Jade and Jordan both have a total of 35 trading cards altogether.
Given, Jade has 28 trading cards. He has 4 times as many trading cards as Jordan.
As, Jade has 28 trading cards
Let Jordan has 'x' trading cards.
Now, as Jade has 4 times as many trading cards as Jordan.
So, 28 = 4x
4x = 28
x = 7
So, Jordan has 7 trading cards.
Now, they both have a total of 35 trading cards altogether.
Hence, Jade and Jordan both have a total of 35 trading cards altogether.
Learn more about Unitary Method here https://brainly.com/question/28627316
#SPJ4
The length of segment AE is 5 centimeters. a. what is the length of segment CD? b. what is the length of segment AB? c. Name a segment that had the same length ...
a) The length of segment CD is; CD = 10 cm
b) The length of segment AB is; AB = 5 cm
c) Another segment with same length as segment AB is;
Segment AC
What is the length of the line segment?From the attached image, we see that Segment AE is a radius of the circle with center of A.
Now, any segment with origin from the center of the Circle that goes on to hit the circumference of the circle, is also a radius, and would be equal in length to segment AE.
a) Segment CD divides the circle into 2 equal parts and as such it will be the diameter of the circle.
Diameter = 2 × radius.
Diameter; CD = 2 × AE
CD = 2 × 5
CD = 10 cm
b) AB is a radius as defined earlier and as such; AB = AE
Thus; AB = 5 cm
c) The other segments that are also radius of the circle and have the same length as segment AB are;
Segment AC
Segment AD
Segment AG
Segment FA
Read more about Line Segment Length at; https://brainly.com/question/27064838
#SPJ1
Factorise the following:
a) x + 3x - 4
b) x-2x-3
c) x +2x-8
The sum of the ages of pam,dion, and their three children, in years, is 5x - 99. where x is dion's age. pam is five years younger than dion. what is the usm of the ages of their children?
The sum of the ages of the children would be 3x - 94 years.
We have the total sum of the ages of pam ,dion and their children
as 5x - 99
here , x is the age of Dion .
we see , pam is five years younger than Dion , so
age of Pam = x - 5
Now as the sum of all the ages = 5x - 99
therefore ,
Age of Dion + Age of Pan + Age of children = 5x - 99
x + x - 5 + Age of children = 5x - 99
2x - 5 + Age of children = 5x - 99
therefore ,
Age of children = 3x - 94
So the age of their children would be 3x - 94 years
Learn more about age related problems here :
https://brainly.com/question/22673152
#SPJ4
how to find the vertex
Answer: To find the vertex: use formula x= -b/2a.
plug x into the given equation to find y value.
now you have (h,k)
find a point on the graph and plug in to the vertex form equation to find "a"
Step-by-step explanation:
Determine which set of side measurements could be used to form a triangle.
A. 13, 19, 7
B. 25, 12, 13
C. 18, 2, 24
D. 3, 1, 5
Option A. The set of side measurement that can be used to form a triangle is given as A. 13, 19, 7
What is a triangle?A triangle in geometry is a three-sided polygon with three edges and three vertices. The fact that a triangle's internal angles add up to 180 degrees is its most crucial characteristic. This characteristic is known as the triangle's angle sum property.
If ABC is a triangle, it is written as ABC, where A, B, and C represent the triangle's vertices. In Euclidean geometry, a triangle is a two-dimensional shape that is represented by three non-collinear points in a single plane.
How to get the measurement that can produce a triangle.
a + b > c = 13 + 19 > 7
a + c > b = 13 + 7 > 19
b + c > a = 7 + 9 > 13
Read more on triangles here: https://brainly.com/question/17335144
#SPJ1
rite the equation for the logarithmic function that has the following
ansformations from the parent logarithmic function. The function will
ave a base of 10. You will not have to write the 10. It is assumed.
- Shifted 3 units left
Vertical compression by a factor of 2
Reflected across the y-axis
Shifted down 5 units
The given function shifted 3 units left is log(x+3), vertical compression by factor 2 is 2log(x+3), Reflection across the y-axis is 2log (-x+3) and shifted down by 5 units is 2log(-x+3)-5.
Given the parent function with base 10.
We want to find the given transformations.
The given parent function is y=log(x)
Firstly, we want to shift the given parent function 3 units left means we will add 3 in the parent function, we get
y=log(x+3)
Now, we want to do vertical compression by a factor of 2 means we will multiply the above function with 2, we get
y=2log(x+3)
Further, we want to reflected the above function across the y-axis means we will multiply the x with minus, we get
y=2log(-x+3)
Furthermore, we want to shift the above function down with 5 units means we will subtract 5 from the above function, we get
y=2log(-x+3)-5
Hence, the given parent function y=log(x) when shifted 3 units left is log(x+3), vertical compression by factor 2 is 2log(x+3), Reflection across the y-axis is 2log (-x+3) and shifted down by 5 units is 2log(-x+3)-5.
Learn more about the logarithmic function transformation from here brainly.com/question/20330517
#SPJ9
A particular car is 16 ft long. A model of it was built with a scale of 1 in: 2 ft. How long is the model car?
The car that is 16 feet long has a length of 8 inches on the scale.
How to find the length of the modelled car?Scale is used to represent the relationship between a measurement on a model and the corresponding measurement on the actual object.
Therefore, the particular car is 16 feet long. A model of it was built with a scale of 1 in: 2 ft. The length of the car can be found as follows:
2 feet = 1 inches
16 feet = ?
cross multiply
length of the model car = 16 / 2
Therefore,
length of the model car = 8 inches
learn more on scale here: https://brainly.com/question/20143411
#SPJ1
the age of children in kindergarten on the first day of school is uniformly distributed between 4.74 and 5.85 years old. a first time kindergarten child is selected at random. round answers to 4 decimal places if possible. the mean of this distribution is the standard deviation is the probability that the the child will be older than 5 years old? the probability that the child will be between 4.84 and 5.34 years old is if such a child is at the 9th percentile, how old is that child? years old.
a) The mean distribution is 5.295.
b) The standard deviation is 0.1026
c) The probability that the child will be older than 5 years old is 0.7657
d) The probability that the child's age is between 4.84 and 5.34 is 0.4504
e) At the 9th percentile, the age of the child is 5.739 years old.
Given interval distribution is
4.74 - 5.85.
a) Firstly, we will find the mean distribution,
Mean distribution = Sum of intervals / Number of intervals
= 4.74+5.85 / 2
= 5.295.
Hence, the mean distribution is 5.295.
b) Now, we will find the standard deviation,
We use the formula:
SD = [tex]\sqrt{\frac{(b-a)^{2} }{12} }[/tex]
b = 5.85
a = 4.74
SD = [tex]\sqrt{\frac{(5.85-4.74)^{2} }{12} }[/tex]
SD = [tex]\sqrt{\frac{(1.11)^{2} }{12} }[/tex]
SD = 0.1026
Hence, the standard deviation is 0.1026
c) The probability that the child will be older than 5 years will be
p(older than 5) = 5.85 - 5 / 5.85 - 4.74
= 0.85 / 1.11
= 0.7657
Hence, the probability that the child will be older than 5 years old is 0.7657
d) The probability that the child will be between 4.84 and 5.34 years old will be
p(between 4.84 and 5.34) = 5.34 - 4.84 / 5.85 - 4.74
= 0.5 / 1.11
= 0.4504
Hence, the probability that the child's age is between 4.84 and 5.34 is 0.4504
e) If the child is at the 9th percentile, the age will be
At the 9th percentile = 4.74 + 9/100 ×(5.85 - 4.74)
= 4.74 +(0.9)(1.11)
= 4.74 + 0.999
= 5.739
Hence, at the 9th percentile, the age of the child is 5.739 years old.
To Learn more about Similar Probability Questions:
https://brainly.com/question/15582698
#SPJ4
if 1,000 points are selected randomly inside the square with all points equally likely to be selected, how many of those points are expected to lie inside the circle?
The number of points that are expected to lie inside the circle is 785.
A circle is a closed two-dimensional figure. In a circle, all points are equidistant from the centre.
As per the given question, the circle is inscribed in a square,
The radius of the circle ( r ) = 1 The side length of the square ( s ) = 2⇒ The area of the circle = π × r × r
= π × 1 × 1
∴ The area of the circle = π
⇒ The area of the square = s × s
= 2 × 2
∴The area of the square = 4
The probability that a randomly selected point inside the square will lie inside the circle,
p = π / 4
The probability that a randomly selected point inside the square will lie outside the circle,
q = 1 - p
q = 1 - ( π / 4 )
⇒ Binomial trial with n = 1000 and p = π / 4,
Number of points expected to lie inside the circle(N) = n × p
= 1000 × ( π / 4 )
= 1000 × ( 3.14 / 4 )
= 1000 × ( 0.785 )
N = 785
Therefore, 785 expected points lie inside the circle.
To know more about circles refer to:
https://brainly.com/question/24810873
#SPJ4
The complete question is
Answer: 56 square
Step-by-step explanation:
Find the value of x.
Answer: 25 degrees
Step-by-step explanation:
Assuming that both triangles are to be connected and that they form a rectangle,
angle x can be found by subtracting 65 degrees from 90 degrees.
(all corners of rectangle=90 degrees)
90-65=25
Suppose that the height (in centimeters) of a candle is a linear function of the amount of time (in hours) it has been burning. after 11 hours of burning, a candle has a height of 19.4 centimeters. after 23 hours of burning, its height is 12.2 centimeters. what is the height of the candle after 15 hours?
The height of the candle after 15 hours of burning is 17 cm.
According to the question,
We have the following information:
Height of the candle after 11 hours of burning = 19.4 cm
Height of the candle after 23 hours of burning = 12.2 cm
Now, we will find the rate at which the height of the candle is decreasing. It means that we will find the decrease in height per centimeter.
Difference between hours and height:
23-11 = 12 hours
19.4-12.2 = 7.2 cm
So, we have:
12 hours = 7.2 cm
1 hour = 7.2/12
1 hour = 0.6 cm
So, the height is decreasing at the rate of 0.6 cm per hour.
Now, we have to find the height after 15 hours.
Height at 11 hours = 19.4 cm
Difference between 15 hours and 11 hours is 4 hours.
Change in height = 0.6*4 cm
Decrease in height = 2.4 cm
So, the height after 15 hours:
19.4-2.4
17 cm
Hence, the height of the candle after 15 hours of burning is 17 cm.
To know more about height of the candle here
https://brainly.com/question/18806271
#SPJ1
Explain why (5 + 4) (5 + 4) could be used to determine the total number of computers.
Answer:
The numbers that we use are expressed in base 10. Every 10 1s equals 1 ten For example, if you are adding 5 + 4, you get: 0101 + 0100.
The function f(t)=9300(0.994)t represents the change in a quantity over t minutes. What does the constant 0.994 reveal about the rate of change of the quantity?
The function is ________exponentially at a rate of _______% every _______.
Please!!!! Help
Answer:
Step-by-step explanation:
NOSEEEEEE
the idea that a large number of sample means or proportions will approximate a normal distribution, regardless of the distribution of the population from which they were drawn, is known as: random error simple random sample sample variance population variance central limit theorem
The Central Limit Theorem gives the idea that a large number of sample means or proportions will approximate a normal distribution, regardless of the distribution of the population from which they were drawn .
Central Limit Theorem : In probability theory , the Central Limit Theorem establishes that , in many situations , when independent random variables are summed up , their properly normalized sum tends toward a normal distribution even if the original variables themselves are not normally distributed .
The Central Limit Theorem gives the idea that a large number of sample means or proportions will approximate a normal distribution, regardless of the distribution of the population from which they were drawn .
To learn more on central limit theorem follow link:
https://brainly.com/question/14781796
#SPJ4
each day for four days, linda traveled for one hour at a speed that resulted in her traveling one mile in an integer number of minutes. each day after the first, her speed decreased so that the number of minutes to travel one mile increased by 5 minutes over the preceding day. each of the four days, her distance traveled was also an integer number of miles. what was the total number of miles for the four trips
The total number of miles for the four trips is 25 miles.
Given that;
Linda traveled for one hour each day for four days at a speed that made her cover one mile in an even number of minutes. After the first day, she started to lose speed, and it took her 5 minutes longer to complete a mile than the day before. Her journey distance was also an integer amount of miles throughout the four days.
We know that,
Distance is a product of speed and time. We need to find the distance here with the use of the given conditions, time is 1 hour.
Speed = Distance / Time
Hence, speed is 1 mile per x minutes because we want to distance by multiplying the time and speed together yielding 60 min * 1 mile / x mins.
Minutes cancel out, so now we have 60/x as our distance for the first day.
The distance for the given case;
⇒ [tex]\frac{60}{x},\frac{60}{x+5},\frac{60}{x+10},\frac{60}{x+15}[/tex]
It is given that x = 5;
⇒ [tex]\frac{60}{5},\frac{60}{10},\frac{60}{15},\frac{60}{20}[/tex]
= 12 + 6 + 4 + 3
= 25
The total number of miles for the four trips is 25 miles.
To learn more about Distance click here:
brainly.com/question/15256256
#SPJ4
Lyle and Ming are painting an art room. They started with 44 gallons of paint. On the first day, Lyle used \frac{1}{2} 2 1 gallon of paint and Ming used 1\frac{1}{4}1 4 1 gallons of paint. How many gallons of paint were left when they completed their first day of painting?
The initial 4 gallons and the fractions of [tex]\frac{1}{2}[/tex] and [tex]1\frac{1}{4}[/tex] gallons of paint used on the first day indicates;
The number of gallons of paint left when they completed the first day of painting is [tex]2\frac{1}{4}[/tex] gallonsWhat is a fraction in mathematics?A fraction is the representation of a number in quotient form such that the value of the number is obtained by dividing the numerator by the denominator.
The amount of paint Lyle and Ming started painting the room with = 4 gallons
Amount of paint Lyle used on the first day = [tex]\dfrac{1}{2}[/tex] gallons of paint
The amount of paint Ming used on the first day = [tex]1\frac{1}{4}[/tex] gallons of paint
Required; The amount of paint remaining after the first day of painting
The paint left after the first day of painting, V, is the difference between the amount of paint with which the painting was started and the amount used by Lyle and Ming on the first day
Therefore; [tex]V = 4 - \left(\dfrac{1}{2} + 1\dfrac{1}{4} \right) = 4 - \left(\dfrac{1}{2} +\dfrac{5}{4} \right) = 4 - \dfrac{7}{4}[/tex]
[tex]V = 4 - \dfrac{7}{4} = \dfrac{16-7}{4} = \dfrac{9}{4} = 2\dfrac{1}{4}[/tex]
The amount of paint left after the first day is [tex]2\frac{1}{4}[/tex] gallonsLearn more about fractions here:
https://brainly.com/question/12950319
#SPJ1
Help me on this please.
The steps and reason to prove the angle theorems is; Table 3
What is the proof of the angles in the triangle?The internal angles of the given triangle are given as;
a, b, c and d.
Now, we know that the sum of interior angles in a triangle is equal to 180°;
∠a + ∠b + ∠c = 180°
Now, ∠c and ∠d are angles that form a straight line and as such they sum up to 180° as they are supplementary angles.
∠c + ∠d = 180°
Thus, by transitive properties, we can say that;
∠a + ∠b + ∠c = ∠c + ∠d
Therefore by subtraction property of equality we have;
∠a + ∠b = ∠d
Read more about Angles in a Triangle at; https://brainly.com/question/7620723
#SPJ1
The image of ΔABC after a reflection across Line E G is ΔA'B'C'.
2 triangles are shown. Line E G is the line of reflection. Line segment D D prime has a midpoint at point F. Line segment C C prime has a midpoint at point G. Points B and B prime share a point. Angle C G F is a right angle.
Which triangle must be a right triangle and why?
ΔBGC is right because Line EG is perpendicular-to CC'.
What is Reflection?A reflection image or reflection point is the mirror image of a figure in the axis or plane of reflection.
Each point of the original figure (the pre-image) has an image that is the same distance from the reflection line as the original point, but is on the other side of the line. This transformation is known as a reflection over line. The size and form of the image in a reflection are identical to those of the pre-image.
Given:
On the line of reflection will be the midpoints of the segments connecting a triangle vertex with its reflected image. The segment will be parallel to the reflection's line.
A triangle will be considered correct in this situation if it has a leg that is a part of the segment connecting the reflected points and a leg that is on the line of reflection. Such a triangle is the BGC.
Hence, BGC is right triangle.
Learn more about reflection here:
https://brainly.com/question/15487308
#SPJ1
Answer: D
Step-by-step explanation: Trust
carter has 24 posters in his room. if he arranges them into 6 equal rows, how many posters will be in each row?
If he arranges them into 6 equal rows, 4 posters will be in each row.
Define division.One of the fundamental arithmetic operations in mathematics is the division, which is the process of dividing a group of items into equal pieces. Every day, we might employ the division approach in various situations. Fraction division differs significantly from natural number division. We must change the division operator into a multiplication operator when dividing fractions. Therefore, the dividend should be multiplied by the inverted divisor.
Given,
Total posters = 24
Arranging them into 6 equal rows,
Dividing:
24÷ 6
Reciprocating,
24 × 1/6
4
If he arranges them into 6 equal rows, 4 posters will be in each row.
To learn more about division, visit:
https://brainly.com/question/21416852
#SPJ4
"I have drawn a polygon who's sum of interior angles is 800"
explain why this is impossie
We know that the sum of all the interior angles of the polygon with sides n is (n - 2)*180.
It is given in the question that,
Sum of all the interior angles of the polygon is 800.
Hence, according to the data given in the question, we can write,
(n - 2)*180 = 800
n - 2 = 800/180
n - 2 = 40/9
n = 40/9 + 2
n = 58/9 = 6.44
As number of sides should always be in integer form, it is not possible to have the sum of all the interior angles of the polygon to be 800 degrees.
To learn more about polygon, here:-
https://brainly.com/question/24464711
#SPJ1
What two numbers = -48 (multiply) and does the two numbers = -13
Answer:
The two numbers are [tex]3[/tex] and [tex]-16[/tex].
Step-by-step explanation:
Two numbers that, when multiplied, result in a product of [tex]-48[/tex]:
[tex]x \cdot y = -48[/tex]
Same two numbers when added get a sum of [tex]-13[/tex]:
[tex]x + y = -13[/tex]
Solve for x in the summation identity:
[tex]y = -13 - x[/tex]
Plug the value back into the product identity and solve for [tex]x[/tex]:
[tex]x \cdot (-13-x) = -48\\-13x - x^2 = - 48\\x^2 + 13x = 48\\x^2 + 13x - 48 = 0\\(x-3)(x+16) = 0[/tex]
The roots we found for [tex]x[/tex] were:
[tex]x = 3\\x = -16[/tex]
Our two numbers are [tex]3[/tex] and [tex]-16[/tex]. We can test this:
[tex]3 + (-16) = -13\\3 * -16 = -48[/tex]
monique and tara each make an ice-cream sundae. monique gets 3 scoops of cherry ice-cream and 1 scoop of mint chocolate chunk ice-cream for a total of 84g of fat. tara has 1 scoop of cherry and 3 scoops of mint chocolate chunk for a total of 60g of fat. how many grams of fat does 1 scoop of each type of ice cream have?
The amount of fat in Cherry ice-cream is 24 grams.
The amount of fat in the Mint Chocolate Chunk ice-cream is 12 grams.
Writing data into equations using Algebra,3C + M = 84...(1)C + 3M = 60...(2)
Multiplying equation (2) by 3 and then subtracting equation (1) from
the result gives, 3 * (C +3M) = 3 × 603C + 9M = 180...(3)(3C + 9M = 180) - (3C + M = 84) = 8M =96M= 12
The amount of fat in the Mint Chocolate Chunk ice-cream, M = 12
grams C + 12*3 = 60C = 60-36 = 24
The amount of fat in Cherry ice-cream C = 24 grams As a result, Cherry ice cream contains 24 grams of fat and Mint Chocolate Chunk ice cream contains 12 grams of fat.
Learn more about Algebra:
brainly.com/question/24875240
#SPJ4
If 1400 dollars is invested in an account for 10 years. find the value of the investment at the end of 10 years if the interest is: (a) 4.6% compounded annually: $ 2195.05 correct (b) 4.6% compounded semiannually: $ (a) 4.6% compounded quarterly: $ 2211.88 correct (b) 4.6% compounded monthly: $ 2215.75 correct (a) 4.6% compounded daily (ignore leap years): $ 2217.63 correct
The compound interest calculated for 10 years annually, semi-annually, quarterly, monthly, and daily are (a) $2195.05, (b) $2206.18 (c) $2211.88 (d) $2215.75, and, (e) $2217.63
The formula for Compound Interest is
Amount = Principal X (1 + r/n100)ⁿˣ
where,
Principal = original mount
n = no. of times the interest is applied
t = time period
Here,
Principal = $1400
x = 10
r = 4.6
a)
Since it is compounded annually, the interest will be given 10 times in 10 years. therefore, once a year
Hence,
n = 1
Amount = 1400 X (1 + 4.6/100)¹⁰
= 1400 X (104.6/100)¹⁰
= 1400 X (1.046)¹⁰
= $2195.05
b)
Since the interest is compounded semi-annually here, it will be calculated twice a year.
Hence, n = 2
Therefore we get
Amount = 1400 X (1 + 4.6/200)²⁰
= 1400 X (204.6/200)²⁰
= 1400 X (1.023)²⁰
= $2206.18
c)
Since it is compounded 4 times a year now,
n = 4
Hence we get
Amount = 1400 X (1 + 4.6/400)⁴⁰
= 1400 X (1.0115)⁴⁰
= $2211.88
d)
Here, the interest is calculated 12 times a year
Hence we get
Amount = 1400 X (1 + 4.6/1200)¹²⁰
= 1400 X (10038)¹²⁰
= $2215.75
e)
Here we are told to ignore leap years, hence we are only going to consider a year to have 365 days.
Hence,
n = 365
Therefore, we get
Amount = 1400 X (1 + 4.6/36500)³⁶⁵⁰
= 1400 X (1 + 4.6/36500)³⁶⁵⁰
= 1400 X (1.00012)³⁶⁵⁰
= $2217.63
Correct Question
If 1400 dollars is invested in an account for 10 years. find the value of the investment at the end of 10 years if the interest is:
(a) 4.6% compounded annually
(b) 4.6% compounded semiannually
(c) 4.6% compounded quarterly
(d) 4.6% compounded monthly
(e) 4.6% compounded daily (ignore leap years)
To know more about Compound Interest visit
https://brainly.com/question/29311315
#SPJ4
Two planes are parallel and each plane contains a line. Are the two lines skew? Explain your reasoning.
If Two planes are parallel and each plane contains a line, the two lines are not skew because In the event that any two lines fall on a single plane, they will either intersect or be parallel to one another. Both instances violate the concept of a skew line because the skew lines are neither parallel nor intersect.
Do two parallel lines on a plane have a skew?Infinitely many lines cross through, yet only one of them is parallel to. Lines that never intersect and are in distinct planes are known as skew lines. Parallel lines and skew lines are distinguished by the fact that they both reside in the same plane, whereas skew lines do not.
The two lines would overlap at some point if the two planes on which they are located weren't parallel, which again defies the definition of skew lines.
Therefore, The skew lines are thus present if and only if both lines fall on a pair of parallel planes.
Learn more about parallel lines from
https://brainly.com/question/24607467
#SPJ1
A bag of chocolate mix that weighed 1/4 of a kilogram could make enough brownies to feed 1/7 of the students at school. How many bags would be needed to feed all of the students?
Answer:
1/28 kilo
Step-by-step explanation:
sb help me on my recent please
flaws in a carpet tend to occur randomly and independently at a rate of one every 270 square feet. what is the probability that a carpet that is 7 feet by 12 feet contains no flaws?
The probability that a carpet that is 7 ft × 12 ft contains no flaws is 0.732
What is the Poisson Distribution Formula?The Normal, Binomial, and Poisson Distributions are the three types of continuous and discrete data-based distributions used in probability and statistics. The distribution of unusual occurrences is another name for the Poisson distribution. This is mostly used to forecast the likelihood of future events based on how frequently the past events occurred. It offers the chance that a specific number of events might happen during a particular time frame.
The formula for Poisson distribution is given below:
P(x) = (e^-x * m^x) / x!
Here we have,
flaws in a carpet tend to occur randomly and independently at a rate of one every 270 square feet
Given the dimensions of carpet = 7 feet × 12 feet
=> area of the carpet = 84 feet²
=> the expected mean of defects m = [1/270]*84 = 0.311
Now use the Poisson formula
P[x] = e^-m × m^x / x!
=> P(x = 0) = e^-(0.31) × 0.31^(0) / 0!
= (0.732 × 1)/1 = 0.732
Therefore,
The probability that a carpet that is 7 ft × 12 ft contains no flaws is 0.732
Learn more about Poisson Distribution at
https://brainly.com/question/28437560
#SPJ4
Which graph represents an odd function?
Answer:
Step-by-step explanation:
Please help me with this question
Answer: The ladder reaches 4.8 ft up the wall
Step-by-step explanation:
Sin 53°=0.80
Cos 53°=0.60
Tan 53°=1.33
Cos 58°/1 = X/8
0.60/1 = X/8
X=4.8
The perimeter of an equilateral triangle is 10 inches more than the perimeter of a square, and the side of the triangle is 6 inches longer than the side of the square. Find the side of the triangle. (Hint: An equilateral triangle has three sides the same length.)
Answer:
The side of the triangle is 14 in======================
Let the sides be t for triangle and s for square.
Difference of perimeters3t = 4s + 10Difference of sidest = s + 6Rearrange the second equations = t - 6Substitute this into first equation and solve for t3t = 4s + 103t = 4(t - 6) + 103t = 4t - 24 + 103t = 4t - 144t - 3t = 14t = 14Answer:
14 inches
Step-by-step explanation:
The side lengths of an equilateral triangle are the congruent.
The side lengths of a square are the congruent.
Let x be the length of one side of the equilateral triangle.
⇒ Perimeter of triangle = 3x
Let y be the length of one side of the square.
⇒ Perimeter square = 4y
Given:
The perimeter of the triangle is 10 inches more than the perimeter of the square.The side of the triangle is 6 inches longer than the side of the square.Create a system of equations with the given information and defined variables:
[tex]\begin{cases}3x = 4y + 10\\x = y + 6\end{cases}[/tex]
Substitute the second equation into the first equation and solve for y:
[tex]\implies 3(y+6)=4y+10[/tex]
[tex]\implies 3y+18=4y+10[/tex]
[tex]\implies 18=y+10[/tex]
[tex]\implies y=8[/tex]
Therefore, the side length of the square is 8 inches.
Substitute the found value of y into the second equation and solve for x:
[tex]\implies x=8+6[/tex]
[tex]\implies x=14[/tex]
Therefore, the side length of the triangle is 14 inches.
how many ways are there to paint each of the integers 2, 3,..., 9 either red, green, or blue so that each number has a dierent color from each of its proper divisors?
432 ways are there to paint each of the integers 2, 3,..., 9 either red, green, or blue so that each number has a different color from each of its proper divisors.
What is counting principle?A rule used to count the entire number of alternative outcomes in a circumstance is known as the fundamental counting principle. It claims that if there are n ways to do something and m ways to do something else after that, then there are n m n*m methods to do both of these acts.
Here,
(1) All prime number can take any of three colors, except one of 2 or 3 as both are connected via 6..
so 2, 5, 7 can have 3 ways each - 3*3*3 = 27 ways
(2) Let us take the multiples of 2..
4 can take any of the remaining 2 colors, while 8 would take the remaining colour. As like 4, 6 can also take any of 2 colors other than the colour of integer 2.
Thus 2*2*1=4
3 is restricted because of 6, so it cannot have the same color as 6 and therefore 3 can have any of the remaining 2 colors.
We could also have taken 3 colors for 6, and then 2 and 3 would have 2 colors each and overall 2*2*3.. We are still getting the same
Only integer left is 9, so it will take any of the 2 colors other than that of 3, so 2 ways..
Total 2*2=4
Combined way of integers = 27∗4∗4=432 ways
There are 432 different methods to paint the numerals 2, 3,..., 9 red, green, or blue so that each number has a different hue from each of its suitable divisors.
To know more about counting principle,
https://brainly.com/question/28384306
#SPJ4