Answer:
y= -20/9
Step-by-step explanation:
4y+5/3=y-5
3y= -(5+5/3)
3y= -20/3
y= -20/9
Answer:
Collect like terms
4y-y=-10/2-5/3
3y=-5-5/3
5-5/3
LCM=3
3/1=3×5=15
3/3=1×5=5
15-5÷3
10/3
3y=10/3÷3
3y=30/3
y=10
find the value of x in each case
in a right triangle, the longer leg is two more than three times the shorter leg, and the area of the triangle is 400. what is the length of the shorter leg?
The length of the shorter leg is 16 units which was found using the given data.
What exactly is a quadratic equation?A quadratic equation is a second-degree algebraic equation in x. In its usual form, the quadratic equation is ax² + bx + c = 0.
Given: The larger leg of a right triangle is twice more than three times the shorter leg, and the triangle's area is 400.
We know that,
Area of triangle = 1/2(larger leg)(shorter leg)
400=1/2(larger leg)(shorter leg) Equation(1)
larger leg = 2 + 3(shorter leg)
We need to substitute this in Equation(1)
400 = 1/2[2+3(shorter leg)](shorter leg)
800 = 2(shorter leg) + 3(shorter leg)²
3(shorter leg)² + 2(shorter leg) - 800 = 0
Solving this quadratic equation,
we get, shorter leg = - 16 or +16
Thus, we found that the length of the shorter leg is 16 units as -16 cannot be the length because it is negative.
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What equation is graphed in this figure?
y−4=−1/3(x+2)
y−3=1/3(x+1)
y+2=−3(x−1)
y−5=3(x−1)
The equation of the graph in point slope form is y + 2 = -3(x - 1)
How to find equation of a graph?The equation of the graph in point slope form can be represented as follows;
y - y₁ = m(x - x₁)
where
m = slopex₁ and y₁ are variableusing two point let's find the slope
(0, 1)(-1, 4)
Hence,
m = 4 - 1 / -1 - 0
m = 3 / -1
m = -3
Therefore, the slope of the line is - 3.
Therefore, using one coordinates(1, -2) from the graph, the equation of the graph in point slope form is y + 2 = -3(x - 1)
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Is -1 8/9 a repeating decimal or Terminating
solve the inequality write the solution in interval notation
-x/3 < 5
The inequality expression given as -x/3 < 5 has a solution of x > -15
How to solve the inequality?From the question, the inequality is given as
-x/3 < 5
The above inequality can be re-written as follows
-x/3 < 5
There is no constant to add or subtract in the expression
So, we start by multiplying both sides of the expression by a constant
Multiply both sides by 3
expression
-x < 15
Divide both sides by -1
So, we have the following representation
x > -15
Hence, the solution to the expression is x > -15
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HELP MEEE PLEASEEEEE
Answer:
XY = 12.4 cm
Step-by-step explanation:
a² + b² = c²
(4 cm)² + (XY)² = (13 cm)²
16 cm² + XY² = 169 cm²
XY² = 153 cm²
XY = √(153 cm²)
XY = 12.4 cm
A triangular number is a number that can be represented by arranging the number of dots in rows to form a triangle. The first four triangular numbers are represented in the diagram. Find the mean, median and range of the first 6 triangular numbers.
mean =
Number
median =
Number
range =
Number
The mean of the triangular dots is 4, the median is 8 and the range is 6.
How to determine the Measures of central tendency?
A measure of central tendency is defined as a single value that attempts to describe a set of data by identifying the central position within the given set of data.
From the question, the parameters are dots that will form triangle as
.
. . .
. . . . .
. . . . . . .
Total mumber of dots is 1+3+5+7=16
These parameters are represented as follows:
The mean is the average of all the dots that formed the triangle
Mean value of the set of data = [tex]\frac{16}{4} =4[/tex]
The median is the middle number when arranged in ascending or descending order of magnitude
The median is [tex]\frac{16}{2} =8[/tex]
The range is the highest value minus the lowest value in the dots
The range is 7-1=6
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A, B and C are points on the circumference of a circle.
XY is a tangent to the circle at the point A.
Angle BAY = 72° and angle ABC = 54°.
Prove that triangle ABC is an isosceles
triangle.
You must give a reason for any statement
that you make or any calculation that you
carry out.
By using tangent property of circle, it has been proved that [tex]\Delta[/tex] ABC is isosceles
What is tangent to a circle?
At first it is important to know about circle.
Circle is a two dimensional round figure in which every point of the circle maintains a fixed distance from a point known as the center. The fixed distance is called the radius of the circle.
The straight line which touches the circle at any point is known as the tangent to a circle.
Tangent property of circle is used here
[tex]\angle BAY = 72^{\circ}[/tex]
[tex]\angle ABC = 54^{\circ}[/tex]
[tex]\angle ACB = 72^{\circ}[/tex] [Angle in alternate segment are equal]
[tex]\angle BAC = 180 - (54 + 72)\\[/tex] [Sum of three angles of a triangle is 180°
= 180 - 126
= 54°
[tex]\Delta ABC[/tex] is isosceles
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Matteo buys a basil plant that is 22 cm tall and grows 1/2 a centimeter every day.
A. Write an equation that can be used to solve for the number of days until the plant has a height of 30 cm. Use d to represent the number of days. Label each part of your equation with what it represents.
B. How much does the plant still have to grow?
C. Solve for the value of d. What does this value represen in this problem?
PLEASE SOLVE ALL
The equation 22+(d-1)0.5 = 30 may be used to determine how many days it will take the plant to reach a height of 30 cm. The value of d is 17, and it stands for the number of days.
What is an arithmetic sequence?There are two definitions for an arithmetic sequence. It is a series where the differences between every two succeeding terms are identical or each term in an arithmetic sequence is formed by adding a fixed number (positive, negative, or zero) to its preceding term.
The following details are available to us:
A 22 cm tall basil plant that is gaining half a centimeter daily was purchased by Matteo.
We now have the arithmetic progression shown below with the common difference, indicated by the letter d:
22, 22.5, 23, 23.5, ...
The formula for calculating the nth term:
When an is the first term, a(n) = a+(n-1)d.
A) 22+(d-1)0.5 = 30
B) The plant still needs to develop 8 cm, as there is a difference of 8 cm between 30 and 22.
C) D's value:
22+(d-1)0.5 = 30
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what is 4x multipied by 7y
Answer:
Step-by-step explanation:
28xy
Solve the inequalityr divided by negative 2.5 is less than or equal to 8.7 for r.
Answer:
r ≤ -21.75
Step-by-step explanation:
Forming the equation,
→ r ÷ (-2.5) ≤ 8.7
Then the value of r will be,
→ r ÷ (-2.5) ≤ 8.7
→ r ≤ 8.7 × (-2.5)
→ r ≤ -21.75
Hence, value of r is -21.75.
potatoes cost $0.85 per pound. Luke bought 2.75 pounds of potatoes. How much did he pay for the potatoes. Round to the nearest cent
Answer:
$2.34
Step-by-step explanation:
2.75 x 0.85 = $2.3375
Since we are rounding, it will round up to $2.34.
Answer:
Step-by-step explanation:
Cost of 2.75 pounds of potato =.
2.75x0.85
= $2.3375
Write down three different factors of
360 with a sum between 90 and 100.
Answer: 90 x 4 x 1
Step-by-step explanation:
90 x 4 x 1 = 360
Please thank and rate <3
Answer:
360
Step-by-step explanation:
2³x3²x5
Please thank you and rate
small airplane flew 104 miles in 50 minutes. At this rate, how many miles can it fly in 3 hours?
An airplane can fly 374.4 miles in 3 hours.
A small airplane flew 104 miles in 50 minutes.
So, the rate would be,
rate = distance / time
rate = 104/50
rate = 2.08 miles/minute
We need to find the distance the airplane can flay in 3 hours.
3 hours = 180 minutes
t = 180 minutes
r = d/t
2.08 = d/180
d = 2.08 * 180
d = 374.4 miles
Therefore, an airplane can fly 374.4 miles in 3 hours.
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A group conducted a survey of 13,000 brides and grooms married in the united states and found that the average cost of a wedding is $23,858. assume that the cost of a wedding is normally distributed with a mean of $23,858 and a standard deviation of $5,900. (a) what is the probability that a wedding costs less than $20,000? (round your answer to four decimal places.) (b) what is the probability that a wedding costs between $20,000 and $32,000? (round your answer to four decimal places.) (c) what is the minimum cost (in dollars) for a wedding to be included among the most expensive 5% of weddings? (round your answer to the nearest dollar.)
The measures, using the normal distribution, are given as follow:
a) Probability that a wedding costs less than $20,000: 0.257 = 25.70%.
b) Probability that a wedding costs between $20,000 and $32,000: 0.659 = 65.90%.
c) Minimum cost of the most expensive 5% of weddings: $33,564
Normal Probability Distribution
The z-score of a measure X of a variable that has to mean symbolized by and standard deviation symbolized by is given by the rule presented as follows:
[tex]Z=\frac{X-\mu}{\sigma}[/tex]
The z-score represents how many standard deviations measure X is above or below the mean of the distribution, depending if the calculated z-score is positive or negative.
Using the z-score table, the p-value associated with the calculated z-score is found, and it represents the percentile of measure X in the distribution.
The mean and the standard deviation for the wedding prices are given as follows:
μ = 23858, σ = 5900
a) The probability that a wedding costs less than $20,000 is the p-value of Z when X = 20000, hence:
[tex]Z=\frac{X-\mu}{\sigma}[/tex]
Z = (20000 - 23858)/5900
Z = -0.65
Z = -0.65 has a p-value of 0.257.
The probability that it costs between $20,000 and $32,000 is the p-value of Z when X = 32000 subtracted by the p-value of Z when X = 20000, found above, hence:
[tex]Z=\frac{X-\mu}{\sigma}[/tex]
Z = (32000 - 23858)/5900
Z = 1.38
Z = 1.38 has a p-value of 0.816.
0.916 - 0.257 = 0.659.
The minimum cost for a wedding to be in the most expensive 5% of weddings is the 95th percentile, which is X when Z = 1.645, hence:
1.645 = (X - 23858)/5900
X - 23858 = 1.645 x 5900
X = $33,564.
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a concert venue is determining the ticket price for concerts in a particular series. the sales team finds that at a price of $38 per ticket, attendance averages 1,000 people per concert. each decrease in price of $5 adds 50 people to the average attendance. find an equation for revenue, r, as a function of p, the price of tickets. what is r(25)?
An equation for revenue (r) as a function of (p) is R = 1380p - 10p²,
and R(25) = 28250.
Given that;
The cost of tickets for a specific series of concerts is set by a concert venue. The sales team discovers that 1,000 people on average attend concerts with tickets costing $38. The average attendance increases by 50 persons for every $5 decrease in price. Then,
Let 'T' be the number of times the price is decreased.
So, price;
p = 38 – 5x
x = (38 - p) / 5
And as per the given condition attendance;
a = 1000 + 50x
So, the Revenue is;
To develop an equation for revenue (r) as a function of p, the price of tickets;
R = p * a
R= p * (1000 + 50x)
But, x = (38 - p) / 5
Then,
R = P * (1000 + 50(38 - p)/5)
= p * (1000 + 380 - 10p)
= p * (1380 – 10p)
= 1380p - 10p² → (I)
To get R(25) from (I);
R(25) = 1380(25) - 10(25)²
= 34500 - 6250
= 28250
Hence, an equation for revenue (r) as a function of (p) is R = 1380p - 10p²,
and R(25) = 28250.
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help meeeeeeeeeeeeeeeeee please
Answer:
324 ft
Step-by-step explanation:
[tex]v=\sqrt{2gh}[/tex]
[tex]v^2=(\sqrt{2gh})^2[/tex]
[tex]v^2=2gh[/tex]
[tex]\frac{v^2}{2g}=\frac{2gh}{2g}[/tex]
[tex]\frac{v^2}{2g}=h[/tex]
[tex]\frac{144^2}{2(32)}=h[/tex]
[tex]\frac{20736}{64}=h[/tex]
[tex]324=h[/tex]
How do I solve this.
Answer:
Step-by-step explanation:
Find the x- and y-intercepts of the graph of -7x+10y=35. State each answer as an integer or an improper fraction in simplest form.
x-intercept
The x-intercept is where y=0.
[tex]-7x+10(0)=35\\\\-7x=35\\\\x=\boxed{-5}[/tex]
y-intercept
The y-intercept is where x=0.
[tex]-7(0)+10y=35\\ \\ 10y=35\\\\y=\boxed{7/2}[/tex]
A 2-pint carton of non-dairy creamer costs $3.36. What is the price per cup?
Answer:
$6.72
Step-by-step explanation:
1 us liquid pint =2 us cups
3.36*2 cups
For triangle XYZ, m∠X = (5g + 18)° and the exterior angle to ∠X measures (8g + 32)°. Find the measure of ∠X and its exterior angle. Interior angle = 68°; exterior angle = 112° Interior angle = 112°; exterior angle = 68° Interior angle = 73°; exterior angle = 105° Interior angle = 105°; exterior angle = 73°
The interior angle and the exterior angle of triangle XYZ is 68° and 112° respectively.
What is a triangle?
A triangle is a plane shape that has three sides.
Recall that, the sum of a interior angle and an exterior angle of a triangle is 180°.
Using the formula,
a+b = 180°............ Equation 1Where:
a = interior angle b = exterior angle.From the question,
Given:
a = m∠X = (5g + 18)° b = ∠X = (8g + 32)°Substitute these values into equation 1
(5g + 18)+ (8g + 32) = 180Solve for g
13g + 50 = 18013g = 130g = 130/13g = 10Hence, interior angle of X = (5×10)+18 = 50+18 = 68° and exterior angle of X = (8×10)+32 = 80+32 = 112°
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Answer: I belive the answer is A
Step-by-step explanation: i could be wrong
15. Find mACB. help me please
The measure of the angle ACB is 87°.
What does the term angle mean?Angles produced by two beams are included in the plane that contains the rays. The intersection of two planes may also produce an angle. Dihedral angles are the name given to them. It is also possible to determine the angle between two crossing curves using the angle created by the rays that are perpendicular to each intersecting curve at that point.
An angle can also refer to a measurement of a rotation or an angle. This number represents the length-to-radius ratio of a circular arc.
When two crossing lines in a plane are not perpendicular to one another, Euclid defined a plane angle as the inclination between those intersecting lines.
In triangle ADE and triangle ACB, the triangles are similar.
So,
∠AED/ ∠ABC = ∠DAE/∠CAB
∠AED = ∠ABC
11x-2 = 6x + 13
11x - 6x = 13 + 2
5x = 15
x = 15/5
x = 3
So, the measure of angle ABC is
∠ ABC = 6(3)+13
∠ ABC = 18+13
∠ ABC = 31°
Now, consider triangle ABC, the sum of all angles = 180°
So, 62° + 31° + ∠ACB = 180°
∠ACB + 93° = 180°
∠ACB = 180° - 93°
∠ACB = 87°
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Consider the system of equations : 2a + 3b - 4c = 7,
a - b + 2c = 6
(a) Find an ordered tripe of numbers (a,b,c) that satisfies both equations.
(b) Can you find a second ordered triple that satisfies both equations.
(c) Solve for b in terms of a, and solve for c in terms of a. How many solutions does this system have?
Answer:
a. 87 b. 9 c. 4
Step-by-step explanation:
Quadrilateral ABCD has vertices A(9, 9), B(—7, 9),
C(-8,-5), and D(4,-5). In terms of units, what is the
perimeter of quadrilateral ABCD?
Round your answer to the nearest tenth.
Answer:get a tutor
Step-by-step explanation:
its free
Please help,
Will mark as brainliest
Answer: D
Step-by-step explanation:
5 x 3 = 15
8 x 3 = 24
the multipliers are both 3
so they are "similar shapes".
The other options don't have the same multipliers so they aren't right :)
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250 bicycles must be manufactured to minimize the cost.
The cost C in dollar of manufacturing x bicycles at a production plant is given by:
C(x) = 3x² - 1500x + 198,500
a. To find number of bicycle that can minimize the cost
differentiate C(x) with respect to x
C'(x) = 6x - 1500
equating C'(x) = 0
6x - 1500 = 0
x = 1500/6
x = 250 , is our stationary point
Differentiate C'(x) = 6x - 1500 again and put x = 250,
C''(x) = 6 (positive)
At x = 250 , cost is minimum
Therefore , 250 bicycles must be manufactured to minimize the cost.
b. C(x) = 3x² - 1500x + 198,500
putting x = 250,
C(x) = 3(250)² - 1500(250) + 198,500
= 187,500 - 375 ,000 + 198,500
= $11,000 is the minimum cost
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A person invests 4500 dollars in a bank. the bank pays 7% interest compounded annually. to the nearest tenth of a year, how long must the person leave the money in the bank until it reaches 14900 dollars?
Answer:
A = Ao * (1+ i)^n amount Ao invested for n yrs at i/yr
14900 = 4500 (1.07)^n
3.311 = (1.07)^n
log 3.311 = n log 1.07 = n* .0294
n = log 3.311 / .0294 = .52 / .0294 = 17.6 yrs
Check:
Money will double about very 70 / 7 = 10 yrs
At 10 yrs around 9000 return
At 20 yrs 18,000 return - result appears reasonable
Wyatt is saving money for a PS5 but has to pay back
the $3 he owes his sister.
#5.
Drag the green points so that the shaded region covers
the range.
#6.
What is the range of this function? (Consider: How do
you think the arrow affects the range?)
Answer:
Step-by-step explanation:
dees
a sock drawer contains 10 white socks, 6 black socks , and 8 blue socks if 2 socks are chosen at random, without replacement
calculate the probability she chooses 2 socks of the same colour
Simply put, probability is the likelihood that something will occur.When we don't know how an event will turn out, we can discuss the likelihood or likelihood of several outcomes.Statistics is the study of events that follow a probability distribution.
calculate the probability she chooses 2 socks of the same colour ?I clarify this because the question uses plural “drawing white socks”. Ok, in our language practice one does usually say socks instead of sock because they usually come in pair.
If it means 1 draw of 1 sock then the probability is 6out of 21. Or about 28.57%
But if it is to draw twice with one sock being drawn in each draw to get a pair of white socks then the probability is 6/21 * /20 = 30/420 = 1/14 or about 7.14%
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The function g(x) = x2 – 10x + 24 is graphed on a coordinate plane. Where will the function cross the x-axis?
(–6, 0) and (–4, 0)
(–2, 0) and (–12, 0)
(4, 0) and (6, 0)
(12, 0) and (2, 0)
The x-intercepts of the quadratic function g(x) = x² - 10x + 24 are given as follows:
(4, 0) and (6, 0).
When does a function crosses the x-axis?A function crosses the x-axis when the numeric value of the function is of y = 0, hence these points are called the x-intercepts of the function.
In this problem, the definition of the function is given as follows:
g(x) = x² - 10x + 24.
This function can be simplified as follows:
g(x) = (x - 6)(x - 4).
Applying the inverse of the Factor Theorem, the x-intercepts are given as follows:
x - 6 = 0 -> x = 6.x - 4 = 0 -> x = 4.Hence the x-intercepts of the function are given by the third option, which is of (4, 0) and (6, 0).
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Answer: C
Step-by-step explanation: trust me