Answers
Answer:
Length YZ is about 16.2 cm (to the first decimal place)
Step-by-step explanation:
In order to find the lenth YZ we need to know the the Pythagorean theorem which is a²+b²=c² (or leg² + leg² = hypothnose)
For this problem let a = line segment XY, let b = YZ and let your hypothnose (c) to be ZX
Substitute your known values in the equation so we know a = 5 cm and c = 17 cm so we can apply it in our equation 5²+ b² = 17² Square your known values in this case 5² and 17² which is 25 and 289 respectively. The equation is now 25+b²=289 Do the inverse operation to Isolate you unknown variable which is b. We do this by subtracting 25 on both sides after doing so the equation is now b²= 264 Square root both sides of the equation the point is to get rid of the squared part of b². After doing so your answer is b = 16.2480768093Round to the first decimal place the two remains the same so the final answer is 16.2 cmRelated Questions
a farmer wants to make a rectangular field with a total area of 2000 square meters. it is surrounded by a fence. it is divided into 4 equal areas by fences. what is the shortest total length of fence this can be done with?
Answers
The shortest total length of fence this can be done with will be 440 m as the total area is 2000 m².
What is perimeter?The length of a shape's outline is its perimeter. You must add the lengths of all four sides of a rectangle or square to determine its perimeter. In this instance, x represents the rectangle's length and y its width. The distance around an object is called the perimeter. For instance, the yard of your home is fenced in. The fence's length serves as the perimeter. Your fence is 200 feet long if the yard is 50 feet by 50 feet.
Here,
The area=2000 m²
xy=2000
x=2000/y
p=4x+2y
p=4*(2000/y)+2y
=8000/y+2y
p'=-8000/y²+2
-8000/y²+2=0
2y²-8000=0
y²-4000=
y²=4000
y= 20 m
p=8000/20+2*20
p=400+40=440 m
Given that the total area is 2000 m², the shortest total length of fence that can be used is 440 m.
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please help . find abc
Answers
The required value of ∠ABC in the given triangle is 50°
Explain the relation between interior and exterior angles?The relation between interior and exterior angles of the triangle are related as, the sum two interior angles of triangle is equal to the opposite exterior angle of that triangle.
As we see in the given question, the sum of angle ∠A and ∠B is equal to the exterior angle which is 145°
According to the question:⇒ 2x° + 95° = 145°
⇒ 2x° = 145° - 95°
⇒ 2x = 50°
Thus, required answer of angle ∠ABC is 50°
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a music store buys instruments and then sells them for more than they paid. during a off sale, the store offers a clarinet for . how much did the store pay for the clarinet?
Answers
The current price of the clarinet and the various discounts and markups illustrate that the amount the store paid was $90.
How to calculate the price?First find out the selling price of the clarinet:
= Discounted price / ( 1 - discount rate)
= 93.60 / ( 1 - 20%)
= $117
This selling price is 30% more than what the store paid so the price the store paid was:
= Selling price / ( 1 + rate of increase)
= 117 / ( 1 + 30%)
= $90
In conclusion, the amount the store paid was $90.
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Complete question
A music store buys instruments and then sells them for 30% more than they paid. During a 20% off sale, the store offers a clarinet for $93.60.
How much did the store pay for the clarinet?
The Clark's updated their living room by purchasing a new chair for $162.98. They paid 9% sales tax on their purchase. If
the Clark's paid $180.98 total, determine if they paid the correct amount.
Answers
162.98 multiplied by 1.09 which is 109 percent is equal to 177.65
11. Using the equation: y + 2 = 3(x - 1).
a) Identify the slope and y-intercept.
b) Graph the equation.
c) Does the point (0,0) satisfy the equation?
Justify your answer.
Answers
For the given equation, the slope is 3 and the y-intercept is -5. From the graph, it is possible to see that the point (0,0) does not satisfy the equation.
Linear Function
An equation can be represented by a linear function. The standard form for the linear equation is: y= mx+b , for example, y=x+19. A line equation also can be represented by the point-slope form: [tex](y-y_1)=m(x-x_1)[/tex].
m= the slope.
[tex](x_1,y_1)[/tex]= the coordinate of a point.
For the given example: m=1 and b=19.
The question gives: y + 2 = 3(x - 1). Therefore,
y + 2 = 3(x - 1)
y=3x-3-2
y=3x-5
Letter A - Identify the slope and y-interceptIf y=3x-5 . Here, you have a standard form of a linear equation y=mx+b. Where:
m= the slope. It can be calculated for Δy/Δx.
b= the constant term that represents the y-intercept
Thus, the slope is 3 and the y-intercept is -5.
Letter B - Graph the equation.For this, you should do a table with points
x y= 3x-5
-2 y=3*(-2)-5=-6-5= -11
-1 y=3*(-1)-5=-3-5= -8
0 y=3*(0)-5=0-5= -5
1 y=3*(1)-5=3-5= -2
2 y=3*(2)-5=6-5= 1
Draw a graph from these points, see the attached image.
Letter C - Does the point (0,0) satisfy the equation?The point (0,0) does not satisfy the equation because when x=0 because y is different than zero (0). See below.
y= 3x-5, for x=0
y=3*0-5
y=0-5
y=-5
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a variable t follows a uniform probability distribution where t is between 0 and 8 what is the probability that the random variable has a value greater than 5?
Answers
There is a 1/3 chance that random variable will have a value higher than 5.
Define the term random variable?A random variable is called with an unknown value or a function that gives values to each of the results of an experiment. Random variables are similarly defined by letters and fall into one of two categories: continuous variables, which can take on any value within a continuous range, or discrete variables, which have specified values.For the variable t, which follows uniform probability distribution.
0 ≤ t ≤ 8
Total variables = 9.
For the probability of value greater than 5 for the random variable.
P(t > 5) = P(t = 6) + P(t = 7) + P(t = 8)
P(t > 5) = 1/9 + 1/9 + 1/9
P(t > 5) = 3/9
P(t > 5) = 1/3
Thus, there is a 1/3 chance that random variable will have a value higher than 5.
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Pls Help Me With this
1. 2.1 x 5.12 =____ 2.12.3 x 1.6 =
Estimate______ Estimate____
3. 6.5 x 3.1 =____ 4. 51.3 x 2.7 = ____
Estimate_____ Estimate______
Answers
The corresponding estimate for numbers in 1,2,3 and 4 are 10, 24, 21 and 153
How to estimate numbers?
Estimation and approximation is the process of using rounded values when presenting numerical data and making rough calculations.
The digits 1,2,3 and are rounded down and digits 5,6,7,8 and 9 are rounded up
1. 2.1 x 5.12 = 2 x 5 = 10
Explanation: The number after the digit 2 in 2.1 is 1, we will round down 2.1 to 2. Also, the number after the digit 5 in 5.12 is 1, we will round down 5.12 to 5
2. 12.3 x 1.6 = 12 x 2 = 24
Explanation: The number after the digit 12 in 12.3 is 3, we will round down 12.3 to 12. Also, the number after the digit 1 in 1.6 is 6, we will round up 1.6 to 2
3. 6.5 x 3.1 = 7 x 3 = 21
Explanation: The number after the digit 6 in 6.5 is 5, we will round up 6.5 to 7. Also, the number after the digit 3 in 3.1 is 1, we will round down 3.1 to 3
4. 51.3 x 2.7 = 51 x 3 = 153
Explanation: The number after the digit 51 in 51.3 is 3, we will round down 51.3 to 51. Also, the number after the digit 2 in 2.7 is 7, we will round up 2.7 to 3
Therefore, the estimate for 1,2,3 and 4 are 10, 24, 21 and 153 respectively
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F(x)=-2x-3 find f(-1)
Answers
Answer:
x = -1
Step-by-step explanation:
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Answer:
-1
Step-by-step explanation:
Replace the variable x with 1 in the expression .
f(1)= 2(1) - 3
Remove the parenthasis
2(1) - 3
Multiply 2 by 1
2 - 3
subtract 2 from 3
-1
on a particular busy section of the garden state parkway in new jersey, police use radar guns to detect speeding drivers. assume the time that elapses between successive speeders is exponentially distributed with the mean of 15 minutes. what is the probability of a waiting time in excess of 25 minutes between successive speeders?
Answers
There is an 18.92% chance that there will be a wait of more than 25 minutes between speeders.
Define probability.Information about the possibility that something will happen is provided by probability. For instance, meteorologists use weather patterns to forecast the likelihood of rain. Probability theory is utilized in epidemiology to comprehend the connection between exposures and the risk of health outcomes. Probability is the likelihood that something will occur or the probability that something will happen. Probability is the measure of how likely it is that a coin will land heads up after being tossed into the air.
Given,
On a particular busy section of the garden state parkway in new jersey, police use radar guns to detect speeding drivers. assume the time that elapses between successive speeders is exponentially distributed with the mean of 15 minutes.
Either the wait is over 25 minutes or it is less than 25 minutes. Decimal 1 represents the total of these events' probabilities. So,
P( X ≤ 25) + P(X > 25) = 1
For P(X > 25):
1 -P(X ≤ 25)
1 - e ⁻⁰⁶⁶⁶⁽²⁵⁾
0.1892
There is an 18.92% chance that there will be a wait of more than 25 minutes between speeders.
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The price of a gallon of gasoline is $2.25. The price when Ryan's mother started driving was 1/5 of the current price. What was the price of gasoline when Ryan's mother started driving?
Answers
The price of gasoline when Ryan's mother started driving is $0. 45
What is a fraction?A fraction can be defined as the part of a whole set, data or element.
The different types of fractions include;
Improper fractionsProper fractionsMixed fractionsSimple fractionsComplex fractionsExample of mixed fractions; 2 1/ 3
Example of simple fractions; 1/ 2
Example of proper fractions; 2/5
From the information given, we have;
Price of a gallon of gasoline is $2. 25
1/ 5 of $2.25
This is represented as;
1/ 5 × $2.25
Multiply the values
$0. 45
Hence, the value is $0. 45
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How can a negative number be written in scientific notation?
PLS AWNSER
For example, what is ‒0.0026 written in scientific notation?
Does any part of the process change because the number being converted is negative?
Answers
Answer:
-2.6 x 10-3
Step-by-step explanation:
if you enter the equation into a calculator it will do it for you. If you want to do it with a calculator heres how to. You would move the decimal to the first whole number for example in this case 2. How many places is that? 3. Whenever a decimal point moves to the right the spot is negative. You would then write it 2.6 with 10 (exponent -3)
Answer:
Step-by-step explanation:
To rewrite in scientific notation means to add an exponent such as e-3 in this case or [tex]10^{x}[/tex] where x is the exponent.
you would convert -0.0026 to -2.6e-3 or [tex]-2.6*10^{-3}[/tex]
The basic way of converting to scientific notation is to move your number a certain amount of decimal places until there is one number left before the decimal mark. Then the amount of values moved turns into you're exponent. A negative exponent means your are going towards a smaller number. Make sure to keep the current sign of the number
[tex]x^{2}-6x+1=0[/tex]
Solve the quadratic equation using the quadratic formula.
Show exact answers in simplified radical form; no rounded decimals.
Answers
The solutions of the quadratic equation using the quadratic formula is x = 3 + 2√2 and x = 3 - 2√2
Solving Quadratic equation using the Quadratic formulaFrom the question, we are to solve the given quadratic equation using the quadratic formula
The given quadratic equation is
x² - 6x + 1 = 0
Using the quadratic formula,
x = [-b±√(b² - 4ac)] / 2a
a = 1, b = -6, and c = 1
Thus,
x = [-(-6) ±√((-6)² - 4(1)(1))] / 2(1)
x = [6 ±√(36 - 4)] / 2
x = [6 ±√(32)] / 2
x = [6 ± 4√2] / 2
x = [2(3 ± 2√2)] / 2
x = 2(3 ± 2√2) / 2
x = (3 ± 2√2)
x = 3 + 2√2 and 3 - 2√2
Hence, the roots are 3 + 2√2 and 3 - 2√2
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a gardener has 1040 feet of fencing to fence in a rectangular garden. one side of the garden is bordered by a river and so it does not need any fencing. garden bordered by a river what dimensions would guarantee that the garden has the greatest possible area?
Answers
The dimensions 520 by 360 feet would guarantee that the garden has the greatest possible area .
Let length be l and width be b of garden .
According to question ,
l + 2b = 1040
Area of garden = l * b
Substituting value of l in formula for area ,
Area = ( 1040 - 2b ) * b = 1040b - 2[tex]b^{2}[/tex]
Taking derivative of Area wrt. b and putting it equal to 0 ,
1040 - 4b = 0
b = 1040 / 4
b = 260 feet
Therefore , l = 1040 - 520 = 520 feet .
Maximum Area = 260 * 520 = 135200 [tex]feet^{2}[/tex] .
Hence , the dimensions 520 by 360 feet would guarantee that the garden has the greatest possible area .
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Which of these strategies would eliminate a variable in the system of equations?
Answers
The strategy which would eliminate a variable in the system of equations is to multiply the top equation by 6 ,multiply the bottom equation by -5 then add the equation and is denoted as option B.
What is Equation?This is a mathematical term which is made up of two expressions and is connected by an equal sign.
In the example given below:
8x + 5y = -7
-7x + 6y = -4
We can multiply the top by 6 and the bottom by -5 which will result in:
48x + 30y = -42
35x - 30y = 20
They are then added to each other to give:
48x + 35x + 30y - 30y = -42 + 20
83x = - 22
x = -22/83
From this we can notice that the variable y was eliminated which is why option B is the correct choice.
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There are 15 circles and 6 squares. What is the simplest ratio of squares to total shapes?
Answers
Answer:
2/7Step-by-step explanation:
There are 15 circles and 6 squares.
Total shapes:
15 + 6 = 21Ratio of squares to total shapes:
6/21 = 2/7Answer:
the answer is 2:7
Step-by-step explanation:
6÷3 : 21÷3
=2:7
The altitude y in feet of a hawk that is descending can be represented by the equation y=−20x+350, where x represents the time in minutes. The equation y=−10x+400 represents the altitude y in feet of an eagle after descending x minutes.
Which bird is closer to the ground after 8 minutes?
The
eagle
is closer to the ground.
How much closer?
feet
hurry
Answers
The hawk is closer to the ground after 8 minutes
It is 130 feet closer
How to determine the valuesWe have the equation as;
y = −20x+350. This represents the altitude y in feet of a hawky=−10x+400. This represents the altitude y in feet of the eagleAlso, x represents the descending time in minutes
Now, let's substitute the value of x as 8 minutes in the equations
If x = 8
For equation (1)
y = - 20(8) + 350
expand the bracket
y = - 160 + 350
y = 190 feet
For equation (2)
y = -10(8) + 400
expand the bracket
y = -80 + 400
y = 320 feet
The hawk is closer after 8 minutes
The distance from the ground(eagle) - The distance from the ground(hawk)
320 - 190
130 feet
Hence, the hawk is closer to the ground
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Darryl’s portfolio includes 66 shares of Essentia Inc., 95 shares of SFT Legal, and 180 shares of Grath Oil. If Essentia Inc. pays a yearly dividend of $1.79 per share, SFT Legal pays $2.62 per share, and Grath Oil pays $1.18 per share, how much does Darryl receive in dividends every year?
Answers
Darryl receive $579.44 in dividends every year .
In the question ,
it is given that
Darryl's portfolio
number of shares of Essentia Inc. = 66
dividend received from each share in a year = $1.79 per share
So , amount of dividend received from Essentia Inc. = 66 × 1.79
= $118.14
number of shares of SFT Legal = 95
dividend received from each share in a year = $2.62 per share
So , amount of dividend received from SFT Legal = 95 × 2.62
= $248.9
number of shares of Grath Oil = 180
dividend received from each share in a year = $1.18 per share
So , amount of dividend received from Essentia Inc. = 180 × 1.18
= $212.4
So , total dividend Darryl receives = $118.14 + $248.9 + $212.4
= $579.44
Therefore , amount of dividend received by Darryl each year is $579.44 .
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Substitution
2x-6y=18
x = 3y + 9
Answers
Answer:
x=17/14 y=5/21
What is the mathematical answer to 5x=3.75
Answers
Answer:
x=0.75
Step-by-step explanation:
5x=3.75
/5. /5
x=0.75
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(THIS FOR A TEST. WILL GIVE BRAINLIEST) 5. A banquet hall has two types of tables, rectangular and round. The rectangular tables can fit 8 people sitting around them. The round tables can fit 6 people sitting around them. The hall will be hosting a banquet for 192 people. Assume all tables will have the maximum number of people seated at the table.
a. Write an equation in standard form showing the relationship between the number of rectangular tables, z, and the number of round tables, y, that are needed to seat 192 people.
b. Find the z-intercept and explain its meaning in the context of the problem.
c. Find the y-intercept and explain its meaning in the context of the problem.
Answers
Answer:
its A.
Step-by-step explanation:
Solve for x.
4(2x-17)=4x+(-5)
Answers
Step-by-step explanation:
4(2x-17) = 4x+(-5)
Open the bracket
8x - 68 = 4x - 5
Collect like terms
8x - 4x = -5 + 68
2x = 63
x = 63/2
x = 31.5
8x-68=4x-5
Move variables to one side.
4x=73
Divide.
x=18.25 or 73
—
4
Rewrite the following equation in slope-intercept form.
y − 8 = 2(x + 6)
Answers
Use distributive property, then add 8 to both sides. Hope this helps :)
In order to get this answer u must distribute 2 into the parenthesis, when h done u must move the constant (which is 8) to the right side of the equation. After u combine like terms and u will have ur final answer
Kyra ha a rock collection. When he put her rock into 2 equal pille , there are no rock left over. When he put her rock into 3 equal pile , there are till no rock left over. When he put her rock into 4 equal pile , there are till no rock left over. How many rock could Kira have ?
Answers
By applying the lowest common multiple approach, Kyra may have acquired up to 12 rocks.
What does common factor mean?
A common factor is a whole number that is a factor of at least two other numbers. The highest common factor is the largest factor that will divide into two or more numbers (HCF). The phrase "lowest common multiple" refers to the smallest multiple that two or more numbers have in common (LCM).
The least common multiple of 2, 3, and 4 can be used to determine how much rock Kyra has.
Several of:
2 = 2, 4, 6, 8, 10, 12, 14, 16, 18, 20
3 = 3, 6, 9, 12, 15, 18, 21
4 = 4, 8, 12, 16, 20
The smallest number that 2, 3, and 4 have in common is 12. There are therefore 12 rock piles in Kyra's possession.
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If the price of gas was $3.12 on the first day of school and $3.55 on the fifth day, what was the rate of change in the price of gas per day)
Answers
it's a easy question I think you can solve it
the number of defectives in 10 different samples of 50 observations each is the following: 5, 1, 1, 2, 3, 3, 1, 4, 2, 3. what is the estimate of the population proportion of defectives?
Answers
The estimate of the population proportion of defectives is 0.05.
Given that,
There are 10 different samples of 50 observations, that is, total of 500 observations.
To find : The estimate of the population proportion of defectives
And total number of defectives from 500 observations is (5+1+1+2+3+3+1+4+2+3) = 25
Thus, the point estimate for the population proportion defectives will be,
=25/500=0.05
or just obtain the individual proportion of each sample and then take their average to obtain the same result.
Thus, the point estimate for the population proportion defectives will be 0.05
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A cycle Wheel does 1645 full turns in 7 minutes
work out the number of full turns per minute
Answers
The number of full turns per minute is 235.
Given that, a cycle Wheel does 1645 full turns in 7 minutes.
What is the unitary method?The unitary method is a technique for solving a problem by first finding the value of a single unit, and then finding the necessary value by multiplying the single unit value.
Here,
The number of full turns per minute = Number of full turns/Number of minutes
= 1645/7
= 235 full turns per minute
Therefore, the number of full turns per minute is 235.
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help meeeeeeeeeeeeeeeeeee pleaseeee rn rnnnnnnnnnn!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
help meeeeeeeeeeeeeeeeeee pleaseeee rn rnnnnnnnnnn!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
Answers
-2 axis
Downwards
Given: ABCD trapeziod, AB=DC, BK - altitude, AB=8, AK=4
Find: m
Answers
The value of angle A and B are 60° and 120° respectively.
How to calculate the angles?It is important to note that in isosceles trapezoid, the angles adjacent to the bases are congruent.
Therefore A = D
B = C
When in the right angle, the hypothenuse is twice the leg, the angle opposite it will be:
ABK = 30°
Also, KBC = 90°
Therefore, B = 30° + 90° = 120°
A = D = 180° - 120° = 60°
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Complete question:
Given: ABCD trapeziod, AB=DC, BK - altitude, AB=8, AK=4
Find: mA and mB.
Solve for the value of v.
123°
(2v+1)°
Answers
Step-by-step explanation:
the angles between 2 intersecting lines must be the same on both sides of either line, they are just left-right mirrored.
so,
123 = 2v + 1
2v = 122
v = 61
A football team lost 5 yards on each of 3 plays. Explain how you could use a number line to find the team's change in field positive after the 3 plays. Then find and interpret the change in position.
Answers
The total spots moved, after the 3 plays is 15 spots to the left.
What is the unitary method?The unitary method is a method for solving a problem by the first value of a single unit and then finding the value by multiplying the single value.
Given that the football team lost 5 yards on each 3 plays.
Assume that a number line to be able to see how far in the field did they lost in 3 games.
Therefore,
1 : 5 (1 game is to 5 yards)
3 : 15 (3 games is to 15 yards )
After the first play, we would move to the left on the line 5 spots (to simulate 5 yards lost) and then make a dot to show your new position.
The total spots moved, after the 3 plays is 15 spots to the left.
Hence, All they lost 15 yards in 3 games.
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