If the area of a trapezoid is 46 sq. cm. and its height is 4 cm. Find the shorter base if itslonger base is 15 cm.
Answers
We are given the following information about a trapezoid.
Area = 46 sq cm
Height = 4 cm
Longer base = 15 cm
We are asked to find the shorter base of the trapezoid.
Recall that the area of a trapezoid is given by
[tex]A=\frac{a+b}{2}\cdot h[/tex]Let us substitute the given values and solve for the shorter side of the trapezoid.
[tex]\begin{gathered} 46=(\frac{a+15}{2})\cdot4 \\ 2\cdot46=(a+15)\cdot4 \\ 92=(a+15)\cdot4 \\ \frac{92}{4}=a+15 \\ 23=a+15 \\ a=23-15 \\ a=8\; cm \end{gathered}[/tex]Therefore, the shorter base of the trapezoid is 8 cm
Related Questions
An automobile battery manufacturer claims that its midgrade battery has amean life of 50 months with a standard deviation of 6 months. Suppose thedistribution of battery lives of this particular brand is approximately normal.ba. On the assumption that the manufacturer's claims are true, find theprobability that a randomly selected battery of this type will last less than 48months.Your answer6b. On the same assumption, find the probability that the mean of a randomsample of 36 such batteries will be less than 48 months.
Answers
Given data:
The given mean life is m=50 months.
The given standard deviation is s=6 months.
The given value of battery life is x= 48 months.
The expression for the probability of that a randomly selected battery will last less than 48 months is,
[tex]\begin{gathered} P(Z<\frac{x-m}{s})=P(Z<\frac{48-50}{6}) \\ =P(Z<-\frac{1}{3}) \end{gathered}[/tex]Refere the Z-table the value of the above expression is 0.3707.
Thus, the probability that a randomly selected battery will last less than 48 months is 0.3707.
Factor the numbers in a sequence that will have you using 21 numbers.
Answers
The sequence of numbers uses 21 numbers whereas each number in the sequence must be a factor or multiple of the previous number is 1, 7, 21.
We are given numbers from 1 to 24.
We need to find the longest sequence using the number 21 such that each number in the sequence must be a factor or multiple of the previous number.
Let the last number be 21.
The previous number of 21 must be a factor or multiple of 21.
From the given numbers we can only choose 7 as it is a factor of 21.
So, the sequence will be ...., 7, 21.
Now,
The previous number of 7 must be a factor or multiple of 7.
From the given numbers we can only choose 1 as it is a factor of 7.
So, the sequence will be 1, 7, 21.
There is not any previous number to 1.
So, our final sequence will be 1, 7, 21.
Thus, the sequence of numbers uses 21 numbers whereas each number in the sequence must be a factor or multiple of the previous number is 1, 7, 21.
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For the function f(x) = x^2 + 4, identify the values of f(0), f(1/2), and f(-1).
Answers
Explanation:
The function is given below as
[tex]f(x)=x^2+4[/tex]Find
[tex]\begin{gathered} f(0) \\ put\text{ }x=0 \\ f(0)=(0)^2+4 \\ f(0)=4 \end{gathered}[/tex][tex]\begin{gathered} f(\frac{1}{2}) \\ put\text{ }x=\frac{1}{2} \\ f(\frac{1}{2})=(\frac{1}{2})^2+4 \\ f(\frac{1}{2})=\frac{1}{4}+4 \\ f(\frac{1}{2})=\frac{17}{4} \end{gathered}[/tex][tex]\begin{gathered} f(-1) \\ put\text{ }x=-1 \\ f(-1)=(-1)^2+4 \\ f(-1)=1+4 \\ f(-1)=5 \end{gathered}[/tex]Hence,
The final answer is
[tex]4,\frac{17}{4},5[/tex]The FIRST OPTION is the correct answer
Solve for m 18 = -6m
Answers
we have the expression
18 = -6m
solve for m
that means
isolate the variable m
so
Divide both sides by -6
18/-6=-6m/-6
simplify
-3=m
Rewrite
m=-3Evaluate expressions with parenthesesWhere can we put parentheses in 45 – 22 + 9 to make it equivalent to 14?Choose 1 answer:A45 – (22 +9)(45 – 22) +9Stuck? Review related articles/videos or use a hint.Report
Answers
Answer
45 – (22 +9)
Explanation
Given the expression
45 - 22 + 9
In order to rearrange the expression to get 14, this can be expressed as:
= 45 - (22 + 9)
= 45 - 31
= 14
Hence the required answer is 45 – (22 +9)
Problem 1. Find the measure of each angle in the diagram below 85° (2x) x 35°
Answers
Answer:
x =80 degrees
2x = 160 degrees
Explanation:
The sum of angles at a point is 360 degrees. Therefore:
[tex]\begin{gathered} 85\degree+2x+x+35\degree=360\degree \\ 3x=360\degree-85-35 \\ 3x=240 \\ x=\frac{240}{3} \\ x=80 \end{gathered}[/tex]Therefore, the measure of the other angle is:
[tex]2x=2\times80=160^0[/tex]Click an item in the list or group of pictures at the bottom of the problem and, holding the button down, drag it into thecorrect position in the answer box. Release your mouse button when the item is place. If you change your mind, dragthe item to the trashcan. Click the trashcan to clear all your answers.y1098765B'C'43BсA'D'3456789 10ADХ-2 -1-2What is the length of CC' ?
Answers
as we can see from the graph coordinates of point C are (2,2) and coordinates of point C' are (7,4)
So by distance formula CC' will be
[tex]\begin{gathered} \text{length of cc'=}\sqrt[]{(7-2)^2+(4-2)^2}^{} \\ =\sqrt[]{25+4} \\ =\sqrt[]{29} \end{gathered}[/tex]So length of CC' is
[tex]\sqrt[]{29}[/tex]Construct parametric equations describing the graph of the following equation.x = 3y +3If y = 4 + 1, find the parametric equation for x.
Answers
Given:
[tex]x=4y+3,y=4+t[/tex]Required: Parametric equation of y.
Explanation:
Substitute 4+t for y into the equation of x.
[tex]\begin{gathered} x=4(4+t)+3 \\ =16+4t+3 \\ =4t+19 \end{gathered}[/tex]So, the parametric equation for x is x = 4t+19.
Final Answer: The parametric equation of x is x = 4t + 19.
I you could just give me the answer that would be great no explanation needed:)
Answers
f(n) = -1.2n + 38.1
Hence, for an additional race
the finishing time, f(n+1), is given
f(n+1) = -1.2(n+1) + 38.1 = -1.2n + 38.1 -1.2
Which implies that
f(n+1) = f(n) - 1.2
This implies that the finishing time decreases by 1.2minutes
The model predicts that for each additional race a runner has run, the finishing time decreases by about 1.2 minutes
Solve for y: y + 10 = -15
Answers
According to the given data we have the following equation:
y + 10 = -15
To solve the variable y of the equation above we would make the following:
y + 10 = -15
We would move the number 10 to the other side, so it would change its sign.
y=-15-10
Finally add the numbers So:
y=-25
The result of the y would be -25
y + 10=-15
y=-15-10
y=-25
Early last summer, Xavier planted a flower. Let y be the flower's height (incentimeters) x days after he planted it. Use the table to relate the independent variable x to thedependent variable y. First describe the relationship in words. Then write an equation. Use theequation to find the flower's height after 3 days.
Answers
i) The equation is; y = x + 16
ii) After 3 days, the height of the flower is 19 centimeters
Here, we want to describe a relationship
We start by describing the relationship between the flower's height and the number of days after it was planted
As we can see from the table, the value of x plus 16 equals the value of y
In the equation from, we have this as;
[tex]x+16\text{ = y}[/tex]To find the height of the flower after 3 days, we simply substitute the value of 3 for y
We have this as;
[tex]\begin{gathered} y\text{ = 16 + 3} \\ y\text{ = 19 } \end{gathered}[/tex]The legs of a right triangle have lengths of 15 cm and 112 cm. What is the length of the hypotenuse?
Answers
ANSWER
113 cm
EXPLANATION
The Pythagorean Theorem states that for a right triangle with leg lengths a and b, and hypotenuse c, the square of the hypotenuse is equal to the sum of the squares of the legs,
[tex]c^2=a^2+b^2[/tex]In this case, the lengths of the legs are 15 cm and 112 cm, so the length of the hypotenuse is,
[tex]c=\sqrt{15^2+112^2}=\sqrt{225+12544}=\sqrt{12769}=113cm[/tex]Hence, the length of the hypotenuse is 113 cm.
Christine ran a video game competition and recorded the scores of all the contestants. Score Number of people 426 4 572 1 859 2 900 1 1 951 2 X is the score that a randomly chosen person scored. What is the expected value of X? Write your answer as a decimal.
Answers
The expected value is defined by
[tex]E=\Sigma x\cdot P(x)[/tex]We have to multiply each score by its probability
[tex]\begin{gathered} E=426\cdot\frac{4}{10}+572\cdot\frac{1}{10}+859\cdot\frac{2}{10}+900\cdot\frac{1}{10}+951\cdot\frac{2}{10} \\ E=170.4+57.2+171.8+90+190.2 \\ E=679.6 \end{gathered}[/tex]Hence, the expected value is 679.6.write each percent as a fraction in simplest form 1. 80%=
Answers
4/5
Explanation:
80%
[tex]\begin{gathered} \frac{80}{100}=\text{ }\frac{8}{10} \\ \text{this we divided both numerator an denominator by 10 } \end{gathered}[/tex]dividing both numerator an denominator by 2:
[tex]\frac{8}{10}=\text{ }\frac{4}{5}[/tex]fraction in simplest form = 4/5
please help, and answer quickly my brainly keeps crashing. please answer quickly.
Answers
We will have the following:
We calculate the total surface area as follows:
[tex]A_s=4(\frac{11in\ast10in}{2})+(11in)^2\Rightarrow A_s=341in^2[/tex]So, the total surface area of the pyramid is 341 in^2.
15. Bryson and Fady work at a PS4 factory, Bryson arrived at work before Fady and began making PS4's. Bryson had already made 30 PS4's when Fady began his work. Bryson was producing PS4's at a rate of 5 PS4's per hour. Fady was able to produce PS4's at a rate of 8 PS4's per hour. At some point, Bryson and Fady will have produced the same number of PS4's. Part A: Write a system of equations to represent the situation. Let x = hours and y=PS4's.
Answers
Bryson:
Already made PS4's = 30
Number of PS4's per hour = 5
Fady :
Number of PS4's per hour = 8
x= hours
y= ps4's
Bryson equation:
y= 30+5x
The number od PS4's made by Bryson (y), must be equal to the sum of the already made PS4's (30) and the product of the number of PS4's made per hour (5) and the number of hours (x)
Fady:
y= 8x
System of equations:
y= 30+5x
y= 8x
find the sum of the first 46 terms of the following series to the nearest integer 12,15,18
Answers
Here, we want to find the sum of the first 46 terms of the series
Here, what we have is a series with a first term of 12 and a common difference of 15-12=18-15 = 3
Before we proceed to get the sum of the first 46 terms, we can calculate the last term
The last term is given as;
[tex]\begin{gathered} a_n\text{ = a + (n-1)d} \\ \\ a_{46}\text{ = 12 + (46-1)3} \\ \\ a_{46}\text{ = 12 + 45(3)} \\ \\ a_{46}\text{ = 12 + 135 = 147} \end{gathered}[/tex]Now, we can apply the formula to get the sum
The formula is given as;
[tex]\begin{gathered} Sn\text{ = }\frac{n}{2}\text{ (a + l)} \\ \\ S_{46}\text{ = }\frac{46}{2}(12\text{ + 147)} \\ \\ S_{46}\text{ = 23(159)} \\ \\ S_{46}\text{ = 23 }\times\text{ 159 = 3657} \\ \text{Where the last term is given as l above} \end{gathered}[/tex]Solve y - 3x = 13 for y.у=
Answers
square pyramid volume 225 cubic inches , base Edge 5 in . Determine the height of the pyramid
Answers
The volume of a pyramid is:
[tex]V=\frac{1}{3}\times B\times h[/tex]Where B is the area of the base and h is the height.
Since it's a square pyramid, the base has the shape of a square. So it's area is:
[tex]B=5in\times5in=25in^{2}[/tex]And we have that the volume is 225in³. We can replace these values into the formula for the volume and solve for h:
[tex]\begin{gathered} 225in^3=\frac{1}{3}\times25in^2\times h \\ \frac{3\times225in^{3}}{25in^2}=h \\ h=27in \end{gathered}[/tex]The height of the pyramid is 27 inches
Write a system of equations to describe the situation below, solve using elimination, and fill in the blanks. To keep in shape, Tisha exercises at a track near her home. She requires 24 minutes to do 6 laps running and 3 laps walking. In contrast, she requires 20 minutes to do 6 laps running and 2 laps walking. Assuming she maintains a consistent pace while running and while walking, how long does Tisha take to complete a lap? Tisha takes minutes to run a lap and minutes to walk a lap.
Answers
Let R be the minutes Tisha runs and W be the minutes Tisha walks. Since she requires 24 minutes to do 6 laps running and 3 laps walking, we have the following equation:
[tex]6R+3W=24[/tex]Now, when she requires 20 minutes to do 6 laps running and 2 laps walking, we have:
[tex]6R+2W=20[/tex]So, we have the following system of equations:
[tex]\mleft\{\begin{aligned}6R+3W=24 \\ 6R+2W=20\end{aligned}\mright.[/tex]We are going to solve it by elimination. Notice that the coefficients of R are the same, so we just have to multiply one equation by -1 and add it altogether to the other equation:
[tex]\begin{gathered} (6R+2W=20)(-1) \\ \Rightarrow-6R-2W=-20 \end{gathered}[/tex]Then:
[tex]\begin{gathered} 6R+3W=24\rbrack \\ -6R-2W=20 \\ \Rightarrow(6R-6R)+(3W-2W)=24-20 \\ \Rightarrow W=4 \end{gathered}[/tex]Now we use the value W=4 to find R:
[tex]\begin{gathered} W=4 \\ 6R+3W=24 \\ \Rightarrow6R+3\cdot4=24 \\ \Rightarrow6R=24-12=12 \\ \Rightarrow6R=12 \\ \Rightarrow R=\frac{12}{6}=2 \\ R=2 \end{gathered}[/tex]Therefore, it takes Tisha to complete a lap 2 minutes if she's running and 4 minutes if she's walking.
Solve for y.2(y – 11) = 16HURRYYYY!!!
Answers
The initial expression is:
2 ( y - 11 ) = 16
Using the distributive property:
2y - 2*11 = 16
2y - 22 = 16
Adding 22 on both sides:
2y - 22 + 22 = 16 + 22
2y = 38
Dividing by 2 on both sides:
[tex]\begin{gathered} \frac{2y}{2}=\frac{38}{2} \\ y=19 \end{gathered}[/tex]Answer: y = 19
you have p fewer pizza than sam who has 15 slices. what expression shows how many slices of pizza you have?
Answers
where y are my slices of pizza
Randall is buying house for $242,000. His down payment is 55% of the price. The mortgage ratefor a 5-year term is 8.2% per annum, compounded semi-annually, amortized over 25 years, andpaid monthly.a) For how much is the mortgage, once the down payment is deducted and compounded?b) How much are the monthly payments,,,,,
Answers
SOLUTION
Given the question in the image, the following are the solution steps to answer the question.
STEP 1: Write the given values
[tex]\begin{gathered} Total\text{ payment}=242000 \\ down\text{ payment}=55\% \\ rate\text{ for compunding}=8.2\%=\frac{8.2}{100}=0.082 \\ n=2\text{ since it is compounded semi-annually} \\ t=5\text{ years} \end{gathered}[/tex]STEP 2: Find the mortgage value
[tex]mortgage\text{ }value=Total\text{ payment}-Down\text{ payment}[/tex]Down payment will be calculated:
[tex]\begin{gathered} 55\%\text{ of \$242000} \\ \frac{55}{100}\cdot242000=0.55\cdot242000=\text{ \$}133100 \end{gathered}[/tex]To calculate the mortgage value, we first calculate the compounded amount,
[tex]\begin{gathered} A = P(1 + \frac{r}{n})^{nt} \\ A=108900\cdot(1+\frac{0.082}{2})^{2\cdot5} \\ A=108900\cdot(1.041)^{10} \\ A=162755.3131\approx\text{ \$}162755.31 \end{gathered}[/tex]Hence, the mortgage value will be approximately $162755.31
Then we calculate the monthly payments
Number of months between 25 years will be:
[tex]\begin{gathered} 1\text{ year}=12\text{ months} \\ 25\text{ years}=25\cdot12=300\text{ months} \end{gathered}[/tex]Therefore, the monthly payments will be:
[tex]\text{ }\frac{\text{ \$}162755.31}{300}=542.5177\approx\text{ \$}542.52[/tex]The monthly payments will be approximately $542.52
Find the missing arc:
Arc BC =
Answers
Let the measure of arc [tex]BC[/tex] be [tex]\alpha[/tex].
[tex]\frac{70+\alpha}{2}=85 \\ \\ 70+\alpha=170 \\ \\ \alpha=\boxed{100^{\circ}}[/tex]
Students sold 342 tickets to the school carnival at $11.75 each. Nine tickets were refunded. Estimate the amount of money that the school took in. Is your estimate and over estimate or underestimate?
Answers
Let:
x = Number of tickets
a = Price of each ticket
T = Total amount of money
so:
[tex]\begin{gathered} T=ax \\ \end{gathered}[/tex]Since nine tickets were refunded,
let:
y = Number of tickets refunded.
[tex]\begin{gathered} T=ax-ay \\ where\colon \\ a=11.75 \\ x=342 \\ y=9 \\ so\colon \\ T=11.75(342)-11.75(9) \\ T=4018.5-105.75 \\ T=3912.75 \end{gathered}[/tex]Answer:
$3912.75
Which of the following equations correctly describes the graphed line?y = -1/2x - 5y = -1/2x + 5y = 1/2x + 5y = 1/2x - 5
Answers
We can see in the graph that the y-intercept is equal to +5. According to that, the correct options could be second and third options.
The line has a positive slope and the third option has a positive slope (1/2), therefore, this is the correct answer. (Since the second option has a negative slope (-1/2)).
The answer is y= 1/2x + 5
could u please help me by writing this out as a example ? solve for x
Answers
ANSWER:
In the given expression, we have to solve for 'x', and show the steps.
[tex]r\text{ =}\frac{5+x}{w}[/tex]Next, I am gonna solve it for 'x'
[tex]\begin{gathered} r=\frac{5+x}{w} \\ M\text{ultiplying both sides by 'w' and subtracting 5 from both sides gives.} \\ wr=5+x \\ x=wr-5 \end{gathered}[/tex]We have solved for 'x'.
multiple both sides by w
rw = 5 + x
subtract both sides by 5
rw - 5 = x
switch sides
x = rw - 5
Write an equivalent expression using the distributive property:
2(3x+4b)
Answers
Answer:
[tex]2(3x + 4b ) = 6x + 8b[/tex]
A car advertisement states that a certain car can accelerate from rest to 72 km/h in 12.5 seconds.
Initially the car is at rest, so the initial velocity is ______
m/s.
The car speeds up to 72 km/h which is equivalent to _______
m/s. Find the car’s average acceleration.
The acceleration of the car is _______
m/s2
Answers
The motion of the car (velocity and acceleration) based on the advertisement can be described as follows;
The initial velocity of the car is 0 m/s
72 km/h is equivalent to 20 m/s
The acceleration of the car is 1.6 m/s²
What is velocity and acceleration?Velocity is the rate of change of displacement
Acceleration is the rate of change of velocity with time
The car accelerates from rest indicates that the initial velocity of the car is 0 m/sThe speed to which the car accelerates to is 72 k m/h
To convert from km/h to m/s, the conversion factor is1000/3600
Therefore;
72 km/h = 72 × 1000/3600 m/s = 20 m/s
The speed of the car of 72 km/h is equivalent to 20 m/sAcceleration can be found from the rate of change of the velocity as follows;
[tex]Acceleration = \dfrac{Change\, in \, \, velocity}{Time}[/tex]
The time it takes the car to increase from 0 to 72 kph (20 m/s) = 12.5 seconds
The acceleration of the car is therefore;
[tex]a = \dfrac{20 - 0}{12.5 - 0} = 1.6[/tex]
The acceleration of the car is 1.6 m/s²Learn more about velocity and acceleration here:
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Pls make sure u explain how u did part A no big words thank u
Answers
We need to calculate the following quotient:
[tex]\frac{8n^6-16n^4}{4n^3}[/tex]We know that:
[tex]\begin{gathered} 8n^6=4n^3\cdot2n^3 \\ 16n^4=4n^3\cdot4n \end{gathered}[/tex]Then:
[tex]\frac{8n^6-16n^4}{4n^3}=\frac{4n^3\cdot2n^3-4n^3\cdot4n}{4n^3}[/tex]Using the distributive property of multiplication, we factor the 4n³ term of the numerator:
[tex]\begin{gathered} \Rightarrow\frac{4n^3\cdot2n^3-4n^3\cdot4n}{4n^3}=\frac{4n^3(2n^3-4n)}{4n^3} \\ \therefore\frac{8n^6-16n^4}{4n^3}=2n^3-4n \end{gathered}[/tex]