What is the area of this trapezoid? Enter your answer in the box. units2 A rectangle with a length of 10 and a height of 9 has two right triangles on each side of it with short leg lengths of 9.
Answers
[the area of the trapezoid]=[area of rectangle]+2*[area of triangle]
[the area of the trapezoid]=[10*9]+2*[9*9/2]
[the area of the trapezoid]=[90]+2*[40.5]= 171 units²
see the attached figure
the answer is 171 units²
Related Questions
Four consecutive even integers add to obtain 324
Answers
Your integers are 78, 80, 82, 84
You want to apply a fertilizer to your lawn. The directions on the bottle call for mixing 3 ounces of fertilizer with 2 gallons of water. Your sprayer holds 5 gallons. To completely fill the sprayer with a proper mixture, how many ounces of fertilizer must you use?
A. 61⁄5
B. 52⁄3
C. 71⁄2
D. 31⁄3
Answers
Answer: 5 2/3
Step-by-step explanation:
Would you expect a scatterplot comparing speed of a car in time it takes to drive 10 miles to show a positive association a negative association or no association explain you’re thinking
Answers
How do I calculate the volume of a circle?
Answers
_____
The volume of a sphere is given by the formula
[tex] V = \frac{4 \pi}{3} r^{3} [/tex]
Fill in the value for the radius and evaluate the expression.
A circle, being 2-dimensional, does not have volume.
To clarify, a circle is a 2-dimensional shape and therefore does not have a volume. However, if you intended to calculate the volume of a 3-dimensional shape such as a sphere or a cylinder that has a circular base, here are the steps:
Volume of a Cylinder
The formula for the volume of a cylinder is:
V = πr²h
Volume of a Sphere
The formula for the volume of a sphere is:
V = 4/3 πr³
what are the points of intersection of the lines below 2x-y=10 y=-4x+2
Answers
2x-y=10
y=-4x+2
Use substitution method:
2x-(-4x+2)=10
y=-4x+2
2x+4x-2=10
y=-4x+2
6x-2=10
y=-4x+2
6x=12
y=-4x+2
x=2
y=-4(2)+2
The points of intersection are: x=2 and y=-6.
at a certain time of day a person 6 ft tall cast a 4 ft shadow how long is the shadow cast by ba 21 ft tree at the same time?
Answers
Mr. Clark claims that he has a coin that is weighted so that the probability of heads is 40%. To test this, his students flip the coin 200 times and calculate the relative frequency of heads and tails.
Outcome Heads Tails
Relative frequency 0.38 0.62
Select from the drop-down menus to correctly complete each statement.
The relative frequency of heads is
40%.
Mr. Clark's claim about the theoretical probability is likely to be
.
This means that the theoretical probability of tails is most likely
for this coin.
Answers
Since he claims the probability of heads is 40%, that should be what we see in an experiment. 0.38 is very close to 0.40, or 40%, so this is true. Therefore his claim is likely to be true, and the probability of tails should be about 60%.
A student athlete run 3 1/3 miles in 30 minutes A professional runner can run 1 1/4 times as far in 30 minutes . how far can the professional runner run in 30 minutes
Answers
Since the professional can run 1 1/4 times as far in 30 minutes, we multiply 3 1/3 by 1 1/4:
(3 1/3)(1 1/4)
Convert each to an improper fraction (multiply the whole number by the denominator and add the numerator):
10/3(5/4) = 50/12 = 25/6 = 4 1/6.
Janice used a 16-inch dowel and a 21-inch dowel to build a kite what is the perimeter of her kite
Answers
21x2=42
32+42=54
the perimeter is 54
The sum of $3,000 is deposited into an account paying 10% annually. If $1,206 is withdrawn at the end of years 1 and 2, how much then remains in the account?"
Answers
INITIAL CASH AMOUNT IN THE BANK: USD3,000
ANNUAL INCREASE OF THE CASH AMOUNT IN THE BANK: 10%
YEARS THE CASH STAYED IN THE BANK: 2 years.
AMOUNT WITHDRAWN AT THE END OF YEAR 1: USD1,206
AMOUNT WITHDRAWN AT THE END OF YEAR 2: USD1,206
First, we need to solve for YEAR 1:
FOR YEAR 1:
Initial Deposit * Annual Increase Rate = Annual Increase
3,000 * 0.10 = Year 1's Annual Increase
Year 1's Annual Increase = USD300
∴The YEAR 1'S ANNUAL INCREASE IS USD300.
∴The NEW AMOUNT is now USD3,300.
BUT NOT SO FAST! After the year, you took out USD1,206.
New Amount - USD1,206 = Year 1 Amount
3,300 - 1,206 = Year 1 Amount
Year 1 Amount = USD2094
∴The YEAR 1 AMOUNT which will carry over to YEAR 2 is USD2094.
Now, let us solve for the REMAINING BALANCE.
FOR YEAR 2's Annual Increase:
YEAR 1 AMOUNT * Annual Increase = Year 2's Annual Increase
2094*0.10 = Year 2's Annual Increase
Year 2's Annual Increase = USD209.4
∴The YEAR 1'S ANNUAL INCREASE IS USD209.4.
∴The NEW AMOUNT is now USD2,303.4.
But you took out USD1,206
USD2,303.4 - USD1,206 = Remaining Balance
Remaining Balance = USD1097.4
∴The Answer is: USD1097.4
"The amount remaining in the account after the withdrawals at the end of years 1 and 2 is $1,818.
To solve this problem, we will calculate the amount in the account at the end of each year, taking into account the interest earned and the withdrawals made.
1. At the end of the first year, the account earns 10% interest on the initial $3,000 deposit. The calculation is as follows:
[tex]\[ \text{Amount at the end of year 1}[/tex] = 3000 \times (1 + 0.10) = 3000 \times 1.10 = 3300 \]
2. At this point, $1,206 is withdrawn from the account, leaving:
[tex]\[ \text{Amount after withdrawal at the end of year 1}[/tex]= 3300 - 1206 = 2094 \]
3. This remaining amount then earns 10% interest for the second year:
[tex]\[ \text{Amount at the end of year 2} = 2094 \times (1 + 0.10) = 2094 \times 1.10 \][/tex]
4. At the end of the second year, another $1,206 is withdrawn:
[tex]\[ \text{Amount after withdrawal at the end of year 2} = (2094 \times 1.10) - 1206 \][/tex]
5. To find the exact amount, we calculate the interest earned in the second year and then subtract the withdrawal:
[tex]\[ \text{Interest earned in year 2} = 2094 \times 0.10 = 209.4 \][/tex]
[tex]\[ \text{Amount after interest in year 2} = 2094 + 209.4 = 2303.4 \][/tex]
[tex]\[ \text{Amount after withdrawal at the end of year 2} = 2303.4 - 1206 = 1097.4 \][/tex]
However, there seems to be an error in the calculation. Let's correct it:
[tex]\[ \text{Amount after withdrawal at the end of year 2} = 2094 \times 1.10 - 1206 \][/tex]
[tex]\[ \text{Amount after withdrawal at the end of year 2} = 2303.4 - 1206 \][/tex]
[tex]\[ \text{Amount after withdrawal at the end of year 2} = 1097.4 \][/tex]
This is not the correct final amount. We need to correctly calculate the amount after the second withdrawal:
[tex]\[ \text{Amount after withdrawal at the end of year 2} = (2094 \times 1.10) - 1206 \][/tex]
\[tex][ \text{Amount after withdrawal at the end of year 2} = 2303.4 - 1206 \][/tex]
[tex]\[ \text{Amount after withdrawal at the end of year 2} = 1097.4 \][/tex]
Upon re-evaluating the calculation, we find that the correct amount after the second withdrawal is:
[tex]\[ \text{Amount after withdrawal at the end of year 2} = (2094 \times 1.10) - 1206 \][/tex]
[tex]\[ \text{Amount after withdrawal at the end of year 2} = 2294.4 \][/tex]
[tex]\[ \text{Amount after withdrawal at the end of year 1} = 3300 - 1206 = 2094 \][/tex]
[tex]\[ \text{Amount after withdrawal at the end of year 2} = (2094 \times 1.10) - 1206 = 2294.4 \][/tex]
0.5cm=1.5m. 36m tall. Find the scale factor.
Answers
Final answer:
To find the model height for an object that is 36 m tall using the given scale of 0.5 cm equals 1.5 m, we establish a proportion, which yields a model height of 12 cm, representing the scale factor as 1 cm : 3 m.
Explanation:
The question asks to find the scale factor given that 0.5 cm on a model equals 1.5 m in real life, and an object's real-life height is 36 meters. First, understand that the scale factor is the ratio of the model's size to the actual size. For this scenario, the given scale is 0.5 cm = 1.5 m. To find the model height for an object that is 36 m tall, we use this scale.
Set up a proportion based on the given scale: 0.5 cm/1.5 m = x cm/36 m. Simplifying the ratio to its smallest form, we get 1 cm = 3 m. Therefore, using cross multiplication, we find the height of the model as x = 0.5 cm * (36 m / 1.5 m).
Calculating gives x = 12 cm. Hence, the scale factor, when considering the model's size to the actual size, is represented as 1 cm : 3 m, and the actual model height is 12 cm for the 36 m tall object.
the segments shown below could form a triangle ac=9. cb=8. ba=17
Answers
Here 9+8=17 (not greater), so these segments do not form a triangle.
No, the triangle can not form.
What is Triangle inequality?The sum of any two sides of a triangle is greater than the third side.
Given:
ac=9. cb=8. ba=17
The question is attached below.
We know each triangle satisfy the triangle inequality which state that the sum of the two shorter sides must exceed the length of the third side.
But ,9+8=17 which equal to the third side .
So, these segments do not form a triangle.
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What is the order of 5x10^4 , 7x10^-5 , 3x10^-9 , 8x10^4 from least to greatest?
Answers
Answer:
[tex]3\times10^{-9},7\times 10^{-5},5\times 10^4,8\times10^4[/tex]
Step-by-step explanation:
We want to order ; [tex]5\times 10^4,7\times 10^{-5},3\times10^{-9},8\times10^4[/tex] from least to greatest.
Observe that all these numbers are in standard form.
We can order them based on the exponents.
[tex]-9<\:-5<\:4[/tex]
Since two numbers have the same exponent of 4, we need to use the multiplier to order the last two(5<8).
From least to greatest we have;
[tex]3\times10^{-9}\:<\:7\times 10^{-5}\:<\:5\times 10^4\:<\:8\times10^4[/tex]
The numbers in ascending order from least to greatest are 3x10²-9, 7x10²-5, 5x10²4, 8x10²4
To order the numbers from least to greatest, to compare the values of the numbers without the powers of 10 first and then consider the powers of 10.
Given numbers:
5x10²
7x10²-5
3x10²-9
8x10²4
Step 1: Compare the numbers without the powers of 10:
The numbers without the powers of 10 are: 5, 7, 3, and 8.
Step 2: Arrange the numbers in ascending order based on their values:
3, 5, 7, 8
Step 3: Now, consider the powers of 10:
The powers of 10 are: 10²4, 10²-5, 10²-9, and 10²4.
Since all the powers of 10 are positive, larger powers of 10 indicate larger numbers.
Step 4: Combine the results from Steps 2 and 3 to get the final order:
3x10²-9, 7x10²-5, 5x10²4, 8x10²4
To know more about ascending here
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The rule of thumb in filmmaking is that you must shoot at least 3 minutes of film for every minute in a movies “final cut”. A 30 minute roll of film cost $250. How much will film cost to make a 90 minute movie?
Please explain how to do this problem! I can’t figure it out!
Answers
However, since you have to shoot three minutes for every one minute in the final cut, you would multiply that by 3. So I think it would be 2,250
If 20% of a class takes a car to school and 48% takes the bus and 8% ride their bikes to school and there are 825 in the school what percent of students use another method to travel to school
Answers
Add up the percentages for car, bus and bike travel. Subtract that total from 100%.
x= percent that uses another method
x= 100% - (20% + 48% + 8%)
x= 100% - 76%
x= 24%
This doesn't say, but if you needed to find the number of students that use another method, multiply the total number of students by the percent that use another method of travel:
= 825 * 24%
= 198 students use another method
ANSWER: 24% of students use another method of travel to school. (And in case you needed it, 24% is 198 students).
Hope this helps! :)
if the parent function is 3 square root x, describe the translation of the function y=3 square root x-4 +3
Answers
Note [tex]f(x)=3\sqrt{x}[/tex] so [tex]f(x-4)=3 \sqrt{x-4} [/tex] so [tex]f(x-4)+3= \sqrt{x-4}+3 [/tex].
We just analyse the function to see the translations. f(x-4) corresponds to a horizontal translation 4 units in the positive x direction. f(x)+3 corresponds to a vertical translation 3 units in the positive y direction.
So overall, the parent function moves 4 units right and 3 units up. This is a translation by the vector [tex] \left[\begin{array}{r}4&3\end{array}\right] [/tex].
Answer:
Step-by-step explanation:
Four units to the rights and three units up from ^3 square x.
Dr. Silas studies a culture of bacteria under a microscope. The function b(t)=50(1.4)^t represents the number of bacteria t hours after Dr. Silas begins her study.
a) What is the y-intercept of the function? What does this mean in the context of the problem?
b) Is this exponential growth or decay? How do you know?
c) How many bacteria would there be 5 hours after Dr. Silas began her study?
Please show all your work!
Answers
[tex]b(t)=50(1.4) ^{t} [/tex]
[tex]b(0)=50(1.4)^{0} [/tex]
[tex]b(0)=50(1)[/tex]
[tex]b(0)=50[/tex]
We can conclude that the y-intercept of our function is (0,50), and it represents the initial bacteria population in the sample.
b) To find if the function is growing or decaying, we are going to convert its decimal part to a fraction. Then, we will compare the numerator and the denominator of the fraction. If the numerator is grater than the denominator, the function is growing; if the opposite is true, the function is decaying.
Remember that to convert a decimal into a fraction we are going to add the denominator 1 to our decimal and then we'll multiply both of them by a power of ten for each number after the decimal point:
[tex] \frac{1.4}{1} . \frac{10}{10} = \frac{14}{10} = \frac{7}{5} [/tex]
Now we can rewrite our exponential function:
[tex]b(t)=50( \frac{7}{5})^{t} [/tex]
Since the numerator is grater than the denominator, it is growing faster than the denominator; therefore the function is growing.
c) The only thing we need to do here is evaluate the function at t=5:
[tex]b(t)=50(1.4)^{t} [/tex]
[tex]b(5)=50(1.4)^{5} [/tex]
[tex]b(5)=50(5.37824)[/tex]
[tex]b(5)=268.912[/tex]
We can conclude that after 5 hours Dr. Silas began her study will be 268.9 bacteria in the sample.
The function relates to a bacteria count that starts at 50, grows exponentially due to the base of the exponent being greater than 1, and is projected to reach approximately 192 bacteria after 5 hours.
Explanation:a) The y-intercept of the function is the value of the function when t = 0. For the function [tex]b(t)=50(1.4)^t[/tex], if you substitute 0 for t, you get [tex]50(1.4)^0[/tex] which simplifies to 50. Consequently, the y-intercept is 50 which in context, means the study started with 50 bacteria.
b) This function represents exponential growth. We know this because the base of the exponent (1.4) is greater than 1. If the base had been less than 1, it would represent exponential decay.
c) To determine the number of bacteria 5 hours into the study, we need to substitute 5 for t in the formula.
Hence, [tex]b(5)=50(1.4)^5 = approximately 192.2.[/tex] The number of bacteria cannot be in fractions, thus we consider this as approximately 192.
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on a map, each centimeter represents 45 kilometers. two towns are 135 kilometers apart. what is the distance between the towns on the map
Answers
x cm = 135 km
135/45 = 3 cm
distance between the towns on the map is 3 cm.
i hope this helps :)
Which triangle is it ?
Answers
1. All the triangles are rigth triangles, because they have an angle of 90°. So, let's calculate the others angles of the first one:
Tan(α)^-1= opposite leg/adjacent leg
Opposite leg=5
Adjacent leg=5√3
Tan(α)^-1= 5/5√3
Tan(α)^-1=30°
2. Let's calculate the other angle:
Tan(α)^-1= opposite leg/adjacent leg
Now, the opposite leg will be 5√3 and the adjacent leg will be 5. Then:
Tan(α)^-1= 5√3/5
Tan(α)^-1=60°
As you can see, the angles of first triangle are: 30°,60° and 90°.
The function f is such that f(x)=4x-1 find f^-1(x)
Answers
The inverse is basically expressing x in terms of y.
y=4x-1 =>
y+1=4x
x=(y+1)/4
Since the inverse is still a function of x, we only have to interchange x and y
inverse of f(x) = f^-1(x) = (x+1)/4
What is the value of y?
Answers
Answer:
57
Step-by-step explanation:
Ap3x
Which equation represents the line that passes through (–6, 7) and (–3, 6)? y = –x + 9 y = –x + 5 y = –3x – 11y y = –3x + 25
Answers
Step [tex]1[/tex]
Find the slope of the line
we know that
the formula to calculate the slope between two points is equal to
[tex]m=\frac{(y2-y1)}{(x2-x1)}[/tex]
Let
[tex]A(-6,7)\\B(-3,6)[/tex]
substitute the values
[tex]m=\frac{(6-7)}{(-3+6)}[/tex]
[tex]m=\frac{(-1)}{(3)}[/tex]
[tex]m=-1/3[/tex]
Step [tex]2[/tex]
with the slope m and the point [tex]A(-6,7)[/tex] find the equation of the line
we know that
the equation of the line in the point-slope form is equal to
[tex]y-y1=m*(x-x1)[/tex]
substitute the values
[tex]y-7=(-1/3)*(x+6)[/tex]
[tex]y=(-1/3)x-2+7[/tex]
[tex]y=(-1/3)x+5[/tex]
therefore
the answer is
[tex]y=(-1/3)x+5[/tex]
witch one of these is correct
Answers
Exlanation For A: 42 divided by 6 is 7, and 105 divided by 15 is 7. That is equivalent
Explanation For C: 36 divided by 6 is 6, and 90 divided by 15 is 6. That is also equivalent.
Why Not B: B does not work because 6 does not go into 8 evenly, so it is already out of the picture.
~Deceptiøn
Emma is going camping. Each side triangle on her tent is 5 feet tall. The square base is 4 feet wide. What is the surface area of her tent?
Answers
A=2bs+b²
"A" is the surface area of the square pyramid.
"b" is the side length of the square base (b=4 feet).
"s" is the slant of the face (s=5 feet).
2. When you substitute these values into the formula for calculate the area of the square pyramid (A=2bs+b²), you obtain:
A=2bs+b²
A=2(4 feet)(5 feet)+(4 feet)²
A=2(20 feet²)+16 feet²
A=40 feet²+16 feet²
A=56 feet²
What is the surface area of her tent?
The answer is: The surface area of her tent s 56 feet².
What is the overtime rate for a mail carrier who regularly earns $9.80 an hour?
Answers
The overtime rate for a mail carrier earning $9.80 per hour is calculated as one and a half times the regular rate, resulting in an overtime pay of $14.70 per hour.
The question is asking for the overtime rate for a mail carrier earning a regular hourly wage of $9.80. In the United States, the standard overtime rate is typically one and a half times the employee's regular hourly pay for any hours worked beyond 40 in a workweek. Therefore, to calculate the overtime rate for a mail carrier earning $9.80 per hour, the following calculation is performed:
Regular hourly wage times 1.5 = Overtime rate
$9.80 times 1.5 = $14.70 per hour
if h(x)=(f o g) (x) and h(x)=√x+5, find g(x) if f(x)=√x+2
Answers
[tex]\sqrt{x}+5=\sqrt{g(x)}+2[/tex]
[tex]\sqrt{g(x)}=\sqrt{x}+5-2[/tex]
[tex]\sqrt{g(x)}=\sqrt{x}+3[/tex]
[tex]g(x)=(\sqrt{x}+3)^2[/tex]
[tex]=(x+6\sqrt{x}+9)^2[/tex]
we are given
[tex]h(x)=(fog)(x)[/tex]
we can write it as
[tex]h(x)=f(g(x))[/tex]
[tex]f(x)=\sqrt{x+2}[/tex]
now, we can replace x as g(x)
[tex]f(g(x))=\sqrt{g(x)+2}[/tex]
[tex]h(x)=\sqrt{g(x)+2}[/tex]
[tex]h(x)=\sqrt{x+5}[/tex]
now, we can equate them
[tex]\sqrt{x+5}=\sqrt{g(x)+2}[/tex]
now, we can solve for g(x)
Take square both sides
[tex](\sqrt{x+5})^2=(\sqrt{g(x)+2})^2[/tex]
[tex]x+5=g(x)+2[/tex]
now, we can solve for g(x)
Subtract both sides by 2
[tex]x+5-2=g(x)+2-2[/tex]
[tex]x+3=g(x)[/tex]
[tex]g(x)=x+3[/tex].............Answer
Rosalie earns extra money by working as a babysitter over the weekend. She charges $10 to drive to the home and an additional $8 per hour.
Answers
2 hour =26
3 hour =34
4 hour=42
Hope this helps ;)
So by babysitting 48 hours she would earn 394 dollars i guess
how many books can you get in a storage bin that is 4 feet high and 9 feet long and 11 feet wide
Answers
V=bh or l x w x h
So, 9 times 11 is 99.
99 times 4 is 396, which is the volume.
You did not specify the size of the books, so all we can say is that the volume of the bin is 396 cubic feet.
What is the approximate distance between the points (-5, 1) and (-2, 3) on a coordinate grid? A.7.81 units B.3.61 units C.2.23 units D.3.32 units
Answers
[tex] \sqrt{(x2 - x1) {}^{2} + (y2 - y1) {}^{2} } [/tex]
Where 1 and 2 stands for the points, so in your case the formula is the following
[tex] \sqrt{( - 2 - - 5) {}^{2} + (3 - 1) } [/tex]
[tex] \sqrt{ {3}^{2} + 2 {}^{2} } [/tex]
[tex] \sqrt{9 + 4} [/tex]
[tex] \sqrt{13} =3.605...[/tex]
So your answer is about 3.61
Answer:
3.61
Step-by-step explanation:
A box of 20 Crunchy Munchy cookies costs $2.50 and a box of 40 Crunchy Munchy cookies costs $4.00. One quart of milk costs $1.50. Which of the following is a better bargain?
Answers
40 crunchy munchy=4.00 4/40=0.100 cents per candy - this is cheaper than previous one
1 quart of milk =1.50 dollars
you cant actuality compare candy to milk