Sonia makes a wooden frame around a square picture. The frame is made of 4 congruent trapezoids. The shorter base is 9 in., the longer base is 12 in., and the height is 1.5 in. What is the area of the picture frame? PLEASE tell me why the answer is that answer.
Answers
Final answer:
The area of Sonia's picture frame is determined by calculating the area of one trapezoid with given dimensions and multiplying by four. The area of each trapezoid is 15.75 square inches, resulting in a total frame area of 63 square inches.
Explanation:
The area of Sonia's picture frame can be calculated by finding the area of one of the congruent trapezoids and then multiplying it by four, since there are four trapezoids making up the entire frame. The formula to calculate the area of a trapezoid is: Area = (1/2) × (base1 + base2) × height. In this case, the shorter base (base1) is 9 inches, the longer base (base2) is 12 inches, and the height is 1.5 inches. Substituting these values into the formula gives us: Area of one trapezoid = (1/2) × (9 in + 12 in) × 1.5 in = (1/2) × 21 in × 1.5 in = 15.75 in2. The total area of the frame is then four times this amount, which equals 63 in2. This answer explains how to calculate the area of a trapezoid and then applies the concept to find the total frame area.
Related Questions
What is the measure of angle x? m∠x
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x = 180 - 44 - 53 = 83 degrees
Can anyone explain this to me??
Answers
hey does anyone know this
the volume of a cone is 27 pi cm cubed
and the radius is 3 cm
what is the height of the cone
Answers
- Plug into the equation. 27π(cubed)=π∙3(2)∙h
-Solve. 27π(3)=9π∙h
27π/9π=3π
I believe the height is 3π.
Hope this helps
if Anne's age is represented by the variable (a) then.... Epress Jenny's age in terms of (a) if Jenny is 3 years less than 1/2 of Anne's age.
Express Fraz's age in terms of (a) if Fraz is twice the sum of Anne's age and 7
Answers
Jenny's age in terms of Anne's age is j = (1/2)a - 3 and Fraz's age in terms of Anne's age is f = 2(a + 7).
Explanation:To express Jenny's age in terms of Anne's age (a), we can use the information given that Jenny is 3 years less than 1/2 of Anne's age. Therefore, Jenny's age (j) can be expressed as:
j = (1/2)a - 3
To express Fraz's age in terms of Anne's age (a), we can use the information given that Fraz is twice the sum of Anne's age and 7. Therefore, Fraz's age (f) can be expressed as:
f = 2(a + 7)
Learn more about Expressions here:https://brainly.com/question/14083225
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PLEASE HELP = simplify 3/4(-10+2/5)
Answers
If you use the distributive property, you need to distribute 3/4 to -10 and 2/5. Distribute means you will multiply it so your resulting equation will be this:
[tex] \frac{-30}{4} - \frac{6}{20} [/tex]
Before you can add, you need to first make them like terms because you cannot add unlike fractions. Get the LCD and form your new equation:
[tex] \frac{-150+6}{20} [/tex]
Now you can just add them together to get:
[tex] \frac{-144}{20} [/tex]
and then simplify your fraction:
[tex] \frac{-36}{5} [/tex] or - [tex] \frac{36}{5} [/tex]
The whole fraction becomes negative because when you divide integers and of them is negative, the final answer will be negative.
Answer:-7.2
Step-by-step explanation: -10+2/5 = -9.6 than -9.6 x 3/4 = 7.2
What is the area of this figure? Enter your answer in the box.
Answers
Answer:
35
Step-by-step explanation:
Archie went to an arcade to play video games he paid $2 for every 11 tokens he bought he spent a total of $16 on tokens which equation can be used to determine t the number of tokens Fred bought
Answers
Rachel has 60 scones. She sells them to Robbie, Cameron, Louis, Tom and Charlie in that order. Each customer buys more scones then the last and the increase is the same number in each case. Robbie and Cameron's combined total number of scones is three sevenths of the total of Louis, Tom and Charlie. How many scones does each boy buy?
Answers
Let's use n for amount that each following customer increases.
We have:
Robbie=x
Cameron=x+n
Louis=x+n+n
Tom=x+n+n+n
Charlie=x+n+n+n+n
We know that they bought total of 60 scones.
Robbie + Cameron + Louis + Tom + Charlie = 60
x + x+n + x+n+n + x+n+n+n + x+n+n+n+n = 60
5x + 10n = 60 /:5
x + 2n = 12
We are also given this information:
(Robbie + Cameron) = 3/7 * (Louis + Tom + Charlie)
We insert the equations from above:
(x + x+n) = 3/7 * (x+n+n + x+n+n+n + x+n+n+n+n)
2x + n = 3/7 * (3x + 9n) /*7
14x + 7n = 3* (3x + 9n)
14x +7n = 9x + 27n
We take everything on the left side.
14x + 7n - 9x - 27n = 0
5x - 20n = 0/:5
x - 4n = 0
Now we have two equations:
x + 2n = 12
x - 4n = 0
We solve second one for x and insert it into first one.
x + 2n = 12
x = 4n
4n + 2n =12
6n = 12 /:6
n = 2
x=4*2
x=8
Now we can solve for the amount for each customer.
Robbie=x = 8
Cameron=x+n = 8 + 2 = 10
Louis=x+n+n = 8 + 2 + 2 = 12
Tom=x+n+n+n = 8 + 2 + 2 + 2 = 14
Charlie=x+n+n+n+n = 8 + 2 + 2 + 2 + 2 = 16
Which expression is equivalent to 2 3 (3x + 9y) + 1 2 (4x - 2y)? A) x + 4y B) 8x - y C) 4x + 5y D) 2x + 5y
Answers
We use the Distributive Property on both parts of this:
2/3(3x + 9y) + 1/2(4x - 2y)
= 2/3(3x) + 2/3(9y) + 1/2(4x) - 1/2(2y)
= 6/3x + 18/3y + 4/2x - 2/2y
= 2x + 6y + 2x - 1y
Combine like terms and we have:
4x + 5y
Find the distance (-2,-6), (2,-2)
Answers
(6x^3+x^5+2x^2−7−4x)−(3x^2−5x+2+5x^5+3x^4)
Answers
Distribute the Negative Sign:=6x3+x5+2x2−7−4x+−1(3x2−5x+2+5x5+3x4)=6x3+x5+2x2+−7+−4x+−1(3x2)+−1(−5x)+(−1)(2)+−1(5x5)+−1(3x4)=6x3+x5+2x2+−7+−4x+−3x2+5x+−2+−5x5+−3x4
Combine Like Terms:=6x3+x5+2x2+−7+−4x+−3x2+5x+−2+−5x5+−3x4=(x5+−5x5)+(−3x4)+(6x3)+(2x2+−3x2)+(−4x+5x)+(−7+−2)= −4x5+−3x4+6x3+−x2+x+−9
Answer:= −4x5−3x4+6x3−x2+x−9
Answer:
-6x^2+10x+7
Step-by-step explanation:
a(n)=−6−4(n−1)
Find the 4th term in the sequence
Answers
Answer:
The 4th term is -18.
Step-by-step explanation:
This is an explicit formula.
All we have to do is plug n = 4 in the formula to find the 4th term
a (4) = -6 - 4 (4 - 1)
= -18
Subtract 1/4 w + 4 from 1/2 w +3
A: 1/4 w + 7
B: 1/4 w -1
C: -1/4 w +1
D: -1/4 w +7
Answers
everything in second parentheses becomes negative
=1/2w+3 -1/4w - 4
combine like terms
=1/2w-1/4w+3-4
=1/4w-1
ANSWER: B) 1/4w-1
Hope this helps! :)
Attila the Hun was a ruler of the Hunnic Empire. The Romans feared him greatly until his death since he made quite a habit of invading. The Romans no longer feared him after his death in 453. Let x represent any year. Write an inequality in terms of x and 453 that is true only for values of x that represent years after the year that Attila died.
Answers
Also, if it helps, I think of inequalities as an alligator's mouth, trying to eat the bigger quantity.
Hope this helps!
Mrs. Lewis make some orange juice after making another 850 mL of juice she now has 4 880 mL of orange juice how much orange juice did mrs Lewis make up first
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Please help!
5xy-6x2+1/2*3y
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write 27% percent as a fraction in its simplist form
Answers
The third grade class is going on a field trip by bus to the museum. The bus leaves the school at 9: 45 am. The bus ride takes 47 minutes. At what time does the bus arrive at museum
Answers
10:32 a.m.
Answer:
at 10:32
Step-by-step explanation:
I hope this will help you
PLEASE HELP!!!
The concentration, in parts per million, of a type of antibiotic in a human's bloodstream after h hours can be modeled by the polynomial function C(h) = −0.09h2 + 3.5h + 8. What is the concentration of the antibiotic after 3 hours in parts per million to the nearest hundredths?
A) 17.69
B) 18.77
C) 38.69
D) 42.34
Answers
You just substitute the h for 3
Mrs. Darnell is going to visit her cousins in Mexico over her summer vacation. She will be gone for one month and fifteen days. She leaves on June 19th. When does she return?
A. July 19
B. July 20
C. August 3
D. August 4
Answers
Mr. Hines was arranging desks into rows for his classroom . Mr. Hines has 20 desks in his class. Draw an array to show how Mr. Hines classroom would look if he put 5 desks in each row
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Each line is a desk
I I I I I
I I I I I
I I I I I
I I I I I
Fabric comes in rolls that are 60 inches wide. Draw a diagram of how you can cut the fabric from a roll that is 10 feet long. Tell me the dimensions.
Answers
To cut fabric from a roll that is 10 feet long and 60 inches wide, you can create strips that are 10 feet long and 60 inches wide or cut pieces that are 10 feet long and less than 60 inches wide.
Explanation:To cut fabric from a roll that is 10 feet long and 60 inches wide, you can create strips that are 10 feet long and 60 inches wide, or you can cut pieces that are 10 feet long and less than 60 inches wide.
For example, you can divide the 60-inch width into two 30-inch wide pieces.
Dimensions: Strips: 10 feet long x 60 inches wide Pieces: 10 feet long x 30 inches wide
The ratio of boys to girls in the sixth grade is 2:3, if there are 75 students, how many more girls are there than boys?
Answers
[tex]2 + 3 = 5 \\ 75 \div 5 = 15 \\ 15 \times 2 = 30 \\ 15 \times 3 = 45 \\ [/tex]
so there are 15 more girls than boys
Ben has Type 180 word in can type 30 words per minute. Millie has Type 60 words and can type 50 word per minute. How many minutes will it take Millie to catch up with Ben?
Answers
If x= minutes,
180+30x=60+50x
120=20x
6=x
180+30x=60+50x
Now let’s subtract 60 from each side.
120+30x=50x
Let’s subtract 30x from each side.
120=20x
Let’s divide each side by 20.
6=x
It will take 6 minutes for Millie to catch up with Ben.
What is the y-intercept of the continuous function in the table?
Answers
The y-intercept of a function is where the graph crosses the y-axis, represented by 'b' in the equation y = mx + b. If a table doesn't show x as zero, one can use the line of best fit by inserting the median x and y values and the slope into the formula b = y - mx to calculate the y-intercept.
Explanation:The y-intercept of a continuous function can be understood as the point where the function's graph crosses the y-axis. It is typically represented by the variable b in the slope-intercept form of a linear equation, which is y = mx + b, where m is the slope and b is the y-intercept. In the context of the problem provided, if the student is examining a table of values representing a linear relationship, they should look for the value of y when x equals zero to determine the y-intercept directly.
However, if the data does not include an x-value of zero, they could use the line of best fit to calculate the y-intercept by plugging the median x and y values, along with the determined slope, into the formula b = y - mx, where y and x are the medians. For example, if given a slope (m) of 0.09, sum of median x values as 1264, and sum of median y values as 219.5, the y-intercept (b) would be calculated as b = 219.5 - 0.09(1264), which simplifies to approximately 35.25.
This calculation would be necessary if the student is working with data that does not directly provide a scenario where x = 0, such as exam scores or years in a dataset stating from year 1. It's important to note that in some real-world applications, a y-intercept may not be meaningful if the x-value cannot be zero, like in the case of time-based data where the year 0 does not exist.
The y-intercept of the continuous function is (-2). This means that the graph of the function intersects the y-axis at the point (0,-2).
The y-intercept of a continuous function represents the point where the graph of the function intersects the y-axis. In other words, it is the value of y when x is equal to zero.
Looking at the given points:
(0,-6), (-2, 0), (-6, 0), (0,-2), and 0
We can determine the y-intercepts by identifying the points where x is equal to zero.
Let's go through the points one by one:
1. (0,-6): This point does not have a y-intercept because the x-coordinate is not zero.
2. (-2, 0): This point also does not have a y-intercept because the x-coordinate is not zero.
3. (-6, 0): Again, this point does not have a y-intercept because the x-coordinate is not zero.
4. (0,-2): Finally, this point does have a y-intercept because the x-coordinate is zero. Therefore, the y-intercept is -2.
5. 0: This is not a point, but simply the value of zero. It does not have a y-intercept because it does not represent a point on the graph.
To summarize, the y-intercept of the continuous function is (-2). This means that the graph of the function intersects the y-axis at the point (0,-2).
what is the correct way to classify a triangle with angles that measure 52 degeers, 68 and 60 degrees?
Answers
look at the number below
75，74，72，69，65，...
describe the pattern
Answers
75 - 1 = 74
74 - 2 = 72
72 - 3 = 69
69 - 4 = 65
and so on...
I hope this helps! : )
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insert the greater than, less than, or equal sign to make each statement true. a. 45/45_1 b. 1_6/3 c. 2/7_ 1 d. 64/23_1
Answers
B. < (6/3 = 2 > 1.)
C. < (2/7 + 5/7 = 1.)
D. > (64/23 = 3 > 1)
Answer:
[tex]\frac{45}{45}=1[/tex]
[tex]1<\frac{6}{3}[/tex]
[tex]\frac{2}{7}<1[/tex]
[tex]\frac{64}{23}>1[/tex]
Step-by-step explanation:
Given the statements
we have to insert the greater than, less than, or equal sign to make each statement true.
[tex]\text{Statement 1: }\frac{45}{45}?1[/tex]
[tex]\frac{45}{45}...1[/tex]
[tex]1...1[/tex]
which are equal
∴ [tex]1=1[/tex]
[tex]\text{Statement 2: }1?\frac{6}{3}[/tex]
[tex]1...\frac{6}{3}[/tex]
[tex]1...2[/tex]
2 is greater than 1
∴ [tex]1<2[/tex]
[tex]\text{Statement 3: }\frac{2}{7}?1[/tex]
[tex]\frac{2}{7}...1[/tex]
[tex]0.286...1[/tex]
1 is greater than 0.286
∴ [tex]0.286<1[/tex]
[tex]\text{Statement 4: }\frac{64}{23}?1[/tex]
[tex]\frac{64}{23}...1[/tex]
[tex]2.783...1[/tex]
2.783 is greater than 1
∴ [tex]2.783>1[/tex]
What is the solution of the system use a graph.
Y=2x+1
Y=-3x-1
Can anybody graph this and show me a picture ?
Answers
The solution is (x, y) = (-2/5, 1/5)
Sand is stored in a shed that is 3 m long, 2 m wide, and 2 m tall. Which is the correct unit of measurement to use to figure out how much sand will fill the shed? A. m3 B. m C. m2