Answers
Answer:
60 cm²
Step-by-step explanation:
We can split this figure into two simpler polygons (a triangle and rectangle), solve for the area of each one, then add their areas together to get the total area of the figure.
Step 1: Rectangle
The easiest shape to recognize is the large rectangle in the lower half of the figure. We can find its area using the formula:
[tex]A = l \cdot w[/tex],
where [tex]l[/tex] is the rectangle's length and [tex]w[/tex] is its width.
[tex]A = 12 \text{ cm} \cdot 4\text{ cm}[/tex]
[tex]A = 48 \text{ cm}^2[/tex]
So, the area of the rectangle is 48 cm².
Step 2: Triangle
We can see there is a triangle in the top half of the figure. The area of a triangle is defined as:
[tex]A = \dfrac{1}{2} \cdot b \cdot h[/tex],
where [tex]b[/tex] is the length of the triangle's base and [tex]h[/tex] is its height.
The trick here is to find out the triangle's base and height measurements.
We can solve for the height by subtracting the height of the bottom half (height of the rectangle) from the total height.
[tex]h = 8 \text{ cm} - 4 \text{ cm}[/tex]
[tex]h = 4 \text{ cm}[/tex]
We can solve for the width by subtracting the lengths next to the triangle from the total width of the figure.
[tex]w = 12 \text{ cm} - 3\text{ cm} - 3\text{ cm}[/tex]
[tex]w = 6 \text{ cm}^2[/tex]
Now, we can plug these values into the area formula:
[tex]A = \dfrac{1}{2} \cdot 6\text{ cm} \cdot 4\text{ cm}[/tex]
[tex]A = 3\text{ cm} \cdot 4\text{ cm}[/tex]
[tex]A = 12\text{ cm}^2[/tex]
So, the area of the triangle is 12 cm².
Step 3: Total Area
Finally, we can solve for the total area of the figure by adding the area of the rectangle and the area of the triangle.
[tex]A = 48 \text{ cm}^2 + 12\text{ cm}^2[/tex]
[tex]\boxed{A = 60\text{ cm}^2}[/tex]
The total area of the figure is 60 cm².
Solution: 48+12=60
Related Questions
Negative Exponent Rule: Which expressions are equivalent to 10−6? Select all that apply.
Answers
Answer:
[tex]\large\boxed{\textsf{See Below.}}[/tex]
Step-by-step explanation:
[tex]\textsf{We are asked which expressions are equivalent to 10}^{\tt -6}.[/tex]
[tex]\textsf{We are given that we need to use the \underline{Negative Exponent Rule}.}[/tex]
[tex]\large\underline{\textsf{What is the Negative Exponent Rule?}}[/tex]
[tex]\textsf{The Negative Exponent Rule is a rule that describe how to evaluate negative}[/tex]
[tex]\textsf{exponents.}[/tex]
[tex]\large\underline{\textsf{How do we use the Negative Exponent Rule?}}[/tex]
[tex]\textsf{We use the negative exponent rule to multiply the denominator of a number by}[/tex]
[tex]\textsf{itself how many times the value of the exponent is.}[/tex]
[tex]\underline{\textsf{Example of the Negative Exponent Rule;}}[/tex]
[tex]\tt 10^{-2}. \ \textsf{Start with 10}^{\tt 1}, \ \textsf{then continue.}[/tex]
[tex]\tt 10^{1} = \frac{10}{1} \rightarrow 10^{\tt 0} = \frac{10}{1 \times 10} = \frac{10}{10} \rightarrow 10^{\tt -1} = \frac{10}{10 \times 10} = \frac{10}{100} \rightarrow 10^{\tt -2} = \frac{10}{100 \times 10} = \boxed{ \frac{10}{1000} }[/tex]
[tex]\large\underline{\textsf{Use the Negative Exponent Rule for our given expressions;}}[/tex]
[tex]\tt \frac{1}{10 \times 10 \times 10 \times 10 \times 10 \times 10} \overset{\textsf{is the same as}} \rightarrow \frac{1}{10^{6}}[/tex]
[tex]\textsf{There is a fraction for this expression, meaning that the exponent is negative.}[/tex]
[tex]\tt \frac{1}{10^{6}} = 10^{\tt -6}[/tex]
[tex]\large\boxed{\tt \frac{1}{10 \times 10 \times 10 \times 10 \times 10 \times 10} = 10^{\tt -6}}[/tex]
-------------------------------------------------------------------------
[tex]\tt 10^{\tt -3} \times 10^{\tt 2}[/tex]
[tex]\textsf{Remember that when exponents multiply, they're going to add together due to}[/tex]
[tex]\textsf{this expression having at least 2 constants.}[/tex]
[tex]\tt 10^{\tt -3} \times 10^{\tt 2} \rightarrow 10^{\tt -3+2} \rightarrow 10^{\tt -1}[/tex]
[tex]\large\boxed{\tt 10^{\tt -3} \times 10^{\tt 2} \neq 10^{\tt -6}}[/tex]
-------------------------------------------------------------------------
[tex]\tt 10^{\tt -3} + 10^{\tt -3}[/tex]
[tex]\textsf{We should know that adding exponents is not like adding whole numbers/terms.}[/tex]
[tex]\textsf{We will need to evaluate 10}^{\tt -3} \ \textsf{using the Negative Exponent Rule.}[/tex]
[tex]\tt 10^{\tt 0} = \frac{10}{10} \rightarrow \tt 10^{\tt -1} = \frac{10}{10 \times 10} = \frac{10}{100} \rightarrow \tt 10^{\tt -2} = \frac{10}{100 \times 10} = \frac{10}{1000} \rightarrow \tt 10^{\tt -3} = \frac{10}{1000 \times 10} = \boxed{\frac{10}{10000}}[/tex]
[tex]\tt \frac{10}{10000} \ \textsf{can reduce to} \ \boxed{\tt \frac{1}{1000}}[/tex]
[tex]\underline{\textsf{We are now adding;}}[/tex]
[tex]\tt \frac{1}{1000} + \frac{1}{1000} = \frac{2}{1000} \rightarrow \boxed{\frac{1}{500} }[/tex]
[tex]\textsf{This does \underline{not} evaluate to 10}^{\tt -6}[/tex]
[tex]\large\boxed{\tt 10^{\tt -3} + 10^{\tt -3} \neq 10^{\tt -6}}[/tex]
-------------------------------------------------------------------------
[tex]\tt \frac{1}{10^{\tt 6}}[/tex]
[tex]\textsf{Because there's a fraction, the exponent is negative.}[/tex]
[tex]\large\boxed{\tt \frac{1}{10^{\tt 6}} = 10^{\tt -6}}[/tex]
-------------------------------------------------------------------------
[tex]\tt \frac{10^{\tt 3}}{10^{\tt 9}}[/tex]
[tex]\textsf{Remember that when dividing exponents, they are going to subtract due to both}[/tex]
[tex]\textsf{of these numbers are constants.}[/tex]
[tex]\tt \frac{10^{\tt 3}}{10^{\tt 9}} \rightarrow \tt 10^{\tt 3-9} = 10^{\tt -6}[/tex]
[tex]\large\boxed{\frac{10^{\tt 3}}{10^{\tt 9}} = 10^{\tt -6}}[/tex]
[tex]\large\underline{\textsf{Hence;}}[/tex]
[tex]\large\boxed{\tt \frac{1}{10 \times 10 \times 10 \times 10 \times 10 \times 10} = 10^{\tt -6}}[/tex]
[tex]\large\boxed{\tt 10^{\tt -3} \times 10^{\tt 2} \neq 10^{\tt -6}}[/tex]
[tex]\large\boxed{\tt 10^{\tt -3} + 10^{\tt -3} \neq 10^{\tt -6}}[/tex]
[tex]\large\boxed{\tt \frac{1}{10^{\tt 6}} = 10^{\tt -6}}[/tex]
[tex]\large\boxed{\frac{10^{\tt 3}}{10^{\tt 9}} = 10^{\tt -6}}[/tex]
i need help with this.
Answers
PLEASE HELP QUICK
Complete the following tables:
Answers
Answer:
Step-by-step explanation:
A telephone pole 60 feet high casts a shadow 80 feet long at the same time that a tree casts a shadow 120 feet. What is the height of the tree
Answers
help meeeeeeeeeeeeeee...i don't understand how i got this answer
Answers
Linear Inequalities
The length of a rectangle is 5cm less than twice it's width. If the perimeter of the rectangle is no more than 80cm, what are the maximum possible dimensions?
Answers
Answer:
15 cm and 25 cm
Step-by-step explanation:
First let's mark the width with the letter b, and the length with a:
width: b
length: a = (2b - 5)
Then we have an inequality (P = 2a + 2b):
2 × (2b - 5) + 2b ≤ 80
4b - 10 + 2b ≤ 80
6b ≤ 80 + 10
6b ≤ 90 / : 6
b ≤ 15
a ≤ 2 × 15 - 5
a ≤ 25
Answer:15 cm and 25 cm
Step-by-step explanation:
PLEASE HELP ME!!!! IM FAILING AND GOING TO BE HELD BACK!!!!
Corinna has $64. She wants to buy a $229 plane ticket. She will save up her earnings from working at the museum where she earns $15 per hour. Which inequality shows the number of hours, n, Corinna must work so that she has a total of at least $229?
A.
n ≤ 10
B.
n ≤ 11
C.
n ≥ 11
D.
n ≥ 10
Answers
Good luck i hope you pass <3
Answer:
A. n ≤ 10
Step-by-step explanation:
Corinna wants to buy a $229 plane ticket. She currently has $64, so she needs to save up $229 - $64 = $165. Since she earns $15 per hour, we can set up the equation n * 15 = 165, where n represents the number of hours Corinna needs to work. Solving for n, we get n = 11.1, which we can round down to 11 hours. Therefore, Corinna must work at least 11 hours to save up enough money to buy the $229 plane ticket. Answer choice A is the correct answer.
Note: Rounding down to 11 is not required, as long as we do not round up to 12. Rounded or unrounded, 11 is the smallest integer greater than or equal to 11.1, so it is the minimum number of hours Corinna would need to work to save up enough money for the plane ticket.
Explanation:
15 times 11 = 165
165 + 64 (she has 64 already)
= 299!
Hope this helped!
Simplify:
(3 · 5) − 10 + 50
Answers
Answer:
55
Step-by-step explanation:
U dum for this problem
3x5=15
15-10=5
5+50=65029452
Answer: 55.
Step-by-step explanation:
Using PEMDAS rules, first do 3 times 5. (15) after this subtract 10 from 15. You will get 5. Add the 50 at the end, and you will get 55.
I hope this helped you! A brainilist is highly appreciated and helpful! <3
write each expression without using the absolute value symbol |14-(x-6)|
THIS IS 15 POINTS PLSSSSSSSSSSSSSS HELP
Answers
To start, we need to recognize that absolute value is a way of expressing the magnitude of a number, regardless of its sign. Thus, to get rid of the absolute value, we need to consider the two cases in which the expression can have either a positive or a negative sign.
For the case of a positive sign, we can simply write the expression as: 14-(x-6)
For the case of a negative sign, we can multiply both sides of the equation by -1 to get: -14 + (x-6)
Overall, we can express the expression without the absolute value symbol as:
14-(x-6) or -14 + (x-6)
The Cherry Creek Middle School band held a car wash to raise money for new uniforms. The band charged $10 for cars and $15 for larger vehicles, like vans or SUVs. In the first hour of the car wash, band members washed a total of 10 vehicles and raised $120 toward their uniforms.
GRAPH THE ANSWER
Answers
Answer: 6 cars and 4 larger vehicles:
Step-by-step explanation:
(10×6)+(4×15)= 120
60+60=120
Answer:6 cars and 4 larger vehicles
Step-by-step explanation:
Find the surface area of the cube shown below.
a. 625 cm2
b. 1121 cm2
c. 726 cm2
Answers
The surface area of a solid is the area of its faces. The surface area of a cube is just 6*side length^2 since the faces are the same and the faces are squares. So, we have 6 * 11^2 = 726.
1/5 divided by 5
HEEEEELP!!!
Answers
math again please help
Answers
Answer:
Step-by-step explanation:
, vb .c c.,v.,c.,b v.b,c.,.bevy b,. cvb,c,v,,v2883/?soo200993
What is the equation of the line containing the points (–6.4, –2.6) and (5.2, 9)?
Answers
y + 3 = 3/5(x - 6)
Your welcome
HELP I HAVE ! HOUR I NEED YOUR HELP
Answers
What scale factor was used to produce figure 1 from figure 2?
two triangles labeled figure 1 and figure 2, where figure 1 has legs that are 2 units long and figure 2 has legs that are 4 units long
4
2
one half
one fourth
Answers
Answer: the first dude is wrong the answer is two
Step-by-step explanation:
its double the size of figure 1... so the answer is obviously 2
Please help me I need help
Answers
Answer: B
Step-by-step explanation: it says twice aka 2x the only one that has 2x is B
Write and Evaluate Algebraic Expressions
Haddie makes and sells knit scarves. Next week she will pay a $25 fee for the use of a booth at a craft fair. She will charge $12 for each scarf she sells at the fair. Write an expression to determine Haddie's profit for selling s scraves after paying the fee for the use of the booth
Answers
Answer:
p = 12s -25
Step-by-step explanation:
You want an expression for Haddie's profit from the sale of s scarves when she has revenue of $12 each and a cost of $25.
ProfitProfit is the difference between revenue and cost. Haddie's revenue from sale of s scarves is ...
revenue = 12s
Haddie's cost is the fee she pays for the booth rental:
cost = 25
Her profit (p) is the difference between these values:
profit = revenue - cost
p = 12s -25
PLEASE HURRYYYY!!!!!!
Answers
Answer:
n-m/800
Step-by-step explanation:
I had this before and got it right
Which angles are complementary to each other? Select all that apply.
please help ive been on this IXL assignment for 20 hours.
Answers
The reasoning is if you estimated, DFE is around 15 degrees and EFA is around 70. added up would be around 90. That is estimating though, but that seems like the more practical answer. using a protractor would be better.
The reasoning is if you estimated, DE is around 15 degrees and EFA is around 70. added up would be around 90.
help for 10 points :DDDDDDDDDDDDDDDDDDDDDDDDDDDDDD
Answers
Answer: 339 1/2
Step-by-step explanation: To solve, you have to do 48 1/2 x 7, and you will get 339 1/2
Answer:
339 1/2 ounces
Step-by-step explanation:
48.5 x 7= 339.5=339 1/2
I need so much help whats 45+90 ???
Answers
Answer: 135
Step-by-step explanation:
45 + 90
take 10 of 45 and add it to 90 = 100
100 + 35 = 135
Answer:
135
Step-by-step explanation:
Brainliest ONLY if correct
Polygon PSRT is drawn with vertices at P(1, 5), S(1, 0), R(−2, −3), T(−4, 2). Determine the image vertices of R′ if the preimage is rotated 270° counterclockwise.
R′(−3, 2)
R′(2, 3)
R′(3, −2)
R′(−2, −3)
Answers
Answer: R'(2, 3)
Step-by-step explanation: I think
evaluate -3|x|+2x if x=-5
THIS IS 15 POINTS PLS HELP!!
Answers
Answer:
-3|-5| + 2(-5)
= -3(5) + 2(-5)
= -15 + (-10) = -25
Switch the absolute value
-3x5-2(-5)
Solve
-25
1/5 divided by 4
Brainliest if get it right!
Answers
Answer:
1/20 is your answer
Step-by-step explanation:
Write in complete sentences to explain what a budget is, how to make one, and how to balance it
Answers
Answer:
Budget is the name given for the evaluation or speculative calculation of the cost of a work or service to be provided.
Step-by-step explanation:
The definition of a budget normally takes into account two main characteristics: the revenue, that is, the amount collected or available, and the expense, which would be the amount to be spent for the completion or maintenance of something. Budgets are present in various aspects of everyday life, from planning for a renovation of the house, to the amounts that will be earmarked for the maintenance of public government services, which directly or indirectly affect the lives of citizens.
Balancing a budget seems easy, but it requires a lot of self-control and discipline. Some strategies for achieving this balance are: do not spend more than what you earn, do not buy anything on impulse, do not borrow, renegotiate your debts and save on expenses that are superfluous.
Isaac has 1.17 pounds of cat food. He uses 0.13 pound of cat food to feed one cat. How Sometimes Isaac has kittens. Each kitten has
1/3
as much cat food as a full-grown cat. How many kittens can Isaac feed with the 1.17 pounds?
Answers
Answer:
¨Isaac has 1.17 pounds of cat food. He uses 0.13 pounds of cat food to feed one cat. How many cats can Isaac feed with the cat food he has?¨ the answer is 9
Answer:
9
Step-by-step explanation:
1.17 divided by 0.13
Step #1: 0.13 x 5 = .65
1.17 - 0.65 = 0.52
Step #2: 0.13 x 4 = 0.52
0.52 - 0.52 = 0
Step #3: 5 + 4 = 9.
Ling makes bracelets and necklaces and sells them at different craft fairs the table shows how much strings is used to make each item Ling plans to make at least 20 bracelets right in solving inequality to determine the minimum length of strings that she needs to buy what is the least number of inches of string lingual need
Answers
20 × 7 1/2 = 150 inches
Therefore, Ling needs to buy at least 150 inches of string.
We can write the inequality to represent this situation as:
length of string ≥ 150
Hope this helps!!
Answer:
150 inches of string
Step-by-step explanation:
Sara had 136 dollars to spend on 8 books. After buying them she had 16 dollars. How much did each book cost ?
Answers
Answer:
Each book cost 15 dollars.
Here’s the work: Sara had 136 dollars and spent some money on 8 books. After buying them she had 16 dollars left. So she spent 136 - 16 = 120 dollars on books. Since she bought 8 books with that money, each book cost her 120 / 8 = 15 dollars.
Explanation:
Sara had $16 left, so
136-16=120
this means she spent $120 on books
She bought 8 books, so
120/8= 15
therefore, 1 book costs $15
I only have 2 hours helppp