Part A. The equivalent expression for the area of the rectangle without parenthesis is 5x + 40 sq meters and
Part B. The term represents that the area has been increased by 5 times the amount of the extension.
What are the area and perimeter of a rectangle?We know the perimeter of any 2D figure is the sum of the lengths of all the sides except the circle and the area of a rectangle is the product of its length and width.
We know the area of a rectangle is (length×width).
So, The area of the rectangle before the length extension is,
= (5×8) sq meters.
= 40 sq meters.
Now, The length is extended by 'x' meters.
Therefore, The area of the rectangle after an extension in length is,
= 5(x + 8) sq meters.
= 5x + 40 sq meters.
The expression's phrase indicates that the area has grown by five times as much as the extension.
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The actual length (1) of a rectangle is 122 inches. Use the scale drawing of the rectangle to find the actual width (w).
W 1.8 in.
6.1 in.
A
3.38 in.
B
36 in
С.
67.77 in
D
219.6 in
Answer:
B. 36 in.
Step-by-step explanation:
Length of the scale drawing (L) = 6.1 in.
Width of the scale drawing (W) = 1.8 in.
Actual length = 122 in.
Using the scale drawing we can apply the rules of three of proportions to find the actual width.
Thus, set the ratio of the scale drawing length to width, equal to the ratio of the actual length to width:
[tex] \frac{6.1}{1.8} = \frac{122}{x} [/tex]
Cross multiply
[tex] 6.1*x = 122*1.8 [/tex]
Divide both sides by 6.1
[tex] x = \frac{122*1.8}{6.1} [/tex]
[tex] x = 36 [/tex]
Actual width of the rectangle = 36 in.
The expression 200 - 16t2 models the height in feet of an object that falls from the initial height of 200 feet t seconds after being dropped. Find the height of the object after 0.75 seconds. Make sure and include the units of feet in your answer for full credit. Round your answer to the nearest hundredth place.
Answer:
Concept: Modeling expressions
We are given the equation [tex]200 - 16 {t}^{2} [/tex]We want to find the time after 0.75 seconds given that t is represented in seconds.Hence we do [tex]200 - 16(0.75)^{2} [/tex]Hence we get the answer to 191 feetThe height of the object that falls after 0.75 seconds given that t is represented in seconds is 191 feet.
What is a quadratic equation?A quadratic equation is the second-order degree algebraic expression in a variable. the standard form of this expression is ax² + bx + c = 0 where a. b are coefficients and x is the variable and c is a constant.
The expression 200 - 16t^2 models the height in feet of an object that falls from the initial height of 200 feet t seconds after being dropped.
We need to find the time after 0.75 seconds given that t is represented in seconds.
The expression is given
[tex]200 - 16t^2[/tex]
time t = 0.75
Substitute the value of t in the given expression
= 200 - 16(0.75)^2
= 200 - 9
= 191
Hence we get the answer to 191 feet.
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Which statement best describes the triangle formed by joining the points A(-3,6),B(-11,2),C(-4,-2)
Answer:
Isosceles triangle
Step-by-step explanation:
Length of side AB = [tex]\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}[/tex]
= [tex]\sqrt{(-11+3)^2+(2-6)^2}[/tex]
= [tex]\sqrt{64+16}[/tex]
= [tex]\sqrt{80}[/tex]
= 4[tex]\sqrt{5}[/tex]
Length of BC = [tex]\sqrt{(-4+11)^2+(-2-2)^2}[/tex]
= [tex]\sqrt{49+16}[/tex]
= [tex]\sqrt{65}[/tex]
Length of AC = [tex]\sqrt{(-3+4)^2+(6+2)^2}[/tex]
= [tex]\sqrt{1+64}[/tex]
= [tex]\sqrt{65}[/tex]
Since, AC = BC, ΔABC will be an isosceles triangle.
Find the value of g7) for the function below.
g(x)= 7/8x -1/2
Answer:
[tex]g(7) = \frac{45}{8} \\ \: or \: \\ 5 \frac{5}{8} [/tex]
Step-by-step explanation:
We would just apply the 7 in g(7) as all the x
g(x)= 7/8x - 1/2
g(7)= 7/8(7) -1/2
[tex] \frac{7}{8} \times \frac{7}{1} = \frac{49}{8} [/tex]
Simplify
g(7)= 49/8 -1/2
Multiply -1/2 by 4/4 to get the denominators the same
[tex] \frac{49}{8} - \frac{4}{8} = \frac{45}{8} [/tex]
answer: g(7)=45/8
(simplified): g(7)=5 5/8
Please help!!
What is 2% of 180?
Answer: 3.6
Step-by-step explanation:
0.02*180=3.6 :)
Answer:
3.6
Step-by-step explanation:
Find the product of the percentage and the value:
180 · 0.02 = 3.6
Therefore, 2% of 180 is 3.6.
Determine the nth term rule and find the 45th term for the arithmetic sequence with a10=1 and d-6
Answer: -209
Step-by-step explanation:
Formula for arithmetic progression
= a + (n - 1)d
Since a10 = 1 and d = -6
a10 = a + 9d
a + 9(-6) = 1
a - 54 = 1
a = 1 + 54
a = 55
Therefore, 45th term = a + (n - 1)d
= a + (45 - 1)d
= a + 44d
= 55 + 44(-6)
= 55 - 264
= -209
please help me on this will give you brainliest
Answer:
11×9=99 99 rounded would be 99.000
The area of a circle, in terms of π, is 54π m2.
Find the value of the radius.
Give your answer as a simplified surd.
Pls helpppppp
Answer:
3√6 m
Step-by-step explanation:
The formula for area of a circle is
A = πr^2
r= √A/π
Since;
A= 54π m2
r = √54π/π
r = √54
r = √54 = √6 * √9 = 3√6
r = 3√6 m
Write an expression for "the product of 6 and q."
Please answer and not steal my points
Answer:
6q
Step-by-step explanation:
Answer:
i think it is 6q
Step-by-step explanation:
2- Justin decided to skip work and go swimming with his friends. Normally he would have worked 3 hours. Assuming he
makes $11 an hour and the swimming trip cost $8 in gas, what was his opportunity cost to go swimming instead of
work?
accumulate over the
Answer:
69
Step-by-step explanation:
Tekashi
how many solutions does this system of equations have?
please help
this is due at noon so anyone who knows this help me.
Answer:
70x+4^2+3
Step-by-step explanation:
0.4 of 1 minute.
Help please
Answer:
24 seconds
Step-by-step explanation:
HELP PLEASE! WHAT IS THE ANSWER!
Not sure if it's right?? but I clicked yes
Answer:
yes you are right it is yes
Step-by-step explanation:
triangle abc is similar to triangle def. the lengths of the sides of triangle abc are 5, 8, and 11. what is the length of the shortest side of triangle def if its perimeter is 60?
Answer:
The shortest sides is 12.5.
Step-by-step explanation:
5 + 8 + 11 = 24
60 / 24 = 2.5
So 2.5 * 5 = 12.5
The length of the shortest side of triangle DEF is 12.5 units.
What is a Triangle?Triangle is defined as a basic polygonal shape of a triangle that has three sides and three interior angles. It is one of the fundamental shapes in geometry and is represented by the symbolΔ.
Since triangle ABC is similar to triangle DEF, the ratio of the corresponding sides of the two triangles is the same.
Let x be the length of the shortest side of triangle DEF.
The length of the shortest side of triangle DEF, x, is in the same ratio to the length of the shortest side of triangle ABC, 5, as the other sides of triangle DEF are in relation to the other sides of triangle ABC.
The perimeter of triangle ABC is:5 + 8 + 11 = 24
The perimeter of triangle DEF is 60.
So 60 / 24 = 2.5
So the length of the shortest side: 2.5 x 5 = 12.5
Therefore, the length of the shortest side of triangle DEF is 12.5 units.
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Did I get this right? Please explain how I got it right if I did
Answer:
no 6 hours
Step-by-step explanation:
no it would be 6 hours
25% = 7.5 hours
5% = 1.5 hours
7.5 - 1.5 = 6 hours
Can anyone help with this?
Answer: 1. Not a right triangle 2. Right Triangle 3. Right triangle 4. Right triangle 5. Not a right triangle
Step-by-step explanation:
the right triangle has to have a pattern to go by, so only evens or only odd sides.
No Solutions
6x - 3x + 4 - 2x= _ + _
box is filled with six yellow cards six red cards and three blue cards a card is chosen at random from the bag what is the probability that the card is not read
Answer:
There is a 9/15 or 3/5
Step-by-step explanation:
There are a total of 15 cards, of those, 6 are red, so if you subtract 6 from 15, you get 9, which is the total amount of yellow and blue cards, which is what you were to not get a red card.
step by set
0000000000000000000000000000000011111111111111111111111111111111111111111111010101010000000000001010101000000011110101010101010101010111010010001
Answer:
2 2/3 or 8/3
Step-by-step explanation:
Step by step I am guessing? (Is that what each question is for?)
STEP 1
First we have to find 1/3 of 23:
23/3= 1/3 of 23
Then:
5/1 = 15/3
STEP 2
Subtract:
23-15= 8/3
8/3 or 2 2/3
Combine like terms in the following expression
6 - 5z + 8 - 4z + 1
Answer:
15-9z
Step-by-step explanation:
combine like terms,, the like terms we have are the terms (z) and the whole numbers so we combine 6,8, and 1-- and combine -5z and -4z to get the solution.
. Caroline had 400 stamps in her collection. 1 10 th of them were Indian stamps, Onethird of the remaining stamps were from Europe and 100 stamps were from Africa. The rest were from the United States of America. How many American stamps were there?
Answer:
So 400 stamps
African---> 100
Indian------> 1/10 x 400
= 40
European---> 400-40=360
1/3 x 360
= 120
so 120+40+100= 260
400-260
= 140 stams from US
I need help ASAP!! Currently failing math ✌️
Find the lower quartile of the following numbers: 1, -2, 7, 9, 0, 10
Answer:
0
Step-by-step explanation:
The first step is to locate the median.
The median is the middle value of the numbers arranged in ascending order. If there is no exact middle value then it is the average of the numbers either side of the middle.
- 2, 0, 1, 7, 9, 10 ← ascending order
↑ middle
median = [tex]\frac{1+7}{2}[/tex] = [tex]\frac{8}{2}[/tex] = 4
The lower quartile Q₁ is the middle value of the numbers to the left of the median, that is
- 2, 0, 1
↑
lower quartile Q₁ = 0
Cheryl borrowed $7,000 from her parents to purchase a car interest free. she makes one payment on the loan to her parents each month. if the loan amount decreases by $300 each month, which of the following functions represents the loan amount, L(x), after x months?
A. L(x) = $6,700x
b. L(x) = $300x
C. L(x) = $300 - $7,000x
D. L(x) = $7,000 - $300x
Answer:
the answer should be D
Step-by-step explanation:
because she took the enital 7,000 then she started taking 300 a month and x equals the amount of months
Complete the pairs of corresponding parts if △RST ≅ △TXY.
∠S =
∠ TXY
∠ XTY
∠ XYT
Answer:
∡S corresponds to ∡X
∡TXY = ∡RST
∡XTY = ∡SRT
∡XYT = ∡STR
Step-by-step explanation:
Answer: im thinking angle txy for the answer, but i mean, why can't you guys who answer just say "_ = _" or "the answer is _" with an explanation below?!?!
Step-by-step explanation: :|
plzz helpp guys
At the beginning of an environmental study, a forest covered an area of 1500 km . Since then, this area has decreased by 2.4% each year. Lett be the number of years since the start of the study. Let y be the area that the forest covers in km². Write an exponential function showing the relationship between y and t.
Answer:
[tex]y = 1500(0.024)^t[/tex]
Step-by-step explanation:
Given
[tex]a = 1500km[/tex] -- initial area
[tex]b = 2.4\%[/tex] -- rate
[tex]t = time[/tex] --- (years)
Required
Represent as an exponential function
An exponential function has the form:
[tex]y = ab^t[/tex]
Where
[tex]a = initial\ value[/tex]
[tex]b = rate[/tex] and [tex]b \ne 1[/tex]
[tex]t= time[/tex]
Substitute values for a and b, we have:
[tex]y = 1500 * (2.4\%)^t[/tex]
Convert percentage to decimal
[tex]y = 1500 * (0.024)^t[/tex]
[tex]y = 1500(0.024)^t[/tex]
Hence, the exponential function that represents the scenario is: [tex]y = 1500(0.024)^t[/tex]
Use the Rectangle to the right for Questions 1-4
Answer:
1. 34
2. 56
3. 112
4. 68
Step-by-step explanation:
For the first one, the angle measuring 112 is a vertical angle to angle 9 so angle 9 is also 112. So 180-112 (180 because the measure of every triangle is 180.) is 68. Then you divide 68 by 2 and get 34 because the angles 1 and 8 measure the same.
For the second one, you would first find the measure of angle 10 by subtracting 180-112 again and getting 68 (the measure of a flat line is 180.) Then you would get 112 for the remaining angles and divide that by two because once again, the two angles are the same measure. So 112 divided by 2 is 56.
For the third one, I already stated that the measure of angle 9 is 112.
And finally, for the fourth one, I also previously stated that the measure of angle 10 is 68.
One spring day, Zoey noted the time of day and the temperature, in degrees
Fahrenheit. During that time, the temperature rose, stayed steady, and fell, at
different rates! On the set of axes below, Zoey created a graph of temperature over
time.
How long did the temperature hold steady for?
Answer:
2 hours
Step-by-step explanation:
Each square=1 hour
2 squares= 2 hours
