8*3 = 24 + 28 = 52 total square feet
he is painting at 8 sq m per hour
so A(t) = -8t +52
Answer:
[tex]A(t)=-8t+52[/tex]
Step-by-step explanation:
Let
A(t)------> the area to paint
t------> the time in hours
Step 1
Find the total area of the room
[tex]A=8*3+28=52\ m^{2}[/tex]
Step 2
Find the linear equation that represent the situation
[tex]A(t)=-8t+52[/tex]
The perimeter of this shape is 82 cm. what is the length of side d? cm
Which of the following is not a pair of similar polygons?
Answer: The answer is the last figure, figure (D). Attached the image.
Step-by-step explanation: We are given four pairs of polygons and we are to select the pair in which the two polygons are not similar.
In the first pair of polygons, the ratio of the corresponding sides will be same as follows:
[tex]\dfrac{2}{\frac{2}{3}}=\dfrac{4}{\frac{4}{3}}=3.[/tex]
So, the polygons are similar.
In the second pair of polygons, the ratio of the corresponding sides will be same as follows:
[tex]\dfrac{2.82}{1.41}=\dfrac{2.24}{1.12}=\dfrac{3}{1.5}=2.[/tex]
So, the polygons are similar.
In the third pair of polygons, the ratio of the corresponding sides will be same as follows:
[tex]\dfrac{1.41}{1.41}=\dfrac{1.12}{1.12}=\dfrac{1.5}{1.5}=1.[/tex]
So, the polygons are similar.
In the fourth pair of polygons, we have
[tex]\dfrac{12}{\frac{4}{3}}=12\times\dfrac{3}{4}=9,[/tex]
and
[tex]\dfrac{4}{\frac{2}{3}}=4\times\dfrac{3}{2}=6\neq 9.[/tex]
So, the polygons are not similar in this case.
Thus, the last figure, attached herewith, is the correct option.
All of the figures are pair of similar polygons
What are similar shapes?Similar shapes have the same shape but may differ in size.
Their corresponding angles are equal, and their corresponding sides are in proportion.
This property allows for resizing through a constant scale factor while maintaining identical angles.
We can test of the polygons are similar by checking the ratio of their corresponding sides are equal.
Fig 1 = 2/2/3 = 3
4/4/3 = 3
therefore the pair of polygons in fig1 are similar.
fig 2 = 3/1.5 = 2
2.82/1.41 = 2
therefore fig2 is a pair of similar polygons.
Therefore, all of the figures are pair of similar polygons
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For a data set, the mean is 3.17 and the range is 1.4. The data set is transformed by adding 0.5 to each data value. What are the mean and range of the new data set?
a. mean: 3.67; range: 1.9
b. mean: 3.67; range: 1.4
c. mean: 3.17; range: 1.9
d. mean: 3.17; range: 1.4
Adding 0.5 to each value in the data set increases the mean to 3.67 while the range remains at 1.4. Hence, the correct answer is option b.
When a constant is added to each data value in a data set, the mean of the data set increases by that constant, while the range remains unchanged. In this case, adding 0.5 to each data value will increase the mean by 0.5 but the range will stay the same.
Given the original mean: 3.17 and original range: 1.4:
New mean = 3.17 + 0.5 = 3.67
New range = 1.4
Therefore, the correct answer is option b: mean: 3.67; range: 1.4.
in diagram below, fg=10 and HJ=10. Which additional facts would guarantee that fghj is a parallelogram? Check all that apply.
Jasmine bought computer which was discounted from 350 to 273. What is the discount rate
subtract the 2 numbers to find amount of discount
350 - 273 = 77
now divide 77 by 350 = 0.22
0.22 = 22% discount
Answer:
22%
Step-by-step explanation:
The discount rate given on the cost of an item is the ratio of the discount to the old price expressed as a percentage.
The discount is the difference between the old and new price while the new price is known as the discounted price.
the discount = $350 - $273
= $77
The discount rate
= $77/$350
= 0.22
= 22%
What are 3 consecutive integers who's sum is 396?
Ethan invested £500 in the bank for 2 years. he earned £40 simple interest in total. what was the simple interest rate per annum
Answer:
4%.
Step-by-step explanation:
We have been given that Ethan invested £500 in the bank for 2 years. He earned £40 simple interest in total. We are asked to find the annual interest rate.
We will use simple interest formula to solve our given problem.
[tex]I=Prt[/tex], where,
I = Amount of interest,
P = Principal amount,
r = Annual interest rate in decimal form,
t = Time in years.
Upon substituting our given values in above formula, we will get:
[tex]40=500*r*2[/tex]
[tex]40=1000*r[/tex]
Now, we will divide both sides of our given equation by 100.
[tex]\frac{40}{1000}=\frac{1000*r}{1000}[/tex]
[tex]\frac{4}{100}=r[/tex]
[tex]\frac{1}{25}=r[/tex]
[tex]0.04=r[/tex]
Since our given interest rate is in decimal form, so we need to convert it in percentage.
[tex]0.04\times 100\%=4\%[/tex]
Therefore, the simple interest rate per annum is 4%.
Owen jarred 10 liters of jam after 2 days. How many days did Owen spend making jam if he jarred 15 liters of jam?
Hi! Please help me with this question! 12 points and brainliest to whoever answers it correctly first!
1. Given: -3x + y = 1. Write the equation in general form Ax + By + C =0.
3x - y + 1 = 0
-3x + y - 1 = 0 (not this one)
3x - y = -1
ΔMNP is an isosceles triangle with MN ≈NP. If ∠ M = 3x + 1 and ∠ N = x - 11. What is the measure of ∠P?
x= r-h/y
solve for h and r
To solve for h, rearrange the equation to h = r - xy, and to solve for r, rearrange it to r = xy + h. This process involves basic algebraic manipulation to isolate each variable on one side of the equation.
Explanation:The original equation given is x = r - h/y. To solve for h, we need to get h by itself on one side of the equation. First, we can rearrange the equation to isolate h:
Multiply both sides by y to get rid of the fraction: xy = r - h.Move all terms containing h to one side and the rest to the opposite side: h = r - xy.To solve for r, we take the original equation and solve for r explicitly:
First, isolate the term containing r: r = xy + h.Now we have both variables solved in terms of x, y, and each other.
What are four different ways of representing functions? how can you tell if a relationship is a function?
Functions can be represented verbally, algebraically, graphically, and numerically. A relationship is a function when for every input, there is exactly one output which is described by the vertical line test. Graphs for different types of functions vary in shape.
Explanation:Functions can be represented in four various ways: verbally, algebraically, graphically, and numerically. For instance, verbal representation uses words to describe the function. Algebraically, we express the function via an equation. Graphically, we visually represent the function through graphs. Numerically, we represent the function using a table.
A relationship is a function if for every input, there is exactly one output. In a graph, this corresponds to an instance where a vertical line drawn anywhere on the graph would intersect it at only one point. This is also known as the vertical line test.
Examples of different types of functions graphically could include (a) a linear graph, showing a straight line, (b) a quadratic graph, parabolic in shape, (c) an inverse graph, where y decreases as x increases, and (d) an exponential graph, where the rate of growth is proportional to the function's current value.
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A baseball player got 102 hits in the last 300 times at bat.
What percent of the times at-bat did the player get a hit?
The player got a hit ? % of the time.
Mary invests £12000 in a savings account. The account pays 1.5% compound interest per year. Work out the value of her investment after 2 years
I shuffle a standard deck with 52 cards and randomly draw the ace of hearts, then put it to one side. what is the probability that the next card i draw is either an ace or a heart?
An investment is currently worth 2.125 × 10^4 dollars . Ten years ago, the investment was worth 1.25 × 10^3 dollars. How many times greater is the value of the investment today than the value of the investment ten years ago?
The investment today is 17 times greater than it was ten years ago.
To find out how many times greater the value of the investment is today compared to ten years ago, you can divide the current value by the value ten years ago.
So, let's do the calculation:
Current value = 2.125 × 10^4 dollars
Value ten years ago = 1.25 × 10^3 dollars
[tex]\( \text{Times Greater} = \frac{\text{Current Value}}{\text{Value Ten Years Ago}} \)[/tex]
Substitute the values:
[tex]\( \text{Times Greater} = \frac{2.125 \times 10^4}{1.25 \times 10^3} \)[/tex]
To divide these numbers, subtract the exponents:
[tex]\( 10^4 \div 10^3 = 10^{4-3} = 10^1 = 10 \)[/tex]
So,
[tex]\( \text{Times Greater} = \frac{2.125}{1.25} \times 10 = 1.7 \times 10 = 17 \)[/tex]
Therefore, the value of the investment today is 17 times greater than the value of the investment ten years ago.
Which phrase best describes a rock? A. a chemical arranged in a lattice B. a gabbro of minerals C. a mixture of crystals D. a fire-formed crystal
The graph illustrates a reflection of . What is the line of reflection?
A.
x-axis
B.
y-axis
C.
y=x
D.
y=2x
Answer:
A. x-axis
Step-by-step explanation:
It is a mirror image. The doesn't change.
The figure J'K'M' is just reflected over the x-axis.
So it is reflection about the x-axis.
Therefore, answer is A. x-axis
Hope this will helpful.
Thank you.
Find the length of the hypotenuse if the legs of a triangle are 5cm and 12 cm.
Question 5 options:
7cm
13cm
17cm
169cm
Two cars leave the origin; one goes north at 45 mph and the other goes south at 40 mph. after how many hours will they be 350 miles apart?
To find the time when two cars traveling in opposite directions are 350 miles apart, we calculate their relative speed, which is 85 mph. We then divide the distance (350 miles) by this speed to get approximately 4 hours and 7 minutes.
Explanation:The question is asking to find out after how many hours two cars traveling in opposite directions will be 350 miles apart, with one car going north at 45 mph and the other south at 40 mph. To solve this, we need to apply the concept of relative speed.
The relative speed is the sum of the individual speeds when two objects are moving in opposite directions. In this case, it's 45 mph + 40 mph = 85 mph. This is the speed at which the distance between the two cars is increasing.
Next, to find the time 't' when they will be 350 miles apart, we use the formula:
Distance = Speed × Time
350 miles = 85 mph × t
To solve for 't', we divide both sides by 85 mph:
t = 350 miles / 85 mph = 4.1176 hours, or approximately 4 hours and 7 minutes.
what is the average rate of change from x = 0 to x=4
A. 0
B. 1
C. 4
D. 8
c) Solve the equation you wrote in part b to find how many hours you would have to work to pay for the first year of video streaming service. Show your work and round your answer to the nearest tenth.
The container that holds the water for the football team is 7/10 full. after pouring out 6 gallons of water, it is 1/2 full. how many gallons can the container hold?
The total capacity of the container is 30 gallons in volume.
What is unitary method?The unitary method is a technique for solving a problem by first finding the value of a single unit, and then finding the necessary value by multiplying it with the value of a single unit.
Given is that the container that holds the water for the football team is 7/10 full. After pouring out 6 gallons of water, it is 1/2 full.
Assume that the container total capacity is [x] gallons. Then, according to the question -
7x/10 - 6 = x/2
7x/10 - x/2 = 6
x(0.7 - 0.5) = 6
0.2x = 6
x = 6/0.2
x = 6/(1/5)
x = 30 gallons
Therefore, the total capacity of the container is 30 gallons in volume.
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Which ordered triple is a solution of this system?
2x + y - z = 7
-x - 2y + 4z = -15
x + 2y - 5z = 17
a) (3, 1, 0)
b) (1, 3, -2)
c) (2, 5, 2)
d) (-2, 6, -5)
Answer:
b) (1, 3, -2)
Step-by-step explanation:
A suitable calculator can give you the answer to this right away. Or, you can try the answer choices in the equations to see which works.
The answer choice that works is choice B.
2·1 +3 -(-2) = 7
-1 -2(3) +4(-2) = -15
1 +2(3) -5(-2) = 17
TRUE OR FALSE
"All 4 sides are equal in a rhombus but not in a parallelogram"?
Expand and simplify 2(2x-3)+2(3x+4)
Triangle lmn is similar to triangle nop. both are right triangles. which statements about the two triangles must be true? choose all answers that are correct.
a. sides ln and np have the same slope.
b. sides ln and np are congruent.
c. triangle lmn and nop are congruent.
d. sides lm and mn are proportional to sides no and op.
"sides ln and np have the same slope." and "sides lm and mn are proportional to sides no and op." are correct for Triangle lmn is similar to triangle nop. both are right triangles.
What are Similar Triangles?Two triangles are said to be similar if their corresponding angles are congruent and the corresponding sides are in proportion .
"Congruent" means the same
Two triangles are said to be congruent if they both have same length and same angles.
"Similar" means the area and sides will be proportional, it means when we divide or multiply with a number we get the measure of the other.
If triangle lmn is similar to triangle nop. both are right triangles.
Then we need to check which options will be correct and holds.
a. sides ln and np have the same slope it is correct because the triangle will have same slopes
b. It must not be true "sides ln and np are congruent" because as they are congruent the sides should be same.
c. triangle lmn and nop are congruent, is not true because there measures are different.
d. As the triangles are similar " sides lm and mn are proportional to sides no and op." must be true, because of proportionality.
Hence "sides ln and np have the same slope." and "sides lm and mn are proportional to sides no and op." are correct for Triangle lmn is similar to triangle nop. both are right triangles.
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A bag contains equal numbers of green and blue marbles. You can divide all the green marbles into groups of 12 and all the blue marbles into groups of 16. What is the least number of each color of marble that can be in that bags?
To solve this problem, we need to find for the LCM of each number. That is:
12: 12, 24, 36, 48, 60
16: 16, 32, 48, 64, 80
So we can see that the LCM is 48.
Therefore the least number of each color of marble must be 48.
Answer:48
Step-by-step explanation:love ya thank me later
Explain in detail why the degree of the polynomial below is not 6. 3x^2+6xy-10x^5+y^6-10x^3y^5
Triangle XYZ is shown on the coordinate plane below:
Triangle XYZ on the coordinate plane with ordered pairs at X 3, negative 1, at Y 4, negative 4, at Z 1, negative 2
If triangle XYZ is reflected across the line y = 1 to create triangle X'Y'Z', what is the ordered pair of X'?
The ordered pair of [tex]X'[/tex] is [tex](3,3)[/tex]
Explanation
According to the below diagram, the co ordinates of [tex]\triangle XYZ[/tex] are: [tex]X(3, -1), Y(4,-4)[/tex] and [tex]Z(1,-2)[/tex]
The triangle [tex]XYZ[/tex] is reflected across the line [tex]y=1[/tex] to create triangle [tex]X'Y'Z'[/tex]
Distance of the point [tex]X[/tex] from the line [tex]y=1[/tex] is 2 units.
So, the point [tex]X'[/tex] will be also 2 units above the line [tex]y=1[/tex]. As the triangle is reflected across a horizontal line, so the [tex]x[/tex] co-ordinate of the point will remain same.
[tex]y[/tex] co-ordinate of the point [tex]X'[/tex] will be: [tex]y=1+2 =3[/tex]
So, the ordered pair of [tex]X'[/tex] is [tex](3,3)[/tex]