Answer:
1.5
Step-by-step explanation:
To determine the scale factor used to create the image, we can compare the distances between corresponding vertices of the two triangles.
Let's start by finding the distance between A and B in triangle ABC:
distance AB = sqrt[(x_B - x_A)^2 + (y_B - y_A)^2]
= sqrt[(-2 - (-6))^2 + (-4 - (-4))^2]
= sqrt[16 + 0]
= 4
Now let's find the distance between A' and B' in triangle A'B'C':
distance A'B' = sqrt[(x_B' - x_A')^2 + (y_B' - y_A')^2]
= sqrt[(-3 - (-9))^2 + (-6 - (-6))^2]
= sqrt[36 + 0]
= 6
To find the scale factor, we can divide the distance between corresponding vertices in the image triangle by the distance between the corresponding vertices in the original triangle:
scale factor = distance A'B' / distance AB
= 6 / 4
= 1.5
Therefore, the scale factor used to create the image is 1.5.
To find the scale factor of a dilation, one can divide a side length of the enlarged shape by the corresponding side length of the original shape. In this case, the scale factor from triangle ABC to A'B'C' is 6/4 = 1.5.
Explanation:In Mathematics, we can find the scale factor of a dilation by comparing corresponding distances in the original shape and its image. The scale factor can be found by dividing a side length of the enlarged shape (triangle A′B′C′) by the corresponding side length of the original shape (triangle ABC).
For example, the distance between points A and B in the original triangle ABC is 4 units (-2 - (-6) = 4), and the distance between points A′ and B′ in the enlarged triangle A′B′C′ is 6 units (-3 - (-9) = 6). So, the scale factor from ABC to A'B'C' is 6/4 = 1.5.
Therefore, the scale factor used to create the image of triangle A'B'C' from triangle ABC is 1.5.
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Solve the equations:
5_r-2)^2[tex]9x^2=36[/tex]
[tex]5(r-2)^2=35\\[/tex]
[tex]-4(k-8)^2=16[/tex]
1. The solution of 5(r-2)² = 35 is r = ±√7 + 2.
2. The solution of -4(k-8)² = 16 is k = (16 ± √(-16)) / 2.
1. 5(r-2)² = 35
First, divide both side by 5 we get
5(r-2)²/5 = 35 /5
(r-2)² = 7
Take square root on both side
r-2 = ±√7
r = ±√7 + 2
2. -4(k-8)² = 16
Divide both side by -4 we get
(k-8)² = -4
k² + 64 - 16k + 4 = 0
k² - 16k + 68 = 0
On solving the quadratic equation we get
k = (16 ± √(-16)) / 2
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Michelle Michelle opened an interest-bearing savings account. She deposited 8750$ into the account. If the account earns 1.3% simple interest. What will be Michelle’s balance after two years
Michelle's balance after two years would be $8977.50.
How to calculate Michelle’s balance after two yearsusing the formula to find Michelle’s balance after two years:
balance = principal + (interest rate * principal * time)
where:
- principal = the initial deposit of $8750
- interest rate = 1.3% = 0.013 (as a decimal)
- time = 2 years
Substituting the values, we get:
balance = 8750 + (0.013 * 8750 * 2)
balance = 8750 + 227.5
balance = $8977.50
Therefore, Michelle's balance after two years will be $8977.50.
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8. Look at the graph. A vertex of a rectangle ABCD is located at A(5,-3).
10
9
8
7
6
5
4
3
2
1
-10-9-8-7-6-5-4-3 -2 -1 0
-1
-2
-3
-4
-5
-6
-8
-9
-10
1
3
5 678 9 10
The vertex B is located 5 units upward from A. The vertex D is located 3 units to the
right of A. What is the area of the rectangle ABCD?
A. 15 units²
B. 16 units²
C. 6 units²
D. 14 units²
The area of the rectangle ABCD is ,
A. 15 units²
Now, For the area of the rectangle ABCD, we need to first locate the position of the other two vertices, C and D.
Since, We know that vertex B is located 5 units upward from A, so the y-coordinate of B is,
-3 + 5 = 2.
We also know that vertex D is located 3 units to the right of A, so the x-coordinate of D is,
5 + 3 = 8.
Now we can calculate the length and width of the rectangle.
The length is the distance between A and B, which is,
2 - (-3) = 5 units.
The width is the distance between A and D, which is,
8 - 5 = 3 units.
Hence, we can calculate the area of the rectangle by multiplying the length and width:
5 units x 3 units = 15 units².
Therefore, the area of the rectangle ABCD is ,
A. 15 units²
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Help Quickly! For every 7 feet of rise, a hill runs 15 feet. What is the hill’s slope?
A. -8
B. 7/15
C. 15/7
D. 8
Answer:
I believe it's D
Sorry if incorrect
A researcher posts a newspaper advertisement offering $10 in exchange for participation in a short study. The researcher accepts the first 10
people who respond to the advertisement. Which of the following statements is true about the sample?
A. It is not a valid sample because it is only a short study.
B. It is a valid sample because money is offered to participants.
C. It is a valid sample because the first 10 people were selected to participate.
D. It is not a valid sample because it is not a random sample of the population.
The correct answer is D: It is not a valid sample because it is not a random sample of the population.
For a sample to be valid and representative of the population, it should be selected randomly. In this case, the researcher accepted the first 10 people who responded to the advertisement. This is a non-random sampling method known as convenience sampling and is prone to biases.
The other statements are incorrect:
A) The length of the study does not affect whether the sample is valid.
B) Offering compensation does not automatically make the sample valid.
C) Selecting the first 10 people does not make the sample valid - it needs to be selected randomly.
So in summary, the key issue here is that the sample was not selected randomly from the population, making it not a valid representative sample.
Which of the answers choices below has the same solution set as the inequality y-8<-2
The same choice of solution as the inequality y-8≤-2 would be y - 8 + 2 ≤ -2 + 2. Option D
How do we identify the right solution for the inequality presented?we can identify the right solution for the inequality by solving each solution presented. First we solve for the inequality y-8≤-2 ⇒ y ≤ -2+8 ⇒ y≤6
a. y - 8 + 8 ≥ -2 + 8 ⇒ y ≥ 6 which is different from y ≤ 6
b. y-8 + 8 < -2 + 8 ⇒ y < 6 is different from y ≤ 6
c. y - 8 + 2 ≤ -2 + 8 ⇒ y ≤ 12 is not y ≤ 6
d. y - 8 + 2 ≤ -2 + 2 ⇒ y ≤ 6 is the same as y ≤ 6
The above answer is in response to the full question below;
Which of the answers choices below has the same solution set as the inequality y-8≤-2.
a. y - 8 + 8 ≥ -2 + 8
b. y-8 + 8 < -2 + 8
c. y - 8 + 2 ≤ -2 + 8
d. y - 8 + 2 ≤ -2 + 2
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8. Which, if any, of the points is a hole of f(x)?
Ext10
f(x)=x2+9x+18
A. A hole exists on f(x) where x = -3.
B. A hole exists on f(x) where x = 5.
C. A hole exists on f(x) where x = -6,
D. The function does not have any holes.
hholow was obtained by tran
QUESTION 4 4.1 Translate each of the following into a mathematical equation: 4.1.1 If we multiply a number by four and then add six, the answer is 42 4.1.2 If we divide a number by three and then add seven, the answer is twenty (2) (2)
When each of the following mathematical equations are translated, the following is gotten;
4 4.1 = 4x+6
4 4.2 = X/3+ 7
How to translate the given statement into mathematical equations?To translate the given statement into mathematical equations, the following steps should be taken.
The first statement;
multiply a number by four and then add six. Let the unknown number be = X
That is ; 4(x)+6
The second statement;
divide a number by three and then add seven.
That is; X/3+ 7.
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square root of 64 one is 8 what is the other
PLEASE HELP I HAVE A TEST TOMORROW AND IM SO CONFUSED
The scale factor of the given diagram above would be = 4
How to calculate the scale factor?To calculate the scale factor of a given figure, the formula that should be used is given below. That is;
Scale factor = Bigger dimensions/smaller dimensions
where;
Surface area of bigger dimension = 1000 ft²
Surface area of smaller dimension = 250 ft²
Therefore scale factor = 1000/250 = 4.
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PLEASE HELP!!! MARKING AS BRAINLIST
Answer:
0.23
Step-by-step explanation:
area of triangle = (bh)/2
= (10*24)/2= 240/2 = 120
area of circle = πr^2
= π * 13^2 = 530.92916
So 120/530.92916 = 0.22601, which rounded to the hundredth is 0.23
Help me please and thank you..
Answer:
You will move each point of this shape 1 unit into the right. Then will move each point of this shape 2 units down. The draw line between each point.Can someone help explaining this problem so that I may understand.
(13, -2) is the solution of the system of equations
The given system of equations are 5x+15y=35
6x+20y=38
The missing entries in the row operations are 1/5, -6, 1/2, -3
Lets find solution for x and y
30x+90y=210
30x+100y=190
Subtract both the equations
30x+90y-30x-100y=210-190
-10y=20
y=-2
So 5x+15(-2)=35
5x-30=35
5x=65
x=13
Hence, (13, -2) is the solution of the system of equations
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Melanie is investing $13, 336 into a savings account. The savings account earns a 1.5% interest rate compounded biannually
can someone help me this!
Answer:
Start at 0, going right close circled.
Step-by-step explanation:
We know that we start at 0 because the inequality starts at 0. It is closed circle because it could also be equal to 0. the arrow is pointing right because it is greater or equal to 0.
50 points
Solve for x. Round to the nearest tenth of a degree, if necessary.
The value of angle x = 56.63 degree.
In the Given figure
EF = 4.4
FD = 8
∠F = x degree
Since we know that
CosΘ = (adjacent of a)/hypotenuse
Therefore,
Cosx = 4.4/8
= 0.55
Take inverse of cos both sides,
x = 56.63 degree
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3 friends share 4/5 of a pizza. What fraction of pizza does each person get?
Answer:
Step-by-step explanation:
1/3
parallelogram what is it
Answer:
a four-sided plane rectilinear figure with opposite sides parallel.
Step-by-step explanation:
basically take a square or rectangle and angle the interior angles of the corners acute angles.
simplify
5ab7c³(4a6b²c4)
Answer:
[tex]20a^7b^9c^7[/tex]
Step-by-step explanation:
I don't have an explanation... because it's right.
Find the surface area of the composite solid to the nearest hundredth.
3 ft.
4 ft
2 ft
The surface area is about
square feet.
The surface area of the composite solid is about 39 square feet to the nearest hundredth.
The surface area of the composite solid need to break it down into its component shapes and calculate their surface areas separately then add them up.
From the given dimensions we can see that the composite solid consists of a rectangular prism with dimensions 3 ft by 4 ft by 2 ft and a pyramid with a square base of side 3 ft and a height of 2 ft.
The surface area of the rectangular prism is the sum of the areas of its six faces.
The top and bottom faces are rectangles with dimensions 3 ft by 4 ft and the four side faces are rectangles with dimensions 3 ft by 2 ft or 4 ft by 2 ft.
The surface area of the rectangular prism is:
2(3 ft × 4 ft) + 2(3 ft × 2 ft) + 2(4 ft × 2 ft) = 24 ft²
The surface area of the pyramid is the sum of the areas of its five faces. The base is a square with an area of 3 ft × 3 ft = 9 ft².
Each of the four triangular faces has an area of (1/2) × base × height, where the base is 3 ft and the height is 2 ft.
The surface area of the pyramid is:
9 ft² + 4(1/2)(3 ft × 2 ft) = 15 ft²
The total surface area of the composite solid is the sum of the surface areas of the rectangular prism and the pyramid:
24 ft² + 15 ft² = 39 ft²
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4. Reyes meter family's water consumption is 117 m³. If their previous water reading was 0531, what is their present water meter reading?
5. Last month, the water meter reading of a household was 1552 m3. The following month, it was 1596 m3. If the basic charge of water consumption per cubic meter is P2.55, how much will they need to pay?
4. The present water meter reading for the Reyes family is 0648.
5. The household needs to pay P112.20 for their water consumption.
4. To find the present water meter reading for the Reyes family, we need to add their previous water reading to their water consumption.
Previous water reading: 0531
Water consumption: 117 m³
To add the two values, we can simply add the numerical part and keep the leading zeros:
0531 + 117 = 0648
Therefore, the present water meter reading for the Reyes family is 0648.
5. To calculate the amount the household needs to pay for water consumption, we need to find the difference in water meter readings and multiply it by the basic charge per cubic meter.
Previous water meter reading: 1552 m³
Present water meter reading: 1596 m³
Water consumption: 1596 - 1552 = 44 m³
Basic charge per cubic meter: P2.55
To calculate the payment, we multiply the water consumption by the basic charge per cubic meter:
Payment = 44 m³ * P2.55/m³ = P112.20
Therefore, the household needs to pay P112.20 for their water consumption.
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75% to a fraction convert reduce to lowest terms
Answer:
3/4
Step-by-step explanation:
A family has two cars. During one particular week, the first car consumed 15 gallons of gas and the second consumed 25 gallons of gas. The two cars drove a combined total of 1525miles, and the sum of their fuel efficiencies was 75 miles per gallon. What were the fuel efficiencies of each of the cars that week?
The fuel efficiency of the first car is approximately 101.67 miles per gallon, and the fuel efficiency of the second car is approximately 61 miles per gallon.
Let's assume the fuel efficiency of the first car is x miles per gallon, and the fuel efficiency of the second car is y miles per gallon.
Given information:
First car consumption: 15 gallons
Second car consumption: 25 gallons
Total distance driven: 1525 miles
Sum of fuel efficiencies: 75 miles per gallon
From the given information, we can set up the following equations:
Equation 1: First car consumption = Distance driven / Fuel efficiency of the first car
15 gallons = 1525 miles / x miles per gallon
Equation 2: Second car consumption = Distance driven / Fuel efficiency of the second car
25 gallons = 1525 miles / y miles per gallon
Equation 3: Sum of fuel efficiencies
x + y = 75 miles per gallon
We can rearrange Equation 1 and Equation 2 to solve for the fuel efficiencies:
x = 1525 miles / 15 gallons
y = 1525 miles / 25 gallons
Simplifying:
x = 101.67 miles per gallon
y = 61 miles per gallon.
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100 POINTS!
In the figure below, lines l and m are parallel. Suppose that m1 = 36 degrees and m2 = 45 degrees.
What are the measures of the other angles?
m3 = __
m4 = __
m5 = __
Please help. This is for a math test. Best answer gets Brainliest.
In the figure below, lines l and m are parallel. Suppose that m1 = 36 degrees and m2 = 45 degrees, then
m3 = 99°
m4 = 36°
m5 = 45°
How is this so?Note that 1, 2, and 3 are on a straight line.
since angles on a Straightline = 180°, thus,
∠3 = 180 - (45+36)
∠3 = 99
Note that angle 4 and angle 1 are corresponding angles and are thus, equal.
So
∠4 = 36°
∠5 is and alternate angle to ∠2 hence,
∠5 = 45°
Checking the sum of all three angles, we have 180 degrees, which confirms that the angels are correct since angles 3, 4 and 5 are for a triangle.
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Pls im struggling help me with it
Answer: 48 (degrees), b= 16.7, c = 22.4
Step-by-step explanation:
3. The table below shows the results of an experiment involving the growth of bateria. Find an equation for
the curve of best fit, then estimate the bacteria's growth after 20 minutes. Round to the nearest integer.
Time
Number of Bacteria
1
3
3
24
5
80
7
177
9
315
11
502
An equation for the curve of best fit is y = 3 - 0.5x.
The estimated bacteria's growth after 20 minutes is 876.5 bacteria.
How to determine the equation for the curve of best fit?In this scenario, the time (in minutes) would be plotted on the x-axis (x-coordinate) of the scatter plot while the number of bacteria would be plotted on the y-axis (y-coordinate) of the scatter plot through the use of Microsoft Excel.
On the Microsoft Excel worksheet, you should right click on any data point on the scatter plot, select format trend line, and then tick the box to display a linear equation for the curve of best fit on the scatter plot.
From the scatter plot (see attachment) which models the relationship between the time (in minutes) and the number of bacteria, a linear equation for the curve of best fit is given by:
y = 49.5x - 113.5
When x = 20 minutes, the bacteria's growth can be determined as follows;
y = 49.5(20) - 113.5
y = 876.5.
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A playground swing has chains that are 8 feet long. A child swings through 12° on
either side of the vertical. Through what angle, in radians, does the child swing? How
long is the arc through which the child travels?
The angle in radians is 0.209 radians
The length of the arc is 1.672 feet
How to find the length of the arcTo find the angle in radians we first need to convert 12° to radians
= 12° × π / 180
= 0.209 radians
The length of the arc
arc length = radius × angle in radians
where
the radius is the length of the chains = 8 feet:
arc length = 8 feet × 0.209 = 1.672 feet
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Find the solution of the system of equations.
3x-10y=-46
8x+10y=24
Answer:
(-2, 4)
(x,y)
Step-by-step explanation:
task 7:Answer the given situation write your answer in your paper. Explain your answer.
Get a medium size chocolate box and a medium sized powdered milk carton. Which do you think has a greater volume? How will you test whick box has a greater volume?
The box or carton which would have greater volume is that which has the greater dimension.
Volume of a bodyThe volume possessed by an object would be affected by it's dimension which are the height and width of the object.
Depending on the carton of Milk or box of chocolate chosen, the one which has a greater dimension would have greater volume.
Testing for VolumeThe boxes may be filled with water. Using a measuring tool, the amount of water held by each box will be measured. The box which hold the larger amount of water would have greater volume.
Hence, either of the boxes could have greater volume depending on the dimension.
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what is the domain of this function?
Answer:
(-∝,∝),{x x∈R}
Step-by-step explanation:
i think it's a
have a great day and thx for your inquiry :)
