By rigid transformations, the image of the parabola y = x² is equal to parabola y = x² + 4.
How to determine the image of a parabola
In this problem, we need to determine the image of a parabola by means of a rigid transformation known as vertical translation:
y = f(x) → y = f(x) + k, where k represents a translation upwards and f(x) is the original function.
If we know that f(x) = x² and k = 4, then the image of the function is:
f(x) = x² + 4
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If sales tax on a 16.00 DVD is $1.32 find the sales tax on a $120.00 DVD player
write an indirect proof..if two angles are supplementary, than they both cannot be obtuse angles.
Answer:
They cannot. They have to be obtuse and acute.
Two cars start at the same time, but travel in opposite directions. One car's average speed is 30 miles per hour (mph). At the end of 4 hours, the two cars are 400 miles apart. Find the average speed in mph of the other car.
Final answer:
The average speed of the second car is calculated by subtracting the distance traveled by the first car from the total distance after both cars have traveled in opposite directions for the same amount of time. The second car's average speed is found to be 70 mph.
Explanation:
To find the average speed of the second car, we first need to establish the total distance covered by both cars. Since they are moving in opposite directions, we can add their distances together to determine the total distance.
Let's designate the distance the first car travels as D1 and the distance the second car travels as D2. The average speed of the first car is given as 30 mph, and both cars travel for 4 hours. Therefore, D1 can be calculated as follows:
D1 = average speed of first car × time = 30 mph × 4 h = 120 miles
Since we know that the combined distance D1 + D2 is 400 miles, we can find D2 by subtracting D1 from the total distance:
D2 = total distance - D1 = 400 miles - 120 miles = 280 miles
Now, to find the average speed of the second car, we divide D2 by the time, which is 4 hours:
Average speed of the second car = D2 / time = 280 miles / 4 h = 70 mph
Therefore, the average speed of the second car is 70 mph.
Gas is $2.09 per gallon; how much will it cost to get 10 gallons of gas?
$20.90
$12.09
$7.91
$4.10
Convert 18532.6 into scientific notation
move the decimal point 4 places to the left to get
1.85326 x 10^4
Alice and Brian have cookies in a ratio of 4:3. Brian and Cori have cookies in a ratio of 6:4. What is the ratio of Alice’s cookies to Cori’s cookies?
4:4
Alice and Cori have the same amount of cookies
A skydiver jumps out of an airplane. After 0.8 seconds, she has fallen 100 feet. After 3.1 seconds, she has fallen 500 feet. Emtiaz says that the skydiver should fall about 187.5 feet in 1.5 seconds. Is his answer reasonable? Explain.
Equivalent name for 57
What's the answer and work of 42.3-(-18.7)
What is 15% higher than 60?
A.9
B.24
C.69
D.75
X(X^2+4)(X-1) as a sum of monomials in standard form
If parallelogram ABCD was reflected over the y-axis, reflected over the x-axis, and rotated 180°, where would point A' lie?
[Hint: Place your coordinates in the blank with no parentheses and a space after the comma in the form: x, y]
Answer:
The point A' lie at (-4,1).
Step-by-step explanation:
From the given figure it is clear that the coordinates of A are (-4,1).
If parallelogram ABCD was reflected over the y-axis, then
[tex](x,y)\rightarrow (-x,y)[/tex]
[tex]A(-4,1)\rightarrow A_1(4,1)[/tex]
Then it reflected over the x-axis,
[tex](x,y)\rightarrow (x,-y)[/tex]
[tex]A_1(4,1)\rightarrow A_2(4,-1)[/tex]
After that, it rotated 180° about the origin,
[tex](x,y)\rightarrow (-x,-y)[/tex]
[tex]A_2(4,-1)\rightarrow A'(-4,1)[/tex]
Therefore the point A' lie at (-4,1).
On a map, two locations are 0.75 centimeter apart. Their actual distance is 15 kilometers apart.
Answer:
The answer is:
B. 0.4 centimeter = 8 kilometers
C. 0.75 centimeter = 15 kilometers
D. 3 centimeters = 60 kilometers
Step-by-step explanation:
Got it right in 2021
yasmine bought 6 gallons of apple juice. after filing up 4 bottles of the same juice, she had 0.3 gallons of apple juice left. What's the amount of apple juice in each bottle?
A softball is thrown straight up, reaching a maximum height of 20 meters, what is the ball's approximate vertical speed when it hits the ground?
Velocity is the rate of change of distance over time.
The ball's approximate vertical speed when it hits the ground is 19.8m/s
The maximum height of an object, thrown up is calculated as:
[tex]\mathbf{h_{max} = \frac{v^2}{2g}}[/tex]
Where:
[tex]\mathbf{h_{max} = 20m}[/tex] --- the maximum height
[tex]\mathbf{v = ??}[/tex] --- final velocity
[tex]\mathbf{g = 9.8ms^{-2}}[/tex] --- acceleration due to gravity
So, we have:
[tex]\mathbf{h_{max} = \frac{v^2}{2g}}[/tex]
[tex]\mathbf{20 = \frac{v^2}{2 \times 9.8}}[/tex]
Solve for v^2
[tex]\mathbf{v^2 = 2 \times 9.8 \times 20}[/tex]
[tex]\mathbf{v^2 = 392}[/tex]
Take square roots of both sides
[tex]\mathbf{v = 19.8ms^{-1}}[/tex]
Hence, the ball's approximate vertical speed when it hits the ground is 19.8m/s
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When a softball is thrown straight up and reaches a maximum height of 20 meters, the approximate vertical speed when it hits the ground can be determined by taking into account the initial vertical velocity and the time it takes to reach the maximum height and fall back down. Using the given information, the initial vertical velocity is calculated using the equation v0y = sqrt(2gh), where g is the acceleration due to gravity and h is the maximum height. Substituting the values, the approximate vertical speed is 19.80 m/s.
Explanation:When a softball is thrown straight up and reaches a maximum height of 20 meters, its approximate vertical speed when it hits the ground can be determined using the principles of projectile motion. The vertical speed of the ball when it hits the ground can be calculated by taking into account the initial vertical velocity and the time it takes for the ball to reach its maximum height and then fall back down. In this case, since the ball is thrown straight up, the vertical speed when it hits the ground will be equal to the initial vertical speed.
Using the given information, we know that the ball reaches a maximum height of 20 meters. We can calculate the time it takes for the ball to reach this height using the equation for vertical displacement:
h = v0yt + (1/2)gt2
Where:
h is the vertical displacement (20 meters in this case)v0y is the initial vertical velocity (which we need to find)t is the time it takes to reach the maximum heightg is the acceleration due to gravity (approximately 9.8 m/s2)Since we know the maximum height and the acceleration due to gravity, we can rearrange the equation to solve for the initial vertical velocity:
v0y = sqrt(2gh)
where:
sqrt represents the square rootg is the acceleration due to gravity (approximately 9.8 m/s2)h is the maximum height (20 meters in this case)Substituting the values into the equation, we get:
v0y = sqrt(2 * 9.8 * 20)
Simplifying further:
v0y = sqrt(392)
v0y ≈ 19.80 m/s
Therefore, the approximate vertical speed of the ball when it hits the ground is 19.80 m/s.
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The table shows the time a patient spends at the dentist and the amount of the bill.
What is the correlation coefficient for the data in the table?
–0.93
–0.27
0.27
0.93
Answer-
Correlation coefficient for the data in the table was found to be 0.93.
Solution-
Taking the independent variable or input variable as, the time a patient spends at the dentist and the dependent variable or output variable as the amount of the bill.
We know that,
[tex]r=\frac{n(\sum xy)-\sum x \sum y}{\sqrt{[n\sum x^{2} -({\sum x})^{2}]\times [n\sum y^{2} -({\sum y})^{2}]}}[/tex]
Calculating the values from the table, then putting it in the formula
[tex]r=\frac{4 \times 3130.9 \ - \ 6.45 \times 1473}{\sqrt{[4\times 12.3725 \ - \ 6.45^{2}][4 \times 877475 \ - \ 1473^2]}}[/tex]
[tex]\Rightarrow r=0.929720561 \approx 0.93[/tex]
∴ Correlation coefficient for the data is 0.93.
The correlation coefficient for the data in the table would be 0.93. So, the correct option is A.
What is the correlation coefficient?The correlation coefficient is used to measure the strong relationship between the two variables.
It is given that the first column is labeled time spent at the dentist (in hours) with entries 1.4, 2.7, 0.75, and 1.6.
The second column is labeled bill amount (in dollars) with entries 235, 867, 156, and 215.
The numbers between -1 and 1 should be one of the values related to the bill amount.
By assuming the independent variable or input variable as, the time a patient spends at the dentist and the dependent variable as the amount of the bill.
Hence, The correlation coefficient for the data in the table was found to be 0.93.
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The lengths of the sides of a triangle are consecutive odd integers. If the perimeter is 1 less than 4 times the shortest side, find the length of each side
10 questions very simple. Lots of points.
1 Simplify the given equation.
5x + 2(x - 3) = -2(x - 1)
a. 7x - 6 = -2x + 2
b. 7x - 3 = -2x - 1
2 Solve for x.
3(x + 2) = 12
a. x = 2
b. x = 3 1/3
c. x = 4 2/3
3 Solve for x.
7(x + 1) = 21
a. x = 2
b. x = 20/7
c. x = 4
4 Solve for x.
4(x + 2) = 48
a. x = 7 1/2
b. x = 10
c. x = 14
5 Solve for x.
13(x - 3) = 39
a. x = 1
b. x = 4
c. x = 6
6 Solve for x.
5(x + 1) = 4(x + 8)
a. x = 7
b. x = 27
c. x = 37
7 Solve for x.
7(x + 2) = 6(x + 5)
a. x = -16
b. x = 16
c. x = 44
8 Solve for x.
3(x + 2) + 4(x - 5) = 10
a. x = 36/7
b. x = 24/7
c. x = 16/7
9 Solve for x.
7(x - 3) + 3(4 - x) = -8
a. x = 1/4
b. x = 25/10
c. x = -41/10
10 Solve for x.
7(3 - x) = 8(4 - 2x)
a. x = -5/9
b. x = 11/23
c. x = 11/9
see attached picture for the answers:
Charlie made four out of 23 free-throw shots. What percentage of shots does he make? Round to the nearest whole number
Each small square on the grid is 1 ft².
Which estimate best describes the area of this figure?
25 ft²
35 ft²
50 ft²
65 ft²
Answer:
50 ft²
Step-by-step explanation:
As you can see the polygon on the grid is not a regular polygon, so to calculate the area would be very complicated without having the right tools, what we can doo is to draw a squre that covers the whole height but not the total length, that way we can take a close estimate of the area, the closest square that can be formed would be a 6x9 square, and the estimated area would be 54, that would be the maximun area, so the answer would be 50 squared feet.
given the number, two-fifths,generate its equivalents forms as a fraction, a decimal, and a percent. in addition, give a real world example in which each form might be used
Whitch best describes the resulting three-dimensional figure !?
The statement which best describes the resulting three-dimensional figure is:
A cylinder with a base radius of 14 cm.Step-by-step explanation:We know that when a rectangle is rotated about a line then the resulting figure so obtained is a cylinder.
Hence, the three dimensional figure will be a cylinder.Also, the breadth of the rectangle will be the radius of the cylinder.
Here the perimeter of the rectangle is: 76 cm.
Also the length of the rectangle is: 24 cm.
Let b be the breadth of the rectangle.
We know that the perimeter of rectangle is given by the formula:
[tex]Perimeter=2(l+b)[/tex]
where l is the length of the rectangle and b is the breadth of the rectangle.
Here we have: l=24 cm
Hence,
[tex]76=2(24+b)\\\\i.e.\\\\24+b=\dfrac{76}{2}\\\\i.e.\\\\24+b=38\\\\i.e.\\\\b=38-24\\\\i.e.\\\\b=14\ cm[/tex]
Hence, the radius of the cylinder is: 14 cm.
Solve for x. The triangles in each pair are similar.
Melvin and Sylvia are married with no children, and they're filing their federal income tax return. Melvin had a gross income of $44,500 last year, while Sylvia had a gross income of $51,200, and they plan to use the standard deduction. They're trying to decide whether to file their return jointly or separately, so they want to calculate how much less they would pay in federal income taxes if they filed jointly rather than separately.
Part I: When filing separately, both Melvin and Sylvia have a standard deduction of $5700, and each can claim him/herself as an exemption for $3650. Neither has any additional adjustments to income. What is Melvin's taxable income? How about Sylvia's taxable income?
add standard deduction and exemption: 5700 + 3650 = 9350
subtract from each of their incomes and that will be the taxable income:
Melvin: 44500 - 9350 = 35150 taxable income
Sylvia: 51200 - 9350 = 41850 taxable income
Melvin's taxable income is $34,150 and Sylvia's taxable income is $42,850.
Explanation:To calculate Melvin's taxable income, we need to subtract his standard deduction and exemption from his gross income. Melvin's gross income was $44,500 and his standard deduction is $5700. He can also claim himself as an exemption for $3650. Therefore, Melvin's taxable income would be $44,500 - ($5700 + $3650) = $34,150.
In a similar way, to calculate Sylvia's taxable income, we subtract her standard deduction and exemption from her gross income. Sylvia's gross income was $51,200 and her standard deduction is $5700. She can also claim herself as an exemption for $3650. Therefore, Sylvia's taxable income would be $51,200 - ($5700 + $3650) = $42,850.
Graph y−2=−34(x−6) using the point and slope given in the equation.
Use the line tool and select two points on the line.
Answer:
Point-slope form: An equation of a straight line in the form [tex]y -y_1 = m(x -x_1)[/tex];
where
m is the slope of the line and [tex](x_1, y_1)[/tex] are the coordinates of a given point on the line.
Given the equation: [tex]y-2=-\frac{3}{4}(x-6)[/tex] ......[1]
On comparing with Point slope form equation we have;
m = [tex]-\frac{3}{4}[/tex] and point (6 , 2)
Now, find the Intercept of the given equation:
x-intercept: The graph crosses the the x-axis i.e,
Substitute y =0 in [1] and solve for x;
[tex]0-2=-\frac{3}{4}(x-6)[/tex]
[tex]-2=-\frac{3}{4}(x-6)[/tex]
Using distributive property: [tex]a\cdot(b+c) = a\cdot b +a\cdot c[/tex]
[tex]-2 = -\frac{3}{4}x + \frac{18}{4}[/tex]
Subtract [tex]\frac{18}{4}[/tex] on both sides we get;
[tex]-2-\frac{18}{4}= -\frac{3}{4}x + \frac{18}{4} -\frac{18}{4} [/tex]
Simplify:
[tex]-\frac{26}{4} = -\frac{3}{4}x[/tex]
or
-26 = -3x
Divide both sides by -3 we get;
x = 8.667
x-intercept: (8.667, 0)
Similarly, for
y-intercept:
Substitute x = 0 in [1] and solve for y;
[tex]y-2=-\frac{3}{4}(0-6)[/tex]
[tex]y-2=\frac{18}{4}[/tex]
Add 2 on both sides we get;
[tex]y-2+2=\frac{18}{4}+2[/tex]
Simplify:
[tex]y=\frac{26}{4} =6.5[/tex]
y-intercept: (0, 6.5)
Now, using these two points (8.667, 0) and (0, 6.5) you can plot the graph using line tool as shown below.
25=2y-5 solve the equation for y
which side correspond to TA
Answer:
The correct option is 3.
Step-by-step explanation:
In ΔACT and ΔDGO.
[tex]\angle A=\angle D[/tex] (Given)
[tex]\angle AC=\angle DG[/tex] (Given)
[tex]\angle C=\angle G[/tex] (Given)
By ASA property of congruent triangles.
[tex]\triangle ACT\cong \triangle DGO[/tex]
The congruent part of congruent triangles are congruent.
[tex]TA=OD[/tex] (CPCTC)
The side TA is corresponding to OD.
Therefore the correct option is 3.
Consider each of the following relationships: the heights of fathers and the heights of their adults sons, the heights of husbands and the heights of their wives, and the heights of women at age 4 and their heights at age 18. Rank the correlation between these pairs of variables from largest to smallest. Explain your reasoning
We would expect the height of women at age 4 and their height as women at age 18 to be the highest correlation since it is rational to think taller children to turn out to be taller adults and shorter children to become shorter adults. The next highest would be the correlation between the father and their adult sons. Tall fathers be likely to have tall sons, but naturally not as tall, and similarly for shorter fathers. The lowest correlation would be between husbands and their wives. Husbands may be taller than their wives in common, but there is no purpose to expect anything more than a weak positive correlation.
The heights of fathers and their adult sons have the highest correlation due to genetics, followed by the heights of husbands and wives influenced by assortative mating. Lastly, the correlation between the heights of women at age 4 and their heights at age 18 is weaker due to the intervening growth factors.
Explanation:To rank the correlation between these pairs of variables, we should consider how closely related they are likely to be based on genetic, environmental, and social factors. Genetics plays a significant role in the height of fathers and their adult sons because height is a highly heritable trait. Therefore, we can expect a high correlation here. Social factors influence the heights of husbands and their wives since people may choose partners similar to themselves in height, a phenomenon known as assortative mating, but the correlation is likely to be weaker than genetic influence. Lastly, for the heights of women at age 4 and their heights at age 18, while early childhood height can be an indicator of adult height, there's substantial growth and development between these ages, affected by environmental and genetic factors, resulting in a lower correlation compared to the direct genetic link between fathers and sons.
If we were to rank the correlation from largest to smallest, it would be:
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Which line on the graph below has a slope of zero?
m=1/2 (d1+d2) solve for d1
Answer: The required solution for [tex]d_1[/tex] is [tex]d_1=2m-d_2.[/tex]
Step-by-step explanation: We are given to solve the following equation for [tex]d_1:[/tex]
[tex]m=\dfrac{1}{2}(d_1+d_2)~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~(i)[/tex]
To solve the given equation for [tex]d_1,[/tex] we must take all the other terms on the right side of the equation.
From equation (i), we get
[tex]m=\dfrac{1}{2}(d_1+d_2)\\\\\\\Rightarrow 2m=d_1+d_2\\\\\Rightarrow d_1=2m-d_2.[/tex]
Thus, the required solution for [tex]d_1[/tex] is [tex]d_1=2m-d_2.[/tex]