Answer:
The minimum value of the function is ƒ(3) = 5.
Step-by-step explanation:
To find the minimum value of ƒ(x), we need to find the vertex of the parabola represented by the function. We can do this by completing the square:
ƒ(x) = x² - 6x + 14
ƒ(x) = (x - 3)² - 9 + 14 (adding and subtracting the square of half the x coefficient, which is -3)
ƒ(x) = (x - 3)² + 5
The vertex of the parabola is at (3, 5), and since the coefficient of the squared term is positive, the parabola opens upward. Therefore, the minimum value of the function is ƒ(3) = 5.
Which of the following describes the transformations of g(x)--(2)**-2 from the parent function f(x)=2*?
O shift 4 units left, reflect over the x-axis, shift 2 units down
O shift 4 units left, reflect over the y-axis, shift 2 units down
O shift 4 units right, reflect over the x-axis, shift 2 units down
O shift 4 units right, reflect over the y-axis, shift 2 units down
Shift 4 units right, reflect over the y-axis, shift 2 units down is the transformation applied.
The parent function f(x) = 2x is transformed to g(x) = (2x-2)⁻²
To determine the transformations applied to f(x), we can work from the inside out, starting with the expression 2x-2:
Shift 2 units to the right: This can be achieved by replacing x with (x-2).
This gives us the expression 2(x-2) = 2x-4.
Reflect over the y-axis: This can be achieved by replacing x with (-x).
This gives us the expression 2(-x)-4 = -2x-4.
Square and take the reciprocal: This can be achieved by applying the transformation f(x) -> 1/f(x)².
This gives us the expression (-1/2x-4)².
Therefore, the transformations applied to f(x) are shift 2 units to the right, reflect over the y-axis, and square and take the reciprocal.
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In a study of computer use, 1000 randomly selected Canadian Internet users were asked how much time they spend using the Internet in a typical week. The mean of the sample observations was 12.7 hours.
A button hyperlink to the SALT program that reads: Use SALT.
(a)
The sample standard deviation was not reported, but suppose that it was 5 hours. Carry out a hypothesis test with a significance level of 0.05 to decide if there is convincing evidence that the mean time spent using the Internet by Canadians is greater than 12.5 hours. (Use a statistical computer package to calculate the P-value. Round your test statistic to two decimal places and your P-value to four decimal places.)
According to the given sample data, and assuming a sample standard deviation of 5 hours, the results of the hypothesis test suggest that there is substantial evidence to support the assertion that the average time spent using the internet by Canadians exceeds 12.5 hours.
To conduct the hypothesis test, we first set the null and alternative hypotheses. The null hypothesis (H0) states that the mean time spent by Canadians on the internet is equal to or less than 12.5 hours. The alternative hypothesis (Ha) states that the mean time spent by Canadians on the internet is greater than 12.5 hours.
Using the given sample data, and assuming a sample standard deviation of 5 hours, we calculate the test statistic and the p-value. To calculate the test statistic, we use the formula t = (x - μ) / (s / √n), where x is the sample mean, μ is the hypothesized population mean, s is the sample standard deviation, and n is the sample size.
We find that the test statistic is 1.78 (rounded to two decimal places). If the p-value is less than the significance level of 0.05, we reject the null hypothesis and conclude that there is strong evidence that the mean time spent using the internet by Canadians is greater than 12.5 hours.
If the p-value is greater than 0.05, we fail to reject the null hypothesis and conclude that there is insufficient evidence to support the claim that the mean time spent using the internet by Canadians is greater than 12.5 hours.
In this case, assuming a significance level of 0.05, we calculate the p-value to be 0.0397 (rounded to four decimal places). Since the p-value is less than the significance level, we reject the null hypothesis and conclude that there is substantial evidence that the mean time spent using the internet by Canadians is greater than 12.5 hours.
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The net below shows a square pyramid. What is the lateral surface area?
After considering the given options we come to the conclusion that the answer is 112 in² which is Option B.
The lateral surface area of a square pyramid is the summation of the areas of the side faces only, on the other hand
surface area = lateral area + area of the base.
The lateral area of a square pyramid = 2al (or) 2a√ [ (a 2 /4) + h² ].
Now, to get the surface area, we have to add the area of the base (which is a 2) to each of these formulas.
For the given case, we are given a square pyramid. Hence, all four sides are equivalent in length. We can apply Pythagoras theorem to evaluate the slant height (h) of the pyramid.
The slant height is given by h = √(a² + l²),
Here
a = length of one side
l = height of the pyramid.
Applying this information, we can evaluate the lateral surface area of the square pyramid
Lateral surface area = 2a * √((a²)/4 + l²)
= 2 * 8 * √((8²)/4 + 10²)
= 112 in²
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The complete question is
The net below shows a square pyramid. What is the lateral surface area?
A. 176 in^2
B. 112 in^2
C. 64 in^2
D. 210 in^2
A ball is thrown from an initial height of 3 meters with an initial upward velocity of 7 m/s.
following.
h=3+7t-5t²
Find all values of t for which the ball's height is 4 meters.
Round your answer(s) to the nearest hundredth.
(If there is more than one answer, use the "or" button.)
initial
height
4
h
ground
t = seconds
The only valid value for t is approximately 1.53 seconds when the ball's height is 4 meters.
How to solve the equationWe are given the equation for the height of the ball h as a function of time t:
h(t) = 3 + 7t - 5t²
We want to find all values of t for which the height h is 4 meters. So, we set h(t) equal to 4 and solve for t:
4 = 3 + 7t - 5t²
Rearrange the equation to form a quadratic equation:
0 = 5t² - 7t - 1
Now, we can use the quadratic formula to solve for t:
t = (-b ± √(b² - 4ac)) / 2a
In our equation, a = 5, b = -7, and c = -1. Plugging these values into the quadratic formula, we get:
t = (7 ± √((-7)² - 4 * 5 * (-1))) / (2 * 5)
t = (7 ± √(49 + 20)) / 10
t = (7 ± √69) / 10
We have two possible solutions for t:
t = (7 + √69) / 10 ≈ 1.53 (rounded to the nearest hundredth)
t = (7 - √69) / 10 ≈ -0.13(rounded to the nearest hundredth)
Since time cannot be negative, we discard the second solution.
So, the only valid value for t is approximately 1.39 seconds when the ball's height is 4 meters.
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Hello please, I did not understand this exercise. In the plane referred to an orthonormal reference (o, i, j) place the points A, B, C and D defined by: A(6; 4); B(3; 7); C(12; -2); D(9; 7).
Show that C is the image of A by dilation with center B and ratio 3.
We have shown that C is the image of A by dilation with center B and ratio 3.
Now, To show that C is the image of A by dilation with center B and ratio 3, we need to follow these steps:
Firstly, Find the vector AB by subtracting the coordinates of B from the coordinates of A:
AB = A - B = (6 - 3, 4 - 7) = (3, -3)
Multiply the vector AB by the dilation ratio of 3:
3 AB = 3 (3, -3) = (9, -9)
Add the resulting vector to the coordinates of the center B:
BC = B + 3 AB = (3, 7) + (9, -9)
BC = (12, -2)
Hence, Compare the resulting point BC to the coordinates of C to show that they are the same:
BC = (12, -2) = C
Therefore, we have shown that C is the image of A by dilation with center B and ratio 3.
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Can someone please help me and show work
Line, line segment, angle,ray
Polygon ABCD with vertices at A(-4, 6), B(-2, 2), C(4,-2), D(4, 4) is dilated using a scale factor of to create polygon A'B'C'D'. Determine the vertices of polygon
4
A'B'C'D'.
OA(-3, 4.5), B(-1.5, 1.5), C(3, -1.5), D'(3, 3)
OA(-12, 18), B(-6, 6), C(12,-6), D'(12, 12)
OA(3, -4.5), B(1.5, -1.5), C(-3, 1.5), D'(-3,-3)
OA (4.5, -3), B(1.5, -1.5), C(-1.5, 3), D'(3, 3)
Answer:
The correct answer is: OA(3, -4.5), B(1.5, -1.5), C(-3, 1.5), D'(-3,-3).
To dilate a point using a scale factor of 4, we multiply each coordinate of the original point by 4.
Thus, the coordinates of A' are (-4 * 4, 6 * 4) = (-16, 24)
The coordinates of B' are (-2 * 4, 2 * 4) = (-8, 8)
The coordinates of C' are (4 * 4, -2 * 4) = (16, -8)
The coordinates of D' are (4 * 4, 4 * 4) = (16, 16)
To check our work, we can plot these points on a graph and compare with the original polygon:
Original Polygon:
A(-4, 6) B(-2, 2)
* *
\ /
\ /
\ /
\ /
\ /
* *
C(4,-2) D(4,4)
Dilated Polygon:
A'(-16, 24) B'(-8, 8)
* *
\ /
\ /
\ /
*
C'(16,-8) D'(16,16)
If we divide the coordinates of the dilated polygon by 4, we get the answer:
A'(-16/4, 24/4) = (-4, 6)
B'(-8/4, 8/4) = (-2, 2)
C'(16/4, -8/4) = (4, -2)
D'(16/4, 16/4) = (4, 4)
So the vertices of polygon A'B'C'D' are OA (3, -4.5), B(1.5, -1.5), C(-3, 1.5), and D'(-3,-3).
Find the value of x for which m||n.
A) 21
B) 19
C) 8
D) Can't be determined
Answer:
X = 20.25°
Step-by-step explanation:
Interior angle of the same side are suplementery which means their sum is equal to 180° .
So 38° +( 8x - 26°) = 180°
12° + 8x = 180° .... Simplify 38 and 26
8x = 180°- 12° .... taking 12 to the left side it
change the sighn to -ve
8x = 162° .... simplify
8x/8 = 162°/8 .... dividing both side 8
x = 20.25°
need help will give brainlist
The expressions that shows a correct way to set up the slope formula for the line that passes through the points (3,6) and (-7,-4) is (-4-6) / (-7 - 3) (option c).
To find the slope of a line that passes through two points, we can use the slope formula, which is:
slope = (change in y) / (change in x)
This formula tells us how much the y-coordinate changes (rise) for every one unit of change in the x-coordinate (run).
Now let's use the given points (3,6) and (-7,-4) to set up the slope formula. We'll call the first point (x₁, y₁) and the second point (x₂, y₂). Then we can plug these values into the slope formula:
slope = (y₂ - y₁) / (x₂ - x₁)
Plugging in the coordinates of the two given points, we get:
slope = (-4 - 6) / (-7 - 3)
We simplify this expression to get:
slope = (-10) / (-10)
Which simplifies further to:
slope = 1
So the correct way to set up the slope formula for the line that passes through the points (3,6) and (-7,-4) is:
slope = (y₂ - y₁) / (x₂ - x₁)
= (-4 - 6) / (-7 - 3)
= 1
Therefore, the slope of the line passing through these two points is 1.
Hence the correct option is (c).
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need some help asap thank you
Answer:
quadratic
Step-by-step explanation:
linear is a straight line
exponential is a simple curved graph
A vending machines coin box contains nickels dimes and quarters the total number of coins in the box is 312 the number of dimes is three times the number of nickels and quarters together and the box contains $31.30 find the number of nickels dimes and quarters that it contains
Answer:
58 nickels; 234 dimes; 20 quarters
Step-by-step explanation:
number of dimes = d
number of nickels = n
number of quarters = q
n + d + q = 312
d = 3(n + q)
0.05n + 0.1d + 0.25q = 31.3
n + d + q = 312
d = 3n + 3q
5n + 10d + 25q = 3130
n + 3n + 3q + q = 312
5n + 30n + 30q + 25q = 3130
4n + 4q = 312
35n + 55q = 3130
n + q = 78
7n + 11q = 626
n = 78 - q
7(78 - q) + 11q = 626
546 - 7q + 11q = 626
4q = 80
q = 20
n = 78 - 20 = 58
d = 3(58 + 20) = 3(78) = 234
Answer: 58 nickels; 234 dimes; 20 quarters
Number 11 on the worksheet
Answer:
24
Step-by-step explanation:
Compare the known similar sides - - -
10 is to 30, and 14 is to 42. Triangle B is 3x Triangle A.
So the unknown side in Triangle B is 3x 8cm, so 24cm.
Make t the subject of c=t³ - 8v
The variable t becomes the subject of the equation c=t³ - 8v by adding 8v to both sides and taking the cube root, giving t = ∛(c + 8v).
Explanation:We need to make t the subject of the equation c=t³ - 8v. To do this, we first add 8v to both sides of the equation to isolate t³ on one side, giving us t³ = c + 8v. We then need to take the cube root of both sides to solve for t. Hence, t = ∛(c + 8v). Now, t is the subject of the equation.
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Help xangle, x and
∠
y
∠yangle, y are supplementary angles.
∠
y
∠yangle, y measures
14
2
∘
142
∘
142, degrees.
What is the measure of
∠
x
∠xangle
Answer:
∠x = 38°
Step-by-step explanation:
∠x + ∠y = 180°
∠x + 142° = 180°
∠x = 180° - 142
∠x = 38°
#CMIIWWhat is the surface area of the cylinder with height 6 km and radius 4 km? Round your answer to the nearest thousandth.
Answer:
251.327 km² (nearest thousandth)
Step-by-step explanation:
The formula for the surface area of a cylinder is:
[tex]\boxed{S.A. = 2\pi r^2 + 2\pi rh}[/tex]
where r is the radius and h is the height of the cylinder.
Substitute the given values of r = 4 km and h = 6 km into the formula and solve:
[tex]\begin{aligned}S.A. &= 2\pi (4)^2 + 2\pi (4)(6)\\&=2\pi (16)+2 \pi (24)\\&=32 \pi+ 48 \pi\\&=80 \pi\\&=251.327412...\\&=251.327\; \sf km^2 \end{aligned}[/tex]
Therefore, the surface area of the cylinder with height 6 km and radius 4 km is 251.327 square kilometers, rounded to the nearest thousandth.
Answer:
Curved surface area is 150.796 km²,Total surface area is 251.327 km².-------------------------
Curved surface area of a cylinder:
CSA = 2πrhSubstitute 6 for h and 4 for r:
CSA = 2π(6)(4) = 150.796447372 ≈ 150.796 km² (rounded)Total surface area adds top and bottom faces:
TSA = 2πrh + 2πr² TSA = 2πr(r + h)TSA = 2π(4)(4 + 6) = 251.327412287 ≈ 251.327 km² (rounded)If g(x) is the inverse of f(x), what is the value of f(g(2))?
Answer:
The answer is C) 2.
Step-by-step explanation:
Since g(x) is the inverse of f(x), we know that f(g(x)) = x for all x in the domain of g.
Therefore, f(g(2)) = 2.
The answer is C) 2.
I need help with the answer
Answer:
Correct equation:
x + 22 + x + 22 + 10 = 48
ASAP PLEASE ANSWER
AND IF U COULD PLEASE ANSWER MY OTHER QUESTIONS THAT ARE FOR COLLEGE, I ACCIDENTALLY PRESSED COLLEGE INSTEAD OF MIDDLE SCHOOL
The statement "Each additional serving will require 1 additional can of beans" is not correct.
How to explain the informationIt should be noted that to make more than 3 servings, Robert will need to increase the amount of both beans and ground turkey used in the recipe.
Assuming that the recipe calls for one 18-ounce can of beans for 3 servings, Robert will need to use 6 cans of beans for 12 servings.
This is because each serving requires 6 ounces of beans (18 ounces ÷ 3 servings), and 12 servings would require a total of 72 ounces of beans (12 servings × 6 ounces per serving).
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A school is constructing a rectangular play area against an exterior wall of school building. It uses 120 feet of fencing material to enclose three sides of the play area. a Complete the table by giving the length and area for each build. b write an equation to represent l, the length of the play area in feet, as a function of w, the width in feet. c write an equation to represent A, the area in square feet, as a function of w, the width in feet.
An equation to represent A, the area in square feet, as a function of w, the width in feet will be; A = 120W -2W²
Here, the perimeter of the rectangle will give:
120 = L + 2W
Area = LW
We know that the area of a rectangle is l × w
When w =10, length = 120 - 20 = 100, area = 100 x 10 = 1000
When w = 20, length = 120 - 40 = 80, area = 80 x 20 = 1600
When w = 40, length = 120 - 80 = 40. area = 40 x 40 = 1600.
So, the completed table will be
Width Length Area
10 100 1000
20 80 1600
40 40 1600
w 120 - 2w (120 - 2w) w
To maximize the area with the given fencing, from the equation written above, then w = 30 feet and l = 60
On substituting, we have,
A = LW = (120 - 2W) W
L = 120 - 2W,
On simplification, we have
A = 120W -2W²
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Ahmed placed salt water in a beaker and left it on his desk for a week. After a week, there was only salt. Which best explains the missing water from the beaker?
A. The water became a new substance.
B. The water evaporated.
C. The water disappeared forever.
D. The water condensed.
The water evaporated.
Option B is the correct answer.
We have,
When a liquid is left open in a container, it can undergo a phase change to become a gas or vapor, which is known as evaporation.
In this case,
The water in the beaker would have evaporated, leaving behind the salt. The water did not disappear forever but instead changed state to become a gas in the air.
Thus,
The water evaporated.
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Factor the following expressions completely. Show and check all work on your own paper.
4x4+8x3+4x2
The complete factorization of the original expression is:
4x² (x + 1)²
We have,
First, we can factor out 4x².
4x² (x² + 2x + 1)
Next, we can see that the expression inside the parentheses is a perfect square trinomial, which means it can be factored as:
4x² (x + 1)²
Thus,
The complete factorization of the original expression is:
4x² (x + 1)²
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using the Pythagorean Identity to find the exact value (i.e. Radicals and fractions, not rounded decimals) of sin θ if cosθ=1/2 and θ terminates in Quadrant IV
1) 〖 sin〗^2 θ+〖cos〗^2 θ=1
Step 1: Pythagorean Identity
2) 〖sin〗^2 θ+〖(1/2)〗^2=1 Step 2: Substitute 1/2 for cos θ
The exact value of sin θ, given that cosθ = 1/2 and θ terminates in Quadrant IV, is -√(3)/2.
The Pythagorean Identity states that sin²θ + cos²θ = 1. This identity can be used to find the value of sinθ, given the value of cosθ, and vice versa.
In Quadrant IV, the cosine function is positive, and the sine function is negative. This is because in Quadrant IV, the x-coordinate is positive, and the y-coordinate is negative.
Given that cosθ=1/2, we can use the Pythagorean Identity to find the value of sin²θ.
sin²θ + cos²θ = 1
sin²θ + (1/2)² = 1
sin²θ + 1/4 = 1
sin²θ = 1 - 1/4
sin²θ = 3/4
To find the value of sinθ, we take the square root of both sides of the equation:
sinθ = ±√(3/4)
However, since θ terminates in Quadrant IV, sinθ is negative. Therefore, we take the negative square root of 3/4:
sinθ = -√(3/4)
We can simplify this expression by writing 3/4 as a fraction in terms of its square roots:
sinθ = -√(3/4)
sinθ = -√(3)/√(4)
sinθ = -√(3)/2
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please helppp !!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
Using Pythagorean trigonometric identity, the value of cosθ is √2/2
What is the value of cosθTo find the value of cosθ, we can use Pythagorean identity to do this. However, we are also told that θ terminates in the the first quadrant.
sinθ = √2/2
sin²θ + cos²θ = 1
Substituting the value of sin θ into the formula above
cos²θ + (√2/2)² = 1
cos²θ + 1/2 = 1
collect like terms
cos²θ = 1 - 1/2
cos²θ = 1/2
cosθ = √(1/2)
cosθ = √2/2
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Please help and show workkkkk please I really need help
Answer:
L = 9
Step-by-step explanation:
6x8=48
432÷48=9
Suppose a four-year bond is purchased for $5700. The face value of the bond when it matures is $6669. Find the APR.
The bond's APR is%
(Type an integer or a decimal.)
The bond's APR is 4.25%.
The formula for face value of the bond is given as following
F=P(1+rt) where F=face value, P= Purchase value, r=Annual rate & t=time of bond.
The given values are P=$5700, t=4 years & F=$6669
Substituting the above values we get
6669=5700(1+r*4)
0.17=4r
r=4.25%.
Hence, the APR for the given bond is 4.25%.
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Find the total surface are of this triangular prism, Picture is provided.
The total surface area of this triangular prism is 976 square cm.
Here, we have,
Total surface area of a figure
The total surface area is the sum of the area of the faces of a figure.
The given shape is made up of three rectangles and 2 triangles.
Surface area = 2[25*10] + (14 * 10) + (24 * 14)
Surface area = 2(250) + 140 + 336
Surface area = 976 square cm
Hence the total surface area of this triangular prism is 976 square cm
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Simplify 3[tex]\sqrt[/tex]2-√2
Answer: (√2)(2) = 2√2
Step-by-step explanation:
To simplify the expression 3√2 - √2, you can factor out the common term √2:
3√2 - √2 = (√2)(3 - 1)
Now, subtract the numbers in parentheses:
(3 - 1) = 2
(√2)(2) = 2√2
solve the following system by graphing.
x-2y=4
x+3y=14
The y-coordinate of the solution is y=
The solution of the system of equations is (8, 2).
Given is a system of equations x-2y = 4 and x+3y = 14, we need to find the solution of the system of equations,
So, the equations are =
x-2y = 4
x = 2y + 4......(i)
x+3y = 14
x = -3y + 14..........(ii)
Equating the equations since their LHS is same,
2y + 4 = -3y + 14
5y = 10
y = 2
Put y = 2 in any equation to find the value of x,
So,
x = 2(2)+4
x = 8
Hence the solution of the system of equations is (8, 2).
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In the function above, the slope will be multiplied by -9, and the y-value of the y-intercept will be increased by 2 units. Which of the following graphs best represents the new function
The equation of the new line will be y = -9x + 4. Then the correct option is B.
Given that:
Linear equation, y = x + 2
The linear equation is given as,
y = mx + c
Where m is the slope of the line and c is the y-intercept of the line.
The y-value of the y-intercept will be raised by 2 units, and the slope will be multiplied by -9.
Then the slope of the equation will be given as,
m = -9 x 1
m = - 9
The y-intercept of the equation is given as,
c = 2 + 2
c = 4
The equation of the new line will be y = -9x + 4. Then the correct option is B.
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In the function y = x + 2, the slope will be multiplied by -9, and the y-value of the y-intercept will be increased by 2 units. Which of the following graphs best represents the new function
