Select the correct answer.
Four equivalent forms of a quadratic function are given. Which form displays the zeros of function h?
A. h(x) = -4(x − 2)(x + 2)
B. h(x) = -4(x2 − 4)
C. h(x) = -4x2 + 16
D. h(x) = -2(2x2 − 8)

The tan(t−π) = 74of the given trigonometric function, tan(t−π), is 74

From the question, we are to determine the value of trigonometric function tan(t−π) using the given information.

The given information is tan(t) = 74

We can use the following identity to solve this problem:

tan(t - π) = tan(t) - tan(π) / 1 + tan(t)tan(π)

Since tan(π) = 0

This can be simplified into

tan(t - π) = tan(t) / (1 - 0)

tan(t - π) = tan(t)

Thus,

We just need to find tan(t)

Given that tan(t) = 74.

Hence, tan(t−π) = 74

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a)

The class modal interval is 24 ≤ a < 26.

b)

The Mean age of the employee is 23.

It is the average value of the set given.

It is calculated as:

Mean = Sum of all the values of the set given / Number of values in the set

We have,

Age                 Frequency (f)      Midpoint (x)    fx

18 ≤ a < 20       3                            19                 57

20 ≤ a < 22      2                           21                  42

22 ≤ a < 24      7                           23                  161

24 ≤ a < 26      8                           25                  200

26 ≤ a               0                

Now,

Sum of all the frequencies.

N = 3 + 2 + 7 + 8 = 20

Sum of fx.

= 57 + 42 + 161 + 200

= 460

Now,

Mean = 460/20

Mean = 23

Now,

Class modal interval.

= 24 ≤ a < 26

Because in the class interval, the frequency is the highest.

Thus,

The class modal interval is 24 ≤ a < 26.

The Mean is 23.

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Answer:

Stefan borrowed $8000 on his car loan and $4000 on his student loan.

Step-by-step explanation:

a. Let x be the amount of money Stefan borrowed on his car loan and y be the amount he borrowed on his student loan. According to the problem, Stefan borrowed twice as much on his car loan as on his student loan, so x = 2y.

b. The annual interest on the car loan is $360 more than the interest on the student loan. We can set up an equation as follows:

0.08x - 0.07y = 360

c. Substituting x = 2y from equation (a) into equation (b), we get:

0.08(2y) - 0.07y = 360

0.16y - 0.07y = 360

0.09y = 360

y = 4000

So, Stefan borrowed $4000 on his student loan. Using equation (a), we can find the amount he borrowed on his car loan:

x = 2y = 2(4000) = 8000

Therefore, Stefan borrowed $8000 on his car loan and $4000 on his student loan.

all the applications are true.

What is simple interest?

A quick and simple way to figure out interest on money is to use the simple interest technique, which adds interest at the same rate for each time cycle and always to the initial principal amount. Any bank where we deposit our funds will pay us interest on our investment. One of the different types of interest charged by banks is simple interest. Now, before exploring the idea of basic curiosity in further detail,

Solution: Start by using:

2012 indicates that x=1

So A = 900 (1.05) = 900 × 1,05=945

B = 1100 (1.038) = 1100 × 1038 = 1141.8 \sC = 5000 (0,85) = 5000 x0.85 = 4250 \s4250 1141.8945

So, Ture is the first applicant.

Applying the second: 1.05-1=0.055% Ture

The third application is 1-0.85=0.15=15%. False

Applying the fourth: A 1.05+=0.05=5%

B: \s11038-1=0.038=3.8% \s5% > 3.8% Ture

Hence all the apply are true.

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Answer:

Variables:

x = number of lollipops sold

y = number of candy bars sold

Inequality: 2x + 4y ≥ 180

In the attachment......

The two lines have same slope with opposite signs thus, the linear routes are perpendicular, and Ty and Leo will pass through a common coordinate.

A perpendicular is a straight line in mathematics that forms a right angle (90 degrees) with another line. In other words, two lines are perpendicular to one another if they connect at a right angle. If two segments PQ and RS connect at right angles, we may say that they are perpendicular to one another.

For the given coordinates of Ty and Leo let us calculate the slope of the line.

The slope of the line is given as:

m = (y2 - y1) / (x2 - x1)

For Ty:

m = (1 - 3) / (0 + 1) = -2

For Leo:

m = (2 - 4) / (0 - 1) = 2

The two lines have same slope with opposite signs thus, the lines are perpendicular, and Ty and Leo will pass through a common coordinate.

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The total length is 115 km.

Let "x" be the complete lengh. So, in order to find 20% of that length we need to multiply by 0.2, which equals 20%. And it needs to equal 23 km. Hence the equation should be the following:

[tex]0.2x=23[/tex]

[tex]\frac{0.2x}{0.2} =\frac{23}{0.2} \\ \\x=115[/tex]

To verify the answer, calculate 20% of the result (115), and it should equal 23 km. Let's see!

[tex]115*0.2=\\ \\23[/tex]

The total length is 115 km.

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3.43 liters of Can A, and 4.57 liters of Can B  should be used from each can to obtain 5 liters of paint which is half blue and half yellow.

A word problem is a few sentences describing a 'real-life' scenario where a problem needs to be solved by way of a mathematical calculation.

From the question,

Can A is 9 parts of blue  1 part yellow= 90% blue, 10% yellow

Can B is 20% blue, 80% yellow.

let

A + B = 8 Liters

90% A + 20% B = 50% (Blue)

10% A + 80% B = 50% (Yellow)

resolving

90% A + 20% B = 10% A + 80% B

80% A = 60% B

Go back to A + B = 8 and solve for one of the variables.

B = 8 - A

80% A = 60% (8 - A)

80% A = 480% - 60% A

140% A = 480%

A = 3 43 liters

B = 8 - A = 4.57 liters

Hence, 3.43 liters of Can A, and 4.57 liters of Can B should be used.

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Answer:

Step-by-step explanation:

Absolute Change:

The absolute change in the politician's support is calculated as the difference between the final support percentage (53%) and the initial support percentage (32%):

53% - 32% = 21 percentage points

So, the absolute change in the politician's support is 21 percentage points.

Relative Change:

The relative change in the politician's support is calculated as the absolute change divided by the initial support percentage, multiplied by 100 to express it as a percentage:

(21 / 32) * 100 = 65.625%

Rounding to the nearest tenth of a percent, the relative change in the politician's support is 65.6%.

So, the absolute change in the politician's support is 21 percentage points, and the relative change is 65.6%.

In this case, the absolute change in the politician's support is an increase of 21 percentage points, and the relative change is an increase of 65.6%.

In this situation, the absolute change in the politician's support can be calculated by subtracting the original value from the new value. So, 53% (new value) - 32% (original value) = 21%. Thus, the absolute change in support is 21 percentage points.

The relative change is the absolute change divided by the original value. So, 21% (absolute change) ÷ 32% (original value) = 0.65625. To get the relative change as a percentage, we need to multiply this decimal by 100, and round to the nearest tenth of a percent, which gives us 65.6%.

Therefore, the politician's support has increased by an absolute change of 21 percentage points, and a relative change of 65.6%.

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In a case whereby Koji is installing a rectangular window in an office building. The window is 8 2/3 feet wide and 5 3/4 feet high using the  formula for the area of a rectangle is A=bh, the area of the window is 49 5/6.

The concept that will be used here is area of a rectangle. Since window can be seen to be like a  rectangle then area of window  can be take as area of rectangle which can be calculated as

Area = Length × breadth

The Length=82/3 = 26/3

the breadth= 5 3/4 = 23/4

Then Area =( 26/3 * 23/4) = 299/6 = 49 5/6

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Answer: 49 5/6 square feet

Step-by-step explanation: The width/breadth = 8 2/3 = 26/3

the height = 5 3/4 = 23/4

Area = (26/3 * 23/4) = 598/12 = 49 5/6

Answer: the right option is (A) II only

Step-by-step explanation:

The radius of the sphere is half of its diameter, so the radius is 30/2 = 15 inches.

The formula for the volume of a sphere is V = (4/3)πr³, where r is the radius.

Substituting the given values, we get:

V = (4/3)π(15)³

V = (4/3)π(3375)

V = 4500π

Therefore, the volume of the sphere is 4500π cubic inches.

The journal entry for the business receiving $ 6, 000 for a 10 month service contract is :

Date                     Account and Explanation               Debit           Credit

December 1          Cash                                           $ 6, 000

                            Unearned Service Revenue                             $ 6, 000

                            Being revenue received for services

                             not yet rendered

When a business receives money for a service that it is yet to perform for the client, this is called unearned service revenue. The amount is to be debited to the cash account as it is an asset and assets are debited when they increase.

Unearned service revenue will then be credited by the same amount because it represents a liability that the company owes to the client.

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The volume of the solid generated is V=8π and 32/5π

Given functions are  x=y²,  x=2  and  y=0

The equation y=x² is a parabola opening to right and has a vertex at  O(0,0)

and another y=0 is the x-axis and  x=2  is a line parallel to the y-axis

The region bounded by the above will be formed once their intersection points are known.

y²=2⟹y=±√2

OFB is bounded by  O(0,0), F(2,0) and  B(2,√2)

Let  V be the volume of solid generated when the region  OFB  is revolved around line x=2.

[tex]V=\pi \int\limits^2_0 {x^4} \, dx \\[/tex]

V=π[x⁵/5]²₀

V=π[(2)⁵/5]

V=32/5 π.

[tex]V=\pi \int\limits^4_0 {(2^2)_2-(\sqrt{y}^2)_3 } \, dy\\\\ V=\int\limits^4_0 {(4-y)} \, dx[/tex]

V=8π.

when the shaded region revolves the bout x-axis:

[tex]V=\pi \int\limits^b_a {y^2} \, dx \\\\V=\pi \int\limits^2_0 {y^2} \, dx =\pi \int\limits^2_0 {x^4} \, dx =\pi [\frac{1}{5}.x^5]_0^2\\\\ V=\pi [\frac{32}{5}-0][/tex]

V=32/5

when the shaded region revolves the bout y-axis:

[tex]V=\pi \int\limits^c_d [(x^2)_2-(x^2)_1} \, dx \\V=\pi \int\limits^4_0 [(2^2)_2-(\sqrt{y} ^2)_1} \, dy \\V=\pi \int\limits^4_0 {(4-y)} \, dy =\pi [4y-\frac{1}{2}y^2]_0^4[/tex]

V=π[16-8]

V=8π

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The average weight of carry-on luggage by passengers in airplanes is (15.7, 20.3) pounds.

The margin of error to be used is 2.3 pounds.

where z is the Z-score that corresponds to the desired confidence level (95% confidence corresponds to a Z-score of 1.96), standard deviation is the population standard deviation (7.5 pounds), and sample size is the number of items in the sample (25).

       Margin of Error = 1.96 * (7.5 / sqrt(25)) = 2.3 pounds

        (average weight - margin of error, average weight + margin of error)

         = (18 - 2.3, 18 + 2.3) = (15.7, 20.3) pounds.

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Answer:

$12,000

Step-by-step explanation:

2000([tex](1 + \frac{.05}{2}) ^{2(3)}[/tex]

12,000

Answer:

3 miles

Step-by-step explanation:

The distance between Arati and Ava can be calculated using the Law of Cosines. Let's call the distance between Arati and Ava as "d". We know that:

a = 2 (distance skied by Arati)

b = 3 (distance skied by Ava ) c = d (distance between Arati and Ava) A = 45 (angle between a and b)

Plugging these values into the Law of Cosines formula:

d^2 = 2^2 + 3^2 - 2 * 2 * 3 * cos(45)

d^2 = 4 + 9 - 12 * (√2 / 2)

d^2 = 13 - 12 * √2

d = √(13 - 12 * √2)

To the nearest mile, the distance between Arati and Ava is approximately 3 miles.

Bode plots depict the frequency response, or the magnitude and phase changes as a function of frequency. This is accomplished using two semi-log scale plots. Using MATLAB, plot Bode diagrams of G1(s) and G2(s) given below.

(a) The first function is:

G1(s) = (1 + s)/(1 + 2s)

MATLAB Code:

%G1(s)

n1 = [1 1]                %coefficients of numerator

d1 = [2 1]               %coefficients of denominator

sys1 = f(n1,d1)      %the transfer function

bode(sys1)           %bode plot

grid on

Command Window:

>> Untitled

n1 = 1 1

d1 = 2 1

sys1 = (1 + s)/(1 + 2s)

Continuous-time transfer function.

(b) The second function is:

G(s) = (1 - s)/(1 - 2s)

MATLAB Code:

%G2(s)

n2 = [-1 1]                    %coefficients of numerator

d2 = [2 1]                   %coefficients of denominator

sys2 = f(n2, d2)       %the transfer function

bode(sys2)               %bode plot

grid on

Command Window:

>> Untitled

n2 = -1 1

d2 = 2 1

sys2 = (1 - s)/(1 - 2s)

Continuous-time transfer function.

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The complete question is:

Using MATLAB, plot Bode diagrams of G1(s) and G2(s) given below:

G1(s) = (1 + s)/(1 + 2s)

G2(s) = (1 - s)/(1 - 2s)

Note that the second transfer function is a non-minimum phase system; meaning it has a zero on the right-half plane. Note how the phase plot is affected.

So, adjusted to three decimal places, the lacking angles in the triangle are B = 80°24', a = 1.042 cm, and c = 5.852 cm.

The number of important digits is the total number of digits, excluding the decimal point, all leading zeros, and some following zeroes. The number of decimal points is the number to the left of the decimals.

We are given that triangle ABC is a right triangle with C = 90°, A = 9° 36', and b = 5.812 cm.

To find B, we can use the fact that the sum of the angles in a triangle is 180°. Therefore, we have:

B + A + C = 180°

B + 9°36' + 90° = 180°

B = 80°24'

To find a, we can use the trigonometric function tangent.

We have:

tan A = opposite/adjacent

tan 9°36' = a/b

Solving for a, we get:

a = b tan A = 5.812 cm tan 9°36' ≈ 1.042 cm

The Pythagorean theorem, which says that in a right triangle, the square of the hypotenuse equals the total of the squares of the two sides (a and b), can be used to determine c.

We have:

c² = a² + b²

c² = (1.042 cm)² + (5.812 cm)²

c² ≈ 34.235 cm²

c ≈ √34.235 cm²

c ≈ 5.852 cm

Therefore, the missing parts of the triangle are B ≈ 80°24', a ≈ 1.042 cm, and c ≈ 5.852 cm, rounded to three decimal places.

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The derivative of y relative to x is given as follows:

dy/dx = 8xsin(x)cos(x) + 4x²(cos²(x) - sin²(x)).

The function for this problem is defined as follows:

y = 4x²sin(x)cos(x)

The function is a product of three functions, hence the product rule is applied, as follows:

dy/dx = [4x²]'sin(x)cos(x) + 4x²[sin(x)]'cos(x) + 4x²sin(x)[cos(x)]'.

The derivatives are given as follows:

Hence the derivative of the function is defined as follows:

dy/dx = 8xsin(x)cos(x) + 4x²cos²(x) - 4x²sin²(x)

dy/dx = 8xsin(x)cos(x) + 4x²(cos²(x) - sin²(x)).

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Answer:

m∠Y = 60

WY = 7 in

Step-by-step explanation:

It's an isosceles triangle (2 sides are equal), therefore m∠W = m∠Y because the base angles of an isosceles triangle are equal.

Sum of interior angles of a triangle is 180.

let x = m∠W = m∠Y

2x + 60 = 180

2x = 180 - 60 = 120

x = 120/2 = 60

m∠Y = 60

Since all 3 angles = 60, now we know it's an equilateral triangle, therefore WY = 7 in

Hence, Reese would need 2/5 yards of blue ribbon for every yard of gold ribbon. Thus, the correct option will be (c)

A ratio is an ordered pair of numbers a and b, written a / b where b does not equal 0. A proportion is an equation in which two ratios are set equal to each other. For example, if there is 1 boy and 3 girls you could write the ratio as:

1 : 3 (for every one boy there are 3 girls)

and if there is 2 pen and 4 copy in your bag the the ratio is

1 : 2 (for every 1 pen there is 2 copy)

We know that

Reese needs 1/4 yards of blue ribbon for every 5/8 yards of gold ribbon.

To know the total blue ribbon she would need for each yard of gold ribbon, we use the following proportion.

(1/4)/x=(5/8)

the x = 5/8 = 4x

x = 2/5

Reese needs 1/4 yards of blue ribbon for every 5/8 yards of gold ribbon.

To know the total blue ribbon she would need for each yard of gold ribbon, we use the following proportion.

Then, we solve for x.

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The question is incomplete, the complete question is:

Standard based practice compare two fractions jasmine cut 3/8 yard of blue ribbon and 1/3 yard of red ribbon to decorate will be:

a) 0

b) 4/7

c) 2/5

d) 3/9

Answer:

92

Step-by-step explanation:

2x49=98-6=92

Answer:

f(7) = 92

Step-by-step explanation:

To find f(7), substitute x = 7 into the given function.

[tex]\begin{aligned}f(7)&=2(7)^2-6\\&=2(49)-6\\&=98-6\\&=92\end{aligned}[/tex]

Answer:

Step-by-step explanation:

The distance between two numbers on the real number line is simply the absolute value of their difference. So, to find the distance between the numbers a = 12 and b = 3, we calculate:

distance = |a - b| = |12 - 3| = |9| = 9

Therefore, the distance between the numbers a = 12 and b = 3 on the real number line is 9 units.

Answer:

Step-by-step explanation:

12.1+|-11|=12

The equation is satisfied for the gcd(30, 21) and it is: -30 + 21 = 3.

For the gcd(a, b) values in exercise 1.9, the extended Euclidean algorithm (Theorem 1.11) can be used to find integers u and v such that au + bv = gcd(a, b).

We start by using the Euclidean algorithm to calculate the gcd(a, b). We then iteratively calculate the remainder, quotient, and coefficients for each step. We use the equation a = qb + r, where q is the quotient and r is the remainder. We then use the equation r = a - qb to find the value of u and v.

For example, consider gcd(30, 21). We use the Euclidean algorithm to calculate the gcd. We get that gcd(30, 21) = 3. We then use the equation a = qb + r to calculate the remainder, quotient, and coefficients. We get that 30 = 1(21) + 9. We then use the equation r = a - qb to find the values of u and v. So, 9 = 30 - 1(21), which gives us that u = -1 and v = 1. This means that the equation is satisfied for the gcd(30, 21) and it is: -30 + 21 = 3.

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1. Using the conversion rate of 1 kilometer = 0.621371 miles, Oskar determine the distance of his trip in miles.

2. Oskar's 165 kilometer trip is equivalent to 101.87995 miles.

3. The difference between kilometers and miles is that a kilometer is a metric unit of length and a mile is an imperial unit of length.

Paragraph 1: To convert kilometers to miles, Oskar will need to use the conversion rate of 1 kilometer = 0.621371 miles.

This conversion rate can be found on any formula sheet, and it will help Oskar determine the distance of his trip in miles.

Paragraph 2: To convert 165 kilometers into miles, Oskar will simply need to multiply 165 by 0.621371.

The result will give him the distance in miles.

For example, 165 * 0.621371 = 101.87995 miles. Therefore, Oskar's 165 kilometer trip is equivalent to 101.87995 miles.

Paragraph 3: Oskar might be traveling in a country where the maps are labeled in kilometers instead of miles. This is common in many countries, including most of Europe and many countries in Asia. The difference between kilometers and miles is that a kilometer is a metric unit of length and a mile is an imperial unit of length. A kilometer is equal to 0.621371 miles, while a mile is equal to 1.60934 kilometers. It's important to be aware of the units used in different countries to ensure accurate navigation.

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Answer:

the awnser is C

Step-by-step explanation:

Answer:

The sine function for the given parameters is y = 4 sin ( pi/2 * x ) + 1. The period is 12, the amplitude is 4, the midline is y = 1 and the y-intercept is (0, 1). The function is not a reflection of its parent function over the x-axis.

Step-by-step explanation:

To solve a sine function with the given features, one must first identify the midline, amplitude, period, and phase shift of the function. The midline is the average of the maximum and minimum values of the graph, while the amplitude is half of the difference between these two values. The period is the length of one cycle in radians, and the phase shift is how much it has been shifted from its parent function over the x-axis.

The shortest distance between the two lines L1 and L2 is 0.

The shortest distance between two lines can be found using the cross product of their direction vectors.

The direction vectors of line L1 and L2 can be found as:

L1 = B - A = (2 - 3, 1 - 2, 0 - 1) = (-1, -1, -1)

L2 = D - C = (3 - 2, 0 - 4, -2 - (-1)) = (1, -4, -3)

The cross product of the direction vectors of L1 and L2 gives the normal vector to the plane formed by the two lines:

cross(L1, L2) = (1 + 4, -1 - 4, 3 + 1) = (5, -5, 4)

The normal vector of the plane formed by the two lines, and a point on line L1 (A = (3, 2, 1)), can be used to find the equation of the plane:

5x - 5y + 4z = d

5 * 3 - 5 * 2 + 4 * 1 = d

15 - 10 + 4 = d

9 = d

So the equation of the plane formed by the two lines is:

5x - 5y + 4z = 9

The shortest distance between the two lines is equal to the distance between a point on line L1 (A = (3, 2, 1)) and the plane formed by the two lines:

d = abs(9 - (5 * 3 - 5 * 2 + 4 * 1)) / sqrt(5^2 + (-5)^2 + 4^2)

d = abs(9 - 9) / sqrt(29)

d = 0 / sqrt(29)

d = 0

Therefore, the shortest distance between the two lines L1 and L2 is 0.

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