5. Select all the statements that are true about AJKL and ALMN. (20 pts) The have only one pair of congruent angles. They have two pairs of congruent angles. AJKL has angles 50°, 60°, and 70°. ALMN has angles 50°, 60°, and 70°. AJKL and ALMN are similar.
​

The necessary information to carry out the hypothesis are given below.

For carrying out a hypothesis examination on the information, we need to do the following steps:

Step 1: Express the null and alternative hypotheses

Step 2: Pick the pertinent measure of value and significance level

Step 3: Compute the test statistic

Step 4: Estimate the p-value

Step 5: Draw a conclusion and interpret the results

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Answer:

y = (x - [tex]\frac{7}{2}[/tex])² - [tex]\frac{21}{4}[/tex]

Step-by-step explanation:

y = x² −7x + 7

Complete the square for y = x² −7x + 7

(x - [tex]\frac{7}{2}[/tex])² - [tex]\frac{21}{4}[/tex]

Set y equal to the new right side.

y = (x - [tex]\frac{7}{2}[/tex])² - [tex]\frac{21}{4}[/tex]

So, the answer is y = (x - [tex]\frac{7}{2}[/tex])² - [tex]\frac{21}{4}[/tex]

The quadratic function with roots -9 and 7 is f(x) = x² + 2x - 63

First, recall that a quadratic function has the form:

f(x) = ax² + bx + c

where a, b, and c are constants.

Given the roots of the quadratic function:

-9 and 7
x = -9 and x = 7 are the two distinct solutions to the quadratic equation.

Hence:

x + 9 and x - 7 are the factors of the quadratic equation.

( x + 9 ) ( x - 7 )

Expanding this expression Using FOIL method:

x( x - 7 ) + 9( x - 7 )

x² - 7x + 9x - 63

Collect and add like terms

x² + 2x - 63

Therefore, the function is f(x) = x² + 2x - 63.

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Answer:

2 2/3 cups flour

Step-by-step explanation:

32 cookies

by my calculations

The area of the region in this problem is given as follows:

A = 1 square unit.

The curve represented in this problem is given as follows:

y = sin(x).

The bounds of the region are given as follows:

Hence the area of the region is represented by the definite integral presented as follows:

[tex]\int_{0}^{\frac{\pi}{2}} \sin{x} dx[/tex]

The integral of the sine is the negative cosine, hence the area is:

A = -cos(x), from x = 0 to x = π/2.

Applying the Fundamental Theorem of Calculus, we have that the area is given as follows:

A = -cos(π/2) + cos(0)

A = -0 + 1

A = 1 square unit.

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The missing statement about base angles of the isosceles trapezoid is ∠TPR ≅ ∠ TAR.

The base angles of isosceles trapezoids are congruent.

In an isosceles trapezoid, the base angles (the angles formed by one of the bases and a leg) are congruent.

Since the opposite angles in an isosceles trapezoid are congruent, the base angles must also be congruent.

In the given diagram, we will identify the base angles as follows;

∠TPR ≅ ∠ TAR

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The distances in meters are:

a) 1241 m

b) 6002 m

c) 5168 m

d) 3400 m

e) 21320 m

f) 895 m

We have,

To convert kilometers (km) to meters (m), we need to multiply the distance by 1000.

a) 1.241 km = 1.241 × 1000 m = 1241 m

b) 6.002 km = 6.002 × 1000 m = 6002 m

c) 5.168 km = 5.168 × 1000 m = 5168 m

d) 3.4 km = 3.4 × 1000 m = 3400 m

e) 21.32 km = 21.32 × 1000 m = 21320 m

f) 0.895 km = 0.895 × 1000 m = 895 m

Therefore,

The distances in meters are:

a) 1241 m

b) 6002 m

c) 5168 m

d) 3400 m

e) 21320 m

f) 895 m

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B) gas mileage decreases with increase of car weight.

The value of the angle y is 86 degrees

To determine the value of the variable, we need to take note of the properties of a parallelogram. They include;

Also, note that angles on a straight line is equal to 180 degrees.

From the information shown on the diagram, we have;

y + 94 = 180

collect the like terms

y = 180 - 94

Subtract the terms

y =86 degrees

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Answer:

Step-by-step explanation:

The product of two given vectors is 48.

Given that, |v|=8, |w|=12 and the angle between v and w is 60 degrees.

We know that, |a|·|b|=|a|×|b|×cosθ.

Here, |v|·|w|=8×12×cos60°

= 96× 1/2

= 48

Therefore, the product of two given vectors is 48.

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Based on its second derivative and given initial values, the function is equal to f(x) = (1 / 3) · x³ - 6 · sin x + 8 · x + 4.

In this problem we find the definition of the second derivative of a function, whose form must be dertermined by integration and the use of initial values. First, write the second derivative:

f''(x) = 2 · x + 6 · sin x

Second, determine the first derivative of the function:

f'(x) = x² - 6 · cos x + C

2 = 0² - 6 · cos 0 + C

2 = - 6 + C

C = 8

f'(x) = x² - 6 · cos x + 8

Third, determine the function:

f(x) = (1 / 3) · x³ - 6 · sin x + 8 · x + C

4 = (1 / 3) · 0³ - 6 · sin 0 + 8 · 0 + C

4 = C

C = 4

f(x) = (1 / 3) · x³ - 6 · sin x + 8 · x + 4

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The angle that is an obtuse angle (that is, greater than 90° but less than 180°) is 120°. The correct option is B. 120°

An obtuse angle is an angle that is greater than 90° but less than 180°. Thus, if x is an obtuse angle, the range of values for x are

90° < x < 180°

From the given question, we are to determine the angle which obtuse.

In the given figure, to determine the angle which is obtuse, we will determine the angle that is greater than 90° but less than 180°.

The angle that is greater than 90° but less than 180° is 120°.

Thus,

The obtuse angle is the angle that measures 120°

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The surface area of the rectangular prism is 216 square cm

From the question, we have the following parameters that can be used in our computation:

10 cm by 3 cm by 6 cm

The surface area of the rectangular prism is calculated as

Area = 2 * (3 * 10 + 3 * 6 + 10 * 6)

Evaluate

Area = 216

Hence, the area is 216 square cm

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The amount of soil to fill the garden box is V = 1,134 inches³

Given data ,

Let the volume of the first rectangular box be V₁

Let the volume of the second rectangular box be V₂

where Volume of Rectangle = Length x Width x Height

So , V₁ = 21 x 7 x 2

V₁ = 294 inches³

And , V₂ = 12 x 10 x ( 7 )

V₂ = 120 x 7

V₂ = 840 inches³

And , the total soil in the garden box = V₁ + V₂

Amount of soil in garden box = 1,134 inches³

Hence , the volume is V = 1,134 inches³

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The measure of ∠EAC is 25°

It is given that the measure of ∠DAB is 25°

let AD = x and AB = y. Then, AE = 2 x and AC = 2 y, since AE and AC are 2 times longer than AD and AB, respectively.

AB / AC = AD / AE

y / 2 y = x / 2 x

1 / 2 = 1 / 2

We know that if two triangles are similar, then the ratio of its corresponding sides will be equal.

So triangle BAD similar to triangle CAE

So ∠DAB = ∠EAC

∠EAC =25°

Therefore, the measure of ∠EAC is 25°

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The exponential function in this problem represents a decay, with a percentage rate of 6%.

An exponential function has the definition presented as follows:

y = ab^x.

In which the parameters are given as follows:

The function is classified as growth or decay as follows:

The function in this problem is defined as follows:

y = 15(0.94)^x.

As |b| = 0.94 < 1, the function is a decay function, and the rate is obtained as follows:

1 - r = 0.94

r = 1 - 0.94

r = 0.06

r = 6%.

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The y- intercept for both function is 0 and 5.8.

We have First function

y= [tex]9^x[/tex]

Now , the y intercept of the equation is when x = 0

So , when x = 0

y= [tex]9^0[/tex]

y= 0

and, the second function is

y= [tex]9^{0.8[/tex]

y= 5.799

Hence, second function have intercept 5.8.

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Answer:

(x + 1)² + y² = 3

Step-by-step explanation:

the equation of a circle in standard form is

(x - h)² + (y - k)² = r²

where (h, k ) are the coordinates of the centre and r is the radius

here (h, k ) = (- 1, 0 ) and r = [tex]\sqrt{3}[/tex] , then

(x - (- 1) )² + (y - 0)² = ([tex]\sqrt{3}[/tex] )² , that is

(x + 1)² + y² = 3

The results of factoring the polynomials are (x - 6)(x + 6), 3(x - 2)(x + 2), (x + 3)² and 4(x + 3)(x - 5)

First, we have

x² – 36

Applying the property of difference of squares, we have

(x - 6)(x + 6)

Next, we have

3x² - 12

Factor out 3

3(x² - 4)

Applying the property of difference of squares, we have

3(x - 2)(x + 2)

First, we have

x² + 6x + 9

Expand and factorize

x² + 6x + 9 = x² + 3x + 3x + 9 = (x + 3)²

Next, we have

4x² - 8x - 60

Expand and factorize

4x² - 8x - 60 = 4(x² - 2x - 15) = 4(x + 3)(x - 5)

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The trigonometry identity value of sin(A) is -2/5

From the question, we have the following parameters that can be used in our computation:

The value of sin(A) has already been given

However, because the angle A is in Quadrant IV, the value of the trigonometry identity would be negative (sine are negative in the 4th quadrants)

So, we have

sin(A) = -2/5

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Answer:

Step-by-step explanation:

211

welcome hun

Based on the above, Since Ana bought 3/4 kg of lanzones and 1/2 kg of apples,  Ana bought 1  1/4 kilograms of fruits in all.

To be able to find out how many kilograms of fruits Ana bought in total, you have to add the amount of lanzones and apples she have.

Ana = 3/4 kg of lanzones

Ana = 1/2 kg of apples

So it will be:

3/4 + 2/4 = 5/4

Therefore, Ana will have bought a total of 5/4 kilograms of fruits.

To convert it to a mixed number, you need to divide the numerator by the denominator:

5 ÷ 4 = 1 remainder 1

So, the mixed fraction will  be 1  1/4 kg.

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See full question below

Ana bought 3/4 kg of lanzones and 1/2 kg of apples. How many kilograms of fruits did she buy in all?​

The measures the angle 3 is given by 45°.

Hence the correct option is (B).

The quadrilateral which has four equal sides and the adjacent sides of which are in perpendicular that is called Square.

The given figure is a Square.

We know that the angle between two adjacent sides = 90°.

We also know that the diagonal of square divides angles into two equal parts of angles.

So here angle 3 is a one equal part of angle between two adjacent sides of  square.

So angle 3 is given by = (1/2)*90° = 45°.

Hence the correct option will be (B).

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Mandy's solution makes sense since it entails multiplying the total number of persons in those entire rows (142) by the number of people in each row (ten).

Similarly, multiplying the total number of people in the remaining seats (142) by the number of people in each row (2) yields the total number of people in the remaining seats. The total number of persons in the theater is calculated by adding these two components.

This is a viable use of multiplication's distributive property, in which we break down a multiplication issue into simpler products and then add them up. As a result, Mandy's approach is a viable method for determining the total number of people in the theater.

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The 96% confidence interval for the population mean μ is approximately (18.06, 20.54).

We have,

To construct a 96% confidence interval about the population mean(μ) with a sample size of n = 57,

we can use the following formula:

CI = x ± z (s/√n)

where x is the sample mean, s is the sample standard deviation, n is the sample size, z is the z-score associated with the desired confidence level (96% in this case), and √n is the square root of the sample size.

The z-score corresponding to a 96% confidence level can be found using a standard normal distribution table or calculator.

For a two-tailed test, the z-score is 1.96.

Substituting the given values, we have:

CI = 19.3 ± 1.96 (4.8/√57)

Calculating the standard error of the mean (s/√n):

s/√n = 4.8/√57 ≈ 0.634

Substituting this value into the formula:

CI = 19.3 ± 1.96*0.634

Calculating the upper and lower bounds of the confidence interval:

lower bound = 19.3 - 1.96*0.634 ≈ 18.06

upper bound = 19.3 + 1.96*0.634 ≈ 20.54

Therefore,

The 96% confidence interval for the population mean μ is approximately (18.06, 20.54).

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To construct a 96% confidence interval for the population mean, use the formula x ± z*(s/√n) with z being the z-score for the 96% level, x being the sample mean, s being the sample standard deviation, and n being the sample size. Substituting the given values will give the lower and upper bound of the confidence interval.

The question is asking for the construction of a 96% confidence interval for a population mean u, given a sample size (n) of 57, a sample mean (x) of 19.3 and a sample standard deviation (s) of 4.8.

To find the confidence interval, we need to use the formula: x ± z*(s/√n) where z is the z-score associated with our confidence level. For a 96% confidence interval, the z-score is approximately 2.05 (you can find this from a standard z-table).

Substituting the given values into the formula gives: 19.3 ± 2.05*(4.8/√57)

Calculating the above expression will give the lower and upper bound of the 96% confidence interval.

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The statement is false, a triangle can't have two angles of 90°.

Remember that for any triangle, the sum of the 3 interior angles should be equal to 180°.

So if the 3 interior angles are A, B, and C we have.

A + B + C = 180°

In this case we know that two of the angles are of  90°, so let's say that:

A = 90°

B = 90°

Replacing that we will get:

90° + 90° + C = 180°

C = 180° - 90° - 90°

C = 0°

And we can't have a 0° degree angle, so the statement is false, triangles with two 90° don't exist.

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The two triangles are congruent since they have equal angles and equal sides.

Congruent triangles are two triangles that have exactly the same size and shape.

In other words we can say that they have the same angles and the same side lengths.

So when two triangles are congruent, all of their corresponding parts including the angles and sides are equal.

For the given triangles

The missing value of angle C = 180 - (18 + 110) = 52⁰

The missing value of angle F = 180 - (18 + 52) = 110⁰

So it is obvious that the two triangles are congruent since they have equal angles and equal sides.

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The inequality that represents the situation is w ≥ 32.

To graph the inequality, we first need to solve it for w:

3/4w ≤ 24

We can isolate w by multiplying both sides by 4/3 (which is the reciprocal of 3/4), remembering to reverse the inequality because we're multiplying by a negative number:

w ≥ 24 × 4/3

w ≥ 32

So the solution to the inequality is w ≥ 32.

To graph this, we draw a number line and put a closed circle at 32 (because the inequality includes "equal to"), and shade to the right of 32 to represent all the values that satisfy the inequality given in the attached image.

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