I dint know the answers to this and its SUPER important I get it right.

The equation of the axis of symmetry is x = 2

The equation of the axis of symmetry is the value of x that divides the parabola into equal halves (mirror images).

The value of x which gives the mirror images is the value of x coordinate of the vertex. The vertex is at (2, 0). The x coordinate = 2

From the graph, we can also see it occurred at x = 2

The axis of symmetry: x = x-coordinate of the vertex

The equation of the axis of symmetry is x = 2

ANSWER

• x = 12

• y = 16

• z = 7

EXPLANATION

Because the triangles are similar, we have that:

• The ratio between corresponding sides is constant:

• Corresponding angles are congruent:

We know that the measure of angle E is 16°, so the measure of angle G must be the same because they are congruent,

With this equation, we can find x. First, divide both sides by 2,

And then, add 4 to both sides,

Hence, x = 12.

Now we know that the length of side EF is,

To find y and z, we will use the proportions we got at the top of this explanation,

Replace with the known values and the expressions with y and z,

With the first two, we can find z,

Simplify the right side,

Rise both sides to the exponent -1 - i.e. flip both sides of the equation,

Multiply both sides by 25,

Subtract 8 from both sides,

And divide both sides by 6,

Hence, z = 7.

Finally, with the last two proportions, we can find y,

The first two steps are the same we did to find z: simplify the left side and flip both sides,

Multiply both sides by 24,

And divide both sides by 3,

Hence, y = 16.

The sum of all interior angles of a triangle is 180° thus the measure of the exterior angle m∠K is 102° so option (B) is correct.

A triangle is a 3-sided shape that is occasionally referred to as a triangle. There are 3 sides and three angles in every triangle, some of which may be the same.

Triangle is a very common figure to deal with in our daily life.

It is known that the sum of all three angles inside a triangle will be 180°.

So,   m∠A +  m∠B +  m∠C = 180°

m∠C = 180° - 58° -  44°

m∠C = 78°.

The exterior angle of C = 180- 78 = 102°.

Hence "The sum of all interior angles of a triangle is 180° thus the measure of the exterior angle to m∠K is 102°".

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Answer:

136

Using the exterior angle theorem,

Step-by-step explanation:

(a) Amount of data entered

(b) R

(c) Average temperature

Answer:

[tex]\textsf{Radical form}: \quad \sqrt[4]{2}\\\\\textsf{Exponent form}: \quad 2^{\frac{1}{4}}[/tex]

Step-by-step explanation:

Given expression:

[tex]\sqrt{8} \div \sqrt[4]{32}[/tex]

[tex]\textsf{Apply the exponent rule} \quad \sqrt[n]{a}=a^{\frac{1}{n}}:[/tex]

[tex]\implies 8^{\frac{1}{2}} \div 32^{\frac{1}{4}}[/tex]

Rewrite 8 as 2³ and 32 as 2⁵:

[tex]\implies (2^3)^{\frac{1}{2}} \div (2^5)^{\frac{1}{4}}[/tex]

[tex]\textsf{Apply the exponent rule} \quad (a^b)^c=a^{bc}:[/tex]

[tex]\implies 2^{\frac{3}{2}} \div 2^{\frac{5}{4}}[/tex]

[tex]\textsf{Apply the exponent rule} \quad a^b \div a^c=a^{b-c}:[/tex]

[tex]\implies 2^{\frac{3}{2}-\frac{5}{4}}[/tex]

[tex]\implies 2^{\frac{6}{4}-\frac{5}{4}}[/tex]

[tex]\implies 2^{\frac{1}{4}}[/tex]

[tex]\textsf{Apply the exponent rule} \quad \sqrt[n]{a}=a^{\frac{1}{n}}:[/tex]

[tex]\implies \sqrt[4]{2}[/tex]

The desired monthly yield at the retirement time will be equal to $565,714.28.

Compound Interest may be defined as the interest earned by the bank on the basis of principle and also accumulated interest which increases exponentially and not linearly with respect to time. In calculating compound interest, the amount earned at the end of first year becomes principle for the next year and so on. Compound interest can be calculated, annually, half-yearly or quarterly etc.

Time for which work is planned = 40 years, Principle = $4500 and APR = 8.4% = 0.084/12 = 0.007.

The value of n = 12 × 25 = 300

The amount can be calculated by the formula A = P/r [1 - (1 + r) ⁻ⁿ]

A = (4500/0.007) [1 - (1 + 0.007) ⁻³⁰⁰]

A = 642,857.14 [1 - 0.12]

A = 642,857.14 × 0.88

A = $565,714.28 which is required amount.

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Complete Question:

You plan to work for 40 years and then retire using a 25-year annuity. You want to arrange a retirement income of $4500 per month. You have access to an account that pays an APR of 8.4% compounded monthly. What monthly deposits are required to achieve the desired monthly yield at retirement?

8a. The length of the robot arm, and the angle in radian and degrees are as follows

8b. The length of the robot arm, and the angle in radian and degrees are as follows

8a

i. let the length of the robot arm be r

The length of the lever arm using the points is done by

r^2 = ( -26 )^2 + ( -15 )^2

r^2 = 676 + 225

r^2 = 900

r = √ 900

r = 30

ii. theta in radian

tan θ = opposite / adjacent

tan θ = y direction / x direction

tan θ = -15 / -26

tan θ = 15/26

θ = Arc tan ( 15/26 )

θ = 29.9816 degrees

θ ≈ 30 degrees

θ ≈ 30 degrees + 180 = 210 degrees

In radian

π = 180 degrees

? = 210 degrees

we cross multiply to get

? * 180 degrees =  π * 210 degrees

? =  π * 210 degrees / 180 degrees

= 7π/6 radian

8b

i. let the length of the lever arm be r

The length of the lever arm using the points is done by

r^2 = ( -30 )^2 + ( 52 )^2

r^2 = 900 + 2704

r^2 = 3604

r = √ 3604

r = 60.033

r ≈ 60

ii. theta in radian

tan θ = opposite / adjacent

tan θ = y direction / x direction

tan θ = -30 / 52

tan θ = -30/52

θ = Arc tan ( -30/52 )

θ = -29.9816 degrees

θ ≈ -30 degrees (clockwise direction)

In radian

π = 180 degrees

? = 30 degrees

we cross multiply to get

? * 180 degrees =  π * 30 degrees

? =  π * 30 degrees / 180 degrees

= π/6 radian

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Since y is a parabolla, there will be two values for y = 19. We already know that x = 1 is one value, to find the other, we can substitute y = 19 on the equation and solve for x to get the following:

the solutions of the equation are x = 1 and x = -7. Since we already have that (1,19) is a point on the graph, then we have that the other point is (-7,19)

I would start by stating the Fundamental Theorem of Calculus which states that;

If a function f is continuous on a closed interval [a,b] and F is an antiderivative of f on the interval [a,b], then

Let

Recall that;

That implies that,

Applying the Fundamental Theorem of Calculus, where a=0, b=3

So the answer is -27/4

To solve this problem, we will use the two pair of points to find the slope of the equation of each line. Then, by comparing these slopes, we can determine either if they are perpendicular or parallel.

Slope calculations

To calcula the slopes, given the pairs of points, we are going to use the following formula: Given points (a,b) and (c,d) the slope of the line that passes through them is given by the formula

Let us calculate first the slope of the line that passes through the points (7,5) and (-14,-9). In this case, we have a=7,b=5,c=-14 and d=-9. So we get

Now, let us calculate the slope of the line that passes through the points (0,1) and (4,-5). In this case, we have a=0,b=1,c=4 and d=-5. So we get

Slope comparison

Now, we compare the slopes to determine if the lines are perpendicular or parallel. Recall that two lines are parallel if they have the same slope and they are perpendicular if the product of their slopes is -1. From our calculations, we can see that the slopes are not equal. Let us confirm that they are perpendicular. To do so, we multiply both slopes. So we get

Since their product is -1, this confirms that both lines are perpendicular.

Answer:

Step-by-step explanation:

The triangles are congruent because they follow the SSS triangle congruence postulate. As the SSS postulate says that all 3 sides of one triangle are congruent to another triangle's sides, these triangles shown have all three of their sides congruent to each other.

Answer: I am no sure but the only way to decide whether a pair of triangles are congruent would be to measure all of the sides and angles, and these triangles do not look the same so I would say that these tringles are not congruent.

Step-by-step explanation:

Answer:

I don't know your answer choices but...

Step-by-step explanation:

( 15 • 3) - 20 is equal to:

45-20

25

(5)(3)(3)-20

Answer:

Formula for slope of line is given as y2-y1 ÷ x2-x1 or y1-y2 ÷ x1-x2, where x and y are the coordinates of the points.

First, identify the coordinates of the two points shown on the graph.

First coordinate is (0,-1) and second coordinate is (3,1).

After that, find the slope of the line using the formula.

Slope = (1-(-1))÷(3-0)

= 2/3

Answer:

B

Step-by-step explanation:

hello the question is if it took 12 men 5 hours to build an age is working at the same rate how many additional men could have been hired in order for the job to have taken 1 hour less ok so we have to find that how many extra may be required to complete the job for a strip 1 hour less than five hours that is 4 hours ok bye have to complete the airstrip in 4 hours and they have to find that how many experiment we have to required for that we will assume that let extra number of number of extra man bhi X show the number of men when we are finishing in it in 4 hours would be 12 + X ok

would be the number of men now and time required would be equal to 1 hour less than 5 hours that is 4 hours ok no from the given data we can say that one cares if strip x 12 men and fibres ok so all vacancy job correct so vacancy job per man are would be 1 divided by 12 in 25 this is the job or the amount of a strip that is completed when

one man works for one hour ok so this is the amount of the job that is done for men power and we have we have this number of men that are not want working and the number of hours that their working for so for one job we will need for one job would be best job per man per hour into number of men into number of hour ok and we have 1 equal to number of Doberman per Rs 1 by 2 11 25 and number of men we have already know that 12 + 6 is the number of men that we will require 12 + X number

forces were less than 5 that is 44 4312 so it would give us 12 + X / 3515 1 to 15 of this site it would give us 12 + X equal to 15 which implies X is equals to 15 - 12 and X is equals to 3 significant required 3 more men to complete the job in Porus dancer is 3 which is given is be in the question make you

Let's suppose that 1 = TRUE and 0 = FALSE, we want to find how many combinations we can do with 11 zeros and ones, in fact, it's:

To evaluate the number of combinations we can do:

2 because we can pick 2 different options (true or false) and 11 because it's the number of questions, then

We have 2048 different ways that this test can be completed.

ANSWER :

yes

EXPLANATION :

From the problem, we have the inequality :

To check if a number is a solution, substitute it to the inequality and check the truthfulness.

Check if 0 is a solution :

Since 2 is greater than -4, therefore 0 is a solution

Answer:

D

Step-by-step explanation:

37.50 ÷ 2 = 18.75. jdjdjfbffcv

Explanation:

The following is a proof that ∆ABC ~ ∆FED.

1. AB║EF, AC║FD . . . . given

2. ∠BCA ≅ ∠EDF . . . . alternate exterior angles theorem

3. ∠ABC ≅ ∠FED . . . . alternate interior angles theorem

4. ∆ABC ~ ∆FED . . . . AA similarity postulate

they answer is 6a because you mines 10-4 and you get 6 then just put the loke 6a

log ( √2.86668684 ) is value of logarithm 18 .

What is logarithm used for in math?

[tex]log_{b} \sqrt{18}[/tex]  = [tex]log_{b} = log_{b} \sqrt{15} + log_{b} \sqrt{3}[/tex]

                 = log( √15 + √3 )

                = log ( √1.0986 * 1.6094  + √1.0986 )

                = log ( √1.76808684 + √1.0986 )

                = log ( √2.86668684 )

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The value of (x) that satisfy the equation → - 3 - 23x = - 14(x - 21) - 15(x + 33) is x = - 33.

An equation is a mathematical statement with an 'equal to' symbol between two expressions that have equal values.

Given is the following equation -

- 3 - 23x = - 14(x - 21) - 15(x + 33)

The given equation is -

- 3 - 23x = - 14(x - 21) - 15(x + 33)

Simplifying for (x), we get -

- 3 - 23x = - 14x + 294 - 15x - 495

- 23x + 14x + 15x = 3 + 294 - 495

6x = - 198

x = - 33

Therefore, the value of (x) that satisfy the equation → - 3 - 23x = - 14(x - 21) - 15(x + 33) is x = - 33.

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Convert the Mixed number to an Improper fraction:

- Multiply the Whole number by the denominator.

- Add the product to the numerator.

- Use the same denominator.

Then:

Then, the total amount of macaroni and cheese Mr. Morales brought was:

After the kids ate macaronis and cheese, the amount he took home was:

After he gave some macaroni and cheese to Mr. Kang the next day, the amount of macaroni and cheese (in pounds) left for mr. Morales to eat, is the following:

The answer is:

The simplification form of the given mathematical equation 4^5 x 4^3 x 4^2 x 4^3 / 4^2 x 4 x 4^2 is [tex]4^{8}[/tex]

In the given question, it is given

We know the simplification property of the division of numbers as,

Division in exponential form

[tex]\frac{a^{x} }{a^{y} }[/tex] = [tex]a^{x-y}[/tex] , and

Multiplication in exponential form

[tex]a^{x} . a^{y}[/tex] = [tex]a^{x+y}[/tex]

Similarly, we'll apply the same property to solve this question,

[tex]4^{5+3+2+3 + ( -2 -1 -2)}[/tex]

[tex]4^{5+3+2+3 - ( 2 + 1 + 2)}[/tex]

[tex]4^{13 - 5}[/tex]

[tex]4^{8}[/tex]

Hence, the simplification form of the given mathematical equation 4^5 x 4^3 x 4^2 x 4^3 / 4^2 x 4 x 4^2 is [tex]4^{8}[/tex]

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Explanation:

Given the function:

First, we find the vertex of the parabola.

Vertex

The equation of the axis of symmetry is calculated using the formula:

From the function: a=2, b=-12

Substitute x=3 into y to find the y-coordinate at the vertex.

The vertex is at (3, -3).

Two points to the left of the vertex

When x=2

When x=1

Two points to the right of the vertex

When x=4

When x=5

Answer:

Plot these points on the graph: (3, -3), (2,-1), (1,5), (4,-1), and (5,5).

Answer:

[tex]\frac{-8}{5}[/tex]

Step-by-step explanation:

Slope is the change in y over the change in x

[tex]\frac{y_{2 - y_{1} } }{x_{2 - y_{1} } }[/tex]

(-2,4) is ([tex]x_{1}[/tex], [tex]y_{1}[/tex])

(3. -4) is ([tex]x_{2}[/tex],[tex]y_{2}[/tex])

[tex]\frac{-4 - 4}{3 - -2}[/tex] = [tex]\frac{-8}{3+ 2}[/tex] = [tex]\frac{-8}{5}[/tex]

Answer:

-8 / 5

Step-by-step explanation:

We can use the slope formula

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

    = ( -4 -4)/( 3 - -2)

   = -8/ ( 3+2)

   = -8 / 5

The area of a triangular shape is given by the following formula

where,

base, b = 10 ft

height, h = 7 ft

therefore,

thus, the answer is 35 ft^2

y= 3x +14 (a)

y=-4x (b)

Replace the value of y (b) on equation (a), and solve for x

-4x = 3x+14

-4x-3x = 14

-7x = 14

x= 14/-7

x = -2

Replace the value of x on any initial equation and solve for y:

y= -4 (-2) = 8

y=8

Answer:

1*v=3,0.1+14y=-1 : v=3,y=-0.07857

[1.v=3}

[0.1+14y=-1]

v=3,y=-0.07857

Step-by-step explanation:

n > 39/4 is value of quartic equation.

What does quartic equation mean?

A fourth-degree equation, often known as a quartic equation, is one that reduces a quartic polynomial to zero and has the formula: where a 0. A quartic function's derivative is a cubic function.

For a quadratic ax² + bx +c , the sign of its determinant, given by

 Δ = b²- 4ac

"determines" the nature of its roots. In particular, if Δ<0 , then the quadratic has two distinct non-real roots.

Now, we have

3z² - 9z = n - 3

3z² - 9z - (n - 3)  = 0

with determinant

Δ = (-9)² - 4 .3( n - 3 ) = 117 - 12n

Solve for  such that Δ < 0

Δ = 117 - 12n < 0 ⇒  12n > 117

n > 117/12

n > 39/4

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The area between the solid line (y=x+4) and the dotted line (y=-2x-2) represents the system of inequalities solution set.

Two linear inequalities system on a coordinate plane. The first has a solid line graphed with a negative slope of one, a negative y-intercept, and a shaded origin area. The area encompassing the origin is shaded, and the second is a dashed vertical line 3 units to the left of the origin.

x ≥ –3; y ≥ x – 2

x > –3; 5y ≥ –4x – 10

x > –3; y ≥ –x + 1

x > –2; y ≥ –x – 1

The solution set for the system of inequalities is represented by the region between the solid line (y=x+4) and the dotted line (y=-2x-2).

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Given:

Area of the square shaped lawn = 224.9 ft²

A square has all four side lengths equal.

To find the side length of this lawn, use the formula for area of a square below:

Take the square root of both sides to find the sile length L:

Therefore, the measurement that is closest to the side length in feet is 15 ft

ANSWER:

15 ft