write the equation in standard form. identify A,B, and C

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:

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

(a) Amount of data entered

(b) R

(c) Average temperature

Jake's weekly rate of eating of cake slices is 11.6

Given,

Number of equal slices of cake = 12

Number of slices Jake eaten after 3 days = 5

We have to find the weekly rate of eating;

Here,

Number of days in a week = 7

Jake eaten 5 slices in 3 days so, 7 - 3 = 4

Again after 3 days 5 slices.

Then,

4 - 3 = 1

That is, Jake eaten 10 slices of cake in 6 days.

Number of cake slices eaten in 1 day = 5/3 = 1.6

Therefore,

Weekly rate of eating is 10 + 1.6 = 11.6

That is,

Jake's weekly rate of eating of cake slices is 11.6

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In order to find the center of the circunscribed circle, we can use the midpoint theorem because the center point is in the middle of any two vertices

that is, if we take points (9,23) and (8,16) the midpoint C is given as

which gives

So the center of the circle is the point (8.5,19.5)

On the other hand, the radius is equal to the distance from any vertex to the center. If we take the vertex (8,16), we get

which gives

so, the radius measure 3.54 units.

Now, lets prove that the answer are correct. In order to do that, we can choose the other vertices and apply the same procedure as above.

So the vertices are (5,20) and (12,19). Again, the center is the midpoint between these points and is given as

which is the same center as above.

Now, the distance from the center to vertec (5,20) is

which is the same radius obtained above. Then, the answers are correct.

Answer:

Given that,

To find the sum of the first 5 terms.

First, to find the first 5 terms of the given sequence.

The given sequence is 2,-8,32,-128,...

It follows geometric series with initial term 2, and common ratio as -4

The explicit formula of the given sequence is,

To find the 5th term of the sequence,

Put n=5 in the above equation we get,

Since common ratio is less than 1, we get the sum of the series formula as,

Substituting the values we get,

The sum of the first 5 terms of the given series is 410.

Answer is: option B: 410

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?

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 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:

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

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)

Answer:

D

Step-by-step explanation:

37.50 ÷ 2 = 18.75. jdjdjfbffcv

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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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

Based on the given equivalences, you have:

7 m = 7(100 cm) = 700 cm

700 cm = 700 (2.54 in) = 1,778 in

Hence, there are 1,778 inches in 7 meters

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 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:

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:

Let's call C the weight of the Cashews and B the weight of the Brazil nuts.

Since the professor wants to sel a 32 pound mixture, we have the following equation:

Now, since the price of the mixture will be $5.37 per pound, this means the price of the whole mixture will be

This leads us to the followin equation:

Now we have a system of equations:

To solve it, let's isolate one of the variables in the first equation by subtracting B from both sides of it:

Now, let's use this value of C in the second equation:

To solve this equation, let's subtract 198.4 from both sides of it:

Then, let's divide both sides by -1.9:

Using this value of B in the first equation will give us:

These would be the values of B and C round to two decimals. If we want, we can also write them as integer numbers. so the mix would need to have 18 pounds of cashews and 14 pounds of Brazil nuts.

Answer:

B

Step-by-step explanation:

if the number is x then 3 times the number is 3x

the difference is the subtraction of 3x and 4 , that is

3x - 4

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

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.

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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By Calculating the Constant of Proportionality, we get,

1. 5 cups of yellow paint is required for 1 cup of blue paint.

2. For 4 cups of blue paint, 20 cups of yellow paint is required.

   For 5 cups of blue paint, 25 cups of yellow paint are required.

3. Cups of Yellow Paints = 5* Cups of Blue Paints

4. The constant of Proportionality is 5.

Let the cups of blue paint = x

and cups of yellow paint = y

From the table, we can infer that to make the same shade of green, we need to mix 5 cups of yellow color with 1 cup of blue.

We have, To make the same shade of green,

we need to mix 5 cups of yellow color with 1 cup of blue.

we need to mix 10 cups of yellow color with 2 cups of blue.

we need to mix 15 cups of yellow color with 3 cups of blue.

So, here we can see a relationship between the two colors, blue (x) and green(y)  

Let k be the constant of proportionality, then, we have :

10 = k *2

k =[tex]\frac{10}{2} = 5[/tex]

Hence, For one cup of blue paint, we need 5 cups of yellow paint to make the same shade of green.

And the equation of the same is y =kx, that is y =5x....equation(1)

To make new pair of numbers that would make the same shade of green.

We can use the equation 1,

for x = 4, we need y = 20

foe x =5, we need y = 25

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Let's begin by identifying key information given to us in the graph:

The reciprocal parent function is given as 1/f(x). This is better written as shown below

When the value for x is greater than zero, the function is positive as shown below:

When the value of x is lesser than zero, the function is negative as shown below:

Therefore, the correct answer is option A (The function is negative when x < 0)

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).

The values in Manu’s list of rational roots he should try in the synthetic division, in light of these findings is

"Manu should try first +1/4,+1/2 and +1."

This is further explained below.

Generally, Because the lower and higher bonds are located between -6 and 1, Manu should have only analyzed the potential rational zeros that fall between those two numbers.

A lower bond indicates that the feasible rational zero cannot be lower than -6, and therefore the higher number that may be achieved cannot be more than 1.

In this manner, Manu will get an opportunity to test. This approach of rationalization based on bonds aims to reduce the number of potential solutions.

Therefore, if Manu discovers through the synthetic division that the possible roots are +1/4,+1/2,+1,+5/4,+2,+5/2,+4,+5,+10,+20, then he should only consider those inside the intervals marked by the lower and upper bounds, which are +1/4,+1/2,+1, because the rest is greater than 1. This is because the rest of the possible roots are higher than 1.

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CQ

Manu determines the roots of a polynomial equation p(x)=0 by applying the theorems he knows. He organizes the results of these theorems. From the fundamental theorems of algebra, Manu knows there are 3 roots to the equation. From Descartes' rule of sign, Manu finds no sign changes in p(x) and 3 sign changes in p(-x). The rational root theorem yields +1/4,+1/2,+1,+5/4,+2,+5/2,+4,+5,+10,+20 as a list of possible rational roots. The lower bound of the polynomial is -6. The upper bound of the polynomial is 1. What values in Manu's list of rational roots should he try in synthetic division in light of these findings?

The box has 3 white balls and 4 black balls.

Total number of balls = 3 + 4 = 7

First draw:

The probability of getting a white ball is given by

Second draw:

Notice that after the first draw the ball is put back in the box.

The probability of getting a white ball is given by

At least one of the balls is white means that one white ball or two white balls.

We have already found the probability of getting one white ball that is P(x=1) = 3/7

The probability of getting two white balls is

Finally, the probability of at least one white ball is

Therefore, the probability of the event that at least one of the balls is white is 30/49

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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