What is equidistant from the angles of a triangle?

Part A: The system of equations  is

6x + 4y= 212

3x + 5y= 202

Part B: The solution of the system of equation is x= 14 and y= 32

Parte C: The solution means that the price of t-shirts and the price of swatshirts are $14 and $32 respectively.

A system of linear equations is a set of two or more equations of the first degree, in which two or more unknowns are related.

A solution to a system of two or more linear equations is a solution that simultaneously satisfies all the equations in the system.

In this case, a system of linear equations must be proposed taking into account that:

You know:

The system of equations to be solved is

6x + 4y= 212

3x + 5y= 202

There are several methods to solve a system of equations, it is decided to solve it using the substitution method, which consists of clearing one of the two variables in one of the equations of the system and substituting its value in the other equation.

In this case, isolating the variable "y" from the first equation:

4y= 212 - 6x

y= (212 - 6x)÷ 4

y= 212÷4 - 6÷4x

y= 53 - 3/2x

Substituting this expression in the second equation:

3x + 5×(53 - 3/2x)= 202

Solving:

3x + 5×53 - 5×3/2x= 202

3x + 265- 15/2x= 202

3x - 15/2x= 202 - 265

-9/2x=-63

x= (-63)÷ (-9/2)

x= 14

Remembering that y= 53 - 3/2x, you get:

y= 53 - 3/2×14

y= 32

The solution of the system of equation is x= 14 and y= 32. This means that the price of t-shirts is $14 and the price of swatshirts is $ 32.

Learn more about system of equations:

brainly.com/question/14323743

brainly.com/question/1365672

brainly.com/question/20533585

brainly.com/question/20379472

#SPJ1

L((7,8)) = (-9,23).  To find the value of L((7,8)), we can use the linearity property of the linear operator L.

Since L is a linear operator, we can express any vector in R² as a linear combination of the basis vectors (1,0) and (0,1).

We have L((1,2)) = (-2,3) and L((1,-1)) = (5,2). Therefore, we can express (7,8) as (7,8) = 7(1,2) + 1(1,-1).

Using the linearity property, we can distribute the linear operator L over the linear combination:

L((7,8)) = L(7(1,2) + 1(1,-1))

= 7L((1,2)) + L((1,-1))

= 7(-2,3) + (5,2)

= (-14,21) + (5,2)

= (-9,23)

Know more about linearity property here:

https://brainly.com/question/28709894

#SPJ11

The addition of three variables to the model is statistically significant as the p-value is less than the significance level of 0.05. Therefore, we reject the null hypothesis and conclude that the added variables have a significant effect on the dependent variable.

The null hypothesis (H₀) states that the coefficients of all three added variables (x₃, x₄, x₅) in the model are equal to zero, indicating that these variables have no significant impact on the dependent variable. The alternative hypothesis (Ha) suggests that at least one of the coefficients is not equal to zero, implying that the added variables have a significant effect.

To test the null hypothesis at the 5% level of significance, we can use the F-test. The F-statistic is calculated by dividing the difference in the sums of squared errors (SSE) between the reduced and full models by the difference in degrees of freedom.

In this case, the reduced model (H₀) has SSE = 785, while the full model (Ha) has SSE = 580. The degrees of freedom difference is the number of added variables, which is 3 in this case.

The formula for calculating the F-statistic is: F = [(SSEᵣₑᵤcₑd - SSEfᵤₗₗ) / q] / [SSEfᵤₗₗ / (n - p)]

where SSEᵣₑᵤcₑd is the SSE of the reduced model, SSEfᵤₗₗ is the SSE of the full model, q is the number of added variables, n is the sample size, and p is the total number of variables in the full model.

Substituting the given values into the formula:

F = [(785 - 580) / 3] / [580 / (25 - 5)]

Simplifying the equation:

F = 205 / 580 * 20/3

Calculating the F-statistic:

F ≈ 11.95

To find the p-value associated with this F-statistic, we can refer to an F-distribution table or use statistical software. The p-value represents the probability of obtaining a test statistic as extreme as the observed F-statistic under the null hypothesis.

The p-value for an F-statistic of 11.95 can be calculated to be approximately 0.0002.

Since the p-value is less than the significance level of 0.05, we reject the null hypothesis (H₀) and conclude that the addition of the three independent variables (x₃, x₄, x₅) is statistically significant in explaining the dependent variable.

To know more about F-tests, refer here:

https://brainly.com/question/32391559#

#SPJ11

Answer:

900

Step-by-step explanation:

3*300=900

Answer:

3 x 300=900

brainly me pls

Consumer surplus $5 as we solve the Q by given data

Consumer surplus is the difference between the consumer's willingness to pay and the price of the commodity.

Consumer surplus in economics, also called social surplus or consumer surplus, is the difference between the price a consumer pays for a commodity and the price the consumer is willing to pay in exchange for giving it up.

Producer surplus is the difference between the price of a commodity and the lowest price at which a seller is willing to sell it.

Consumer Surplus = Willingness to Pay - Price of the Good.

Item Price = $35 - $10 = $25

$30 - $25 = $5

Producer surplus is the difference between the price of a commodity and the lowest price at which a seller is willing to sell it.

know more about consumer surplus click here;

https://brainly.com/question/14852681

#SPJ4

Answer:

1930.47

Step-by-step explanation: formula=bh+(surface 1+surface 2+surface 3)H

The final equation for the tangent plane to the graph of f at the point (a, b) is z = 2e^a(x - a) - y + 2e^a - 2b. This equation represents the plane that is tangent to the graph of f at the specified point (a, b).

To find the equation for the tangent plane to the graph of the function f(x, y) = 2e^x - y at a given point (x0, y0), we need to calculate the partial derivatives of f with respect to x and y at that point.

The partial derivative of f with respect to x, denoted as ∂f/∂x or fₓ, represents the rate of change of f with respect to x while keeping y constant. Similarly, the partial derivative of f with respect to y, denoted as ∂f/∂y or fᵧ, represents the rate of change of f with respect to y while keeping x constant.

Let's calculate these partial derivatives:

fₓ = d/dx(2e^x - y) = 2e^x

fᵧ = d/dy(2e^x - y) = -1

Now, we have the partial derivatives evaluated at the point (x0, y0). Let's assume our point of interest is (a, b), where a = x0 and b = y0.

At the point (a, b), the equation for the tangent plane is given by:

z - f(a, b) = fₓ(a, b)(x - a) + fᵧ(a, b)(y - b)

Substituting fₓ(a, b) = 2e^a and fᵧ(a, b) = -1, we have:

z - f(a, b) = 2e^a(x - a) - (y - b)

Now, let's substitute f(a, b) = 2e^a - b:

z - (2e^a - b) = 2e^a(x - a) - (y - b)

Rearranging and simplifying:

z = 2e^a(x - a) - (y - b) + 2e^a - b

The final equation for the tangent plane to the graph of f at the point (a, b) is z = 2e^a(x - a) - y + 2e^a - 2b.

This equation represents the plane that is tangent to the graph of f at the specified point (a, b).

Learn more about tangent here:

https://brainly.com/question/10053881

#SPJ11

Answer:

Substitution

Step-by-step explanation:

New function that is a horizontal stretch of F(x)=\((x+2)^{3} + 5\) is F(\(\frac{x}{k}\))=\((\frac{x}{k} +2)^{3} + 5\)

The point (x, y) on the graph of f(x) is changed to the point (x/k, y) on the graph of g when the graph is stretched or contracted horizontally by a factor of 1/k (x).Only when the input value is also increased by a, can a graph be stretched horizontally by a factor of 1/a. The x-coordinates should be multiplied by a once f(x) has been stretched horizontally to f(ax). Keep the y-intercepts where they are. The resulting function might have a different domain, but it will have the same range. If a point (m, n) is stretched horizontally, it becomes (am, n).

F(x)=\((x+2)^{3} + 5\)

F(\(\frac{x}{k}\))=\((\frac{x}{k} +2)^{3} + 5\)ch visit :
To learn more about horizontal stretch visit :

brainly.com/question/25753477

#SPJ9

The proportion of students who scored higher than Willa is 0.7389. Hence, Option B is correct.

The given information is:

Mean (μ) = 78, Standard deviation (σ) = 5, and Willa scores = 74.8

The formula for the Z-score is:

Z = (x-μ) / σ

Where, x is the value, μ is the mean and σ is the standard deviation.

Substitute the values in the above formula, we get:

Z = (74.8 - 78) / 5

= -0.64

The negative sign indicates that Willa's score is less than the mean score.

Now, find the proportion of students who scored higher than Willa.

It can be done in two steps as shown below:

Step 1: Find the area under the standard normal distribution curve corresponding to the calculated Z-score.

The Z-table gives the area to the left of Z = -0.64.

The area to the right of Z is 1 - area to the left of Z.= 1 - 0.2611

= 0.7389

Therefore, the proportion of students who scored higher than Willa is 0.7389.

Hence, Option B is correct.

To know more about proportion visit:

https://brainly.com/question/31548894

#SPJ11

Answer:

It looks different. Can you provide some formulae based on it. I may help you out in the comment section!

The diameter of the circle is 48 in.

A circle's sector is a pie-shaped portion made up of the arc and its two radii. At both ends of the arc, when a section of the circle's circumference (also known as an arc) and two of its radii meet, a sector is produced. A sector of a circle resembles a piece of pizza or a pie in shape.

As per the given data:

Central angle of the sector (θ) = 30°

Area of the sector (A) = 150 in²

A = (1/2) × r² × θ {where θ is in radian and r is radius}

Converting 30° to radian.

= 30 × (π/180)

= π/6

150 = (1/2) × r² × π/6

r = √(1800/π)

r = √(576)

r = 24 in

Diameter = 2r

= 2 × 24 in

= 48 in

Hence, the diameter of the circle is 48 in.

To learn more about the sector, click:

brainly.com/question/15591260

#SPJ2

The correct option is Ray 2.When light passes from one medium to another of different optical densities, it bends from its initial path, this bending is called refraction.

The amount of refraction is determined by the refractive index of the media. The refractive index of the media is the ratio of the speed of light in the medium to the speed of light in a vacuum. The refracted ray for ray 1 is Ray 2.The direction of light in air or vacuum will change when it enters water.

The angle of incidence of the light ray and the angle of refraction of the light ray will determine how much the direction will change. Because light moves from a medium with a lower index of refraction (air) to one with a higher index of refraction (water), the ray is bent away from the normal as it enters the water.

The incident ray 1 in air, the refracted ray 2 in water, and the normal line, are in the same plane. The angle of incidence and angle of refraction are related through Snell's law, which states that n1 sin θ1 = n2 sin θ2, where n1 and n2 are the indices of refraction in the incident and refracted media.

The refracted ray 2 will be bent towards the normal. Thus, the correct option is Ray 2.

For more question on refraction

https://brainly.com/question/27932095

#SPJ8

x = 1.43 is the solution to the equation 6 • e^x = 25, rounded to two decimal places

The length of one side of the equilateral triangle is 5x + 10 units

What is an equilateral triangle ?

An equilateral triangle is a triangle that has all of its sides equal. Let a, b and c be the sides of the equilateral triangle. Since all the sides are equal, then a = b = c.

The perimeter of the triangle is the sum of all the sides of the triangle.

P  = a + b+ c

GIVEN THE PERIMETER OF THE EQUILATERAL TRIANGLE AS P = 15 x + 30 units and a = b = c, then;

15 x + 30 = a + b + c

15 x + 30 = a + a + a (since all sides are equal)

15 x + 30 = 3a

3a = 15 x + 30

3a = 3(5x+10)

Dividing both sides by 3 will give;

3a/3 =   3(5x+10)/3

a = 5x+10

Hence, the length of one side of the equilateral triangle is 5x + 10 units.

to know more about equilateral triangle , visit:

https://brainly.com/question/17264112

#SPJ4

ANSWER:

(x+7)^2=16

Step-by-step explanation:

x^2-14x+49=16

x^2-14x+49-16=0

x^2-14x+33=0

subtract -33 on both sides

x^2-14x+33-33=-33

x^2-14x=-33

Add 49 on both sides

x^2-14x+49=-33+49

x^2-14x+49=16

x^2-7x-7x+49=16

x(x-7)-7(x-7)=16

(x-7)(x-7)=16

(x-7)^2=16

In this case, the proportionality constant is 3.5 (y = kx), and when x = 28, we can substitute it into the equation to find the value of y:

y = 3.5 * 28 = 98.

Therefore, when x = 28, the value of y is 98.

If the value of y is directly proportional to the value of x, then the ratio between y and x is constant. Let this constant be represented by k. Then we can write:

y = kx

To find the value of y when x = 28, we need to know the value of k. We can find k by using the fact that when x = 7, y = 21:

21 = k * 7

k = 3

Now we can substitute k into our equation to find the value of y when x = 28:

y = 3.5 * 28 = 98

Therefore, when x = 28, the value of y is 98.

Learn more about :  

ratio : brainly.com/question/31945112

#SPJ11

The correct answer is A. The selling price of a bond is affected by the coupon rate and the market interest rate.

If the coupon rate is less than the market interest rate, investors will not be interested in buying the bond because they can get a higher return elsewhere. This results in the selling price of the bond being less than its face value of $10,000.
The selling price of a $10,000 5-year bond will be less than $10,000 if the:
A. Coupon rate is less than the market interest rate

This is because when the coupon rate (the interest paid by the bond) is lower than the market interest rate, investors would prefer to invest in other options that offer a higher return. Therefore, to attract buyers, the bond's selling price would be discounted to compensate for the lower coupon rate.

Learn more about price:

brainly.com/question/19091385

#SPJ11

Answer:

480 People.

Step-by-step explanation:

120,000(0.004) = 480

Answer:

quadratic binomial

\({ \boxed{ \bf{a {x}^{2} + bx + c }}} \\ 2 {g}^{2} + 3g - g\)

Answer:

\(\\\sf7x^3 - 2x^2 - 5\)

Step-by-step explanation:

\(\\\sf(6x^3 + 3x^2 - 2) + (x^3 - 5x^2 - 3)\)

Remove parenthesis.

6x^3 + 3x^2 - 2 + x^3 - 5x^2 - 3

Rearrange:

6x^3 + x^3 + 3x^2 - 5x^2 - 2 - 3

Combine like terms to get:

----------------------------------------

More on adding polynomials: https://brainly.com/question/30791478

Hope this helps! :)

Answer:

7x³ - 2x² - 5

Step-by-step explanation:

(6x³ + 3x² - 2) + (x³ - 5x² - 3)

Remove the round brackets.

= 6x³ + 3x² - 2 + x³ - 5x² - 3

Put like terms together.

= 6x³ + x³ + 3x² - 5x² - 2 - 3

Do the operations.

= 7x³ - 2x² - 5

____________

hope this helps!

Answer:

Well the slope of this is 49 and y intercept is 28, hooe this helped

Answer:

Slope: 2/2 = 1

y-intercept: 2

Step-by-step explanation:

Step-by-step explanation:

you mean it is 6° less, right ?

supplement means together they have 180°.

complement means together they have 90°.

x is our angle.

180 - x is the supplement angle.

90 - x is the complement angle.

180 - x = 90 - x - 6

90 = -6

you see, that is not possible.

the difference between the supplementary angle and the complementary angle is always 90°.

e.g.

x = 30°

supplement = 180-30 = 150°

complement = 90-30 = 60°

the difference is : 150 - 60 = 90°

x = 80°

supplement = 180 - 80 = 100°

complement = 90-80 = 10°

the difference is : 100 - 10 = 90°

and so on.

so, again, there is no angle that satisfies that criteria.

either you made a mistake in the problem description, or your teacher tried to be tricky.

remember, as x has also a complementary angle, it must be smaller than 90°.

so, the supplementary angle of x must be larger than 90°, and therefore larger than the complementary angle.

there is no angle, for which the supplementary angle is smaller than the complementary angle.

 (-1/24)(x^4 + 4)^(-6) + (1/7)(x^4 + 4)^(-7) + C is the integration of the above mentioned integrals.

To evaluate the indefinite integral ∫x^2/(x^4 + 4)^8 dx, we can use the substitution method.

Let's perform the following substitution:

u = x^4 + 4
du/dx = 4x^3

Now, solve for x^3 dx:

x^3 dx = (1/4) du

Now, we can rewrite the integral in terms of u:

∫x^2/(x^4 + 4)^8 dx = ∫(x^2/u^8)((1/4) du)

We need to rewrite x^2 in terms of u:

x^2 = u - 4

Substitute this expression for x^2 back into the integral:

(1/4) ∫(u - 4)/u^8 du

Now, split the integral into two parts:

(1/4) [∫u/u^8 du - ∫4/u^8 du]

Simplify the integrals:

(1/4) [∫u^(-7) du - ∫4u^(-8) du]

Now, integrate each term with respect to u:

(1/4) [(u^(-6)/(-6)) - (4u^(-7)/(-7)) + C]

Simplify the expression:

(-1/24)u^(-6) + (1/7)u^(-7) + C

Now, substitute x^4 + 4 back for u:

answer: (-1/24)(x^4 + 4)^(-6) + (1/7)(x^4 + 4)^(-7) + C

learn more on finding indefinite integrals on:https://brainly.com/question/22008756

#SPJ11

Answer:

I think non of these! Cuz we use the CHOOSE function to model the scenario.

Hope this helps ❤️

Answer:

Vertex form: y = 3(x + 2)² + 2

Step-by-step explanation:

Given the graph of an upward-facing parabola, whose vertex occurs at point (-2, 2):

The vertex form of a quadratic equation is given by:  y = a(x - h)² + k

where:

(h, k) ⇒ vertex

h =  indicates a horizontal translation of the graph.

k =  indicates a vertical translation of the parabola.

x = h ⇒ axis of symmetry: the imaginary vertical line that divides the graph into two symmetrical parts.

a = direction of the parabola's opening; determines the wideness of the graph.

Now that we have established the necessary terms related to understanding the concept of quadratic equations, we can proceed with determining the equation of the graph.

Besides the vertex, (-2, 2), we must choose another point on the graph to solve for the value of a.  Using the point from the graph, (-1, 5), along with the vertex, substitute these values into the vertex form to solve for a:

y = a(x - h)² + k

5 = a[-1 - (-2)]² + 2

5 = a(-1 + 2)² + 2

5 = a(1)² + 2

5 = a + 2

Subtract 2 from both sides:

5 - 2 = a + 2 - 2

3 = a

Therefore, the vertex form of the given graph of a parabola is:

y = 3(x + 2)² + 2

Answer:

B

Step-by-step explanation:

have a nice day :)

Answer:

n ÷ 20.7 = 9

Step-by-step explanation:

Let n be the unknown number

Quotient is division and is means equals.

n ÷ 20.7 = 9

The area of each of the given triangle is:

4. 21 units²; 5. 12 units²; 6. 12 units²

7. 35 ft²; 8. 8 in.²; 9. 24 cm²

To find the area of a triangle, find one-half the product of the height and the base length of the triangle.

Therefore, area = 1/2(base * height).

4. A = 1/2 * 6 * 7 = 21 units²

5. A = 1/2 * 4 * 6 = 12 units²

6. A = 1/2 * 6 * 4 = 12 units²

7. A = 1/2 * 7 * 10 = 35 ft²

8. A = 1/2 * 8 * 8 = 8 in.²

9. A = 1/2 * 6 * 8 = 24 cm²

Learn more about the area of a triangle on:

https://brainly.com/question/21735282

#SPJ1