Given: Triangle ABC
Prove: mA = 64°
A
(4x)
B
(90)
C
(x+10)

Answer:

[tex](-5)[/tex] and [tex]3[/tex].

Step-by-step explanation:

The [tex]x[/tex]-intercepts of a graph refer to points where the graph intersects the [tex]x\![/tex]-axis. These are [tex]x\!\![/tex] values for which [tex]f(x) = 0[/tex].

For example, since [tex]x = (-5)[/tex] is one of the [tex]x[/tex]-intercepts of [tex]y = f(x)[/tex], it must be true that [tex]f(-5) = 0[/tex]. Likewise, since [tex]3[/tex] is one of the [tex]x[/tex]-intercepts of [tex]y = f(x)\![/tex], [tex]f(3) = 0[/tex].

Since [tex]f(-5) = 0[/tex], the expression [tex]7\, f(-5)[/tex] would also evaluate to [tex]0[/tex] (that is, [tex]7\, f(-5) = (7)\, (0) = 0[/tex].) Thus, [tex]x = (-5)[/tex] would be an [tex]x[/tex]-intercept of the new graph [tex]y = 7\, f(x)[/tex].

Likewise, since [tex]f(3) = 0[/tex], [tex]7\, f(3) = (7)\, (0) = 0[/tex], such that [tex]x = 3[/tex] would also be an [tex]x[/tex]-intercept of the new graph [tex]y = 7\, f(x)[/tex].

No other points could be an [tex]x[/tex]-intercept of the new graph [tex]y = 7\, f(x)[/tex] without being an [tex]x\![/tex]-intercept of [tex]y = f(x)[/tex]. For example, assume that [tex]x = x_{0}[/tex] is an [tex]x[/tex]-intercept of [tex]y = 7\, f(x)[/tex] but not [tex]y = f(x)[/tex]. [tex]7\, f(x_{0}) = 0[/tex], such that [tex]f(x_{0}) = (1/7)\, (7\, f(x_{0})) = (1/7)\, (0) = 0[/tex]- contradiction.

Therefore, the [tex]x[/tex]-intercepts of the new graph would be [tex]x = (-5)[/tex] and [tex]x = 3[/tex].

Answer:

3x+4x-1+x+2=73

8x+1=73

8x=73-1

8x=72

8x/8=72/8

x=9

Perimeter (p) of a triangle:

[tex]p = a + b + c[/tex]

P = 73 units

To find the value of x

[tex]73 = 3x + 4x - 1 + x + 2[/tex]

→[tex]73 = 8x + 1 \\ 73 - 1 = 8x[/tex]

→[tex]8x = 72[/tex]

→[tex] \frac{8x}{8} = \frac{72}{8} [/tex]

[tex]x = 9[/tex]

Answer:

The slope of the line is -1.

We can find this by using the slope formula, where [tex]\frac{y_{2} -y_{1} }{x_{2}-x_{1} }[/tex]. Substitute in our points; [tex]\frac{7-4}{6-9} =\frac{3}{-3}[/tex]. Remember that a negative in either the numerator or the denominator of a fraction makes the entire fraction negative, so [tex]\frac{3}{-3}=-\frac{3}{3}[/tex] Remember that an identical numerator and denominator is equal to 1. Same rule applies here, except it's negative, so the slope of the line is -1. You can see this in action if you were to use a graphing tool. I recommend checking out desmos graphing calculator.

Answer:

Number of 12$ Shares? 25

Number of 14$ Shares? 57

Step-by-step explanation:

Let x = number of $12 shares.

Let y = number of $14 shares.

"Ivan has $1098 worth of $12 and $14 stock shares."
12x + 14y = 1098

The number of $14 shares is seven more than twice the number of $12 shares.

y = 2x + 7

We have a system of equations.

12x + 14y = 1098

y = 2x + 7

We can use the substitution method since the second equation is already solved for y. Substitute 2x + 7 for y in the first equation.

12x + 14(2x + 7) = 1098

12x + 28x + 98 = 1098

40x = 1000

x = 25

There are 25 $12 shares.

y = 2x + 7 = 2(25) + 7 = 57

There are 57 $14 shares.

Check:

25 × $12 + 57 × $1`4 = $300 + $798 = $1098

The total value is correct, so the answer is correct.

Answer:
y = x - 4

Step-by-Step Explanation:

Perpendicular lines have slopes that are negative reciprocals—multiplying their slopes result in -1.Given the slope of a line m = -1, then it means that the slope of the other line must be 1 (because multiplying the slope of line 1  (m1 = -1), and the slope of the other line (m2 = 1) results in: -1 × 1 = -1).Therefore, given the slope of line 2 (m2 = 1), and the point (2, -2), we could plug these values into the slope-intercept form and solve for the y-intercept (b):y = mx + b-2 = 1(2) + b-2 = 2 + bSubtract 2 from both sides to solve for b:-2 - 2 = 2 - 2 + b-4 = bTherefore, the y-intercept (b) = -4.Hence, the equation of the perpendicular line is: y = x - 4

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Answer:

See picture below.

Step-by-step explanation:

Answer:

B and D

Step-by-step explanation:

The wording in the answer choices make a huge difference. It is possible implies that there is a possibility

A is false. The range of a function is the output value of the function for the input value in the domain of the function. So we can say with certainty that 7 is in the range since it is an output. But we cannot state that 4 is in the range because we have only one output value 7 for g(4)

A good example is a constant function such as g(x) = 7. Here, whatever the value of x, the y value is always 7. This represents a horizontal line passing through y = 7. So the range is just a single number {7}

B can be true. It is possible but not a certainty that f(a) = 4 for some value of a. For example, consider the function g(x) = x + 3.

At x = 4, g(4) = 4 .1 + 3 = 7

At x = 1, g(1) = 1 + 3 = 4 so it is possible for 4 to be an output

C is false. A well-defined function has only a unique value for a specific input of x. So we cannot get two different values for a single x value.

D is true. Since at x =4, y = g(x) = 7, this corresponds to a point on the graph. The point will be (x=4, y =7) or (4,7)

E is false. The x, y coordinates have been interchanged in this answer choice

The true statements are B and D.

The wording in the answer choices make a huge difference.

It is possible implies that there is a possibility

A. 4 is in the range of g.

A is false.

The range of a function is the output value of the function for the input value in the domain of the function. So we can say with certainty that 7 is in the range since it is an output. But we cannot state that 4 is in the range because we have only one output value 7 for g(4)

A good example is a constant function such as g(x) = 7.

Here, whatever the value of x, the y value is always 7.

This represents a horizontal line passing through y = 7.

So the range is just a single number {7}

B. For a value a, it is possible that g (a) = 4.

B can be true.

It is possible but not a certainty that f(a) = 4 for some value of a.

For example, consider the function g(x) = x + 3.

At x = 4, g(4) = 4 .1 + 3 = 7

At x = 1, g(1) = 1 + 3 = 4 so it is possible for 4 to be an output.

C. For a value y, it is possible that g (4) = y.

C is false.

A well-defined function has only a unique value for a specific input of x. So we cannot get two different values for a single x value.

D. The point (4,7) is on the graph of y = g (x).

D is true.

Since at x =4, y = g(x) = 7, this corresponds to a point on the graph.

The point will be (x=4, y =7) or (4,7)

E. The point (7, 4) is on the graph y = g(x).

False. The statement doesn't provide any information about g(7), and we cannot determine whether the point (7, 4) lies on the graph of the function y = g(x) based solely on the given information.

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The equation of a line perpendicular to the line is y = (-1/2)x - 9

Slope of the line perpendicular to y = 2x - 1, m =-1/2;

Therefore, equation of line perpendicular to given line in slope- intercept form is; y = (-1/2) x + c;

This line passes through (-8, -5); therefore;

-5 = (-1/2)(-8) + c;

c = -9;

Therefore, equation of required line is y = (-1/2)x - 9;

Perpendicular lines are two non-vertical lines in the same plane that intersect at a right angle. Horizontal and vertical lines are perpendicular to one other, forming the coordinate plane's axes. Negative reciprocals are the slopes of two perpendicular lines.

Vertical and horizontal lines are parallel to each other. In this scenario, the slope of the perpendicular line is equal to the slope of a horizontal line, which is 0. The slope of the parallel line is 0 while the slope of the perpendicular line is unknown.

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Answer:

-3

Step-by-step explanation:

Hope this helps!

Answer:

-3

Step-by-step explanation:

if its negative then it will continue to be unless 7 is added into -6. So, adding 3 to that would make it -3

The 48 inches allowable minimum height of a rider and the 52 and 2.5 mean and standard deviation of the height of the children in the camp of 140 campers, by the Z–Score gives the number of campers allowed as approximately 132 campers.

The required height of riders is at least 48 inches.

The mean height of the children = 52 inches

The standard deviation of the children's height = 2.5 inches

The number of campers at the camp, n = 140

Required: The number of the 140 campers that will be allowed on the ride

Solution:

The Z–Score of the allowable campers is found using the equation;

[tex]z = \frac{x - \mu}{ \sigma} [/tex]

Which gives;

[tex]z = \frac{48 - 52}{2.5} = - 1.6[/tex]

From the Z–Score table, the probability (proportion) of a camper's height to be less than 48 inches is P(x < 48) = 0.05480

Therefore;

The probability that the height of a camper is more than 48 inches is given by the equation;

P(x > 48) = 1 - P(x < 48) = 1 - 0.05480

Which gives;

P(x > 48) = 1 - 0.05480 = 0.9452

Which gives;

The number of campers allowed, c, is given by the equation;

c = n × P(x > 48)

c = 140 × 0.9452 = 132.328 ≈ 132

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Answer:

Domain: [-2, infinity)

Range: [-4, infinity)

Step-by-step explanation:

There's only one graph I see.

Domain is how far the graph extends on the x axis.

Range is how far the graph extends on the y axis.

The value of the given expression is equivalent to -3

Linear equations are equation that has a linear degree of 1.

The statement three eighths times the quantity 1 plus the square root of 49 end quantity squared minus the quantity four minus one end quantity cubed is written mathematically as:

3/8(1+√49)² - (4-1)³

Expand to have:

3/8(1+7)² - 3³

3/8(8)² -27

3/8(64) - 27

3(8) - 27

24 - 27

-3

Hence the value of the given expression is equivalent to -3

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Answer:

The total amount of apples sold is 63.  There were 49 red apples and 14 green apples

Step-by-step explanation:

red: green : total

7          2       7+2

7          2          9

When we use the ratios, the total is 9

We are given the total is 63

63 divided by 9 is 7

We need to multiply each number by 7

red: green : total

7*7      2*7       9*7

49       14             63

The total amount of apples sold is 63.  There were 49 red apples and 14 green apples

Answer:

the answer is red apples 49 and green apples 14.

Answer:

(n ÷ 4) + 6 = 8

Step-by-step explanation:

Quotient means The answer when you divide' So we are working in the division.

n ÷ 4 is the division part

It says 'and' which can also mean addition. So we add 6. So far our equation is: (n ÷ 4) + 6 (Brackets are needed as we are dividing n by 4 and not dividing n by 4+6)

Lastly it says the answer must be 8 so we add that at the end. So the answer is:

(n ÷ 4) + 6 = 8

Answer: Point B will be at (4,-3)

Point C will be (-2,-3)

Point D will be (6,3)

The distance between the two points rounding to the nearest tenth is

9.2 units.

Given that the two points are (-1,4) and (8,2).

We are required to find the distance between two given points.

Distance is basically a numerical or occasionally qualitative measurement of how far apart objects or points are.

The points are (-1,4) and (8,2).

The formula to calculate the distance between two points (x,y),(,a,b) is as under:

Distance=[tex]\sqrt{(a-x)^{2} +(b-y)^{2} }[/tex]

Distance=[tex]\sqrt{(8+1)^{2} +(2-4)^{2} }[/tex]

=[tex]\sqrt{(9)^{2} +(-2)^{2} }[/tex]

=[tex]\sqrt{81+4}[/tex]

=[tex]\sqrt{85}[/tex]

=9.2195

After rounding off to nearest tenth we will get 9.2.

Hence the distance between the two points rounding to the nearest tenth is 9.2 units.

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The Lagrangian is

[tex]L(x,y,\lambda) = x^2 + y^2 - \lambda (x + y - 1)[/tex]

Find its critical points.

[tex]\dfrac{\partial L}{\partial x} = 2x - \lambda = 0 \implies x = \dfrac\lambda2[/tex]

[tex]\dfrac{\partial L}{\partial y} = 2y - \lambda = 0 \implies y = \dfrac\lambda2[/tex]

[tex]\dfrac{\partial L}{\partial\lambda} = -(x+y-1) = 0 \implies x + y = 1[/tex]

From the first two conditions, [tex]x=y[/tex], so

[tex]x + y = 2x = 1 \implies x = y = \dfrac12[/tex]

At the point (1/2, 1/2), compute the Hessian determinant of [tex]f(x,y)[/tex].

[tex]H(x,y) = \begin{bmatrix} \dfrac{\partial^2f}{\partial x^2} & \dfrac{\partial^2f}{\partial x \partial y} \\\\ \dfrac{\partial^2f}{\partial y\partial x} & \dfrac{\partial^2f}{\partial y^2} \end{bmatrix} = \begin{bmatrix}2&0\\0&2\end{bmatrix}[/tex]

[tex]H(x,y)[/tex] is positive definite for all [tex]x,y[/tex], which indeed indicates a local minimum at (1/2, 1/2), so that

[tex]\min\left\{x^2+y^2 \mid x+y=1\right\} = f\left(\dfrac12,\dfrac12\right) = \dfrac14+\dfrac14 = \boxed{\dfrac12}[/tex]

The cost to carpet this room area is $2764.8.

What is the area?

Area of room = 32*24 (product is equal to the area of carpet)

Cost of carpet per square foot = $3.6 (three. six)

Cost of carpet = Area of carpet * Cost of carpet per square foot (product)

 = 32 x 24 x 3.6

 = 2764.8

The cost to carpet this room area is $2764.8.

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Answer:

40°

Step-by-step explanation:

At point C, the angle is shown as 110°.
Since a line is 180°, you now know that the other side of point C is 70°.
Line A-B and A-C are equal (shown by the short lines), meaning the angle at point B is also 70°,
A triangle is 180° in total, so the equation would be 180° - 2(70°) = 180° - 140° = 40°

This range defines that the babies delivered weigh between 6.9 and 9.5 pounds.

Part 1.

Given inequality is  | x − 8.1 |  ≤ 1.3

Simplifying this inequality as

x - 8.2 ≤ 1.3 or x - 8.2 ≥ -1.3

Solving x - 8.2 ≤ 1.3  we get, x ≤ 9.5

And

Solving x - 8.2 ≥ -1.3 we have, x ≥ 6.9

Now combining the ranges we get,

6.9 ≤ x ≤ 9.5

Part 2.

This range defines that the babies delivered weigh between 6.9 and 9.5 pounds.

Hence, This range indicates that the babies' weights fall within the range of 6.9 to 9.5 pounds.

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The ordered pair for each letter on the graph would be A at (2, 4), B at (-1, 2), C at (-3, -2), D at (2, 0), E at (0, 4), and F at (5, -5).

A graph can be defined as a pictorial representation or a diagram that represents data or values.

As per the given graph,

The coordinates of point A would be (2, 4)

The coordinates of point B would be (-1, 2)

The coordinates of point C would be (-3, -2)

The coordinates of point D would be (2, 0)

The coordinates of point E would be (0, 4)

The coordinates of point F would be (5, -5)

Therefore, the ordered pair for each letter on the graph would be A at (2, 4), B at (-1, 2), C at (-3, -2), D at (2, 0), E at (0, 4), and F at (5, -5).

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Answer:

375

Step-by-step explanation:

Let the number of hamburgers sold be x. Then, x-66 cheeseburgers were sold.

[tex]x+x-66=684 \\ \\ 2x=750 \\ \\ x=375[/tex]

Answer:  27. 10 < x < 20

29. 10 < x < 20

Step-by-step explanation:

Taking into account the definition of a system of linear equations, the system of equations that could be used to determine the number of games Kadeesha played and the number of rides Kadeesha went on is:

[tex]\left \{ {{2.50G+4.75R=48.75} \atop {G=2R}} \right.[/tex]

where G is the number of games Kadeesha played and R is the number of rides Kadeesha went on.

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.

Solving a system of equations consists of finding the value of each unknown so that all the equations of the system are satisfied. That is to say, the values ​​of the unknowns give the solution proposed in both equations.

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

On the other hand, you know:

So, the system of equations to be solved is

[tex]\left \{ {{2.50G+4.75R=48.75} \atop {G=2R}} \right.[/tex]

Among the different existing methods to solve the system of equations, it is decided to solve it using the substitution method. This method 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, substituting the second equation in the first one you get:

2.50×2R+4.75R=48.75

Solving:

5R+4.75R=48.75

9.75R=48.75

R= 48.75÷ 9.75

R= 5

Remembering that G=2R, you obtain that G=2×5= 10

In summary, the system of equations that could be used to determine the number of games Kadeesha played and the number of rides Kadeesha went on is:

[tex]\left \{ {{2.50G+4.75R=48.75} \atop {G=2R}} \right.[/tex]

where G is the number of games Kadeesha played and R is the number of rides Kadeesha went on.

Finally, the number of games played is 10 while the number of rides she went on is 5.

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Explanation:

Imagine drawing a circle and splitting it into 3 equal slices. Repeat this process to get 12 identical such circles. We have 12*3 = 36 slices so far.

Then add a 13th circle that has 2 of the 3 slices shaded, to represent 2/3. So we add 2 extra slices to the 36 original to get 36+2 = 38 total slices.

Each slice represents 1/3 of a cup. So each full circle represents 1 full cup.

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

Another approach:

Let's convert the mixed number 12 & 2/3 into an improper fraction

We use the formula

a & b/c = (a*c+b)/c

So,

12 & 2/3 = (12*3+2)/3 = (36+2)/3 = 38/3

Then rewrite the 38/3 as 38*(1/3) to show we have 38 copies of the 1/3 cup.

Answer: 38 cups

Step-by-step explanation:

       We will divide 12 2/3 cups by our measurement, 1/3 cup, to find how many 1/3 cups will be needed.

(12 + 2/3) / (1/3) = 38 cups

Using Gaussian elimination, the solution to the given system of equations is given as follows:

x = 5, y = -11, z = 3.

A system of equations is when multiple variables are related, and equations are built to find the values of each variable, according to the relations given in the problem.

For this problem, the variables are x, y and z, and the system is given as follows:

There are multiple ways in which a system can be solved, and for this one, Gaussian elimination will be used.

The first step is writing the augmented matrix of the system, as follows:

[tex]\left[\begin{array}{cccc}2&-1&4&33\\1&2&-3&-26\\-5&-3&5&23\end{array}\right][/tex]

Then, the first column, which is equivalent to be coefficient of y, has to be of zero on the second and on the third row, hence:

The updated matrix will be given by:

[tex]\left[\begin{array}{cccc}2&-1&4&33\\0&5&-10&-85\\0&-11&30&211\end{array}\right][/tex]

Then, the second column, equivalent to the coefficient of y, on the third row has to be zero, hence:

R3 -> 11R2 + 5R3.

Then the matrix is:

[tex]\left[\begin{array}{cccc}2&-1&4&33\\0&5&-10&-85\\0&0&40&120\end{array}\right][/tex]

From each row of the system, from bottom up, we find the variables, as follows:

40z = 120

z = 120/40

z = 3.

5y - 10z = -85

5y - 30 = -85

5y = -55

y = -11.

2x - y + 4z = 33

2x + 11 + 12 = 33

2x = 10

x = 5.

Hence the solution for the system is:

x = 5, y = -11, z = 3.

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Answer:

32

Step-by-step explanation:

That is a weird question. Usually questions like that include a variable. Its like saying n = 32. It just gives the answer. Assuming you didn't miss anything, this is the answer.