what does the variable, r, stand for in the equation 16- r/7 = 21

The length of the semi-major axis of the ellipse is 7.

What is the semi-major axis of an ellipse?

The semi-major axis of an ellipse is the half of the longest diameter passing through its vertex and focus.

The general equation of an ellipse is :

⇒ x²/a²+y²/b²=1, where a is the semi-major axis and b, is the semi-minor axis

x²/49+y²/36=1

x²/(7²)+y²/(6²)=1

x²/a²+y²/b²=1

a=7

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The class interval of the distribution of ages is 10

To determine the class interval, we simply make use of the first class limits

5 up to 15

Rewrite the first class limits as:

5 - 15

Calculate the difference between the upper and the lower limits

Class interval = 15 - 5

Evaluate the difference

Class interval = 10

Hence, the class interval of the distribution of ages is 10

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The fraction of the area of polygon H of polygon G's area would be: 1/16.

When a polygon is formed by enlarging or reducing an original polygon by a scale factor, the new polygon formed is similar to the original polygon.

The scale factor = new dimension/original dimension

Given that polygon H is the new polygon formed when polygon G is reduced by a scale factor of 1/4, thus, we would have the following:

Area of polygon H/Area of polygon G = square of the side of polygon H/square of the side of polygon G = square of the scale factor of dilation

Area of polygon H/Area of polygon G = 1²/4² = 1/16

This implies that the area of polygon G is 16 units² while the area of polygon H is 1 units².

Thus, the fraction of the area of polygon H of polygon G's area would be: 1/16.

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The second pair of points representing the solution set of the system of equations is (-6, 29).

To find the second pair of points representing the solution set of the system of equations, we need to substitute the x-coordinate of the second point into one of the equations and solve for y.

Given the system of equations:

y = x^2 - 2x - 19

y + 4x = 5

Substituting the x-coordinate of the second point (-6) into equation 2:

y + 4(-6) = 5

y - 24 = 5

y = 5 + 24

y = 29

Therefore, the second pair of points representing the solution set of the system of equations is (-6, 29).

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Question

Type the correct answer in the box. Use numerals instead of words. If necessary, use / for the fraction bar.

y = x2 − 2x − 19

y + 4x = 5

The pair of points representing the solution set of this system of equations is (-6, 29) and

_________.

Answer:

\(\boxed{11.78}\)

Step-by-step explanation:

From observations, we can note that BC is the hypotenuse.

As the length of hypotenuse is not given, we can only use tangent as our trig function.

tan(θ) = opposite/adjacent

tan(67) = x/5

5 tan(67) = x

11.77926182 = x

x ≈ 11.78

Answer:

the angle is acute angle

Answer:

The type of angle shown is an acute angle

Step-by-step explanation:

there are 4 main types of angles. this is an acute angle as it is less than 90°.

Types of angles:

The 4 main types of angles are: acute, obtuse, right angles, reflex angles.

Acute angles- Acute angles are angles less than 90°.

Obtuse Angles-Obtuse angles are angles greater than 90° but less than 180°.

Right Angles- Right angles are angles of 90°.

Reflex Angles- Reflex angles are angles greater than 180° but less than 360°.

The solution of the equations 6x = 52 − 2y and 5x + 7y = 70 by elimination method will be (7, 5).

In other words, the collection of all feasible values for the parameters that satisfy the specified mathematical equation is the convenient storage of the bunch of equations.

The equations are given below.

6x = 52 - 2y

6x + 2y = 52

3x + y = 26                   ...1

5x + 7y = 70

(5/7)x + y = 10              ...2

Subtraction equation 2 from equation 1, then we have

3x - (5/7)x = 26 - 10

(16/7)x = 16

x = 7

Then the value of 'y' is given as,

3(7) + y = 26

21 + y = 26

y = 5

The solution of the equations 6x = 52 − 2y and 5x + 7y = 70 by elimination method will be (7, 5).

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Answer:

7 / 10 14 / 20 21 / 30

Step-by-step explanation:

7 out of 10 is its simplest form the equivalent ratio of 7 * 210 * 2 equals 14 / 27 / 10 * 3 * 3 equals 21/30 letter answer

None of the given answer options (-10, 10, 16, ¾/1) correspond to the correct slope of -1/2.

To find the slope of the red line given that it is perpendicular to the green line with a slope of 2, we can use the property that perpendicular lines have slopes that are negative reciprocals of each other.

The slope of the green line is 2. To find the slope of the red line, we take the negative reciprocal of 2. The negative reciprocal is obtained by taking the reciprocal (flipping the fraction) and changing the sign.

Reciprocal of 2: 1/2

Negative reciprocal: -1/2

Therefore, the slope of the red line is -1/2.

However, none of the given answer options (-10, 10, 16, ¾/1) correspond to the correct slope of -1/2.

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let's take a peek at the picture above, hmmm let's notice the vertex is at (-1 , 2), now let's get a point besides the vertex hmmm let's see it passes through (-2 , -1).

So we can reword that as what's the equation of a quadratic whose vertex is at (-1 , 2) and it passes through (-2 , -1)?

\(~~~~~~\textit{vertical parabola vertex form} \\\\ y=a(x- h)^2+ k\qquad \begin{cases} \stackrel{vertex}{(h,k)}\\\\ \stackrel{a~is~negative}{op ens~\cap}\qquad \stackrel{a~is~positive}{op ens~\cup} \end{cases} \\\\[-0.35em] ~\dotfill\)

\(\begin{cases} h=-1\\ k=2\\ \end{cases}\implies y=a(~~x-(-1)~~)^2 + 2\hspace{4em}\textit{we also know that} \begin{cases} x=-2\\ y=-1 \end{cases} \\\\\\ -1=a( ~~-2-(-1) ~~ )^2 + 2\implies -3=a(-2+1)^2\implies -3=a \\\\\\ ~\hfill~ {\Large \begin{array}{llll} y=-3(x+1)^2 + 2 \end{array}} ~\hfill~\)

Answer:

y = -3(x + 1)^2 + 2

Step-by-step explanation:

y = a(x - h)^2 + k is the vertex form of a quadratic, where

Finding (h, k):

We see from the graph that the vertex is a maximum and its coordinates are (-1, 2).  Thus h is -1 and k is 2.  Since h becomes negative, it will be 1 in the parentheses: (x - (-1) = (x + 1).

Finding a:

In order to find a, we will need to plug in a point on the parabola for (x, y) and (-1, 2) for h and k.  We see that (0, -1) lies on the parabola so we can use this point for (x, y).

-1 = a(0 - (-1))^2 + 2

-1 = a(0 + 1)^2 + 2

-3 = a(1)^2

-3 = a

Thus, a = -3.

Thus, the exact equation in vertex form of the parabola is:

y = -3(x + 1)^2 + 2

I attached a picture from Desmos Graphing Calculator that shows how the equation I provided works and contains the two points you marked on the parabola, including (-1, 2) aka the maximum, and (0, -1) aka the y-intercept.

Answer:

(100°)

Step-by-step explanation:

first join point 162° to 98° to form a triangle

then add

162°+98°

=260°

an angle totally has 360°

so you minus 260° from 360°

360°-260°

=100°

(sorry,thanks and hope I helped)

the inequality of the number line will be -6<x<2.

What is number line?

A number line is an image of numbers plotted on a straight line, either horizontally or vertically. We can compare numbers and execute simple arithmetic operations on them easily by writing the numbers down on a number line. The starting point of a number line is often regarded as zero (0). These numbers to the left of zero are all negative while the numbers just on right of zero are all positive. As a result, we can argue that on a number line, the value of numbers grows as we approach the right. The numbers on the right are therefore larger than the ones on the left, according to this statement.

In this number line the max point its marked is 2

and the minimum point is -6

So the value of unknown x should lie in between

-6<x<2

So, the inequality of the number line will be -6<x<2.

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Peter should pay a minimum amount of $960 in rent for the other half of the duplex in order to pay off the mortgage in 30 years.

An addition operation in mathematics adds values on either side of the operator.

For example 4 + 2 = 6

The rent Peter should charge will be computed as follows:

Peter will pay 90% of his purchase price after a 10% down payment:

90% of the buying price = 226,950*0.9 = $204255

Assuming the mortgage is compounded monthly, the total monthly mortgage payment is calculated using the amortization formula:

A=P(i(1+i)ⁿ)/((1+i)ⁿ-1)

where

A = monthly payment

P = amount borrowed (present value) = $204255

i = monthly interest = 0.0625/12

n = number of months = 30*12 = 360

Calculating the monthly payment:

A = 204255(.0625/12 (1+.0625/12)³⁶⁰)/((1+.0625)³⁶⁰-1)

A = $1257.63

His monthly payment is 10% of his monthly earnings.

10% of $2985 = $298.50 monthly payment

As a result, the minimum rent is 1257.63 minus $298.50.

The minimum rent is $959.13.

As a result, Peter should charge a minimum of $960 for the other half of the duplex.

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Answer: its B

Peter should increase the rent by $60.

Step-by-step explanation:

There is no real Value of k that will satisfy the equation 2x² - x + 8k = 0 if a and 1/a are the roots of the polynomial.

(i) Zeroes of the polynomial:

In the graph, we have two points where the curve intersects the x-axis: one is at (-1,0), and the other is at (2,0).The corresponding values of x are -1 and 2, and they are the zeros of the polynomial. Therefore, the zeros of the polynomial are -1 and 2.(ii) Forming the quadratic polynomial:

From the graph, we can observe that the curve intersects the y-axis at the point (0,5), implying that the constant term of the polynomial is 5.

We can use the formula to find the quadratic polynomial if we have two zeros and one constant term. Thus, the quadratic polynomial is given by:(x + 1)(x - 2) = x² - x - 2x + 2 = x² - 3x + 2. Therefore, the quadratic polynomial is x² - 3x + 2.(iii) Value of k if a, 1/a are the zeroes of the polynomial 2x² - x + 8k:

We know that a and 1/a are the zeroes of the polynomial 2x² - x + 8k. Therefore, we can find the sum and product of the roots and use them to determine the value of k.

The sum of the roots is a + 1/a, and their product is a(1/a) = 1. Using the sum and product of the roots, we can write: a + 1/a = 1/2 (1/2 is the coefficient of x)Substituting a with 1/a in the above equation, we get: 1/a + a = 1/2Multiplying both sides of the equation by 2a, we get: 2 + 2a² = a

Simplifying the equation, we get: 2a² - a + 2 = 0Multiplying both sides by 2,

we get: 4a² - 2a + 4 = 0Dividing both sides by 2, we get: 2a² - a + 2 = 0

Using the quadratic formula, we get: a = [1 ± √(1 - 4(2)(2))]/(2(2))

Simplifying, we get: a = [1 ± √(-31)]/4Since the discriminant of the quadratic formula is negative, the roots are imaginary. Therefore, there is no real value of k that will satisfy the equation 2x² - x + 8k = 0 if a and 1/a are the roots of the polynomial.

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By analyzing the graph and evaluating the objective function at each vertex of the feasible region, we can find the optimal solution, which is the vertex that maximizes the objective function z = 3x + y.

To find the optimal solution of the given problem using the graphical method, we need to plot the feasible region determined by the given constraints and then identify the point within that region that maximizes the objective function.

Let's start by graphing the constraints:

1. Plot the line 2x - y = 5. To do this, find two points on the line by setting x = 0 and solving for y, and setting y = 0 and solving for x. Connect the two points to draw the line.

2. Plot the line -x + 3y = 6 using a similar process.

3. The x-axis and y-axis represent the constraints x ≥ 0 and y ≥ 0, respectively.

Next, identify the feasible region, which is the region where all the constraints are satisfied. This region will be the intersection of the shaded regions determined by each constraint.

Finally, we need to identify the point within the feasible region that maximizes the objective function z = 3x + y. The optimal solution will be the vertex of the feasible region that gives the highest value for the objective function. This can be determined by evaluating the objective function at each vertex and comparing the values.

Note: Without a specific graph or additional information, it is not possible to provide the precise coordinates of the optimal solution in this case.

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Answer: 0.35

Step-by-step explanation:

Times 7 = 2. 45kg

Yes, she did buy additional carrot seed. No, the total number of seeds was 1120. No, the total price is $171. She did buy more maize and beans than carrots.

Multiplication is one of the four basic mathematical operations of arithmetic, along with addition, subtraction, and division. A product is the outcome of a multiplication operation. Multiplication is a way of calculating the product of two or more integers in mathematics. It is one of the most fundamental mathematical operations that we utilize every day. When we multiply two numbers, the result is known as the product. The multiplicand is the number of items in each group, and the multiplier is the number of such equal groupings. In our situation, the multiplicand is, the multiplier is, and the product is 6.

Here,

Beans=12*40

=480

cost of beans=12*5

=$60

Carrot=15*36

=540

cost of carrot=15*7

=$105

Corn=2*50

=100

cost of corn=2*3

=$6

Total seeds=1120

Total cost=$171

Yes she bought more of carrot seed. No the total seeds was 1120. No the total cost is $171. Yes she bought more corn and beans than carrot.

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By conducting mathematical operations, we know that John's gross pay will be $1,012 if he works 44 hours a week.

A mathematical "operation" is the process of calculating a value utilizing operands and a math operator.

The supplied operands or integers must adhere to a set of predefined rules that are connected to the symbol of the math operator.

The order of operations refers to the rules that specify how to solve an expression including many operations.

Parentheses, Exponents, Multiplication, Division, Addition, and Subtraction are all referred to as PEMDAS (from left to right).

So, we know that:

John earns $22 per hour for the first 40 hours of a week.

After every additional hour, he earns 1.5 times $22 each hour.

22 * 1.5 = $33

So, John's gross pay if he worked 44 hours will be:

22*40 + 33*4

880 + 132

$1,012

Therefore, by conducting mathematical operations, we know that John's gross pay will be $1,012 if he works 44 hours a week.

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Step-by-step explanation:

1) -5n+10n

= 5n

2) -x-9+2x-10

= 2x-x-9-10

= x-19

3) -5(x-10)-x

= -5x+50-x

= -6x+50

4) 9-5(1-7x)

= 9-5+35x

= 35x+4

5) y^2-x

= 3^2-2

= 9-2

= 7

Do the remain questions by yourself, you can do it!

Answer:

33

Step-by-step explanation:

I am did my diagnostic too.

The required chance of that a random donor has type A blood is given as 11/25. Option B is correct.

Probability can be defined as the ratio of favorable outcomes to the total number of events.

Here,
Total blood donor = 31 + 33 + 9 + 2 = 75
Donors has type A blood = 33

Now, the chance that a random donor has type A blood,

= Donors has type A blood / Total blood donor

= 33 / 75
= 11 / 25

Thus, the required chance of that a random donor has type A blood is given as 11/25.

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Answer:

what we have to find or to prove.

The solution of the given quadratic equation is -2 ± √6.

Quadratic expressions are polynomial equations of second degree.

The general form of a quadratic equation is ax² + b x + c = 0.

Solution of a quadratic equation ax² + b x + c = 0 can be found by,

x = [-b ± \(\sqrt{b^2-4ac}\)] / 2a, where \(b^2-4ac\) is called discriminant.

Given quadratic equation is x² + 4x - 2 = 0.

Discriminant = 4² - (4 × 1 × -2) = 16 + 8 = 24

x = [-4 ± √24] / 2

  = [-4 ± 2√6] / 2

  = -2 ± √6

Hence the solution of the given quadratic equation is -2 ± √6.

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Answer:A school bus provides a safe way of transportation for your child. Learn resources to talk to your child about school bus and bus stop safety.

Step-by-step explanation:

The measure of the arc or angle is:

m∠NLM = 60 deg

From the given figure, line LN is the diameter. Thus, the measure of arc LN is 180° (semicircle).

Thus, we can say:

arc NM + arc ML = 180°

(3x + 21) + (8x + 16) =  180°

11x + 37 = 180

11x = 180 - 37

11x = 143

x = 143/11

x = 13

arc NM = 8x + 16

put x = 13:

arc NM = 8(13) + 16 = 120°

Recall that:

The measure of inscribed angle is half the measure of its intercepted arc. That is:

m∠NLM = 1/2 * 120°

m∠NLM = 60°

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Answer:

a = -3

Step-by-step explanation:

3a - 6a + 2 = 8a + 20 - 5a

Combine Like Terms

-3a + 2 = 3a + 20

       -2            -2

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

-3a = 3a + 18

-3a  -3a

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

-6a = 18

----   ----

-6     -6

a  =  -3

To maximize the volume, of the rectangular prism, the carton should have dimensions of approximately 10.74 inches (length), 10.74 inches (width), and 5.37 inches (height).

Assuming the height of the rectangular prism is h inches.

According to the given information, the length and width of the prism will be twice the height, which means the length is 2h inches and the width is also 2h inches.

The total surface area of the rectangular prism is given by the formula:

Surface Area = 2lw + 2lh + 2wh

Substituting the values, we have:

576 = 2(2h)(2h) + 2(2h)(h) + 2(2h)(h)

576 = 8h² + 4h² + 4h²

576 = 16h² + 4h²

576 = 20²

h² = 576/20

h² = 28.8

h = √28.8

h = 5.37

The height of the prism is approximately 5.37 inches.

The length and width will be twice the height, so the length is approximately 2 * 5.37 = 10.74 inches, and the width is also approximately 2 * 5.37 = 10.74 inches.

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Add 7 to both sides.

Add −4 and 7 to get 3.

Multiply both sides by 3, the reciprocal of 1/3 . Since 1/3 is >0, the direction of inequality remains the same.

Multiply 3 and 3 to get 9.

Answer:

Sqrt 80 = 8.94

Step-by-step explanation:

d = sqrt[(x-x)^2 + (y-y)^2]

d = sqrt [(6-2)^2 + (-9 - - 1)^2]

d = sqrt [(4)^2 + (-8)^2]

d = sqrt (16 + 64)

d = sqrt 80

d = 4 sqrt 5 = 8.94

Answer:

c

Step-by-step explanation: