Solve by using substitution.
a =5b-4
-2a +10b = 5​

Answer:

The standard form of the equation of a circle with center at (h, k) and radius r is:

(x - h)^2 + (y - k)^2 = r^2

We are given that the center of the circle is (4, -1), so h = 4 and k = -1. We also know that the circle passes through the point (-4, 1), which means that the distance from the center of the circle to (-4, 1) is the radius of the circle.

The distance between two points (x1, y1) and (x2, y2) is given by the distance formula:

d = sqrt((x2 - x1)^2 + (y2 - y1)^2)

So the radius of the circle is:

r = sqrt((-4 - 4)^2 + (1 - (-1))^2) = sqrt(100) = 10

Now we can substitute the values of h, k, and r into the standard form equation of a circle:

(x - 4)^2 + (y + 1)^2 = 10^2

Expanding the equation gives:

x^2 - 8x + 16 + y^2 + 2y + 1 = 100

Simplifying and putting the equation in standard form, we get:

x^2 + y^2 - 8x + 2y - 83 = 0

Therefore, the equation in standard form of the circle with center at (4, −1) and that passes through the point (−4, 1) is:

x^2 + y^2 - 8x + 2y - 83 = 0

If Saquon Barkley lost \(7\frac{2}{3}\) yards on the first play, and gained \(9\frac{5}{8}\) yards on the next play, then the total gain for the running during the first two plays is  \(1\frac{23}{24}\) yards

The amount he lost on the first play =  \(7\frac{2}{3}\) yards

Convert the mixed fraction to the simple fraction

\(7\frac{2}{3}\) yards = 23/3 yards

The amount he gained on the second play =  \(9\frac{5}{8}\) yards

Convert the mixed fraction to the simple fraction

\(9\frac{5}{8}\) yards = 77/8 yards

The total gain for the running during the first two plays = The amount he gained on the next play - The amount he lost on the first play

Substitute the values in the equation

= 77/8 - 23/3

= 47/24 yards

Convert the simple fraction to the mixed fraction

47/24 yards = \(1\frac{23}{24}\) yards

Hence, if Saquon Barkley lost \(7\frac{2}{3}\) yards on the first play, and gained \(9\frac{5}{8}\) yards on the next play, then the total gain for the running during the first two plays is  \(1\frac{23}{24}\) yards.

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Answer:

Step-by-step explanation:

Answer:

Step-by-step explanation:

Two consecutive numbers be 2x , (2x + 2)

(2x)(2x + 2) = 360

2x*2x + 2x *2 = 360

4x² + 4x = 360 {divide the equation by 4}

x² + x = 90

x² + x - 90 = 0

x² + 10x - 9x - 9*10 = 0

x(x + 10) - 9(x + 10) = 0

(x + 10)(x -9) = 0

x + 10 = 0

x = -10

2x = 2*(-10) = -20

2x + 2 = -20 + 2 = 18

(-20 , -18)

The zeros of the function f(x) = 2x⁴ + 11x³ + 16x² + x - 6 are x = -3, x = -2,

x = -1 and x = 1/2 respectively

The zero of a real-, complex-, or generally vector-valued function f, is a member x of the domain of f such that f(x) vanishes at x; that is, the function f attains the value of 0 at x, or equivalently, x is the solution to the equation f(x) = 0. Graphically, the real zero of a function is where the graph of the function crosses the x‐axis; that is, the real zero of a function is the x‐intercept(s) of the graph of the function.

In the given problem, the zero of the function;

f(x) = 2x⁴ + 11x³ + 16x² + x - 6; -3 are

f(-3) = 2(-3)⁴ + 11(-3)³ + 16(-3)² -3 - 6 = 0

f(-2) = 2(-2)⁴ + 11(-2)³ + 16(-2)² - 2 - 6 = 0

f(-1) = 2(-1)⁴ + 11(-1)³ + 16(-1)² - 1 - 6 = 0

f(1/2) = 2(1/2)⁴ + 11(1/2)³ + 16(1/2)² - 1/2 - 6 = 0

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Given:

The function is,

The graph of the above function is dilated by x. It is given as,

The points on h(x) is (-3,0),(0,-3),(1,-4),(2,-5).

Now, dilate the graph by multiplying x values.

The graph is given as,

Answer:

is c

Step-by-step explanation:

The length of the curve x = y3/2/3 - y1/2 from y = 3 to y = 11 is 5.75 + (1/4)ln|11.5| - (1/4)ln|3.5|.

Curve is a mathematical term that refers to the shape of a line or surface. It is used to describe the shape of a graph or a three-dimensional object. A curve can be either smooth or jagged, and can have a variety of shapes, including circles, ellipses, parabolas, and hyperbolas. In mathematics, curves are used to model physical objects and phenomena, such as the earth's surface or the shape of a molecule.

We can use the formula for the arc length of a function given by:
L = ∫a b √1+(f′(x))2dx
In this case, we have:
f(x) = y3/2/3 - y1/2
Taking the derivative of this function gives us:
f′(x) = 3/2y1/2/3 - 1/2y-1/2
Plugging this into the formula, we get:
L = ∫3 11√1+(3/2y1/2/3 - 1/2y-1/2)2dx
Integrating this expression yields:
L = [3/2y3/2/3 - 1/2y1/2 + (1/4)ln|y+1/2|]3-11
Substituting in the limits of integration, we get:
L = [3/2(11)3/2/3 - 1/2(3)1/2 + (1/4)ln|11+1/2|] - [3/2(3)3/2/3 - 1/2(3)1/2 + (1/4)ln|3+1/2|]
Simplifying this expression gives us:
L = [6.5 - 0.75 + (1/4)ln|11.5|] - [1.5 - 0.75 + (1/4)ln|3.5|]
Evaluating this expression yields:
L = 5.75 + (1/4)ln|11.5| - (1/4)ln|3.5|
Therefore, the length of the curve x = y3/2/3 - y1/2 from y = 3 to y = 11 is 5.75 + (1/4)ln|11.5| - (1/4)ln|3.5|.

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Answer:

2A9

Step-by-step explanation:

Answer:

p = 7

Step-by-step explanation:

trust me

Answer:

p = 7

Step-by-step explanation:

Given value of q = 4 so,

5p - 11 = 6 × 4

=> 5p = 24 + 11

=> 5p = 35

\( = > p = \frac{35}{5} \)

=> p = 7(Ans)

The slope of the graph is equal to 1 for all x between x= 0 and x=3.

Starting at x=3 the function value y increases as x increases.

The slope of the graph is equal to 3 for x between x=3 and x=5

For x between x=0 and x=4, the function value of y is ≤ 0.

For x between x=4 and x=8 the function of value y is ≥ 0.

In Mathematics and Geometry, the slope of any straight line can be determined by using the following mathematical equation;

Slope (m) = (Change in y-axis, Δy)/(Change in x-axis, Δx)

Slope (m) = rise/run

Slope (m) = (y₂ - y₁)/(x₂ - x₁)

By substituting the given data points into the formula for the slope of a line, we have the following;

Slope (m) = (0 - 3)/(3 - 0)

Slope (m) = -3/3

Slope (m) = -1.

For x between x=3 and x=5, the slope is given by;

Slope (m) = (3 + 3)/(5 - 3)

Slope (m) = 6/2

Slope (m) = 3.

By critically observing the graph of this function, we can logically deduce that the function value of y is less than or equal to 0 for x between x=0 and x=4 and greater than or equal to 0 for x between x=4 and x=8.

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When the former image is rotated, the dots will be located at section 2 and 7.

When an image is rotated, the constituents within it also changes its position as the object is moves from a point to another about a pivot junction.

From the given image above, after the rotation of the initial image, the dot should be located at number 2 and 7 of the new image.

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Answer:

129

Step-by-step explanation:

the 2 angles together will equal 180 because that is half of a circle a circle is 360so what you do is subtract 180 minus 51 and get 129

Answer:

\(Probability = 0.068\)

Step-by-step explanation:

Let P(S) represent the probability that stock market will go up in a day

Given

\(P(S) = 51\%\)

Required

Determine the probability that stock will go up 4 consecutive days

Start by converting P(S) from percentage to decimal

\(P(S) = 51\%\)

\(P(S) = \frac{51}{100}\)

\(P(S) = 0.51\)

The above expression represents the probability in a day;

For 4 days; we have:

\(Probability = P(S) * P(S) * P(S) * P(S)\)

\(Probability = (P(S))^4\)

Substitute 0.51 for P(S)

\(Probability = (0.51)^4\)

\(Probability = 0.06765201\)

\(Probability = 0.068\) -- Approximated

Hence, the probability that stock will rise for 4 consecutive days is 0.068

Answer:

90/9 = 10, the length of the pool.  This can be proven as 10 x 9 = 90²

Step-by-step explanation:

There are 120 different combinations of 3 programmers that can be chosen to transfer to the new department

From the question, we have

Total number of programmers, n = 10

Numbers to programmers to select, r = 3

The number of ways of selection could be drawn is calculated using the following combination formula

Total = ⁿCᵣ

Where

n = 10 and r = 3

Substitute the known values in the above equation

Total = ¹⁰C₃

Apply the combination formula

ⁿCᵣ = n!/(n - r)!r!

So, we have

Total = 10!/(7! * 3!)

Evaluate

Total = 120

Hence, the number of ways is 120

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Using trigonometry ratio

x = 277.5 ft

The coefficient of variation for A is 20.37% and for B is 15.98%.

What is coefficient of variation?

In statistics, the relative standard deviation (RSD), commonly referred to as the coefficient of variation formula (CV), is a standardized way to assess how widely spaced out a probability distribution or frequency distribution is. Lower values of the coefficient of variation indicate that the data is highly stable and less variable.

We know that formula for coefficient of variation is

CV = Standard Deviation / Mean

A. $31,100, $25,800, $36,300, $30,200, $30,000, $19,800, $22,300, $22,600, $34,900, $21,700, $36,900, $30,800, $31,700, $37,100

Mean = 411200 / 14

Mean = $29371.42

Similarly,

Standard Deviation = $5984.52

So,

CV = 5984.52 / 29371.42 * 100

CV = 20.37%

B. 3.18, 4.24, 4.27, 4.38, 3.87, 4.75, 3.43, 3.35, 4.16, 4.81, 2.98

Mean = 43.42 / 11

Mean = $3.94

Similarly,

Standard Deviation = $0.63

So,

CV = 0.63 / 3.94 * 100

CV = 15.98%

Hence, the coefficient of variation for A is 20.37% and for B is 15.98%.

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The art teacher can make a maximum of 24 identical kits using all the crayons and drawing paper for proper distribution.

To determine the largest number of identical kits the art teacher can make using all the crayons and drawing paper, we need to find the greatest common divisor (GCD) of the quantities.

The GCD represents the largest number that can divide all the quantities without leaving a remainder.

The GCD of the quantities of crayons can be found by considering the prime factorization:

72 = 2³ × 3²

48 = 2⁴ × 3

48 = 2⁴ × 3

48 = 2⁴ × 3

The GCD of the crayons is 2³ × 3 , which is 24.

Now, we need to find the GCD of the quantity of drawing paper:

120 = 2³ × 3 × 5

The GCD of the drawing paper is also 2³ × 3 , which is 24.

Since the GCD of both the crayons and drawing paper is 24, the art teacher can make a maximum of 24 identical kits using all the crayons and drawing paper.

Each kit would contain an equal distribution of crayons and drawing paper.

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Answer:

x = 35

Step-by-step explanation:

since the figures are similar then the ratios of corresponding parts are in proportion, that is

\(\frac{x}{10}\) = \(\frac{14}{4}\) = \(\frac{7}{2}\) ( cross- multiply )

2x = 7 × 10 = 70 ( divide both sides by 2 )

x = 35

The visual that can help you in  creating a  3D structure using rectangular prism and others is given in the image attached.

3D structure creation is the method of planning and building three-dimensional structures or objects utilizing various materials and methods. This may make use of physical development with the use of materials such as wood, metal, and plastic, as well as virtual development utilizing computer program programs.

In virtual 3D structure creation, creators make use of program to make 3D models of structures or objects. These models can be seen and controlled in virtual space, and can be utilized to reenact how the structure  will see and work within the real world.

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See text below



1. Start by creating a rectangular prism

as the base of your structure. This will

be the main structure that includes

the walls and interior rooms.

2. Add a cylindrical tower to one corner of the rectangular prism. Adjust the size and height to your liking.

3. Add another cylindrical tower to the opposite corner of the rectangular

prism. Again, adjust the size and

height to your liking.

4. Add a pyramid-shaped roof to one of the cylindrical towers, and a cone-

shaped roof to the other cylindrical tower.

5. Add a second rectangular prism on top of the first one, with a different orientation or size. This can serve as an additional room or tower.

6. Add a pyramid-shaped roof to the second rectangular prism, and a cone-shaped roof to the cylindrical tower that does not have one yet.

7. Add a rectangular prism

perpendicular to the main structure,

creating an L-shape. This can be a

separate building or an extension of

the main structure.

8. Add a pyramid-shaped roof to the new

rectangular prism, and a cone-shaped roof to the cylindrical tower on the

opposite side of the main structure. 9. Finally, add spheres as decorative

elements to the walls and towers. You can also add other shapes, such as additional rectangular prisms,

pyramids, or cones, as long as you have at least 2 of each of the 5

required shapes.

Answer:

b

Step-by-step explanation:

I mean I believe its b it looks like theres three

The probability that the melon will have a diameter greater than 137 mm is 21.19%.

Probability is a way to gauge how likely something is to happen. According to the probability formula, the likelihood that an event will occur is equal to the proportion of positive outcomes to all outcomes. The probability that an event will occur P(E) is equal to the ratio of favorable outcomes to total outcomes. The likelihood of an event occurring might range from 0 to 1.

Given A grocery store purchases melons from two distributors, J & K,

for distributor J,

mean of melons = μ = 133 mm

standard deviation  = σ = 5 mm

to find the probability  that the melon will have a diameter greater than 137 mm,

x = 137 mm

P(x > 137)

using z score formula

z = (x - μ)/σ

z = (137 - 133)/5

z = 0.8

P-value from Z-Table:

P(x < 137) = 0.78814

P(x > 137) = 1 - P(x < 137) = 0.21186

probability in percent = P(x > 137) = 0.21186*100 = 21.186%

P(x > 137) = 21.19%

Hence probability for melon will have a diameter greater than 137 mm is 21.19%.

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The complete question is,

A grocery store purchases melons from two distributors, J & K. Distributor J provides melons from organic farms. The distribution of the diameters of the melons from distributor J is approximately normal with mean with 133 millimeters and standard deviation 5 mm. For a melon selected at random from distributor J, what is the probability that the melon will have a diameter greater than 137mm?

Answer:

Step-by-step explanation:  If you roll the die twice, the probability of getting a even number both times is (1/2)(1/2) ... A probability experiment consists of rolling a 6 sided die

Answer:

The distance is 1.41 to nearest hundredth.

Step-by-step explanation:

The line y = x + 3 passes through the point (0, 3) on the yaxis.

Find the perpendicular line passing through this point:

y  - 3 = -1(x + 0)

y = -x + 3

Now find the point where this line intersects the line y = x + 1:

y = -x + 3

y = x + 1

-x + 3 = x  + 1

3 -1 = x + x

2x = 2

x = 1

and y = 2

So this point is (1, 2)

We require the distance between this point and (0, 3)

This = √((3-2)^2 + (0-1)^2) = √2

= 1.4142

Answer:

toooo what?

Step-by-step explanation: