Nina, Shanti and Belle run a 1000 m race at a constant speed. When Nina crossed the inish line irst,
she was 200 m ahead of Shanti and 400 m ahead of Belle. When Shanti crossed the inish line, how far
ahead of Belle was she?

Answer:

(2, -32)

Step-by-step explanation:

1) Expand them.

y = 2(x² - 6x + 2x - 12)

y = 2(x² - 4x - 12)

y = 2x² - 8x - 24.

2) Complete the square to find the vertex.

y = 2([x² - 4x)] - 24

y = 2[(x - 2)² - 4] - 24

y = 2(x - 2)² - 8 - 24

y = 2(x - 2)² - 32

The vertex: (2, -32)

or you can use this: x = -b/2a

x = -(-8)/2(2)

x = 8/4

x = 2

Substitute the value into the original equation for y.

y = 2(2)² - 8(2) - 24

y = 2(4) - 16 - 24

y = 8 - 16 - 24

y = -32

Vertex: (2, -32)

Answer:

  (2, -32)

Step-by-step explanation:

The vertex of the graph of a quadratic equation is on the line of symmetry, halfway between the x-intercepts. It can be found by evaluating the equation at that point.

The given function is written in factored form, so the x-intercepts are easy to find. They are the values of x that make the factors zero:

  (x +2) = 0   ⇒   x = -2

  (x -6) = 0   ⇒   x = 6

The midpoint between these values of x is their average:

  x = (-2 +6)/2 = 4/2

Then the x-coordinate of the vertex, and the equation of the line of symmetry is ...

  x = 2

Using this value of x in the quadratic relation, we find the y-value at the vertex to be ...

  y = 2(2 +2)(2 -6) = 2(4)(-4)

  y = -32

The coordinates of the vertex are (x, y) = (2, -32).

Based on the information provided and the requirements to organize the students, Jon most likely has 23 students.

In general, Jon will need a number that is not prime as this type of number will not allow him to complete all the grid.

20 = A rectangular grid of 5 x 4 seats can be arranged

21= A rectangular grid of 7 x 3 can be arranged

22 = A rectangular grid of 2 x 11 can be arranged

23 = It is impossible to organize 23 seats in a rectangular grid without gaps

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Jon has 23 students in his class.

Number of students = Least 20 and most 28

In this case, we are getting a 1 * x rectangle of desks, which is the only possible arrangement.

'x' is a prime number.

Since his classes can't have less than 20 and more than 28, it means we are  looking out for a prime number between 20 and 28.

Let's sort out a prime number between the numbers, 20 and 28

20: 1,2,4,5,10,20

21: 1,3,7,21

22: 1,2,11,22

23: 1,23

24: 1,2,3,4,6,8,12,24

25: 1,5,25

26: 1,2,13,26

27: 1,3,9,27

28: 1,2,4,7,14,28

From what we have, 23 is a prime number because it is only divisible by one and itself.

Therefore, Jon has 23 students in his class.

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Answer:

Step-by-step explanation:

1/2 pi is an angle ( in radians)

in degrees its 90 degrees.

cos 90 = 0.

Answer:

Step-by-step explanation:

Using proportions, the scenario modeled by the equation 0.6x = 86.46 is:

D. A picnic table is on sale for 40 percent off. The original price of the picnic table is x, $144.10.

A proportion is a fraction of a total amount, and the measures are related using a rule of three.

When a product is 40% off, 100 - 40 = 60% of the original price x is paid, hence the expression for the price is:

0.6x.

In this problem, the expression is:

0.6x = 86.46

x = 86.46/0.6

x = 144.1.

Hence option D is correct.

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Answer:

1/5

Step-by-step explanation:

P(event) = # of favorable outcomes / # of total outcomes. Multiples of 5 are 5, 10, 15, 20, 25, 30, 35, 40 ... and there are 3 multiples of 5 within 1 to 15. So the # of favorable outcomes is 3. # of total outcomes is 15 because there are 15 equal-sized sections.

P = 3/15 = 1/5

The given relation is function, because the curve of y = p(x) has its exist for every x in its domain(-6, 3) and the range of the function is lies between (-1, 9).

Functions is the relationship between sets of values. e g y=f(x), for every value of x there is its exists in set of y. x is independent while Y is dependent variable.

As Clearly the shows in the graph the structure is decreasing, increasing and then decreasing. And implies, curve is continuous in its limits and for every x (-6,3) there is exist in range of y(-1, 9).

Thus, The given relation is function, and domain is (-6, 3) and the range of the function is lies between (-1, 9).

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The equivalent expressions for the costs are 8 * (14 + c) and 112 + 8c

The given parameters are:

Number of uniform = 8

Cost of each = $14

The cost of the uniforms and the shorts is then calculated as:

Cost = Number of uniforms * (Cost of uniform + Cost of short)

This gives

Cost= 8 * (14 + c)

Expand

Cost = 112 + 8c

Hence, the equivalent expressions for the costs are 8 * (14 + c) and 112 + 8c

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The points where both coordinates are integers lie within the intersection of these circles, including its boundary are 8 points.

To answer the question, we need to find the equation of the circles.

The equation of a circle with center (h, k) and radius r is

(x - h)² + (y - k)² = r²

Given that the first circle has

Its equation is

(x - 0)² + (y - 0)² = 5²

x² + y² = 25  (1)

Given that the second circle has

Its equation is

(x - 8)² + (y - 0)² = 5²

x² - 16x + 64 + y² = 25  (2)

To find the point of intersection of both circles, subtracting (1) from (2), we have

x² - 16x + 64 + y² = 25  (2)

-

x² + y² = 25  (1)

-16x + 64 = 0

-16x = -64

x = -64/-16

x = 4

Substituting x = 4 into (1), we have

x² + y² = 25

4² + y² = 25

16 + y² = 25

y² = 25 - 16

y² = 9

y = ±√9

y = ±3

So, the circles intersect at (4,-3) and (4, 3).

So, all the points that lie within their points of intersection where both coordinates are integers including their points of intersection are

So, there are 8 points.

So, all the points where both coordinates are integers lie within the intersection of these circles, including its boundary are 8 points.

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Both the computers will take 18 minutes to do the job together.

The slower computer sends all the company's email in 45 minutes.

The faster computer completes the same job in 30 minutes.

Let's take minutes t  to complete the task together.

As they complete one job, we get the following equation:

[tex]\frac{t}{45}[/tex]+[tex]\frac{t}{30}[/tex]=1

LCM of 45 and 30 is:

45 = 3 x 3 x 5

30 = 2 x 3 x 5

LCM = 2 x 3 x 3 x 5 = 90

Now, solving for t;

⇒[tex]\frac{2t+3t}{90} = 1\\\frac{5t}{90} =1\\5t=90\\[/tex]

Dividing both sides by 5;

[tex]\frac{5t}{5}=\frac{90}{5}[/tex]

We get t = 18

Hence, it will take both the computers 18 minutes to do the job together.

A company has two large computers. The slower computer can send all the company's emails in 45 minutes. The faster computer can complete the same job in 30 minutes. If both computers are working together, how long will it take them to do the job?

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Answer:

C. 2y²

Step-by-step explanation:

[tex] \sf{( {3}^{0}y) {}^{2} \times 2(xy {)}^{0} = }[/tex]

[tex]\sf{ = (\red{1} \times y)^{2} \times (2 \times \red{1}) }[/tex]

[tex]\sf{ = (y)^{2} \times 2 }[/tex]

[tex]\sf{ =2 {y}^{2} }[/tex]

Answer:

[tex]\textsf{C.} \quad 2y^2[/tex]

Step-by-step explanation:

Given:

[tex](3^0y)^2 \times 2(xy)^0[/tex]

[tex]\textsf{Apply exponent rule} \quad a=a^1:[/tex]

[tex](3^0y^1)^2 \times 2(x^1y^1)^0[/tex]

[tex]\textsf{Apply exponent rule} \quad(a^n)^c=a^{nc} \implies (a^nb^n)^c=a^{nc}b^{nc}:[/tex]

[tex]\implies 3^{(0 \times 2)}y^{(1 \times 2)} \times 2 \left(x^{(1 \times 0)}y^{(1 \times 0)} \right)[/tex]

[tex]\implies 3^0y^2 \times 2\left(x^0y^0\right)[/tex]

[tex]\textsf{Apply exponent rule} \quad a^0=1:[/tex]

[tex]\implies (1)y^2 \times 2\left(1 \times 1 \right)[/tex]

Simplify:

[tex]\implies (1)y^2 \times 2(1)[/tex]

[tex]\implies y^2 \times 2[/tex]

[tex]\implies 2y^2[/tex]

The value of x is 103.

The value of x is 59.

The value of x is 134.

The value of x is 12

The value of x is 50

The value of x is 135

The sum of angles on a straight line add up to 180 degrees.

180 - 77 = 103

180 - 121 = 59

180 - 46 = 134

12 x + 36 = 180

12x = 180 - 36

12x = 144

x = 12

24 + 3x + 6 = 180

3x = 180 - 24 - 6

3x = 150

x - 50

[tex]\frac{x}{3}[/tex] + 99 + 36 = 180

[tex]\frac{x}{3}[/tex] = 180 - 36 - 99

[tex]\frac{x}{3}[/tex] = 45

x = 45 x 3

x = 135

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33) [tex]AC=6[/tex] and [tex]BD=6[/tex], so [tex]AC/BD=1[/tex]

34) By the distance formula,

[tex]AE=\sqrt{(-2-4)^2 + (8-0)^2 }=10\\[/tex]

Also, EC = 8. So, [tex]AE/EC = 5/4[/tex].

35) [tex]\frac{8-0}{4-2}=4[/tex]

36) [tex]\frac{8-0}{4-8}=-2[/tex]

Answer:

Volume = 64

Step-by-step explanation:

To find the volume of the cube use the formula.

Formula: l×b×h

l=length

b=base

h=height

Use the information given to solve using the formula.

4×4×4=64

The volume of this cube is 64.

Hope this helps!

If not, I am sorry.

Recall the Pythagorean identity,

[tex]\sin^2(x) + \cos^2(x) = 1[/tex]

Then we can rewrite the equation as

[tex]\sin(3x) + 2 \cos^2(3x) = 1[/tex]

[tex]\sin(3x) + 2 (1 - \sin^2(3x)) = 1[/tex]

[tex]1 + \sin(3x) - 2 \sin^2(3x) = 0[/tex]

Factorize the left side.

[tex](1 + 2 \sin(3x)) (1 - \sin(3x)) = 0[/tex]

Then we have

[tex]1 + 2\sin(3x) = 0 \text{ or } 1 - \sin(3x) = 0[/tex]

[tex]\sin(3x) = -\dfrac12 \text{ or } \sin(3x) = 1[/tex]

Solve for [tex]x[/tex]. We get two families of solutions:

[tex]3x = \sin^{-1}\left(-\dfrac12\right) + 2n\pi \text{ or } 3x = \pi - \sin^{-1}\left(-\dfrac12\right) + 2n\pi[/tex]

[tex]\implies 3x = -\dfrac\pi6 + 2n\pi \text{ or } 3x = \dfrac{7\pi}6 + 2n\pi[/tex]

[tex]\implies \boxed{x = -\dfrac\pi{18} + \dfrac{2n\pi}3} \text{ or } \boxed{x = \dfrac{7\pi}{18} + \dfrac{2n\pi}3}[/tex]

and

[tex]3x = \sin^{-1}(1) + 2n\pi[/tex]

[tex]\implies 3x = \dfrac\pi2 + 2n\pi[/tex]

[tex]\implies \boxed{x = \dfrac\pi6 + \dfrac{2n\pi}3}[/tex]

(where [tex]n[/tex] is any integer)

Answer:

8x^2

Explanation:

First, do prime factorization of each of the coefficients:

32   ⇒   2^5

24   ⇒   2^3, 3

The greatest common factor (GCF) of the coefficients is 2^3 = 8.

Next, find the GCF of the variables:

x^2

x^2, y

The GCF of the variables is x^2.

Finally, multiply the GCF of the coefficients by the GCF of the variables to get:

8x^2

Answer: 4x^2

Step-by-step explanation: I took the test and got this answer right

The expression 3⁴ × 3² when rewritten in the form 3ⁿ is;  (3²)³

We want to find the expression;

3⁴ × 3²

Now, according to law of exponents, we know that;

y² × y³ = y⁽² ⁺ ³⁾

Thus, applying that exponent form to our question gives us;

3⁴ × 3² = 3⁽⁴ ⁺ ²⁾ = 3⁶

Now, we want to find the answer in the form 3ⁿ. Thus;

3⁶ = (3²)³

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Answer: 3^6 on khan academy

Step-by-step explanation: add the exponents 4 and 2 and you get the exponent 6

Answer: m=-1.

Step-by-step explanation:

[tex]Q(x)=x^2+mx-12\ \ \ \ Q(-3)=0\ \ \ \ \ m=?\\Q(-3)=(-3)^2+m*(-3)-12=0\\9-3m-12=0\\-3m-3=0\\3m=-3\ |:3\\m=-1.[/tex]

The required equation is g+300-900-900=1300.

The value of g is 2800 pounds.

The definition of an equation in algebra is a mathematical statement that demonstrates the equality of two mathematical expressions.

Initially, there is a mound of g pounds of gravel, then 300 pounds are added, and then two orders of 900 pounds are sold. At the end of the day, the mound has 1,300 pounds of gravel.

The equation for the given information is formed as follows:

g+300-900-900=1300

Solve the equation to find the value of g,

g+300-1800=1300

g-1500=1300

g=1300+1500

g=2800

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First of all, a pair of angles that are complementary means that they add up to 90 degrees. In this case, angle b + 63 degree = 90 degree (because they are complementary), which mean angle b = 90 - 63 = 27 degree.

Answer: 27°

Step-by-step explanation:

Hello.

Complementary angles add up to 90°

Therefore,

63° + ? = 90°

Now we can subtract!

90° - 63° = 27°

Hope this helps and have a nice day :)

Answer:

In slope-intercept form:

[tex]y = - \frac{1}{4} x - 5[/tex]

In standard form:

[tex]x + 4y = - 20[/tex]

Step-by-step explanation:

[tex] - 3 = - \frac{1}{4} ( - 8) + b[/tex]

[tex] - 3 = 2 + b[/tex]

[tex]b = - 5[/tex]

[tex]y = - \frac{1}{4} x - 5[/tex]

[tex] - 4y = x + 20[/tex]

[tex] - x - 4y = 20[/tex]

[tex]x + 4y = - 20[/tex]

Cubing of integers from 1 to 5 will have their cubes in the interval 1 to 200. There are such 5 positive numbers (1,2,3,4,5).

To calculate the variety of integers, locate and subtract the integers of the hobby after which subtract 1. As evidence of the concept, calculate the wide variety of integers that fall between five and 10 on more than a few lines. We realize there are four (6, 7, 8, 9).

All entire numbers are integers (and all herbal numbers are integers), however now not all integers are whole numbers or natural numbers. as an example, -five is an integer but not an entire variety or a natural quantity. An integer is an entire variety (not a fractional number) that can be fine, bad, or 0. Examples of integers are: -5, 1, 5, 8, 97, and 3,043. Examples of numbers that are not integers are: -1.forty three, 1 3/four, three.14, . 09, and five,643.1.

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The population of viruses in the dish A is 3,391 viruses.

Population density measures the amount of organisms in 1 square millimeters of a place (in this case the dish)

Population density = population / area

Population = population density x area

1.2 x 2826 = 3,391 viruses

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Answer:

The distance is 7.3 units.

Step-by-step explanation:

Two given points: (-3, 1) and (4, -1)

[tex]\sf Distance \ between \ two \ points = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2}[/tex]

Here given:

Applying the formula:

[tex]\sf d = \sqrt{(4 - (-3))^2 + (-1 - 1)^2}[/tex]

[tex]\sf d = \sqrt{(7)^2 + (-2)^2}[/tex]

[tex]\sf d = \sqrt{49 + 4}[/tex]

[tex]\sf d = \sqrt{53} \ \approx \ 7.28 \ \approx \ 7.3 \ (rounded)[/tex]

Answer:

7.3

Step-by-step explanation:

The distance of a line segment between two points (x1, y1) and (x2, y2) is given by the formula

[tex]d = \sqrt{(x2-x1)^2 + (y2-y1)^2}[/tex]

If we look at the graph,

the leftmost point of the line is at (-3, 1). Let's call this (x1, y1)

the rightmost point is at (4, -1). Let's call this (x2, y2)

Substituting these values into the distance formula gives us

[tex]d = \sqrt{(4-(-3)^2 + (1-(1)^2} \\ \\d = \sqrt{(7)^2 + (-2)^2} \\ \\d = \sqrt{49 + 4} \\\\d = \sqrt{(x2-x1)^2 + (y2-y1)^2}\\\\d = \sqrt{53} = 7.28[/tex]

Rounded to one decimal place, this is 7.3

Using the bisection concept, it is found that the measure of angle PQR is of 130º.

A bisection divides an angle into two equal angles. In this problem, the angles are given as follows:

Hence the value of x is given as follows:

3x + 5 = 2x + 25

x = 20º.

Hence the measure of angle PQR is given as follows:

m<PQR = 3x + 5 + 2x + 25 = 5x + 30 = 5 x 20º + 30º = 130º.

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A scale factor is a contracting scale such that x < 1, where x is the scale factor.

For example, if the scale factor x is less than 1, then it must be decreasing in size, and thus be contracting in size.

But, if the scale factor is greater than 1, then it is expanding in size and increasing.

1) -5 is expanding. It is greater than one.

2) -1/4 is contracting. It is less than one.

3) 3.5 is expanding. It is greater than one.

4) 6/7 is contracting. It is less than one.

Answer:

False, False, True

Step-by-step explanation:

Matrix addition or subtraction can only be performed on two matrices if they are the same dimensions.  The number of rows for both must match, and the number of columns for both must match.  If either is different, they cannot be combined with addition or subtraction.

So, the first two questions are false because the first number from each pair doesn't match (and neither does the second number from each pair, but we just need one mismatch for it to fail).

The last question is true because both of the first numbers are a 3, and both of the second numbers are a 4.

Step-by-step explanation:

ATTACHED IS THE SOLUTION!!

Answer:

y is the variable in that expression.

Answer:  36 square units

Work Shown:

area = base*height/2

area = 12*6/2

area = 72/2

area = 36

The base and height are always perpendicular to each other. The triangle formula above applies to obtuse triangles, as well as any other type of triangle. It might help to rotate the triangle so that side IJ is at the bottom rather than the top.