Out of the 21 students in Mrs. Clark's class, 5of the class are boys and of the class are girls. How many students in the
class are girls and how many are boys?
(SHOW WORK)

Answer:

Step-by-step explanation:

[tex]3(x-4)-5=x-3\qquad\text{use the distributive property}\\3x-12-5=x-3\\3x-17=x-3\qquad\text{add 17 to both sides}\\3x-17+17=x-3+17\\3x=x+14\qquad\text{subtract}\ x\ \text{from both sides}\\3x-x=x-x+14\\2x=14\qquad\text{divide both sides by 2}\\\dfrac{2x}{2}=\dfrac{14}{2}\\\\x=7[/tex]

Answer:

540

Step-by-step explanation:

f(x) = x(x - 1)

g(x) = 3x

(f* g)(x) = x(x - 1) 3x

            = (x^2 -x) * 3x

            = 3x^3 -3x^2

            =3x^2(x-1)

Let x = 6

(f* g)(6) = 3*6^2( 6-1)

            =   3*36 *5

                   540        

Answer:

540

Step-by-step explanation:

(f*g)(6)=f(6)*g(6).

Now we need to find f(6) and g(6).  Once we find their values we multiply them.

f(6) means to replace x in x(x-1) with 6:

6(6-1)

6(5)

30

So f(6)=30.

g(6) means to replace x in 3x with 6:

3(6)

18

So g(6)=18.

(f*g)(6)=f(6)*g(6)=30*18=540.

Answer:

6 which is none of your answers.

Are you sure your function is right?

Is value to plug in x=-8?

Step-by-step explanation:

To find the value of the function at x=-8, you replace x with -8 in the function.

g(x)=3(x+10)

g(-8)=3(-8+10)

g(-8)=3(2)

g(-8)=6

g(-8) = 6.

The value of g(x) = 3(x + 10) when x = -8 is:

Substituting x = -8 in the function g(x)

g(-8) = 3 (-8+ 10)

Solving the operation in the  parenthesis

g(-8) = 3 (-8 + 10)

g(-8) = 3 (2)

Solving the multiplication

g(-8) = 6

The correct answer is: True

A parallelogram means that the lines will not intersect.

As you can see the ^ on both sides witch indicates that they will not touch.

Hope this helps! :3

The figure Hijk is definitely a parallelogram is true.

That quadrilateral in which opposite sides are parallel is called a parallelogram.

Thus, a parallelogram is always a quadrilateral but a quadrilateral can or cannot be a parallelogram.

We are given that;

The figure of parallelogram

Now,

IH is parallel to JK

IJ is parallel to HK

Angle H and angle J are equal by alternate interior angles

Therefore, by given parallelogram the answer will be true.

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Answer:

a,b

Step-by-step explanation:

in the rectangle when bisected

if mid point is taken as O

BO=OD

AO=OC

X=2a

mid point of X=2a/2=a

Y=2b

y mid point = b

The midpoint of BD will be ( a,b ) so option (C) will be correct.

A line section that can connect two places is referred to as a segment.

In other terms, a line segment is merely a section of a larger, straight line that extends indefinitely in both directions.

The line is here! It extends endlessly in both directions and has no beginning or conclusion.

The midpoint of a line associated with two coordinates is given by

(x₁ + x₂)/2 and (y₁ + y₂)/2

Given that B (0,2b) D (2a,0)

So midpoint

(0 + 2a)/2 and (2b + 0)/2

⇒ (a,b) so the midpoint will be this.

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Answer:

3.2

Step-by-step explanation:

If there are 2 secont lines intersecting inside a circle like the picture shown, then the theorem tells us that "the product of 2 segments of one secant line is equal to the product of 2 segments of other secant line"

Thus, we can say that:

x * 10 = 8 * 4

10x = 32

x = 32/10

x = 3.2

Feel free to ask for any doubts.

Please mark Brainliest if this helps!

Divide the number of cans by the number of sheets to find the constant.

36 cans / 2 sheets = 18 cans per sheet.

180 cans / 10 sheets = 18 cans per sheet.

The proportionality constant is 18 cans per sheet.

Answer:

The graph in the attached figure

Step-by-step explanation:

we have

[tex]y=2x^{2}+6x+3[/tex]

This is the equation of a vertical parabola open up

The vertex is a minimum

Convert to vertex form

Complete squares

[tex]y-3=2x^{2}+6x[/tex]

Factor the leading coefficient

[tex]y-3=2(x^{2}+3x)[/tex]

[tex]y-3+4.5=2(x^{2}+3x+2.25)[/tex]

[tex]y+1.5=2(x^{2}+3x+2.25)[/tex]

Rewrite as perfect squares

[tex]y+1.5=2(x+1.5)^{2}[/tex]

The vertex is the point (-1.5,-1.5)

Find the zeros of the function

For y=0

[tex]2(x+1.5)^{2}=1.5[/tex]

[tex](x+1.5)^{2}=3/4[/tex]

square root both sides

[tex]x+\frac{3}{2} =(+/-)\frac{\sqrt{3}}{2}[/tex]

[tex]x=-\frac{3}{2}(+/-)\frac{\sqrt{3}}{2}[/tex]

[tex]x=-\frac{3}{2}(+)\frac{\sqrt{3}}{2}=\frac{-3+\sqrt{3}}{2}=-0.634[/tex]

[tex]x=-\frac{3}{2}(-)\frac{\sqrt{3}}{2}=\frac{-3-\sqrt{3}}{2}=-2.366[/tex]

Find the y-intercept

For x=0

[tex]y=3[/tex]

The y-intercept is the point (0,3)

therefore

The graph in the attached figure

Answer: graph a

Step-by-step explanation: a p e x

Answer:

Step-by-step explanation:

There is not possible solution in the real number system or the complex field.

Oddly, before I answer your question, I would point out that the equation given is a perfectly legitimate equation in some computer languages. It has the meaning of

But that is not what you are being asked about.

The blank you could put in 4

so 4 = 4 - 5

4 = - 1

The second blank will give you the result of 4 = - 1 which can't be true in a million years.

Answer:

-6

Step-by-step explanation:

The average rate of a function f(x) on the interval from x=a to x=b is [tex]\frac{f(b)-f(a)}{b-a}[/tex].

So in the problem you have from [tex]x=2[/tex] to [tex]x=4[/tex].

The average rate of the function from x=2 to x=4 is

[tex]\frac{f(4)-f(2)}{4-2}=\frac{f(4)-f(2)}{2}[/tex].

Now we need to find f(4) and f(2).

f(4) means what is the y-coordinate that corresponds to x=4 on the curve.

f(4)=-15 since the ordered pair at x=4 is (4,-15).

f(2) means what is the y-coordinate that corresponds to x=2 on the curve.

f(2)=-3 since the ordered pair at x=2 is (2,-3).

So let's plug in those values:

[tex]\frac{f(4)-f(2)}{4-2}=\frac{-15-(-3))}{2}[/tex].

Now we just simplify:

[tex]\frac{-15+3}{2}[/tex]

[tex]\frac{-12}{2}[/tex]

[tex]-6[/tex]

Answer:

Option C is correct.

Step-by-step explanation:

The rate of change can be found by finding the slope of given ordered pairs.

y₂=12, y₁=7,x₂=1,x₁=0

rate of change = y₂-y₁/x₂-x₁

rate of change = 12-7/1-0

rate of change = 5/1 = 5

Now considering next two points,

y₂=17, y₁=7,x₂=2,x₁=1

rate of change = y₂-y₁/x₂-x₁

rate of change = 17-12/2-1

rate of change = 5/1 = 5

So, the rate of change for this set of ordered pairs is 5.

Option C is correct.

Ration expressions cause excluded values wherever the denominator equals zero.

So, for any expression like

[tex]h(x)=\dfrac{f(x)}{g(x)}[/tex]

-5 is an excluded value if [tex]g(-5)=0[/tex]

For example, the simplest one would be

[tex]h(x) = \dfrac{1}{x+5}[/tex]

In fact, if you try to evaluate this function at -5, you'd have

[tex]h(-5)=\dfrac{1}{5+5}=\dfrac{1}{0}[/tex]

which is undefined, and thus you can't evaluate the function, and thus -5 is an excluded value.

Answer:

6/x+5

Step-by-step explanation:

Answer:

10x

Step-by-step explanation:

The greatest common factor of the polynomial 30x³ - 20x is 10x.

Option B is the correct answer.

We have,

To find the greatest common factor (GCF) of the polynomial

30x³ - 20x, we need to determine the largest expression that can be factored out from both terms.

Let's look at the coefficients first.

The coefficients of the terms are 30 and -20.

Both numbers are divisible by 10, so we can factor out 10.

Now let's consider the variable, x. In the first term, we have x³, and in the second term, we have x.

The lowest power of x that appears in both terms is x, so we can factor out x.

Putting it together, we can factor out the GCF of 10x:

GCF(30x³ - 20x) = 10x

Therefore,

The greatest common factor of the polynomial 30x³ - 20x is 10x.

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Answer:

4960.

Try that, And good luck

Answer:

lwh = 4960

Step-by-step explanation:

To solve for volume, we use the formula V = lwh. Let's plug in our values:

lwh = l*w*h

      = 8*31*20

      = 4960

Answer:

a

Step-by-step explanation:

Given:

triangle XYZ  is rotated by a composition of 50°+40°=90° both about point y

Now when a geometrical figure is rotated by any degree then its shape or size does not change and remain same.

As the triangle is rotated clockwise by 90  degrees about point y then diagram attached is formed .

option a is correct.

Answer:

The correct option is A.

Step-by-step explanation:

If the direct of rotation is not mentioned, then it is consider as counterclockwise rotation.

It is given that triangle XYZ rotated 50 degrees and a 40 degrees, both about point Y.

It means the figure triangle XYZ rotated 90 degrees counterclockwise  about the point Y.

In option A, triangle XYZ rotated 90 degrees counterclockwise  about the point Y.

In option B, triangle XYZ rotated 180 degrees counterclockwise about the point Y.

In option C, triangle XYZ rotated 270 degrees counterclockwise  about the point Y.

In option D, triangle XYZ rotated 360 degrees counterclockwise  about the point Y.

Therefore the correct option is A.

First, to get applied by the fraction rule: [tex]\displaystyle\frac{3^4}{1}[/tex], then, the applied rule [tex]\displaystyle\frac{a}{1}=a[/tex]. Finally, simplify to find the answer. [tex]\displaystyle3^4=3*3*3*3=81[/tex], the correct answer is 81. I hope this will help you. Have a wonderful day!

[tex]\left(\dfrac{1}{3}\right)^{-4}=3^4=81[/tex]

Answer:

[tex]\frac{(x--3)^2}{49} -\frac{(y-6)^2}{32}=1[/tex]

Step-by-step explanation:

The standard equation of a horizontal hyperbola with center (h,k) is

[tex]\frac{(x-h)^2}{a^2}-\frac{(y-k)^2}{b^2}=1[/tex]

The given hyperbola has vertices at (–10, 6) and (4, 6).

The length of its major axis is [tex]2a=|4--10|[/tex].

[tex]\implies 2a=|14|[/tex]

[tex]\implies 2a=14[/tex]

[tex]\implies a=7[/tex]

The center is the midpoint of the vertices (–10, 6) and (4, 6).

The center is [tex](\frac{-10+4}{2},\frac{6+6}{2}=(-3,6)[/tex]

We need to use the relation [tex]a^2+b^2=c^2[/tex] to find [tex]b^2[/tex].

The c-value is the distance from the center (-3,6) to one of the foci (6,6)

[tex]c=|6--3|=9[/tex]

[tex]\implies 7^2+b^2=9^2[/tex]

[tex]\implies b^2=9^2-7^2[/tex]

[tex]\implies b^2=81-49[/tex]

[tex]\implies b^2=32[/tex]

We substitute these values into the standard equation of the hyperbola to obtain:

[tex]\frac{(x--3)^2}{7^2} - \frac{(y-6)^2}{32}=1[/tex]

[tex]\frac{(x+3)^2}{49} -\frac{(y-6)^2}{32}=1[/tex]

Final answer:

The final cost of the shoes after a 30% discount and a 6.5% sales tax is $67.08, with each step of the calculation rounding to the nearest cent.

Explanation:

Calculating Final Price with Discount and Sales Tax

To calculate the final cost of a pair of shoes with an original price of $89.99 and a discount of 30%, along with an additional 6.5% sales tax, follow these steps:

The final cost of the shoes after applying the discount and including sales tax is $67.08.

Answer:

x=5

Step-by-step explanation:

If the equation is:

3(x+1)=7(x-2) -3

Solution:

Multiply (x+1) by 3 and (x-2) by 7

3x+3 = 7x-14 -3

3x+3 = 7x -17

Now combine the like terms:

3+17 = 7x-3x

20 = 4x

Now divide both the terms by 4

20/4 = 4x/4

5 = x

You can write it as x=5

Thus the value of x is 5 ....

Answer:

It is 100. You round the 6 to the 9 which makes the 9 round the 99 which makes it 100.

Answer:

x^2+11x+10

or

(x+1)(x+10) since you can factor x^2+11x+10

Step-by-step explanation:

Let's do synthetic division.

We are dividing by x+2, so -2 will be on the outside. Like this:

-2 |         1          13          32         20

   |                     -2        -22         -20

   |___________________________

             1          11           10            0

The remainder is 0, so (x+2) is indeed a factor of x^3+13x^2+32x+20.

The other factor we found by doing this is (x^2+11x+10).

You can find more factors by factoring x^2+11x+10.

Two numbers that multiply to be 10 and add to be 11 is 10 and 1 so the factored form of x^2+11x+10 is (x+10)(x+1).

Answer:

In picture.

Step-by-step explanation:

I'm going to look at y=3x+2 first.

This is a linear equation in slope-intercept form.

Slope-intercept form is y=mx+b.

It is called slope-intercept form because it tells us m, the slope, and b ,the y-intercept.

So I'm going to draw a point at 2 on the y-axis (because 2 is our y-intercept).

From that point, I'm going to count up 3 and right once because our slope is 3 (which is 3/1; slope=rise/run).  So my next point will be at (1,5).

Now let's go back to y>3x+2.

Since it says y>, then we shade above.

If it had said y<, then we shade below.

There is only one more thing to consider, and that is the lack of or there of of the equal sign.

If the equal sign part is there, your line will be solid.

If the equal sign is not there, your line will be dashed or broken.

Answer:

Step-by-step explanation:

Answer:

[tex]\frac{\pi }{4}[/tex]

Step-by-step explanation:

To convert from degrees to radians

radian measure = degree measure × [tex]\frac{\pi }{180}[/tex]

given degree measure = 45°, then

radian = 45 × [tex]\frac{\pi }{180}[/tex] ( divide 45 and 180 by 45 )

           = [tex]\frac{\pi }{4}[/tex]

Answer:

π/4 radians.

Step-by-step explanation:

To convert to radians we multiply degrees by π/180.

So 45 degrees = 45 * π / 180

= π/4 radians.

Answer:

y-3=2(x-1)

Step-by-step explanation:

So it looks like your line goes through (2,5) and (1,3) based on what you have said.

Looking at 5 to 3, that is down 2.

Locking at 2 to 1, that is left 1.

So the slope is -2/-1 =2/1=2.

Plug in the (x1,y1)=(1,3) and slope=m=2.

So using point slope form we have y-3=2(x-1).

Answer:

Step 3

Step-by-step explanation:

Just did the test

Answer:

x = - 5, x = - 1

Step-by-step explanation:

To find the x- intercepts let f(x) = 0, that is

x² + 6x + 5 = 0 ← in standard form

Consider the factors of the constant term (+ 5) which sum to give the coefficient of the x- term ( + 6)

The factors are + 5 and + 1, since

5 × 1 = 5 and 5 + 1 = + 6, hence

(x + 5)(x + 1) = 0 ← in factored form

Equate each factor to zero and solve for x

x + 5 = 0 ⇒ x = - 5 ⇒ (- 5, 0 )

x + 1 = 0 ⇒ x = - 1 ⇒ (- 1, 0)

Answer:

-5 -1

Step-by-step explanation:

on edge

Answer:

1001 ways

Step-by-step explanation:

Total number of people who applied for the job = 8 + 6 = 14

Number of people to be chosen = 4

This is a combination problem because the order of selection does not matter. A group selection involves the combinations. So here we have to find the combinations of 14 people taken 4 at a time. The formula for the combination is:

[tex]^{n}C_{r} = \frac{n!}{r!(n-r)!}[/tex]

Here, n is the total number of objects which is 14 in this case.

r is the number of objects to be chosen which is 4 in this case.

Using these values, we get:

[tex]^{14}C_{4}=\frac{14!}{4!(14-4)!}\\\\ = \frac{14!}{4! \times 10!}\\\\ =1001[/tex]

Thus, there are 1001 ways to select 4 applicants from 8 men and 6 women for the second interview.

bearing in mind that standard form for a linear equation means

• all coefficients must be integers, no fractions

• only the constant on the right-hand-side

• all variables on the left-hand-side, sorted

• "x" must not have a negative coefficient

[tex]\bf (\stackrel{x_1}{-3}~,~\stackrel{y_1}{2})\qquad (\stackrel{x_2}{2}~,~\stackrel{y_2}{1}) \\\\\\ slope = m\implies \cfrac{\stackrel{rise}{ y_2- y_1}}{\stackrel{run}{ x_2- x_1}}\implies \cfrac{1-2}{2-(-3)}\implies \cfrac{1-2}{2+3}\implies -\cfrac{1}{5} \\\\\\ \begin{array}{|c|ll} \cline{1-1} \textit{point-slope form}\\ \cline{1-1} \\ y-y_1=m(x-x_1) \\\\ \cline{1-1} \end{array}\implies y-2=-\cfrac{1}{5}[x-(-3)]\implies y-2=-\cfrac{1}{5}(x+3)[/tex]

[tex]\bf y-2=-\cfrac{1}{5}x-\cfrac{3}{5}\implies y=-\cfrac{1}{5}x-\cfrac{3}{5}+2\implies y=-\cfrac{1}{5}x+\cfrac{7}{5} \\\\\\ \stackrel{\textit{multiplying both sides by }\stackrel{LCD}{5}}{5(y)=5\left( -\cfrac{1}{5}x+\cfrac{7}{5} \right)}\implies 5y=-x+7\implies \blacktriangleright x+5y=7 \blacktriangleleft[/tex]

The equation of the line passing through points (-3,2) and (2,15) is calculated using the point-slope formula after calculating the slope. The derived equation is y = 2.6x + 7.8.

The question is asking to find the equation of the line that passes through two given points: (-3,2) and (2,15). To tackle this, firstly we need to calculate the slope (m) of the line, which is given by the formula: (y2 - y1) / (x2 - x1). Secondly, we apply the point-slope formula, y - y1 = m(x - x1), where (x1, y1) can be either point.

Now, calculating the slope using the given points, we find (15-2) / (2- (-3)) equals to 13/5 or 2.6. Next, we use the point-slope formula to write the equation. If using point (-3,2) we find y - 2 = 2.6 (x - (-3)). Thus, the equation for the line that passes through (-3,2) and (2,15) is y = 2.6x + 7.8 after simplifying the equation.

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Answer:

Function.

Step-by-step explanation:

A relation is a function every x that in your domain only gets assigned to exactly one number in your range.

Basically if you have a set of points and you see that the same x is being used more than once, then it isn't a function (unless for some reason they repeated the same point).

So the x's I see in the order that your points are is 3,1,-1,-2.  All of these x's are different so it is a function.

Answer: Yes, it is a function.

Step-by-step explanation:

Usually we denote the input value as 'x' and the output value as 'y'.

The given relation: {(3, −5), (1, 2), (−1, −4), (−2, 2)}

Here , each input value corresponds an unique output value.

Therefore , the given relation is a function.