Please Explain step-by-step

An algebra class contains 30 students. Forty
percent of the students in the class are girls. How
many boys are in the class?

Answer:

EF = 2 units

Step-by-step explanation:

Given:

Line segment DF and point E on it.

DF = 11 unit

DE = 9 Unit

Find:

EF

Computation:

We know that,

DF = DE + EF

11 = 9 + EF

EF = 11-9

EF = 2 units

Answer:

9

Step-by-step explanation:

x = c - b/a

x = 10 - 2/2

x = 10 - 1

x = 9

Answer:

x = c - b (divided by) a

Step-by-step explanation:

x = 10 - 2over2

x = 10 - 1

x = 9

try 18/2 since that part is a fraction.

Answer:

18 inches by 36 inches.

Step-by-step explanation:

Since we have given that

The generic version was basedOn the brand name and was 2/3

And given Dimensions of generic version is given by 12inches ×24inches

If we use the first dimensions of 12inches we have

12=2/3 × brand

12×3/2 = brand

=18inches= brand

we use the first dimensions of 24 inches we have

24=2/3 × brand

24×3/2 = brand

=36 inches= brand

brand= 36 inches

Therefore,the dimensions of brand name will be 18 inches by 36 inches.

Answer:

3(2x-5)(x+2)

Step-by-step explanation:

Factor out the 3.

3(2x²-x-10)

Factor the remaining.

3(2x-5)(x+2)

(I don‘t know what grid they’re talking about.)

Answer:

. an=4(2n−1)

Step-by-step explanation:

Answer: he will save $42.50

Step-by-step explanation:

45÷3=15

45÷2+35=57.50

57.50-15= $42.50

Answer:

Step-by-step explanation:

Since the figure above is a right angled triangle we can use trigonometric ratios to find x

To find x we use sine

sin ∅ = opposite / hypotenuse

From the question

The hypotenuse is 12

The opposite is x

Substitute the values into the above formula and solve for x

That's

[tex] \sin(60) = \frac{x}{12} [/tex]

[tex] \sin(60) = \frac{ \sqrt{3} }{2} [/tex]

[tex]x = \frac{ \sqrt{3} }{2} \times 12[/tex]

We have the final answer as

Hope this helps you

Answer:

Factoring is finding what to multiply to find an expression. It is like splitting expression into a multiplication of simplified expression.

Greatest common factor or GCF of two numbers is the largest number that divides evenly in both numbers, GCF works the same in polynomials, which divide the expression evenly .

Factoring take away the multiplication, to factorize a polynomial it means take apart what  is multiplied. the best example is a²+b²+2ab ( multiplied)

factorize :(a+b)(a+b)   take apart what is multiplied

x²-25  =(x+5)(x-5)

3x²-12x-15 = 3(x²-4x-5)  GCF=3

3(x-5)(x+1)

x³+2x²+3x+6  (x+2) common factor

(x+2)(x²+3)

the key features are the vertex, axis of symmetry, x and y intercept

parabola : y=ax²+bx+c

ex: 3x²-12x-15

find vertex (h,k)

h=-b/2a =-(-12)/2(3)=2

k=f(h)=f(2)=3(2)²-12(2)-15

k=12-24-15=-27

vertex=(2,-27)

x intercept is when the graph =0 (y=0)

y intercept when x=0 then y= the constant c and where the graph cross the y axis

axis of symmetry is the x of the vertex: is a line about which a parabola is symmetrical and vertical when the axis of symmetric is vertical.

factor a polynomial helps us understand more about equations,factoring helps us rewrite the polynomial into simpler expression.

example from real life:

A homeowner has a back yard and wants to turn it to garden beds so he can plant his vegetables, he wants to fill it with dirt he needs 240 cubic feet to fill it  the length is 4 feet than the width , and the height is 4

solve:

length=W+4

height=1/3 w

V=length* width* height

240=(w+4)(w)(4)

351= 4w²+16w

4w²+16w-240=0

take 4 as common factor

4(w²+4w-60)

now factorize:

4(w-6)(w+10)=0

Answer:

[tex]\large \boxed{\sf \bf \ \ y=3x^2-6x-1 \ \ }[/tex]

Step-by-step explanation:

Hello, please consider the following.

We can read from the graph that the vertex is (1,-4) , it means that the equation is, a being a real number.

[tex]y=a(x-1)^2-4[/tex]

And the point (0,-1) is on the graph so we can write.

[tex]a\cdot 1^2-4=-1 \\\\a-4+4=-1+4\\\\a = 3[/tex]

So the equation is.

[tex]y=3(x-1)^2-4\\\\=3(x^2-2x+1)-4\\\\=3x^2-6x+3-4\\\\=3x^2-6x-1\\\\=\boxed{3}x^2\boxed{-6}x\boxed{-1}[/tex]

Hope this helps.

Do not hesitate if you need further explanation.

Thank you

Answer:

[tex]y=3x^{2} -6x-1[/tex]

Step-by-step explanation:

Problem 2

Josh forgot to apply the square root to 16 when he went from [tex](x-3)^2 = 16[/tex] to [tex]x-3 = 16[/tex]

Also, he forgot about the plus/minus.

This is what his steps should look like

[tex]x^2 - 6x - 7 = 0\\\\x^2 - 6x = 7\\\\x^2 - 6x +9= 7+9\\\\(x-3)^2= 16\\\\x-3= \pm\sqrt{16}\\\\x-3= 4 \text{ or } x-3= -4\\\\x= 7 \text{ or } x= -1\\\\[/tex]

There are two solutions and they are x = 7 or x = -1. To check each solution, you plug it back into the original equation

Let's try out x = 7

x^2 - 6x - 7 = 0

7^2 - 6(7) - 7 = 0

49 - 42 - 7 = 0

0 = 0 ... solution x = 7 is confirmed. I'll let you check x = -1

====================================================

Problem 3

We will have

a = 1, b = -4, c = 3

plugged into the quadratic formula below to get...

[tex]x = \frac{-b\pm\sqrt{b^2-4ac}}{2a}\\\\x = \frac{-(-4)\pm\sqrt{(-4)^2-4(1)(3)}}{2(1)}\\\\x = \frac{4\pm\sqrt{4}}{2}\\\\x = \frac{4\pm2}{2}\\\\x = \frac{4+2}{2} \ \text{ or } \ x = \frac{4-2}{2}\\\\x = \frac{6}{2} \ \text{ or } \ x = \frac{2}{2}\\\\x = 3 \ \text{ or } \ x = 1\\\\[/tex]

The two solutions are x = 3 or x = 1. You would check this by plugging x = 3 back into the original expression x^2 - 4x + 3. The result should be zero. The same applies to x = 1 as well.

Answer:

y = 5/2x - 5

Step-by-step explanation:

You have to rearrange the equation so that it is equal to y.

5x - 2y = 10

(5x - 2y) - 5x = -5x + 10

-2y = -5x + 10

(-2y)/-2 = (-5x)/-2 + (10)/-2

y = 5/2x - 5

Answer:

|BC| = 9.4 m

Step-by-step explanation:

Angle bxy = angle abc (reason, corresponding angles)

Angle ayx = angle acb ( reason , corresponding angles)

So angle abc= 62°

Angle acb = 51°

Angle acb + and + bac = 180 (reason, sum of angles in a triangle)

Anlge bac = 180-62-51

Angle bac= 180-113

Angle back = 67°

Using sine formula

|BC| /sin 67 = 9/sin 62

|BC| = sin 67 *9/sin62

|BC| = 9.4 m

Answer:

1) x²+4x=2700

2) 50x50

Step-by-step explanation:

Pony area = x²

line-up area=4x

x²+4x=2700

x²+4x-2700=0

(x-50)(x+54)

So x= 50 or -54.  Since it can’t be a negative number, it must be 50.

CHECK:

Square = 50x50 = 2500

Line up area = 50x4 = 200

2500+200=2700 YES

Answer: A. mean: 10, median: 8, mode: none

Step-by-step explanation:

Given : The number of patients treated at Dr. Jason's dentist office each day was recorded for seven days: 3, 8, 11, 22, 17, 5, 4.

First we arrange it order.

3, 4, 5, 8, 11, 17, 22

Mean = (Sum of observations) ÷ (Number of observations)

Number of observations = 7

Sum of observations = 3+4+5+8+11+17+22 =70

Mean = 70 ÷7 = 10

Median = Middle-most value

= 8

Mode = Most repeatted value

= none

Hence, the mean, median, and mode for this sample = A. mean: 10, median: 8, mode: none

Answer:

t5 = 1250

Step-by-step explanation:

Each term is derived by multiplying the previous term by 2.5

t2 = t1 * 2.5

t2 = 32 * 2.5

t2 = 80

===========

tn = a*b^(n - 1)

t3 = 32*2.5^2

t3 = 200

That's just to test the formula. It does work.

===============

t5 = 32*2.5^(5 -1)

t5 = 32*2.5^4

t5 = 1250

Answer:

[tex]radius = \sqrt{13}[/tex] or [tex]radius = 3.61[/tex]

Step-by-step explanation:

Given

Points:

A(-3,2) and B(-2,3)

Required

Determine the radius of the circle

First, we have to determine the center of the circle;

Since the circle has its center on the x axis; the coordinates of the center is;

[tex]Center = (x,0)[/tex]

Next is to determine the value of x through the formula of radius;

[tex]radius = \sqrt{(x_1 - x)^2 + (y_1 - y)^2} = \sqrt{(x_2 - x)^2 + (y_2 - y)^2}[/tex]

Considering the given points

[tex]A(x_1,y_1) = A(-3,2)[/tex]

[tex]B(x_2,y_2) = B(-2,3)[/tex]

[tex]Center(x,y) =Center (x,0)[/tex]

Substitute values for [tex]x,y,x_1,y_1,x_2,y_2[/tex] in the above formula

We have:

[tex]\sqrt{(-3 - x)^2 + (2 - 0)^2} = \sqrt{(-2 - x)^2 + (3 - 0)^2}[/tex]

Evaluate the brackets

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

[tex]\sqrt{(-(3 + x))^2 + 4} = \sqrt{(-(2 + x))^2 + 9}[/tex]

Eva;uate all squares

[tex]\sqrt{(-(3 + x))(-(3 + x)) + 4} = \sqrt{(-(2 + x))(-(2 + x)) + 9}[/tex]

[tex]\sqrt{(3 + x)(3 + x) + 4} = \sqrt{(2 + x)(2 + x) + 9}[/tex]

Take square of both sides

[tex](3 + x)(3 + x) + 4 = (2 + x)(2 + x) + 9[/tex]

Evaluate the brackets

[tex]3(3 + x) +x(3 + x) + 4 = 2(2 + x) +x(2 + x) + 9[/tex]

[tex]9 + 3x +3x + x^2 + 4 = 4 + 2x +2x + x^2 + 9[/tex]

[tex]9 + 6x + x^2 + 4 = 4 + 4x + x^2 + 9[/tex]

Collect Like Terms

[tex]6x -4x + x^2 -x^2 = 4 -4 + 9 - 9[/tex]

[tex]2x = 0[/tex]

Divide both sides by 2

[tex]x = 0[/tex]

This implies the the center of the circle is

[tex]Center = (x,0)[/tex]

Substitute 0 for x

[tex]Center = (0,0)[/tex]

Substitute 0 for x and y in any of the radius formula

[tex]radius = \sqrt{(x_1 - 0)^2 + (y_1 - 0)^2}[/tex]

[tex]radius = \sqrt{(x_1)^2 + (y_1)^2}[/tex]

Considering that we used x1 and y1;

In this case we have that; [tex]A(x_1,y_1) = A(-3,2)[/tex]

Substitute -3 for x1 and 2 for y1

[tex]radius = \sqrt{(-3)^2 + (2)^2}[/tex]

[tex]radius = \sqrt{13}[/tex]

[tex]radius = 3.61[/tex] ---Approximated

Answer:

( 6,6) is outside

Step-by-step explanation:

(x - 2)^2 + (y - 1)^2 = 25

This is of the form

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

where ( h,k) is the center and r is the radius

(x - 2)^2 + (y - 1)^2 = 5^2

The center is at ( 2,1) and the radius is 5

P(0,5), Q(2,2) R(5,-2), and S(6,6)

Adding the radius to the y coordinate gives us 6 so the only point with a y coordinate on the circle is ( 2,6)

( 6,6) is outside the circle

Answer:

B. Yes; diagonals of a parallelogram bisect each other.

Step-by-step explanation:

The diagonals of a parallelogram bisect each other. If the diagonals of a quadrilateral bisect each other, the quadrilateral is a parallelogram.

Answer: B. Yes; diagonals of a parallelogram bisect each other.

If AE=EC and BE=DE then quadrilateral ABCD is a parallelogram because  diagonals of parallelogram bisect each other.

A parallelogram is a 2 dimensional figure whose opposite sides are equal to each other and parallel to each other. Area of parallelogram is base*height.

To be parallelogram ΔAEB and ΔEDC should be congruent.

Angle AEB= Angle DEC

AE=EC

DE=EB

so both triangles are congruent by side, side, angle.

Similarly AE=EC , DE=EB and vertical angles AED= Vertical angle BEC.

Therefore triangle AED and BEC are congruent and that makes all their corresponding sides are also congruent.

And AB=DC.

Hence both pairs of opposite sides of a quadrilateral are congruent ,then the quadrilateral is a parallelogram.

Learn more about parallelogram at https://brainly.com/question/970600

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Answer:

126

Step-by-step explanation:

Let x be the missing length

The triangles are similar:

● UE/140 = 45/x

From the graph we deduce that:

● UE = 140 - 90 = 50

Replace UE by its value

● 50/ 140 = 45/x

Switch x and 50

● x / 140 = 45/50

45/50 is 9/10 wich is 0.9

● x/140 = 0.9

Multiply 0.9 by 140

● x = 140 × 0.9

● x = 126

Answer:

I think its c 126

Step-by-step explanation:

Answer:

Micheal sent 40 messages, Christine sent 20, and Dave sent 11.

Step-by-step explanation:

Christine, Dale, and Michael sent a total of 71 messages

C + D + M = 71

Dale sent 9 fewer messages than Christine

D = C - 9

Michael sent 2 times as many messages as Christine

M = 2C

Plug-in the numbers.

C + C - 9 + 2C = 71

4C - 9 = 71

4C = 80

C = 20

Now, plug in to other equations for other results.

D = (20) - 9

D = 11

M = 2(20)

M = 40

Micheal sent 40 messages, Christine sent 20, and Dave sent 11.

Verify?

40 + 20 + 11 = 71.

Answer:

The slope is -2, the y-intercept is 12

Step-by-step explanation:

[tex] slope (m) = \frac{y_2 - y_1}{x_2 - x_1} [/tex]

Chose any two coordinates pair. Let's make use of:

[tex] (0, 12) = (x_1, y_1) [/tex]

[tex] (3, 6) = (x_2, y_2) [/tex]

Thus,

[tex] slope (m) = \frac{6 - 12}{3 - 0} [/tex]

[tex] slope (m) = \frac{-6}{3} [/tex]

[tex] slope (m) = -2 [/tex]

Using the slope-intercept equation, find the y-intercept, b, as follows:

[tex] y = mx + b [/tex]

Use any coordinate pair as x and y, then solve for b.

Let's use (3, 6)

[tex] 6 = (-2)(3) + b [/tex]

[tex] 6 = -6 + b [/tex]

Add 6 to both sides

[tex] 6 + 6 = - 6 + b + 6 [/tex]

[tex] 12 = b [/tex]

The slope (m) of the linear function that is represented by the table is -2, while the y-intercept (b), is 12.

Answer:

The slope is –2, and the y-intercept is 12.

Step-by-step explanation:

I used it and got it right

Answer:

Step-by-step explanation:

[tex](1,5)=(x_1,y_1)\\(9,0) = (x_2,y_2)\\\\d = \sqrt{(x_2-x_1)^2+(y_2-y_1)^2} \\\\d = \sqrt{(9-1)^2 +(0-5)^2}\\ \\d = \sqrt{(8)^2+(-5)^2}\\ \\d = \sqrt{64+25}\\ \\d = \sqrt{89}\\[/tex]

The distance between the points (1, 5) and (9, 0) is √89 units.

In Mathematics and Geometry, the distance between two (2) end points that are on a coordinate plane can be calculated by using the following mathematical equation:

Distance = √[(x₂ - x₁)² + (y₂ - y₁)²]

Where:

x and y represent the data points (coordinates) on a cartesian coordinate.

By substituting the given end points (1, 5) and (9, 0) into the distance formula, we have the following;

Distance = √[(9 - 1)² + (0 - 5)²]

Distance = √[(8)² + (-5)²]

Distance = √[64 + 25]

Distance = √89 units.

Read more on distance here: brainly.com/question/12470464

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Answer:

D. 4x+5x=180

Step-by-step explanation:

Answer:

D. 4x + 5x = 180

Step-by-step explanation:

The two angles form a straight line and a straight line equals 180°. So, the sum of the two angles has to equal 180°.

4x + 5x = 180

9x = 180

x = 20°

Hope that helps.

Answer:

1522km^2

Step-by-step explanation:

To solve this, first convert the percentage to a decimal. That would be .0475.

Now subtract that from 1.0 to get the factor it decreases by. This would be 1-.0475 = .9525

Multiply 2600 x (.9525)^11 = 1522.258 which rounds to 1522 km^2

Answer:

The area will be 1292.98 km² after 11 years.

Step-by-step explanation:

To find what decreases by 4.57% each year in kilometers:

2600 × 4.57/100 = 26 × 4.57

= 118.82 km²

To find the area after 11 years:

118.82 × 11 = 1307.02

2600 - 1307.02 = 1292.98 km²

1292.98 km² is the answer.

Answer:

Hey there!

-4/3-4/5

-20/15-12/15

-32/15

Let me know if this helps :)

Answer:

Step-by-step explanation:

volume=7.3×1760×3×30×1760×3×1/12=73×176×90×440=508780800 ft³

Answer:

508,780,800 ft³ of rain

Step-by-step explanation:

In order to do the computation, we need to express all the given lengths in feet.

recall that 1 mile = 5280 feet

hence,

width = 7.3 miles = 7.3 x 5280 = 38,544 feet

length = 30 miles = 30 x 5280 = 158,400 feet

also recall that 1 inch = 1/12 feet

hence,

depth of rainfall = 1 inch = 1/12 feet

Volume of rain = width of beach x length of beach x depth of rainfall

= 38,544 x 158,400 x (1/12)

= 508,780,800 ft³ of rain

Answer:

Step-by-step explanation:

We first need to figure out what the equation is for this set of circumstances before we can answer any questions. We will use the equation

[tex]A(t)=P(1+r)^t[/tex] which is just another form of an exponential equation where

(1 + r) is the growth rate, P is the initial investment, and t is the time in years. We will fill in the values we know first to create the equation:

[tex]A(t)=4000(1+.11)^t[/tex] which simplifies to

[tex]A(t)=4000(1.11)^t[/tex]

Now we'll just sub in a 1 for t and solve, then a 2 for t and solve.

When t = 1:

A(t) = 4000(1.11) so

A(t) = 4440

When t = 2:

[tex]A(t)=4000(1.11)^2[/tex] which simplifies to

A(t) = 4000(1.2321) so

A(t) = 4928.40

Answer:

Step-by-step explanation:

Answer:

Hey there!

The answer would be C. 4/15.

4/5(1/3)=4/15

Let me know if this helps :)

Answer:

3438.

Step-by-step explanation:

6³ ÷ 4 + 2 × 9 (32 × 8 - 17 × 4)

= 6³ ÷ 4 + 2 × 9 (256 - 68)

= 6³ ÷ 4 + 2 × 9 × 188

= 216 ÷ 4 + 2 × 9 × 188

= 54 + 2 × 9 × 188

= 54 + 3384

= 3438

3438 is the answer.

Answer:

5 cm

Step-by-step explanation:

The volume (V) of milk in the container is calculated as

V = 8 × 15 × 12 = 480 cm³

After change of position with depth d then

8 × 15 × d = 480

120d = 480 ( divide both sides by 120 )

d = 4 cm