What value of c makes the equation true?
(PLEASE HELP, and look at the picture)

[tex]\implies {\blue {\boxed {\boxed {\purple {\sf { \: (r - 7)(r - 3) }}}}}}[/tex]

[tex]\sf \bf {\boxed {\mathbb {STEP-BY-STEP\:\:EXPLANATION:}}}[/tex]

[tex] {r}^{2} - 10r + 21[/tex]

[tex] = {r}^{2} - 7r - 3r + 21[/tex]

Taking [tex]r[/tex] as common from first two terms and [tex]3[/tex] from last two terms, we have

[tex] = r(r - 7) - 3(r - 7)[/tex]

Taking the factor [tex](x-7)[/tex] as common,

[tex] = (r - 7)(r - 3)[/tex]

[tex]\bold{ \green{ \star{ \orange{Mystique35}}}}⋆[/tex]

Step-by-step explanation:

Your Answer with

Explanation is given in the attachment

Hope it is helpful to you

✌️✌️✌️✌️✌️✌️✌️

Answer:

8050 m²

Step-by-step explanation:

We can divide the diagram up into two components: a rectangle with a width of 60 m and a height of 80 m, and a triangle with a base of 130 m (190 - 60) and a height of 50 m (80 - 30).

The area of the rectangle:

A = lw

A = 60 m (80 m)

A = 4800 m²

The area of the triangle:

A = 1/2 b*h

A = 1/2 (130 m) (50 m)

A = 1/2 (6500 m²)

A = 3250 m²

Now, we can add the areas of the two separate components:

A = 4800 m² + 3250 m²

A = 8050 m²

Answer:

x- intercept = - 4

Step-by-step explanation:

The equation of a line in slope- intercept form is

y = mx + c ( m is the slope and c the y- intercept )

Here m = - [tex]\frac{1}{2}[/tex] and c = - 2 , then

y = - [tex]\frac{1}{2}[/tex] x - 2 ← equation of line

To find the x- intercept let y = 0

0 = - [tex]\frac{1}{2}[/tex] x - 2 ( add 2 to both sides )

2 = - [tex]\frac{1}{2}[/tex] x ( multiply both sides by - 2 to clear the fraction )

- 4 = x

The x- intercept is - 4

Answer:

A

8.5 is the answer

If you test is going on so

all the best!

Answer:

octagon which has eight sides.. (1st option )

Answer:

- [tex]\frac{2\sqrt{3} }{3}[/tex]

Step-by-step explanation:

Using the identity and the exact value

csc x = [tex]\frac{1}{sinx}[/tex]  and sin60° = [tex]\frac{\sqrt{3} }{2}[/tex]

- 120° is in the third quadrant where sin < 0 , then

csc - 120° = - sin60° , then

csc - 120°

= [tex]\frac{1}{-sin60}[/tex]

= - [tex]\frac{1}{\frac{\sqrt{3} }{2} }[/tex]

= - [tex]\frac{2}{\sqrt{3} }[/tex] ( rationalise the denominator )

= - [tex]\frac{2}{\sqrt{3} }[/tex] × [tex]\frac{\sqrt{3} }{\sqrt{3} }[/tex]

= - [tex]\frac{2\sqrt{3} }{3}[/tex]

The equivalent value of the trigonometric relation cosec ( -120 )° = 2√3/3

Trigonometry is the study of the relationships between the angles and the lengths of the sides of triangles

The six trigonometric functions are sin , cos , tan , cosec , sec and cot

Let the angle be θ , such that

sin θ = opposite / hypotenuse

cos θ = adjacent / hypotenuse

tan θ = opposite / adjacent

tan θ = sin θ / cos θ

cosec θ = 1/sin θ

sec θ = 1/cos θ

cot θ = 1/tan θ

Given data ,

We know that the cosecant function is defined as the reciprocal of the sine function:

cosec (θ) = 1 / sin(θ)

Therefore, to evaluate cosec(-120°), we first need to find sin(-120°).

We know that sine is an odd function, which means that sin(-θ) = -sin(θ). Therefore,

sin(-120°) = -sin(120°)

We can now use the fact that the sine function has a period of 360 degrees, which means that sin(120°) is the same as sin(120° - 360°) = sin(-240°).

Using the same logic as before, we get:

sin(-240°) = -sin(240°)

Now , from the trigonometric relations , we get

Now, we can use the fact that sin(240°) = sin(240° - 360°) = sin(-120°), which means that:

sin(-240°) = -sin(-120°)

Therefore, we have:

sin(-120°) = -sin(120°) = -sin(-240°) = sin(240°)

Now, we can use the unit circle or trigonometric identities to find sin(240°). One way to do this is to draw a 30-60-90 degree triangle in the third quadrant of the unit circle, with the angle of 240° as the reference angle:

In this triangle, the opposite side (O) has a length of √3, the adjacent side (A) has a length of -1, and the hypotenuse (H) has a length of 2.

Therefore, sin(240°) = O/H = (√3)/2.

Finally, we can use the definition of the cosecant function to find cosec(-120°):

cosec(-120°) = 1/sin(-120°) = 1/sin(240°) = 1/((√3)/2) = 2/√3 = (2√3)/3.

Hence , cosec(-120°) is equal to (2√3)/3.

To learn more about trigonometric relations click :

https://brainly.com/question/14746686

#SPJ2

Answer:

g(x)=f(x+3)+5

Step-by-step explanation:

Answer:

By the Substitution property, the measure of angle ABC is equal to GHI.

Step-by-step explanation:

According to the Question,

Since we have,

On substituting the value of from equation (1) to equation (2)

We get, ∠ABC = ∠GHI ∴ ∠ABC ≅ ∠GHI

Thus, By the Substitution property  

The measure of angle ABC is equal to angle GHI.

Answer:

[tex]7z + 15 + 27 \\ 7z + 42 \\ z = 42 \div 7 \\ z = 6[/tex]

Answer:

The value of P(AUB) = 0.438

Step-by-step explanation:

Given:

P(A) = 0.36

P(B) = 0.2

P(A∩B) = 0.122

Find:

The value of P(AUB)

Computation:

P(AUB) = P(A) + P(B) - P(A∩B)

The value of P(AUB) = 0.36 + 0.2 - 0.122

The value of P(AUB) = 0.56 - 0.122

The value of P(AUB) = 0.438

Answer:

[tex]f^{-1}(f(58))=58[/tex]

[tex]f(f(5))=11[/tex]

Step-by-step explanation:

We are given that the table which shows some inputs and outputs of the invertible function f with domain all real numbers.

We are given that

x         f(x)

5         9

3         -2

1          -5

18          -1

0           1

9           11

We have to find

[tex]f^{-1}(f(58))[/tex] [tex]f(f(5))[/tex]

We know that

[tex]f^{-1}(f(x))=x[/tex]

Using the property

[tex]f^{-1}(f(58))=58[/tex]

[tex]f(5)=9[/tex]

[tex]f(f(5))=f(9)[/tex]

[tex]f(f(5))=11[/tex]

Answer:

10 friends can go to the amusement park

Step-by-step explanation:

214.25 = 6.75 + 20.75x

207.50 = 20.75x

x = 10 friends can go

Answer:

Step-by-step explanation:

To get the selling price.

Selling price=100÷ 100-x × 85

Where x is the markup.

Sp= 100 ÷ 100-35× 85

Sp= 100÷ 65×85

Sp= $130.7692

Answer:

x = 3     y = 5

Step-by-step explanation:

     y=x+2

+    y=-x +8

2y = 10

y = 5

y = -x + 8

5 = -x + 8

x = 3

Answer:

this as a equation looks like this

-1/2x+1+x=11

1/2x=10

x=20

Hope This Helps!!!

20 dollars were originally in the box

Two or more expressions with an Equal sign is called as Equation.

Given,

In an office there was a small cash box.

One day ann took half of the money plus$1 more

Then dan took half of the remaining money plus$1 more

Stan then took the remaining $11

-1/2x+1+x=11

Subtract 1/2x from both sides

1/2x=10

Multiply 2 on both sides

x=20

Hence, 20 dollars were originally in the box

To learn more on Equation:

https://brainly.com/question/10413253

#SPJ5

Answer:

2nd option

Step-by-step explanation:

f(x) + g(x)

= 4x - 5 + 3x + 7 ← collect like terms

= 7x + 2

domain is all real numbers

Answer:

Kindly check attached picture

Step-by-step explanation:

Based d on the instruction given.

1.)

-3 * 6 = 18

6 * - 2 = - 12

-3 * - 2 = 6

2.)

We use logical reasoning to find 2 numbers whichbwhen multiplied gives the number in the box in between :

The answers are given in the picture attached.

Answer:

3, 5, 7

Step-by-step explanation:

Substitute n = 1, 2, 3 into the nth term rule

a₁ = 2(1) + 1 = 2 + 1 = 3

a₂ = 2(2) + 1 = 4 + 1 = 5

a₃ = 2(3) + 1 = 6 + 1 = 7

Answer:

3, 5, 7

Step-by-step explanation:

n = 1, 2, 3 into the nth term rule

a₁ = 2(1)+1=2+1=3

a2=2(2)+1=4+1=5

a3 = 2(3)+1=6+1=7

Answer:

[tex]9p^2-16q^2[/tex]

[tex](3p)^{2} -(4p)^{2}[/tex]

[tex]\underline{x^2-y^2=\left(x+y\right)\left(x-y\right)}[/tex]

[tex]\left(3p\right)^2-\left(4q\right)^2=\left(3p+4q\right)\left(3p-4q\right)[/tex]

[tex]=\left(3p+4q\right)\left(3p-4q\right)[/tex]

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

hope it helps....

have a great day!!

Answer:

60

Step-by-step explanation:

Subsitute the number if large vehicles

5x + 10(50) = 800

5x + 500 = 800

5x =300

X =60

Answer:

60

Step-by-step explanation:

Substitute y = 50 into the equation and solve for x

5x + 10(50) = 800 , that is

5x + 500 = 800 ( subtract 500 from both sides )

5x = 300 ( divide both sides by 5 )

x = 60

That is 60 small vehicles were washed in total

Answer:

22 cm

Step-by-step explanation:

the perimeter = AB+BG+GF+FE+ED+DC+CA

= 65 cm

7+7+7+FE+7+DC+7=65 => FE = CD

35+ 2FE = 65

2FE = 65-35

= 30

FE = 30/2 = 15

so, GE = GF + FE

= 7+15 = 22 cm

Answer:

6:9 ÷3

2:3

Step-by-step explanation:

1st write the ratio then simplify it with dividing with the Highest common factor on both sides

Answer:

(B) 30

Step-by-step explanation:

Imagine you drew a line from Point T until it touched Line PR. Let's call that point where it touched Line PR "Point Z".

That line (called Line TZ) would be perpendicular to PR, forming a 90 degree angle.

Now, TZW is a triangle.

To find x, we need to find the angle measurment of Angle ZTW.

This is where we use the hexagon.

A hexagon's interior angle sum is 720, meaning each interior angle is equal to 120 degrees. So Angle UTS would equal 120 degrees.

However, Line TZ bisects that 120 degree angle, so Angle ZTW would equal 60 degrees (because 120/2 = 60).

Now we have two angles of the triangle: 90 & 60.

A triangle's interior angle sum is 180.

Add 90 & 60, which is 150, and subtract 150 from 180.

The result is 30, which is the angle measurement of x.

Hope it helps (●'◡'●)

Given:

The given statement is "6 less than the difference of 5 and a number".

To find:

The variable expression for the given statement.

Solution:

Let n be the unknown number or the variable.

We know that minus sign is used to represent the difference between two numbers.

Difference of 5 and a number is [tex](5-n)[/tex].

6 less than the difference of 5 and a number is [tex](5-n)-6[/tex].

The required expression for the given statement is [tex](5-n)-6[/tex].

Therefore, the correct option is C.

Answer:

[tex]\displaystyle A = \frac{32}{3}[/tex]

General Formulas and Concepts:

Calculus

Integrals

Integration Rule [Reverse Power Rule]:                                                                   [tex]\displaystyle \int {x^n} \, dx = \frac{x^{n + 1}}{n + 1} + C[/tex]

Integration Rule [Fundamental Theorem of Calculus 1]:                                        [tex]\displaystyle \int\limits^b_a {f(x)} \, dx = F(b) - F(a)[/tex]

Integration Property [Multiplied Constant]:                                                             [tex]\displaystyle \int {cf(x)} \, dx = c \int {f(x)} \, dx[/tex]

Integration Property [Addition/Subtraction]:                                                           [tex]\displaystyle \int {[f(x) \pm g(x)]} \, dx = \int {f(x)} \, dx \pm \int {g(x)} \, dx[/tex]

Area of a Region Formula:                                                                                       [tex]\displaystyle A = \int\limits^b_a {[f(x) - g(x)]} \, dx[/tex]

Step-by-step explanation:

Step 1: Define

Identify

Curve: x³ + 2x² - 3x

Interval: [-3, 1]

Step 2: Find Area

Topic: AP Calculus AB/BC (Calculus I/I + II)

Unit: Integration

Book: College Calculus 10e

Answer:

1452628383763637£838

Answer:

B

Step-by-step explanation:

Answer:

y is 4

Step-by-step explanation:

x is 3

y is 4 coordinate is (3,4)

Answer:

4

Step-by-step explanation: