Find the area of the shaded regions:

Answer:

y = mx + b

m = slope = -2

To find the y-intercept(b), substitute the points into the function:

-3 = -2(-5)  + b

-3 = 10 + b

b = -3 - 10 = -13

Therefore, y = -2x - 13

Answer:

Step-by-step explanation:

Step-by-step explanation:

The Rational Roots Test states that for a polynomial with integer coefficients, the factors of the constant / the factors of the leading coefficient are the possible rational roots.

Here, the constant (the value without an x attached to it) is -12 and the leading coefficient (the value that the x to the highest degree is multiplied by) is 1 as x⁴ is multiplied by 1. The factors of -12 are

±(1, 2, 3, 4, 6, 12), so the possible rational roots are ±(1, 2, 3, 4, 6, 12)/1 (as 1 is the only factor of 1).

Trying out a few roots until we get one that works using synthetic division, we can try

x+1 (the root is x=-1)

-1  |     1       1        -6         -14         -12

    |            -1          0          6           8

    __________________________

          1     0        -6            -8         -4

the remainder is -4, so this does not work

x+2 (the root is x=-2)

-2 |     1       1        -6         -14         -12

    |            -2          2          8          12

    __________________________

          1      -1       -4           -6         0

Therefore, x=-2 is a root and x+2 is a factor of the polynomial. The quotient of the polynomial and x+2 is

-6 + (-4)x + (-1)* x² + 1 * x³ = x³-x²-4x-6

Using the rational roots theorem, the possible roots of x³-x²-4x-6 are

±(1,2,3,6)

Starting with

x-1 (root is x=1), we have

1 |     1       -1        -4         -6      

    |            1          0         -4        

    _____________________

          1      0       -4           -10

there is a remainder, so this is not a root

next, x-2 (root is x=2)

2 |     1       -1        -4         -6      

    |            2         2         -4        

    _____________________

          1      1       -2           -10      

there is a remainder, so this is not a root

next, x-3 (root is x=3)

3|     1       -1        -4         -6      

    |            3         6         6        

    _____________________

          1      2      2          0

x-3 is a factor and 3 is a root. the quotient of (x³-x²-4x-6)/(x-3) is x²+2x+2

Answer: the answer to this is 3x-2

Step-by-step explanation:

Answer:

12 starfish

Step-by-step explanation:

Create a system of equations where x is the number of starfish he has and y is the number of spiders he has:

x + y = 19

5x + 8y = 116

Solve by elimination by multiplying the top equation by -8:

-8x - 8y = -152

5x + 8y = 116

Add these together and solve for x:

-3x = -36

x = 12

So, he has 12 starfish.

The total number of starfish is 12 starfishes

What is an Equation?

Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.

It demonstrates the equality of the relationship between the expressions printed on the left and right sides.

Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.

Given data ,

Let the number of starfish be = x

Let the number of spiders be = y

The number of legs for spiders = 8

The number of legs for starfish = 5

So , the equation will be

The total number of legs for x starfish = 5x

The total number of legs for y spiders = 8y

The total number of creatures = 19

So , x + y = 19   be equation (1)

And ,

The total number of legs = 116

So , 5x + 8y = 116   be equation (2)

Now , from equation (1) , x = 19 - y

Substituting the value of equation (1) in equation (2) , we get

5x + 8y = 116

5 ( 19 - y ) + 8y = 116

95 - 5y + 8y = 116

95 + 3y = 116

Subtracting 95 on both sides , we get

3y = 21

Divide by 3 on both sides , we get

y = 7

So , the number of spiders is 7 spiders

Substituting the value of y in equation (1) , we get

x + y = 19

x + 7 = 19

Subtract 7 on both sides , we get

x = 12

Therefore , the value of x is 12

Hence , The total number of starfish is 12 starfishes

To learn more about equations click :

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Answer:

this is the same quiestion i was doing if u get answer plz send me

Answer:

Step-by-step explanation:

7(x-2) -3(x+3) = 5(x-3) +x , distribute in parenthesis

7x -14 -3x -9 = 5x -15 +x , isolate like terms

7x -3x -5x -x = 14 +9 -15, combine like terms

-2x = 8, divide both sides by -2

x= -4

Answer:

A is the answer...........

Explanation

8x+3=3x+8

8x-3x=8-3

5x=5

x=5/5

x=1

Answer:

D

Step-by-step explanation:

(the line is a / shape, so the slope is positive)

(the line crosses the y axis at (0,-2))

(using the above information, we can conclude that the equation is y=2x-2)

or

slope = m = rise/run = 2/1 = 2

y=mx+b

y=2x+b

Choose any point on the line) (1,0)

0=2(1)+b

b=-2

y=2x-2

1.) 10+2√21

2.) 8-2√15

3.) 38+2√10

solution to all the answers:

NUMBER 1:

=> use (a + b)^2 + 2ab + b^2 to expand the expression (√3 +√7)^2, then it should look like this: 3 + 2√21 + 7.

=> add the numbers: 10 + 2√21.

NUMBER 2:

=> use (a + b)^2 + 2ab + b^2 to expand the expression (√5 -√3)^2, then it should look like this: 5 - 2√15 + 3.

=> add the numbers: 8 - 2√15.

NUMBER 3:

=> use (a + b)^2 + 2ab + b^2 to expand the expression (2√5 + 3√2)^2, then it should look like this: 20 + 12√10 + 18.

=> add the numbers: 38 + 12√10.

I HOPE THIS HELPED!!

Answer:

I dont know. sorry sorry

Step-by-step explanation:

her it go u can see it.. have a nice Day

Answer:

45°

Step-by-step explanation:

Segments GJ and HK intersect at F.

That makes angles JFK and GFH vertical angles and congruent.

An arc has the same measure as its central angle.

m<GFH = 45°

m<JFK = m<GFH

m<JFK = 45°

Answer:

in 3.04 years the will give required intrest

Answer:

B

Step-by-step explanation:

when logarithms of the same base (the base in this case is 'b') are being subtracted, divide the arguments ( 'a' and 'd')

Answer:

To find the leading coefficient, first expand the function:

[tex]y= -(x+3)^{2} -5\\\\y=-(x^{2} +6x+9)-5\\\\y=-x^{2} -6x-9-5\\\\y=-x^{2} -6x-14[/tex]

The leading coefficient is the coefficient of the highest-order term, which, in this case, would be the -1 from -x².

To find the vertex: see image below

Vertex = (-3, -5)

Answer:

Amira is currently 24 years old and Pam is currently 12 years old

Step-by-step explanation:

Let Amira's age be [tex]a[/tex] and Pam's age be [tex]p[/tex]. Currently, Amira is twice as old as Pam. Therefore, we can write the equation [tex]a=2p[/tex].

We can write a second equation using the other information given in the question. Nine years ago, Amira and Pam's combined ages was 18. If Amira and Pam are currently [tex]a[/tex] and [tex]p[/tex] years old, respectively, then their respective ages 9 years ago would ben [tex]a-9[/tex] and [tex]p-9[/tex]. Since these add up to 18, we have the equation [tex](a-9)+(p-9)=18[/tex].

Therefore, we have a system of equations:

[tex]\begin{cases}a=2p,\\a-9+p-9=18\end{cases}[/tex]

Substitute the first equation into the second one:

[tex]2p-9+p-9=18[/tex]

Combine like terms:

[tex]3p-18=18[/tex]

Add 18 to both sides:

[tex]3p=36[/tex]

Divide both sides by 3:

[tex]p=\frac{36}{3}=\boxed{12}[/tex]

Now substitute this into any of the equations (I'll choose the first):

[tex]a=2p,\\a=2(12),\\a=\boxed{24}[/tex]

Therefore, Amira is currently 24 years old and Pam is currently 12 years old.

Answer:

70 [milliliters]

Step-by-step explanation:

Since the solution consists of 90% alcohol, the 63 milliliters of alcohol must represent 90% of the entire solution. Let the solution have [tex]x[/tex] milliliters in total. We have the following equation:

[tex]0.9x=63[/tex]

Divide both sides by 0.9:

[tex]x=\frac{63}{0.9}=\boxed{70}[/tex]

Therefore, there are 70 milliliters in the solution.

Answer:

[tex]thank \: you[/tex]

Answer:

C.

0.5; 13.5; 1093.5

Step-by-step explanation:

msin²x+cos²x=m-1

since the interval are 0 and π/4

Therefore

msin²(0)+cos²(0)=m-1

m(0)+1=m-1

1=m-1

m=2

use π/4 now

msin²(π/4)+cos²(π/4)=m-1

m(1/2)+(1/2)=m-1

m+1=2(m-1)

m+1=2m-2

-m=-3

m=3

Therefore

m=2 or 3

Step-by-step explanation:

here's the answer to your question

Answer:

Last option. She didn't use the reciprocal.

Answer:

The second, third, and fourth

Step-by-step explanation:

When you multiply two fractions, you multiply the numerator and denominator, not add them. Also, when you divide by a fraction and want to turn it into multiplication, you multiply by the reciprocal, which she didn't do. Hope this helps!

Answer: A. 20 is the answer.

Step-by-step explanation:

x+40 = 3x

or, 40 = 3x-x

or, 2x = 40

or, x = 40/2

so, x = 20

[tex] \frac{9}{41} [/tex]

Step-by-step explanation:

The ratio cosine tell us that

In other words,

[tex] \cos(x) = \frac{adj}{hyp} [/tex]

The side adjacent to angle a is 9. The hypotenuse is 41.

So

[tex] \cos(a) = \frac{9}{41} [/tex]

Answer:

c. 20/21

Step-by-step explanation:

You just multiply straight

3×7 = 21

4×5 =20

21/20 <---- and it can't be reduced farther than this.

Answer:

C. ²¹⁄₂₀

Step-by-step explanation:

OKOKOK DON'T WORRY I'M HERE :)))

--

When multiplying fractions, you multiply the numerators together and then multiply the denominators together.

The numerators here are 3 and 7. Multiply those and you get 21 (7 x 3 = 21).

The denominators here are 4 and 5. Multiply those and you get 20 (4 x 5 = 20).

Then you put the newly-multiplied numerator over the newly-multiplied denominator and you get ²¹⁄₂₀.

Hope this helped!!

Answer:

arithmetic

Step-by-step explanation:

because it bounced double

Answer:

[×1] +16=10

×=10-16

×=-6

Answer:

x=5 and x=-5

Step-by-step explanation:

First subtract 16 from both sides.

Then solve for x+1=6 and x+1=-6

you answer should be x=5 and x=-5

Answer:

See explanation

Step-by-step explanation:

The question is incomplete, as the required number line is not included in the question.

A general explanation is as follows:

An open circle means > or <

A closed circle means >= or <=

Take, for instance, the attached number line:

The open dot on -3 means >-3 or <-3

The arrow points to the right direction, means >-3 i.e. greater than -3

Hence, the inequality is:

[tex]x > -3[/tex]

Answer:

36

Step-by-step explanation:

a1 = 4

an=an-1 *3

a2 = a1 *3 = 4*3 = 12

a3 = a2*3 = 12*3 = 36

Answer:

82,83,84,80,84,86,91,96,95,99,97,92