If a line passes through the points (1,3) and (-2,-9), the equation of the line is y-3=4(x-__)

Answer:

-18  

Step-by-step explanation:

f(x) = x² - 3x -10

f(-10) = (-10)² – 3(-10) – 10

f(-10) = 100 + 30 - 10

f(-10) = 120

f(-5) = (-5)² – 3(-5) – 10

f(-5) = 25 + 15 - 10

f(-5) = 30

=====

The average rate of change is the slope m of the straight line joining the two points.

m = (y₂ - y₁)/(x₂ - x₁)

m = (30 - 120)/(-5 – (-10))

m = -90/(-5+10)

m = -90/5

m = -18

[tex]\log_ab=c\iff a^c=b\\\\4^{x+2}=\dfrac{1}{2}\qquad\text{use}\ a^{-1}=\dfrac{1}{a}\\\\(2^2)^{x+2}=2^{-1}\qquad\text{use}\ (a^n)^m=a^{nm}\\\\2^{2(x+2)}=2^{-1}\iff2(x+2)=-1\qquad\text{use distributive property}\\\\(2)(x)+(2)(2)=-1\\\\2x+4=-1\qquad\text{subtract 4 from both sides}\\\\2x=-3\qquad\text{divide both sides by 2}\\\\\boxed{x=-1.5}[/tex]

Answer:

m<1=134

m<2=46

x=13

Step-by-step explanation:

Angle 2 can be set equal to 180 since the angle is supplementary after transferring angle 2 to its alternate interior.

4x-6+10x+4=180

Combine like terms

14x-2=180

Solve for x

14x=182

x=13

Now plug x in for the two angles

10(13)+4

130+4

m<1=134

4(13)-6

52-6

m<2=46

134+46=180, verified

Answer:

Step-by-step explanation: Thew figures are similar becasue 5/15 equals 3/9. They bothe equal one third. This shows that they are bhoth orportionate to eachoither. The ratios of the lengths of their corresponding sides are equal.

Answer:

length =25 and width =4

Step-by-step explanation:

If the area of a rectangle is 100, then the length is 25 and the width is 4. The counterexample is length = 20, width = 5.

If the area of a rectangle is 100, and the length is 25, we can find the width by dividing the area by the length: 100 ÷ 25 = 4. So the width is 4. To find the counterexample, we need to find another pair of length and width that give a different area.

Let's try length = 20 and width = 5. The area of this rectangle would be 20 × 5 = 100, which is the same as the original rectangle.

https://brainly.com/question/31566854

#SPJ2

The values of x and y for the Isosceles triangle are 90° and 43° respect.

By observation, the triangle ∆ABC is an Isosceles triangle with the markings on both legs of the triangle so the base angles are equal,

angle C = angle B = 47°.

Since the line AD bisects the angle A, then line AD is perpendicular to the base BC and so angle x is a right angle

x = 90°

Considering the right triangle ∆ADB can evaluate for y as follows;

x + y + angle B = 180° {sum of interior angles of a triangle}

y + 90 + 47 = 180

y + 137 = 180

y = 180 - 137

y = 43°.

Therefore, the values of the x is equal to 90° and that of y is 43° for the Isosceles triangle ∆ABC.

Answer:

(B) [tex]477=6(1+0.20)^t[/tex]

Step-by-step explanation:

we can use formula

[tex]P(t)=P_0(1+r)^t[/tex]

where

Po is the initial population

r is the growth rate

t is the time in months

We are given

initial population of insects

so, Po=6

The scientists find that the insect population, x, is growing exponentially 20% per month

so, r=0.20

now, we can plug these values

[tex]P(t)=6(1+0.20)^t[/tex]

there to be a population of 477 insects

so, P(t)=477

now, we plug it

and we get

[tex]477=6(1+0.20)^t[/tex]

Answer:

{1}

Step-by-step explanation:

We find determinant for the given matrix and set it equal to -1

To find determinant we apply formula

[tex]|A| = a_{11}(a_{22}a_{33} − a_{32}a_{23}) - a_{12}(a_{21}a_{33} − a_{31}a_{23})+a_{13}(a_{21}a_{32} - a_{31}a_{22})[/tex]

[tex]|A| = x(1x - 2) - 0(7-7) + 0(14-7x) [/tex]

|A| = x^2 - 2x

Now we set the determinant = -1

[tex]x^2 - 2x=-1[/tex]

Add 1 on both sides

[tex]x^2 - 2x + 1=0[/tex]

Now factor it

(x-1)(x-1) = 0

Set each factor =0  and solve for x

x- 1=0 so x=1

Answer:

1. -6 ≤ x < -1, conjunction

2. x > 10   or   x ≤ 6, disjunction

3. 7 ≤ x ≤ 12, conjunction

4. x ≥ -3   or   x < -9, disjunction

Step-by-step explanation:

These inequalities are called "compound inequalities." Each compound inequality is made up of two simple inequalities.

A compound inequality of the type 5 < x < 8 means x > 5 and x < 8. Since the word between the simple inequalities is "and", it is a conjunction.

A compound inequality of the type "x < 3 or x > 12" uses the word "or" between the simple inequalities. It is called a disjunction.

1.

-4 ≤ x + 2 < 1

Conjunction

For this type of inequality, do what you need to do to get x alone in the middle section. Do the same to all three "sides" of the inequality.

The middle section has x + 2. We want x alone,s o w must subtract 2. We subtract 2 from all three sides.

-4 - 2 ≤ x + 2 - 2 < 1 - 2

-6 ≤ x < -1

2. 5x - 4 > 46 or 4x ≤ 3x + 6

Disjunction

In this type of compound inequality, solve each inequality by itself, and always keep the word "or" between the inequalities.

5x - 4 > 46 or 4x ≤ 3x + 6

5x - 4 + 4 > 46 + 4   or   4x - 3x ≤ 3x - 3x + 6

5x > 50   or   x ≤ 6

x > 10   or   x ≤ 6

3. Similar to problem 1.

Conjunction

10 ≤ 2x - 4 ≤ 20

Add 4 to all sections.

14 ≤ 2x ≤ 24

Divide all sections by 2.

7 ≤ x ≤ 12

4.

6 - 2x ≤ 12 or 7 + 2x < -11

Disjunction

-2x ≤ 6   or   2x < -18

x ≥ -3   or   x < -9

Answer:

1. -6≤x<-1

conjunction

2.x>10   or     x≤6

Disjunction

3.7≤x≤12

Conjunction    

4.x ≥-6                    or                           x < -6

Disjunction

5.2≤x≤5

Conjunction

6. x ≤ 54                                        or               x≥66

Disjunction

7.  39< x≤43

Conjunction

Step-by-step explanation:

conjunction is "and"  like a sandwich between 2 points

disjunction is " or"  like boat oars with a gap for the boat in the middle

1. -4≤x+2<1

Subtract 2 from all sides

-4-2≤x+2-2<1 -2

-6≤x<-1

conjunction

2. 5x-4>46"                                 or          " 4x≤3x+6

Add 4 to each side                                  Subtract 3x from each side

5x-4+4 > 46+4                                           4x-3x≤3x-3x+6

5x >50                                                           x≤6

Divide by 5                                                  

5x/5 >50/5

x>10   or     x≤6

Disjunction

3. 10≤2x-4≤20

Add 4 to all sides

10≤2x-4≤20

10+4 ≤2x-4+4≤20+4

14≤2x≤24

Divide by 2 on all sides

14/2≤2x/2≤24/2

7≤x≤12

Conjunction    

4. 6-2x≤12" or                             " 7+2x<-11

Subtract 6 from each side       Subtract 7 from each side

6-6-2x≤12                                or " 7-7+2x<-11-7

-2x≤12                                        2x<-18

Divide by -2                                Divide by 2

Flips the inequality

-2x/-2≥12/-2                             2x/2 <-18/2

x ≥-6                    or                           x < -6

Disjunction

5. 5≤2x+1≤11

Subtract 1 from all sides

5-1≤2x+1-1≤11-1

4≤2x≤10

Divide all sides by 2

4/2≤2x/2≤10/2

2≤x≤5

Conjunction

6. 2/3 x-20≤16"                            or " x/3+10≥32

Add 20 from each side                     Subtract 10 from each side

2/3 x-20+20 ≤16+20                     x/3 +10-10 ≥32 -10

2/3 x ≤36                                                x/3≥22

Multiply by 3/2 on each side            Multiply by 3 on each side

3/2 * 2/3x ≤ 36*3/2                      x/3*3 ≥22 *3

x ≤ 54                                        or               x≥66

Disjunction

7. 10<1/4 (x+1)≤11

Multiply all sides by 4

4*10<1/4*4 (x+1)≤11*4

40< (x+1)≤44

Subtract 1 from all sides

40-1< (x+1-1)≤44-1  

39< x≤43

Conjunction

Answer:

C. 12x + 6y = 30

Step-by-step explanation:

A. x  3 4 5  

   y   3    6     9

We need to make and equation

slope = (y2-y1)/(x2-x1)

    = (9-3)/(5-3)

    6/2

  3

The slope is 3

Using point slope form

y-y1 = m(x-x1)

y-3  = 3(x-3)

Distribute

y-3 = 3x-9

Add 3 to each side

y = 3x-9+3

y = 3x-6

Let x=0

y = 0-6

y = -6

B. y = 4x – 7

Let x = 0

y = 0-7

y = -7

C. 12x + 6y = 30

Let x = 0

12(0) + 6 y = 30

6y = 30

Divide by 6

6y/6 = 30/6

y =5

D. A linear function that goes through point 1, negative 1 and point 0, 4

The point ((0,4) says when x=0   y=4

y =4

y=5  is the max so the answer is C

Answer:

15

Step-by-step explanation:

you have to divide 975/65=$15 per person

Answer:

(x - 6)(x + 3)

Step-by-step explanation:

Consider the product of the factors of the constant term which sum to give the coefficient of the x-term

product = - 18 and sum = - 3

The factors are - 6 and + 3, hence

x² - 3x - 18 = (x - 6)(x + 3)

Answer:

none of the solutions

Step-by-step explanation:

if k(x) = 2x-3x

We can substitute x=9 to find k(9)

k(9) = 2(9) -3(9)

      = 18 -27

      = -9

Answer:

2 decimal places

Step-by-step explanation:

When you multiply two decimals, the largest possible number of decimal places in the product is the sum of the number of the decimal places of the factors. Here, the product has 2 decimal places. One factor is an integer, so it has no decimal places. The other factor must have at least 2 decimal places.

Answer: [tex]398.5750[/tex]

Step-by-step explanation:

It is important to remember that the fourth digit after the decimal point is in the ten-thousandth place.

Then, given the  following number:

[tex]398.574986215[/tex]

You can follow these steps in order ti round it to the nearest ten-thousandth:

1. You can identify that the digit in the ten-thousandth place is:

[tex]9[/tex]

2. Identify the digit to the right of [tex]9[/tex]. This is:

[tex]8[/tex]

3. Since:

 [tex]8>5[/tex]

 You must round up. Increase the digit [tex]9[/tex] by 1. (Notice that [tex]9+1=10[/tex], then the digit to the left of  [tex]9[/tex] increases by 1 too). Then:

[tex]398.5750[/tex]

<, > - opened circle

≤, ≥ - closed circle

<, ≤ - draw line to left

>, ≥ - draw line to right

Answer in the attachment.

<,> - dotted line

≤, ≥ - solid line

<, ≤ - shadow to left

>, ≥ - shadow to right

x = -6 - its a vertical line

Answer:

It takes 2.5 seconds for the ball to reach its  highest point

Maximum height is 196 feet

Step-by-step explanation:

h(t) = -16t^2+80t +96

a=-16, b= 80, c=96

To find the maximum height , we need to find vertex

Let find x coordinate of vertex

[tex]t=\frac{-b}{2a}[/tex]

Plug in the values

[tex]t=\frac{-80}{2(-16)}= 2.5[/tex]

It takes 2.5 seconds for the ball to reach its  highest point

Now plug in 2.5 for t to find maximum height

[tex]h(t) = -16t^2+80t +96[/tex]

[tex]h(2.5) = -16(2.5)^2+80(2.5) +96=196[/tex]

Maximum height is 196 feet

Answer:

200

Step-by-step explanation:

8x2=16

12 1/2x16=200

Answer:

The length of each side is 12.2 ft

The complete factor of the expression x⁴ + 8x² – 9 will be (x² + 9), (x - 1), and (x + 1). Then the correct option is B.

It is a method for dividing a polynomial into pieces that will be multiplied together. At this moment, the polynomial's value will be zero.

The expression is given as,

⇒ x⁴ + 8x² – 9

Factorize the expression, then we have

⇒ x⁴ + 8x² - 9

⇒ x⁴ + 9x² - x² - 9

⇒ x²(x² + 9) - 1(x² + 9)

⇒ (x² + 9)(x² - 1)

⇒ (x² + 9)(x - 1)(x + 1)

The complete factor of the expression x⁴ + 8x² – 9 will be (x² + 9), (x - 1), and (x + 1). Then the correct option is B.

More about the factorization link is given below.

https://brainly.com/question/6810544

#SPJ7

The complete question is attached below.

Answer:

60,000 i believe :)

Answer:

120

Step-by-step explanation:

Answer:

I) B = 20 m², h = 4 m are NOT possible dimensions for the area of the base and the height of the prism.

Step-by-step explanation:

Given that the triangular prism has a volume = 240 m³, we can use the formula for the volume of a triangular prism to check the given answers for possible dimensions.  V = Bh, where B = the area of the base and h = height of the prism.  In this case, we simply need to multiply each of the given dimensions together to see if they equal 240 m³:

F) B = 48 m², h = 5 m:  v = 48 x 5 = 240 m³ (possible)

G) B = 24 m², h = 10 m; v = 24 x 10 = 240 m³ (possible)

H) B = 12 m², h = 20 m: v = 12 x 24 = 240 m³ (possible)

I) B = 20 m², h = 4 m: v = 20 x 4 = 80 m³ (NOT possible)

Answer:

No

Yes

Yes

No

Step-by-step explanation:

X's repeat

X's don't repeat

X's don't repeat

X Values repeat

Answer:7

Step-by-step explanation: 14%=14/100. (14/100)*50=7

Answer:

7

Step-by-step explanation:

to find your answer multiply .14 (14 as a fraction)  by 50 to get 7

Answer:

The equation of this line would be y = 3x - 1

Step-by-step explanation:

In order to find this equation we must first find the slope of the original line. The original slope (the coefficient of x) is 3, which means the new slope will also be 3 because parallel lines have the same slope. Now, we can use this slope along with the point in point-slope form to find the equation of the line.

y - y1 = m(x - x1)

y + 7 = 3(x + 2)

y + 7 = 3x + 6

y = 3x - 1