Vicki and Tamra are working on their math homework together. Vicki has worked p problems, and Tamra has worked 4 times as many problems as Vicki. The expression shows how many problems they have worked altogether.

Hi there!

[tex]\large\boxed{(n - 8)(n + 5)}[/tex]

n² - 3n - 40

Find two numbers that sum up to -3 and multiply into -40. We get:

-8, 5

Thus:

(n - 8)(n + 5)

Answer:

8x^2 - 4x - 5

See the steps below for better explanation:

Answer:

D

Step-by-step explanation:

từ O hạ đường vuông góc xuống các cạnh AB, AC, BC các đường vuông góc đó sẽ bằng nhau

520 x 12 months x 4 years = 24960

24960 + 3000 deposit = 27,960 total paid.

27,960 - 13,000 = 14,960 total interest paid

The point [tex](-2,2)[/tex] is a solution of the system given by [tex]y<2x+8[/tex] and [tex]y \geq -x-3[/tex]

Given point: [tex](-2,2)[/tex]

Given systems:

To find: The system to which the given point is a solution

If a point is a solution of a system, then the coordinates of the point satisfies all the equation(s) or inequation(s) of the system. So, we can substitute the x & y coordinates of the given point into the inequalities of each of the given systems and check if the inequalities are satisfied by the coordinates of the point.

(1) [tex]y>-2x+2[/tex] and [tex]y>x+5[/tex]

Substitute the coordinates of the point [tex](-2,2)[/tex] into the inequalities of the system.

Put [tex]x=-2,y=2[/tex] in [tex]y>-2x+2[/tex] to get,

[tex]2>-2(-2)+2[/tex]

[tex]2>4+2[/tex]

[tex]2>6[/tex]

The above inequality is clearly impossible and thus, the coordinates of the given point does not satisfy this inequality.

This implies that the given point is not a solution of this system.

(2) [tex]y<x+2[/tex] and [tex]y>x-1[/tex]

Substitute the coordinates of the point [tex](-2,2)[/tex] into the inequalities of the system.

Put [tex]x=-2,y=2[/tex] in [tex]y<x+2[/tex] to get,

[tex]2<-2+2[/tex]

[tex]2<0[/tex]

The above inequality is clearly impossible and thus, the coordinates of the given point does not satisfy this inequality.

This implies that the given point is not a solution of this system.

(3) [tex]y<2x+8[/tex] and [tex]y \geq -x-3[/tex]

Substitute the coordinates of the point [tex](-2,2)[/tex] into the inequalities of the system.

Put [tex]x=-2,y=2[/tex] in [tex]y<2x+8[/tex] to get,

[tex]2<2(-2)+8[/tex]

[tex]2<-4+8[/tex]

[tex]2<4[/tex]

This is a true inequality. Then, the given point satisfies the first inequality of the system.

We will now check if the point satisfies the second inequality of the system.

Put [tex]x=-2,y=2[/tex] in [tex]y \geq -x-3[/tex] to get,

[tex]2 \geq -(-2)-3[/tex]

[tex]2 \geq 2-3[/tex]

[tex]2 \geq -1[/tex]

This is also a true inequality. Then, the given point also satisfies the second inequality of the system.

Thus, the given point is a solution of this system.

(4) [tex]y<2x+3[/tex] and [tex]y \geq -2x-5[/tex]

Substitute the coordinates of the point [tex](-2,2)[/tex] into the inequalities of the system.

Put [tex]x=-2,y=2[/tex] in [tex]y<2x+3[/tex] to get,

[tex]2<2(-2)+3[/tex]

[tex]2<-4+3[/tex]

[tex]2<-1[/tex]

The above inequality is clearly impossible and thus, the coordinates of the given point does not satisfy this inequality.

This implies that the given point is not a solution of this system.

Thus, we can see that the coordinates of the given point [tex](-2,2)[/tex] satisfies the inequalities of the third system only.

Then, the point [tex](-2,2)[/tex] is a solution of the system given by [tex]y<2x+8[/tex] and [tex]y \geq -x-3[/tex].

Learn more about geometric solutions of system of linear inequalities here:

https://brainly.com/question/17174433

[tex]\\ \sf\longmapsto 2x+y=2[/tex]

[tex]\\ \sf\longmapsto 2x=2-y[/tex]

[tex]\\ \sf\longmapsto x=\dfrac{2-y}{2}\dots(1)[/tex]

And

[tex]\\ \sf\longmapsto x+1=y+2[/tex]

[tex]\\ \sf\longmapsto x=y+2-1[/tex]

[tex]\\ \sf\longmapsto x=y+1[/tex]

[tex]\\ \sf\longmapsto \dfrac{2-y}{2}=y+1[/tex]

[tex]\\ \sf\longmapsto 2-y=2(y+1)[/tex]

[tex]\\ \sf\longmapsto 2-y=2y+2[/tex]

[tex]\\ \sf\longmapsto 2-2=2y+y[/tex]

[tex]\\ \sf\longmapsto 3y=0[/tex]

[tex]\\ \sf\longmapsto y=\dfrac{0}{3}[/tex]

[tex]\\ \sf\longmapsto y=\infty[/tex]

[tex]\\ \sf\longmapsto x=\dfrac{2-y}{2}[/tex]

[tex]\\ \sf\longmapsto x=\dfrac{2-\infty}{2}[/tex]

[tex]\\ \sf\longmapsto x=\dfrac{2}{2}[/tex]

[tex]\\ \sf\longmapsto x=1[/tex]

Answer:

x=1 , y=0

Step-by-step explanation:

2x+y=2.......1

x+1=y+2

x-y=2-1

x-y=1...... 2

from equation 2 we get ,

x-y=1

x=1+y

putting the value of x in equation 1 we get,

2*(1+y) +y=2

2+2y+y=2

2+3y=2

3y=2-2

3y=0

y=0/3

y=0

putting the value of y in equation 2 we get,

x-0=1

x=1+0

x=1

hence x=1 , y=0

Answer:

A (3,3)

J (5,2)

L (0,0)

Step-by-step explanation:

.........................

Answer:

5x + 10y

5*4 + 10*5

20+50 = $70

Step-by-step explanation:

Answer:

5, 12, 13

Step-by-step explanation:

let x be the longer leg then x + 1 is the hypotenuse and x - 7 the shorter leg

Using Pythagoras' identity in the right triangle

x² + (x - 7)² = (x + 1)² ← expand using FOIL

x² + x² - 14x + 49 = x² + 2x + 1

2x² - 14x + 49 = x² + 2x + 1 ( subtract x² + 2x + 1 from both sides )

x² - 16x + 48 = 0 ← in standard form

(x - 4)(x - 12) = 0 ← in factored form

Equate each factor to zero and solve for x

x - 4 = 0 ⇒ x = 4

x - 12 = 0 ⇒ x = 12

x = 4 , then x - 7 = 4 - 7 = - 3 ← not possible

x = 12, then x - 7 = 12 - 7 = 5 and x + 1 = 12 + 1 = 13

The lengths of the 3 sides are

longer leg = 12 m , shorter leg = 5 m and hypotenuse = 13 m

y............. xnxnxnxnxnccncncncnnncncjcjnf

Answer:

a(n)= 1/2 * (-8) n-1

Step-by-step explanation:

In a geometric sequence, the ratio between successive terms is constant. This means that we can move from any term to the next one by multiplying by a constant value. Let's calculate this ratio over the first few terms:

\dfrac{-256}{32}=\dfrac{32}{-4}=\dfrac{-4}{\frac12}=\blue{-8}  

32

−256

​

=  

−4

32

​

=  

2

1

​

−4

​

=−8start fraction, minus, 256, divided by, 32, end fraction, equals, start fraction, 32, divided by, minus, 4, end fraction, equals, start fraction, minus, 4, divided by, start fraction, 1, divided by, 2, end fraction, end fraction, equals, start color #6495ed, minus, 8, end color #6495ed

We see that the constant ratio between successive terms is \blue{-8}−8start color #6495ed, minus, 8, end color #6495ed. In other words, we can find any term by starting with the first term and multiplying by \blue{-8}−8start color #6495ed, minus, 8, end color #6495ed repeatedly until we get to the desired term.

Let's look at the first few terms expressed as products:

nn 111 222 333 444

h(n)\!\!\!\!\!h(n)h, left parenthesis, n, right parenthesis \red{\dfrac12}\cdot\!\!\!\left(\blue{-8}\right)^{\,\large0}\!\!\!\!\!\!  

2

1

​

⋅(−8)  

0

start color #df0030, start fraction, 1, divided by, 2, end fraction, end color #df0030, dot, left parenthesis, start color #6495ed, minus, 8, end color #6495ed, right parenthesis, start superscript, 0, end superscript \red{\dfrac12}\cdot\!\!\!\left(\blue{-8}\right)^{\,\large1}\!\!\!\!\!\!  

2

1

​

⋅(−8)  

1

start color #df0030, start fraction, 1, divided by, 2, end fraction, end color #df0030, dot, left parenthesis, start color #6495ed, minus, 8, end color #6495ed, right parenthesis, start superscript, 1, end superscript \red{\dfrac12}\cdot\!\!\!\left(\blue{-8}\right)^{\,\large2}\!\!\!\!\!\!  

2

1

​

⋅(−8)  

2

start color #df0030, start fraction, 1, divided by, 2, end fraction, end color #df0030, dot, left parenthesis, start color #6495ed, minus, 8, end color #6495ed, right parenthesis, squared \red{\dfrac12}\cdot\!\!\!\left(\blue{-8}\right)^{\,\large3}  

2

1

​

⋅(−8)  

3

start color #df0030, start fraction, 1, divided by, 2, end fraction, end color #df0030, dot, left parenthesis, start color #6495ed, minus, 8, end color #6495ed, right parenthesis, cubed

We can see that every term is the product of the first term, \red{\dfrac12}  

2

1

​

start color #df0030, start fraction, 1, divided by, 2, end fraction, end color #df0030, and a power of the constant ratio, \blue{-8}−8start color #6495ed, minus, 8, end color #6495ed. Note that this power is always one less than the term number nnn. This is because the first term is the product of itself and plainly 111, which is like taking the constant ratio to the zeroth power.

Thus, we arrive at the following explicit formula (Note that \red{\dfrac12}  

2

1

​

start color #df0030, start fraction, 1, divided by, 2, end fraction, end color #df0030 is the first term and \blue{-8}−8start color #6495ed, minus, 8, end color #6495ed is the constant ratio):

a(n)=\red{\dfrac12}\cdot\left(\blue{-8}\right)^{\large{\,n-1}}a(n)=  

2

1

​

⋅(−8)  

n−1

a, left parenthesis, n, right parenthesis, equals, start color #df0030, start fraction, 1, divided by, 2, end fraction, end color #df0030, dot, left parenthesis, start color #6495ed, minus, 8, end color #6495ed, right parenthesis, start superscript, n, minus, 1, end superscript

Note that this solution strategy results in this formula; however, an equally correct solution can be written in other equivalent forms as well.

Answer:

A: population

Step-by-step explanation:

Um its just the definition of the word i think.

Population: a collection of persons, things, or objects under study.

Answer:

Step-by-step explanation:

The easiest way to explain this is to use slope and then writing equations for lines. The reason for that is because we are told that the production uniformly increases. That "uniform increase" is the rate of change, and since the rate of change is constant, we are talking about the slope of a line, where the rate of change is constant throughout the whole length of the line.

Create coordinates from the info given:

In the third year, 600 units were made. Time is always an x thing, so the coordinate is (3, 600). Likewise for the other bit of info. Time is always an x thing, so the coordinate is (7, 700). Applying the slope formula:

[tex]m=\frac{700-600}{7-3}=\frac{100}{4}=25[/tex]  which means that 25 units per year are produced. Write the equation to find the number of units produced in any year. I used the point-slope form of a line to do this:

y - 600 = 25(x - 3) and

y - 600 = 25x - 75 so

y = 25x + 525

If we want to know the number of units in the first year, we will replace x with 1 and do the math:

y = 25(1) + 525 so

y = 550 units, choice C.

Answer:

Angelica's house is 11 miles away from the gas station.

Step-by-step explanation:

The most simple path from Angelica's house is 11 blocks away from the gas station and each unit/block is 1 mile. So 11 miles.

Answer:

here are the points (0,-6), (-2,1), (2,2), (6,3)

Step-by-step explanation:

you just use the rise over run rule, which means that the top number is the rise and the bottom number is the run. In this case the rise is 1 and the run is 4. So, you would move up one space then move 4 spaces to the right, but because the graph is cut off you can reverse it and it would be the same thing, it would just be in a different area of the graph. So you go, down 1 and left 4 instead. hope this helps :)

Answer:

O Prime

Step-by-step explanation:

x^2 - 7x - 10

What two numbers multiply to -10 and add to -7

There are no two number that multiply to -10 and add to -7

Answer:

x^2 - 7x - 10

Think about it like this: What two numbers multiply to get -10 and add to get -7?

But no matter what we try, this doesn't work. And that's because x^2 - 7x - 10 is actually prime.

So "Prime" is the correct answer.

Let me know if this helps.

Answer:

Step-by-step explanation:

If you plot these points on a graph, you would see that this is definitely a line. Let's find the slope of the line first:

[tex]m=\frac{2-1}{6-5}=1[/tex] (I used the last 2 coordinates on the table because I don't like negatives; and since the slope is the same for the whole entire line, it doesn't matter which points you pick to go into your slope formula)

And then use that slope and any other point in the table to write the equation. I am going to use (4, 0), since I like the 0 (less work!)

In point-slope form:

y - 0 = 1(x - 4) and

y = x - 4

That's the function rule (aka equation) for the table.

Answer:

x=2  true solution

x=-3 extraneous

Step-by-step explanation:

sqrt(x+7) -1 = x

Add 1 to each side

sqrt(x+7) -1+1 = x+1

sqrt(x+7)  = x+1

Square each side

(sqrt(x+7))^2  = (x+1)^2

x+7 = x^2 +2x+1

Subtract x from each side

7 = x^2 +x +1

Subtract 7 from each side

0 = x^2 +x - 6

Factor

0 = (x+3)(x-2)

Using the zero product property

x+3 = 0   x-2 =0

x=-3  x=2

Check solutions

x=-3

sqrt(-3+7) -1 = -3

sqrt(4) -1 = -3

3 =-3  extraneous

x=2

sqrt(2+7) -1 = 2

sqrt(9) -1 = 2

3 -1 =2

2 =2  true

Answer:

A

Step-by-step explanation:

Multiply 28 by 5.5

28 × 5.5 = 154 words → A

Answer:

the awnser is a=154

hope that helps

Step-by-step explanation:

can u give me brainliest

Answer:

false

Step-by-step explanation:

correlation doesn't mean causation-

one doesn't necessarily affect the other, can just be conditions (such as weather) or coincidence

Answer:

[tex]5^{-2}[/tex]

Step-by-step explanation:

Using the rule of exponents

[tex]a^{-m}[/tex] ⇔ [tex]\frac{1}{a^{m} }[/tex] , then

[tex]\frac{1}{25}[/tex] = [tex]\frac{1}{5^{2} }[/tex] = [tex]5^{-2}[/tex]

In exponent form, it should be written as [tex]5^{-2}[/tex].

Given that,

Based on the above information, the calculation is as follows:

[tex]a^{-m} = \frac{1}{a^{m}} \\\\\frac{1}{25} = \frac{1}{5^{2}}[/tex]

[tex]5^{-2}[/tex]

Learn more: brainly.com/question/17429689

Answer:

The mean will be 22.436363636364.. or 22.4 (rounded to the nearest tenth)

you add them then divide by 22 since it has 22 terms, to find the mean

Answer:

use a calculator and add all values and divide by 22

u et final value as ( as per me not sure..maybe mistake) is

493.6/22 and ans Is 22.4363636364

The choices :

Three

B , E , D

Answer:

x = 10

Step-by-step explanation:

7(x+1+7)=6(x+5+6)

or, 7(x+8)=6(x+11)

or, 7x+56=6x+66

or, 7x-6x=66-56

or, x=10

Answered by GAUTHMATH

Answer: 7m⁵ -3m³ - 3

Working:

= (6m⁵ + 3 - m³ - 4m) -(-m⁵ + 2m³- 4m +6)

= 6m⁵ + 3 - m³ - 4m +m⁵-2m³+4m - 6

= 6m⁵ + m⁵-m³ -2m³ -4m + 4m - 6 +3

= 7m⁵ -3m³ - 3

Answered by Gauthmath must click thanks and mark brainliest

Answer:

8^18

Step-by-step explanation:

We know that a^b ÷ a^c = a^(b-c)

8^15÷8^−3

8^(15 - -3)

8^(15+3)

8^18

Step-by-step explanation:

cos(90) = 0

around this point the cos function "mirrors" with opposite signs. cos(<90) is positive and cos(>90) is negative.

but |cos(90-a)| = |cos(90+a)| for 0 <= a <= 90

75 = 90 - 15

105 = 90 + 15

so, a = 15

and because of

|cos(90-a)| = |cos(90+a)| for 0 <= a <= 90

cos (90-15) = cos(75) = -cos(90+15) = -cos(105)