The table below shows how much Joe earns, y, after working x hours.

Joe’s Earnings

Hours worked
Money earned
4
$30
10
$75
12
$90
22
$165

The relationship between money earned and hours worked is linear. Joe computes the slope between (4, 30) and (12, 90), then computes the slope between (4, 30) and (10, 75). How do the two slopes compare?
The slope between (4, 30) and (12, 90) is greater because the ordered pairs are farther apart on the x-axis.
The slope between (4, 30) and (12, 90) is greater because the ordered pairs are farther apart on the y-axis.
The slope between (4, 30) and (12, 90) and between (4, 30) and (10, 75) is the same.
The slope between (4, 30) and (12, 90) is less because 4 is a factor of 12 and 30 is a factor of 90.

Answer:

Area of a Sector of Circle = (θ/360º) × πr²

[tex]area \: = \: \frac{70}{360} \times \frac{22}{7} \times 10 {}^{2} \\ = 61.11[/tex]

on rounding off to two decimal places:-

Answer:

m = -1

n= -8

Step-by-step explanation:

5m -3n = 19

m - 6 = -7

solve for m:

m = -7+6

m = -1

plug in m

5(-1) - 3n = 19

-5 - 3n = 19

-3n = 24

n = -8

is good answer the x value and y value

Answer:

No, the inverse function does not pass the horizontal line test.

Step-by-step explanation:

Answer: C. 225

Step-by-step explanation:

Answer:

There is a non-removable discontinuity at x = 3

Step-by-step explanation:

We are  given that

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

We have to find true statement about given function.

[tex]\lim_{x\rightarrow 3}f(x)=\lim_{x\rightarrow 3}\frac{x^2+9}{x-3}[/tex]

=[tex]\infty[/tex]

It is not removable discontinuity.

x-3=0

x=3

The function f(x) is not define at x=3. Therefore, the function f(x) is continuous for all real numbers except x=3.

Therefore, x=3 is non- removable discontinuity of function f(x).

Hence, option B is correct.

Answer:

y - 2 = 36(x - 4)

Step-by-step explanation:

The equation of a line in point- slope form is

y - b = m(x - a)

where m is the slope and (a, b) a point on the line

Here m = 36 and (a, b ) = (4, 2 ) , then

y - 2 = 36(x - 4) ← equation of line

Answer:

B

Step-by-step explanation:

Answer:

B=-5

Step-by-step explanation:

Slope=rise/run

The line passes in

P1(-1,3)

and

P2(0,-2)

So slope=(3-(-2))/(-1-0)=5/-1=-5

Hello,

[tex]u_0=4000\\u_1=4000*1.05 (for\ year\ 2011)\\\\u_n=4000*1.05^n\\So:\\year\ 2017: u_7=4000*1.05^7=5628,401690625\ \approx{5628}[/tex]

Using an exponential function, the number of students y in the graduating class 7 years after 2010 i.e. in 2017 will be 5628.4

y = abˣ, where a is the initial population, b is the rate, and x is the time, is the standard exponential function.

Here initial student population = 4000.

Rate = 5% = (100 + 5)/100 = 1.05

Time = 7 years.

Now, in 2017, the population will be y = 4000 * (1.05)⁷ = 5628.401691 ≅ 5628.4.

Therefore, using an exponential function, the number of students y in the graduating class 7 years after 2010 i.e. in 2017 will be 5628.4

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Answer:

the answer is A, if you need explanation comment

Step-by-step explanation:

Answer:

1. 25

2. 44

3. 9

Step-by-step explanation:

Answer:

Step-by-step explanation:

Given:

The expression is:

[tex]2x^3+mx^2+nx+c[/tex]

It leaves the same remainder when divided by x -2 or by x+1.

To prove:

[tex]m+n=-6[/tex]

Solution:

Remainder theorem: If a polynomial P(x) is divided by (x-c), thent he remainder is P(c).

Let the given polynomial is:

[tex]P(x)=2x^3+mx^2+nx+c[/tex]

It leaves the same remainder when divided by x -2 or by x+1. By using remainder theorem, we can say that

[tex]P(2)=P(-1)[/tex]              ...(i)

Substituting [tex]x=-1[/tex] in the given polynomial.

[tex]P(-1)=2(-1)^3+m(-1)^2+n(-1)+c[/tex]

[tex]P(-1)=-2+m-n+c[/tex]

Substituting [tex]x=2[/tex] in the given polynomial.

[tex]P(2)=2(2)^3+m(2)^2+n(2)+c[/tex]

[tex]P(2)=2(8)+m(4)+2n+c[/tex]

[tex]P(2)=16+4m+2n+c[/tex]

Now, substitute the values of P(2) and P(-1) in (i), we get

[tex]16+4m+2n+c=-2+m-n+c[/tex]

[tex]16+4m+2n+c+2-m+n-c=0[/tex]

[tex]18+3m+3n=0[/tex]

[tex]3m+3n=-18[/tex]

Divide both sides by 3.

[tex]\dfrac{3m+3n}{3}=\dfrac{-18}{3}[/tex]

[tex]m+n=-6[/tex]

Hence proved.

Answer:

C. non collinear and coplanar

Option (C) non-collinear and co planar is the correct answer about the points R, L, and S.

A set of points in space are co planar, if there exists a geometric plane that contains them all.

Non-collinear points are points that do not lie on one straight line. The points are not collinear, when they are joined with each other, they form a triangle, which is a three-sided polygon.

For the given situation,

The diagram shows the plane M and the triangle.

In the diagram, all the points are lie on the same plane but the points are not lie on the same line.

Three points are always co planar, and if the points are distinct and non-collinear, the plane they determine is unique.

Hence we can conclude that option (C) non-collinear and co planar is the correct answer about the points R, L, and S.

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Answer:the awnser would b 2

Step-by-step explanation: it’s telling you if you look at the triangle from ABC it’s 54 degrees, but if you look at it from BAC it’s 30 degrees so you can only draw 2 triangles because no other combination is given the only other information we know is the line connecting A and B is 5 in some length which is a line not a triangle it would be a triangle thou if lines BC and AC were given. Long story short it’s B) 2

Answer:

x = 4

Step-by-step explanation:

steps are in the pic above.

Answer:

Find the circumference of the semicircle:

Find the outer perimeter:

Answer:

the answer is 108

Step-by-step explanation:

please stop deleting my answer and i am right i was researching it you need to multiply and add the 10+8x6

Answer: [tex]1456\ ft^2[/tex]

Step-by-step explanation:

Given

Length of whole fence is 155 feet

If the length of rectangle is 45.5 ft

Suppose width is w

Length of whole fence is perimeter which is given by

[tex]\Rightarrow 155=2(45.5+w)\\\Rightarrow 77.5=45.5+w\\\Rightarrow w=32\ ft[/tex]

Area of the rectangle is given by the product of length and width

[tex]\Rightarrow A=lw\\\Rightarrow A=45.5\times 32\\\Rightarrow A=1456\ ft^2[/tex]

Thus, total area of pasture is [tex]1456\ ft^2[/tex]

Answer:

slope= difference in y ÷difference in x

=y-y1÷x-x1

=-3-(-1)÷-3-1

=-3+1÷-3-1

=-2÷-4

=1/2

Step-by-step explanation:

hope this is helpful

Y2 -Y1 ÷ X2-X1

-1 - 1 ÷ -3 - -3= 0.5 or 1/2

Answer:

C

Step-by-step explanation:

[tex]4(x + 3) \leqslant 44 \\ \\ 4x + 12 \leqslant 44 \\ 4x \leqslant 44 - 12 \\ 4x \leqslant 32 \\ 4x \div 4 \leqslant 32 \div 4 \\ x \leqslant 8[/tex]

Answer:

Step-by-step explanation:

(a+b+c)²=a²+b²+c²+2ab+2bc+2ca

(2x-3y+4z)²=(2x)²+(-3y)²+(4z)²+2(2x)(-3y)+2(-3y)(4z)+2(4z)(2x)

=4x²+9y²+16z²-12xy-24yz+16zx

We know that,

→ (a + b + c)² = a² + b² + c² + 2ab + 2bc + 2ca

Now Putting 2x = a, -3y = b and 4z = c , we get

→ (2x - 3y + 4z)²

→ (2x)² + (- 3y)² + (4z)² + 2 × 2x × (- 3y) + 2 × (- 3y) × 4z + 2 × 4z × 2x

→ 4x² + 9y² + 16z² - 12xy - 24yz + 16zx

Arranging according to the like terms, we get

→ 4x² - 12xy + 16zx + 9y² - 24yz + 16z²

Answer:

Step-by-step explanation:

Let "ab" represent the digits of the number. The value of "ab" is 10a+b.

a+b = 7

The value of "ba" is 10b+a

(10b+a) - (10a+b) = 9b-9a = 27

b-a = 3

a+b = 7

b-a = 3

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

2b = 10

b = 5

a = 2

The number is 25.

Answer:

x = 5

Step-by-step explanation:

Sides of large triangle: 4x and 15

Corresponding sides of small triangle: 3x + 1 and 12

[tex] \dfrac{4x}{15} = \dfrac{3x + 1}{12} [/tex]

[tex] 60 \times \dfrac{4x}{15} = 60 \times \dfrac{3x + 1}{12} [/tex]

[tex] 16x = 15x + 5 [/tex]

[tex] x = 5 [/tex]

Given:

The expressions are:

[tex]6+3[/tex]

[tex]6+(-4)[/tex]

[tex]6+(-6)[/tex]

To find:

The value of given expression by using integer tiles.

Solution:

We have,

[tex]6+3[/tex]

Here, both number are positive. When we add 6 and 3 positive integer tiles, we get 9 positive integer tiles as shown in the below figure. So,

[tex]6+3=9[/tex]

Similarly,

[tex]6+(-4)[/tex]

Here, 6 is positive and -4 is negative. It means we have 6 positive integer tiles and 4 negative integer tiles.

When we cancel the positive and negative integer tiles, we get 2 positive integer tiles as shown in the below figure. So,

[tex]6+(-4)=2[/tex]

[tex]6+(-6)[/tex]

Here, 6 is positive and -6 is negative. It means we have 6 positive integer tiles and 6 negative integer tiles.

When we cancel the positive and negative integer tiles, we get 0 integer tiles as shown in the below figure. So,

[tex]6+(-6)=0[/tex]

Therefore, [tex]6+3=9, 6+(-4)=2,6+(-6)=0[/tex].

Answer:

1=9

2=2

3=0

Step-by-step explanation:

Step-by-step explanation:

just use (a+b)(a-b) = [tex]a^{2} - b^{2}[/tex][tex](4+\sqrt{3}) (4-\sqrt{3)} = 4^{2} - (\sqrt{3} )^{2} = 16 - 3 = 13[/tex]

answer is 13

Answer:

65/264 or 0.2462

Step-by-step explanation:

The given series is

(1/1.2.3) + (1/2.3.4) + (1/3.4.5) + ………………

If we denote the series by

u(1) + u(2) + u(3) + u(4) +……………..u(n),

where u(n) is the nth term, then

u(n) = 1/[n(n+1)(n+2)] , n = 1,2,3,4,………n.

which can be written as

u(n) = (1/2) [1/n(n+1) - 1/(n+1)(n+2)] ………………………(1)

In the question, the number of terms n =10, thereby restricting us only to first 10 terms of the series and we have to find the sum for this truncated series. Let S(10) denote the required sum. We have then from (1),

u(1) = (1/2) (1/1.2 - 1/2.3)

u(2) = (1/2) (1/2.3 - 1/3.4)

u(3) = (1/2) (1/3.4 - 1/4.5)

u(4) = (1/2) (1/4.5 - 1/5.6)

u(5) = (1/2) (1/5.6 - 1/6.7)

u(6) = (1/2) (1/6.7 - 1/7.8)

u(7) = (1/2) (1/7.8 - 1/8.9)

u(8) = (1/2) (1/8.9 - 1/9.10)

u(9) = (1/2) (1/9.10 - 1/10.11)

u(10) = (1/2) (1/10.11 - 1/11.12)

Let us now add the terms on LHS and the terms on RHS independently. The sum of LHS is nothing but the sum S(10) of the series up to 10 terms. On the RHS, alternate terms cancel and we are left with only the first and the last term. Therefore,

S(10) = (1/2) (1/1.2 - 1/11.12) = (1/2) (66–1)/132 = [65/(132.2)]

= 65/264

= 0.2462 (correct to four decimal places)

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Answer:

Below.

Step-by-step explanation:

Ok so since 71 +25 = 96. A line segment is 180 so 180-96= 84. Hope this is right little hard to see.

Answer:

1096 more water

Step-by-step explanation:

Let;

x = the water used in general

but used 3 times of the original = 3x

3*(548) = 1644 water a day

How much more water =New - original

where:

new = 1644

original= 548

1644 - 548

=1096 more water

Answer:

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

Answer:

17

Step-by-step explanation: