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3 years ago

There are 122 fourth grade and 11 teachers going on a field trip

1 answer:

5 0

For the first part of this question, you will write the following division problem to represent this situation:

(122 + 11)/16 =
133/16 =8.3125

Mrs. Reyes is NOT correct! You will need one more bus because 8 groups of 16 is 128, and you need to fit 133 people on the buses.

To show the place value models, you will need 4 individual boxes, 3 rows of 10 (30), 5 - 10 x 10 models (500) and 1 cube that is 10 x 10 x 10 (1000).

1000 + 500 + 30 + 4

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Simplifying Rational Expressions

Evgen [1.6K]

B^-2 / b^-3 = b^(-2-(-3) = b^1 = b

answer is d

4 0

3 years ago

Suppose you have $5000 to invest. A certificate of deposit (CD) earn 6% annual interest, while bonds, which are riskier, earn 8%

Travka [436]

$2000(1.06)+3000(1.08)-5000=360$
$2000(1.06)^2+3000(1.08)^2-5000=746.4$

6 0

4 years ago

What is the distance from ( -3 4 ) to ( 4 , -3)?

Hoochie [10]

Answer:

Answer:

Exact form: 7√2

Decimal form: 9.89949493

Step-by-step explanation:

Also i'm going to assume you meant (-3, 4) instead of

"( -3 4 )."

5 0

3 years ago

The average smoker typically pays 15% higher life insurance costs than the average non-smoker. If the monthly cost to a non-smok

algol13

Answer:

$575 per month

Step-by-step explanation:

$500 x 15% = $75

(15% of 500 = $75)

therefore

500 + 75 = $575 a non smoker must pay for insurance

6 0

3 years ago

Maths functions <br> please help!

Vlad [161]

Answer:

$\textsf{1)} \quad f(x)=-x+3$

2) A = (3, 0) and C = (-3, 0)

$\textsf{3)} \quad g(x)=x^2-9$

4) AC = 6 units and OB = 9 units

Step-by-step explanation:

Given functions:

$\begin{cases}f(x)=mx+c\\g(x)=ax^2+b \end{cases}$

Given points:

H = (-1, 4)
T = (4, -1)

As points H and T lie on f(x), substitute the two points into the function to create two equations:

$\textsf{Equation 1}: \quad f(-1)=m(-1)+c=4 \implies -m+c=4$

$\textsf{Equation 2}: \quad f(4)=m(4)+c=-1 \implies 4m+c=-1$

Subtract the first equation from the second to eliminate c:

$\begin{array}{r l} 4m+c & = -1\\- \quad -m+c & = \phantom{))}4\\\cline{1-2}5m \phantom{))))}}& = -5}\end{aligned}$

Therefore m = -1.

Substitute the found value of m and one of the points into the function and solve for c:

$\implies f(4)=-1(4)+c=-1$

$\implies c=-1-(-4)=3$

Therefore the equation for function f(x) is:

$f(x)=-x+3$

Function f(x) crosses the x-axis at point A. Therefore, f(x) = 0 at point A.

To find the x-value of point A, set f(x) to zero and solve for x:

$\implies f(x)=0$

$\implies -x+3=0$

$\implies x=3$

Therefore, A = (3, 0).

As g(x) = ax² + b, its axis of symmetry is x = 0.

A parabola's axis of symmetry is the midpoint of its x-intercepts.

Therefore, if A = (3, 0) then C = (-3, 0).

Points on function g(x):

A = (3, 0)
G = (1, -8)

Substitute the points into the given function g(x) to create two equations:

$\textsf{Equation 1}: \quad g(3)=a(3)^2+b=0 \implies 9a+b=0$

$\textsf{Equation 2}: \quad g(1)=a(1)^2+b=-8 \implies a+b=-8$

Subtract the second equation from the first to eliminate b:

$\begin{array}{r l} 9a+b & = \phantom{))}0\\- \quad a+b & =-8\\\cline{1-2}8a \phantom{))))}}& = \phantom{))}8}\end{aligned}$

Therefore a = 1.

Substitute the found value of a and one of the points into the function and solve for b:

$\implies g(3)=1(3^2)+b=0$

$\implies 9+b=0\implies b=-9$

Therefore the equation for function g(x) is:

$g(x)=x^2-9$

The length AC is the difference between the x-values of points A and C.

$\implies x_A-x_C=3-(-3)=6$

Point B is the y-intercept of g(x), so when x = 0:

$\implies g(0)=(0)^2-9=-9$

Therefore, B = (0, -9).

The length OB is the difference between the y-values of the origin and point B.

$\implies y_O-y_B=0-(-9)=9$

Therefore, AC = 6 units and OB = 9 units

3 0

2 years ago

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