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4 years ago

The graph below belongs to which function family?

Mathematics

2 answers:

svet-max [94.6K]4 years ago

6 0

The answer is the last one (absolute value)

I am Lyosha [343]4 years ago

6 0

The graph shown in the diagram belongs to the family of absolute function value.

The parent function $f(x)=|x|$ has the graph (red graph in attached diagram).

Reflect this graph across the x-axis and translate 3 units up to get given graph (see blue graph in attached diagram). The function rule will be $g(x)=-|x|+3.$

Answer: correct choice is D.

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A rectangular field is 75 yards wide and 105 yards long

nika2105 [10]

Answer:

width = 72 yards

length = 108 yards

Step-by-step explanation:

Given:

Width = 75 yards
Length = 105 yards

Area of the field with the given values:

$\begin{aligned}\textsf{Area of a rectangle}&=\sf width \times length\\& = \sf 75 \times 105\\& = \sf 7875\:\: yd^2\end{aligned}$

To maintain the same perimeter, but change the area, either:

decrease the width and increase the length by the same amount, or
increase the width and decrease the length by the same amount.

In geometry, length pertains to the longest side of the rectangle while width is the shorter side. Therefore, we should choose:

decrease the width and increase the length by the same amount.

Define the variables:

Let x = the amount by which to decrease/increase the width and length.

Therefore:

$\implies \sf width \times length < 7875\:\:yd^2$

$\implies (75-x)(105+x) < 7875$

Solve the inequality:

$\begin{aligned}(75-x)(105+x) & < 7875\\7875-30x-x^2 & < 7875\\-x^2-30x & < 0\\-x(x+30) & < 0\\x(x+30) & > 0\\\implies x & > 0 \:\: \textsf{ or }\:\:x < - 30\end{aligned}$

Therefore, as distance is positive only and the maximum width is 75 yd (since we are subtracting from the original width):

$\begin{cases}\textsf{width} = 75 - x\\\textsf{length} = 105 + x\end{cases}$

$\textsf{where } 0 < x < 75$

Therefore, to find the width and length of another rectangular field that has the same perimeter but a smaller area than the first field, simply substitute a value of x from the restricted interval into the found expressions for width and length:

Example 1:

Let x = 3

⇒ Width = 75 - 3 = 72 yd

⇒ Length = 105 + 3 = 108 yd

⇒ Perimeter = 2(72 + 108) = 360 yd

⇒ Area = 72 × 108 = 7776 yd²

Example 2:

Let x = 74

⇒ Width = 75 - 74 = 1 yd

⇒ Length = 105 + 74 = 179 yd

⇒ Perimeter = 2(1 + 179) = 360 yd

⇒ Area = 1 × 179 = 179 yd²

4 0

2 years ago

Read 2 more answers

Mileage tests are conducted for a particular model of automobile. If a 98% confidence interval with a margin of error of 1 mile

kipiarov [429]

Answer: 37

Step-by-step explanation:

As per given description in the question, we have

Population standard deviation : $\sigma=2.6\text{ miles per gallon}$

Critical value for 98% confidence interval = $z_{\alpha/2}=2.33$

Margin of error : E= 1 mile per gallon

Formula we use to find the sample size :

$n=(\dfrac{z_{\alpha/2}\cdot \sigma}{E})^2$

i.e. $n=(\dfrac{(2.33)\cdot(2.6)}{1})^2$

$\Rightarrow\ n=36.699364\approx37$

Therefore , the number of automobiles should be used in the test =37

4 0

3 years ago

What is 32+56•45? Please answer!

otez555 [7]

32+56*45

Remember PEMDAS, so we have to solve the multiplication part of the expression first....

32+2520

Now we solve for the addition

2552

Answer=2552

5 0

4 years ago

Read 2 more answers

If you apply the changes below to the linear parent function, Fx) = x, what is

Inga [223]

Answer: A. G(x)= ax=y= - f(x) is flip over x-axis. Therefore, f(x) =14x would become f(x) =-14x. Therefore, final transformed function f(x)=-14x is vertically stretch by a factor of 14 and flip over the x-axis.

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4 years ago

The system of equations graphed below has how many solutions?

Montano1993 [528]

Because these two lines have the same slope, they are parallel. Since they are parallel, they never intersect and therefore have no solutions, so the answer is C

5 0

3 years ago