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3 years ago

9

if x =

s="latex-formula"> , y = 2, and z = $\frac{1}{2}$ , then $x^{2}$ - 5yz + $y^{2}$

1 answer:

irina1246 [14]3 years ago

4 0

Answer:

2

Step-by-step explanation:

Substitute all the variables in.

$\sqrt{3} ^2-5(2)(\frac{1}{2} )+2^2$

Use the order of operations to solve.

3-5+4

2

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Rewrite the radical as a rational exponent. the cube root of 2 to the seventh power 2 to the 3 over 7 power 2 to the 7 over 3 po

Deffense [45]

$\sqrt[3]{2^7} =2^{ \frac{7}{3} }$

8 0

3 years ago

Read 2 more answers

The stopping distance d of an automobile is directly proportional to the square of its speed s. On one road, a car requires 75 f

Anton [14]

Answer:

The car requires 192 feet to stop from a speed of 48 miles per hour on the same road

Step-by-step explanation:

Direct proportion means that two quantities increase or decrease in the same ratio

If y is directly proportional to x (y ∝ x) , then $\frac{y_{1}}{y_{2}}=\frac{x_{1}}{x_{2}}$ <em>OR</em> y = k x, where k is the constant of proportionality

∵ The stopping distance d of an automobile is directly

proportional to the square of its speed s

- That means d ∝ s²

∴ $\frac{d_{1}}{d_{2}}=\frac{(s_{1})^{2}}{(s_{2})^{2}}$

∵ A car requires 75 feet to stop from a speed of 30 miles per hour

∴ d = 75 feet

∴ s = 30 miles/hour

- Change the mile to feet

∵ 1 mile = 5280 feet

∴ 30 miles/hour = 30 × 5280 = 158400 feet/hour

∵ The car require to stop from a speed of 48 miles per hour

on the same road

- Change the mile to feet

∴ 48 miles/hour = 48 × 5280 = 253440 feet/hour

∵ $\frac{d_{1}}{d_{2}}=\frac{(s_{1})^{2}}{(s_{2})^{2}}$

- Substitute the values of $d_{1}$ by 75 feet, $s_{1}$ by 158400 feet/hour

and $s_{2}$ by 253440 feet/hour

∴ $\frac{75}{d_{2}}=\frac{(158400)^{2}}{(253440)^{2}}$

∴ $\frac{75}{d_{2}}=\frac{25}{64}$

- By using cross multiplication

∴ 25 × $d_{2}$ = 75 × 64

- Divide both sides by 25

∴ $d_{2}$ = 192 feet

The car requires 192 feet to stop from a speed of 48 miles per hour on the same road

4 0

3 years ago

Fins the zeros, multiplicity, and effect on the graph of the function in

tekilochka [14]

Answer:

See explanation

Step-by-step explanation:

Zeroe of the function is such velue of x at which f(x)=0.

1. Consider the function $f(x)=-x(3x-2)^2 (x+9)^5.$

Zeros are:

$-x(3x-2)^2(x+9)^5=0\\ \\x=0\text{ or }x=\dfrac{2}{3}\text{ or }x=-9.$

Zero $x=0$ has multiplicity of 1, zero $x=\dfrac{2}{3}$ has multiplicity of 2, zero $x=-9$ has multiplicity of 5.

At $x=0$ or $x=-9$ the graph of the function crosses the x-axis, at $x=\dfrac{2}{3}$ the graph of the function touches the x-axis.

2. Consider the function $f(x)=x^3+10x^2+25x=x(x^2+10x+25)=x(x+5)^2.$

Zeros are:

$x(x+5)^2=0\\ \\x=0\text{ or }x=-5.$

Zero $x=0$ has multiplicity of 1, zero $x=-5$ has multiplicity of 2.

At $x=0$ the graph of the function crosses the x-axis, at $x=-5$ the graph of the function touches the x-axis.

8 0

4 years ago

A recent poll of 1971 home owners in West Virginia showed that the average price of a house in the U.S. is $319,000

siniylev [52]

Answer:

A) Sample statistic

Step-by-step explanation:

A sample statistic is a number computed from values that belongs to a sample, to represent a whole population.

In this case the sample is the home owners in West Virginia that respond this poll in 1971, and the population is U.S.

3 0

3 years ago

Part 2: NO LINKS!! NOT MULTIPLE CHOICE! Please help me

Dmitry_Shevchenko [17]

Answer:

(see attachment for tree diagram)

$\sf Probability\:of\:an\:event\:occurring = \dfrac{Number\:of\:ways\:it\:can\:occur}{Total\:number\:of\:possible\:outcomes}$

<h3><u>Part (a)</u></h3>

$\textsf{P(Head) and P(3)}=\sf \dfrac{1}{2} \times \dfrac{1}{6}=\dfrac{1}{12}$

<h3><u>Part (b)</u></h3>

$\textsf{P(Tail) and P(even)}=\sf \dfrac{1}{2} \times \dfrac{3}{6}=\dfrac{3}{12}=\dfrac{1}{4}$

<h3><u>Part (c)</u></h3>

$\textsf{P(not 6)}=\sf 1-\textsf{P(6)}=1-\dfrac{1}{6}=\dfrac{5}{6}$

$\implies \textsf{P(Head) and P(not 6)}=\sf \dfrac{1}{2} \times \dfrac{5}{6}=\dfrac{5}{12}$

<h3><u>Part (d)</u></h3>

As the six-sided die does not have a side labelled "7", the probability of rolling a 7 is zero.

$\implies \textsf{P(Head) and P(7)}=\sf \dfrac{1}{2} \times 0=0$

7 0

2 years ago