The height of a triangle is 2 more than

Suppose a parabola has an axis of symmetry at x=-5, a maximum height of 9, and passes through the point (-7,1). Write the equati

Nutka1998 [239]

the parabola has maximum at 9, meaning is a vertical parabola and it opens downwards.

it has a symmetry at x = -5, namely its vertex's x-coordinate is -5.

check the picture below.

so then, we can pretty much tell its vertex is at (-5 , 9), and we also know it passes through (-7, 1)

$\bf ~~~~~~\textit{parabola vertex form} \\\\ \begin{array}{llll} y=a(x- h)^2+ k\qquad \leftarrow \textit{using this one}\\\\ x=a(y- k)^2+ h \end{array} \qquad\qquad vertex~~(\stackrel{}{ h},\stackrel{}{ k}) \\\\[-0.35em] \rule{34em}{0.25pt}\\\\ \begin{cases} h=-5\\ k=9 \end{cases}\implies y=a[x-(-5)]^2+9\implies y=a(x+5)^2+9$

$\bf \textit{we also know that } \begin{cases} x=-7\\ y=1 \end{cases}\implies 1=a(-7+5)^2+9 \\\\\\ -8=a(-2)^2\implies -8=4a\implies \cfrac{-8}{4}=a\implies -2=a \\\\[-0.35em] ~\dotfill\\\\ ~\hfill y=-2(x+5)^2+9~\hfill$

7 0

3 years ago

this month salespersons a made 11% of $67,530. salesperson b made 8% of $85,740. who made more commission this month? how much d

Paul [167]

Salesperson A made $7428.30
Salesperson B made $6859.20
Salesperson A made more commission this month and made $7428.30

7 0

4 years ago

Read 2 more answers

Symposium is part of a larger work referred to as Plato's Dialogues. Wishart and Leach† found that about 21.4% of five-syllable

notsponge [240]

Complete Question

ymposium is part of a larger work referred to as Plato's Dialogues. Wishart and Leach† found that about 21.4% of five-syllable sequences in Symposium are of the type in which four are short and one is long. Suppose an antiquities store in Athens has a very old manuscript that the owner claims is part of Plato's Dialogues. A random sample of 498 five-syllable sequences from this manuscript showed that 129 were of the type four short and one long. Do the data indicate that the population proportion of this type of five-syllable sequence is higher than that found in Plato's Symposium? Use = 0.01.

a. What is the value of the sample test statistic? (Round your answer to two decimal places.)

b. Find the P-value of the test statistic. (Round your answer to four decimal places.)

Answer:

a) $Z=2.45$

b) $P Value=0.0073$

Step-by-step explanation:

From the question we are told that:

Probability of Wishart and Leach $P=21.4=>0.214$

Population Size $N=498$

Sample size $n=12$

Therefore

$P'=\frac{129}{498}$

$P'=0.2590$

Generally the Null and Alternative Hypothesis is mathematically given by

$H_0:P=0.214$

$H_a:=P>0.214$

Test Statistics

$Z=\frac{P'-P}{\sqrt{\frac{P(1-P)}{n}}}$

$Z=\frac{0.2590-0.214}{\sqrt{\frac{0.214(1-0.214)}{498}}}$

$Z=2.45$

Therefore P Value is given as

$P Value =P(Z\geq 2.45)$

$P Value =1-P(Z\leq 2.45)$

$P Value =1-0.99268525$

$P Value=0.0073$

7 0

3 years ago

6. Find the perimeter of the figure below

liraira [26]

Answer:

26 in.

Step-by-step explanation:

» <u>Concepts</u>

The perimeter for a shape is the total distance around it measured in units. The formula to find the perimeter of a trapezoid is a + b + c + d, where a & b are the bases, and c & d are the lengths of the other sides.

» <u>Solution</u>

Adding up all the sides, we get: