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2 years ago

The triangles below are similar. Find x.

Mathematics

1 answer:

Anni [7]2 years ago

8 0

Answer: 105

Step-by-step explanation:

Corresponding sides of similar triangles are proportional, so

$\frac{x}{14}=\frac{97.5}{13}\\\\=\frac{x}{14}=7.5\\\\x=\boxed{105}$

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The fraction 5/3 has what as the denominator

Lyrx [107]

Answer:3

Step-by-step explanation:

6 0

3 years ago

Read 2 more answers

Find the area of a rectangle with a length of (5x – 4) and a width of (-3x – 6).

Inessa05 [86]

Use this simple calcula tor to find the area and perimeter of a rectangle. ... Suppose the length is a = 6 inches and the width is b = 4 inches.

4 0

2 years ago

If the scientist is accurate, what is the probability that the proportion of airborne viruses in a sample of 477 viruses would d

melisa1 [442]

Answer:

0.01596

Step-by-step explanation:

A scientist claims that 8% of the viruses are airborne

Given that:

The population proportion p = 8%

The sample size = 477

We can calculate the standard deviation of the population proportion by using the formula:

$\sigma_p = \sqrt{\dfrac{p(1-p)}{n}}$

$\sigma_p = \sqrt{\dfrac{0.8(1-0.8)}{477}}$

$\sigma_p = \sqrt{\dfrac{0.0736}{477}}$

$\sigma_p = 0.02098$

The required probability can be calculated as:

$P(| \hat p - p| > 0.03) = P(\hat p - p< -0.03 \ or \ \hat p - p > 0.03)$

$= P \bigg ( \dfrac{\hat p -p }{\sqrt{\dfrac{p(1-p)}{n}}} < -\dfrac{0.03}{0.0124} \bigg ) + P \bigg ( \dfrac{\hat p -p }{\sqrt{\dfrac{p(1-p)}{n}}} >\dfrac{0.03}{0.0124} \bigg )$

= P(Z < -2.41) + P(Z > 2.41)

= P(Z < -2.41) + P(Z < -2.41)

= 2P( Z< - 2.41)

From the Z-tables;

$P(| \hat p - p| > 0.03)$ = 2 ( 0.00798

$P(| \hat p - p| > 0.03)$ = 0.01596

Thus, the required probability = 0.01596

3 0

3 years ago

A circle is centered at the point (-7, -1) and passes through the point (8, 7).

Sergeu [11.5K]

we know the circle's center is at -7, -1, and we know the circle itself passes through 8,7, the distance from the center to a point on it is by definition its radius, therefore

$\bf ~~~~~~~~~~~~\textit{distance between 2 points}\\\\\stackrel{center}{(\stackrel{x_1}{-7}~,~\stackrel{y_1}{-1})}\qquad (\stackrel{x_2}{8}~,~\stackrel{y_2}{7})\qquad \qquad d = \sqrt{( x_2- x_1)^2 + ( y_2- y_1)^2}\\\\\\\stackrel{radius}{r}=\sqrt{[8-(-7)]^2+[7-(-1)]^2}\implies r=\sqrt{(8+7)^2+(7+1)^2}\\\\\\r=\sqrt{15^2+8^2}\implies r=\sqrt{225+64}\implies \boxed{r=17}$

and since we know that x = -15 for such a point, then

$\bf \textit{equation of a circle}\\\\ (x- h)^2+(y- k)^2= r^2\qquad center~~(\stackrel{-7}{ h},\stackrel{-1}{ k})\qquad \qquad radius=\stackrel{17}{ r}\\\\\\\[x-(-7)]^2+[y-(-1)]^2=17^2\implies (x+7)^2+(y+1)^2=289\\\\\\\stackrel{\textit{since we know x = -15}}{(-15+7)^2+(y+1)^2=289}\implies (-8)^2+\stackrel{FOIL}{(y^2+2y+1^2)}=289\\\\\\64+y^2+2y+1=289\implies y^2+2y=224\implies y^2+2y-224=0\\\\\\(y+16)(y-14)=0\implies y=\begin{cases}-16\\14\end{cases}$

since it's a circle, it touches x = -15 twice, check the picture below.

6 0

3 years ago

Find the coordinates of the vertex of the graph of the function. y = 4x2 – 7x + 4

Zanzabum

Answer:

vertex (0.875, 0.9375) AoS x=0.875

Step-by-step explanation:

5 0

3 years ago