Determine if the triangles below are similar. If they are, give the rule that you used to determine similarity.

Distance:-

[tex]\\ \sf\longmapsto \sqrt{(x_2-x_1)^2+(y_2-y_1)^2}[/tex]

[tex]\\ \sf\longmapsto \sqrt{(3+2)^2+(7-5)^2}[/tex]

[tex]\\ \sf\longmapsto \sqrt{5^2+2^2}[/tex]

[tex]\\ \sf\longmapsto \sqrt{25+4}[/tex]

[tex]\\ \sf\longmapsto \sqrt{29}[/tex]

[tex]\\ \sf\longmapsto 5.2[/tex]

[tex]\begin{gathered} {\underline{\boxed{ \rm {\red{Distance \: = \: \sqrt{(x_2 - x_1) \: + \: (y_2 - y_1)} }}}}}\end{gathered}[/tex]

[tex] \begin{cases}\large\bf{\blue{ \implies}} \tt \: Distance \: = \: \sqrt{ \bigg(3 - [ - 2] \bigg) \: + \: (7 - 5)}\\ \\ \large\bf{\blue{ \implies}} \tt \: Distance \: = \: \sqrt{ (3 + 2 ) \: + \: (7 - 5)} \\ \\ \large\bf{\blue{ \implies}} \tt \: Distance \: = \: \sqrt{ {5} \: ^{2} + \: {2}^{2} } \\ \\ \large\bf{\blue{ \implies}} \tt \: Distance \: = \: \: \sqrt{25 \: + \: 4} \\ \\ \large\bf{\blue{ \implies}} \tt \: Distance \: = \: \: \ \sqrt{29} \\ \\\large\bf{\blue{ \implies}} \tt \: Distance \: = \: \:5.38 \: \: units \end{cases}[/tex]

Answer:

The equation is y= -4x -8

Step-by-step explanation:

The -4 is the slope and the -8 is the y intercept

Answer:

Slope: -4

Line type: Straight and diagonal from left to right going down.

Rate of change: a decrease by 4 for every x vaule

y-intercept is: (0,-8)

x-intercept is: (-2,0)

Step-by-step explanation:

Slope calculations:

y2 - y1 over x2 - x1

0 - 4

-2 - ( -3) or -2 + 3

=

-4/1 =

-4

More slope info on my answer here: https://brainly.com/question/17148844

Hope this helps, and have a good day.

Graduation is 4 years away and you want to have $500 available for a trip. If your bank is offering a 4-year CD (certificate of deposit) paying 2.3% simple interest, how much do you need to put in this CD to have the money for your trip?

P: Principal, the amount you need to put in the CD

r: interest rate

t: time

A: total amount

________________________________

P(1+rt) = A

P(1+0.023×4) = 500

P(0.092) = 500

P = 500/0.092 = 5434.78

[Hence, you need $5434.78 to put in this CD to have the money for your trip ]

Answer:

cccccccccccccccçccccccccc

Answer:

if the dot is filled (black) it is ≤ or ≥

if it is not filled it is  < or >

you graph goes from 6 to 10

the unfilled one is 6 the filled one is 10

thus 6 < x ≤ 10

which says x is greater than 6 and also less than or equal to 10

Step-by-step explanation:

Answer:

5/12

Step-by-step explanation:

3/4-1/3=

9/12-4/12=

5/12

Answer:

It is undefined.

Step-by-step explanation:

Let's take a look at the first equation- if we simplify and move the terms, it becomes sqrt of 6 = 0, which results in an undefined value of x. The second equation works with x=0 but not the first so the value of x is undefined.

Answer:

(5*sqrt(2), 5pi/4)

Step-by-step explanation:

In Polar coordinates, tan(theta)=y/x and r=sqrt(x^2+y^2)

tan(theta)=-5/5=-1. Theta=5pi/4

r=sqrt(5^2+5^2)=5*sqrt(2)

Hence the Polar coordinate is (5*sqrt(2), 5pi/4)

The polar coordinate is [tex](5\sqrt{2},\frac{-\pi }{4} )[/tex].

The polar coordinate system is a two-dimensional coordinate system in which each point on a plane is determined by a distance from a reference point and an angle from a reference direction.

To convert rectangular coordinate (x, y) to polar coordinate(r, θ) by using some formula

tanθ = y/x and [tex]r =\sqrt{x^{2} +y^{2} }[/tex]

According to the given question

We have

A rectangular coordinate (5, -5).

⇒ x = 5 and y = -5

Therefore,

[tex]r=\sqrt{(5)^{2} +(-5)^{2} } =\sqrt{25+25} =\sqrt{50} =5\sqrt{2}[/tex]

and

tanθ = [tex]\frac{-5}{5} =-1[/tex]

⇒ θ = [tex]tan^{-1} (-1)[/tex] = [tex]-\frac{\pi }{4}[/tex]

Therefore, the polar coordinate is [tex](5\sqrt{2},\frac{-\pi }{4} )[/tex].

Learn more about polar coordinates here:

https://brainly.com/question/1269731

#SPJ2

Answer:

Step-by-step explanation:

answer is 71.08745247

in mix form or in short form it is =

71/23/263

Answer:

[tex] {(x + 1)}^{2} + {(y - 1)}^{2} = 9[/tex]

[tex] {x} ^{2} + {y} ^{2} + 2x - 2y - 7 = 0 [/tex]

Answer:

(a) The 26th percentile for the number of chocolate chips in a bag is 1185

(b) The number of chocolate chips in a bag that makes up the middle 96% of the bags is between 1020 and 1504

Step-by-step explanation:

From the question, we have the following values:

μ =1262 and σ =118

(a) Let the value of x represents the 26th percentile. So the 26th percentile means 26% data is less than x. We can use the standard normal table to get the particular z-value that corresponds to this percentile.

P( Z<-0.65 )=0.2578 which is approximately 0.26

So for 26th percentile z-score will be -0.65.

Mathematically;

z-score = (x-mean)/SD

-0.65 = (x-1262)/118

-76.7 = x -1262

x = 1262-76.7 = 1185.3

This value is approximately 1,185

(b) Using a graph of standard normal distribution curve, if middle is 96% , then at both tails 2% each.

From z-table, we can find the closest probability;

P(-2.05<z<2.05) = 0.96

So we have two x values to get from the individual z-scores

-2.05 = (x-1262)/118

x = 1020(approximately)

For 2.05, we have

2.05 = (x-1262)/118

x = 1262 + 2.05(118) = 1504 (approximately)

Answer:

Step-by-step explanation:

We will use the set notation to solve this question.

let n(U) be the total number of students surveyed = 100

n(M) be the number of student that took math = 34

n(E) be the number of student that took English = 59

n(M∩E) be the number of student that took both classes= 12

n(M∪E)' be the number of student that took neither class = ?

Using the formula n(U) = n(M∪E) + n(M∪E)'

n(M∪E)' = n(U)-n(M∪E)

Before we can get the number of student that took neither class i.e n(M∪E)'  we need to  get n(M∪E).

n(M∪E) = n(M)+n(E)- n(M∩E)

n(M∪E) = 34+59-12

n(M∪E)  = 81

Since n(M∪E)' = n(U)-n(M∪E);

n(M∪E)' = 100-81

n(M∪E)' = 19

Hence 19 students took neither class as a freshmen.

Answer:

10

Step-by-step explanation:

Let the no. of sodas be x

Price of each soda = $2

Therefore, no . of sodas you can buy = $2x

2x=20

=>x=[tex]\frac{20}{2}[/tex]

=>x=10

you can buy 10 sodas

Answer: 10 sodas

Step-by-step explanation:

2x = 20       Divide both sides by 2  

x = 10

If I brought 20 dollars and I  want to by only sodas and each sodas cost 2 dollars, then I will divide the total amount of money that I brought  by 2 to find out how many sodas I could by.

Answer:

(a) {5}

(b) {1, 2, 5, 6}

(c) {1, 2, 5, 6}

Answer:

see below

Step-by-step explanation:

7g can be "split" as 7 * g. The "*" means multiplication so a verbal form of this expression could be "7 times a number g" or "The product of 7 and a number g".

By Green's theorem,

[tex]\displaystyle\int_{x^2+y^2=16}(3y-e^{\sin x})\,\mathrm dx+(7x+y^4+1)\,\mathrm dy[/tex]

[tex]=\displaystyle\iint_{x^2+y^2\le16}\frac{\partial(7x+y^4+1)}{\partial x}-\frac{\partial(3y-e^{\sin x})}{\partial y}\,\mathrm dx\,\mathrm dy[/tex]

[tex]=\displaystyle4\iint_{x^2+y^2\le16}\mathrm dx\,\mathrm dy[/tex]

The remaining integral is just the area of the circle; its radius is 4, so it has an area of 16π, and the value of the integral is 64π.

We'll verify this by actually computing the integral. Convert to polar coordinates, setting

[tex]\begin{cases}x=r\cos\theta\\y=r\sin\theta\end{cases}\implies\mathrm dx\,\mathrm dy=r\,\mathrm dr\,\mathrm d\theta[/tex]

The interior of the circle is the set

[tex]\{(r,\theta)\mid0\le r\le4\land0\le\theta\le2\pi\}[/tex]

So we have

[tex]\displaystyle4\iint_{x^2+y^2\le16}\mathrm dx\,\mathrm dy=4\int_0^{2\pi}\int_0^4r\,\mathrm dr\,\mathrm d\theta=8\pi\int_0^4r\,\mathrm dr=64\pi[/tex]

as expected.

Answer:

B) 3

Step-by-step explanation:

4+5+1/3=10/3=3.333~3

Answer:

B) 3

Step-by-step explanation:  

The predictive value of a positive test is is 0.43.

------------------

This question is solved using the concepts of sensitivity and specificity.

------------------

------------------

The predictive value of a positive test is:

Probability of a positive test, which is 40% of 90% plus 70% of 10%, so:

[tex]p = 0.4\times0.9 + 0.7\times0.1 = 0.43[/tex]

The predictive value of a positive test is is 0.43.

A similar question is given at https://brainly.com/question/22373775

Answer:

Tetragonal unit cell.

Step-by-step explanation:

A unit cell is the smallest part of a material which is formed by a well arranged lattice points. Some common types are; face centered, body center, tetragonal, cubic etc

Tetragonal unit cell has a square top and base, with rectangular sides. The internal angles are [tex]90^{0}[/tex] each, and consists of molecules, atoms, or ions (lattice points) arranged at each corners of the unit cell.

The crystal as described in the given question is a tetragonal unit cell.

Answer:

16,807

Step-by-step explanation:

Answer:

The mean is about 68 (67.5555)

Step-by-step explanation:

(63+64+66+66+67+68+69+71+74) / 9 ≈ 68

Answer:

B = 34.2°

C = 105.8°

c = 12.0 units

Step-by-step Explanation:

Given:

A = 40°

a = 8

b = 7

Required:

Find B, C, and c.

SOLUTION:

Using the Law of Sines, find <B:

[tex] \frac{sin(A)}{a} = \frac{sin(B)}{b} [/tex]

[tex] \frac{sin(40)}{8} = \frac{sin(B)}{7} [/tex]

Multiply both sides by 7

[tex] \frac{sin(40)}{8}*7 = \frac{sin(B)}{7}*7 [/tex]

[tex] \frac{sin(40)*7}{8} = sin(B) [/tex]

[tex] 0.5624 = sin(B) [/tex]

[tex] B = sin^{-1}(0.5624) [/tex]

[tex] B = 34.2 [/tex] (to nearest tenth).

Find <C:

C = 180 - (34.2+40°) (sum of angles in a triangle)

C = 180 - 74.2 = 105.8°

Using the Law of Sines, find c.

[tex] \frac{c}{sin(C)} = \frac{b}{sin(B)} [/tex]

[tex]\frac{c}{sin(105.8)} = \frac{7}{sin(34.2)}[/tex]

Multiply both sides by sin(105.8)

[tex]\frac{c}{sin(105.8)}*sin(105.8) = \frac{7}{sin(34.2)}*sin(105.8)[/tex]

[tex] c = \frac{7*sin(105.8)}{sin(34.2)} [/tex]

[tex] c = 12.0 [/tex]

Answer:

0.22

Step-by-step explanation:

Probability distribution is the function which describes the likelihood of possible values assuming a random variable. The alkalinity of lake is determined by dividing the high shallow depthness by the total of lake alkalinity. The shallow depth is 209 and the total alkalinity of the lake is 966. By dividing the depthness with alkalinity we get 0.22.

209/966 = 0.219

approximately 0.22

Step-by-step explanation:

hope it helps u..........

and pls mark as brainliat ans

Answer:

90 degrees

Step-by-step explanation:

the right angles in the top right and bottom left mean its a square

Answer:

2,044

Step-by-step explanation:

S9=G1 (1r^n)/1-r

G9=G1r^8, r=2

S9=(4)(-511)/-1=2,044

Answer: 2,044

Step-by-step explanation:

I just took the quiz!

Answer:

[tex]\frac{5}{24}[/tex]

Step-by-step explanation:

If we have the division statement [tex]\frac{5}{6} \div \frac{4}{1}[/tex], we can multiply by the reciprocal and find the quotient.

[tex]\frac{5}{6} \cdot \frac{1}{4} = \frac{5}{24}[/tex].

Hope this helped!

Answer:

5/24

Step-by-step explanation:

Because the 5 is being divided by both the 6 and the 4, you just multiply these two and get 24. So it is 5 over 24.

Step-by-step explanation:

Consider the following rules.

even + odd = odd

even - odd = odd

even × odd = even

even ÷ odd = even (if divisible)

Now for the two consectives terms...

One will surely be even and the other, odd.

So using the rule

Their product will always be odd

Hope it helps....

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