20 POINTS

(SSS)
If the lengths of the ______sides of two triangles are______, then the triangles are similar.
(SAS)
If an angle of one triangle is______to an angle of a second triangle and the lengths of the sides including these angles are______, then the triangles are similar.

The answer is:

The correct option is:

A) The function g(x) has a higher y-intercept.

To solve the problem, we need to find the y-intercept of the g(x) function, and then, compare to the y-intercept of the f(x) function which is equal to -1 (we can see it on the picture).

Also, we need to remember the slope-interception form of the line:

[tex]y=mx+b[/tex]

So,

Finding the y-intercept of the g(x) function, we have:

Calculating the slope of the function, using the first two points (4,9) and (6,13), we have:

[tex]m=\frac{y_2-y_1}{x_2-x_1}\\\\m=\frac{13-9}{6-4}=\frac{4}{2}=2[/tex]

Now,

Calculating the value of "b", we have:

Using the first point (4,9), the slope of the function, and the slope-intercept form of the function, we have:

[tex]y=mx+b[/tex]

[tex]y=2x+b[/tex]

[tex]9=2*(4)+b[/tex]

[tex]9=8+b[/tex]

[tex]9-8=b[/tex]

[tex]b=1[/tex]

So, the equation of the line will be:

[tex]y=2x+1[/tex]

We know that "b" represents the y-intercept, so, the function g(x) has its y-intercept at y equal to 1.

Comparing, we have that the function f(x) has a y-intercept located at y equal to "-1" and the g(x) function has a y-intercept located at y equal to "1".

Hence, the correct option is:

A) The function g(x) has a higher y-intercept.

Have a nice day!

Answer:

has two rays that share a common end point.

Answer:

Angle has two rays that share a common endpoint.

Step-by-step explanation:

Given : Angle.

To find : Which is a property of an angle.

Solution : We have given properties of an angle .

Angle : the space between two intersecting lines or surfaces at or close to the point where they meet.

Vertex is also called the angle.

Therefore, Angle has two rays that share a common endpoint.

Answer:

[tex]\large\boxed{x=-\dfrac{1}{5}}[/tex]

Step-by-step explanation:

[tex]\dfrac{a-x}{x-a}=5x\\\\\dfrac{(a-x)}{-(a-x)}=5x\qquad\text{cancel}\ (a-x)\\\\-1=5x\qquad\text{divide both sides by 5}\\\\-\dfrac{1}{5}=\dfrac{5x}{5}\to\boxed{x=-\dfrac{1}{5}}[/tex]

Answer:

A) x+y=4

B) x-y=-6​

We add both equations and get

2x = -2 so x = -1

and y = 5

So the ordered pair (-1, 5) is the solution to the equations.

Step-by-step explanation:

Answer:

The square root of 130 would be 11.4017543. Rounding to the nearest tenth, we would get 11.4, because the value 0 is below 5. Rounding 11.4 to the nearest whole number, we would get 11, because the value 4 is below 5. So either 11 or 11.4 works, depending on if you are looking for a decimal or a whole number.

Hope this helps ya :D

Final answer:

The simplified square root of 130 is √130 and cannot be further simplified using integers as 130 does not have pairs of identical prime factors.

Explanation:

The question asks for the simplified form of the square root of 130. To simplify a square root, you want to factor the number under the square root into its prime factors and look for pairs of identical factors, because the square root of a pair of identical factors is just that number. In this case, 130 = 2 x 5 x 13, and since there are no pairs of identical factors, we cannot simplify it further without using a decimal or fractional answer. Therefore, the simplified square root of 130 is √130, which cannot be further simplified using integers.

Answer: 1,760 centimeters

Step-by-step explanation: Your Answer is above

Answer:

Step-by-step explanation:

To determine which equations have a lower unit rate than the rate in the table, calculate the unit rate or slope from the table and compare it to the slopes of the other equations. Equations with a smaller slope have a lower unit rate.

To answer this question, we need to calculate the unit rate of the original equation. The unit rate is the ratio of the increase in the dependent variable (usually represented by y) to the increase in the independent variable (usually represented by x).

For example, if the table shows x increasing by 2 and y increasing by 4, then the unit rate is 4/2 = 2 which is the slope.

The equations with a lower unit rate than this would have a smaller ratio of the increase in y to the increase in x. For instance, if the slope of another equation is 1, that means for each unit increase in x, y increases by only 1, which is less than the original rate of 2.

Therefore, to decide which equations have a lower unit rate, compare the slopes of the equations to the unit rate calculated from the original table. Any equation with a smaller slope has a lower unit rate.

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Answer:

64% as a fraction and decimal: 16/25 and .64

1/8 as a percent and decimal: 12.5% and .125

1.4 as a percent and fraction: 140% and 1 2/5

2 3/4 as a percent and decimal: 275% and 2.75

8 percent as a decimal and fraction: .08 and 2/25

Step-by-step explanation:

Answer:

k = 2cw

Step-by-step explanation:

1. 11cw + 2k = 15cw

2. Subtract 11cw from both sides:

2k = 4cw

3. Divide by 2 on both sides:

k = 2cw

Answer:

19 -  8√3

Step-by-step explanation:

(-4 + √2)^2

= (-4)^2 + 2(-4)(√3) + √3)^2

= 16 - 8√3 + 3

= 19 -  8√3

Answer:

D

Step-by-step explanation:

note that ([tex]\sqrt{3}[/tex] )² = 3

Given

(- 4 + [tex]\sqrt{3}[/tex] )² = (- 4 + [tex]\sqrt{3}[/tex])(- 4 + [tex]\sqrt{3}[/tex])

Expand using (a + b)² = a² + 2ab + b²

= (- 4 )² + 2(- 4[tex]\sqrt{3}[/tex] ) + ( [tex]\sqrt{3}[/tex] )²

= 16 - 8[tex]\sqrt{3}[/tex] + 3

= 19 - 8[tex]\sqrt{3}[/tex]

The mean is the average, add the numbers together and divide by the quantity of numbers:

10 + 12 + 15 + 12 + 13 + 11 + 10 + 13 = 96

96 / 8 = 12

The mean is 12

The median is the middle value.

Rearrange the numbers from smallest to largest:

10 , 10 , 11 , 12 , 12 , 13 , 13 , 15

There are an even amount of numbers, so find the middle two values, add together and divide by 2:

12 + 12 = 24 /2

Median = 12

2y^2- 14y+ 20

By splitting the middle term:

2y^2 -10y -4y +20

By taking the common outside:

2y(y-5) -4(y-5)

=(2y-4)(y-5)

=2(y-2)(y-5)

Therefore D is the right answer

Answer:

D

Step-by-step explanation:

Given

2y² - 14y + 20 ← factor out 2 from each term

= 2(y² - 7y + 10)

To factor the quadratic

Consider the factors of the constant term (+ 10) which sum to give the coefficient of the y- term (- 7)

The factors are - 2 and - 5, since

- 2 × - 5 = 10 and - 2 - 5 = - 7, so

y² - 7y + 10 = (y - 2)(y - 5) and

2y² - 14y + 20 = 2(y - 2)(y - 5) → D

Answer:

It would take them 6.667 minutes to paint 50 square feet together.

Step-by-step explanation:

This is a classic work problem.  If Sam can do the job in 10 minutes, she can get done 1/10 of the job in one minute.  If you can do the job in 5 minutes, you can 1/5 of the job done in one minute.  To find out how many minutes it will take them together to paint 25 square feet, set the addition of their times equal to 1/x:

[tex]\frac{1}{10}+\frac{1}{5}=\frac{1}{x}[/tex]

x is how long it takes them to get the job done together.  Find the common denominator and multiply it through be everything to get rid of the denominators altogether.  That denominator is 10x:

[tex](10x)\frac{1}{10}+(10x)\frac{1}{5}=(10x)\frac{1}{x}[/tex]

Simplify to get the simple equation x + 2x = 10 and 3x = 10.  That means that x=3 1/3.  That's how long it takes to do 25 square feet.  Double that time for 50 square feet.

-35

First, add the contents of the parentheses. 3 + 4 = 7. This gives you -5 * 7.

Now, just multiply. -5 * 7 = -35, so -35 is the answer.

Answer:

x^5 - 5 x^4 + 9 x^3 - 9 x^2 + 12 x - 12

Step-by-step explanation:

(x ^4 - 3x^3 + 3x^2 - 3x + 6) (x - 2)

Distribute the x to all the terms in the first parentheses

(x^ 4  *x - 3x^ 3  *x + 3x^ 2   *x - 3x   *x + 6*x)

Then simplify

(x^5 - 3x^4 + 3x^ 3 - 3x2 + 6x)

Distribute the -2 to all the terms in the first parentheses

(x^ 4  *(-2) - 3x^ 3  *(-2) + 3x^ 2   *(-2) - 3x   *(-2) + 6*(-2))

Then simplify

(-2x^4 +6x^3 -6x^ 2 +6x -12)

Add the terms together

(x^5 - 3x^4 + 3x^ 3 - 3x2 + 6x) +(-2x^4 +6x^3 -6x^ 2 +6x -12)

x^5 - 5 x^4 + 9 x^3 - 9 x^2 + 12 x - 12

Answer:

x^3 -x^2 + x -1 + 4/x-2

Step-by-step explanation:

;)

The area of a kite is half the product of the diagonals.  

Area = ½(d1 x d2)  

Plug in the values of the diagonals.

Area = ½(7.8 * 6)  

Multiply, and you should get -

Area = 23.4 ft²

Answer: Option 'A' is correct.

Step-by-step explanation:

Since we have given that

Diagonals of kite are as follows:

7.8 ft and 6 ft

As we know the formula for "Area of kite":

Area of kite is given by

[tex]\dfrac{1}{2}\times d_1\times d_2\\\\=\dfrac{1}{2}\times 7.8\times 6\\\\=3\times 7.8\\\\=23.\ ft^2[/tex]

Hence, Option 'A' is correct.

.25 is the answer because the next number should be half of the previous number and the opposite sign of the previous number.

0.25 is the best answer for the sequence :D

Answer:

[tex](f + g) (2) = -4[/tex]

Step-by-step explanation:

We have the functions

[tex]F(x) =-3x^2-2[/tex]

And

[tex]g(x)=4x+2[/tex]

We want to find [tex](f + g) (x)[/tex]

Then

[tex](f+g)(x) = f(x) + g(x)\\\\(f+g)(x) = -3x^2-2 + 4x+2\\\\(f+g)(x)= -3x^2 +4x[/tex]

finally we find [tex](f + g) (2)[/tex]

[tex](f + g) (2) = -3(2)^2 + 4(2)\\\\(f + g) (2) = -3*4 + 8\\\\(f + g) (2) = -12+ 8\\\\(f + g) (2) = -4[/tex]

Answer:

(f+g)2 = 20

Step-by-step explanation:

18. if F(x) =-3x2-2 and g(x)=4x+2 what is value of (f+g)(2)?

We know, (f+g)2= f(2) + g(2)

We will put 2 in the place of x for f(x) and g(x) and then find their result.

Solving:

(f+g)2= f(2) + g(2)

         =3(2)^2 -2 + 4(2) +2

         = 3(4) -2 + 8 +2

         = 12 -2 +8 +2

         = 20

So, (f+g)2 = 20

Answer:

She would need to complete 5.57 each noght to reach her goal of 100%.

Step-by-step explanation:

39/7 is equal to 5.57

sqrt (b^2 -4ac ) =sqrt (4-4•3•4) = sqrt (-44) so the parabola does not have real solutions. Answer C)

Answer:

c

Step-by-step explanation:

Answer: Because there are no values

Step-by-step explanation: Since there are no numbers in the problem, there is no sum. making it 0. You can't add two letters to make another letter, So it becomes a 0. anything with a variable subtracted, divided, added, ect by another variable, is 0

Answer:

1. Simple random sampling

2. Systematic random sampling

Answer:

0.18 cents

Step-by-step explanation:

2.34 divided by 13= 0.18

To check my answer, 0.18 x 13 = 2.34

Answer:

$0.18/ounce

Step-by-step explanation:

Divide the price by the weight.

($2.34)/(13 ounces) = $0.18/ounce

Answer:

[tex]\boxed{0.2}[/tex]

Step-by-step explanation:

Convert [tex]\dfrac{12}{60}[/tex] to a decimal

Step 1. Reduce the fraction to its lowest terms.

Divide both numerator and denominator by their greatest common factor (12)

[tex]\dfrac{12}{60} =\dfrac{1}{5}[/tex]

Step 2. Convert the denominator to a power of 10

Multiply both numerator and denominator by 2.

[tex]\dfrac{1}{5} \times \dfrac{2}{2} = \dfrac{2}{10}[/tex]

Step 3. Divide the numerator by the denominator

Dividing by 10 moves the decimal point one place to the left.

[tex]\dfrac{2}{10} = \boxed{0.2}[/tex]

Check the picture below.

Answer:

=53 seconds.

Step-by-step explanation:

24ft=7sec

180

180 x 7

_______=52.5=53

24

Answer:

800 meters

Step-by-step explanation:

y is inversely proportional to x is the same as y is inversely proportional to [tex]\frac{1}{x},[/tex] that means

[tex]y=\dfrac{k}{x}.[/tex]

If a wave with a frequency of x=720 kilohertz has a length of y=500 meters, then

[tex]500=\dfrac{k}{720}\\ \\k=500\cdot 720=360000.[/tex]

Hence, the length of a wave y with a frequency of x=450 kilohertz is

[tex]y=\dfrac{360000}{450}=800[/tex]

The relationship between the frequency and wavelength of a wave is given by the formula:
\[ c = f \times \lambda \]
where:
- \( c \) is the speed of light (or the speed of the wave in another medium, but for radio waves in the air or vacuum, it's approximately the speed of light),
- \( f \) is the frequency of the wave,
- \( \lambda \) is the wavelength of the wave.
Given that the relationship is inverse, when the frequency goes up, the wavelength goes down, and vice versa.
We are given that a wave with frequency 720 kilohertz has a length of 500 meters. We can represent this with the equation:
\[ c = 720 \times 500 \]
We are asked to find the wavelength when the frequency is 450 kilohertz. Since the speed of light doesn't change, we set up the proportion using the formula, keeping \( c \) constant:
\[ 720 \times 500 = 450 \times \lambda_{\text{new}} \]
Now we solve for \( \lambda_{\text{new}} \):
\[ \lambda_{\text{new}} = \frac{720 \times 500}{450} \]
To simplify this, we can divide both the numerator and the denominator by a common factor. In this case, let's divide by 90:
\[ 720 \div 90 = 8 \]
\[ 450 \div 90 = 5 \]
\[ 500 \text{ remains unchanged} \]
Now we can substitute these simplified numbers back into our equation:
\[ \lambda_{\text{new}} = \frac{8 \times 500}{5} \]
\[ \lambda_{\text{new}} = \frac{4000}{5} \]
\[ \lambda_{\text{new}} = 800 \]
So the length of a wave with a frequency of 450 kilohertz is 800 meters.

Answer:

The probability of not drawing a black marble is : 8/10, 4/5, 80%

The probability of drawing a red marble is: 3/10, or 30%

Step-by-step explanation:

Blue marbles: 5

Black marbles: 2

Red marbles: 3

Total marbles: 10

The probability of not drawing a black marble is :

NOT drawing a black marble means you'll draw either a blue or a red one.  Combined, red and blue marbles account for 8 marbles out of 10.

So the probability of NOT drawing a black marble is 8/10, 4/5 or 80%

The probability of drawing a red marble is:

There are 3 red marbles, out of 10 marbles.... so the probability of drawing a red marble is 3/10, or 30%

Answer:

[tex]m=\frac{3}{4}[/tex]

Step-by-step explanation:

We can use the slope formula in order to find the slope of the line

[tex]m=\frac{-2-2}{0-(-3)} \\m=\frac{-4}{3}[/tex]

For a line to be perpendicular, it must have a slope that is the negative reciprocal, so that means that we swap the numerator and denominator and then multiply it by -1, this means that

[tex]m=\frac{-4}{3}\\\\m=\frac{3}{-4} \\\\m=\frac{-3}{-4} \\\\m=\frac{3}{4}[/tex]