what else would need to be congruent to show that ABC = DEF by SAS?

Answer:  1.  286 different combinations of players are possible.

2.  The probability of selecting a team of 5 girls and 5 boys is [tex]\frac{63}{143}[/tex] and the decimal is 0.4405...

Step-by-step explanation:

1.  Number of girls is 6 and number of boys is 7.

So, the total number of players = 6+7 = 13

A team of 10 players is to be selected from the class.

So, the total possible number of different combinations of players will be:  [tex]^1^3C_{10} = \frac{13!}{10! (13-10)!}=\frac{13*12*11*10!}{10!*3!}= \frac{13*12*11}{6}=286[/tex]

2.   Number of girls is 6 and number of boys is 7.

The possible number of teams by selecting 5 girls and 5 boys will be:  [tex]^6C_{5}\times ^7C_{5} =6\times 21= 126[/tex]

and the number of total possible teams of 10 players [tex]= ^1^3C_{10} =286[/tex]

Thus, the probability of selecting a team of 5 girls and 5 boys [tex]=\frac{126}{286}= \frac{63}{143}[/tex] or [tex]0.4405...[/tex]

We are given function f(a) = 1.07a for total amount including sales tax.

g(b) = b+50 total cost including delivery.

We need to write function g(f(a)).

g(f(a)) = g of f(a).

We need to substitute function f(a) in g(b) function for b.

g(f(a)) = g(1.07a) = 1.07a +50.

We are given mattress price a = $1125.

In order to find the total cost including delivery charges, we need to plug a= 1125 in the above function 1.07a +50.

Plugging a= $1125, we get

g(1125) = 1.07a +50 = 1.07*1125 +50 = 1203.75 +50 = 1253.75.

Answer:

g(f(a)) = 1.07a +50.

Total cost including delivery charges is $1253.75.

The equation of the line that is parallel to y = -x + 9 and passes through the point (7, -13) is y = -x - 6.

Now, we want to find the equation of a line that is parallel to this given line and passes through the point (7, -13). Since the new line is parallel, it will have the same slope of -1. Let's denote the equation of the new line as y = mx + b. We know the slope (m = -1), and we have a point (7, -13) that the line passes through. We can use this information to find the value of b.

To find b, we can plug in the coordinates of the point (7, -13) into the equation y = -x + b:

-13 = -1 * 7 + b

Now, solve for b:

b = -13 + 7

b = -6

Therefore, the value of b is -6.

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As per your defention, horses are the only thing considered "not small".  To find the percentage, you take the number of what you are trying to find the percentage of divided by the total number.

So, 7 dogs + 13 cats + 3 ferrets = 23 Small animals

7 dogs + 13 cats + 3 ferrets + 4 horses = 27 total animals.

So,

[tex]\frac{23}{27}*100[/tex]

The reason we multiply by 100 is because the division gives us a decimal, and a percentage is a part out of 100.

So by doing the calculation we get

85.18%

Mathematics defines a percentage as a number or ratio expressed as fraction of 100.

It is denoted using % sign.

General formula to calculate percentage is:

                                   [tex]\rm Percentage=\dfrac{\rm Value}{\rm Total\: value} \times 100%.[/tex]

For the given question, percentage of small animals is [tex]\rm 85.19\%.[/tex]

[tex]\begin{aligned} \rm Total\: animals &= 7 + 13 + 4 + 3\\&= 27 \end[/tex]

[tex]\begin{aligned} \rm Number\:of\:small\:animals &= 7 + 13 + 3\\&= 23\end[/tex]

Small animals includes all animals except horses.

Therefore, percentage of small animals will be:

         [tex]\rm \begin{aligned}\rm Percentage &= \dfrac{\rm Small \:animals}{\rm Total\:animals} \times 100\\\\ &= \dfrac{23}{27} \times 100\\\\ &= 85.19\% \end{aligned}[/tex]

Percentage of patients to be small animals is [tex]\rm 85.19\%[/tex].

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[tex]Domain:\ x\geq0\\\\5\sqrt[3]{x}+9\sqrt[3]{x}=(5+9)\sqrt[3]{x}=14\sqrt[3]{x}[/tex]

That will be 1, since 17 can only be factored by itself and 1

Even though 6 can be factored by 3 and 2, the least common factor between 17 and 6 will be 1.

Hello there,

The correct answer is 2 the (LCM) or Least common factor of 17 and 6 is 2

If my answered helped you understand more greatly please mark me as brainliest thank you and have the best day ever!

0.09

-hope this helps

The decimal equivalent of the mixed number, '9 and 11/27', is found by first converting the fraction into a decimal, followed by adding it to the whole number part. The answer is 9.4074.

To find the decimal equivalent of a mixed number like 9 and 11/27, we first need to convert the fractional part into the decimal form. We do this by dividing the numerator (11) by the denominator (27).

The fraction 11/27, when written in decimal form, is approximately 0.4074

Then, the decimal equivalent of the mixed number '9 and 11/27' is found by adding this decimal (0.4074) to the whole number part (9). Hence, the answer is 9.4074.

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Solution 1:

The compound interest formula to be used here is given by:

[tex]A=P(1+r)^{t}[/tex]

Now we are given:

P=$500

r=10% or 0.1

t=5 years

Plugging them in the formula ,

[tex]A=500(1+0.1)^{5}[/tex]

A=$802.255

Answer : After 5 years I will have $802.255 in my account.

Solution 2:

The formula for compound interest here is given by:

[tex]A=P(1+\frac{r}{n})^{nt}[/tex]

Here interest is compounded after every two years, so n=2

r=2% or 0.02

t=6 years

P= $100

Plugging these into the formula:

[tex]A=100(1+\frac{0.02}{2})^{2*6}[/tex]

[tex]A=100(1+0.01)^{12}[/tex]

[tex]A=100(1.01)^{12}[/tex]

A=$112.683

Answer: The balance after 6 years would be $112.683.

Solution 4:

In this situation:

a. Ax+By

Ax represents duration of Podcast A episodes

By represents duration of Podcast B episodes

Ax+By represents total duration of Podcast A and Podcast B songs.

b. A+B

A+B represents total number of episodes of Podcast A and Podcast B.

First, we need to solve the equation 4x+5y=7 to make it slope intercept form and find the slope of the line, because parallel lines have the same slope.

4x+5y=7

Subtract 4x from both sides.

5y=-4x+7

Divide both sides by 5.

y=-4/5x+7/5

The slope of the line is -4/5x. Plug that in to the blank slope intercept form equation, y=mx+b, with m being the slope and b being the y-intercept.

y=-4/5x+b

Now, we need to solve for the y-intercept. We can do this by plugging in the given coordinates (4,-3) into the above equation for x and y respectively:

-3=-4/5(4)+b

-3=-16/5+b

Add -16/5 to both sides.

1/5=b

The y-intercept is 1/5, plug this into the equation:

[tex]y=-\frac{4}{5}x+\frac{1}{5}[/tex]

Your equation is the above equation.

I hope this helps :)

Final answer:

To find the slope-intercept form of a line parallel to 4x + 5y = 7 and passing through (4, -3), first find the slope of the given line, then use the point-slope form with the given point to derive the final slope-intercept form, which is y = (-4/5)x + 1/5.

Explanation:

The student is asking for the slope-intercept equation of a line parallel to another line. Since parallel lines have the same slope, we first need to find the slope of the given line, 4x + 5y = 7. To do this, we solve for y to get it into the slope-intercept form, y = mx + b, where m is the slope.

To convert 4x + 5y = 7 into slope-intercept form, we subtract 4x from both sides to get 5y = -4x + 7, and then divide by 5, resulting in y = (-4/5)x + 7/5. The slope of this line is -4/5. Hence, our new line must have the same slope of -4/5 to be parallel.

We use the point-slope form of the equation, which is y - y1 = m(x - x1), to get the equation of the line passing through the point (4, -3). Plugging in the values, we have y - (-3) = (-4/5)(x - 4), which simplifies to y + 3 = (-4/5)x + 16/5. To get the slope-intercept form, we subtract 3 from each side and get y = (-4/5)x + 16/5 - 15/5, leading to y = (-4/5)x + 1/5.

The measure of angle A is 61 degrees.

Given that

Angle A and angle B are complementary angles.

If the measure of angle B is 29 degrees.

We have to determine

The measure of angle A?

According to the question

The measure of angle A is determined in the following steps given below.

When adding the two complementary angles the sum of the angle is equal to 90 degrees.

[tex]\rm \angle A + \angle B = 90[/tex]

The measure of angle B is 29 degrees.

Then,

The measure of angle A is,

[tex]\rm \angle A + \angle B = 90\\\\\rm \angle A + 29= 90\\\\\rm \angle A =90-29\\\\\rm \angle A =61[/tex]

Hence, the measure of angle A is 61 degrees.

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laps per minute by:

- Mai- 12/3 = 4 laps

- Lena- 48/6= 8 laps

- Susan- 30/5= 6 laps

thus, the person who drove fastest was Lena, who drove 8 laps per minute.

The answer is 83.2%, Hope this helps

The change in height from the starting platform to the stopping point of the roller coaster is 40.75 feet above the ground.

To determine the change in height from where the friends started on the platform to where they stop, we need to calculate the total distance the car traveled vertically. The car first ascends 80 and one half feet and then descends 50 and one fourth feet. The starting platform is 10 and one half feet above the ground.

First, we add the height of the platform to the initial ascent:

Next, we subtract the descent:

The change in height is the final position above the ground minus the starting position, yielding a total change in height of 40.75 feet.

You do what you did in your head if you know the answer is 65 and it's not on the paper.

If your friend answered it for you then sorry I can't help cause I'm horrible at word problems.

Final answer:

0.8 divided by 0.6 is 1.33333... which, when rounded to the nearest hundredth, is 1.33. The rounding should be done to the nearest hundredth as 'rounding to the nearest hundred' typically does not apply to decimals.

Explanation:

To calculate 0.8 divided by 0.6, we simply perform the division:

0.8 ÷ 0.6 = 1.33333...

When we round this to the nearest hundredth, we look at the third decimal place. Since it's 3, we do not round up the second decimal place. Thus, 1.33333... rounded to the nearest hundredth is 1.33.

Rounding numbers and understanding division are fundamental skills in mathematics. They are essential for various applications, such as converting fractions to percentages or when dealing with metrics and customary units.

However, the question asked to round to the nearest hundred, which seems to be a typographical mistake, because we usually round numbers to the nearest hundredth or to the nearest hundred as a whole number, but not to the nearest hundred as a decimal. Assuming it's a typo and meant the hundredth, the result is 1.33. Otherwise, 1.33 rounded to the nearest hundred as a whole number is simply 100 (since this is the closest hundred to 1.33).

Domain: {-10, -5, 0, 5}

Range: {-7, -4, -1, 2}

you just find the x and y values of the plotted points my friend!! make sure they're in order from least to greatest

Let

n-------> the lesser even number

n+2----> the greater even number

we know that

[tex]3(n+2)=(n-10)[/tex]

Solve for n

[tex]3n+6=n-10[/tex]

Combine like terms

[tex]3n-n=-10-6[/tex]

[tex]2n=-16[/tex]

[tex]n=-8[/tex]

so

[tex]n=-8\\n+2=-8+2=-6[/tex]

therefore

the answer is

the lesser even number is [tex]-8[/tex]

the greater even number is [tex]-6[/tex]

Hey there!

First, let's multiply each side of the equation by 3 to get rid of the fraction [tex]\frac{2}{3}[/tex].

9 + 2x = [tex]\frac{6}{5}[/tex]

Next we can multiply each side of the equation by 5 to get rid of the fraction [tex]\frac{6}{5}[/tex].

45 + 10x = 6

There's your answer!

Hope this helps!

change each to improper fractions

21 1/2 = (2*21 +1)/2 = 43/2

2/3 = 2/3

43/2  divided by 2/3    

copy dot flip

43/2 * 3/2

129/4 = 32 1/4

Answer:

Speed of Victoria, [tex]v=32\dfrac{1}{4}\ miles/hour[/tex]

Step-by-step explanation:

It is given that,

Distance covered by Victoria, [tex]d=21\dfrac{1}{2}\ miles=\dfrac{43}{2}\ miles[/tex]

Time taken, [tex]t=\dfrac{2}{3}\ hour[/tex]          

Speed (v) of Victoria is given by total distance divided by total time taken. It is given by :

[tex]v=\dfrac{d}{t}[/tex]

[tex]v=\dfrac{\dfrac{43}{2}\ miles}{\dfrac{2}{3}\ hour}[/tex]

[tex]v=\dfrac{129}{4}\ miles/hour[/tex]

or

[tex]v=32\dfrac{1}{4}\ miles/hour[/tex]

So, the speed of Victoria is [tex]32\dfrac{1}{4}\ miles/hour[/tex]. Hence, this is the required solution.

To find the price per pound, simply add 0.65 + 0.75 then divide.

0.65 + 0.75 = 1.40    13.65 / 1.40 = 9.75

Danny paid $9.75 per pound!

Lets go through the steps

1) Add the weights together which gives us 1.4 lb

2) Divide the cost by the weight 13.65/1.4 = $9.75 lb

(0,1) I hope that helped                                                                    

The only time that f(x) will equal g(x) occurs at x = 0.

If "the sum of 3 and a number is 16" is given, we can rewrite it as an equation (note that "a number" refers to a variable, commonly x):

3 + x = 16

Now, simply use the Subtraction Property of Equality (subtract 3 from both sides):

3 + x - 3 = 16 - 3

x = 13

Therefore, the number, or x, is equal to 13.

Hope this short response helps! :)

2p² - p - 10 = 0

2 = a

- 1 = b

- 10 = c

To factor, find two numbers that multiply to equal a·c and also that have a sum of b

2p² + 4p - 5p - 10 = 0

2p (p + 2) - 5 (p + 2) = 0

If the horizontal plan passes through the cone that have horizontal base, the shaped form will be circular.

B AND C I THINK BUT IM NOT SURE

For the interval (-∞, 1), put x = 0.5, then y = - 0.5 + 3 = 2.5.

Therefore, (0.5, 2.5) is a point on y = -x + 3.

Put x = - 1, then y = -(-1) + 3 = 1 + 3 = 4.

Therefore, (-1, 4) is another point on y = -x + 3.

Joining (0.5, 2.5) and (-1, 4), we get the graph of the line y = -x + 3.

For the interval [1, ∞), put x = 1, then y = 2(1) - 4 = -2.

Therefore, (1, -2) is a point on y = 2x - 4.

Put x = 2, then y = 2(2) - 4 = 4 - 4 = 0.

Therefore, (2, 0) is another point on y = 2x - 4.

Joining (1, -2) and (2, 0), we get the graph of the line y = 2x - 4.

The graph of the piecewise-defined function is: [tex]function \(y = \begin{cases} 3 & \text{if } x < -2 \\ 0 & \text{if } x = 1 \\ -1 & \text{if } x > 1 \end{cases}\)[/tex]is attached accordingly.

A piecewise-defined function is a mathematical function that is defined by different rules or formulas over different intervals or regions of its domain.

The graph of the piecewise function is attached accordingly.

The graph of the piecewise function [tex]\(y\)[/tex] consists of two linear segments with a clear transition at [tex]\(x = 1\)[/tex]:

1. For [tex]\(x < 1\)[/tex], the equation [tex]\(y = -x + 3\)[/tex] defines a downward-sloping line that intersects the y-axis at [tex]\(y = 3\)[/tex].

2. For , the equation [tex]\(y = 2x - 4\)[/tex] defines an upward-sloping line that intersects the y-axis at [tex]\(y = -4\)[/tex].

These two segments meet at the point (1, -1), creating a kink in the graph. This piecewise function effectively combines two linear functions with different slopes, resulting in a non-continuous graph at [tex]\(x = 1\)[/tex].

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the vertex of the quadratic function

[tex]f(x)= \frac{1}{2}x^2+3x+\frac{3}{2}[/tex]

To find vertex we use formula x= -b/2a

from the given equation , a= 1/2  and b = 3

Now we plug in the values in the formula

[tex]x = \frac{-b}{2a}[/tex]

[tex]x= \frac{-3}{2\frac{1}{2}}=-3[/tex]

x coordinate of vertex is -3

Now plug in -3 for x  in f(x)

[tex]f(-3)= \frac{1}{2}(-3)^2+3(-3)+\frac{3}{2}[/tex]

f(-3) = -3

the y coordinate of vertex is -3

So vertex is (-3,-3)

Answer:

(-3, -3)

Step-by-step explanation:

The standard form of a quadratic equation is [tex]y = ax^2+bx+c[/tex] where the coordinates of the highest point (x, y) indicate the vertex.

Here, [tex]a= \frac{1}{2} , b = 3[/tex] and  [tex]c= \frac{3}{2}[/tex].

We know the formula to find the x coordinate = [tex]\frac{-b}{2a}[/tex]

[tex]x= \frac{-3}{2(\frac{1}{2}) }[/tex] = [tex]-3[/tex]

To find y, put this value of x in the function to get:

[tex]y = \frac{1}{2} x^2+3x+\frac{3}{2}[/tex]

[tex]y = \frac{1}{2} (-3)^2+3(-3)+\frac{3}{2}[/tex]

[tex]y = -3[/tex]

Therefore, the vertex (x, y) = (-3, -3)

Slope Formula: (y² - y¹) / (x² - x¹)

1 + 7 = 8

-1-1 = -2

8/2 = 4

-2/2 = 1

4/1 = -4

Your answer is B.

Hope this Helps!!

The slope-intercept form:

[tex]y=mx+b\\\\m=\dfrac{y_2-y_1}{x_2-x_1}[/tex]

We have (1, -7) and (-1, 1).

Substitute:

[tex]m=\dfrac{1-(-7)}{-1-1}=\dfrac{8}{2}=4[/tex]

Therefore we have

[tex]y=4x+b[/tex]

Substitute the coordinates of the first point to the equation of line:

[tex]-7=-4(1)+b[/tex]

Answer:

[tex]\dfrac{1+7}{-1-1}=-4;\ -7=-4(1)+b[/tex]