Together Mike and Sara ran 42 laps on the
track. Sara ran twice as many laps as
Mike did. Write a system of equations and
solve it to see how many laps they each ran.

Answer:

B

Step-by-step explanation:

Using the cosine ratio in the right triangle and the exact value

cos45° = [tex]\frac{1}{\sqrt{2} }[/tex] , then

cos45° = [tex]\frac{adjacent}{hypotenuse}[/tex] = [tex]\frac{3}{c}[/tex] = [tex]\frac{1}{\sqrt{2} }[/tex] ( cross- multiply )

c = 3[tex]\sqrt{2}[/tex]

Answer:

D

Step-by-step explanation:

D starts low on both sides but is highest in the middle

Answer: https://brainly.com/question/22661875?answering=true&answeringSource=feedPublic%2FhomePage%2F10

Step-by-step explanation: hope tis helps

Answer:

m = -1, b = 5.

Step-by-step explanation:

We can find the slope, m, by plugging in our coordinates into the slope formula: [tex]\frac{y2-y1}{x2-x1} =\frac{2-7}{3-(-2)}=\frac{-5}{5}=-\frac{5}{5}=-\frac{1}{1}=-1[/tex]. That gives us the slope. Now we can fill that in the slope intercept formula: [tex]y=-1x+b[/tex]. We know one of the coordinates and the slope, which allows to find the y-intercept. We know that for every 1 unit down on the line, we move 1 unit right, and vice versa. Meaning we can just count down (or up in this case), so, (-2, 7), (-1, 6), (0, 5). Therefore, our y intercept is 5.

Answer:

45.5

Step-by-step explanation:

To find 35% of 70, you have to use the equation...

70 x 35/100

70 x 35 = 2,450

2,450/100 = 24.5

24.5 is 35% of 70, so the item is now $24.5 less than the original price.

70 - 24.5 = 45.5

The selling price is $45.5

Answer:

4 ) reflexive property of congrunce

5 ) Definition of Equilateral Triangle

Step-by-step explanation:

4) the lines are equal to each other

5) if one triangle is equal to another triangle than they must be the same triangle

Answer:

6.5

Step-by-step explanation:

Answer:

6.5 centimeters (proof below!)

Step-by-step explanation:

Answer:

B

Step-by-step explanation:

C = πd = 3.14 * 32 = 100.48in

Answer:

the ratio of 6 kg 400 gram is 1:662

Answer:

1/52 OR 0.01923076923 (unusual)

Step-by-step explanation:

So, since it is only asking for 1 card and there is 52 cards in a deck, you have a in 52 chance to pick that card.

Hope that helps!

Answer:

y = 31

Step-by-step explanation:

Given

y = [tex]x^{5}[/tex] + 32 ← substitute x = - 2

y = [tex](-2)^{5}[/tex] + 63 = - 32 + 63 = 31

Answer:

-5

Step-by-step explanation:

1*1=1

1-6= -5

Hope this helped!

Answer:

x ≈ 8.1 units

Step-by-step explanation:

Using the tangent ratio in the right triangle

tan72° = [tex]\frac{opposite}{adjacent}[/tex] = [tex]\frac{25}{x}[/tex] ( multiply both sides by x )

x × tan72° = 25 ( divide both sides by tan72° )

x = [tex]\frac{25}{tan72}[/tex] ≈ 8.1 ( to the nearest tenth )

Answer:

true

Step-by-step explanation:

Answer:

Sorry, I can't complete this without knowing the radius, or diameter.

Step-by-step explanation:

*☆*――*☆*――*☆*――*☆*――*☆*――*☆*――*☆*――*☆**☆*――*☆*――*☆*――*☆

Answer: 27528 ft^3

Explanation:

24 x 31 x 37 = 27528

I hope this helped!

<!> Brainliest is appreciated! <!>

- Zack Slocum

*☆*――*☆*――*☆*――*☆*――*☆*――*☆*――*☆*――*☆**☆*――*☆*――*☆*――*☆

Given:

The vertices of a right triangle are:

[tex](-3,4),(3,4),(3,-4)[/tex]

To find:

The length of the hypotenuse of the given right triangle.

Solution:

Let the vertices of the right triangle are [tex]A(-3,4),B(3,4),C(3,-4)[/tex].

The distance formula is:

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

Using distance formula, we get

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

[tex]AB=\sqrt{(3+3)^2+(0)^2}[/tex]

[tex]AB=\sqrt{(6)^2+0}[/tex]

[tex]AB=\sqrt{36}[/tex]

[tex]AB=6[/tex]

Similarly,

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

[tex]BC=\sqrt{(0)^2+(-8)^2}[/tex]

[tex]BC=\sqrt{64}[/tex]

[tex]BC=8[/tex]

And,

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

[tex]AC=\sqrt{(6)^2+(-8)^2}[/tex]

[tex]AC=\sqrt{36+64}[/tex]

[tex]AC=\sqrt{100}[/tex]

[tex]AC=10[/tex]

Now, taking sum of squares of two smaller sides, we get

[tex]AB^2+BC^2=6^2+8^2[/tex]

[tex]AB^2+BC^2=36+64[/tex]

[tex]AB^2+BC^2=100[/tex]

[tex]AB^2+BC^2=AC^2[/tex]

By the definition of the Pythagoras theorem, AC is the hypotenuse of the given triangle.

Therefore, the length of the hypotenuse is 10 units.

Answer:

The answer is D

Equations:

[tex]x+6=5+x[/tex]

[tex]-2(x-3)=-2x+6[/tex]

[tex]4-4x=3x+2[/tex]

[tex]4(x+1)=3(x+2)[/tex]

[tex]5-3x=-3x+4[/tex]

Answer:

[tex]x+6=5+x[/tex]

[tex]5-3x=-3x+4[/tex]

Step-by-step explanation:

Given

[tex]x+6=5+x[/tex]

[tex]-2(x-3)=-2x+6[/tex]

[tex]4-4x=3x+2[/tex]

[tex]4(x+1)=3(x+2)[/tex]

[tex]5-3x=-3x+4[/tex]

Required:

Which have no solution

[tex]x+6=5+x[/tex]

Subtract x from both sides

[tex]x -x+6 = 5 + x - x[/tex]

[tex]6 = 5[/tex]

[tex]x+6=5+x[/tex] has no solution because [tex]6 \ne 5[/tex]

[tex]-2(x-3)=-2x+6[/tex]

Open bracket

[tex]-2x + 6 = -2x + 6[/tex]

Both sides are equal.

Hence, there is an [tex]Infinite\ Number[/tex] of Solutions

[tex]4-4x=3x+2[/tex]

Collect like terms

[tex]-3x - 4x = 2 - 4[/tex]

[tex]-7x = -2[/tex]

Solve for x

[tex]x = \frac{-2}{-7}[/tex]

[tex]x = \frac{2}{7}[/tex] --- This has a solution

[tex]4(x+1)=3(x+2)[/tex]

Open brackets

[tex]4x + 4 = 3x + 6[/tex]

Collect like terms

[tex]4x-3x = 6 - 4[/tex]

[tex]x = 2[/tex] --- This has a solution

[tex]5-3x=-3x+4[/tex]

Add 3x to both sides

[tex]5 - 3x + 3x = -3x + 3x + 4[/tex]

[tex]5 = 4[/tex]

[tex]5-3x=-3x+4[/tex] has no solution because [tex]5 \ne 4[/tex]

Answer:

y=4

Step-by-step explanation:

3(9) +4y= 43

27+4y=43

4y=16

y=4

Answer:

a/8 = b/15

Step-by-step explanation:

a/b = 8/15  -- divide both side by 8 and multiple both side by b

a/8 = b/15

Answer:

+/-11

Step-by-step explanation:

It's plus or minus eleven

Answer:

x=5 and y=16

Step-by-step explanation:

x = number of pants

y = number of shirts

Set up equations:

Set the equations up as a system:

25x+14.5y=357

x+y=21

Steps:

Solve the system by substitution.

(You can also solve this system by elimination.)

25x + 14.5y=  357

x + y = 21

Step 1: Solve x+y=21 for x:

(x + y) − y = (21) − y(Subtract y from both sides)

x = −y + 21

Step 2: Substitute −y + 21 for x in 25x + 14.5y = 357:

25x + 14.5y = 357

25(−y + 21) + 14.5y = 357

−10.5y + 525 = 357 (Simplify both sides of the equation)

(−10.5y + 525) − 525 = (357) − 525(Subtract 525 to both sides)

−10.5y =  −168

−10.5y / −10.5 = −168 / −10.5 (Divide both sides by -10.5)

y = 16

Step 3: Substitute 16 for y in x = −y + 21:

x = −y + 21

x = −16 + 21

x = 5 (Simplify both sides of the equation)

Answer:

x=5 and y=16

Answer:

$80

Step-by-step explanation:

10x + 30 = y

He wants to rent it for 5 hours, so we replace x with 5.

10(5) + 30 = 80

He should expect to pay $80 for the rental.

Answer:

0,-1

Step-by-step explanation:

Answer: [tex]25^{\circ}[/tex]

Step-by-step explanation:

Given

The highest temperature recorded is [tex]18^{\circ}[/tex]

The lowest temperature recorded is [tex]-7^{\circ}[/tex]

The amount of change between the high and the low temperatures is

[tex]\Rightarrow 18-(-7)=18+7\\\Rightarrow 25^{\circ}[/tex]