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3 years ago

10

Kendra has $ 7.75 $7.75 in nickels and quarters. if she has 13 13 more quarters than nickels, how many of each coin does she hav

e?

1 answer:

Ludmilka [50]3 years ago

7 0

Total of $7.75
13 more quarters than nickels

15 nickels = $0.75
28 quarters = $7.00

28 - 15 = 13 coins
$7.00 + $0.75 = $7.75

She has 15 nickels and 28 quarters.

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Sellus Evaluate the expression when m=25. m + 2(m-5) = [?]

stiv31 [10]

Answer:

65

Step-by-step explanation:

So we have the expression:

$m+2(m-5)$

And we want to evaluate it for m=25.

So, substitute 25 for m:

$=(25)+2((25)-5)$

Subtract:

$=25+2(20)$

Multiply:

$=25+40$

Add:

$=65$

So, our answer is 65.

And we're done!

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3 years ago

Circle the following 2 terms that correspond with the domain of a function:

Nitella [24]

Answer:

x-values

independent variable

Step-by-step explanation:

x (the independent variable) is the domain

y (the dependent variable) is the range

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3 years ago

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X squared+ y squared = 2 y = 2x squared – 3 Which of the following describes the system?

cluponka [151]

Answer:

$x=-1,1,-\sqrt{\frac{7}{4} },\sqrt{\frac{7}{4}}$ and $y=-1,\frac{1}{2}$

The ordered pair solutions are $(-\sqrt{\frac{7}{4}},0.5)$ , $(\sqrt{\frac{7}{4}},0.5)$ , $(-1,-1)$ , and $(1,-1)$ .

Step-by-step explanation:

I'm assuming the system is $\left \{ {x^2+y^2=2} \atop {y=2x^2-3}} \right.$ :

$x^2+y^2=2$

$x^2+(2x^2-3)^2=2$

$x^2+(4x^4-12x^2+9)=2$

$x^2+4x^4-12x^2+9=2$

$4x^4-11x^2+9=2$

$4x^4-11x^2+7=0$

$x^4-11x^2+28=0$

$(x^2-7)(x^2-4)=0$

$(4x^2-7)(x^2-1)=0$

$4x^2-7=0$

$4x^2=7$

$x^2=\frac{7}{4}$

$x=\pm\sqrt{\frac{7}{4}}$

$x^2-1=0$

$x^2=1$

$x=\pm1$

$y=2x^2-3$

$y=2(\pm\sqrt{\frac{7}{4}})^2-3$

$y=2({\frac{7}{4}})-3$

$y=\frac{7}{2}-3$

$y=\frac{1}{2}$

$y=2x^2-3$

$y=2(\pm1)^2-3$

$y=2(1)-3$

$y=2-3$

$y=-1$

Therefore, $x=-1,1,-\sqrt{\frac{7}{4} },\sqrt{\frac{7}{4}}$ and $y=-1,\frac{1}{2}$

The ordered pair solutions are $(-\sqrt{\frac{7}{4}},0.5)$ , $(\sqrt{\frac{7}{4}},0.5)$ , $(-1,-1)$ , and $(1,-1)$ .

4 0

2 years ago

In a right triangle ABC, CD is an altitude, such that AD=BC. Find AC, if AB=3 cm, and CD=√2 cm.

Zielflug [23.3K]

Given that triangle ABC is right angle triangle. CD is altitude such that AD=BC

ABC is a right angle triangle so apply Pythogorean theorem

$AC^{2} + BC^{2} = AB^{2}$

$AC^{2} + AD^{2} = AB^{2}$ (Given that AD = BC)

$AC^{2} + AD^{2} = 3^{2}$ (Given that AB=3)

$AC^{2} + AD^{2} = 9$ ...(i)

ADC is a right angle triangle so apply Pythogorean theorem

$AD^{2} + CD^{2} = AC^{2}$

$AD^{2}+(\sqrt{2})^2= AC^{2}$

$AD^{2}+2= AC^{2}$

$AD^{2}=AC^{2} -2$ ...(ii)

Plug value (ii) into (i)

$AC^{2} + AC^{2}-2 = 9$

$2AC^{2} -2=9$

$2AC^{2} =11$

$AC^{2} =\frac{11}{2}$

$AC=\sqrt{\frac{11}{2} }$

Hence final answer is $AC=\sqrt{\frac{11}{2} }$

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3 years ago

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Write the equation of the line in fully simplified slope-intercept form.

Aneli [31]

Answer:

$y = -\frac{1}{5}x -1$

Step-by-step explanation:

Given

The attached graph

Required

Determine the line equation

First, list out two points from the graph

$(x_1,y_1) = (-5,0)$

$(x_2,y_2) = (0,-1)$

Next, calculate the slope (m)

$m = \frac{y_2 - y_1}{x_2 - x_1}$

$m = \frac{-1-0}{0 -(-5)}$

$m = \frac{-1}{0 +5}$

$m = -\frac{1}{5}$

The equation in slope intercept form is:

$y = m(x - x_1) + y_1$

This gives:

$y = -\frac{1}{5}(x - (-5)) + 0$

$y = -\frac{1}{5}(x +5)$

Open bracket

$y = -\frac{1}{5}x -1$

4 0

3 years ago