1) Set up, but do not solve, a system of equations for the following application: A nurse mixes a 100% saline solution with a 20% saline solution to produce 160 milliliters of a 25% saline solution. How much of the 100% saline solution and how much of the 20% saline solution were used?

Answer:

45%

Step-by-step explanation:

Divide 27/60, which gives you 0.45. Multiply that by 100, you get 45 percent.

Answer:

45%

Step-by-step explanation:

27/60

Answer:

[tex] {x}^{2} - 7x + 10 = 0[/tex]

Step-by-step explanation:

[tex](x -2)(x - 5) = 0[/tex]

[tex] {x}^{2} - 7x + 10 = 0[/tex]

Answer:

Octagon

Step-by-step explanation:

Formula for a polygon is :

Since a regular octagon has 8 sides, and a regular hexagon has 6, the octagon will have the greater area due to greater perimeter.

Answer:

-6

Step-by-step explanation:

h(x) = −3 |x + 1| evaluate h (-3)

h (-3) means x = -3

Plug in:

h(x) = −3 |(-3) + 1| → h(x) = −3 |-3 + 1|

h(x) = −3 |-2|       since -2 is an absolute value it becomes 2

h(x) = −3(2)

h(x) = -6

Let me know if you have anymore questions,

Good Luck studying :) YOU GOT THIS !!!

Answer:

19

Step-by-step explanation:

3(4)(2) - 5

3 * 4 = 12 * 2 = 24

24 - 5 = 19

Answer:

M = 2

Step-by-step explanation:

3M+4/3 = 28/3 -M

3M+M +4/3-28/3 = 0

4M -8 = 0

4M = 8 ( divide 4 in both sides)

M=8/4

M=2

The expression in the 6th term in the binomial expression is [tex]265781250y^6[/tex]

The expression is given as:

(5y + 3)^10

The above expression is a binomial expression, and the xth term can be represented using:

[tex]^nC_x (a)^x * (b)^{n-x}[/tex]

So, we have:

[tex]^{10}C_6 * (5y)^6 * (3)^4[/tex]

Evaluate the combination expression

[tex]210 * (5y)^6 * (3)^4[/tex]

Evaluate the exponents

[tex]210 * 15625y^6 * 81[/tex]

Evaluate the product

[tex]265781250y^6[/tex]

Hence, the expression in the 6th term is [tex]265781250y^6[/tex]

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The system of equations that we need to solve is:

And the solution is x = 49 and y = 101.

Let's define the variables:

We know that the total number of CDs is 150, then:

x + y = 150

And we know that:

y = 2x + 3

Then the two equations that represent the information (and conform a system of equations) are:

x + y = 150

y = 2x + 3

b) The graphs of the two equations can be seen below.

c) To find the solution, we just need to see where the graphs intercept.

We can see that the intercept is (49, 101), this means that:

Isabella has 49 rock music CDs and 101 alternative music CDs.

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Answer:

Step-by-step explanation:

that should help

Answer:

I like to use Desmos when I graph parabolas. But I’m this case it would be 3 down and one to the left so the vertex should be (-1,-3) and then just graph x^2

Step-by-step explanation:

Hope this helps! ;-)

There were 14 boys at Mina's disco for her birthday.

A ratio is a quantitative value that shows the number of times a certain value is in another value.

It is given that for every 2 boys at the disco, there were 3 girls. This means that the ratio of boys to girls at the disco is 2:3.

Let the proportionality constant be x.

Therefore total boys and girls are 2x and 3x respectively.

There are 35 kids at the disco. This means that the number of boys plus girls is 35. It can be written as shown below:

2x + 3x = 35

⇒ x = 35/5

⇒ x = 7

Total number of boys = 2x

= 2 * 7

= 14 boys

Therefore the total number of boys at the disco is 14.

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Answer:

See below ~

Step-by-step explanation:

The three inequalities (listed below) have been plotted on a graph :

Answer:

[tex]160[/tex] °

Step-by-step explanation:

An alternative method is to use the exterior angle.

the sum of the exterior angles is ALWAYS 360 °

So you can find the size of the exterior angles of a regular polygon quite easily:

If there are 18 sides ( n = 18 ) , then each exterior angle is:

[tex]\frac{360}{n} =\frac{360}{18} = 20[/tex]°

The sum of the exterior and interior angles is 180° because they are adjacent angles on a straight line.

∴ each interior angle is 180° - 20° = 160°

Since events a and b are independent P(a and b) = P(a) × P(b)

To answer the question, we need to know what probability is

Probability is the likelihood of an event to occur. The probability of the event P(event) = number of required outcomes/total number of outcomes

If we have two independent event sa and b that have probabilities of occuring P(a) and P(b) respectively, the probability P(a and b) = P(a) × P(b)

So, P(a and b) = P(a) × P(b)

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Answer:

Choice E.

Step-by-step explanation:

sin^2 2x = 1

sin 2x = ± 1

So 2x = 90, 270 , 450, 630  etc

x = 45, 135, 225, 315   etc

=  45 + 360n, 135 + 360n, 225 + 360n, 315 + 360n

Answer:

140 ounces of Vegetables

Step-by-step explanation:

23 ounces of carrots x 2 = 46 ounces

47 ounces of broccoli x 2 = 94 ounces

46 ounces of carrots + 94 Ounces of Broccoli = 140 Ounces of Vegetables

Answer:

140 oz of vetables

Step-by-step explanation:

23 x 2 = 46

47 x 2 = 94

46 + 94 = 140

The probability of pulling a white marble from the jar is 0.

Probability determines the odds that an event would happen. The odds usually lie between 0 and 1.

The probability of pulling a white marble = total number of white marbles / total number of marbles

0 / 40 = 0

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Answer:

    43. (2) $2.00

Step-by-step explanation:

Question 43

Subtract Equation 2 from Equation 1.

Answer:

(2)  $2.00

Step-by-step explanation:

Jack's order

3 slices of cheese pizza and 4 slices of mushroom pizza = $12.50

Grace's order

3 slices of cheese pizza and 2 slices of mushroom pizza = $8.50

The difference between the two orders is 2 slices of mushroom pizza.

The difference between the cost of the two orders is:

$12.50 - $8.50 = $4.00

Therefore, 2 slices of mushroom pizza costs $4.00

So the cost of 1 slice of mushroom pizza is:

$4.00 ÷ 2 = $2.00

Answer:

Here is the ans ..hope it helps

The fraction 11/20 can not be converted to a mixed fraction since it belongs to the proper fraction, I mean that the numerator is less than the denominator.

Only improper fractions can be mixed.

[tex]\: \: \: \: \: \: \: \: \qquad\bold{\Rightarrow \dfrac{20}{11}= 1\dfrac{9}{11} }[/tex]

So no the fraction 11/20 cannot be a mixed fraction.

Answer:

Solve the set of two reals for the following exponential equation:

\Large\text{${\dfrac{27^x\:-\:3^x}{9^x\:-\:3^x} = 82}$}

[tex]~~~~~~~\cos 45^{\circ} = \dfrac{\text{Base}}{\text{Hypotenuse}}\\\\\\\implies \dfrac 1{\sqrt 2} = \dfrac{\sqrt 3}{x}\\\\\\\implies x = \sqrt 3 \cdot \sqrt 2\\\\\\\implies x = \sqrt {3 \times 2}\\\\\\\implies x = \sqrt 6[/tex]

[tex]\csc 2x+1[/tex]

Step-by-step explanation:

Answer:

Step-by-step explanation:

21/7=3

5*3=15 width

3*3=9 height

The area of the pentagon, rounded to the nearest tenth will be 32.7 square cm. Then the correct option is C.

The polygon is a 2D geometry that has a finite number of sides. And all the sides of the polygon are straight lines connected to each other side by side.

A regular pentagon has an apothem measuring 3 cm and a perimeter of 21.8 cm.

Then the side length of the pentagon will be

5 x Side length = 21.8 cm

     Side length = 4.36 cm

Then the area of the pentagon, rounded to the nearest tenth will be

Area of pentagon = 5 x area of triangle

Area of pentagon = 5 x 1/2 x 4.36 x 3

Area of pentagon = 32.7 square cm

Thus, the correct option is C.

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Answer:

D. is the correct option

Step-by-step explanation:

There is a total of 5 people, so we can either split the pizza cost into 5, or into 10 and multiply by 2 (since each guest ate 2 slices) We'll do the first option since it's simpler.

$17.49 ÷ 5 = 3.489 or rounded up to $3.50

Next, we'll add $1.19 to $3.59 which equals $4.69

Hope this helps!

Answer:

130

Step-by-step explanation:

[tex](35*4)-(10*1)-(5*0)=130[/tex]

Answers:

=======================================================

Part (a)

Let's find the distance from point D to point E.

In other words, this will compute the length of segment DE.

[tex]D = (x_1,y_1) = (0,-6) \text{ and } E = (x_2, y_2) = (3,1)\\\\d = \sqrt{(x_1 - x_2)^2 + (y_1 - y_2)^2}\\\\d = \sqrt{(0-3)^2 + (-6-1)^2}\\\\d = \sqrt{(-3)^2 + (-7)^2}\\\\d = \sqrt{9 + 49}\\\\d = \sqrt{58}\\\\d \approx 7.6158\\\\[/tex]

Segment DE is roughly 7.6158 units long.

Let's repeat these steps to find the length of segment EF.

[tex]E = (x_1,y_1) = (3,1) \text{ and } F = (x_2, y_2) = (-2,1)\\\\d = \sqrt{(x_1 - x_2)^2 + (y_1 - y_2)^2}\\\\d = \sqrt{(3-(-2))^2 + (1-1)^2}\\\\d = \sqrt{(3+2)^2 + (1-1)^2}\\\\d = \sqrt{(5)^2 + (0)^2}\\\\d = \sqrt{25 + 0}\\\\d = \sqrt{25}\\\\d = 5\\\\[/tex]

Segment EF is exactly 5 units long.

Lastly, we'll compute the length of segment FD.

[tex](x_1,y_1) = (-2,1) \text{ and } (x_2, y_2) = (0,-6)\\\\d = \sqrt{(x_1 - x_2)^2 + (y_1 - y_2)^2}\\\\d = \sqrt{(-2-0)^2 + (1-(-6))^2}\\\\d = \sqrt{(-2-0)^2 + (1+6)^2}\\\\d = \sqrt{(-2)^2 + (7)^2}\\\\d = \sqrt{4 + 49}\\\\d = \sqrt{53}\\\\d \approx 7.2801\\\\[/tex]

Segment FD is about 7.2801 units long.

This is close to the length of DE, but not quite.

To recap, we found these segment lengths:

As you can see, all three sides are different lengths. Therefore, triangle DEF is scalene.

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

For part (b), follow the same template as part (a).

I'll be skipping the steps.

This is what you should get for the lengths of triangle TRI

Segments TR and IT are the same length (both exactly [tex]\sqrt{37}[/tex] units long), which means triangle TRI is isosceles.

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

For part (c), I'll also be skipping steps.

Here are the lengths you should find

All three lengths are different, making this triangle scalene.

Answer:

the answer willl be D

Step-by-step explanation:

Answer:

The surface area of this solid is:

b. 107

Step-by-step explanation:

To understand this answer we need to analyze it. First, we have different geometric figures composing the solid. A pyramid and a rectangular prism. We need to obtain the surface, not the volume so we need to obtain the area of all the figures composing the pyramid and the prism without the hidden part of the pyramid base. We need to obtain the following areas:

2 rectangles with the following measures= W=2 L= 8

1 rectangle with the following measures= W=3 L=8

1 rectangle with the following measures= W=3 L 5

2 rectangles with the following measures= W=2 L=3

4 triangles with the following measures= B=3 H=4

Following the formula for the rectangles W x L we obtain a total area for them of 83 square meters.

Following the formula for the triangles b x h / 2 we obtain the following area: 24 square meters. Then we add both and obtain 107 square meters.

Answer:

Step-by-step explanation:

We know that vertical angles are congruent.

Use this property to set up equation.

Substitute the values of angles and solve for x.

The value of x is 9