Mr. and Mrs. Rivers left their house at 10:00 a.m. driving in opposite directions. Mr. Rivers drove at an average speed of 48 mph and Mrs. Rivers drove at an average speed of 36 mph. How far apart are they at 10:30 a.m.?

Answer:

[tex]\large\boxed{D.\ y=-\dfrac{1}{5}x+\dfrac{32}{5}}[/tex]

Step-by-step explanation:

The slope-intercept form of an equation of a line:

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

m - slope

b - y-intercept

We have the slope m = -1/5. Substitute:

[tex]y=-\dfrac{1}{5}x+b[/tex]

Put the coordinates of the given point (-3, 7) to the equation:

[tex]7=-\dfrac{1}{5}(-3)+b[/tex]

[tex]7=\dfrac{3}{5}+b[/tex]            subtract 3/5 from both sides

[tex]6\dfrac{2}{5}=b\to b=\dfrac{6\cdot5+2}{5}=\dfrac{32}{5}[/tex]

Answer:

Approx. 39.7%

Step-by-step explanation:

All you have to do is

17,892÷45,128

Answer:

40 %

Step-by-step explanation:

Percent = Responses/total surveys × 100 %

             = 17 892/45 128 × 100 %

             ≈ 40 %

Approximately 40 % of people responded to the survey.

North Carolina = 3 * Utah

North Carolina = 2 * Oregon

Arkansas = Oregon - 1,000,000

North Carolina + Utah + Oregon + Arkansas = 27,000,000

North Carolina = 3 * Utah

Utah = 1/3 * North Carolina

Utah = 1/3 * (2 * Oregon)

(2 * Oregon) + (1/3 * (2 * Oregon)) + Oregon + (Oregon - 1,000,000) = 27,000,000

2O + (1/3 * 2O) + O + O - 1,000,000 = 27,000,000

2O + 2/3O + O + O - 1,000,000 = 27,000,000

4 2/3 O - 1,000,000 = 27,000,000

4 2/3 O = 28,000,000

O = 6,008,584

NC = 2O

NC = 2(6,008,584)

NC = 12,017,167

A = O - 1,000,000

A = 6,008,584 - 1,000,000

A = 5,008,584

NC = 3U

12,017,167 = 3U

U = 4,005,722

The populations of the four states are as follows:

- Utah has a population of 4 million.

- Oregon has a population of 6 million.

- North Carolina has a population of 12 million.

- Arkansas has a population of 5 million.

Let's denote the population of Utah, Oregon, and Arkansas as U, O, and A, respectively. According to the information given:

1. North Carolina has three times the population of Utah: [tex]\( NC = 3U \).[/tex]

2. North Carolina has twice the population of Oregon: [tex]\( NC = 2O \).[/tex]

3. Arkansas has 1 million people fewer than Oregon: [tex]\( A = O - 1 \).[/tex]

4. The total population of these four states is 27 million: [tex]\( U + O + A + NC = 27 \).[/tex]

From equations (1) and (2), we can equate the populations of Utah and Oregon since both are related to the population of North Carolina:

[tex]\( 3U = 2O \) or \( O = \frac{3}{2}U \).[/tex]

Now, substitute the value of O from equation (3) into the total population equation (4):

[tex]\( U + \frac{3}{2}U + ( \frac{3}{2}U - 1 ) + 3U = 27 \).[/tex]

Combine like terms:

[tex]\( U + \frac{3}{2}U + \frac{3}{2}U - 1 + 3U = 27 \),[/tex]

[tex]\( U + 3U + 3U - 1 = 27 \),[/tex]

[tex]\( 7U - 1 = 27 \).[/tex]

Now, solve for U:

[tex]\( 7U = 27 + 1 \),[/tex]

[tex]\( 7U = 28 \),[/tex]

[tex]\( U = \frac{28}{7} \),[/tex]

[tex]\( U = 4 \)[/tex] million.

Now that we have the population of Utah, we can find the populations of the other states:

[tex]\( O = \frac{3}{2}U = \frac{3}{2} \times 4 = 6 \)[/tex] million,

[tex]\( NC = 2O = 2 \times 6 = 12 \)[/tex] million,

[tex]\( A = O - 1 = 6 - 1 = 5 \)[/tex] million.

?

Step-by-step explanation:

first you have to add the PIC to have us answer

Answer:

your answer would be: x=1±√11 all divided by 2

Hope this helps

~QueenSupreme AKA Trinity

Answer:   [tex]\bold{\dfrac{1\pm \sqrt{11}}{2}}[/tex]

Step-by-step explanation:

[tex]x^2-x-\frac{5}{2}=0\quad \text{multiply by 2 to get:}\\\\2x^2-2x-5=0\quad \rightarrow \quad a=2,\ b=-2,\ c=-5\\\\\text{Quadratic formula is: }x=\dfrac{-b\pm \sqrt{b^2-4ac}}{2a}\\\\\\x=\dfrac{-(-2)\pm \sqrt{(-2)^2-4(2)(-5)}}{2(2)}\\\\\\.\ =\dfrac{2\pm \sqrt{40}}{2(2)}\\\\\\.\ =\dfrac{2\pm \sqrt{44}}{2(2)}\\\\\\.\ =\dfrac{2\pm 2\sqrt{11}}{2(2)}\\\\\\.\ =\boxed{\dfrac{1\pm \sqrt{11}}{2}}[/tex]

Answer:B.

Step-by-step explanation:

Answer:

C

Step-by-step explanation:

it is C because A, B, and D are triangular prisms.

Answer:

[tex]S.A=96\pi m^2[/tex]

Step-by-step explanation:

The surface area of a right circular cylinder is given by the formula;

[tex]S.A=2\pi r(r+h)[/tex]

where [tex]h=8m[/tex] is the height of the cylinder and

[tex]r=4m[/tex] is the radius of the cylinder.

We plug in these values into the formula to obtain;

[tex]S.A=2\pi \times4(4+8)[/tex]

[tex]S.A=8 \times12 \pi[/tex]

[tex]S.A=96\pi m^2[/tex]

Answer:

The answer is C, 220 units.

Answer:

The answer is 0.42525 TONS (METRIC)

♫ - - - - - - - - - - - - - - - ~Hello There!~ - - - - - - - - - - - - - - - ♫

➷ x=-2, no explanation

✽

➶ Hope This Helps You!

➶ Good Luck (:

➶ Have A Great Day ^-^

TROLLER

There always needs to be an explanation so you understand it!

Follow this step by step.

#1. Remove all -1 on both sides.

You are left with 2(x+3)+x=0.

#2. Expand the equation.

2x+6+x=0.

#3. Simplify 2x + 6 + x to 3x + 6.

3x+6=0

#4. Subtract 6 from each side.

3x=−6.

#5. Divide both sides by 3.

x = -6/3.

#6. Simplify 6/3 to 2.

x = 2.

Therefore, you get [tex]\fbox{x = 2}[/tex].

Final answer:

To factor the expression 3x² - 19x + 20, we find two numbers that multiply to 60 and add up to -19, which are -4 and -15. The expression can then be rewritten and factored by grouping to obtain the factors (x - 5)(3x - 4).

Explanation:

The question asks to factor the quadratic expression

3x² - 19x + 20

To factor this expression, we need to find two numbers that multiply to give the product of the coefficient of x² (which is 3) and the constant term (which is 20), and at the same time, add up to give the coefficient of x (which is -19). The two numbers that satisfy these conditions are -4 and -15, as (-4) * (-15) = 60 and (-4) + (-15) = -19.

Now, we can rewrite the expression by splitting the middle term:

3x² - 4x - 15x + 20

Factor by grouping: x(3x - 4) - 5(3x - 4)

The factors are: (x - 5)(3x - 4)

Answer:

C

Step-by-step explanation:

Answer:

The inequality is

6+4r>17

The miminum number of runs per inning is  

3.

Step-by-step explanation:

C is the one you're looking for

Answer:

All are True

a) 30a^6-24a^2=3à^2(10a^4-8)

b) 24a^4+18=6(4a^⁴+3)

c) 16a^5-20a^3=4a^3(4a^2-5)

D) 12a^3+8a=4(3a^3+2a)​

Step-by-step explanation:

a) 30a^6-24a^2=3à^2(10a^4-8)

since; 3à^2(10a^4-8)

        = 30a^6 - 24a^2

b) 24a^4+18=6(4a^⁴+3)

Since; 6(4a^⁴+3) opening the brackets

           = 24a^4 + 18

c) 16a^5-20a^3=4a^3(4a^2-5)

Since; 4a^3(4a^2-5) , opening the brackets we get

         = 16a^5 - 20^3

D) 12a^3+8a=4(3a^3+2a)​

Since;4(3a^3+2a)​, opening the bracket we get;

        = 12a^3 + 8a

Answer:

2

Step-by-step explanation:

The car would be about 90 ft

Answer:

[tex]90cm^2[/tex]

Step-by-step explanation:

The side length AB of triangle ABC corresponds to side length of PQ of triangle PQR.

The scale factor from ABC to PQR is [tex]k=\frac{6}{4}=1.5[/tex]

The area of triangle PQR will change by [tex]k^2=1.5^2=2.25[/tex] centimeters square.

Since we know the area of triangle ABC to be [tex]40cm^2[/tex], the area of triangle PQR [tex]=2.25\times 40=90cm^2[/tex]

Answer:

The area of the triangle PQR is 90 cm^2.

Step-by-step explanation:

We are given two triangles, ABC and PQR, which are similar to each other.

If two triangles are similar, then the ratio of their areas is the square of the ratio of their sides.

Given that area of the triangle ABC is [tex]40cm^2[/tex], we are to find the area of the triangle PQR.

Finding the scale factor [tex]k=\frac{6}{4} =1.5[/tex]

So square of this scale factor will be [tex]k^2=(1.5)^2=2.25[/tex]

Area of triangle PQR = [tex]2.25 \times 40[/tex] = 90cm^2

Answer:

Plane = 441 mi/h; wind =  63 mi/h

Step-by-step explanation:

distance = rate × time

 Let p = the plane's speed in still air

and w = the wind speed . Then,

p + w = speed with wind

 p - w = speed against wind

We have two conditions:

(1)  756 = (p - w) × 2

(2) 756 = (p + w) × 1.5

Distribute the constants                  (3)    756 = 2p - 2w

                                                          (4)   756 = 1.5p + 1.5 w  

Multiply Equation (3) by 3                (5) 2268 = 6p  -  6w

Multiply Equation (4) by 4                (6) 3024 = 6p + 6w

Add Equations (5) and (6)                     5292 = 12p

Divide each side by 12                     (7)        p = 441 mi/h

Substitute (7) into Equation(3)                 756 = 882 - 2w

Add 2w to each side                      2w + 756 = 882

Subtract 756 from each side                    2w = 126

Divide each side by 2                                 w = 63 mph

The plane's speed in still air is 441 mi/h.

The wind speed is 63 mph.

Check:

(1) 756 = (441 - 63) × 2     (2) 756 = (441 + 63) × 1.5

   756 = 378 × 2                   756 = 504 × 1.5

   756 = 756                         756 = 756

The speed of the plane in still air is 420 miles per hour and the wind speed is 84 miles per hour.

To solve Dave and Sandy Hartranft's problem, we set up two equations for flying into and with the wind. For Dave and Sandy flying into the wind, we use the formula speed equals distance over time: P - W = 756 miles / 2 hours. This represents the plane's speed minus the wind speed equaling the distance traveled divided by the time taken. We denote P as plane's speed and W as wind speed.

On the return trip, with the wind behind them, we calculate plane's speed plus the wind speed based on the same formula: P + W = 756 miles / 1.5 hours. Solving these two equations, you get: P = 420 miles per hour (plane's speed in still air) and W = 84 miles per hour (wind speed).

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The solution to the number 8000 in scientific notation is 8  * 10³

From the question, we have the following parameters that can be used in our computation:

Number = 8000

Multiply the number by 1

So, we have

Number = 8000 * 1

Express 1 as 1000/1000

So, we have the following representation

Number = 8000 * 1000/1000

Next, we have

Number = 8 * 1000

Express 1000 as 10³

So, we have

Number = 8 * 10³

Hence, the solution is 8  * 10³

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[tex]AB\: is \:the \:diameter\Rightarrow \widehat{ACB}=90°\Rightarrow \widehat{ABC}=180°-90°-30°=60° \: (1) \\ \bigtriangleup OBC \: has \: OB=OC=R\Rightarrow \bigtriangleup OBC \: is \: an \: isosceles \: triangle \: (2) \\ (1),(2)\Rightarrow \bigtriangleup OBC \: is \: an \: equilateral \: t riangle \Rightarrow \widehat{COB} =\widehat{COD} = 60° \\ CD \: tangents \: (O) \: at \: C\Rightarrow OC\perp OD \: at \: C\Rightarrow \widehat{OCD}=90° \\ \widehat{CDO}=180°-\widehat{OCD}-\widehat{COD}=180°-90°-60°=30° \\ In\: \bigtriangleup ACD,\widehat{CAD}=\widehat{CDA}=30°\\\Rightarrow \bigtriangleup ACD\: is\: an\: isosceles\: triangle\: at\: C[/tex]

Triangle ACD is an isosceles triangle, with AC = AD.

A triangle is a 2-D figure with three sides and three angles.

The sum of the angles is 180 degrees.

We can have an obtuse triangle, an acute triangle, or a right triangle.

We have,

Let O be the center of the circle, and let E be the point where the tangent line to the circle at point C intersects diameter AB.

Since OC is perpendicular to CE (tangent line at C), and OD is perpendicular to AB, angle ECD and angle OAD are alternate angles, and hence congruent.

Now,

Since the measure of the angle between diameter AB and chord AC is 30°, the measure of angle AOC is 60°.

The measure of angle OAD is also 60°.

Now,

Since angles ACD and OAD are congruent, and angle AOC is 60°,

we have:

angle ACD = angle OAD = 60°

Also,

Since OC is perpendicular to AC (radius of the circle),

we have angle OCA = 90°.

Now,

angle ACB

= angle OCA - angle AC0

= 90° - 30°

= 60°

Since angle ACD is equal to angle ACB, and angle AOC is also equal to 60°,

We have:

angle ACD = angle ACB = 60°

angle AOC = 60°

Therefore,

Triangle ACD is an isosceles triangle, with AC = AD.

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Answer:

m<2 = 63

m<3 = 117

Step-by-step explanation:

<1 and <2 are alternate interior angles and are therefore equal. M<1 = 63 degrees,  so m<2 must be the same thing.

<2 and <3 are on the same straight line.

They are supplementary.

Therefore they equal 180 degrees.

63 + m<3 = 180                  Subtract 63 from both sides.

63 - 63 +m<3 = 180 - 63   Collect like terms

m<3 = 117

Answer:

Although variables wouldn't really fit for this problem, if you were to graph it, the pizza types would be on the x axis and the cost would be on the y axis since the cost of the pizzas technically "depend" on the type of pizza.

Answer:

[tex]x \geq -56[/tex]

Step-by-step explanation:

You can solve inequalities the same way as equations as long as whenever you multiply or divide by a negative number, or flip fractions, you change the direction of the sign.

We don't have to do that here, here is the worked solution:

[tex]-12 \leq 44 + x[/tex]

[tex]-56 \leq x[/tex]

[tex]x \geq -56[/tex]

Answer:

x ≥ -56

Step-by-step explanation:

Solve for x by simplifying both sides of the equation, then isolating the variable.

Hope this helps,

Davinia.

Answer:

c)Q3

Step-by-step explanation:

In the third quadrant, tangent and cotangent are positive while cosine and thus secant are negative. Therefore, the solution is C. Q3

It’s the second one from the right

Since there’s a - behind x it means it has to be facing down so it’s either 2 or 4

Now it’s x-2 and we know that x moves the opposite so it needs to move 2 to the right so the answer is 2

Answer: (-1, -4) and (4, 6)

Step-by-step explanation:

The pair of solution to the equations y = 2x - 2  and y = x² - x - 6

are (4, 6) and (-1, -4).

It is defined as the relation between two variables, if we plot the graph of the linear equation we will get a straight line.

If in the linear equation, one variable is present, then the equation is known as the linear equation in one variable.

We have two equations:

y = 2x - 2

y = x² - x - 6

Equate both equations:

2x - 2 = x² - x - 6

x² - 3x - 4 = 0

Solving using the quadratic formula:

[tex]\rm x_{1,\:2}=\dfrac{-\left(-3\right)\pm \sqrt{\left(-3\right)^2-4\cdot \:1\cdot \left(-4\right)}}{2\cdot \:1}[/tex]

x = 4, -1

y = 6, -4

Thus, the pair of solution to the equations y = 2x - 2  and y = x² - x - 6

are (4, 6) and (-1, -4).

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Answer:

x + y = -1

Step-by-step explanation:

To write the equation of a line, find the slope and use it with a point in the point slope form.

You can find the slope using the slope formula.

[tex]m = \frac{y_2-y_1}{x_2-x_1} = \frac{5--3}{-6-2} = \frac{8}{-8}=-1[/tex]

Substitute m = -1 and the point (2,-3) into the point slope form.

[tex]y - y_1 = m(x-x_1)\\y --3 = -1(x-2)\\y+3=-1(x-2)[/tex]

Convert to standard form by applying the distributive property and rearranging the terms.

y+3 = -1(x-2)

y + 3 = -x + 2

x + y + 3 = 2

x + y = -1

Answer:

radius=3.5 Diameter=7 Circumference=21.99 area=38.48

Step-by-step explanation: These are the answers, hope you found them helpful :)