Ralph and Waldo start in towns that are 70 miles apart and travel in opposite directions for 4 hours.

Ralph travels
15 miles per hour faster than Waldo.

Let w stand for Waldo's speed and write algebraic expressions to answer the
following questions


a. How far did Waldo travel?


miles



b. What was Ralph's speed?


mph



C. How far did Ralph travel?


miles



d. What is the distance between Ralph and Waldo after the 4 hours?


miles

Answer:

x1=-11 x2=-1 y=11

Step-by-step explanation:

you can see the explanation in the pics

Answer:

Step-by-step explanation:

You would simplify 5/2, making it 2 and 1/2.  this would go in between 2 and 3 on a graph.

Step-by-step explanation:

5/2 = 2.5

see attached to find where 2.5 is located on the number line.

Answer:

Part 2) Option b. 5.4

Part 3) Option c. 8

Part 4) Option a. 15

Part 5) Option d. 8.9

Step-by-step explanation:

Part 2) Find the value of x to the nearest tenth

we know that

x is the radius of the circle

Applying the Pythagoras Theorem

[tex]x^{2}=3.6^{2}+(8/2)^{2}[/tex]

[tex]x^{2}=28.96[/tex]

[tex]x=5.4\ units[/tex]

Part 3) Find the value of x

In this problem

x=8

Verify

step 1

Find the radius of the circle

Let

r -----> the radius of the circle

Applying the Pythagoras Theorem

[tex]r^{2}=8^{2}+(15/2)^{2}[/tex]

[tex]r^{2}=120.25[/tex]

[tex]r=\sqrt{120.25}[/tex]

step 2

Find the value of x

Applying the Pythagoras Theorem

[tex]r^{2}=x^{2}+(15/2)^{2}[/tex]

substitute

[tex]120.25=x^{2}+56.25[/tex]

[tex]x^{2}=120.25-56.25[/tex]

[tex]x^{2}=64[/tex]

[tex]x=8\ units[/tex]

Part 4) Find the value of x

In this problem

x=OP=15

Verify

step 1

Find the radius of the circle

Let

r -----> the radius of the circle

In the right triangle FPO

Applying the Pythagoras Theorem

[tex]r^{2}=15^{2}+(40/2)^{2}[/tex]

[tex]r^{2}=625[/tex]

[tex]r=25[/tex]

step 2

Find the value of x

In the right triangle RQO

Applying the Pythagoras Theorem

[tex]25^{2}=x^{2}+(40/2)^{2}[/tex]

[tex]625=x^{2}+400[/tex]      

[tex]x^{2}=625-400[/tex]

[tex]x^{2}=225[/tex]

[tex]x=15\ units[/tex]

Part 5) Find the value of x

Applying the Pythagoras Theorem

[tex]6^{2}=4^{2}+(x/2)^{2}[/tex]

[tex]36=16+(x/2)^{2}[/tex]

[tex](x/2)^{2}=36-16[/tex]

[tex](x/2)^{2}=20[/tex]

[tex](x/2)=4.47[/tex]

[tex]x=8.9[/tex]

Answer:

sqrt.(a) * absolutevalue(b)

Step-by-step explanation:

You do abs value when you have an even exponent with an odd exponent result from b^2 to b^1.

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Answer: Hello there!

Well, the square root is the inverse function of the square potential.

This is if you have [tex](\sqrt{x} )^{2}  = x[/tex] and [tex]\sqrt{x^{2} }  = +-x[/tex]

A interesting part of the square root is that (-4)*(-4) = 16, and 4*4 = 16, so the solutions for [tex]\sqrt{16}[/tex] are -4 and 4. For this is that you see a +- symbol in the second equation.

Now, if you have the number [tex](a*b)^{2}[/tex]

Now, we put this inside a square root: [tex]\sqrt{(a*b)^{2} } = +-a*b[/tex]

So the solutions for the square root of (a*b)^2 are a*b and - a*b.

Answer:

Step 1  1200/ ?

Step-by-step explanation:

There is a mistake in the very first step

He is writing par over whole

100% is the original amount of tickets x

150% is the 1200 tickets

150       1200

-----  =  ------------

100          ?

Answer:

a

Step-by-step explanation:

Answer:ZTSU

Step-by-step explanation:

Another way to name ∠UST is ∠TSU.

Option B is correct.

We have,

Angles are the figure formed by the intersection of two lines or rays by sharing a common point. This point is called the vertex of the angle.

Angles are usually measured in degrees or radians.

The angle mentioned in the figure is at the point S.

This angle is the smaller angle formed at the point S.

An angle can be represented in two ways, from left to right or from right to left.

Suppose, an angle is ∠ABC.

We can represent this as ∠CBA.

So, the angle represented is ∠TSU.

Hence the angle is ∠TSU.

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Answer:

Option B

The solution in the attached figure

Step-by-step explanation:

we have

Inequality A

[tex]y > -\frac{1}{3}x+1[/tex]

we know that

The solution of the inequality A is the shaded area above the dashed line

The equation of the dashed line is [tex]y=-\frac{1}{3}x+1[/tex]

The slope of the dashed line is negative [tex]m=-\frac{1}{3}[/tex]

Inequality B

[tex]y > 2x-1[/tex]

we know that

The solution of the inequality B is the shaded area above the dashed line

The equation of the dashed line is [tex]y=2x-1[/tex]

The slope of the dashed line is positive [tex]m=2[/tex]

therefore

The solution in the attached figure

The correct graph is:

                Graph B

First inequality is given by:

             [tex]y>\dfrac{-1}{3}x+1[/tex]

The inequality is a straight line that passes through (0,1) and (3,0) and also the line is dotted since the inequality is strict.

The shaded region is away from the origin since the inequality does not pass the zero point test.

Second inequality is given by:

            [tex]y>2x-1[/tex]

The graph of this inequality is a dotted line (since the inequality is strict) and passes through (0,-1) and (1/2,0) and the shaded region is towards the origin

( since the line passes the zero point test )

Graph B represents the system of inequality.

Answer:

[tex]\large\boxed{V_A=1512\ m^3}[/tex]

Step-by-step explanation:

[tex]\text{If a prism A is similar to a prism B with a scale k, then:}\\\\\text{1.\ The ratio of the lengths of the corresponding edges is equal to the scale k}\\\\\dfrac{a}{b}=k\\\\\text{2. The ratio of the surface area of the prisms is equal}\\\text{to the square of the scale k}\\\\\dfrac{S.A._A}{S.A._B}=k^2\\\\\text{3. The ratio of the prism volume is equal to the cube of the scale k}\\\\\dfrac{V_A}{V_B}=k^3[/tex]

[tex]\text{We have}\\\\k=6:5=\dfrac{6}{5}\\\\V_B=875\ m^3\\\\V_A=x\\\\\text{Substitute to 3.}\\\\\dfrac{x}{875}=\left(\dfrac{6}{5}\right)^3\\\\\dfrac{x}{875}=\dfrac{216}{125}\qquad\text{cross multiply}\\\\125x=(875)(216)\qquad\text{divide both sides by 125}\\\\x=\dfrac{(875)(216)}{125}\\\\x=\dfrac{(7)(216)}{1}\\\\x=1512\ m^3[/tex]

Prism A is similar to Prism B with a scale factor of 6:5. If the volume of Prism B is 875 m2. The volume of prism B is 1512 meter square.

Suppose the initial measurement of a figure was x units.

And let the figure is scaled and the new measurement is of y units.

Since the scaling is done by multiplication of some constant, that constant is called the scale factor.

Let that constant be 's'.

Then we have:

[tex]s \times x = y\\s = \dfrac{y}{x}[/tex]

Thus, the scale factor is the ratio of the new measurement to the old measurement.

Prism A is similar to Prism B with a scale factor of 6:5.

If the volume of Prism B is 875 m2, find the volume of Prism A.

scale factor = 6/5

The ratio of the surface area of the prism A to the prism B

A1 / A2 = k^2

The ratio of the prism is equal to the cube of the scale k.

V1 / V2 = k^3

Let x be the volume of Prism A.

x / 875 = (6/5)^2

x / 875 = 216 / 125

x = 875 * 216 / 125

x = 1512

Therefore, the volume of prism B is 1512 meter square.

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ANSWER

shifts up 7 units.

EXPLANATION

The given function is

[tex]f(x) = {x}^{2} [/tex]

This is the base of the quadratic function without any transformation.

It is also refer to as the parent function.

The transformed function has equation:

[tex]f(x) = {x}^{2} + 7[/tex]

This transformation is of the form

[tex]y = f(x) + k[/tex]

This transformation shifts the graph of the base function up by k units.

Since k=7, the base function is shifted up by 7 units.

Answer:

2. the process of breeding only organisms with desirable traits

Step-by-step explanation:

Answer:

the answer is the second one

Step-by-step explanation:

Answer:

P(6, 12 )

Step-by-step explanation:

Using the Section formula, then

[tex]x_{P}[/tex] = [tex]\frac{7(7)+1(-1)}{1+7}[/tex] = [tex]\frac{49-1}{8}[/tex] = [tex]\frac{48}{8}[/tex] = 6

[tex]y_{P}[/tex] = [tex]\frac{7(14)+1(-2)}{1+7}[/tex] = [tex]\frac{98-2}{8}[/tex] = [tex]\frac{96}{8}[/tex] = 12

Hence P(6, 12 )

in total: thirty-six (36) markers.

Answer:

2 is the bigger number

Step-by-step explanation:

Answer:7

Step-by-step explanation:

Think about it this way your looking at a number line and at this point your looking at number -5 and then do bunny hops from -5 to 2 and however many hops you took is the difference between

Step-by-step explanation:

The product of a and b is equal to a · b.

Let w - width and l - length, then the product of the width and the lenght is

w · h = wh

The product of width(w) and height(h) is equal to w.h.

Let ;

w - width

l - length

∴ the product of the width and the length is w · h = wh

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Answer:

The new volume is 8 times smaller than the original volume

Step-by-step explanation:

we know that

If two figures are similar, then the ratio of its volumes is equal to the scale factor elevated to the cube

Let

z-----> the scale factor

x ----> the volume of the reduced sphere

y ----> the volume of the original sphere

so

[tex]z^{3}=\frac{x}{y}[/tex]

we have

[tex]z=1/2[/tex] ----> scale factor

substitute

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

[tex](1/8)=\frac{x}{y}[/tex]

[tex]x=\frac{y}{8}[/tex]

therefore

The new volume is 8 times smaller than the original volume

Verify

The volume of the original sphere is

[tex]r=18/2=9\ cm[/tex] ---> the radius is half the diameter

[tex]V=\frac{4}{3}\pi (9)^{3}=972\pi \ cm^{3}[/tex]

the volume of the reduced sphere is

[tex]r=9/2=4.5\ cm[/tex] ---> the radius is half the diameter

[tex]V=\frac{4}{3}\pi (4.5)^{3}=121.5\pi \ cm^{3}[/tex]

Divide the volumes

[tex]972\pi \ cm^{3}/121.5\pi \ cm^{3}=8[/tex]

Answer:

Correct answer is "A"

Step-by-step explanation:

It is a tranformation about 90° in anti-clock wise direction

In geometry, transformations are used to move a point or points from one position to another. The transformation of [tex](x,y) \to (-y,x)[/tex] is a 90 degrees rotation about the origin.

Given that:

[tex]A(-1,1) \to A'(-1,-1)[/tex]

[tex]B(1,1) \to B'(-1,1)[/tex]

[tex]C(1,4) \to C'(-4,1)[/tex]

The transformation rule is:

[tex](x,y) \to (-y,x)[/tex]

When a point is rotated through [tex](x,y) \to (-y,x)[/tex]

Such point has undergone a 90 degrees counterclockwise rotation.

Hence, option (a) is correct.

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a = interest rate for first bond.

b = interest rate for second bond.

we know the rates add up to 3%, so a + b = 3.

we also know that investing the same amount hmm say $X gives us the amounts of 360 and 480 respectively.

let's recall that to get a percentage of something we simply [tex]\bf \begin{array}{|c|ll} \cline{1-1} \textit{a\% of b}\\ \cline{1-1} \\ \left( \cfrac{a}{100} \right)\cdot b \\\\ \cline{1-1} \end{array}[/tex]

so then, "a percent" of X is just (a/100)X = 360.

and "b percent" of X is just (b/100)X = 480.

[tex]\bf a+b=3\qquad \implies \qquad \boxed{b}=3-a~\hfill \begin{cases} \left( \frac{a}{100} \right)X=360\\\\ \left( \frac{b}{100} \right)X=480 \end{cases} \\\\[-0.35em] ~\dotfill\\\\ \left( \cfrac{a}{100} \right)X=360\implies X=\cfrac{360}{~~\frac{a}{100}~~}\implies X=\cfrac{36000}{a} \\\\\\ \left( \cfrac{b}{100} \right)X=480\implies X=\cfrac{480}{~~\frac{b}{100}~~}\implies X=\cfrac{48000}{b} \\\\[-0.35em] ~\dotfill[/tex]

[tex]\bf X=X\qquad thus\qquad \implies \cfrac{36000}{a}=\cfrac{48000}{b}\implies \cfrac{36000}{a}=\cfrac{48000}{\boxed{3-a}} \\\\\\ (3-a)36000=48000a\implies \cfrac{3-a}{a}=\cfrac{48000}{36000}\implies \cfrac{3-a}{a}=\cfrac{4}{3} \\\\\\ 9-3a=4a\implies 9=7a\implies \cfrac{9}{7}=a\implies 1\frac{2}{7}=a\implies \stackrel{\mathbb{LOWER~RATE}}{\blacktriangleright 1.29\approx a \blacktriangleleft}[/tex]

[tex]\bf \stackrel{\textit{since we know that}}{b=3-a}\implies b=3-\cfrac{9}{7}\implies b=\cfrac{12}{7}\implies b=1\frac{5}{7}\implies \blacktriangleright b \approx 1.71 \blacktriangleleft[/tex]

[tex]1\cdot4\cdot3\cdot2+2\cdot4\cdot3\cdot2=24+48=72[/tex]

Answer:

72

Step-by-step explanation:

There are five possible digits to choose from: 3, 4, 5, 6, and 7.

The number must be greater than 5000, so there are 3 possibilities for the first digit: 5, 6, or 7.

There's no repetition, so the second digit is one of 4 remaining possible digits.

That leaves 3 possible digits for the third digit.  And 2 possible digits for the fourth digit.

So the number of possible four-digit numbers that can be formed is:

3 × 4 × 3 × 2 = 72

Answer:

Step-by-step explanation:

Begin with process of elimination: As seen on the graph, there is a discontinuity at x=3. this means that x>=3. so  we can eliminate B and C

Now you can see that at x = 3, two things happen. When moving to the left, x<3. when moving tot he right x>=3 so because of this you can eliminate D. The answer is A

Answer:

[tex]g(x)=-2x[/tex]

Step-by-step explanation:

A point reflected across the y-axis maintains its y-coordinate, but its x-coordinate switches signs. So, a positive x-coordinate becomes negative, and a negative x-coordinate becomes positive.

Let's take a few points from the original function, f(x). Remember, if we know the function, we can find the y-coordinate for any x-coordiante by simply plugging it into the function's equation.

Generally, [tex]f(x)=2x[/tex]

So:

[tex]f(0)=2(0)=0\\f(1)=2(1)=2\\f(2)=2(2)=4[/tex]

Leading us to have the plot points (0,0), (1,2) and (2,4).

To reflect this across the y-axis for the g(x) equation, we just need to turn the x-coordinates negative, resulting in a set of (0,0), (-1,2), and (-2,4).

Since we know this is a linear function (because there are no exponents in the equation), we can calculate the slope of this new set of points by using just 2 of them. The slope will give us our equation, because since (0,0) is a point on our line, we know that the y-intercept is zero.

[tex]slope=\frac{(y_{2}-y_{1})}{(x_{2}-x_{1})} \\slope=\frac{(4-2)}{((-2)-(-1))} \\slope=\frac{2}{-1}\\slope=-2\\\\g(x)=-2(x)[/tex]

Answer:

2x^2 +2x-2

Step-by-step explanation:

f(x)=-x^2+6x-1

g(x)=3x^2-4x-1

(f+g)(x)= -x^2+6x-1 +3x^2-4x-1

          =  2x^2 +2x-2

Answer:

B. The system may have infinitely many solutions

D. The system may have no solution

Step-by-step explanation:

we know that

If a system of linear equations contains two equations with the same slope

then

we may have two cases

case 1) The two equations are identical, in this case we are going to have infinite solutions

case 2) The two equations have the same slope but different y-intercept, (parallel lines) in that case the system has no solution.

Answer:

[tex]\sigma=6.16[/tex]

Step-by-step explanation:

By definition, the variance V of a population is defined as:

[tex]V = \sigma^2[/tex]

Where [tex]\sigma[/tex] is the standard deviation

We know that [tex]V = 38[/tex], then we can solve the equation for the standard deviation [tex]\sigma[/tex]

[tex]38 = \sigma^2[/tex]

[tex]\sigma^2=38[/tex]

[tex]\sigma=\sqrt{38}[/tex]

[tex]\sigma=6.16[/tex]

Finally  the standard deviation is: [tex]\sigma=6.16[/tex]

Check the picture below.

Answer:

1/16

Step-by-step explanation:

You need to know the following property

[tex]a^{(-b)} = \frac{1}{a^b}[/tex]

That means

[tex]4^{-2} = \frac{1}{4^2} = \frac{1}{4*4} = \boxed{\frac{1}{16}}[/tex]

[tex]-\dfrac{5}{7}\cdot\dfrac{1}{5}=-\dfrac{1}{7}[/tex]

Answer: The value of x = 1

Step-by-step explanation:

Given : Parallelogram ABCD, diagonals AC and BD intersect at point E.

such that

[tex]AE = 11x -3 \text{ and} CE = 12- 4x.[/tex]

We know that the diagonal of a parallelogram bisects each other.

Therefore , we have the following equation :-

[tex]11x -3= 12- 4x\\\\\Righatrrow11x+4x=12+3\\\\\rightarrow\ 15x=15\\\\\Rightarrow\x=\dfrac{15}{15}=1[/tex]

Hence, the value of x = 1

For this case we have the following equation:

[tex]2 (x + 2) = x-4[/tex]

Applying distributive property to the terms within the parentheses on the left side of the equation we have:

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

Subtracting "x" on both sides of the equation we have:

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

Subtracting 4 on both sides of the equation we have:

[tex]x = -4-4\\x = -8[/tex]

Answer:

[tex]x = -8[/tex]

Answer:

x = -8

Step-by-step explanation:

We are given that Manuela solved following equation and we are to find its solution:

[tex] 2 ( x + 2 ) = x - 4 [/tex]

Expanding the left side of the equation by multiplying the terms inside the bracket by 2:

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

Arranging the equation in a way such that like terms are on each side (variables on the left and constants on the right):

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

x = -8

The recent percentage of people that go out dancing at least one night a month, considering an initial percentage of 78% in 2010 and a recent increase of 2%, is 80%.

The percentage of people who went out dancing at least once a month in 2010 was 78%. If the number has recently increased by 2%, we need to add these two percentages together to find the recent percentage. In mathematics, when an increase is given in percentage, it's added to the original.

So, let's do the calculation:

78% (percentage in 2010) + 2% (recent increase) = 80% (recent percentage).

So, the recent percentage of people who go out dancing at least once a month is 80%.

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Answer:

Third option: 2x^3-11x^2+16x-3

Step-by-step explanation:

The product to be found is:

[tex](x-3)(2x^2-5x+1)[/tex]

Distributive property will be used for the product:

[tex]x(2x^2-5x+1)-3(2x^2-5x+1)\\[/tex]

Multiplication will give us:

[tex]=2x^3-5x^2+x-6x^2+15x-3\\Combining\ alike\ terms\\=2x^3-5x^2-6x^2+x+15x-3\\=2x^3-11x^2+16x-3[/tex]

The product is: 2x^3-11x^2+16x-3

Hence, third option is the correct answer ..

Answer:

The product is 2x³ - 11x² + 16x - 3 ⇒ 3rd answer

Step-by-step explanation:

* Lets explain how to find the product of binomial by trinomial

- If (ax² ± bx ± c) and (dx ± e) are trinomial and binomial, where

 a , b , c , d , e  are constant, their product is:

# Multiply (ax²) by (dx) ⇒ 1st term in the trinomial and 1st term in the  

 binomial

# Multiply (ax²) by (e) ⇒ 1st term in the trinomial and 2nd term in

the binomial

# Multiply (bx) by (dx) ⇒ 2nd term the trinomial and 1st term in  

the binomial

# Multiply (bx) by (e) ⇒ 2nd term in the trinomial and 2nd term in    the binomial

# Multiply (c) by (dx) ⇒ 3rd term in the trinomial and 1st term in  

 the binomial

# Multiply (c) by (e) ⇒ 3rd term the trinomial and 2nd term in  

the binomial

# (ax² ± bx ± c)(dx ± e) = adx³ ± aex² ± bdx² ± bex ± cdx ± ce

- Add the terms aex² and bdx² because they are like terms

- Add the terms bex and cdx because they are like terms

* Now lets solve the problem

∵ The binomial is (x - 3) and the trinomial is (2x² - 5x + 1)

∴ (x)(2x²) = 2x³

∵ (x)(-5x) = -5x²

∵ (x)(1) = x

∵ (-3)(2x²) = -6x²

∵ (-3)(-5x) = 15x

∵ (-3)(1) = -3

∴ (x - 3)(2x² - 5x + 1) = 2x³ + -5x² + x + -6x² + 15x + -3

- Add the like terms

∵ -5x² and -6x² are like term

∴ Their sum is -11x²

∵ x and 15 x are like terms

∴ Their sum = 16x

∴ (x - 3)(2x² - 5x + 1) = 2x³ - 11x² + 16x - 3

* The product is 2x³ - 11x² + 16x - 3