On the way to visit her grandmother, Sally drove at an average speed of 85 mph. On the way home (taking the same route) she only averaged 65 mph. If the total round trip took 18 hours, how many hours did it take Sally to drive to her grandmother's? Write your answer as a decimal.​

Answer: 10

Step-by-step explanation:

If [tex]-5 < x < 5[/tex], then [tex]|x-5|=5-x[/tex] and [tex]|x+5|=x+5[/tex].

So, the expression is equal to 10.

Answer:

x = 753.6 ft

Step-by-step explanation:

One leg is x.

The other leg is given.

The trig function that relates the two legs of a right triangle is the tangent.

tan A = opp/adj

tan 37° = x/1000ft

x = 1000 ft × tan 37°

x = 753.6 ft

Answer: 753.6 feet

Step-by-step explanation:

The angle, theta, is 37 degrees. However, we're not given the length of the hypotenuse in this case. So sine would be x by the hypotenuse and cosine would be 1,000 by the hypotenuse. In this case, we can use tangent, which is sine/cosine. In this case, tan 37 = x/1,000.

Hence,

tan 37 = x/1,000

x = tan 37 * 1000

x is approximately 753.6, rounded to the nearest tenth.

Answer: [tex]y-8=-2(x+3)[/tex]

Step-by-step explanation:

See attached image, it's direct formula substitution.

Answer:

4, 4√3

Step-by-step explanation:

In a 30-60-90 triangle:

The leg opposite of the 30-degree angle is 1/2 of the hypotenuse: 8/2 = 4

The longer leg is √3 times the shorter leg: 4*√3 = 4√3

Check work: 4^2+(4√3)^2 = 8^2 --> 16+48 = 64 --> 64 = 64

Step-by-step explanation:

pythogoras theorem = Q²=P²+R²

P=P

Q= 57.6

R=33.8 =

(57.8)²=(P)²+(33.8)²

=3,340.84=(P)²+1142.44

=3340.84-1142.44=P²

=2,198.4=P²

[tex] = \sqrt{2198.4} = p \\ = 46.8 = p[/tex]

Answer:

  (d)  1 unit

Step-by-step explanation:

The length of the dilated line segment is the product of the dilation factor and the length of the original line segment. It can also be computed as the length of the segment between the dilated coordinates.

The length of the original horizontal line segment BC is the difference of its x-coordinates:

  BC = 6 -4 = 2 . . . . units

(We know the segment is horizontal because the y-coordinates of the end points are the same.)

Multiplying the length of the original segment by the dilation factor, we find the length of B'C':

  B'C' = dilation factor × BC

  B'C' = 0.5×(2 units)

  B'C' = 1 unit

The dilation factor multiplies each coordinate value:

  B' = 0.5B = 0.5(4, 3) = (2, 1.5)

  C' = 0.5C = 0.5(6, 3) = (3, 1.5)

The length of B'C' is the difference of x-coordinates: 3 -2 = 1 unit.

Nani could purchase her pineapple from stores A, D, and E.

Given Information

It is given that Nani needs to purchase  8 cups of pineapple.

The unit prices of pineapple at each store is as follows,

Store A : 0.49

Store B : 0.51

Store C : 0.55

Store D : 0.48

Store E : 0.45

Amount that Nani has = $4

Reason Behind Purchasing From Either A, D, or E

Since Nani has amount of $4, she can purchase pineapple only from the stores where the total cost of 8 pineapple cups adds up to less than $4. The purchase of 8 pineapple cups at each store would be given as,

Store A : 0.49(8) = $3.92

Store B : 0.51(8) = $4.08

Store C : 0.55(8) = $4.40

Store D : 0.48(8) = $3.84

Store E : 0.45(8) = $3.60

As it can be seen, Nani can purchase from the store A, D, and E as it falls within her budget of $4.

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The correct answer is (40, 35) because by plugging in,  40 +35 = 75 and

(40 x 5) + (35 x 3) > 300

Word problem can be solved by interpreting the problem into its best fit equation. The equation may be linear, quadratic or simultaneous equations.

Given that

5x + 3y > 300

x + y = 75

Let us first assume that 5x + 3y = 300. That is,

5x + 3y = 300

x + y = 75

Eliminate y by multiplying equation 2 by 3

5x + 3y = 300

3x + 3y = 225

2x = 75

x = 75/2

x = 37.5

Substitute x in equation 2

37.5 + y = 75

y = 75 - 37.5

y = 37.5

The correct answer is (40, 35) because 40 +35 = 75 and

(40 x 5) + (35 x 3) > 300

Therefore,  the solution to the system is (40, 35)

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The equation of a parabola whose vertex is (0, 0) and focus is (1 / 8, 0) is equal to x = 2 · y².

Herein we have the case of a parabola whose axis of symmetry is parallel to the x-axis. The standard form of the equation of this parabola is shown below:

(x - h) = [1 / (4 · p)] · (y - k)²     (1)

Where:

The distance from the vertex to the focus is 1 / 8. If we know that the location of the vertex is (0, 0), then the standard form of the equation of the parabola is:

x = 2 · y²     (1)

The equation of a parabola whose vertex is (0, 0) and focus is (1 / 8, 0) is equal to x = 2 · y².

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Answer:

f(2) = 3

Step-by-step explanation:

Plug in 2 for x

Using Percentage, the eighth graders voted for Luke is of 72 percentage or 72%.

According to the question,

They are 450 eighth graders at Wilson Middle School. In the class president, 324 students voted for Luke, 81 students voted for Alice, and 45 students voted for Chris.

In order to find the percentage of eighth graders voted for Luke only if 252 divided by 350.

[tex]\frac{252}{350} = 0.72[/tex]

To convert decimal into Percentage multiply 0.72 into 100.

0.72*100 = 72%.

Hence, the percentage of the eighth graders voted for Luke is of 72 percentage or 72%.

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Answer: a

Step-by-step explanation:

The slope is the rate at which a line goes up or down (i.e., how steep it is). It is measured by the slope formula, which is [tex]\frac{y_2-y_1}{x_2-x_1}[/tex], where (x1, y1) and (x2, y2) are two points on the line.

Below, (x1, y1) are (c, d) and (x2, y2) are (a, b).

When all variables are plugged in, the slope is

[tex]\frac{b-d}{a-c}[/tex]

The value of f(-2) is 0

The graph of the function is added as an attachment

The graph is given as:

y = f(x)

When x =-2. we have

y = f(-2)

From the graph, we have:

x = -2 and y = 0

So, we have

f(-2) = 0

Hence, the value of f(-2) is 0

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Step-by-step explanation:

18z+10z+40z+5+1=360

68z+6=360

68z=360-6

68z=364

z≈5.353

Answer:

218,048. skeins

Step-by-step explanation:

This question is built to throw you off by not telling you about the information in order.

First, the polypay sheep produces 9.9 pounds of wool.

Then, each pound produces 10.95 miles of yarn.

And finally, the yarn is packaged into skeins that are 175 yards each.

Each polypay sheep is 9.9 pounds. And we will use that total weight to find the amount of yarn in miles.
Then we will split up that yarn into equal pieces to make skeins.

BUT, the pieces are measured in yards, so we will have to convert the miles of yarn into an equivalent amount in yards as well. (Unmatched units of measurements don't mix well).

So, our equation will look like this:

(#of sheep) [tex]\times[/tex] (9.9 pounds per sheep) [tex]\times[/tex] (10.95 miles per yarn) [tex]\times[/tex] (1760 yards per mile) [tex]\div[/tex] (175 skeins per yard)

The number of sheep Bill has is 200.

So, we plug that into the number model we made.

[tex]200\times9.9\times10.95\times1760\div175[/tex]

We end up with:

218,048.914

The decimal indicates that there is a remaining amount of yarn that couldn't be properly packaged into a skein.

Since, that remainder is not a complete skein, we must ignore its existence.

So the number of skeins expected is:

218,048

The number of skeins of yarn is Bill's flock expected to produce in one year is 1819.

The unitary method is a technique for solving a problem by first finding the value of a single unit, and then finding the necessary value by multiplying the single unit value.

Given that, a polypay sheep produces an average 9.9 pounds of wool annually.

Farmer Bill has a flock of 200 polypay sheeps

So, total weight of wool is 9.9×200

= 1980 pounds

One pound of wool makes 10.95 miles of yarn.

So, the number of yarns = 1980/10.95

= 180.82 miles of yarn

We know that, 1 mile =1760 yards

Then, 180.82 miles

= 318243.2 yards

This wool is cleaned, spun into yarn and then packaged into skeins of 175 yards of yarn each.

Number of skeins = 318243.2/175

= 1819

Therefore, the number of skeins of yarn Bill's flock expected to produce in one year is 1819.

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One can know if an equation is extraneous if after plugging it in the original equation, it shows a false meaning or the value is undefined.

It should be noted that an extraneous equation means a root of a transformed equation that isn't the root of the original equation due to the fact that it's excluded from the domain of the original equation.

In this case, one can know if an equation is extraneous if after plugging it in the original equation, it shows a false meaning or the value is undefined.

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The wavelength of X-rays for the given frequency is [tex]$1 \times 10^{-10} \mathrm{~m}$[/tex].

The distance between the two crests or troughs of the light wave is known as the wavelength of light.

The color of light is determined by its wavelength, and the pitch of sound is determined by its wavelength. The visible spectrum of light has wavelengths between around 700 nm (red) to 400 nm (violet). The range of audible sound wavelengths is roughly 17 mm to 17 m.

To calculate the wavelength of light, we use the equation:

[tex]$\lambda=\frac{c}{\nu}$[/tex]

where,

λ = wavelength of the light  

c = speed of light = [tex]$3 \times 10^{8} \mathrm{~m} / \mathrm{s}$[/tex]

ν= frequency of light = [tex]$3 \times 10^{18} s^{-1}$[/tex]

Putting the above value in equation,

[tex]$\lambda=\frac{3 \times 10^{8} \mathrm{~m} / \mathrm{s}}{3 \times 10^{19} \mathrm{~s}-1}=1 \times 10^{-10} \mathrm{~m}$[/tex]

Hence, the wavelength of X-rays for the given frequency is [tex]$1 \times 10^{-10} \mathrm{~m}$[/tex].

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The surface area of the composite figure is equal to 233.6 square centimeters.

The surface area is the area of all faces of a solid. Since the surface area of the figure is a combination of triangles and quadrilaterals, we must sum all the areas to determine the surface area of the figure. Now we proceed to determine this:

A = 4 · (1/2) · (3 cm) · (2 cm) + 2 · (6 cm) · (3 cm) + 2 · (8 cm) · (6 cm) + 2 · (8 cm) · (2 cm) + 2 · (8 cm) · (3.6 cm)

A = 233.6 cm²

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A set of vectors {v1,v2,...,vk} is linearly independent if the vector equation x1v1 + x2v2 + .......... + xkvk = 0 has only the trivial solution

x1 = x2 = .... = xk =0. Then the set  {v1,v2,...,vk} is linearly dependent otherwise.

So putting in the formula we get

x1u1 + x2u2 + x3u3 = 0

x1u1 + x2u2 = -x3u3

au1 + bu2 = u3               ∵ (-x1/x3 = a & -x2/x3 = b)

On putting in the values

a(3,-1) + b(4,5) = (-4,7)

(3a+4b,-a+5b) = (-4,7)

On comparing we get

3a + 4b = -4 -(1)

-a + 5b = 7  -(2)

on solving these equations we get

b = 17/19 and a= -48/19

which is non trivial.

Thus the following form linearly dependent sets of vectors.

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Answer:

[tex]\sf Tan \ D = \dfrac{4}{3}[/tex]

Step-by-step explanation:

Trigonometry ratios:

       [tex]\sf \boxed{\bf \tan \ D =\dfrac{opposite \ side \ of \ \angle \ D}{adjacent \ side \ of \ \angle D}}[/tex]

                   [tex]\sf =\dfrac{BC}{DC}\\\\ =\dfrac{32}{24}\\\\=\dfrac{4}{3}[/tex]

Answer:

Given:

mu = 200 lb, the mean sigma = 25 the standard deviation

For the random variable x = 250 lb, the

z-score is z = (x - mu) / sigma = (250 - 200) / 25 = 2

From standard tables for the normal distribution, obtain

P(x < 250) = 0.977

Answer: 0.977

The proportional relationship that represents the market that sells their carrots at a lower rate per pound is: y = 1.6x.

A proportional relationship is a function in which the output variable is given by the input variable multiplied by a constant of proportionality, that is:

y = kx

In which k is the constant of proportionality.

From the table, the rate is:

k = $8.8/4.4 = 2.

From the market, the rate is:

k = $4.8/3 = $1.6.

Hence the equation is y = 1.6x.

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Using the relation between velocity, distance and time, it is found that a reasonable estimation of the current is of 1 mph.

Velocity is distance divided by time, hence:

[tex]v = \frac{d}{t}[/tex]

Upstream, against the current, he traveled 3 miles in t hours, hence the equation is:

[tex]2 - c = \frac{3}{t}[/tex]

[tex]c = 2 - \frac{3}{t}[/tex]

Downstream, with the current, he traveled 3 miles in 4 - t hours, hence the equation is:

[tex]2 + c = \frac{3}{4 - t}[/tex]

Hence:

[tex]c = \frac{3}{4 - t} - 2[/tex]

Then, taking the two equal equations:

[tex]2 - \frac{3}{t} = \frac{3}{4 - t} - 2[/tex]

[tex]\frac{3}{4 - t} + \frac{3}{t} = 4[/tex]

[tex]\frac{3t + 12 - 3t}{t(4 - t)} = 4[/tex]

12 = -4t² + 16t

4t² - 16t + 12 = 0

t² - 4t + 3 = 0

(t - 3)(t - 1) = 0.

The current is positive, hence:

[tex]c = 2 - \frac{3}{3}[/tex]

c = 2 - 1

c = 1 mph.

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Answer:

1.2

2.4√3÷3

3. x=45, y=15

Step-by-step explanation:

OK,

1. So the first part requires the Pythagoreanism formula which is: b²=a²+c²:

AC²=AB²+BC²====> AC²=(1)²+(√3)²===> AC²=4===> AC=2

2.The second part requires the formula of tan:

tan A=BC÷AB===> tan A=√3÷1===> tan A=√3

tan C=AB÷BC===> tan C=1÷√3===> tan C=√3/3

tan A+tan C=√3+√3/3===> 4√3÷3

3.And the last part requires the equation of angles:

A+B+C=180===>

x+y+x-y+90=180===> 2x=90===> x=45, y=15

Rewrite the second expression as

[tex]\dfrac1{1+x^m + x^{-n}} = \dfrac{x^{\ell+n}}{x^{\ell+n} + x^{\ell+m+n}+x^\ell} = \dfrac{x^{-m}}{x^{-m} + 1 + x^\ell}[/tex]

and the third expression as

[tex]\dfrac1{1 + x^n + x^{-\ell}} = \dfrac{x^\ell}{x^\ell + x^{\ell+n} + 1} = \dfrac{x^\ell}{x^\ell + x^{-m} + 1}[/tex]

so the fractions all have the same denominator.

Then combining the fractions gives the desired result,

[tex]\dfrac1{1+x^\ell+x^{-m}} + \dfrac1{1+x^m+x^{-n}} + \dfrac1{1+x^n+x^{-\ell}} = \dfrac{1+ x^\ell + x^{-m}}{1+x^\ell+x^{-m}} = \boxed{1}[/tex]

Answer:

The measure of the acute angle = 90 - a

Leg 1 = a cos(a)

Leg 2 = a sin(a)

Step-by-step explanation:

In a right triangle ,the two acute angles are complementary

We are given that the measure of one of the acute angles is ‘a’

Then

The measure of the other one is ‘90 - a’

Now, we use the law of sine to determine the length of the legs :

Let x and y be respectively the length of the two legs.

[tex]\frac{x}{\sin \left( 90-a\right) } =\frac{a}{\sin \left( 90\right) }[/tex]

[tex]\Longleftrightarrow \frac{x}{\sin \left( 90-a\right) } =a[/tex]

[tex]\Longleftrightarrow x = a \times\sin \left( 90-a\right)[/tex]

[tex]\Longleftrightarrow x = a \times\cos \left( a\right)[/tex]

On the other hand,

[tex]\frac{y}{\sin \left( a\right) } =\frac{a}{\sin \left( 90\right) }=a[/tex]

Then

[tex]y = a \times \sin(a)[/tex]

As the value of x increases and the function of f(x) also increases since it is moving in the upward direction. The x-intercept is (-3,0)

A function is a set of input values into a program that produces the desired output. In mathematical terms, we can say a function is a set of x values that maps to a set of y values.

Functions can also be represented on the graph called graphical representation.

From the given graphical information, as the value of x increases, the function of f(x) also increases since it is moving in the upward direction.

The x-intercept is the value where the line cuts the horizontal x-axis when y is zero, therefore the x-intercept is (-3,0)

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