For a limited time, Sammy’s gas station is offering a discount on the cost of gasoline when amounts greater than 5 gallons are purchased. The table below shows the cost for different amounts of gasoline.

Which of these could be used to determine c, the cost for purchasing g gallons of gasoline with the discount?

A: C=2.65g
B: C=2.65g-12

We have three similar triangles, because each has a right angle and shares an angle.   Let's write the angles in order: opposite to short leg, long leg, hypotenuse.

CAB similar to BAD similar to CBD

Or as ratios,

CA:AB:CB = BA:AD:BD = CB:BD:CD

We also know

AC = AD + CD

(AD+CD):AB:CB = BA:AD:BD = CB:BD:CD

(AD+CD)/CB=CB/CD

We have CB=6, AD=5 and seek x=CD.

[tex](5 + x)/6 = 6/x[/tex]

[tex]x(x+5) = 36[/tex]

[tex]x^2 +5x - 36 = 0[/tex]

[tex](x+9)(x-4) = 0[/tex]

We reject the negative root and conclude x=4

Answer: 4

From opposite to the short leg, long leg, and hypotenuse DC is A) 4

A triangle is a three-sided closed-plane figure formed by joining three noncolinear points. Based on the side property triangles are of three types they are Equilateral triangle, Scalene triangle, and Isosceles triangle.

Because each triangle has a right angle and shares an angle, we have three comparable triangles. The angles should be written from opposite to the short leg, long leg, and hypotenuse.

CAB is similar to BAD similar to CBD

CA : AB : CB = BA : AD : BD = CB : BD : CD

We also know

AC = AD + CD

(AD + CD) : AB : CB = BA : AD : BD = CB : BD : CD

(AD + CD)/CB = CB/CD

We have CB = 6, AD = 5, and x = CD.

∴ (5 + x)/6 = 6/x.

x(5 + x) = 36.

5x + x² = 36.

x² + 5x - 36 = 0.

x² + 9x - 4x - 36 = 0.

x(x + 9) - 4(x + 9) = 0.

(x + 9)(x - 4) = 0.

x = - 9 Or x = 4.   (length can not be negative).

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Answer:

• The water bottle loses 0.5 an ounce of water per minute

Step-by-step explanation:

The definition of the variables tells you that m stands for minutes and that W stands for the water remaining in the bottle. So, the -0.5m in the equation has the effect of reducing the remaining water by 0.5 each time m increases by 1. That is, there are 0.5 fewer ounces of water after each additional minute: the bottle loses 0.5 ounces per minute.

Answer:

  D)  If Jack drives 200 miles, it will cost anywhere between $30 and $42

Step-by-step explanation:

The cost is said to be a range of possibilities. The first three answer choices seem to assume the cost is at one extreme or the other. They incorrectly interpret the statement of cost.

Answer:

Option C. [tex]452.16\ cm^{2}[/tex]

Step-by-step explanation:

step 1

Find the circumference

The circumference of a circle is equal to

[tex]C=2\pi r[/tex]

we have

[tex]r=3\ cm[/tex]

[tex]\pi=3.14[/tex]

substitute

[tex]C=2(3.14)(3)=18.84\ cm[/tex]

step 2

Find the area of the rectangle made by the circumference and height of the cylinder

The area of the rectangle is equal to

[tex]A=C*h[/tex]

substitute the values

[tex]A=(18.84)(24)=452.16\ cm^{2}[/tex]

Answer:

C

Step-by-step explanation:

Answer:

60 meters

Step-by-step explanation:

The standard form for parabolic motion is

[tex]h(x)=-5x^2+v_{0}x+h_{0}[/tex]

where [tex]v_{0}[/tex] is the initial upwards velocity and [tex]h_{0}[/tex] is the initial launching height.  If I am understanding your question, this is what you are looking for.  So the height AT the time of launch was 60 meters.

Answer:

The height of the object at the time of the launch is [tex]60m[/tex]

Step-by-step explanation:

We know that the height in meters, x seconds after the launch is modeled by the following function :

[tex]h(x)=-5x^{2}+20x+60[/tex]

For example, after [tex]x=3s[/tex] from the launch the height of the object is :

[tex]h(3s)=-5.(3^{2})+20.(3)+60=75[/tex]

[tex]h(3s)=75m[/tex]

If we want to know the height of the object at the time of the launch we will need to find the height of the object at [tex]x=0s[/tex] because that is the instant where the object is launched.

If we use [tex]x=0s[/tex] in [tex]h(x)[/tex] ⇒

[tex]h(0s)=-5.(0^{2})+20.(0)+60=60[/tex]

We find that the height of the object at the time of launch is [tex]60m[/tex]

Final answer:

The correct statement for a 45-45-90 triangle is that the legs are equal in length, and the hypotenuse is the length of a leg multiplied by √2, following from the Pythagorean Theorem.

Explanation:

The correct statement for 45-45-90 triangles is that they are special right triangles featuring two 45-degree angles and one 90-degree angle. In such triangles, the lengths of the legs are equal, and the length of the hypotenuse is √2 times the length of a leg. This arises from the fact that in a 45-45-90 triangle, the two legs opposite the 45-degree angles are congruent, which also means that their corresponding sides are in a ratio of 1:1, and the hypotenuse can be found by multiplying one of the legs by √2.

This is a consequence of the Pythagorean Theorem where, for a right-angle triangle with sides 'a' and 'b' and hypotenuse 'c', the relationship is c^2 = a^2 + b^2. Since 'a' and 'b' are equal in a 45-45-90 triangle (let's call each side 's'), the equation simplifies to c^2 = 2s^2, implying c = s√2. This ratio is essential to understanding the properties of these triangles and is used frequently in various geometry and trigonometry problems.

Answer:

you must solve the question.

Step-by-step explanation:

it would be when we're solving a formula for himself a variable we must solve it.

Answer:

isolate

Step-by-step explanation:

Answer:

The custodian can make 128 pails.

Step-by-step explanation:

first, you convert 1/8 to 0.125.

then, you divide 16 by 0.125 to get 128.

Answer: Divide by 9 ------- APEX

Step-by-step explanation:

i got it wrong and that was the right answer eiahhh

To check her register for transposing errors, Lia needs to subtract the balances and divide the difference by 9. so. the correct option is A.

Suppose that there are k things which are to be divided in P parts, then

K÷ P will give the amount that each one of P parts would get from k, which will make equal distribution of k things in P parts.

Lia is comparing her check register to her bank statement, and the ending balances don't seem to match.

To balance her check register, Lia needs to subtract the balances and divide the difference by 9.

If entries in her bank statement do not appear in her check register or vice versa.

To check her register for transposing errors, Lia needs to subtract the balances and divide the difference by 9. so. the correct option is A.

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Answer:

It is 12.5

Step-by-step explanation:

It is because the formula of finding the volume of a rectangular prism is area of the base x height.

So you do 200 divided by 16 (Which is the height) which equals 12.5

Answer:

The height of the prism is 12.5 units.

Step-by-step explanation:

Volume formula:  V = (length)(width)(height)

or                           V = (area of base)(height)

Here, we want to calculate the height.  The appropriate formula is

(height) = (volume) / (area of base) = (200 units³) / (16 units²) = 12.5 units

The height of the prism is 12.5 units.

Answer:

tallest man height is more extreme.

Step-by-step explanation:

Given:

Heights of men at that time had a mean of 173.73 cm and a standard deviation of 8.65 cm.

Concept used:

Convert height into z scores for comparison of deviation from the mean.

Solution:

Tallest man height = 265 cm

[tex]Z_{tall} =\frac{265-173.73}{8.65} \\=10.55[/tex]

Shortest man height = 109.1 cm

[tex]Z_{short} =\frac{109.1-173.73}{8.65} \\=-7.47[/tex]

Thus we find that tallest man is 10.55 std deviations from the mean to the right and shortest man is 7.47 std deviations from the mean to the left.

Hence tallest man height is more extreme.

The tallest living man at one time had a more extreme height compared to the shortest living man at that time.

In this question, we are given the heights of the tallest and shortest living men at a specific time, as well as the mean and standard deviation of heights at that time. To determine which man had a more extreme height, we need to compare their heights to the mean and see how many standard deviations away they are.

The tallest man had a height of 265 cm, which is 265 - 173.73 = 91.27 cm above the mean.

The shortest man had a height of 109.1 cm, which is 173.73 - 109.1 = 64.63 cm below the mean.

Since the tallest man's height is significantly farther away from the mean compared to the shortest man's height, we can conclude that the tallest man had a more extreme height.

Answer:

-10

Step-by-step explanation:

Velocity is the derivative of position.  Derivative is defined as:

f'(x) = lim(h->0) [ f(x+h) - f(x) ] / h

s(t) = 1 - 10t

s(t+h) = 1 - 10(t+h)

Plugging in:

s'(t) = lim(h->0) [ 1 - 10(t+h) - (1 - 10t) ] / h

s'(t) = lim(h->0) (1 - 10t - 10h - 1 + 10t) / h

s'(t) = lim(h->0) (-10h) / h

s'(t) = lim(h->0) -10

s'(t) = -10

v(t) = -10

So at t=0, v(0) = -10.

The instantaneous velocity at [tex]t = 10[/tex] is 10.

The instantaneous Velocity of the object at a time [tex]t[/tex] is determined by mathematical concept of Derivative, whose description is shown below:

[tex]v = \lim_{h \to 0} \frac{s(t+h) - s(t)}{h}[/tex] (1)

Where:

[tex]h[/tex] - Time difference.

[tex]s(t)[/tex] - Function position evaluated at time [tex]t[/tex].

If we know that [tex]s(t) = 1 - 10\cdot t[/tex], then the instantaneous Velocity of the object is:

[tex]v = \lim_{h \to 0} \frac{1-10\cdot (t+h)-1+10\cdot t}{h}[/tex]

[tex]v = \lim_{h \to 0} \frac{10\cdot h}{h}[/tex]

[tex]v = \lim_{h \to 0} 10[/tex]

[tex]v = 10[/tex]

As instantaneous velocity is a constant function, it means that objects travels at constant velocity. Hence, we conclude that the instantaneous velocity at [tex]t = 10[/tex] is 10.

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Answer:

Step-by-step explanation:

Center

x = 5

y = - 3

r = 4

(x - 5)^2 + (y - - 3)^2 = 4^2

(x - 5)^2 + (y + 3)^2 = 16

Hello there! The answer is B. (3, 21).

So you want to be able to substitute one of the equations into the other. We can't do this right now since both of the equations are y = something, so we need to change the second equation to x = something so we can plug it in to the value of x in the first equation.

y = x + 18 can translate to x = y - 18. Now, plug "y - 18" into x in the first equation.

y = 10(y-18) - 9 and solve.

y = 10y - 180 - 9

-9y = - 180 - 9

-9y = -189

y = 21.

Now we have our y value, but we need our x value. Well, remember that y = x + 18? So, since y is 21, what plus 18 is equal to 21? The answer is 3, making our x value 3.

If x = 3 and y = 21, the ordered pair is (3, 21) or option B. I hope this was helpful and have a great day! :)

Hello

10x-9=x+18

10x-x=18+9

9x=27

x=3

=30-9=21

(3,21)

Good Luck

Goodbye ♥

Number 3 is the correct answer

Tell me if you want further explanation

Answer:

f(x) = –2(x – 2)(x – 4)

Step-by-step explanation:

In the first two possible answer choices we have a 2 and a 4, whose product is 8, whereas we need a y-intercept of -16.  So omit the first two choices.

If the x-intercepts are at (2, 0) and (4, 0), the corresponding factors must be (x - 2)(x - 4), so the third answer, f(x) = –2(x – 2)(x – 4), must be the correct one.

Answer:

A box of 50 stickers would cost $13

Explanation:

1- getting the equation representing the price:

We have two variables; the number of stickers and the price of the box

We can note that the price is the dependent variable (y) while the number of stickers is the independent one (x)

We are given that:

A box of 15 stickers cost $6..........> first point is (15,6)

A box of 25 stickers cost $8 ........> second point is (25,8)

The general equation of the linear line is:

y = mx + c

where m is the slope and c is the y-intercept

i. getting the slope:

[tex]m=\frac{y_{2}-y_{1}}{x_{2}-x_{1}}=\frac{8-6}{25-15}=0.2[/tex]

The equation now became: y = 0.2x + c

ii. getting the y-intercept:

To get the y-intercept, use any of the given points and substitute in the equation we got in part i. I will use the point (15,6)

y = 0.2x + c

6 = 0.2(15) + c

c = 6 - 0.2(15) = 3

The final equation is:

y = 0.2x + 3

where y is the price of the box and x is the number of stickers it contains

2- getting the price of a box with 50 stickers:

To get the price of a box of 50 stickers, simply substitute with x = 50 in the equation we got from part 1

This is done as follows:

y = 0.2(50) + 3 = 13

Therefore, a box of 50 stickers will cost $13

Hope this helps :)

Answer:

Perimeter = 32.44 units

Area = 30 square units

Step-by-step explanation:

Given

Vertices

A(2,8), B(16,2) and C(6,2)

WE have to determine the lengths of all sides before finding the perimeter and area.

The formula of modulus is:

[tex]d = \sqrt{(x_{2}- x_{1})^{2} +(y_{2}-y_{1})^{2}}\\AB=\sqrt{(16-2)^{2} +(2-8)^{2}}\\=\sqrt{(14)^{2} +(-6)^{2}}\\=\sqrt{196+36}\\ =\sqrt{232}\\=15.23\\\\BC=\sqrt{(6-16)^{2} +(2-2)^{2}}\\=\sqrt{(-10)^{2} +(0)^{2}}\\=\sqrt{100+0}\\ =\sqrt{100}\\=10\\\\AC=\sqrt{(6-2)^{2} +(2-8)^{2}}\\=\sqrt{(4)^{2} +(-6)^{2}}\\=\sqrt{16+36}\\ =\sqrt{52}\\=7.21\\\\[/tex]

So the perimeter is:

[tex]Perimeter=AB+BC+AC\\=15.23+10+7.21\\=32.44\ units[/tex]

Using hero's formula,

[tex]s=\frac{perimeter}{2}\\s=\frac{32.44}{2}\\ s=16.22\\Area=\sqrt{s(s-a)(s-b)(s-c)}\\=\sqrt{16.22(16.22-15.23)(16.22-10)(16.22-7.21)}\\=\sqrt{(16.22)(0.99)(6.22)(9.01)}\\=\sqrt{899.91}\\=29.99\ square\ units[/tex]

Rounding off will give us 30 square units ..

Answer:

30 square units

Step-by-step explanation:

Recall that the area of an equilateral triangle with side length [tex]s[/tex] is [tex]\dfrac{\sqrt3}4s^2[/tex].

In the [tex]x-y[/tex] plane, the base is given by two equations:

[tex]x^2+y^2=9\implies y=\pm\sqrt{9-x^2}[/tex]

so that for any given [tex]x[/tex], the vertical distance between the two sides of the circle is

[tex]\sqrt{9-x^2}-\left(-\sqrt{9-x^2}\right)=2\sqrt{9-x^2}[/tex]

and this is the side of length of each triangular cross-section for each [tex]x[/tex]. Then the area of each cross-section is

[tex]\dfrac{\sqrt3}4(2\sqrt{9-x^2})^2=\sqrt3(9-x^2)[/tex]

and the volume of the solid is

[tex]\displaystyle\int_{-3}^3\sqrt3(9-x^2)\,\mathrm dx=\boxed{36\sqrt3}[/tex]

[tex](-\infty, +\infty)[/tex]

Hope this helps.

r3t40

Answer:

Step-by-step explanation:

4 miles = 1hour

5miles = 1hour and 25 minutes

10miles = 2 hours and 50 min

15miles = 4hours and 15min

x miles = 5 hours

20 miles = 5 hours

tell me if i got it wrong sry

Answer:

$30

Step-by-step explanation:

$500 x 0.02 x 3 = 30

Answer:

$30   is the    answer  

Answer:

x = 12.5

Step-by-step explanation:

The given triangle is a right angle triangle.

We cannot use the Pythagoras theorem as the lengths of all sides are not known. We will use triangular ratios here to solve the given problem.  

As it is clear from the diagram that x is the hypotenuse of the triangle and 11 is the length of the base. We will use a ratio in which base and hypotenuse are used.

So,

cos ⁡θ= base/hypotenuse

cos⁡ 28=11/x

x=11/cos⁡28  

x=11/0.8829

x=12.45

Rounding off to nearest 10

x=12.5

The value of x is 12.5 in the triangle by using cosine function, option B is correct.

We need to find the value of x in the triangle.

The given triangle is a right angles triangle.

We find value of x by using cosine function.

Cosine function is a ratio of Adjacent side and hypotenuse.

Cosθ = Adj side/hypotenuse.

Here θ = 28 degrees.

Adjacent side = 11.

Hypotenuse = x.

Plug in these values in above formula:

Cos28 degrees = 11/x

x=11/cos28

x=11/0.882

x=12.47

x=12.5

Hence, the value of x is 12.5.

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Answer:

120 ways.

Step-by-step explanation:

We have been given that you have 6 reindeer, Prancer, Rudy, Balthazar, Quentin, Jebediah, and Lancer, and you want to have 3 fly your sleigh. You always have your reindeer fly in a single-file line.

We will use permutation formula to solve our given problem as:

[tex]_{r}^{n}\textrm{C}=\frac{n!}{(n-r)!}[/tex]

[tex]_{3}^{6}\textrm{C}=\frac{6!}{(6-3)!}[/tex]

[tex]_{3}^{6}\textrm{C}=\frac{6\cdot 5\cdot 4\cdot 3!}{3!}[/tex]

[tex]_{3}^{6}\textrm{C}=6\cdot 5\cdot 4[/tex]

[tex]_{3}^{6}\textrm{C}=120[/tex]

Therefore, you can arrange your reindeer in 120 different ways.

For this case we have the following functions:

[tex]f (x) = 3x\\g (x) = x ^ 2 + 1[/tex]

We must find (f + g) (x). By definition of operations with functions we have to:

(f + g) (x) = f (x) + g (x)

So we have to:

[tex](f + g) (x) = 3x + (x ^ 2 + 1)\\(f + g) (x) = x ^ 2 + 3x + 1[/tex]

Answer:

[tex](f + g) (x) = x ^ 2 + 3x + 1[/tex]

Option B

Answer:

B.  16 hrs

Step-by-step explanation:

Distance = rate × time

The best way to do this is to make a table with the info.  We are concerned with the trip There and the Return trip.  Set it up accordingly:

                    d     =     r     ×     t

There    

Return

The train made a trip from A to B and then back to A again, so the distances are both the same.  We don't know what the distance is, but it doesn't matter.  Just go with it for now.  It'll be important later.

               d     =     r     ×     t

There      d    

Return     d

We are also told the rates.  There is 70 km/hr and return is 80 km/hr

               d     =     r     ×     t

There      d     =    70

Return     d     =    80

All that's left is the time column now.  We don't know how long it took to get there or back, but if it took 2 hours longer to get There than on the Return, the Return trip took t and the There trip took t + 2:

                      d     =     r     ×     t

There             d     =    70   ×    t+2

Return            d     =    80   ×     t

The distances, remember, are the same for both trips, so that means that by the transitive property of equality, their equations can be set equal to each other:

70(t + 2) = 80t

70t + 140 = 80t

140 = 10t

14 = t

That t represents the Return trip's time.  Add 2 hours to it since the There trip's time is t+2.  So 14 + 2 = 16.  

B.  16 hours

It’s a frequency table, you find the middle number from the prices of mail received and you would multiply it. Not sure what with but if you search on Google Frequency tables there should be a good explanation.

Hope this helped you!

C. bc chickens have two legs each making it 12 chickens times 2 legs equal 24 plus the remaining 25 animals (pigs) would be 25x4=100+24 chicken legs = 124

For this case we have that the pigs have 4 legs while the hens have 2.

We propose a system of equations:

x: Variable representing the number of pigs

y: Variable representing the number of chickens

[tex]x + y = 37\\4x + 2y = 124[/tex]

We multiply by -4 the first equation:

[tex]-4x-4y = -148[/tex]

We add the equations:

[tex]-4x-4y = -148\\4x + 2y = 124\\-4y + 2y = -148 + 124\\-2y = -24\\y = \frac {24} {2}\\y = 12[/tex]

So, there are 12 chickens.

[tex]x + 12 = 37\\x = 37-12\\x = 25[/tex]

There are 25 pigs.

ANswer:

25 pigs

12 chickens

Option C

Answer:

[tex]\boxed{\text{D. }3\sqrt{2}}[/tex]

Step-by-step explanation:

Multiply numerator and denominator by √2

[tex]\dfrac{6}{\sqrt{2}} = \dfrac{6}{\sqrt{2}} \times \dfrac{\sqrt{2}}{\sqrt{2}}\\\\= \dfrac{6\sqrt{2}}{2}\\\\= \boxed{3\sqrt{2}}[/tex]

Answer: D. [tex]3\sqrt{2}[/tex]

Step-by-step explanation:

The given fraction : [tex]\dfrac{6}{\sqrt{2}}[/tex]

Here, the denominator is in radical form which makes it not an simplified form.

So , we rationalize it by multiplying [tex]\sqrt{2}[/tex] to the numerator and the denominator , we get

[tex]\dfrac{6}{\sqrt{2}}\times\dfrac{\sqrt{2}}{\sqrt{2}=\dfrac{6\sqrt{2}}{2}}\\\\=\dfrac{2\times3\times\sqrt{2}}{2}\\\\=3\sqrt{2}[/tex]  [Cancel 2 from the numerator and the denominator.]

Hence, the choice is equivalent to the given fraction = [tex]3\sqrt{2}[/tex]

Hence, the correct option is D. [tex]3\sqrt{2}[/tex]

Answer:

It cannot be simplified any further.

The simplified form of the quantity y−squared plus 7y plus 12 over the quantity y−squared minus 2y minus 15 is (y-4)/(y-5) .

(y^2-y+12)/(y^2-2y-15)  factor both the numerator and denominator...

(y^2-4y-3y+12)/(y^2-5y+3y-15)

(y(y-4)-3(y-4))/(y(y-5)+3(y-5))

((y-4)(y-3))/((y-5)(y+3))  so the (y+3) and (y-3) cancel leaving

(y-4)/(y-5)

(y-4)/(y-5) the simplified form of the quantity y−squared plus 7y plus 12 over the quantity y−squared minus 2y minus 15.

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Answer:

Step-by-step explanation:

Area of a circle is ...

  A = πr² . . . r is the radius

Area of a sphere is ...

  A = 4πr²

Lateral area of a cylinder is ...

  A = πdh = 2πrh . . . h is the height

Volume of a cylinder is ...

  V = πr²h

Volume of a sphere is ...

  V = (4/3)πr³

___

The area of the composite figure is the sum of the areas ...

  total area = base circle area + cylinder lateral area + 1/2 sphere area

  = πr² + 2πrh + (1/2)4πr² = (πr)(r +2h +2r)

  = πr(3r +2h)

For the given dimensions, r=3 in, h = 13 in, this is ...

  total area = π(3 in)((3·3 +2·13) in) = 105π in²

___

The volume of the composite figure is the sum of the volumes ...

  total volume = cylinder volume + 1/2 sphere volume

  = πr²h + (1/2)(4/3)πr³ = πr²(h + 2/3r)

  = π(3 in)²((13 +2/3·3) in) = 135π in³