Rodolpho uses a prepaid gas card to spend $35 each week for gas. After the first week, he has $140 left on the card. After everything he second week he has $105, and so on. Which equation represents the cash balance on his card after t weeks

Answer:

p = - 6, p = - 2

Step-by-step explanation:

Given

- 2p² = 16p + 24

Subtract 16p + 24 from both sides

- 2p² - 16p - 24 = 0 ← in standard form ( divide all terms by - 2)

p² + 8p + 12 = 0

To factor the quadratic

Consider the factors of the constant term (+ 12) which sum to give the coefficient of the p- term (+ 8)

The factors are + 6 and + 2, since

6 × 2 = 12 and 6 + 2 = 8, thus

(p + 6)(p + 2) = 0

Equate each factor to zero and solve for p

p + 6 = 0 ⇒ p = - 6

p + 2 = 0 ⇒ p = - 2

The line in the middle has a right angle, so the angle just above the Y would be 90 degrees.

The angle to the right of y is given as 48.

The three inside angles of a triangle need to equal 180.

So y  = 180 - 90 - 48 = 42 degrees.

Answer:

Step-by-step explanation:

First step:

Calculate the hypotenuse of a right triangle.

Use the Pythagorean theorem:

[tex]h^2=3^2+4^2\\\\h^2=9+16\\\\h^2=25\to h=\sqrt{25}\\\\h=5\ cm[/tex]

Second step:

We have

two right triangles with legs a = 3cm and b = 4 cm

one rectangle 4cm × 2cm

one rectangle 3cm × 2cm

one rectangle 5cm × 2cm

Calculate each area:

The formula of an area of a right triangle:

[tex]A=\dfrac{ab}{2}[/tex]

Substitute:

[tex]A_1=\dfrac{(3)(4)}{2}=(3)(2)=6\ cm^2[/tex]

The formula of an area of a rectangle l × w:

[tex]A=lw[/tex]

Substitute:

[tex]A_2=(4)(2)=8\ cm^2\\\\A_3=(3)(2)=6\ cm^2\\\\A_4=(5)(2)=10\ cm^2[/tex]

Third step:

Calculate the Surface Area of the figure:

[tex]S.A.=2A_1+A_2+A_3+A_4[/tex]

Substitute:

[tex]S.A.=2(6)+8+6+10=36\ cm^2[/tex]

$22.75

Start by finding the cost of each topping. Subtract $17.50 minus $14.00 to find that adding 2 toppings costs $3.50. Now, divide $3.50 by 2 to find that the cost for adding only one topping is $1.75.

Then, multiply $1.75 by 5 to find how much it costs to add 5 toppings. You get $8.75.

Finally, add the cost of 5 toppings to the cost of a large pizza with no toppings. $14.00 plus $8.75 equals $22.75, so a large pizza with 5 toppings costs $22.75.

Answer: $22.75

Step-by-step explanation:

Given : The cost in dollars, y, of a large pizza with x toppings from Pat’s Pizzeria can be modeled by a linear function.

A linear function is given by :-

[tex]y=mx+c[/tex]                            (1)

, where m is slope (rate of change of y w.r.t x) and c is the y-intercept.

A large pizza with no toppings costs $14.00.

i.e. for x=0 , y= 14

Put theses values in (1) , we get

[tex]14=m(0)+c\\\Rightarrow\ c=14[/tex]   (2)

A large pizza with 2 toppings costs $17.50.

i.e. for x=2 , y= 17.50

Put theses values in (1) , we get

[tex]17.50=m(2)+c[/tex]      

Put value of c from (2)

[tex]17.50=2m+14\\\\[/tex]      

Subtract 14 from both sides , we get

[tex]3.50=2m[/tex]

Divide both sides by 2 , we get

[tex]1.75=m[/tex]

Put m= 1.75 and c= 14 in (1) , the linear function representing cost of large pizza becomes [tex]y=1.75x+14[/tex]

At x= 5

[tex]y=1.75(5)+14=8.75+14=22.75[/tex]

Thus , the cost of a pizza with 5 toppings= $22.75

Answer:

C. 3Pi/2 or 270 degrees

Step-by-step explanation:

The first step is to ignore the negative sign and then evaluate the arcsin of 1 to obtain the reference angle of θ in the first quadrant;

θ = arcsin(1)

θ = 90 degrees or equivalently pi/2

Since the sine of θ was given as -1, this will imply that θ lies either in the third or forth quadrant where the sine of an angle is negative.

To obtain the value of θ in the third quadrant we simply add 180 degrees of pi radians to our reference angle;

90 + 180 = 270 degrees

pi/2 + pi = 3/2 pi

Answer:

20% it would be 10% if there was 10 items. 5 items mean every item has 20%.

Step-by-step explanation:

Answer:  0.20

Step-by-step explanation:

Given : The number of side dishes for the lunch menu =6

The number of ways to select 3 dishes from 6 :

Total outcomes : [tex]^6C_3=\dfrac{6!}{3!(6-3!)} \ \ [\because\ ^nC_r=\dfrac{n!}{r!(n-r)!}\ ][/tex]                  

If applesauce and broccoli is already selected , then we need to select only one dish out of remaining 4 dishes.

Number of ways to select 1 dish from 4 :

Favorable outcomes: [tex]^4C_1=\dfrac{4!}{1!(4-1)!)}=4[/tex]

Now, the theoretical probability that applesauce and broccoli will both be offered on Monday :-

[tex]\dfrac{\text{Favorable outcomes}}{\text{Total outcomes}}\\\\=\dfrac{4}{20}=0.20[/tex]

Hence, the theoretical probability that applesauce and broccoli will both be offered on Monday = 0.20

Answer:

900 miles

Step-by-step explanation:

Well, 200 miles is 1 inch. 100 miles is 1/2 an inch.

Answer:

900

Step-by-step explanation:

Given: 1/4 in. = 50 miles

Find the amount of miles per inch. Multiply 4 to both sides of the equation.

(1/4 in.) x (4) = (50 miles) x (4)

4/4 in. = 200 miles

1 in. = 200 miles

Now, find the amount of miles for 4 1/2 in. Multiply 4 1/2 to both sides.

Note that 4 1/2 = 4.5

(1 in.)(4.5) = (200 miles) x (4.5)

4.5 = 200 x 4.5

4.5 = 900

900 miles is your answer.

~

The answer is y = 3x - 2

Y=3x-2

The formula y=mx+b is the slope intercept formula. You would enter the information of the problem into the equation.

You would place the slope in the place of m and the y intercept in the place of b.

Since it is a negative slope it would be -2 instead of +2 if it was positive.

Answer:

42 units^2.

Step-by-step explanation:

We are given that it is a rectangle so its area is the product of the length of adjacent sides.

Length  of the horizontal line = 11 - 4 = 7 units ( from the first 2 points) and  the length of an adjacent side is 9 - 3 = 6 units (from the second and third points).

Area = 7 * 6 = 42.

Answer:

area of rectangle = 42

Step-by-step explanation:

area of rectangle = length × width

                             = 7 × 6

                             = 42

Answer:

p = 2 , q = 0

Step-by-step explanation:

Solve the following system:

{-28 = -14 p - 40 q | (equation 1)

10 q + 4 = 2 p | (equation 2)

Express the system in standard form:

{14 p + 40 q = 28 | (equation 1)

-(2 p) + 10 q = -4 | (equation 2)

Add 1/7 × (equation 1) to equation 2:

{14 p + 40 q = 28 | (equation 1)

0 p+(110 q)/7 = 0 | (equation 2)

Divide equation 1 by 2:

{7 p + 20 q = 14 | (equation 1)

0 p+(110 q)/7 = 0 | (equation 2)

Multiply equation 2 by 7/110:

{7 p + 20 q = 14 | (equation 1)

0 p+q = 0 | (equation 2)

Subtract 20 × (equation 2) from equation 1:

{7 p+0 q = 14 | (equation 1)

0 p+q = 0 | (equation 2)

Divide equation 1 by 7:

{p+0 q = 2 | (equation 1)

0 p+q = 0 | (equation 2)

Collect results:

Answer:  {p = 2 , q = 0

Answer:

p = 2 , q = 0

Step-by-step explanation:

Trust me

Answer:

Choice B: BD/DA = CE/EA

Step-by-step explanation:

Slope is rise over run. For the two slopes to be equal, the rise over run of the two triangles must be equal.

The rise over run for triangle ABD is BD/DA.

The rise over run of triangle ACE is CE/EA.

For the slopes to be equal, BD/DA = CE/EA

Answer: Choice B.

Step-by-step explanation:

Mean is the average and that means you add up all the numbers and divide it by its amount.

Interquartile Range is the range of Quartile 3 minus Quartile 1

Range is the highest number minus the lowest number

mean the sum of a set of data divided by the number of items in the set

range the difference between the largest and smallest data points

interquartile range  the difference between the upper quartile and the lower quartile

Answer:

The third alternative is correct

Step-by-step explanation:

In hypothesis testing, the null hypothesis H0 is the hypothesis of no difference and as such it always contains an equality sign. The equality sign could be either of the following alternatives;

=, equal to

≤, less than or equal to

≥, greater than or equal to

In the question presented the claim is that students who practice taking all of their regular tests on the computer will do better on the state's final exam than the students taking their regular tests by paper and pencil.  

This implies that the average on the state exam of students using paper and pencil tests is less than the average of the students using computer tests. Since the null hypothesis must contain an equality sign, the third alternative becomes our null hypothesis, H0.

Answer:

y - 4 = -1/2(x+6).

Step-by-step explanation:

The equation of the line is: y - y0 = m(x-x0)

If the line passes through the points (x1, y1)=(-6, 4) and (x1, y1)=(2, 0). Then, the slope is:

[tex]m = \frac{y1-y0}{x1-x0} = \frac{0-4}{2-(-6)} = -\frac{1}{2} [/tex]

Then, the equation is: y - 4 = -1/2(x+6).

Answer:

The money was invested for 16 years

Step-by-step explanation:

This is a compound interest problem and the following information has been provided;

Principal, P = 2500

Rate, r = 0.05 compounded semiannually. This will imply an effective rate of 0.05/2 = 0.025 effective per semiannual period.

Accumulated amount, A = 5509.39

We are required to determine the duration of investment in years. We let the number of years be n. We then use the compound interest formula;

[tex]A=P(1+r)^{n}\\\\5509.39=2500(1+0.025)^{2n}[/tex]

We raise to power 2n since there are 2n semiannual periods in n years. The next step is to divide both sides by 2500;

[tex]2.203756=1.025^{2n}\\[/tex]

We introduce logs in order to solve for n;

[tex]ln(2.203756)=2nln(1.025)\\\\2n=\frac{ln(2.203756)}{ln(1.025)}\\ \\2n=32\\\\n=16[/tex]

c increased by 17

Increased = +

c + 17 is the answer

Answer:

Error question or wrong

Answer:

Option B

Step-by-step explanation:

we know that

A line perpendicular to the x-axis is a line parallel to the y-axis

so

the equation of the line is of the form x=(+/-)a

The slope of the line is undefined

where

a is a real number

therefore

x=6 is a line perpendicular to the x-axis

Answer:

B. [tex]x = 6[/tex]

Step-by-step explanation:

The x-axis is the line of [tex]0 = y[/tex] [horizontal line], therefore the ONLY live perpendicular to that would be [tex]x = 6[/tex], which is a vertical line, giving you a right angle in the centre.

I am joyous to assist you anytime.

Answer: C.

Step-by-step explanation:

Diameter = Radius/2

So, the radius would be 6.5 in.

The formula for the volume of a sphere is: V = 4/3 (3.14) r^3.

So, once you "plug in" the radius, you get an equation of V = 4/3 (3.14) r^3.

And, once you solve the equation, you get and answer of 1,150 in.^3, rounded to the nearest cubic inch.

The volume of a sphere with a diameter of 13 inches, using the formula V = 4/3 * π * r³ and rounding off to the nearest cubic inch, is approximately 1151 cubic inches or choice C, 1150 in³.

To find the volume of a sphere, you can use the formula V = 4/3 * π * r³, where V is the volume and r is the radius. In this case, the diameter of the sphere is given as 13 inches. So, the radius would be half the diameter, which is 6.5 inches.

Plugging the values into the formula, we get V = 4/3 * 3.14 * (6.5)³. Calculating this gives an approximate value of 1151 cubic inches. Since we need to round to the nearest cubic inch, the final volume is 1151 in³.

So, the correct choice is C. 1150 in³.

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z÷x

-6÷3

=-2

Answer is -2

Answer:

(-6)/3 = -2

Step-by-step explanation:

you have to change the variables with the numbers

Answer:

High positive correlation

Step-by-step explanation:

Perfect correlation is 1 or -1(0 is no correlation), the correlation coefficient is .8

It is positive because it is a positive number (closest to positive 1).

This value is close to 1 so it's a high positive correlation.

Answer:

Answer Is C.

Step-by-step explanation:

Answer:

4.5

Step-by-step explanation:

because 2 3 4 4 5 7 9 11

4.5 is the middle number, between 4 and 5 since you find what the middle number is

Here is some fun:

[tex]mean=\frac{\Sigma_{0}^{n}a_r}{n}=\frac{a_0+a_1+\dots+a_{\infty}}{\infty}[/tex]

[tex]

mean=\frac{4+5+9+2+7+4+3+11}{8}=\frac{45}{8}=\boxed{5.625}

[/tex]

And now the real work:

[tex]median=\frac{2+7}{2}=\boxed{4.5}[/tex]

The answer is B. 4,5

Hope this helps.

r3t40

Answer:

n = 4

Step-by-step explanation:

Given

10n + 2 = 7n + 14

Collect terms in n on the left side and numbers on the right side

Subtract 7n from both sides

3n + 2 = 14 ( subtract 2 from both sides )

3n = 12 ( divide both sides by 3 )

n = 4

Answer n=4

Step-by-step explanation: Collect the like terms 10n-7n=14-2

3n=12 divide both sides by 3

For this case we have that by definition, the formula to count the total number of different permutations is:

[tex]nP_ {r} = \frac {n!} {(n-r)!}[/tex]

SUstituyendo:

[tex]n = 8\\r = 5[/tex]

We have:

[tex]8P_ {5} = \frac {8!} {(8-5)!} = \frac {8!} {3!} = \frac {8 * 7 * 6 * 5 * 4 * 3!} {3! } = 6720[/tex]

ANswer:

[tex]8P_ {5} = 6720[/tex]

Answer:

(1+10)+18=11+18=29; 1+(10+18)=1+28=29

Step-by-step explanation:

the associative property of addition means that no matter in what order you group the numbers for addition the results come out to be the same.

using the associative property of addition to find the total of 1,10, and 18 in two different ways

first: (1+10)+18

=11+18

=29

second: 1+(10+18)

=1+28

=29!

Answer:

Check attached graph

Step-by-step explanation:

Given inequality is [tex]-2a-5>3[/tex].

Now we need to graph the given inequality to find the correct choice.

[tex]-2a-5>3[/tex]

[tex]-2a-5+5>3+5[/tex]

[tex]-2a>8[/tex]

[tex]-\frac{2a}{-2}<\frac{8}{-2}[/tex]

[tex]a<-4[/tex]

that means line will go on the left side of -4.

since we have <, so there will be an open circle at -4.

Hence final graph of the given problem looks like:

Answer:

The diagonal is 39.54 in

Step-by-step explanation:

First we use the Pythagorean theorem to calculate the length of the diagonal of the base.

If the base measures 13 inches by 35 inches then the diagonal is:

[tex]c = \sqrt{13^2 +35^2}\\\\c= 37.34\ in[/tex]

Now we use the Pythagorean theorem again to find the diagonal of the cube.

If the height of the box is 13 inches and the diagonal of the base is 37.34 inches then the diagonal of the cube will be

[tex]z = \sqrt{37.34^2 +13^2}\\\\z= 39.54\ in[/tex]

The baton will fit in the box if it is placed in the direction of the diagonal of the cube, since:

39.54\ in > 38 inches

Using the 3D Pythagorean theorem, the diagonal of the box is calculated to be approximately 39.53 inches, which means that Kylie's 38-inch baton will fit inside the box diagonally.

Kylie needs to check if her 38-inch long baton will fit diagonally in a box with dimensions of 13 inches by 35 inches by 13 inches. To determine whether the baton will fit, she needs to find the length of the longest diagonal of the box. This is solved by using the 3D Pythagorean theorem, which is an extension of the traditional Pythagorean theorem applied to three dimensions.

To find the length of the diagonal (d), we use the formula:

d = √(l² + w² + h²)

Where l is the length, w is the width, and h is the height of the box. Substituting the given values:

d = √(13² + 35² + 13²)

d = √(169 + 1225 + 169)

d = √1563

d ≈ 39.53 inches

The calculated diagonal length of approximately 39.53 inches indicates that Kylie's baton, which measures 38 inches, will indeed fit inside the box diagonally.

-10t+6=-44

-10t=-50

t= 5

ANSWER

[tex]h(5) = - 44[/tex]

EXPLANATION

The given expression is :

h(t)=-10t+6

We want to find the value of t that will evaluate to -44.

We equate the function to -44 and solve for t.

[tex]-10t+6 = - 44[/tex]

Subtract 6 from both sides of the equation,

[tex]-10t = - 44 - 6[/tex]

[tex]-10t = - 50[/tex]

Divide both sides by -10

[tex]t = 5[/tex]

Answer:

Option B.

Step-by-step explanation:

The constant of proportionality is the constant value of the ratio of two proportional quantities x and y; usually written y = kx, where k is the factor of proportionality.

Given that the graph is a straight line, we can find the constant of proporctionality just by selecting a point, and then dividing the y-value by the x-value.

We can see from the graph that when y=5, x=4. Then, the constant of proportionality comes to be:

k = 5/4 = 1.25.

Then, the correct option is Option B.

It was 2 hours

A bicyclist ride 3 mph (miles per hour) to cover 12 miles in 4 hours

The distance of the first ride, ridden for 120 minutes at 18 mph, was 36 miles. To cover 12 miles in 4 hours, the bicyclist must ride at a speed of 3 mph.

To find the distance of the first ride, we can use the formula:

Distance = Speed × Time

Given that the bicyclist rides for 120 minutes (2 hours) at an average speed of 18 miles per hour:

Distance = 18 miles/hour × 2 hours = 36 miles

So, the distance of the first ride was 36 miles.

To find the speed the bicyclist must ride to cover 12 miles in 4 hours, we use the same formula:

Speed = Distance / Time

Given that the distance is 12 miles and the time is 4 hours:

Speed = 12 miles / 4 hours = 3 miles per hour

The bicyclist must ride at a speed of 3 miles per hour to cover 12 miles in 4 hours.

To know more about speed:

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Answer:

[tex]x=6\sqrt{5}\\ \\y=3\sqrt{5}\\ \\z=6[/tex]

Step-by-step explanation:

The height of the right triangle drawn to the hypotenuse is geometric mean of two segments of hypotenuse, so

[tex]z^2=12\cdot 3\\ \\z^2=36\\ \\z=6[/tex]

By the Pythagorean theorem,

[tex]x^2=12^2+z^2\\ \\x^2=144+6^2\\ \\x^2=144+36\\ \\x^2=180\\ \\x=6\sqrt{5}[/tex]

and

[tex]y^2=z^2+3^2\\ \\y^2=6^2+9\\ \\y^2=36+9\\ \\y^2=45\\ \\y=3\sqrt{5}[/tex]