jason had $32. he spent all the money buying four cds for x dollars each and two magazines for y dollars each. if jason had bought five cds and two magazines, he would have run short by $4. the following system of equations models this scenario: 4x 2y

Answers

Answer 1

Step-by-step explanation:

The given system of equations models the scenario where Jason spent all of his money on buying CDs and magazines, and that if he had bought one more CD, he would have run out of money. The system of equations is:

4x + 2y = 32 (Equation 1)

5x + 2y = 36 (Equation 2)

The first equation represents the total amount of money Jason spent on 4 CDs (x dollars each) and 2 magazines (y dollars each). The second equation represents the total amount of money Jason would have spent if he had bought one more CD. By subtracting equation 1 from equation 2, we get:

x = 4 (Equation 3)

This equation tells us that each CD costs $4.

By substituting this value into equation 1, we get:

4(4) + 2y = 32

16 + 2y = 32

2y = 16

y = 8 (Equation 4)

This equation tells us that each magazine costs $8.

So, Jason spent $4 for each CD and $8 for each magazine.


Related Questions

Interpreting Polynomials
5x+9
A. 5
B. 9
C.
O
D. 1
What is the degree of the
polynomial?
Choice A
O Choice B
Choice C
O Choice D

Answers

Answer:

Give the degree of the polynomial.

6x5+5x4−3x2+x7

Answers:

18

5

6

9

7

Hope it helps :)

For the first question it's 1 and for the second question it is 5

find the equations of the lines that pass through the point (5,6) and are parallel to and perpendicular to the line with equation y =4x

Answers

The equation of  this parallel line is y = 4x - 22.  Railroad tracks, sidewalk edges, ladder rails, endless rail tracks, opposing sides of a ruler, opposite edges of a pen, an eraser, and other real-world objects are instances of parallel lines.

What is meant by parallel line?In a plane, lines that are consistently spaced apart from one another are referred to as parallel. Parallel lines don't ever intersect. Perpendicular lines are those that intersect at a 90-degree angle.Parallel lines are two lines that are never crossed and are equally spaced apart from one another.They could be horizontal or vertical. Parallel lines can be found in our daily life in the form of nearby train tracks, rows of notebooks, and zebra crossings.

Since there is no "b" in the conventional equation y = mx + b, the line y = 4x has a slope of 4 and an intercept of 0. Any parallel line will have the same slope as the slope (m = 4) in this case. The slope of all parallel lines will be the same.

So let's return to the conventional format and replace the m with a "4".

y = 4x + b

Now that the values have been entered into the equation, let's solve for "b" using the point that sits on the line.

-6 = 4(4) + b

-6 - 16 = b

b = -22

The equation of  this parallel line is y = 4x - 22

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2. If -2 is the root of a quadratic equation x²-5x+c=0, find
a: the value of c
b: the other root

Answers

The value of c according to the given equation as described is; -14.

The other root of the equation in discuss is; 7.

What is the value of c and determine the other root?

As evident in the task content; if -2 is the root of a quadratic equation x²-5x+c=0, then x = -2 holds true for the equation; therefore, we have;

a). (-2)² - 5 (-2) + c = 0

4 + 10 + c = 0

c = -14

Hence, the value of c is; -14.

b). By substituting into the equation; we have;

x² - 5x - 14 = 0

(x - 7) (x + 2) = 0

x = 7 OR x = -2.

Therefore, the other root of the equation is; 7.

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Evaluate the integral below by interpreting it in terms of areas. In other words, draw a picture of the region the integral represents, and find the area using geometry.-5 ∫5 sqrt(5^2−x^2) dx my lower limit is -5 and my upper is 5. How do I solve this problem? do i graph this equation and use left or right approximation?

Answers

Answer:

[tex]\frac{25\pi}{2}\approx39.27\text{ units}^2[/tex]

Step-by-step explanation:

I assume your problem is [tex]\displaystyle \int\limits^{5}_{-5} {\sqrt{5^2-x^2}} \, dx[/tex]. Recognize that [tex]\sqrt{5^2-x^2}=\sqrt{25-x^2}[/tex] is a semi-circle directly above the x-axis with a radius of 5. The bounds cover the whole area of the semicircle, so its area is just half the area of a circle with a radius of 5. You probably know that the area of a circle is [tex]A=\pi r^2[/tex], so the area of a semicircle would be [tex]A=\frac{\pi r^2}{2}[/tex]. Thus, the area using geometry is [tex]A=\frac{\pi (5)^2}{2}=\frac{25\pi}{2}\approx39.27\text{ units}^2[/tex].

4x-3y<9 x-3y>6 .... how does it look on a graph

Answers

A graph of the solution to this system of inequalities on a coordinate plane is shown in the image attached below.

How to graph the solution to this system of inequalities?

In order to to graph the solution to the given system of inequalities on a coordinate plane, we would use an online graphing calculator to plot the given system of inequalities and then take note of the point of intersection;

4x - 3 < 9

x - 3y > 6

Based on the graph (see attachment), we can logically deduce that the solution to the given system of inequalities is the shaded region and the point of intersection of the lines on the graph representing each, which is given by the ordered pair (3, -1).

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Mariah made a cylinder out of clay that had a radius of 6 cm and a volume of 72π cm^3. She painted the entire surface of the cylinder purple. How many square centimeters of the cylinder did Mariah paint in terms of π?

Enter the correct answer in the box/blank in terms of π.
_______ cm^2 (squared)

Answers

[tex]Answer:\ \boxed{96\pi }\ cm^2[/tex]

Step-by-step explanation:

[tex]R=6\ cm \ \ \ \ V_c=72\pi \ cm^3\ \ \ \ S_c=?[/tex]

[tex]V_c=\pi R^2H\\[/tex]

[tex]72\pi =\pi 6^2H\\\\72=36H\\[/tex]

Divide both parts of the equation by 36:

[tex]2=H\\\\Thus,\ H=2\ cm[/tex]

[tex]S_c=2(\pi R^2)+2\pi R(H)\\\\S_c=2\pi (6^2)+2\pi 6(2)\\\\S_c=2\pi(36)+12\pi (2) \\\\S_c=72\pi +24\pi \\\\S_c=96\pi\ cm^2[/tex]

A school is arranging a field trip to the zoo. The school spends 885.69 dollars on passes for 37 students and 2 teachers. The school also spends 325.23 dollars on lunch for just the students. How much money was spent on a pass and lunch for each student?

Answers

The $31.309 money was spent on a pass and lunch for each student

What is Equation?

Two or more expressions with an Equal sign is called as Equation.

School spends on a pass for each student,885.69/39

$22.97

School spends on a lunch for each student,

325.23/39

$8.339

Therefore, total money spent on a pass and lunch for each student

= 22.97 + 8.339

= $31.309

Hence, the $31.309 money was spent on a pass and lunch for each student

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Three softball players discussed their batting averages after a game.


Probability
Player 1 six tenths
Player 2 five ninths
Player 3 four sevenths


Compare the probabilities and interpret the likelihood. Which statement is true?
.
.
A. Player 1 is more likely to hit the ball than Player 2 because P(Player 1) > P(Player 2)
B. Player 2 is more likely to hit the ball than Player 1 because P(Player 2) > P(Player 1)
C. Player 3 is more likely to hit the ball than Player 1 because P(Player 3) > P(Player 1)
D. Player 2 is more likely to hit the ball than Player 3 because P(Player 2) > P(Player 3)

Answers

Comparibg the probabilities and interpreting the likelihood, the true statement is that:

A. Player 1 is more likely to hit the ball than Player 2 because P(Player 1) > P(Player 2)

How to calculate the probability?

Probability simply means the chance that a particular thing or event will happen. It is the occurence of likely events. It is simply the area of mathematics that deals with the numerical estimates of the chance that an event will occur.

Player 1 = six tenths = 0.6

Player 2 = five ninths = 0.56

Player 3 four sevenths = 0.57

This shows that player 2 has the highest probability. The correct option is A.

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Find the volume of the solid obtained by rotating the region bounded by the given curves about the specified line. sketch the region, the solid, and a typical disk or washer.
y=2−12x, y=0, x=1, x=2; rotate about the x-axis.

Answers

The Volume of the solid obtained by rotating the region bounded by the curves is 5 cm³.

Volume of a solid plain:

The volume of a solid is a measure of the space occupied by an object. It is measured by the number of unit cubes required to fill the solid.

Given in the question:

y = 2 - 1/2x

y = 0 , x = 1 and x = 2

As we know that:

We can write 19π / 12 as

(19× 22/7 )÷ 12

=  209/ 42

= 4.97 ≈ 5 cm³

Therefore, the volume is 5 cm³

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A trapezium ABCD is inscribed into a semi-circle of radius l so that the base AD of the trapezium is diameter and the vertices B and C lie on the circumference. Then the value of base angle θ (in degree) of the trapezium ABCD which has the greatest perimeter, is

Answers

The value of base angle θ (in degree) of the trapezium ABCD which has the greatest perimeter, is 60°

Given, AD = 2I

From ΔABD,

cos∅=[tex]\frac{AB}{AD}[/tex]

⇒ AB = AD cos∅

⇒ AB = 2I cos∅

and x = ABcos∅ = 2I [tex]cos^{2}[/tex]∅

Now perimeter,

P = 2I+ 2I - 2x + 2AB

P = 4I - 4I [tex]cos^{2}[/tex]∅ + 4Icos∅

P = 4I (1 - cos²∅ +  cos∅)

Differentiating with respect to ∅, we get

dP/d∅= 4I(2 cos∅ sin∅ - sin∅)

For max/min,

dP/d∅ = O

2 cos∅ sin∅ - sin∅ = 0

⇒ cos∅ = [tex]\frac{1}{2}[/tex]  (∅ [tex]\neq[/tex] 0)

            = 60°

[tex]d^{2}[/tex]P/d∅ = 4i(2 cos2∅ - cos∅)

[tex]d^{2}[/tex]P/d∅ < 0  

∅ = 60°

Therefore, Perimeter is maximum when ∅ = 60°

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A kite is flying 20 ft off the ground. It’s line is pulled taut and casts a 15 feet shadow

Answers

Answer:ts line is pulled taut and casts a 15 ft - shadow. Find the length of the line. If necessary, round your answer to the nearest tenth.

Step-by-step explanation:

The segments GA and GB are tangent to a circle at A and B, and AGB is a 48-degree angle. Given that GA = 12 cm, find the distance from G to the nearest point on the circle.

Answers

The distance from G to the nearest point on the circle is going to be 5.61 cm.

The given figure (image attached below) has the segments GA and GB tangent to a circle at A and B, and AGB is at a 48-degree angle. We have been told that GA = 12 cm. We have to find the distance from G to the nearest point on the circle.

For this, first what we need to do is draw radii to A and B. Next draw OG which bisects the 48-angle G into two 24-angles. Let P be the point where OG intersects the circle. This becomes the distance from G to the nearest point on the circle which we need to find (image attached below).

In the right triangle AOG, radius AO is the side opposite angle AGO-

= Tangent = Perpendicular / Base

= tan(24) = r / 12

= r = 12tan(24)            (i)

For OG -

= cos(24) = Base / Hypotenuse = 12 / OG

= OG = 12cos(24)        (ii)

Now, we subtract (i) and (ii) -

= 12tan(24) - 12cos(24)    

= 5.61 cm

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Divide the following and then check by multiplying.
7)84
Select the correct choice below and, if necessary, fill in the answer box to complete your choice
OA. The quotient does not have a remainder. The quotient is
B. The quotient has a remainder not equal to 0. The quotient is
OC. The quotient is undefined.

Answers

When dividing 84 by 7 then the quotient does not have a reminder and the quotient will be 12.

What is division?

A division in mathematics is the process of dividing a specific amount into equal parts. The division is the inverse of multiplication.

We can find a division fact if we know a multiplication fact: For instance, 3 5 = 15, so 15 / 5 = 3.

Also 15 / 3 = 5.

Here given that,

We have to divide 87/7,

By dividing,

we know that 8/7 gives reminder 1, and a quotient of 1.

Then divide 14 by 7,

which gives reminder 0 and quotient 2.

So by dividing 84 / 7 we get reminder 0 with a quotient of 12.

Therefore the correct option is option A. With a quotient of 12.

Hence, When dividing 84 by 7 then the quotient does not have a reminder and the quotient will be 12.

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Examine the number line,and then choose the correct symbol to complete each statement

Answers

After examine the number line,and then the correct symbol to complete each statement is -2/4<-1/4; 3/4>2/4;-1/4<0.

What is Number line ?

A number line is a diagram of a graduated straight line used to represent real numbers in introductory mathematics. It is assumed that every point on a number line corresponds to a real number, and that every real number corresponds to a point.

What is Symbol?

A mark, sign, or term that denotes, denotes, or is taken to denote an idea, an item, or a relationship is known as a symbol. By connecting seemingly unrelated ideas and events, symbols help people look beyond the known and the visible.

In the question given some relation between the real number which are

a) -2/4 < -1/4 because negative number has the property that the those numbers which is smaller is always greater.

b) 3/4 > 2/4 both numbers are positive so clearly it 3/4 comes after 2/4 so it is greater.

c)  -1/4 < 0 zero is always greater than the negative numbers

So, after examine the number line,and then the correct symbol to complete each statement is -2/4<-1/4; 3/4>2/4;-1/4<0.

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The acceleration function (in m/s2) and the initial velocity are given for a particle moving along a line.
a(t) = t + 4, v(0) = 3, 0 ≤ t ≤ 11(a) Find the velocity at time t. 3 m/s (b) Find the distance traveled during the given time interval.

Answers

The distance traveled during the given time interval be 2024 m.

What is meant by acceleration function?

An object's rate of change in velocity is referred to as its acceleration. The rate of change in velocity is known as acceleration. Acceleration typically signals a change in speed, though this is not always the case. Because of the shifting direction of its velocity, an item moving on a circular path at a constant speed is still accelerating.

By integrating the velocity v in terms of time t, v = gt, we can determine acceleration, which is the rate of change of velocity with respect to time.

Let the function be a(t) = t + 4

time = 11

substitute the value of t in the above equation, we get

a(11) = 11 + 6 = 17 m/s²

a = v/t, so v = at

finally v = (17 m/s²) (11s)

v = 187 m/s

b) Find the distance traveled during the given time interval

[tex]$$V_{total} = V_{final} - V_{ initial[/tex]

V final = 187 m/s, Vinitial = 3 m/s

V total = 187 - 3 = 184 m/s

Let the equation of velocity be

Velocity = distance/time

distance = velocity × time

distance = 184 m/s × 11 s

distance = 2024 m

Therefore, the distance traveled during the given time interval be 2024 m.

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A man bought one almirah for Rs 3640 and the other for Rs 4800. He sold the first almirah for a loss of 15% and the other at a profit of 13 1/3 %. How much did he gain or lose in the whole transaction.
Please tell the answer .​

Answers

Answer:

Rs. 94

Step-by-step explanation:

We will denote the almirahs as A1 and A2 for ease of explanation. I am omitting currency until the final answer

For the following computations note that x% = x/100 in decimal so
15% = 15/100 = 0.15
13 1/3% = 13 1/3 ÷ 100 = 40/3 ÷ 100 = 40/300

Cost of A1 = 4800

A1 was sold for a loss of 15%

Loss = 15% of 3640 = 0.15 x 3640  = Rs 546

A2 bought at 4800 was sold at a gain of 13 1/3%

Gain from sale = 13 1/3% of 4800 = 40/300 x 4800 =Rs 640

We have to treat gain as positive and loss as negative to arrive at the answer

Net gain/loss = 640  - 546 = Rs. 94

Find a vector (u ) with magnitude 4 in the opposite direction as v =⟨−2,3⟩ Give EXACT answer. You do NOT have to simplify your radicals!
u =

Answers

A vector (u) with magnitude 4 in the opposite direction as v =⟨−2,3⟩ is u = ⟨-2/√13, 3/√13⟩.

A vector in the opposite direction of a given vector can be found by multiplying that vector by -1. The magnitude of a vector is the length of the vector and it can be found by using the Pythagorean theorem on the coordinates of the vector.

The magnitude of the vector v = ⟨-2,3⟩ is:

|v| = √(-2)^2 + 3^2 = √4 + 9 = √13

To find a vector with magnitude 4 in the opposite direction as v, we can first normalize the vector v by dividing it by its magnitude,

then multiply it by 4:

u = (-1) * (1/|v|) * v

= (-1) * (1/√13) * ⟨-2,3⟩

= ⟨2/√13, -3/√13⟩

So, a vector (u) with magnitude 4 in the opposite direction as v =⟨−2,3⟩ is u = ⟨2/√13, -3/√13⟩

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Airline passengers get heavier In response to the increasing weight of airline passengers, the Federal Aviation Administration (FAA) in 2003 told airlines to assume that passengers average 190 pounds in the summer, including clothes and carry-on baggage. But passengers vary, and the FAA did not specify a standard deviation. A reasonable standard deviation is 35 pounds. Weights are not Normally distributed, especially when the population includes both men and women, but they are not very non-Normal. A commuter plane carries 30 passengers.
• (a) Explain why you cannot calculate the probability that a randomly selected passenger weighs more than 200 pounds.
• (b) Find the probability that the total weight of the passengers on a full flight exceeds 6000 pounds. Show your work. (Hint: To apply the central limit theorem, restate the problem in terms of the mean weight.)

Answers

The probability that the total weight of the passengers on a full flight exceeds 6000 pounds is about 0.0147 or 1.47%.

What is the Central Limit Theorem?

The Central Limit Theorem states that the sum of a large number of independent and identically distributed random variables is approximately Normally distributed.

(a) The reason why you cannot calculate the probability that a randomly selected passenger weighs more than 200 pounds is that the weight of passengers is not Normally distributed.

The Normal distribution is a symmetric bell-shaped distribution that is defined by its mean and standard deviation.

The weight of passengers is not symmetric and it may not follow a bell shape.

Therefore, we cannot use the Normal distribution to calculate the probability of a weight greater than 200 pounds.

(b) To calculate the probability that the total weight of the passengers on a full flight exceeds 6000 pounds, we can use the Central Limit Theorem.

Since we don't know the exact distribution of the weight of the passengers, we can use the Central Limit Theorem to approximate the total weight of the passengers on a full flight.

The mean weight of a passenger is 190 pounds, and the standard deviation is 35 pounds. Since a full flight carries 30 passengers, the mean weight of the passengers on a full flight is 19030 = 5700 pounds and the standard deviation is 35sqrt(30) = 175 pounds.

To find the probability that the total weight of the passengers on a full flight exceeds 6000 pounds, we can use the standard normal distribution table.

z = (6000 - 5700) / 175 = 2.2857

Probability P(X > 6000) = P(Z > 2.2857) = 1 - P(Z < 2.2857) = 1 - 0.9853 = 0.0147

Hence, the probability that the total weight of the passengers on a full flight exceeds 6000 pounds is about 0.0147 or 1.47%.

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You buy 4 small candles and 2 large candles for $14. Your friend buys 5 small candles and 3 large candles for $20. What is the cost of each small candle? of each large candle?
Each small candle costs $_ and each large candle costs $_.

Answers

Using simultaneous equations, each small candle costs $1.00 and each large candle costs $5.00.

What are simultaneous equations?

Simultaneous equations are two or more equations solved concurrently.

Simultaneous equations are also known as a system of equations.

                 Small Candle   Large Candle   Total Cost

You buy             4                       2                    $14

A friend buys    5                       3                   $20

Let the cost of the small candle each = s and the cost of the large candle each = l

Equations:

Equation 1: 4s + 2l = 14

Equation 2: 5s + 3l = 20

Multiply Equation 1 by 1.5:

Equation 3: 6s + 3l = 21

Subtract Equation 2 from Equation 3:

6s + 3l = 21

-

5s + 3l = 20

s = 1

= $1

From Equation 1:

4s + 2l = 14

4 + 2l = 14

2l = 10

l = 5

= $5

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Benjamin gets to go to festival with his friend for $120 The cost covers $45 for his lodging and 2 tickets to the festival, including all of his meals.
How much is a ticket to the festival?

Answers

Answer:

is $27.50 per each teacket

A rectangle is partitioned into 5 regions as shown. Each region is to be painted a solid color-red. orange, yellow, blue, or green-so that regions that touch are painted different colors, and colors can be used more than once. How many different colorings are possible? (A) 120 (B) 270 (C) 360 (D) 540 (E) 720

Answers

The 5 different colorings are possible.

The rectangle is partitioned into 5 regions.

The objective is to find the different of color.

There are 5 rectangle and 5 colors

Each region is to be painted a solid color-red. orange, yellow, blue, or green

Need to color 5 rectangles by using given five colors.

Then, we need to use 5! colors.

The factorial of a whole number is the function that multiplies the number by every natural number below it. Symbolically, a factorial can be represented by using the symbol "!". So, "n factorial" is the product of the first n natural numbers and is represented as n!

The formula for n factorial is:

n! = n × (n - 1)!

=5×4×3×2×1

=120

Therefore, the possible colorings are 5.

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Consider the following data: 13,11,5,2,9,14 Step of 3 : Calculate the value of the sampe variance Round your answer to one decimal place.Refer to Exercise 3. Calculate and interpret the standard deviation of the random variable X.

Answers

The sample variance of the given data 13,11,15,2,9,14 is 356.6.

Sample variance can be defined as the expectation of the squared difference of data points from the mean of the data set. It is an absolute measure of dispersion and is used to check the deviation of data points with respect to the data's average.

we have data 13, 11, 5, 2, 9, 14, and we have to determine the sample variance of given data.

Sample variance is given by,

[tex]S^2=\frac{\sum^n_1(X_i-X')^2}{(n-1)}[/tex]

where X' is the sample mean,

the mean of given data is,

[tex]X'=\frac{(13+11+5+2+9+14)}{6} \\\\X'=\frac{54}{6} \\\\X'=9[/tex]

now the sample variance is given by,

[tex]S^2=\frac{(13+9)^2+(11+9)^2+(5+9)^2+(9+9)^2+(14+9)^2}{6-1} \\\\S^2=\frac{(484+400+289+81+529)}{5} \\\\S^2=356.6[/tex]

Hence the sample variance is 356.6.

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LA REPRESA POZA HONDA ALMACENA 11 MILLONES DE METROS CÚBICOS DE AGUA. ¿CUÁNTOS KILÓMETROS DE AGUA ALMACENA?

Porfavor ayudenme es para Matematicas

Answers

Answer: 11/1000 o 1.1%

Step-by-step explanation:

11 ÷ 1000

0.011

11/1000 o 1.1%

Caitlyn needs to mail a USB drive to a friend. She uses 42 -cent stamps and 5 -cent stamps to pay $1.71 in postage. How many of each stamp did Caitlyn use?

Answers

Solving an equation we will see that Caitlyn used 3 of the 42-cent stamps and 9 of the 5-cent ones.

How many of each stamp does she use?

Let's define the variables that we will be using:

x = number of 42-cent stapms.y = number of 5-cent stamps.

Then the total value of the stamps, in dollars, is:

x*0.42 + y*0.5

And we know that the value must be $1.71, then we can write the equation:

x*0.42 + y*0.05 = 1.71

y = (1.71 - x*0.42)/0.05

To find the values of x and y, we can just evaluate in different whole values of x, until we get a whole value of y.

using x = 1 we get:

y = (1.71 - 0.42)/0.05 = 2.58

This is not a solution.

if x = 3

y = (1.71 - 0.42*3)/0.05 = 9

This is the solution, she used 3 of the 42-cent and 9 of the 5-cent.

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PLEASE HELPPPP

An equilateral triangle has sides of length (3x+7). Find the perimeter of triangle.

Answers

Answer:

9x + 21

Step-by-step explanation:

An equilateral triangle is a triangle with three equal sides. If we know the length of one side, we can find the perimeter by multiplying by three.

3(3x + 7) = 9x + 21

711
Put the measures of the angles in order from least to greatest

Answers

Answer: [tex]m\angle YOZ, m\angle VOS, m\angle UOZ, m\angle XOS, m\angle TOZ[/tex]

Step-by-step explanation:

[tex]m\angle VOS=90^{\circ}\\\\m\angle UOZ=180^{\circ}-56^{\circ}=124^{\circ}\\\\m\angle YOZ=180^{\circ}-143^{\circ}=37^{\circ}\\\\m\angle XOS=126^{\circ}\\\\m\angle TOZ=180^{\circ}-33^{\circ}=147^{\circ}[/tex]

In an interval whose length is z seconds, a body moves (32z + 2z^ 2 ) ft. What is the average speed v of the body in this interval?

Answers

The average speed of the body in the given interval is 32 + 2z ft/s.

The average speed v of a body in an interval of z seconds can be calculated using the formula v = d/t, where d is the distance traveled and t is the time taken.

In this case, the distance d is (32z + 2z^ 2 ) ft and the time taken is z seconds.

Therefore, the average speed v of the body in this interval is:

v = (32z + 2z^ 2 ) ft / zs

v = 32 + 2z ft/s

Therefore, the average speed of the body in the given interval is 32 + 2z ft/s.

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given vector u equals open angled bracket negative 10 comma negative 3 close angled bracket and vector v equals open angled bracket 4 comma 8 close angled bracket comma what is projvu? open angled bracket negative 640 over 109 comma negative 192 over 169 close angled bracket open angled bracket negative 256 over 109 comma negative 512 over 109 close angled bracket open angled bracket negative 8 comma negative 3 close angled bracket open angled bracket negative 16 over 5 comma negative 32 over 5 close angled bracket

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The correct answer is open angled bracket negative 16 over 5 comma negative 32 over 5 close angled bracket, as it is the vector u.

The projection of vector u onto vector v is given by the formula:

projv(u) = (u . v/||v||^2) * v

where u . v is the dot product of vectors u and v,and ||v|| is the magnitude of vector v

Given that u = <-10, -3> and v = <4, 8>, we can substitute these values into the formula and find projv(u)

projv(u) = ( (-10)(4) + (-3)(8) )/ (4^2 + 8^2) * <4,8>

projv(u) = ((-40 - 24)/ (16 + 64))* <4,8>

projv(u) = (-64/80) * <4,8>

projv(u) = (-4/5) * <4,8>

projv(u) = <-16/5,-32/5>

The vector u is already parallel to the vector v, that's why the projection of vector u on vector v is equal to vector u itself.

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Find the 10th term of the sequence below

Answers

Answer:

10th term = 94

Step-by-step explanation:

Given equation,

→ Tn = n² - n + 4

Now the 10th term will be,

→ Tn = n² - n + 4

→ T10 = (10)² - 10 + 4

→ T10 = 100 - 6

→ [ T10 = 94 ]

Hence, the answer is 94.

the sums of the measures of the interior angles of a polygon is three times the sum of its exterior angles. how many sides does it have. please help

Answers

The sums of the measures of the interior angles of a polygon is three times the sum of its exterior angles then it has 8 sides .

What is Polygon?

A polygon is a two-dimensional, closed form that is flat or planar and is limited by straight sides. Its sides are not curled. A polygon's edges are another name for its sides. The vertices (or corners) of a polygon are the places where two sides converge. Here are some illustrations of polygons.

What is interior angles?

Interior angles are those that are located within the confines of two parallel lines that are intersected by a transversal.

What is exterior angles?

The angles that are created outside of a triangle are its external angles. In other terms, the angle created between one of a triangle's sides and its neighboring extended side is the triangle's external angle.

We know that sum of interior angle of regular polygon is ;

(n-2) x 180°

Where n = no. of sides

We also know that sum of exterior angle of regular polygon is 360°.

The fact that the sum of a polygon's internal angles is three times the sum of its outside angles is now a given;

Therefore;

sum of interior angles of a regular polygon = 3 x sum of exterior angle

⇒ (n-2) x 180°

⇒3 x 360°

Simplify the equation we have above by:

⇒(n-2) = 3 x 360°/180° = 6

⇒ n = 6+2 = 8

Therefore the sides of the regular polygon  is 8.

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