Find the value of x in 4^x+64^x= 272

Answers

Answer 1

Answer:

1.342

Step-by-step explanation:

4^x+64^x=272

4^x+(4^3)^x=272

4^3x+4^x=272

(4^x)^3+4^x=272

(4^x)^3+4^x-272=0

u^3+u-272=0 ==> substitute 4^x with u

Now, use synthetic division to find roots:

\(\sqrt[3]{272}\)31   |    1    0              1             -272

                       \(\sqrt[3]{272}\)1     \(\sqrt[3]{272^2}\)      272

                 1    \(\sqrt[3]{272}\)1      \(\sqrt[3]{272^2}\)       0

4^x=\(\sqrt[3]{272}\)

log 4 (4^x)=log 4 (\(\sqrt[3]{272}\))=1.342


Related Questions

A) Do the following lengths form a right triangle? Prove it by SHOWING YOUR WORK. 0 6 8 9

Answers

Answer:

friend me on here and imma send you the link Step-by-step explanation:

Choose the correct way to simplify 4(5-3) using the distributive property of multiplication over subtraction.

Answers

━━━━━━━☆☆━━━━━━━

▹ Answer

20 - 12 or 8 (depending on what you need to find)

▹ Step-by-Step Explanation

4(5 - 3)

Distribute 4 * 5 and 4 * -3

This will give 20 - 12

If you are looking for the final answer, it would be 8.

Hope this helps!

CloutAnswers ❁

Brainliest is greatly appreciated!

━━━━━━━☆☆━━━━━━━

you multiply 4 and 5 and then 4 and 3 and subtract those 2 answers

someone help meee nowww pleasee

someone help meee nowww pleasee

Answers

Answer:

149.28 m²

Step-by-step explanation:

Bottom and two sides of the rectangle: 3x4x6=72

Two square ends of the rectangle: 2x4x4=32

Two triangular sides of the prism: 2x1/2x2x6=12

Back of prism: 2x4=8

Top of prism: 4x6.32=25.28

72+32+12+8+25.28=149.28

Let P(x) = -50x+20,000x-1,5000,000 represent the profit function for manufacturing a particular model of recreational
vehicle (RV) and x represent the number of RVS produced monthly. Use a compound inequality to state the range of the
number of RVs that need to be sold each month for the company to make a profit.
O 0 100 200 none of the answer choices
O 0 O 100

Let P(x) = -50x+20,000x-1,5000,000 represent the profit function for manufacturing a particular model

Answers

Among the given answer choices, the correct option that represents this range is "0 100 200 none of the answer choices".

To determine the range of the number of RVs that need to be sold each month for the company to make a profit, we need to consider the profit function and find the values of x that result in a positive profit.

The profit function is given by P(x) = -50x + 20,000x - 1,500,000.

To make a profit, the value of P(x) must be greater than zero (P(x) > 0). We can set up the inequality:

-50x + 20,000x - 1,500,000 > 0.

Combining like terms, we have:

19,950x - 1,500,000 > 0.

Now, let's solve this inequality for x:

19,950x > 1,500,000.

Dividing both sides by 19,950, we get:

x > 1,500,000 / 19,950.

Simplifying the right side, we have:

x > 75.

The range of the number of RVs that need to be sold each month for the company to make a profit is x > 75.

Among the given answer choices, the correct option that represents this range is "0 100 200 none of the answer choices".

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For each pair of functions f and g below, find f(g(x)) and g (f(x)).
Then, determine whether fand g are inverses of each other.
Simplify your answers as much as possible.
(Assume that your expressions are defined for all x in the domain of the composition.
You do not have to indicate the domain.)

f(x) = x+4
g (x) = x+4

Answers

The Function  f(g(x)) = g(f(x)) = x + 8.

The functions are: f(x) = x + 4 and g(x) = x + 4. We can find f(g(x)) by substituting g(x) in place of x in f(x).

f(g(x)) = f(x + 4) = (x + 4) + 4 = x + 8

Similarly, we can find g(f(x)) by substituting f(x) in place of x in g(x).g(f(x)) = g(x + 4) = (x + 4) + 4 = x + 8

Thus, we can see that f(g(x)) and g(f(x)) are equal to each other,

which is x + 8.

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A ball pit contains 190 balls.
50 are orange, 100 are purple and 40 are yellow.
What is the ratio of yellow to purple balls in its simplest form?

Answers

Step-by-step explanation:

40 :100        yellow to purple,  divide both sides by 20

2:5

Answer:

the ratio of yellow to purple is 40:100 that is 2:5 in the simplest form.

Step-by-step explanation:

Hope it helps.

Solve the inequality.

Question 1
3y≤−9
The solution is

Answers

The solution of the given inequality is y ≤ -3.

The given inequality is -

3y ≤ −9

We have to solve this given inequality.

Now, we have the inequality as -

3y ≤ −9

=> y ≤ -3

Thus, the solution of the given inequality is y ≤ -3.

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FIND THE EQUATION OF THE LINE FROM THE FOLLOWING GRAPH. please give steps​​

FIND THE EQUATION OF THE LINE FROM THE FOLLOWING GRAPH. please give steps

Answers

Answer:

I can't tell

Step-by-step explanation:

I'm on an ocps school laptop and i can't see the image

Answer:

D. x+2y=12

Step-by-step explanation:

From the graph we know that the y-intercept is 6. (0,6) and the x-intercept is 12. (12,0)

The graph is going down so the slope is negative, from (0,6) count down to (0,0) and count right 12 unit to reach the x-intercept(12,0) the slope is -6/12 or -1/2.

the equation of the line is y=-1/2+6 or x+2y=12

x+2y=12

2y=-x+12

y=-1/2x+6

The monthly worldwide average number of air- plane crashes of commercial airlines is 3.5. What is the probability that there will be
(a) at least 2 such accidents in the next month?
(b) at most 1 accident in the next month?

Answers

Answer:

The probability that there will be

(a) at least 2 such accidents in the next month?

= 0.864

(b) at most 1 accident in the next month?

= 0.136

Step-by-step explanation:

This is a Poisson Distribution question.

The formula is given as:

For X = x ,

= λ^x × e^-λ/x!

The monthly worldwide average number of air- plane crashes of commercial airlines is 3.5. What is the probability that there will be

(a) at least 2 such accidents in the next month?

= λ^x × e^-λ/x!

λ = 3.5

x = at least 2 such accidents

x ≥ 2

= 1 - [P(x = 0) + P(x = 1)]

= 1 - [(3.5^0 × e^-3.5/0!)+ (3.5^1 × e^-3.5/1!)]

= 1 - [ 1 × 0.0301973834 + 3.5 × 0.0301973834]

1 - [ 0.0301973834+ 0.105690842]

= 0.8641117746

≈ 0.864

(b) at most 1 accident in the next month?

= λ^x × e^-λ/x!

λ = 3.5

x = at most 1 such accidents

x ≤ 1

= [P(x = 0) + P(x = 1)]

= [(3.5^0 × e^-3.5/0!)+ (3.5^1 × e^-3.5/1!)]

= [ (1 × 0.0301973834) + (3.5 × 0.0301973834)]

[ 0.0301973834+ 0.105690842]

= 0.1358882254

≈ 0.136

The water usage at a car wash is modeled by the equation W(x) = 5x3 + 9x2 − 14x + 9, where W is the amount of water in cubic feet and x is the number of hours the car wash is open. The owners of the car wash want to cut back their water usage during a drought and decide to close the car wash early two days a week. The amount of decrease in water used is modeled by D(x) = x3 + 2x2 + 15, where D is the amount of water in cubic feet and x is time in hours. Write a function, C(x), to model the water used by the car wash on a shorter day. C(x) = 5x3 + 7x2 − 14x − 6 C(x) = 4x3 + 7x2 − 14x + 6 C(x) = 4x3 + 7x2 − 14x − 6 C(x) = 5x3 + 7x2 − 14x + 6

Answers

To model the water used by the car wash on a shorter day, we need to find the difference between the water usage over a full day and the water usage over a reduced day (i.e., with the car wash closed for two hours less than it would be on a full day). Let the number of hours the car wash is open on a full day be x hours. Then the amount of water used on a full day would be W(x). And the amount of water used on the reduced day (i.e., with the car wash closed for two hours less than on a full day) would be C(x). Therefore, we have:


W(x) - C(x) = 2(W(x) - C(x))


Solving this equation for C(x), we get:


C(x) = (W(x) - 2W(x))
= W(x)(1 - 2)
= (5x3 + 9x2 - 14x + 9)(1 - 2)
= (5x3 + 7x2 - 14x + 6)


Therefore, the function C(x) to model the water used by the car wash on a shorter day is:
C(x) = (5x3 + 7x2 - 14x + 6)

9. Write an equation of a parabola that opens to the right, has a vertex at the origin, and a focus at (7,0).

Answers

Answer:

\(x = \frac{1}{28} y^{2}\)

Step-by-step explanation:

parabola equation with vertex (0 , 0) and focus length |f| = 7

4*f*(x - h) = (y - k)²

4*7*(x-0)=(y-0)²

28x = y²

\(x = \frac{1}{28} y^{2}\)

9. Write an equation of a parabola that opens to the right, has a vertex at the origin, and a focus at

HELO PLEASE HELP ME WITH THIS I BADLY NEED THIS RN I'LL MARK AS BRA!NLIEST!! SOLVE THE VARIABLES!! IT'S OKAY IF YOU ONLY ANSWER 1 BUT PLEASE PUT THE SOLUTION!! ​

HELO PLEASE HELP ME WITH THIS I BADLY NEED THIS RN I'LL MARK AS BRA!NLIEST!! SOLVE THE VARIABLES!! IT'S

Answers

(1) The missing sides of the right triangle is r = 8√2, and t = 8.

(2) The missing sides of the right triangle cannot be determined.

(3) The missing sides of the right triangle is 60√2.

(4) The missing sides of the right triangle is y = 20, and z = 20√3.

(5) The missing sides of the right triangle is m = 2, and n = 4.

(6) The missing sides of the right triangle is p = 5√3, and O = 5.

What are the values of the missing sides of the right triangle?

The values of the missing sides of the right triangle is calculated as follows;

For question 1; the lengths of the right triangle is calculated as;

sin 45 = 8/r

r = 8/sin 45

r = 8√2

tan 45 = t/8

t = 8 tan(45)

t = 8

For question 2;

The value of g cannot be determined since we don't know if the triangle is a right triangle.

For question 3;  the lengths of the right triangle is calculated as;

Assuming the triangle is 45, 45, 90 triangle, then the value of x is calculated as;

sin 45 = 60/x

x = 60/sin 45

x = 60√2

For question 4;  the lengths of the right triangle is calculated as;

sin 30 = Y/40

Y = 40 x 0.5

Y = 20

cos 30 = z/40

z = 40 x cos30

z = 20√3

for question 5;  the lengths of the right triangle is calculated as;

tan 30 = m/2√3

m = 2√3  x tan30

m = 2

sin 30 = m/n

n = m/sin30

n = 2/0.5

n = 4

For question 6;  the lengths of the right triangle is calculated as;

sin 60 = p/10

p = 10 x sin60

p = 5√3

sin 30 = O/10

O = 10 x sin(30)

O = 5

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Suppose we want to chose 2 objects without replacement from 3 objects how many ways can this be done with choice matter and with choice does not Matter

Answers

There are 6 ways tο chοοse 2 οbjects withοut replacement frοm 3 οbjects if the chοice matters and 3 ways tο chοοse 2 οbjects withοut replacement frοm 3 οbjects if the chοice dοes nοt matter.

What is the factοrial?

The prοduct οf all pοsitive integers less than οr equal tο a given pοsitive integer and denοted by that integer and an exclamatiοn pοint. Thus, factοrial seven is written 7!, meaning 1 × 2 × 3 × 4 × 5 × 6 × 7. Factοrial zerο is defined as equal tο 1.

If the chοice matters (i.e., the οrder οf the chοsen οbjects matters), then there are 3 pοssible chοices fοr the first οbject and 2 pοssible chοices fοr the secοnd οbject.

Thus, there are 3 * 2 = 6 ways tο chοοse 2 οbjects withοut replacement frοm 3 οbjects if the chοice matters.

If the chοice dοes nοt matter (i.e., the οrder οf the chοsen οbjects dοes nοt matter), then there are 3 chοοse 2 = 3!/((3-2)!*2!) = 3 ways tο chοοse 2 οbjects withοut replacement frοm 3 οbjects if the chοice dοes nοt matter.

Therefοre,  there are 6 ways tο chοοse 2 οbjects withοut replacement frοm 3 οbjects if the chοice matters and 3 ways tο chοοse 2 οbjects withοut replacement frοm 3 οbjects if the chοice dοes nοt matter.

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replace the values of m and n to show solutions of this equation: x^2+6x-5=0

Answers

The answer is x=5/8 hope this helps

Krista designs quilts using the pattern shown. The table of values describes the shaded area of the pattern in square units, y, as a function of the length of a side,X units. Which equation describes this relationship?

Krista designs quilts using the pattern shown. The table of values describes the shaded area of the pattern

Answers

The equation which describes the relationship between the side length and shaded area of the quilt is y=0.5x²

Modeling relationship between two variables

Side length, x = 1,3,4,5,8

Shaded Area, y = 0.5, 4.5, 8, 12.5, 32

The relationship can be modeled as a quadratic function. Using a graphing calculator for the quadratic function written in the form y = ax² + bx + c

a = 0.5 ; b = 0 ; c = 0

Therefore, the quadratic function can be written as y = 0.5x²

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Krista designs quilts using the pattern shown. The table of values describes the shaded area of the pattern

Which of the following equations represents a linear function? y equals one fourth times x squared y equals two thirds times x minus 7 x = 4 3x − 5 = 18

Answers

An equation that represents a linear function include the following: B. y = 2/3(x) - 7.

What is a linear function?

In Mathematics, a linear function is a type of function whose equation is graphically represented by a straight line on the cartesian coordinate.

This ultimately implies that, a linear function has the same slope and it is typically used for uniquely mapping an input variable to an output variable, which both increases or decreases simultaneously;

y = mx + c

Where:

m represent the slope or rate of change.x and y are the points.c represent the y-intercept or initial value.

In conclusion, only the equation y = 2/3(x) - 7 represent a linear function.

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Missing information:

The question is incomplete and the complete question is shown in the attached picture.

Which of the following equations represents a linear function? y equals one fourth times x squared y

the temperatures at midday on march 1st in five cities are shown in the bar chart below. What is the difference in temperature between rome and munich?

Answers

The difference in temperature between Rome and Munich is given as follows:

6ºC.

How to obtain the difference in temperatures?

The difference in temperature between Rome and Munich is given by the subtraction of Rome's temperature by Munich's temperature.

The bar graph in the context of this problem gives the temperature for each town.

From the bar graph given by the image presented at the end of the answer, the temperatures for Rome and Munich are given as follows:

Rome: 11 ºC.Munich: 5 ºC.

Hence the difference in temperature between Rome and Munich is given as follows:

11 - 5 = 6ºC.

Missing Information

The graph is given by the image presented at the end of the answer.

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the temperatures at midday on march 1st in five cities are shown in the bar chart below. What is the

please answer within 7 minutes !!

please answer within 7 minutes !!

Answers

Step-by-step explanation:

x = by - 3/2

x + 3/2 = by

y = x/b + 3/(2b)

now compare this to the first equation :

y = 2x + 3

the system has infinite solutions, if both equations are actually identical.

and they are only identical, if b = 1/2

y = x/(1/2) + 3/(2 × 1/2) = 2x + 3

A makeup artist purchased some lipsticks and wants to wrap them individually with gift wrap. Each lipstick has a radius of 0.6 inch and a height of 2.4 inches. How many total square inches of gift wrap will the makeup artist need to wrap 4 lipsticks? Leave the answer in terms of π.

2.26π square inches
9.04π square inches
10.8π square inches
14.4π square inches

Answers

Total square inches of gift wrap will the makeup artist need to wrap 4 lipsticks is 14.4π square inches. Therefore, option D is the correct answer.

What is total surface area of cylinder?

The surface area of a cylinder refers to the total area that the cylinder's curved surface and circular bases cover. The total surface area of the cylinder includes the area of the 2 bases of the cylinder (each of which is in the shape of a circle) and the area of the curved surface.

We know that, the total surface area of a cylinder is 2πr(r + h).

Given that, lipstick has a radius of 0.6 inch and a height of 2.4 inches.

Here, surface area of a lipstick = 2×π×0.6(06+2.4)

= 2×π×0.6×3

= 3.6π

Paper needed to wrap 4 lipsticks = 3.6π×4

= 14.4π

Therefore, option D is the correct answer.

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Sara hiked down a mountain for 3 hours. Each hour, her elevation decreased by 60 meters. Compute
her change in elevation in meters relative to her starting point.

Answers

Answer:

180m

Step-by-step explanation:

If her elevation decreases by 60 m every hour, then after 3 hours her elevation will decrease by...

3*60m=180m

Solve the equation or formula for the indicated variable.
T=2rh + 2r^2 ; for h

Answers

ugh I hated learning these, they are so confusing

so we need to isolate the part that has h

so we would subtract 2r^2

T - 2r^2 = 2rh

the we would need to divide by 2r

(T - 2r^2)/2r = h

but we can simplify the left side

T/2r - 2r = h

I think that's right but not 100% sure

For what value of Θ is cotΘ undefined?



180°
270°

Answers

The value of such that = k * 180, where k is an integer, is the value at which cotangent is undefinable.

Cotangent, or cot, is one of the six standard trigonometric functions. Cotangent of an angle is defined as the ratio of the adjacent side to the opposite side of a right-angled triangle.

The value of cotangent is undefined when the denominator is zero. This implies that cotangent is undefined at angles where the value of sine is zero.

Since the sine function is periodic and has a period of 360 degrees, the values of sine repeat themselves after every 360 degrees.

For this reason, cotangent is undefined at angles such that θ = k * 180, where k is an integer.

That is, cotangent is undefined at 0°, 180°, 360°, and so on. It is also important to note that cotangent is a periodic function, and its values repeat every 180 degrees.

Therefore, cotangent is undefined at 0° + k * 180°, where k is an integer.

To summarize, the value of Θ at which cotangent is undefined is such that θ = k * 180, where k is an integer.

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P(x)=(x-2)(x-4)(x-5)

Px=(x-2)(x-4)(x+5)

Px=1/2(x-2)(x-4)(x+5)

Px=5(x-2)(x-4)(x+5)

Px=-5(x-2)(x-4)(x+5)

What are the constants?

Answers

The constants of a polynomial is the term that has no variable attached to it.

The constant term

To determine the constant, we simply multiply the constant term in each factor of the polynomial.

So, we have:

Polynomial P(x) = (x-2)(x-4)(x-5)

\(Constant = -2 \times -4 \times -5\)

\(Constant = -40\)

Hence, the constant is -40

Polynomial P(x) = (x-2)(x-4)(x+5)

\(Constant = -2 \times -4 \times 5\)

\(Constant = 40\)

Hence, the constant is 40

Polynomial P(x) =1/2(x-2)(x-4)(x+5)

\(Constant = \frac 12 \times -2 \times -4 \times 5\)

\(Constant = 20\)

Hence, the constant is 20

Polynomial P(x) = 5(x-2)(x-4)(x+5)

\(Constant = 5 \times -2 \times -4 \times 5\)

\(Constant = 200\)

Hence, the constant is 200

P(x) =-5(x-2)(x-4)(x+5)

\(Constant = -5 \times -2 \times -4 \times 5\)

\(Constant = -200\)

Hence, the constant is -200

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0.02 X 100 = 0.02 X_____=_____

Answers

Answer:

0.02 × 100 = 2

Step-by-step explanation:

move the decimal 2 steps backward according to the numbers of zeros behind the multiplier(100).

0.02 × 100 = 2

please mark brainliest

what is inequalities​

Answers

Inequalities are used in various branches of mathematics, as well as in real-world applications such as economics, physics, and social sciences, to describe relationships, make comparisons, and analyze data.

Inequalities are mathematical statements that describe a relationship between two values or expressions, indicating that one is greater than, less than, or not equal to the other. Inequalities are used to compare quantities and express their relative sizes or order.

The most common symbols used in inequalities are:

">" (greater than): indicates that the value on the left side is larger than the value on the right side.

"<" (less than): indicates that the value on the left side is smaller than the value on the right side.

"≥" (greater than or equal to): indicates that the value on the left side is greater than or equal to the value on the right side.

"≤" (less than or equal to): indicates that the value on the left side is less than or equal to the value on the right side.

"≠" (not equal to): indicates that the values on both sides are not equal.

Inequalities can be represented using variables, constants, and mathematical operations such as addition, subtraction, multiplication, and division. Solutions to inequalities are often expressed as intervals or sets of values that satisfy the given inequality.

Inequalities are used in various branches of mathematics, as well as in real-world applications such as economics, physics, and social sciences, to describe relationships, make comparisons, and analyze data.

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2.8 Combined Transformations 25 Pts

2.8 Combined Transformations 25 Pts

Answers

2a) The coordinates of the vertex are: (5,-4).

2b) The coordinates of the vertex are: (2,4).

2c) The coordinates of the vertex are: (2,-8).

3a) The vertex-form definition of the quadratic equation is given as follows: g(x) = (x + 1)² + 7.

3b) The function was shifted left one unit and up seven units.

How to obtain the coordinates of the vertex?

The coordinates of the vertex are obtained considering the transformations applied to the function, they are applied to all the ordered pairs of the function.

Hence, the coordinates of the vertex in problem 2 are given as follows:

a) shift right of 3 units, due to the rule x -> x - 3, hence the vertex is at (5,-4).b) reflection over the x-axis, due to the rule y = -g(x), hence the vertex is at (2,4).c) vertical stretch by a factor of 2, due to the rule y = 2g(x), hence the vertex is at (2,-8).

For problem 3, the vertex-form definition of the function is obtained completing the squares, as follows:

x² + 2x + 8 = (x + 1)² + 7.

Which means that the transformations relative to the standard quadratic equation y = x² are given as follows:

x -> (x + 1): shift left of one unit.y -> y + 7: shift up of seven units.

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During halftime of a football game, a sling shot launches T-shirts at the crowd A T-shirt is launched from a height of 6 feet with an initial upward velocity of 72 feet per second Use the
equation h(t) = -16 +72t+6, where t is time in seconds and h(t) is height. How long will it take the T-shirt to reach its maximum height? What is the maximum height?

Answers

Answer:

Hope this helps ;)

Step-by-step explanation:

To find the time it takes the T-shirt to reach its maximum height, we need to find the value of t when the velocity of the T-shirt is zero, because at this point the T-shirt has reached its maximum height and starts falling back down. We can find the velocity of the T-shirt by taking the derivative of the height equation with respect to time:

v(t) = h'(t) = 72

The velocity of the T-shirt is a constant 72 feet per second, so it will never reach a velocity of zero and will never reach its maximum height. The T-shirt will keep going up indefinitely.

If the problem had specified that the T-shirt was launched with an initial upward velocity of -72 feet per second (meaning it was launched downward), then we could have found the time it takes the T-shirt to reach its maximum height by setting v(t) = 0 and solving for t. In this case, we would find that t = 1, so it would take the T-shirt 1 second to reach its maximum height. The maximum height would be h(1) = -16 + 72(1) + 6 = 62 feet.

Find the distance between the points A(-4, -3) and B(-8, 7). Round your answers to the nearest tenth.

Answers

Answer:

distance = 10.8

Step-by-step explanation:

the distance between 2 points is the Hypotenuse of the right angled triangle of the x and y coordinate differences.

so, Pythagoras is used.

c² = a² + b²

c = the Hypotenuse (the side of the triangle being opposite to the 90 degree angle).

x- difference : -4 - -8 = +4

y- difference : -3 - 7 = -10

c² = +4² + (-10)² = 16 + 100 = 116

c = sqrt(116) = 10.8

160 students went on a field trip. Five buses were filled and 15 students traveled in cars. How many students were in each bus?

Each bus had ____ students.

Answers

each bus has 29 students.

HELP URGENT WILL GIVE
BRAINLIEST!!!
Elsa is putting money into a
savings account. She starts
with $550 in the savings
account, and each week she
adds $70.
Let S represent the total
amount of money in the
savings account (in dollars),
and let W represent the
number of weeks Elsa has
been adding money. Write
an equation relating S to W
Then use this equation to
find the total amount of
money in the savings
account after 11 weeks.

Equation:__

Total amount of money after
11 weeks:

$__

Answers

Answer:

S x W + 550 = answer

Step-by-step explanation:

eh u dont need to know, yw

Answer:

Step-by-step explanation:

S= total amount in savings acc.
W= # of weeks
You have 550 in your acc and your adding 70 every week?
S= 550+70w

Then for 11 weeks: Equation- S=550+70*11

70*11=770

S= 550+770 - S= 1320

Total after 11 weeks is 1320

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