add the polynomials

3x^5-2x^3+4x
+ 4x^6-5x^5+4x^3-x^2

Answer:

A. (x , y) = ( 1,  4) is the SOLUTION of the given system of equations.

Step-by-step explanation:

Here, the given set of equations is:

2 y + 5x = 13  ....... (1)

2y - 3x = 5    ...... (2)

Now, to solve this question by SUBSTITUTION:

From (1), we get:

2 y + 5x = 13   ⇒   2 y = 13 - 5 x

or, [tex]y = \frac{13 - 5x}{2}[/tex]

Put this value of y in (2) . We get

[tex]2y - 3x = 5  \implies 2\times\frac{(13-5x)}{2}  - 3x = 5\\\implies 13 - 5 x - 3x = 5\\\implies- 8x  = -8\\\implies x = 1[/tex]

Now, x = 1, put this value of x  in (1),

2 y + 5x = 13     ⇒ 2y + 5(1) = 13

or, 2 y = 13- 5 = 8

or, y = 8 / 2  = 4,   ⇒ y = 4

Hence, x  = 1, y = 4 is the SOLUTION of the given system of equations.

Ms. Brown has been reading for 18 weeks so far.

To find out how many weeks Ms. Brown has been reading so far, we can set up a proportion based on the rate at which she reads books.

Ms. Brown reads 2 books every 3 weeks, so we can write this as the ratio:

[tex]\[ \frac{2 \text{ books}}{3 \text{ weeks}} \][/tex]

Now, we can set up a proportion to find out how many weeks she has been reading to reach a total of 12 books.

Let ( x) represent the number of weeks she has been reading so far. So, we set up the proportion:

[tex]\[ \frac{2 \text{ books}}{3 \text{ weeks}} = \frac{12 \text{ books}}{x \text{ weeks}} \][/tex]

Now, we can solve for ( x ) by cross-multiplying:

[tex]\[ 2 \times x = 3 \times 12 \][/tex]

[tex]\[ 2x = 36 \][/tex]

Divide both sides by 2 to solve for ( x ):

[tex]\[ x = \frac{36}{2} \][/tex]

[tex]\[ x = 18 \][/tex]

So, Ms. Brown has been reading for 18 weeks so far.

complete question given below:

Ms. Brown is reading 2 books every 3 weeks. She has read 12 books so tar. How many weeks has she been reading so far?

Answer:

AD=23

Step-by-step explanation:

18+5=23      combined factors

Answer:

AD=23

Step-by-step explanation:

Answer:

24:36:72

Step-by-step explanation:

multiply 2,3,and 6 by 12 and you got the ratio 24:36:72, which adds to 132

Answer:

y = 0.5x

Step-by-step explanation:

Given that x and y vary directly then the equation relating them is

y = kx ← k is the constant of variation

To find k use the condition x = 1, y = 0.5

k = [tex]\frac{y}{x}[/tex] = [tex]\frac{0.5}{1}[/tex] = 0.5

y = 0.5x ← equation of variation

Answer: 0.5

Step-by-step explanation:

Answer:

The equation of the line in point slope form is equal to

[tex](y-4)=\frac{4}{3}(x+2)[/tex]

The graph in the attached figure

Step-by-step explanation:

we know that

The equation of a line in point-slope form is equal to

[tex]y-y1=m(x-x1)[/tex]

we have

[tex]3y-12=4x+8[/tex]

Convert to point slope form

Factor 3 left side and factor 4 right side

[tex]3(y-4)=4(x+2)[/tex]

Divide by 3 both sides

[tex](y-4)=\frac{4}{3}(x+2)[/tex]

In this equation

the point is (-2,4)

the slope is [tex]m=\frac{4}{3}[/tex]

using a graphing tool

The graph in the attached figure

This question is incomplete, here is the complete question:

On a recent day, 8 euros were worth $9 and 24 euros were worth $27. Write an equation of the form y = kx to show the relationship between the number of euros and the value in dollars.

The equation that represents the relationship between the number of euros and the value in dollars is y = 1.125 x

Step-by-step explanation:

On a resent day;

We need to write an equation of the form y = kx to show the relationship between the number of euros and the value in dollars

∵ The form of the equation is y = kx, where x is the number of

   euros and y is the value in dollars

∵  8 euros were worth $9

∴ (8 , 9) is an ordered pair belong to the equation

∵ 24 euros were worth $27

∴ (24 , 27) is another ordered pair belong to the equation

To find k substitute x and y in the equation by the coordinates of one of these two points

∵ x = 8 and y = 9

∵ y = kx

∴ 9 = 8k

- Divide both sides by 8

∴ 1.125 = k

- Substitute the value of k in the equation

∴ y = 1.125 x

To check the equation substitute x by the x coordinate of the 2nd point if it gives the same value of the y-coordinate of the point then the equation is true

∵ x = 24

∵ y = 1.125 x

∴ y = 1.125(24)

∴ y = 27 the same value of the y-coordinate of the point

∴ The equation is true

The equation that represents the relationship between the number of euros and the value in dollars is y = 1.125 x

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Answer:

35.33 km/h.

Step-by-step explanation:

Given: Distance= 212 km.

           Times= 6 hours

Now, finding unit rate (speed) for the situation.

Formula; Speed= [tex]\frac{Distance}{time}[/tex]

Speed (rate)= [tex]\frac{212}{6} = 35.3333\ km/h[/tex]

Speed (rate)= 35.3333≅ 35.33 km/h (nearest hundredth).

∴ Rate of the unit is 35.33 km/h

Answer:

C. 1/2

Step-by-step explanation:

SOHCAHTOA

Cosine is adjacent over hypotenuse. For the angle that is 60 the adjacent is 1 and the hypotenuse is 2.

Answer:

60 minutes

Step-by-step explanation:

There are 3 feet in a yard, so a football field is 300 feet long.

Dive 300 by 5 to find the total minutes.

300 / 5 = 60

Answer:

1 hour

Step-by-step explanation:

100 yards = 300 feet

300 / 5 = 60

60 min = 1 hour

Answer: It would take 1 hour for sloths to walk across a 100-yard football field.

Answer:

y=125x+75

Step-by-step explanation:

Y= 125x+B

700=125(5)+B

700=625+B

700-625=625-625+B

75=B

The initial value, or deposit, for the vacation home is $75. The rate of change, or the cost per day, is $125. This constitutes a linear relationship where the total cost increases by a constant daily fee as the number of rental days increases.

In this problem, the total cost of the vacation home equals the deposit plus (daily rental fee * number of days). The total cost came out to be $700 when the family rented the home for 5 days. Given that the daily rental rate is $125, that means that the cost of the rental alone was $125 * 5 = $625.

Subtract the cost of the rental from the total cost to find the deposit: $700 - $625 = $75. Therefore, the initial value is $75, which represents the deposit.

The rate of change, which is the cost per day, is $125. This means for every additional day the family rents the vacation home, they are charged an additional $125. So the relationship is linear because the total cost increases by a constant rate - the daily fee - as the number of days increases.

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This solution uses the formula for the area of a triangle together with the Pythagorean theorem to determine the length of the missing side in a right triangle. Assuming one side and the area of the triangle are given, the step involves rearranging the area formula to solve for the missing side. The Pythagorean theorem guarantees the accuracy of this method.

The subject of this question is Mathematics. The grade of this question is Middle School. Based on the information given, we are asked to find a missing side of a triangle with a given area.

Since this is a right triangle, we can use the Pythagorean theorem, which states that the square of the length of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the lengths of the other two sides. This can be written as x² + y² = h².

Assuming we know one side and the area of the triangle, we can use the formula for the area of a triangle, which is 1/2 * base * height = 50. If we know one of the other sides, let's say 'y', we can solve for the other side 'x' by rearranging this formula to solve for 'x', then substituting the known values.

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Answer:

40

Step-by-step explanation:

if 3/8 equals 15 that means 1/8 equals 5 because 15/3=5. now if we multiply 5 by 8 then we get 40 years

If jay has been working for his current company for 15 years, then his age is 40 years.

A fraction is written in the form of p/q, where q ≠ 0.

Fractions are of two types they are proper fractions in which the numerator is smaller than the denominator and improper fractions where the numerator is greater than the denominator.

Given, jay spent 3/8ths of his life working for a company and he has been working for his current company for 15 years.

Assuming Jay's age to be x years.

∴ (3/8) of x is 15 years.

(3/8)x = 15.

x = 15×(8/3).

x = 40.

So, Jay's age is 40 years.

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The answer is $11200.

Answer:

$11,200 or its D

Step-by-step explanation:

got it right on edge

Good evening ,

Step-by-step explanation:

we know that, x-1 = (-1)×(1-x) and 1-x=(-1)×(x-1)

then each of 1-x and x-1 is a multiple of the other one,

if x>1 then x-1>0 and 1-x<0 then x-1>1-x

therefore in this case the least common multiple of x-1 and 1-x is x-1.

if x<1 then x-1<0 and 1-x>0 Then 1-x>x-1

therefore in this case the least common multiple of x-1 and 1-x is 1-x.

:)

Answer:

k = 4

Step-by-step explanation:

Given that a varies directly as b then the equation relating them is

a = kb ← k is the constant of variation

To find k use the condition a = 8 when b = 2

k = [tex]\frac{a}{b}[/tex] = [tex]\frac{8}{2}[/tex] = 4

Answer:

K = 4

Step-by-step explanation:

Given that varies a directly as b then the equation relating them is

Simply implies that a is directly proportional to b, that is increase in a will cause increase in, and decrease in a will cause decrease in b, and vice versa, where k remains constant.

a α b

a = kb, where k is constant

To find k use the condition a = 8 when b = 2, we make k the subject of the formular

K = a/b

K = 8/2

K = 4

Answer:

The answer is 34

To solve this, percentage calculations were used. The geologist visited 6 volcanoes in California, which is 15% of 40, and the remaining 34 in Alaska.

The question requires us to calculate the number of volcanoes the geologist visited in California and Alaska. The total number of volcanoes visited is 40, and 15% are in California. To find the number of volcanoes in each state, we employ basic percentage calculations.

First, to find the number of volcanoes in California, we multiply the total number by 15% (or 0.15):
Number of volcanoes in California = 40 * 0.15 = 6.

To find the number of volcanoes in Alaska, we subtract the number of volcanoes in California from the total:
Number of volcanoes in Alaska = 40 - 6 = 34.

Therefore, the geologist visits 6 volcanoes in California and 34 volcanoes in Alaska.

Final answer:

Juanita has 18 magazines and wants to divide them into 3 equal piles. By dividing the total number of magazines (18) by the number of piles (3), we find that there will be 6 magazines in each pile.

Explanation:

The question asked by the student is a simple division problem in which Juanita needs to organize her magazines into 3 equal piles, and she has a total of 18 magazines. To find out how many magazines are in each pile, we divide the total number of magazines by the number of piles.

To solve this, we perform the following calculation:

So, the calculation is 18 \/ 3 = 6 magazines per pile.

Answer:

$79.20

Step-by-step explanation:

fixed charged of $19 x 4 months = $76.00

additional charged of $0.04 x 20 = $0.80 x 4 months = $3.20

Therefore, $76.00 + $3.20 = $79.20

Answer:

f=10

Step-by-step explanation:

Answer:

88°

Step-by-step explanation:

Alternate interior angles are congruent. So, set the angles equal to each other and solve for x.

2x + 30 = 3x + 1

x = 29

So, ∠5 = 3x + 1 = 3(29) + 1 = 88°

Answer:

94

Step-by-step explanation:

had question on usa test prep

Answer:

The two numbers are -365 and -1825.

Step-by-step explanation:

5x=y

x-y=1460

--------------

x-5x=1460

-4x=1460

x=1460/-4

x=-365

-365-y=1460

y=-365-1460=-1825

Answer:

[tex]y\leq -\frac{1}{3}x+1[/tex]

Step-by-step explanation:

Given:

From the graph, the x and y intercepts are at the points (3, 0) and (0, 1) respectively.

Now, for a line with two points [tex](x_1,y_1)\ and\ (x_2,y_2)[/tex], the slope is given as:

[tex]m=\frac{y_2-y_1}{x_2-x_1}[/tex]

Here, [tex](x_1,y_1)=(3,0)\ and\ (x_2,y_2)=(0,1)[/tex]. Therefore,

[tex]m=\frac{1-0}{0-3}=-\frac{1}{3}[/tex]

Now, y-intercept is [tex]b=1[/tex]

Therefore, the standard form of a line is of the form: [tex]y=mx+b[/tex]. So, the equation of the line on the graph is:

[tex]y=-\frac{1}{3}x+1[/tex]

Now, from the graph, the region is below the line including all the points on the line. Therefore, the inequality used is less than or equal to. This gives,

[tex]y\leq -\frac{1}{3}x+1[/tex]

Answer:

y-1=-x+2

Step-by-step explanation:

m=-1

y-1=-1(x-2)

y-1=-x+2

Answer:

C. Both x is a function of y and y is a function of x

Step-by-step explanation:

A function is a relationship which assigns to each input (from the domain) value, a unique output (from the range).

y is a function of x means x is from domain, y is from range

x is a function of y means y is from domain, x is from range

1. Given [tex]y=16-x[/tex]

y is a function of x because for each x there is exactly one y corresponding to this x.

2. Rewrite [tex]y=16-x[/tex] expressing x in terms of y:

[tex]y-16=-x\\ \\-x=y-16\\ \\x=16-y[/tex]

x is a function of y because for each y there is exactly one x corresponding to this x.

Final answer:

In the equation y = 16 - x, both x and y are functions of each other since each variable can be expressed as having a unique output for each input of the other. The correct answer is c. both x is a function of y and y is a function of x.

Explanation:

To determine which statement is true regarding the equation y = 16 - x, we need to understand the concept of a function. A function, in mathematical terms, is a relationship between two sets that assigns to each element of the first set exactly one element of the second set. In simpler terms, for a variable to be a function of another variable, each input should give us exactly one output. This leads us to the vertical line test, which is a visual way to determine if a curve is a graph of a function of x.

Looking at the given equation, y is expressed in terms of x, implying that for each value of x, there is exactly one value of y. This satisfies the definition of a function, so y is a function of x. Conversely, if we solve the equation for x, we get x = 16 - y, which similarly means that for each value of y, there is exactly one value of x, so x is also a function of y.

Given these points, the correct answer is c. both x is a function of y and y is a function of x. This is because each variable can be expressed as having a unique output for each input of the other variable, therefore both variables are functions of each other.

Answer:43%

Step-by-step explanation:

just finished test

Answer:

Step-by-step explanation:

The events describe is about picking a card, and placing it back into the deck. This means that the total number of event won't change in each trial.

We know that there are 4 queens of 52 cards. So, the probability of picking a card and be a queen is

[tex]P=\frac{4}{52}=\frac{1}{13}[/tex]

However, in this case, we have to apply the experimental probability definition, because we have several attempts. This experimental probability is defined as the ratio between the time the event occurs (4) and the total number of trials (7). That is

[tex]P_{exp}=\frac{4}{7}=0.57 \ (or \ 57\%)[/tex]

Therefore, the right answer is C.

Answer:

a=-2 and b=-2

Step-by-step explanation:

So I just used Elimination I made the top part the same as b then I just subtract and did some other stuff,hope the pic helps

Answer:

9/20 yes, 4/15 not. See below

Step-by-step explanation:

Pick 9/20 and multiply numerator and denominator by 5:

9/20 = 45/100

We know that if we divide a number by 100 we need to move the coma as two places left, so:

9/20 = 45/100 = 0.45

And this is a terminal decimal as we know where it ends.

On the other hand if we pick 4/15 let try to divide it (here I will do it 'manually'):

4 |_ 15

we can divide 4 by 15, so we use 40 and begin with a comma

40 |_ 15

      0.

15 enters 2 times in 40 with a rest of 10, so:

40 |_ 15

  30  0.2

  100

100 divided by 15 is 6 and we have 10 as rest again, and again and again...

40 |_ 15

  30  0.266.....

  100

    100

      ....

So, we will have 0.266666666666666 infinitely. The decimal for 4/15 is non terminating and is 0.26666666666666666...