Every month, Theresa sets aside $410.60 of her paycheck to use as spending money. This month, she plans to use 2/5 of her spending money for groceries. How much money would Theresa have this month to spend on items other than groceries?

Answer:

y < 3x + 2

y> -2x + 2  The symbol should be > with a line under it to show greater than or equal to

Step-by-step explanation:

The answers are -0.5, 2.2, 3.8, and 9.0

We need to evaluate the expression 3.8 + 0 + y for the given values of y.

Let x = 3.8 + 0 + y

The values of y are -4.3, -1.6, 0, and 5.2

Let's substitute the value of y in the expression and calculate the values of x.

Refer to the attached image for the values of the expression corresponding to the values of y.

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Answer:

-0.5, 2.2, 3.8, and 9.0

Step-by-step explanation:

All the values of x that solve the given system of equations are as follows:

x = 17/2.

A system of equations is when multiple variables are related by equations, which are solved to find the values of each variable. Usually, these relations are linear, but they may also be quadratic, as is the case in this problem.

For this problem, we are given two equations, as follows:

From the second equation, we have that:

x = 9 - 3y.

Replacing in the first, we have that:

(9 - 3y)² - 9y² = 72.

9y² - 54y + 81 = 72.

54y = 9.

y = 9/54

y = 1/6, as 9/9 = 1, 54/9 = 6.

Hence the solution for x of the system of equations is found by replacement, as follows:

x = 9 - 3y = 9 - 3/6 = 9 - 1/2 = 18/2 - 1/2 = 17/2.

The solution is x = 17/2.

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Answer:

1/5 needs to be 20 words long

Answer:

maybe if you learn you will know

Step-by-step explanation:

Step-by-step explanation:

٨-٥٢.....................

At (4.472 , 4.236) in the first quadrant , the line with equation y = 0.5 x + 2 intersect the circle with radius 5 and center (0, 2) .

The equation of circle with center (h,k) and radius r can be written as

(x-h)²+(y-k)²=r²

In the given question

the center of the circle is (0,2) and the radius of the circle is 5 .

So the equation of circle become

(x-0)²+(y-2)²=5²

x²+(y-2)²=25     ...(i)

It is given that y=0.5x+2 intersects the circle

y = 0.5x+2

Rewriting the equation we get

y-2=0.5x

(y-2)=0.5x

x=(y-2)/0.5

x = 2(y-2)        ...(as 0.5=1/2)       ....(ii)

Squaring both sides

x² = (2(y-2))²

x² = 2²(y-2)²

x² = 4(y-2)²     ...(iii)

Substituting the value of equation (iii) in equation (i) we get ,

4(y-2)²+(y-2)²=25

5(y-2)²=25

(y-2)²=25/5

(y-2)²=5

Taking Square root both the sides , we get

√(y-2)²=√5

y-2 = √5

y=(√5)+2

y=2.236+2

y=4.236

Substituting the value of y in (ii) we get

x=2(4.236-2)

x=2*2.236

x=4.472

Therefore ,  the circle with radius 5 and center (0, 2) will intersect  the line with equation y = 0.5 x + 2  in the first quadrant at (4.472 , 4.236).

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THE ANSWER IS IN THE PHOTO

The amount that the bidder needs to put into a kitty for the other bidders to be compensated will be $57600.

It should be noted that 5 people can claim joint ownership of an item and intend to divide it by the Method of Sealed Bids and the winner offers a bid of $72,000.

Therefore, the fair share will be:

= Bids / Number of people

= 72000 / 5

= 14400

Therefore, the amount that the bidder needs to put into a kitty for the other bidders to be compensated will be:

= $72000 - $14400

= $57600

Therefore, the amount that the bidder needs to put into a kitty for the other bidders to be compensated will be $57600.

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Answer: 90 degrees

Step-by-step explanation:

Dilations preserve angle measure.

Answer:

-8756 %

Step-by-step explanation:

Because 5 is a strong number

Answer:

R 19734.32

Step-by-step explanation:

If an amount P is deposited at R% interest compounded annually for n years, the amount at the end of n years is given by the formula

[tex]P = P(1 + r)^t[/tex]

r = R/100

Note

Interest rate 8% = 8/100 =0.08 for computation

Interest rate 9% = 8/100 =0.09 for computation

Since the interest rate changes after 3 years, the first thing to do is to find out how much the value is after 3 years

[tex]V(3 years) = 6000(1 + 0.08)^3[/tex] = 6000 x1.08³ = 6000 x 1.259712 = 7558.27

After 3rd year interest changes to 9%(0..09) but an additional amount is deposited

Let's find the value after the 4th year at 9% compounded annually using the general formula with r = 0.09 and t =1

V (after 4th year) = 7558.27(1.09)¹ = 7558.27 x 1.09 = 8238.51

We are depositing 7000 at the end of the 4th year so the principal becomes 8238.51 + 7000 = 15,238.51

This new amount accrues interest at 9% for 3 more years (7-4)

So value of savings at end of 7th year is

V = 15238.51(1+0.09)³ = 15238.51 x 1.259712 = 19734.32

Answer:

R19734.32

Step-by-step explanation:

Annual Compound Interest Formula

[tex]\large \text{$ \sf A=P\left(1+r\right)^{t} $}[/tex]

where:

Given:

Substitute the given values into the formula and solve for A:

[tex]\implies \sf A=6000(1+0.08)^3[/tex]

[tex]\implies \sf A=6000(1.08)^3[/tex]

[tex]\implies \sf A=6000(1.259712)[/tex]

[tex]\implies \sf A=7558.272[/tex]

Therefore, the amount in the account after 3 years was R7558.272.

The interest rate changed to 9%.

Given:

Substitute the given values into the formula and solve for A:

[tex]\implies \sf A=7558.272(1+0.09)^1[/tex]

[tex]\implies \sf A=7558.272(1.09)[/tex]

[tex]\implies \sf A=8238.51648[/tex]

Therefore, the value of savings at the end of the 4th year was R8238.51648.

After four years, R7000 was added to the account.

Given:

Substitute the given values into the formula and solve for A:

[tex]\implies \sf A=15238.21648(1+0.09)^3[/tex]

[tex]\implies \sf A=15238.21648(1.09)^3[/tex]

[tex]\implies \sf A=15238.21648(1.295029)[/tex]

[tex]\implies \sf A=19734.3207...[/tex]

Therefore, the value of the savings at the end of the seventh year is R19734.32.

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Answer:

5x+10

Step-by-step explanation:

[tex](f \circ g)(x)=f(g(x)) \\ \\ =f(-5x-6) \\ \\ =-(-5x-6)+4 \\ \\ =5x+6+4 \\ \\ =5x+10[/tex]

The values of all the variables are:

Given equations:

To find the values of x, y, w, and z:

Substitute (w = -3) in z + w = 2:

Substitute (w = -3) and (z = 5) in 3y + 18z + 6w = 24:

Substitute (y = - 16), (w = -3) and (z = 5) in -4x - 8y - 2z - 6w = 5

Therefore, the values of all the variables are:

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Answer:

1/15

Step-by-step explanation:

3/10 x 2/9 = /90  Dived the top and bottom by 6 and you will get 1/15.

The first time there were 10 marbles and she wanted red.  There were only 3 red so the chances of getting a red is 3/10.  Now she only has 9 marbles left.  She was a blue so her chances are 2/9.

[16] f(-3) = -5

      #17 is asking us to find what the function equals when x is equal to -3. We will find x = -3 on the graph, then find what y equals.

[17] f(4) = 0

      #17 is quite similar, it is asking us to find what the function equals when x is equal to 4. We will find x = 4 on the graph, then find what y equals.

You asked in the comments for #16 and #17, I hope this helps.

Answer:

x = 21

Step-by-step explanation:

Adding numbers:

3x+ 18 + 4x + 15 = 180

3x + 33 + 4x = 180

Combine Like terms:

3x + 33 + 4x = 180

7x + 33 = 180

Subtract:

7x + 33 - 33 = 180-33

7x = 147

Divide:

An equation of the function in standard form is equal to -x²/4 + 1 = 0.

A quadratic function can be defined as a mathematical expression (equation) that can be used to define and represent the relationship that exists between two or more variable on a graph.

In Mathematics, the standard form of a quadratic equation is given by;

ax² + bx + c = 0

y = f(x) = ax² + bx + c

Next, we would formulate a system of equations from the data contained in the table above:

-3 = a(-4)² + b(-4) + c  ⇒ -3 = 16a - 4b + c      .......equation 1.

0 = a(-2)² + b(-2) + c  ⇒   0 = 4a - 2b + c      .......equation 2.

1 = a(0)² + b(0) + c  ⇒   1 = c                            .......equation 3.

Substituting the value of c into eqn. 1 and eqn. 2, we have:

-4 = 16a - 4b        .......equation 4.

-1 = 4a - 2b          .......equation 5.

Multiplying eqn. 5 by 2 and solving simultaneously, we have:

-4 = 16a - 4b

-2 = 8a - 4b

-2 = 8a

a = -2/8

a = -1/4  

For the value of b, we have:

-1 = 4a - 2b

-1 = 4(-1/4) - 2b

-1 = -1 - 2b

2b = 0

b = 0

Substituting the values of a, b and c into the standard form of a quadratic equation:

ax² + bx + c = 0

-1/4x² + (0)x + 1 = 0

-x²/4 + 1 = 0

Check:

When x = 2, we have:

-x²/4 + 1 = 0

-2²/4 + 1 = 0

-4/4 + 1 = 0

-1 + 1 = 0

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(0,0) because that is the center

Answer:

your answer is 55 as shown by above photo ^^

Answer:

55

Step-by-step explanation:

Answer:

35 yd

Step-by-step explanation:

Answer:

Answer:

  $2780

Step-by-step explanation:

Given an income tax of 10% of the first $7000 and 16% of all after that, you want the tax on $20,000.

Manuel's income is more than $7000, so the tax is computed in two parts.

First $7000

The tax on the first $7000 of income is 10%:

  tax = $7000 × 0.10 = $700

Amount Over $7000

The amount over $7000 is ...

  $20,000 -7,000 = $13,000

The tax on that amount is 16%:

  tax = $13,000 × 0.16 = $2080

Total tax due

The tax Manuel must pay is the total of these two amounts:

  $700 +2080 = $2780

Manuel must pay $2780 in income tax for last year.

We need 65 ml of 50% mixture to obtain the desired solution.

Here, we need to make a 25% alcohol solution by mixing some amount of 50% alcohol mixture with 325 mL of a 20% alcohol mixture.

Let the amount of 50% alcohol solution be x

The the quantity of alcohol in 50% alcohol solution = 50% of x

= 0.5x

Similarly the the quantity of alcohol in 20% alcohol solution = 20% of 325

= 65ml

The total quantity of 25% alcohol solution = (325 + x) ml

Thus, the the quantity of alcohol in 25% alcohol solution = 25% of (325 + x)

= 0.25 (325 + x)

= 81.25 + 0.25x

Thus, we can form the following equation-

0.5x + 65 = 81.25 + 0.25x

0.5x - 0.25x = 81.25 - 65

0.25x = 16.25

x = 16.25/ 0.25

x = 65

Thus, we need 65 ml of 50% mixture to obtain the desired solution.

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The  option which represents the situation described if a is the number of shares of Stock X purchased and b is the number of shares of Stock Y purchased is:

D. 22a + 35b ≤ 4,500

a + b ≥ 100

a ≥ 20

b ≥ 15

What does at least and no more than mean in this instance?

At least is interpreted in inequalities as greater than or equals to whereas "no more than" implies that it cannot be greater, hence, can be less than or equals to, as a result, the following relationships are determined:

a≥20(the least number of X shares is a, which is 20)

b≥ 15(the least number of Y shares is a, which is 15)

total amount spent on X=22*a=22a

total amount spent  on Y=35*b=35b

maximum amount to invest=4500(less than or equals to)

22a+35b≤ 4500

sum of X and Y shares altogether(least)=100

a+b≥100

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Full question:

Heinrich must buy at least 100 shares of stock for his portfolio. The shares he buys will be from Stock X, which costs $22 per share and Stock Y, which costs $35 per share. His budget for buying stock is no more than $4,500. He must buy at least 20 shares of Stock X and 15 shares of Stock Y. Which of the following represents the situation described if a is the number of shares of Stock X purchased and b is the number of shares of Stock Y purchased?

A. 22a + 35b ≤ 4,500

a + b ≥ 100

a ≤ 20

b ≤ 15

B. 22a + 35b ≤ 4,500

a + b ≤ 100

a ≤ 20

b ≤ 15

C. 22a + 35b ≤ 4,500

a + b ≤ 100

a ≥ 20

b ≥ 15

D. 22a + 35b ≤ 4,500

a + b ≥ 100

a ≥ 20

b ≥ 15

Answer:

Step-by-step explanation:

y = f(x) = 3x -2

When x = -4,

y = 3(-4) -2 = -12-2 = -14

When x = 2,

y = 3(2) -2 = 6-2 = 4

When x = 3,

y = 3(3) -2 = 9-2 = 7

The relationship between distances biked and distances run is

D(bike) = 2 × D(run)

Here, we have been shown that when distance run is, lets say x then distance run is 2x

When distance run is 2 then distance biked is 4, twice as distance run.

Again in distance run 3[tex]\frac{1}{2}[/tex], distance biked is 7, so this proves that

D(bike) = 2 × D(run)

The measurement of distance between two objects or points can be quantitative or occasionally qualitative. Distance in physics or common language can refer to a physical length or an assumption based on other factors (e.g. "two counties over").

Since spatial thinking is a rich source of conceptual metaphors in human thought, the term is also frequently used metaphorically to denote a measure of the degree of separation or the statistical distance between two similar objects (such as edit distance between strings of text or statistical distance between probability distributions) (as exemplified by distance between people in a social network).

A metric space is a mathematical concept that is used to define the majority of these conceptions of distance, both literal and figurative.

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