Jonas earns $9 per hour as a lifeguard and $11 per hour as a swim instructor. Last week he worked a total of 40 hours at the pool, 10 of which were teaching swim lessons. Which expression and value show the total amount of money that he earned last week? 9 × 10 + 11 × 30; $420 9 × 10 + 11 × 30; $210 9 × 30 + 11 × 10; $419 9 × 30 + 11 × 10; $380

Answer:

350 people

Step-by-step explanation:

you would cross multiply

98/100 times 343/x

98x = 34300

34300/98= 350

So the answer is 350 people

Answer:

Center = (0, -4)

Radius = [tex]\sqrt{7}[/tex] units

Step-by-step explanation:

We are given;

The equation of a circle;

[tex]x^2+y^2+4y=3[/tex]

We are required to determine the radius and the center of the circle;

To do this we are going to use completing square method;

[tex]x^2+y^2+4y=3[/tex]

Since we don't have the x term then;

[tex]x^2+ox+y^2+4y=3[/tex]

We add the square of half the coefficients of x and y on both sides of the equation;

That is;

[tex]x^2+0x+(0^2)+y^2+4y + (2^2)=3+0+(2^2)[/tex]

We get;

[tex]x^2+0x+(0^2)+y^2+4y + (2^2)=7[/tex]

Taking the squares;

[tex](x+0)^2+(y+4)^2=7[/tex]

But we know when the equation of a circle is written in the form of;

[tex](x-a)^2+(y-b)^2=r^2[/tex], where (a,b) is the center and r is the radius of the circle.

Thus, in this case;

[tex](x+0)^2+(y+4)^2=7[/tex]

Center = (0, -4)

Radius = [tex]\sqrt{7}[/tex] units

Answer:

The Correct option is C ) 25

Therefore the value of x is 25 when y =40.

Step-by-step explanation:

Given:

Variable 'y' is directly proportional to the variable 'x'.

[tex]\therefore y=kx[/tex]     ......Direct Variation

Where,

k = Constant of proportionality

To Find:

value of x = ? when y = 40

Solution:

First we need to find Constant of proportionality

When x = 20 and y = 32

Substituting the values we get

[tex]32=k\times 20\\k=\dfrac{32}{20}=1.6\\\\k=1.6[/tex]

Now when k =1.6 , y = 40 then x will be

[tex]40=1.6\times x\\\\x=\dfrac{40}{1.6}=25\\\\x=25[/tex]

Therefore the value of x is 25 when y =40.

Final answer:

The value of x when y is 40 is C) 25.

Explanation:

The variable y is directly proportional to the variable x.

This means that as x increases or decreases, y does so at a constant rate.

This relationship can be written as y = kx, where k is the constant of proportionality.

To find k, we use the information that y = 32 when x = 20, leading to the equation 32 = k * 20.

Solving this gives us k = 32 / 20 or k = 1.6.

With the constant k known, we can find the value of x when y = 40 by setting up the equation 40 = 1.6x.

Dividing both sides by 1.6 gives us x = 40 / 1.6, which results in x = 25.

Therefore, the correct answer is C) 25.

Answer:

70 miles

Step-by-step explanation:

30 minn+30 min=1 hour/60 min

30 min=35 miles

add the minutes together then add the miles together witch will give you

1 hour/60 min=70 miles

Answer:

70 miles

1 hour= 60 minutes

[tex]60 \div 30 = 2[/tex]

Take 35 and multiply it by your first equations sum

[tex]35 \times 2 = [/tex]

=70

Answer:

A) -2/3

Step-by-step explanation:

We are given the equation;

5 - 2m - 3m² = 0

We are required to get the sum of the roots of the equation;

Rearranging the equation;

3m² + 2m - 5 = 0

product = -15 m²

sum = 2 m

Terms = 5m and -3m

Therefore;

3m² + 5m - 3m - 5 = 0

Factorizing by pairing

m(3m + 5) - 1 (3m + 5) = 0

Thus;

(m - 1) (3m + 5) = 0

This means;

m - 1 = 0 or 3m + 5 =0

Hence; the roots of the equation are;

m = 1 or m = -5/3

Thus, the sum of the roots is;

= 1 + -5/3

= -2/3

Hence, the sum of the roots of the equation is -2/3

Perimeter of a rectangle = 6x + 8

Solution:

Given area of a rectangle = [tex]2x^2+7x+3[/tex]

Let us first factor the given polynomial.

[tex]2x^2+7x+3=2x^2+x+6x+3[/tex]

                    [tex]=(2x^2+x)+(6x+3)[/tex]

Taking out common terms in the above expression

                    [tex]=x(2x+1)+3(2x+1)[/tex]

Taking out common term [tex]2x+1[/tex] in the above expression

                    [tex]=(2x+1)(x+3)[/tex]

[tex]2x^2+7x+3=(2x+1)(x+3)[/tex]

Area of a rectangle = l × b

Therefore, [tex]l=2x+1[/tex] and [tex]b=x+3[/tex]

Perimeter of a rectangle = 2(l + b)

                                         [tex]=2[(2x+1)+(x+3)][/tex]

                                         [tex]=2(2x+1+x+3)[/tex]

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

                                         [tex]=6x+8[/tex]

The answer is same if you take l = x + 3 and b = 2x + 1.

Hence, perimeter of a rectangle = 6x + 8.

Answer:

Total cost of the meal is $ 27.32.

Step-by-step explanation:

Given:

Cost of the meal = $25.30

Tax levied on it = 8%

We have to find the total cost.

Total cost of the meal = Summation of cost of the meal and levied tax.

So,

We have to calculate the tax.

⇒ [tex]8\%\ of\ \$25.30[/tex]

⇒ [tex]\frac{8}{100}\times \$25.30[/tex]

⇒ [tex]0.08\times \$25.30[/tex]

⇒ [tex]\$2.024[/tex]

Tax imposed = [tex]\$2.024[/tex]

Now,

Total cost of the meal =Tax + Meal cost

⇒ [tex]\$(2.024+25.30)[/tex]

⇒ [tex]\$27.324[/tex]

Total cost of the meal is $ 27.32.

Answer:

Step-by-step explanation:

The polynomial f(x)=x^4+2x^3−27x−54 has x+2 as a factor. The complete factorization of f(x) after polynomial division and analysis is (x + 2)(x^2 - 3x + 9)(x + 3).

To show that x+2 is a factor of f(x)=x^4+2x^3−27x−54, we need to use the Factor theorem which states that if a polynomial f(x) has a factor of the form x - k, then f(k) = 0.

So, if x + 2 is a factor of the function, then f(-2) should equal 0. Let's apply this to our function:

f(-2) = (-2)^4 + 2(-2)^3 - 27(-2) -54 = 16 -16+54 -54 = 0. So x+2 is indeed a factor.

To factor f(x) completely, we will perform polynomial division of f(x) by the factor (x+2) which will give us g(x) = x^3 - 27. This can be further factored to x^3 - 3^3 which is a difference of cubes. Consequently, the complete factorization of f(x) would be:

f(x) = (x + 2)(x^2 - 3x + 9)(x + 3).

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Without the markup percentage or discount percentage, it is impossible to calculate the actual cost price the store paid for the trumpet. One needs this additional information to provide a precise answer.

The question "if the price tag on a trumpet says $104, how much did the store pay for it" cannot be answered with the information provided. To calculate how much the store paid for the trumpet, we need additional details such as the markup percentage or the discount percentage. Retail stores typically apply a markup to the cost of the goods they purchase from suppliers to cover their operating expenses and make a profit.

Let's assume the markup percentage is known. For example, if a store generally marks up items by 50%, and the selling price of the trumpet is $104, we can calculate the store's cost using the formula: Cost Price = Selling Price / (1 + Markup Percentage). So the cost would be $104 / (1 + 0.50), which is $69.33.

Without the markup or discount information, it is impossible to determine the exact cost price that the store paid for the trumpet.

Answer:

The two congruent segments are EF and GF, and EH and GH.

Step-by-step explanation:

That being said, your answer is A because EF and GF are in fact congruent segments.

I hope this helps!

- sincerelynini

Answer:

I believe the answer to this question is: 3/2 simplified to 1  1/2.

I hope this help you with what you need

You are correct. The scale factor is 1/5 = 0.2

Nice work.

Answer:12

Step-by-step explanation:

Answer:

X=-1

Step-by-step explanation:

Isolate the variable by dividing each side by factors that don't contain the variable.

Answer: 4/3

Explanation: To write the fraction 8/6 in lowest terms, we divide the numerator and the denominator by the greatest common factor of 8 and 6.

Since the factor of 8 are 1, 2, 4, and 8 and the factors of 6 are 1, 2, 3, and 6, the greatest common factor of 8 and 6 is 3 so we divide the numerator and the denominator of 8/6 by 2 and we get 4/3.

So 8/6 can be simplified to 4/3.

4/3 can also be changed to the mixed number 1 and 1/3.

Good evening

Answer:

RM ≈ 8.25

Step-by-step explanation:

√((10-2)^2+(6-4)^2)

= √(8^2+2^2)

=√(64+4)

=√(68)

=8.246211251235

Distance RM To the nearest hundredth 8.25

:)

Answer:

Step-by-step explanation:

-(-3)-[-(-4)]-2+7 = 3 - [4] - 2 + 7 = 3 - 4 - 2 + 7 = (3+7) - (4+2) = 10 - 6 = 4

Answer:

The similarity statement: FGHI ~ BCDE

Similarity ratio: 5:1

Step-by-step explanation:

The similarity statement is quite obvious, as there are only two rectangles shown, and the other one is "BCDE".

The similarity ratio is 5:1 because everything in the 1st (FGHI) rectangle is multiplied 5 times the values in the 2nd (BCDE) rectangle.

Since 9 is 3², each digit in base nine takes two digits in base 3.

2₉ = 02₃

6₉ = 20₃

7₉ = 21₃

1₉ = 01₃

Putting it together

2671₉ = 2202101₃

Answer:

29 1/3

Step-by-step explanation:

1/3 (4 + 18) 4

1/3 (22) 4

7 1/3 x 4

29 1/3

Twenty nine and one third is your answer.

Final answer:

The expression 1/3 (4+18) 4 evaluates to approximately 29.333 following the order of operations; first the addition inside the parentheses, then multiplication by 1/3, and lastly by 4.

Explanation:

When evaluating the expression 1/3 (4+18) 4, it's essential to follow the orders of operation, often remembered by the acronym PEMDAS (Parentheses, Exponents, Multiplication, and Division (from left to right), Addition and Subtraction (from left to right)). Let's break down the problem step by step:

Now, perform the multiplication: 22 * 4 = 88. Since we are multiplying by a division by 3 (22/3), it is the same as dividing 88 by 3, which gives us the final answer: 88 divided by 3 equals 29 with a remainder of 1, or as a decimal, approximately 29.333.

The correct answer to the expression 1/3 (4+18) 4 is therefore approximately 29.333. It is crucial to always follow the order of operations in any math problem to get the correct result.

Answer:

H = 21.7

Step-by-step explanation:

A = 1/2 x b x h

26 = 1/2 x2.4xh

26= 1.2h

divide both sides by 1.2

26/1.2 = 1.2/1.2 h

h = 21.7

Answer:

12.5

Step-by-step explanation:

1) Original equation: 3(2) - 18x +225 = 6

2) Simplify: 6 - 18x + 225 = 6

3) Move 18x over to the right: 6 + 225 = 6 + 18x

4) Move the 6 on the right over to the left: 225 = 18x

5) Divide both sides by 18 to isolate x: 225/18, 18x/18

6) x = 12.5

Answer:

Approximately 43 feet of minimum cable is needed.

Step-by-step explanation:

This problem can be solved using Trigonometry and Pythagorean theorem. Pythagorean theorem applies on right-triangles (which are known to have one 90° angle). The theorem states that the square of the Hypotenuse is obtained by the squared sum of the other two sides of the triangle (i.e the two sides forming the 90° angle - with the hypotenuse side being across it as:

[tex]h^2=a^2+b^2[/tex]           Eqn. (1)

where

[tex]h[/tex] is the hypotenuse

[tex]a[/tex] is a side

[tex]b[/tex] is a side

Now in this case, the utility pole must be perpendicular to the ground and the anchor being parallel to the ground, and a 90° angle formed between them. Conclusively the cable length will be represented by the hypotenuse in a right triangle. So here we have [tex]a=40ft[/tex] and [tex]b=15ft[/tex]. Plugging in Eqn.(1) and solving for [tex]h[/tex] we have:

[tex]h^2=40^2+15^2\\h=\sqrt{40^2+15^2} \\h=\sqrt{1600+225}\\ h=\sqrt{1825}\\ h=5\sqrt{73}\\ h=42.72ft[/tex]

So we conclude that the minimum length of cable needed by Lamont is

≈43 feet (rounded up).

Answer:

1,800

Step-by-step explanation:

Answer:

11.55

Step-by-step explanation:

An equilateral triangle is one which all it sides are equal.

10cm altitude means the height is 10cm.

Using Pythagoras theorem,

x² = 10² + (x/2)²

Assume that the side of the triangle is xcm

x² - x²/4 = 100

3x²/4 = 100

x = √(400/3)

x = 11.55cm

9514 1404 393

Answer:

  5

Step-by-step explanation:

The evaluation can be easier if terms are collected first.

  3xy+7x^2−3x^2y+3y^2x−2x^2−2xy+4x^2y−2y^2x

  = x^2y(-3+4) +xy^2(3-2) +x^2(7-2) +xy(3-2)

  = x^2y +xy^2 +5x^2 +xy

  = x(xy +y^2 +5x +y)

Filling in the numbers, we have ...

  = (1)(1(-2) +(-2)^2 +5(1) +(-2))

  = -2 +4 +5 -2

  = 5

The value of the polynomial is 5.

Answer:

The answer is that 5x to the third times 6 is 30x³

Step-by-step explanation:

Let's answer the question, this way:

5x to the third = 5x³

5x³ times 6 = 5x³ * 6 = 30x³

The answer is that 5x to the third times 6 is 30x³

Answer:

B, hope this helps you!

Both the variable and constant terms in Yari's equation are identical on each side after simplification, leading to the conclusion that both sides are exactly the same.

Analysing Yari's equation step-by-step, we can see that after expanding and simplifying both sides of the equation:

Comparing both sides of the simplified equation 2x + 3 = 3 + 2x, we notice that both the variable terms (2x) and the constant terms (3) are identical on each side.

Therefore, the correct answer is:

B) Both sides are exactly the same.

Answer:no

Step-by-step explanation:

Because it can not get any smaller