Paula’s paycheck varies directly with the number of hours she works. If she earns $52.50 for 6h of work, how much will she earn for 11 h of work? Round your answer to the nearest cent

Answer:

There are 12 bills of 10$ and 11 bills of 20$

Step-by-step explanation:

Let

x ------> number of 10$ bills

y -----> number of 20$ bills

we know that

x+y=23 -----> x=23-y -----> equation A

10x+20y=340 ----> equation B

substitute equation A in equation B and solve for y

10(23-y)+20y=340

230-10y+20y=340

10y=340-230

y=110/10=11

Find the value of x

x=23-y ----> x=23-11=12

therefore

There are 12 bills of 10$ and 11 bills of 20$

The solution to the inequality is [tex]\( \{ x \,|\, x < \frac{15}{2} \} \),[/tex] indicating all real numbers less than [tex]\( \frac{15}{2} \).[/tex]

To solve the inequality [tex]\(2x - 8 < 7\)[/tex], we'll isolate  x by adding 8 to both sides and then dividing both sides by 2.

Here's the step-by-step calculation:

Starting inequality:

[tex]\[ 2x - 8 < 7 \][/tex]

Add 8 to both sides:

[tex]\[ 2x - 8 + 8 < 7 + 8 \][/tex]

[tex]\[ 2x < 15 \][/tex]

Divide both sides by 2:

[tex]\[ \frac{2x}{2} < \frac{15}{2} \][/tex]

[tex]\[ x < \frac{15}{2} \][/tex]

So, the solution to the inequality is [tex]\(x < \frac{15}{2}\).[/tex]

Now, let's express the solution set in set-builder notation. The solution set for x consists of all real numbers less than [tex]\( \frac{15}{2} \)[/tex]. This can be written as:

[tex]\[ \{ x \,|\, x < \frac{15}{2} \} \][/tex]

So, the correct option is:

[tex]\[ \boxed{\{ x \,|\, x < \frac{15}{2} \}} \][/tex]

Answer: No

Step-by-step explanation: 5/3 is greater than 1 because 1 is the same as 3/3 and 5/3 is greater than 3/3 making 5/3 greater than 1.

Answer:

[tex]A=779.4\ cm^{2}[/tex]

Step-by-step explanation:

we know that

The area of a regular hexagon is equal to the area of six equilateral triangles

Applying the law of sines

The area of six equilateral triangles is equal

[tex]A=6[\frac{1}{2}b^{2}sin(60)][/tex]

where

b is the side length of the regular hexagon

we have

[tex]b=10\sqrt{3}\ cm[/tex]

[tex]sin(60\°)=\sqrt{3}/2\ cm[/tex]

substitute

[tex]A=6[\frac{1}{2}(10\sqrt{3})^{2}(\sqrt{3}/2)][/tex]

[tex]A=450\sqrt{3}=779.4\ cm^{2}[/tex]

Answer: The slope is -2

Step-by-step explanation:

It is important to remember that the equation of the line in Slope-Intercept form is the following:

[tex]y=mx+b[/tex]

Where "m" is the slope of the line and "b" is the y-intercept.

In this case you can observe that the given equation of the line [tex]y=-2x+3[/tex] is written in Slope-Intercept form.

Therefore, you can identify that the slope "m" is:

[tex]m=-2[/tex]

And the y-intercept "b" is:

[tex]b=3[/tex]

Answer:

700 square feet

Step-by-step explanation:

We can simply divide 630 by 0.9 to find the value:

[tex]\frac{630}{0.90}=700[/tex]

Checking, if she goes for 700 sq ft at $0.90 per square feet, she would need:

700 * 0.90 = $630

Yes, that's the max, so 700 sq. feet apartment is what she can afford.

Answer:

x ≥ -5

Step-by-step explanation:

If we have a translation to left c units, we write " x + c " in the function, and

If we have a translation to right c units, we write " x - c" in the function

If we have vertical translation up b units, we "add b to the function", and

If we have vertical translation down b units, we "subtract b to the function"

The parent function is  [tex]f(x)=\sqrt{x}[/tex]

Since translation left 5 units and up 3 units, we can write:

[tex]f(x)=\sqrt{x+5} + 3[/tex]

The domain is affected by the square root sign and we know the number under the square root CANNOT be negative, so we can say:

x + 5 ≥ 0

x ≥ -5

This is the domain.

The domain of the function g(x), which is the translated version of f(x) = √x, is all x ≥ -5 after being shifted left 5 units and up 3 units.

The function g(x) resulting from translating f(x) = √x left 5 units and up 3 units is expressed as g(x) = √(x+5) + 3. Because we cannot take the square root of a negative number in the set of real numbers, the domain of f(x) is all x ≥ 0. After the translation, the domain of g(x) will also be shifted 5 units to the left. Therefore, the domain of g(x) is all x ≥ -5, as this is the new point where the function starts to produce real number outputs.

Answer:

x = 4

Step-by-step explanation:

2x + y = 6 ... (i)

x - 6 = y ... (ii)

y = 6 - 2x ... (i)

y = x - 6 ... (ii)

So,

6 - 2x = x - 6

x + 2x = 6 + 6

3x = 12

x = 12/3 = 4

Answer:

A

Step-by-step explanation:

For a 1 mile ride, plug in 1 into m.

Total = 0.40(1) + 1.75

= 0.40+1.75 = 2.15.

Because no other answer but A has 2.15, you're answer is A

Answer:A

Step-by-step explanation:

Answer:

A. rolling a two and landing on tails

Answer:

C) 35 Degrees

Step-by-step explanation:

To find the degree of an exterior angle, subtract the larger arc, DE, degree by the smaller arc, BC, and then divide by 2! Which is 35. 118-48/ 2 = 35.

Answer:

x = -8

Step-by-step explanation:

We are given the following expression which we are to solve for [tex]x[/tex]:

[tex] 2 7 ^ x = 9 ^ { x - 4 } [/tex]

For this expression, we will make the bases same on both sides of the equation and then equate the exponents equal to each other.

[tex](3^3)^x = (3^2)^{x-4}[/tex]

Multiplying the exponents and equating them to get:

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

[tex] 3 x = 2 x - 8 [/tex]

[tex] 3 x - 2 x = - 8 [/tex]

x = -8

For this case we must solve the following equation:

[tex]27 ^ x = 9 ^ {x-4}[/tex]

We rewrite:

[tex]27 = 3 * 3 * 3 = 3 ^ 3\\9 = 3 * 3 = 3 ^ 2[/tex]

So:

[tex]3^{3(x)}=3^{2(x-4)}[/tex]

Since the bases are the same, the two expressions are only equal if the exponents are also equal. So, we have:

[tex]3 (x) = 2 (x-4)\\3x = 2x-8[/tex]

Subtracting 2x on both sides:

[tex]3x-2x = -8\\x = -8[/tex]

Answer:

[tex]x = -8[/tex]

The total cost of a taxi ride includes a $5 flat fee plus $0.50 for every mile traveled. The total cost can be calculated using the formula: Total cost = $5 flat fee + ($0.50 × number of miles). For instance, a 10-mile trip would cost $10.

The total cost of a taxi ride is dependent on the distance traveled in miles. The taxi driver charges a $5 flat fee to enter the car and $0.50 per mile. To find the total cost, you can use the equation:

Total cost = Flat fee + (Cost per mile × Number of miles traveled)

For example, if you traveled 10 miles, the total cost would be:

Total cost = $5 + ($0.50 × 10) = $5 + $5 = $10

This formula will give you the total expense for any number of miles traveled in the taxi.

Pre-Image < Image, then the scale factor is k >1.

Pre-Image > Image, then the Scale factor will be lies between,

0 < k < 1.

It exists given that Rectangle Q has an area of 2 square units.

Thea Drew a scaled version of Rectangle Q and labeled it as R.

As you must keep in mind If we draw a scaled copy of the pre-image, then the two images.

Therefore, Pre-image and Image are similar.

Consider the Scale factor of transformation = k

Rectangle Q = Pre - image,

Rectangle R= Image

If, Pre-Image < Image, then the scale factor is k >1.

But If, Pre-Image > Image, then the Scale factor will be lies between,

0 < k < 1.

To learn more about the Scale factor of a rectangle

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All you need to do to solve this is multiply 2 to both sides. This will cancel out 2 from the denominator and isolate x...

2([tex]\frac{x}{2}[/tex]) = -7 * 2

x = -14

Hope this helped!

~Just a girl in love with Shawn Mendes

Hello There!

The Answer is -14

If we substitute -14 in the equation as x, -14 ÷ 2 ≈ -7

A negative number divided by a positive number gives us a negative number.

4-9=5

-2--8=6

y=mx+b

slope/mx=6/1

base/y intercept=5

Answer: The equation for the line in  point-slope form :[tex] (y+2)=\dfrac{-6}{5}(x-4)[/tex]

The equation in slope-intercept form : [tex]y=\dfrac{-6}{5}x+\dfrac{14}{5}[/tex]

Step-by-step explanation:

The equation of a line in point slope form passing through points (a,b) and (c,d) is given by :-

[tex](y-b)=\dfrac{d-b}{c-a}(x-a)[/tex]

Now, the point slope form passing through points (4, -2) and (9, -8) is given by :-

[tex](y-(-2))=\dfrac{-8-(-2)}{9-4}(x-4)\\\\\Rightarrow (y+2)=\dfrac{-6}{5}(x-4)[/tex]

The equation for the line in  point-slope form :[tex] (y+2)=\dfrac{-6}{5}(x-4)[/tex]

Further if we simplify the equation , we get

[tex] y+2=\dfrac{-6}{5}x+\dfrac{24}{5}\\\\\Rightarrow\ y=\dfrac{-6}{5}x+\dfrac{24}{5}-2\\\\\Rightarrow\ y=\dfrac{-6}{5}x+\dfrac{14}{5}[/tex]

The equation in slope-intercept form : [tex]y=\dfrac{-6}{5}x+\dfrac{14}{5}[/tex]

Answer:

6 ft.

Step-by-step explanation:

solution :

360 degree = pie r².

1 degree =pie r²/360

50degree=5pie r²/36

5pie = 5 pie r²/36

r²=36

r=6

Therefore radius = 6 ft.

Answer:

x = -345

Step-by-step explanation

2.3 + .02x + .4 - 4.8 = -9

2.7 - 4.8 + .02x = -9

-2.1 + .02x = -9

.02x = 6.9

x = -6.9 / .02

x = -345

Answer: x = -345

Step-by-step explanation:

2.3 + .02(x + 20) - 4.8 = -9

2.3 + (.02x + .4) - 4.8 = -9

-2.1 + .02x = -9

+2.1             +2.1

.02x = -6.9

.02/.02  -6.9/.02

x = -345

Let R = greatest number of rectangular lots.

R = (910 • 300)/(120 • 65)

R = 273,000 ÷ 7800

R = 35

Answer:60%

Step-by-step explanation:

Final answer:

Lucinda will mark up the price of her flower arrangements by 60% to make a $6.00 profit on each one, which costs her $10.00 to prepare. The correct answer is option a.

Explanation:

Lucinda wishes to make a profit of $6.00 on each flower arrangement she sells, on top of the $10.00 it costs her to prepare one. To calculate the percentage markup, we use the formula: Markup Percentage = (Profit / Cost) × 100%. In Lucinda's case, the profit is $6.00 and the cost is $10.00.

So, the calculation will look like this:

Markup Percentage = ($6.00 / $10.00) × 100% = 0.6 × 100% = 60%.

Therefore, Lucinda will mark up the price by 60% to achieve her desired profit. The correct answer to the question is option a.

Answer: 5.25 miles per hour.

Step-by-step explanation:

21/4 = 5.25

Hello There!

WHAT WE KNOW Shelly biked 21 miles in 4 hours. We know that Shelly's average speed = 5.25 miles / hour because "21 divided by 4 equals 5.25"

Answer:

18 square units.

Step-by-step explanation:

graph the square or find the difference then multiply the base by the hight.

Answer:

The value of the expression for x=2 is 2.

Step-by-step explanation:

Consider the provided expression.

[tex]4(x - 3) + 5x - x^2 [/tex]

We need to find the value of expression for x=2.

Substitute the value of x=2 in provided expression and simplify as shown.

[tex]4(2 - 3) + 5(2) - 2^2 [/tex]

[tex]4(-1) + 10 - 4 [/tex]

[tex]-4 + 6 [/tex]

[tex]2 [/tex]

Hence, the value of the expression for x=2 is 2.

The numerical value of the expression 4(x - 3) + 5x - x² when x = 2 is 2.

Given the expression in the question:

4(x - 3) + 5x - x²

x = 2

To evaluate the expression 4(x - 3) + 5x - x² for x = 2, repalce all the occurences of x in the expression with 2 and simplify:

4(x - 3) + 5x - x²

Plug in x = 2:

4(2 - 3) + 5(2) - (2)²

Subtract 3 from 2:

4(-1) + 5(2) - (2)²

Take the square of 2:

4(-1) + 5(2) - 4

Multiply 4 and -1:

-4 + 5(2) - 4

Multiply 5 and 2:

-4 + 10 - 4

Add the 3 numbers:

2

Therefore, the value of the expression is 2.

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Answer:

Dan has £54 left

Step-by-step explanation:

Dan's weekly wages are £540.

Then his spending includes (2/5)w + (5/10()w, or (9/10)w, and this is subtracted from Dan's wages:  £540 - (expenses)

                                                    £540 - (9/10)(£540) = £54

Dan has £54 left after having spent 9/10 of his weekly wages on rent and food.

[tex]\bf \qquad \qquad \textit{inverse proportional variation} \\\\ \textit{\underline{y} varies inversely with \underline{x}}\qquad \qquad y=\cfrac{k}{x}\impliedby \begin{array}{llll} k=constant\ of\\ \qquad variation \end{array} \\\\[-0.35em] \rule{34em}{0.25pt}\\\\ k=5\qquad \qquad y=\cfrac{5}{x}[/tex]

Answer:

C. Y=5/x

Step-by-step explanation:

Inverse variation is given by

xy = k  where k is a constant

Divide each side by x

xy/x = k/x

y = k/x  where k is a constant

Let k=5

y = 5/x  is an equation that is inverse variation

Answer:

y=9.01

Step-by-step explanation:

In this question you apply the Pythagoras Theorem to generate relationships which will enable you to form equations and solve for the unknown.

The Pythagoras Theorem states that when you have a right-angle triangle and squares are made at each of the three sides, the sum of squares of the two small sides will equal the square of the longest side.

It is expressed as a²+b²=c² where;

In the question we can use three triangles to form expressions using this theorem

First triangle

The relationship you can form is;

[tex]3^2+y^2=z^2\\9+y^2=z^2\\y^2=z^2-9------------------------(1)[/tex]

In this equation you make y² the subject of the formula

Second Triangle

Hence the relationship you can form is

[tex]27^2+y^2=x^2\\729+y^2=x^2\\y^2=x^2-729[/tex]

In this equation you make y² the subject of the formula

Third Triangle

The relationship you can form is;

[tex]z^2+x^2=30^2\\x^2=30^2-z^2---------------------(3)[/tex]

Here x² is the subject of the formula

Equations

[tex]y^2=z^2-9\\y^2=x^2-729\\x^2=900-z^2[/tex]

Substitute equation 3 in equation 2

[tex]y^2=x^2-729-------------2\\\\x^2=900-z^2-------------3\\\\y^2=900-z^2-729\\\\y^2=171-z^2---------------4[/tex]

Substitute equation 4 in equation 1

[tex]y^2=171-z^2---------------4\\\\y^2=z^2-9------------1\\\\z^2-9=171-z^2\\\\2z^2=171+9\\\\z^2=180\\\\z=\sqrt{180} \\\\z=9.487\\\\z=9.5[/tex]

Use the value of z in equation 1 to get value of y

[tex]z^2-3^2=y^2\\\\9.5^2-9=y^2\\\\90.25-9=y^2\\\\81.25=y^2\\\\\sqrt{81.25} =y\\\\y=9.01[/tex]

Answer:

4. h(t)=2000t+800

Step-by-step explanation:

800 is his starting elevation we dont not multiply it

every hour he gains 2000ft in elevation and t shows the hours 2000ft * t (hours) + 800

Answer:

(0,2/3)

Step-by-step explanation:

I would go for elimination on this one.

This will require we manipulate at least one equation.

I'm going to multiply bottom equation by -2:   -2x-12y=-8

So we have

2x+3y=2

-2x-12y=-8

---------------add the two equations

 0 -9y=-6

     -9y=-6

         y=6/9=2/3

2x+3y=2

2x+3(2/3)=2

2x+2=2

2x=0

x=0

(0,2/3)

Answer: The Answer is A X=0 Y=2/3

Step-by-step explanation:

2x+3y=2

X+6y=4

step one: substitute in the value of x into the equation

2x +3y = 2

x= 4-6y

Step two: Solve with the X substitution

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

You get Y= 2/3

Step three: plug in 2/3 for X

X= 4-6(2/3)

You get 0

therefore: X = 0 and Y=2/3