(Help)Find the value of X.
15-18

x will represent the number of tickets.

y will represent the fixed fee given by the ticket agency

6x + y = 135

3x + y = 75

To solve, we can use the process of elimination by multiplying the second equation by -2 so that 6y will cancel:

-6x - 2y = -150

+6y + y = 135

Now we simplify by adding/subtracting:

-y = -15 or y = 15

Plug the value of y into any of the two equations and solve for x. I will use the second equation:

3x + 15 = 75

3x = 60

x = 20

To set this up in slope intercept form (y = mx + b), we need to identify what m and b are.

m is x because it is not a fixed number, and b is y because it is a fixed number (price of “fixed” fee). This brings us to y = 20x + 15

Answer:

=5x+3

Step-by-step explanation:

Hope this helps!

Answer:

annnnnnn

Step-by-step explanation:

u r wronggggggggggggggggggggggggggg

(2√5 )²

= 2√5 × 2√5

= 4×5

= 20

Answer:

Step-by-step explanation:

The given question says that, the man is standing 50 ft away from the statue.

Looking at the top of the statue, the  angle of elevation is 8°.

Hence, where the man is standing, from that horizontal plane, the distance of the top of the statue is [tex]50 tan 8°[/tex].

Similarly, looking down towards the base, the angle is 14°.

Hence, the height from the base of the statue to the horizontal plane, where the man is standing is [tex]50 tan 14°[/tex].

The total height of the statue is [tex]50 tan 8° + 50 tan 14° = 50( tan 8° + tan 14°)[/tex] = 22.24475804 ≅22.24 ft.

Answer:

The answer is the first choice: 10x - 12 + x + 10x - 12 + x

Step-by-step explanation:

Let the length of a table 2.5x - 3 and let the width of the table be x.

Four tables with identical dimensions are placed together.

So we can say that width of the new table formed by placing the four tables side to side will be the same as the width of one table, that is x.

And the two sides of the new table which will represent the width will be the width of one table at one end and the width of the table at the other end, that is x + x.length

Now as we saw before there are are two widths which are part of the perimeter there are also two lengths which are part of the perimeter.

The perimeter of a table is given by (2 × length) + (2 × width).

Now one length of the new table will be equal to (4 × length of one table) = 4 × (2.5 x - 3) = 10x -12

Therefore perimeter of the new table is given from the formula of the perimeter = Length + width + Length + width

     =   10x - 12  + x  +  10x -12 + x

Answer:

Equation: [tex]8.5t+6.5=57.5[/tex]

Solution: [tex]t=6[/tex]

Step-by-step explanation:

Let be "t" the number of movie tickets bought by the group of friends.

According to the information given in the exercise, the price of each movie ticket is: $8.50.

Then, you can represent the amount (in dollars) the group of friends spent in movie tickets, with this expression:

[tex]8.5t[/tex]

You know that one person spent $6.50, then the expression that represents the total amount (in dollars) the group of friends spent in food and movie tickets, is:

[tex]8.5t+6.5[/tex]

Since that total amount spent is given in the exercise, you can write the following equation to determine how many tickets were bought:

[tex]8.5t+6.5=57.5[/tex]

Finally, you can solve for "t" in order to find the solution of the equation. This is:

[tex]8.5t=57.5-6.5\\\\t=\frac{51}{8.5}\\\\t=6[/tex]

Final answer:

The group purchased 6 movie tickets. The equation formulated to determine this is t × $8.50 + $6.50 = $57.50, where t stands for the number of tickets. Subtracting the food cost and dividing the remainder by the ticket cost gives us the answer.

Explanation:

To determine how many movie tickets were bought by the group, we can set up the following equation:

t × $8.50 + $6.50 = $57.50

Here, t represents the number of tickets. The cost of one movie ticket is $8.50 and the cost of the food is $6.50. The total amount spent by the group is $57.50.

To solve for t, subtract the cost of the food from the total amount:

$57.50 - $6.50 = $51

Now divide the remaining amount by the cost of one ticket to find the number of tickets:

$51 ÷ $8.50 = 6

Therefore, the group purchased 6 movie tickets.

Answer:

5 is greater

Step-by-step explanation:

Answer:

3x-5y

Step-by-step explanation:

Combine like terms

To simplify the expression 13x + 2y - 10x - 7y, combine the like terms together. The simplified expression is 3x - 5y.

To simplify the expression 13x + 2y - 10x - 7y, combine the like terms together. Start by combining the x terms and then combine the y terms.

13x - 10x = 3x

2y - 7y = -5y

Therefore, the simplified expression is "3x - 5y."

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Answer:

Slope [tex]\dfrac{20}{3}[/tex]

y-intercept [tex]\dfrac{10}{3}[/tex]

Equation [tex]y=\dfrac{20}{3}x+\dfrac{10}{3}[/tex]

150 miles traveled

Step-by-step explanation:

The line shown on the diagram passes through the points (4,30) and (7,50). Find the slope of the line:

[tex]\dfrac{y_2-y_1}{x_2-x_1}=\dfrac{50-30}{7-4}=\dfrac{20}{3}[/tex]

The equation of the line is

[tex]y-30=\dfrac{20}{3}(x-4)\\ \\y=\dfrac{20}{3}x+\dfrac{10}{3}[/tex]

Hence, y-intercept is [tex]\dfrac{10}{3}[/tex]

When [tex]x=22,[/tex] then

[tex]y=\dfrac{20}{3}\cdot 22+\dfrac{10}{3}=\dfrac{440+10}{3}=150\ miles[/tex]

Answer: [tex]27a^6[/tex]

Step-by-step explanation:

The question is not clear. So, assuming that the expression you need to simplify is this one:

[tex](3a^2)^3[/tex]

You need to remember a property called "Power of a power property". This property states the following:

[tex](b^m)^n=b^{(m*n)}=b^{(mn)}[/tex]

Therefore, you need to apply the Power of a power property explained before, in order to simplify the expression provided in the exercise, multiplying the exponents inside the parentheses by the exponent outside of the parentheses. Then:

[tex](3a^2)^3=3^{(1*3)}a^{(2*3)}=3^3a^6[/tex]

Now, you must remember that:

[tex]3^3=3*3*3=27[/tex]

Finally, you get:

[tex]=27 a^6[/tex]

Answer:

D

Step-by-step explanation:

Please look at the attached picture for full solution.

Method 1 is using the shoelace method to find the area of the rectangle. Shoelace method can be used to find the areas of any polygons given their coordinates. The coordinates have to be taken in an anticlockwise order and ending with the first coordinate.

Method 2 is making use of the distance formula of two points. The formula is as shown below:

[tex] \sqrt{(x1 - x2) ^{2} + (y1 - y2)^{2} } [/tex]

Having found the distance of the length and breadth of the rectangle, you can now find its area since area of rectangle= length × breadth.

Answer:

y = x - 1

Step-by-step explanation:

The equation of a line in slope- intercept form is

y = mx + c ( m is the slope and c the y- intercept )

y = - x - 1 ← is in slope- intercept form

with slope m = - 1

Given a line with slope m then the slope of a line perpendicular to it is

[tex]m_{perpendicular}[/tex] = - [tex]\frac{1}{m}[/tex] = - [tex]\frac{1}{-1}[/tex] = 1, thus

y = x + c ← is the partial equation of the perpendicular line

To find c substitute (- 1, - 2) into the partial equation

- 2 = - 1 + c ⇒ c = - 2 + 1 = - 1

y = x - 1 ← equation of perpendicular line

The perimeter of triangle ABC can be calculated by adding the distance between points A and B, B and C, and A and C. The respective distances are roughly 5, 4.12, and 5.1, thus, the estimated perimeter of the triangle is 14.22.

To calculate the approximate perimeter of a triangle given its vertices, one should first calculate the distance between each pair of vertices. In the context of the triangle △ABC with vertices at A(3,4), B(−1,1), and C(−2,5), the distance formula, which stems from the Pythagorean Theorem, is applied. The formula is as follows: D = √[(x2-x1)² + (y2-y1)²].

For the distance between A and B, the formula would play out as follows: D = √[((-1)-3)² + (1-4)²] = √[16 + 9] = √25 = 5.

For AB to C, the calculation would be: D = √[((-2)-(-1))² + (5-1)²] = √[1+16] = √17 ≈ 4.12

For AC: D = √[((-2)-3)² + ((5-4)²] = √[25 + 1]= √26 ≈ 5.1.

Essentially, you sum these distances up to get the perimeter, which in this case is approximately: 5 + 4.12 + 5.1 = 14.22

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To find the approximate perimeter of triangle ABC, we use the distance formula to calculate the lengths of the sides.

To find the approximate perimeter of triangle ABC, we need to calculate the distances between its vertices. Using the distance formula, we can calculate the length of each side.

Side AB: sqrt((3-(-1))^2 + (4-1)^2) = sqrt(16+9) = sqrt(25) = 5

Side BC: sqrt((-1-(-2))^2 + (1-5)^2) = sqrt(1+16) = sqrt(17)

Side AC: sqrt((3-(-2))^2 + (4-5)^2) = sqrt(25+1) = sqrt(26)

The perimeter of triangle ABC is approximately 5 + sqrt(17) + sqrt(26).

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Answer:

[tex]c\leq \$17[/tex]

Step-by-step explanation:

Let

c -----> the additional amount (in dollars) David will spend

we know that

The word " at most" in this context means "less than or equal to"

The amount David has spent plus possible additional amounts he will spend must be less than or equal to $39

so

The inequality that represent this situation is

[tex]22+c\leq 39[/tex]

solve for c

subtract 22 both sides

[tex]c\leq 39-22[/tex]

[tex]c\leq \$17[/tex]

The maximum amount he could spend is $17

Answer:

TV is 3 inches tall.

Step-by-step explanation:

Given: Diagonal length of TV is 5 inch

            Width of TV is 4 inches.

Considering TV to be in rectangle shape.

Lets assume the TV height to be "x"

Diagonal form a right angle triangle as shown on picture attached.

∴ using pathagorean theoram to find the height of TV.

[tex]h^{2} = a^{2} + b^{2}[/tex], where h is hypotenous, a is width or adjacent and b is height or opposite side.

∴ [tex]5^{2} = 4^{2} + x^{2}[/tex]

⇒[tex]25= 16+x^{2}[/tex]

subtracting both side by 16

⇒[tex]25-16= x^{2}[/tex]

⇒[tex]x^{2} = 9[/tex]

Taking sqaure root on both side.

Remember, √a²= a

⇒[tex]x= \sqrt{9}[/tex]

∴[tex]x= 3[/tex]

Hence, the height of TV is 3 inches.

Answer:

D is correct

Step-by-step explanation:

The total length of ribbon needed to line the two long sides of the hat is 22 inches.

Given that, the sides above the right angles are (3x + 5) inches and (5x + 1) inches. The sides below the right angle are (2x + 1) inches and 5 inches.

A kite is a quadrilateral that has 2 pairs of equal adjacent sides. The angles where the adjacent pairs of sides meet are equal.

Now, (3x + 5)=(5x + 1)

⇒x=2

2x+1=5

⇒x=2

Thus, (3x + 5)=11 inches

Now, 11+11=22 inches

Therefore, the required answer is 22 inches.

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Answer: daughter = 6 years

mother = 30 years

Step-by-step explanation:

Let the daughter's age be x and the mother's age be y , then from the first statement

y = 5x  .......................... equation 1

In 6 years time , the mother will be y + 6 and the daughter will be x + 6 ,from the second statement , we have

y + 6 = 3 ( x + 6 )

y + 6 = 3x + 18 ..................................... equation 2

substituting equation 1 into equation 2 , we have

5x + 6 = 3x + 18

5x - 3x = 18 - 6

2x = 12

x = 6

Therefore , the daughter's age is 6 years ,then the mother's age will be 6x5 = 30 years

Answer:

[tex]\begin{array}{cccc}&\text{Like pizza}&\text{Do not like pizza}&\text{Total}\\ \\\text{Like burritos}&165&10&175\\\text{Do not like burritos}&70&5&75\\ \text{Total}&235&15&250\end{array}[/tex]

Step-by-step explanation:

250 people are surveyed. 15 of them do not like pizza, then

250 - 15 = 235 like pizza.

30% do not like burritos. 30% of 250 is

[tex]250\cdot 0.3=75[/tex] people which do not like burritos and 250 - 75 = 175 people like burritos.

Then the incomplete two way frequency table is

[tex]\begin{array}{cccc}&\text{Like pizza}&\text{Do not like pizza}&\text{Total}\\ \\\text{Like burritos}&&&175\\\text{Do not like burritos}&&&75\\ \text{Total}&235&15&250\end{array}[/tex]

66% like pizza and burritos. Then

[tex]250\cdot 0.66=165[/tex] people like pizza and burritos.

Hence,

[tex]235-165=70[/tex] people like pizza and do not like burritos

[tex]175-165=10[/tex] people like burritos and do not like pizza

[tex]250-165-70-10=5[/tex] people do not like pizza and do not like burritos

Hence the complete two way frequency table is

[tex]\begin{array}{cccc}&\text{Like pizza}&\text{Do not like pizza}&\text{Total}\\ \\\text{Like burritos}&165&10&175\\\text{Do not like burritos}&70&5&75\\ \text{Total}&235&15&250\end{array}[/tex]

Answer: [tex]=24+(1+92)[/tex]

Step-by-step explanation:

For this exercise you need to remember a property called "Associative Property".

The Associative Property states that it does not matter how you group the numbers, because you will always obtained the same result.

For Additiion, the Associentive property states the following:

[tex]a + (b + c) = (a + b) + c[/tex]

Where "a", "b" and "c" are Real numbers.

In this case you have:

[tex](24+1)+92[/tex]

As you can notice, the number 24 and the number 1 are grouped inside the parentheses, but you can also regroup the numbers 1 and 92 using parentheses and you will have the same result.

Therefore, based on the Associative Property explained before, you can conclude that:

[tex](24+1)+92=24+(1+92)[/tex]

The diameter of hemisphere is 61.4 units

Solution:

Given that, volume of hemisphere is 60570 cubic units

To find: Diameter of hemisphere

The formula for volume of hemisphere is given as:

[tex]V = \frac{2}{3} \pi r^3[/tex]

Where, "r" is the radius of hemisphere

Substituting the values we get,

[tex]60570 = \frac{2}{3} \times 3.14 \times r^3\\\\60570 = 2.093 \times r^3\\\\r^3 = \frac{60570}{2.093}\\\\r^3 = 28939.32\\\\\text{Take cube root on both sides }\\\\r = \sqrt[3]{28939.32} \\\\r = 30.7017248 \approx 30.7[/tex]

We know diameter is twice of radius

[tex]Diameter = 2 \times radius\\\\Diameter = 2 \times 30.7\\\\Diameter = 61.4[/tex]

Thus diameter of hemisphere is 61.4 units

The diameter of the hemisphere is [tex]\( 60.2 \, \text{cm} \)[/tex].

To find the diameter of a hemisphere with a volume of [tex]\( 60,570 \, \text{cm}^3 \)[/tex], we can follow these steps:

Step 1: Write a hemisphere's volume formula.

A hemisphere's volume (V) is determined by:

[tex]\[ V = \frac{2}{3} \pi r^3 \][/tex]

where ( r ) is the radius.

Step 2: Set up the equation with the given volume

Given [tex]\( V = 60,570 \, \text{cm}^3 \)[/tex], we substitute into the formula:

[tex]\[ 60,570 = \frac{2}{3} \pi r^3 \][/tex]

Step 3: Find the value of [tex]\( r^3 \)[/tex]

First, isolate [tex]\( r^3 \)[/tex]:

[tex]\[ r^3 = \frac{60,570 \times 3}{2 \pi} \][/tex]

Step 4: Calculate the value inside the equation

[tex]\[ r^3 = \frac{181,710}{2 \pi} \approx \frac{181,710}{6.2832} \approx 28,931.89 \][/tex]

Step 5: Solve for ( r )

Take the cube root of both sides to find ( r ):

[tex]\[ r = \sqrt[3]{28,931.89} \approx 30.1 \][/tex]

Step 6: Calculate the diameter

Two times the radius is the diameter (D):

[tex]\[ D = 2r \approx 2 \times 30.1 = 60.2 \][/tex]

Thus, the diameter of the hemisphere is [tex]\( 60.2 \, \text{cm} \)[/tex].

Complete Question:

What is the diameter of a hemisphere with a volume of 60570 [tex]cm^{3}[/tex] , to the nearest tenth of a centimeter?

Answer:

86.4 km

Step-by-step explanation:

Since the cyclist travels 1.8km in a minute, he will travel 48 times that in 48 minutes:

[tex]48*1.8 = 86.4[/tex]

Answer:

V=(4/3)πr^3

Step-by-step explanation:

This is the equation to find the volume of a sphere

V=(4/3)πr^3

than plug in 6 for x, and solve

The volume of a sphere with a radius of 6 units is represented by the expression [tex]\frac{4}{3}[/tex] πr³, which calculates to V = [tex]\frac{4}{3}[/tex] π(6)³, cubic units. If two such spheres combine, the volume doubles, and the new radius is the cube root of the new volume.

The expression that represents the volume of a sphere with a given radius in cubic units is given by the formula V = [tex]\frac{4}{3}[/tex] πr³. For a sphere with a radius of 6 units, you can substitute the value of the radius into this formula to calculate the volume.

The calculated volume V would be V = [tex]\frac{4}{3}[/tex] π(6)³, which simplifies to V = [tex]\frac{4}{3}[/tex] π(216), or V = 288π cubic units. Therefore, the volume of the sphere is 288 times π cubic units.

Answer:

12:45

Step-by-step explanation:

quik maths

Answer:12:45

Step-by-step explanation:

Answer:

The answer is 9 on edgggggggggggg

Step-by-step explanation:

Based on the information given, the value of h is 9.

Firstly, it should be noted that the sum of the angles that are on a straight line is 180°.

In this case, we'll have to equate both values that are given and this will be:

3h + 18° + 15h = 180°

Collect like terms

3h + 15h = 180° - 18°

18h = 162°

Divide both sides by 18

18h/18 = 162°/18

h = 9

Therefore, the value of h will be 9

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Answer:

Step-by-step explanation:

Area of rectangle A = L × W

Length L = n - 3

Width = 2

Area = 24square unit

:- 24 = (n - 3)2

24 = 2n - 6 ...... This the equation

24 + 6 = 2n

30 = 2n

n = 30/2

n = 15

Nina makes 11.25 per hour.

Step-by-step explanation:

Given,

Number of hours worked by Nina = 32 hours

Amount earned by Nina = 360

Let,

x represent the amount earned by Nina per hour.

Amount per hour * Number of hours = Amount earned

[tex]32*x=360\\32x=360[/tex]

Dividing both sides by 32

[tex]\frac{32x}{32}=\frac{360}{32}\\x=11.25[/tex]

Nina makes 11.25 per hour.

Keywords: variable, equation

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