"71 points". Match the proportional relationships to their corresponding equations.
11 pounds of apples for $40.59
12 gallons of gasoline for $44.16
15 magazines for $54.75
14 sandwiches for $50.68
t = $3.69n
arrowBoth
t = $3.62n
arrowBoth
t = $3.65n
arrowBoth
t = $3.68n
arrowBoth

Answer:

a) c = 65.532 cm

P = 145.532 cm

b) A = 751.754 cm²

Step-by-step explanation:

This is an isosceles triangle.  The given angle is obtuse, so it must be the vertex angle.

a) One way to find the length of the third side is law of cosine:

c² = a² + b² − 2ab cos C

c² = 40² + 40² − 2(40)(40) cos 110°

c = 65.532

Another way is to cut the triangle in half and use sine.

sin (110°/2) = (c/2) / 40

c = 80 sin 55°

c = 65.532

The perimeter is the sum of the sides:

P = 40 + 40 + 65.532

P = 145.532

b) You can find the area using the SAS equation:

A = ½ ab sin C

A = ½ (40)(40) sin 110°

A = 800 sin 110°

A = 751.754

Another way is to split the triangle in half, find the height using cosine, then use half the base times height.

cos (110°/2) = h / 40

h = 40 cos 55°

h = 22.943

A = ½ ch

A = ½ (65.532) (22.943)

A = 751.754

Answer:

(0,2.5), (-1.25,0) and (3,8.5)

Step-by-step explanation:

we have

[tex]-4x+2y-5=0[/tex]

This is a linear equation (equation of a line)

If a ordered pair is a solution of the linear equation, the the ordered pair must satisfy the linear equation

1) Find the y-intercept

The y-intercept is the value of the y when the value of x is equal to zero

For x=0

substitute the value of x in the linear equation and solve for y

[tex]-4(0)+2y-5=0[/tex]

[tex]2y=5[/tex]

[tex]y=2.5[/tex]

The ordered pair is (0,2.5)

2) Find the x-intercept

The x-intercept is the value of the x when the value of y is equal to zero

For y=0

substitute the value of y in the linear equation and solve for x

[tex]-4x+2(0)-5=0[/tex]

[tex]-4x=5[/tex]

[tex]x=-1.25[/tex]

The ordered pair is (-1.25,0)

3) Assume any value of x or y and solve for the other variable

For x=3

[tex]-4(3)+2y-5=0[/tex]

[tex]-12+2y-5=0[/tex]

[tex]2y=17[/tex]

[tex]y=8.5[/tex]

The ordered pair is (3,8.5)

Answer:

3

Step-by-step explanation:

To solve this you have to work backwards with what you are given.

16-7=9

Then we know that a number has to be multiplied by itself to equal nine the only number that follows that criteria is 3

3*3=9+7=16

Answer:

3

Step-by-step explanation:

Work backwards. 16 Subtract 7. Take square root. We take the square root because that is how to undo a number that was multiplied by itself.

16-7=9 √(9)=3

Check this by going through the same steps listed in the question:

A positive number is multiplied by itself. then 7 is added. the answer is 16

3×3=9

9+7=16

Answer:

y = 7 is the equation of the line that passes through the point ( -2, 7 ) and has a slope of zero.

Step-by-step explanation:

Given:

Let,

A ≡ ( x1 , y1 ) ≡ ( -2, 7 )

Slope = m = 0

To Find :

Equation of Line:

Solution:

Formula for , equation of a line passing through a point (  x1 , y1 ) and having a slope m is given by

[tex](y - y_{1})=m(x-x_{1})[/tex]

Now substituting the values of x1 = -2 and y1 = 7 and slope m = 0 we get,

[tex]y-7=0\times(x--2) \\y-7=0\times (x+2)\\y-7=0\\\therefore y=7[/tex]

Which is the required equation of a line passing through the point ( -2, 7 ) and slope zero

The equation of a line that passes through a point is an algebraic equation. It can also be referred to as the Slope-Intercept Equation.

The equation of the line that passes through the point (-2, 7) and has a slope of zero is written as: y = 7

The equation of the line through a point (x1, y1) can be represented by the algebraic equation:

y = mx + c

where:

m = slope

c = y - intercept

From the question,

(x1, y1) = (-2, 7)

m = slope = 0

Substituting these values into the algebraic equation,

7 = (0 x -2) + c

7 = 0

Hence, y = 7

The equation of the line that passes through the point (-2, 7) and has a slope of zero is y = 7

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The total bill is $14.64 ⇒ last answer

Step-by-step explanation:

The given is;

Sandwiches

Side Orders

Beverages

∵ You order 2 veggieburgers, one salad, one fries and 2 coffees

∵ The price of the 1 veggieburgers = $3.25

∵ The price of the 1 salad = $2.5

∵ The price of the 1 fries = $1.5

∵ The price of the 1 of one coffee = $0.9

∴ The cost of the order = 2(3.25) + 1(2.5) + 1(1.5) + 2(0.9)

∴ The cost of the order = 6.5 + 2.5 + 1.5 + 1.8 = $12.3

∵ There is a tax 4%

∴ The tax = 4% × 12.3 = [tex]\frac{4}{100}[/tex] × 12.3 = $0.492

∵ There is a tip 15%

∴ The tip = 15% × 12.3 = [tex]\frac{15}{100}[/tex] × 12.3 = $1.845

To find the total bill add the cost of the order, the tax and the tip

∵ The total bill = cost of the order + tax + bill

∴ The total bill = 12.3 + 0.492 + 1.845

∴ The total bill = $14.637 ≅ $14.64

The total bill is $14.64

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Answer:

Option C is the correct choice that is [tex]y<-\frac{5}{2}x-2[/tex]

Step-by-step explanation:

As this is a multiple choice question we will reduce the options and work on it with the given points [tex](0,-2),(-2,-3)[/tex]

Note:We know that [tex]\leq ,\geq[/tex] where there is [tex]=[/tex] sign associated with it have a straight line graph there is no breaking in the line.

And when there is simply [tex]<,>[/tex] we have a dashed line when we plot it on a graph.

So option B and D are discarded.

Now one-by one we will put the values [tex](x,y)\ (-2,3)[/tex] to know which equation it satisfies.

If we put [tex]y=3[/tex] then [tex]x=-2[/tex].

So working with option A.

[tex]y<-\frac{2}{5}x-2[/tex]

Plugging the values.

[tex]3<-\frac{2}{5}x-2\ ,3<\frac{-2x-10}{5}\ ,15<-2x-10\ ,15+10< -2x\ ,x=\frac{25}{-2}=-12.5[/tex]

And we know that [tex]x[/tex] must be equal to [tex]-2[/tex] so this is not the right answer.

We are left with only one choice that is C .

So option C is the correct option of the above inequality.

Answer:

Y = - 2

Step-by-step explanation:

Put your finger at x= 0 or (0,0) and go down until you hit the black line, thats your y

Answer:

814 - 64 = 750

750 ÷ 2 = 375

375 + 64 = 439

The problem can be solved by setting up two equations based on the given information, substituting one equation into the other, and then solving for the variable. In this case, 375 adult tickets were sold.

The subject of this problem is mathematics, particularly a class of problems known as linear equations. Let's assign variables to each type of ticket: A for the number of adult tickets and S for the number of student tickets.

According to the problem, S = A + 64 (because there were 64 more student tickets sold) and S + A = 814 (because a total of 814 tickets were sold).

With these two equations, you can substitute the value of S from the first equation into the second equation. Therefore, (A + 64) + A = 814. Simplify this to get 2A + 64 = 814.

To find the number of adult tickets, solve the simplified equation for A. Subtract 64 from both sides to get 2A = 750, and then divide by 2 to find that A = 375.

So, 375 adult tickets were sold.

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Answer:22/24 or 11/12

Step-by-step explanation:

Answer:

Six books are removed from the shelves, so $24-6=18$ books remain. Of these, $10-2=8$ are math books. Therefore, $8/18=\boxed{4/9}$ of the books remaining are math books.

Step-by-step explanation:

4/9

Answer:

Probability that the sum of the two dice is greater than 12 is ZERO.

Step-by-step explanation:

Here, when two dices are rolled together, the sample space is given as:

(1, 1), (1, 2), (1, 3), (1, 4), (1, 5), (1, 6),

(2, 1), (2, 2), (2, 3), (2, 4), (2, 5), (2, 6),

(3, 1), (3, 2), (3, 3), (3, 4), (3, 5), (3, 6),

(4, 1), (4, 2), (4, 3), (4, 4), (4, 5), (4, 6)

(5, 1), (5, 2), (5, 3), (5, 4), (5, 5), (5,6)

(6, 1), (6, 2), (6, 3), (6, 4),(6,5), (6,6)  = Total 36 outcomes

Now, E :  Event of getting a  sum greater than 12.

So here, number of possible outcomes  = 0

So, the probability that the sum of the two dice is greater than 12  = 0/36  = 0

So, it is an IMPOSSIBLE EVENT.

It is impossible to roll a sum greater than 12 with two standard six-sided dice, as the maximum sum possible is 12. Therefore, the probability of rolling a sum greater than 12 is zero.

The student asked about the probability that the sum of two standard six-sided dice is greater than 12. Since the highest sum one can achieve with two six-sided dice is 12 (when both dice show a 6), it is impossible to roll a sum greater than 12. Therefore, the probability of this event is zero.

When considering every outcome of rolling a die, we must include all possible individual results, which range from 1 to 6 for each die. The sum of two dice ranges from a minimum of 2 (both dice showing 1) to a maximum of 12 (both dice showing 6). Consequently, there are no combinations of dice that can result in a sum that exceeds 12.

The highest sum achievable on two six-sided dice is 6 + 6 which equals 12. This makes sums greater than 12 unattainable, and highlights the importance of considering the specified number of sides on dice when calculating probabilities related to their sums.

Answer:

I think it would be either (-10, 5) or (35, -20)

Step-by-step explanation:

Answer:

It Is C

Step-by-step explanation:

Edg 2020

Answer:

7 grams

Step-by-step explanation:

If you're asking me grams specifically, and not kilograms, subtract 68 from 75 to get your answer. If it's only kilograms subtract 324 from 405. If it's both of them added together subtract 399 from 473, you're welcome!

Answer:

7 grams

Step-by-step explanation:

Answer:

y=-2

Step-by-step explanation:

y-y1=m(x-x1)

m=slope & (x1, y1) is a point on the line

m=(y2-y1)/(x2-x1)

m=(-2-(-2))/(-3-5)

m=(-2+2)/(-8)

m=0

y-(-2)=0(x-5)

y+2=0

y=0-2

y=-2

Answer: 17 and 31

Step-by-step explanation:

first number = x

second number = y

x+y=48

-(x-y=14)

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

2y=34

y=17

x=31

Answer:

17 and 31

Step-by-step explanation:

17 + 31 = 48, I basically just plugged in random numbers until I got the answer.

Answer:

The number of students who prefer chocolate milk is 780 .

Step-by-step explanation:

Given as :

The total number of students in the school = 1200

The percentage of students who prefer plain white milk = 35 %

Let the number of students who prefer chocolate milk = x

Now, ∵ The percentage of students who prefer plain white milk = 35 %

∴ The percentage of students who prefer chocolate milk = 100 % - 35 % = 65%

So , As The number of  students who prefer chocolate milk = x

Or, 65 % of total number of students in school = x

So, x = [tex]\frac{65}{100}[/tex] × 1200

or, x = [tex]\frac{65\times 1200 }{100}[/tex]

∴  x = 780

So, the number of students who prefer chocolate milk = x = 780

And  students who prefer plain white milk = 1200 - x = 1200 - 780 = 420

Hence, The number of students who prefer chocolate milk is 780 . Answer

If you are given the slope and y-intercept of a line, you can conclude several things about the line and use them to write the equation of the line in slope-intercept form, which is \( y = mx + b \), where \( m \) is the slope and \( b \) is the y-intercept.

For the values you've given:

- The slope (m) is 35.
- The y-intercept (b) is 550.

From these pieces of information, you can conclude:

1. **Slope (Steepness and Direction):** Since the slope is 35, this tells us that the line is relatively steep and rises quickly. The slope is positive, which means the line slants upwards from left to right. Specifically, for every one unit that x increases, y increases by 35 units.

2. **Y-intercept (Starting Point):** The y-intercept is where the line crosses the y-axis. Since the y-intercept is 550, it indicates that the line will cross the y-axis at the point (0, 550). This is the starting point of the line if you begin plotting from the y-axis.

With these conclusions, you can write the equation of the line in slope-intercept form:

\[ y = 35x + 550 \]

This equation allows you to predict or calculate the value of y for any given value of x along the line. It also enables you to graph the line by plotting the y-intercept and using the slope to determine the direction and steepness of the line. Remember, a line extends infinitely in both directions on the graph, so the portion you draw depends on the context or constraints of the particular situation you are modeling with the line.

Answer:

3x^3-18x^2+26x-8

Step-by-step explanation:

(x-4)(3x^2-6x+2)

3x^3-6x^2+2x-12x^2+24x-8

3x^3-6x^2-12x^2+2x+24x-8

3x^3-18x^2+26x-8

3 is the least possible number that satisfied these conditions

The solution set is: x≥3

Step-by-step explanation:

Let x be the number

Then according to given statement

If five times a number is increased by four

[tex]5x+4[/tex]

At least 19 means that the result will be equal to or greater than 19

so,

[tex]5x+4\geq 19[/tex]

subtracting 4 from both sides

[tex]5x+4-4 \geq 19-4\\5x \geq 15[/tex]

Dividing both sides by 5

[tex]\frac{5x}{5} \geq \frac{15}{5}\\x\geq 3[/tex]

3 is the least possible number that satisfied these conditions

The solution set is: x≥3

Keywords: Inequality, Variables

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Answer:

217

Step-by-step explanation:

868/4=217

Answer:

217

Step-by-step explanation:

Answer: 0.8660254038

Answer:

1 inch = 41 miles

Step-by-step explanation:

205 / 5 = 41

1 inch = 41 miles

Answer:

41 miles per inch

could be answered as 41/1 or 41:1

Step-by-step explanation:

Use a ratio to find the scale.

205/5

Divide the numerator and denominator by 5 to simplify.

41/1

There were 980 student desks originally before the purchase was made.

Step-by-step explanation:

Total desks purchased = 295

As 50 new desks are for teachers, therefore, we will subtract this amount from total;

Desks purchased for students = 295-50 = 245

Let,

x be the number of original student desks, therefore,

[tex]\frac{1}{4}\ of\ x=245\\\frac{x}{4}=245[/tex]

Multiplying both sides by 4

[tex]4*\frac{x}{4}=245*4\\x=980[/tex]

There were 980 student desks originally before the purchase was made.

Keywords: subtraction, fractions

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Answer:

m ∠ AMC = 75°

Step-by-step explanation:

Given:

In Δ ABC, m ∠C=90°

m∠ B =30°

CM is angle bisector

We need to find m ∠AMC

In Δ ABC Sum of all angle is 180° so we get,

[tex]m\angle A+m\angle B+m\angle C =180\\m\angle A+90+30 =180\\m\angle A+120 =180\\m\angle A=180-120\\m\angle A=60[/tex]

Now we know that CM is angle bisector of ∠C

∴ [tex]m\angle ACM +m\angle BCM =90\\m\angle ACM +m\angle ACM =90\\2m\angle ACM =90\\m\angle ACM =\frac{90}{2}=45[/tex]

Now in Δ ACM we know that Sum of all angles is 180

[tex]m\angle ACM + m\angle AMC + m\angle A=180\\45 + m\angle AMC + 60 =180\\105 + m\angle AMC =180\\m\angle AMC =180 -105 =75[/tex]

Hence m ∠ AMC = 75°

Answer:

[tex]15x^7y^5[/tex]

Step-by-step explanation:

Given

[tex]5x^3y^2\times 3x^4y^3[/tex]

Rewrite it as

[tex](5\cdot 3)\times (x^3\cdot x^4)\times (y^2\cdot y^3)[/tex]

Use power property:

[tex]a^m\cdot a^n=a^{m+n},[/tex]

so

[tex]x^3\cdot x^4=x^{3+4}=x^7\\ \\y^2\cdot y^3=y^{2+3}=y^5[/tex]

Then

[tex](5\cdot 3)\times (x^3\cdot x^4)\times (y^2\cdot y^3)=15\times x^7\times y^5=15x^7y^5[/tex]

Answer:

look at above image for answer. thank you for the question

Using the given conditions, we formed two equations: x + y = -11 and x - y = -3. We then solved these simultaneous equations to find that the two numbers are -7 and -4.

We have been given two conditions to find the values of two numbers, represented by x and y. The first condition can be expressed as the equation x + y = -11. The second condition gives us the second equation x - y = -3.

adding the first and second equation:

(x + y) + (x - y) = -11 + (-3)
2x = -14
x = -7

We can then substitute the value of x back into one of the original equations to solve for y:

-7 + y = -11
y = -11 + 7
y = -4

Thus, the two numbers are -7 and -4.

Answer:

5x² - 13x + 6

Step-by-step explanation:

8x² - 6x + 2 - (3x² +7x -4)

Simplify the expression:

8x² - 6x + 2 - 3x² -7x + 4

Combine like terms:

5x² - 13x + 6

Answer:

There can be 180 apples in that box.

Step-by-step explanation:

1. Let's review the information given to answer the question correctly:

Number of apples in a box < 200

2. It is known that 2, 3, 4, 5, or 6 kids can share these apples evenly. How many apples can be in that box?

The answer is that the number of apples that can be in the box is the highest multiple of 2, 3, 4, 5, and 6 that is close to 200.

The common multiples for this set of numbers are 60, 120, 180, 240, 300 and so on with 60 as the constant.

Therefore, the highest number that is multiple for this set of numbers and at the same time lower than 200 is 180.

There can be 180 apples in that box.

Answer:

120 or 180 apples

Step-by-step explanation:

It hasd to be divisible by 5 so it can only end in fives and zeroes next it has to be divisible by 2 so that narrows it tdown to only number that end in zero the it has to be divisible by 3 once yo find that you have two answers

120 or 180 and that is how many apples can be in the box

Answer:

Step-by-step explanation:

50% of 60? 0.5*60=30

10% of 60? 0.1*60=6

75% of 60? 0.75*60=45

50percent of 60 minutes is 30 minutes, 10percent of 60 minutes is 6 minutes, and 75percent of 60 minutes is 45 minutes.

50percent of 60 minutes: 50percent of 60 minutes is half of 60, which equals 30 minutes.

10percent of 60 minutes: 10percent of 60 minutes is 6 minutes (10percent of 60 is 6).

75percent of 60 minutes: 75percent of 60 minutes is 45 minutes (75percent of 60 is 0.75 * 60 = 45).

After solving for x1, we get

[tex]x_1 = 2M-x_2[/tex]

Step-by-step explanation:

Given formula is:

[tex]M = \frac{x_1+x_2}{2}[/tex]

In order to solve for x1, we have to isolate x1 on one side of the equation

So,

Multiplying the whole equation by 2:

[tex]2M = \frac{x_1+x_2}{2} * 2\\2M = x_1+x_2[/tex]

Subtracting x2 from both sides

[tex]2M-x_2 = x_1+x_2-x_2\\2M-x_2 = x_1[/tex]

so,

After solving for x1, we get

[tex]x_1 = 2M-x_2[/tex]

Keywords: Formulas, Solving for a variable

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