4. Tomas uses 12 gallons of water to prepare lemonade for a party. The lemonade recipe states that for every 2 quarts of water, he should add cup of lemon juice and cup 1 of sugar. How much lemon juice does Tomas need?​

Answer:

y = 41.65

Step-by-step explanation:

Given y varies directly as x then the equation relating them is

y = kx ← k is the constant of variation

To find k use the condition y = 49 when x = 40

49 = 40k ( divide both sides by 40 )

[tex]\frac{49}{40}[/tex] = k = 1.225

y = 1.225x ← equation of variation

When x = 34 , then

y = 1.225 × 34 = 41.65

Answer: 69

Step-by-step explanation:

Answer:

18

Step-by-step explanation:

The x coordinate of vertex J and L are same of x= -2, JL // Y axis

Height is the perpendicular segment (KD) from K to JL, KD // X axis

area = JL * KD /2 = ((1 - -5)* (4 - -2)) / 2 = (6 * 6) / 2 = 18

Problem 1

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

Explanation:

The first task is to determine the function for f(x). Because it's linear, it's in the form y = mx+b. Let's find the slope m.

Select any two columns to pick out (x,y) points from the f(x) function. I'll pick the first two columns to select the points (-6,15) and (-4,11). Apply the slope formula to these two points to get...

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

m = (11-15)/(-4-(-6))

m = (11-15)/(-4+6)

m = -4/2

m = -2

Then use this m value along with any of the points of the table to determine the y intercept b. I'll use the point (-6,15)

y = mx+b

b = y-mx

b = 15-(-2)*(-6)

b = 15-12

b = 3

The y = mx+b equation becomes y = -2x+3 and that leads directly to the function f(x) = -2x+3.

Repeat all of those steps but do so for g(x) this time. I'll skip those steps over but you should get the function g(x) = 5x-6.

The y intercepts of f(x) and g(x) found were 3 and -6 respectively. Subtract those values to find the y intercept of h(x) = (f-g)(x) = f(x)-g(x).

So we get 3-(-6) = 3+6 = 9 which leads to the location (0, 9).

=========================================================

Problem 2

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

Explanation:

Through trial and error, the factor by grouping method, or using your graphing calculator, factor the denominator to get

g(x) = x^3+2x^2-x-2 = (x+2)(x+1)(x-1)

The factors (x+2), (x+1) and (x-1) lead to the roots of x = -2, x = -1, and x = 1 in that order. Those three roots of g(x) will make g(x) = 0 and cause a division by zero error in the denominator. So we must kick out those three values from the domain. Every other real number is allowed in the domain. So that's how we get the notation for choice A. It starts off saying x is a real number. Then it goes onto say that -2, -1 and 1 aren't allowed.

So overall the domain is described as: "x can be almost any real number except x cannot be -2, cannot be -1, and it cannot be 1".

Side note: We don't involve the numerator function at all.

=========================================================

Problem 3

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

Explanation:

The height is x, which we can factor out like this

2x^3-5x^2-3x

2x^2*x - 5x*x - 3*x

x(2x^2-5x-3)

Effectively you would use the distribution rule in reverse.

Now let's factor the remaining expression in the parenthesis.

I'll use the factor by grouping method.

2x^2-5x-3

2x^2-6x+1x-3

(2x^2-6x) + (1x-3)

2x(x-3) + 1(x-3)

(2x+1)(x-3)

Therefore, the full factorization is

x(2x+1)(x-3)

which shows we have the dimensions of x, (2x+1) and (x-3). The order doesn't matter so we could easily have (2x+1) the length and (x-3) the width, or we could have it the other way around.

You can verify that (2x+1)(x-3) expands out to 2x^2-5x-3 using either the FOIL method or the box method.

Answer:

76%

Step-by-step explanation:

First, we know that 6 tables of 6 are already seated. We can go ahead and multiply 6 by 6, which is 36.

This means that 36 of the 150 seats are already taken.

But, we want to find the amount of seats that are still empty. So, we subtract 36 from 150 to get 114 seats.

The question is asking for the percentage, so we can divide 114 by 150 seats to get 0.76. Then, we have to move the decimal to the right 2 spaces to get 76%

Answer:

76% of the restaurant is still empty

Step-by-step explanation:

6 tables of 6 seated means there are currently 36 people seated. If the restaurant can seat 150 people, 76% of the restaurant is still empty.

[tex]6\times6=36\text{ | there are 36 guests}\\36\div150=0.24\text{ | 24\% of the restaurant is filled}\\1-0.24=0.76\text{ | 76\% of the restaurant is not filled}[/tex]

Answer:

boom bam ba boom bam ba

Answer: -3/4

Step-by-step explanation:

The y value is decreasing by -0.75

-3.75 - 0.75 = -4.5

-4.5 - 0.75 = -5.25

-5.25 - 0.75 = -6

ect.

-0.75 in fraction form is -3/4

s = number of slices for a large pizza

so if "s" is the number of slices in 1 large pizza, the total for 1 pizza will just be 1s, for two pizzas will be 2s and so on, so for 4 pizzas the total will just be 4s.

we also know there were an extra 3 slices, and we also know that whatever 4s is plus 3 will give us the total of 51 slices of pizza.

[tex]4s + 3 = 51\implies 4s = 48\implies s = \cfrac{48}{4}\implies \boxed{s = 12}[/tex]

Answer:

m∠DEB = _70_°

m∠BCD= _110_°

m∠EAB= _73_°​

Step-by-step explanation:

To find ∠DEB:

Take the angle of ∠EDC, which is 110°. We know the total degree in a triangle is 180°. So, we do 180° - 110° to get 70°.

To find ∠BCD:

Because EBCD is an isosceles trapezoid, this means that ∠D and ∠C both have the congruent angles. Since we know ∠EDC is 110°, this means that ∠C is also 110°.

To find ∠EAB:

We know that m∠ABC is 133° and ∠DEA is 114°. However, both angles count both the triangle and trapezoid. Previously we figured out that ∠DEB is 70°. We'll take the angle of ∠DEA and subtract the angle of ∠DEB from it, which gets us 44°. To figure out the angle of ∠B, we take the angle of ∠ABC and subtract 70° or the angle of ∠DEB, which gets us 63°. Now we take the total degree of a triangle, 180° and minus both 44° and 63° from it, which is 73°.

- 2021 Edmentum

Answer:

8 tablespoons1/2 cup4 ounces10 tablespoons plus 2 teaspoons2/3 cup5.2 ounces12 tablespoons3/4 cup6 ounces16 tablespoons1 cup8 ounces

Answer:

[tex]m = 2[/tex]

Step-by-step explanation:

Using mental math to find the slope of the line:

If you think about the formula, then you set up the points in your head, you will notice that the first point is on top of the second point. And that way makes it easy to simplify. All you would need to do is subtract down in your head: For example:

(0, 0)

(4, 8)

As you can see, the first point is on top of the other, and that way you can just subtract from bottom to top. If you do it that way, it is set up (Remember, you would do this all in your head)

Answer:

Step-by-step explanation:

r = 2.1 feet

h = 14 feet

V = pi r^2 h

V = 3.14 * 2.1^2 * 14

V = 193.85

Let h = 28 feet

V = pi * r^2 * h

V = 3.14 * 3.2^2 * 28

V = 387.72

If you divide 387.72 by 2 you get 193.86

The difference in the hundreds place comes about because of the rounding that took place.

The answer to your question is you must double the height,

Answer:

[tex]2\sqrt{5}[/tex]

Step-by-step explanation:

Since it is tangent to the center, the perpendicular line passes through the center, (2,-3). We find the slope of the perpendicular line to be -1/2 (perpendicular to a slope of 2). We can use point slope form to find the line from the tangent line to the center:

y+3=-1/2(x-2)

We can simplify this to

y= -1/2x-2

We can then check the point of intersection:

-1/2x-2=2x+3

-5=2.5x

x=-2

we can plug this in to the first equation to get y=2(-2)+3=-1

So the point of intersection of the circle and the tangent line is (-2,-1)

Then we find the distance of this point to (2,-3) and we can use pythagorean theorem.

[tex]\sqrt{(-2-2)^{2}+(-1-(-3))^{2} } =\sqrt{(-4)^{2}+2^{2} } =\sqrt{20} =2\sqrt{5}[/tex]

The radius of the circle is [tex]2\sqrt{5}[/tex]

For Line y=2x+3 is tangent to a circle with center (2,-3) then the length of the radius of the circle is 10/√5

The length along a line or line segment between two points on the line or line segment.

Distance=√(x₂-x₁)²+(y₂-y₁)²

The line y=2x+3 is tangent to the circle with center (2,-3)

The distance from the center of the circle to the line is equal to the radius of the circle.

The distance from a point (x₁, y₁) to a line Ax + By + C = 0 is given by the formula:

d = |Ax₁+ By₁ + C| /√A² + B²

The equation of the line is y = 2x + 3, which can be written in the form Ax + By + C = 0 as (-2)x + y - 3 = 0.

d = |-2(2) + (-3) - 3| / √(-2)² + 1²

d=10/√5

The radius of the circle is equal to the distance from the center to the tangent line, which is:

radius = 10/√5

Hence, for Line y=2x+3 is tangent to a circle with center (2,-3) then the length of the radius of the circle is 10/√5

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Answer:

D. 144km

Step-by-step explanation:

If the vehicle travels 72km every hour, in two hours, it will drive 144km. (72x2=144)

Ans. 450

Solve.

Add 100and you will get the ans

Answer:

1.is a function

2. is a function

3. is a function

4. is not a function

Step-by-step explanation:

Answer: 3500x1 or 35x100

Step-by-step explanation:

350x10=3500

3500x1=3500

35x100=3500

Answer:

0,1,2,3,4,5,6,7,8,9

Step-by-step explanation:

: probability of meeting someone with a phone number that ends with 3 .....

= 3/total amount of no ×100

3÷10= 0.3

: 0.3×100= 30% probability.

Assuming a phone number is 10 digits long and the last digit can be any of the 10 digits (0, 1, 2, 3, 4, 5, 6, 7, 8, or 9) with equal probability, the probability of randomly meeting someone with a phone number that ends in 3 is 1/10, or 0.1.

Probability is a number that expresses the likelihood or chance that a specific event will take place. Both proportions ranging from 0 to 1 and percentages ranging from 0% to 100% can be used to describe probabilities.

If the phone number is 10 digits long, there are 10 possible digits that could be at the end. Since only one of those digits is a 3,

the probability of randomly selecting a phone number that ends in 3 is:

1/10 = 0.1 or 10%

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Answer:

I don't know

Step-by-step explanation:

Answer:

11/18

Explanation:

Find the LCM

6 × 3 = 18

9 × 2 = 18

Since you found the LCM, multiply the numerators by the number you multiplied the denominators by.

[tex]\frac{5 *3}{6*3}= \frac{15}{18}[/tex]

[tex]\frac{2*2}{9*2}=\frac{4}{18}[/tex]

Now subtract.

[tex]\frac{15}{18} -\frac{4}{18} =\frac{11}{18}[/tex]

Answer:

$48

Step-by-step explanation:

Each ticket costs 4 dollars.

Answer:

n=6 , n=-2

Step-by-step explanation:

[tex]n^{2}-4n-12=0[/tex]

Factorise to give:

[tex](n-6)(n+2)[/tex]

Set first one to equal 0:

[tex]n-6=0[/tex]

[tex]n=6[/tex]

Set second one to equal 0:

[tex]n+2=0[/tex]

[tex]n=-2[/tex]

Reason for 2 solutions:

All quadratics can have a maximum of 2 solutions like this one or a minimum of 0.

The solution(s) is the point where the graph crosses the x-axis

The image below shows the graph of the equation:

[tex]n^{2}-4n-12[/tex]

When y=0:

It intercepts the x-axis at 6 and -2 giving why n has 2 solutions

Answer:

-3/5

Step-by-step explanation:

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

m=(6-3)/(-1-4)

m=3/(-5)

m=-3/5

Mary having a credit card could be beneficial to her present situation as it gives her the ability to move to the new apartment without making immediate cash payments.

A credit card is a payment card issued by a bank or financial services company to a cardholder to enable the cardholder to purchase goods and services on credit and later pay for them.

Credit cards and their interest rates are issued based on the user's credit rating.

Some of the benefits that Mary can derive from using credit cards include:

Thus, with a credit card, Mary can move to the new apartment by borrowing the required funds for advance payment, including additional moving expenses.

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Answer:

the graph is in link

Step-by-step explanation:

y ..... means full  line and shading above the line

Y< ......means  doted  line and shading below the line

A) solution is overlapping shaded part

B) (10,5)

plug in point in inequalities and check if it's true; if it's true you showed that solution is correct

1. 5-1/2*10 + 2 1/2

 5 -5 + 2 1/2

 5 -2 1/2 TRUE

2. 51/5*10 + 6

  5< 2 + 6

5< 8  TRUE

Answer:

Game #1B is the correct answer i guess so

To reach a raise of $ 700, you can sell 20 entire cheesecakes and 63 slices, or 10 entire cheesecakes and 132 slices, or 15 entire cheesecakes and 98 slices.

To determine, if they want to raise at least $ 700, how many of each could they sell, listing three possible combinations of entire cheesecakes and slices of cheesecake the players could sell to reach their goal, the following calculation must be performed:

Therefore, to reach a raise of $ 700, you can sell 20 entire cheesecakes and 63 slices, or 10 entire cheesecakes and 132 slices, or 15 entire cheesecakes and 98 slices.

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Answer:

x=3

Step-by-step explanation:

factoring

set to 0

Answer:

-3<lxl<5

Step-by-step explanation:

take least number than use x in absolute value bars than take highest number sorry if this is wrong I'm just a kid