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Answer:

24 ounces.

Step-by-step explanation:

Given that the ratio of blue paint to yellow paint in a green paint mixture is 2:3.

Actual ounces used for blue paint = 16

By ratio and proportion property we have

2:3 = 16:x where x is the actual ounces of yellow paint used.

Simplify using ratio rules

if a:b = c:d then ad = bc

We get

2x=3(16) = 48

Divide by 2

x = 24

Hence 24 ounces of yellow paint to be used.

Answer:

24 ounces. to be exact

Step-by-step explanation:

-3.

Hope this helped.

Answer:

x = -3

Step-by-step explanation:

Solving for value of x

−x + (−3) = x + 3              

-x -3 = x + 3                     [subtract x from both side]

-x -3 -x = x + 3 -x

-2x -3 = 3                       [add 3 to both side]

-2x -3 + 3 = 3 + 3

-2x = 6                          [divide both side by -2]

[tex]\frac{-2x}{-2}[/tex] = [tex]\frac{6}{-2}[/tex]

x = -3

The first thing you would do is "bring" the 10 over by subtracting 10 from both sides

[tex]3x^2+13x-10=0[/tex]

Now, you would want to factor

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

Then, set each factor equal to zero, and solve

3x-2 = 0

3x = 2

x = 2/3

AND

x+5 = 0

x=-5

An equation is a mathematical statement that is made up of two expressions connected by an equal sign.

The determinant is given as:

D = -b ±√(b² - 4ac) / 2a

The values of x are:

x = (-13 + √17) / 6

x = (-13 - √17 ) / 6

An equation is a mathematical statement that is made up of two expressions connected by an equal sign.

Example:

x + 3 = 4 is an equation.

3x + 4x = 4 is an equation.

We have,

3x² + 13x = 10

This can be written as:

3x² + 13x - 10 = 0

Using the Middle term factorization.

3x² + (10 + 3)x - 10 = 0

3x² + 10x + 3x - 10 = 0

This is not possible so,

Using determinant.

3x² + 13x - 10 = 0

a = 3, b = 13 and c = -10

Now,

Determinant is given as:

D = -b ±√(b² - 4ac) / 2a

D = -b + √(b² - 4ac) / 2a

D = [-13 + √(169 + 120)] / 6

D = (-13 + √17) / 6 _____(1)

D = -b - √(b² - 4ac) / 2a

D = -13 - √(169 + 120) / 6

D = (-13 - √17 ) / 6 ______(2)

Thus,

The values of x are:

x = (-13 + √17) / 6

x = (-13 - √17 ) / 6

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Answer:

15.5

Step-by-step explanation:

Answer: x = -1, -3, 7 + √62, 7 - √62

Step-by-step explanation:

q                                    p

x⁴ - 10x³ - 66x² - 94x - 39

[tex]\frac{p}{q}[/tex] = +/- [tex]\frac{1*3*13*39}{1}[/tex]

possible rational factors: 1, -1, 3, -3, 13, -13, 39, -39

Use synthetic division or long division to see which factor will leave a remainder of 0.

try x + 1 = 0  ⇒   x = -1

-1   |  1     -10     -66     -94     -39

    |  ↓     -1        11        55      39

       1     -11      -55     -39       0

(x + 1)(x³ - 11x² - 55x - 39)        

next, try x + 3 = 0  ⇒   x = -3   for the new polynomial

-3   |  1     -11     -55     -39

     |  ↓     -3       42     39

        1     -14      -13       0  

(x + 1)(x + 3)(x² - 14x - 13)

Lastly: find the zeros by setting each factor equal to zero and solve.

x + 1 = 0  ⇒  x = -1

x + 3 = 0   ⇒ x = -3

x² - 14x - 13 = 0

[tex]x = \frac{-(b) +/- \sqrt{(b)^{2} -4(a)(c)}}{2(a)}[/tex]

  [tex]= \frac{-(-14) +/- \sqrt{(-14)^{2} -4(1)(-13)}}{2(1)}[/tex]

  [tex]= \frac{14 +/- \sqrt{196+52}}{2}[/tex]

  [tex]= \frac{14 +/- \sqrt{248}}{2}[/tex]

  [tex]= \frac{14 +/- 2\sqrt{62}}{2}[/tex]

  [tex]= 7 +/- \sqrt{62}[/tex]

Answer:

The man got a 8% raise.

Step-by-step explanation:

Percentage change        = [Increase or decrease in value / Original Value]*100

Increase in hourly wage = [tex]13.5-12.5[/tex]

                                         =[tex]1[/tex]

Percentage raise             = [Increase in hourly wage / Initial hourly wage]*100

                                         =[tex]\frac{1}{12.5} *100[/tex]

                                         = [tex]8[/tex]%

The man got a 8% raise.

The man's hourly wage increased from $12.50 to $13.50 which, following the formula for calculating percentage change, indicates that he received an 8 percent raise in his hourly wage.

Given that the man's hourly wage increased from $12.50 to $13.50, we can use the formula for calculating the percentage change to find out what percent raise he got.

The formula for calculating the percentage change is as follows:

[(change in quantity)/(original quantity)] × 100

In this case, the change in quantity (the man's wage increase) is $1.00 (13.50 - 12.50), and the original quantity (the man's original wage) is $12.50.

Plugging these values into the formula, we get:

[1.00/12.50] × 100

This calculates to an 8 percent wage increase. Therefore, the man got an 8 percent raise in his hourly wage.

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[tex]5\cdot5\cdot4\cdot4\cdot3\cdot3\cdot2\cdot2\cdot1\cdot1\cdot2=28,800[/tex]

Its x^2 if x > -1

x = 3  so the answer is 3^2  = 9

Initial velocity of the ball (u) = 80 ft/ sec

Final velocity of the ball after reaching the ground (v) = 0

Distance covered by the ball to reach the ground (s) = 8 ft

Let "a" be the acceleration of the ball.

We know, [tex]2as=v^{2}-u^{2}[/tex]

[tex]2a(8)=0-80^{2}=-6400[/tex]

[tex]a=-\frac{6400}{16}[/tex]

[tex]a=-400ft/s^{2}[/tex]

Let "t" be the time required to reach the ground.

We know,

[tex]v=u+at[/tex]

[tex]t=\frac{v-u}{a}[/tex]

[tex]t=\frac{0-80}{-400}[/tex]

[tex]t=0.2s[/tex]

The ball will hit the ground in 0.2 second.

A

f(x) = 2x + 1

f(3) = 2*3 + 1 = 7

B

g(x) = x^2

g(7) = 7^2

g(7)= 49

C

f(g(x)) = 2(g(x) + 1

f(g(x)) = 2 x^2 + 1

f(g(3) = 2* 3^2 + 1

f(g(3) = 19

D

g(f(x)) = (f(x))^2

g(f(x)) = (2x + 1)^2

g(f(3)) = (2*3 + 1)^2 = (6 + 1)^2 = 49

E

f(g(x)) = 2*g(x) + 1

f(g(x)) = 2*x^2 + 1

f(g(3)) = 2*3^2 + 1

f(g(3)) = 2 * 9 + 1

f(g(3)) = 18 + 1

f(g(3) = 19

F

f(g(x)) = 2(g(x)) + 1

f(g(x)) = 2*x^2 + 1  

We are given a figure where M, N , O and P points are given.

We need to explain if points O, N, and P collinear or not.

Note: All co-linear points are in a straight line.

From the figure, we can see that O and N points are in a straight line but point P is aside.

So, the points O, N, and P are not collinear.

Therefore, correct option is "No, the three points are not collinear".

10 -:- 5. This is the answer. Hope this helps:)

The function for the given situation is f=60h+75.

Given that, a plumber's fees f are $75 for house calls and $60 per hour h for each hour worked.

We need to model a function for the given situation.

Functions are the fundamental part of calculus in mathematics. The functions are the special types of relations. A function in math is visualized as a rule, which gives a unique output for every input x. Mapping or transformation is used to denote a function in math. These functions are usually denoted by letters such as f, g, and h.

According to the question, we can model function as follows:

f=60h+75

Therefore, the function for the given situation is f=60h+75.

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place x to the other side of the equation

x=15/2.5

x=6

Answer:

6

Step-by-step explanation:

If you take 15 and divide it. by 2.5 you. get 6

Answer:

If you can maintain this speed you will travel 120 km in 1 hour.

Explanation:

The translated question is, A cheetah can travel 20 kilometers in 10 minutes. If I could maintain this speed for one hour, how many kilometers would you travel?.

 Let us find the speed of cheetah

            Distance traveled =  20 km

            Time taken = 10 minutes = 10/60 = 1/6 hours

            So speed = [tex]\frac{20}{\frac{1}{6} } =120[/tex]km/hr.

 So speed of cheetah = 120 km/hr, which means cheetah will travel 120 km in 1 hour.

If you can maintain this speed you will also travel 120 km in 1 hour.

Apply the vertical line test. Think of a vertical line moving from left to right in the graph. If the graph of the relation intersects the vertical line in more than one point in any position of the vertical line, then the relation is not a function.

The only graph that passes the vertical line test is the graph at the bottom right.

The graph at the bottom right is a function. All others are not.

Answer:

option d

Step-by-step explanation:

Solve each inequality and check which inequality has -12 as a solution

a. [tex]x+6<-8[/tex]

Subtract 6 from both sides

[tex]x<-14[/tex]

b. [tex]x+4>-6[/tex]

Subtract 4 from both sides of the inequality to get x alone

[tex]x>-10[/tex]

c.[tex]x-3>-0[/tex]

Add 3 on both sides

x>3

d. [tex]x+5<-4[/tex]

Subtract 5 from both sides

x<-9

-12 lies below -9. So x<-9 has -12 in its solution

Starting with 113+ (2x+5)=180, combine like terms and to get 118+2x=180.  Subtract 180-118, which gives you 62.  Then you have 2x=62.  Divide both sides by 2 to get a final answer of x=31.

Hey there!!

Given :

... 113 + ( 2x + 5 ) = 180

Subtract 113 on both sides

... 2x + 5 = 180 - 113

... 2x + 5 = 67

Subtract 5 on both sides

... 2x = 62

Divide by 2 on both sides

... x = 31

The value of x is 31.

Hope my answer helps!!

Answer:

81

Step-by-step explanation:

x^2 − 18x + 9^2 = 17 + 9^2

=> x^2 − 18x + 81 = 17 + 81

The queen might've asked the king to measure the rug to demonstrate humility, responsibility, highlight practical skills, or grasp the concept of measurement. Without specific context, however, it's hard to pinpoint an exact reason.

Without specific context, it's difficult to provide an exact reason for the queen asking the king to measure a rug. However, in general, English literature often showcases rulers partaking in ordinary tasks as a means of demonstrating humility, responsibility, or attention to detail. For instance, the queen might have wanted the king to measure the rug in order to prove that he can attend to ordinary matters as well as royal duties, or perhaps to prove himself practical and not merely ceremonial. It could also be a ploy to make the king grasp the concept of measurement, size or area, by doing the task himself.

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(18)

2.5% of 129,500 is

$129500 * 0.025 = $3237.50 is the commission on the sale

(19)

sales $3012

commission 3.5% of sales: 0.035 * 3012 = $105.42

Raquelle's total earnings: $290 + 105.42 = $395.42

Answer:

Option D

0.6

Step-by-step explanation:

Given that there are 5 colour marbles in a large bag.

The colours are red, orange, yellow, blue and green.

Also given that there are equal amounts of each colour

Let n be the no of marbles of each colour.

Then total no of marbles = 5(n) = 5n

No of red,blue and yellow marbles = n+n+n = 3n

Prob of drawing a red or blue or yellow = P(red)+P(blue)+P(yellow)

= [tex]\frac{n}{5n} +\frac{n}{5n} +\frac{n}{5n}  = \frac{3n}{5n}[/tex]

= 0.60

Here are the answers below that I got. Hope this helps mate. Cheers.

Answer:

As mention in the explanation steps.

Step-by-step explanation:

The following expression or phrase to each box are helpful to complete the proof.

(1). We say that ∠ACB and ∠BCD are supplementary, from linear pair of postulate.

(2). ∠ACB + ∠BCD =180°, because ∠ACB and ∠BCD are supplementary (from the difinition of supplementary angles).

(3). ∠ACB +45° = 180° because ∠BCD =45°(substitute).

(4).Subtraction properties of equality ( because we subtract 45 degree from both sides of the previous equation).

(5). ∠ABC is obtuse, because m∠ABC grater than 90°.

(6). From the definition of obtuse triangle (ΔACB is an obtuse triangle because ∠ACB =135 degree which is grater than 90 degree).

Answer:

Amount John gets paid per hour [tex]6.92[/tex] Dollars per hour ,

Step-by-step explanation:

To find how much he gets paid per hour we need to divide the total payment he received by the total number of hours he worked.

Amount John gets paid per hour = [tex]\frac{173}{25}[/tex] Dollars per hour.

                                                       =[tex]6.92[/tex] Dollars per hour

$6 dollars on candy because 35+25+10=70, 76-70=$6

14.50 times 0.20 = 2.9

He would give a $2.90 as a tip of 20% from a bill of $14.50

1. 4x = 7(x - 3)   GIVEN

4x = (7)(x) + (7)(-3)

2. 4x = 7x - 21     DISTRIBUTIVE PROPERTY

4x - 7x = 7x - 7x - 21

3. -3x = -21    SUBTRACTION PROPERTY OF EQUALITY

-3x : (-3) = -21 : (-3)

4. x = 7      DIVISION PROPERTY OF EQUALITY

1. Given

2. Distributive Property

3.Subtraction Property of Equality

4. Division Property of Equality

So, the product of (9x - 2)(3x - 8) in standard form is: [tex]27x^2 - 78x + 16[/tex]

To multiply the expressions (9x - 2) and (3x - 8)

Step 1: Use the distributive property

(9x - 2)(3x - 8) = 9x * (3x) + 9x * (-8)

(9x - 2)(3x - 8) = -2 * (3x) - 2 * (-8)

So , perform the multiplications:

Multiply the terms:

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

9x * (-8) = -72x

-2 * 3x = -6x

-2 * (-8) = 16

Combine like terms:

[tex]27x^2 - 72x - 6x + 16[/tex]

Simplify further by combining like terms:

27x^2 - 78x + 16

So, the product of (9x - 2)(3x - 8) in standard form is: [tex]27x^2 - 78x + 16[/tex]

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