Apply the distributive property to factor out the greatest common factor.
{25p + 50q} =25p+50q=25, p, plus, 50, q, equals

Answer:

d. The cost of natural gas (y) = $0.83 per unit

Step-by-step explanation:

The explanation is shown below:-

the equation of system is:

750x + 17y = 141.61  (i)        

300x + 30y =75.90 (ii)

as x indicates the cost of electricity and y indicates the costs of natural gas.

we will solve the both equation with the help of multiplication for (i) by 30 and for (ii) 75

[tex]30\times (750x + 17y) 30\times 141.61\\\\[/tex]

after solve the above equation we will get

22,500x + 510y = 4248.3 (iii)

[tex]75\times (330x + 30y) = 75\times 75.90[/tex]

after solve the above equation we will get

22500x + 2250y = 5692.5 (iv)

After deducting the equation (iii) and (iv) we will get

1740 y = 1444.2

After Dividing by 15 both sides,

116y = 96.28

So, Katrina simplify the above system using linear equation and reach at the equation that is

116 y = 96.28

By Division property of equality defines that divide the equal no. of both sides of an equation:

by  Division of 116 to both sides of an equation, to get y:

[tex]\frac{116y}{116} = \frac{96.28}{116}[/tex]

y = 0.83

So, the natural gas is $0.83 per unit

Answer:

d

Step-by-step explanation:

Answer:

5 < 10x – 3

Step-by-step explanation:

The inequality is 5 - 2x < 8x - 3.

5 < 6x – 3 is incorrect because 8x + 2x = 10x, not 6x.

3x < 8x – 3 is incorrect because 5 - 2x is not 3x, you can't subtract those terms as they are not like terms.

5 < 10x – 3 is correct because 8x + 2x = 10x.

2 – 2x < 8x is incorrect because 5 + 3 = 8, not 2.

Answer:

C on edg

Step-by-step explanation:

Answer:

Linear symmetry.

Step-by-step explanation:

The word 'TOOT' can be reflected  in y-axis if a point (0,0) on cartesian plane divides the words' TO' and 'OT' equally.

Answer:

  (A) see the attachments

Step-by-step explanation:

The graph is constant from x=2 to x=10. This eliminates all descriptions except A, which is the correct one.

Answer:

12√5

Step-by-step explanation:

6√5 + 6√5 = (6 + 6) * √5 = 12 * √5 = 12√5.

Answer:

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

Step-by-step explanation:

When you add the surds which are the same type, (both are root 5), just add the integers before them together.

do you know where is India

becz I am an Indian

Answer:

2,49/4,10/9

Step-by-step explanation:

[tex]1.\sqrt{4} =2\\2.\sqrt{x} =3+\frac{1}{2} =\frac{7}{2} \\x=\frac{49}{4} \\3.\sqrt{x} =3+\frac{1}{3} =\frac{10}{3} \\x=\frac{100}{9}[/tex]

Answer:

Step-by-step explanation:

To find x we use cosine

That's

cos ∅ = adjacent / hypotenuse

From the question

The adjacent is x

The hypotenuse is 28

So we have

cos 43 = x / 28

x = 28 cos 43

x = 20.477

x = 20 to the nearest tenth

Hope this helps you

Answer:

1kg of salami cost $9.1

Step-by-step explanation:

Hailey paid $13 for 1 3/7 kg of sliced salami.

What was the cost per kilogram of salami?

Cost of 1 3/7 kg of sliced salami=$13

1 3/7 kg=10/7kg

Let x=1 kg of sliced salami

10/7 kg of x=$13

$13=10/7x

13=10/7*x

x=13 ÷ 10/7

=13×7/10

=91/10

=9.1

x=$9.1

Therefore, 1kg of salami cost $9.1

Answer: x=-10

Step-by-step explanation:

5*(12+x)=10

Distribute

60+5x=10

Subtract(60)

5x=-50

x=-10

Hope it helps <3

Answer:

Heeyyy hope it helps

Step-by-step explanation:

Ok, so the product is the answer to a multiplication problem.

The product of 5 and the sum of a number(X) and 3 is

5(X + 3) = 12

5X + 15 = 12

5X = 12 - 15

5X = -3

X = -3/5

I'll be using the following properties about exponents:

[tex]a^b \times a^c=a^{b+c}[/tex]

[tex]a^b \div a^c=a^{b-c}[/tex]

[tex](a^b)^c=a^{bc}[/tex]

where a, b, and c are some positive integers

Part a:

[tex]8^5 \times 8^4 = 8^{5+4}=8^9[/tex]

Part b:

[tex]3^{11} \times 3 = 3^{11} \times 3^{1} = 3^{11+1} = 3^{12}[/tex]

Part c:

[tex]9^3 \times 9^7 = 9^{3+7}=9^{10}[/tex]

Part d:

[tex]7^7 \div 7 = 7^7 \div 7^1 = 7^{7-1}=7^6[/tex]

Part e:

[tex]12^{10} \div 12^5 = 12^{10-5}=12^5[/tex]

Part f:

[tex](6^3)^6 = 6^{6 \times 3} = 6^{18}[/tex]

These should be all the answers. Let me know if you need any clarifications, thanks!

Answer:

25

Step-by-step explanation:

let his age be x, then

5 years ago his age was x - 5 and in 5 years will be x + 5 , thus

(x - 5)(x + 5) = 600 ← expand factors using FOIL

x² - 25 = 600 ( add 25 to both sides )

x² = 625 ( take the square root of both sides )

x = [tex]\sqrt{625}[/tex] = 25

Answer:

[tex]\boxed{Age \ of \ man = 25 \ years}[/tex]

Step-by-step explanation:

Let the age be x

Then, the given condition is:

(x-5)(x+5) = 600     [ x-5 for age 5 years ago and x+5 for age 5 years after ]

Using Formula [tex](a+b)(a-b) = a^2-b^2[/tex]

[tex]x^2-25 = 600[/tex]

Adding 25 to both sides

[tex]x^2 = 600+25[/tex]

[tex]x^2 = 625[/tex]

Taking sqrt on both sides

[tex]x = 25[/tex] years

Answer:

30 degrees

Step-by-step explanation:

25 cm in length, radius 3.5cm

Answer and Step-by-step explanation:

a. As the friend claim is wrong as he flipped the coin very less i.e 10 only which reflects the number of time he flipped the coins. And we know that the probability is based on an imagination that could have a long series with respect to indefinite trails i.e unlimited

b. Since your friend flipped very less i.e only 10 which is not sufficient to get the nearest estimate your friend should flipped many times so that he would able to come very close.

Answer:

The answer is

Step-by-step explanation:

Equation of a line is y = mx + c

where

m is the slope

c is the y intercept

To find the equation of the line we must first find the slope

That's

Slope of the line using points

(8,-8) and (-5,-8) is

[tex]m = \frac{ - 8 + 8}{ - 5 - 8} = \frac{0}{ - 13} = 0[/tex]

So the equation of the line using point (8,-8) is

y + 8 = 0(x - 8)

y + 8 = 0

We have the final answer as

Hope this helps you

Answer:

The base is 10cm. The other two sides are 20cm each

Step-by-step explanation:

I believe that "the base is twice shorter" means that the two equal sides of the iscosceles triangle are twice the length of the base.

Using the equation x + 2x +2x = 50 where x is the length of the base, we can simplify it to

5x=50. Then divide both sides by 5 to get the results:

x=10 for the base and

2x=20 for the other two sides.

Answer:

3[tex]a^{4}[/tex] - 48

Step-by-step explanation:

Given

(a + 2)(3a² + 12)(a - 2)

= (a + 2)(a - 2)(3a² + 12) ← expand the first pair of parenthesis using FOIL

=(a² - 4)(3a² + 12) ← expand using FOIL

= 3[tex]a^{4}[/tex] + 12a² - 12a² - 48 ← collect like terms

= 3[tex]a^{4}[/tex] - 48

Answer:

exact form: n=378/13

decimal form: n=29.0769....

mixed number form: n=[tex]29\frac{1}{13}[/tex]

Step-by-step explanation:

Answer:

n = 21

Step-by-step explanation:

[tex]\frac{n}{2}-\frac{3n}{9}+\frac{5n}{9}=21\\\\\frac{9n}{18}-\frac{6n}{18}+\frac{10n}{18}=21\\\\\frac{3n}{18}+\frac{10n}{18}=21\\\\\frac{13n}{18}=21\\\\13n=273\\\\n=21[/tex]

Steps:

1. Write as fractions

2. Make the fractions have the same denominator

3. Collect like terms

4. Collect like terms

5. Multiply both sides by 18

6. Divide both sides by 13.

Answer:

SAT vs. IQ because the data points are closer to the trend line.

Step-by-step explanation: The accuracy of linear model is based on the sum of the squared error between the actual and predicted data. Therefore in drawing our trend line, we want one in which gives the least sum of squared error(distance between trend line and the actual data point). With such a trend line, we'll get a more accurate prediction from our model. The rate of change does not rely dictate accuracy of a model, it only explains how a variable changes in relation to another. From both graphs, the data point on the SAT v IQ graph AR closer to the trend lines and as such will produce a lower sum of squared error than the GPA v IQ model.

Answer:

a

Step-by-step explanation:

Answer:

D

Step-by-step explanation:

You know that you have to find y, so eliminate choice B. She reads 30 per day, which is c, so you will have 30x. She also read 15 pages separately, so the 15 will be added on separately. With this, you get y = 30x + 15.

Answer:

D.

Step-by-step explanation:

Since she already read 15 pages in the bookstore, those 15 pages are constant since she cannot unread those pages. Those pages are the y-intercept of the equation.

Gwen is reading 30 pages per day, so her slope will be 30.

D. y = 30x + 15 will be her equation.

Hope this helps!

Answer:

one ticket is $1.20

Step-by-step explanation:

6 / 5 = 1.2, then check it by multiplying 1.2 x 5. Its easier than you think. Im positive im correct. All you have to do is one but if u want to make sure you can do all of them

Answer:

$1.20

Step-by-step explanation:

If you divide the price of a ticket bundle by the amount of tickets, you get the individual ticket price.

5 tickets for $6.

6/5 = 1.2

10 tickets for $12.

12/10 = 1.2

15 tickets for $18

18/15 = 1.2

Answer:

Step-by-step explanation:

Given the expression after 4 has been subtracted from both sides as

1/2 x = - 1/2 x, the original expression will be gotten by adding back 4 to both sides of the resulting expression as shown;

1/2 x + 4 = - 1/2 x + 4

x/2 + 4 = -x/2 + 4

Find the LCM of both equation;

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

Multiplying both sides by 2 will give;

x+8 = -x+8

Collecting the like terms;

x+x = 8-8

2x = 0

x = 0/2

x = 0

Hence, the value of x is 0

Answer:

0

Step-by-step explanation:

Answer:

77

Step-by-step explanation:

slope equation

Answer:

6510ml

Step-by-step explanation:

1cl = 10ml

651cl = ?

651 × 10 = 6510ml

Answer is 6510ml

Answer:

The function has two real roots and crosses the x-axis in two places.

The solutions of the given function are

x = (-0.4495, 4.4495)

Step-by-step explanation:

The given quadratic equation is

[tex]G(x) = -x^2 + 4x + 2[/tex]

A quadratic equation has always 2 solutions (roots) but the nature of solutions might be different depending upon the equation.

Recall that the general form of a quadratic equation is given by

[tex]a^2 + bx + c[/tex]

Comparing the general form with the given quadratic equation, we get

[tex]a = -1 \\\\b = 4\\\\c = 2[/tex]

The nature of the solutions can be found using

If [tex]b^2- 4ac = 0[/tex] then we get two real and equal solutions

If [tex]b^2- 4ac > 0[/tex] then we get two real and different solutions

If [tex]b^2- 4ac < 0[/tex] then we get two imaginary solutions

For the given case,

[tex]b^2- 4ac \\\\(4)^2- 4(-1)(2) \\\\16 - (-8) \\\\16 + 8 \\\\24 \\\\[/tex]

Since 24 > 0

we got two real and different solutions which means that the function crosses the x-axis at two different places.

Therefore, the correct option is the last one.

The function has two real roots and crosses the x-axis in two places.

The solutions (roots) of the equation may be found by using the quadratic formula

[tex]$x=\frac{-b\pm\sqrt{b^2-4ac}}{2a}$[/tex]

[tex]x=\frac{-(4)\pm\sqrt{(4)^2-4(-1)(2)}}{2(-1)} \\\\x=\frac{-4\pm\sqrt{(16 - (-8)}}{-2} \\\\x=\frac{-4\pm\sqrt{(24}}{-2} \\\\x=\frac{-4\pm 4.899}{-2} \\\\x=\frac{-4 + 4.899}{-2} \: and \: x=\frac{-4 - 4.899}{-2}\\\\x= -0.4495 \: and \: x = 4.4495 \\\\[/tex]

Therefore, the solutions of the given function are

x = (-0.4495, 4.4495)

A graph of the given function is also attached where you can see that the function crosses the x-axis at these two points.

Answer:

x=1

x=-2

Step-by-step explanation:

(3x-3)(x+2)

x=1

x=-2

Answer:

D. so you don't confuse properties of the model with properties of the real thing.

2-Mathematical and computer models are similar because both involve using calculation to represent an object or system

3- Some models can illustrate a system. What does the term system refer to

A. a collection of interacting things

4-J.J. Thomson's Plum Pudding Model is an example of _____B. an analogy

5. An advantage of describing a cell as being like a factory is that it _____

A. makes cells easier to understand

6- C. cheaper and more complex

7-C. clearly explained where electrons were located in an atom

8-C. a physical model

9-B. can be easier to change

GOOD LUCK

Answer:

Misty is the more consistent employee

Step-by-step explanation:

The given data are

Misty: 11, 13, 12, 14, 10, 16, 14

Brock: 8, 15, 10, 11, 16, 10, 9

The mean of Misty's successfully answered questions = ∑x/n = 90/7 = 12.86

Misty's data standard deviation = √(∑(x - μ)²/n) = 1.884

The mean of Brock's successfully answered questions = ∑x/n = 79/7 = 11.29

Brock's data  standard deviation = √(∑(x - μ)²/n) = 2.81

Therefore, based on the value of the standard deviation which is a measure of variability, whereby the standard deviation of Brock's number of successfully answered questions is larger than the standard deviation of Misty's number of tech supported successfully answered questions, Misty is the more consistent employee.

Answer:

333 cars

Step-by-step explanation:

Assuming among 6 agents, the working efficiency is the same and constant. Fixing number of agents:

    6 agents can sell 333 cars in 3 months.

=> 6 agents can sell 333/3 cars in 3/3 month.

=> 6 agents can sell 111 cars in 1 month.

Fixing number of months:

=> 6/2 agents can sell 111/2 cars in 1 month.

=>  3 agents can sell 111/2 cars in 1 month.

Then considering that 3 agents worked in 6 months:

=> 3 agents can sell 6 x 111/2 cars in 6 x 1 months.

=> 3 agents can sell 333 cars in 6 months.

Answer:

  1.999396

Step-by-step explanation:

2 = (√2)² = 1.414² = 1.999396

Answer: B

Step-by-step explanation:

Answer:

b

Step-by-step explanation: