What is the solution to this system of equations?

2x - y = 8
x + y = 4
A. (2, -4)
B. (4, 0)
C. (6, 4)
D. (12, -8)

Option C

Math teacher would need to buy 130 prizes

Solution:

Given that,

Math teacher currently has 109 students and the box has 88 prizes in it

The math teacher likes to keep at least twice as many prizes in the box as she has students

So, she wants the number of prizes to be twice the number of students

Therefore,

number of prizes = 2 x 109 students

number of prizes = 2 x 109 = 218 prizes

The box has 88 prizes in it

Therefore, number of prizes she would need to buy is:

⇒ 218 - 88 = 130

Thus she would need to buy 130 prizes

Answer:

y>- 22/63

Step-by-step explanation

-65y+19<-2y+41

-65y+2y<41-19

-63y<22

y>-22/63

The solution to the inequality is y > -22/63.

To solve the inequality -65y + 19 < -2y + 41 for y, we'll follow these steps:

-65y + 19 < -2y + 41

First, we'll combine like terms by moving the terms with y to the left side and the constant terms to the right side:

-65y + 2y < 41 - 19

-63y < 22

Next, we'll isolate y by dividing both sides of the inequality by -63. Remember that when we divide by a negative number, the inequality sign flips:

y > 22 / -63

Simplifying the fraction:

y > -22/63

Therefore, the solution to the inequality is y > -22/63.

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Answer:

17576 Combinations.

Step-by-step explanation:

There are 26 letters in the Current English Lexicon (Alphabet), If there are 3 letters in a person's initials, then our equation would turn out to be "26³ =  17576". So, There are 17576 different possible combinations.

Final answer:

The total number of possible initials a person can have, using the first letters of their first name, middle name, and last name in the English alphabet, is 17,576. This is calculated by multiplying the number of alphabet letters (26) for each initial, resulting in a product of 26 x 26 x 26.

Explanation:

To calculate the number of possible initials a person can have from their first name, middle name, and last name, we must consider that each initial can be any letter from the English alphabet, which has 26 letters. Since each initial is independent of the others, the total number of possible initials is found by multiplying the number of options for each initial together.

The calculation is as follows:

First name initial: 26 possibilities (A-Z)

Middle name initial: 26 possibilities (A-Z)

Last name initial: 26 possibilities (A-Z)

So, the total number of possible initials would be:

26 (for the first name) x 26 (for the middle name) x 26 (for the last name) = 17,576 possible initials.

Answer:

253.75

Step-by-step explanation:

Answer:

it is B 2.5

Step-by-step explanation:

The height of the pan that he should use for the batter to completely fill the pan is 2.5 inches.

From this interactive, formula for volume is V = l w h (volume equals length times width times height) and can also be written V = B h (volume equals the area of the base times the height).

The volume is equal to the product of the area and height of the shape. Volume = Base Area x Height.

Given:

Base Area= 45 sq. inches

Volume= 112.5 cubic inches

So,

Volume= Base Area x Height

112.5 = 45 x Height

Height= 112.5 / 45

Height =  2.5 inches

Hence, the height of the pan that he should use for the batter to completely fill the pan is 2.5 inches.

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5x^2 + 7x -6

Rewrite the middle term whose product equals first term x last term: 5 x -6 = -30 and whose sum equals the middle term.

Rewrite 7 as -3 + 10

5x^2 +(-3+10)x -6

Use distributive property:

5x^2 -3x + 10x -6

Group the first two terms and last two terms:

(5x^2 -3x) (10x -6)

Factor out greatest common factor of each group to get final answer:

(5x-3)(x+2)

Answer:

It is 5 to 3

Step-by-step explanation:

Answer:

d

Step-by-step explanation:

Answer: The five exponent properties are

Product of Powers: When you are multiplying like terms with exponents, use the product of powers rule as a shortcut to finding the answer. It states that when you are multiplying two terms that have the same base, just add their exponents to find your answer.

Power to a Power.: When raising a power to a power in an exponential expression, you find the new power by multiplying the two powers together. ... Then multiply the two expressions together. You get to see multiplying exponents (raising a power to a power) and adding exponents (multiplying same bases).

Quotient of Powers.:  When you are dividing like terms with exponents, use the Quotient of Powers Rule to simplify the problem. This rule states that when you are dividing terms that have the same base, just subtract their exponents to find your answer. The key is to only subtract those exponents whose bases are the same.

Power of a Product: The Power of a Product rule is another way to simplify exponents. ... When you have a number or variable raised to a power, it is called the base, while the superscript number, or the number after the '^' mark, is called the exponent or power.

Power of a Quotient.: The Power of a Quotient rule is another way you can simplify an algebraic expression with exponents. When you have a number or variable raised to a power, the number (or variable) is called the base, while the superscript number is called the exponent or power

You can use these any way you want to rewrite an equation.

Hope this helped

:D

The properties of exponents are rules to simplify expressions with powers, which include adding exponents when multiplying like bases, multiplying exponents when raising powers to powers, and subtracting exponents when dividing like bases.

The properties of exponents are mathematical rules used to rewrite expressions involving powers in simpler or alternative forms. These properties are essential for performing operations with exponents and include rules for multiplying, dividing, and raising powers to powers.

Examples of Exponent Properties

Multiplying Powers with the Same Base: 10³ × 10² = 10³+2 = 10µ.

Raising a Power to a Power: (5³)⁴ = 5³×4 = 5¹², or 5 multiplied by itself 12 times.

Negative Exponents: 2.4 x 10⁻² tells you to move the decimal point to the left twice, which equals 0.024.

Application of Exponent Properties

To apply these properties, you would systematically use the appropriate rule based on the operation you're performing. For multiplication, add the exponents when the bases are the same. For powers, multiply the exponents. For division, subtract the exponents when the bases are the same. Using these rules simplifies complex expressions and makes it easier to work with exponents in algebra and science.

Answer: x=279,936

Step-by-step explanation:

See attachment

Answer:

Step-by-step explanation:

The volume formula for a cylinder is B*h

B : the area of the base

h : the height

Cylinder 1

The volume is 8pi

Cylinder 2

The volume is 32pi

Cylinder 3

The volume is 72pi

Answer:

Cylinder 1:  V = 8π

Cylinder 2:  V = 32π

Cylinder 3:  V = 72π

Step-by-step explanation:

The volume of the cylinder of radius r and height h is calculated using the form:  V = π r² h

Cylinder 1:  r = 1 cm  and  h = 8 cm

Volume of Cylinder 1 = π r² h = π 1² * 8 = 8π

Cylinder 2:  r = 2 cm  and  h = 8 cm

Volume of Cylinder 2 = π r² h = π 2² * 8 =  π * 4 * 8 = 32π

Cylinder 3:  r = 3 cm  and  h = 8 cm

Volume of Cylinder 1 = π r² h = π 3² * 8 = π * 9 * 8 = 72π

Answer:

r > -178

Step-by-step explanation:

Solving the equations means to find what "r" can be for the equation to be true.

If the sign < confuses you, you can always write = then change it back.

To find "r", we need to isolate it. To do this, we move "r" to the left side, and every other number to the right side. When you move something to the other side, remember you need to do the reverse operation on both sides.

I want to move -195 first. The opposite is +195.

-17 < -195 - r

-17 + 195< -195 + 195- r    Add 195 to both sides. 195 cancels out on the right

-17 + 195 < -r           Simplify left right by add 195 to -17

178 < -r             The opposite of multiply by -1 is divide by -1.

178/-1 < -r/-1          Divide both sides by -1.

178/-1 < r          "r" is isolated now. Simplify left side

-178 < r          Answer is found. Put variable on left side. Remember the keep the open side of the symbol facing "r".

r > -178         The solution is when "r" is greater than -178.

Answer:8:24

Step-by-step explanation:

So since it is 1:3 and 2 dozen is 24 so 24 divided by 3 = 8 so now it’s 8:24

Answer:

1. This equation of m<a + m<c = m<b - m<c wouldn't be correct unless the measure of angle c was 0. So technically there is no statment to make that equation true.

2. Angle addition postulate.

3. Transitive property of equality.  

4. Substitution property.

Step-by-step explanation:

You might want to recheck and see if these are the correct answer they seem to be to me. Im only in 10th grade so i kind of just learned this.

If you have any questions feel free to ask in the comments - Mark

Also when you have the chance please mark me brainliest.

Answer:

equation of line m is x=3

equation of line n is y=-4

Step-by-step explanation:

Line m has no y intercept, and its x-intercept is (3,0).

When a line has no y intercept then it is a vertical line

for any vertical line the equation is x= x1

(3,0) is (x1,y1)

so equation of line m is x=3

Line n has no x intercept and its  y -intercepts is (0-4).

When a line has no x intercept then it is a horizontal  line

for any horizontal line the equation is y= y1

(0,-4) is (x1,y1)

so , the equation of line n is y=-4

You divide 20 by 100

Answer:

Step-by-step explanation:

Answer:

Step-by-step explanation:

-0.5(3x + 5)   and   -1.5x + 2.5

-0.5(3x + 5)...distribute the -0.5 thru the parenthesis

-1.5x - 2.5

no, these are not equivalent.... one is -1.5x + 2.5 and the other is -1.5x - 2.5....not the same

Answer:

Both expressions are not equal

Step-by-step explanation:

First expression is

-0.5(3x + 5)

By multiplying

-1.5x - 2.5

2nd expression is

-1.5x + 2.5

Only Sign is different with 2.5 in both cases

Answer: 50 words per minute

Step-by-step explanation: You need to find the unit rate, so you solve 150=3x to get x=50

Answer: x=−3 or x=−5

Step-by-step explanation:

Step 1: Factor left side of equation.

(x+3)(x+5)=0

Step 2: Set factors equal to 0.

x+3=0 or x+5=0

x=−3 or x=−5

Answer:

These are the answers

Step-by-step explanation:

Answer:

The 4th Image

Step-by-step explanation:

Answer: 36

Step-by-step explanation:

120 students is the same as 100%, so you would divide 120 by 100 and your quotient would be 1.2 Then you multiply 30 by 1.2, since you would multiply 100 by 1.2 to get 120. 30×1.2=36. So 36 seventh graders have completed their science project.

Answer:

a

Step-by-step explanation:

Answer:

133

Step-by-step explanation:

Evaluate g(- 5) then substitute the value obtained into f(x)

g(- 5) = - 5 - 3 = - 8, then

f(- 8) = 2(- 8)² + 5 = 2(64) + 5 = 128 + 5 = 133

Answer:

1/4

Step-by-step explanation:

It is 1/4 because you divide the fraction by its highest multiple for 6 and 24 its 6, so you divide the numerator and denominator by 6.

Answer:

y = 2.50 , x = 1.25

Step-by-step explanation:

x = soft tacos

y = double deckers

Dory:

3x + 3y = 11.25 

Nemo:

4x + 2y = 10.00

---Now to solve for x and y---

---We find LCM of either x or y then make them cancel each other---

Dory multiply by 2:

6x + 6y = 22.50

Nemo multiply by 3:

12x + 6y = 30.00

--eliminate y--- 

Nemo subtract Dory:

6x = 7.50

Therefore x = 7.50 ÷ 6 = 1.25

---Now substitute x = 1.25 in either equation.---

Dory:

3.75 + 3y = 11.25

Therefore 3y = 11.25 - 3.75

therefore 3y = 7.50

there fore y = 2.50

y = 2.50 , x = 1.25

Answer:

x= $2.50, y= $1.25

Step-by-step explanation:

X= soft taco

Y= double deckers

$11.25= 3x+3y

$10.00= 4x+2y

first eliminate 1 variable, lets say d, to do this we must cancel them out, to do this multiply the top by -2 and the bottom by 3

 -2 ($11.25= 3x+3y)                                      -$22.50= -6x-6y

 3 ($10.00= 4x+2y)     which becomes.          $30.00=12x+6y

then the -6y and the positive 6y cancel out and you are left with 1 variable  

after this add the remaining parts to get.

$7.50=6x  divide by 6, then put x back into one of your original equations and solve for d then you have found how much each item costs and are finished with the system of equations

Answer:

[tex]\frac{(3m^{-1}n^2)^4}{(2m^{-2}n)^3}[/tex] [tex]=\frac{81m^{2}n^{5}}{8}[/tex]

Step-by-step explanation:

[tex]\frac{(3m^{-1}n^2)^4}{(2m^{-2}n)^3}[/tex]

[tex]=\frac{(3^4m^{-4}n^8)}{2^3m^{-6}n^3}[/tex]

[tex]=\frac{(3^4m^{-4+6}n^{8-3})}{2^3}[/tex]

[tex]=\frac{3^4m^{2}n^{5}}{2^3}[/tex]

[tex]=\frac{81m^{2}n^{5}}{8}[/tex]

Answer:

see here our answer is 60 degrees now how I will tell u see u know the sum of triangle that is 180 degrees now add up. y +y + 60 = 180 and solve it u will get ur correct answer

comment if u have doubt

Answer:

60

Step-by-step explanation:

Because you would 180/3 and will get 60

Yo sup??

Since you haven't mentioned the reference potential therefore we will consider it to be ground.

Since just before hitting the ground there is negligible amount of kinetic energy and also the velocity is very high hence we can say that it will have more kinetic energy than potential energy.

Hope this helps.

Answer:

[6 , +∞[

Step-by-step explanation:

Domain of g is all x≥4

domain of f is all real numbers

domain of goh is all real numbers x that verify 2x-8≥4 ⇒ x≥6

The restriction on the domain of goh is x ≥ 4.

To find the restrictions on the domain of goh, we need to consider the compositions of the two functions g(x) and h(x).

It is important to note that the square root function √x has a restriction on its domain. The expression inside the square root must be greater than or equal to zero. So, for g(x), we have x - 4 ≥ 0. Solving for x, we find that x ≥ 4.

Now, let's consider the composition goh(x). We substitute h(x) into g(x) as follows: goh(x) = g(h(x)) = g(2x-8).

The domain of h(x) is all real numbers, so we don't have any restriction for h(x). However, when we substitute h(x) into g(x), we must make sure that the resulting expression is within the domain of g(x), which is x ≥ 4. Therefore, the restriction on the domain of goh is x ≥ 4.

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