Use substitution to solve the system of equations.
x-2y=1
3x-6y=3

Answer:

34 degrees; 56 degrees

The measures of each of the acute angles are 56 degrees and 34 degrees.

Step-by-step explanation:

The measures of a triangle add up to 180 degrees.

One angle has the measure of 90 degrees since it is marked as a right angle.

Using this info we can create an equation to solve for x.

(19x-1)+(13x-5)+90=180

Now solve for x.

32x-6+90=180

32x=96

x=3

Now to find the measure of each angle subsitute the value of x.

(19x-1)=19*3-1=56 degrees

(13x-5)=13*3-5=34 degrees

The measures of each of the acute angles are 56 degrees and 34 degrees.

Answer:

19x - 1 ➡ 19 × 3 - 1 = 56°

13x - 5 ➡ 13 × 3 - 5 = 34°

Step-by-step explanation:

The given triangle is a right triangle which means one of the angle has a measurement of 90° and since the sum of interior angles in a triangle is equal to 180° the sum of other two angles must be 90°

19x - 1 + 13x - 5 = 90 add like terms

32x - 6 = 90 add 6 to both sides

32x = 96 divide both sides by 32

x = 3

19x - 1 ➡ 19 × 3 - 1 = 56°

13x - 5 ➡ 13 × 3 - 5 = 34°

Answer:

30 ÷ 6 =5 so

5 is to the power 6

Answer:

I think he might need 100ml.

Step-by-step explanation:

Brandon needs to use 100 ml of water to make 250 ml of hand sanitizer.

The percentage is defined as a ratio expressed as a fraction of 100.

To save money, Brandon made his own hand sanitizer. Hand sanitizer needs 60% alcohol to be effective.

We have to determine the amount of water to manufacture 250ml of hand sanitizer.

To make 250ml of hand sanitizer with 60% alcohol, Brandon needs to use 250ml x 60% = 150ml of alcohol.

Since the total volume of the hand sanitizer is 250ml,

Brandon needs to use 250ml - 150ml = 100ml of water to make 250ml of hand sanitizer.

Therefore, he needs to use 100 ml of water to make 250 ml of hand sanitizer.

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The product is expressed as an exponent as 6 x 6 = 6².

Given data:

To write the product 6 x 6 using an exponent, we can express it as 6².

The different Laws of exponents are:

mᵃ×mᵇ = mᵃ⁺ᵇ

mᵃ / mᵇ = mᵃ⁻ᵇ

( mᵃ )ᵇ = mᵃᵇ

mᵃ / nᵃ = ( m / n )ᵃ

m⁰ = 1

m⁻ᵃ = ( 1 / mᵃ )

When we multiply a number by itself, we can represent the repeated multiplication using an exponent. In this case, we have 6 multiplied by 6, which is the same as saying 6 raised to the power of 2 (6²).

The exponent 2 indicates that we are multiplying 6 by itself 2 times.

Hence, the product 6 x 6 can be written as 6².

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Answer:

The equation to determine the normal price of each cookie is

7(x - 0.75) = 2.80

The normal price of each cookie = $1.15

Step-by-step explanation:

Let us represent the normal price of a cookie as : x

We are told that:

Today each cookie costs \$0.75less than the normal price.

The price of a cookie today is

x - 0.75

Right now if you buy 7 of them it will only cost you \$2.80$

Hence:

7(x - 0.75) = 2.80

Solving for x

7x - 5.25 = 2.80

7x = 2.80 + 5.25

7x = 8.05

x = 8.05/7

x = $1.15

The normal price of each cookie = $1.15

Answer:

$ 1.15

Step-by-step explanation:

7(c-0.75) = 2.80 is the equation

$1.15 is the total for C

I did this khan before and this is correct

Hope this helps!

;)

Answer:

The answer is $21

Step-by-step explanation:

The amount of money for 12 yards of fabric is $ 21.00

Given data:

To determine the cost of 12 yards of fabric, we can use the information provided in the table. We observe that the cost of fabric increases linearly with the number of yards.

The table shows that 3 yards of fabric cost $5.25. To find the cost per yard, we divide the total cost by the number of yards:

$5.25 / 3 = $1.75

On simplifying the equation:

Now we can use this cost per yard to calculate the cost of 12 yards:

$1.75 × 12 = $21.00

Hence, 12 yards of fabric would cost $21.00.

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The complete question is attached below:

The table below shows the amount of money needed to buy certain amounts of fabric.Fabric Cost

Yards of Fabric

Total

Cost

3

$5.25

6

$10.50

9

$15.75

12

?

If the price is the same for each yard, how much money would 12 yards of fabric cost?

$18.00

$21.00

$24.75

$26.25

Answer:

2 1/5 meters

Step-by-step explanation:

Given that:

Area of kitchen = 3 3/4

Width of kitchen = 1 1/2

Length = x

Recall : Area of rectangle = Length * width

Area of kitchen = length * width

3 3/4 = x * 1 1/2

15 / 4 = x * 3/2

x = 15/4 ÷ 3/2

x = 15/4 * 2/3

x = 30/12 = 2 6/30

x = 2 1/5

Answer:

Commission= $53.82

Step-by-step explanation:

First, we need to calculate the gross profit of the sale:

Gross profit= sale price - total cost

Gross profit= 899 - 600

Gross profit= $299

Now, the commission made by the seller:

Commission= gross profit*commission rate

Commission= 299*0.28

Commission= $53.82

Answer:A IS THE LINEAR FUNCTION

Step-by-step explanation: NO NEED FOR EXPLANATION

Answer:

thetht

Step-by-step explanation:jtejr

Answer:

x = 7

Step-by-step explanation:

Let the number added to the numerator is x.

ATQ,

[tex]\dfrac{3+x}{7+2x}=\dfrac{10}{21}[/tex]

Cross multiplying each side,

[tex]\dfrac{3+x}{7+2x}=\dfrac{10}{21}\\\\63+21x=70+20x\\\\21x-20x=70-63\\\\x=7[/tex]

Hence, the person that is added is 7.

Answer:

Traditional = 162

Modern = 90

Step-by-step explanation:

Given that:

12 songs per hour for 15 hours

8 songs per hour for the rest of the day ; (24 - 15) = 9 hours ;

That is ; 8 songs per hour for 9 hours

Total number of songs played per day :

(12 * 15) + (8 * 9) = 252 songs

If songs are mixed using the ratio 9:5 (traditional : modern)

Traditional songs :

(9 * 252) / (9 + 5) = 162

Modern songs :

(5 * 252) / (9 + 5) = 90

Answer:

223.2725

Step-by-step explanation:

223.2725

Answer:

3.32,3.325,335,7320

Answer:

3.32, 3.325, 335, 7,320

Hope it helps

Step-by-step explanation:

Answer:

For a confined, constant volume of gas, the ratio

P

T

is therefore constant (i.e.,

P

T

=

k

). If the gas is initially in “Condition 1” (with P = P1 and T = T1), and then changes to “Condition 2” (with P = P2 and T = T2), we have that

P

1

T

1

=

k

and

P

2

T

2

=

k

, which reduces to

P

1

T

1

=

P

2

T

2

Answer:

Property of Addition

Step-by-step explanation:

Step-by-step explanation:

4(sin⁴ 60° + cos⁴ 60°) = 1 + 3(sin²60° - Cos² 60°)​

sin 60°=[tex]\frac{\sqrt{3} }{2}[/tex]

Cos 60°= [tex]\frac{1}{2}[/tex]

​[tex]4(( \frac{\sqrt{3} }{2}) ^{4} +(\frac{1}{2}) ^{4} )=1+3(( \frac{\sqrt{3} }{2}) ^{2} +(\frac{1}{2}) ^{2} )[/tex]

then do it by the calculator and they will be equal 2.5

I hope it will help

Answer: 20 feet

Step-by-step explanation: you want to do 2.5 x 8

Answer:

3x³ + 5x² + 4x + 4

Step-by-step explanation:

Given

(x + 2)(x² + x + 2) + 2(x³ + x²)

To expand the product, each term in the second factor is multiplied by each term in the first factor, that is

x(x² + x + 2) + 2(x² + x + 2) + 2(x³ + x²) ← distribute the parenthesis

= x³ + x² + 2x + 2x² + 2x + 4 + 2x³ + 2x² ← collect like terms

= 3x³ + 5x² + 4x + 4

The present age of Ahmed and Ahmed's father is 12 and 36 respectively.

Step-by-step explanation:

Given : Ahmed's father is thrice as old as Ahmed. After 12 years, his age will be twice that of his son.

To Find : Their present age ?

Solution :

Let the Ahmed's age be 'x'.

Ahmed's father is thrice as old as Ahmed.

i.e. Ahmed's father age is '3x'

After 12 years, his age will be twice that of his son.

i.e. 3x+12 = 2(x+12)3x+12=2(x+12)

Solving the equation,

3x+12 = 2x+243x+12=2x+24

x=12x=12

So, Ahmed's age is 12.

Ahmed's father age is 3\times 12=363×12=36

Therefore, The present age of Ahmed and Ahmed's father is 12 and 36 respectively.

Answer:

-9x-2

Step-by-step explanation:

Answer:

-9x -2

Step-by-step explanation:

-3x + 1 – 3 – 6x

Combine like terms

-3x -6x  +1 -3

-9x -2

Answer:

-150

General Formulas and Concepts:

Pre-Algebra

Order of Operations: BPEMDAS

Step-by-step explanation:

Step 1: Define

-6x + 150

x = 50

Step 2: Evaluate

Answer:

10. 9

In the first question we can solve using the Pythagorean theorem. It states that the hypotenuse in a right triangle or the longest side of the triangle, squared is equal to the other 2 sides, squared. Its expressed as so: C^2 = A^2 + b^2 where c is the hypotenuse and a and b are the other sides oft eh triangle.

Therefore,

15^2 = 12^2+x^2

225=144+x^2

81=x^2

x=9

__________________________________________________________

11. x=12

In this figure, there are 2 right triangles on the sides of the square. If we can find the lengths of the base of both triangles then we can find x using the Pythagorean theorem. the total base is 21 and the square is 11. 11+a+b=21. We can assume that both triangles are congruent and therefore we can solve this equation:

11+a+b=21

a+b=10

5+5=10

b=5

a=5

The bases of the two triangles are 5 and the hypotenuse is 13. Now we can solve using the Pythagorean theorem:

c^2 = a^2+b^2

13^2=5^2+x^2

169=25+x^2

144=x^2

144= 12 x 12

x=12

__________________________________________________________

12.

The diagnol of a triangle is the hypotenuse and since the length is the square root of 3, we have all the information we need.

c^2 = a^2+b^2

2^2 = (square root of 3)^2+b^2

4=3+b^2

1=b^2

b=1

Step-by-step explanation:

Answer:

f = 54°

Step-by-step explanation:

54° and f are vertical angles and are congruent, thus

f = 54°

Answer:

la respuesta es 28 porque 32 dividido por 112 es 28

Answer:

24

Step-by-step explanation:

4*6=24