an exterior angle of a triangle is 105 and its two opposite interior angles are equal . Find the angles​

Answer: 1 \(\frac{11}{20}\)

Step-by-step explanation:

First, we will subtract 2 from 3.

     3 - 2 = 1

Next, we will subtract the fractions by getting common denominators.

     \(\displaystyle \frac{3}{4} -\frac{1}{5} =\frac{3*5}{4*5} -\frac{1*4}{5*4} =\frac{15}{20} -\frac{4}{20} =\frac{11}{20}\)

This leaves us with an answer of 1 \(\frac{11}{20}\).

Answer:

\(\displaystyle{ 1\dfrac{11}{20}}\)

Step-by-step explanation:

First, focus on the fractions. Start by finding LCM of 4 and 5 which is 20. Multiply 3/4 by 5/5 to make the denominator equivalent to LCM (20). Then Multiply 1/5 by 5/5. Thus,

\(\displaystyle{3 \dfrac{15}{20} - 2\dfrac{4}{20}}\)

Since the minuend (left) is higher than subtrahend (right), we can subtract normally. Therefore, 3-2 = 1 and 15-4 = 11. Hence,

\(\displaystyle{3 \dfrac{15}{20} - 2\dfrac{4}{20} = 1\dfrac{11}{20}}\)

Also make sure that you're not treating 1 like 1x = x here. Always add 1, do not treat like a variable term!

The ages of Sari and her mother is 15 and 36 respectively

It is important to note that linear equations are defined as equations having the greatest degree of x as 1.

From the information given, we have that;

Let Sari's age be x

Let her mother's age be y

Then, we have that;

2x + 1/2y = 48

3x = y + 9

Make 'y' the subject from equation 2, we have;

y = 3x - 9

Substitute the value in equation 1

2x + 3x - 9/2 = 48

Find the LCM

4x + 3x - 9/2 = 48

cross multiply

7x - 9 = 96

collect like terms

7x = 105

Sari's age, x = 15 years

Her mother's age = 45 - 9 = 36 years

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The age of Sari and her mother is 15 and 36 years respectively.

The sum of twice Sari's age and half her mother's age is 48. Triple sari's age is 9 years more than her mother's age.

Therefore, the age of Sari and her mother are as follows:

let

x = Sari's age

y = mother's age

Hence,

2x + 1 / 2y = 48

3x = y + 9

Therefore,

4x + y = 96

3x - y = 9

add the equations

7x = 105

x = 105 / 7

x = 15

Therefore, let's find y

y = 96 - 4(15)

y = 96 - 60

y = 36

Hence,

Sari's age = 15 years

Mother's age = 36 years

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Answer:

9 1/2= 19/2 & 1 6/7= 13/7

Now equalising denominator we will get,

133/14 & 26/14

Now finding difference:

(133-26)/14

= 107/14 is the difference

Answer:

107/14

Step-by-step explanation:

Hope this helps

Short & Simple Answer:

0.027

Answer:

0.027

Step-by-step explanation:

0.3x0.3x0.3

Answer:

x = 15

Step-by-step explanation:

3x+1+4x-3 = 103

7x = 105

x = 15

The time take to fill the pool will be 494 hours.

Inlet pipe fills in  38 hours = 1 pool

Inlet pipe fills in 1 hours = 1/38

Drain pipe empty in 39 hours = 1 pool

Drain pipe empty in 1 hour = 1/39

If both pipes are opened together then in pool fills in 1 hour =  1/38 - 1/39

= 1/1482

Therefore, 1/1482 fills in 1 hour.

. Therefore, 1/3 will be:

= 1/3 × 1482

= 494 hours.

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Answer: n = 0

Step-by-step explanation:

Given expression

(-3/4) (8n + 12) = 3 (n - 3)

Expand parentheses and apply the distributive property

-6n - 9 = 3n - 9

Add 9 on both sides

-6n - 9 + 9 = 3n - 9 + 9

-6n = 3n

Subtract 3n on both sides

-6n - 3n = 3n - 3n

-9n = 0

Divide -9 on both sides

-9n / -9 = 0 / -9

\(\boxed{n=0}\)

Hope this helps!! :)

Please let me know if you have any questions

Answer:

0

Step-by-step explanation:

-3/4(8n+12)=3(n-3)

-24/4n-36/4=3n-9

-6n-9=3n-9

-6n-3n-9=-9

-9n-9=-9

-9n=-9+9

-9n=0

n=0/-9

n=0

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Answer:

First, set up equations for total cost for both Happy Paws and Woof Watchers.

x= number of hours

y= total cost

Happy Paws

y=3.50x +16

Woof Watchers

y=4.75x+11

4.75x+11=3.50x+16

x=4

You can check your answer by doing the following:

Happy Paws: (3.50)(4)+16= 30

Woof Watchers: (4.75)(4)+11= 30

The y-intercept of the line y = 14 / 17 x + 14 is 14.

The equation of a line can be represented in different form such as slope intercept form, point slope form, standard form and general form.

Therefore, let's represent it in slope intercept form.

y = mx + b

where

Therefore, using the equation of a line in slope intercept form, the y-intercept of the equation y = 14 / 17 x + 14 is 14.

The y-intercept of a line is the value of y when x = 0.

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The quadratic regressiοn equatiοn fοr the given data pοints is y = 5x² - 20x + 7

A secοnd-degree equatiοn οf the fοrm ax² + bx + c = 0 is knοwn as a quadratic equatiοn in mathematics. Here, x is the variable, c is the cοnstant term, and a and b are the cοefficients.

Tο find the quadratic regressiοn equatiοn fοr the given data pοints, we need tο fit a quadratic equatiοn οf the fοrm y = ax² + bx + c tο the data.

We can start by using the three given pοints tο set up a system οf three equatiοns:

\((1,-8): a(1)^2 + b(1) + c = -8\\\\(2,-4): a(2)^2 + b(2) + c = -4\\\\(3,6): a(3)^2 + b(3) + c = 6\)

SimpIifying each equatiοn, we get:

a + b + c = -8 (equatiοn 1)

4a + 2b + c = -4 (equatiοn 2)

9a + 3b + c = 6 (equatiοn 3)

AIternativeIy, we can use technοIοgy such as a caIcuIatοr οr spreadsheet tο sοIve the system.

SοIving the system using technοIοgy, we get:

a = 5

b = -20

c = 7

Therefοre, the quadratic regressiοn equatiοn fοr the given data pοints is:

y = 5x² - 20x + 7

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Answer: 5th week

Step-by-step explanation:

E= -12w+568

520= -12w+568

520+12w=568

12w=48

w=4

4+1=5th week

Answer:

GFBH

Step-by-step explanation:

1 (- 3, - 2 ) ⇒ G

2 (3, 4 ) ⇒ F

3 (2, 0 ) ⇒ B

4 (1, - 3 ) ⇒ H

The code is GFBH

Answer:

72

Step-by-step explanation:

8 = 2×2^2

18 = 2×3^2

32 = 2×4^2

50 = 2×5^2

72 = 2×6^2

A system of equations are 9x+7y=77 and 3x+5y=49. Therefore, cost to rent each chair is $1.75 and cost to rent each table is $8.75.

A system of linear equations consists of two or more equations made up of two or more variables such that all equations in the system are considered simultaneously. The solution to a system of linear equations in two variables is any ordered pair that satisfies each equation independently.

a) From the table, first costumer brought 9 chairs and 7 tables per $77

Second costumer brought 3 chairs and 5 tables per $49

Let x be the cost (in dollars) to rent a chair

Let y be the cost (in dollars) to rent a table

Here, 9x+7y=77 --------(I)

3x+5y=49 --------(II)

b) Multiply equation (II) by 3

9x+15y=147 --------(III)

Subtract equation (I) from (III), we get

9x+15y-(9x+7y)=147-77

⇒ 8y=70

⇒ y=8.75

Substitute y=8.75 in (I), we get

9x+7×8.75=77

⇒ 9x+61.25=77

⇒ 9x=77-61.25

⇒ 9x=15.75

⇒ x=1.75

Therefore, the system of linear equations are 9x+7y=77 and 3x+5y=49.

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Answer:

V=0

Step-by-step explanation:

9V + 19 =19

9V=19-19

9V=0

V=0

The domain and range of function p for the intervals (0, 14) and (0, 80) respectively.

The domain of the function includes all possible x values of a function, and the range includes all possible y values of the function.

We have been given a graph that has Function p representing the number of people in the library on a Monday as a function of hours since the library opened.

Based on the graph and the situation, the required solution would be as:

The domain at intervals (0, 14) and range at intervals (0, 80) for function p.

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Answer: 0.5699

Step-by-step explanation:

In the number 56.99, the point is after two places from the right and in 0.01 also the point is after two places from the right. Hence, the point is after four places from the right.

Multiply the numbers without considering the points i.e. multiply 5699 and 1, the answer will be 5699*1= 5699

put the point after four places from the right i.e. 0.5699.

Answer:

\(0.5699\)

Step-by-step explanation:

\(56.99X0.01\)\(=0.5699\)

The conditional probability is given as follows:

P(B|A) = 1/2, option C.

A probability is calculated as the division of the desired number of outcomes by the total number of outcomes in the context of a problem/experiment.

The events are given as follows:

P(B|A) is the probability that the second digit is even, considering that the first digit was odd. As the digits cannot repeat, and there will be 8 remaining digits, out of which 4 will be even, the probability is given as follows:

P(B|A) = 4/8 = 1/2.

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Step-by-step explanation:

so to get y all you need to do the equation so let's start with the first 1 which is 2 so 3×2=9-5=4 so y equals to 4

so to find X we need to do the opposite so let's do the second one which y is 4 so instead of subtracting we will add 5 which is 9 then we devide by 3 which is 3 that's how to do it

7+5=12÷3=4

5×3=15-5=10

Answer: Yes, It is. (True)

Step-by-step explanation:

Answer:

the answer is 3.36 please mark brainliest

Step-by-step explanation:

The correct value of Z for the solution to true system is -2

From the question, we have the following parameters that can be used in our computation:

2x + 3y - z = 4

x - 3y + 2z = -3

3x + y - z = 5

Transform the third equation

So we have

2x + 3y - z = 4

x - 3y + 2z = -3

9x + 3y - 3z = 15

Eliminate y in the equations by subtraction

So we have

x - 3z = 7

10x - z = 12

Multiply x - 3z = 7 by 10

10x - 30z = 70

10x - z = 12

Subtract the equations

-29z = 58

So, we have

z = -2

Hence, the correct value of Z  is -2

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The data in the table can be modeled by this linear equation in slope-intercept form: y = 8x - 5.

The slope is 8, which means the wages earned increases at rate of 8 dollars per hour as the time increases.

The y-intercept is -5 and it represent the initial wages earned.

In Mathematics and Geometry, the slope-intercept form of the equation of a straight line is represented by this mathematical expression;

y = mx + c

Where:

First of all, we would determine the slope of this line;

Slope (m) = (y₂ - y₁)/(x₂ - x₁)

Slope (m) = (24.00 - 8.00)/(3 - 1)

Slope (m) = 16.00/2

Slope (m) = 8

At data point (1, 3), a linear equation in slope-intercept form for this line can be calculated as follows:

y - y₁ = m(x - x₁)

y - 3 = 8(x - 1)

y = 8x - 8 + 3

y = 8x - 5

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The domain of the function f(x) = -3x + 2 is (-∞, +∞), representing all real numbers, and the range is (-∞, 2], representing all real numbers less than or equal to 2.

The function f(x) = -3x + 2 is a linear function defined by a straight line. To determine the domain of this function, we need to identify the range of values for which the function is defined.

The domain of a linear function is typically all real numbers unless there are any restrictions. In this case, there is no explicit restriction mentioned, so we can assume that the function is defined for all real numbers.

Therefore, the domain of the function f(x) = -3x + 2 is (-∞, +∞), which represents all real numbers.

Now, let's analyze the range of the function. The range of a linear function can be determined by observing the slope of the line. In this case, the slope of the line is -3, which means that as x increases, the function values will decrease.

Since the slope is negative, the range of the function f(x) = -3x + 2 will be all real numbers less than or equal to the y-intercept, which is 2.

Therefore, the range of the function is (-∞, 2] since the function values cannot exceed 2.

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Applying exponent rules, the factored expression is given as follows:

125^6 - 27^15 = 5^18 - 3^45.

The expression is factored according to the like terms of the expression, which are placed into evidence.

For this problem, the expression is:

125^6 - 27^15

First, we have to factor 125 and 27, finding it's prime factors, hence:

Thus the expression can be written as:

125^6 - 27^15 = (5³)^6 - (3³)^15

There will be no like terms on the expression, as the bases are different,  of 3 and 5, hence we just apply the exponent rules, as follows:

a^b^c = a^(b x c), which is the power of power rule.

Hence:

Hence the simplified expression is given as follows:

(5³)^6 - (3³)^15 = 5^18 - 3^45.

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Answer:

Answers are below!

Step-by-step explanation:

(2 + g) (8)

= (2 + g) (8)

Add a 8 after the 2, and flip.

= (2)(8) + (g)(8)

= 16 + 8g

= 8g + 16

= (4) (8 + -5g)

Add another 4, then flip.

= (4) (8) + (4) (-5g)

= 32 − 20g

= - 20g + 32

−7 (5-n)

= (−7) (5 + -n)

Add another 7, then flip.

= (−7) (5) + (-7) (-n)

= −35 + 7n

= 7n - 35

Use the distributive property.

a (b + c) = ab + ac

a = 8

b = 2m

c = 1

= 8 × 2m + 8 × 1

Simplify, you get 16m + 8.

Use the distributive property.

a (b + c) = ab + ac

a = 6x

b = y

c = z

= 6xy - 6xz is the answer.

\(\mathrm{Apply\:the\:distributive\:law}:\quad \\\:a\left(b+c\right)=ab+ac\)

\(a=-3,\:b=2b,\:c=2a\)

\(=-3\cdot \:2b+\left(-3\right)\cdot \:2a\)

Apply minus plus rules.

\(=-3\cdot \:2b+\left(-3\right)\cdot \:2a\)

Multiply the numbers.

3 x 2 = 6

Answer:

9. -35+7n

10. 16m+8

11. 6xy-6xz

Step-by-step explanation:

You multiplying the terms inside the ( ) by the outside factor.

This is call distributive property, a(b+c)=ab+ac.

Also, a(b+c)=(b+c)a by commutative property.

It also works over the operation subtraction since subtraction is just a disguised addition (addition of the opposite). That is, a(b-c)=ab-ac.

Anyhow, let's look at 9.,10., and 11..

9.

-7(5-n)

(-7)(5-n)

(-7)(5)-(-7)(n)

-35+7n

10.

8(2m+1)

(8)(2m)+(8)(1)

16m+8

11.

6x(y-z)

(6x)(y-z)

(6x)(y)-(6x)(z)

6xy-6xz

Hint on 7. It's like all the other problems. That is, it is equivalent to doing 8(2+g).

If you want comment below, if you want me to check any of yours or if you have any questions.

Answer:

To convert euros to pounds, we have to multiply the amount in euros by the exchange rate. So, the sunglasses cost 90 * 0.875 = 78.75 pounds.

To use a suitable approximation, we can round the exchange rate to the nearest hundredth, which is 0.88. This makes the calculation easier and gives a close estimate of the actual value.

Using the rounded exchange rate, the sunglasses cost 90 * 0.88 = 79.2 pounds.

We can see that both the exact and the approximate values are greater than 70 pounds, so Elyas is wrong. The sunglasses cost more than 70 pounds

Step-by-step explanation:

The value of y is 48

y= kx

let's solve for k which is the constant

y= 8 , x= 4

k= 8/4

k= 2

Next is to calculate the value of y when x is 24

y = 2 × 24

y= 48

Hence the value of y is 48

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