What is the measure of each base angle of a 140 degree

Answer:

c=12.04

Explanation:

You can use the formula given: c=√a^2+b^2

c=√8^2+9^2=√64+81=√145=12.04

The exact values are:

sin(α + β) = (-6√5 - 8)/25

cos(α + β) = (4√5 - 6)/25

sin(α - β) = (-6√5 + 8)/25

tan(α - β) = (-9√5 + 45)/4

We have,

Recall the trigonometric identities:

sin(a + b) = sin(a)cos(b) + cos(a)sin(b)

cos(a + b) = cos(a)cos(b) - sin(a)sin(b)

sin(a - b) = sin(a)cos(b) - cos(a)sin(b)

cos(a - b) = cos(a)cos(b) + sin(a)sin(b)

tan(a - b) = (tan(a) - tan(b))/(1 + tan(a)tan(b))

Using these identities, we can find the exact values of the expressions given.

(a) Sin (α + β)

sin(α + β) = sin(α)cos(β) + cos(α)sin(β)

= (√5/5)(-3/5) + (2/5)(-4/5) (using the values given for sin and cos)

= -6√5/25 - 8/25

= (-6√5 - 8)/25

(b) Cos (α + β)

cos(α + β) = cos(α)cos(β) - sin(α)sin(β)

= (2/5)(-3/5) - (√5/5)(-4/5) (using the values given for sin and cos)

= -6/25 + 4√5/25

= (4√5 - 6)/25

(c) Sin (α - β)

sin(α - β) = sin(α)cos(β) - cos(α)sin(β)

= (√5/5)(-3/5) - (2/5)(-4/5) (using the values given for sin and cos)

= -6√5/25 + 8/25

= (-6√5 + 8)/25

(d) tan (α - β)

tan(α - β) = (tan(α) - tan(β))/(1 + tan(α)tan(β))

= ((√5/5) - (-4/5))/(1 + (√5/5)(-4/5)) (using the values given for sin and cos)

= (9√5/5)/(1 - 4/5√5)

= (-9√5 + 45)/4

Therefore,

The exact values are:

sin(α + β) = (-6√5 - 8)/25

cos(α + β) = (4√5 - 6)/25

sin(α - β) = (-6√5 + 8)/25

tan(α - β) = (-9√5 + 45)/4

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0.15 cups of flour will be in each pancake.

As per the given data:

Desmond is making chocolate chip pancakes for his whole family.

He uses 3 cups of flour to make the 20 equal-sized pancakes.

Here we have to determine that how many cups of flour will be in each pancake.

Here we use the unitary method to find the number of cups of flour will be in each pancake.

Unitary method: The unitary approach is a strategy for problem-solving that involves first determining the value of a single unit, then multiplying that value to determine the required value.

Number of cups of flour in each pancake = \($\frac{3}{20}\)

= 0.15

Therefore 0.15 cup of flour in each pancake.

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Answer:

Step-by-step explanation:

NOTE: kindly find attached the graphical analysis/solution.

Given the data, we are expected to maximize the profit of Gillian’s Restaurant

let X be icecream

and Y be yogurt

Our objective function is

4.15X+3.6Y=P

Constraints

a. 0.75X+0.93Y<90

b. X+Y<115

c. X>=2Y = X-2Y>=0

X>=0, Y>=0      

a. 0.75X+0.93Y=90

X=0  

      0.75(0)+0.93Y=90

       0.93Y=90

                Y=90/0.93

                 Y=96.77

Y=0

       0.75X+0.93(0)=90

       0.75X=90

                X=90/0.75

                 X=120

b. X+Y<115

    X=0  

               X+Y=115

               0+Y=115

                Y=115

Y=0

        X+0=115

               X+0=115

                X=115

c. X>=2Y = X-2Y>=0

 X=0  

               X-2Y=0

               0+2Y=0

                Y=0

Y=0  

               X-2(0)=0

               X+0=0

                X=0

From the graph profit is maximum at

X=80 and Y=30

4.15(80)+3.6(30)=P

332+108=P

440=P

P=$440

We are expected to maximize the profit of Gillian’s Restaurant:

let

Objective function =4.15X+3.6Y=P

a. 0.75X+0.93Y<90

b. X+Y<115

             0.75X+0.93Y=90

X=0  

      0.75(0)+0.93Y=90

      0.93Y=90

      Y=90/0.93

       Y=96.77

Y=0

      0.75X+0.93(0)=90

      0.75X=90

       X=90/0.75

        X=120

            X+Y<115

 X=0  

Y=0

The graph profit is maximum at

X=80 and Y=30

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Answer:

\( \sqrt{98} = \sqrt{49 \times 2} = \sqrt{49} \sqrt{2} = 7 \sqrt{2} \)

Answer:

12.5

Step-by-step explanation:

divide 43.75 by 3.5 to get your answer

Answer:

131072

Step-by-step explanation:

Answer: The answer is 131072.

Step-by-step explanation:

Using a calculator, we find that \(2^{17}=\boxed{131072}.\)

Answer:

0.8

Step-by-step explanation:

It is 0.8 because since you have y=1.8-0.2x (which is in the form of y=mx+b); and you have the value that x=5, all that you have to do is plug in 5 into the X in the equation.

Here is shown work:

y=1.8-0.2x

y=1.8-0.2(5)

y=1.8-1

y=0.8

Hopefully this helps! :)

The predicted depth value when the velocity value is 5 will be 0.8 feets

Given the regression model :

yˆ=1.8−0.2x

yˆ = Predicted value

x = velocity

To calculate the predicted depth, at a given velocity, x ;

Substitute the value of x and solve for yˆ in the equation

When x = 5

yˆ=1.8−0.2(5)

yˆ=1.8− 1.0

yˆ = 0.8

Therefore, the predicted depth value in feet is 0.8

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On solving the inequalities The solution for this is option D

(D)All real numbers

For this case we must find the solution set of the following inequalities:

The solution is given by all values of x greater than -5.

The solution is given by all values of x greater than -5.

This is the union of both the inequalities a hence all the real numbers will justify the inequalities.

Then, the solution set is given by all real numbers.

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The ordered pair that completes the function is (0, 0)

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

((15,21), (17,26). (21,37), (25,40), (30,45)

Missing pair = 1

Total pairs = 6

For a relation to be a function, the x values must point to different y values

This means that the pair (0, 0) can complete the function

This is so because it does not stop the relation from being a function

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Answer:

n = 19

Step-by-step explanation:

2n > 36 ( divide both sides by 2 )

n > 18

and

5n < 100 ( divide both sides by 5 )

n < 20

so n > 18 and n < 20

thus n = 19

Answer:

-11

Step-by-step explanation:

Notice how

\(f(x)=x^{2} +8x+1\)

So when we have

\(f(-6)=(-6)^{2} +8(-6)+1= 36-48+1=-11\)

The answer is:

f(-6) = -11

Step-by-step explanation:

Plug in -6 for x:

\(\sf{f(x)=x^2+8x+1}\)

\(\sf{f(-6)=(-6)^2+8(-6)+1}\)

Simplify this:

\(\sf{f(-6)=36-48+1}\)

\(\sf{f(-6)=-12+1}\)

\(\sf{f(-6)=-11}\)

Answer: About 72%

Step-by-step explanation:

It's a conditional probability.

(Number of graduates on financial aid)/(Number of graduates)

\(\frac{1879}{2610} =0.7199\)

0.7199 = 71.99% ≈ 72%

Answer:

4x+10+2x-1=9x-15;

6x+9=9x-15;

6x-9x=-15-9;

-3x=-24;

3x=24;

from which

x=24:3=8

Then:

DF=9x-15=(9×8)-15=72-15=57

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Step-by-step explanation:

9 inches

Answer:

x - 4 yards.

Step-by-step explanation:

Given:

Area of rectangle = 3x^2 - 12x square yards

Width = 3x yards

To find:

Length of rectangle

Solution:

The area of a rectangle is equal to the product of its length and width.

Area of rectangle = Length * Width

Substituting the given values, we get:

3x^2 - 12x = Length * 3x

Length =( 3x^2 - 12x )3x

Length = x-4

Therefore, the length of the rectangle is x - 4 yards.

Answer: The length of the rectangle is x - 4 yards.

Step-by-step explanation:

We can create an equation to solve this word problem, where the variable L = length.

3x  ×  L  = \(3x^2 - 12x\)

We need to solve for the variable L, to find the length of the rectangle.

First lets factor the right side of the equation to make it easier to divide with.

3x  ×  L  = \(3x^2 - 12x\)

We can factor out 3x from the right side of the equation.

3x  ×  L  = 3x(x - 4)

Now we need to get the variable L by itself (isolating the variable). In order to do that, we can divide both sides by 3x.

3x ×  L  = 3x(x - 4)

/3x           /3x

L = x - 4

The length of the rectangle is x - 4 yards.

Answer:

1 is answer

2x+1=5x-2

5x-2x=1+2

3x=3

x=3

Answer:

x = 2 and y = -2

Step-by-step explanation:

a) 5x-4y = 18

b) x+3y = -4

b) x = -3y - 4

a) 5 (-3y - 4) - 4y = 18 (substitution)

a) - 15y - 20 - 4y = 18

a) -19y = 18 + 20

a) y = 38/-19

y = -2

b) x + 3(-2) = -4

b) x - 6 = -4

x = 6-4 = 2

Given statement solution is :- If the expression is set equal to 10x + 5, then there would be one solution.

If the expression is set equal to 10x + 7, then there would be no solution.

If the expression is set equal to -10x + 5, then there would be one solution.

If the expression 12x - 6x + 5 + 4x is set equal to 10x + 5, then there would be solution(s).

If the expression is set equal to 10x + 5, then there would be one solution.

If the expression is set equal to 10x + 7, then there would be no solution.

If the expression is set equal to -10x + 5, then there would be one solution.

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Answer:

white

Step-by-step explanation:

plato

The solution is Option D.

The missing color from the tree diagram is given by the equation A = white

Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.

It demonstrates the equality of the relationship between the expressions printed on the left and right sides.

Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.

Given data ,

Let the missing color from the tree diagram be represented as A

Now , the value of A is

Jenson has 3 clean T-shirts of white , red and orange

Jenson has 2 clean pairs of jeans of blue and gray

Now , substituting the values in the equation , we get

For every blue jeans = { white , red , orange }

For every gray jeans = { A , red , orange }

From the equation , we get

The value of A = white

Therefore, the value of A is white

Hence , the missing color is white

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Answer:

130 degrees

Step-by-step explanation:

DE+DA=130

Answer:

4300

Step-by-step explanation:

The difference between their yearly incomes is $31,304.

To calculate each person's yearly income, we need to multiply their weekly income by the number of weeks in a year. Assuming there are 52 weeks in a year, the yearly income can be calculated as follows:

For the student who drops out of high school:

Yearly Income = Weekly Income x Number of Weeks

= 451 x 52

= 23,452

For someone with a bachelor's degree:

Yearly Income = Weekly Income x Number of Weeks

= 1053 x 52

= 54,756

The difference between their yearly incomes can be found by subtracting the student's yearly income from the bachelor's degree holder's yearly income:

Difference = Bachelor's Yearly Income - Student's Yearly Income

= 54,756 - 23,452

= 31,304

Therefore, the difference between their yearly incomes is $31,304.

It is important to note that these calculations are based on the given information and assumptions. The actual yearly incomes may vary depending on factors such as work hours, additional income sources, deductions, and other financial considerations.

Additionally, it is worth considering that educational attainment is just one factor that can influence income, and there are other variables such as experience, job type, and market conditions that may also impact individuals' earnings.

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Answer:

(From left to right) 2  5  8

Step-by-step explanation:

1. Find the gap (between the first and last terms) 11 - (-1) = 12

2. Divide by the number of times the linear term is added: 12/4=3

3. Use the common difference to find the missing values.

Answer:

Step-by-step explanation:

Therefore, the values of

a

1

and r are 2 and -1, respectively.

The values of a₁ and r of the geometric series are 2 and -1 respectively.

Any term divided by the preceding term is a constant in a geometric series. The common ratio of the sequence is the name given to this constant. Any term in the sequence can be divided by the prior term to determine the common ratio.

We have the series 2, -2, 2, -2, ......

Here, The first term is 2.

and, the Common Ratio = -2 / 2

                                        = 2/(-2)

                                         = -1

So, the first term is 2 and r is -1.

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All given equations are false, by using subtraction we get a) 22 b) 868 c) 44 d) 702 e) -100.

The equation is a declaration of equivalence between two expressions with variable- and/or number-filled expressions. In essence, solutions are questions, and efforts to discover a method for answering them have fueled the growth of mathematics.

Equations come in two varieties: truths and conditional equations. All possible values of those variables result in an identity. Only certain combinations of the variables' values make a conditional equation true.

Two expressions joined by the equals symbol ("=") form an equation.

Option 1: 34-12= 22      ≠14  (false)

Option 2: 916−48= 868 ≠58 (false)

Option 3: 78-34= 44      ≠18  (false)

Option 4:715-13= 702    ≠615 (false)

Option 5:12-120=-100    ≠1020 (false)

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Answer: 2a < 2b

Step-by-step explanation:

We are given a statement:

a < b and b < c, then 2a ____ 2b

We can use simple numbers that make the statement true.

Where,

a = 2

b = 3

c = 4

Now lets plug it in.

2 < 3 and 3 < 4, then 2(2) ____ 2(3)

and lets simplify:

2 < 3 and 3 < 4, then 4 ____ 6

We can see that 4 is less than 6,

so as a is less than b, 2a is less than 2b.

The only thing changing is the coefficient being multiplied by the variables a and b.

Answer:

d/ ( a+b) = x

Step-by-step explanation:

d=ax+bx

Factor out x

d = x( a+b)

Divide each side by (a+b)

d/ ( a+b) = x (a+b)/ (a+b)

d/ ( a+b) = x