Use Figure 1 to evaluate each trigonometric function of angle A . The side adjacent to angle A has length 4 and the side opposite angle A has length 10.

The least number of balls we require to take out to be sure that we have two green or two red balls is 14.

In the bag, there are a total number of balls of;

Total number of balls = 12 + 7 = 19 balls

Inside the bag, we have 12 red balls and 7 green balls.

The balls are selected without replacement, and this means that they are removed from the bag, and replaced back.

In theory, we could pick 12 balls, and all 12 being red, while also 13, with 12 red and 1 green e.t.c

Therefore, at least 14 balls are needed to guarantee that there are at least 2 green or two red balls

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The one time joining fee found from the linear relationship between total cost and the number of months of membership is $250

A linear relationship is a relationship between two variables that has a straight line when graphed.

The total cost of the gym membership = C

The number of months of membership = t

The table in the question is presented as follows;

t (Time in months)     [tex]{}[/tex]                 C (Total cost)

2      [tex]{}[/tex]                                            200

4     [tex]{}[/tex]                                             250

9     [tex]{}[/tex]                                             375

The linear equation that represents the value in the table is found as follows;

Slope of the line, m = (375 - 250)/(9 - 4) = 25

The equation of the line in point and slope form is therefore;

(C - 375) = 25·(t - 9)

C = 25·(t - 9) + 375

C = 25·t - 225 + 375 = 25·t + 250

C = 25·t + 250

The joining fee is the amount paid at the start when t = 0, therefore;

Joining fee = 25 × 0 + 250 = 250

The one time joining fee is $250

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Answer: The skis cost $117.60.

Step-by-step explanation:

A pair of skis costing $210 is 30% off.

30% of $210 is $147

Then two weeks later, it will be 20% off THAT price.

20% of $147 is $117.60

Therefore, $117.60 is the clearence price of the skis. Hope this helps!

Lois’ pay before the tax had been deducted is £660.

Given:

Lois Denominator, a mathematics examiner, receives £514.80 after tax has been deducted at 22% for marking papers.

22% = 514.80

divide by 22 on both sides

22%/22 = 514.80/22

1%= 23.4

= 514.8/0.78

= 5148/10/78/100

= 5148*100/10*78

= 66*100/10

= 66*10

= £660.

Therefore Lois’ pay before the tax had been deducted is £660.

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Answer:

The answer is x=4.5

Step-by-step explanation:

I hope this helps

There are 6 circles and 9 squares. What is the simplest ratio of circles to squares?

There are 6 circles and 9 squares.

Factors of 6: 1,2,3,6

Factors of 9: 1,3,9

Common factors: 1,3

GCF (greatest common factor): 3

6:9

Unsimplified ratio

÷3↓↓÷3

Reduce out GCF

2:3

Simplified ratio

Visual representation:

6

2

9

Answer:

Step-by-step explanation:

1. Nine squares to three circles. You can right it as a ratio by using a colon to seperate its ratio!

9 to 3= 9:3

2. If a ratio is not simplified, always simplify it like fractions.

9:3= 3:1

3. Answer: 3:1

Answer:

168

Step-by-step explanation:

Let the area of the square be [tex]x[/tex].

[tex]\frac{4}{7}x-\frac{5}{6}\left(\frac{3}{7}x \right)=36 \\ \\ \frac{4}{7}x-\frac{5}{14}x=36 \\ \\ \frac{8}{14}x-\frac{5}{14}x=36 \\ \\ \frac{3}{14}x=36 \\ \\ \frac{1}{14}x=12 \\ \\ x=168[/tex]

The number of cups that Mr Colton need to make 2 pounds of dough is 3.08 cups.

Ratio demonstrates how many times one number can fit into another number. Ratios contrast two numbers by ordinarily dividing them. A/B will be the formula if one is comparing one data point (A) to another data point (B). This indicates that you're dividing information A by B. For instance, the ratio will be 5/10 if A is 5 and B is 10

Let the number of cups be represented by x.

This will be expressed as:

2/3 = x/4.62

Cross multiply

3x = 2 × 4.62

3x = 9.24

Divide

x = 9.24 / 3

x = 3.08

Therefore, 3.08 cups are needed.

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Answer:

The number of cups that Mr Colton need to make 2 pounds of dough is 3.08 cups.

Step-by-step explanation:

The solution to the system of equations, in terms of x, considering the augmented matrix, is of:

The augmented matrix of a system of equations is built as follows:

In this problem, there are three columns before the |, the there are three variables given as follows:

x,y and z.

The expression from the first row is:

x -0.05z = 2.

The expression from the second row is:

y + 2z = 1.

The third row is all zero, meaning that there is a free variable, hence the solution to the system is written as a function of x as follows:

x - 0.05z = 2

0.05z = x - 2.

z = (x - 2)/0.05

z = 20x - 40.

Hence the solution for y is:

y = 1 - 2z

y = 1 - 40x + 80

y = -40x + 81.

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The value of 32/25 as mixed number is 1 7/25

A fraction represented with its quotient and remainder is a mixed fraction. For example, 2 1/7 is a mixed fraction, where 2 is the quotient, 1 is the remainder. So, a mixed fraction is a combination of a whole number and a proper fraction.

A mixed fraction can be obtained wen there is improper fraction. Improper fraction is a fraction that it's numerator is larger than denominator for example 32/25.

To convert to mixed fraction we find the number of times 25 can go in 32, which is 1 and the remainder is 7

Therefore 32/25 = 1 7/25.

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Answer:

Line v:  y = x + 5

Step-by-step explanation:

Given two lines are perpendicular and the equation of one line, we use the following formula to find the slope of the other line where m1 is the slope of the line we're given and m2 is the slope of the line we want to find:

[tex]m_{2}=-\frac{1}{m_{1} }\\m_{2}=1[/tex]

The general equation of a line is y = mx + b, where m is the slope and b is the y-intercept.  

Therefore we plug in our slope and the point (-3, 2) to find the y-intercept of line v:

[tex]2=1(-3)+b\\2=-3+b\\5=b[/tex]

In the given triangle JKL , NO = 26 units and JK = (7x + 17) units, then the value of x is equal to 5 units.

As given in the question,

In the given triangle JKL,

M, N ,O are the mid-points of the side JK, JL, KL of the triangle respectively.

Measure of NO is equal to 26 units

Measure of JK is equal to (7x + 17) units

Using mid- point theorem we have,

In triangle JKL,

NO is half the measure of opposite side JK

NO = 1/2 ( JK)

⇒ 26 = 1/2 ( 7x + 17 )

⇒ 7x + 17 = 26 × 2

⇒ 7x + 17 = 52

⇒ 7x = 52 - 17

⇒ 7x = 35

⇒ x= 5 units

Therefore, for the given triangle JKL , NO = 26 units and JK = (7x + 17) units, then the value of x is equal to 5 units.

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Answer:

[tex]y-7=-\frac{4}{3}(x+7)[/tex]

Step-by-step explanation:

The slope of the line is [tex]\frac{-9-7}{5-(-7)}=-\frac{4}{3}[/tex].

The equation of the line passing through the point [tex](x_1, y_1)[/tex] and slope [tex]m[/tex] is [tex]y-y_1=m(x-x_1)[/tex], so the equation is [tex]y-7=-\frac{4}{3}(x+7)[/tex].

Complete steps to find domain of function is describe below.

Domain is defined as the all input values which satisfy the function or can say all inputs any function have.

suppose we have a function f(x) = 6x^2 + 5x - 4

For domain solve it for x

⇒ 6x^2 + 5x - 4

⇒ 6x^2+ 8x - 3x - 4

⇒ 2x(3x + 4)· -1(3x + 4)

⇒ (3x + 4) (2x - 1)

values of x are positive for quadratic  equation,

⇒ (3x + 4) (2x - 1)≥0

⇒ x ≥ 1/2  or  x ≥ -4/3

These  are the domain of function.

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The cost of each ticket of the amusement park is $15.

One or many equations having the same number of unknowns that can be solved simultaneously called as simultaneous equation. And simultaneous equation is the system of equation.

Given:

Two student groups went to an amusement park on the same day.

Group 1 bought 9 tickets and received a $120 discount.

Group 2 bought 3 tickets and received a $30 discount.

Let x be the amount of one ticket and y be the total amount.

According to the question:

We have system of equation,

y = 9x - 120    equation1

y = 3x - 30    equation 2

Subtract the equation 2 to equation 1.

So, 6x = 90

x = 15

Therefore,  $15 is the cost of each ticket.

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The analysis of the given functions is as follows;

i. y = 16ˣ ⇒ Graph C

ii. y = 0.25ˣ ⇒ Graph B

iii. y = 4.5ˣ ⇒ Graph D

iv. y = 0.5ˣ ⇒ Graph A

v. y = 10·x + 1 ⇒ Graph E

(b) The equation of the exponential function is; y = 0.375ˣ

(c) The equation of the line is; y = 10·x - 4

(d) y = 25ˣ

(e) The equation of the perpendicular line is; y ≈ 5 - 0.1·x

An exponential function in which the argument is the index value such that the power to which a constant is raised, is the argument.

i. The values of the function y = 16ˣ is given by the function that has a value of 4 when x = 0.5, which corresponds with the graph C

ii. The function, y = 0.25ˣ decreases as the value of x increases, from negative to positive which corresponds to the graph B

iii. The function y = 4.5ˣ has a value of 4.5 when x = 1, which corresponds with the graph D

iv. The function, y = 0.5ˣ also decreases as x increases and has a value of  5 when x = -1, which corresponds to the graph A

v. The function, y = 10·x + 1 is a linear function which corresponds with the graph E

(b) The exponential function of graph A and B are y = 0.5ˣ and y = 0.25ˣ respectively

An exponential function that lies between graph A and graph B is obtained by adjusting the y-intercept value to be between 0.5 and 0,25 as follows;

[tex]y =\left(\dfrac{ 0.5 + 0.25}{2}\right)^x = 0.375^x[/tex]

The exponential function that is located between  graph A and B is 0.375ˣ

(c) The equation of the function of graph E is; y = 10·x  + 1, which is of the form y = m·x + c

Where comparing, we get, m = 10 = The slope of the graph

The slope of parallel lines are congruent, therefore, the slope of the line parallel to the line E is also 10

The equation of the line passing through (0, -4), and parallel to the graph E in point and slope form is y - (-4) = 10·(x - 0)

y + 4 = 10·x

The equation of the line is; y = 10·x - 4

(d) An equation for an exponential function with a higher constant percent rate than graph C, y = i6ˣ is y = 25ˣ

(e) The slope of the line perpendicular to the line E, y = 10·x + 1, that has a slope m, is found as follows;

[tex]m_{\perp} = -\dfrac{1}{m}[/tex]

[tex]m_{\perp} = -\dfrac{1}{10} = -0.1[/tex]
The equation of the line is therefore; y - 5 = -0.1 × (x - 0)

y = -0.1·x + 5 = 5 - 0.1·x

The equation of the line perpendicular to line E  is y = 5 - 0.1·x

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The required solution to the given expression is 3 which is determined by the division operation.

In mathematics, divides left-hand operands into right-hand operands in the division operation.

To determine the evaluation of expression 4 ÷ 4/3

When considering multiplying the fractions together, After that, you would multiply the denominator across and the numerator across, respectively. Your final answer should be 12/4 However, if you simplify it by 4, your final answer will be 3.

Thus, the required solution to the given expression is 3.

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The expression without the summation notation is Sₙ = 4(n² - 1)/n²

Summation notation is used to write a very long sum (of elements) in a very concise manner. It is also called Sigma notation

Given:

[tex]\displaystyle \sum\limits_{i = 1}^n \frac{12k(k-1)}{n^{3} }[/tex]

Below are the useful summation formulas you will need in order to rewrite the expression without the summation notation:

[tex]\displaystyle \sum\limits_{i = 1}^n i = \frac{{n\left( {n + 1} \right)}}{2}[/tex]

[tex]\displaystyle \sum\limits_{i = 1}^n {{i^2}} = \frac{{n\left( {n + 1} \right)\left( {2n + 1} \right)}}{6}[/tex]

Where i is a variable

Since 12 and n are constants, we can rewrite the given equation as follows:

[tex]\displaystyle \sum\limits_{i = 1}^n \frac{12k(k-1)}{n^{3} } = \displaystyle \frac{12}{n^{3} } \displaystyle\sum\limits_{i = 1}^n k(k-1)[/tex]

                       [tex]= \displaystyle \frac{12}{n^{3} } \displaystyle\sum\limits_{i = 1}^n k(k-1)[/tex]

                     [tex]= \displaystyle \frac{12}{n^{3} } \displaystyle\sum\limits_{i = 1}^n (k^{2}-k)[/tex]

                    [tex]= \displaystyle \frac{12}{n^{3} } ( \displaystyle\sum\limits_{i = 1}^n k^{2} - \displaystyle\sum\limits_{i = 1}^n k )[/tex]

Using the formula, we have:

                   = 12/n³ ( n(n+1)(2n+1)/6 - n(n+1)/2 )      Factorise n(n+1) out

                   = 12n(n+1)/n³ ( (2n+1)/6 - 1/2 )

                   = 12(n+1)/n² ( (2n+1-3)/2 )

                   = 12(n+1)/n² ( (2n-2/6) )

                   = 2(n+1)/n² (2n-2)

                  =  ( (2n+2)(2n-2) )/n²

                 = (4n² - 4)/n²

                 = 4(n² - 1)/n²

Therefore, using summation formulas to rewrite the expression without the summation notation gives Sₙ = 4(n² - 1)/n²

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The amount that should be invested to the nearest ten dollars is $930.

When an amount is compounded daily, it means that the investment increases in value everyday over the investment period.

In order to determine how much should be invested today, the present value of $1890 has to be determined.

The formula for determining the present value is:

PV = FV ÷ (1 + r)^nm

Where:

PV = 1890  ÷ (1.00016)^(12 x 365) = 930

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The y-intercept of the line passes through the point (-4,5) with slope 2 is y = 13.

Given:

(-4,5) and slope m = 2

substitute in y=mx+c

5 = 2*(-4) + c

5 = -8 + c

c = 5 + 8

c = 13.

c value in y = 2x + c

y = 2x + 13

To find y-intercept put x = 0.

y = 2(0) + 13

y = 0+13

y = 13

Therefore the y-intercept of the line passes through the point (-4,5) with slope 2 is y = 13.

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Answer:

Z-Grand Shipping Company manufactures boxes in the shape of a cube.

The formula for the surface area of a cube is 6s, where s is the length of one side.

Z-Grand Shipping Company manufactures large boxes with a side length of 6 feet. The surface area of each large box is 216

square feet

The company also manufactures small boxes with a side length of 3 feet. The surface area of each small box is 54

square feet

The surface area of the large box is 4 times larger than the small box.

{So for the first line which is The surface area of each large box is

square feet.}

Ans;216

{The second line which is The surface area of each small box is

square feet.]

Ans;54

{The Third line which is The surface area of the large box is times larger than the small box.}

Ans;4

Answer:

Z-Grand Shipping Company manufactures boxes in the shape of a cube.

The formula for the surface area of a cube is 6s, where s is the length of one side.

Z-Grand Shipping Company manufactures large boxes with a side length of 6 feet. The surface area of each large box is 216

square feet

The company also manufactures small boxes with a side length of 3 feet. The surface area of each small box is 54

square feet

The surface area of the large box is 4 times larger than the small box.

{So for the first line which is The surface area of each large box is

square feet.}

Ans;216

{The second line which is The surface area of each small box is

square feet.]

Ans;54

{The Third line which is The surface area of the large box is times larger than the small box.}

Ans;4

Answer:

(2x+6) = (x+9) ; x = 3

Step-by-step explanation:

-x both sides ; 2x-x = x and -6 both sides which is x = 3

The two operations that are needed to write the expression that represents "five less than the quotient of a number and three" are Division and subtraction.

What is the quotient?

A result is obtained by dividing two amounts.

The quotient is the result of a division.

The term "less than" represents subtraction.

So, the two operations that are needed to write the expression that represents "five less than the quotient of a number and three" are Division and subtraction.

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Answer:

y=60°, x=60°

Step-by-step explanation:

X=60° Angles in a Equaliteral triangles are all 60°

Alternate angle to get the base angle close to y

Y=60° because of Isoceless angles

Answer:

the answer for x when h(x) is 2.9

The length of triangle AB is 22.5.

Triangle A = 7.5

Triangle B = 15

Whole = 22.5

As per the given question

Figure is made of 2 triangles.

Triangle A

Triangle B

9

7

As it is 2 triangles so

So A = 7.5

      B = 15

The whole is = 15 + 7.5

                             =22.5

Each part is 7.5 and 15 respectively and whole is 22.5 per square unit.

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The missing terms in the two column proof are;

Reason 1; Perpendicular bisector

Reason 2; Definition of perpendicular bisector

Statement 3; CO ≅ BO

Reason 3; Segment division

Reason 4; Reflexive Property of Congruence

Reason 5; Definition of Isosceles Triangle

Reason 6; AAS Congruency Postulate

From the given image, we want to use the two column proof to prove that ΔAOB ≅ ΔAOC

Now, we have the two column proof as follows;

Statement 1; AO ⊥ BC

Reason 1; Perpendicular bisector

Statement 2; ∠AOB and ∠AOC are right angles

Reason 2; Definition of perpendicular bisector

Statement 3; CO ≅ BO

Reason 3; Segment division

Statement 4; AO ≅ AO

Reason 4; Reflexive Property of Congruence

Statement 5; AB ≅ AC

Reason 5; Definition of Isosceles Triangle

Statement 6; ΔAOB ≅ ΔAOC

Reason 6; AAS Congruency Postulate

The final proof is AAS Congruency postulate because it has 2 congruent angles and the non-included congruent side.

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Answer:

[tex]-9,-18,-27,-36[/tex]

Step-by-step explanation:

If the first term of a sequence is [tex]-9[/tex] and the common difference is [tex]-9[/tex], then each successive term in the sequence is [tex]9[/tex] less than the previous term:

[tex]a_n=-9n[/tex]

Therefore, the first term is [tex]-9[/tex], followed by [tex]-18[/tex], [tex]-27[/tex], and [tex]-36[/tex].

The required solution of the given absolute value equation is z = 4/3 and z = 1/3.

Given that,
To solve the absolute value equation |6z-3|=5

The equation is the relationship between variables and represented as y = ax + b is an example of a polynomial equation.

here,
Given the absolute value equation,
|6z-3|=5
Simplify,
6z - 3 = ± 5
Taking (+)

6z - 3 = 5
6z = 8
z = 4/3
Taking (-)
6z -3 = -5
z = -1/3

Thus, the required solution of the given absolute value equation is

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