Write the equation of the line with a slope of 3/2that contains the point ( — 4, − 2).

Answer:

[tex]y+10=\frac{13}{8}(x-20)[/tex]

Step-by-step explanation:

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].

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

Using trigonometric ratios, tan a + cot a = (cos a + sin a) / sin a * cos a

The six trigonometric ratios are sine (sin), cosine (cos), tangent (tan), cotangent (cot), cosecant (cosec), and secant (sec). In geometry, trigonometry is a branch of mathematics that deals with the sides and angles of a right-angled triangle. Therefore, trigonometric ratios are evaluated with respect to sides and angles.

In the question given, the trig ratio is

tan a + cot a

We can simplify this as

tan a = sin a / cos a

cot a = 1 / tan a = 1 / sin a / cos a = cos a / sin a

Adding both ratios together

tan a + cot a = (sin a / cos a) + (cos a / sin a)

tan a + cot a = (cos a + sin a) / sin a * cos a

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The first mechanic worked for 10 hours and second mechanic worked for 5 hours.

Given,

Price of first mechanic service =$85/hr

Price of second mechanic service=$45/hr

Total time they worked together=15 hours

Total combined price charged=$1075

Let

Time spend by first mechanic on work =x

Time spend by second mechanic on work =y

Price charged by first mechanic on total work =85x

Price charged by second mechanic on total work=45y

Equation for total time spend by them together on work can be written as,

[tex]x+y=15.....i\\\\y=15-x[/tex]

Equation for total price charged by them can be written as,

[tex]85x+45y=1075\\[/tex]

Substituting y,

[tex]85x+45(15-x)=1075\\\\85x+675-45x=1075\\\\40x+675=1075\\\\40x=1075-675\\\\40x=400\\\\x=10\\[/tex]

Substituting x in eq.[tex]i[/tex],

[tex]10+y=15\\\\y=15-10\\\\y=5[/tex]

Hence, the first mechanic worked for 10 hours and second mechanic worked for 5 hours.

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Considering the given translation, the vertex that is not part of the image is:

H(3,0).

The translations to an image are represented as follows:

The vector notation of a translation is given as follows:

{x ± a, y ± a}

In this problem, this notation is:

{3, -3}.

Hence the rule applied to each vertex of the image is:

(x,y) -> (x + 3, y - 3).

The vertices of the original figure are as follows:

( -7, 3), (- 4,6), ( -1, 3) and (-4, 0)

Applying the translation rule, the vertices of the image are given as follows:

(-4, 0), (-1, 3), (2, 0), (-1, -3).

The lone coordinate without a vertex of the image is H(3,0).

The problem is given by the image at the end of the answer.

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Answer:

use AAA congurency rule

Step-by-step explanation:

angle a=angle f

angle b=angle e

angle c= angle d(a+b+c=180 when the triangle 2 sides are equal that means 3 is also equal)

The seal's new position relative to the surface of the ocean is 47 meters below.

It is important to note that that question has to do with elevation which is the change in position with regards to the sea or ocean level.

In this case, the harbour seal dives 35 metres below the ocean's surface and then it dives down an additional 12 metres

The new position will be;

= -35 - 12

= -47

This implies that it's 47 meters below the ocean surface.

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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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If the function be f(x) = (2[tex]$$x^4[/tex] + 1) sin 2[tex]$$x^5[/tex] then by differentiating the equation with respect to x, we get sin (2)(18[tex]$$x^8[/tex] + 5[tex]$$x^4[/tex]).

Let the given function be f(x) = (2[tex]$$x^4[/tex] + 1) sin 2[tex]$$x^5[/tex]

Differentiating with respect to x, we get

d/dx((2[tex]$$x^4[/tex] + 1) sin 2[tex]$$x^5[/tex])

= sin (2) (d/dx(2[tex]$$x^4[/tex] + 1) [tex]$$x^5[/tex] + d/dx ([tex]$$x^5[/tex])  (2[tex]$$x^4[/tex] + 1)

d/dx (2[tex]$$x^4[/tex] + 1) = 8x³

d/dx ([tex]$$x^5[/tex]) = 5[tex]$$x^4[/tex]

= sin (2) (8x³ + 5[tex]$$x^4[/tex] (  (2[tex]$$x^4[/tex] + 1)

Simplify

= sin (2) (8x³ + 5[tex]$$x^4[/tex] (  (2[tex]$$x^4[/tex] + 1)

= sin (2) (18[tex]$$x^8[/tex] +  5[tex]$$x^4[/tex]

Therefore, the function be f(x) = (2[tex]$$x^4[/tex] + 1) sin 2[tex]$$x^5[/tex] then by differentiating the equation with respect to x, we get sin (2)(18[tex]$$x^8[/tex] + 5[tex]$$x^4[/tex]).

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The solution for the given inequality has been graphed in detail.

A linear inequality can be gives the values for a variable in an interval of numbers.

Given inequalities are as below,

2x - 7 > 3 and 4 - x < -4

They can be simplified as,

2x - 7 > 3    

=> 2x > 10    

=> x > 5

And,  

4 - x < -4

=> x - 4 > 4

=> x > 8

The solution of the given inequality is the intersection of two solutions x > 5 and x > 8, which is x > 8.

This is graphed as follows,

Hence, the given inequality has solution x > 8 which has been graphed.

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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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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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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 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 exponential growth of 16.63% will take approximately 10.80 years to reach a population of 1134

An exponential function is a mathematical function, which is used in many real-world situations. It is mainly used to find the exponential decay or exponential growth or to compute investments, model populations and so on.

Data;

f(x) = P(1 + r)ˣ

x = time

Substituting the values

1134 = 215(1 + 0.1663)^ˣ

x = 10.80

It will take approximately 10.8 years to reach a growth of 1134

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Answer: The correct answer is "10.0 years"

Step-by-step explanation:

I took the test

The total weight of the metal bar is 45.002 grams.

Given:

While mining, Peter found a large metal bar that contained 33 grams of gold.

Peter also determined that the bar was 73.33% gold.

73.33% = 33 grams

divide by 73.33 on both sides

73.33%/73.33 = 33/73.33 grams

1% = 0.45002 grams

Multiply on 100 on both sides

1%*100 = 0.45002*100

100% = 45.002 grams.

Therefore the total weight of the metal bar is 45.002 grams.

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68 calls she received in each evening .

A straight line equation and equations with a maximum order of one are referred to as "linear equations." The formula for the linear equation can be written as Y = mx + b, where m is the slope of the line, b is the y-intercept, and x and y are the variables. Slopes tell us the direction and steepness of a line. The value of y when x is 0 is referred to as the y-intercept because (0,y) is the point where the line crosses the y-axis.

Let's say the number of calls on the second night was x.

The first evening was then x+7.

The third evening she received 4x calls.

Add them up to make 109 calls....

x + x+7 + 4x = 109

6x + 7 = 109

6x = 102

x = 17 calls

x+7 = 24 calls

4x = 68 calls

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Answer:

There isn't one. There is no solution.

Step-by-step explanation:

There are multiple ways to solve this system, but here's what I did:

Solve the both equations for s:

   s/2 + 5t = 3 + 5t  ⇒  s = 6

   3t - 6s = 9 + 3t  ⇒  s = -3/2

Since s cannot equal both 6 and -3/2 at the same time, there is no real solution to this system.

The total number of movies that the students saw is 105.

I got the answer by adding all of the values that the students saw. So I add 14,10,16,15...etc. which gives me the total of 105.

The probability that the fish is at most 0.5 meters away from the center of the container, considering the volume of the cube, is given as follows:

0.0723 = 7.23%.

The volume of a cube of side length s is given by the side length cubed, that is:

V = s³.

The cube in this problem has a side length of 1.2 meters, hence the volume is given as follows:

V = 1.2³ = 1.728 cubic meters.

Considering only the inner 0.5 meters of the cube, the volume is given as follows:

V = 0.5³ = 0.125 cubic meters.

A probability is given by the division of the number of desired outcomes by the number of total outcomes, hence:

p = 0.125/1.728 = 0.0723 = 7.23%.

(desired volume is of 0.125 m³, total is of 1.728 m³).

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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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For isosceles triangle RST  the measure of angle T is 34 degree

In this question, we have been given a isosceles triangle RST with RS = RT.

So, by isosceles triangle theorem,

angle S = angle T

So, angle T = (3x - 2)°

We know that the sum of all angles of triangle is 180°

∠R + ∠S + ∠T = 180°

9x + 4 + 3x - 2 + 3x - 2 = 180°

15x + 4 - 4 = 180°

15x = 180°

x = 12

So, 3x - 2 = 3(12) - 2

                = 34°

Therefore, for triangle RST  the measure of angle T is 34 degree

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Mr. Pinello wants each container to contain the same number of coloured pencils and markers, the most containers he can create is 16.

What is the Greatest Common Factor?

The biggest positive integer that divides evenly into all the numbers with no remainder is the greatest common factor (GCF, GCD, or HCF) of a collection of whole numbers.

We have,

The number of coloured pencils Mr. Pinello has = 80.

The number of markers and pencils Mr. Pinello has = 60.

The most containers Mr. Pinello can create to ensure that each one contains an identical amount of coloured pencils and markers.

The GCD of the number of coloured pencils and markers will be the largest number of containers to have the same number of items when the same number of items must be preserved.

Calculating the gcd of  and 80 and 64 is:

The greatest common divisor (GCD) of both 80 and 64 is 16.

∴ GCD = 16

Therefore, If Mr. Pinello wants each container to contain the same number of coloured pencils and markers, the most containers he can create is 16.

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The measure of the line AC is 15√3/2

The measure of the line BC is 15/2

Triangle ABC is the display style for a triangle with vertices A, B, and C.

In Euclidean geometry, any three points that are not collinear produce a singular triangle and a singular plane (i.e. a two-dimensional Euclidean space). All triangles are enclosed in a single plane if all of geometry is the Euclidean plane, however this is no longer true in higher-dimensional Euclidean spaces.

One of the internal angles of a right triangle (also known as a right-angled triangle) measures 90 degrees (a right angle). The hypotenuse, the triangle's longest side, is the side that faces the right angle. The triangle's other two sides are referred to as its legs, Right triangles follow the Pythagorean theorem, which states that the square of the length of the hypotenuse is equal to the sum of the squares of the lengths of the two legs of a right triangle (a2 + b2 = c2). Special right triangles have extra characteristics that simplify computations involving them. The 3-4-5 right triangle is one of the two most well-known.

Sin 60⁰=x/15

√3/2=x/15

x=15√3/2

The measure of the line AC is 15√3/2

Cos 60⁰= y/15

1/2=y/15

y=15/2

The measure of the line BC is 15/2

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Option B. The appropriate conclusion at the 5% significance level is to Reject the null hypothesis, the population mean is significantly different from 123

H0: mean = 123

H1 : mean ≠ 123

We have the p value of the statistics stated already in the question as p value = 0.0037.

The level is significance that we have been given in the question is 5% = 0.05

We are to test here if the true mean is different from 123.

Hence we would be testing the p value against the significance level.

We can see that P value is  < level of significance.

0.0037 < 0.05

Hence we would reject the null hypothesis.

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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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