Create a slope intercept equation with given information (3,1) m =0

The zeros with each multiplicity are given as follows:

The factor theorem is used to define the functions, which states that the function is defined as a product of it's linear factors, if x = a is a root, then x - a is a linear factor of the function.

Considering the linear factors of the function in this problem, the zeros are given as follows:

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The values of a, b and c are given as follows:

\(a = 6\sqrt{3}\), b = 21, \(c = 6\sqrt{2}\)

The three trigonometric ratios are the sine, the cosine and the tangent, and they are defined as follows:

For the length a, we have that it is opposite to an angle of 60º, while the adjacent length is of 6, hence:

\(\tan{60^\circ} = \frac{a}{6}\)

\(a = 6\sqrt{3}\)

Applying the 30-60-90 triangle theorem, the length b is given as follows:

b = 2 x 6

b = 12.

Length c is adjacent to an angle of 45º, while the hypotenuse is of 12 units, hence:

\(\cos{45^\circ} = \frac{c}{12}\)

\(c = 12 \times \frac{\sqrt{2}}{2}\)

\(c = 6\sqrt{2}\)

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The initial investment of the function is 20 dollars.

The rate growth in percentage is 4%.

The investment after 10 years is 29.6 dollars.

The function \(y=20(1.04)^{t}\) represents the value y of a saving account after t years.

Therefore, the initial investment of the function is 20 dollars.

The rate growth in percentage can be calculated as follows;

rate growth in percent = 0.04 × 100

rate growth in percent = 4 %

Let's find the value of the investment after 10 years.

Therefore,

\(y=20(1.04)^{t}\)

t = 10

\(y=20(1.04)^{10}\)

\(y=20(1.48024428492)\)

y = 29.6048856984

Therefore, the investment after 10 years is as follows:

y = 29.6 dollars

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The two other ways to name plane R are PTV and SVT

The figure that completes the question is added as an attachment

For a figure to be a plane, the figure must have at least three points

From the attached diagram, we have the following points on plane R

The above points can be combined as;

PTV and SVT

Hence, the two other ways to name plane R are PTV and SVT

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Answer:228m

Step-by-step explanation: 19m x 12m = 228m

Answer: 228m

Step-by-step explanation: Just multiply 19m by 12m. That's how you find area.

Answer:

-5/6

Step-by-step explanation:

(9, 5) and (21, -5)

slope = m = (difference in y)/(difference in x)

m = (-5 - 5)/(21 - 9)

m = -10/12

m = -5/6

Answer: -5/6

The slope of the line that passes through points (9,5) and (21,-5) is -5/6.

We can use the two-point formula to find the slope for the given line. The formula is as follows:

(y2 - y1) = m*(x2 - x1)

Where (x1, y1, x2, and y2) represent the points on the line, and m is the slope of the line.

In the given case:

x1=9, x2=21

y1=5, y2=-5

Using these values in the two-point formula, we get:

(-5-5)=m*(21-9)

-10=m*12

m=-10/12

m=-5/6

Hence the slope of the line is -5/6.

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The position vector of point P, MP, is given by MP = 6i - j.

To find the position vector of point P, which is the midpoint of NO, we can use the midpoint formula.

The midpoint formula states that the midpoint of a line segment with endpoints (x₁, y₁) and (x₂, y₂) is given by:

Midpoint (Mᵖ) = ((x₁ + x₂) / 2, (y₁ + y₂) / 2)

Let's find the position vector of point P using the given information:

Point N: N = 4i - 5j

Point O: O = 8i + 3j

Using the midpoint formula, we can find the coordinates of point P:

x-coordinate of P: (x₁ + x₂) / 2 = (4i + 8i) / 2 = 12i / 2 = 6i

y-coordinate of P: (y₁ + y₂) / 2 = (-5j + 3j) / 2 = -2j / 2 = -j

Therefore, the position vector of point P, MP, is given by:

MP = 6i - j

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Answer:

63

Step-by-step explanation:

y = x - 4 is  the equation of the line in slope-intercept form.

How do you interpret a slope-intercept form?

The data provided by that form can be used to graph a linear equation in slope-intercept form. As an illustration, the equation y=2x+3 indicates that the line's slope is 2 and that its y-intercept is located at (0,3). This reveals the single point at which the line passes as well as the direction in which we should draw the full line after that.

Point from graph = (2, -2 )

                slope (m) = y/x

                                = -2/2

                                = 1

slope-intercept form ⇒ y = mx + c    

                                        -2 = 1 * 2 + c

                                          - 2 = 2 + c

                                               c = -4

 slope-intercept form ⇒ y = x - 4

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Answer:

  $0.25 per ream

Step-by-step explanation:

The costs per ream are ...

  X: $40/(8 reams) = $5/ream

  Y: $19/(4 reams) = $4.75/ream

The savings per ream is $5.00 -4.75 = $0.25 for the cheapest brand.

Ha:mu<10  is the appropriate alternative hypothesis that the consumer group wishes to test .

How would you define hypothesis?

An assumption or notion is called a hypothesis when it is put forth with the purpose of debating whether it might be true.

                               In the scientific process, the hypothesis is developed prior to the completion of any relevant study, other than a brief background review.

Ha:mu<10

Because A consumer group is suspicious of this claim, believing that the weight lose is, on average, much less.

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Answer:

the approximate population of the city after 14 years will be 7.96 thousand residents.

Step-by-step explanation:

to calculate the approximate population of the city after 14 years, we need to take into account the annual growth rate.

Given that the city's population grows by around 420 persons each year, we can calculate the total growth over 14 years by multiplying the annual growth rate by the number of years:

14 years × 420 persons/year = 5,880 persons

To find the approximate population after 14 years, we add the total growth to the current population:

2.08 thousand + 5.88 thousand = 7.96 thousand

Answer:

4

Step-by-step explanation:

Bc if you want 24 servings but it serves 6 you have to multiply it by 4 do it's 1*4 =4 because 6*4 =24

Answer:

4/14 as a fraction

Step-by-step explanation:

i did the test

The number of sodas sold at the baseball game was 119, while the number of hot dogs sold was 72.

Let's assume the number of sodas sold as 'x' and the number of hot dogs sold as 'y'.

According to the problem, the total number of sodas and hot dogs sold is 191, so we can write the equation:

x + y = 191   ...(1)

The problem also states that the number of hot dogs sold was 47 less than the number of sodas sold. Mathematically, we can express this as:

y = x - 47   ...(2)

To find the values of x and y, we can solve the system of equations (1) and (2). Substituting equation (2) into equation (1), we have:

x + (x - 47) = 191

Simplifying the equation:

2x - 47 = 191

2x = 191 + 47

2x = 238

Dividing both sides by 2:

x = 238/2

x = 119

Substituting the value of x back into equation (2):

y = 119 - 47

y = 72

As a result, the total amount of sodas sold is 119, and the total amount of hot dogs sold is 72.

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Answer:

y = 2x+4

Step-by-step explanation:

When we substitute the value of x in y =2x+4. The output of function is exactly like in the table shown.

x = 1 —> y = 2(1)+4 = 6

x = 3 —> y = 2(3)+4 = 10

x = 5 —> y = 2(5)+4 = 14

x = 7 —> y = 2(7)+4 = 18

x = 9 —> y = 2(9)+4 = 22

Since the output is exactly like in the table. Therefore, y = 2x+4 represents the following table.

Answer:

So the diameter of the pipe with the insulation around it is approximately 18.84 inches / 2 = 9.42 inches.

Step-by-step explanation:

To find the diameter of the pipe with the insulation around it, we can use the formula for the circumference of a circle:

C = 2 * π * r

Where:

· C = circumference of the pipe

· π = the mathematical constant approximately equal to 3.14

· r = the radius of the pipe

Using the given information, we know that the pipe’s diameter is 2.5 inches and that the insulation around the pipe is 0.5 inch thick. Therefore, the radius of the pipe with the insulation around it is:

r = 2.5 inches + 0.5 inch = 3 inches

Plugging in the values:

C = 2 * π * 3

C = 6.28 * 3

C = 18.84 inches

Note that this is only an approximation, as the thickness of the insulation is slightly larger than the diameter of the pipe. To obtain a more accurate result, we would need to use a geometric area formula or a numerical integration technique.

Answer:

105000000

Step-by-step explanation:

Since the exponent of the scientific notation is positive, move the decimal point 8  places to the right.

After writing the expression in standard form we get 105000000

An exponent is a number or letter written above and to the right of a mathematical expression called the base. It indicates that the base is to be raised to a certain power.

The given question is 1.05 * 10⁸

It has to be written in the standard format

The exponent 8 on 10 means base 10 is multiplied 8 times.

therefore

1.05 * 10*10*10*10*10*10*10*10

On solving this we get

105000000 is what we get after writing the expression in standard form.

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Answer: it b

Step-by-step explanation:

IT B

Answer:

74 and 18

Step-by-step explanation:

Answer:

100

Step-by-step explanation:

The length of e is given as follows:

e = 29.5 inches.

Suppose we have a triangle in which:

The lengths and the sine of the angles are related as follows:

\(\frac{\sin{A}}{a} = \frac{\sin{B}}{b} = \frac{\sin{C}}{c}\)

Considering that the sum of the measures of the internal angles of a triangle is of 180º, the measure of angle E is given as follows:

<E = 180 - (140 + 5)

<E = 35º.

Hence the length e is obtained applying the law of sines as follows:

sin(35º)/e = sin(140º)/33

e = 33 x sine of 35 degrees/sine of 140 degrees

e = 29.5 inches.

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Answer:

10

Step-by-step explanation:

7+15/5

Answer:

10

Step-by-step explanation:

subsitute

7+15/5=10

Answer:

\( \huge\mathfrak\pink{S} \huge\mathfrak\purple{o} \huge\mathfrak\blue{l} \huge\mathfrak\red{u} \huge\mathfrak\green{t} \huge\mathfrak\pink{i}\huge\mathfrak\purple{o}\huge\mathfrak\red{n}\huge\mathfrak\orange{➔}\ \)

by using Pythagoras law:

h²=p²+b²

6²=x²+3²

x²=36-9

x=√27 units

Answer:

53°, 127°, 127°

Step-by-step explanation:

Two intersecting lines form two pairs of angles:

So if one of the angles is measured 53°, then the other angles are:

The missing step of the congruent triangles is ΔMDA ≅ ΔMBC by ASA theorem

Given data ,

Let the two triangles be represented as ΔMDA and ΔMBC

Now , the measure of side MD ≅ MB ( given )

And , the measure of angle ∠DMA ≅ ∠BMC ( vertical angles theorem )

Now , the measure of ∠MDA ≅ measure of ∠MBC ( alternate interior angles)

Two angles are the same and a corresponding side is the same (ASA: angle, side, angle)

So , ΔMDA ≅ ΔMBC by ASA theorem

Hence , the congruent triangles are solved

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The lengths of the sides of a triangle can be the set of numbers {12, 13, 20}, making option D the right choice.

According to the triangle inequality theorem, any two sides' sums in a triangle must be bigger than the length of the third side. If a, b, and c are the lengths of a triangle's sides, then the sum of a and b's lengths is greater than c's length. Similar to how a+ c > b, b + c > a. It is not possible to create a triangle using the specified side lengths in any instance where they are unable to satisfy these requirements.

In the question, we are asked for the set of numbers from the options that could be the lengths of the sides of a triangle.

Thus, the lengths of the sides of a triangle can be the set of numbers {12, 13, 20}, making option D the right choice.

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Answer:

1) x= -3

2) x=-4

Step-by-step explanation:

The first equation is :

-3x+8=17

solving for x

-3x=17-8 ------------by collecting like terms

-3x=9

Divide both sides by -3

-3x/-3=9/-3

x= -3

In the second equation

1+4x= -15

solving for x

4x=-15-1

4x = -16

x=-16/4

x= -4

Answer:

Dimension of the pen: 13x4

Step-by-step explanation:

area = 52m²

width = x (I'd put 'w' but let's work with 'x' cause we are used to)

length = 2x + 5

x * (2x + 5) = 52

2x² + 5x = 52

2x² + 5x - 52 = 0 (that's a quadratic equation)

delta = 5² - 4*2*(-52)

delta = 25 + 416

delta = 441

x1 = (-5 + \(\sqrt{441}\)) / 2*2

x1 = (-5 + 21) / 4

x1 = 16 / 4

x1 = 4

width = 4

x2 = (-5 - 21) / 4

x2 = -26 / 4

x2 = -6.5 (cannot be this one for width because it's a negative value)

length = 2 * 4 + 5

length = 8 + 5

length = 13

PS: I don't know if there is an easier way to do it but that's the one I figured.