Given (x – 7)2 = 36, select the values of x. x = 13 x = 1 x = –29 x = 42

Consuelo deposited an amount of money in a savings account that earned 6. 3% simple interest. After 20 years , she had earned $5’922 in interest then the initial deposit was $4700

Use the simple interest formula

I = P r t

where I = simple interest

P = principal

r= rate of interest

t= number of years

5922=Px6.3%x20

5922=Px1.26

P=5922/1.26

P=4700

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The amount of honey that Bert’s new beehive hold would be; 200.

The unitary method is a method for solving a problem by the first value of a single unit and then finding the value by multiplying the single value.

Given data that the Number of frame beehive = 6

The Pound of honey = 40

The Current Frame beehive = 30

First step is to formulate an equation and then use the formulated equation;

40 × 30 ÷ 6

Hence, 40 × 5

= 200 honey

Therefore, the number of honey would be; 200.

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Thus, it takes 1.5 minutes {30 seconds} for filling a 3-litre bowl

We can conclude that train A is moving faster than train B

The general equation of a straight line is -

[y] = [m]x + [c]

where -

[m] is slope of line which tells the unit rate of change of [y] with respect to [x].

[c] is the y - intercept i.e. the point where the graph cuts the [y] axis.

The equation of a straight line can be also written as -

Ax + By + C = 0

By = - Ax - C

y = (- A/B)x - (C/A)

We have the following problem -

The distance y (in miles) that train A travels in [x] amount of time is represented by the equality y = 78x. The graph shows the distance that train B travels.

Train A is moving with speed s[A] = 78 miles/hour {As slope of the equation is 78}. The train B will move with speed given by -

s[B] = (132 - 66)/(2 - 1) = 66 miles/hour

Therefore, we can conclude that train A is moving faster than train B

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[In the complete question it is asking to find which train is moving faster]

21/8 must be added to the terms to give the result as 6. The answer will be in a fraction.

What is a fraction?

In general, any number of equal pieces is represented by a fraction, which is a portion of the entire. In ordinary English, a fraction refers to the number of parts of a specific size.

Main Body:

Let the term to be added be x.

3+3/8+x =6

on solving this we will get the value of  x= 21/8

Hence the answer of this question is 21/8.

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The Area of the circle is 149.6 when the radius is 6.9cm.

Given that,

The radius is 6.9cm when the pi value is 3.142

Find the circle's area is what we must do.

We know that,

Radius is 6.9cm

r= 6.9cm

The space a circle occupies in a two-dimensional plane is referred to as its area. As an alternative, the area of a circle is the area included within the circle's perimeter.

Area of the circle is πr²

Area of the circle= 3.142×6.9²

Area of the circle= 3.142×47.61

Area of the circle=149.6

Therefore, The Area of the circle is 149.6 when the radius is 6.9cm.

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Answer:

150

Step-by-step explanation:

The sum of the interior angles, in degrees, of a regular polygon is given by the formula 180(n – 2), where n is the number of sides. The problem concerns a polygon with twelve sides, so we will let n = 12. The sum of the interior angles in this polygon would be 180(12 – 2) = 180(10) = 1800.

One of the unknown adjacent angle measures 48.3 degrees.

The adjacent angles are next to each other and hence are calculated by performing addition of the constituent angles. Let us assume the unknown adjacent angle be x.

Forming the equation based on x, adjacent angles and it's sum

104.7 + x = 153

Rewriting the equation as per the x

x = 153 - 104.7

Performing subtraction on Right Hand Side of the equation to find the value of x

x = 48.3 degrees

Thus, the measure of the adjacent angle is 48.3 degrees.

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Answer: its 48.3

Step-by-step explanation:

x+104.7= 153                                                                                                                 -104.7     -104.7                                                                                                                      =48.3

Step-by-step explanation:

6.

the factors need to be zero for the x-intercepts.

but (-3 - 3) = -6 and not 0.

the same for (-7 - 7) = -14 and not 0.

his mistake was the signs.

what do I need to add to -3 to get 0 ? 3. and 7 to -7.

so, the correct f(x) is

f(x) = (x + 3)(x + 7)

to get x-intercepts at -3 and -7.

7.

in the same way we get the factors here : for a given x the y value has to be 0.

how is y turning 0 for a polynomial in factor form ? well, at least one of the factors has to be 0.

therefore, for (-6, 0) the factor has to be

(x + 6) as -6 + 6 = 0

for (2, 0) the factor has to be

(x - 2) as 2 - 2 = 0

pick one of them as your answer. they are both correct factors for f(x).

The given circle equation  [tex]x^2+4x+y^2-2y-4[/tex]=0 has center(-2,1) and radius r=3.

What is circle equation?

 For all values of g, f, and c, the general equation of any type of circle is written as x2 + y2 + 2gx + 2fy + c = 0. The collection of all points in a plane that maintain a fixed, finite distance r from a fixed point is known as a circle. O = (a,b). The definition of a circle on the coordinate plane can be expressed using the equation of a circle. The equation is where r is the radius and if the centre of the circle is at the origin of the coordinate plane.

Here the given circle equation is,

=> [tex]x^2+4x+y^2-2y-4[/tex]=0

=>[tex]x^2+4x+y^2-2y =4[/tex]

[tex]= > x^2+4x+4+y^2-2y+1=4+4+1\\= > (x+2)^2+(y-1)^2=9[/tex]

we know that equation of circle is [tex](x-a)^2+(y-b)^2=r^2[/tex]

Here (a,b)= center and r is radius.

=> [tex](x+2)^2+(y-1)^2=3^2[/tex]

Then the Center (a,b)=(-2,1) and radius r=3.

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By taking the product between the mass and the acceleration, we will see that the force is:

F = 640 N

By the second Newton's law, we know that a force can cause motion on a body by accelerating it, such that the force is equal to the product between the mass of the object and the acceleration.

F = m*a

Here we know that:

m = 80kg

a = 8 m/s^2

Replacing that we get:

F = (80 kg)*( 8 m/s^2) = 640 N

Where N is the unit Newton.

1 N = 1 kg*m/s^2

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The factored form of x² + 2x - 15 is (x + 5)(x - 3).

Factorisation is a process of finding the factors of algebraic equations and representing them in simple form instead of expanded form.

Therefore, let's factor x² + 2x - 15

x² + 2x - 15

let's find two numbers we can add to get 2 and multiply to get - 15. The two numbers are -3 and 5.

Therefore,

x² - 3x + 5x - 15

x(x - 3) + 5(x - 3)

(x + 5)(x - 3)

Therefore,

x² + 2x - 15 = (x + 5)(x - 3)

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The amount received by Charis on Simple interest in 2 years will be $8.4

What is Simple Interest?

The process of figuring out how much interest will accrue on a given principal sum of money is known as simple interest (S.I.).

It's formula is given by S.I. = PRT/100  where P = principle amount

R= rate and T = time.

Main Body:

P= $140

R= 3%

T= 2 years

so S.I. = 140*2*3/100

S.I. = $ 8.4

Hence total amount received by Charis at the end of 2 years will be $8.4

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The equation of a line for y-intercept and the coordinate point is y=3x-1.

Given that, y-intercept is -1 and the line passes through the point (3, 8).

In Maths, an intercept is a point on the y-axis, through which the slope of the line passes. It is the y-coordinate of a point where a straight line or a curve intersects the y-axis. This is represented when we write the equation for a line, y = mx+c, where m is slope and c is the y-intercept.

Put, c=-1 and (x, y)=(3, 8) in y = mx+c, we get

8=m(3)-1

⇒ 3m=9

⇒ m=3

Substitute c=-1 and m=3 in y = mx+c, we get

y=3x-1

Therefore, the equation of a line for y-intercept and the coordinate point is y=3x-1.

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Answer:

-4/5

Step-by-step explanation:

do -3/2to get your answer

Step-by-step explanation:

You find the image of triangle by translation

Answer: I would say it is 2 and 3

Step-by-step explanation:

I can't be 1 ben franklin was not the one fooling the king and France

It can't be 4 because Mesmers force did not exist.

The jar of chemicals contains 176 grams of zinc.

Using ratio and proportion to calculate the amount of zinc. Let us assume the mass of zinc to be x. Equating the ratios.

4 : 11 = x : 484

Rewriting the equation in terms of x

x = (484 × 4) ÷ 11

Performing multiplication in numerator on Right Hand Side of the equation to find the value of x

x = 1936 ÷ 11

Performing division on Right Hand Side of the equation to find the value of x

x = 176

Thus, the mass of zinc is 176 grams.

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False, the leftmost end point of a line segment cannot be specified as the start point of the line

A line segment in geometry has two different points on it that define its boundaries. A line segment is sometimes referred to as a section of a line that links two places. The difference between a line and a line segment is that a line has no endpoints and can go on forever in either direction. A line segment is either an edge (of that polygon or polyhedron) if its end points are adjacent vertices, or a diagonal more generally when both of its end points are vertices of a polygon or polyhedron. A line segment is referred to as a chord when both of its end points are located on a curve, like a circle.

Given,

False, the leftmost end point of a line segment cannot be specified as the start point of the line.

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Answer:

p=17

Step-by-step explanation:

P = 3n+2r+t -1

when n=3, r=2, and t=5?

we will just substitute for the values

p=3(3)+2(2)+5-1

p=9+4+4

p=9+8

p=17

;- The value for p is 17

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The equation could be used to determine cc is 5.25x + 133 = 579.25 and cost of labor per hour is $85.

Given:

The technician at the store worked on the computer for 5.25 hours and charged her $133 for parts.

Total charged = 579.25

Let x be the charge per hour.

so the equation = 5.25x + 133 = 579.25.

Technician charge  = 579.25 - 133 = 446.25

5.25 hours = 446.25

divide by 5.25 on both sides

5.25 hours / 5.25 = 446.25/5.25

1 hour = $85

Therefore The equation could be used to determine cc is 5.25x + 133 = 579.25 and cost of labor per hour is $85.

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The number of  boys and girls in a class of 150 students is 90 and 60 respectively.

RATIO:

Comparing two quantities of the same units and determining the ratio tells us how much of one quantity is in the other.

i.e., it shows how many times a number contains another.

Total number of students = 150

ratio of boys to girls = 3 : 2

B:G = 3 : 2

now

3x + 2x = 150

5x = 150

x = 30

the number of boys = 3x = 3 X 30 = 90 boys.

the number of girls = 2x = 2 X 30 = 60 girls.

The number of  boys and girls in a class of 150 students is 90 and 60 respectively.

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4, 7/4, -1/2, -11/4, is Arithmetic progression.

What is Arithmetic progression ?

An arithmetic progression or arithmetic sequence ( AP ) is a sequence of numbers such that the difference between the consecutive terms is constant.

Here the series is given

4, 7/4, -1/2, -11/4,.....

In series, take 1st and 2nd terms to know common difference.

the common difference is = 7/4 - 4

                                              = (7 - 16) / 4 = -9/4

Now, take 3rd and 2nd term

common difference = -1/2 - 7/4

                                 = (-2 - 7) / 4 = - 9/4

so, we get the common difference is -9/4.

By that we can clearly say that given sequence of series is a Arithmetic sequence.

Hence, 4, 7/4, -1/2, -11/4, is Arithmetic progression

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The perimeter of Ragans new mural is 530cm.

Rectangle:

A rectangle is a type of quadrilateral, whose opposite sides are equal and parallel. It is a four-sided polygon that has four angles, equal to 90 degrees. A rectangle is a two-dimensional shape.

Here it is given that the measure of the rectangle is 238 cm and 435cm.

The Raegan creates a mural that is 27cm.

The formula to calculate the perimeter of a rectangle:

Perimeter = 2(length + breadth)

Earlier the length is 238cm and the breadth is 435cm.

Now replace the breath 435cm to 27cm.

length = 238cm

breadth = 27cm

Therefore we get the perimeter of the rectangle:

Perimeter = 2( 238 + 27)

= 2( 265)

=530cm

Therefore the perimeter is 530cm.

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Answer:

1400

Step-by-step explanation:

The number of pets per capita is 0.24

Given,

Number of pets in a town = 11,357

Population of the town = 47,500

We have to find the number of pets per capita;

Per capita;-

The Latin phrase "per capita" means "by head." It is used to calculate the average for each individual in a certain measurement. Per capita is frequently used, for instance, to calculate a population's per capita gross domestic product (GDP).

Here,

Number of pets per capita = Number of pets / Population

Number of pets per capita = 11,357 / 47,500

Number of pets per capita = 0.24

That is,

The number of pets per capita is 0.24

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Answer:

y = 8x - 6

Step-by-step explanation:

The slope-intercept form is y = mx + b, where m is the slope and b is the y-intercept.

We know that the y-intercept occurs when x = 0 so from the table, it's b = -6

We can use the slope formula to find the slope:

[tex]\frac{y_{2}-y_{1} }{x_{2}-x_{1} }\\ \frac{2-(-6)}{1-0} \\\frac{2+6}{1-0} \\8=m[/tex]

The number of times Aarf the Dog bark for 15 seconds if the dog starts barking at midnight and stops at 1:01 AM is 91.5 times

Total time of barking and silence = 15 seconds + 25 seconds

= 40 seconds

Difference in time = 1:01 AM - 12:00 am

= 1 hour 1 minutes

Convert hours and minutes to seconds

1 hour 1 minutes = 61 minutes × 60 seconds

= 3,660 seconds

Number of times Aarf the Dog bark for 15 seconds = Total hours Aarf dog barks / Total time of barking and silence

= 3,660 / 40

= 91.5 times

So therefore, the number of Aarf the Dog bark for 15 seconds is 91.5 times

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Answer:

(f ￮ g)(0) = 3

Step-by-step explanation:

evaluate g(0) then substitute the value obtained into f(x)

g(0) means what is the value of g(x) when x = 0

from the graph g(0) = 2 , then

f(2) , that is what is the value of f(x) when x = 2

from the graph  f(2) = 3

then

(f ￮ g)(0) = 3

The length of the road in the simplest radial form is 10[tex]\sqrt{29}[/tex].

Here a rectangle of dimensions is 20m by 50m. So the length of 50m and the breadth is 20m

As the road is diagonal of the rectangle.

So we have to find the length of the diagonal of the rectangle.

Formula to find the diagonal of rectangle:

Diagonal = [tex]\sqrt{l^{2} + b^{2} }[/tex]

length (l) = 50m

Breadth(b) = 20m

Diagonal = [tex]\sqrt{50^{2} + 20^{2} }[/tex]

               = [tex]\sqrt{2500 + 400}[/tex]

               = √2900

              = 10√29

Therefore the length of the road is 10√29.

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Answer:

4f^2/3 divided 1/4f 16f^3/3 f/3 3/16f^3 3/f

✓ Lets use algebra and simplify:[tex]\frac{\frac{4f^{2}}{3}}{\frac{1}{4f}} \\=\frac{4f^{2}}{3}* \frac{4f}{1} \\=…