Suppose you had D dollars in your bank account. you spent $12 but have at least $51 left. how much money did you have initially? write and solve an inquality that represents this situation

Answer:

a) 27 b) 5 c) 16 d) 7

Step-by-step explanation:

Answer:

  x = 4

Step-by-step explanation:

You want to know the value of x in the arithmetic sequence x, 2x+4, 5x.

Terms of an arithmetic sequence have a common difference. This means ...

  (2x+4) -x = 5x -(2x+4)

  x +4 = 3x -4 . . . . . . . . . . simplify

  8 = 2x . . . . . . . . add 4-x

  4 = x . . . . . . divide by 2

The value of x is 4.

__

Additional comment

The common difference is x+4 = 8. The sequence is ...

  4, 12, 20, ...

Slope is 9.

A line's steepness can be determined by looking at its slope. Slope is calculated mathematically as "rise over run" (change in y divided by change in x). A line or a part of a line that connects two locations is said to have a slope, which is a measure of how steep it is. Or. The ratio of how much y grows as x grows by a certain amount is known as a line's slope. A line's slope often indicates the steepness and direction of the line. By calculating the difference between the coordinates of the two points, (x1,y1) and (x2,y2), it is simple to calculate the slope of a straight line between them. The letter "m" is frequently used to denote slope.

Given Data

Equation

Y=9-x/8

Slope

y = mx + b

Slope is 9.

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Answer:

Explanations:

Dilation is a transformation technique that changes the size of an object in a xy-plane.

From the given figure, there was an enlargement from AJV to A'J'V'. This shows that the scale factor is greater than 1:

Using one of the coordinates V and V'

V = (0, 1)

V' = (0, 4)

Determine the scale factor

Scale factor = V'/V

Scale factor = 4/1

Scale factor = 4

Hence the scale factor of triangle AJV till A'J'V' is 4

The equation of the line that represents Saturn Avenue is; y = 4.

The equation of a line can be ascertained using the formula,

y = mx + c

where m is the line's slope and c is just the y - intercept.

m = vertical change/ horizontal change

m = Δy/Δx

m = (y₂ - y₁)/(x₂ - x₁)

In this question, draw a line through the cleaners as well as perpendicular to Planet Drive.

We can discover the slope of the equation by contemplating two points just on line.

Consider the following points: (8, 4) and (16, 4).

Put the value sin slope.

m = (4 - 4)/(16 - 8)

m = 0/8

m = 0

So we got that,

y - intercept = 4

slope = 0  

Put back the values in equation of line.

y = mx + c

y = (0)x + 4

y = 4

As a result, y = 4 is the equation of the line which represents Saturn Avenue, given that Christopher decides that another road named Saturn Avenue, which will run past this same cleaners and be perpendicular to Planet Drive, is required.

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The point ([tex]-3\frac{1}{2}[/tex], [tex]-1\frac{1}{4}[/tex] ) on the coordinate plane is shown in the figure .

The Coordinate plane can be defined as a 2 D plane formed by the intersection of two line ,

where the horizontal line is called x axis and

the vertical line is called y axis .

In the question ,

the point is given

the point is  ([tex]-3\frac{1}{2}[/tex] , [tex]-1\frac{1}{4}[/tex] )

writing the mixed fraction  in decimal form , we get

x coordinate = [tex]-3\frac{1}{2}[/tex] ⇒ -(3*2+1)/2 = -7/2 = -3.5

y coordinate = [tex]-1\frac{1}{4}[/tex] ⇒ -(1*4+1)/4 = -5/4 = -1.25

So, the point to be plotted on the coordinate plane becomes (-3.5,-1.25)

the points plotted are shown in the figure below .

Therefore , the point ( [tex]-3\frac{1}{2}[/tex], [tex]-1\frac{1}{4}[/tex] ) on the coordinate plane is shown in the figure .

The given question is incomplete , the complete question is

Where is ([tex]-3\frac{1}{2}[/tex] , [tex]-1\frac{1}{4}[/tex]  ) on the coordinate plane?

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Answer:

3037 trttthdhsbdhwhsshs

Answer:

x

=

7

2

−

y

2

Step-by-step explanation:

Answer:

The slope is -5/2

Step-by-step explanation

I tried to show how I solved this problem in the image, but its not too great, so I hope this helps. :)

Answer:

c

Step-by-step explanation:

Bertha's dive is 5 times farther than the end of Vernon's dive

A ratio can defined mathematical as an ordered pair of numbers, like variables b and c, when written form b / c with the denominator greater than the value zero.

It explains how many times a particular number is composed of another number in a given proportion.

It is also seen as the comparison of two quantities, elements or numbers having the same unit measure. It goes further to explain how much of one of the element or quantity contains another.

This is done on the basis of  their magnitude or sizes.

Given that;

Bertha's dive ended = -25 m

Vernon's dive ended = -5 m

Divide the values

= -25/-5

= 5 times

Hence, the value is 5 times

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The average rate of change from

3 to 5 is -16.

0 to 2 is -4

-3 to 0 is -6.

It represents the typical amount by which the function changed for each unit over that time. On the function graph, it is calculated using the slope of the line connecting the interval's ends.

Given Data

Equation = 4 -2x²

Formula-

[tex]\frac{f(a)-f(b)}{a-b}[/tex]

a)To find the average rate of change from 3 to 5

a = 5, b = 3

Equating values in the formula

[tex]\frac{4-2(5^{2} )-(4-(3)}{5-3}[/tex]²

[tex]\frac{-46+14}{2}[/tex]

-[tex]\frac{32}{2}[/tex]

-16

The average ROC 3 to 5 is -16.

b) The average ROC from 0 to 2

a = 2 b=0

Equating values in the formula

[tex]\frac{4-2(2^{2})-(4-2(0) }{2-0}[/tex]

[tex]\frac{-4-4}{2}[/tex]

[tex]\frac{-8}{2}[/tex]

-4

The average ROC from 0 to 2 is -4

c)The average ROC from -3 to 0

a= 0 b = -3

Equating values in the formula

[tex]\frac{4-2(0)-(4-2(3^{2} )}{-3-0}[/tex]

[tex]\frac{4+14}{-3}[/tex]

-[tex]\frac{18}{3}[/tex]

-6

The average ROC from -3 to 0 is -6.

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The GCF of 10, 30, and 50 is 10.

Given numbers are 10, 30, and 50.

To calculate the Greatest Common Factor of the numbers, list the prime factors of each number.

10 = 2 × 5

30 = 3 × 2 × 5

50 = 2 × 5²

GCF is the result of the factors that each of the given numbers has in common.

So, GCF = 2 × 5 = 10

Therefore, 10 is the greatest positive integer that divides 10, 30, and 50 without leaving any remainder.

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The scale factor of model of Eiffel tower is 3:1640.

The scale factor is the ratio of measure of small length to large length. The base of both actual tower and scale down model is mentioned in question. Keep the values in ratio to find the scale factor.

Scale factor = 0.75 : 410

Removing decimal to get the whole number

Scale factor = 75:41000

Dividing the both parts of ratio by 25 to find the scale factor of mentioned model

Scale factor = 3:1640

As the Eiffel tower is scaled down in the model, the scale factor is 3:1640.

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[tex]\displaystyle \int -\tan(\theta )\cdot \ln(3\cos(\theta )) ~~ d\theta \\\\[-0.35em] ~\dotfill\\\\ u=\ln(3\cos(\theta ))\implies \cfrac{du}{d\theta }=\cfrac{1}{3\cos(\theta )}\cdot -3\sin(\theta ) \\\\\\ \cfrac{du}{d\theta }=-\tan(\theta )\implies \cfrac{du}{-\tan(\theta )}=d\theta \\\\[-0.35em] ~\dotfill\\\\ \displaystyle \int -\tan(\theta )\cdot u\cdot \cfrac{du}{-\tan(\theta )}\implies \int u\cdot du[/tex]

Percentage - The amount to pay for the policy $596,774.19

What is Percent ?

A percentage is a figure or ratio stated as a fraction of 100 in mathematics. Although the abbreviations "pct.", "pct.", and occasionally "pc" are also used, the percent symbol, "%," is frequently used to indicate it. A % is a number without dimensions and without a measurement system.

Given that,

Investment policy pay
PV = $37,000 year;
investment return: 6.2%
r = 6.2%
r = 6.2/100
r = 0.062

We must use one year as the number of periods even if we just need to calculate the value for one year. We employ: to determine the FV of a lump sum.

FV=PV/r
FV=37,000/0.062
FV= $596774.1935
to 2 decimal point
FV=$596,774.19

Hence, $596,774.19 is to pay for the policy

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Answer:

f(-1) = 6

Explanation:

Looking at the piecewise function given, we see that

f(x) = -3x -5

for x different from -1

And

f(x) = 6

for x = -1

So, we choose the suitable one, since x = -1

Answer:

6 liters

Step-by-step explanation:

Given:

The 9 litre of 50% acidic liquid.

Required:

What quantity of water should be added to reduce 9 liters of 50% acidic liquid to 30% acidic liquid ?

Explanation:

The solution steps are:

Acidic liquid in 9 liters lotion = (50/100) * 9 = 4.5 liters

Then water = 9 - 4.5 = 4.5 liters

Let 'x' liters be the required quantity of water.

Then :-

[tex]\frac{4.5}{9+x} = \frac{30}{100} = \frac{3}{10}[/tex]

That leads to :-

[tex]3(9+x) = 45 == > 3x = 18[/tex]

Which gives us :-

[tex]x=6[/tex]

Thus required quantity of water = 6 liters

Final answer:

6 liters

(Hi fyi this answer took a lot of time & effort to make sure it was accurate, precise and to the point to be produced, so if you could opt this answer as the brainliest it would mean the world to me,)

Stay positive and Take care,

A fellow mate,

Cheers !

Given:

The distance travelled by the ball is, d = 40 m.

The maximum height the ball reached is, h = 3 m.

The objective is to find the distance travelled by the ball at a height of h' = 2 m.

. (vertex)

n, the

The value of x can be calculated using the general form of the equation of parabola,

Here, (p,q) stands for the vertex of the parabola (20,3).

To find the value of a, consider a coordinate (0,0) and substitute the obtained values in the general equation of parabola.

Now, consider the coordinate of the required distance x of the ball, (x,2).

Substitute the above coordinate, the value of a and the vertex in the equation of parabola.

To solve the square on RHS, take square root on both sides of the equation.

Since, the height of 2 m of ball can be obtained at either side of the vertex.

So the distance between the vertex and the required position is

Then, the other possible position of the ball is,

Hence, the height of the ball will be 2m, either at a distance of 8.5m from origin or 31.5m from the origin.

(a) 291/2020

Divide the total for the 10-14 year column by the total.

(b) 77/465

There are 465 people from the east, 77 of which were loyal for 10 to 14 years

(c) 437/1010

There are 291+583=874 people who were loyal for at least 10 years. Divide this by the total of 2020 people.

(d) 145/376

376 people are from the West, (45+100)=145 of which are at least 10.

(e) 32/157

157 people were loyal for less than a year, 32 of which were from the East.

(f) 53/157

157 people were loyal for less than a year, 53 of which were from the South.

(g) 433/465

465-32=433 people were loyal for at least 1 year out of the 465 people from the East.

(h) 335/376

376-41=355 people were loyal for at least 1 year out of the 376 people from the West.

Answer:

B. 5a² + 3b + 6a

Step-By-Step Explanation:

First, see what has like terms. 7a² and -2a² both have the exponent 2 and the letter a, so you can combine those to get 5a². 3b and 6a cannot be combined because they have a different letter. So, 5a² + 3b + 6a is your answer.

Answer:

False

Step-by-step explanation:

No data points pass through 2 or more vertical lines

The side length of his patio will be 3·√42 ft long.

The area of a square can be calculated as the square of the sides of a given figure.

The area of a square = side x side

Given  that Vince wants to make a square patio in his yard and has enough concrete to pave an area of 378 square feet

The parameters given are;

The Area of the square patio = 378 square feet

Lets 's' be the side of the square;

Therefore, the dimensions of the sides of a patio that has an area of 378 ft.² is ;

s² = 378

Take square root on both sides

Therefore, s = √378

s = √(9 × 42)

s = 3·√42 ft

Hence, The side length of his patio will be 3·√42 ft long.

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The force exerted by the prism on the floor = 450N

Given: height = 3m, volume = 10m³

Pressure = 75 N/m², prism

To find force

Solution:

Volume of prism = Area of base x height

= Аrеа х 3

Area = 18 = 6m²

Now,

Pressure: force / Area ⇒ 75 = force 6

force= 75×6 = 450N.

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Answer:

espiritu satninon

Step-by-step explanation:

hello! it would help if you gave more information so we could better answer the question ^^

Solution:

First of all, we must find the 20% of 180 minutes:

180 x 0.20 = 36 minutes.

That means that the bus takes an extra 36 minutes in traffic. So that, if there

was no traffic congestion the total time is:

180-36 = 144 minutes.

So that, we can conclude that the correct answer is:

144 minutes.

1) given

2) base angles theorem

3) PN=QN

4) [tex]\angle 3=\angle 4[/tex]

5) MP=OQ

7) PQ, QP

8) MQ=PO

9) ASA

Answer:

2

Step-by-step explanation:

if you plug it in for the first equation you get 2-2 +8 which is 8

Then for the second one it would be 3(2) +2 which is 8