Write an inequality using variables x and y whose graph is described by the given information. The points (2,5) and (-3,-5) lie on the boundary line. The points (6,5) and (-2,-3) are solutions of the inequality.

The product of two consecutive non-negative integers is 240 and the integers are 15,16.

What are consecutive integers?

Let the numbers be x, x+1

Product is x(x+1)=240

x² + x = 240

x² + x − 240 = 0

x² + 16x − 15x − 240 = 0

x(x+16) − 15(x+16) = 0

(x+16)(x−15)=0

x = 15,−16

So, the product of two consecutive non-negative integers is 240,then numbers are 15, 16.

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Based on the information given: A. c║d; converse of alternate exterior angles theorem.

Exterior alternate angles are congruent based on the alternate exterior angles theorem. Conversely, it can also be stated that if two angles, which are exterior alternate angles, are congruent to each other, therefore the lines they lie on that is crossed by a transversal are proven to be parallel to each other based on the converse of alternate exterior angles theorem.

Given that angles 11 and 13 are congruent angles, the diagram also shows that they are alternate exterior angles. They lie on each lines, c and d, that are crossed by transversal a.

Therefore, based on the converse of alternate exterior angles theorem, lines c and d are parallel.

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The x-intercept is (8.75,0) and

The y-intercept is (0,700)

The ordered pairs are (2.5,500) and (5,300).

Given that,

In the picture we have a graph with line.

We have to find the x-intercept and y-intercept of the scenario and the ordered pairs (2.5, ___) and (___ , 300)

We know that,

The x intercept is the location where the line touches the x axis. The y intercept is the location where the line touches the y axis.

So,

The x-intercept is (8.75,0) and

The y-intercept is (0,700)

The ordered pairs are (2.5,500) and (5,300).

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The equation of the function in slope-intercept form with slope of 2 is y = 2x+19.

According to the question,

We have the following information:

Slope = 2 (Note that slope of a line is denoted by m.)

Points through which function is passing = (-8,3)

So, we have x' = -8 and y' = 3.

We know that the following equation is used to find the equation of the function or line:

(y-y') = m(x-x')

y-3 = 2{x-(-8)}

y-3 = 2(x+8)

y-3 = 2x+16

y = 2x+16+3

y = 2x+19

Hence, the equation of the function in slope-intercept form with slope of 2 is y = 2x+19.

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The sale price of the oil change after the discount can be found to be $25.50.

When given a discount, the selling price of an item is found by the formula:

= Price of item before discount - Discount

The discount on the oil change, given the price of the oil change and the coupon is:

= Price of oil change x Coupon rate

= 30 x 15%

= $4.50

The sale price after the oil change is:

= Price of oil change before discount - discount

= 30 - 4.50

= $25. 50

The first part of the question is:

An oil change at city auto is regularly $30. Mr Allen has a coupon for 15% off.

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Answer: -1.73 ft

Step-by-step explanation:

(-2.54 - 3.16 - 2.82 + 1.6) / 4 = -1.73

Answer:

Determine the distance between each set of ordered pairs

(6 7/8,2) and (-3,2)

Step-by-step explanation:

Well if you do delta y over delta x you do -2 - 2 over 3 - 67/8 which will be -4 over -5.375 which will equal 32 over 43 which is you M you b is one point (your choice) then y = mx + b so 2 = 32/43(-3) + b 2 = -96/43 + b then add -96/43 to both sides and you'll get -10/43 = b so y = 32/43x + -10/43

equation - y = 32/43x + -10/43

Answer:

70 dogs

Step-by-step explanation:

total animal is 98

total ratio is 5+2 = 7

calculate how much each ratio has

98/7 = 14

5 ratio are dogs, so multiply 14 with 5 to get 70 dogs

you can also do:

5/7 × 98 = 70

It quickly becomes apparent that 174 is much too large, so n must be 144.The value of the n is 144.

Taking the given equation modulo 2,3, and 5, respectively, we have

n⁵≡(mod 2)

n⁵≡(mod 3)

n⁵≡( mod 5)

By either Fermat's Little Theorem (FLT) or inspection, we get

n≡(mod 2)

n≡(mod 3)

n≡( mod 5)

By either the Chinese Remainder Theorem (CRT) or inspection, we get n≡ 24 ( mod 30)

It is clear that n>133, so the possible values for n are 144,174,204,...Note that

n⁵ = 133⁵ + 110⁵ + 84⁵ + 27⁵

n⁵ < 133⁵ + 110⁵ +( 84 + 27)⁵

n⁵ =133⁵ + 110⁵ + 111⁵

n⁵ < 3.133⁵

From which (n/133)⁵ < 3

If n>= 174 then,

(n/133)⁵ > 1.3⁵

(n/133)⁵ = 3

which arrives at a contradiction. Therefore, we conclude that n=144

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Answer:

Step-by-step explanation:

add 23+14=37-90= 53

answer=53

Answer:

133/7 = 19

Step-by-step explanation:

"Find the average change in the zoo's tiger food supply each day."

And what does that have to do with anything? It's not like there is a change in diet that we can then easily calculate using derivatives.

Answer:

x = -9

Step-by-step explanation:

(x1, y1) = (-4, 3)  &  (x2, y2) = (x, 4)

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

-1/5 = (4 - 3)/(x - (-4) = 1/(x+4)

-(x + 4) = 5

-x - 4 = 5

-x = 5 + 4 = 9

2276 large a sample should be taken to obtain a margin of error of 0.027 for the estimation of a population proportion.

Given:

At 99% confidence, how large a sample should be taken to obtain a margin of error of 0.027 for the estimation of a population proportion.

Error e = 0.027

z score at 99%:

z = 2.576.

sample size n = p(1-p)(z/e)^2

= 0.5(1-0.5)(2.576/0.027)^2

= 0.5*0.5*9102.573

= 0.25*9102.573

= 2275.64

≈ 2276

Therefore 2276 large a sample should be taken to obtain a margin of error of 0.027 for the estimation of a population proportion.

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The equation of the graph is given by y = ( x + 2 )² + 3

Graphs behave differently at various x-intercepts. Sometimes the graph will cross over the x-axis at an intercept. Other times the graph will touch the x-axis and bounce off.

Identify the even and odd multiplicities of the polynomial functions' zeros.

Using end behavior, turning points, intercepts, and the Intermediate Value Theorem, plot the graph of a polynomial function.

The graphs cross or are tangent to the x-axis at these x-values for zeros with even multiplicities. The graphs cross or intersect the x-axis at these x-values for zeros with odd multiplicities

Given data ,

Let the equation be represented as A

Now , the value of A is

y = ( x + 2 )² + 3

The given equation is in the standard vertex form of a parabola:

y = a(x - h)² + k

where (h, k) is the vertex of the parabola.

By comparing the given equation with the standard vertex form, we can see that:

a = 1, h = -2, and k = 3

Hence , the vertex of the parabola is at the point (-2, 3) and the graph is plotted

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The force of attraction is 2.78 Newton when m = 2 kilograms and d = 15 meters.

According to the question,

We have the following information:

The force of attraction, F of a body varies directly as its mass (m) and inversely as the square of the distance (d) from the body. And when m=8kg and d=5meters then F=100 Newtons.

Now, let's take the constant for this case to be k.

We have the following expression:

F = km/[tex]d^{2}[/tex]

Putting the values in this expression to find the value of k:

100 = 8k/(5*5)

Using the cross multiplication method:

2500 = 8k

k = 2500/8

k = 312.5

Now, we have the following value of F:

F = 312.5*2/15*15

F = 625/225

F = 2.78 Newton

Hence, the force of attraction is 2.78 Newton when m = 2 kilograms and d = 15 meters.

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The reflection of function f(x) across the x-axis is [tex]-x^{2} -4[/tex].

It is given to us that the function is -

[tex]f(x)=x^{2} +4[/tex] --- (1)

and a function g

We have to find out the reflection of f(x) across the x-axis.

A function can be defined as an expression that assigns the value of each element of a given set to the another specific element of another given set.

To find out the reflection of f(x) across the x-axis, we have to take -f(x) instead of f(x).

Now,

[tex]-f(x)=-(x^{2} +4)\\= > -f(x)=-x^{2} -4[/tex]

Thus, the reflection of function f(x) across the x-axis is [tex]-x^{2} -4[/tex].

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Answer:

in six years, Mo will have roughly $393090.4 in savings bonds.

Step-by-step explanation:

(This might not be the most efficient way to do it.)

year one - 290000 x 1.052 = 305080

year two - 305080 x 1.052 = 320944.16

year three - 320944.16 x 1.052 = 337633.256

year four - 337633.256 x 1.052 = 355190.185

year five - 355190.185 x 1.052 = 373660.075

year six - 373660.075 x 1.052 = 393090.399

in six years, Mo will have roughly $393090.4 in savings bonds.

Answer:

[tex]0 < x < 60[/tex]

Step-by-step explanation:

By the Triangle Inequality Theorem:

30 + 30 > x, so 60 > x ----> x < 60

30 + x > 30, so x > 0

x + 30 > 30, so x > 0

Putting these inequalities together, we have 0 < x < 60. So the length of the third side can be greater than 0 inches but less than 60 inches.

Answer: About 140,514 ft²

Step-by-step explanation:

The area of a parallelogram is base × height. The base is already determined as 740 ft. You can find the height(h) with trigonometry:

[tex]sin(88)=\frac{h}{190}\\ \\h=190sin(88)=189.88425713[/tex]

Now, multiply the values together:

[tex]740*189.88425713=140514.350[/tex]

The simplified expression is 11 (1/6).

A fraction is a part of the whole represented by a/b, where a and b are any integers.

The given expression is 7 (5/12) - (-3 (3/4)).

Simplify the expression as follows:

7 (5/12) - (-3 (3/4))

= 89/12 +15/4

= (89+45)/12

= 134/12

= 11 (1/6)

Hence, the simplified expression is 11 (1/6).

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Explicit formula for this sequence is (C) an= 6+ (n-1)(-4)

Given sequence,

6, 2, -2, -6.....

First term = a = 6

Difference = d = 2 - 6

                        = -4

No. of terms = n

Therefore, an = a + (n-1)d

                       = 6 + (n-1)(-4)

Hence, an= 6+ (n-1)(-4).

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Answer:

  4 pairs

Step-by-step explanation:

You want the number of pairs of integers (m, n) such that m > n and m² -n² = 96.

The difference of squares is factored as ...

  m² -n² = (m -n)(m +n)

In order for the difference to be 96, these factors must be factors of 96.

The prime factorization of 96 is ...

  96 = 2^5 · 3

The number of divisors of 96 is the product of the exponents of these factors, each increased by 1:

  (5+1)(1+1) = 12

That is, there are 12/2 = 6 factor pairs ab such that a<b. They are ...

   96 = 1·96 = 2·48 = 3·32 = 4·24 = 6·16 = 8·12

The values of m and n relate to the values of 'a' and 'b' by ...

  m = (a+b)/2

  n = (b-a)/2

In order for m and n to be integers, the values of 'a' and 'b' must both have the same parity. That is, they must both be even, or both be odd. This eliminates the factor pairs 1·96 and 3·32, leaving 4 (a, b) pairs, hence 4 (m, n) pairs. Possible ordered pairs are ...

  (m, n) ∈ {(25, 23), (14, 10), (11, 5), (10, 2)} . . . . . 4 pairs

Coffee shops per capita in city is 7235.294118

What is per capita?

The Latin phrase "per capita" means "by head." In statistics, the term "per capita" is sometimes used in place of "per person" to denote the average per person.

Main Body:

total population of city = 246000

Total coffee shops = 34

Per capita shops for population can be calculated by dividing total population by total shops.

calculatiing,

Per capita shops = total population/ total shops

                            = 246000/34

                            = 7235.294118

Hence number of coffee shops per capita is 7235.294118

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Hey, so because you didn't include the image this is impossible to get the number values.  But, essentially you'd solve it something like this.

Remember, the Y axis goes up, and its located when you are at X = 0.  

The y intercept is the value of Y, when is 0.  

The slope of a line is referred to as "rise/run"

Basically, you take any given spot.  For example, from x = 0 to x = 2.  The run is 2, because thats how much x value the line covers.  So, in that "run" how much do you go up or go down?  Lets say in those 2 x's that you travelled, how much did the height change?  If you changed by going up 4 units, it would be (rise/run) 4/2 = 2.  The slope would be 2.  That means that for every time x increases by 1, Y goes up 2.

Answer:

False.

Step-by-step explanation:

A point is a zero-dimensional object as it has no length, width or height. It has no size.

And it would be great if you can spell "point" correctly.

The minimum number of pizzas that john must deliver to earn back the money he spent on the car he bought  is 715 pizzas   .

In the question,

it is given that ,

the amount for which John bought the used car for pizza delivery = $5000

the amount John gets for 1 pizza he delivers = $10

the amount John spend on gas for 1 pizza he delivers = $3

So , the amount that John earned for 1 pizza delivered is = 10 - 3 = $7 .

the number of pizza required to sell = (price of car)/(amount earned from 1 pizza)

Substituting the values , we get

number of pizza required to sell = 5000/7 = 714.2857

rounding the answer to  whole number ,

we get

= 715 pizzas

Therefore , The minimum number of pizzas that John must deliver to earn back the money he spent on the car he bought  is 715 pizzas   .

The given question is incomplete , the complete question is

John recently bought a used car for $5000 for his pizza delivery job. he gets $10 for each pizza he delivers, but he has to spend $3 on gas for each pizza he delivers. what is the minimum whole number of pizzas john must deliver in order to earn back the money he spent on the car he bought ?

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Answer:

y= [tex]\frac{5}{9}[/tex]x - 2

Step-by-step explanation:

You want to get y alone so divide both sides by -9 to get: y = [tex]\frac{5}{9}[/tex]x- 2

this is because 2 negatives (-5x and -9) make a positive

Using the concepts of confidence interval, we got that is he interval estimate for the population proportion if we suppose 1,608 of 2,400 registered voters sampled said they planned to vote for the republican candidate for president.

We know that population proportion is given by the fraction of number of positive results to the total number of results

Therefore, Population Control(P)=1608/2400

                                                =>P   =0.67

Now, we are given that confidence interval is 0.95 degree or 95%

For 95%,confidence interval is given by =P±√[P×(1-P)]/n

where n is the total number of registered voters, and P is the population control.

confidence interval=0.67±√[0.67×(1-0.67)]/2400

                               =0.67±√(0.67×0.33)/2400

                                =0.67±√0.2211/2400

                                =0.67±(0.47/48.98)

                                =0.67±0.0095

                                 =0.660 and 0.679

Hence, if we suppose 1,608 of 2,400 registered voters sampled said they planned to vote for the republican candidate for president. using the 0.95 degree of confidence,  the interval estimate for the population proportion  is (0.660,0.679)

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