A rectangle is drawn so the width is 6 inches longer than the height. If the rectangle's
diagonal measurement is 49 inches, find the height.

The two numbers whose sum is 2 and product is -24 are 6 and -4

A quadratic equation is a second-order polynomial equation in a single variable x

a[tex]x^{2}[/tex]+bx+c=0

with a ≠ 0 . Because it is a second-order polynomial equation, the fundamental theorem of algebra guarantees that it has at least one solution. The solution may be real or complex.

Let the two numbers be x and y

so that

x + y = 2 ----------------1

xy = -24 -----------------2

from equation 1 make x the subject of the equation, so that it becomes

x = 2 - y ---------------3

substitute x in equation 3 in equation 2

y(2-y) = - 24

multiply out the bracket

2y - [tex]y^{2}[/tex] = -24

taking all terms to one side of the equation, it becomes

[tex]y^{2}[/tex] -2y -24 = 0

factorizing the equation

[tex]y^{2}[/tex] -6y + 4y - 24 = 0

y(y - 6) +4(y - 6) = 0

taking the terms outside bracket and putting them in a new bracket we have

(y + 4) (y - 6) = 0

so y + 4 = 0 or y - 6  = 0

y = -4 or y = 6

using y = -4 and substituting in equation 3

x = 2 - - 4

x = 6

In conclusion the two numbers are 6 and -4

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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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Answer:

25%

Step-by-step explanation:

cause i did marh

Answer:

k=297.54

Step-by-step explanation:

i can't really explain it

The value of k that satisfies the equation k/34.2 = 8.7 is approximately 297.54. So, correct option is B.

To determine the value of k in the equation k/34.2 = 8.7, we can solve for k by isolating it on one side of the equation.

We can start by multiplying both sides of the equation by 34.2 to eliminate the denominator:

k/34.2 * 34.2 = 8.7 * 34.2

This simplifies to:

k = 8.7 * 34.2

Evaluating the right side of the equation:

k ≈ 297.54

The correct option from the given choices is 297.54. So, correct option is B.

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Answer:

45mi/h

Step-by-step explanation:

4 to 8 = 4 hours

v = space / time

v = 180/4 = 45 mi/h

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 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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Answer: 33 pages in 1 hour

Step-by-step explanation:

You could cross multiply

[tex]\frac{11}{1/3}[/tex] = [tex]\frac{x}{1}[/tex]

11=1/3x

x=33

The P(a, b and c)  is 0.0432 when P(a) = 0.90, p(b) = 0.96, p(c) = 0.05.

From the given question, we know that

Probability of event 'a' occurring, P(a) = 0.90

Probability of event 'b' occurring, P(b) = 0.96

Probability of event 'c' occurring, P(c) = 0.05

We have been told that these three events are independent.

Thus, we can use the multiplication rule of probability, which states that the probability of three independent events a, b, and, c occurring is equal to the products of the probability of each individual event occurring.

p(a, b and c) = p(a) × p(b) × p(c)

                    = 0.90 × 0.96 × 0.05

                    = 0.0432

Hence, the probability(a, b, and c) is 0.0432.

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a)  no solution

b) only one solution

c) only one solution

d) infinite many solution.

e)  only one solution

f) no solution

g) infinite many solution.

h)  infinite many solution.

i)  no solution

j) only one solution

k) infinite many solution.

Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.

It demonstrates the equality of the relationship between the expressions printed on the left and right sides. LHS = RHS is a common mathematical formula.

Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.

Given:

We know depending upon the types of lines there are different type of solution

if there are two equations

[tex]a_1 x+ b_1 y+ c_1= 0[/tex] and [tex]a_2 x+ b_2 y+ c_2= 0[/tex]

For Intersecting Lines

[tex]a_1/a_2[/tex] ≠ [tex]b_1/b_2[/tex]

and, have only one solution

For parallel lines:

[tex]a_1/a_2[/tex] = [tex]b_1/b_2[/tex] ≠ [tex]c_1/c_2[/tex]

and, have no solution

For co- incident line

[tex]a_1/a_2[/tex] = [tex]b_1/b_2[/tex] = [tex]c_1/c_2[/tex]

and, have infinite many solution.

a) y= -5x + 4  --> 5x + y = 4

5x+y= -3

So, [tex]a_1/a_2[/tex] = [tex]b_1/b_2[/tex] ≠ [tex]c_1/c_2[/tex]

and, have no solution

b) y=3/4 x+5

y= 4/3 x + 5

so, [tex]a_1/a_2[/tex] ≠ [tex]b_1/b_2[/tex]

and, have only one solution

c) y= -3/4x+5

y=3/4x+5

[tex]a_1/a_2[/tex] ≠ [tex]b_1/b_2[/tex]

and, have only one solution

d) y= 3/4 x + 5

y= 5+ 3/4x

So, [tex]a_1/a_2[/tex] = [tex]b_1/b_2[/tex] = [tex]c_1/c_2[/tex]

and, have infinite many solution.

e) y= 3/4x +5

y=  x + 2

So, [tex]a_1/a_2[/tex] ≠ [tex]b_1/b_2[/tex]

and, have only one solution

f) y= 3/4x + 5

y= 3/4x + 2

So, [tex]a_1/a_2[/tex] = [tex]b_1/b_2[/tex] ≠ [tex]c_1/c_2[/tex]

and, have no solution

g) 6x -y = 5

-6x + y= -5

So, [tex]a_1/a_2[/tex] = [tex]b_1/b_2[/tex] = [tex]c_1/c_2[/tex]

and, have infinite many solution.

h) 2x- y +5 =0

2x- y+ 5 =0

So, [tex]a_1/a_2[/tex] = [tex]b_1/b_2[/tex] = [tex]c_1/c_2[/tex]

and, have infinite many solution.

i) 4x- y+ 5 =0

4x- y +3 = 0

So, [tex]a_1/a_2[/tex] = [tex]b_1/b_2[/tex] ≠ [tex]c_1/c_2[/tex]

and, have no solution

j) 3x- y +5 = 0

2x -y +5 =0

So, [tex]a_1/a_2[/tex] ≠ [tex]b_1/b_2[/tex]

and, have only one solution

k) 2x+ y -1 = 0

2x + y- 1= 0

So, [tex]a_1/a_2[/tex] = [tex]b_1/b_2[/tex] = [tex]c_1/c_2[/tex]

and, have infinite many solution.

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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.

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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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:

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

Answer:

I'm not sure, but it could be "inverse"

Step-by-step explanation:

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

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

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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Answer:

m<T = 60°

m<U = 60°

TS = 13

SU = 13

Step-by-step explanation:

Triangle TSU is an equilateral triangle.

All interior angles has equal measures and each = 60° since the sum of interior angles in a triangle is equal to 180 and this divided by 3 = 60

all side lengths are also equal to one another, TU is given as 13 cm so the length of TS and SU is also = 13

The exponential number 7⁴ we get expression as 2401.

Given that,

The exponential number is 7⁴.

We have to find the expression.

A number's exponent tells us how many times it has been multiplied by itself.

Exponent-related issues are resolved utilising exponentiation rules or exponentiation attributes.

How many times we must multiply the reciprocal of the base is indicated by a negative exponent is the exponential with negative symbol

A fractional exponent is one where the exponent of a number is a fraction.

Take the exponential number.

7⁴

7×7×7×7

2401

Therefore, The exponential number 7⁴ we get expression as 2401.

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Answer:

Step-by-step explanation:

add 23+14=37-90= 53

answer=53

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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The scale factor for a a pair of corresponding sides will be;

⇒ 3 / 2

What is Proportional?

The equality between two ratio is called Proportional.

Given that;

DEFG has been dilated to D'EF'G'.

Now,

Let the coordinates of DEFG are for side DG are;

D = (- 6, 3)

G = (- 3, 3)

And, The coordinates of D'E'F'G' are for side D'G' are;

D' = (- 4, 2)

G' = (- 2, 2)

So, The length of side DG is;

DG = √ (- 3 - (-6))² + (3 - 3)²

     = √ 3²

     = 3

And, The length of side D'G' is;

D'G' = √ (- 2 - (-4))² + (2 - 2)²

     = √ 2²

     = 2

Thus, The scale factor for a a pair of corresponding sides will be;

⇒ DG / D'G' = 3 / 2

Therefore, The scale factor for a a pair of corresponding sides will be;

⇒ 3 / 2

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Answer:

Only the third one is incorrect. First 2 and last 1 are correct.

The new volume of the container will be 120 ft³

Volume is defined as the space occupied within the boundaries of an object in three-dimensional space. It is also known as the capacity of the object.

Given a container with dimensions 3ft by 4ft by 5ft

Its volume need to be twice.

Volume of container = length*width*height

Original volume = 3*4*5 = 60 ft³

After doubling = 60*2 = 120 ft³

New dimensions are = 4ft by 5ft by 6ft

Hence, The new volume of the container will be 120 ft³ and New dimensions are 4ft by 5ft by 6ft

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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:

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.

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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