2.
How many solutions does the following equation have?
8.5m +8 = 8.5m
infinitely many solutions
O exactly one solution
Ono solutions
O exactly two solutions

Answer:

Step-by-step explanation:

slope=-5/4

b=5

y=-5/4x+5

Answer:

a

Step-by-step explanation:

Answer:

The answer is: A. Hope it helps.

f(x) = Area = (length)(width)

width = x

The length is 16 yards greater than 3 times x

length = 3x+16

f(x) = (3x+16)(x) = 3x^2 + 16x

Answer:

Step-by-step explanation:

We have been given that -- The length of a rectangular parking lot is 16 yards greater than 3 times its width, x, in yards

Length of parking lot is 16 + 3x

Width of parking lot is x

We have to write the function f(x) that describes the area, in square yards, as a function of the width, x

Area of rectangle is Length × width

[tex] \sf Area = f(x) [/tex]

put value of length and width here,

[tex] \sf f(x) = (16 + 3x)(x )[/tex]

[tex] \sf f(x) = 3x^2 + 16x [/tex]

Therefore, f(x) = 3x² + 16x

The mean and the standard deviation of D are given as follows:

Variable D is the average amount of money earned, and the number of $10 bills grabbed has the distribution with mean and standard deviation given as follows:

(as stated in the problem).

We want now the mean and the distribution for the total amount of money, meaning that the entire distribution is multiplied by 10, and thus:

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The equation of line r which is parallel to line q and passes through point (5,-4) is y = (-3/5)x - 1.

The slope-intercept form is expressed as;

y  = mx + b

The point-slope formula is expressed as

y - y₁ = m( x - x₁ )

Given the data in the question;

First, determine the slope of the line q using the slope intercept-form.

y = mx + b

3x + 5y = 10

5y = -3x + 10

y = (-3/5)x + 10/5

y = (-3/5)x + 2

Hence;

Slope of line q m = -3/5

Since, line r is parallel to line q, they both have the same slope.

Therefore, slope of line r will be m  = -3/5

Now, plug the point  (5,-4) and and slope m = -3/5 into the point slope formula and solve for y.

y - y₁ = m( x - x₁ )

y - (-4) = (-3/5)( x - 5 )

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

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

y = (-3/5)x - 1

Therefore, the equation of line r is  y = (-3/5)x - 1.

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Answer:

  (c)  ∠acb ≅ ∠dcb

Step-by-step explanation:

You want to know what additional information is required to show ∆abc ≅ ∆dbc by SAS, given ac ≅ dc.

This postulate tells you triangles are congruent if two corresponding sides are congruent, and the angles between them are congruent.

In the given geometry, the corresponding sides are given as congruent, so the additional information required is that the angles between them are congruent.

The angle between sides ac and bc is ∠acb.

The angle between sides dc and bc is ∠dbc.

The additional information required is ...

  ∠acb ≅ ∠dcb . . . . . matches choice C

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Answer:

Step-by-step explanation:

you could do is buy 2x on the x-axis

Answer: 248

Step-by-step explanation: First, you add 4 + 6 to get 10, then you multiply that by 5 to get 50. Then you multiply 50 by 5 to get 250, so 250-2 = 248. I hoped this solved your problem.

Answer:

248

Step-by-step explanation:

(4+6)x5x5-2

10x5x5-2

50x5-2

250-2

248

(if wrong sorry)

Answer:

m4 - 11 = 1

Step-by-step explanation:

Given information,

→ m4 - 11

→ m = 3

Now the value of expression is,

→ m4 - 11

→ (3)4 - 11

→ 12 - 11 = 1

Hence, value of expression is 1.

Based on the definition of similar quadrilaterals, the measure of side MN is: 14.1 units.

If two quadrilaterals are similar to each other, then the measure of their corresponding sides will have a ratio that is equal. This means they will have proportional side measures.

Since we are told that quadrilaterals GHIJ and KLMN are similar to each other, then their corresponding sides will have measures that are proportional to each other.

Therefore:

IJ/MN = GJ/KN

IJ = 35

MN = ?

GJ = 52

KN = 21

Substitute:

35/MN = 52/21

Cross multiply:

MN(52) = (35)(21)

MN(52) = 735

MN = 735/52

MN = 14.1 units

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By using testing of hypothesis, it can be concluded that-

The correct set of hypotheses is

[tex]H_0 : \mu \geq 85[/tex]

[tex]H_a : \mu < 85[/tex]

What is testing of hypothesis?

Suppose there is a data at hand and there is a hypothesis to be tested. Testing of hypothesis determines whether the given hypothesis can be supported with the data at hand.

A student believes that the average grade on the final examination in statistics is at least 85.

The null hypothesis is [tex]\mu \geq 85[/tex]

The alternative hypothesis is [tex]\mu < 85[/tex]

So, the correct set of hypotheses is

[tex]H_0 : \mu \geq 85[/tex]

[tex]H_a : \mu < 85[/tex]

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Answer:

1 hour and 20 minutes I think

Step-by-step explanation:

add all of them up then divide by 60

The number of supervisors for baby unicorns is 9 times the number of unicorns.

Let 'n' be the number of supervisors.

Let there be u number of unicorns.

A unicorn daycare center needs two supervisors for every 18 unicorns, according to the question.

As a result, mathematically, it is stated as

9/u = 2/18

9n = u

As a result, the relationship between the number of supervisors and unicorns was established.

Hence, there are nine times as many supervisors as unicorns.

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The percentage of all customers prefer port drink and tea is 17.55%. The result is obtained by multiplying the two percentages of the data.

We have a number of customers.

Of all customers, find the percentage that they prefer port drink and tea!

If 55% prefer soda over port drink, then the ones who prefer port drink is

100% - 55% = 45%

Of the customers who prefer port drink, 61% prefer coffee over tea. So, the ones who prefer tea is

100% - 61% = 39%

From that information, we can get the ones who prefer port drink and tea. Let's say pt = port drink and tea.

pt = 39% × 45%

pt = 0.39 × 0.45

pt = 0.1755

pt = 17.55%

Hence, of all customers, the percentage who prefer port drink and tea is 17.55%.

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Using the given triangle shown in the image, we know that the PR, the distance across the river is 198.94ft.

A polygon with three edges and three vertices is called a triangle. It is one of the fundamental geometric shapes.

ABC refers to a triangle with vertices A, B, and C.

In Euclidean geometry, any three points that are not collinear produce a distinct triangle and a distinct plane.

So, the triangles PRE and POC appear to be comparable triangles in the diagram.

Utilizing the similarity theorem:

PR/RE = PR+RO/OC

x/135 = (x+140)/230

By cross-multiply:
230x = 135(x+ 140)

230x = 135x + 18,900

230x - 135x = 18,900

95x = 18900

x =18900/95

x = 198.94

Therefore, using the given triangle shown in the image, we know that the PR, the distance across the river is 198.94ft.

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Correct question:
To indirectly measure the distance across a river, Nolan stands on one side of the river and uses sight lines to a landmark on the opposite bank. Nolan draws the diagram below to show the lengths and angles that he measured. Find PRPR, the distance across the river. Round your answer to the nearest foot.

The whole numbers are closed under subtraction only by distributive property else they are not closed under subtraction.

Whole numbers constitute natural numbers including zero. The subset is given by {0, 1, 2, 3, 4, 5, …}, the set does not include fractions, decimals, and negative integers. The set of whole numbers is represented by ‘W’={0, 1, 2, 3, 4, 5, …...}

To check if the whole numbers are closed under subtraction or not we will check out the four properties namely, the closure property, the commutative property, the associative property, and the distributive property.

Let us consider each property one by one -

1. The closure property-

let's take two whole numbers say 5 and 2.

now 5-2=3, but 2-5= -3 which is not a whole number.

Thus, whole numbers are not closed under subtraction by closure property.

2. The commutative property-

let's take two whole numbers say 5 and 2.

now 5-2=3 and 2-5=-3

hence, we get 2-5 ≠ 5-2.

Thus, whole numbers are not closed under subtraction by commutative property.

3. The associative property-

let's take three whole numbers say 5, 3, and 2.

now (5-3)-2 = 0 and 5-(3-2)= 4

hence, we get (5-3)-2 ≠ 5-(3-2).

Thus, whole numbers are not closed under subtraction by associative property.

4. The distributive property-

let's take three whole numbers say 20, 6, and 5.

now, 20 × ( 6 – 5 ) =  20 × 6 – 20 × 5  = 20

         and 20 × ( 6 – 5 ) = 20 × 1 = 20

Hence, 20=20.

Thus, whole numbers are closed under subtraction only by distributive property.

Hence, we can conclude that whole numbers are closed under subtraction only by distributive property.

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The slope of a line perpendicular to Y =-7 is 7. We may use this as a substitution in the inverse slope formula because the slope of Y = -7 is -1.

To find the slope of a line perpendicular to Y = -7, we need to use the inverse slope formula.

The inverse slope formula is m = -1/m1

where m1 represents the original line's slope.

We may use this as a substitution in the inverse slope formula because the slope of Y = -7 is -1.

m = -1/-1

This simplifies to m = 1.

As a result, a line's slope that is perpendicular to Y = -7 is 7.

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The number which is less than that of -2.67 are -2.8, -2.9, -3.0.

What is a fraction?

If the numerator is bigger, it is referred to as an improper fraction and can also be expressed as a mixed number, which is a whole-number quotient with a proper-fraction remainder.

Any fraction can be expressed in decimal form by dividing it by its denominator. One or more digits may continue to repeat indefinitely or the result may come to a stop at some point.

Which numbers are less than –8/3 = -2.67

So given in the option which is less than -2.67

Numberless -2.7 are

-2.8, -2.9, -3.0.

Hence the number is less than that of -2.67 are -2.8, -2.9, -3.0.

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Complete Question.
Which numbers are less than-8/3 Select all that apply.
A. -2.6 (repeating)
B.-2.76
C.-2 1/4
D. -11/4
E. -2

The simplified form would be 338√x -72√2y.

If a fraction's top and bottom share only one additional common factor, it is said to be in its simplest form. In other words, the top and bottom cannot be divided further and remain full numbers.

The simplest form is also referred to as "lowest words."

the given expression is :

2(4√16x) - 2(4√2y) + 34√81x - 4(4√32y)

⇒ 8(√16x) - 8(√2y) + 34√81x - 16√32y  

⇒8×4√x - 8√2y + 34×9√x - 16√16×2y     [∵ √16 = 4 and √81 = 9]

⇒32√x - 8√2y + 306√x - 16×4√2y

⇒(32√x + 306√x) - 8√2y  - 16×4√2y      

⇒338√x -72√2y

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Answer:

The probability for the green one is 6/10

and for the next one, it is 4/10  

Step-by-step explanation:

The graph of y = f(x) has end behavior as x ⇒ ∞, y ⇒ - ∞ and

as x ⇒ - ∞, y ⇒ ∞.

A polynomial function's final behavior is how its graph behaves as x gets closer to positive or negative infinity.

The graph's final behavior is determined by a polynomial function's degree and leading coefficient.

The given function f(x) has end behavior as x approaches infinity y approaches negative infinity and as x approaches negative infinity y approaches infinity.

As when x value is positive y value is negative and when y value is negative x value is positive.

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By evaluating the function graphically ,  f (4) = -4

An expression, rule, or law in mathematics that establishes the relationship between an independent variable and a dependent variable (the dependent variable).

The x-axis is indicated with the input values. The vertical displacement from the x-axis is the appropriate output value for any input value. For instance, the output is identical to f when x = a. (a).

According to the Given information

f( x ) = y

where x is an input and y is an output

We need to find the value for f(4)

f( 4 ) = y

For x = 4 we have a corresponding value at y axis as -4 in fourth quadrant

f (4) = -4

By evaluating the function graphically ,  f (4) = -4

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By using algebra (5, 4) is not a solution of the inequality.

Boundary does not contain in the given graph this is the error was made when graphed.

What is inequality?

In mathematics, inequalities describe the relationship between two values that are not equal. Equal means to be equal, not. The "not equal symbol (≠)" is typically used to indicate that two values are not equal. But different inequalities are used to compare the values to determine whether they are less than or greater than.

Consider, the given inequality

x + 2y ≤ 12

Here the inequality contain ≤ .

Since, if there is ≤  sign then graph must contain boundary line.

The boundary line is solid line need to use in the graph.

But in the given graph the boundary line is dotted.

Boundary does not contain in the graph.

Hence, this is the error was made when graphed.

Also from graph we can see that the point (5, 4) is not contain in the graph.

Hence, (5, 4) is not a solution of the inequality.

Now prove by using algebra.

Plug x = 5, y = 4 in the given inequality

⇒  5 + 2(4) ≤ 12

         5 + 8 ≤  12

             13 ≤  12

It is not possible that 13 ≤  12.

Hence, (5, 4) is not a solution of the inequality.

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Answer:

3 km

Step-by-step explanation:

Dividing by 3, the kangaroo travels 3 km in 1 min.

The given function is  x² - 7x + 5 and the most general antiderivative of the function  is F(x) = x³/3 - 7x²/2 + 5x + c.

The antiderivative of a function (also called the integration of a function) is the reverse of the differentiation of that function. Given a function f(x), its integration, F(x), can be calculated as follows;

F(x) = ∫f(x)dx

From the question, f(x) = x² - 7x + 5

Therefore,

F(x) = ∫x² - 7x + 5

F(x) = x³/3 - 7x²/2 + 5x + c

Where c is the constant of the integration (antiderivative).

The constant of integration is used for indefinite integrals and allows to express integration of a function in its most general form.

Therefore,  F(x) = x³/3 - 7x²/2 + 5x + c is the most general antiderivative of the function.

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The money that Peter gets paid after 7 hours is 43.75

What are Functions?

A function is an expression, rule, or law in mathematics that describes a connection between one variable (the independent variable) and another variable (the dependent variable).

Solution:

The question given is quite straight forward.

Sinec, we are given with the function y = 6.25x

where x is the hours and y is the pay

To find the pay for 7 hrs

we need to replace x by 7

y = 6.25 * 7

y = 43.75 units

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The rule of reflection for the triangle △JKL to △J'K'L' is x = -4.

What is a triangle?

A polygon with three edges and three vertices is called a triangle. It is one of the fundamental geometric shapes. Triangle ABC is the designation for a triangle with vertices A, B, and C. In Euclidean geometry, any three points that are not collinear produce a distinct triangle and a distinct plane.

Given that the vertices of △JKL are J(1, 0), K(-5, 2), L(4, -4).

The vertices of △J'K'L' are J'(-9, 0), K'(-3, 2), L'(-12, -4).

The formula of midpoint of (x₁, y₁) and (x₂, y₂) is

((x₁+x₂)/2,  (y₁+y₂)/2)

The midpoint of J(1, 0) and J'(-9, 0) is ((1+(-9)/2,(0+0)/2) = (-8/2,0) = (-4,0)

The midpoint of K(-5, 2) and K'(-3, 2) is ((-5+(-3)/2,(2+2)/2) = (-8/2,4/2) = (-4,2)

The midpoint of L(4, -4) and L'(-12, -4) is ((4+(-12)/2,(-4+(-4))/2) = (-8/2,-8/2) = (-4,-4)

Thus the x-coordinate of the midpoint is the same.

Thus the line of reflection is x = -4.

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The graph is given below.

The coordinates in a graph indicate the location of a point with respect to the x-axis and y-axis.

The coordinates in a graph show the relationship between the information plotted on the given x-axis and y-axis.

We have,

y = 1.5x - 2

We can have the following coordinates on the graph.

x = 1, y = 1.5 - 2 = -0.5

(1, -0.5)

x = 2, y = 3 - 2 = 1

(2, 1)

x = 3, y = 4.5 - 2 = 2.5

(3, 2.5)

x = 4, y = 6 - 2 = 4

(4, 4)

And so on.

The graph of y = 1.5x - 2 is given below.

Thus,

Some of the coordinates on the graph are:

(1, -0.5), (2, 1), (3, 25), (4, 4), and so on.

The graph is given below.

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Answer:

two or four

Step-by-step explanation:

Any degree-X polynomial can have up to 8 zeros (some of them can have multiciplity higher than 1).

The polynomial can be written as:

f(x) = (x-a)(x-b)(x-c)(x-d)(x-e)(x-f)(x-g)(x-h)

and we're already told that there are 2 x-intercepts, one with multiplicity 1. Let's assign those x-intercepts a and b=c=d (multiplicity 3).

We're left with (x-e)(x-f)(x-g)(x-h), where e, f, g and h need to be non-real complex numbers (otherwise they'd provide x-intercepts).

The complex zeros (more accurate term than imaginary) must come in pairs - if a number c is a zero of the function, its conjugate is a zero too. That means that we need to have an even number of complex zeros.

We can either have 4 distinct complex zeros, or 2 complex zeros, each with multiplicity of 2.