if you horizontally stretch the quadratic parent function, f(x)=x^2, by a factor of 5, what is the equation of the new function?

Answer:

I think it's =

Step-by-step explanation:

they both equal 32.

Answer:

=

Step-by-step explanation:

6^2 - 2^2

36 - 4

32

4 (6 + 2)

24 + 8

32

Steve walked a total of 1.5 miles from the library to school.

A numerical expression is a mathematical statement written in the form of numbers and unknown variables. We can form numerical expressions from statements.

From the given diagram we can conclude that Steve walked a total of

(1.5 + 2) km = 2.5 km from the library to the school.

Now we know 1 km is equal to 0.6 miles.

∴ 2.5 km = (2.5×0.6) miles = 1.5 miles.

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Answer:

x = 5.59

Step-by-step explanation:

tan 90⁰ = 16/x

x = atan 90⁰/16

= 5.5852 (to 5 significant figures)

= 5.59 (to 3 significant figures)

Answer:

85,000 i think

Step-by-step explanation:

Answer:x=2

Step-by-step explanation:

4(x-2) goes to 4x -8 which then goes to 4x=8 which then divided by 4 equals x=2

The solution of the system of functions can be found graphically by locating the point of intersection of the graphs of the different functions.

A function is a rule that maps the elements of one set A to the elements of another set B such that each element of A maps directly to only one element of B.

The solution of an equation, which is the expression of equality of two or more functions is found by locating the point of intersection of the graphs of both functions, which corresponds to the point at which the same input value to both functions produces the same output

The graph of the exponential function y = 2ˣ + 1, (which increases exponentially through the points (-1, 1.5), (0, 2), (2, 5)) and the function y = (1/2)ˣ which decreases exponentially from (-3, 8), (-1, 2), (3, 0.125), intersect at the point given by the solution of the equation;

[tex]2^x + 1= \left(\dfrac{1}{2} \right)^x[/tex]

2ˣ×2ˣ + 2ˣ = 1

[tex]2^{2\cdot x} + 2^x = 1[/tex]

[tex]2^{2\cdot x} + 2^x - 1 = 0[/tex]

Let a = 2ˣ

a² + a - 1 = 0

Therefore;

[tex]a = \dfrac{-1\pm \sqrt{1-4\times 1\times (-1)} }{2} = \dfrac{-1\pm \sqrt{5} }{2}[/tex]

[tex]2^x= \dfrac{-1\pm \sqrt{5} }{2}[/tex]

[tex]x=\dfrac{ ln\left( \dfrac{-1\pm \sqrt{5} }{2}\right)}{ln(2)}\approx -0.694[/tex]

y = 2ˣ + 1

[tex]y = 2^{-0.694} + 1 \approx 1.618[/tex]

Which gives;

The solution of the equation, [tex]2^x + 1= \left(\dfrac{1}{2} \right)^x[/tex]is (x, y) = (-0.694, 1.618)

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The table considering the numeric values of the function y = 6x - 2 is given as follows:

x | y

-1 | -8

0 | -2

1 | 4

5 | 28

To obtain the numeric value of a function or of an expression, we replace each instance of the variable in the function or in the expression by the value at which we want to find the numeric value.

In this problem, the function is:

y = 6x - 2.

Hence the numeric values are obtained replacing the lone instance of x by it's attributed value.

At x = -1, the numeric value is:

y = 6(-1) - 2 = -6 - 2 = -8.

At x = 0, the numeric value is:

y = 6(0) - 2 = 0 - 2 = -2.

At x = 1, the numeric value is:

y = 6(1) - 2 = 6 - 2 = 4.

At x = 5, the numeric value is:

y = 6(5) - 2 = 30 - 2 = 28.

The problem asks to complete the table with the numeric values as follows:

x | y

-1 | _

0 | _

1 | _

5 | _

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Answer:

3

Step-by-step explanation:

1) Substitute x with 2

b^8

b^2

2) subtract the index

b^8-2

=b^6

3)b^6 ≠ b^8

therefore, 3 is a lie

1/4(10x+8)= -(1/2x+13) + 3(x+5) being examined by three Math Club members for all possible values of x.

Given that,

The formulas 1/4(10x+8) and -(1/2x+13) + 3(x+5) are being examined by three Math Club members for all possible values of x. According to the findings in the table, each student asserts that the expressions are connected.

We have to find which student is right.

Take the

1/4(10x+8) = 10/4x+8/4 = 5/2x+2

-(1/2x+13) + 3(x+5) = -1/2x-13+3x+15 = 5/2x+2

So, 1/4(10x+8)= -(1/2x+13) + 3(x+5)

Therefore, 1/4(10x+8)= -(1/2x+13) + 3(x+5) being examined by three Math Club members for all possible values of x.

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The function given f(x) = 4/x² + 1 concaves upward on (-∞,0)∪(∞,0) and has no point of inflection.

A point of inflection of the graph of a function f(x) is a point where the second derivative f′′(x) is 0. We have to wait a minute to clarify the geometric meaning of this.

A piece of the graph of f is concave upward if the curve ‘bends’ upward. For example, the popular parabola y=x2 is concave upward in its entirety.

A piece of the graph of f is concave downward if the curve ‘bends’ downward. For example, a ‘flipped’ version y=−x² of the popular parabola is concave downward in its entirety.

The relation of points of inflection to intervals where the curve is concave up or down is exactly the same as the relation of critical points to intervals where the function is increasing or decreasing. That is, the points of inflection mark the boundaries of the two different sort of behavior. Further, only one sample value of f′′ need be taken between each pair of consecutive inflection points in order to see whether the curve bends up or down along that interval.

In the function f(x) = 4 / x² + 1 has no points of inflection but it's concave upwards along (-∞, 0) ∪ (0, ∞)

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Answer:

x=12 degrees so c

Step-by-step explanation:

Since they are supplementary angles on transversal, 11x+4x=180.

15x=180 so x=12 degrees.

The required cost function is c(b) = 35b + 475, and the completed table is shown.

A function is a relation where every input is connected to only one possible output from a set of available inputs.

Given that, the cost of the plane ticket is $475 and the cost per checked bag is $35.

The cost of b checked bags is $35b.

Therefore, the total cost is:

c(b) = 35b + 475

The completed table is:

               Number of bags(b)                                  Total cost c(b)

                            0                                                          475

                            1                                                            510

                            2                                                           542

                            3                                                           580

                            4                                                           615

                            6                                                           685

                            8                                                           755

Hence, the required cost function is c(b) = 35b + 475.

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The given system of equations has no solution.

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 general equation of a quadratic equation is -

y = ax² + bx + c

We have the following equations -

y = x² + 6x + 3

y = 3x - 7​

Plot the graph of both equations and the points of intersection would be the solution set. Refer to the graph below. There are no points of intersection, hence these set of equations have no solution.

Therefore, the set of equations of line -

y = x² + 6x + 3

y = 3x - 7​

have no solution

Therefore, the given system of equations has no solution.

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Answer:

D: y = -4/7x + 7

Step-by-step explanation:

Answer:

[tex]y=-\frac{4}{7}x+7[/tex] or option D

Step-by-step explanation:

y=mx+b is the form where m is the slope and b is the y intercept so just fill those in

y=-4/7x+7

Hopes this helps please mark brainliest

Answer:

See below

Step-by-step explanation:

Sqrt(2x + 29)     - 7    = x        <===answering this version

       add 7 to both sides to get

sqrt(2x+29) = x+7            square both sides

2x+29  =   x^2 + 14x + 49      simplify

x^2 +12x + 20 = 0                  factor

(x+10)(x+2) = 0      shows x can be   -10  or -2

     sub in these values in the original equation to find only the answer

            x = -2 works       then the answer x = -10 is extraneous answer

Answer:

(0, -8)

Step-by-step explanation:

The y-intercept of the line is -8, meaning the coordinate point is (0, -8),

The perimeter of the rectangle with area of 108 cm is 48 cm.

The perimeter of a rectangle is the sum of the whole sides of the rectangle. A rectangle is a quadrilateral with opposite side equal to each other.

Therefore,

area of a rectangle = lw

where

Therefore,

l = 3w

108 = 3w(w)

108 = 3w²

w² = 108 / 3

w = √36

w = 6

Hence,

length = 3(6) = 18

Therefore,

perimeter of the rectangle = 2(l + w)

perimeter of the rectangle = 2(18 + 6)

perimeter of the rectangle = 2(24)

perimeter of the rectangle = 48 cm

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The possible real zeros for the function will be:

Positive: 4 or 2

Negative: 1

The Descartes rule of sign is technique which helps us  to find no. of real positive/negative and imaginary zeros a function has.

To apply the rule:

1. Arrange the function in the decreasing value of exponents of variables.

2. The no. of positive real zeros of f(x) will be either equal to the number of sign change or less than the number of sign changes by an even number.

3. For real negative real zeros it will be the same but we will check the sign change of f(-x).

now let's look at the function.

f(x) = 6[tex]x^{7}[/tex] -3[tex]x^{4}[/tex] + 6[tex]x^{3}[/tex] + 9[tex]x^{2}[/tex] - 7x + 4

The sign change here is 4 times so the value of +ve zeros of f(x) will be either 4 or 2.

similarly  let's take f(-x) for negative zeros.

f(x) = 6[tex](-x)^{7}[/tex] -3[tex](-x)^{4}[/tex] + 6[tex](-x)^{3}[/tex] + 9[tex](-x)^{2}[/tex] - 7(-x) + 4

Here sign change is 1 which cannot be decreased by an even no. so it is the only value.

Therefore the positive and negative zeros of the function will be 2 or 4 and 1 respectively.

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the coordinates of A after translation is (-2, 0)

What is a co-ordinate?

In geometry, a coordinate system may be a system that uses one or a lot of numbers, or coordinates, to unambiguously confirm the position of the points or alternative geometric components on a manifold like Euclidean space.

Main body:

point A = (-5,3)

According to question:

translated by the rules (x,y)- (x+3,y-3)

we need to add 3 to x coordinate and subtract 3 from y coordinate.

New coordinate of A are (-5+3 , 3-3)

Hence New coordinate of A are (-2,0)

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Answer:

B.

Step-by-step explanation:

The simplified expression of 8x + 4 - 6y - 3x + y is 5x - 5y + 1

Expression:

An expression is any mathematical statement that consists of numbers, variables and an arithmetic operation between them.

Given,

Here we have the expression 8x + 4 - 6y - 3x + y.

Now, we have to simplify the expression.

To simplify the expression, first we have to write the given expression,

=> 8x + 4 - 6y - 3x + y

Now, we have to combine the like terms, then we get,

=> (8x - 3x) + (-6y + y) + (4 - 3)

Now, we have to perform the appropriate arithmetic operations on it, then we get,

> 5x + (-5y) +1

Therefore, the simplified form of the given expression is 5x - 5y + 1

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Answer:

x is equal to 10 times 5 is the ans

The value of fractions are

The given Fractions are :

1. [tex]\frac{3}{4} +\frac{1}{6} =\frac{3*3+2*1}{12} = \frac{9+2}{12} = \frac{11}{12}[/tex]

2. [tex]\frac{8}{9} +\frac{1}{3} =\frac{8*1+3*1}{9} =\frac{8+3}{9} =\frac{11}{9}[/tex]

3. [tex]8\frac{5}{6} +4\frac{7}{10} = \frac{53}{6} +\frac{47}{10} =\frac{5*53+3*47}{30} =\frac{406}{30}= \frac{203}{15}[/tex]

4. [tex]\frac{3}{4} -\frac{7}{16} =\frac{12-7}{16} =\frac{5}{16}[/tex]

5. [tex]9\frac{11}{24} -7\frac{3}{8} =\frac{227}{22} -\frac{59}{8} =\frac{908 - 649}{88} =\frac{259}{88}[/tex]

6. [tex]2\frac{5}{6} -1\frac{1}{4} =\frac{17}{6} -\frac{5}{4} =\frac17*2-3*5}{12} =\frac{34-15}{12} =\frac{19}{12}[/tex]

7. [tex]\frac{2}{3} +\frac{1}{12} = \frac{4*2+1*1}{12} =\frac{8+1}{12} =\frac{9}{12} =\frac{3}{4}[/tex]

8. [tex]5\frac{4}{5} -2\frac{9}{20} =\frac{29}{5} -\frac{49}{20} =\frac{4*29-49*1}{20} =\frac{116-49}{20} =\frac{67}{20}[/tex]

9. [tex]1\frac{3}{4} +1\frac{3}{10} =\frac{7}{4}+\frac{13}{10} =\frac{35+26}{20} = \frac{61}{20}[/tex]

10. [tex]6 -3 \frac{1}{2} = \frac{6}{1} -\frac{7}{2} =\frac{12-7}{2} =\frac{5}{2}[/tex]

11. [tex]3\frac{1}{2} -1\frac{2}{3} =\frac{7}{2} -\frac{5}{3} =\frac{21-10}{6} =\frac{11}{6}[/tex]

12. [tex]8\frac{3}{4} -3\frac{4}{5} =\frac{35}{4} -\frac{19}{5} =\frac{175-76}{20} =\frac{99}{20}[/tex]

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Answer:

Step-by-step explanation:

-5x-25=78

-5x-25+25=78+25

-5x=103

divide both sides by -5

-5x/-5 = 103/-5

x=-103/5

The number of these patients on average per day that do not have insurance and thus pay cash price for their visits would be = 504 people.

An insurance coverage is defined as the official coverage an individual has over unforseen and inexperienced financial demands.

The average number of patients seen in a day = 22.4.

The number of months patients where seen = 3 months = 90 days

Total number of patients seen would be= 22.4 × 90 = 2,016

The fraction of patients that has insurance= 3/4

Therefore the fraction that doesn't have insurance= 1/4 of 2,016

= 2,016/4

= 504 people.

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Answer: x=18 inches.

Step-by-step explanation:

You can use the Pythagorean Theorem for help.

To find the length of the third side of a right triangle, you have to do

10 square + 15 square=x square.

100+225=x square

325=x square

x=  [tex]\sqrt{325}[/tex].

The nearest inch would be x= 18 inches.

Answer:  The correct answer is 18 inches

Step-by-step explanation:

Using the Pythagorean Theorem:

c= [tex]\sqrt{a^2+b^2}[/tex]

c=[tex]\sqrt{10^2+15^2}[/tex]

c=18.02776

c= 18 inches

The measure of arc AB is 30 degrees , so option B is correct .

What is an arc?

An "arc" in mathematics is a straight line that connects two endpoints. An arc is typically one of a circle's parts. In essence, it is a portion of a circle's circumference.

A curve contains an arc. A circle is the most common example of an arc, yet it can also be a section of other curved shapes like an ellipse.

Main Body:

We know that:

The measure of arc AB is equal to the measure of angle 1 by central angle so,

arc AB = m∠1 = 30° -----> by central angle

we have

m∠1= 30°

therefore,

arc AB = 30°, option B is correct.

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