Given f(x) and g(x) = f(x) + k, use the graph to determine the value of k.

Answer:

  1 ≤ x < 7/4

Step-by-step explanation:

The function f(x) is defined as increasing on the domain (-8, 4), so the ordering of the arguments is not changed by the function. We can solve the inequality as though f(x) = x, which is increasing everywhere.

  f(4x -3) ≥ f(2 -x²)

  4x -3 ≥ 2 -x² . . . . . . using our assumed definition of f(x)

  x² +4x -5 ≥ 0 . . . . . subtract 2-x²

  (x -1)(x +4) ≥ 0 . . . . factored form; zeros at -4, +1

The values of x that make this true are ones that make the factors have the same signs: x ≤ -4 or x ≥ 1.

The domain of f(x) is -8 < x < 4, so we require the arguments of f be restricted to those values

Left side

  -8 < 4x -3 < 4

  -5 < 4x < 7

  -5/4 < x < 7/4

Right side

  -8 < 2 -x² < 4 . . . . . right side is always true

  x² < 10 . . . . . . . . . . . add x² +8

  |x| < √10 . . . . . . . . . . less restrictive than the the left-side restriction

With the given domain restrictions on f(x), the inequality will be true on the interval ...

  1 ≤ x < 7/4

__

Additional comment

The attached graph shows the left-side function argument (dashed blue) and the right-side function argument (dashed green) with the given domain restrictions. The red curve is the difference in function values for the function defined as above. It is only non-negative between 1 and 1.75 as we found above.

This general behavior is applicable for any f(x) that can be described as in the problem statement. For example, f(x) = √(x+8) also gives an increasing curve for the difference f(4x-3)-f(2-x²) on the interval (-5/4, 7/4) with an x-intercept of +1.

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Answer:

a set of numbers that are used to find the hypotenuse

Step-by-step explanation:

brainliest

The integer solutions to the Pythagorean theorem, are called Pythagoras triples.

The integer solutions to the Pythagorean theorem, [tex]a^{2} +b^{2} =c^{2}[/tex] are called Pythagorean triples which contains three positive integers a, b and c.

For example:

(3, 4, 5)

By evaluating we get

[tex]3^{2} +4^{2} =5^{2}[/tex]

⇒ 9 + 16 = 25

Hence, 3, 4 and 5 are Pythagorean triples.

Learn more about Pythagorean Triples here:

https://brainly.com/question/15190643

#SPJ2

Answer:

1/9

Step-by-step explanation:

Given:

2 red marbles

4 white marbles

3 purple marbles

He will randomly select 2 marbles from the bag one at a time without

replacement.

To Find:

What is the probability that he will choose a red marble first and then a white marble?

Solution:

Since red marbles =2

White = 4

Total = 2+4+3 = 9

Select first time = 2/9

Select second time = 4/8

And then = Multiply

2/9 * 4/8 = 8/72

8/72 Simplify

1/9

[RevyBreeze]

Answer:

1. three hundred ninety six thousand twenty four

2. five million two hundred thousand ninety

3. four million six hundred six thousand two hundred twenty

First graph

#A

Use quadratic formula

[tex]\\ \rm\rightarrowtail x=\dfrac{-b\pm\sqrt{b^2-4ac}}{2a}[/tex]

[tex]\\ \rm\rightarrowtail x=\dfrac{-22\pm\sqrt{484+192}}{-32}[/tex]

[tex]\\ \rm\rightarrowtail x=\dfrac{-22\pm\sqrt{676}}{-32}]/tex]

[tex]\\ \rm\rightarrowtail x=\dfrac{-22\pm 26}{-32}[/tex]

[tex]\\ \rm\rightarrowtail x=\dfrac{-1}{8}\:or\:\dfrac{3}{2}[/tex]

[tex]\\ \rm\rightarrowtail x=-0.125\:or\:1.5[/tex]

#B

Vertex will be maximum

Coordinates are

#C

[tex]\sf f(x) = -16x^2 + 22x + 3[/tex]

Part A

To find x-intercepts, the f(x) will be 0

[tex]\sf \hookrightarrow -16x^2 + 22x + 3=0[/tex]

[tex]\sf \hookrightarrow -16x^2 + 24x -2x+ 3=0[/tex]

[tex]\sf \hookrightarrow -8x(2x-3)-1(2x- 3)=0[/tex]

[tex]\sf \hookrightarrow (-8x-1)(2x+ 3)=0[/tex]

[tex]\sf \hookrightarrow -8x-1=0 , \ 2x+ 3=0[/tex]

[tex]\sf \hookrightarrow x=-0.125 , \ x=1.5[/tex]

find y-intercept:

to find y-intercept, x will be 0

[tex]\sf f(x) = -16(0)^2 + 22(0) + 3[/tex]

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

Part B

To find vertex use the formula: x = -b/2(a)

[tex]\sf \rightarrow x = \dfrac{-22}{2(-16)}[/tex]

[tex]\sf \rightarrow x = 0.6875[/tex]

find y coordinates:

[tex]\sf f(x) = -16(0.6875)^2 + 22(0.6875) + 3[/tex]

[tex]\sf f(x) =10.5625[/tex]

coordinates of vertex: (0.6875, 10.5625)

As its positive and greater than 0, the vertex will be Maximum.

part C

To draw the graph, simplify point the vertex on the graph. Then point both the x-intercepts. Also the y-intercept and draw the curve with free hand.

Graph attached:

[tex]\green{ \underline { \boxed{ \sf{Average = \frac{Sum \:of \: observation}{Number \:of \: observation}}}}}[/tex]

[tex]\longrightarrow[/tex]Here, no of observation are 5

Now,

[tex]\begin{gathered}\\\implies\quad \sf Average = \frac{1+9+11+13+26}{5} \\\end{gathered} [/tex]

[tex]\begin{gathered}\\\implies\quad \sf Average = \frac{60}{5} \\\end{gathered} [/tex]

[tex]\begin{gathered}\\\implies\quad \sf Average = 12 \\\end{gathered} [/tex]

[tex]\longrightarrow[/tex]The Average of given set of numbers is 12 .

[tex]\therefore\: [/tex] Option A) is correct ✔️

The net square pyramid and its given dimension as shown has a total surface area of 1040 ft².

Surface area of a square pyramid = A + 1 / 2 ps

where

Therefore,

A = l²

where

A = 20² = 400 ft²

p = 4l = 4 × 20 = 80 ft

s = 16 ft

Therefore,

Surface area = 400 + 1 / 2 × 80 × 16

Surface area = 400 + 1280 / 2

Surface area = 400 + 640

Surface area = 1040 ft²

learn more on surface area here: https://brainly.com/question/2835293

Answer:

Acc to ques

7x-3x = 60

x = 15

so they made total of 10x = 150

Answer:

[1,∞)

Step-by-step explanation:

Brackets indicate equal to while parentheses indicate not equal to this bound.

Answer:

the width is 9in

Step-by-step explanation:

perimeter of triangle =3×16 = 48

let w= width of rectangle

perimeter of triangle = perimeter of rectangle

48= 2(15 +w)

24= 15 + w

w= 9

Answer:

The solution is 9.01.

Step-by-step explanation:

To prove that 9.1 isn't the solution we have to plug 9.1 into the equation. By replacing n with 9.1 we get 2.7 which isn't equal to 2.61.

To find the solution we must add 6.4 to both sides of the equation.

Answer:

20

Step-by-step explanation:

from the numbers i was seeing my answer is 20 i am so sorry if it not right.

Answer:

It will take 5 seconds

By rewriting the weights in decimal form and applying them to the correspondent percentages, we will see that the final grade is 92.8%.

The final grade will be given by:

G = a₁*x₁ + a₂*x₂ + ...

Where the values "a" are the weights, and the values "x" are the averages of Jeorge.

We know that the weights are:

Then we can write the weights in decimal form:

a₁ = 0.3

a₂ = 0.1

a₃ = 0.4

a₄ = 0.2

And the scores are:

So the final math grade will be:

G = 0.3*92 + 0.1*98 + 0.4*91 + 0.2*95 = 92.8%

If you want to learn more about percentages, you can read:

https://brainly.com/question/843074

Answer:

the answer is 92.8%

Step-by-step explanation:

Answer:

  (a)  6 months

Step-by-step explanation:

The formula for figuring the monthly payment on an amortized loan can be used for finding the length of time it takes to pay off the loan.

That formula is ...

  A = P(r/12)/(1 -(1 +r/12)^(-12t))

where A is the monthly payment, P is the principal value of the loan, r is the annual interest rate, and t is the number of years.

__

Using the given information, we can solve for t:

  300 = 1568(0.113/12)/(1 -(1 +0.113/12)^(-12t))

  1 -(1 +0.113/12)^(-12t) = 1568(0.113)/(12(300))

  (1 +0.113/12)^(-12t) = 1 -(1568·0.113)/(12·300) ≈ 0.950782

Taking logs, we get ...

  -12t·log(1 +0.113/12) = log(0.950782)

  t = log(0.950782)/(-12·log(1 +0.113/12)) ≈ 0.448739 . . . . years

This fraction of a year is ...

  (12 months/year)(0.448739 years) = 5.38 months

It will take you 6 months to pay off the loan.

Answer:

Number 1 is b

I found the answer on a website

keeping in mind that perpendicular lines have negative reciprocal slopes, let's check for the slope of the equation above

[tex]y = \stackrel{\stackrel{m}{\downarrow }}{\cfrac{5}{6}}x+\cfrac{7}{6}\qquad \impliedby \begin{array}{|c|ll} \cline{1-1} slope-intercept~form\\ \cline{1-1} \\ y=\underset{y-intercept}{\stackrel{slope\qquad }{\stackrel{\downarrow }{m}x+\underset{\uparrow }{b}}} \\\\ \cline{1-1} \end{array}[/tex]

so we can say that

[tex]\stackrel{~\hspace{5em}\textit{perpendicular lines have \underline{negative reciprocal} slopes}~\hspace{5em}} {\stackrel{slope}{\cfrac{5}{6}} ~\hfill \stackrel{reciprocal}{\cfrac{6}{5}} ~\hfill \stackrel{negative~reciprocal}{-\cfrac{6}{5}}}[/tex]

so we're really looking for the equation of a line with a slope of -6/5 and that passes through (-8 , 9)

[tex](\stackrel{x_1}{-8}~,~\stackrel{y_1}{9})\qquad\qquad \stackrel{slope}{m}\implies -\cfrac{6}{5} \\\\\\ \begin{array}{|c|ll} \cline{1-1} \textit{point-slope form}\\ \cline{1-1} \\ y-y_1=m(x-x_1) \\\\ \cline{1-1} \end{array}\implies y-\stackrel{y_1}{9}=\stackrel{m}{-\cfrac{6}{5}}(x-\stackrel{x_1}{(-8)})\implies y-9=-\cfrac{6}{5}(x+8) \\\\\\ y-9=-\cfrac{6}{5}x-\cfrac{48}{5}\implies y=-\cfrac{6}{5}x-\cfrac{48}{5}+9\implies y=-\cfrac{6}{5}x-\cfrac{3}{5}[/tex]

The quotient of 36 and -4 is -9.

36/-4 = -9

==========================================================

Let's simplify the expression:-

[tex]\bigstar{\boxed{\frac{3}{1} *\frac{1}{2}}[/tex]

Multiply 3 times 1 and 1 times 2:-

[tex]\bigstar{\boxed{\pmb{\frac{3}{2} }}[/tex]

======================================================

Hope everything is clear; if you need any clarification/explanation, kindly let me know, and I'll comment and/or edit my answer :)

Answer:

$149 - skateboard price

$52 - carly's money

$20 × 5 cars = $100

$100 + $52 = $152

$152 - $149 = $3 left

Answer:

it’s C. 2.5

Step-by-step explanation:

Answer:

False

Step-by-step explanation:

The sides are not equal

[tex]|-16-x|=0\\\\\implies -16-x = 0\\\\\implies x = -16[/tex]

Answer:

I'm not to sure of this answer

Answer:

45

Step-by-step explanation:

Put in '5' where 'x' is

2 (5)^2 - 5 = 45

What is the equation: [tex]2x^2-5[/tex]

What do we want to find: f(5)

To find f(5), we must plug the value '5'

     ⇒ into the 'x' position

        ⇒ f(x)

So: [tex]f(5) = 2(5^2)-5 = 2 * 25 - 5 = 50 -5 = 45[/tex]

Thus f(5) = 45

Hope that helps!

Answer:

T

Step-by-step explanation:

The regression line is flat when there is no ability to predict whatsoever. The regression line is sloped at an angle when there is a relationship. The extent to which the regression line is sloped, however, represents the degree to which we are able to predict the y scores with the x scores

Answer:

x=7

Step-by-step explanation:

In a 45 45 90 triangle the two legs are equal so you set 33=5x-2 and then solve the equation.

Answer:

  a.  $150

  b.  $158.25

Step-by-step explanation:

The amount of tax is the product of the tax rate and the price being taxed. This relation can let us solve for the price.

  tax = tax rate × price

  price = tax/(tax rate) = $8.25/0.055 = $150.00

The purchase price of the table saw is $150.00.

__

The total price is the sum of the purchase price and the tax.

  total price = price + tax

  total price = $150.00 +8.25 = $158.25

The total price of the table saw is $158.25.