The following figures are not drawn to scale but AB and CD are straight lines. Find x

Answer:

Option B. x In 5 = In 7

Step-by-step explanation:

we have

[tex]5^{x}+4=11[/tex]

step 1

[tex]5^{x}+4=11[/tex]

step 2

Subtract 4 both sides

[tex]5^{x}+4-4=11-4[/tex]

[tex]5^{x}=7[/tex]

step 3

Apply ln both sides

[tex]ln(5^{x})=ln(7)[/tex]

step 4

[tex]xln(5)=ln(7)[/tex]

step 5

Divide by ln(5) both sides

[tex]x=ln(7)/ln(5)[/tex]

Answer:

  2π ≈ 6.283

Step-by-step explanation:

The average value of the function is the area under it, divided by the base. This function describes a semicircle of radius 8, so its area is ...

  A = 1/2πr² = 1/2π·8² = 32π

The width of the base is the diameter of the semicircle, so is 16. Then the average value is ...

  32π/16 = 2π . . . . . average value of y

Answer:

  3

Step-by-step explanation:

Solving the inequality gives ...

  x/9 < 2/5

  x < 18/5 . . . . multiply by 9

Applying the problem restrictions, we have ...

  0 < x < 3.6 . . . . . x is an integer

Solutions are {1, 2, 3}. There are 3 distinct possible values for x.

Amplitude = 2; period T = π; midline y = 1.

This sinusoidal wave is a even function which means that it has a positive half-cycle and a negative half-circle of equal size, from the image we can see that the midline is y = 1 which is the point where the function is centered.

The amplitude is the measure from the midline to the positive half-cycle, and the midline to the negative half-cycle which is 2.

The period corresponds to a complete cycle of the function or the repetition of the wave seen from a point. In this case, we can see that the wave, starting from π/2 it repeat in 3π/2. So, to calculate the period just substract 3π/2 by π/2

T = 3π/2 - π/2 = (3π - π)/2

T = 2π/2

T = π

Answer:

Option B. [tex]F(x)=x^{2}+1[/tex]

Step-by-step explanation:

we know that

[tex]G(x)=x^{2}[/tex]

This is the equation of a vertical parabola open upward wit vertex at (0,0)

The rule of the translation of G(x) to F(x) is equal to

(x,y) ----> (x,y+1)

therefore

The vertex of the function f(x) is the point (0,1) and the equation is equal to

[tex]F(x)=x^{2}+1[/tex]

Answer:

  3520 ft/min

Step-by-step explanation:

40 mi/h = (40 mi/h)×(5280 ft/mi)×(1 h)/(60 min) = 3520 ft/min

_____

Each conversion factor has a value of 1 (numerator = denominator), so changes the units without changing the speed.

Final answer:

To convert 40 mi/h to feet per minute, multiply by 5280 feet per mile and then divide by 60 minutes per hour, resulting in a speed of 2400 ft/min. So the correct option is a. 2,400 ft/min.

Explanation:

To convert the speed of a car from miles per hour (mi/h) to feet per minute (ft/min), we need to know the following conversions:

1 hour = 60 minutes

Now, we can use these conversions to calculate the speed:

40 mi/h
40 mi/h = 40
(5280 ft/mi)
(60 min/hour) = 2,400 ft/min.

The car is driving at a speed of  2,400 ft/min.

Come on, now. Incomplete question.

Answer:

is it late now

Step-by-step explanation:

For this case we must factor the following expression:

[tex]4x ^ 3 + x ^ 2-8x-2[/tex]

We group the first two and the last two terms:

[tex](4x ^ 3 + x ^ 2) + (- 8x-2)[/tex]

We factor the highest common denominator of each group:

[tex]x ^ 2 (4x + 1) -2 (4x + 1)[/tex]

We take the common factor[tex]4x + 1:[/tex]

[tex](4x + 1) (x ^ 2-2)[/tex]

Answer:

[tex](4x + 1) (x ^ 2-2)[/tex]

Answer:

see explanation

Step-by-step explanation:

1

The equation of a line in slope- intercept form is

y = mx + c ( m is the slope and c the y- intercept )

here m = - [tex]\frac{1}{4}[/tex], hence

y = - [tex]\frac{1}{4}[/tex] x + c ← is the partial equation

To find c substitute (8, - 1) into the partial equation

- 1 = - 2 + c ⇒ c = - 1 + 2 = 1

y = - [tex]\frac{1}{4}[/tex] x + 1 ← in slope- intercept form

2

The equation of a line in point- slope form is

y - b = m(x - a)

where m is the slope and (a, b) a point on the line

here m = - 1 and (a, b) = (- 2, 5), hence

y - 5 = - (x - (- 2)), that is

y - 5 = - (x + 2)

Answer:

  84.5 m

Step-by-step explanation:

It is often helpful to draw a diagram for word problems involving geometric relationships. One for this problem is shown below.

The mnemonic SOH CAH TOA reminds you of the relationship between sides of a right triangle:

  Tan = Opposite/Adjacent

Here we're given angles of depression measured from the horizontal (as shown in the diagram), but it is more convenient to use angles measured from the vertical. In particular, ∠BAO is the complement of 60°, and its tangent is the ratio OB/OA:

  tan(30°) = OB/OA

  OB = (200 m)·tan(30°) ≈ 115.47 m . . . . . . multiply by OA, use OA=200 m

Likewise, we have ...

  OC = (200 m)·tan(45°) = 200 m

Then the width of the river is the difference between these values:

  BC = OC -OB = 200 m - 115.47 m = 84.53 m

Answer:

  3

Step-by-step explanation:

Fill in the known values in the vertex form equation and solve for the coefficient.

  y = a(x -h)^2 +k

  -1 = a(3 -2)^2 -4 = a -4 . . . . fill in the values and simplify

  3 = a . . . . . . . . . . . . . . . . . . .add 4

The coefficient of the squared expression is 3.

Final answer:

The coefficient of the squared term in the parabola's equation, given the vertex (2, -4) and a point (3, -1) on the parabola, is found to be 3 by substituting these values into the vertex form of a parabola's equation.

Explanation:

The student is asking how to determine the coefficient of the squared term in a parabola's equation, given the vertex and a point on the parabola. The standard form of a parabola's equation with vertex (h, k) is  [tex]y = a(x - h)^2 + k,[/tex] where a is the coefficient in question. Knowing the vertex at (2, -4) and a point (3, -1) on the parabola, we can substitute these into the equation to find a.

Substituting the vertex into the equation gives us the form [tex]y = a(x - 2)^2 - 4.[/tex] Then we substitute the point (3, -1):

[tex]-1 = a(3 - 2)^2 - 4[/tex]

[tex]-1 = a(1)^2 - 4[/tex]

-1 + 4 = a · 1

a = 3

Therefore, the coefficient of the squared expression in the parabola's equation is 3.

Answer:

  $227.64

Step-by-step explanation:

The relevant relations are ...

  sales + tax = total

  tax = 7% × sales

Using the second equation, we can write sales in terms of the tax as ...

  sales = tax/0.07

Substituting this into the first equation gives ...

  tax/.07 + tax = total . . . . . substitute for sales

  tax(1/0.07 + 1) = total . . . . factor out tax

  tax ((1 +.07)/.07) = total . . . simplify to a single fraction

Multiply by the inverse of this fraction:

  tax = .07/1.07 × total = (7/107)($3479.64)

  tax = $227.64

For this case we have that by definition, the area of the trapezoid is given by:

[tex]A = \frac {1} {2} (B + b) * h[/tex]

Where:

B: It is the major base

b: It is the minor base

h: It's the height

Substituting the values according to the data of the figure:

[tex]A = \frac {1} {2} (2.1 + 0.9) * 1.3\\A = \frac {1} {2} (3) * 1.3\\A = \frac {1} {2} * 3.9\\A = 1.95[/tex]

Thus, the area of the trapezoid is[tex]1.95 m ^ 2[/tex]

ANswer:

Option B

The expression that represents the height of the rectangular prism is 3x + (10 / (2x - 4)) found by dividing the given volume expression by the base area expression.

To find the expression that represents the height of the rectangular prism, we need to rearrange the formula for the volume of a prism, which is Volume = Base Area x Height. Given the volume of the rectangular prism as 6x^2
- 2x + 8 and the base area as 2x - 4, we divide the volume by the base area to find the height:

Height = Volume / Base Area

Height = (6x^2 - 2x + 8) / (2x - 4)

This simplifies to:

Height = 3x + (10 / (2x - 4))

Therefore, the expression that represents the height is 3x + (10 / (2x - 4)).

Answer:

vertex (-3,5) and another pt (-2,4)

Step-by-step explanation:

It is in vertex form so the vertex is (-3,5)...

Now just plug in a value for x say like -2...

f(-2)=-(-2+3)^2+5

f(-2)=-(1)^2+5

f(-2)=-1+5

f(-2)=4

So another point is (-2,4)

Answer:

y-int = 5

roots: sqrt(5)-3 or -3 - sqrt(5)

TP @ (-3,5)

Step-by-step explanation:

y intercept = 5 (when x = 0)

Roots:

When y = 0

5 - (x + 3)^2 = 0

(x+3)^2 = 5

Square both sides:

x + 3 = Sqrt[5] or x + 3 = - Sqrt[5]

x = Sqrt[5] - 3 or x= - 3 - Sqrt[5]

Turning point (Critical Point):

dy/dx (5-(x+3)^2) = - 2 (x+3)

Solve -2 (x+3) = 0

x = - 3

y = 5

Max point at (-3,5)

Following are the description on the function behavior:

Given:  

[tex]\bold{f(x) = -3x^4 + 7x^2 - 12x + 13}[/tex]

To find:

Function behavior=?

Solution:

We use Power and Polynomial Functions features in the absence of technology. As the function [tex]\bold{f(x) = -3x^4 + 7x^2 -12x + 13}[/tex]

For final behaviour of power functions of such form[tex]\bold{f(x)=ax^n}[/tex] wherein n is a non-negative integer depends on the power and the constant.

 So, the leading term, [tex]\bold{f(x)=-3x^4}[/tex]

When the negative constant and even power are:  

[tex]\to x \to \infty\\\\\to f(x) \to -\infty[/tex]

At  

[tex]x \to -\infty\\\\f(x) \to -\infty[/tex]

 Therefore, the final answer is "Down on the left down on the right "

Learn more:

brainly.com/question/13821048

The end behavior of [tex]\( f(x) = -3x^4 + 7x^2 - 12x + 13 \)[/tex] is described as "Down on the left, down on the right," The correct answer is option a) Down on the left, down on the right.

To determine the end behavior of the polynomial [tex]\( f(x) = -3x^4 + 7x^2 - 12x + 13 \)[/tex] without using technology, we analyze the leading term, which dominates the behavior of the function as x approaches positive or negative infinity.

1. Identify the leading term: The leading term of [tex]\( f(x) \) is \( -3x^4 \)[/tex].

2. Consider the degree and leading coefficient:

  - The degree of the polynomial is 4.

  - The leading coefficient (coefficient of the term with the highest power of [tex]\( x \)) is \( -3 \)[/tex].

3. Determine the end behavior:

  - As [tex]\( x \to +\infty \), \( -3x^4 \)[/tex] approaches [tex]\( -\infty \)[/tex] because [tex]\( x^4 \)[/tex] grows much faster than the negative coefficient affects it. Therefore, [tex]\( f(x) \to -\infty \)[/tex].

  - As [tex]\( x \to -\infty \)[/tex], [tex]\( -3x^4 \)[/tex] also approaches [tex]\( -\infty \)[/tex] for the same reason. Hence, [tex]\( f(x) \to -\infty \)[/tex].

4. Conclusion: Based on the analysis:

  - The polynomial [tex]\( f(x) = -3x^4 + 7x^2 - 12x + 13 \)[/tex] decreases to [tex]\( -\infty \)[/tex] as x goes to both positive and negative infinity.

Therefore, the end behavior of [tex]\( f(x) \)[/tex] is described as "Down on the left, down on the right", which corresponds to option a). This indicates that the graph of [tex]\( f(x) \)[/tex] starts high on the left and continues downward indefinitely in both directions.

Complete question : Without using technology, describe the end behavior of f(x) = −3x4 + 7x2 − 12x + 13.

a Down on the left, down on the right

b Down on the left, up on the right

c Up on the left, down on the right

d Up on the left, up on the right

ANSWER

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

EXPLANATION

The vertex form of a parabola has equation:

[tex]f(x) = a ({x - h)}^{2} + k[/tex]

where V(h,k) is the vertex of the parabola and 'a' is the leading coefficient.

From the question, we have that, the vertex is

[tex](1,-1)[/tex]

and the leading coefficient is

[tex]a= 2[/tex]

We substitute the vertex and the leading coefficient into the vertex form to get:

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

We simplify to get:

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

The graph of this function is shown in the attachment.

The graph that has a vertex of (1,-1) and a leading coefficient of a=2 is a parabola.

The graph that has a vertex of (1,-1) and a leading coefficient of a=2 is a parabola. The leading coefficient, which is the coefficient of the squared term, determines the nature of the parabola.

Since the leading coefficient is positive, the parabola opens upward. The equation of the parabola can be written in the form y = ax^2 + bx + c, where a represents the leading coefficient.

Therefore, the equation of the graph is y = 2x^2 - 4x + 1.

Answer:

r=4ft

h=8ft

Area of cyclender=?

by using formula,

A=πr²h

=22/7×4²×8

=402.28ft²Ans.

ANSWER

301.6 ft²

EXPLANATION

The surface area of a cylinder is calculated using the formula;

[tex]S.A = 2\pi \: r(r + h)[/tex]

From the diagram the height of the cylinder is 8 feet and the radius is 4 feet.

We substitute the values into the formula to obtain,

[tex]S.A = 2\pi \: 4(4+ 8)[/tex]

This simplifies to:

[tex]S.A = 8\pi \: (12)[/tex]

[tex]S.A = 96\pi[/tex]

Or

[tex]S.A = 301.6 {ft}^{2} [/tex]

to the nearest tenth.

Answer:

D

Step-by-step explanation:

3 and 7 are the main factors so you add them and get 10 but since it’s two equilateral trapezoids then you get another 10 being 20 square feet.

Answer:

D) 20 square feet

Step-by-step explanation:

We are given two congruent isosceles trapezoids and placed together formed to make a corner of the desk.

We need to find the area.

We know that the area of a trapezoid = [tex]\frac{h}{2} [base 1+ base 2][/tex]

Where "h" is the height of the trapezoid.

Given: h = 2 ft, base 1 = 7ft and base 2 = 3ft

Now plug in these values in the above formula, we get

Area of a 1 trapezoid = [tex]\frac{2}{2} [7 + 3][/tex]

= 10 square feet

The two trapezoids are congruent.

So the area of the given figure = 2(10) = 20 square feet.

Answer:

5

Step-by-step explanation:

Blue: when x = - 3, y = 5

Green: when x = -3, y = 0

The difference between the two graphs at X = -3 : 5 - 0 = 5

Answer

5

Answer:

12

Step-by-step explanation:

The only possible answer if 12 because all of the other choices come to the conclusion that 8h ≤ 64

if h=12 then 8h= 8 * 12 = 96 > 64

The value of h is 12.

Multiply the length, width, and height of a rectangular prism to determine its volume. Cubic measurements are used to express volume.

Given,

The only possible answer is 12 because all of the other choices come to the conclusion that 8h ≤ 64

if h=12 then 8h= [tex]8 * 12[/tex] = 96 > 64

To know more about rectangular prism  refer to :

https://brainly.com/question/477459

#SPJ2

Answer:

(1,2) and (2,-1)

Step-by-step explanation:

we have

[tex]y&lt; 5-2x[/tex] ----> inequality A

The solution of the inequality A is the shaded area below the dashed line [tex]y=5-2x[/tex]

[tex]x+5y&gt;-7[/tex] ---->inequality B

The solution of the inequality B is the shaded area above the dashed line [tex]x+5y=-7[/tex]

The solution of the system of inequalities is the triangular shaded area between the two dashed lines

If a ordered pair is a solution of the system of inequalities, then the ordered pair must lie on the shaded area

Two points in the solution are(1,2) and (2,-1)see the attached figure

Answer:

3%

Step-by-step explanation:

We are given the data of number of cars observed waiting in line at the beginning of 2 minute intervals between 3 and 5 p.m. on Friday.

We are to find the probability (in percent) that there is no one in line.

Sum of frequencies = 2 + 9 + 16 + 12 + 8 + 6 + 4 + 2 + 1 = 60

Frequency of no car in line = 2

P (no car in line) = 2 / 60 × 100 = 3.3% ≈ 3%

Answer:

2x^2-x+1

Step-by-step explanation:

Answer:

2x² - x + 1

Step-by-step explanation:

[tex]\frac{(2x^{2}-x+1)(x+1)}{(x+1)} = 2x^{2}-x+1[/tex]

Very Likely

think of it this way

you have a 7/8 chance of getting electrocuted by sticking your hand in the toaster

you have a 1/8 chance of this event not occurring when you stick said hand in the toaster

so its VERY LIKELY that you will be electrocuted if you stick your hand in a toaster

hope that helps!

Step-by-step explanation:

49-30=19, then add 19+16, then you get the answer of 35!

Hope this helps!

Answer:

d

Step-by-step explanation:

what does ' f ' represent?

The exponential function for the total number of ill students is [tex]f(x) = 10 * (1.20)^x,[/tex] where x is the number of hours after the outbreak. To reach at least 100 ill students, it takes about 13 hours. So correct answer is option B.

To represent the total number of ill students f(x) as an exponential function where x is the number of hours after the outbreak, we use the initial value of 10 people sick and an hourly increase rate of 20%. The function is: [tex]f(x) = 10 * (1 + 0.20)^x[/tex].

To find how long it takes for at least 100 people to be ill, we set f(x) \\>= 100 and solve for x:

[tex]10 * (1.20)^x \ > = 100\\(1.20)^x \ > = 10x\\\\log(1.20) \ > = \log(10)\\x > = \log(10) \\ \\log(1.20)\\x = 12.2[/tex]

Therefore, it takes about 13 hours for at least 100 people to be ill. So the answer is b. About 13 hours.

See the attached picture for the answer.

Answer:

(10, −13); (15, −20)

Step-by-step explanation:

Answer:

Vertical A @ x=3 and x=1

Horizontal A nowhere since degree on top is higher than degree on bottom

Slant A @ y=x-1  

Step-by-step explanation:

I'm going to look for vertical first:

I'm going to factor the bottom first:  (x-3)(x-1)

So we have possible vertical asymptotes at x=3 and at x=1

To check I'm going to see if (x-3) is a factor of the top by plugging in 3 and seeing if I receive 0 (If I receive 0 then x=3 gives me a hole)

3^3-5(3)^2+4(3)-25=-31 so it isn't a factor of the top so you have a vertical asymptote at x=3

Let's check x=1

1^3-5(1)^2+4(1)-25=-25 so we have a vertical asymptote at x=1 also

There is no horizontal asymptote because degree of top is bigger than degree of bottom

There is a slant asympote because the degree of top is one more than degree of bottom (We can find this by doing long division)

                       x   -1

                --------------------------------------------------

x^2-4x+3 |      x^3-5x^2+4x-25

                  - ( x^3-4x^2+3x)

                   --------------------------------

                            -x^2 +x  -25

                       -   (-x^2+4x-3)

                          ---------------------

                                   -3x-22

So the slant asymptote is to x-1

Answer: D

Step-by-step explanation:

EDGE 2021