BRAINLEST Use the function f(x) = 2x^2 − 5x + 3 to answer the questions. Part A: Completely factor f(x). Part B: What are the x-intercepts of the graph of f(x)? Show your work.

Answer:

$947

Step-by-step explanation:

12,000(1 + .05/1)^(15*1) = $24,947.14

12,000 + (12,000*.07*15) = $24,600

difference is $947

Answer:

86.7

Step-by-step explanation:

Answer:

86.7%

Step-by-step explanation:

Correct on Edge2020

Answer:

4 miles

Step-by-step explanation:

Solution:-

- This question pertains to special right angle triangles.

- This requires the use of special angles like ( 30°, 45°, 60° ) for all three trigonometric ratios that give us exact answers in the form of radicals.

- We will make a table of all three trigonometric ratios for the 3 special angles given above as follows:

                          30°           45°            60°

     sin               1/2           1/√2        √3 / 2

      cos           √3 / 2        1/√2           1/2

      tan             1 /√3          1              √3

- Now take a look at the figure and determine the appropriate trigonometric ratio that could be used to determine the distance ( q ). We are given an opposite angle ( θ = 45° ) and hypotenuse of the right angle triangle ( H = 4√2 mi )

- We see that the sine ratio is the most appropriate which can be written as:

                       sin ( θ ) = q / H = q / 4√2

                       sin ( 45° ) = q / 4√2  

                       q = 4√2  *  sin ( 45° )   ... Use above table for sin ( 45° )

                       q = 4√2  *  [ 1 / √2 ]

                       q = 4 miles  ... Answer

Answer:

E: all real numbers

Step-by-step explanation:

Answer:

16 and 24 ft

Step-by-step explanation:

If we call the length of one piece x, the length of the other piece is x + 8, therefore, we can write the following equation:

x + x + 8 = 40

2x + 8 = 40

2x = 32

x = 16 so x + 8 = 16 + 8 = 24.

Answer:

24 and 16

Step-by-step explanation:

x + x+8=40

2x+8=40

2x=32

x=16

16 and 24

Answer:

Step-by-step explanation:

The average number of runs scored by a Little League team in a game is 5.7. If he chooses five games at random in which his team scored 5 , 9, 4, 11, and 8 runs, their average score of the five games is expressed as shown;

Average score of 5 games = (5+9+4+11+8)/5

Average score of 5 games  = 37/5

Average score of 5 games  = 7.4

Comparing the average score in 5 games to the the average number of runs scored nationally, it can be seen that their difference is 7.4 - 5.7 which is 1.7. Since the difference is quite significant, then it is most likely that his team's scores is different from the national distribution.  

Hey there! I'm happy to help!

To find the volume of a cylinder, you multiply the base by the height and then divide by three. The volume of a cone is the same as the volume of a cylinder with the same dimensions divided by three.

So, since a cone's volume is 1/3 of that of a cylinder, we just divide 72 by 3!

72/3=24

Therefore, the volume of the cone is 24 feet cubed.

Have a wonderful day! :D

Answer: its 24.

Step-by-step explanation:

Answer:

[tex]f(-1) = 8[/tex]

[tex]f^{-1}(x) = \frac{5}{3} - \frac{x}{3}[/tex]

Step-by-step explanation:

Given

[tex]f(x) = 5 - 3x[/tex]

Required

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

Solving for f(-1)

Substitute -1 for x in [tex]f(x) = 5 - 3x[/tex]

[tex]f(-1) = 5 - 3(-1)[/tex]

[tex]f(-1) = 5 + 3[/tex]

[tex]f(-1) = 8[/tex]

Solving for [tex]f^{-1}(x)[/tex]

Let y = f(x)

[tex]y = 5 - 3x[/tex]

Interchange the position of x and y

[tex]x = 5 - 3y[/tex]

Make y the subject of formula (add 3y to both sides)

[tex]3y + x = 5 - 3y + 3y[/tex]

[tex]3y + x = 5[/tex]

Subtract x from both sides

[tex]3y + x - x = 5 - x[/tex]

[tex]3y = 5 - x[/tex]

Divide through by 3

[tex]\frac{3y}{3} = \frac{5}{3} - \frac{x}{3}[/tex]

[tex]y = \frac{5}{3} - \frac{x}{3}[/tex]

Replace y with [tex]f^{-1}(x)[/tex]

[tex]f^{-1}(x) = \frac{5}{3} - \frac{x}{3}[/tex]

Answer:1.0111111111

Step-by-step explanation:

18.2 - 18 = .2-18 =1.0111111

Answer:

28.142m

Step-by-step explanation:

area of rectangle=width x lenght

so; (rotating the formula with what is given)

area of rectangle/width=lenght

197/7=lenght

28.142m =lenght

Answer:

Length is 18 m and width is 11 m

Step-by-step explanation:

So based on the information given length is seven cm more than your width, and since we don’t know the values of these, we can plot this information into a formula that looks like this: (x+7)(x)=198, which is basically how you take the area of the plot of land.

If you multiply your values, you will get a quadratic equation that looks like this x²+7x-198. If you follow the quadratic formula to solve this equation, the positive result you will get for x is 11, this is your width. And since length exceeds by 7, you just add 7 to 11 to find the length, which ends up being 18.

to verify, you can simply multiply these two values

Answer:

a) CD = 41 m

b) 77.32°

c) 1380 square metres

Step-by-step explanation:

We can divide the trapezium as shown in the diagram below.

a) To find CD, we use Pythagoras Rule:

[tex]CD^2 = 9^2 + 40^2[/tex]

[tex]CD^2 = 81 + 1600\\\\CD^2 = 1681\\\\=> CD = 41 m[/tex]

b) To find <BCD, we use trigonometric function SOHCAHTOA:

sin(BCD) = opp / hyp

sin(BCD) = 40 / 41

sin(BCD) = 0.9756

=> <BCD = 77.32°

c) The area of a trapezium is given as:

A = 1/2 (a + b) * h

where h = height = 40 m

a = top length = 30 m

b = bottom length = 39 m

A = 1/2 * (30 + 39) * 40

A = 1/2 * 69 * 40

A = 1380 square metres

Answer:

a

Step-by-step explanation:

If the lines DE and BC were parallel then

Δ ADE and Δ ABC would be similar and the ratios of corresponding sides would be equal, that is

[tex]\frac{AD}{AB}[/tex] = [tex]\frac{AE}{AC}[/tex] , substituting values

[tex]\frac{4}{10}[/tex] = [tex]\frac{6}{14}[/tex]

but

[tex]\frac{4}{10}[/tex] ≠ [tex]\frac{6}{14}[/tex]

That is 4 : 10 ≠ 6 : 14 → a

Answer:

The correct answer is option:

D) ΔABC and ΔA″B″C″ are congruent triangles.

Step-by-step explanation:

Given

To find: The true statement among the given options.

Solution:

Let the triangle be situated in 1st quadrant.

It is rotated about the origin by [tex]270^\circ[/tex].

Now, it moves towards quadrant 2 if it is rotated clockwise. It is termed as

[tex]\triangle A'B'C'[/tex].

It is given that now it is translated 10 units upwards. i.e. 10 units added to x coordinate of each vertex to form [tex]\triangle A''B''C''[/tex].

Now, we can see that there is no change in the dimensions of the triangle. We are just changing the location of the triangle.

So, all its angles will be equal to each other and all the sides will be equal to each other.

i.e.

[tex]\angle A = \angle A''\\\angle B = \angle B''\\\angle C = \angle C''\\Side\ AB = Side\ A''B''\\Side\ BC = Side\ B''C''\\Side\ AC = Side\ A''C''[/tex]

Hence, the correct option is:

D)ΔABC and ΔA″B″C″ are congruent triangles.

Answer:A-B

Step-by-step explanation:

Answer:

[tex]\frac{20}{25}[/tex]

Step-by-step explanation:

See Attachment for Complete Question

Given

[tex]Ratio = \frac{12}{15}[/tex]

Required

Determine its equivalent proportion

[tex]Ratio = \frac{12}{15}[/tex]

Factorize the given expression

[tex]Ratio = \frac{3 * 4}{3 * 5}[/tex]

Divide the numerator and denominator by 3

[tex]Ratio = \frac{4}{5}[/tex]

We apply the same steps to the given options as follows:

1.

[tex]Ratio = \frac{21}{28}[/tex]

Factorize

[tex]Ratio = \frac{7 * 3}{7 * 4}[/tex]

Divide the numerator and denominator by 7

[tex]Ratio = \frac{3}{4}[/tex]

This is not an equivalent proportion of [tex]\frac{12}{15}[/tex]

2.

[tex]Ratio = \frac{20}{25}[/tex]

Factorize

[tex]Ratio = \frac{5 * 4}{5 * 5}[/tex]

Divide the numerator and denominator by 5

[tex]Ratio = \frac{4}{5}[/tex]

This is equivalent to [tex]\frac{12}{15}[/tex] because they both simplify to [tex]\frac{4}{5}[/tex]

There's no need to check the last option;

Hence, the option that answers the question is [tex]\frac{20}{25}[/tex]

Answer: The answer is D.

Step-by-step explanation: Ok, we start by simplifing the equation to 3√x^2 - 3√x=2. Now, by plugging the possible options in, we can find the answer. You find that -1 is a possible answer for x, so that eliminates E. Since there is no cube root for 2, we elimate A and B. By plugging in C and D, you find that C=6, not C=2. So D must be the answer.

Answer:

The rate at which the biomass is increasing when t = 5 is 180.36 g/week

Step-by-step explanation:

Given that :

t = 5 weeks

Population N(t) = 824 guppies

Growth Rate [tex]\dfrac{dN(t)}{dt}= 50 \ guppies /week[/tex]

average mass M(t) = 1.3 g

increase rate of biomass  [tex]\dfrac{dM (t)}{t}[/tex]= 0.14 g/week

Therefore; the rate at which the biomass is increasing when t = 5 is:

[tex]\dfrac{dB(t)}{dt}= M(t) * \dfrac{dN(t)}{dt}+ N(t)* \dfrac{dM (t)}{t}[/tex]

[tex]\dfrac{dB(t)}{dt}=1.3 * 50+ 824* 0.14[/tex]

[tex]\dfrac{dB(t)}{dt}=65+115.36[/tex]

[tex]\mathbf{\dfrac{dB(t)}{dt}=180.36 \ g/week}[/tex]

The rate at which the biomass is increasing when t = 5 is 180.36 g/week

The rate at which the biomass is increasing when t = 5 is 180.36 g/week

Since time = 5 weeks, Population N(t) = 824 guppies, and growth rate = 50 guppies / week, average mass = 1.3g, and the increase rate of biomass is 0.14g/week

So,

[tex]= 1.3\times 50 + 824 \times 0.14[/tex]

= 65 + 115.36

= 180.35 g/weel

Learn more about mass here: https://brainly.com/question/3943429

Answer:

Step-by-step explanation:

[tex]6\: km\: in \:10\: minutes\\First\:lets\:convert\:10\:min\:to\:seconds\\\\1\:minute \:\:\:\:=60\:seconds\\\\10\:minutes = x \:seconds\\\\x = 60\times 10\\x = 600seconds\\\\6km\: = 600\:seconds\\x\:km = 1 \:second\\\\Cross\:Multiply\\600x =6\\\frac{600x}{600} =\frac{6}{600} \\\\x = 1/100\\\\ =0.01km[/tex]

Answer:

[tex]Probability = 51\%[/tex]

Step-by-step explanation:

Given

Radius of inner circle = 5ft

Radius of outer circle = 7ft

Required

Determine the probability that the thumbtack will be placed on the inner circle

We start by calculating the area of both circles;

Inner Circle

[tex]Area = \pi r^2[/tex]

[tex]Area = 3.14 * 5^2[/tex]

[tex]Area = 3.14 * 25[/tex]

[tex]Area = 78.5[/tex]

Outer Circle

[tex]Area = \pi R^2[/tex]

[tex]Area = 3.14 * 7^2[/tex]

[tex]Area = 3.14 * 49[/tex]

[tex]Area = 153.86[/tex]

At this point, the probability can be calculated;

The probability = Area of Inner Circle / Area of Outer Circle

[tex]Probability = \frac{78.5}{153.86}[/tex]

[tex]Probability = 0.51020408163[/tex]

Convert to percentage

[tex]Probability = 0.51020408163 * 100\%[/tex]

[tex]Probability = 51.020408163\%[/tex]

Approximate

[tex]Probability = 51\%[/tex]

Answer:

Step-by-step explanation:

Volume of cartoon = 5 cm × 8 cm × 15 cm

= 600 cm³

Volume of milk = 5 cm × 8 cm × 12 cm

= 480 cm³

Space = 600 cm³ - 480 cm³ = 120 cm³

Let depth be ' h '

15 × 5 × h = 480

Multiply the numbers

75h = 480

Divide both sides of the equation by 75

75 h / 75 = 480 / 75

Calculate

h = 6.4 cm

therefore, The depth of the milk is 6.4 cm

Hope this helps...

Best regards!!

The definition of sin is the opposite/hypotnuse and since the hypotnuse has to be greater or equal to the other sides, the maximum possible value of sine is 1.

Answer:

the number is -6  (assuming "3 lots of" means 3 times)

Step-by-step explanation:

Let the number be x

1 less than a doubled number

2x-1

5 more than 3 lots of (times???) the number

3x+5

Solve for x

2x-1 = 3x + 5

-x = 5+1

x = -6

Answer:

N

Step-by-step explanation:

Since this hexagon has six sides, and to end up back at E again we’d need to rotate 360°, this means for every side we cross it’s a 60° turn.

Therefore, [tex]60 \cdot 2 = 120[/tex]° would be two sides.

Since we are moving counter-clockwise, the image for E would be to the left of it.

Two sides/points to the left of E is N, so the image of E for a 120° counterclockwise rotation around the center of this shape would be N.

Hope this helped!

Answer:

11.25

Step-by-step explanation:

12*12/12-3/4

PEMDAS says multiply and divide first

from left to right

144/12 - 3/4

12 -3/4

12 - .75

Then add and subtract

11.25

Answer:

[tex]\frac{45}{4}[/tex]

Step-by-step explanation:

Apply PEDMAS

P - parenthesis

E - exponents

D - division

M - multiplication

A - addition and S - subtraction  

Division is first.

12 × [tex]\frac{12}{12}[/tex] - [tex]\frac{3}{4}[/tex]

12 × 1 - [tex]\frac{3}{4}[/tex]

Followed by multiplication.

12 - [tex]\frac{3}{4}[/tex]

Subtract the numbers next.

[tex]\frac{12}{1} -\frac{3}{4}[/tex]

Make the denominators same by LCM.

[tex]\frac{48}{4} -\frac{3}{4}[/tex]

[tex]\frac{45}{4}[/tex]

Answer:

She did not represent the two original factors correctly on the headers.

Step-by-step explanation:

Adi Algebra titles method is based on the field of values. In the given question the representation of of the product is not correct. The two negative titles must be in the top header so the correct sign in incorporated with the variables.

Answer:

A. She used the algebra tiles correctly.

Step-by-step explanation:

She represents each step of the equation with algebra tiles correctly, even if it could be simplified more.

Answer:

x = 3.25

Step-by-step explanation:

Isolate the variable, x. Note the equal sign, what you do to one side, you do to the other. Do the opposite of PEMDAS.

PEMDAS =

Parenthesis

Exponents (& Roots)

Multiplication

Division

Addition

Subtraction

...and is the order of operation.

First, subtract 3 from both sides of the equation:

4x + 3 = 16

4x + 3 (-3) = 16 (-3)

4x = 16 -3

4x = 13

Next, dvide 4 from both sides:

(4x)/4 = (13)/4

x = 13/4

x = 3.25

x = 3.25 is your answer.

~

Answer:

x = 3.25

Step-by-step explanation:

4x + 3 = 16

4x + 3 - 3 = 16 - 3

4x = 13

4x/4 = 13/4

x = 3.25

Answer:

n = 60.22

Step-by-step explanation:

Hello

To find Sn, we need to draw out equations for each a₇ and a₁₉

In an arithmetic progression,

Sn = a + (n-1)d

Where Sn = sum of the A.P

a = first term

d = common difference

a₇ = 32

32 = a + (7-1)d

32 = a + 6d ........equation (i)

a₁₉ = 140

140 = a + (19-1)d

140 = a + 18d .........equation (ii)

Solve equation (i) and (ii) simultaneously

From equation (i)

32 = a + 6d

Make a the subject of formula

a = 32 - 6d .....equation (iii)

Put equation (iii) into equation (ii)

140 = (32 - 6d) + 18d

140 = 32 - 6d + 18d

Collect like terms

140 - 32 = 12d

12d = 108

d = 108 / 12

d = 9

Put d = 9 in equation (i)

32 = a + 6(9)

32 = a + 54

a = 32 - 54

a = -22

When Sn = 511

Sn = a + (n - 1)d

Substitute and solve for n

511 = -22 + (n-1) × 9

511 = -22 + 9n - 9

511 = -31 + 9n

511 + 31 = 9n

542 = 9n

n = 542 / 9

n = 60.22

Answer:

Hello There!

`~~~~~~~~~~~~~~~~~~`

You added no fraction so i thought you wanted the definition

Convert Fractions to Percents. Divide the top of the fraction by the bottom, multiply by 100 and add a "%" sign.

Hope this helped you. Brainliest wouldbe nice!

Answer:

20/29

Step-by-step explanation:

SOH CAH TOA

so its opposite/hyp...

20/29

is the answer

Answer:

73 degrees

Step-by-step explanation:

Given

A Shaped Frame of two congruent sides

Required

Determine the angle made with the ground

Given that there are two congruent sides, this implies that the A frame is an isosceles triangle;

Let the two angles made with the ground be represented by x

Angles in a triangle when added equals 180;

Hence;

[tex]x + x + 34 = 180[/tex]

[tex]2x + 34 = 180[/tex]

Subtract 34 from both sides

[tex]2x + 34 - 34 = 180 - 34[/tex]

[tex]2x = 180 - 34[/tex]

[tex]2x = 146[/tex]

Divide both sides by 2

[tex]\frac{2x}{2} = \frac{146}{2}[/tex]

[tex]x = \frac{146}{2}[/tex]

[tex]x = 73[/tex]

Hence, the angle with the ground is 73 degrees