Find the value of m.
28
3
35°
| | (1 d.p.)

The factorized expression of the equation of the function given as lf(x) = 4x³ - x² + 16x - 4 is f(x) = (x² + 4)(4x - 1)

The equation of the function is given as

f(x) = 4x³ - x² + 16x - 4

Factor out x from the equation of the function

So, we have

f(x) = 4x³ - x² + 16x - 4

Group the terms in 2's

f(x) = (4x³ - x²) + (16x - 4)

Factorize the expression in the bracket

So, we have

f(x) = x²(4x - 1) + 4(4x - 1)

Factor out 4x - 1

So, we have

f(x) = (x² + 4)(4x - 1)

Hence, the factorized expression is f(x) = (x² + 4)(4x - 1)

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Using equation, the number of hours Ajay spent washing car and tutoring are 2 and 4 hours respectively.

Ajay is working two summer jobs working $8 per hour washing cars and $11 per hour tutoring.

Last week Ajay worked 2 more hours tutoring than hours washing cars and earned a total of $60.

The system of equation that could be used to determine the number of hours Ajay worked washing cars last week and the number of hours he worked tutoring last week can be calculated as follows:

let

x = number of hours washing cars

y = number of hours tutoring

Therefore,

y = 2 + x

Hence,

8(x) + 11(2 + x) = 60

8x + 22 + 11x = 60

19x  = 60 - 22

19x = 38

x = 38 / 19

x = 2

Therefore,

y = 2 + 2

y = 4

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Answer:

variables :

Let = w = The number of hours washing car.

let = t = The number of hours tutoring.

system of equations:

8w + 11t = 60

t = w + 2

Step-by-step explanation:

The distance between two points having coordinates (4, -4) and (9, -2) plotted on the cartesian plane, and rounded to the nearest tenth, will be 5.40 units.

As per the question statement, two points having coordinates (4, -4) and

(9, -2) plotted on the cartesian plane.

We are required to calculate the distance between the above mentioned two points, rounded to the nearest tenth.

To solve this question,  we need to know the Distance-formula which goes as,

"The distance between any two points (x₁, y₁) and (x₂, y₂) can be given by √[(x₂ - x₁)² + (y₂ - y₁)²]"

Assuming that [(x₁, y₁) = (4, -4)] and [(x₂, y₂) = (9, -2)], and substituting these values in the above-mentioned distance formula, we get,

√[(9 - 4)² + {(-2) - (-4)}²]

= √[(9 - 4)² + {(-2) + 4}²]

= √[(9 - 4)² + (4 - 2)²]

=√[(5)² + (2)²]

=√(25 + 4)

=√29

= 5.38 units.

Therefore, rounding (5.38) to the nearest tenth, we get, 5.40.

That is, the distance between two points having coordinates (4, -4) and (9, -2) plotted on the cartesian plane, and rounded to the nearest tenth, will be 5.40 units.

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A linear function which has the same y-intercept of 5 as the one that is represented by the graph is: table 1.

Mathematically, the slope of any linear function can be calculated by using this formula;

Slope, m = (Change in y-axis, Δy)/(Change in x-axis, Δx)

Slope, m = (y₂ - y₁)/(x₂ - x₁)

At points (-3, -4) and (-1, 2), the slope of the line is given by:

Slope, m = (2 + 4)/(-1 + 3)

Slope, m = 6/2

Slope, m = 3.

Note: The y-intercept of the line shown on the graph is 5.

At points (-3, -4), the y-intercept of this line can be calculated by using the slope-intercept form:

y = mx + c

Where:

Making y-intercept (c) the subject of formula, we have:

y-intercept, c = y - mx

y-intercept, c = -4 - 3(-3)

y-intercept, c = -4 + 9

y-intercept, c = 5.

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Complete Question:

Which linear function has the same y-intercept as the one that is represented by the graph?

[tex]\qquad \textit{Amount for Exponential Decay} \\\\ A=P(1 - r)^t\qquad \begin{cases} A=\textit{current amount}\dotfill & \$2607\\ P=\textit{initial amount}\dotfill &6400\\ r=rate\to r\%\to \frac{r}{100}\\ t=\textit{elapsed time}\dotfill &22\\ \end{cases} \\\\\\ 2607=6400(1 - \frac{r}{100})^{22} \implies \cfrac{2607}{6400}=\left( \cfrac{100-r}{100} \right)^{22} \implies \sqrt[22]{\cfrac{2607}{6400}}=\cfrac{100-r}{100}[/tex]

[tex]\cfrac{r-100}{100}=-\sqrt[22]{\cfrac{2607}{6400}}\implies r-100=-100\sqrt[22]{\cfrac{2607}{6400}} \\\\\\ r=100-100\sqrt[22]{\cfrac{2607}{6400}}\implies {\Large \begin{array}{llll} r\approx 4 \end{array}}[/tex]

a. A car travels 97.5 miles in 1.5 hours.

b. A car takes 2 hours to travel 130 miles.

c. Mai's equation matches the story because it is algebraic form of the formula of speed.

In this question, we have been given a car is going 65 miles per hour down the highway.

Part a.

A car is going 65 miles per hour.

This means, in 1 hour car traveled 65 miles.

Let car travels 'm' miles in 1.5 hours.

So, m = 1.5 × 65

m = 97.5 miles

Thus, a car travels 97.5 miles in 1.5 hours

Part b.

Suppose that it will take t hours to travel 130 miles.

We have been given 1 hour = 65 miles

So, we get an equation,

t = 130 / 65

t = 2 hours

This means, a car takes 2 hours to travel 130 miles.

Part c.

Mai wrote the equation y = 65x, with x representing the time traveled, in hours, and y representing the distance traveled, in miles.

We know that the formula of speed.

speed = distance / time

⇒ distance = speed × time

here, speed = 65 miles per hour

⇒ distance = 65 × time

Assuming distance = y  and time = x

y = 65x

This means,  Mai's equation matches the story.

Therefore, a. A car travels 97.5 miles in 1.5 hours.

b. A car takes 2 hours to travel 130 miles.

c. Mai's equation matches the story because it is algebraic form of the formula of speed.

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Answer:

y>-7

Step-by-step explanation:

Answer:

the answer is option 3

Step-by-step explanation:

18+6y<42

6y<42-18

6y<24

y<4

Answer: the value of a = 14.72 and if you evaluate it.

Have a good day

Answer:

12.25

Step-by-step explanation:

P, which is the principal invested is $7,000 whereas the T is 0.75

What is simple interest?

The simple interest on an investment such as that of Ryan, can be determined as the principal multiplied by the simple interest  rate and the time whose formula is as given below:

I=PRT

I=simple interest amount in dollars=unknown

P=principal investment=actual amount invested on simple interest basis=$7000

R=annual simple interest rate=8.3%

T=period of investment measured in years=9/12=0.75(9months divided by 12months in a year gives 0.75 years)

I=$7000*0.083*0.75

I=$435.75

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Answer: 91 ft

Step-by-step explanation:

Since WZ=1287ft .XY=54ft

WX is congruent to YZ

so WX= 1/2 (128-54)

= 1/2 x(<—times) 74

=37ft

WY= WX + XY

=37+54

= 91ft

Answer:

4 seconds

Step-by-step explanation:

First I substitute the Y with 0 and then I move the 16x^2 to the left side of the equation and then I divide both sides with 16 leaving me with x^2 then I get the square root of both sides and then I evaluate it and then I got the answer x = 4

Answer:

4 seconds

Step-by-step explanation:

We have a quadtratic equation, that is, we have a function to the highest degree of x^2.

When solving this, we can either solve using the quadratic equation, or by solving for X which would be the easiest and quickest way to do it.

256 -16x^2=0

-16x^2=-256

x^2=16 (divide both sides by -16)

[tex]\sqrt{x} =\sqrt{16}[/tex]

Which leaves x=4 as your answer.

To check this, we can simply input 4 back into the equation, and we will find that it does indeed equal 0.

To further visualize this, when we solve the equation for x, we are finding where the x value that intersects the x axis.  We are finding where x=0, or when it touches the ground.

By analyzing the geometric system, the measure of the angle RSP is equal to 49°.

In this problem we find a geometric system formed by two triangles, in which the line segment QR is parallel to the line segment PS. Then, we can obtain the following system of linear equations:

Intern alternate angles between parallel line segments

m ∠ QRP = m ∠ RPS

5 · y + 14 = 8 · y - 13

27 = 3 · y

y = 9

Internal angles of a triangles

m ∠ RPS + m ∠ PRS + m ∠ RSP = 180°

(8 · y - 13) + 3 · x + (2 · x + 1) = 180

8 · y + 5 · x - 12 = 180

8 · y = 180 + 12 - 5 · x

5 · x = 192 - 8 · y

x = (192 - 8 · y) / 5

x = (192 - 8 · 9) / 5

x = (192 - 72) / 5

x = 120 / 5

x = 24

Finally, the measure of the angle RSP is:

m ∠ RSP = 2 · x + 1

m ∠ RSP = 2 · 24 + 1

m ∠ RSP = 49

The measure of the angle RSP is equal to 49°.

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g = a - [tex]\frac{h}{2}[/tex]

The coordinates of T are (13, -6) which s is the midpoint of rt r(-9,4) and s(2,-1).

A midpoint is defined as in the middle of the line connecting two points a position known as a midpoint. A location in the middle of a line connecting the two points that are equally far from both points is the midpoint.

Let two points A (x₁, y₁) and B (x₂, y₂), the midpoint between A and B is given by,

M(x, y) = (x₁ + x₂)/2, (y₁ + y₂)/2

Assuming that S is the midpoint of the line segment RT, where point R's coordinates are (-9, 4) and S's coordinates are (2, -1).

We have to determine the coordinates of point T.

The midpoint is the average of both endpoints. i.e., (x₁, y₁) and (x₂, y₂).

In this case, the midpoint is given by M = S(2, -1).

Let R(x₁, y₁) = R(-9, 4) and we will determine T(x₂, y₂).

2 = (-9 + x₂)/2

-9 + x₂ = 4

x₂ = 13

-1 = (4 + y₂)/2

4 + y₂ = -2

y₂ = -6

Therefore, the coordinates of T are (13, -6).

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The question seems to be incomplete the correct question would be

Find the missing endpoint if s is the midpoint of rt r(-9,4) and s(2,-1) ; find T

Calculating a projectile's vertical upward firing is possible using the function h(t)=-16t²+900t+175.  12.65<t<43.59 will the projectile be above the ground at a height more than 9000 feet.

Given that,

Calculating a projectile's vertical upward firing is possible using the function h(t)=-16t²+900t+175.

We have to find how long will the projectile be above the ground at a height more than 9000 feet.

Answers should be rounded to the closest hundredth.

The function is

h(t)=-16t²+900t+175

-16t²+900t+175>9000

-16t²+900t+175-9000>0

-16t²+900t-8825>0

The simplest method for locating a quadratic equation's roots is the quadratic formula. There are some quadratic equations that are difficult to factor, and in these cases we can quickly discover the roots by using the quadratic formula.

Gives the roots of a quadratic equation ax² + bx + c = 0.

x = [-b ± √(b² - 4ac)]/2a.

Now, We get

t= [-900 ± √((900)² - 4(-16)(-8825))]/2(-16)

t=[-900 ± √(810000-564800)]/-32

t=[-900 ± √(245200)]/-32

t=[-900 ± 495.17]/-32

First,

t=[-900 + 495.17]/-32

t=[-404.83]/-32

t=12.65

Second,

t=[-900 - 495.17]/-32

t=[-1395.17]/-32

t=43.59

Therefore, 12.65<t<43.59 will the projectile be above the ground at a height more than 9000 feet.

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The slope of the line in the given diagram = rise/run = 1/2.

The slope of a line is determined as the ratio of the rise of the line to the run of the line.

The rise of a line = change in y

The run of a line = change in x.

The red line in the image attached below shows the rise of the line which is, 1 units.

The blue line represents the run, which is, 2 units.

The slope of the line = 1 units/2 units = 1/2.

Therefore, we can state that the slope of the line = 1/2.

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AAnswer:

Step-by-step explanation:

The percentage is calculated by dividing the required value by the total value and multiplying by 100.

The total amount earned in a week including the commission is $605 working for 40 hours.

The hourly rate is $15.125.

The percentage is calculated by dividing the required value by the total value and multiplying by 100.

Example:

Required percentage value = a

total value = b

Percentage = a/b x 100

We have,

The amount earned in a week = $350

Amount earned in commission = 3% of $8,500

= 3% of 8500

= 3/100 x 8500

= 3 x 85

= $255

The number of hours worked = 40 hours.

The hourly rate for the week:

= (350 + 255) / 40

= 605 / 40

= $15.125

Thus,

The hourly rate is $15.125.

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Answer:

∠ R = 75°

Step-by-step explanation:

you are correct with answers to a, b, c

d

the sum of the 3 angles in Δ QRS = 180° , that is

∠ Q +∠ R + ∠ S = 180° , so

55° + ∠ R + 50° = 180°

∠ R + 105° = 180° ( subtract 105° from both sides )

∠ R = 75°

Answer:wish i could help

Step-by-step explanation:......

Answer:

No solution

Step-by-step explanation:

6 + 2x = 2(x - 3)

6 + 2x = 2x-6

No solution

The most appropriate choice for ratio will be given by-

Ratio of red and orange to the other Skittles  = 8 : 9

What is ratio?

Ratio determines how many times one number is bigger than the other number, provided both the numbers has the same unit.

The first part of the ratio is called antecedent and the second part of the ratio is called consequent

Here,

Number of red Skittles Rory has = 5

Number of yellow Skittles Rory has = 8

Number of purple Skittles Rory has = 6

Number of green Skittles Rory has = 4

Number of orange Skittles Rory has = 11

Total number of red and orange skittles = 5 + 11

                                                                   = 16

Total number of other skittles = 8 + 6 + 4

                                                  = 18

Ratio of red and orange to the other Skittles = 16 : 18

                                                                         = 8 : 9

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The slope of the line h is 3

Let m1 be the slope of line g and m2 be the slope of line h.

Line g passes through points (2, 3) and (5, 2).

Using the formula of slope,

m1 = (2 - 3)/(5 - 2)

m1 = -1 / 3

Line h is perpendicular to line g.

We know that the product of slopes of the perpendicular lines is -1.

m1 * m2 = -1

(-1/3) * m2 = -1

m2 = 3

Therefore, the slope of the line h is 3

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The number of solutions in the equation where the equation is given as 7x + 3 - 8 = 2(5x - 4)  is one solution

The equation is given as

7x + 3 - 8 = 2(5x - 4)

The above equation is a linear function with one variable

So, we have

7x + 3 - 8 = 2(5x - 4)

Open the brackets

So, we have

7x + 3 - 8 = 10x - 8

Subtract 10x from both sides of the equation

So, we have

-3x + 3 - 8 = - 8

Subtract (3 - 8) from both sides of the equation

So, we have

-3x = - 3

Divide by -3

x = 1

The above equation is true because it has a definite solution

Hence, the number of solutions in the equation is one

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Answer:

Step-by-step explanation:

Step: 1

-Graph the 6x: It will start at (0,0) and will have a rise of 6 and a run of 1

Step: 2

-Graph the 90: From what I understand it should be a horizontal line with its point on 90y

Sorry if this doesn't help very late where I am.

 3/4mile part of her walk completed by Sonia once she has walked 3/5 mile of 4/5 mile distance.

As given in the question,

Sonia takes a walk everyday which is equal to

= 4/5 mile

Moreover, she has completed a part of her daily targeted distance =  3/5 mile

We need to find, what part of the total distance which Sonia covers daily, has she covered just now by covering 3/5 mile of distance.

Part of the total distance which Sonia covers daily, from the distance she has covered just now by covering 3/5 mile of distance

= (Distance covered by Sonia)/ (Total distance covered by Sonia)

= (3/5) / (4/5)

= (3/5) × (5/4)

= 3/4 mile

Therefore,,   3/4mile part of her walk completed by Sonia once she has walked 3/5 mile of 4/5 mile distance.

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Using an exponential function, the sound intensity of a noise that is 130 dB is of I = 10 watts/m².

The sound level, in dB, of a sound of intensity given by I is given according to the following equation:

[tex]B = 10\log{\left(\frac{I}{I_0}\right)}[/tex]

In which [tex]I_0[/tex] is the smallest sound heard by the human ear, which is of [tex]I_0 =  10^{-12}[/tex] watts/meter.

Hence, for a sound of 130 db, the intensity I is found as follows:

[tex]130 = 10\log{\left(\frac{I}{10^{-12}}\right)}[/tex]

Isolating the logarithm, the equation is:

[tex]\log{\left(\frac{I}{10^{-12}}\right)} = 13[/tex]

The power of 10 and the logarithm are inverse functions, hence the power of 10 is applied to both sides of the equation to isolate the intensity creating the exponential function given as follows:

[tex]10^{\log{\left(\frac{I}{10^{-12}}\right)}} = 10^{13}[/tex]

[tex]\frac{l}{10^{-12}} = 10^{13}[/tex]

[tex]l = 10^{-12} \times 10^{13}[/tex]

Multiplying two terms with the same base and different exponents, we keep the base and add the exponents, hence the intensity is given as follows:

I = 10 watts/m².

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According to the solving the factorized value of the given equation is:

(4x-5). (3x+1).

Writing a number or any mathematical object as the sum of several factors—typically smaller or simpler objects that use the same known as factorization or factoring. For instance, 3 5 factors the polynomial x2 - 4 as well as the integer 15.

Factoring is a crucial procedure that aids in our understanding of our equations. We factorize our polynomials to create a simpler form, and when we factorize equations, we obtain a wealth of important information.

Detailed explanation:

12x² - 11x-5

12x²+4x-15x-5

4x(3x+1) - 5(3x+1)

(4x-5). (3x+1)

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There is nothing more we can do with these binomials, so we break them up and combine like terms.

-2x - 13 + 19 + 5x
5x - 2x + 19 - 13
3x + 19 - 13
3x + 6

Answer:

[tex]\boxed{\sf 3x+6}[/tex]

Step-by-step explanation:

[tex]\sf \left(-2x-13\right)+\left(19+5x\right)[/tex]

Simplify:-

[tex]\sf -2x-13+19+5x[/tex]

Combine like terms/Add numbers:-

[tex]\sf -2x+5x-13+19[/tex]

[tex]\sf (-2x+5x)=\bf 3x[/tex]

[tex]\sf (-13+19)=\bf 6[/tex]

[tex]\boxed{\sf 3x+6}[/tex]

Therefore, your answer is D. 3x + 6!!

_______________________

Hope this helps!

Have a great day!