Xintercept for the quadratic function f(x)=x²-8x

Answer:

A

Step-by-step explanation:

To rite the equation of the function, take two points from the table. Let them be (1,21) and (3,15).

The slope of the function is

[tex]\dfrac{21-15}{1-3}=\dfrac{6}{-2}=-3[/tex]

Thus, the equation of the function in slope-intercept form is

[tex]f(n)=-3n+b[/tex]

Find b by substituting coordinates of the first point into the function expression:

[tex]21=-3\cdot 1+b\\ \\b=21+3\\ \\b=24[/tex]

Therefore,

[tex]f(n)=-3n+24[/tex]

Answer: x=4.25

Step-by-step explanation:

-30=4-8x

subtract 4 from both sides

-8x=-34

divide by -8 on both sides

x=4.25

Answer: No  

Step-by-step explanation:

Answer:

No

Step-by-step explanation:

It doesn't tell you how many teams there but if there are two teams that have extra player it is obviously not proportional.

<X = 48 degrees, <Y = 8X-3, W = 18X+5

Since it's a triangle we know that it equals 180 degrees.

So take 8X-3+18X+5+48=180

Add your like terms together which makes, 26X+50=180

Now you're going to subtract 50 from 180 which leaves you with 26X=130

Now divide your sums which leaves you X which = 5

You should be able to plug X back into your equation to find <Z. Hope this helps.

Answer:

f light is imagined as a flow of particles, the particles are called photons with each photon carrying a discrete packet of energy.

Answer:

Bro XD lol just simplify it.

the answer is 3

Answer:

3

Step-by-step explanation:

Answer:

The answer is B. 5/8 quarts

Step-by-step explanation:

1 ounce is equal to .03125 quarts so to find the amount of quarts, you multiply 20 times .03125 to get .625 or 5/8.

Final answer:

There are 5/8 quarts of soda in a 20 ounce bottle, which is found by dividing 20 by the conversion factor of 32 ounces per quart.

Explanation:

The student has asked how many quarts of soda are in a 20 ounce bottle. To convert ounces to quarts, we use the conversion factor that there are 32 ounces in a quart. To find the number of quarts in 20 ounces, we divide 20 by 32.

20 oz ÷ 32 oz/qt = 0.625 qt

This can also be written as 5/8 quarts, which is option B. Therefore, there are 5/8 quarts of soda in a 20 ounce bottle.

5 million, four thousand, three hundered in standard form is [tex]5.0043 \times 10^{6}[/tex]

Need to represent 5 million, four thousand, three hundered in standard form

5 million = 5000000

4 thousand = 4000

3 hundred = 300

5 million, four thousand, three hundred =  5000000 + 4000 + 300 = 5004300

In standard form, decimal comes after first digit and multiply to power of 10 dependency on total digits of number.

In our case, given number is 5004300.

So we need decimal after first and after that multiplying it by appropriate power of 10. So,

[tex]5004300=5.0043 \times 10^{6}[/tex]

Hence [tex]5.0043 \times 10^{6}[/tex] is standard form of 5004300 that is standard form of  5 million, four thousand, three hundred.

The number '5 million, four thousand, three hundred' is written in standard form as 5,004,300. Standard form notation uses commas to split up large numbers into thousands, millions, etc.

The standard form notation for representing numbers is a helpful way to write large or very small numbers in a more compact format. In this case, the number '5 million, four thousand, three hundred' in standard form would be represented as 5,004,300. This combines all the components: millions, thousands, and hundreds into one concise figure.

In standard form, this value is written by placing commas every three digits, starting from the right. So, '5 million' is written as 5,000,000. 'Four thousand' is written as 4,000 and 'three hundred' as 300. When you add these values together, you get 5,004,300.

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Answer:

Lenghts of the sides: [tex]26\ cm[/tex]

Lenghts of the diagonals: [tex]48\ cm[/tex] and [tex]20\ cm[/tex]

Step-by-step explanation:

Look at the rhombus ABCD shown attached, where AC and BD de diagonals of the rhombus.

The sides of a rhombus have equal lenght. Then, since the perimeter of this one is 104 centimeters, you can find the lenght of each side as following:

[tex]AB=BC=CD=DA=\frac{104\ cm}{4}= 26\ cm[/tex]

You know that the diagonals are in the ratio [tex]5:12[/tex]

Then, let the diagonal AC be:

[tex]AC=12x[/tex]

This means that AE is:

[tex]AE=\frac{12x}{2}=6x[/tex]

And let the diagonal BD be:

[tex]BD=5x[/tex]

So BE is:

[tex]BE=\frac{5x}{2}=2.5x[/tex]

Since the diagonals of a rhombus are perpendicular to each other, four right triangles are formed, so you can use the Pythagorean Theorem:

[tex]a^2=b^2+c^2[/tex]

Where "a" is the hypotenuse and "b" and "c" are the legs.

In this case, you can choose the triangle ABE. Then:

[tex]a=AB=26\\b=AE=6x\\c=BE=2.5x[/tex]

Substituting values and solving for "x", you get:

[tex]26^2=(6x)^2+(2.5x)^2\\\\676=36x^2+6.25x^2\\\\\sqrt{\frac{676}{42.25}}=x\\\\x=4[/tex]

Therefore, the lenghts of the diagonals are:

[tex]AC=12(4)\ cm=48\ cm[/tex]

[tex]BD=5(4)\ cm=20\ cm[/tex]

Answer:

(3x + 5) and (x - 6).

Step-by-step explanation:

3x^2-13x-30

Use the 'ac' method:

a * c = 3*-30 = -90.

We need two numbers whose product is -90 and whose  sum is -13. They are  -18  and + 5, so we have

3x^2 - 18x + 5x - 30     Factor by grouping:

= 3x(x - 6) + 5(x - 6)

= (3x + 5)(x - 6).

Answer:

A (3x + 5) and (x - 6

Step-by-step explanation:

The width of the picture is 14 inches and the height is 10 inches, resulting in dimensions of 14 inches by 10 inches.

This problem can be solved by using the formula for the area of a rectangle, which is area = length x width. We are given that the area is 140 square inches, and that the height of the picture is 5/7 of its width. Therefore, we can create the equation 140 = width x (5/7)width.

By simplifying this equation, we can then solve for the width:

So the width of the picture is 14 inches. To find the height, we multiply the width by 5/7: height = 14 x (5/7) = 10 inches.

Therefore, the dimensions of the picture are 14 inches by 10 inches.

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Answer:

b=-1

Step-by-step explanation:

1=(6/-15)(-5)+b

-6/15=-2/5

(-2/5)(-5)=10/5=2

2+b=1

b=1-2=-1

Answer:

Domain: All Real Numbers

Range: All Integers

Step-by-step explanation:

Integers are numbers positive and negative and 0 but cannot be partial numbers. Partial numbers are decimal or fractional numbers when most simplified.

Real numbers are positive and negative and 0 and can be partials, decimal numbers, fractions, radicals, anything considered a number.

The domain is all real numbers. Since the graph has lines that show between the grid lines, decimal numbers are included.

The range is all integers because there are only number on the grid lines. Real numbers would include all of the decimal numbers that not in the white spaces.

Answer:

the bottom right

Step-by-step explanation:

range cannot be all real numbers because they have to be integers(for example, 3/4 is a real number but it is not an integer)as the lines are on integer numbers. But the domain can be all real numbers because the lines go through all real numbers

Answer:

[tex]8x+12y\leq 300[/tex]

[tex]x\geq 6[/tex]

[tex]y\leq 12[/tex]

[tex]x\geq 2y[/tex]

Step-by-step explanation:

We are given that

x=Number of small vases

y=Number of large vases

Total number of roses not more than 300 in vases.

Number of roses in small vase atleast=8

Number of roses in large vase not more than =12

We have to find the constraints are placed on the variables in the given situation.

According to question

[tex]8x+12y\leq 300[/tex]

[tex]x\geq 6[/tex]

[tex]y\leq 12[/tex]

[tex]x\geq 2y[/tex]

Answer:

x=43/8

Step-by-step explanation:

2-8x+41=0

-8x+43=0

-8x=0-43

-8x=-43

8x=43

x=43/8

Answer:

0.05

Step-by-step explanation:

1/20=5/100=0.05

Answer:

0.05

Step-by-step explanation:

To find the decimal equivalent of the fraction 1/20, this is shown as shown in the attachment.

1/20 = 0.05

The decimal equivalent of 1/20 is 0.05

Answer:

X=13

Step-by-step explanation:

15x-15= 180

15x-15+15=180+15

15x/15=195/15

X=13

Now just plug X in to every equation

(Q) 4(13)-22= 30

(P) 10(13)-4= 126

(R) 1(13)+11=24

Answer:

p(x) = 5(x + 3)² - 45

Step-by-step explanation:

Sandra wrote the function as p(x) = 30x + 5x².

So, this is a formula of a parabola, and this we have to convert into vertex form.

Now, rearranging the function we get

p(x) = 5(x² + 6x)

⇒ p(x) = 5(x² + 6x + 9) - 45

⇒ p(x) = 5(x + 3)² - 45

So, this is the vertex form and the vertex of the parabola is (-3,-45).

We know the formula of a parabola having vertex at (m,n) and axis parallel to positive y-axis is given by

(x - m)² = 4a(y - n)

⇒ [tex]y = \frac{1}{4a} (x - m)^{2} + n[/tex] (Answer)

Answer:C

Step-by-step explanation:

The required rational function is F(x) = x-5/3x. Option C is correct.

From the options correct rational function is  to be determined.

A rational number is defined as the number written in the form of the f ratio.

Here,
The property of rational function is it contains function on both numerator and denominator.
By looking to the property, only function F(x) = x-5/3x seems to rational functions.

Thus, the required rational bis F(x) = x-5/3x.

Learn more about rational numbers here
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Answer: Choice B) (2,0)

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

Set the first piece equal to zero and solve for x

x^2 - 4 = 0

x^2 = 4

x = sqrt(4) or x = -sqrt(4)

x = 2 or x = -2

Keep in mind that the first piece y = x^2-4 is only graphed when x = 2 or larger, so we ignore x = -2. This is one x intercept, but there may be more. Let's check the other graph to see what we get.

----------

Set the second piece equal to zero and solve for x

x-2 = 0

x-2+2 = 0+2

x = 2

We get the same result as above in the prior section. Because of this, the two pieces connect at this junction point.

The x intercept x = 2 leads to the location (2,0). The x intercept always occurs when y = 0.

The graph below shows this.

side note: the red piece y = x^2 - 4 looks linear, but it's actually not a straight line. It's just a really stretched out curve.

Answer:

hope this helped i was kinda confused by the question

Step-by-step explanation:

3 x 11 = 33

4 x 5 = 20

33 + 20 = 53

10 x 4 = 40

80 - 40 = 40

53 > 40

60 - 50 = 10

3 x 10 = 30

5 x 15 = 75

50 = 20 = 70

11 + 33 = 44

35 x 15 = 525

42 + 35 = 77

9 x 8 = 72

Answer: [tex]g(-3)=-28[/tex]

Step-by-step explanation:

For this exercise it is important to remember the multiplication of signs:

[tex](+)(+)=+\\(-)(-)=+\\(-)(+)=-\\(-)(+)=-[/tex]

You have the following function g(x) provided in the exercise:

[tex]g(x) = 2x - 22[/tex]

The problem asks to find the value of [tex]g(-3)[/tex]. In order to find it, you need to substitute [tex]x=-3[/tex] into the function g(x):

[tex]g(-3) = 2(-3) - 22[/tex]

The final step is to evaluate.

Applying this procedure, you get that the value of [tex]g(-3)[/tex] is:

[tex]g(-3) = -6 - 22\\\\g(-3)=-28[/tex]

Answer:

15 : 11 : 16

Step-by-step explanation:

If A, B, and C are in the ratio x : y : z, then we can say that there is x quantity of A, y quantity of B and z quantity of C.

Therefore, the 15 quantity of white paint. 11 quantity of black paint and 16 quantity of blue paint are in the ratio of 15 : 11 : 16.

Since there is no common factor between 15, 11 and 16 then the ratio is in the simplest form and the ratio is 15 : 11 : 16. (Answer)

A student memorized the statement the product of any rational number and an irrational number is irrational holds true for non-zero rational number

Solution:

A rational number is a number that can be written as a fraction.

When a rational number fraction is divided to form a decimal value,

it becomes a terminating or repeating decimal.

An Irrational Number is a real number that cannot be written as a simple fraction. It cannot be expressed as a fraction with integer values in the numerator and denominator.

When an irrational number is expressed in decimal form, it goes on forever without repeating.

"The product of a rational number and an irrational number is SOMETIMES irrational."

If you multiply any irrational number by the rational number zero, the result will be zero, which is rational.

Any other situation, however, of a product of rational and irrational will be irrational.

A better statement would be:

"The product of a non-zero rational number and an irrational number is irrational."

Let us understand this with a example

[tex]\text { non - zero rational number } \times \text { irrational number }=\text { irrational number }[/tex]

Consider [tex]\frac{1}{2} \rightarrow rational number[/tex]

[tex]\frac{\sqrt{3}}{4} \rightarrow irrational number[/tex]

Now multiply both,

[tex]\frac{1}{2} \times \frac{\sqrt{3}}{2}=\frac{\sqrt{3}}{4}=0.433012701[/tex]

We got 0.433012701 which is a irrational number because in decimal form, it goes on forever without repeating.

Thus we can frame two statements:

Answer:

Step-by-step explanation:

"The product of any rational number and an irrational number is irrational"

To know if the statement is true or false, we can test an example. Lets use the rational number [tex]\frac{3}{2}[/tex] and the irrational number [tex]\pi[/tex]. Id we calculate the product of these two we would have:

[tex]\frac{3}{2}\pi= 4.71238898038469...[/tex]

As you can observe, the product is an irrational number, because it's infinite and not periodic, it doesn't have any pattern.

Therefore, the statement is true.

Answer:

The temperature outside is  75.6°F

Step-by-step explanation:

We are given the following in the question:

The temperature of dry ice = - 109.3°F

Let x be the temperature outside in Fahrenheit.

It is given that the temperature of dry ice  is 184.9°F less than  the outside temperature.

Thus, we can write the equation:

[tex]x - 184.9 = -109.3[/tex]

Solving, the above equation, we get:

[tex]x - 184.9 = -109.3\\x = -109.3 + 184.9\\x = 75.6[/tex]

Thus, the temperature outside is  75.6°F

Question:

A car that travels 20 miles in 1/2 hour at constant speed is traveling at the same speed as a car that travels 30 miles in 3/4 hour at constant speed.  Explain

Answer:

Both the car travels at  the same speed of  40 miles per hour .

Step-by-step explanation:

Given:

car 1  :

Distance travel car 1 travels =20 miles  

Time taken = 1/2 hour

car 2 :

Distance travel car 1 travels =30 miles  

Time taken = 3/4 hour

Solution:

Let the speed at which car 1 travels be x

Let the speed at which car 2 travels be y  

Finding the speed of car 1 :

Speed of car 1,[tex]x =\frac{distance}{time}[/tex]

=>[tex]x=\frac{20}{(\frac{1}{2})}[/tex]

=>[tex]x=20\times \frac{2}{1}[/tex]

=>x = 40 miles per hour

Finding the speed of car 2 :

Speed of car 2,[tex]y =\frac{distance}{time}[/tex]

=>[tex]y=\frac{30}{(\frac{3}{4})}[/tex]

=>[tex]y=30\times \frac{4}{3}[/tex]

=>[tex]y=\frac{120}{3}[/tex]

=>x = 40 miles per hour

Answer:

Time taken by the ball to reach its maximum height is 3.4 sec

maximum height reached by the ball is 185.6ft

Step-by-step explanation:

h(t) = -16[tex]t^{2}[/tex] + 109t

height is maximum ⇔ [tex]\frac{d}{dt}[/tex](h) = 0 and [tex]\frac{d^{2} }{dt^{2} }[/tex](h) < 0

[tex]\frac{d}{dt}[/tex](h) = 0 ⇒ -32t + 109 = 0

⇒t = [tex]\frac{109}{32}[/tex] ⇒ t = 3.4sec

[tex]\frac{d^{2} }{dt^{2} }[/tex](h) = -32 < 0

∴h(t) is maximum at t = 3.4

and maximum height is h(3.4) = -16×[tex]3.4^{2}[/tex] + 109×3.4 ⇒ h = 185.6ft

Answer:

The maximum height with rounding by the nearest tenth is [tex]280.56\ m[/tex]

Explanation:

Initial velocity of ball [tex]=109\ ft/sec[/tex]

Quadratic function [tex]$h(t)=-16t x^{2} +109t$[/tex]

Maximum  height[tex]=?[/tex]

Step 1:

This ball has its height related to time by a parabola with the equation:

[tex]$s=\frac{1}{2} \times a \times t^{2}+v_{0} \times t+s_{0}$[/tex]

where [tex]$s$[/tex] is the height so is the starting height, [tex]v_{0}[/tex]  is its starting velocity [tex]$=109 \ {ft} / \mathrm{s}$[/tex]

[tex]$a$[/tex] is the acceleration of gravity, which is [tex]$-16 \ {ft} / \mathrm{s}$[/tex] every second.

Step 2:

Time required to reach its maximum height:

[tex]$v=a^{*} t+v_{0}[/tex]  (its velocity is the acceleration of gravity × time [tex]+ v_0[/tex]) [tex]$v$[/tex] will slow down from [tex]$109 \ {ft} / \ s[/tex] to [tex]$0 \mathrm{ft} / \mathrm{s}$[/tex]  

And it slowing down at [tex]$16 \mathrm{ft} / \mathrm{s}$[/tex] :

[tex]t(s)=0,1,2,3,4,5,6[/tex]

[tex]V (m/s)=109,93,77,61,45,29,13[/tex]

Before [tex]$7 \mathrm{~s}$[/tex], it will hit the ground.

Exact calculation [tex]$t=\frac{109 f t / s}{16 f t / s}=6.81 s$[/tex]

Thus we can say at the height of,

[tex]$\mathrm{t}_{\max }=\frac{6.81}{2} \\=3.4\ sec[/tex]  

Step 3:

Plug the [tex]t_m_a_x[/tex] sec value back into equation:

[tex]$h(t)=t \cdot(-16 t+109)$[/tex]

[tex]$h_{\max }=3.4 \cdot(-16.4 .1875+109)$[/tex]

[tex]$h_{\max }= 185.6\ m[/tex]

Hence, the maximum height is [tex]185\ m[/tex]

To learn more about vertically upward ball, refer:

Answer:

Number of panels produced by Plant B is 8,000.

Step-by-step explanation:

The number of panels produced by Plant A  = 16,000

The number of defective panels from A = 5%

Now, 5% of 16,000 = [tex]\frac{5}{100}  \times 16,000 = 800[/tex]

So, out of  16,000 panels produced by pant A , 800 are defective. .. (1)

Let us assume number of panels produced by Plant B  = m

The number of defective panels from B = 2%

Now, 2% of m = [tex]\frac{2}{100}  \times m = 0.02 m[/tex]

So, out of total m panels produced by pant B , 0.02 m are defective. .. (2)

Now, total panels produced over all = Panels by A  + Panels by B

= 16,000 + m

The percentage of defected panels over all = 4%

Now, 4% of (16,000 + m) = [tex]\frac{4}{100}  \times (16,000+m)  = (0.04)(16,000 + m)[/tex]

Also, the total number of defective panels = Defective from A  + Defective from B

⇒(0.04)(16,000 + m)  =  800 +   0.02 m   from (1) and (2)

or, 640 + 0.04 m = 800 + 0.02

or, 0.02 m = 160

⇒ m = 160 /0.02 = 8,000

or, m = 8,000

Hence, Number of panels produced by Plant B is 8,000.

The number of panels produced by Plant B can be calculated by setting up an equation representing the total number of defective panels from both plants. Solving this equation yields a result of 20,000 panels for Plant B.

Let's denote the number of panels produced by Plant B as X. According to the problem, 5% of the panels produced by Plant A were defective, which is 0.05*16,000 = 800. Since 2% of the panels produced by Plant B were defective, that's 0.02*X panels.

The total number of defective panels from both plants was 4% of the total production, which means it was equivalent to 0.04 * (16,000+X). Setting this equation equal to the sum of defective panels from both plants, we get the equation 0.04*(16,000+X) = 800 + 0.02*X.

Solving the above equation, we get X = 20,000. Therefore, "Plant B produced 20,000 panels".

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Answer:

1. x<4

2. x>9/4

Step-by-step explanation:

Answer:

the answer is b

Step-by-step explanation:

Answer:

Step-by-step explanation:

Solved by elim: it is similar (diff size, but not congruent, same size) and B is twice the size of A, not half.