Finding Intercepts of Quadratic FunctionsConsider the function f(x) = x2 + 12x + 11.

x-intercepts:

0 = x2 + 12x + 11

0 = (x + 1)(x+ 11)



y-intercept:

f(0) = (0)2 + 12(0) + 11
What are the intercepts of the function?

The x-intercepts are .



The y-intercept is .

To solve this you must use a proportion like so...

[tex]\frac{part}{whole} = \frac{part}{whole}[/tex]

60 is a percent and percents are always taken out of the 100. This means that one proportion will have 60 as the part and 100 as the whole

We want to know out of what number is 12 60%. This means 12 is the part and the unknown (let's make this x) is the whole

[tex]\frac{12}{x} =\frac{60}{100}[/tex]

Now you must cross multiply

12*100 = 60*x

1200 = 60x

To isolate x divide 60 to both sides

1200/60 = 60x/60

20 = x

This means that 60% of 20 is 12

Hope this helped!

~Just a girl in love with Shawn Mendes

The number that 60% of 20 is 12.

We know that 60 is a percent and percent is always taken out of the 100. which  means that one proportion will have 60 as the part and 100 as the whole

We need  to know out of what number is 12 60%. This means 12 is the part and the unknown, x is the whole

Now we must cross multiply;

12*100 = 60*x

1200 = 60x

To isolate x divide 60 to both side;

1200/60 = 60x/60

20 = x

This, means that 60% of 20 is 12

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Answer:

12.5 times larger is the storage capacity of Meredith's new hard drive

Step-by-step explanation:

Meredith's new computer storage capacity = 1.5 x 10^12

Meredith's old computer storage capacity = 1.2 X 10^11

times the storage capacity of Meredith's new hard drive is larger = Meredith's new computer storage capacity/Meredith's old computer storage capacity

= 1.5X10^12/1.2X10^11

= 12.5

So, 12.5 times larger is the storage capacity of Meredith's new hard drive

Answer:

Step-by-step explanation:

Givens

To find how many times larger is the new hard drive thatn the old one, we just need to divide

[tex]\frac{1.5 \times 10^{12}bytes }{1.2 \times 10^{11} bytes }=1.25 \times 10 = 12.5[/tex]

Therefore, the new hard driave can store 12.5 times more than the old hard drive.

Answer:

True

Step-by-step explanation:

When you are given an equation of a line in the plane, it´s like if they´ve given you the map to a line, and in this case it´s really easy to calculate the value of the different points on X and Y and by that you just have to immagine a value for one of the variables to calculate the other one, most cases is always X the one that you give the value to, and then you just calculate the Y.

Answer:

True.

Step-by-step explanation:

An equation for a line in the plane allows you to find x- and y-coordinates of any point on that line.

Answer:

75.00

Step-by-step explanation:

1500*0.05

because 5% is her interest you convert 5% into a decimal = 0.05

then you multiply 1500 by 0.05 and you get 75.00

Answer:

13/102

Step-by-step explanation:

There are 52 cards in a standard deck (not including the jokers).

So let's start with the first thing... the red part. Half the deck is red which means 52/2=26 cards are red.

So the probability of the red being drawn is 26/52 (I'm going to keep it an un-reduced form for now)

So now since it says we don't replace (we don't put the card back into the deck), there is only 51 cards to choose from now.  There are 4 suits so there are 13 of each kind of suit. So to draw a spade, the probability would be 13/51.

So the end: The probability of drawing a red then a spade without replacing is the multiplication of these probabilities I found:

So the answer is 26/52  * 13/51=13/102

Answer:

[tex]x<-2\\\\y\leq-x-2[/tex]

Step-by-step explanation:

From the given graph , the shaded region is bounded by two lines ( one is dotted and another is solid line).

Dotted line :  It is parallel to y-axis and intersecting the x -axis at .

so the equation of the line is x=-2.

But it is represented in dotted form it means the inequality sign used here is strictly less than.

i.e. the equation for dotted line = [tex]x<-2[/tex]

Solid line : It is passing through (-2,0) and (-1,-1).

Equation of line passing through (a,b) and (c,d) :-

[tex](y-a)=\dfrac{d-b}{c-a}(x-b)[/tex]

Then equation of sold line:

[tex](y-0)=\dfrac{-1-0}{-1-(-2)}(x-(-2))\\\\\Rightarrow\ y=\dfrac{-1}{-1+2}(x+2)\\\\\Rightarrow\ y=\dfrac{-1}{1}(x+2)\\\\\Rightarrow\ y=-x-2[/tex]

Hence, the inequality represents solid line(≤)= [tex]y\leq-x-2[/tex]

Hence, the system of linear inequalities is graphed will be :-

[tex]x<-2\\\\y\leq-x-2[/tex]

Answer:

3.75

Step-by-step explanation:

It would cost Casey $3.75

If you divide 52.50 by 14 you get 3.75

this is a way to find the cost of one gallon

Hope this helps :)

If it does please mark brainliest :D

- A.Hazle <3

Answer:

E)82

Step-by-step explanation:

The formula is

A^2 + B^2= C^2

the two sides that make up the right angle is always A and B

Answer:

E

Step-by-step explanation:

Since the triangle is right use Pythagoras' theorem to solve for BC

The square on the hypotenuse (BC) is equal to the sum of the squares on the other 2 sides, that is

BC² = 80² + 18² = 6400 + 324 = 6724 ( take the square root of both sides )

BC = [tex]\sqrt{6724}[/tex] = 82 → E

Answer:

I think B is right because,

5x-3y=-6

or,5x_3y+6=o

now,we representing quadratic formula

The equation that represents a quadratic function is y = 2x² - 12x + 9

Which of the equations represents a quadratic function?

From the question, we have the following parameters that can be used in our computation:

The equations

By definition

A quadratic function is represented as any of the following forms

y = ax² + bx + c

y = a(x - h)² + k

Using the above as a guide, we have the following:

The equation that is a quadratic function is y = 2x² - 12x + 9

Others are not quadratic functions

Answer:

no

Step-by-step explanation:

to know if a number is divisible by 4, you need to look only at the last two digits and see if that is divisible, 15 is not divisible by 4 and therefore the whole number isnt.

if you tried to divided 262,015 by 4 you would get 65503.75, a decimial so not divisible

Answer:

No, 262,015 will not divide evenly into 4.

Step-by-step explanation:

262,015 ÷ 4 = 65503.75.

Therefore, it will not divide evenly into 4.

Another way to do this is to check if the last two digits are divisible by 4.

The last two digits are 15. 15 is not divisible by 4. Therefore, the entire number will not be divisible by 4.

Answer:

-1

Step-by-step explanation:

A-(b+c)

Let a=2 b=-5 c=8

2 - (-5+8)

2 - (3)

2-3

-1

Answer:

c) (3-7x^2)(x-3)

Step-by-step explanation:

-7x^3+21x^2+3x-9

Factor out a -7x^2 from the first two terms and a 3 from the last two terms

-7x^2 (x -3) +3(x-3)

Now factor out (x-3)

(x-3) (-7x^2+3)

Rearranging)

(x-3) (3-7x^2)

Answer:

Option C. 7,000 − 36x

Step-by-step explanation:

Let

y ----> depreciated value of the car

x---> rate of depreciation

t ----> the time in months

we know that

The linear equation that represent this situation is

y=7,000-xt

For

t=3 years

Convert to months

t=3*12=36 months

substitute

y=7,000-x(36)

y=7,000-36x

Answer:

9

Step-by-step explanation:

9x5 is 45

Answer:

308.65 Pounds

Step-by-step explanation:

Since one kilogram is 2.20462 pounds you can multiply 140 by 2.20462 to get 308.6468 and rounded to the nearest hundredth it would be 308.65.

The weight of a 140 kilogram person in pounds is approximately 308.64 pounds, when rounded to the nearest hundredth.

To find the weight of a 140-kilogram person in pounds, we first need to understand that weight is a measure of the force of gravity on an object and can be calculated by multiplying the mass of the object by the acceleration due to gravity.

However, here, we are converting kilograms to pounds, which is a conversion of mass units, not weight. The conversion factor from kilograms to pounds is approximately 2.2046.

Therefore, to convert 140 kilograms into pounds, we multiply 140 by 2.2046:

140 kg * 2.2046 = 308.644 pounds.

And rounded to the nearest hundredth, we get 308.64 pounds.

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Answer:

[tex]\large\boxed{\text{the sloe}\ m=\dfrac{2}{3}}[/tex]

Step-by-step explanation:

[tex]\text{Let}\\\\k:y=m_1x+b_1\\\\l:y=m_2x+b_2\\\\l\ \parallel\ k\iff m_1=m_2\\\\l\ \perp\ k\iff m_1m_2=-1\to m_2=-\dfrac{1}{m_1}[/tex]

[tex]\text{We have the slope}\ m_1=\dfrac{2}{5}.\\\\\text{The slope of parallel line is the same:}\ m_2=\dfrac{2}{5}[/tex]

Answer:

x=8

Step-by-step explanation:

Cause 8+1 =9

Answer:

8

Explanation:

to get the answer we have to use the opposite of addition which is subtraction. we flip around the equation so now it would be 9 - 1 = ?

9 minus 1 is 8.

that is how you get the answer.

ANSWER

The equivalent form is 8.

EXPLANATION

The given expression is

[tex] ({16}^{ \frac{3}{2} } )^{ \frac{1}{2} } [/tex]

This is the same as:

[tex] {16}^{ \frac{3}{2} \times \frac{1}{2} } [/tex]

[tex]{16}^{ \frac{3}{4}} [/tex]

[tex]{16}^{ \frac{3}{4}} = { {2}^{4 \times } }^{ \frac{3}{4}} [/tex]

We cancel out the common factors in the exponents to get,

[tex]{2}^{3} = 8[/tex]

The correct answer is B.

Answer:

B) 9.2

Step-by-step explanation:

To find an average, you have to combine all of your numbers and then divide by how many there are.

So first, combine the values.

9.7 + 8.6 + 9.3 = 27.6

Now, divide by how many numbers you had, which is 3.

27.6 ÷ 3 = 9.2

Firstly , combine the all values

[tex]9.7 + 8.6 + 9.3 = 27.6[/tex]

Now , divided by 3

[tex] 27.6 \div 3 \\ \\ \frac{27.6}{3} \\ \\ 9.2 [/tex]

The correct answer is 9.2 - option (b) (✔)

Answer:

Rule:

a_n = 9^(n - 1)

8th term:

a_8 = 9^(8 - 1) = 9^7 = 4,782,969

Step-by-step explanation:

a_1 = 1 = 9^0

a_2 = 1 * 9 = 9^1

a_3 = 1 * 9 * 9 = 9^2

a_4 = 1 * 9 * 9 * 9 = 9^3

Notice that the exponent on the 9 is always 1 less than the number of the term.

Rule:

a_n = 9^(n - 1)

8th term:

a_8 = 9^(8 - 1) = 9^7 = 4,782,969

[tex]\textbf{$\left[\begin{array}{cc}x & y\\-3 & 12\\-6 & 24\\-9 & 36\end{array}\right]$}[/tex]

Two variables have a proportional relationship if the ratios are equivalent. In other words, in this type of cases two quantities vary directly with each other, so we can write this in a mathematical language as follows:

[tex]y=kx[/tex]

Here [tex]k[/tex] is the slope of the linear equation defined above. So, verifying that k is constant we have:

[tex]k=\frac{24-12}{-6-(-3))}=\frac{36-24}{-9-(-6)}=\frac{36-12}{-9-(-3)}=-4 \\ \\ \therefore \boxed{k=-4}[/tex]

One way to prove this is by writing the equation that represents the table. From the two-point intercept form of the equation of a line we have:

[tex]y-y_{1}=\frac{y_{2}-y_{1}}{x_{2}-x_{1}}(x-x_{1}) \\ \\ P(x_{1},y_{1})=P(-3,12) \\ \\ P(x_{2},y_{2})=P(-6,24) \\ \\ Subtituting \ x_{1}, x_{2}, y_{1}, y_{2}: \\ \\ y-12=\frac{24-12}{-6-(-3)}(x-(-3)) \\ \\ y-12=-4(x+3) \\ \\ Solving: \\ \\ y-12=-4x-12 \\ \\ Adding \ 12 \ to \ both \ sides: \\ \\ y-12+12=-4x-12+12 \\ \\ \boxed{y=-4x}[/tex]

So, this implies that the ordered pairs of the last option represent a proportional relationship

Answer:

Step-by-step explanation:

In this case, an proportional realtionship refer to the existence of a contant ratio of change between variables, that is, each y-value can be found by multiplying each x-value with this constant ratio of change.

So, notice that in the first table, is we multiply by four, you can get the first two pairs, but the last one doesn't fall into the ratio. That's not the answer.

Similarly, the second table doesn't have a constant ratio of change, because the last pair has different ratio.

However, the last table shows a constant ratio of change, because each x-value can be multiplied by -4, to get each y-value, that is

-3 x -4 = 12

-6 x -4 = 24

-9 x -4 = 36

Therefore, the right answer is the last table.

Answer:

It turns out that all three altitudes always intersect at the same point - the so-called orthocenter of the triangle. The orthocenter is not always inside the triangle. If the triangle is obtuse, it will be outside. To make this happen the altitude lines have to be extended so they cross.

Check the picture below.

The measure of an angle formed by intersecting secants is half the sum of the measures of the intercepted arcs is:    [tex]\[m\angle L = \frac{1}{2}(mAB + mCD)\][/tex]

The correct option is (B).

The problem step by step:

1. Given Information:

  - We have a circle with intersecting secants labeled as A, B, C, and D.

  - We need to find the correct equation that describes the relationship between the measures of angles and arcs formed by these intersecting secants.

2. Understanding the Problem:

  - When two secants intersect inside a circle, they create several angles and arcs.

  - Let's focus on angle[tex]\(m\angle L\)[/tex] and the corresponding arcs AB and CD.

3. Relationship Between Angle and Arc:

  - The measure of an angle formed by intersecting secants is half the sum of the measures of the intercepted arcs.

  - In other words:

[tex]\[m\angle L = \frac{1}{2}(mAB + mCD)\][/tex]

4. Answer:

  - The correct equation is:

   [tex]\[m\angle L = \frac{1}{2}(mAB + mCD)\][/tex]

Answer:

5x³ + 2x - 1

Step-by-step explanation:

(f + g)(x)

= f(x) + g(x)

= 5x³ - 2 + 2x + 1 ← collect like terms

= 5x³ + 2x - 1

Answer:

A.

Step-by-step explanation:

To find a significant figure you just count how many numbers are before and after the decimal place but if the first number is zero then it does not count.

Final answer:

The values with 3 significant figures are A. 10.1 and D. 129, as non-zero numbers are always significant, and there are no leading, captive, or trailing zeros to consider in these cases.

Explanation:

The values that have 3 significant figures are:

A. 10.1

D. 129

In A, all the digits are significant because they are all non-zero numbers. In D, similarly, all digits are significant since non-zero numbers are always counted as significant figures.

For the options not chosen:

B. 100.05 has 5 significant figures because zeros between non-zero numbers are significant and so are the ending non-zero numbers.

C. 120 may be seen as having 2 or 3 significant figures depending on whether the zero is considered significant; additional context such as writing the number in scientific notation or a decimal point (120.) is needed to clarify its significance.

Answer:

1/10

Step-by-step explanation:

The length of the rope swing for the considered case is found being of 5 meters approximately.

If we've got:

Then, we get:

[tex]T \approx 2\pi \sqrt{\dfrac{L}{g}}[/tex]

This is the period of oscillation, the time taken for a complete cycle in a simple gravity pendulum.

Using the above formula, as for this case, we're specified that:

Then, the length of the rope is obtained as:

[tex]T \approx 2\pi \sqrt{\dfrac{L}{g}} \: \rm \:sec\\\\L = \dfrac{T^2g}{4\pi^2} \: \rm meters\\\\\L \approx \dfrac{(4.5)^2\times 2\times (9.8)}{4\pi^2} \approx 5 \: \rm meters[/tex]

Thus, the length of the rope swing for the considered case is found being of 5 meters approximately

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The closing bracket ']' in the inequality solution set (–∞, 6.5] indicates that 6.5 is included, making it a solution to the inequality.

The solution to an inequality is (–∞, 6.5]. To determine if 6.5 is a solution to the inequality, we look at the notation used. The parenthesis '(' indicates that the number at this end of the interval is not included in the solution set, while the bracket ']' indicates that the number at this end is included. Since 6.5 is associated with a closing bracket, it means that 6.5 is indeed a solution to the inequality. Therefore, any number less than or equal to 6.5 is a solution to this particular inequality.

The correct explanation among the given options is the following:

"The solution includes numbers from negative infinity to 6.5. Because a bracket is used, the solution includes 6.5."

In interval notation, brackets ([ and ]) indicate that the endpoint is included in the solution, while parentheses (( and )) indicate that the endpoint is not included.

Here, with (-∞, 6.5], the closing bracket means 6.5 is included in the solution to the inequality.

Thus, 6.5 is a valid solution to the inequality.

The complete question is : The solution to an inequality is (-, 6.5]. Is 6.5 a solution to the inequality? Explain your answer

The solution includes numbers from negative infinity to 6.5. Because a bracket is used, the salution does not

include 6.5. The solution includes numbers from 6.5 to infinity. Because a parenthesis is used, the solution does not include 6.5.

The solution is the point(, 6.5). Because a bracket is used, 6.5 is a solution to the inequality.

The solution includes numbers from negative infinity to 6.5. Because a bracket is used, the solution includes 6.5.

Answer:

0.63

Step-by-step explanation:

The fraction is 5/8. It is equivalent to ...

5/8 = (5·125)/(8·125) = 625/1000 = 0.625

This exact decimal equivalent rounds to 0.63.

_____

It can be useful to memorize the decimal equivalents of common fractions, including multiples of 1/3, 1/4, 1/5, 1/6, 1/7, 1/8, 1/9, 1/10.

Answer:

A Quadratic Equation can have upto 2 roots maximum. So,if one of the roots is a Real number, there are following two possibilities:

1) The other root is also a real number, but a different number

2) Its a repeated root, so the other root is the same number.

The other root cannot be a complex number as its not possible for one root to be real and other to be complex. Either no root will be complex or both will be complex roots.

Following are 3 possibilities for the roots of a quadratic equation: