evaluate 3|-3|

a. -6
b. 6
c. 9
d. -9

Answer:

The vertex form is:

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

Where the vertex of the function is (4, 2).

Step-by-step explanation:

We want to find the vertex and the vertex form of the quadratic function:

[tex]f(x)=-2x^2+16x-30[/tex]

We have two methods of converting from standard form to vertex form: (1) by using the vertex formulas or (2) by completing the square.

Method 1) Using Formulas:

First, note that the leading coefficient of our function is -2.

The vertex of a quadratic equation is given by the formulas:

[tex]\displaystyle \text{Vertex}=\left(-\frac{b}{2a}, f\left(-\frac{b}{2a}\right)\right)[/tex]

In this case, a = -2, b = 16, and c = -30. Find the x-coordinate of the vertex:

[tex]\displaystyle x=-\frac{(16)}{2(-2)}=\frac{-16}{-4}=4[/tex]

In order to find the y-coordinate of the vertex, we substitute this value back in. Hence:

[tex]f(4)=-2(4)^2+16(4)-30=2[/tex]

Therefore, our vertex is (4, 2).

Vertex form is:

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

Where a is the leading coefficient and (h, k) is the vertex.

Substitute. Our leading coefficient is -2 and our vertex is (4, 2). Therefore:

[tex]\displaystyle f(x)=-2(x-4)^2+2[/tex]

Method 2) Completing the Square:

To complete the square, we first factor out the leading coefficient from the first two terms:

[tex]f(x)=-2(x^2-8x)-30[/tex]

Then, we divide the coefficient of the b term by half and square it. This yields:

[tex]\displaystyle \left(\frac{-8}{2}\right)^2=16[/tex]

We will add this value inside of the parentheses. Since we added 16 inside the parentheses, we will subtract 16 outside of the parenthese to remain the equality of the function. However, since the parentheses is multiplied by -2, we technically added -2(16) = -32 inside. So, we will subtract -32 outside. Thus:

[tex]f(x)=-2(x^2-8x+16)-30-(-32)[/tex]

Simplify:

[tex]f(x)=-2(x^2-8x+16)+2[/tex]

Factor using the perfect square trinomial:

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

We acquire the same result.

Answer:

Purple

Step-by-step explanation:

Because the graph has the circle filled in at the point 11, we know that it is a valid solution and that we are looking for a sign with the line under it. However, because we know that the number line extends to the right of 11, these would include answers such as 12, 13, 14, 15, etc. Because all these values are "greater than or equal to" 11, our answer is 11 <or= a, which is the purple one or the one on the right.

❀ [tex]\huge\underline{ \underline{ \tt {ANSWER :-}}}[/tex]

⁺˚*･༓☾✧.* ☽༓･*˚⁺‧

⟹ Jada will have a profit because she sold the bag for money than she had bought it for.

[tex]85 - 75 \\ = 10[/tex]

⟹ She'll have about 10 (currency name) as the profit.

⁺˚*･༓☾✧.* ☽༓･*˚⁺‧

ʰᵒᵖᵉ ⁱᵗ ʰᵉˡᵖˢ ツ

[tex]\underbrace{ \overbrace{ \tt{Carry \: On \: Learning}}}[/tex]

꧁❣ ʀᴀɪɴʙᴏᴡˢᵃˡᵗ2²2² ࿐

Answer:

8/10+7/9+39/90

Step-by-step explanation:

expressing something in the form p/q means basically make it a fraction.

.8 = 80/100

.7bar= .77777777777 (7/9)

0.43 (bar on 3 only is)= 0.433333333333333

how to make a fraction for .777777bar

10x = 7.777777777

X = .7777777777

subtract 10x-x  

we get 7/9 for .7777 (10x-x = 9 thats the denominator and, 7.7777-.7777 = 7.)

how to make a fraction for .43bar for 3 only

100x = 43.3333333333

10x = 4.33333333333

100x-10x = 43-4

43-4 = 39, and the 333333333 cancel out 39/90

Answer:

(x+1)²+(y-5.5)²=45/4.

Step-by-step explanation:

1)  the common form of the required equation is: (x-a)²+(y-b)²=r², where 'a' and 'b' are the coordinates of the centre of the given circle, r - radius of the given circle.

2) the midpoint of the diameter is the centre of the given circle, its coordinates are:

[tex]\frac{2-4}{2}=-1; \ and \ \frac{4+7}{2}=5.5.[/tex]

3) the length of the radius of the given circle is:

[tex]r=\frac{1}{2}*\sqrt{(2+4)^2+(4-7)^2)}=\sqrt{\frac{45}{4}}.[/tex]

4) according to the common form and calculated the centre O(-1;5.5) and the radius it is possible to make up the required equation of the circle:

[tex](x+1)^2+(y-5.5)^2=\frac{45}{4}.[/tex]

Answer:

The correct answer is (x+1)^2 + (y−11/2)^2 = 45/4

Step-by-step explanation:

This is how the system wants it put in. See question 12

The area of the sector of the given circle is: 40 units²

A circle is a round-shaped figure that has no corners or edges. In geometry, a circle can be defined as a closed, two-dimensional curved shape.

The set of all points on a plane that are a fixed distance from a center,

A circle is a special kind of ellipse in which the eccentricity is zero and the two foci are coincident.

The circle is the shape with the largest area for a given length of perimeter.

Given the following:

r = 8

θ = 1.25 radians

Area of sector = (1/2) × r²θ = (1/2) × (8²)(1.25)

Hence, the Area of sector = 40 units²

Learn more about the circles on:

https://brainly.com/question/29142813

#SPJ7

Answer:

B

Step-by-step explanation:

For this problem, let us find the respective speeds of Jasmine and Caroline and compare the two. All we have to do is divide #minutes by #miles to find the time spent per one mile.

Jasmine:

[tex]\frac{42.5}{5} =\\\\[/tex]

[tex]8.5[/tex] minutes per mile

Caroline:

[tex]\frac{26.4}{3} =\\[/tex]

[tex]8.8[/tex] minutes per mile

Since Caroline takes longer to run a mile than Jasmine, We now know that Jasmine ran at a faster pace:

[tex]8.8-8.5=0.3[/tex]

B. Jasmine ran at a faster pace because she ran 0.3 minutes faster per mile.

I hope this helps! Let me know if you hae any questions :)

Answer:

JM = 18 units

Step-by-step explanation:

∆MHN and ∆JKH are similar (by A.A.A axiom)

so, their sides are proportional

i.e.

(JM+18)/(20+15) = 18/15

or, JM + 18 = 540/15

or, JM = 36-18

hence, JM = 18

Answer:

49

Step-by-step explanation:

b^c

Let b = 7 and c = 2

7^2

7*7 = 49

Answer:

49

Step-by-step explanation:

you fill in the equation so that it's 7^2. which is 7*7. this equals 49

Answer:

45 inches

Step-by-step explanation:

Create a proportion where x is the perimeter of the smaller triangle:

[tex]\frac{5}{3}[/tex] = [tex]\frac{75}{x}[/tex]

Cross multiply and solve for x:

5x = 225

x = 45

So, the perimeter of the smaller triangle is 45 inches

Answer:

B.

Step-by-step explanation:

If you add 3x + x, it would be 3x^2

Answer:

y = (-3/2)x + 4

Step-by-step explanation:

The slope of the given line is 2/3.  The slope of any line perpendicular to the given line is the negative reciprocal of 2/3, which comes out to -3/2.

Now we have the slope of the new line and know that it passes through (0, 4).  (0, 4) happens to be the y-intercept, b, in y = mx + b:

Substituting -3/2 for m and 4 for b, we get y = (-3/2)x + 4.

Answer:

y=[tex]-\frac{4}{3}[/tex]x+2

Step-by-step explanation:

To write the equation for this line, we are going to use slope-intercept form, which is written as

y=mx+b.

Here are the meanings of each variable:

y= basically the "name" of the function and it always stays as y.

m= slope, which is rise over run.

x= variable that is always on the right of the slope and it always stays as x.

b= y-intercept, or the value that crosses the y-axis.

We will substitute numbers into the equation along the way. The first thing we will want to do is find b, which is the easiest.

The line crosses the y-axis at 2, so that is our value of b.

Our new equation is

y=mx+2.

Next, we will find the slope. The most efficient way of doing this is looking at the lowest point that is already provided, (3, -2), and finding a way to rise and run to the highest point, (0, 2).

If you look closely at the graph, we need to rise up 4 and run over -3 to get to the other point. Therefore, the slope is [tex]-\frac{4}{3}[/tex], and we can substitute it into our equation, which is completed and is now

y=[tex]-\frac{4}{3}[/tex]x+2

I hope this helps you out!! Have an awesome day ^^

Answer:

"D" (2,4), (-2,-4)

Step-by-step explanation:

Hi there!

Before we get into translation or transformation of a graph. Let's understand how the graph of cube root of x looks like.

1. How does an original graph, or a graph without any translations look like?

2. Translations/Transformation of the graph.

3. Conclusion and Answer

I hope this helps! Let me know if you have any doubts regarding your question or my answer.

Answer:

4/5 ÷ 1/10 = 40/5 as simplified as 8/1 in fraction form.

4/5 ÷ 1/10 = 8 in decimal form.

This calculator, formula, step by step calculation and associated information for fraction 4/5 divided by 1/10 may help students, teachers, parents or professionals to learn, teach, practice or verify such division between two fractions calculations efficiently.

Step-by-step explanation:

hope it helps...

Answer:

8/1

Step-by-step explanation:

4/5 change × 10/1= 8/1 hope helpful answer to your question have a good time to you

Answer:

14

Step-by-step explanation:

Find HCF

Year 7: 70 students

7x5x2=70

Year 8: 98 students

7x7x2=98

HCF: 14

The largest team size she can use is 14 students.

Grade 7: 5 teams

Grade 8: 7 teams

Brainliest please, thanks!

Answer: D

Step-by-step explanation:

Answer:

Answer: It can be written as 1.47x10-³

Step-by-step explanation:

0.00147 = 1.47

1.47 = 1.47 x 10 -^3

Answer:

its the last one.

Step-by-step explanation:

easy way to do inverse functions:

write out equation :

y = 2[tex]x^{2}[/tex] + 2

Switch the x and y:

x = 2[tex]y^{2}[/tex] + 2

Solve for y :

x = 2[tex]y^{2}[/tex] + 2

subtract 2 both sides

x - 2 = 2[tex]y^{2}[/tex]

Divide both sides by 2

[tex]\frac{x}{2}[/tex] - [tex]\frac{2}{2}[/tex] = [tex]y^{2}[/tex]

reduce fraction and square root both sides

Answer:

Step-by-step explanation:

The total number of students is 1800 + 1200 =  3000

The % of boys who did not pass is 100% - 32% = 68%

The number of boys who did not pass is 68/100 * 1800 =       1224

The % of the girls who did not pass is 100%  - 50% = 50%

The number of girls who did not pass was 50/100 * 1200 =    600

The total number who did not pass was                                  1824

The % who did not pass was 1824/3000 * 100 = 60.8%

Answer:

q = 55

Step-by-step explanation:

      [tex]p\ \alpha\ \frac{1}q} \\\\p = k \times \frac{1}{q}\\\\22 = k \times \frac{1}{5}\\\\22 \times 5 = k\\\\k = 110\\\\[/tex]

Find q when p = 2

   [tex]p = k \times \frac{1}{q}\\\\2 = 110 \times \frac{1}{q}\\\\2 \times q = 110\\\\q = \frac{110}{2}\\\\q = 55[/tex]

Answer:

A directly proportionality between x and y is written as:

y = k*x

where k is the constant of proportionality.

Then, if p is directly proportional to (q + p)^2

We can write this as:

p = k*(q + p)^2

Now we know that q = 1 when p = 1

Then we can replace these values in the above equation to find the value of k

1 = k*(1 + 1)^2

1 = k*2^2 = k*4

1/4 = k

Then the equation is:

p = (1/4)(p + q)^2

Now we want to find the value of q when p = 10

So we just replace p by 10, and solve the equation

10 = (1/4)*(q + 10)^2

10*4 = (q + 10)^2

40 = q^2 + 2*q*10 + 10^2

40 = q^2 + 20*q + 100

This is a quadratic equation for q, such that:

q^2 + 20*q + 100 - 40 = 0

q^2 +20*q + 60 = 0

This is the equation that gives the value of q when p = 10

To solve this, we can use Bhaskara's equation, which says that for a quadratic equation:

a*x^2 + b*x + c = 0

The solutions are given by:

[tex]x = \frac{-b \pm \sqrt{b^2 - 4*a*c} }{2*a}[/tex]

In this case, the solutions for q are:

[tex]q = \frac{-20 \pm \sqrt{20^2 - 4*1*60} }{2*1} = \frac{-20 \pm 12.65}{2}[/tex]

Then we have two possible values for q:

q = (-20 + 12.65)/2 = -3.675

q = (-20 - 12.65)/2 = -16.325

Answer:

The volume of cube is 32.7 inches³

Step-by-step explanation:

Given :-

To Find :-

Volume of cube

Formula Used :-

Volume of cube = ( side)³

Solution :-

Using Formula

Volume of cube = ( side) ³

Where,

Calculation being :-

⟼ Volume of cube = ( 3.2 inches) ³

⟼ Volume of cube = 32.768 inches ³

Hence, the volume of cube is 32.768 inches³.

Round nearest hundred = 32.7 inches³.

Answer:

-3/5

Step-by-step explanation:

7 * -3/7 * 1/5

Rewritng

7/7 * -3/5 *1

Simplifying fractions

1 * -3/5 *1

-3/5

Given:

[tex](3^5-5^3+2)[/tex] divided by [tex]4^2[/tex].

To find:

The simplified form of the given expression.

Solution:

We have, [tex](3^5-5^3+2)[/tex] divided by [tex]4^2[/tex]. Mathematically it can be written as:

[tex]\dfrac{3^5-5^3+2}{4^2}=\dfrac{243-125+2}{16}[/tex]

[tex]\dfrac{3^5-5^3+2}{4^2}=\dfrac{120}{16}[/tex]

[tex]\dfrac{3^5-5^3+2}{4^2}=\dfrac{15}{2}[/tex]

[tex]\dfrac{3^5-5^3+2}{4^2}=7.5[/tex]

Therefore, the simplified form of the given expression is 7.5.

Answer:

140°

Step-by-step explanation:

a° = 180°-(75°-35°) = 180°-40° = 140°