Question 2 of 10
If you apply the changes below to the quadratic parent function, f(x) = x2,
what is the equation of the new function?
• Shift 1 unit left.
• Vertically stretch by a factor of 3.
• Reflect over the x-axis.
A. g(x) = -3(x-1)2
B. g(x) = -3(x + 1)2
C. g(x) = (-3x+1)
D. g(x) = -3x2 - 1

[tex]\huge\color{purple}\boxed{\colorbox{black}{♡Solution}}[/tex]

8.

[tex]7 {x}^{3} + 3 {x}^{2} + 4x + 10 - 10 - 8x - 3 {x}^{3} \\ = 7 {x}^{3} - 3 {x}^{3} + 3 {x}^{2} + 4x - 8x + 10 - 10 \\ = 4 {x}^{3} + 3 {x}^{2}- 4x[/tex]

9.

[tex]5 {x}^{4} - 4 {x}^{3} - 3x - 4 - 2x + 6 {x}^{3} + 2 {x}^{4} \\ = 5 {x}^{4} + 2 {x}^{4} - 4 {x}^{3} + 6 {x}^{3} - 3x - 2x - 4 \\ = 7 {x}^{4} + 2 {x}^{3} - 5x - 4[/tex]

10.

[tex]7 {x}^{3} - 9 {x}^{2} - 7x - 8 - 8 + 4 {x}^{2} + 6 {x}^{3} \\ = 7 {x}^{3} + 6 {x}^{3} - 9 {x}^{2} + 4 {x}^{2} - 7x - 8 - 8 \\ = 13 {x}^{3} - 5 {x}^{2} - 7x - 16[/tex]

11.

[tex]4a + 20 - 5 {a}^{2} + 20a - 35 \\ = - 5 {a}^{2} + 24a - 15[/tex]

12.

[tex]8y + 48 - 6 {y}^{2} + 36y - 24 \\ = - 6 {y}^{2} + 44y + 24 \\ = 2( - 3 {y}^{2} + 22y + 12)[/tex]

13.

[tex]3c - 12 - 5 {c}^{2} - 20c + 40 \\ = - 5 {c}^{2} - 17c + 28[/tex]

[tex]\large\mathfrak{{\pmb{\underline{\orange{Mystique }}{\orange{♡}}}}}[/tex]

Answer:

y=3/4x + 10

Step-by-step explanation:

First, lets put this into Point-Slope form: y-4 = 3/4(x+8)

Now, lets modify the equation in our favor, getting the "y" alone on the left hand side:  y-4 = 3/4(x+8)

                     +4                   +4

-----------------------------------------------

                  y=3/4(x+8)+4

Now, lets simplify....

                  y=3/4x + 6 + 4 = y = 3/4x+10

And we are done!

Answer:

5.83 ft

Step-by-step explanation:

Pythagorean Theorem:

a² + b² = c²

3² + 5² = c²

9 + 25 = c²

34 = c²

c ≈ 5.8309 ≈ 5.83

If my answer is incorrect, pls correct me!

If you like my answer and explanation, mark me as brainliest!

-Chetan K

Answer:

11.2square feet

Step-by-step explanation:

Area of a sector = theta/360 * πr²

theta is the central angle = 80degrees

radius r = PC = 4ft

Substitute

Area of the sector = 80/360 * 3.14 * 4²

Area of the sector = 80/360 * 3.14 * 16

Area of the sector = 4,019.2/360

Area of the sector = 11.2ft²

Hence tthe area of the blue sector is 11.2square feet

Answer:

B and E

Step-by-step explanation:

3^-8/3^-4 = 1/81 or .01234567...

I suggest that if you're having difficulty with a question like this again you go through all the answers individually so you can see what they equal! This method can really help in tests or where you can't get help.

3^-12 = 1/531441 <- not the answer

3^-4 = 1/81 <- answer!

3^2 = 9

1/3^2 = 1/9

1/3^4 = 1/81

1/3^12 = 1/531441

its also good to remember

3^-8/3^-4 would mean -8+4 = 3^-4 which would help you get your first answer.

Hope this helps!

[tex]B. \: {3}^{ - 4} \:✅\\ \\ E. \: \: \frac{1}{ {3}^{4} }\:✅ [/tex]

Step-by-step explanation:

[tex] \frac{ {3}^{ - 8} }{ {3}^{ - 4} } \\ \\ we \: know \: that \: \: \: \frac{ {a}^{m} }{ {a}^{n} } \: = \: {a}^{m - n} \\ \\= {3}^{ - 8 - ( - 4)} \\ \\ = {3}^{ - 8 + 4} \: ( \: ∵\: - \times - = + ) \\ \\ = {3}^{ - 4} \\ \\ ( \: or \: ) \\ \\= \frac{1}{ {3}^{4} } \\ \\( \: ∵\: {a}^{ - m} = \frac{1}{ {a}^{m} } \: ) \\\: [/tex]

[tex]\large\mathfrak{{\pmb{\underline{\orange{Happy\:learning }}{\orange{!}}}}}[/tex]

Answer:

Price = 20, Amount = 14

Step-by-step explanation:

A = Amount of Mangoes

P = Price for 1 Mango

P = A + 6

280 = P * A

insert A+6 for P

280 = (A+6) * A

280 = 6A + A²

280=1*a^2+6*a  | Vertausche beide Seiten der Gleichung.

1*a^2+6*a=280  | quadratische Ergänzung: ergänze auf beiden Seiten (3)^2

1*a^2+6*a+(3)^2=3^2+280  | Rechne 3 hoch 2 aus.

1*a^2+6*a+(3)^2=9+280  | addiere 9 und 280

1*a^2+6*a+(3)^2=9+280  | Fasse die rechte Seite mit Hilfe der binomischen Formel zusammen.

1*(1*a+(3))^2=289  | Auf beiden Seiten Quadratwurzel ziehen.

1*a+(3)=+-*289^0.5  

1*a_1+(3)=289^0.5  

1*a_1+3=289^0.5  | Ziehe die Wurzel aus 289

1*a_1+3=17  | -3

1*a_1=14  

The total number of mangoes bought by Kumar are 14.

"An equation is a mathematical statement with an 'equal to' symbol between two expressions that have equal values is called mathematical equation. For example, 3x + 5 = 15. There are different types of equations like linear, quadratic, cubic, etc."

We have,

Total amount for mangoes(P) =  280

Price of one mango is equal to 6 more than the total number of mangoes (A) i.e., P = A+6

By using mathematical equation from the question

P×A = 280.....(1)

Substitute P = A+6 in equation (1)

⇒ (A+6) × A = 280

⇒[tex]A^{2}+6A =280[/tex]

Add [tex]3^{2}[/tex] on both sides of above equation

⇒[tex]A^{2}+6A+3^{2} = 280+3^{2}[/tex]

⇒[tex]A^{2}+2.(1)(3A)+3^{2} =289[/tex]          (∵ [tex](a+b)^{2} = a^{2}+2ab+b^{2}[/tex])

⇒[tex](A+3)^{2} =289[/tex]

⇒[tex]A+3 = \sqrt{289}[/tex]

⇒[tex]A=17-3[/tex]

⇒[tex]A=14[/tex]

Hence, The total number of mangoes bought by Kumar are 14.

Learn more about mathematical equation here

https://brainly.com/question/15389595

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Answer:

THREE AND SIX OR FOUR AND FIVE

Step-by-step explanation:

They're just opposite ends !

Step-by-step explanation:

Alternate Interior Angles: 3 and 6

Alternate Exterior Angles: 2 and 7

Answer:

4.50

Step-by-step explanation:

[tex] \sin(40) \times 7 = 4.499513268[/tex]

round it up

[tex] = 4.50[/tex]

Answer:

y = -0.2(x) + 3

Step-by-step explanation:

One way to find an equation for a line is to find two points and go from there. To find the second point, we can note that the y intercept means when x=0. In the line y=3, y is always 3, so when x=0, y = 3.

Our two points are then (5, 2) and (0,3)

To find the slope, we can use

[tex]\frac{y_2 - y_1}{x_2-x_1} = \frac{3-2}{0-5} \\= \frac{1}{-5} \\= -0.2[/tex]

Using the formula y = mx + b and the slope m = -0.2, plugging into (5, 2) and solving for b, we get

2 = -0.2 (5)  +b

2 = -1 + b

add 1 to both sides to isolate the b

b = 3

Our formula is thus

y = -0.2(x) + 3

Answer:

[tex]y=-2x+2[/tex]

Step-by-step explanation:

[tex]y=mx+b[/tex] is the slope intercept

[tex]m[/tex] is the slope

[tex]b[/tex] is the y-intercept

The slope in the graph is 4/2 or 2 simplified. From point (-2,6), you have to go down 4 and right 2 to get to the point (0,2)

The y-intercept is 2 because the line crosses the y axis at exactly 2.

Hope this helps

Answer:

A general sinusoidal equation is:

y = A*sin(w*x + p) + M

where:

A is the amplitude

w is the angular frequency

p is the phase shift

M is the midline.

Now, we know that:

Amplitude must be 6, so A = 6

period is 2*pi/3

Remember that the frequency is the inverse of the period, then:

f = 1/T

f = 1/(2*pi/3) = 3/(2*pi)

And the angular frequency is 2*pi times the normal frequency, then:

w = 2*pi*f = 2*pi*(3/2*pi) = 3

w = 3

Here we not have information about the midline, so M = 0.

And we know that the phase shift is one unit to the left.

Remember horizontal translations:

for a function f(x), an horizontal translation of N units is written as:

g(x) = f(x + N)

if N > 0, then the translation is to the left

if N < 0 , then the translation is to the right,

Here we know that the phase shift is to the left, so p must be positive, and we know that the shift is 1 unit to the left, then:

p = +1

Replacing these in the equation we get:

y = 6*sin(3*x + 1) + 0

y = 6*sin(3*x + 1)

Answer:

I want to help but I don't understand the question. Can you plz send a picture of the question

Answer:

85%

Step-by-step explanation:

(40 - 6)/40 * 100%

34/40 * 100%

85%

hola quien habla español bueno ya no Adios :)

Answer:

C.(B and D

Step-by-step explanation:

Answer:

Ok so the probability  would be 16%(can be round to)

Step-by-step explanation:

Answer:

Rida is 10 years old and her father is 40 years old.

Step-by-step explanation:

Given:

Present age

Present age of Rida = x

Present age of Rida's father = 4x

Age after 5 years

Age of Radi after 5 years = x + 5

Age of Radi's father after 5 years = 3(x + 5)

What To Find:

The present age of Rida and Rida's father.

Solution:

According to the statement the equation will be,

⇒ 4x + 5 = 3(x + 5)

Remove and solve the brackets,

⇒ 4x + 5 = 3x + 15

Take numbers to RHS and variable to LHS,

⇒ 4x - 3x = 15 - 5

Subtract 3x from 4x and 5 from 15,

⇒ x = 10

Now substitute the values of Rida's age and Rida's father's age,

Rida's age = x = 10 years

Rida's father's age = 4x = 4(10) = 40 years

Answer:

15.6

Step-by-step explanation:

We see a dilation. So the ratio between UT and XW is 2:7.8. That is 1:3.9. If we put 4 in the 1 place, then we get 15.6

Please give brainliest

Hope this helped

Answer:

The answer is negative, the one you chose in the picture.

Step-by-step explanation:

Positive slope would be going upwards.

Negative slope would be going downwards.

Slopes that are zero would be horizontal.

Slopes that are undefined would be vertical.

So, the reason why the slope is negative is that the line is going downhill.

Hope this is helpful

Given:

The expressions are:

[tex]2x(x^2-6x+3)[/tex]

[tex]2a^2(5b^2+3ab+6a+1)[/tex]

To find:

The product of each expression.

Solution:

According to the distributive property of multiplication over addition, we get

[tex]a(b+c)=ab+ac[/tex]

The first expression is:

[tex]2x(x^2-6x+3)[/tex]

Using distributive property of multiplication over addition, we get

[tex]2x(x^2-6x+3)=(2x)(x^2)+(2x)(-6x)+(2x)(3)[/tex]

[tex]2x(x^2-6x+3)=2x^3-12x^2+6x[/tex]

Therefore, the product of [tex]2x(x^2-6x+3)[/tex] is [tex]2x^3-12x^2+6x[/tex].

The second expression is:

[tex]2a^2(5b^2+3ab+6a+1)[/tex]

Using distributive property of multiplication over addition, we get

[tex]2a^2(5b^2+3ab+6a+1)=(2a^2)(5b^2)+(2a^2)(3ab)+(2a^2)(6a)+(2a^2)(1)[/tex]

[tex]2a^2(5b^2+3ab+6a+1)=10a^2b^2+6a^3b+12a^3+2a^2[/tex]

Therefore, the product of [tex]2a^2(5b^2+3ab+6a+1)[/tex] is [tex]10a^2b^2+6a^3b+12a^3+2a^2[/tex].

Answer:

6:

[tex] {x}^{2} - 2x - 3 \\ = (x - 3)(x + 1) \\ when \: y = 2 \\ x = 1 \\ vertex \: is \: (1, \: 2)[/tex]

7:

[tex] {x}^{2} = - 625 \\ x = \sqrt{ - 625} \\ x = \sqrt{625} \times \sqrt{ - 1} \\ x = 25 \times \sqrt{ {i}^{2} } \\ x = 25 \times i \\ x = 25i[/tex]

Answer:

a^2 + b^2 = c^2

6^2 + 6^2 = c^2

36 + 36 = c^2

c^2 = 72

c = [tex]\sqrt{72}[/tex]

c=3[tex]\sqrt{8}[/tex]

c=8.485281374

Step-by-step explanation:

Answer:

4th option 0,5,10,15

Step-by-step explanation:

Let's check if the first choice is geometric.

2*3 = 6. is 6*3 = 18, yes! is  18*3 = 54. Yep! its geometric

the second option multiplies by -2, it is geometric

the third option multiplies by 1/5, it is geometric

The fourth option does not multiply by anything common, it is Not geometric

Answer:

0,5,10,15 is not the sequence of geometric.

Generally, to check whether a given sequence is geometric, one simply checks whether successive entries in the sequence all have the same ratio. The common ratio of a geometric series may be negative, resulting in an alternating sequence.

Step-by-step explanation:

This is totally correct!

Answer:

452.4 mi^2

Step-by-step explanation:

area of circle=πr^2

=22/7*(12)^2

=3.142*144

=452.448

=452.4 mi^2

Answer:

C)    452.4 mi²

Step-by-step explanation:

a = πr²

a = π * 12²

a = π * 144

a = 452.3893421169

a = 452.4

Answer:

80°

because its diagnol so the one in the top corner is the same as x

Answer:

x = 140°

Step-by-step explanation:

Sum of exterior angles of polygon is 360°

That is, x + 70 + 80 + 70 = 360

           x + 220 = 360

           x = 360 - 220 = 140°

y = -19

I started by adding 18 to both sides(inverse operation) then dividing by -2 to isolate the variable. What you do to one side must be done to the other

Answer:

[tex]p(x) = k(x -1)^{3} * (x -4)^{2} * (x +3)[/tex] --- General polynomial

The degree is 6

[tex]p(x) = -\frac{1}{3}(x -1)^{3} * (x -4)^{2} * (x +3)[/tex] --- The polynomial precisely

Step-by-step explanation:

Given

[tex](a,b,c)= (1,4,-3)[/tex] --- zeros

[tex](m_1,m_2,m_3) =(3,2,1)[/tex] --- multiplicities

Solving (a): The polynomial

The polynomial is represented as:

[tex]p(x) = (x -a)^{m_1} * (x -b)^{m_2} * (x -c)^{m_3}[/tex]

So, we have:

[tex]p(x) = (x -1)^{3} * (x -4)^{2} * (x +3)^{1}[/tex]

[tex]p(x) = (x -1)^{3} * (x -4)^{2} * (x +3)[/tex]

Include constant k; So, the polynomial becomes

[tex]p(x) = k(x -1)^{3} * (x -4)^{2} * (x +3)[/tex]

Solving (b): The degree (d)

To do this, add up the multiplicities

[tex]d = m_1 +m_2 +m_3[/tex]

[tex]d = 3+2+1[/tex]

[tex]d = 6[/tex]

The degree is 6

Solving (c): The actual polynomial

In (a), we have:

[tex]p(x) = k(x -1)^{3} * (x -4)^{2} * (x +3)[/tex]

[tex]p(0)=16[/tex] means:

[tex](x,p(x)) = (0,16)[/tex]

This gives:

[tex]16 = k(0 -1)^{3} * (0 -4)^{2} * (0 +3)[/tex]

[tex]16 = k(-1)^{3} * (-4)^{2} * (3)[/tex]

[tex]16 = k*-48[/tex]

Solve for k

[tex]k = \frac{16}{-48}[/tex]

[tex]k = -\frac{1}{3}[/tex]

So:

[tex]p(x) = k(x -1)^{3} * (x -4)^{2} * (x +3)[/tex]

[tex]p(x) = -\frac{1}{3}(x -1)^{3} * (x -4)^{2} * (x +3)[/tex]

Answer:

14.286% increase

Step-by-step explanation:

Since the admission to the amusement park increased by $10 we need to find what percentage of $70 equals $10.

We can find this percentage by multiplying 10 (the difference in money) by 100 (a hundred percent), and dividing that by 70 (the initial cost)

[tex]10*100/70=14.286[/tex]