The function y = (x - 4)2 + 3 is a transformation of the function y = x?. How is the function's vertex affected by the
transformation?
The vertex of the graph of y = x? is shifted to the left 4 units and down 3 units.
The vertex of the graph of y = x? is shifted to the left 3 units and down 4 units.
The vertex of the graph of y = x is shifted to the right 3 units and up 4 units.
The vertex of the graph of y = x?is shifted to the right 4 units and up 3 units.

In 1 minute, bison runs 3520 feet

In 60 minutes, the bison would run

3520*60 feet

211200 feet per hour.

These are equivalent to;

40 miles per hour since 1 mile is equivalent to 5280 feet.

The bison is faster by 10 miles per hour

Answer:

C

Step-by-step explanation:

Given

f(x) = 3x - 40 and f(x) = 8 , then equate the right sides, that is

3x - 40 = 8 ( add 40 to both sides )

3x = 48 ( divide both sides by 3 )

x = 16 → C

Answer:

25

Step-by-step explanation:

97-72= 25

Hope this helped!

Answer:

25

Step-by-step explanation:

97-72= 25

Answer:

Step-by-step explanation:

a = 1 m 60 cm = 1.6 m

b = 1 m 80 cm = 1.8 m

c = 2 m

perimeter = a + b + c = 1.6 + 1.8 + 2 = 5.4 m = 5 m 40 cm

★ AnsWer :

➨ 540 cm

★ Step by step Explaination :

Let triangle be ABC,

1m = 100 cm

[tex]\begin{lgathered}\bullet\:\:\textsf{AB = 1m 60cm = \textbf{160 cm}}\\\bullet\:\:\textsf{BC = 1m 80cm = \textbf{180 cm}}\\\bullet\:\:\textsf{CA = 2m = \textbf{200 cm}}\end{lgathered}[/tex]

[tex]\setlength{\unitlength}{1.5cm}\begin{picture}(6,8)\linethickness{0.5mm}\qbezier(1,.5)(2,1)(4,2)\qbezier(4,2)(2,3)(2,3)\qbezier(2,3)(2,3)(1,0.5)\put(.7, .3){$C$}\put(4.05, 1.9){$B$}\put(1.7, 2.95){$A$}\put(3.2, 2.5){\sf{160 cm}}\put(0.7,1.7){\sf{200 cm}}\put(2.7, 1.05){\sf{180 cm}}\end{picture}[/tex]

[tex]\rule{130}1[/tex]

[tex]\underline{ \large \purple{ \mathscr{\dag\:A \bf{ccording} \: to \: \mathscr {Q} \bf{uestion} ....}}}[/tex]

[tex]\begin{lgathered}\dashrightarrow\tt\:\: Perimeter_{{\tiny\triangle ABC}}=Sum\:of\:all\:sides\\\\\\\dashrightarrow\tt\:\: Perimeter_{{\tiny\triangle ABC}} = AB + BC + CA\\\\\\\dashrightarrow\tt\:\: Perimeter_{{\tiny\triangle ABC}} = 160 + 180 + 200\\\\\\\dashrightarrow\:\:\underline{\boxed{\tt Perimeter_{{\tiny\triangle ABC}} = 540 \:cm}}\end{lgathered}[/tex]

[tex]\therefore\:\underline{\textsf{Perimeter of triangle ABC is \textbf{540 cm}}}.[/tex]

Answer:

13) The planes ABF and FHG are  perpendicular

14)  Segments Ab and CD are parallel.

Step-by-step explanation:

13)

Planes ABF and FHG are perpendicular (they intersect along side EF)

14)

In order to find out about the segments AB and CD, let's use the formula for the slope that joins any two points [tex](x_1,y_1)\,\,\&\,\,(x_2,y_2)[/tex] on the plane:

[tex]slope=\frac{y_2-y_1}{x_2-x_1}[/tex]

Therefore, given:

A = (-3, 2)

B = (1, 4)

C = (-3, -1)

D = (1, 1)

we have for segment AB the following slope:

[tex]slope_{AB}=\frac{4-2}{1+3} =\frac{2}{4} =\frac{1}{2}[/tex]

and for segment CD the following slope:

[tex]slope_{CD}=\frac{1+1}{1+3} =\frac{2}{4} =\frac{1}{2}[/tex]

Since they show the same slope, these two segments are parallel.

Answer:

First term is [tex]\frac{3}{2}[/tex].

Common difference: -1

Step-by-step explanation:

Given the sequence:

[tex]\frac{3}{2} , \frac{1}{2} , -\frac{1}{2}, -\frac{3}{2}, ...[/tex]

we notice that one term is generated from the previous one by subtracting from it "1". That means that the common difference for this sequence is "-1", and its first term is [tex]\frac{3}{2}[/tex].

Answer:

144

Step-by-step explanation:

Using the rule of radicals

[tex]\sqrt{a}[/tex] × [tex]\sqrt{b}[/tex] ⇔ [tex]\sqrt{ab}[/tex]

Given

4[tex]\sqrt{2}[/tex] × 6[tex]\sqrt{18}[/tex]

= 4 × 6 × [tex]\sqrt{2}[/tex] × [tex]\sqrt{18}[/tex]

= 24 × [tex]\sqrt{36}[/tex]

= 24 × 6

= 144

Step-by-step explanation:

Hey, there!!

You can get your answer simply, just remember the two point formula,

Given, the points are (0,2),(8,8).

We have, Formula for two points is,

[tex](y - y1) = \frac{y2 - y1}{x2 - x1} (x - x1) [/tex]

Put all values here,

[tex](y - 2) = \frac{8 - 2}{8 - 0} (x - 0)[/tex]

[tex](y - 2) = \frac{6}{8} (x -0)[/tex]

[tex](y - 2) = \frac{3}{4} (x - 0)[/tex]

multiply (y-4) by 4 and (x-0) by 3.

[tex](4y - 8) = 3x[/tex]

Bringing 4y and -8 on same side of 3x.

[tex]0 = 3x - 4y + 8[/tex]

[tex]or \: 3x - 4y + 8 = 0[/tex]

Therefore, 3x-4y+8=0..... is the required equation.

Hope it helps..

Answer:

8x+2y+2

Step-by-step explanation:

First, write it out as it's given:

3y+2+3x-y+5x

Then, combine the x-terms first:

3y+2-y+8x

Next, combine the y-terms:

2+2y+8x

Answer:

2(x-5)

Step-by-step explanation:

the number will be ''x''

difference between the number (x) and 5 =

                 x-5

twice the difference is =

            2(x-5)

Hey there! I'm happy to help!

QUESTION 100

Here, we are looking for the number of permutations. A permutation is the number of possible arrangements you can make from a given set of things (order matters). If you have 6 kids standing in alphabetical order in line, that is one permutation. If you do reverse alphabetical order, that is a different permutation.

We are asked to find the number of permutations using the given format:

[tex]_{n}P_{r}\\[/tex]

This is simply a representation of what we want to find. The P means we are looking for the number of permutations. The n is the total number of objects in the set (for example, if there were 26 kids we could choose from to make this 6 person line, n would be 26). The r is the number of things chosen from the set (in our line example, the r would be six because we are choosing 6 kids).

The formula for finding the number of permutations is [tex]\frac{n!}{(n-r)!}[/tex]. The ! is factorial, it means you multiply that number by every integer counting backwards towards 1. 6! is 6×5×4×3×2×1. There is an option to do this on your calculator, though.

Let's solve this problem.

[tex]_{5}P_{4}=\frac{5!}{(5-4)!}= \frac{120}{1} =120[/tex]

This means that there are 120 permutations.

QUESTION 101

Now we have a C. This is similar to permutations but with combinations order does not matter. With our line example, having the same six kids in alphabetical order is a different permutation than having it in backwards alphabetical order. With combinations, if you have those specific six kids, it is just one combination; the order does not matter.

The formula for combinations is [tex]\frac {n!}{r!(n-r)!}[/tex]. Let's plug in our numbers and solve for this.

[tex]_{8}C_{2}=\frac{8!}{2!(8-2)!} =\frac{8!}{2!(6!)}=\frac{40320}{1440} =28[/tex]

QUESTION 102

Quick note: 0! is equal to 1. I don't really know why but there's probably proof somewhere.

[tex]_{7}C_{0}=\frac{7!}{0!(7-0)!} =\frac{7!}{7!} =1[/tex]

And I believe you already have Question 103 figured out.

4!=4×3×2×1=24

Have a wonderful day! :D

Answer: a piecewise function is a function that is defined on a sequence of intervals.

Step-by-step explanation:

A piecewise function is a function that is "different" at different intervals.

The function may behave linearly between x = 0 and x = 10, and after that point, the function may be constant for a while, then change again.

This type of functions can be written as:

f(x) = g(x) if x1 ≤ x ≤ x2

f(x) = h(x) if x2 ≤ x ≤ x3

f(x) = k(x) if x3 ≤ x ≤ x4

and so on, where g(x), h(x) and k(x) are different functions, and those functions only act on the givenintervals: (x1, x2), (x2, x3) and (x3, x4)

Answer:

m=5/6

Step-by-step explanation:

arrange all the "m's" at the left side and the numbers at the right side doing that we get

m-m+m=1-2/3+1/2

m=5/6

Answer:

B The graph of g(x) is the graph of f(x) shifted to the right 6 unit

Relation between the graph of g(x) and f(x) is option (B) The graph of g(x) is the graph of f(x) shifted to right 6 units

Function, in mathematics, an expression, rule, or law that defines a relationship between one variable (the independent variable) and another variable (the dependent variable).

Given,

[tex]f(x) =10^{x}[/tex]

[tex]g(x)=f(x-6)=10^{(x-6)}[/tex]

f(x)  shift right 6 units to get f(x-6)

Given that

g(x) = f(x-6)

Therefore graph of g(x) is the graph of f(x) shifted to the right 6 units

Hence, Relation between the graph of g(x) and f(x) is option (B) The graph of g(x) is the graph of f(x) shifted to right 6 units

Learn more about Function here

https://brainly.com/question/12431044

#SPJ2

Answer:

x = 80.4

Step-by-step explanation:

Step 1: Realize you have to use tangent to solve

[tex]tan()=\frac{o}{a}[/tex]

Step 2: Use tangent to solve

o = x

a = 300

[tex]tan()=\frac{o}{a} \\tan(15)=\frac{x}{300}\\x = 300tan(15)\\x = 80.4[/tex]

Therefore x is equal to 80.4 rounded to the nearest tenth

Answer:

Step-by-step explanation:

[tex]Opposite = x\\Adjacent = 300\\\alpha =15\\Using \: SOHCAHTOA\\\\Tan \alpha = \frac{Opposite}{Adjacent} \\\\Tan 15 =\frac{x}{300} \\\\2-\sqrt{3} = \frac{x}{300}\\\\ 2-\sqrt{3} \times 300=x\\\\80.384=x\\\\x = 80.4[/tex]

Answer:

[tex]\frac{1}{6}\\[/tex]

Step-by-step explanation:

To find the probability, divide the number of desired outcomes by the total:

This will be 3/18, since there are 3 convertibles and there are 18 total cars

Simplify 3/18

= [tex]\frac{1}{6}[/tex]

Answer:

-4x+26

Step-by-step explanation:

Answer:

[tex] \boxed{ \bold{ { \boxed{ \sf{8 {x}^{3} - {x}^{2} - 4x + 4}}}}}[/tex]

Step-by-step explanation:

[tex] \sf{(8 {x}^{3} - 3 {x}^{2} + x) + (2 {x}^{2} - 5x + 4)}[/tex]

When there is a ( + ) in front of an expression in parentheses , no need to change the sign of each term. That means , The expression remains the same. Also , remove the unnecessary parentheses

⇒[tex] \sf{8 {x}^{3} - 3 {x}^{2} + x + 2 {x}^{2} - 5x + 4}[/tex]

Collect like terms

⇒[tex] \sf{8 {x}^{3} - 3 {x}^{2} + 2 {x}^{2} - 5x + x + 4}[/tex]

⇒[tex] \sf{8 {x}^{3} - {x}^{2} - 4x + 4}[/tex]

Hope I helped!

Best regards!!

Answer:

the second one

Step-by-step explanation:

Answer:

length: 30 meters

width: 12 meters

Step-by-step explanation:

2(a+b) = 84

a = 2b + 6

a = length

b = width

then:

2((2b+6)+b) = 84

2b + 6 + b = 84/2

3b + 6 = 42

3b = 42 - 6

3b = 36

b = 36/3

b = 12

a = 2b + 6

a = 2*12 + 6

a = 24 + 6

a = 30

Check:

84 = 2(12+30)

84 = 2*42

Answer:

If a = B and b = C, then

a = C

Answer:

opens UP and has a minimum value.

Step-by-step explanation:

The given quadratic function opens UP (the branches of the associated parabola open up) because the coefficient that accompanies the leading term (leading coefficient) is positive.

Since the graph is a parabola with arms pointing up, the graph should have a minimum located at the vertex of the parabola.

Answer:

Step-by-step explanation:

Given the exponential growth formula expressed as [tex]P = Ae^{kt}[/tex] where P is the countrys population and t is the time.

Initially in 1991, at t= 0, P = 147 million

[tex]P = Ae^{kt}\\147 = Ae^{k(0)}\\147 = Ae^0\\147 = A(1)\\A = 147[/tex]

If by 1998 it was 153 million, this means that the population is 153 million 7 years later i.e when t = 7, P = 153. On substituting into the formula to get the constant 'k';

[tex]P = Ae^{kt}\\153 = 147e^{k(7)}\\153 = 147e^{7k}\\153/147 = e^{7k}\\e^{7k} = 1.041\\Taking \ ln \ of \ both \ sides\\lne^{7k} = ln 1.041\\7k = 0.04018\\k = 0.04018/7\\k = 0.00574[/tex]

To estimate the population in 2017, to number of years from 1991 to 2017 is 26 years. Hence we are to find the value of P given t = 27, A = 147 and k = 0.00574

[tex]P = Ae^{kt}\\P = 147e^{0.00574*26}\\P = 147e^0.14924\\P = 147*1.16095\\P = 170.659[/tex]

Hence the population in 2017 using exponential growth formula to the nearest million is 171 million.

Answer:

  yes

Step-by-step explanation:

Every polynomial has "all real numbers" in its domain. 5 is a real number, so is in the domain of f(x).

Answer:

Your value expression is 10

Step-by-step explanation:

We know that [tex]1\frac{1}{2}=\frac{3}{2}=1.5[/tex]

The value experssion:

Giving: [tex]\frac{9.5-3(1\frac{1}{2}) }{0.5}[/tex]

Change [tex]1\frac{1}{2}[/tex] into a whole number:  [tex]\frac{9.5-3(1.5)}{0.5}[/tex]

Multiply 3 into 1.5: [tex]\frac{9.5-4.5}{0.5}[/tex]

Divide: [tex]\frac{5}{0.5}[/tex]

Your answer equals: 10

Answer:

A

Step-by-step explanation:

We would like to find the value of x.

Since the triangle is isosceles, the drawn altitude bisects the base of length 8. This means that the big triangle is split into two congruent triangles with base 4 and height 5.

Notice that by definition, as well, the altitude of 5 is perpendicular to the base of length 8. So, we have two right triangles, each with legs of 4 and 5 and hypotenuse x.

We apply the Pythagorean Theorem, which states that for a right triangle with legs a and b and hypotenuse c:

a² + b² = c²

Here, we have:

4² + 5² = x²

16 + 25 = x²

41 = x²

x = √41

The answer is thus A.

~ an aesthetics lover

Answer:

B

Step-by-step explanation:

Answer:

6 1/4 cup of soda for one cup of pineapple

Step-by-step explanation:

2/ 5 of pineapple for every 2 1/2 cups of soda

1 cup of pine apple         ??

(2 1/2)/(2/5)

5/2 ÷2/5    ( when divide fraction,change ÷ to × and flip the fraction (reciprocal)

5/2×5/2=25/4   or  6 1/4

Answer:

Step-by-step explanation:

f(x) = 7x - 4

g(x) = -3x + 2

To find (f+g)(x) add g(x) to f(x)

That's

We have the final answer as

Hope this helps you

Answer:

[tex]\Large \boxed{(f + g)(x) = 4x - 2}[/tex]

Step-by-step explanation:

We have two functions.

f(x) = 7x - 4

g(x) = -3x + 2

To find (f+g)(x), we have to find the sum of f(x) and g(x).

(f+g)(x) = f(x) + g(x)

(f + g)(x) = 7x - 4 + -3x + 2

Combining like terms.

(f+g)(x) = 7x - 3x - 4 + 2

(f + g)(x) = 4x - 2

Answer:

8 feet

Step-by-step explanation:

Distance can be explained as the way to measure how far a thing or something is apart from each other numerically, it shows how close or far apart between two point

From the question, we are given two point

Point1= 12 feet

Point 2= 4 feet

Then Distance between the two point= 12feet-4feet

= 8feet

Hence the distance= 8 feet