If you horizontally stretch the quadratic parent function, f(x)= x^2, by a factor of 4, what is the equation of the new function

Step-by-step explanation:

You need to remember that

[tex] log( \frac{a}{b} ) = log(a) - log(b) [/tex]

and

[tex] log(ab) = log(a) + log(b) [/tex]

then the solution is

[tex] log( \frac{r}{st} ) = log(r) - log(st) \\ = log(r) - ( log(s) + log(t) ) \\ = log(r) - log(s) - log(t) [/tex]

Answer: Whats the whole question?

Step-by-step explanation:

Answer:

a,b,d,f

Step-by-step explanation:

If the diameter of a circle is 50 yards the radius must be 25 yards.

This is because the radius is always half the diameter of the circle. Since we know the diameter is 50 yards, half of 50 is 25 so the radius must be 25 yards.

Have a great day!

The radius of the circle is 25 yards.

A circle is a round shaped figure which has all its points in one plane and the distance between all the points on its circumference to the center of the circle is equal .

It is given that

Diameter of a circle is 50 yards.

Radius of a circle =  Diameter of circle / 2

Radius of the circle = 50/2 = 25 yards

Therefore the radius of the circle is 25 yards.

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Answer:

log x

Step-by-step explanation:

Using the rule of logarithms

• log [tex]x^{n}[/tex] ⇔ n log x

Hence

log [tex]x^{4}[/tex] - log x³

= 4 log x - 3 log x

=log x

The value of logx⁴ - logx³ will be logx.

The exponent indicates the power to which a base number is raised to produce a given number called a logarithm.

In another word, a logarithm is a different way to denote any number.

If you want to write 1 in logarithm then it will be log(base).

The first method →

Given,

⇒ logx⁴ - logx³

By log property that loga7 = 7loga

⇒ 4logx - 3 logx

⇒ logx

The second method →

This question can also be solved by another log property that

logm - logn = log(m/n)

Since given,

logx⁴ - logx³ = log(x⁴/x³) = logx

Hence, The value of logx⁴ - logx³ will be logx.

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Step-by-step explanation:

2 * (x + 1) = 8   | :2

x + 1 = 4   | -1

x = 3

Answer:

x = 3

Step-by-step explanation:

2 ( x + 1 ) = 8

⇒ Expand brackets

2 x + 2 = 8

⇒ Minus 2 from both sides

2 x = 6

⇒ Divide by 2 from both sides to isolate x

x = 3

To find the measure of ∠ONK in rectangle MPKN with given conditions, it's determined through the congruency of triangles and properties of a rectangle that ∠ONK is 72°.

The question involves finding the measure of ∠ONK in rectangle MPKN, where the diagonals intersect at point O, and a line segment OA is an altitude of triangle MOP with m∠AOP = 18°. Given the properties of a rectangle, we know that its diagonals bisect each other and are equal in length. Therefore, triangles MOP and NOP are congruent.

Because OA is the altitude to hypotenuse MP of triangle MOP, it creates two right triangles, OAM and OAP. The angle ∠AOP is given as 18°, which means ∠MOA = 90° - 18° = 72° since triangle OAM is a right-angled triangle. Because the diagonals of the rectangle bisect each other at O, triangle ONP is congruent to triangle OMP, and hence ∠ONK (which is also ∠ONP) is equal to 72° as angle ∠ONP is supplementary to ∠MOA in rectangle MPKN.

ANSWER

Option D

EXPLANATION

The given function is

[tex]y = \sqrt{16x - 32} - 3[/tex]

We factor 16 under the radical.

[tex]y = \sqrt{16(x - 2)} - 3[/tex]

[tex]y = \sqrt{16} \times \sqrt{(x - 2)} - 3[/tex]

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

This is the graph of

[tex]y = 4\sqrt{x } [/tex]

translated 2 units right and 3 units down.

The last option is the correct choice.

Answer:

Step-by-step explanation:

[tex]4y^2-37=27\qquad\text{add 37 to both sides}\\\\4y^2=64\qquad\text{divide both sides by 4}\\\\y^2=16\to y=\pm\sqrt{16}\\\\y=-4\ or\ y=4[/tex]

To solve for 'y' in the equation 4y^2 - 37 = 27, you isolate y^2, take the positive square root, and find that the positive value of y is y = 4.

To find the positive value of 'y' from the equation 4y^2 - 37 = 27, we first need to isolate y. Starting with 4y^2 - 37 = 27, add 37 to both sides to get 4y^2 = 64. Divide both sides by 4 to isolate y^2, leading to y^2 = 16. Finally, take the square root of both sides. Remember that the square root of a number gives both positive and negative solutions. However, because the question asks for the positive value, we ignore the negative root. Thus, the positive value of y is y = 4.

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ANSWER

D. x=55

EXPLANATION

The given radical equation is

[tex] \sqrt{x - 6} + 3 = 10[/tex]

Add -3 to both sides

[tex] \sqrt{x - 6} = 10 - 3[/tex]

[tex] \sqrt{x - 6} =7[/tex]

Square both sides.

[tex] { (\sqrt{x - 6})}^{2} = {7}^{2} [/tex]

[tex]x - 6 = 49[/tex]

Solve for x to get:

[tex]x = 49 + 6 = 55[/tex]

Answer:

Step-by-step explanation:

10 contain both chocolate and caramel

There are 18 candies.

3 don't contain either chocolate or caramel

12 contain chocolate.

There are 18 - 12 - 3 that are not accounted for. So we have 3 that are not mentioned. Those 3 must contain just caramel.

So it should be filled out like this

contain caramel      Do not contain Caramel

         10                          2

          3                           3

Answer:

Statements that are true with out any given proof

Step-by-step explanation:

There is no information needed for you to get your answer

Answer:

Statements that are true with out any given proof

Step-by-step explanation:

its basicly the def of it

Answer: The answer is 15 * 14

Step-by-step explanation:

You start with 15 people to choose from to select a president, so you have 15. After removing one person 15-1,=14 you have fourteen people to choose from, to select a vice president. This gives you 15*14.

The expression that can be used to represent the number of ways that a president and a vice-president can be chosen out of a group of 15 people is 15×14 or ¹⁵P₂.

Permutation helps us to know the number of ways an object can be arranged in a particular manner. A permutation is denoted by 'P'.

[tex]^nP_r = \dfrac{n!}{(n-r)!}[/tex]

where,

n is the number of choices available,

r is the choices to be made.

The number of people that are available for the post of the president is 15, while the number of people that are available for the post of vice-president after the president is selected is 14. Therefore,

Number of ways in which president and vice-president can be selected

= ¹⁵P₂

= 15 × 14

Hence, the expression that can be used to represent the number of ways that a president and a vice-president can be chosen out of a group of 15 people is 15×14 or ¹⁵P₂.

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Answer:

C, [tex]4e^{i(7\pi/4)}[/tex]

Step-by-step explanation:

To remind you, Euler's formula gives a link between trigonometric and exponential functions in a very profound way:

[tex]e^{ix}=\cos{x}+i\sin{x}[/tex]

Given the complex number [tex]2\sqrt{2}-2i\sqrt{2}[/tex], we want to try to get it in the same form as the right side of Euler's formula. As things are, though, we're unable to, and the reason for that has to do with the fact that both the sine and cosine functions are bound between the values 1 and -1, and 2√2 and -2√2 both lie outside that range.

One thing we could try would be to factor out a 2 to reduce both of those terms, giving us the expression [tex]2(\sqrt{2}-i\sqrt{2})[/tex]

Still no good. √2 and -√2 are still greater than 1 and less than -1 respectively, so we'll have to reduce them a little more. With some clever thinking, you could factor out another 2, giving us the expression [tex]4\left(\frac{\sqrt{2}}{2} -i\frac{\sqrt{2}}{2}\right)[/tex] , and now we have something to work with.

Looking back at Euler's formula [tex]e^{ix}=\cos{x}+i\sin{x}[/tex], we can map our expression inside the parentheses to the one on the right side of the formula, giving us [tex]\cos{x}=\frac{\sqrt2}{2}[/tex] and [tex]\sin{x}=-\frac{\sqrt2}{2}[/tex], or equivalently:

[tex]\cos^{-1}{\frac{\sqrt2}{2} }=\sin^{-1}-\frac{\sqrt2}{2} =x[/tex]

At this point, we can look at the unit circle (attached) to see the angle satisfying these two values for sine and cosine is 7π/4, so [tex]x=\frac{7\pi}{4}[/tex], and we can finally replace our expression in parentheses with its exponential equivalent:

[tex]4\left(\frac{\sqrt2}{2}-i\frac{\sqrt2}{2}\right)=4e^{i(7\pi/4)}[/tex]

Which is c on the multiple choice section.

Answer: V=7.605π

Step-by-step explanation:

The cylinder formula is V=πr^2h

Substitute the values into the equation.

V=π(1.3)^2(4.5)

V=π(1.69)(4.5)

V=7.605π

Hope this helps!

Answer:

9.5%

Step-by-step explanation:

Buying price of the part= $ 8.75

Selling price of the part= $ 9.98

sale tax= $0.40

Selling price before sale tax= $9.98-$ 0.40 = $ 9.58

Make-up amount charged= $9.58- $8.75 = $ 0.83

As a percentage= (0.83/ 8.75) ×100

=9.5%

Answer:

The correct option is C.

Step-by-step explanation:

If a line passing through two point then the equation of line is

[tex]y-y_1=\frac{y_2-y_1}{x_2-x_1}(x-x_1)[/tex]

From the given graph it is clear that the line of best fit passing through the points (0,0) and (14,45). So, the equation of line of best fit is

[tex]y-0=\frac{45-0}{14-0}(x-0)[/tex]

[tex]y=\frac{45}{14}x[/tex]

The equation of line of best fit is [tex]y=\frac{45}{14}x[/tex], therefore the correct option is C.

To subtract the given expressions, first, simplify each expression separately by combining like terms. Then subtract the second expression from the first expression by distributing a negative sign and adding it to the first expression.

To subtract the given expressions, (2x^3+7x^2-4) - (2x^2+4x-10), we need to simplify each expression separately and then subtract them. First, combine like terms within each expression. Then, subtract the terms of the second expression from the first expression. This can be done by distributing a negative sign to each term in the second expression and then adding it to the first expression.

So, (2x^3+7x^2-4) - (2x^2+4x-10) = 2x^3+7x^2-4 - 2x^2-4x+10.

Combining like terms, we get 2x^3+(7x^2-2x^2)+(-4-4x)+(10). Simplifying further, we have 2x^3 + 5x^2 - 4x + 6. Therefore, the result of the subtraction is 2x^3 + 5x^2 - 4x + 6.

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Answer:

(q-9) (5+c)

Step-by-step explanation:

Factor out the common factor.  In this case, q-9.

5(q-9) + c(q-9)

(q-9) (5+c)

Answer:

P = (4.8, 11)

Step-by-step explanation:

P = 3R + 2W

RP + PW

= 3(4,5) + 2(6,20)

2 + 3

= (12,15) + (12,40)

5

= (24,55) = (4.8, 11)

5

Line segment RW has endpoints R(4, 5) and W(6, 20). Point P is

on RW such that RP: PW is 2:3. the coordinates of point P would be (0, 11).

Suppose that there is a line segment {AB} such that a point P(x,y) lying on that line segment{AB} divides the line segment {AB} in m:n, then, the coordinates of the point P is given by:

[tex](x,y) = \left( \dfrac{mx_2 + nx_1}{m+n} , \dfrac{my_2 + ny_1}{m+n} \right)[/tex]

where we have:

the coordinate of A is (x_1, y_1)

and the coordinate of B is (x_2, y_2)

Line segment RW has endpoints R(4, 5) and W(6, 20). Point P is

on RW such that RP: PW is 2:3.

[tex](x,y) = \left( \dfrac{2(6) + 3(-4)}{2+3} , \dfrac{2(20) + 3(5)}{2+3} \right)\\\\(x,y) = \left( \dfrac{12- 12}{5} , \dfrac{40+15}{5} \right)\\\\(x,y) = \left( \dfrac{0}{5} , \dfrac{55}{5} \right)\\\\(x,y) = (0, 11)[/tex]

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Answer:

Step-by-step explanation:đáp án a

∆=b²-4ac= 1² - 4*3*(-11)=133

=>√∆=√133

X=(-b±√∆)/2a

X=(-(-1)±√133)/2*6

X=(1±√133)/6

Answer:

10

Step-by-step explanation:

Mean is all the given numbers in the set added together then divided by the total amount of numbers

6+7+10+12+12+13= 60

60÷6=10

Answer:10

Step-by-step explanation: Mean is all the given numbers in the set added together ,then divided by the total amount of numbers

6+7+10+12+12+13= 60

60÷6=10

Square root x=13

x=169

Hope you get it!

To solve the equation x^2√x-8+2=7, follow these steps: combine like terms, square both sides, simplify, take the cube root, and simplify again to find x = 3.

To solve the equation x2√x-8+2=7, we need to isolate the variable x. Here are the steps:

Therefore, the solution to the equation is x = 3.

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[tex]\frac{3}{5}(x - 5) \leq 27[/tex]

Hope this helped!

~Just a girl in love with Shawn Mendes

Answer: Option D

The inequality that represents the  situation is:

[tex]\frac{3}{5}(x-5)\leq 27[/tex]

following situation

Step-by-step explanation:

Suppose an unknown number X.

That number minus 5 is:

[tex]x-5[/tex]

Now, [tex]\frac{3}{5}[/tex] times the unknown number minus 5 is:

[tex]\frac{3}{5}(x-5)[/tex]

We know that all this expression is not greater than 27.

Then we use the symbol "less or equal than" ([tex]\leq[/tex]) to represent the situation

[tex]\frac{3}{5}(x-5)\leq 27[/tex]

Answer:

Can you take a pic of the problem if you can't type it out?

Step-by-step explanation:

Answer:

3/10a

Step-by-step explanation:

4/5a - 1/2a

4 × 2a - 1 × 5a/5a × 2a

8a - 5a/10a²

3a/10a²

3/10a

-TheUnknownScientist

To find the original price before the increase, divide the new price by 1 + the percent of increase.

198 / 1.20 = 165

The original price was $165

The price before the increase was $ 165

Percentage can be said as a part of a whole expressed in hundredths .

Let the price of the watch be $ x

According to the problem,

So, we can write x + 20x/100 = 198

⇒ 6x/5  = 198

⇒ x = 165

∴ The price before the increase was $ 165

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Answer:

no i don't sry

Step-by-step explanation:

Fulton Virtual provides competency based, personalized middle and high school learning options for FCS students throughout the district. This page is where students request and access Fulton Virtual courses. Parents can access the Fulton Virtual parent portal here too.

25) proportion is 3:6=7:14

26) proportion is 2:6=5:15

27) proportion is 2:4=7:14

28) proportion is 1:2=2:4

29) proportion is 4:8=5:10

30) proportion is 2:8=3:12

Answer:

a) P(a)= 0.0001

b) P(b)= 0.0024

Step-by-step explanation:

Given:

Chosen number = 3079

Possible numbers that have chance of winning from 0000 to 9999= 10,000

Winning condition=  if made choice matches the winning digits

Now

a)What is the probability that the winning number matches your number exactly?

From 0000 to 9999, only one time can the number 3079 can be the winning number, so

P(a)= 1/10000

     = 0.0001

b)What is the probability that the winning number has the same digits as your number in any order?

Winning numbers from 0000 to 10000 that have same digits as 3079 are

4 x 3 x 2 x 1 = 24 ways

Following are the 24 numbers from 0000 to 9999 that have matching digits to 3079:

0379

0397

0973

0937

0793

0739

3079

3097

3970

3907

3790

3709

7039

7093

7930

7903

7390

7309

9073

9037

9370

9307

9730

9703

P(b)= 24/10000

     =0.0024 !

y = 218.2. The lenght of side y by  trigonometry is 218.2.

In order to solve this problem we are going to use the angles and sides of a right triangle and its relation by expressions that we call trigonometric ratios.

In the image we can see that the lenght of the opposite leg is 141 , we do not know the lenght of the adjacent leg y and the hypotenuse x. The key to solve this problem is to use trigonometric ratios and the equation tan θ = sin θ/cos θ = opposite leg/adyacent leg = 141/y

Clear for y for the equation tan θ = sin θ/cos θ = 141/y, we obtain:

y = arctan θ (141)

y = arctan (43°)(141) = 218.2