(01.03)

Solve the equation for x.

the square root of the quantity x plus 5 end quantity minus 3 equals 4

Answer:

The vertex is: [tex](6, 8)[/tex]

Step-by-step explanation:

First solve the equation for the variable y

[tex]x^2-4y-12x+68=0[/tex]

Add 4y on both sides of the equation

[tex]4y=x^2-4y+4y-12x+68[/tex]

[tex]4y=x^2-12x+68[/tex]

Notice that now the equation has the general form of a parabola

[tex]ax^2 +bx +c[/tex]

In this case

[tex]a=1\\b=-12\\c=68[/tex]

Add [tex](\frac{b}{2}) ^ 2[/tex] and subtract [tex](\frac{b}{2}) ^ 2[/tex] on the right side of the equation

[tex](\frac{b}{2}) ^ 2=(\frac{-12}{2}) ^ 2\\\\(\frac{b}{2}) ^ 2=(-6) ^ 2\\\\(\frac{b}{2}) ^ 2=36[/tex]

[tex]4y=(x^2-12x+36)-36+68[/tex]

Factor the expression that is inside the parentheses

[tex]4y=(x-6)^2+32[/tex]

Divide both sides of the equality between 4

[tex]\frac{4}{4}y=\frac{1}{4}(x-6)^2+\frac{32}{4}[/tex]

[tex]y=\frac{1}{4}(x-6)^2+8[/tex]

For an equation of the form

[tex]y=a(x-h)^2 +k[/tex]

the vertex is: (h, k)

In this case

[tex]h=6\\k =8[/tex]

the vertex is: [tex](6, 8)[/tex]

Answer: 6, 8

Step-by-step explanation:

Answer:

Number of cards at week n = 10,000(0.85)^(n-1).

At week 6  Dylan has 4437 cards.

Step-by-step explanation:

At the start of week 1 he had 10,000 = 10,000(0.85)^0  cards.

So at the start of week 2 he had 10,000(0.85)^(2-1) cards.

Number of  cards for week n =  10,000(0.85)^(n-1).

Number of he will have at the start of the 6th week

= 10,000(0.85)^(6-1)

=  4437 cards (answer).

The explicit rule for the number of baseball cards Dylan starts with in week n is A(n) = 10,000 * 0.85ⁿ⁻¹. In the 6th week, Dylan will start with approximately 4437 cards.

The number of baseball cards Dylan starts with in week n can be represented by an explicit rule, which is a formula that uses the starting amount of cards and a common ratio to find the amount for any given week. The starting number of cards for week n can be calculated using the geometric sequence formula: A(n) = A(1) * rⁿ⁻¹, where A(1) is the initial number of cards, r is the ratio of the remaining cards per week (85%, or 0.85), and n is the week number.

To calculate the number of cards Dylan starts with in the 6th week, we use the formula with A(1) = 10,000, r = 0.85, and n = 6:
A(6) = 10,000 * 0.85⁶⁻¹

After performing the calculations and rounding to the nearest card, Dylan will start with approximately 4437 cards in the 6th week.

[tex]9^4\cdot26^2=6561\cdot 676=4435236[/tex]

The total number of personal access codes that can be formed is,

= 4435236 possible ways

To multiply means to add a number to itself a particular number of times. Multiplication can be viewed as a process of repeated addition.

Given that;

Total digits of code = 6

Hence, We get;

Code options for first 4 digits = any of 1 - 9 = 9 options

Code option for last 2 digits = A - Z = 26 options

So,

Code number 1 = 9 possible values

Code number 2 = 9 possible values

Code number 3 = 9 possible values

Code number 4 = 9 possible values

Code number 5 = 26 possible values

Code number 6 = 26 possible values

Hence, total number of possible access codes :

= 9 x 9 x 9 x 9 x 26 x 26

= 9⁴ x 26²

= 4435236 possible ways

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Answer:

  72%

Step-by-step explanation:

QT has length 42-24 = 18.

ST has length 42-29 = 13.

The length ST is 13/18 ≈ 72.2% of the length of QT.

Answer:

Probability = 72.2%

Step-by-step explanation:

A number line contains points Q, R, S, and T with coordinated 24, 28, 29, and 42 respectively.

Now if a point lies on QT then the length of QT= coordinate of T - coordinate of Q

= 42 - 24

= 18

If a point lies on ST then the length of ST = coordinate of T - coordinate of S

= 42 - 29

= 13

Now we know Probability of an event = [tex]\frac{\text{Favorable event}}{\text{Total possible events}}\times 100[/tex]

Probability = [tex]\frac{13}{18}\times 100[/tex]

                  = 72.2%

Therefore, probability that a point chosen on QT will lie on ST will be 72.2%

[tex]a^{\log_a b}=b\\\\12^{\log_{12}24}=24[/tex]

Answer:

The correct answer option is A) 24.

Step-by-step explanation:

We are given the following log expression and we are to simplify it:

[tex] 1 2 ^ { log _ { 1 2 } } ^ { 2 4 } [/tex]

Here, we are going to apply the rule for solving a log problem:

[tex]a^{log_a^{(b)}[/tex] [tex] = b[/tex]

So if [tex] 1 2 ^ { log _ { 1 2 } } ^ { 2 4 } [/tex], then it would be equal to 24.

Answer:

Third choice

Step-by-step explanation:

The standard form of a circle is

[tex](x-h)^2+(y-k)^2=r^2[/tex]

where h and k are coordinates of the center and r is the radius squared.  We have h = 2, k = 7, and r = 4 (we will have to square it to fit it into the equation properly).  Filling in accordingly:

[tex](x-2)^2+(y-7)^2=16[/tex]

The third choice is the one you want.

Step-by-step explanation:

add all marbles together:

4 (green) + 3 (red) + 3 (yellow) = 10 marbles total

if we pick a yellow marble out of the bag and do not replace it, then we have 2 yellow marbles left.

we need to add marbles again with one yellow marble subtracted.

4 (green) + 3 (red) + 2 (yellow) =

new Total is 9 marbles.

so then we have 2 yellow marbles out of 9 total marbles.

2:9

or 2/9

or .22 (22%)

is the probability

Answer:

1/15 is the answer guys! Not 2/15 or anything else.

Step-by-step explanation:

Answer:

32 oz

Step-by-step explanation:

Assuming the hole in the bottle is not made any bigger as it loses water, it will lose it at a constant rate.  This makes it a linear function.  We can use the 2 points given to find the slope of the line, then use one of the 2 points to write an equation for the line in point-slope form, change it into slope-intercept form, and the amount of water in the bottle originally will be apparent.  Plugging in to the slope formula:

[tex]m=\frac{20-28}{6-2}=-2[/tex]

Now we will choose one point for the x and y values and plug in to the point-slope form of a line:

y - 28 = -2(x - 2) and

y - 28 = -2x + 4 so

y = -2x + 32

That is in y = mx + b form where m is the slope and b is the y-intercept, the initial value of y when x = 0.  x being the time gone by, when x = 0, that means that no time has gone by, and that means that no water has yet to leak out of your bottle.

Let a = car's age in years and v = value of car.

v = 25000(1 - 0.17)^a 

v = 25000(0.83)^a 

v = 25000(0.83)^a 

We need to find a.

Let v = 10,000

10,000 = 25000(0.83)^a

The value of a is about 4.91758.

Round off to the nearest whole number we get 5.

Answer is after more than 4 years but less than 6 and 8.

Answer:

  B)  T = 2πr/v

Step-by-step explanation:

To solve the given equation for T, multiply it by T/v.

[tex]v=\dfrac{2\pi r}{T}\\\\v\dfrac{T}{v}=\dfrac{2\pi r}{T}\cdot\dfrac{T}{v}\\\\T=\dfrac{2\pi r}{v} \qquad\text{simplify}[/tex]

By the way nice job using Khan Academy, I love it. the answer is the dep. is the numbers of minutes and the ind. is the episodes.

Answer:  The number of episodes you watch → Independent variable

The number of minutes you spend watching anime→ Dependent variable

Step-by-step explanation:

Given : Your favorite anime series has episodes that are 20 minutes long.

In the equation , w is the number of episodes you watch and t is the number of minutes you spend watching anime.

The relationship between these two variables can be expressed by the following equation :-

[tex]t=20w[/tex]

We can see that the time spend on watching anime depends on the number of episodes we watch.

Thus the dependent variable is the number of minutes you spend watching anime i.e. 't'.

The independent variable is the number of episodes you watch i.e. 'w'.

The statement that explains why the squares are similar is

Option C. Translations and dilations preserve betweenness of points; therefore, the corresponding sides of squares T and T″ are proportional.

There are several types of transformations:

Let us now tackle the problem!

[tex]\texttt{ }[/tex]

This problem is about Translation and Dilation.

Properties of Translation of the images compared to pre-images:

[tex]\texttt{ }[/tex]

Properties of Dilation of the images compared to pre-images:

[tex]\texttt{ }[/tex]

From the information above, we can conclude that:

Option A is not true because Dilations do not preserve side length.

Option B is not true because Dilations do not preserve orientation.

Option C is true because Translations and Dilations preserve betweenness of points.

Option D is not true. Although Translation and Dilations preserve collinearity but it cannot be related to the corresponding angles are congruent.

[tex]\texttt{ }[/tex]

Grade: High School

Subject: Mathematics

Chapter: Transformation

Keywords: Function , Trigonometric , Linear , Quadratic , Translation , Reflection , Rotation , Dilation , Graph , Vertex , Vertices , Triangle

Answer:

D

Step-by-step explanation:

x=-3 is a zero means x+3 is a factor

x=5/4 (with multiplicity 2) means you have the factor (x-5/4) two times

Now this may be rewritten so you don't have the fraction

like 4x=5 so you have 4x-5 as a factor two times which means you will see (4x-5)^2

So you one factor of (x+3) and two factors of (4x-5)

so you have

(x+3)(4x-5)^2

or

2(x+3)(4x-5)^2

or

41(x+3)(4x-5)^2

You can put whatever constant multiple in front of the whole thing and it will still satisfy the conditions of the problem.

So the answer is D

Final answer:

The factored form of the polynomial p(x) with a simple zero at x=-3 and a double zero at x=5/4 is (x+3)(4x-5)
, which makes option D the correct answer.

Explanation:

If p(x) is a polynomial that has a simple zero at x=-3 and a double zero at x=5/4, then to identify the correct factored form of p(x), we need to determine the factors that correspond to these zeros. A simple zero at x=-3 suggests that (x+3) must be a factor of p(x). A double zero at x=5/4 indicates that the factor corresponding to this zero should be squared in the polynomial, and since 5/4 can be written as 5/4 = 4/4 + 1/4 = 1 + 1/4, thus, the factor is (x-1-1/4), which simplifies to (x - 5/4) or (4x - 5) when multiplied by 4 to clear the fraction.

Looking at the options presented:

A) p(x)=2(x+3)(5x-4) - This has the correct factor for x=-3 but not the squared factor for x=5/4.

B) p(x)=(x+3)(5x-4)
- This has the correct factor for x=-3 but not the squared factor for x=5/4.

C) p(x)=2(x+3)(4x-5) - This has the correct factors but does not square the (4x-5) factor for the double zero at x=5/4.

D) p(x)=(x+3)(4x-5)² - This option correctly includes (x+3) for the simple zero at x=-3 and (4x-5) squared for the double zero at x=5/4.

Therefore, the correct factored form of p(x) is option D.

Answer:

true

The wording does not quite mean anything,

but what I think was meant to ask is

"if we use some parts of two triangles to prove they are congruent,

can we then use that to prove that

a pair of corresponding parts not used before are congruent?"

The answer is

Yes, of course,

Corresponding Parts of Congruent Triangles are Congruent,

which teachers usually abbreviate as CPCTC.

For example, if we find that

side AB is congruent with side DE,

side BC is congruent with side EF, and

angle ABC is congruent with angle DEF,

we can prove that triangles ABC and DEF are congruent

by Side-Angle-Side (SAS) congruence.

We then, by CPCTC, can conclude that other pairs of corresponding parts are congruent:

side AB is congruent with side DE,

angle BCA is congruent with angle EFD, and

angle CAB is congruent with angle FDE.

It was possible (by CPCTC) to prove those last 3 congruence statements,

after proving the triangles congruent.

The expected answer is FALSE.

Step-by-step explanation:

Answer:

So, 35 degrees is your answer.

Step-by-step explanation:

180 - 100 - 45 = 35 degrees

Hope my answer has helped you!

For this case we have by definition, that the sum of the internal angles of a triangle is 180.

Then, they tell us that two of the angles measure 45 and 100 degrees respectively. If "x" is the missing angle we have:

[tex]45 + 100 + x = 180[/tex]

Clearing the value of "x":

[tex]x = 180-45-100\\x = 35[/tex]

So, the missing angle is 35 degrees

ANswer:

35 degrees

Option B

1. The word is inverse not inverese.

2. Where is the question?

Answer:

yo no vi nada

i don't see anything

Step-by-step explanation:

Answer:

D. 13

Step-by-step explanation:

From the diagram, [tex]\angle BAD=2x\degree[/tex] and [tex]\angle BCD=(10x+24)\degree[/tex]

In an isosceles trapezium, the base angles are equal.

This implies that [tex]\angle ABC=\angle BAD[/tex]  [tex]\implies \angle ABC=2x\degree[/tex]

The side length CB of the trapezoid is a transversal line because CD is parallel to AB.

This means that [tex]\angle ABC=2x\degree[/tex] and [tex]\angle BCD=(10x+24)\degree[/tex] are co-interior angles.

Since co-interior angles are supplementary, we write and solve the following equation for [tex]x[/tex].

[tex]2x\degree+(10x+24)\degree=180\degree[/tex]

Group similar terms

[tex]2x+10x=180-24[/tex]

Simplify both sides of the equation.

[tex]12x=156[/tex]

Divide both sides by 12

[tex]\frac{12x}{12}=\frac{156}{12}[/tex]

[tex]\therefore x=13[/tex]

The correct answer is D.

Answer:

13

Step-by-step explanation:

a pex

[tex]\bf (\stackrel{x_1}{8}~,~\stackrel{y_1}{-8})~\hspace{10em} slope = m\implies \cfrac{3}{4} \\\\\\ \begin{array}{|c|ll} \cline{1-1} \textit{point-slope form}\\ \cline{1-1} \\ y-y_1=m(x-x_1) \\\\ \cline{1-1} \end{array}\implies y-(-8)=\cfrac{3}{4}(x-8)\implies y+8=\cfrac{3}{4}(x-8)[/tex]

Answer:

  opens down; (10, 2); same

Step-by-step explanation:

If the vertex of f(x) is (0, 0) then translating it to (h, k) makes the function look like f(x -h) +k. Changing the sign of f(x) to -f(x) reflects it across the x-axis, so ...

  y = 2 - |x -10|

is the function y = |x| reflected across the x-axis and translated 10 units right and 2 units up. Because there is no horizontal or vertical scale factor, the apparent width of the function is the same as the original.

Final answer:

The graph of the function y = 2 - |x – 10|  a .opens down with a vertex at (10, 2). It has the same width as the graph of y = |x|, meaning it is not stretched or compressed horizontally, but it is shifted upward and to the right.

Explanation:

To determine whether the graph of the function y = 2 - |x – 10| opens up or down, we must understand the behavior of the absolute value function. Since the absolute value function has a V-shape, the negative sign in front of the absolute value in the given function indicates that the graph opens down, creating an upside-down V-shape. Furthermore, the vertex of the graph is at the point where the expression inside the absolute value equals zero. In this case, x – 10 = 0, so x = 10. Plugging this into the function gives us the y-coordinate of the vertex, which is y = 2 - |10 - 10| = 2. Therefore, the vertex is (10, 2).

Comparing the width of the graph to the graph of y = |x|, we notice that there is no multiplication factor affecting the x inside the absolute value, hence the graph of the given function has the same width as the graph of y = |x|. In other words, the graph is neither stretched nor compressed horizontally. Rather, it is vertically shifted upward by 2 units, and horizontally shifted to the right by 10 units due to the x – 10 part of the function.

Answer:25≤x≤35

Step-by-step explanation: This statement means that the person can take more than or 25 mg or the can take less 35 or exactly 35 mg.

Answer:

(x-3,y+2)

Step-by-step explanation:

Answer:  The correct option is

(B) [tex]T^{-1}(x,y)=(x-3,y+2).[/tex]

Step-by-step explanation:  Given that under T, the point (0,2) gets mapped to (3,0).

We are to find the expression for [tex]T^{-1}(x,y).[/tex]

According to the given information, we have

[tex]T(0,2)=(3,0)=(0+3,2-2)\\\\\Rightarrow T(x,y)=(x+3,y-2)\\\\\Rightarrow T^{-1}(x+3,y-2)=(x,y)\\\\\Rightarrow T^{-1}(x+3-3,y-2+2)=(x-3,y+2)\\\\\Rightarrow T^{-1}(x,y)=(x-3,y+2).[/tex]

Thus, the required expression is [tex]T^{-1}(x,y)=(x-3,y+2).[/tex]

Option (B) is CORRECT.

Answer:

d = 13.8 feet

Step-by-step explanation:

Because we are talking about cubic feet of water, we need the formula for the VOLUME of a cylinder.  That formula is

[tex]V=\pi r^2h[/tex]

We will use 3.141592654 for pi; if the tank HALF filled with water is at 20 feet, then the height of the tank is 40 feet, so h = 40; and the volume it can hold in total is 6000 cubic feet.  Filling in then gives us:

[tex]6000=(3.141592654)(r^2)(40)[/tex]

Simplify on the right to get

[tex]6000=125.6637061r^2[/tex]

Divide both sides by 125.6637061 to get that

[tex]r^2=47.74648294[/tex]

Taking the square root of both sides gives you

r = 6.90988299

But the diameter is twice the radius, so multiply that r value by 2 to get that the diameter to the nearest tenth of a foot is 13.8

Answer:

Topmost option

Step-by-step explanation:

(see attached)

Answer:

[tex]\large\boxed{g\bigg(f(6)\bigg)=-\dfrac{4}{3}}[/tex]

Step-by-step explanation:

[tex]f(a)=-\dfrac{1}{4}(a+8)\\\\g(b)=\dfrac{2}{3}b+1\\\\g\bigg(f(6)\bigg)\\\\\text{calculate}\ f(6)\to\text{put}\ a=6\ \text{to the equation of}\ f(a):\\\\f(6)=-\dfrac{1}{4}(6+8)=-\dfrac{1}{4}(14)=-\dfrac{14}{4}=-\dfrac{7}{2}\\\\g\bigg(f(6)\bigg)\to\text{put}\ b=-\dfrac{7}{2}\ \text{to the equation of}\ g(b):\\\\g\bigg(f(6)\bigg)=\dfrac{2}{3}\left(-\dfrac{7}{2}\right)+1=-\dfrac{7}{3}+1=-\dfrac{7}{3}+\dfrac{3}{3}=-\dfrac{4}{3}[/tex]

Answer:

Step-by-step explanation:

Reflection across the line y=x swaps the x- and y-coordinates.

A(-5, 1) becomes A'(1, -5), for example. The coordinates of the other points are swapped in similar fashion.

Answer:

(x,y)→(y,x); A' is at (1, −5)

Step-by-step explanation:

Trapezoid ABCD is shown. A is at negative 5, 1. B is at negative 4, 3. C is at negative 2, 3. D is at negative 1, 1.

(x,y)→(y,−x); A' is at (1, 5)

(x,y)→(y,x); A' is at (1, −5) 

(x,y)→(−x,y); A' is at (5, 1) 

(x,y)→(−x,−y); A' is at (5, −1)

This is the complete question and your answer is :

(x,y)→(y,x); A' is at (1, −5) 

The equation that determines how many minutes it takes Mina to get to work is "30 = one half (x) + 10".

The given statements are:

Katie's commute on the train takes 10 minutes more than one-half as many minutes as Mina's commute by car.

Here, the minutes it takes Mina to get to work is considered as x (variable since it depends on the other terms)

Katie's commute on the train takes 10 minutes more than one-half as many minutes as Mina's commute by car i.e., one-half(x) + 10

It takes Katie 30 minutes to get to work i.e., 30 = one-half(x) + 10

Therefore, the equation is "30 = one-half(x) + 10".

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Answer:

  t ≈ 1.118 . . . seconds

Step-by-step explanation:

Set h=0 and solve for t.

  0 = -16t^2 +20

  0 = t^2 -20/16 . . . . . . . . . . . . . . . divide by the coefficient of t^2

  t = √(5/4) = (1/2)√5 ≈ 1.118 . . . . . add 5/4 and take the square root

The pinecone hits the ground about 1.12 seconds after it drops.

For the mathematical model h = -16t² + 20, corresponding to a pinecone dropping from a tree, the pinecone would hit the ground after approximately 1.118 seconds.

In order to know when a pinecone hits the ground, we would need to solve the equation provided for the variable t when h equals zero, as that would represent the pinecone being on the ground. The equation given is quadratic in nature: h = -16t² + 20. In this equation, h represents the height of the pinecone, and t represents time in seconds.

To find when the pinecone hits the ground (h=0), we set h to zero and solve for t:

0 = -16t² + 20
Therefore, 16t² = 20
So, t² = 20/16 = 1.25
Then, t = sqrt(1.25) = 1.118 (remember we exclude negative root as it doesn't go with time).

The pinecone hits the ground approximately at t = 1.118 seconds.

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Step-by-step explanation:

You forgot to include the formula, but it has to be either a sine wave or cosine wave:

h = A sin(ωt + φ) + B

The coefficient A is called the amplitude.  The diameter of the ferris wheel is double the amplitude.

d = 2A