A chemical company makes two brands of antifreeze. The first brand is 35% anti freeze, and the second brand is 85% pure antifreeze. In order to obtain 150 gallons of a mixture that contains 75% pure antifreeze, how many gallons of each brand of antifreeze must be used.

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:

B

Step-by-step explanation:

Conditional probability is:

P(A given B) = P(A and B) / P(B)

Here, P(A and B) = 0.052 and P(B) = 0.17:

P(A given B) = 0.052 / 0.17

P(A given B) = 0.306

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]

[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:

Topmost option

Step-by-step explanation:

(see attached)

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.

[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:

  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%

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:

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

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.

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:

[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:

x-2y = -12

Step-by-step explanation:

Standard form of a line is in the form Ax + By = C   where A is a positive integer

y − 3 = 1/2(x + 6)

Multiply each side by 2 to eliminate the fractions

2(y-3)= 1/2*2 (x+6)

Distribute

2y -6 = x+6

Subtract x from each side

-x +2y -6 = x-x +6

-x+2y -6 = 6

Add 6 to each side

-x+ 2y -6+6 = 6+6

-x +2y = 12

Multiply each side by -1 to make A a positive integer

x-2y = -12

Answer:

  see below

Step-by-step explanation:

The image is reflected across the origin and enlarged by a factor of 3.

___

The first choice shows some funny combination of translation, rotation, and dilation. The last choice has point N invariant, which means that is the center of the (horizontal only) dilation. Neither of these matches the problem description.

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:

1. Let [tex]a,b,c[/tex] be the three points of intersection, i.e. the solutions to [tex]f(x)=g(x)[/tex]. They are approximately

[tex]a\approx-3.638[/tex]

[tex]b\approx-1.862[/tex]

[tex]c\approx0.889[/tex]

Then the area [tex]R+S[/tex] is

[tex]\displaystyle\int_a^c|f(x)-g(x)|\,\mathrm dx=\int_a^b(g(x)-f(x))\,\mathrm dx+\int_b^c(f(x)-g(x))\,\mathrm dx[/tex]

since over the interval [tex][a,b][/tex] we have [tex]g(x)\ge f(x)[/tex], and over the interval [tex][b,c][/tex] we have [tex]g(x)\le f(x)[/tex].

[tex]\displaystyle\int_a^b\left(\dfrac{x+1}3-\cos x\right)\,\mathrm dx+\int_b^c\left(\cos x-\dfrac{x+1}3\right)\,\mathrm dx\approx\boxed{1.662}[/tex]

2. Using the washer method, we generate washers with inner radius [tex]r_{\rm in}(x)=2-\max\{f(x),g(x)\}[/tex] and outer radius [tex]r_{\rm out}(x)=2-\min\{f(x),g(x)\}[/tex]. Each washer has volume [tex]\pi({r_{\rm out}(x)}^2-{r_{\rm in}(x)}^2)[/tex], so that the volume is given by the integral

[tex]\displaystyle\pi\int_a^b\left((2-\cos x)^2-\left(2-\frac{x+1}3\right)^2\right)\,\mathrm dx+\pi\int_b^c\left(\left(2-\frac{x+1}3\right)^2-(2-\cos x)^2\right)\,\mathrm dx\approx\boxed{18.900}[/tex]

3. Each semicircular cross section has diameter [tex]g(x)-f(x)[/tex]. The area of a semicircle with diameter [tex]d[/tex] is [tex]\dfrac{\pi d^2}8[/tex], so the volume is

[tex]\displaystyle\frac\pi8\int_a^b\left(\frac{x+1}3-\cos x\right)^2\,\mathrm dx\approx\boxed{0.043}[/tex]

4. [tex]f(x)=\cos x[/tex] is continuous and differentiable everywhere, so the the mean value theorem applies. We have

[tex]f'(x)=-\sin x[/tex]

and by the MVT there is at least one [tex]c\in(0,\pi)[/tex] such that

[tex]-\sin c=\dfrac{\cos\pi-\cos0}{\pi-0}[/tex]

[tex]\implies\sin c=\dfrac2\pi[/tex]

[tex]\implies c=\sin^{-1}\dfrac2\pi+2n\pi[/tex]

for integers [tex]n[/tex], but only one solution falls in the interval [tex][0,\pi][/tex] when [tex]n=0[/tex], giving [tex]c=\sin^{-1}\dfrac2\pi\approx\boxed{0.690}[/tex]

5. Take the derivative of the velocity function:

[tex]v'(t)=2t-9[/tex]

We have [tex]v'(t)=0[/tex] when [tex]t=\dfrac92=4.5[/tex]. For [tex]0\le t<4.5[/tex], we see that [tex]v'(t)<0[/tex], while for [tex]4.5<t\le8[/tex], we see that [tex]v'(t)>0[/tex]. So the particle is speeding up on the interval [tex]\boxed{\dfrac92<t\le8}[/tex] and slowing down on the interval [tex]\boxed{0\le t<\dfrac92}[/tex].

The approximate difference in the maximum height achieved by the two projectiles is 5.4 ft. (Option C).

How to calculate the difference between two maximum heights?

The approximate difference in the maximum height achieved by the two projectiles is calculated as follows;

The given function of one of the projectile;

f(x) = -16x² + 42x + 12

The function of the second projectile shown in the table, shows that the maximum of the function, g is 33

g(1) = 33 ft (maximum height)

The maximum height attained by the projectile with f(x) function occurs at x = 1

f(1) = -16(1)² + 42(1) + 12

f(1) = 38 ft

The difference between two maximum heights;

Δh = f(1) - g(1)

Δh = 38 ft - 33 ft

Δh = 5 ft

The option that is approximately 5 ft is option C (5.4 ft).

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

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:

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) 

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

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.

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:

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:

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.