The sum of the digits of a two-digit number is 12. The number with the digits reversed is 15 times the original tens' digit. Find the original number.
I don't need the answer, just the equations! Thanks!

Answer:

I would say your answer is B.

Step-by-step explanation:

5.3 times 10^5 + 3.8 times 10^4

Tirn them into their regular form and add them together you will get the answer

Answer:

(a) 13

(b) LIFO: $19.60; FIFO: $37.50; Avg: $28.26

Step-by-step explanation:

(a) The starting inventory was 12 sets. Added to that were 4, 6, 6, 10, to make a total of 38 paint sets. 25 were sold, so 13 remained at the end of the year.

(b)

LIFO

Sets purchased at the end of the year are sold first (last-in, first-out). So the sets remaining in inventory are the ones purchased at the beginning of the year. Those 13 sets cost 12@1.50 +1@1.60 = $19.60.

FIFO

Sets purchased first are sold first, so the sets remaining in inventory are the ones purchased last. Those 13 sets cost 10@3.00 +3@2.50 = $37.50.

Avg

The total cost of all inventory purchases was ...

... 12@1.50 +4@1.60 +6@2.20 +6@2.50 +10@3.00

... = 18.00 +6.40 +13.20 +15.00 +30.00 = $82.60

Then the value of the remaining 13 of the 38 items bought is ...

... (13/38)·$82.60 = $28.26.

_____

I find it convenient to let a spreadsheet do the arithmetic.

Q. P

12. 1.5. 18.00

4. 1.6. 6.40

6. 2.2. 13.20

6. 2.5. 15

10. 3. 30

__ __. ___

38. 10.8. 82.6

Sales. 25

Ending inventory 25-38=13. Answer a

B) ending inventory under LIFO

12×1.5=18

1×1.6=1.6

___

19.6 Answer

Ending inventory under FIFO

10×3=30

3×2.5=7.5

___

37.5. Answer

Ending inventory under weighted average

82.6÷38=2.17

2.17× 13=28.21 ...Answer

Hope it helps!

D. log₁₀(200) = 2t

Dividing by 5 gives you ...

... 200 = 10^(2t)

Taking the log to the base 10 gives you ...

... log₁₀(200) = 2t . . . . . . matches selection D

You can see that the graph of [tex] g(x) [/tex] is the graph of [tex] f(x) [/tex] translated one unit to the left.

Horizontal translations are given by the transformation

[tex] f(x) \mapsto f(x+k) [/tex]

If [tex] k>0 [/tex] the function is translated k units to the left, else if [tex] k<0 [/tex] the function is translated k units to the right.

So, in your case, [tex] k=1 [/tex]

And thus you have

[tex] g(x) = f(x+1) = 2^{x+1} [/tex]

Answer:

2^x+1

Step-by-step explanation:

2^0=1

2^-2=1/4

(-2)^2=4

-2^2=-4

-2^2,2^-2,2^0,(-2)^2

Answer:

R(x) = 850x + 9600

Step-by-step explanation:

Answer:

Option b. 30.5

Step-by-step explanation:

Given in the picture is a triangle ABC with sides AB = 22.3 and side BC=24.1

The included angle B = 82 degrees

We have to find the third unknown side AC = b

REcollect the cosine formula for triangles.

[tex]b^{2} =a^{2} +c^{2} -2ac cos B[/tex]

substitute for a and c

We get

[tex]b^2 = 22.3^2+24.1^2-2(22.3)(24.1) cos 82\\=928.587[/tex]

b = square root of 928.587

b =30.47=30.5

Thus we get b = 30.5

Answer:

should be the first table

Step-by-step explanation:

The table that can be used to determine how long it would take if Elias and Niko polished the silver together is table B

You can create a table to determine the time it would take Elias and Niko together to polish the silver based on their individual rates of completing the task.

Let's denote:

Elias's rate of polishing = 1 job / 40 minutes

Niko's rate of polishing = 1 job / 50 minutes

To find the combined rate when they work together, you can use the formula:

Combined rate = Elias's rate + Niko's rate

Elias's rate = 1 job / 40 minutes

Niko's rate = 1 job / 50 minutes

So, the combined rate when they work together will be:

Combined rate = 1/40 + 1/50

Combined rate = (5/200) + (4/200)

Combined rate = 9/200

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x ≈ {-3.082, 1.082}

I find the easiest way to answer such a question (with medium accuracy) is to use a graphing calculator. The graph shown in the attachment gives the answers listed above.

___

From vertex form

The graphing calculator also makes it easy to find the vertex of the parabola. If we divide by 3 so the scale factor is 1, then the y-value of the vertex is -13/3 and the vertex form of the equation can be written ...

... y = (x +1)² -13/3

This has x-intercepts easily found.

... 0 = (x +1)² -13/3 . . . . x-intercepts are where y=0

... (x +1)² = 13/3 . . . . . . . add 13/3

... x +1 = ±√(13/3) . . . . . take the square root

... x = -1 ±√(13/3) . . . . . subtract 1

... x ≈ {-3.0816660, 1.0816660}

_____

Using the quadratic formula

This equation has a=3, b=6, c=-10, so we can put these values into the quadratic formula to find the x-interecepts.

... x = (-b±√(b²-4ac))/(2a)

... x = (-6 ±√(6² -4(3)(-10)))/(2(3))

... x = (-6 ±√156)/6 = -1 ±√(13/3) . . .  or . . . -1 ±(√39)/3

Answer:

1/2

Step-by-step explanation:

1/3 ÷ 2/3

We will use copy dot flip

Copy the first number , change the divide to multiply, take the reciprocal of the second number.

1/3 × 3/2

1/2

The volume of the sphere is given by :

V=[tex]\frac{4}{3}\pi r^{3}[/tex]

And volume of cylinder is given as :

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

So, as given to select the radius randomly and the height of the cylinder will be the diameter of the sphere.

The radius are = 3, 5, 8, 10, 12

And height will be = 6, 10, 16, 20, 24

1. Volume of sphere with radius 3 = [tex]\frac{4}{3}*3.14*3*3*3= 113.04[/tex] units

Volume of cylinder with radius 3 and height 6 = [tex]3.14*3*3*6=169.56[/tex] units

2. volume of sphere with radius 5 = 523.60 units

volume of cylinder with height 10 = 785.40 units

3. volume of sphere with radius 8 = 2144.66 units

volume of cylinder with height 16 = 3216.99 units

4. volume of sphere with radius 10 = 4188.79 units

volume of cylinder with height 20 = 6283.19 units

5. volume of sphere with radius 12 = 7238.23 units

volume of cylinder with height 24 = 10857.34 units

Answer:

a. $0.07

Step-by-step explanation:

Profit = Charge -Cost

We want to make a profit of 25 and the cost is 10

25 = Charge -10

Add 10 to each side

25+10 = Charge -10+10

35 = Charge

We need to charge 35 per jar.

Each jar contains 500 marbles

The cost per marble is Cost/ number of marbles

cost per marbles = $35 / 500

                             = $.07

Answer:

Option A : $0.07

Step-by-step explanation:

Given :

A school purchases jars of marbles.

Each jar contains 500 pieces of marbles.

Each jar costs $10.

To Find : How much does the school have to charge for each piece of marbles to make a profit of $25 per  jar?

Solution :

Cost of one jar is $10

Now, school wants to make profit of $25 on each jar .

using formula : Profit = Charge - cost

⇒$25 = charge - $10

⇒$35 = charge

Thus school should charge one jar of marbles of $35.

Since each jar contains 500 marbles.

So,to calculate cost of each marble when charge of jar is $35.

Cost of 500 marbles is $35

Cost of 1 marble = 35/500 = $0.07

cost of each marble when charge of jar is $35 is $0.07

Hence , the school have to charge $0.07 for each piece of marble to make a profit of $25 per  jar.

Option A is correct

Simplify each term: 5x^4y + 7x^4y - 5x^5 - 5x^3z + 3x^3z

Combine like terms: -5x^5 + 12x^4y -2x^3z  

That is the most simplified form.

If necessary, factor:

x^3(-5x^2+12xy-2z)

Answer:

B

Step-by-step explanation:

....

The sequence of translation and dilation of transformation would change two congruent figures into two similar figures that are no longer congruent.

Option B is the correct answer

It is the movement of the shape in the left, right, up, and down directions.

The translated shape will have the same shape and size.

There is a positive value when translated to the right and up.

There is a negative value when translated to the left and down.

We have,

Two congruent figures:

If a translation is applied to the two congruent figures we get the same shape and size.

If we apply a dilation after the translation to the two congruent figures the size of the figures changes.

If translation and dilation are applied to two congruent figures this sequence would change two congruent figures into two similar figures that are no longer congruent.

Thus,

The sequence of translation and dilation of transformation would change two congruent figures into two similar figures that are no longer congruent.

Option B is the correct answer.

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Answer:

The values for both of the missing sides is 8.

Step-by-step explanation:

The hypotenuse of a right triangle = a(square root of 2)

Therefore the other two missing sides equal a.

Therefore, the other two sides equal 8.

now, recalling the pythagorean theorem a little.

the hypotenuse here is 8√2, and then we have the other two sides, BUT, the opposite angle for each is actually the same 45°, if each opposite angle is the same, the length of the side on the other end is also the same.

so we have say side "b" and side "a", but because each has an opposite angle of 45°, that means "b" and "a" are actually twins.

[tex]\bf \textit{using the pythagorean theorem} \\\\ c^2=a^2+b^2\implies (8\sqrt{2})^2=a^2+b^2 \qquad \begin{cases} c=\stackrel{hypotenuse}{8\sqrt{2}}\\ a=adjacent\\ b=opposite\\ \end{cases} \\\\\\ \stackrel{\textit{since we know that \underline{a = b}}}{[8^2(\sqrt{2})^2]=a^2+a^2}\implies 64(2)=2a^2\implies \cfrac{64(2)}{2}=a^2\implies 64=a^2 \\\\\\ \sqrt{64}=a\implies 8=a=b[/tex]

Answer:

60.9

Step-by-step explanation:

Answer:

Marta’s equation has a positive y-intercept, but the scatterplot suggests a negative y-intercept.

Step-by-step explanation:

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Sorry if this does not help

Answer:

A

Step-by-step explanation:

Answer:

5/16

Step-by-step explanation:

In 5/2 the time, we expect that 5/2 × 1/8 = 5/16 of the test will be complete.

_____

5/2 × (2/5 h) = 1 h

Answer:5/16

Step-by-step explanation: In 5/2the time, we expect that 5/2 *1/8= 5:16

The expression written as a square of a monomial is [tex](4x^3)^3[/tex]

Given the indices expression [tex]64x^9[/tex]

We are to express as a square of a monomial. This is expressed as shown:

[tex]=64x^9\\=(4 \times 4 \times 4)(x^3)^3\\= 4^3(x^3)^3\\=(4x^3)^3[/tex]

Hence the expression written as a square of a monomial is [tex](4x^3)^3[/tex]

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Final answer:

To write 64x^9 as a square of a monomial, we can write it as (8x^4)^2. To write it as a cube of a monomial, we can write it as (4x^3)^3.

Explanation:

To write 64x^9 as a square of a monomial, we need to find a monomial that, when squared, equals 64x^9. To do this, we need to identify the square root of 64, which is 8, and the square root of x^9, which is x^4. Therefore, 64x^9 can be written as (8x^4)^2.

To write an expression as a cube of a monomial, we need to find a monomial that, when cubed, equals the given expression. In this case, we need to find the cube root of 64, which is 4, and the cube root of x^9, which is x^3. Therefore, 64x^9 can be written as (4x^3)^3.

check the picture below.

so, we know the radius of this circle is 5 then, namely, the distance from (0,0) to (5,0) is 5.

now, if (√(21) , 2) indeed lies on that circle curve, then the distance from (0,0) to (√(21) , 2) will also be the same radius of 5 units.

[tex]\bf ~~~~~~~~~~~~\textit{distance between 2 points} \\\\ \stackrel{\textit{origin}}{(\stackrel{x_1}{0}~,~\stackrel{y_1}{0})}\qquad (\stackrel{x_2}{\sqrt{21}}~,~\stackrel{y_2}{2})\qquad \qquad d = \sqrt{( x_2- x_1)^2 + ( y_2- y_1)^2} \\\\\\ r=\sqrt{(\sqrt{21}-0)^2+(2-0)^2}\implies r=\sqrt{(\sqrt{21})^2+2^2} \\\\\\ r=\sqrt{21+4}\implies r=\sqrt{25}\implies r=5~~~~\checkmark[/tex]

Answer:

It does. "Proof" below.

Step-by-step explanation:

In order for the given points to lie on the circle, they must both be the same distance from the origin. The Pythagorean theorem is used to make a "distance formula" for computing the distance between two points.

For a point (x, y), its distance (d) to the origin will be ...

... d = √(x² +y²)

For the reference point that we know is on the circle, this distance (the circle's radius) is ...

... d = √(5² +0²) = √25 = 5

For the point in question, the distance to the origin is ...

... d = √((√21)² +2²) = √(21 +4) = √25 = 5

Both points have the same distance to the origin, 5 units, so a circle (of radius 5) centered there will contain both points.

_____

A graph is not proof, but it can confirm the result.

Answer:

C' = (-5, -2)

Step-by-step explanation:

Reflection over the y-axis negates the x-coordinate.

C(5, -2) ⇒ C'(-5, -2)

Answer:

The correct option is 3.

Step-by-step explanation:

The vertices of isosceles trapezoid ABCD are A(2, 0), B(4, 0), C(5, -2), D(1, -2).

If a figure reflected over the y-axis, then the relation between coordinates of preimage and image is defined as

[tex](x,y)\rightarrow (-x,y)[/tex]

It is given that ABCD reflected over the y-axis and coordinates of point C are (5,-2), so the coordinates of C' are

[tex]C(5,-2)\rightarrow C'(-5,-2)[/tex]

The coordinates of C' are(-5,-2). Therefore the correct option is 3.

y +3 = (1/4)(x +3)

The two-point form of the equation for a line is good for this.

... y -y1 = (y2-y1)/(x2-x1)(x -x1)

Substituting your values, we have ...

... y -(-3) = (-1-(-3))/(5-(-3))(x -(-3))

... y +3 = 2/8(x +3)

Since you ask for "an equation," we can leave it in this form.

... y +3 = (1/4)(x +3)

_____

Or we can rearrange it to slope-intercept form:

... y = (1/4)x -(2 1/4)

or put it in standard form:

... x -4y = 9

Answer:

it would be c

Step-by-step explanation:

all you have to do is find the picture that maches the stament

asa means angle side angle so therefore c if im correct

Answer:

Triangle A prime B prime C prime. is obtained by dilating Triangle ABC. by a scale factor of 1 over 2. and then rotating it about the origin by 180 degrees

Step-by-step explanation:

All the coordinates of A'B'C' are -1/2 times those of ABC. The dilation factor is 1/2, and rotation by 180° is indicated.

A'(-1, -1) = (-1/2) × A(2, 2)

B'(-1, -5) = (-1/2) × B(2, 10)

C'(-4, -6) = (-1/2) × C(8, 12)

___

Rotation by 180° negates both coordinates. It is equivalent to reflection across the x-axis and reflection across the y-axis, in either order.

Answer:

its basically B

Step-by-step explanation:

A. y = (-6/5)x +10

The given line has a negative slope (downward to the right). The only equation offered with a negative slope is the one of selection A.

_____

Complete working

A parallel line will have the same slope. If there are less-obvious choices to select from, you need to know the slope of the given line. That is computed from ...

... slope = (change in y)/(change in x)

The coordinates of two points are given, so we can find the slope as ...

... slope = (-4-2)/(-1-(-6)) = -6/5

There are a number of ways to write the equation of a line, but in slope-intercept form, the slope is the coefficient of x. You will be looking for a choice that has an x-coefficient of -6/5.

To find out if a set satisfies the inequality, you can either plug in the points into the equation, or you can plug in the points into the graph.

Any point in the shaded area and on the line satisfy the inequality. If the inequality had a sign of < or >, then the point can not be on the line, only in the shaded area.

A.) This is a solution because they are all in the shaded area

B.) This is not a solution because (7,-2) is outside the shaded area

C.) This is not a solution because (3,3) is outside the shaded area

D.) This is not a solution because (2,1) is outside the shaded area

Answer:

A) {(0, 0), (1, 2), (3, -3)}  

Step-by-step explanation:

Check by inserting values into the inequality.

y ≤ -2x + 4

Set A

(0,0): 0≤ 4 TRUE

(1,2): 2 ≤ -2×1 + 4

       2 ≤ -2 + 4

       2 ≤ 2 TRUE

(3,-3): -3 ≤ -2×3+4

         -3 ≤ -6 + 4

         -3 ≤ -2 TRUE

=====

Set B

(7, -2): -2 ≤ -2×7 + 4

          -2 ≤ -14 + 4

          -2 ≤ -10 FALSE

=====

Set C

(3,3): 3 ≤ -2×3 + 4

        3 ≤ -6 + 4

        3 ≤ -2 FALSE

=====

Set D

(2,1): 1 ≤ -2×2 + 4

       1 ≤ -4 +4

       1 ≤ 0 FALSE

Set A is the one that contains only points that satisfy the inequality.

Answer:

The function r(x) represents a constant rate per unit change in x.

Step-by-step explanation:

This is because when you increase in 2, it goes from 37 to 25, a decrease in 12, then when the x goes from 2 to 3, then it has to drop down by 6, or else it won't be linear. It does. 25-6 is 19. Then it goes from 3 to 5, meaning it has an increase of 2 in x, meaning it has to drop down in 12 to be linear, It does. 19-12 is 7. So it is linear, meaning it has a constant rate per unit change in x.

Answer:

0.153

Step-by-step explanation:

It has been a long time since I've done this, so I hope it is correct:

cos = adjacent side / hypotenuse

cos x = 13 / 85 = 0.153

The decimal value of cos X can be found using a calculator or trigonometric table. Cosine is a trigonometric function that gives the ratio of the length of the adjacent side to the hypotenuse of a right triangle.

The decimal value of cos X can be found using a calculator or trigonometric table. Cosine is a trigonometric function that gives the ratio of the length of the adjacent side to the hypotenuse of a right triangle. For example, if cos X is equal to 0.6, this means that the adjacent side of the triangle is 0.6 times the length of the hypotenuse.

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Answer:

(4,0)

Step-by-step explanation:

insert 0 where the y is located and solve for x

6x – 3y = 24

6x – 3(0) = 24?

6x = 24

6x / 6 = 24 / 6

x = 4

x-intercept = (4, 0)

The x-intercept of the line 6x - 3y = 24 is (4, 0).

The x-intercept of a line represents the point where the line intersects the x-axis. To find the x-intercept of the line 6x - 3y = 24, we need to set y = 0 and solve for x.

Substituting y = 0 into the equation, we get 6x - 3(0) = 24. Simplifying this equation gives us 6x = 24, and dividing both sides by 6 gives x = 4.

Therefore, the x-intercept of the line 6x - 3y = 24 is (4, 0).

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