Question 30 The Royal Fruit Company produces two types of fruit drinks. The first type is pure fruit juice, and the second type is pure fruit juice. The company is attempting to produce a fruit drink that contains pure fruit juice. How many pints of each of the two existing types of drink must be used to make pints of a mixture that is pure fruit juice

Answer:

Largest prime factor of the given expression is 379.

Step-by-step explanation:

Given the expression:

[tex]15^6 - 7^6[/tex]

To find:

The largest prime factor of the given expression.

Solution:

First of all, let us factorize the given expression.

[tex]15^6 - 7^6\\\Rightarrow (15^3)^2 - (7^3)^2\\\\\text{Using } x^{2} -y^2 = (x+y) (x-y)\\\\\Rightarrow (15^3+7^3)(15^3-7^3)[/tex]

Let us learn two formula:

[tex]x^3+y^3 = (x+y)(x^2+y^2-xy)[/tex]

[tex]x^3-y^3 = (x-y)(x^2+y^2+xy)[/tex]

Applying the above formula in the expression written above:

[tex](15^3+7^3) = (15+7)(15^2+7^2-15\times 7)\\\Rightarrow 22(225+49-105 ) = 2 \times 11 \times 169 \\\Rightarrow 2 \times 11\times 13\times 13\\\Rightarrow 2 \times 11\times 13^2[/tex] ...... (1)

Similarly:

[tex](15^3-7^3) = (15-7)(15^2+7^2+15\times 7)\\\Rightarrow 8(225+49+105 ) = 2^3 \times 379[/tex]........ (2)

Multiplying the expressions from (1) and (2) to get the result:

[tex]\therefore 15^6 - 7^6 = 2^4 \times 11 \times \underline{\bold{379}} \times 13 ^2[/tex]

So, largest prime factor of the given expression is 379.

The largest prime divisor of the expression is 379.

The expression will be factorized. This will be:

= (15³)² - (7³)²

= (15 + 7)³(15 - 7)³

This can be illustrated as:

(15 + 7)³ = 2 × 11 × 13²

(15 - 7)³ = 2³ × 379

In conclusion, the largest prime divisor of the expression is 379.

Learn more about divisor on:

https://brainly.com/question/552761

Answer:

Step-by-step explanation:

We will make a table and fill it in according to the information provided. What this question is asking us to find, in the end, is how long did it take the cars to travel the same distance. In other words, how long, t, til car 1's distance = car 2's distance. The table looks like this:

              d     =      r     *     t

car1

car2

We can fill in the rates right away:

             d       =      r     *     t

car1                       40

car2                       60

Now it tells us that car 2 leaves 3 hours after car 1, so logically that means that car 1 has been driving 3 hours longer than car 2:

            d     =      r      *      t

car1                     40         t + 3

car2                     60           t

Because distance = rate * time, the distances fill in like this:

                   d      =      r      *      t

car1    40(t + 3)    =      40        t+3

car2          60t     =       60         t

Going back to the interpretation of the original question, I am looking to solve for t when the distance of car 1 = the distance of car 2. Therefore,

40(t+3) = 60t and

40t + 120 = 60t and

120 = 20t so

t = 6 hours.

Answer: Second choice. Triangle ABX and triangle EDX.

Check out the diagram below. I have color coded the segments that are the same length. The congruent angles are due to the fact we have a pair of vertical angles, which are always the same measure. The green angles are between the red and blue sides for each triangle.

Answer:

Congruent Triangles

Step-by-step explanation:

From the available information, let's concentrate on the fact that lines AX≅EX and lines BX≅DX. This simply means that line AX is equal to line EX and line BX equals DX. since the two lines cross each other to make the vertically opposite angles AXB and DXE equal (AXB≅DXE), then the opposite triangles are congruently sharing two pairs of equal sides and the same.

The congruent triangles are ΔABX and ΔEDX

Answer:

8250

Step-by-step explanation:

I think

Answer:

[tex]2(6x^2y^2+xy-1)\\[/tex]

Step-by-step explanation:

We are to find the product of the given expression. Given the expression

(3xy - 1) (4xy + 2), th product is derives by simply opening up the bracket as shown below;

[tex]= (3xy - 1) (4xy + 2)\\\\= 3xy(4xy)+2(3xy)- 1(4xy)-1(2)\\\\= 12x^2y^2 + 6xy-4xy-2\\\\= 12x^2y^2 + 2xy-2\\\\bringing\ out\ the\ common\ factor;\\\\2(6x^2y^2+xy-1)\\\\[/tex]

The expression 2(6x²y²+xy-1) gives the required product.

Answer:

A

Step-by-step explanation:

consider the form g(x) = aX^2, where a is negative, means the curve is flip upside down.

-3, shifted down for 3 units.

Answer:  b) {-3, 0.5}

Step-by-step explanation:

The new equation is the original equation plus 6.  Move the original graph UP 6 units.  The solutions are where it crosses the x-axis.

[tex]\text{Original equation:}\quad f(x)=\dfrac{15}{x}-\dfrac{9}{x^2}\\\\\\\text{New equation:}\quad\dfrac{15}{x}+6=\dfrac{9}{x^2}\\\\\\.\qquad \qquad f(x)= \dfrac{15}{x}-\dfrac{9}{x^2}+6[/tex]

+6 means it is a transformation UP 6 units.  

Solutions are where it crosses the x-axis.

The curve now crosses the x-axis at x = -3 and x = 0.5.

Answer:

25°

Step-by-step explanation:

Since ∠DBC = 130°, ∠DBC + ∠ABD = 180° (sum of angles on a straight line is 180°). Solving for ∠ABD:

∠DBC + ∠ABD = 180°

130 + ∠ABD  = 180°

∠ABD = 180° - 130°

∠ABD = 50°

∠ABD  is bisected by line BE, therefore ∠ABD = ∠EBA + ∠DBE (angle addition postulate).

The angle addition postulate states that if w is the interior of xyz then ∠XYZ = ∠XYW + ∠ZYW

Since E is the interior of ∠ABD, then:

∠ABD = ∠EBA + ∠DBE

But ∠EBA = ∠DBE

∠ABD = 2∠EBA

50 = 2∠EBA

∠EBA = 25°

Answer:

Answer:

Hey there!

-9x-y=-15

9x+y=15

A solution with integer values would be 9(1)+6=15

Thus, x=1 and y=6

(1, 6)

Hope this helps :)

Answer:

(6,1)

Step-by-step explanation:

Answer:

Lines r and s are parallel as Corresponding Angles given. There are four pairs of corresponding angles: angle 1 and angle 5, angle 2 and angle 6, angle 3 and angle 7, and angle 4 and angle 8. Since r and s are parallel, the slope of r is equal to the slope of s. Since t is a straight line, the slope of t is the same at both intersections, by the definition of a straight line. Thus, the corresponding angles created at both intersections must have the same measure, since the difference of the slopes at each intersection is the same, and the intersections share a common line. So, corresponding angles must have equal measure. Therefore, by definition of congruent angles, corresponding angles are congruent: angle 1 is congruent to angle 5, angle 2 is congruent to angle 6, angle 3 is congruent to angle 7, and angle 4 is congruent to angle 8.

Step-by-step explanation

answer from haven

Answer:

16

Step-by-step explanation:

Let the 1st part of your answer be x , so the 2nd part will be 40-x . From the given information, we can write the equation: (1/4)x = (3/8) × (40-x) . We can simplify this into (1/4)x = (120-3x)/8 ; 8x = 480-12x ; 8x+12x = 480 ; 20x = 480 ; x = 480/20; x = 24

Therefore, the 1st part = 24

Plug this into your 40-x equation to get: 40 - 24 = 16

Answer:

5/8

Step-by-step explanation:

Let the numerator = n.

Let the denominator = d.

The fraction is

n/d

"The denominator of a rational number is greater than its numerator by 3."

d = n + 3

The fraction is

n/(n + 3)

"If 3 is subtracted from the numerator and 2 is added to its denominator, the new number becomes 1/5."

(n - 3)/(n + 3 + 2) = 1/5

(n - 3)/(n + 5) = 1/5

Cross multiply.

5(n - 3) = 1(n + 5)

5n - 15 = n + 5

4n = 20

n = 5

d = n + 3 = 5 + 3 = 8

n/d = 5/8

The original number is 5/8.

Answer:

(-2, -8/3)

Step-by-step explanation:

2(-2) - 6y = 12

-4 -6y = 12

-6y = 16

y = -16/6 = -8/3

Answer:

n = -15 and n = 9. n = -15 is not reasonable because you can't have negative boxes or negative units of measurement.

Step-by-step explanation:

8(n + 2)(n + 4) = 1,144

(n + 2)(n + 4) = 143

n^2 + 2n + 4n + 8 = 143

n^2 + 6n - 135 = 0

(n + 15)(n - 9) = 0

n + 15 = 0

n = -15

n - 9 = 0

n = 9

I got two solutions: n = -15 and n = 9. Only one is reasonable because you cannot have a negative number of boxes or negative weight.

Hope this helps!

Simplify the equation, and set it equal to zero to prepare for factoring.

Multiply the two factors in parentheses using the distributive property:

8(n2 + 2n + 4n + 8) = 1,144

Combine like terms inside the parentheses:

8(n2 + 6n + 8) = 1,144

Multiply the terms inside the parentheses by 8 using the distributive property:

8n2 + 48n + 64 = 1,144

Set the equation equal to zero by subtracting 1,144 from each side:

8n2 + 48n − 1,080 = 0

Factor out the GCF, which is 8:

8n2 + 48n − 1,080 = 0

8(n2 + 6n − 135) = 0

Divide both sides of the equation by 8:

n2 + 6n − 135 = 0

Compare the equation with the standard form ax2 + bx + c = 0, and get a, b, and c:

a = 1, b = 6, c = -135

The leading coefficient of the equation is 1. So, find two numbers that have a sum of 6 and a product of -135:

6 = -9 + 15

-135 = -9 • 15

The two numbers are -9 and 15. Use the two numbers to write the factors of the quadratic expression:

(n − 9)(n + 15) = 0

Use the zero product property, and solve for n:

n − 9 = 0 or n + 15 = 0

n = 9 or n = -15

There are two solutions for n. But since n represents the width of the helmet box, it can’t be negative. Therefore, the only reasonable solution is n = 9

Answer:

30 seconds.

Step-by-step explanation:

So, we have the equation:

[tex]h(t)=-16t^2+h[/tex]

Where t is the time in seconds and h is the initial height.

A barometer falls from a weather balloon at a height of 14,400 feet. In other words, the initial height is 14,400. Substitute for h:

[tex]h(t)=-16t^2+14400[/tex]

We need to find when the barometer hits the ground. Ground level is 0 feet. Therefore, we can substitute h(t) for 0 and solve for the equation (solve for t) in order to find how long (in seconds) it took for the barometer to fall:

[tex]0=-16t^2+14400\\-14400=-16t^2\\900=t^2\\t=\pm\sqrt{900} \\\text{Time cannot be negative.}\\t=\sqrt{900}\\ t=30 \text{ seconds}[/tex]

Therefore, it took 30 seconds for the barometer to hit the ground when it fell at a height of 14,400 feet.

Edit: Spelling.

Answer:

[tex]\frac{2}{7} x[/tex]

Step-by-step explanation:

To find the slope of a line with 2 points we use the following formula.

[tex]\frac{y^2-y^1}{x^2-x^1}[/tex]

So with the following points,

E(-4,4)

D(10,8)

So 8 is y2 and 4 is y1 8-4 = 4

10 - -4 = 14

Slope: 2/7x

Thus,

the slope of the line is 2/7x.

Hope this helps :)

Answer:

5

Step-by-step explanation:

5

Answer:

The annual gross income of the server is $52936

Step-by-step explanation:

The server works four 6-hour shift a week.

the server earns $9.75/h

An average seller sells $1400 in a single shift, and makes 14% tip of a bill.

For the 6-hour shift, the server earns

6 x $9.75 = $58.5 a shift

in a week, the total money made for the four shifts in a week will be

4 x $58.5 = $234

The server makes an average of 14% of a bill, and makes about  $1400 in a single shift.

In a single shift he makes a tip of

14% of $1400 = 0.14 x $1400 = $196

in a week he makes 4 x $196 = $784

Total money the server makes in a week is

==> $234 + $784 = $1018

There are 52 weeks in a year.

The server's annual gross income will be

52 x $1018 = $52936

Answer:

7.8

Step-by-step explanation:

To do this problem you need to know Pythagorean Theorem which is also known as [tex]a^{2} +b^{2} =c^{2}[/tex].

In this problem 6 would be a, 5 would be b, and d would be c. So to do this we would do 5 squared (which is 25)+ 6 squared which is 36) and you would get 61 and when you do that you will just take the square root of that which is 7.81 and round it to the nearest tenth which is 7.8 and that would be the final answer

Answer:

D

Step-by-step explanation:

Given

y = x² + 1

y = x

Equating gives

x² + 1 = x ( subtract x from both sides )

x² - x + 1 = 0

Consider the discriminant Δ = b² - 4ac

with a = 1, b = - 1 and c = 1

b² - 4ac = (- 1)² - (4 × 1 × 1) = 1 - 4 = - 3

Since b² - 4ac < 0 then there are no real solutions

Answer:

125

Step-by-step explanation:

Add all the angles then subtract by 360.

Answer:

Vp-by-step explanation:

Three different whole numbers whose sum and product are equal are 1, 2, and 3.

1 + 2 + 3 = 6

1 x 2 x 3 = 6

As demonstrated above, the sum and product of 1, 2, and 3 is the same.

Hope this helps!! :)

Answer:

1 2 and 3

Step-by-step explanation:

Answer:

Option (C)

Step-by-step explanation:

Domain of any graph is defined by the x-values or the input values of a function.

Similarly, y-values on the graph of a function define the Range.

In the graph attached, x-values varies from (-∞) to (+∞).

Therefore, Domain of the graphed function will be (-∞, ∞)

Or -∞ < x < ∞

Similarly, y-values of the graph varies from (-∞) to (1)

Therefore, range of the graphed function will be (-∞, 1).

Or -∞ < y < 1

Option (C) will be the answer.

You answer is 10404 to get this answer multiply the 102 double time

Answer:

Q5 d

Step-by-step explanation:

(2x-1)2=9

4x-2=9

4x=9+2

4x=11

x=2.75

ans: none of these

Answer:

The completed proportions are;

ED/A_F = CE/CA = CF/CD

Step-by-step explanation:

The given m∠CED = m∠A

∴ Angle ∠CDE = Angle ∠A_FC, (corresponding angles)

Angle ∠ECD = Angle ∠ACF (reflexive property)

Triangle ΔDCE is similar to triangle ΔACF (Angle Angle Angle (AAA) similarity)

In triangle ΔDCE and triangle ΔACF

m∠A is bounded by CA and A_F

m∠CED is bounded by CE and ED

∠DCE is bounded by CE and DE

∠C is bounded by CA and CF

Based on the orientation of the two triangles, we have

ED is the corresponding side to A_F, CD is the  corresponding side to CF, CE is the corresponding side to CA

Therefore, we have;

ED/A_F = CE/CA = CF/CD.

Answer:

Step-by-step explanation:

[tex]x^2+y^2-14x+10y+25=0\\\\x^2-14x\ +\ y^2+10y+25=0\\\\\underline{x^2-14x+49} -49+\underline{y^2+10y+25}=0\\\\\underline{x^2-2\cdot x\cdot7+7^2}-49+\underline{y^2+2\cdot y\cdot5+5^2}=0 \\\\\underline{(x-7)^2}-49+\underline{(y+5)^2}=0\\\\\underline{\underline{(x-7)^2+(y+5)^2=49}}[/tex]

Answer:

The answer to this question can be defined as follows:

In option 1, She buys 4 memory cards.

In option 2, The cost of memory is $40  

Step-by-step explanation:

Given:

Available space is = 105 GB

required space = 1000 GB

256 GB memory cost $10.

Find needed memory:

=  1000 GB - 105 GB

= 895 GB

∴ the available memory is 256 GB.

∵ 256 × 4 = 1024  GB

The total memory she have = 1024 + 105 = 1129 GB

And  she needs to buy 4 memory cards.

The cost of the four memory cards is= 4 ×10 =  $40.

Using proportions, it is found that the least  amount of money Nancy can spend to get the storage she needs is of $40.

------------------------------

The rule of three is of:

1 card - 256 GB

x cards - 895 GB

Applying cross multiplication:

[tex]256x = 895[/tex]

[tex]x = \frac{895}{256}[/tex]

[tex]x = 3.5[/tex]

Rounding, she has to buy 4 cards.

A similar problem is given at https://brainly.com/question/17594062

Answer:

=360

explanation:

When you’re talking about rotation you go counterclockwise and each quadrant is another 90 degrees.

Answer:

360

Step-by-step explanation: