Problem Water boils at 212^\circ212 ∘ 212, degrees Fahrenheit. Write an inequality that is true only for temperatures (t)(t)left parenthesis, t, right parenthesis that are higher than the boiling point of water.

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.

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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:

g(x)= 0.05x represents the amount of bonus, f(x)=x-3,000 represents weekly sales over $3,000.

Step-by-step explanation:

The function f(x) represents how much money earned by sales person weekly over $3000.

And function g(x) represents the amount of bonus earned by salesperson.

An expression, rule, or law that defines a relationship between one variable (the independent variable) and another variable (the dependent variable) is called function.

According to the given question.

The percent of bonus earned by salesperson weekly on sales over $3,000 is 5%.

Also, we have two functions.

[tex]f(x) = x - 3000[/tex]

and [tex]g(x) = 0.05x[/tex]

For the function, f(x) if x is the amount of money earned salesperson in a week, then f(x) will represents how much money salesperson earned apart form $3000.

And the function g(x) represents the amount of bonus earned by the salesperson.

Hence, the function f(x) represents how much money earned by sales person weekly over $3000. And function g(x) represents the amount of bonus earned by salesperson.

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Answer:

45

Step-by-step explanation:

The final had an extra credit as 25, so without it it would be 135. Then, you would divide by three to find that the first test had 45 points.

Answer:

45

Step-by-step explanation:

The final had an extra credit as 25, so without it it would be 135. Then, you would divide by three to find that the first test had 45 points.

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:

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:

[tex]\boxed{Option \ A}[/tex]

Step-by-step explanation:

y-intercept = b = 2   [y-intercept is when x = 0]

Slope = m = -3/7

Putting this in slope-intercept equation

=> [tex]y = mx+b[/tex]

=> [tex]y = -\frac{3}{7}x + 2[/tex]

Answer:

a

Step-by-step explanation:

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:

[tex]39x^2-416xy[/tex]

Step-by-step explanation:

To simplify, we have to distribute the 13x to 3x and -32y. To distribute, we multiply 13x with the first number, and then the second.

[tex]13x*3x=39x^2\\13x-32y=-416xy\\39x^2-416xy[/tex]

The first number is squared ([tex]39x^2[/tex]) because when two [tex]x[/tex]s get multiplied by each other, then it creates a square. We never do this: [tex]39xx[/tex]

Our answer is:

[tex]39x^2-416xy[/tex]

Hope this helps!

Answer:

[tex]\boxed{39x^2-416xy}[/tex]

Step-by-step explanation:

[tex]13x(3x-32y)[/tex]

First step into solving the problem will be to apply the distributive law.

[tex]13x(3x)+13x(-32y)[/tex]

Multiply the terms and simplify.

[tex]39x^2 +-416xy[/tex]

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:

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.

Answer:

yes, by AAS there are two sides of corresponding angles

Step-by-step explanation:

HOPE this helps...

Answer:

Last option..

Yes by AAS

Step-by-step explanation:

the angles which occupy the same relative position at each intersection where a straight line crosses two others. If the two lines are parallel, the corresponding angles are equal

Therefore by this statement we understand that these two are the sides of the corresponding angles!

Hope it helps!

Answer:

Lines a and c.

Step-by-step explanation:

m∠1=42° and m∠3=138°. 42 + 138 = 180, so the two angles form a 180° angle. That means that lines a and c are parallel.

Hope this helps!

Answer:A is parallel to C

Step-by-step explanation:

Statement            |    Reason

42*+138*=180*     |Corresponding angles

There fore A||C aka a parallel to c

42*+140*=180*   | Same side int. angles

Therefore A no || B aka A is not parallel to B

138*=140*            | Same side int. Angles

Therefore B And C are not parallel and A,B. and C are not parallel

The answer is A||C or A is parallel to C

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

here is your formula then

Answer:

8250

Step-by-step explanation:

I think

Answer:

Step-by-step explanation:

The area of a parallelogram is equal to the product of the length of its side and the height of the parallelogram perpendicular to that side.

H = 9 cm

S = 21 cm

A = S•H = 21 cm • 9 cm = 189 cm²

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:

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:

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:

49

Step-by-step explanation:

[tex]3x^2+5x-2 = 0[/tex]

Apply discriminant formula : [tex]D = b^2- 4ac[/tex]

[tex]D=discriminant\\b=5\\a=3\\c=-2[/tex]

[tex]D = b^2- 4ac[/tex]

Plug in the values for a, b, and c.

[tex]D = 5^2- 4(3)(-2)[/tex]

Evaluate.

[tex]D = 25- 12(-2)[/tex]

[tex]D = 25- - 24[/tex]

[tex]D=25+24[/tex]

[tex]D=49[/tex]

Answer:

49

Step-by-step explanation:

3x²+5x-2 = 0

This is in the form

ax^2 + bx + c=0

a=3  b=5  c = -2

The discriminant is

b^2 -4ac

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

25 + 24

49

The discriminant is 49

Answer:

18m square

Step-by-step explanation:

Formula for rectangular- based pyramid is L x W x H divided by 3

= 3 x 5 x 3.6 divided by 3 = 18

So you would need 18 m square for the sculpture

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:

79%

Step-by-step explanation:

To find the median, you need to arrange the numbers in ascending order. Than pick the middle number. If there are two middle numbers then you add them together and then divide by 2.

Answer:

79%

Step-by-step explanation:

Answer:

1290000

Step-by-step explanation: Given that

The volume of the Sun is about = 1.41 x 10^18 cubic kilometers.

The volume of Earth is about 1.09 x 10^12 cubic kilometers.

The number of Earths that can fit inside the Sun can be found by dividing the Sun's volume by Earth's volume.

= Volume of Sun ÷ Volume of the Earth

= 1.41 x 10^18 cubic km/1.09 x 10^12 cubic km

= 1.41 x 10^18/1.09 x 10^12

=(1.42/1.09)× 10^18-12

= 1.29×10^6

n is 1.29×10^6.

Hence the number of Earth that can be fitted in the Sun is 1290000

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: 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

try this answer good luck

Answer:

Answer:  1/2

Step-by-step explanation:

Given : Figure B is a scaled copy of Figure A.

We know that the scale factor is the ratio of the corresponding sides of two similar figures.

From , the graph we assume that that one point = one unit of length.

Then, the dimension of one side of figure A = 4 units and the  dimension of  corresponding side of Figure B = 2.

Then, the scale factor is given by:

k = 2/4 = 1/2

Hence, the  scale factor is 1/2

Answer:

5

Step-by-step explanation:

5