How do you solve this

Answer:

[tex]\large\boxed{8x^3+125=(2x+5)(4x^2-10x+25)}[/tex]

Step-by-step explanation:

[tex]8x^3+125=2^3x^3+5^3=(2x)^3+5^3\\\\\text{use}\ a^3+b^3=(a+b)(a^2-ab+b^2)\\\\=(2x+5)((2x)^2-(2x)(5)+5^2)\\\\=(2x+5)(4x^2-10x+25)[/tex]

➷ Use this formula:

density = mass / volume

Rearrange it for mass:

mass = density x volume

Substitute the values in:

mass = 100 x 19.3

Solve:

mass = 1930g

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Answer:

In parallelogram ABCD

FD is perpendicular to BC

BE is perpendicular to CD

Consider triangle BEC and triangle DFC

FC = EC (Given)

Angle BEC = Angle DFC (=90°)

Angle BCE = Angle DCF (common)

Therefore triangle BEC is congruent to triangle DFC (AAS congruency)

DF = BE (CPCT)

Since the altitudes are equal their bases will also be equal

Therefore BC = DC

Therefore BC = DC = AD = AB

Therefore ABCD is a rhombus

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Since [tex]\(ABCD\)[/tex] is a parallelogram with all four sides congruent, [tex]\(ABCD\)[/tex] is a rhombus. Hence, [tex]\(ABCD\)[/tex] is proven to be a rhombus.

To prove that parallelogram [tex]\(ABCD\)[/tex] is a rhombus, we need to show that all sides are congruent.

Given:

1. [tex]\(ABCD\)[/tex] is a parallelogram.

2. [tex]\(BE \perp CED\).[/tex]

3. [tex]\(DF \perp BFC\).[/tex]

4. [tex]\(CE \cong CF\).[/tex]

Proof:

1. Parallelogram Properties:

  - In a parallelogram, opposite sides are congruent and parallel.

  - Therefore, [tex]\(AB \parallel CD\)[/tex] and [tex]\(AD \parallel BC\)[/tex].

  - Also, [tex]\(AB \cong CD\)[/tex] and [tex]\(AD \cong BC\)[/tex].

2. Congruent Segments:

  - [tex]\(CE \cong CF\) (given).[/tex]

  - Since [tex]\(BE \perp CED\)[/tex] and [tex]\(DF \perp BFC\)[/tex], [tex]\(BE\)[/tex] and [tex]\(DF\)[/tex] are heights from [tex]\(B\)[/tex] and [tex]\(D\)[/tex] respectively to line [tex]\(CED\)[/tex].

3. Triangle Congruence:

  - Consider [tex]\(\triangle CEF\)[/tex]. Since [tex]\(CE \cong CF\)[/tex] and [tex]\(BE \perp CED\)[/tex], [tex]\(DF \perp BFC\)[/tex], [tex]\(\triangle CEF\)[/tex] is isosceles with base [tex]\(EF\)[/tex].

4. Diagonals in Parallelogram:

  - Diagonals of a parallelogram bisect each other.

  - Since [tex]\(\triangle CEF\)[/tex] is isosceles and [tex]\(CE = CF\)[/tex], the diagonals [tex]\(BE\)[/tex] and [tex]\(DF\)[/tex] bisect each other at [tex]\(E\)[/tex] and [tex]\(F\)[/tex].

5. Symmetry and Congruence:

  - Since diagonals bisect each other and the height from [tex]\(B\)[/tex] and [tex]\(D\)[/tex] are equal, segments from [tex]\(B\)[/tex] and [tex]\(D\)[/tex] to the diagonals are congruent.

6. Sides of Parallelogram:

  - From symmetry and congruence, all sides of the parallelogram are equal.

  - Therefore, [tex]\(AB \cong BC \cong CD \cong DA\)[/tex].

Conclusion:

Since [tex]\(ABCD\)[/tex] is a parallelogram with all four sides congruent, [tex]\(ABCD\)[/tex] is a rhombus.

Hence, [tex]\(ABCD\)[/tex] is proven to be a rhombus.

Answer:

Step-by-step explanation:

Area = L * W

2/5 * 1/3 =

2 * 1 = 2

5 * 3 = 15

= 2/15 inches squared

What we do is find area

Area of rectangle=(l*w)

length=2/5

width=1/3

Area=2/5*1/3

Answer=2/15

Answer=2/15

Answer:

21

Step-by-step explanation:

Answer:

3/2

Step-by-step explanation:

mm,m

Based on the calculations below, the slope of this graph is equal to: C. 2/3.

In Mathematics and Euclidean Geometry, the slope of any straight line can be determined by using the following mathematical equation;

Slope (m) = (Change in y-axis, Δy)/(Change in x-axis, Δx)

Slope (m) = rise/run

[tex]Slope(m)=\frac{y_2-y_1}{x_2-x_1}[/tex]

By substituting the given data points (0, -2), and (3, 0) into the formula for the slope of a line, we have the following;

Slope of graph = (0 - (-2))/(3 - 0)

Slope of graph = (0 + 2)/(3 - 0)

Slope of graph = 2/3

Based on the graph, the slope is the change in y-axis with respect to the x-axis, and it is equal to 2/3.

The value of exponential function, which completes the table for variable x at 1/3 is 3. The option B is correct.

Exponential function is the function in which the function growth or decay with the power of the independent variable.

The curve of the exponential function depends on the value of its variable.

The exponential function with dependent variable y and independent variable x can be written as,

[tex]y=a^x[/tex]

Here, [tex]x[/tex] is the variable in the power of a number.

Given information-

The given exponential function in the problem is,

[tex]f(x)=8^x+1[/tex]

The value of function at the value of variable x as 1/3 has to be find to complete the table. Put 1/3 in the above equation on the place of x as,

[tex]f(x)=8^{\frac{1}{3}}+1[/tex]

The number 8 can be written as the [tex]2^3[/tex]. Thus,

[tex]f(x)=(2^3)^{\frac{1}{3}}+1\\f(x)=(2)^{\dfrac{3\times1}{3}}+1\\f(x)=(2)^1+1\\f(x)=2+1\\f(x)=3[/tex]

Thus the value of exponential function, which completes the table for variable x at 1/3 is 3. The option B is correct.

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Answer:

C

Step-by-step explanation:

given

x² = 64 ( take the square root of both sides )

x = ± [tex]\sqrt{64}[/tex] = ± 8

Tamara omitted the negative square root → C

Tamara made the mistake of only finding the positive square root, not the negative square root.

The mistake that Tamara made in finding the solution to the equation x^2=64 is that she only found the positive square root, not the negative square root.

When solving a quadratic equation like this, you need to consider both the positive and negative square roots, because both values satisfy the equation. So the correct solution to x^2=64 is x=8 and x=-8.

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The population of a town decreasing at a rate of 1.5% per year from an initial number of 4500 will drop below 4000 in approximately 9 years, around the year 2019.

The topic of this question concerns a decrease in population over time, which is generally described using exponential decay in mathematics. When we talk about a decrease of 1.5% per year, we're looking at an exponential decay factor of 1 - 0.015 = 0.985. We follow this process to determine the duration for the population to reduce below 4000:

Basically, it means:

4500 * (0.985^n) < 4000

. By solving this inequality, we find that

n ≈ 8.29

. Therefore, we can estimate the town's population will drop below 4000 in the 9th year (since we can't have a fraction of a year), which would be

2019

if we start counting from 2010.

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The population of the town would drop below 4000 in 2024.

To determine the year when the population of the town drops below 4000, we can use the formula for exponential decay:

Population = Initial population × (1 - Decay rate)^Time

where:

Population is the population at a given time

Initial population is the initial population (in 2010, which is 4500)

Decay rate is the decrease rate per year (1.5% or 0.015)

Time is the number of years since 2010

We want to find the Time when the Population is less than 4000. So, we can set up an inequality:

4000 > 4500 × (1 - 0.015)^Time

Dividing both sides by 4500, we get:

0.889 > (1 - 0.015)^Time

Taking the natural logarithm of both sides, we get:

ln(0.889) > Time × ln(1 - 0.015)

Dividing both sides by ln(1 - 0.015), we get:

Time ≈ 13.92

Since we're looking for the year when the population drops below 4000, we round up to the nearest whole year. Therefore, the population of the town would drop below 4000 in 2024.

[tex]The \: money \: of \: each \: after \: Fred \: paid \: his \: debt: \frac{84 - 12}{2} = \$36 \\ John \: gave \: Fred:36 + 12 = \$48[/tex]

Answer:

36

Step-by-step explanation:

Answer:

[tex]\dfrac{7.7.7.7.7}{7.7}[/tex]

Step-by-step explanation:

Finding the expression of the value [tex]\dfrac{7^{5} }{7^{2}}[/tex] is just like taking the spread out value of the two variables raised to their exponents.

[tex]\dfrac{7^{5}}{7^{}}=\dfrac{7.7.7.7.7}{7.7}[/tex]

So if we multiply all the values together we get:

=[tex]\dfrac{16807}{49}[/tex]

=343

This method is just one of the methods that can be used to finding the quotient of a variable raised to an exponent.

Answer:

168

14 times 12

Answer:

x = 1/2

Step-by-step explanation:

Subtract 2x from both sides

4x + 5x - 2x = 6

Combine 4x and -2x to get 2x.

2x + 5 = 6

Subtract 5 from both sides.

2x = 6 - 5

Subtract 5 from 6 to get 1.

2x=1

Divide both sides by 2.

x = 1/2

Answer: FIRST OPTION

Step-by-step explanation:

To solve this problem you must apply the Intersecting Secant-Tangent Theorem. By definition, when a secant line and a tangent lline and a secant segment are drawn to a circle from an exterior point:

[tex](Tangent\ line)^2=(Secant\ line)(External\ Secant\ line)[/tex]

The total measure of the secant shown is:

[tex]18+Diameter[/tex]

If the radius is 7, then the diameter is:

[tex]D=7*2=14[/tex]

Therefore:

[tex]Secant\ line=18+14=32[/tex]

You also know that:

[tex]External\ Secant\ line=18\\Tangent\ line=x[/tex]

Keeping the above on mind, you can substitute values and solve  for x:

[tex]x^{2}=32*18[/tex]

[tex]x=\sqrt{576}\\x=24[/tex]

The measure of the side length of the tangent line PQ to the circle O is 25 units

From the image, Line segment PQ is a tangent line because it touches the curve at point Q.

Therefore, triangle PQO forms a right triangle.

Leg 1 of the right triangle = OQ = 7

Leg 2 of the right triangle = PQ = x

Hypotenuse = PO = 18 + 7 = 25

Now, to solve for the measure of side length x, we use the Pythagoras theorem:

PQ = √( PO² - OQ² )

Plug in the values:

x = √( 25² - 7² )

x = √( 625 - 49 )

x = √576

x = 24

Therefore, the value of x is 24.

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Answer:

Step-by-step explanation:

Find out the price of one bagel by dividing the price by the number of bagels:

350 Bagels = $168

1 Bagel = $0.48

475 Bagels = $209

1 Bagel = $0.44

0.48 > 0.44

This means the second bakery has the lower price.

Louis wants 800 bagels, so multiply the price by 800.

0.44 * 800 = $352

You can check it's lower by comparing it with the first bakery.

0.48 * 800 = $384

384 > 352

Answer:

40 un.

Step-by-step explanation:

The diagonals of the rhombus bisect each other at right angle. This gives us that

By the Pythagorean theorem,

[tex]VE^2=VS^2+ES^2,\\ \\VE^2=6^2+8^2,\\ \\ VE^2=36+64,\\ \\VE^2=100,\\ \\VE=10\ un.[/tex]

The sides of the rhombus are all of the same length, then the perimeter of the rhombus is

[tex]P_{VENU}=4\cdot 10=40\ un.[/tex]

Answer:

70 in³ (answer d)

Step-by-step explanation:

The volume of a pyramid with base area A and height h is

V = (1/3)(A)(h).

Here, V = (1/3)(21 in²)(10 in) = 70 in³

Answer:

Section A: Sally drives from her house to her friend's house.

Section B: Sally stops to visit her friend.

Section C: Sally drives from her friend's house to the post office to drop off a card.

Section D: Sally drives back to her house.

Step-by-step explanation:

As you can see in the graph, the point (0,0) is the location of Sally's house. In that point the distance is 0 and the time is 0.

In Section A she drives 3 miles in 6 minutes from her house to her friend's house.

In Section B, the distance does not change, this means that Sally stopped at her friend's house for 4 minutes.

In Section C she drives (for 4 minutes) 1 mile from her friend's house to some place (In this case the post office).

In Section D she comes back to 0 distance, then, she drives back to home.

The answer is D. C ÷ d = π, where C is circumference and d is diameter.

Answer:

Step-by-step explanation:

[tex]\text{The formula of a circumference of a circle:}\ C=d\pi\\\\d-diameter\\\\d\pi=C\qquad\text{divide both sides by}\ d\\\\\pi=\dfrac{C}{d}[/tex]

Answer:6.928

Step-by-step explanation: formula A=√ 3*(side^2/4)

The area would be 7 cm

See the image

Answer:

75

Step-by-step explanation:

To find the volume of a squared pyramid use the formula:

Volume of a squared pyramid = × base area × height

Base area = Side× side

( A square has the same length and breadth)

= 5 × 5 = 25 in

Volume of a squared pyramid =  [tex]\frac{1}{3}[/tex] × 25 × 9

= 75 [tex]in^{3}[/tex]  

Answer: [tex]\frac{2}{3}[/tex]

Step-by-step explanation:

The greatest GCF is 5 because 5 goes into 15, and 10. Therefor, the answer would be 2/3.

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Answer:

⅔

Step-by-step explanation:

Find all the factors of 10 and 15.

Factors of 10: 1, 2,     5, 10

Factors of 15: 1, 2, 3, 5,      15

The highest factor that is in both 10 and 15 is 5.

To reduce the fraction 10/15, divide both the numerator and denominator

by 5.

10/15 = (10 ÷ 5)/(15 ÷ 5) = ⅔

Answer:

Step-by-step explanation:

The product of three and a number x: 3 · x = 3x

The sum of four and the product of three and a number x:

4 + 3x

Answer:

2

Step-by-step explanation:

In order to solve a system using the additional method, we would need to multiply the first equation by '2' in order for the x’s to add out.

We have the following equations:

[tex] 3 x - y = 3 [/tex] --- (1)

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

We will multiply equation (1) by 2 and equation (2) by 3 to cancel the x's.

[tex] 2 ( 3x - y = 3 ) = [/tex] [tex] 6x - 2 y = 6 [/tex]

[tex] 3 ( -2x + 2 y = 6 ) = -6x + 6y = 36 [/tex]

Exponential decay because it is decreasing

Answer:

2A/h = b

Step-by-step explanation:

The formula for area of a triangle is

A = 1/2 bh

Multiply each side by 2

2A = 2*1/2 bh

2A = bh

Divide each side by h

2A/h = bh/h

2A/h = b

Answer:

b=2A/h

Step-by-step explanation:

The formula for area of a triangle is

A = 1/2 bh

Multiply each side by 2

 2*1/2 bh = 2A

bh = 2A

Divide each side by h

bh/h = 2A/h

b = 2A/h

The linear equation that models the cost of making a call lasting x minutes using a calling card is y = -0.1x + 1.45.

To write a linear equation that models the cost of making a call lasting x minutes using a calling card, we can use the given information about two calls. If a 5-minute call costs $0.95 and a 13-minute call costs $1.75, we can set up two equations:

0.95 = 5m + b

1.75 = 13m + b

Solving these equations, we find that m = -0.1 and b = 1.45. Therefore, the linear equation that models the cost of making a call lasting x minutes is y = -0.1x + 1.45.

Answer:

NO

Step-by-step explanation:

2/10 have a common term of 2.  reduce both the numerator and denominator by dividing both by 2.

2/2 = 1  

10/2 = 5

the reduced fraction woudl be 1/5

Answer:

No 2/10 is not the same as 4/5

Step-by-step explanation:

The reason why is because If you doubled 2/10 then it would be 4/20 not 4/5 and if you divided by 4/5 by 2 then it would be a complex fraction of 2/1/2 that is why the statement 4/5 is equal to 2/10 is false.