Which expression is equivalent to x^2 + 5x - 6? Explain how.

(1) (x + 3) (x - 2)

(2) (x + 2) (x - 3)

(3) (x - 6) (x + 1)

(4) (x + 6) (x - 1)

The ratio is different from the other three is StartFraction 6 Over 10 EndFraction; 6/10.

A ratio is a number representing a comparison between two named things.

StartFraction 2 Over 5 EndFraction = StartFraction 6 Over 10 EndFraction = StartFraction 8 Over 20 EndFraction = StartFraction 12 Over 30 EndFraction

2/5 = 6/10 = 8/20 = 12/30

2/5 = 0.4

6/10 = 0.6

8/20 = 0.4

12/30 = 0.4

Therefore, the ratio is different from the other three is StartFraction 6 Over 10 EndFraction; 6/10

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Answer:

Euler's Formula = F+V=E+2

F=9

V=14

So, 9+14=E+2

23=E+2

23-2=E

21=E

Hence, E (edges) = 21

Step-by-step explanation:

Answer:

Option 2

Step-by-step explanation:

Since theta is in the third quadrant, the sine of theta is negative.

By the Pythagorean identity,

[tex]\sin \theta=-\frac{\sqrt{105}}{13}[/tex]

So, using the double angle formula for sine, we get that

[tex]\sin 2\theta=\frac{16\sqrt{105}}{169}[/tex]

Engine is currently in first gear as mentioned in question

Drive shaft speed be x

Answer:

700 rpm

Step-by-step explanation:

A driveshaft is a shaft that transmits mechanical power.

Its speed is measured in rpm (revolutions per minute).

Engine speed

Given engine speed:

Therefore, the drive-shaft speeds in the different gears are:

First gear

Drive-shaft speed = 2100 ÷ 3 = 700 rpm

Second gear

Drive-shaft speed = 2100 ÷ 1.6 = 1312.5 rpm

Third gear

Drive-shaft speed = 2100 rpm

The expression which shows how the distributive property of the can be used to multiply 8×29 as in the task content is; 8(20 + 9).

It follows from the task content that the given product to be multiplied is; 8×29.

Consequently, it follows from convention that the distributive property of multiplication allows that the multiplication in this case can be rewritten as follows;

8×29 = 8 (20 + 9)

Hence, we have; (8×20) + (8×9).

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Using proportions, it is found that the radian measure of the central angle is given as follows:

[tex]\frac{4\pi}{3}[/tex] radians.

A proportion is a fraction of a total amount, and the measures are related using a rule of three. Due to this, relations between variables, either direct or inverse proportional, can be built to find the desired measures in the problem.

The entire circumference is equivalent to a central angle of [tex]2\pi[/tex] radians. Hence the radian measure of the central angle considering two-thirds of the circumference is given as follows:

[tex]\frac{2}{3} \times 2\pi = \frac{4\pi}{3}[/tex]

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Answer:

Step-by-step explanation:

c edge

Answer:

(3, ∝) or all values of x greater than +3

Step-by-step explanation:

The inequality is [tex]5.5x + 15.5 > 32[/tex]

Subtracting 15.5 from both sides yields

5.5x > 32 - 15.5 or 5.5x > 16.5

Dividing by 5.5 on both sides yields

x > 16.5/5.5 or x > 3

This means the inequality is valid for all values of x > 3

The solution set is the interval (3, ∝ )

7.2 + c = 19

c = 19 - 7.2

c = 11.8

Answer:

Your answer is 5.

Step-by-step explanation:

7.2 + c = 19

or, 14 + c = 19

or, c = 19 - 14

or, c = 5       ans.

Hope its helpful :-)

The length of the side of the square is [tex]44 cm[/tex].

Determine the length of the side of the square:

Radius of circle[tex]=28.[/tex]

Circumference[tex]=2\pi r[/tex]

                        [tex]2\pi (28)=176[/tex]

Side of the square[tex]=\frac{176}{4} =44cm.[/tex]

The length of the side of the square is [tex]44 cm[/tex].

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Answer:

22

Step-by-step explanation:

| 2^3 - 4*3^2 |  - 4 = | 8 - 36| - 4 =  28-4 = 24

Answer:

a) $20,771.76

b) $20,817.67

c) $20,484.80

d) $20,864.52

Step-by-step explanation:

Compound Interest Formula

[tex]\large \text{$ \sf A=P\left(1+\frac{r}{n}\right)^{nt} $}[/tex]

where:

Part (a): semiannually

Given:

Substitute the given values into the formula and solve for A:

[tex]\implies \sf A=15000\left(1+\frac{0.055}{2}\right)^{2 \times 6}[/tex]

[tex]\implies \sf A=15000\left(1.0275}{2}\right)^{12}[/tex]

[tex]\implies \sf A=20771.76[/tex]

Part (b): quarterly

Given:

Substitute the given values into the formula and solve for A:

[tex]\implies \sf A=15000\left(1+\frac{0.055}{4}\right)^{4 \times 6}[/tex]

[tex]\implies \sf A=15000\left(1.01375}\right)^{24}[/tex]

[tex]\implies \sf A=20817.67[/tex]

Part (c): monthly

Given:

Substitute the given values into the formula and solve for A:

[tex]\implies \sf A=15000\left(1+\frac{0.055}{12}\right)^{12 \times 6}[/tex]

[tex]\implies \sf A=15000\left(1+\frac{0.055}{12}\right)^{72}[/tex]

[tex]\implies \sf A=20484.80[/tex]

Continuous Compounding Formula

[tex]\large \text{$ \sf A=Pe^{rt} $}[/tex]

where:

Part (d): continuous

Given:

Substitute the given values into the formula and solve for A:

[tex]\implies \sf A=15000e^{0.055 \times 6}[/tex]

[tex]\implies \sf A=20864.52[/tex]

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The system that can help to model this are

We have the following equation. Remember that a good understanding of the question is what would help us to write the equation

The condition says:

The square of first number is equal to the sum of the second number and 16:

First number = x. Square of x = x²

second number = y + 16

For the second

The difference of 4 times the second number and 1 is equal to the first number multiplied by 7:

second number is y

4*y - 1= x*7

= 4y - 1 = 7x

Hence we would have the following as our equations

x² = y + 16

4y - 1 = 7x

The solution to the equation when graphed = 5, 9

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Based on the percentage discount that one gets from the promotion using a jar, the average discount amount the shoe store can expect to give each customer is $15.

The average discount in percentages will be:

= (3/6 x 10%) + (2/6 x 30%) + (1/6 x 60%)

= 5% + 10% + 10%

= 25%

The average discount in cash amounts is:

= 25% x 60

= $15

In conclusion, the average discount amount that the store can expect to give each customer in dollars is $15.

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Answer:

Step-by-step explanation:

F starts at 200 and ends at 900

V starts at 0 and ends at 100

points(0,200) and (100,900)

200-900/0-100

= -700/-100

=7 which means every 7 it goes you another 100

this is all I got hope it helps

Answer:

I = (PTR)/100

1450=(5000*1*R)/100

1450*100=5000R

145000/50000=R

29=R

Step-by-step explanation:

We know,

[tex] S.I. = \rm\cfrac{P*R*T}{100}[/tex]

Given,

Principal P = 5000

Rate R = R(Assume)

Time T = 1

Interest = 1450

Plug:

[tex]1450 = \frac{5000 \times r \times 1}{100} [/tex]

Solve:

[tex]1450 \times 100 = 5000 \times r[/tex]

[tex]145000 \div 5000 = r[/tex]

[tex]r \: = \: 29 \%[/tex]

Rate = 29

Therefore,the rate of Interest is 29%.

See attachment for the axis of symmetry and maximum point.

To plot the axis of symmetry:

Therefore, the maximum value occurs at the vertex, given by (h,k)=(-2,8).

So, see attachment for the axis of symmetry and maximum point.

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Answer:2

Step-by-step explanation:

Answer: someone already answered this check the link out

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The quadratic equation exists [tex]$x^{2}+3 x+2=0$[/tex].

If a quadratic equation exists [tex]$a x^{2}+b x+c=0$[/tex], the utilizing the quadratic equation the solutions for x will be given by

[tex]$x_{1,2}=\frac{-b \pm \sqrt{b^{2}-4 a c}}{2 a}$$[/tex]

The solution for x exists

[tex]$x=\frac{-3 \pm \sqrt{3^{2}-4(1)(2)}}{2(1)}[/tex]

Comparing equations (1) and (2) we get, a = 1, b = 3 and c = 2.

Therefore, the quadratic equation exists [tex]$x^{2}+3 x+2=0$[/tex].

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Answer:

One guy said it was B. but I'm going with A.

Step-by-step explanation:

Ramiya is using the quadratic formula to solve a quadratic equation. her equation is x = startfraction negative 3 plus or minus startroot 3 squared minus 4(1)(2) endroot over 2(1) endfraction after substituting the values of a, b, and c into the formula. which is ramiya’s quadratic equation?

Answer:

(2)

Step-by-step explanation:

by substituting the values of x into f(x) and evaluating

f(0) = 3(0) - 5 = 0 - 5 = - 5 ≠ 0

f(3) = 3(3) - 5 = 9 - 5 = 4 ← True

f(4) = 3(4) - 5 = 12 - 5 = 7 ≠ 3

f(5) = 3(5) - 5 = 15 - 5 = 10 ≠ 0

Hence, statement 2 is true for the equation f(x) = 3x-5

The definition of an equation in algebra is a mathematical statement that proves two mathematical expressions are equal.

Types of Equations:

 Linear Equation: More than one variable may be present in a linear equation. An equation is said to be linear if the maximum power of the variable is consistently 1.

  Quadratic Equation: This equation is of second order. At least one of the variables in a quadratic equation needs to be raised to exponent 2.

  Cubic Equation: A third-order equation is this one. At least one of the variables in cubic equations needs to be raised to exponent 3.

  Rational Equation: A fractional equation having a variable in the numerator, denominator, or both is referred to as a rational equation.

Substituting the values of x into f(x) and evaluating

f(x) = 3x - 5

put x = 0

f(0) = 3(0) - 5

= 0 - 5 = - 5

put x = 3

f(3) = 3(3) - 5

= 9 - 5

= 4

put x = 4

f(4) = 3(4) - 5

= 12 - 5

= 7

put x = 5

f(5) = 3(5) - 5

= 15 - 5

= 10

hence statement 2 is true.

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The trigonometry illustrates that the four angles whose cosine is the same as cos pi/3 will be 7∏/3, 13∏/3, 19∏/3, and 31∏/3

From the information, given cos (x), the value that is similar to cos x will be the sum of the angle and multiple of 360.

Therefore, for the angle cos(∏/3), the angles that are similar to this angle will be expressed as Cos(2∏n + ∏/3) where n is any positive integer.

Then the other four angles will be 7∏/3, 13∏/3, 19∏/3, and 31∏/3. Also, the statement that all angles that have the same cosine will have the same sine is false. The sine of an angle is simply equal to the cosine of the complementary angle.

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The smallest positive integer having exactly 5 different positive integer divisors is 60.

To find the smallest positive integer having exactly 5 different positive integer divisors:

Therefore, the smallest positive integer having exactly 5 different positive integer divisors is 60.

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The answer of your question is option (B)

The group that would best represent a sample of the study population is: C: one thousand of their customers with a current smart phone data plan.

A sample that best represents a population under study is a sample that is a subset of the entire population, that is, research subjects that are drawn as samples should reflect the general characteristics of the entire population without leaving out any part of the population. Also, a good sample should enable a researcher make generalization.

A sample that is a subset of a population and reflects the characteristics of the general population would not be biased.

Given the situation above, the population of the study are smart phone customers that use dat in the cell phone company. So, a sample that would better represent this general population would be customers that currently have a smart phone plan, since the average amount of data they use is what the cell pone company wants to ascertain.

Therefore, the group that would best represent a sample of the study population is: C: one thousand of their customers with a current smart phone data plan.

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The volume of the cylinder is [tex]384\pi \sqrt{3cm }^{2}[/tex].

Body of the diagonal=24cm.

Assume the length of the side= a.

[tex]a^{2} +(a^{2} +a^{2} )=24^{2}[/tex]

                   [tex]a=\sqrt[8]{3} cm[/tex]

The area of the cylinder base=[tex]\pi R^{2}[/tex]

                                                =[tex]\pi (\frac{1}{2} \sqrt[8]{3} )^{2}[/tex]

                                                =[tex]48cm^{2}[/tex]

The high of the cylinder is[tex]\sqrt[8]{3}cm[/tex]

The volume of the cylinder:

=s*h

=[tex]48\pi *\sqrt[8]{3}[/tex]

=[tex]384\pi \sqrt{3} cm^{3}[/tex]

The volume of the cylinder is [tex]384\pi \sqrt{3cm }^{2}[/tex].

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The biggest possible volume of the cylinder will be [tex]2089.497\hspace{1mm}\text{cm}^3[/tex].

Now, given that the diagonal of the cube is [tex]24[/tex] cm. So, if the side length of the cube is [tex]x[/tex] cm, then we must have

[tex]x\sqrt{3}=24\\\Longrightarrow x=\frac{24}{\sqrt{3}}\\\Longrightarrow x=8\sqrt{3}[/tex]

Thus, the side length of the cube is [tex]8\sqrt{3}[/tex] cm.

So, the height of the cylinder with maximum volume will be [tex]h=8\sqrt{3}[/tex] cm and the diameter will be [tex]d=8\sqrt{3}[/tex]cm i.e. the radius will be [tex]r=\frac{d}{2}=\frac{8\sqrt{3}}{2}=4\sqrt{3}[/tex] cm.

So, using the above formula for the volume of a cylinder, we get

[tex]V=\pi r^{2}h=\pi\times (4\sqrt{3})^2\times 8\sqrt{3}=2089.497\hspace{1mm}\text{cm}^3[/tex].

Therefore, the biggest possible volume of the cylinder will be [tex]2089.497\hspace{1mm}\text{cm}^3[/tex].

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Answer:

(3, -3 8/9)

Step-by-step explanation:

Use a slope calculation or a graph to find the slope of the line.

m = (y-y)/(x-x)

m = (-3- -5)/(7- -2)

m = 2/9

Then write the equation of the line. I used point-slope form. (You could use y=mx+b, slope-intercept form, but you'd have to first calculate b as well)

Point-slope form:

y -Y = m(x-X)

y - -3 = 2/9(x- 7)

y + 3 = 2/9(x - 7)

We know the x-coordinate of the point we're looking for is 3. Fill that in as well and calculate the y that goes with it.

y + 3 = 2/9(3-7)

y+3=2/9(-4)

y = -8/9 - 3

y = -3 8/9

In decimal form this is -3.8888repeating

see image.

The point at x=3 on the line between M(7,-3) and N(-2,-5) is (3, -3 8/9).

Solving a logarithmic equation, it is found that the San Francisco earthquake was 24.71 times more intense than the Columbian earthquake.

As given in the problem, the intensities of the earthquakes are given by logarithms of base 10. Then, supposing that the intensities are R1 and R2, with R1 greater than R2, the ratio of the intensities, that is, how much intense R1 is than R2, is given as follows:

[tex]r = 10^{\frac{R_1}{R_2}}[/tex]

For this problem, the intensities are given as follows:

Then, the ratio of the intensities is given as follows:

[tex]r = 10^{\frac{7.8}{5.6}} = 24.71[/tex]

The San Francisco earthquake was 24.71 times more intense than the Columbian earthquake.

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The unknown angles are as follows;

x = 180 degrees

r = 90 degrees.

The angle subtended by an arc of a circle at its centre is twice the angle it subtends anywhere on the circle's circumference.

Therefore,

x = 2(90)

x = 180

Therefore, the sum of angle in a circle is 360 degrees.

Hence, the 2 angles of the arc are the same.

Therefore,

360 - 180 = 2r

2r = 180

divide both sides by 2

2r / 2 = 180 / 2

r = 90 degrees.

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Answer:

r = 3.75

Step-by-step explanation:

C = 2(pi)r (write equation)

r = c / 2pi (rearrange for r)

r = 23.55 / 2(3.14) (plug in variables)

r = 23.55 / 6.28 (simplify)

r = 3.75 (solve)