What is the quotient (3x2 + 4x − 15) ÷ (x + 3)?

Answer:

3(x - 3)(x + 2)

Step-by-step explanation:

take out a common factor of 3 from each term

= 3(x² - x - 6)

to factor the quadratic consider the factors of - 6 which sum to - 1

These are - 3 and + 2, hence

3x² - 3x - 18 = 3(x - 3)(x + 2) ← in factored form

Answer:

A. (10,1)

Step-by-step explanation:

[tex]Solution,\:solve\:for\:x,\:\frac{5}{6}x=\frac{10}{3}\quad :\quad x=4[/tex]

[tex]Steps[/tex]

[tex]\frac{5}{6}x=\frac{10}{3}[/tex]

[tex]\mathrm{Multiply\:both\:sides\:by\:}6,\\6\cdot \frac{5}{6}x=\frac{10\cdot \:6}{3}[/tex]

[tex]\mathrm{Simplify}:\\\\6\cdot \frac{5}{6}x,\\\mathrm{Multiply\:fractions}:\quad \:a\cdot \frac{b}{c}=\frac{a\:\cdot \:b}{c},\\\frac{5\cdot \:6}{6}x,\\\mathrm{Cancel\:the\:common\:factor:}\:6,\\x\cdot \:5\\\\\frac{10\cdot \:6}{3},\\\mathrm{Multiply\:the\:numbers:}\:10\cdot \:6=60,\\\frac{60}{3},\\\mathrm{Divide\:the\:numbers:}\:\frac{60}{3}=20,\\\\5x=20[/tex]

[tex]\mathrm{Divide\:both\:sides\:by\:}5,\\\frac{5x}{5}=\frac{20}{5}[/tex]

[tex]\mathrm{Simplify},\\x=4[/tex]

[tex]\mathrm{The\:Correct\:Answer\:is\:x=4}[/tex]

[tex]\mathrm{Hope\:This\:Helps!!!}[/tex]

[tex]\mathrm{Please\:Mark\:Brainliest!!!}[/tex]

[tex]\mathrm{-Austint1414}[/tex]

Final answer:

To solve the equation 5/6x = 10/3, multiply both sides by the reciprocal of 5/6 (i.e., 6/5), then simplify the resulting equation to find that x = 4.

Explanation:

Solving the Equation 5/6x = 10/3

To solve for x in the equation 5/6x = 10/3, we aim to isolate x on one side of the equation. First, we would multiply both sides of the equation by the reciprocal of the fraction that is multiplied with x, which is 6/5. Multiplying both sides by 6/5 will cancel the 5/6 on the left side and leave us with x alone.

Here are the steps for the solution:

Multiply both sides of the equation by 6/5: (6/5) imes (5/6)x = (6/5) imes (10/3).

Simplify the left side: x = (6/5) imes (10/3).

Multiply the numerators and the denominators: x = (6 imes 10) / (5 imes 3).

Simplify the multiplication: x = 60 / 15.

Divide 60 by 15: x = 4.

Therefore, the value of x is 4.

For the expression (16y^5/4y^3)^12, you need to simplify the fraction inside the parentheses and then apply the square root to the simplified fraction. The final result is 2y.

The simplification of the expression (16y^5/4y^3)^12 into steps.

Simplify the fraction inside the parentheses:

16y5/4y3

=4y2

Apply the square root to the simplified fraction:

(4y2)12

=2y

By taking the square root, we reduce the exponent by half.

Therefore, the simplified expression is 2y.

Answer:

Add 9 to each side of the equation.

Step-by-step explanation:

To complete the square, we need to add (b/2) ^2 to each side, where b is the coefficient of the x terms.

The coefficient of the x terms is -6

so we need to add (-6/2) ^2 = (-3)^2 = 9.  

Add 9 to each side of the equation.

Answer:

The coefficient of the x terms is -6

so we need to add (-6/2) ^2 = (-3)^2 = 9.    

Add 9 to each side of the equation.

Step-by-step explanation:

[tex]\sin^2q+\cos^2q=1\to \cos^2q=1-\sin^2q\to\cos q=\pm\sqrt{1-\sin^2q}\\\\q\ \text{terminates in the fourth quadrant, therefore}\ \cos q > 0.\\\\\sin q=-\dfrac{3}{5}\to\cos q=\sqrt{1-\left(-\dfrac{3}{5}\right)^2}\\\\\cos q=\sqrt{1-\dfrac{9}{25}}\\\\\cos q=\sqrt{\dfrac{25}{25}-\dfrac{9}{25}}\\\\\cos q=\sqrt{\dfrac{16}{25}}\\\\\cos q=\dfrac{4}{5}[/tex]

[tex]\tan q=\dfrac{\sin q}{\cos q}\\\\\sin2q=2\sin q\cos q\\\\\cos2q=\cos^2q-\sin^2q\\\\\text{therefore}\\\\\tan2q=\dfrac{\sin2q}{\cos2q}=\dfrac{2\sin q\cos q}{\cos^2q-\sin^2q}\\\\\text{substitute}\\\\\tan2q=\dfrac{2\left(-\dfrac{3}{5}\right)\left(\dfrac{4}{5}\right)}{\left(\dfrac{4}{5}\right)^2-\left(-\dfrac{3}{5}\right)^2}=\dfrac{-\dfrac{24}{25}}{\dfrac{16}{25}-\dfrac{9}{25}}=\dfrac{-\dfrac{24}{25}}{\dfrac{7}{25}}=-\dfrac{24}{25}\cdot\dfrac{25}{7}=-\dfrac{24}{7}[/tex]

[tex]Answer:\ \boxed{B:\ -\dfrac{24}{7}}[/tex]

The exact value of tan 2θ will be –24/7. Then the correct option is B.

The connection between the lengths and angles of a triangular shape is the subject of trigonometry.

If sin θ = -3/5.

Then the value of cos θ will be

cos² θ = 1 – sin² θ

cos² θ = 1 – (-3/5)²

cos² θ = 1 – 9/25

cos² θ = 16/25

 cos θ = 4/5

Then the value of tan 2θ will be

[tex]\tan 2\theta = \dfrac{\sin 2\theta }{ \cos 2\theta}\\\\\\\tan 2\theta = \dfrac{2 \sin \theta \cos \theta }{ \cos^2 \theta - \sin ^2 \theta}\\\\\\\tan 2\theta = \dfrac{2 * \frac{-3}{5} * \frac{4}{5} }{( \frac{4}{5})^2 - ( \frac{-3}{5}) ^2 }[/tex]

Simplify the equation, we have

tan 2θ = (–24/25) / (7/25)

tan 2θ = –24/7

Then the correct option is B.

More about the trigonometry link is given below.

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Answer:

Step-by-step explanation:

Remark

You need 2 facts.

That means you can use the Pythagorean Theorem.

If one side of a square is a then the 1 after it is a as well.

Formula

Givens

Solution

Perimeter

P = 4s

You don't need the area. The answer is D

Area

For a square with a diagonal length of 11in, the side length is 11√2/2. The area of the square is then 60.5 square inches and the perimeter is 22√2 inches.

To find the perimeter and area of a square with a given diagonal length, we need to firstly understand the relation between the diagonal and sides of the square. A square's diagonal divides it into two equal right triangles, and according to Pythagoras' theorem, the diagonal, being the hypotenuse in these right triangles, is equal to the square root of the sum of the squares of the sides. But since all sides of a square are equal, let's say the side length is 'a', then the diagonal would be 'a√2'.

Given that the diagonal length is 11in, we then have:

11 = a√2 or a = 11/√2

It's common to rationalize the denominator which gives: a = 11√2/2

Area of a square is a², therefore, Area = (11√2/2)² = 121/2 = 60.5 square inches.

The Perimeter of a square is 4a, therefore, Perimeter = 4 * (11√2/2) = 22√2 inches.

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The measure of the smaller angle, when it is one-fourth the measure of the other supplementary angle, is 36 degrees.

The student is asking about the measures of two supplementary angles where one angle is four times the measure of the other angle. In Mathematics, supplementary angles are two angles whose sum is 180 degrees. Let's call the smaller angle 'x' and the larger angle '4x'. The equation we need to solve is:

x + 4x = 180

This equation simplifies to '5x = 180', meaning that 'x', the smaller angle, is equal to '180 / 5', which calculates to be 36 degrees. Therefore, the measure of the smaller angle is 36 degrees.

Answer:

E.

Step-by-step explanation:

Even though we have a sample of 40 units, we cannot determine that the units that are not in the sample will have the same or similar quality as the units that are in the sample. Thus none of the conclusions can be true.

Answer: Choice B) 100 pieces must be defective

Assuming the sample selected is representative of the population, we have two copies of "25" in that list (row 4; row 8) out of 40 total. So 2/40 = 1/20 = 0.05 = 5% of the items should be defective out of the entire population. Again this is assuming the sample is representative.

So we take 5% of 2000 and we end up with 0.05*2000 = 100 items we expect to be defective from a sample of 2000 items. Keep in mind that the true count will probably not be 100 items but some value close around it (eg: 98 or 101). This value is an estimate and not always perfect.

If choice B said "around 100" or "about 100" or "approximately 100" then I think it would be more technically correct. I think this is what your teacher is after.

Answer:

Andy bought = 13 cakes.

Betty bought = 52 cakes.

Colin bought = 16 cakes.

Step-by-step explanation:      

We are told that Andy buys x cakes. Betty buys 4 times as many cakes as Andy. So number of cakes bought by Betty will be 4*x.

We are also told that Colin buys 3 more cakes than Andy. So number of cakes bought by Colin will be x+3 cakes.

Each cake costs 65 p. The total cost of the cakes is $52.65. We can represent this information as:

[tex]0.65(x+4*x+x+3)=52.65[/tex]

[tex]0.65(2x+4*x+3)=52.65[/tex]

[tex]1.3x+2.6x+1.95=52.65[/tex]  

Let us combine like terms.

[tex](1.3+2.6)x+1.95=52.65[/tex]

[tex]3.9x+1.95=52.65[/tex]

[tex]3.9x=52.65-1.95[/tex]

[tex]3.9x=50.7[/tex]

[tex]x=13[/tex]

Therefore, Andy bought 13 cakes.

Let us find number of cakes bought by Betty by substituting x=13 in expression 4*x.

[tex]\text{Cakes bought by Betty}=4*13[/tex]

[tex]\text{Cakes bought by Betty}=52[/tex]

Therefore, Betty bought 52 cakes.

Now we will find number of cakes bought by Colin by substituting x=13 in expression x+3.

[tex]\text{Cakes bought by Colin}=13+3[/tex]

[tex]\text{Cakes bought by Colin}=16[/tex]

Therefore, Colin bought 16 cakes.

Andy bought 13 cakes, Betty bought 52 cakes, and Colin bought 16 cakes.

Let's break down the given information and solve the problem step by step:

Let the number of cakes bought by Andy be x.

Betty buys 4 times as many cakes as Andy, so she buys 4x cakes.

Colin buys 3 more cakes than Andy, so he buys (x+3) cakes.

The total cost of the cakes is €52.65, and each cake costs 65p.

Now, we can create the equation to find the value of x:

x*(65p) + 4x*(65p) + (x+3)*(65p) = £52.65

Simplifying the equation:

65x + 260x + 65x + 195 = 5265

390x + 195 = 5265

390x = 5070

x = 13

So, Andy bought 13 cakes, Betty bought 4x13 = 52 cakes, and Colin bought (13+3) = 16 cakes.

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Answer: what is the whole question angel?

Step-by-step explanation:

Answer:

See attachment

Step-by-step explanation:

We graph equations by drawing a number line and placing an open circle on the two values. We fill in the circles if we have [tex]\leq or \geq[/tex]. Since we don't, we leave it open. We then shade between the two.

Given these two equations:

1) 5x + y = 2
2) 4x + y = 4

Let's solve for x and y step by step.

Step 1: We start by subtracting equation (2) from equation (1) to eliminate y:

This gives us:

5x - 4x = 2 - 4

Which simplifies to:

x = -2

Step 2: Now, we substitute x = -2 into the equation (1) to find the value of y:

5*(-2) + y = 2

Which simplifies to:

-10 + y = 2
And therefore:

y = 12

So, the solution to the system of equations is x = -2 and y = 12.

Answer:

Option a is correct.

Exponential functions exhibit exponential growth (or decay) which mean the graph will rise or fall more dramatically than a polynomial graph

Step-by-step explanation:

An exponential function is in the form of [tex]y =ab^x[/tex] where a≠0  is a y-intercepts and  b is a positive number other than 1, multiplier this base is constant  , x  is the independent variable  and y is the dependent variable.

Exponential growth:

Exponential decay:

therefore, the graph will rise or fall more dramatically than a polynomial graph

Answer:

D. 13.267 m

Step-by-step explanation:

We can use the Pythagorean theorem to solve this problem

a^2 + b^2 = c^2

where a and b are the legs and c is the hypotenuse

7^2 + b^2 = 15^2

49 + b^2 = 225

Subtract 49 from each side

b^2 = 225-49

b^2 =176

Take the square root of each side

sqrt(b^2) = sqrt(176)

b = sqrt(176)

b = 13.266

Answer:7.50(x) + 24 is the answer

Step-by-step explanation:

Answer:

144 people.

Step-by-step explanation:

Let n be the vertices, where cars are located.

We have been given that the sum of the measures of the angles' vertices is 6120°.

Let us find the number of vertices using formula:

[tex]\text{Sum of all interior angles of a polygon with n sides}=180(n-2)[/tex].

Upon substituting the given sum of the measures of the angles in this formula we will get,

[tex]6120=180(n-2)[/tex]

Using distributive property [tex]a(b+c)=a*b+a*c[/tex] we will get,

[tex]6120=180n-360[/tex]

Adding 360 to both sides of our equation we will get,

[tex]6120+360=180n-360+360[/tex]

[tex]6480=180n[/tex]

Upon dividing both sides of our equation by 180 we will get,

[tex]\frac{6480}{180}=\frac{180n}{180}[/tex]

[tex]36=n[/tex]

As the cars are located on the vertices of regular polygon, so there will be 36 cars in the ride.

We are told that each car holds a maximum of 4 people, so the number of maximum people who can ride at one time will be equal to 4 times 36.

[tex]\text{Maximum number of people who can be on the ride at one time}=4\times 36[/tex]

[tex]\text{Maximum number of people who can be on the ride at one time}=144[/tex]

Therefore, the maximum number of people who can be on the ride at one time is 144 people.

The maximum number of people who can be on the ride at one time is 144, given that each car holds a maximum of four people.

Step 1

To find the maximum number of people who can be on the ride at one time, we need to determine the number of cars first, which is equal to the number of vertices in the regular polygon.

We know that the sum of the measures of the angles at the vertices of a polygon is given by the formula [tex]\(180^\circ \times (n - 2)\)[/tex], where n is the number of sides of the polygon.

Given that the sum of the measures of the angles' vertices is 6120°, we can set up the equation as follows:

[tex]\[180^\circ \times (n - 2) = 6120^\circ\][/tex]

Step 2

Solving for n:

[tex]\[n - 2 = \frac{6120^\circ}{180^\circ}\][/tex]

[tex]\[n - 2 = 34\][/tex]

[tex]\[n = 36\][/tex]

So, there are 36 cars on the ride. Since each car holds a maximum of four people, the maximum number of people who can be on the ride at one time is [tex]\(36 \times 4 = 144\)[/tex] people.

Answer:

Each shirt costs $22.95

Step-by-step explanation:

39.58 + 52.22 = 91.80

91.80/4 = 22.95

Answer:

[tex]2K+12L\geq87[/tex]

Step-by-step explanation:

Let K be the number of kites made by Min-young and L be the number of lamps made by Min-young.

We are told that it takes 2 wooden sticks to make a kite, so number of sticks used to make K kites will be 2K.

We are also told that it takes 12 wooden sticks to make a lamp, so number of sticks used to make L lamps will be 12L.

As Min-Young wants to make kites and lamps using at least 87 wooden sticks, so the total number of sticks used in making K  kites and L lamps will be greater than or equal to 87.

We can represent this information in an inequality as:

[tex]2K+12L\geq87[/tex]

Therefore, the our required inequality will be [tex]2K+12L\geq87[/tex].

An inequality based on the number of wooden sticks needed for making kites and lamps is 22K + 12L ≥ 87, where K represents the number of kites and L represents the number of lamps.

To determine the inequality that represents the condition based on the number of wooden sticks for making kites and lamps, we need to use the given data. It takes 22 wooden sticks to make a kite and 12 wooden sticks to make a lamp. Min-Young wants to use at least 87 wooden sticks.

The inequality will be formed by considering the number of kites (K) and the number of lamps (L) she wants to make. The total number of sticks used will be equal to 22 times the number of kites plus 12 times the number of lamps. This sum must be at least 87, the minimum number of sticks Min-Young wants to use. Therefore, the inequality can be written as 22K + 12L≥ 87.

Answer:KL

Step-by-step explanation:

Answer:

b - 60

Step-by-step explanation:

Let the number of books in the library be b.

The number of books in the library minus the 60 checked out is translated into a variable expression as b - 60

Answer:

[tex]b-60[/tex]

Step-by-step explanation:

We are given that the number of books in the library minus the 60

We have to translate the phrase into a variable expression.

We are given that a letter ''b'' is used for the number of books in the library.

Number of books in the library=b

According to question

[tex]b-60[/tex]

Hence, the required expression is given by

[tex]b-60[/tex]

Answer: Their actual volume in millions is 207×10⁹.

Step-by-step explanation:

Since we have given that

A certain corporation listed their sales in 100s as 20700

We need to find their actual volume in millions,

According to question,

In 100s, their volume = 2070000

In 100000, their volume is given by

[tex]207\times 10^5\\\\=2070000\times 10^5=207\times 10^9[/tex]

Hence, their actual volume in millions is 207×10⁹.

Answer:

see below

Step-by-step explanation:

(a) this is in the second quadrant.

(b) The tangent is negative in this quadrant

(c)

17 pi / 6  = 2 5pi/6

= 5pi/6 (this is the reference angle)

(d) this is equivalent to  -tan (pi/6)

(e)

tan 17pi/6

= tan 5pi/6

-√3/3

The sample mean X¯

X

¯

has normal distribution, mean the population mean μ

μ

, and standard deviation τ=84√

τ

=

8

4

. We want Pr(X¯−μ>2)

Pr

(

X

¯

−

μ

>

2

)

, which is Pr(Z>2τ)

Pr

(

Z

>

2

τ

)

, where Z

Z

is standard normal.

Answer: cotθ

Step-by-step explanation:

 tanθ * cos²θ * csc²θ

=  [tex]\dfrac{sin\theta}{cos\theta} * \dfrac{cos\theta*cos\theta}{} *\dfrac{1}{sin\theta*sin\theta}[/tex]

= [tex]\dfrac{cos\theta}{sin\theta}[/tex]

= cotθ

Answer: B

Step-by-step explanation:

The parent graph is y = x²

The new graph y = -x² + 3 should have the following:

Answers:

Explanation:

[tex]\dfrac{17\pi}{6} - \dfrac{12\pi}{6} = \dfrac{5\pi}{6}[/tex]

a) Quadrant 2 is: [tex]\dfrac{\pi}{2} < \theta < \pi[/tex]

b) In Quadrant 2, cos is negative and sin is positive, so tan is negative

c) [tex]\pi-\dfrac{5\pi}{6}[/tex] = [tex]\dfrac{\pi}{6}[/tex]

d) the reference line is above the x-axis so it is negative -->  [tex]-tan\dfrac{\pi}{6}[/tex]

e) [tex]tan(\dfrac{5\pi}{6})=\dfrac{1}{-\sqrt{3}}=-\dfrac{\sqrt{3}}{3}[/tex]

Answer:

It is equal to that area because 120 times 3 is equal to 360, which is the area of a circle

Step-by-step explanation:

To find this, you simply multiply 120 by 3, the 3 is from 1/3. That gives you ur answer

Answer:25 spaces in a row

Step-by-step explanation: Multiply 6 levels by 15 rows. Answer is 90.

Divide 90 into 2,250 parking spaces.

Answer is 25 spaces in each row.

Answer: D

Step-by-step explanation:

x - 2 = 0   -->   x = 2

Using synthetic division:

2   |   4   -5   3   -1

    |   ↓    8   6   18

        4    3   9   17  ← this is the remainder!

Using remainder theorem:

f(x) = 4x³ - 5x² + 3x - 1

f(2) = 4(2)³ - 5(2)² + 3(2) - 1

     =   32   - 20    +  6    - 1

    = 17