Factor 6x4 – 5x2 + 12x2 – 10 by grouping. What is the resulting expression?

Answer:

[tex]5(a^2b-a^2c-db+dc)[/tex]

Step-by-step explanation:

Given expression is [tex]5a^2b- 5a^2c -5db +5dc[/tex].

Now we need to show the first step of factoring.

We know that first step of factoring in any problem is to find the GCF that is find the greatest common factor. We see that 5 is the only largest number that can divide each term so 5 is the GCF.

Now we write 5 outside parenthesis and divide given terms by 5 to find the terms that goes inside parenthesis.

Hence first step of factoring is given by :

[tex]5a^2b- 5a^2c -5db +5dc[/tex]

[tex]=5(a^2b-a^2c-db+dc)[/tex]

The first step when factoring [tex]\(5a^2b - 5a^2c - 5db + 5dc\)[/tex] by grouping is to group the terms and then factor out the common terms from each group

Let's factor the expression [tex]\(5a^2b - 5a^2c - 5db + 5dc\)[/tex] by grouping.

First, let's group the terms:

[tex]\( (5a^2b - 5a^2c) + (-5db + 5dc) \)[/tex]

Now, let's factor out the common terms from each group:

[tex]\( 5a^2(b - c) + 5d(-b + c) \)[/tex]

Now, we can factor out the common factor of 5 from both terms:

[tex]\( 5(a^2(b - c) + d(-b + c)) \)[/tex]

So, the factored expression is [tex]\(5(a^2(b - c) + d(-b + c))\).[/tex]

In the given expression, we have four terms[tex]: \(5a^2b\), \(-5a^2c\), \(-5db\), and \(5dc\).[/tex]

The first step in factoring by grouping is to group the terms in pairs. Here, we pair [tex]\(5a^2b\)[/tex] with [tex]\(-5a^2c\)[/tex] and [tex]\(-5db\)[/tex] with [tex]\(5dc\).[/tex]

Next, we factor out the common terms from each group. From the first group, we factor out [tex]\(5a^2\)[/tex], and from the second group, we factor out [tex]\(5d\).[/tex] This leaves us with [tex]\(b - c\)[/tex] in the first group and [tex]\(-b + c\)[/tex] in the second group.

Finally, we factor out the common factor of 5 from both terms to get the final factored expression [tex]\(5(a^2(b - c) + d(-b + c))\).[/tex]

So, the first step when factoring [tex]\(5a^2b - 5a^2c - 5db + 5dc\)[/tex] by grouping is to group the terms and then factor out the common terms from each group.

Complete question:

show the first step when factoring [tex]5a^2b- 5a^2c -5db +5dc[/tex] by grouping?

Answer:

Both A and B

Step-by-step explanation:

A = {(3, −5), (4, 6), (−3, 9), (2, 7)}  

-Each x goes to a different y so this is a function

B = {(2, 4), (−1, −7), (5, 6), (4, 3)}

-Each x goes to a different y so this is a function

ANSWER

The value of x is 47°

EXPLANATION

PQ is a tangent to the circle at Q.

This tangent meets the diameter at 90°.

The sum of interior angles of a triangle is 180°

This implies that:

[tex]90 \degree + x + 43 \degree = 180 \degree[/tex]

[tex]133 \degree + x = 180 \degree[/tex]

Group similar terms to obtain;

[tex] x = 180 \degree - 133 \degree[/tex]

Simplify similar terms to get;

[tex]x = 47\degree[/tex]

Answer:

The value of x = 47°

Step-by-step explanation:

From the figure we can see that a circle with center O.

PQ is a tangent to the circle fro point P.

m<P = 43°

Therefore <Q = 90°

To find the value of x

From the given triangle we can write,

x + m<Q + m<P = 180

x = 180 - (m<Q + m<P)

 = 180 - (90 + 43)

 = 180 - 133 = 47°

Therefore the value of x = 47°

Answer:

The top isn't closed.

Step-by-step explanation:

The bottom is enclosed, creating more surface area, but the top is opened.

Answer:

The surface area of a cylinder is given by :

SA=[tex]2 \pi rh+2\pi r^{2}[/tex]

When the base is same but the height is doubled. Doubling the height replaces h with 2h:

New formula becomes:

SA=[tex]2 \pi r(2h)+2\pi r^{2}[/tex]

SA = [tex]4\pi rh+2\pi r^{2}[/tex]

We can see that only the height is doubled not the radius. The formula changes a little bit.

We can take an example-

Lets say the height of cylinder is 10 cm and radius is 4 cm

So, SA in 1st case :

SA=[tex]2\times3.14\times4\times10+ 2\times3.14\times (4)^{2}[/tex]

=[tex]251.2+100.48=351.68[/tex] cm square

SA in 2nd case:

[tex]4\times3.14\times4\times10+ 2\times3.14\times(4)^{2}[/tex]

= [tex]502.4+100.48=602.88[/tex] cm square

We can see that area of lateral surface doubles up in case 2 but the base area remains the same.

Answer:

±i√55

Step-by-step explanation:

Answer:b

Step-by-step explanation:

Answer:

x < 6

Step-by-step explanation:

Let's isolate x first.  Add 3 to both sides, obtaining (1/3)x < 2.  Now multiply both sides by 3 to eliminate the fraction:  x < 6

Answer:

1.  $640

2. About 10.3 years later

Step-by-step explanation:

This is a compound decay problem. The formula is

[tex]F=P(1-r)^t[/tex]

Where

F is the future amount

P is the initial amount

r is the rate of decrease (in decimal), and

t is the time in years

Question 1:

We want to find F after 2 years of a phone initially costing 1000. So,

P = 1000

r = 20% or 0.2

t = 2

plugging into the formula, we solve for F:

[tex]F=P(1-r)^t\\F=1000(1-0.2)^2\\F=1000(0.8)^2\\F=640[/tex]

The phone is worth $640 after 2 years

Question 2:

We want to find when will the phone be worth 10% of original.

10% of 1000 is 0.1 * 1000 = 100

So, we want to figure this out for future value of 100, so F = 100

We know, P = 1000 r = 0.2 and t is unknown.

Let's plug in and solve for t (we need to use logarithms):

[tex]F=P(1-r)^t\\100=1000(1-0.2)^t\\100=1000(0.8)^t\\\frac{100}{1000}=0.8^t\\0.1=0.8^t\\ln(0.1)=ln(0.8^t)\\ln(0.1)=t*ln(0.8)\\t=\frac{ln(0.1)}{ln(0.8)}\\t=10.32[/tex]

So, after 10.32 years, the phone would be worth less than 10% of original value.

Answer: 0, 4, -9

Set the equation equal to zero.

x(x - 4)(x + 9) = 0

Solve for x by setting each factor equal to zero.

The factors in the equation are x, (x - 4), and (x + 9).

        x = 4

        x = -9

The zeros of the function are 0, 4, and -9.

Answer:

Step-by-step explanation:

x% of y equals to 0.01*x*y

Just put the numbers in the formula

33% of 507 = 167.31

48% of 375 = 180

76% of 285 = 216.6

60% of 398 = 238.8

89% of 150 = 133.5

26% of 430 = 111.8

81% of 216 = 174.96

5% of 584 = 29.2

18% of 725 = 130.5

2% of 115 = 2.3

90% of 152 = 136.8

12% of 649 = 77.88

55% of 216 = 118.8

43% of 108 = 46.44

97% of 235 = 227.95

Step-by-step explanation:

(B).(x=5 or -5) is the homogeneous mixture

The first equation has two distinct rational solutions, the expression 2x - 1 can be one of the factors to solve the second equation, the solutions to the third equation are x = -2/5 and x = 0, and the solutions to the fourth equation are x = -1 and x = -5.

1. To find the solutions to the equation x^2 - 1 = 24, we can start by isolating the squared term:

x^2 = 24 + 1

x^2 = 25

Next, we take the square root of both sides to find the values of x:

x = ±√25

Therefore, there are two distinct rational solutions to the equation.

2. In order to solve the quadratic equation 2x^2 - 7x + 3 = 0, Marcus can use the quadratic formula x = (-b ± √(b^2 - 4ac)) / (2a). One of the factors he can write is 2x - 1.

3. The solutions to the equation 5x^2 = -2x are found by getting all the terms to one side and setting the equation equal to zero:

5x^2 + 2x = 0

Next, we factor out the greatest common factor:

x(5x + 2) = 0

Setting each term equal to zero, we get two values for x:

x = 0 or x = -2/5

Therefore, the statement that the solutions are x = -2/5 and x = 0 is true.

4. To find the solutions to the equation (x + 3)^2 - 4 = 0, we isolate the squared quantity:

(x + 3)^2 = 4

Next, we take the square root of both sides, considering both the positive and negative square roots:

x + 3 = ±√4

x + 3 = ±2

Solving for x, we get two solutions:

x = -3 - 2 = -5

x = -3 + 2 = -1

Therefore, the statement that the solutions are x = -1 and x = -5 is true.

https://brainly.com/question/30098550

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Answer:

C

Step-by-step explanation:

Since the triangle is right use Pythagoras' identity to solve for x

The square on the hypotenuse is equal to the sum of the squares on the other two sides.

Note the 2 legs are equal, that is both x, hence

x² + x² = 16²

2x² = 256 ( divide both sides by 2 )

x² = 128 ( take the square root of both sides )

x = [tex]\sqrt{128}[/tex] = [tex]\sqrt{64(2)}[/tex] = [tex]\sqrt{64}[/tex] × [tex]\sqrt{2}[/tex] = 8[tex]\sqrt{2}[/tex]

ANSWER

x=100,y=10

EXPLANATION

The given logarithmic equations are;

[tex] log_{10}( {x}^{2} {y}^{3} ) = 7[/tex]

This implies that,

[tex] {x}^{2} {y}^{3} = {10}^{7} ...(1)[/tex]

and

[tex] log_{10}( \frac{x}{y} ) = 1[/tex]

This implies that,

[tex] \frac{x}{y} = {10}^{1} [/tex]

[tex]x = 10y...(2)[/tex]

Put equation (2) into equation (1)

[tex]{(10y)}^{2} {y}^{3} = {10}^{7}[/tex]

[tex]10 ^{2} y^{2} {y}^{3} = {10}^{7}[/tex]

[tex]{y}^{5} = {10}^{5}[/tex]

Hence y=10.

This implies

[tex]x = 10(10) = 100[/tex]

x = 0, -1, -2

When the function is set equal to zero and solved for, you end up with these three numbers.

The collection of investments in a mutual fund is referred to as a portfolio, which can include a variety of stocks and bonds. Index funds are examples of mutual funds that track the performance of market indexes. Mutual funds are significant in the financial landscape, with many U.S. households investing in them.

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Mutual funds gather stocks or bonds from various companies into one investment vehicle, making it simpler for investors to own a diversified collection without purchasing each security individually.

Investors purchase shares of the mutual fund and receive returns based on the collective performance of the fund's portfolio.

For instance, index funds are types of mutual funds that aim to mimic the performance of a specific market index.

This strategy offers broad market exposure and low operating expenses.

There are also specialized mutual funds that focus on particular sectors or regions, offering different levels of risk and potential return.

In the modern financial landscape, mutual funds play a significant role, with a substantial percentage of U.S. households holding investments in these funds.

Answer:

x = π/2 or

x = π/2 + 2πn (for any value of n)

Step-by-step explanation:

We need to find the numerical value of the trigonometric function sinx+1/sinx=1+cscx

Subtract 1+cscx on both sides

sinx + 1/sinx -(1+csc x) = 1+cscx - (1+cscx)

sinx + 1/sinx -1 -csc x = 0

Taking LCM i.e, sinx and solving

(sinx)(sinx) + 1 - sinx -cscx(sinx) / sinx = 0

Multiplying sinx on both sides

sin^2 x + 1 -sinx - cscx(sinx) =0

as we know, cscx = 1/ sinx

sin^2 x + 1 -sinx - (1/sinx)(sinx) = 0

Solving,

sin^2 x + 1 -sinx - 1 = 0

sin^2 x - sin x =0

Let u = sinx

Putting it in above equation

u^2 - u =0

Solving the equation:

u= 1 , u= 0

Putting back the value of u

sin(x) = 1 and sin(x) = 0

x = sin ⁻¹ (1) and x = sin ⁻¹ (1) =0

x = 90° or π/2 and x = 0 (undefined for the question)

So, x = π/2 or

x = π/2 + 2πn (for any value of n)

ANSWER

9

EXPLANATION

We want to find the distance between the points (3, -5) and (-6, -5).

The given points have the same y-coordinates .

This means it is a horizontal line.

We use the absolute value method to find the distance between the two points.

We find the absolute value of the distance between the x-values.

The distance between the two points is

|3--6|=|3+6|=|9|=9

Answer:

3. Since the range of the original function is limited to y> 6, the domain of the inverse function is x ≥ 6.

Step-by-step explanation:

The domain of a function is the range of its inverse, and vice versa. The only answer choice that expresses this relationship is choice 3.

__

Comment on the answer choice:

The slope of the function is undefined at x=4, so restricting the function domain to the portion with positive slope means the domain restriction of the function is x > 4. That also means the range restriction of the function is y > 6. The domain restriction of the inverse function is the same: x > 6, not x ≥ 6. The answer choice has an error.

The domain of the original function with the positive slope is restricted to x > 4, and the range of f(x) is y ≥ 6. Therefore, the domain of the inverse function is x ≥ 6.

The function given is f(x) = |x – 4| + 6. When restricting the domain to the portion of the graph with a positive slope, the function increases. In the absolute value function, the slope changes at the vertex, which here is when x = 4. For x > 4, the slope is +1 because the graph of the function is increasing. So, considering the domain x > 4 makes the graph of the function only represent the portion with a positive slope.

The range of the original function with the restricted domain is f(x) ≥ 6, because the lowest value of |x – 4| is 0 when x ≥ 4, which results in f(x) = 0 + 6 = 6 when x = 4. Consequently, the corresponding range of the inverse function must be the domain of the original function, and thus, the domain of the inverse function must be x ≥ 6.

Answer: I would just say add a line to the Equal sign so the equation would read

5+5+5≠550, since this way it would say that 5+5+5 ISNT equal to 550 which is technically true, but that might be wrong.

Answer:

The safe dose for the child is:   [tex]640\ \frac{mg}{day}[/tex]

Step-by-step explanation:

We know that the conversion factor is 40 mg/kg/day

The child weighs 16 kg. This means that 40 mg per day corresponds to each kilogram of the child.

So to know how many milligrams per day correspond per day we must multiply 16 kg by the conversion factor

[tex]16\ kg * 40\ \frac{\frac{mg}{kg}}{day} = 640\ \frac{mg}{day}[/tex]

Answer:

The safest dose would be 640 mg per day.

Hope this helps!

Answer:

x = -48, y = 25

Step-by-step explanation:

Both equations have a 5y term, we can work with that.

Let's first convert them into 5y = ... form:

2x + 5y = 29 => 5y = 29 - 2x

3x + 5y = -19 => 5y = -3x - 19

Now we can equate the right-hand sides:

29 - 2x = -3x - 19

And simplify:

29 + 19 = -3x + 2x => x = -48

Let's put this x value in the first:

2*(-48) + 5y = 29 =>

-96 - 29 = -5y =>

-5y = -125 =>

y = 25

Answer:

3C + 5 T = 550

C+T= 122

PUT IN 1  T= 122-C

3C + 5 (122-C)=550

3C -5C + 610=550

-2C= 550 - 610= -30

C= 15

T= 122-15 = 107

Step-by-step explanation:

Answer:  50

Step-by-step explanation:

Let x be the number of cars and y be the number of trucks .

By considering the given information, we get

[tex]x+y=122-----------------(1)\\\\3x+5y=510-------------------(2)[/tex]

Multiply (1) by 3 , we get

[tex]3x+3y=366--------------(3)[/tex]

Eliminate equation (3) from (2), we get

[tex]2y=144\\\\\Rightarrow\ y=72[/tex]

Put y= 72 in equation (1), we get

[tex]x+72=122\\\\\Rightarrow\ x=122-72=50[/tex]

Hence, the number of cars did the club = 50

ANSWER

1. -7

2. no real solution

EXPLANATION

1. The given quadratic equation is:

[tex]12 {x}^{2} - 7x - 9 = 0[/tex]

Comparing this to

[tex]a{x}^{2} + bx + c= 0[/tex]

we have a=12, b=-7 and x=-9.

Therefore the value of b is -7

2. The given quadratic equation is

[tex]3{x}^{2} + 3x + 2= 0[/tex]

We have a=3,b=3 and c=2.

The discriminant of this equation is

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

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

[tex]D= 9- 24 = - 15[/tex]

Since the discriminant is negative, the equation has no real roots.

[tex]12x ^{2}-7x -= 0 \\ \\ x = \frac{7 + \sqrt{481} }{24} \: or \: x = \frac{7 - \sqrt{481} }{24} \\ \: b. \: -7 \\ \\3x^{2} + 3x + 2 = 0 \\ c. \: no \: real \: solutions[/tex]

The answer is:

The second option,

b.) [tex]C(x)=40.60x+201[/tex]

We are given the functions E(x) and K(x), since they both are function of the same variable, we need to add them in order to find the correct option.

From the statement we know the functions:

[tex]E(x)=22.75x+74[/tex]

and

[tex]K(x)=17.85x+127[/tex]

So, adding the functions we have:

[tex]C(x)=E(x)+F(x)[/tex]

[tex]C(x)=(22.75x+74)+(17.85x+127)[/tex]

[tex]C(x)=22.75x+17.85x+74+127[/tex]

[tex]C(x)=40.60x+201[/tex]

Hence, the answer is the second option,

b.) [tex]C(x)=40.60x+201[/tex]

Have a nice day!

Answer:

The answer is b

Step-by-step explanation:

C(x)=40.60x + 201

Answer:

21503 feet²

Step-by-step explanation:

Area of Square 1 = 69 x 69 = 4761

Area of Triangle = 69 x 92 ÷ 2 = 3174

Area of Square 2 = 92 x 92 = 8464

Area of Circle = 57.5² x π ÷ 2 ≈ 5104

Total Area = 21503

Answer:

it is C

Step-by-step explanation:

i hope this helped = ) <3

21.6 x 5.9 x 0.5 = 63.72

The area of the triangle is 63.72 ft²

Answer:

63.72 ft^2

Step-by-step explanation:

The base and the height of the triangle are given:  21.6 ft and 5.9 ft.

Apply the area-of-a-triangle formula:

A = (1/2)(base)(height)

Here, the area is

A = (1/2)(21.6 ft)(5.9 ft) = 63.72 ft^2

Answer:

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

Step-by-step explanation:

Given

sin x = - 1

x = [tex]sin^{-1}[/tex] ( - 1 )

  = [tex]\frac{3\pi }{2}[/tex] + 2kπ k ∈ Z

For 2π < x < 4π, then

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

Answer:

Step-by-step explanation:

[tex]Q+p+Q+p+Q\\\\\text{combine like terms}\\\\=(Q+Q+Q)+(p+p)=3Q+2p[/tex]

Answer:

three hundred

Step-by-step explanation:

Answer:

300

Step-by-step explanation:

5,9 times 540