What is the domain of the function? f(x)=[tex]\frac{x-3}{2x^{2}+x-21 }[/tex] (−∞,3)∪(3,∞) (−∞,−3)∪(−3,72)∪(72,∞) (−∞,−72)∪(−72,∞) (−∞,−72)∪(−72,3)∪(3,∞)

━━━━━━━━━━━━━━━ ♡ ━━━━━━━━━━━━━━━  

To simplify a number, you have to find the greatest common factor (of the numerator and the denominator) and divide each number by the greatest common factor.

The greatest common factor of 3 and 12 is 3.

Now divide each 3 and 12 by 3.

3 ÷ 3 = 1

12 ÷ 3 = 4

Now the numerator is 1 and the denominator is 4.

3/12 in reduced form is 1/4.

━━━━━━━━━━━━━━━ ♡ ━━━━━━━━━━━━━━━  

Answer:

3/12 in reduced form is 1/4

Step-by-step explanation:

find GCF for 3 and 12 which is 3 . step 2 divide numerator and denominator by GCd which is 3 and rewrite the fraction = (3/3) / (12/3) which equals 1/4. Thus 1/4 is the simplified fraction for 3/12 your welcome

Answer:

10 square units

Step-by-step explanation:

Answer:

The family will pay 34722 cents more if they take the van

Step-by-step explanation:

Given

Van = 12 miles per gallon

Sedan = 36 miles per gallon

Distance = 2500 miles

Gas = $2.50 per gallon

First, we need to determine the number of gallons that'll be used by both vehicles

This  is done by dividing total distance by number of miles per gallon

[tex]Van = \frac{2500}{12} \ gallon[/tex]

[tex]Sedan = \frac{2500}{36}\ gallon[/tex]

Next, is to multiply this by the cost of gas per gallon;

This gives the total spendable amount on both vehicles

[tex]Van = \frac{2500}{12} * \$2.50[/tex]

[tex]Van = \frac{\$6250}{12}[/tex]

[tex]Van = \$520.833[/tex]

[tex]Sedan = \frac{2500}{36}* \$2.50[/tex]

[tex]Sedan = \frac{\$6250}{36}[/tex]

[tex]Sedan = \$173.611[/tex]

Next is to get the difference between these amounts

[tex]Difference = \$520.833 - \$173.611[/tex]

[tex]Difference = \$347.222[/tex]

Multiply by 100 to convert to cents

[tex]Difference = 347.222 * 100 cents[/tex]

[tex]Difference = 34722.2 \ cents[/tex]

[tex]Difference = 34722\ cents[/tex] (Approximated)

Hence;

The family will pay 34722 cents more if they take the van

Answer:

you have four techniques to choose from: plugging in the x value, factoring, rationalizing the numerator, and finding the lowest common denominator.

hope that helps : )

Answer:

2, 5, & 6

Step-by-step explanation:

2, because it’s the opposite angle.

5, because it’s parallel.

6, because it’s opposite to 5.

2, 5, & 6 all equal 100°.

1, 3, 4, & 7 all equal 80°.

The angles formed that are congruent to angle measure of 100 degrees when transversal t intersects parallel lines m and n are:

Angle measuring 100 degrees is the given angle measure formed at the point of intersection between line m and transversal t.

Thus, angles that are congruent to 100 degrees will be equal in measure to 100 degrees.

The following are angles congruent to 100 degrees.

<2 is congruent to 100 degrees (vertically opposite angles are congruent).

<5 is congruent to 100 degrees (corresponding angles are congruent).

<6 is congruent to 100 degrees (alternate exterior angles are congruent).

Therefore, the angles formed that are congruent to angle measure of 100 degrees when transversal t intersects parallel lines m and n are:

Learn more here:

https://brainly.com/question/15937977

Answer:

Step-by-step explanation: you sjxhbtdtbd

Answer:

x = 3

Step-by-step explanation:

6x + 2x - 5= 19

8x -5 = 19

8x = 24

x = 3

Answer:

x = 3

Step-by-step explanation:

6x + 2x - 5 = 19

Note the equal sign, what you do to one side, you do to the other. Do the opposite of PEMDAS.

First, combine like terms:

(6x + 2x) - 5 = 19

(8x) - 5 = 19

Next, isolate the variable, x. First, add 5 to both sides:

8x - 5 (+5) = 19 (+5)

8x = 19 + 5

8x = 24

Next, divide 8 from both sides:

(8x)/8 = (24)/8

x = 24/8

x = 3

3 is your answer for x.

~

Answer:

Answer: There is 1 1/2 times more juice than ginger ale; there is 2/3 as much ginger ale as there is punch.

Step-by-step explanation:

Answer:

Answer A:

Step-by-step explanation:

2 parts ginger ale to 3 parts raspberry juice.

Answer:

x = 9, AR = 25 , AM = 40

Step-by-step explanation:

Since AM = AR + RM and AM also = 7x-23

7x - 23 = (2x + 7) + 15

7x - 23 = 2x + 22

    +23          +23

7x = 2x + 45

-2x   -2x

5x = 45

x = 9

Now plug x = 9 into 2x + 7 to find AR

AR = 2x + 7

     = 2 (9) + 7

     = 18 + 7

AR  = 25

Now to find AM plug x = 9 into 7x - 23

AM = 7x - 23

      = 7 (9) - 23

      = 63 - 23

AM = 40

To double check, we already know that RM = 15, so add AR + RM to find AM

AM = 25 + 15

AM = 40

Answer:

9 = x

AR = 25

AM =  40

Step-by-step explanation:

AR + RM = AM

2x+7 +15 = 7x - 23

Combine like terms

2x+22 = 7x -23

Subtract 2x from each side

2x+22 -2x = 7x-2x -23

22 = 5x - 23

Add 23 to each side

22+23 = 5x-23+23

45 = 5x

Divide each side by 5

45/5 = 5x/5

9 = x

AR = 2x+7 = 2*9 +7 = 18+7 = 25

AM = 7x-23 = 7*9 -23 = 63-23 = 40

Answer: 6 hours

Step-by-step explanation:

Let x= the number of hours they've worked

12x+6x=108

Combine like terms

18x=108

Divide 18 on both sides

18/18 x=108/18

x=6

Hope this helps!! :)

Please let me know if you have any question

both the father and son worked for 6 hours each.

Let's denote the number of hours that both the father and son worked as "h".

The father charges $12 per hour, so his earnings for h hours of work would be 12h dollars.

The son charges $6 per hour, so his earnings for h hours of work would be 6h dollars.

Since their combined charge for labor was $108, we can set up the equation:

12h + 6h = 108

Combining like terms:

18h = 108

To solve for h, we divide both sides of the equation by 18:

h = 108 / 18

h = 6

Therefore, both the father and son worked for 6 hours each.

Learn more about work here

https://brainly.com/question/11421188

#SPJ2

Answer:

number 3 I think I'm not sure

Answer:

Hey there!

Total students: 7+9+5+3+12=36

Students that like math: 7

7/36=19.4% of students like math.

Let me know if this helps :)

Answer:

19% (Math)

Step-by-step explanation:

7 divide by total number of students (36) X100% =19%

Answer:

An interesting experiment is given. We need to address various questions based on our knowledge of calculus.

Step 2

Part (a)

Time taken for the radius to grow to 2 cm = t1 = r/0.5 = 2/0.5 = 4 hours

Time taken for the radius to become 0 = t2 and the same can be obtained by solving:

r = 2 - √t2 = 0

Hence, t2 = 22 = 4 hours

Hence, the time duration of the entire experiment (from the introduction of the bacteria until its disappearance) = t1 + t2 = 4 + 4 = 8 hours

Step 3

Part (b)

r(t) = 0.5t for 0 ≤ t ≤ 4

and

r(t) = 2 - √(t - 4) for t > 2

Step-by-step explanation:

Answer: 140°

Step-by-step explanation:

If you look at ∠BXF, you can see that F is at the base of the inner semi circle. Going left, you can see that it stops at 140. Now, we know that m∠BXF is 140°.

Answer:

  m∠BXF = 140°

Step-by-step explanation:

The symbol "<" is "greater than." The symbol "∠" is "angle." When used as "m∠", it refers to "the measure of angle ...".

Here, you're asked for the measure of angle BXF.

You can see that it is an obtuse angle, so will have a measure greater than 90°. The protractor has two scales: one measuring angles counterclockwise, and the other measuring angles clockwise. Ray XF is aligned with the 0 on the inner (counterclockwise) scale, so the angle measure is found where ray XB crosses that scale.

Ray XB crosses the inner scale of the protractor at 140, so ...

  m∠BXF = 140°.

Answer:

A

Step-by-step explanation:

Answer:

See below.

Step-by-step explanation:

So we have the two functions:

[tex]f(x)=-3x\text{ and } g(x)=2x-1[/tex]

And we want to find f(x) + g(x).

So, substitute:

[tex]f(x)+g(x)\\=(-3x)+(2x-1)[/tex]

Combine like terms:

[tex]=(-3x+2x)+(-1)[/tex]

Simplify:

[tex]=-x-1[/tex]

So:

[tex]f(x)+g(x)=-x-1[/tex]

Answer:

[tex]\frac{511\,\,\sqrt{3} }{99}[/tex]  which is an irrational number

Step-by-step explanation:

Recall that the repeating decimal 0.7373737373... can be written in fraction form as: [tex]\frac{73}{99}[/tex]

Now, let's write the number 147 which is inside the square root in factor form to find if it has some perfect square factors:

[tex]147=7^2\,3[/tex]

Then, 7 will be able to go outside the root when we compute the final product requested:

[tex]\frac{73}{99} \,*\,7\,\sqrt{3} =\frac{511\,\,\sqrt{3} }{99}[/tex]

This is an irrational number due to the fact that it is the product of a rational number (quotient between 511 and 99) times the irrational number [tex]\sqrt{3}[/tex]

Answer:

Step-by-step explanation:

(4 + 9x)^3 represents "the cube of the sum of 4 and 9 times x"

and if we divide by "the product of 5 times x and the difference of x and 1," we get

    (4 + 9x)^3

-----------------------

       5x(x - 1)

What exactly do you need to know, or to do?

Answer:

a. [tex]\mathbf{P(\overline x < 68) = 0.9998}[/tex]

b. [tex]\mathbf{P(68 < \overline x < 69 ) =0}[/tex]

c. [tex]\mathbf{P ( \overline x > 66 ) =0.02275}[/tex]

Step-by-step explanation:

Given that ;

Let Y be a random variable In a​ population, where:

mean [tex]\mu_y[/tex] = 65

[tex]\sigma^2_y[/tex] = 49

standard deviation σ  = [tex]\sqrt{49}[/tex] = 7

The objective is to determine the following :

In a random sample of size n​ = 69​, find Pr(Y <68) =

Using the Central limit theorem

[tex]P(\overline x < 68) = \begin {pmatrix} \dfrac{\overline x - \mu }{\dfrac{\sigma}{\sqrt{n}}} < \dfrac{68 - \mu }{\dfrac{\sigma}{\sqrt{n}}} } \end {pmatrix}[/tex]

[tex]P(\overline x < 68) = \begin {pmatrix}Z < \dfrac{68 - 65 }{\dfrac{7}{\sqrt{69}}} } \end {pmatrix}[/tex]

[tex]P(\overline x < 68) = \begin {pmatrix}Z < \dfrac{3 }{\dfrac{7}{8.3066}} } \end {pmatrix}[/tex]

[tex]P(\overline x < 68) = (Z < 3.5599 )[/tex]

From the z tables:

[tex]\mathbf{P(\overline x < 68) = 0.9998}[/tex]

In a random sample of size n​ = 124​, find Pr (68< Y <69)=

[tex]P(68 < \overline x < 69 ) = P \begin {pmatrix} \dfrac{68- \mu}{\dfrac{\sigma}{\sqrt{n}}} < \dfrac{\overline x - \mu}{\dfrac{\sigma}{\sqrt{n}}} < \dfrac{ 69 - \mu}{\dfrac{\sigma}{\sqrt{n}}} \end {pmatrix}[/tex]

[tex]P(68 < \overline x < 69 ) = P \begin {pmatrix} \dfrac{68- 65}{\dfrac{7}{\sqrt{124}}} < Z < \dfrac{ 69 - 65}{\dfrac{7}{\sqrt{124}}} \end {pmatrix}[/tex]

[tex]P(68 < \overline x < 69 ) = P \begin {pmatrix} \dfrac{3}{\dfrac{7}{11.1355}} < Z < \dfrac{ 4}{\dfrac{7}{11.1355}} \end {pmatrix}[/tex]

[tex]P(68 < \overline x < 69 ) = P \begin {pmatrix} 4.7724 < Z < 6.3631 \end {pmatrix}[/tex]

[tex]P(68 < \overline x < 69 ) = P( Z < 6.3631 ) - P ( Z < 4.7724 )[/tex]

From z tables

[tex]P(68 < \overline x < 69 ) = 0.9999 - 0.9999[/tex]

[tex]\mathbf{P(68 < \overline x < 69 ) =0}[/tex]

In a random sample of size n​ = 196​, find Pr (Y >66)=

[tex]P ( \overline x > 66 ) = P ( \dfrac{\overline x -\mu }{\dfrac{\sigma}{\sqrt{n}}} > \dfrac{66 -\mu }{\dfrac{\sigma}{\sqrt{n}}})[/tex]

[tex]P ( \overline x > 66 ) = P ( Z> \dfrac{66 - 65 }{\dfrac{7}{\sqrt{196}}})[/tex]

[tex]P ( \overline x > 66 ) = P ( Z> \dfrac{1 }{\dfrac{7}{14}})[/tex]

[tex]P ( \overline x > 66 ) = P ( Z> \dfrac{14 }{7})[/tex]

[tex]P ( \overline x > 66 ) = P ( Z>2)[/tex]

[tex]P ( \overline x > 66 ) = 1 - P ( Z<2)[/tex]

from z tables

[tex]P ( \overline x > 66 ) = 1 - 0.9773[/tex]

[tex]\mathbf{P ( \overline x > 66 ) =0.02275}[/tex]

Answer:

E. This polynomial could be factored by using grouping or the perfect squares methods.

Step-by-step explanation:

x^2 + 2x + 1

There is no greatest common factor

This is a perfect square

a^2 + 2ab+ b^2 = ( x+1)^2

We can factor this  by grouping

x^2 + 2x + 1

(x^2 +x) + (x+1)

x( x+1)  + x+1

Factor out x+1

( x+1)  ( x+1)

This is not the difference of squares since there is no subtraction

Answer:

SOHCAHTOA.

we have to use SOH(Sin) here because the theta is 65° and the opposite is 13 while the hypotenuse is x.

which is Sin 65°=13/x.

xSin65°=13.

0.906307787x=13.

x=13/0.9063=14.34403619~14.

Answer:

Volume of the lake = 6.44 × 10¹¹ Litres

Step-by-step explanation:

First, let us unify the units of measurement in the problem by converting the depth from feet to miles

1 mile = 5280 feet

1 foot = 1/5280 miles

∴ 51.0 Feet = 51.0 × (1/5280) miles

= 0.009659 miles

Next, let us calculate the volume of the lake.

Volume = surface area × depth

surface area = 16.0 (mi)²

depth = 0.009659 mi

volume = 16.0 × 0.009659 = 0.15454 (mi)³

Next, since we are asked to report the volume in litres, let us convert from cubic miles to litres

1 cubic mile = 4.168 × 10¹² litres

∴ 0.15454 cubic miles = 4.168 × 10¹² × 0.15454

= 6.44 × 10¹¹ Litres

∴ Volume of the lake = 6.44 × 10¹¹ Litres

The volume of the lake is 6.46×10¹¹ liters.

To get the volume of the lake in liters, we need to calculate the volume in square miles and then convert it to liters.

Formula:

Where:

From the question,

Given:

Substitute these values into equation 1

Hence, the volume of the lake is  6.46×10¹¹ liters

Learn more about volume here: https://brainly.com/question/12410983

Answer:

[tex]\int_C F . dr = \pi[/tex]

[tex]C : x = cost , y = sin t, z = sin^2 t - cos^2 t , 0 \leq t \leq 2 \pi[/tex]

Step-by-step explanation:

Given that:

[tex]F(x,y,z) = x^2yi + \dfrac{1}{3}x^3j +xyk[/tex]

Here C is the curve of intersection of the hyperbolic parabolic [tex]z = y^2 - x^2[/tex] and the cylinder [tex]x^2 +y^2 =1[/tex]

Using Stokes' Theorem

[tex]\int_C F . dr =\int \int \limits_s \ curl \ F. \ds[/tex]

From above ;

S = the region under the surface [tex]z = y^2 -x^2[/tex] and above the circle [tex]x^2+y^2 =1[/tex]

Suppose, we consider [tex]f(x,y,z) =z-y^2+x^2[/tex]

therefore, S will be the level curve of f(x,y,z) = 0

Recall that:

[tex]\bigtriangledown f (x,y,z)[/tex] is always normal to the surface S at the point (x,y,z).

∴

This implies that the unit vector [tex]n = \dfrac{\bigtriangledown f}{|| \bigtriangledown ||}[/tex]

So [tex]\bigtriangledown f = <2x, -2y,1 >[/tex]

Also, [tex]|| \bigtriangledown f ||= \sqrt{4x^2+4y^2+1}[/tex]

Similarly ;

[tex]curl \ F = \begin {vmatrix} \begin{array} {ccc}{\dfrac{\partial }{\partial x} }&{\dfrac{\partial }{\partial y} }& {\dfrac{\partial }{\partial z} }\\ \\ x^2y& \dfrac{1}{3}x^3&xy \end {array} \end{vmatrix}[/tex]

[tex]curl \ F = \langle x ,-y,0 \rangle[/tex]

Then:

[tex]\int \int_s curl \ F .ds = \int \int_s curl \ F .nds[/tex]

[tex]\int \int_s curl \ F .ds = \iint_D curl \ F \dfrac{\bigtriangledown f}{ || \bigtriangledown f||} \sqrt{ (\dfrac{\partial z}{\partial x }^2) + \dfrac{\partial z}{\partial x }^2)+1 } \ dA[/tex]

[tex]\int \int_s curl \ F .ds = \iint_D \dfrac{\langle x,-y,0 \rangle * \langle 2x,-2y,1 \rangle }{\sqrt{4x^2 +4y^2 +1 }} \times \sqrt{4x^2 +4y^2 +1 }\ dA[/tex]

[tex]\int \int_s curl \ F .ds = \iint_D (2x^2 + 2y^2) \ dA[/tex]

[tex]\int \int_s curl \ F .ds = 2 \iint_D (x^2 + y^2) \ dA[/tex]

[tex]\int \int_s curl \ F .ds = 2 \int \limits ^{2 \pi} _{0} \int \limits ^1_0r^2.r \ dr \ d\theta[/tex]

converting the integral to polar coordinates

This implies that:

[tex]\int \int_s curl \ F .ds = 2 \int \limits ^{2 \pi} _{0} \int \limits ^1_0r^2.r \ dr \ d\theta[/tex]

⇒ [tex]\int_C F . dr = 2(\theta) ^{2 \pi} _{0} \begin {pmatrix} \dfrac{r^4}{4}^ \end {pmatrix}^1_0[/tex]

[tex]\int_C F . dr = 2(2 \pi) (\dfrac{1}{4})[/tex]

[tex]\int_C F . dr =(4 \pi) (\dfrac{1}{4})[/tex]

[tex]\int_C F . dr = \pi[/tex]

Therefore, the value of [tex]\int_C F . dr = \pi[/tex]

The parametric equations for the curve of intersection of the hyperbolic paraboloid can be expressed as the equations of the plane and cylinder in parametric form . i.e

[tex]z = y^2 - x^2 \ such \ that:\ x=x , y=y , z = y^2 - x^2[/tex]

[tex]x^2 +y^2 =1 \ such \ that \ : x = cos \ t , y= sin \ t, z = z, 0 \leq t \leq 2 \pi[/tex]

Set them equal now,

the Parametric equation of [tex]C : x = cost , y = sin t, z = sin^2 t - cos^2 t , 0 \leq t \leq 2 \pi[/tex]

Answer:

False!

Step-by-step explanation:It is not possible.

Answer:

False

Step-by-step explanation: there is no possible way

plz brainliest

Answer: F (-8, -3), G (-3, -5) and H (-1, -7)

Step-by-step explanation:

A rotation of 180° around the origin is equivalent to a reflection over the x-axis, and then another reflection over the y-axis.

Then, if we have a point (x, y) and we do a rotation of 180°, the point will transform into (-x, -y)

Then if at the start the vertices of the triangle are:

F (8, 3), G (3, 5), and H (1, 7).

After a rotation of 180°, the vertices will be:

F (-8, -3), G (-3, -5) and H (-1, -7)

The correct option is the last one.

Answer:

9

step by step explanation :

390

Hope this helps :)

384 the next greatest number of tens is 390.

Arithmetic operations can also be specified by subtracting, dividing, and multiplying built-in functions.

The operator that performs the arithmetic operation is called the arithmetic operator.

Operators which let do a basic mathematical calculation

Note that the tens place is two moves to the right of the decimal point (if it exists).

To determine the greatest number to the nearest ten (nearest 10),

we use the place of the whole number to determine whether the tens place rounds up or stays the same.

The tens place (8) then look at the digit to the right (4):

⇒ 384

The digit to the right (4) is 4 or below. So, we replace it with a 0 (zero) to get 390 as the answer.

So, 384 the next greatest number of tens is 390.

Learn more about Arithmetic operations here:

brainly.com/question/25834626

#SPJ2

Answer:

The equation used to solve Carey's hourly rate is:

1 + (c/2) = 6

Step-by-step explanation:

Answer:

The equation used to solve Carey's hourly rate is:

1 + (c/2) = 6

Step-by-step explanation:

edg2020

Answer:

6=6

True for all a

Step-by-step explanation:

[tex]2a+6=2a+5+1\\\mathrm{Subtract\:}2a\mathrm{\:from\:both\:sides}\\\mathrm{Simplify}\\6=5+1\\\mathrm{Simplify\:}5+1:\quad 6\\\\6 = 6[/tex]

Answer:

infinite solutions

Step-by-step explanation:

2a+6=2a+5+1

Combine like terms

2a+6 = 2a+6

Subtract 2a from each side

6 =6

Since this is always true, we have infinite solutions

Answer:

The range of the curve is [tex][-9,9][/tex].

Step-by-step explanation:

The domain of the curve corresponds to the values on horizontal axis (x-Axis), where the range of curve corresponds to the values on vertical axis (y-Axis). In addition, the curve is continuous in [tex](-5, 8)[/tex], so that images exists within interval.

The range of the curve is [tex][-9,9][/tex].

Answer:

.00000005708 is your answer. If it's asking you to solve the problem, 49.08

Answer:

[tex]\Huge \boxed{0.00000005708}[/tex]

[tex]\rule[225]{225}{2}[/tex]

Step-by-step explanation:

[tex]5.708 \cdot 10^{-8}[/tex]

Solving for exponent and evaluating:

[tex]\displaystyle 5.708 \cdot \frac{1}{10^8 }[/tex]

[tex]\displaystyle \frac{5.708}{10^8 }[/tex]

[tex]\Rightarrow \ \displaystyle \frac{5.708}{100000000}[/tex]

The decimal place moves 8 units to the left side.

[tex]\Rightarrow \ 0.00000005708[/tex]

[tex]\rule[225]{225}{2}[/tex]