Rationalize the denominator and simplify
12/√7+2

Answer:

$2109

Step-by-step explanation:

We are given that Mr and Mrs Wilson payed a rent of $575 for the banquet hall and a per head of $13 for the catering dinner for their daughter's wedding.

We are to find the total amount they paid.

Amount paid for dinner for 118 people = [tex]118 \times 13[/tex] = $1534

Total amount payed by Mr and Mrs Wilson = $1534 + $575 = $2109

Inverse check:

2109 - 575 = 1534

1534/118 = 13

Answer:

2

Step-by-step explanation:

The rate at which the height increases is 2 inches per hour. That is the slope of the equation.

18 + 2t = 24

The coefficient of t is 2.

Answer:

2

Step-by-step explanation:

We are given that a cylinder container has a  height of 24 inches.

Currently, the container filled with water to a height=18 inches

If the height of the water in the container increase by 2 inches per hour

We are given that an equation which can be used to find the t in number of hours it would take to fill the container

We have to find the coefficient of t

In one hour, height increase=2 inches

In t hours, height increase=2t

According to question

[tex]18+2t=24[/tex]

Therefore, the coefficient of t is 2.

Hence, the number should be the coefficient of t=2

For this case we must find the product of the following expression:

[tex](-3x ^ 5y ^ 2) * (9x ^ 3y ^ 8)[/tex]

Then, by definition of powers of the same base we have to put the same base and add the exponents:

[tex](-3 * 9) x^{5 + 3} (1 * 1)y^{8 + 2} =[/tex]

[tex]-27x ^ 8*1y ^ {10}[/tex]

ANswer:

[tex]-27x ^ 8y ^ {10}[/tex]

Answer:

9y + 54

Step-by-step explanation:

Multiply 9 both terms inside the parentheses

y*9 + 6*9

9y + 54

Answer:

A

Step-by-step explanation:

If you choose any number 'k', then the result of subtracting 5 will be '5 less than k'.

Example: If k=6, k-5 is 1.

1 is 5 less than k=6.

The expression is also written as k less than 5. Then the correct option is C.

The equivalent is the expressions that are in different forms but are equal to the same value.

The expression is given as (k – 5).

The expression is also written as k less than 5.

Then the correct option is C.

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Answer:

option a

Step-by-step explanation:

we know  the equation of a circle is:

(x-x1)^2 +(y-y2)^2= r^2

center= (x1,y2)

radius =r

in this case we have:

center= (5,-2)

r=3

so we have:

(x-5)^2 +(y-(-2))^2=9

finally we have:

(x-5)^2 +(y+2)^2=9

Answer:

So, adding two rationals is the same as adding two such fractions, which will result in another fraction of this same form since integers are closed under addition and multiplication. Thus, adding two rational numbers produces another rational number. Proof: "The product of two rational numbers is rational."

Sum of two rational numbers is always a rational number is always true .

A rational number is a number that can be expressed as the quotient or fraction p/q of two integers, a numerator p and a non-zero denominator q. For example, −3/7 is a rational number, as is every integer

According to the question

The sum of two rational numbers :

Case 1: Consider rational numbers with different denominator : [tex]\frac{4}{5} , \frac{2}{3}[/tex]

Sum of both rational numbers

=  [tex]\frac{4}{5} + \frac{2}{3}[/tex]

= [tex]\frac{12 + 10 }{15}[/tex]

= [tex]\frac{22}{15}[/tex]

Case 2:Consider rational numbers with same denominator : [tex]\frac{4}{5} , \frac{1}{5}[/tex]

= [tex]\frac{4}{5} + \frac{1}{5}[/tex]

= [tex]\frac{5}{5}[/tex]

= [tex]\frac{1}{1}[/tex]

= 1

Sum in both cases are rational numbers

Hence, Sum of two rational numbers is always a rational number is always true .

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CREDIT BELONGS TO Sage24

I think that 3 rolls is wrong and that 6 rolls is right. If you create a 15 by 15 square and draw two lines through the center that connect to the opposite corner, you'll be able to use the Pythagorean Theorem.

Perimeter: 15+15+15+15=60ft.

Length of Line from Corner to Corner:

(15)(15)+(15)(15)=C^2

225+225=C^2

450=C^2

21.2=C

21.2(2)= 42.4ft.

42.4ft.+60ft.= 102.4ft.

102.4ft. divided by 20ft. = 5.12 = 6 rolls

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ANSWER

[tex] \log_{4}(3x + 4) = 2[/tex]

EXPLANATION

Consider the equation:

[tex] \log_{4}(3x + 4) = 2[/tex]

When we rewrite this logarithmic equation in the exponential form, we obtain:

[tex]3x + 4= {4}^{2} [/tex]

Note that to write a logarithmic equation in exponential form, the base of the logarithm is still the base in the exponential form.

We now simplify the RHS.

[tex]3x + 4 = 16[/tex]

Group like terms

[tex]3x = 16 - 4[/tex]

This implies that

[tex]3x = 12[/tex]

Divide both sides by 3

[tex] \frac{3x}{3} = \frac{12}{3} [/tex]

Simplify to get;

[tex]x = 4[/tex]

Hence the equation that has x=4 as a solution is

[tex] \log_{4}(3x + 4) = 2[/tex]

Another way to do this is to substitute x=4 into each equation. The equation that is satisfied is the correct choice.

Answer:

(A)

Step-by-step explanation:

on edg 2021

Answer:

60 more strips were used in the afternoon

Step-by-step explanation:

Bacon used in the morning

17 packages * 15 strips/ package = 255 strips

Bacon used in the afternoon

21 packages * 15 strips/package = 315

Difference = 315-255 =60

60 more were used in the afternoon

Answer:

729

Step-by-step explanation:

9 x 9 x 9

Answer:729

Step-by-step explanation:

third power means squared, and that means that you multiply the number by it's self three times, 9*9=81, that's once. then again 81*9 =728

Answer:

A ray has an endpoint at one end, and goes on infinitely in the other direction.  An endpoint is shown with a point (usually including a label that is typically a single letter), and the infinite direction is shown with an arrow.

Answer:

1,200 doctors use brand X aspirin

Step-by-step explanation:

Out of the 2,000 doctors, the survey showed that 3 out of 5 use brand X. So that means [tex]\frac{3}{5}[/tex] of 2000 doctors use Brand X. So the proportion will then be lke this:

[tex]\dfrac{3}{5} = \dfrac{x}{2000}[/tex]

So we can now solve for x using this equation:

[tex]\dfrac{3}{5} = \dfrac{x}{2000}\\\\\dfrac{(2000)(3)}{5} = x\\\\\dfrac{6000}{5} = x\\\\1200 = x[/tex]

Answer:

m=-4

Step-by-step explanation:

5m-10m=-10m+5m=-(10m-5m)=-5m=20

divide by 5 on both sides, -m=4

miltiply by -1 on both sides, m=-4

Answer:

m = - 4

Step-by-step explanation:

Given

5m - 10m = 20 ← simplify left side by combining terms

- 5m = 20 ( divide both sides by - 5 )

m = - 4

Answer:

-3 3/4, -3, 3 1/10, 3 1/3

Step-by-step explanation:

in negative numbers bigger number is always smaller in value and in fractions bigger numbers yet again if in a small portion is a smaller value

Answer:

The measure of angle JKM is 108°

Step-by-step explanation:

step 1

Find the value of x

we know that

The sum of the interior angles of a triangle must be equal to 180 degrees

so

∠M+∠L+∠MKL=180°

substitute the given values

4x+5x+6x=180°

15x=180°

x=12°

step 2

Find the measure of angle JKM

we know that

Angles MKL and JKM are supplementary angles

so

∠MKL+∠JKM=180°

6x+∠JKM=180°

substitute the value of x

6(12)+∠JKM=180°

∠JKM=180°-72°=108°

Answer:

108

Step-by-step explanation:

We know sum of all the 3 angles in a triangle is equal to 180. We can set up an equation for the triangle KML using the information given:

[tex]4x+5x+6x=180\\15x=180\\x=\frac{180}{15}=12[/tex]

So measure of Angle MKL is 6x, or 6(12) = 72

Now, we know Angle JKM + Angle MKL = 180 (straight line). Thus,

Angle JKM + 72 = 180

Angle JKM = 180 - 72 = 108

They're not equivalent.

[tex]|x|[/tex] (vertical bars) represents the absolute value of x. How it works is that it turns negative numbers positive but leaves 0 and positive numbers alone (hence it gets a number's distance from 0 on the number line).

[tex][x][/tex] (square brackets) usually represents the floor function, which returns the largest integer that is less than or equal to x. (The floor of x can also be written as [tex]\lfloor x \rfloor[/tex] --- it depends on what your textbook/source says).

To solve [tex]|x| - 3 = 7[/tex], you first transform it into the equivalent equation [tex]|x| = 10[/tex]. Then by definition of absolute value, there are only two solutions for the first equation: x = 10 or x = -10.

[x] = 10 has infinitely many solutions. For example, the floor of 10 is 10, so [tex][10] = 10[/tex], thus a solution for the second equation is x = 10

The floor of 10.1 is 10, so [tex][10.1] = 10[/tex], thus another solution for the second equation is x = 10.1.

The two equations do not have the same solution set (as x = 10.1 does not solve |x| - 3 = 7 but solves [x] = 10), so they're not equivalent.

Answer: Another angle would be 65 and two other angles would be 115.

Step-by-step explanation: Attachment shown.

Answer:

3. 32:4

4. three times

Step-by-step explanations:

Answer:

y=5/8  x+1

Step-by-step explanation:

so not 58 but 5/8 is the slope, okay... Did you try looking at your last question as an example for this one?  

y=mx+b

we are given m=5/8 so plug in

y=5/8  x+b

You are given an (x,y) on the line which is (-8,-4) so plug in and find b

-4=5/8  (-8)+b

-4=-5+b

1=b

So the line y=5/8  x+1

Answer:

Step-by-step explanation:

[tex]\left\{\begin{array}{ccc}2x+3y=17&\text{multiply both sides by (-2)}\\3x+6y=30\end{array}\right\\\underline{+\left\{\begin{array}{ccc}-4x-6y=-34\\3x+6y=30\end{array}\right}\qquad\text{add both sides of the equations}\\.\qquad-x=-4\qquad\text{change the signs}\\.\qquad x=4\\\\\text{put the value of x to the first equation:}\\\\2(4)+3y=17\\8+3y=17\qquad\text{subtract 8 from both sides}\\3y=9\qquad\text{divide both sides by 3}\\y=3[/tex]

For this case we must find the domain of the following function:

[tex]y = ln (x + 2)[/tex]

By definition, the domain of a function is given by all the values for which the function is defined.

In this case, the argument of the expression must be greater than 0 to be defined.

[tex]x + 2> 0\\x> -2[/tex]

Thus, the domain of the function is given by all the values of x greater than -2.

Answer:

Domain: [tex]x> -2[/tex]

Answer:

(-∞, ∞).

Step-by-step explanation:

This function can have any real value.

Range = (-∞, ∞).

The range of f(x) = 3/4x – 4 is [tex]\( (-\infty, \infty) \)[/tex].

To find the range of the function [tex]\( f(x) = \frac{3}{4}x - 4 \)[/tex], we need to consider all possible output values of the function as x varies.

The function x is a linear function with a slope of [tex]\( \frac{3}{4} \)[/tex], which means it increases or decreases steadily as x increases or decreases, respectively. Since there are no restrictions on the domain of the function (i.e., x can take any real value), the range of the function is also unrestricted.

To find the range, we can examine the behavior of the function as x approaches positive infinity and negative infinity:

1. As x approaches positive infinity, [tex]\( f(x) \)[/tex] also approaches positive infinity.

2. As x approaches negative infinity, [tex]\( f(x) \)[/tex] also approaches negative infinity.

Therefore, the range of the function [tex]\( f(x) = \frac{3}{4}x - 4 \)[/tex] is all real numbers. In interval notation, we can represent the range as [tex]\( (-\infty, \infty) \)[/tex].

Answer:

see explanation

Step-by-step explanation:

Using the addition identity for sine

sin(x + y) = sinxcosy - cosxsiny

Consider the left side

cos²(45 - A) - sin²(45 - A)

cos²(45 - A) = 1 - sin²(45 - A), thus

1 - sin²(45 - A) - sin²(45 - A)

= 1 - 2sin²(45 - A) ← expand sin(45 - A)

= 1 - 2(sin45cosA - cos45sinA)²

= 1 - 2([tex]\frac{\sqrt{2} }{2}[/tex]cosA - [tex]\frac{\sqrt{2} }{2}[/tex]sinA)²

= 1 - 2([tex]\frac{1}{2}[/tex]cos²A - sinAcosA + [tex]\frac{1}{2}[/tex]sin²A)

= 1 - cos²A + 2sinAcosA - sin²A

= sin²A + 2sinAcosA - sin²A

= 2sinAcosA

= sin2A = right side ⇒ verified

By Using the addition identity for sine; sin(x + y) = sinx cosy - cosx siny.

It is proved that cos²(45 - A) - sin²(45 - A)= Sin2A.

We can use the fact that:

[tex]\sin(\theta ^\circ) = \cos(90 - \theta^\circ)[/tex]

To convert the sine to cosine (but the angles won't stay the same unless it's 45 degrees).

Using the addition identity for sine

sin(x + y) = sinx cosy - cosx siny

Now,

cos²(45 - A) - sin²(45 - A)

cos²(45 - A) = 1 - sin²(45 - A),

1 - sin²(45 - A) - sin²(45 - A)

= 1 - 2sin²(45 - A)  

Expand sin(45 - A)

= 1 - 2(sin45cosA - cos45sinA)²

= 1 - 2(√2/2 cosA - √2/2 sinA)²

= 1 - 2(1/2 cos²A - sinAcosA + 1/2 sin²A)

= 1 - cos²A + 2sinAcosA - sin²A

= sin²A + 2sinAcosA - sin²A

= 2sinAcosA

cos²(45 - A) - sin²(45 - A) = sin2A = right side

Hence, it is verified.

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Answer:

The correct answer option is D. He multiplied the divisor by 100 and dividend by 10.

Step-by-step explanation:

We are given that Miguel completed the division where initially he had to divide 754 by 0.52.

To make it easier, he multiplied both the divisor and the dividend by the same number to get rid of the decimal in the divisor.

If he multiplied the divisor by 100, he should have multiplied the dividend by 100 too. But instead, he mistakenly multiplied the divisor by 100 and dividend by 10.

Answer:

1.5 hours is the correct answer !

Step-by-step explanation:

Speed is the rate of distance over time.

The equations are:

The given parameters are:

[tex]\mathbf{(t_1,d_1) = (1:30pm,35miles)}[/tex]

[tex]\mathbf{(t_2,d_2) = (4:30pm,230miles)}[/tex]

So, the time difference is:

[tex]\mathbf{t=4:30pm - 1:30pm}[/tex]

[tex]\mathbf{t=3\ hours}[/tex]

The distance traveled is:

[tex]\mathbf{d = 230miles - 35miles}[/tex]

[tex]\mathbf{d = 195miles}[/tex]

Speed is calculated as:

[tex]\mathbf{Speed = \frac{Distance}{Time}}[/tex]

So, we have:

[tex]\mathbf{Speed = \frac{195\ miles}{3\ hours}}[/tex]

Multiply both sides by 3 hours

[tex]\mathbf{3\ hours \times Speed = 195\ miles}[/tex]

Divide both sides by Speed

[tex]\mathbf{3\ hours = \frac{195\ miles}{Speed}}[/tex]

Hence, the equations are:

[tex]\mathbf{Speed = \frac{195\ miles}{3\ hours}}[/tex]

[tex]\mathbf{3\ hours \times Speed = 195\ miles}[/tex]

[tex]\mathbf{3\ hours = \frac{195\ miles}{Speed}}[/tex]

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Answer:

4

Step-by-step explanation:

=(1/2)^-2

=(2/1)^2

=2^2

=4

Answer:

C)   {xIx=R (all real #'s) , x>5}

Step-by-step explanation:

If I am reading the options correctly it should be c since after u add 7 to both sides you get x>5

(pls give brainliest)

Answer:

44cm

Step-by-step explanation:

Formula for circumference, C = 2πr

where r is the radius

r = C / 2π

= [tex]\frac{88\pi }{2\pi }[/tex]

=44 cm

Answer:

approximately 44 cm

Step-by-step explanation:

The formula for circumference of a circle of radius r is C = 2π·r.  Solving for r, we get:

         C

r = ------------

         2π

and in this instance, r = 88π cm   /   2π, or 44 cm

Answer:

$29.99

Step-by-step explanation:

This is a division problem.

$209.93/7 = $29.99

Answer: $29.99

Answer:

$29.99

Step-by-step explanation:

$209.93 divided by 7 is $29.99