The table shows values for the functions f(x) and g(x). What are the solutions of X where f(x) = g(x)?



Question 3 options:

x = -1


x = 0


x = 1


x = 2


x = 3


x = 4


x = 5


x = 3

Answer:

[tex] \frac{3}{x - 3} - \frac{5}{x - 2} = \frac{3(x - 2) - 5(x - 3)}{(x - 3)(x - 2)} = \frac{3x - 6 - 5x + 15}{(x - 3)(x - 2)} = \frac{9 - 2x}{(x - 3)(x - 2)} [/tex]

To simplify the expression 3/x-3 - 5/x-2 into one fraction, you need to find a common denominator. The simplified expression is (-2x+9) / [(x-3)(x-2)].

To simplify the expression 3/x-3 - 5/x-2 into one fraction, we need to find a common denominator.

The denominator of the first fraction is x-3 and the denominator of the second fraction is x-2.

The common denominator will be (x-3)(x-2) since that is the product of the two denominators.

Multiplying the numerator and denominator of the first fraction by (x-2) and the numerator and denominator of the second fraction by (x-3), we get:

[(3)(x-2)] / [(x-3)(x-2)] - [(5)(x-3)] / [(x-3)(x-2)]

= (3x-6) / [(x-3)(x-2)] - (5x-15) / [(x-3)(x-2)]

Now that we have a common denominator, we can combine the terms in the numerator:

(3x-6 - 5x+15) / [(x-3)(x-2)] = (-2x+9) / [(x-3)(x-2)]

Therefore, the simplified expression is (-2x+9) / [(x-3)(x-2)].

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:

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:

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: There is no picture ?

Step-by-step explanation:

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:

[tex]x^2 +(y-8)^2=64[/tex]

Step-by-step explanation:

The equation of the circle with center at point [tex](x_0,y_0)[/tex] and radius r is

[tex](x-x_0)^2+(y-y_0)^2=r^2[/tex]

In your case,

So, the equation of the circle with center at (0,8) and radius r=8 is

[tex](x-0)^2+(y-8)^2=8^2\\ \\x^2 +(y-8)^2=64[/tex]

Answer: x² +( y - 8 )² =64

Step-by-step explanation: happy to help :)

Answer:

Option B (3x - 4y = -4).

Step-by-step explanation:

Parallel lines are the straight lines that never meet. This is only possible when the gradients of both the lines are same. This means that the slopes of all the parallel lines in a group can be calculated by calculating the slope of one of the lines. Therefore, the slope of the line that is parallel to the line 3x-4y=7 is the same as the original line. Hence, the gradient can be extracted from the original line by converting the equation in the form y=mx+c, where m is the slope.

3x - 7 = 4y.

y = (3/4)x - 7/4.

The slope of the line which has to be found is 3/4 and it passes through (x0, y0) = (-4, -2). Using the following formula:

(y - y0) = m*(x - x0).

(y + 2) = (3/4)*(x + 4)

Cross multiplying:

4y + 8 = 3x + 12.

3x - 4y = -4.

Hence, Option B is the correct choice!!!

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

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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She earns commission on the amount of sales  over $10,000

Subtract 10,000 from her sales to get the amount she earns commission on:

30,000 - 10,000 = 20,000.

multiply that by the percent:

20,000 x 0.12 = 2400

She earned $2,400 in commission.

Now add that to her salary to find her total pay:

45,000 + 2,400 =  $47,400

Answer:

$47,400.

Step-by-step explanation:

We have been given that Yvette earns 12% commission on any sales over $10,000. Last year Yvette made $30,000 in sales.

The amount on which Yvette will get commission would be [tex]\$30,000-\$10,000=\$20,000[/tex].

Since Yvette gets 12% commission, so amount earned as commission would be 12% of $20,000.

[tex]\text{Commission}=\$20,000\times \frac{12}{100}[/tex]

[tex]\text{Commission}=\$20,000\times 0.12[/tex]

[tex]\text{Commission}=\$2,400[/tex]

Yvette also gets a salary of $45,000, so Yvette's total earnings would be $45,000 plus $2,400.

[tex]\text{Yvette's total earnings}=\$45,000+\$2,400[/tex]

[tex]\text{Yvette's total earnings}=\$47,400[/tex]

Therefore, Yvette's earned $47,400 in salary plus commission.

Hello There!

Statistics is a tool used to help people process, summarize, analyze and interpret data for making better decisions.

It helps us with future events if we know what has happened in past.

Helps us make better decisions.

The better we know about the future of an outcome, the more possibility we have to work around it.

Answer:

Statistic is the art or science of collecting,analysing ,summarising and presenting data by using numbers.

Answer:

We need to find the increasing function with constant slope.

Let us check each option one by one.

A) 6x -5y =10.

Let us solve it for y to get slope-intercept form

6x-5y =10.

-5y =-6x +10.

y =6/5 x-2.

Slope is 6/5 positive, therefore, it's an increasing function.

A linear function always has a constant slope.

Therefore, correct option is option A.

A. 6x -5y =10

All other options are incorrect.

Step-by-step explanation:

Please mark brainliest and have a great day!

Answer:

18

Step-by-step explanation:

thanks..

..

Answer:

C. 18

Step-by-step explanation:

Let x represent number of stereos.

We have been given that a salesman sold each stereo for $1500. He earned a commission of 16.5% on each stereo sold.

The amount of commission earned on each stereo would be 16.5% of 1500.

[tex]1500\times \frac{16.5}{100}=15\times 16.5=247.5[/tex]

The amount of commission earned on x stereos would be [tex]247.5x[/tex].

We are told his base salary is $33,170, so total salary of salesman would be [tex]247.5x+33,170[/tex].

We are also given that last year he earned $37,625. We can represent this information in an equation as:

[tex]247.5x+33,170=37,625[/tex]

[tex]247.5x+33,170-33,170=37,625-33,170[/tex]

[tex]247.5x=4455[/tex]

[tex]\frac{247.5x}{247.5}=\frac{4455}{247.5}[/tex]

[tex]x=18[/tex]

Therefore, the salesman sold 18 stereos last year.

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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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:

300+85670=85970

Answer:

85,970

Step-by-step explanation:

This is simple, just add 300 or 3 hundreds to 85,650 on a calculator to get 85,970. 6 + 3 = 9.

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:

80¢\lb.; 58 667\1000 ft.\sec.

Step-by-step explanation:

Divide the cost by three; multiply 40 by 1.466675.

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

[tex]6 \sqrt{6} [/tex]

EXPLANATION

The given product is

[tex] \sqrt{12} \times \sqrt{18} [/tex]

We rewrite to get;

[tex] \sqrt{4 \times 3} \times \sqrt{9 \times 2} [/tex]

We split the radical sign to get:

[tex]\sqrt{4 } \times \sqrt{3} \times \sqrt{9} \times \sqrt{2} [/tex]

The perfect squares simplifies to:

[tex]2\sqrt{3} \times 3 \sqrt{ 2} [/tex]

This gives us :

[tex]2 \times 3 \sqrt{3 \times 2} [/tex]

This simplifies to;

[tex]6 \sqrt{6} [/tex]

Answer: [tex]b=1[/tex]

Step-by-step explanation:

Given the equation [tex]-3(-8b+7)=3(2b-1)[/tex] you need to solve for the variable "b".

You need to apply Distributive property on both sides of the equation:

[tex]-3(-8b+7)=3(2b-1)\\\\24b-21=6b-3[/tex]

Now you need to add 21 to both sides of the equation:

[tex]24b-21+21=6b-3+21\\\\24b=6b+18[/tex]

Subtract [tex]6b[/tex] from both sides:

[tex]24b-6b=6b+18-6b\\\\18b=18[/tex]

And finally, you can divide both sides of the equation by 18:

[tex]\frac{18b}{18}=\frac{18}{18}\\\\b=1[/tex]

Answer:

b=1

Step-by-step explanation:

You first need to multiply -3 and -8b. That will be 24b. Then you multiply -3 times 7. That will be -21. On the other side, you will multiply 3 times 2b which will equal 6b. Then you multiply 3 by -1. You will get -3. So at this point, the equation should look like this, 24b-21=6b-3. Then add 21 to both sides. You will have this equation, 24b=6b+18. Then subtract 6b from both sides, 18b=18. Finally, divide 18 from both sides to get your final answer of b=1.

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:

x ≥ 6

Step-by-step explanation:

Lets solve the first inequality:

7x - 6 > 8

7x > 8 + 6

7x > 14

x > 14/7

x > 2

And now the second inequality:

3x + 4 ≥ 22

3x ≥ 22 - 4

3x ≥ 18

x ≥ 18/3

x ≥ 6

So, from the 2 answers, which region is overlapping ?? x ≥ 6

So this is the solution.

Note: we disregard x from 2 to 6 because that region is ONLY solution to the first one

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:

[tex]\$635.62[/tex]  

Step-by-step explanation:

The formula to calculate continuously compounded interest is equal to

[tex]A=P(e)^{rt}[/tex]  

where  

A is the Final Investment Value  

P is the Principal amount of money to be invested  

r is the rate of interest in decimal  

t is Number of Time Periods  

e is the mathematical constant number

we have  

[tex]t=3\ years\\ P=\$500\\ r=0.08[/tex]  

substitute in the formula above  

[tex]A=\$500(e)^{0.08*3}[/tex]  

[tex]A=\$635.62[/tex]  

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:

4

Step-by-step explanation:

=(1/2)^-2

=(2/1)^2

=2^2

=4

Answer:

the third one

Step-by-step explanation:

count your factors of 5... I count 6

so the only answer that says you have a factor of 3 and 6 factors of 5 is the third one