Given f(x) = 3x - 1 and g(x) = 2x + 1, find (f +g)(3)

Answer:

C

Step-by-step explanation:

The equation of a line in slope- intercept form is

y = mx + c ( m is the slope and c the y- intercept )

y = [tex]\frac{3}{4}[/tex] x + 4 ← is in slope- intercept form

with slope m = [tex]\frac{3}{4}[/tex]

Parallel lines have equal slopes, thus this is slope of parallel line.

The line crosses the y- axis at (0, 2) ⇒ c = 2

y = [tex]\frac{3}{4}[/tex] x + 2 → C

Answer:

about 37% chance or, rounding to the nearest tenth, 36.5% chance

Step-by-step explanation:

since there are only 6 black face cards out of 52 cards, so the fraction is 6/52

there are also 13 spade cards out of 52 cards, so the fraction is 13/52

to find the percent you have to add the two fractions becuase all you want to do is draw a black face card or a spade card. when you add them you get 19/52

then dividing the fraction gives you .3653846154 on my calculator :)

Answer:

A. Yes

B. Yes

C. No

Step-by-step explanation:

We can substitute each value in to the equation and see if the sides match up. Let's start with a.

[tex]4\cdot(2)-3 = -2\cdot(2)+9\\8-3 = -4+9\\5 = 5[/tex]

So, n = 2 works for equation a. Let's try B.

[tex]9\cdot(\frac{10}{3}) - 19 = 3\cdot(\frac{10}{3}) + 1\\\\\\\frac{90}{3} -19 = \frac{30}{3} + 1 \\ 30 - 19 = 10 + 1\\11 = 11[/tex]

So, m = [tex]\frac{10}{3}[/tex] works for B. Now let's try C.

[tex]3(30+8) = 2\cdot(30)-6\\3(38) = 60-6\\114 \neq 54[/tex]

So y = 30 doesn't work for C.

Hope this helped!

Answer:

x = 6

Step-by-step explanation:

The x-intercept of the equation is where the graph crosses the x-axis when y = 0. So, we simply plug in 0 for y:

2(0) - x = -6

0 - x = -6

-x = -6

x = 6

Alternatively, you can graph the equation into a graphing calc and analyze where the graph crosses the x-axis.

Answer:

The answer is below

Step-by-step explanation:

The shape of the figure attached is the shape of a sector with an angle of 90° (quarter of a circle).

From the sector, AB = AC = radius of the sector (r) = 12. Therefore:

[tex]Area\ of\ sector=\frac{\theta}{360}*\pi r^2 = \frac{90}{360}*\pi * (12)^2 = 0.25 * \pi * 144=36\pi\\\\Area\ of\ triangle\ ABC=\frac{1}{2}*base *height= \frac{1}{2}*AB*BC=\frac{1}{2}*12*12=72\\\\Area \of\ shaded\ region = Area\ of\ sector-Area\ of\ triangle=36\pi-72\\\\Area \of\ shaded\ region =36\pi-72[/tex]

From the triangle: AC² = AB² + BC²

AC² = 12² + 12² = 144 + 144

AC² = 288

AC=√288 = 12√2

[tex]Perimeter\ of\ sector=\frac{\theta}{360}*2\pi r = \frac{90}{360}*2\pi * (12) = 0.25 * 2\pi * 12=6\pi\\\\Perimeter \of\ shaded\ region = Perimeter\ of\ sector+AC=6\pi + 12\sqrt{2}[/tex]

Answer:

yes

Step-by-step explanation: i agree its 3

Answer:

[tex]\large \boxed{\sf \ \ \dfrac{x^2}{x^4+1}=\dfrac{1}{7} \ \ }[/tex]

Step-by-step explanation:

Hello,

We know that (let's assume that x is different from 0 as we cannot divide by 0)

   [tex]x+\dfrac{1}{x}=3[/tex]

and we want to estimate

   [tex]\dfrac{x^2}{x^4+1}[/tex]

Let's take the square.

[tex]9=3^2=(x+\dfrac{1}{x})^2=x^2+2\cdot x \cdot \dfrac{1}{x}+\dfrac{1}{x^2}=x^2+2+\dfrac{1}{x^2}=\dfrac{x^4+1}{x^2}+2[/tex]

So, we can write

[tex]\dfrac{x^4+1}{x^2}=9-2=7 \\ \\\\\text{*** let's take the inverse ***} \\ \\\dfrac{x^2}{x^4+1}=\dfrac{1}{7}[/tex]

Hope this helps.

Do not hesitate if you need further explanation.

Thank you

Answer:

2.625 cups or 21 ounces

Step-by-step explanation:

Ava needs 3/4 cup of blue paint for every 1 cup of white paint. So, the ratio is 0.75 : 1.

She has 28 ounces of white paint. But, you have to convert ounces to cups.

1 cup = 8 ounces

28 ounces ÷ 8 ounces/cup = 3.5 cups

Now set up a ratio.

[tex]\frac{0.75}{1} = \frac{x}{3.5}[/tex]

X (how much blue paint is needed) is over 3.5 cups (the amount of white paint she has)

Cross multiply and divide.

[tex]\frac{0.75}{1} = \frac{x}{3.5}[/tex]

x = 0.75 × 3.5

x = 2.625 cups

To convert to ounces, multiply by 8.

2.625 cups × 8 ounces = 21 ounces

Therefore, Ava needs 2.625 cups or 21 ounces of blue paint.

Hope that helps.

Answer:

SAS Postulate

Step-by-step explanation:

In EDG & ADC ,

1) AD = ED ( given )

2)angle( EDG ) = angle ( ADC )................ [ Vertical Opposite Angles are equal ]

3) GD = CD ( D is the mid - point of CG )

So triangles EDG & ADC are congruent by SAS postulate....

Answer:

[see below]

Step-by-step explanation:

Geo has 3/8 of a pizza. His sister has 7/9 of another pizza.

Add the values:

[tex]\frac{3}{8}+\frac{7}{9}\\\\ \text{The LCM of the denominators is 72.}\\\\\frac{3*9}{8*9}=\frac{27}{72}\\\\\frac{7*8}{8*9}=\frac{56}{72}\\\\\frac{27+56}{72}=\frac{83}{72}\\\\\frac{83}{72}=1\frac{11}{72}\\\\\boxed{\frac{3}{8}+\frac{7}{9} = 1\frac{11}{72}}[/tex]

Answer:

315943/12683

Step-by-step explanation:

Well -9 2/7 * -10 3/7 is 315943/12683

Answer:

540/49

Step-by-step explanation:

Work on the brackets first: (-10✖️3/7)=-30/7

-30/7✖️2/27=-60/49

-60/49✖️-9=540/49

Answer:

x = 1

Step-by-step explanation:

The diagonals of a parallelogram bisect each other, thus

AE = CE , substitute values

11x - 3 = 12 - 4x ( add 4x to both sides )

15x - 3 = 12 ( add 3 to both sides )

15x = 15 ( divide both sides by 15 )

x = 1

Answer:

25x  ²−49y ²

Step-by-step explanation:

We need to find product of (5x+7)(5x−7y)

By using identity (a+b)(a−b)=a −b  ²

We have a=5x,b=7y

Thus (5x+7y)(5x−7y)=(5x)  ²−(7y)  

let me know if it was helpful

25x² - 49y²

Step-by-step explanation:

To Find:

The product of (5x - 7y)(5 x + 7)

How to solve:

Just need to use the formula of a² - b² = (a+b)(a-b)

let's assume a = 5x and b = 7x

Solution:

(5x - 7y)(5 x + 7) = (5x)² - (7y)²

= 25x² - 49y²

Hence required answer is 25x² - 49y².

Answer:

[tex]x = 17[/tex]

Step-by-step explanation:

According to the two tangent theory, tangent MN and tangent NP, which are both from point N, are congruent.

That is, [tex]x + 4 = 21[/tex]

Solve for x

[tex]x + 4 = 21[/tex]

Subtract 4 from both sides

[tex]x + 4 - 4 = 21 - 4[/tex]

[tex]x = 17[/tex]

Answer:

$3,500

Step-by-step explanation:

First, Lets analyze the problem.

LeBron buys 500 shares for $10 a share. So he buys 500 shares for $5,000.

Now the price drops to $3, he had 500 stocks, the stocks are now only worth $1500.

5000-1500=3,500

He has lost $3,500 in the Tiger Corporation shares.

Answer:

8 more unit of tiles

Step-by-step explanation:

The function is given as;

f(x) = x² - 6x + 1

Now, we want to add more unit tiles to complete the square.

The given function(f(x)) is of the order 2 due to the highest power of 2 attached to x, but the side of the square will be of the order 1.

Now, Let's make a general order 1 expression ax + b to be the side of the square.

From the function forming the square after adding some p unit tiles, we have;

f(x) + p = (side of square)²

Thus;

x² - 6x + 1 + p = (ax + b)²

x² - 6x + 1 + p = a²x² + 2abx + b²

Comparing both sides of the equation, we have;

a² = 1

2ab = 6

b² = 1 + p

From a² = 1, a = 1

From 2ab = 6,putting 1 for a, we have;

2(1)b = 6

b = 6/2

b = 3

From b² = 1 + p

Putting 3 for b, we have;

3² = 1 + p

9 = 1 + p

9 - 1 = p

p = 8

Thus, 8 more unit of tiles are required to complete the square.

Hey there!

We see that the first factor is 82.17, which is about 80. Then, we have 7.32, which is about 7.

80 times 7 is just doing 8 times 7 but putting a zero on the end!

So, 80 times 7 is 560, so our best estimate is A.560

Have a wonderful day!

Answer:

[tex]\frac{9}{4}/\frac{3}{2}[/tex]

Step-by-step explanation:

[tex]-2\frac{1}{4}[/tex] is equilavalent to [tex]-\frac{9}{4\\}[/tex].

[tex]-\frac{2}{3}[/tex] can stay put.

The equation is division so neither answers #2 and #3 are the correct ones because when dividing fractions the second fraction has to be flipped in order to continue multiplying instead.

In addition, when two negatives are put together the answer must always be positive.  

Hence the answer is [tex]\frac{9}{4}/\frac{3}{2}[/tex].

Answer:

Reflection

Step-by-step explanation:

Just took the test got a 100%

edg 2021

Answer:

A: Reflection

Step-by-step explanation:

Let's be honest, no one hardly ever pays attiontion to the explanation.

<3

Answer:

Step-by-step explanation:

a = 8

b  = 10

a^3 =8^3 = 512

b^3= 10^3 =1000

a^3 + b^3 = 1512

a^2 = 64

-ab = - 80

b^2 = 100

a + b=18

(a + b) (64 -  80+ 100)

18 * (84)

1512'

Answer:

36 : 6 and -6

12 = [tex]2\sqrt{3} , -2\sqrt{3}[/tex]

1.96 =1.4 and -1.4

0.64 : 0.8 and -0.8

400 : 20 and -20

25/36 = 5/6 and -5/6

Step-by-step explanation:

we know that

(-x)^2 = x^2

ALSO

(x)^2 = x^2

thus, square of both negative and positive number is same positive number.

_________________________________________________

36 = 6*6

36 = -6*-6

hence

square roots of 36 is both -6 and 6

12 = 4*3 = [tex]2^2*\sqrt{3} *\sqrt{3}[/tex]

[tex]\sqrt{12} = 2\sqrt{3}[/tex]

also

12 = [tex]-2\sqrt{3} *-2\sqrt{3}[/tex]

[tex]\sqrt{12} = -2\sqrt{3}[/tex]

___________________________________

1.96 = 196/100 = (14/10)^2

1.96 = 196/100 = (-14/10)^2

hence

[tex]\sqrt{1.96} = 14/10 \ or -14/10[/tex]

_______________________________

0.64 = 64/100 = (8/10)^2 = 0.8^2

0.64 = 64/100 = (-8/10)^2 = (-0.8)^2

Thus, square root of  0.64 = 0.8 and -0.8

_________________________________

400 = 20^2

400 = (-20)^2

[tex]\sqrt{400} = 20\\\sqrt{400} = -20\\[/tex]

__________________________________

25/36 = (5/6)^2

25/36 = (-5/6)^2

[tex]\sqrt{ 25/36} = 5/6 \\\sqrt{ 25/36} = (-5/6[/tex]

Answer:

D.  y + 6 = -3(x - 2)

Step-by-step explanation:

To find the equation in point-slope form, you need to use the slope and a point from that line.  The slope is -3 and the point given is (2, -6).

Point-slope form is y - y₁ = m(x - x₁).  Plug in the slope and point.

y - (-6) = -3(x - 2)

y + 6 = -3(x - 2)

Answer:

D. [tex]y - 2 = -3(x+6 )[/tex]

Step-by-step explanation:

Well point slope form is,

[tex]y - y_{1} = m(x-x_{1} )[/tex]

So we already have slope meaning we can plug that in for m.

[tex]y - y_{1} = -3(x-x_{1} )[/tex]

And with the given point (2,-6),

we can create point slope form.

[tex]y - 2 = -3(x+6 )[/tex]

Therefore,

the answer is d. [tex]y - 2 = -3(x+6 )[/tex].

Hope this helps :)

Answer:

I have:

33 - 3N/44   marbles

N = marbles of Nicole

Step-by-step explanation:

Nicole + me = 44 marbles

m = 44 - N

m = me

N = Nicole

if i lose 1/4 of my marbles

4/4 - 1/4 = 3/4

i have left:

3/4 of my marbles

then:

m = 3(44-N)/4

m = 3*44/4 + 3*-N/44

m = 33 - 3N/44

I have finally:

33 - 3N/44

Answer:

The amount spent on shower water by Trevor's family in the past month is $86.4

Step-by-step explanation:

The given information are;

The number of people in Trevor's family house are 6

The volume of water each person showered with during the month = 72 litres

The water costs = $0.20 per litre

The total volume of water used for shower by the 6 people = 72 × 6 = 432 litres

The amount spent on shower water by Trevor's family in the past month = The total volume of water used for shower × The cost per litre of water

The amount spent on shower water by Trevor's family in the past month = 432 × 0.2 = $86.4.

Answer:

$86.4

Step-by-step explanation:

Let A, B, and C denote the sets of students that have taken calculus, sociology, and Spanish, respectively.

We're given that [tex]A\cup B\cup C[/tex] consists of 187 students.

We want to find the size of [tex]A\cap B\cap C[/tex], given that

• A has 61 students;

• B has 78;

• C has 72;

• [tex]A\cap B[/tex] has 15;

• [tex]A\cap C[/tex] has 20; and

• [tex]B\cap C[/tex] has 13.

Using the inclusion/exclusion principle, we have

[tex]|A\cup B\cup C|=|A|+|B|+|C|-(|A\cap B|+|A\cap C|+|B\cap C|)+|A\cap B\cap C|[/tex]

where |X| denotes the size of the set X. Plug in all the known sizes:

[tex]187=61+78+72-(15+20+13)+|A\cap B\cap C|[/tex]

[tex]\implies|A\cap B\cap C|=24[/tex]

so 24 students have taken all three classes.

Answer:

The third option is correct

Step-by-step explanation:

We can rule out the first option because systems of equations CAN have decimal answers (this certain question cannot because of the domain) Same for the second option.

The last option says that all the numbers of forks knives and spoons must be equal but the question never specified that, in fact it looks like that is impossible since the variables have different coefficients.

The only logical answer is number 3

Answer:

3 1/3 km or 3.33 km (to the hundredth)

Step-by-step explanation:

Using the given formula,

estimated distance = v.t  = velocity * time,

velocity = 5 km/h

time = 40 minutes = [tex]\frac{40}{60}[/tex] hours = [tex]\frac{2}{3}[/tex]  hours

Therefore

distance = 5 km/h * [tex] \frac{2}{3} [/tex]  hours = 10/3 km

= 3.33 km approximately

Answer:

[tex]\boxed{Distance = 3.33\ km}[/tex]

Step-by-step explanation:

Given:

Time = t = 40 min = 40/60 = 0.67 hours

Speed = v = 5 km/hr

Required:

Distance = S = ?

Formula:

Distance = Speed × Time

Solution:

Distance = 5 × 0.67

Distance = 3.33 km

Answer:

Step-by-step explanation:

[tex]x \times 2 + 1 = 10[/tex]

[tex]2x + 1 = 10[/tex]

Move constant to R.H.S and change its sign

[tex]2x = 10 - 1[/tex]

Subtract the numbers

[tex]2x = 9[/tex]

Divide both sides of the equation by 2

[tex] \frac{2x}{2} = \frac{9}{2} [/tex]

Calculate

[tex]x = 4.5[/tex]

Hope this helps..

Best regards!!

Answer:

  x = 5 is the solution

Step-by-step explanation:

See the attachment for table values.

  f(x) = g(x) for x = 5

The solution to the equation ...

  2.5x -10.5 = 64(0.5^x)

is x = 5.

Answer:

Step-by-step explanation:

This is more physics than math, but since "The book of nature is written in the language of mathematics"...

Anyway, the one-dimesional motion equation you want to use here resembles the quadratic we use to model parabolic motion. It is

[tex]v^2=v_0^2+2a[/tex]Δx

where v is the final velocity of the firefighter, v₀ is the initial velocity of the firefighter, a is -9.8 m/s/s (negative because the motion is in the downward direction), and Δx is -34 m. This is also negative because where the firefighter lands is below the point at which he started. This is important, because if you leave the 34 as positive, you end up with a negative radicand...and that's not gonna work. Filling in the formula:

[tex]v^2=(7.5)^2+2(-9.8)(-34)[/tex]

Paying close attention to significant digits here is important (at least it is when I teach physics in school!). Since there are 2 significant digits in 7.5, we need 2 in the product. 7.5 squared is 56.25 which will round to 56. Then on the right side of the plus sign, we need 2 significant digits as well since the number 2 is part of the equation. We don't count it as significant if it is part of the equation. 2(-9.8)(-34) = 666.4 but that will round to 670. NOW, since the rules for significant digits are different in multiplication and addition, you have to round each first, then take the square root of the sum, rounding at the end. In this case we will round to the place that holds the least significance between the 2 numbers. In our case that is the tens place, since the tens place is less significant than is the 1's place. The number 7 is in the tens place. (Following that rule is super tricky, and also quite maddening!)

What we have here is

[tex]v^2=56+670[/tex] and

[tex]v=\sqrt{56+670}[/tex]

That leaves us with

v = 26.94438j

But don't forget we round that to the tens place which comes out in the end, finally, to

v = 30 m/s