12
y
8
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ninate Education, Inc.

[tex]\left( \sqrt 3 + \sqrt 7\right) \left( \sqrt 3 - \sqrt 7\right)\\\\=\left(\sqrt 3 \right)^2 - \left(\sqrt 7 \right)^2\\ \\=3-7\\\\=-4[/tex]

Answer:

- 4

Step-by-step explanation:

([tex]\sqrt{3}[/tex] + [tex]\sqrt{7}[/tex] )([tex]\sqrt{3}[/tex] - [tex]\sqrt{7}[/tex] )

each term in the second factor is multiplied by each term in the first factor.

[tex]\sqrt{3}[/tex] ([tex]\sqrt{3}[/tex] - [tex]\sqrt{7}[/tex] ) + [tex]\sqrt{7}[/tex] ([tex]\sqrt{3}[/tex] - [tex]\sqrt{7}[/tex] ) ← distribute parenthesis

= 3 - [tex]\sqrt{21}[/tex] + [tex]\sqrt{21}[/tex] - 7 ← collect like terms

= - 4

There are 300 different sundaes possible with the given choices of 20 ice cream flavors, 5 toppings, and 3 sizes at the make-your-own sundae bar.

To find the total number of different sundaes possible, we need to multiply the number of choices for each category: ice cream flavors, toppings, and sizes.

Number of ice cream flavors = 20

Number of toppings = 5

Number of sizes = 3

Total number of sundaes = Number of ice cream flavors × Number of toppings × Number of sizes

Total number of sundaes = 20 × 5 × 3

Total number of sundaes = 300

There are 300 different sundaes possible with the given choices of 20 ice cream flavors, 5 toppings, and 3 sizes at the make-your-own sundae bar.

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Answer:

Step-by-step explanation:

keeping in mind that parallel lines have exactly the same slope, let's check for the slope of the equation above

[tex]y = \stackrel{\stackrel{m}{\downarrow }}{\cfrac{1}{3}}x-4\qquad \impliedby \begin{array}{|c|ll} \cline{1-1} slope-intercept~form\\ \cline{1-1} \\ y=\underset{y-intercept}{\stackrel{slope\qquad }{\stackrel{\downarrow }{m}x+\underset{\uparrow }{b}}} \\\\ \cline{1-1} \end{array}[/tex]

so we're really looking for the equation of a line whose slope is 1/3 and passes through (-3 , 2)

[tex](\stackrel{x_1}{-3}~,~\stackrel{y_1}{2})\hspace{10em} \stackrel{slope}{m} ~=~ \cfrac{1}{3} \\\\\\ \begin{array}{|c|ll} \cline{1-1} \textit{point-slope form}\\ \cline{1-1} \\ y-y_1=m(x-x_1) \\\\ \cline{1-1} \end{array}\implies y-\stackrel{y_1}{2}=\stackrel{m}{\cfrac{1}{3}}(x-\stackrel{x_1}{(-3)}) \\\\\\ y-2=\cfrac{1}{3}(x+3)\implies y-2=\cfrac{1}{3}x+1\implies y=\cfrac{1}{3}x+3[/tex]

The true statements are:

Given:

To find the large size meals that came with milk,

71-55= 16.

Therefore, the total number of large size meals ordered was:

16+22+86 = 124.

Hence, options A, D and E are correct.

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The probability that a person selected at random is Ages 16-18 and has prepared a meal for their family

From the table of values, we have:

Age 16 - 18 that has performed meal =  8

Total = 30

The probability is then calculated using:

P(16 - 18) = n(16 - 18)/Total

This gives

P(16 - 18) = 8/30

Simplify

P(16 - 18) = 4/15

Hence, the probability is 4/15

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Answer:

[tex]\boxed{\sf x = -4 \pm 2\sqrt{6} }[/tex]

Explanation:

3x² + 24x - 24 = 0

factor the coefficient

3(x² + 8x) -24 = 0

Halve the second term and square it

3(x + 4)² -24 -3(4)² = 0

simplify the answer

3(x + 4)² -72 = 0

add 72 on both sides

3(x + 4)² = 72

divide both sides by 3

(x + 4)² = 24

square root both sides

x + 4 = ±√24

subtract both sides by 4

x = -4 ± 2√6

Answer:

[tex]x=-4\pm2\sqrt{6}[/tex]

Step-by-step explanation:

Completing the square for quadratic in the form  [tex]ax^2+bx+c=0[/tex]

Given equation:

[tex]3x^2+24x-24=0[/tex]

Factor out 3:

[tex]\implies 3(x^2+8x-8)=0[/tex]

Divide both sides by 3:

[tex]\implies x^2+8x-8=0[/tex]

Add 8 to both sides:

[tex]\implies x^2+8x=8[/tex]

[tex]\textsf{Add }\: \left(\dfrac{b}{2}\right)^2\: \textsf{ to both sides}:[/tex]

[tex]\implies x^2+8x+\left(\dfrac{8}{2}\right)^2=8+\left(\dfrac{8}{2}\right)^2[/tex]

[tex]\implies x^2+8x+16=8+16[/tex]

[tex]\implies x^2+8x+16=24[/tex]

Factor the left side:

[tex]\implies (x+4)^2=24[/tex]

Square root both sides:

[tex]\implies x+4=\pm2\sqrt{6}[/tex]

Subtract 4 from both sides:

[tex]\implies x=-4\pm2\sqrt{6}[/tex]

[tex]\qquad\qquad\huge\underline{{\sf Answer}}[/tex]

The given sequence is in Arithmetic progression, and we have to find its nth term ~

So, let's get it solved ~

First term of the sequence is :

Common difference is :

Now, if we have to write the 2nd Term with respect to first one, we can write :

similarly ~

Therefore, I similar pattern ~

[tex] \qquad \sf  \dashrightarrow \: nth \: term = a + (n - 1)d[/tex]

[tex] \qquad \sf  \dashrightarrow \: nth \: term = 2 + (n - 1)2[/tex]

[tex] \qquad \sf  \dashrightarrow \: nth \: term = 2(1 + (n - 1))[/tex]

[tex] \qquad \sf  \dashrightarrow \: nth \: term = 2(1 + n - 1)[/tex]

[tex] \qquad \sf  \dashrightarrow \: nth \: term = 2 n [/tex]

Feel free to ask your doubts, if you have any ~

Answer:

Step-by-step explanation:

from the number sequence above, each term except the first is generated by adding 2 to the term immediately preceding it.

the nth term of the sequence is usually designated Tn, and it's usually a function of n

from the number sequence

T1= 2

T2 = 2+2= 4

T3= 4+2= 6

T4= 6+2= 8

therefore, Tn= 2+2×(n-1)

= 2+2n-2

=2-2+2n= 2n

Answer:

[tex]\huge\boxed{\sf \$\ 205}[/tex]

Step-by-step explanation:

Work hours = 28 hours

Earning = $8 per hour

1 hour = $8

28 hours = $8 × 28

28 hours = $224

He has earned $224 last month.

Spent = $19

Left:

= Earning - Spent

= $224 - $19

= $205

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

Answer:

26.7

Step-by-step explanation:

Answer:

the person earned one summer = $3,600

We have to show the amount in fraction that Paula spent during the following semester,

they spent for tuition = $2,500 =  × 100

=0.6944 × 100

=  69.44%  

they spent for rent = $650 =   × 100

= 0.1806 × 100

= 18.06%

they spent for food = $430 =   × 100

=0.1194 × 100

= 11.94%

they Spent in tuition, rent and food = 2,500 + 650 + 430 = $3580

Now they spent in miscellaneous expenses = 3600 - 3580 = $20.00   × 100

= 0.056 × 100

= 0.56%

Answer:

5/9

Step-by-step explanation:

Solution

The gradient of the line ment when two segment given (X1, Y1) and (X2, Y1) is points

m =

[tex] \frac{y2 - y1}{x2 - x1 } [/tex]

Here two points given, (-5,-2) and (4,3)

gradient (m):

[tex] \frac{3 - ( - 2)}{4 - ( - 5)} [/tex]

Answer:

$30

Step-by-step explanation:

since 7 = 28

and 1 = 4

divide 1 in half to find the half hour amount

1/2 hr = 2

28 + 2 = 30

your answer is $30

hope this helps:)

Answer:

I can help, but can you label which is base, height, and length

Step-by-step explanation:

Step-by-step explanation:

k has to be replaced by k+1.

so,

4 / ((k+1)(k+1 + 3)) = 4 / ((k+1)(k+4))

I am not sure how far your teacher expects you to go with this.

just in case, I will do also the full multiplications

4 / ((k+1)(k+4)) = 4 / (k² + 4k + k + 4) = 4 / (k² + 5k + 4)

and if you need the factor to go from Pk to Pk+1 :

Pk+1 / Pk = (4/((k+1)(k+4))) / (4/(k(k+3)) =

= (4/((k+1)(k+4))) × (k(k+3))/4 =

= (k(k+3)) / ((k+1)(k+4))

Using a system of equations, it is found that Teresa's password in the 7th day of the month is of 98.

A system of equations is when two or more variables are related, and equations are built to find the values of each variable.

The rule for her password is defined as follows: A whole number that is equal to four times the fourth power of the day of the month divided by two times the square day of the month. Hence, considering n as the day of the month, the equation is given by:

[tex]P = \frac{4n^4}{2n^2} = 2n^2[/tex]

Hence, for the 7th day, the password is given by:

P = 2 x 7² = 98.

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Answer:

Step-by-step explanation:

P(3 and 4)= 1/6×1/6

                =1/36

Answer:

Step-by-step explanation:

Formula

speed = distance / time

Givens

speed = ?

distance = 162 miles.

Time = 3 hours.

Solution

speed = 162 / 3

speed = 54 miles per hour.

Answer:

Company "A"

Step-by-step explanation:

its the highest line on the graph from the 300 point.

[tex]\huge\underline{\red{A}\blue{n}\pink{s}\purple{w}\orange{e}\green{r} -}[/tex]

the following expression can be solved as follows ~

[tex] \frac{x}{3} + 1 = \frac{x}{8} + \frac{1}{11} \\ [/tex]

Taking LCM on both the sides ,

[tex] \frac{x + 3}{3} = \frac{11x + 8}{88} \\ [/tex]

On cross multiplying ,

[tex]( x + 3)88 = (11x + 8)3 \\ \\ \implies \: 88x + 264 = 33x + 24[/tex]

let's now gather the like terms at either sides of the equation and solve ~

[tex]88x - 33x = 24 - 264 \\ \\ \implies \: 55x = - 240 \\ \\ \implies \: x = \cancel\frac{ - 240}{55} \\ [/tex]

on further simplifying ,

[tex]\implies x = \frac{ - 48 }{ 11} \\ [/tex]

hope helpful ~

Answer:

[tex]\textsf{B.} \quad x=\dfrac{1}{2}[/tex]

Step-by-step explanation:

Log laws

[tex]\textsf{Product law}: \quad \log_ax + \log_ay=\log_axy[/tex]

[tex]\textsf{Equality law}: \quad \textsf{if }\: \log_ax=\log_ay\:\textsf{ then }\:x=y[/tex]

Therefore:

[tex]\large \begin{aligned}\log_6 x+ \log_6 3 & =\log_6 (x+1)\\\log_6 (3x) & =\log_6 (x+1)\\3x & =x+1\\2x & =1\\x & =\dfrac{1}{2}\end{aligned}[/tex]

The value of a and b given that the opposite side are equal are 17 and 6 respectively

The kite is a quadrilateral with 4 sides and the opposite side of the side are equal. If they are, then;

2a - 4 = 30
2a = 34

a = 17

Similarly

3b+6 = 24

3b = 18
b = 6

Hence the value of a and b given that the opposite side are equal are 17 and 6 respectively

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Answer:

∠ T = 76°

Step-by-step explanation:

RSTU is a cyclic quadrilateral

the opposite angles of a cyclic quadrilateral sum to 180°

∠ T + ∠ R = 180°

∠ T + 104° = 180° ( subtract 104° from both sides )

∠ T = 76°

The function that has the same minimum value as fx= 3x³ is f(x) = x + 3.

It should be noted that a function simply means a relation or expression that involves two or more variables.

In this case, the function that has the same minimum value as the expression of 3x³ is f = x + 3.

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Answer:

B. f(x) = /x/ + 3

Step-by-step explanation:

edg 22'

x = -2/3 or -4

see the attachment for solution

hope it helps...!!!

Answer:

(x-3)(x+2)

Step-by-step explanation:

¹ you open brackets.

² you put the "x" in both brackets

³ you then check for factors, that will give you a "6" when you multiply them and give you the "x" when you add or subtract them.

Veremos que de los 20 intentos, Mariana metio 16 canastas.

Sabemos que ella tiro 20 veces, y sabemos que ella ha errado 1/5 de los tiros.

Entonces los otros 4/5 tiros entraron. Para obtener el numero de canastas que ha metido, debemos multiplicar la fracción por la cantidad total de tiros al aro:

C = 20*(4/5) = 16

Así, podemos concluir que Mariana ha metido 16 canastas.

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Answer: y  - 6x +46

Step-by-step explanation:

y + 4- 6(x +7)

y + 4 - 6x +42

y  - 6x +46

Answer: the zeros are the xintercepts which are shown on the graph

Step-by-step explanation: