Which expression is equivalent to (4 + 7¡)(3 + 4¡)?

[tex] \frac{2}{3} x + 5 = 1[/tex]

[tex] \frac{2}{3} x = 1 - 5[/tex]

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

[tex]x = ( - 4) \div \frac{2}{3} [/tex]

[tex]x = ( - 4) \times \frac{3}{2} [/tex]

[tex]x = \frac{ - 12}{ \: \: \: 2} [/tex]

[tex]x = ( - 6)[/tex]

[tex]∴ \frac{2}{3} \times ( - 6) + 5 = 1[/tex]

Answer:

The sports shop has 21 part-time employees.

Step-by-step explanation:

Solution:

What is 25% of 84?

.Y is 25% of 84

Equation: Y = P% * X

Solving our equation for Y

Y = P% * X

Y = 25% * 84

Converting percent to decimal:

p = 25%/100 = 0.25

Y = 0.25 * 84

Y = 21

Or another quicker way....

50% is half of the whole, and 25 is half of 50.

84/2/2

equals 21 too, I don't recommend to use it as row form.

The sports shop has 21 part-time employees, found by calculating 25% of 84.

The question asks how many part-time employees a sports shop with 84 employees has if 25% of them work part-time. To find the answer, we need to calculate 25% of 84 employees. The calculation is done as follows:

First, convert the percentage to a decimal by dividing it by 100: 25% = 0.25.

Then, multiply the total number of employees by this decimal: 84  times 0.25 = 21.

Therefore, the sports shop has 21 part-time employees.

Answer:

A) x=2, 8

Step-by-step explanation:

abs(x-5)=3

x-5=3, x-5=-3

x=3+5=8,

x=-3+5=2

Final answer:

option A.  x=2, x=8

Explanation:

To solve the equation |x-5|=3, we need to consider both cases regarding the absolute value function. The absolute value of an expression is equal to 3 if the expression itself is 3 or -3. Therefore, we have two equations to solve:

Solving the first equation:

Solving the second equation:

Thus, the solutions for the equation |x-5|=3 are x=2 and x=8, which corresponds to option A.

Answer:

Substitute the slope  and the coordinates of point D in the equation of the line  y=mx+b and then solve for b in each equation

Step-by-step explanation:

we know that

The first step is calculate the slopes of these two lines. Remember that if two lines are parallel then the slopes are the same (m1=m2) and if two lines are perpendicular then the slopes is equal to m1*m2=-1

The second step is substitute the slope m2 and the coordinates of point D in the equation of the line in slope-intercept form y=mx+b and then solve for b in each equation

Rajeev will pay Rs 6876.10 for the goods.

Step-by-step explanation:

Given,

Worth of goods = Rs 6650

Rebate = 6%

Amount of rebate = 6% of worth of goods

Amount of rebate = [tex]\frac{6}{100}*6650=0.06*6650[/tex]

Amount of rebate = Rs 399

Amount after rebate = 6650 - 399 = Rs 6251

Sales tax = 10%

Amount of sales tax = 10% of amount after rebate

Amount of sales tax = [tex]\frac{10}{100}*6251=0.1*6251[/tex]

Amount of sales tax = Rs 625.10

Total amount of goods paid = Amount after rebate + sales tax

Total amount of goods paid = 6251+625.10 = Rs 6876.10

Rajeev will pay Rs 6876.10 for the goods.

Keywords: addition, percentage

Learn more about percentages at:

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Answer:

[tex]a=2s-b-c[/tex]

Step-by-step explanation:

Given formula:

[tex]s=\frac{a+b+c}{2}[/tex]

To solve for [tex]a[/tex]

In order to solve for [tex]a[/tex] we will try to isolate [tex]a[/tex] on one side of the equation.

Steps to isolate [tex]a[/tex].

1) Multiplying both sides by [tex]2[/tex] to remove fractions.

[tex]2\times s=2\times \frac{a+b+c}{2}[/tex]

[tex]2s=a+b+c[/tex]

2) Subtracting both sides by [tex]b[/tex]

[tex]2s-b=a+b-b+c[/tex]

[tex]2s-b=a+c[/tex]

3) Subtracting both sides by [tex]c[/tex]

[tex]2s-b-c=a+c-c[/tex]

[tex]2s-b-c=a[/tex]

Thus, we successfully isolated [tex]a[/tex] on one side. The formula for [tex]a[/tex] can be given as:

∴ [tex]a=2s-b-c[/tex]

Answer:

7<k+3+2

7<k+5

2<k

which is same as k>2

Answer:

y = mx + b

Step-by-step explanation:

m is slope

b is y-intercept

Answer:

26.82

Step-by-step explanation:

Answer:

$26.82

Step-by-step explanation:

Product Cost: $18

Markup: 49%

Selling Price = (49% / 100% * $18) + $18 = $8.82 + $18 = $26.82

This gives you a price markup of $26.82.

this is my first answer and it could very well be wrong, sorry ;(

Answer:

[tex]x^{2} +7x-170=0[/tex]

Step-by-step explanation:

Here is the complete question: The width of a rectangle is 7 meters greater than its length . If the area of the rectangle is 170 m², write the quadratic equation in standard form for the equation that would represent the area of the rectangle. Let x equal to the length of the rectangle.

Given: Width of rectangle is 7 meter greater than length

           Length of rectangle is x.

           Area of rectangle= 170 m²

Now as given, length is x meter and width is (x+7) meter

we know that, area of rectangle= [tex]length\times width[/tex]

∴ substitute the values to get correction equation.

⇒170= [tex]x\times (x+7)[/tex]

now distributing x into (x+7).

⇒ [tex]170= x^{2} +7x[/tex]

subtracting 170 both side.

[tex]x^{2} +7x-170=0[/tex]

∴ [tex]x^{2} +7x-170=0[/tex] is the quadratic equation in standard form for the equation that would represent the area of the rectangle.

Answer: 36

Step-by-step explanation:

The legs are given to be :

3x - 1 and -x + 27

The base = 5x + 1

One of the properties of an isosceles triangle is that two sides are equal , that is the two legs are equal. This means that

3x - 1 = - x + 27

3x + x = 27 + 1

4x = 28

x = 7

To calculate the length of the base, substitute x = 7 into the length of the base given , that is

Length of the base = 5(7) + 1

L = 35 + 1

L = 36

Answer:

The function through which given point passes is f(x) = 24 x - 12 .

Step-by-step explanation:

Given as :

The points are

[tex]x_1[/tex] , [tex]y_1[/tex] = 1 , 12

[tex]x_2[/tex] , [tex]y_2[/tex] = 2 , 36

now, slope of the line

Let The slope of line = m = [tex]\frac{y_2-y_1}{x_2-x_1}[/tex]

Or, m = [tex]\frac{36 - 12}{2-1}[/tex]

Or, m = 24

So The slope of line = m = 24

Now, equation of line in point-slope form

y - [tex]y_1[/tex] = m × (x - [tex]x_1[/tex] )

Or, y - 12 = 24 × (x - 1 )

or, y - 12 = 24 x - 24

or, y = 24 x - 24 + 12

or, y = 24 x - 12

or , f(x) = 24 x - 12

So, The function through which given point passes is f(x) = 24 x - 12 . Answer

Answer:

For x = 10,  the value of the given function f(x)= 4(x − 11) − 9 is -13.

Step-by-step explanation:

Here, the given expression is:

f(x) = 4(x − 11) − 9

Now, given: f(x)  = -13

⇒ -13  = 4(x − 11) − 9

Now, solving for the value of x, we get:

-13  = 4(x-11) -9

⇒ -13 = 4 x - 44 - 9

or, -13 + 44  + 9 =  4x

or, 4 x = 40

or, x = 40/4 = 10

or, x = 10

Hence, for x = 10,  the value of the given function f(x)= 4(x − 11) − 9 is -13.

Answer:

The answer is B. 6 and 8.

Answer:

B) 6 and 8

Step-by-step explanation:

[tex]3 \times 8 = 24[/tex]

[tex]4 \times 6 = 24[/tex]

[tex]2 \times 12 = 24[/tex]

Good evening ,

Answer:

Step-by-step explanation:

255 = 3×5×17

726 = 2×3×11^2

Then HCF(255,726) = 3.

:)

Answer:

49 cm²

Step-by-step explanation:

The volume (V) of a cube is calculated as

V = s³ ← s is the length of the side, thus

s³ = 343 ( take the cube root of both sides )

s = [tex]\sqrt[3]{343}[/tex] = 7, thus

area of base = s² = 7² = 49 cm²

The amount spent at the movie store is $ 10.5

Given that Davis bought some candy for $ 35

This was seven dollars less than four times what he bought at the movie store

Which means that $ 35 is equal to seven dollars less than four times what he bought at the movie store

Let "m" be the amount spent at the movie store

$ 35 = seven dollars less than four times what he bought at the movie store

35 = 4m - 7

35 + 7 = 4m

42 = 4m

Thus the amount spent at the movie store is $ 10.5

Answer:

The answer is 3024

Step-by-step explanation:

you do 9!/(9-4)! which comes out to 3024

Answer:

x= 1; y= 0; z= -2 and w= 3.

Step-by-step explanation:

Given that,

1) x + 2y - z = 3

2) 2x - y + z - w = -3

3) y + 2z - w = -7

4) x + 3y + 2z + 2w = 3 ​

now, from 1) z = x + 2y -3 →→(5)

from 2) w = 2x -y + z +3

         ⇒w = 2x -y + x + 2y -3 +3  (from (5))

            w = 3x + y →→(6)

Now substitute (5) and (6) in 3), we get

y +2(x + 2y -3) - (3x + y) = -7

⇒ 4y - x = -1 →→→(7)

Now substitute (5) and (6) in 4), we get

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

⇒ 9x +9y = 9

⇒ x + y =1 →→→(8)

⇒ x= 1-y , substituting this in (7) gives 5y -1 = -1

⇒ y = 0 and x = 1

substituting these values in

(5) and (6) gives, z = -2 and w = 3

⇒ x= 1; y= 0; z= -2 and w= 3.

Answer:

[tex]a - 6 \leqslant 15 + 8a[/tex]

[tex] - 7a \leqslant 21[/tex]

[tex]a \geqslant - 3[/tex]

Answer:

y+1=-3/2(x-3)

Step-by-step explanation:

m=(y2-y1)/(x2-x1)

m=(5-(-1))/(-1-3)

m=(5+1)/-4

m=6/-4

simplify

m=-3/2

y-y1=m(x-x1)

y-(-1)=-3/2(x-3)

y+1=-3/2(x-3)

Answer:

Tuesday : Total = 30 : 72 = 5 : 12

Step-by-step explanation:

Monday: 42 miles

Tuesday: 42 - 12 = 30 miles

Monday + Tuesday: 42 + 30 = 72 miles

Tuesday : Total = 30 : 72 = 5 : 12

Answer:

$.56 per can; $.49 per can; 5 cans for $2.45

Step-by-step explanation:

If it were a dollar for two cans, it's pretty easy to figure out each can is 50 cents.  So you use the same idea.  if you have x cans for y dollars, if you divide both numbers by x you get the price of 1 can.

3 cans for 1.68 is 1 can for 1.68/3 = .56 so 56 cents

5 cans for 2.45 is 1 can for 2.45/5 = .49 so 49 cents.

You could use this trick dividing by the price and find how many cans you need to but to pay 1 dollar.

3 cans for 1.68 is 3/1.68 for 1 dollar or 1.786 cans for 1 dollar.  Doesn't make a lot of sense since you can't but part of a can, but I wanted to show you how you could use the logic for other things.

Answer:

The number of adult tickets sold is 894 and the number of kid tickets is 750.

Step-by-step explanation:

Given:

A Six Flags theme park charges $30 for adults and $15 for kids.

Total of 1,644 tickets were sold.

Total amount of tickets $11,250.

Now, to find the number of adult tickets and kid tickets.

Let the number of kid tickets be [tex]x.[/tex]

And the number of adult tickets be [tex]y.[/tex]

So, the total number of tickets:

[tex]x+y=1644.[/tex].....(1)

Solving the equation we get the value of [tex]x[/tex]:

[tex]x=1644-y.[/tex]

Now, the total amount of tickets of adult and kids:

[tex]15x+30y=11250.[/tex]

So, by putting the value of [tex]x[/tex] we get:

[tex]15(1644-y)+30y=11250[/tex]

[tex]24660-15y+30y=11250[/tex]

[tex]24660+15y=11250[/tex]

Subtracting both sides by 24660 we get:

[tex]15y=-13410[/tex]

Dividing both sides by -15 we get:

[tex]y=894[/tex]

Thus number of adult tickets = 894.

Now, putting the value of [tex]y[/tex] in equation (1):

[tex]x+894=1644[/tex]

On solving we get:

[tex]x=1644-894[/tex]

[tex]x=750.[/tex]

So. the number of kid tickets = 750.

Therefore, the number of adult tickets sold is 894 and the number of kid tickets is 750.

Answer: 750

Step-by-step explanation:

Final answer:

The x-value 6.5 in the quadratic function's vertex represents the price of the headphones in dollars at which the company's expected revenue is maximized, according to the revenue function [tex]R= - 5x^2 +65x + 700[/tex].

Explanation:

The question involves understanding the meaning of the x-value in the vertex form of a quadratic function, which in this context represents the price of the headphones for which the company expects to make the maximum revenue. The given function is [tex]R= - 5x^2 +65x + 700[/tex], and the vertex of the graph of this function is given as (6.5, 911.25). The x-value, 6.5, therefore represents the price in dollars at which the revenue of the company is maximized. This is because, in the context of a quadratic revenue model, the vertex represents the maximum point when the parabola opens downwards (which it does, since the coefficient of x² is negative), meaning that increasing or decreasing the price from this point will lead to a decrease in the total revenue.

Answer:

Step-by-step explanation:

Divide 7,200 by 45

The number of t-shirts each employee make in one week is 160 if the clothing factory makes 7,200 t-shirts in one week.

Fraction number consists of two parts, one is the top of the fraction number which is called the numerator and the second is the bottom of the fraction number which is called the denominator.

It is given that:

A clothing factory makes 7,200 t-shirts in one week on average there are 45 employees at the factory.

Let x be the number of t-shirts each employee make in one week

The value of x can be calculated as follows:

x = 7,200/45

x = 160

Thus, the number of t-shirts each employee make in one week is 160 if the clothing factory makes 7,200 t-shirts in one week.

Learn more about the fraction here:

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Answer:

34/9

Step-by-step explanation:

3 7/9 = 9*3+7 =34

34/9

Answer:34/9

Step-by-step explanation:

9*3 = 27

27+7= 34 then add the denominator

Answer:

x>-4

Step-by-step explanation:

13-2x > 21

-13 -13

-2x >8

(-2x)/(-2) >(8)/(-2)

x>-4

Answer:

x=-17/19, y=131/19. (-17/19, 131/19).

Step-by-step explanation:

-19x=26-9

-19x=17

x=-17/19

9(-17/19)=54-9y

-153/19=54-9y

9y=54-(-153/19)

9y=54+153/19

9y=1026/19+153/19

9y=1179/19

y=(1179/19)/9

y=(1179/19)(1/9)

y=1179/171

y=131/19

Answer:

Therefore,

[tex]x=y= 4\sqrt{2}=5.6568\ units[/tex]

Step-by-step explanation:

Given:

Consider In Right Angle Triangle ABC

∠B = 90°

∠C = ∠A = 45°

AB = y

BC = x = adjacent side

AC = 8 = hypotenuse

To Find:

x = ?

y = ?

Solution:

In Right Angle Triangle ABC by Cosine Identity we have

[tex]\cos C = \dfrac{\textrm{side adjacent to angle C}}{Hypotenuse}\\[/tex]

substituting the above given values we get

[tex]\cos 45 = \dfrac{BC}{AC}=\dfrac{x}{8}[/tex]

[tex]\dfrac{1}{\sqrt{2} } =\dfrac{x}{8}\\\therefore x=\dfrac{8}{\sqrt{2} } \\Rationalizing\ we\ get\\\therefore x=\dfrac{8}{\sqrt{2}}\times \dfrac{\sqrt{2} }{\sqrt{2}}}\\\therefore x=4\sqrt{2}=4\times 1.4142=5.6568\ units[/tex]

As The triangle is 45 - 45 - 90

It is an Isosceles Right triangle

[tex]x=y[/tex]..... Isosceles Triangle property

[tex]\therefore y=4\sqrt{2}=4\times 1.4142=5.6568\ units[/tex]

Therefore,

[tex]x=y= 4\sqrt{2}=5.6568\ units[/tex]