1. Which of the following expressions is equivalent to -3(x + 2) + (x – 3)x:
A. -5x – 6
B. -5x + 2
C. x2 - 6x – 6
D. x2 - 6x + 2

The number of boys in the schools is 104.

Step-by-step explanation:

Given,

The ratio of boys and girls is 8:9

Number of girls = 117

Let us take,

Number of boys = 8x

Number of girls = 9x

To find the number of boys.

According to the problem,

9x = 117

or, x = [tex]\frac{117}{9}[/tex]

= 13

Hence, the number of boys = 13×8 = 104

Two numbers multiply into (-24) and adds up to (-10) are 2 & -12

Step-by-step explanation:

Here we need to find two numbers , with the following info:

Let us assume that two numbers are x & y .

two numbers multiply into (-24):

Two numbers are x and y , and there multiply is -24 i.e.

⇒ [tex]x(y) = -24[/tex]

two numbers adds up to (-10):

Two numbers are x and y , and there addition is -10 i.e.

⇒ [tex]x+y = -10[/tex] . .............. (1)

Let's solve this :

We know that , [tex](x+y)^2 = x^2 +y^2 +2xy[/tex]

⇒ [tex](x+y)^2 = x^2 +y^2 +2xy[/tex]

⇒ [tex](-10)^2 = x^2 +y^2 +2(-24)[/tex]

⇒ [tex]100 = x^2 +y^2 -48[/tex]

⇒ [tex]x^2 +y^2 =148[/tex]

Now,

⇒ [tex](x-y)^2 = x^2 +y^2 -2xy[/tex]

⇒ [tex](x-y)^2 = (148) -2(-24)[/tex]

⇒ [tex](x-y)^2 = (148) +48=196 = 14^2[/tex]

⇒ [tex]x-y = 14[/tex]     .......... (2)

Let's solve equation 1 & 2 by adding (1)+(2):

⇒ [tex](x+y)+(x-y) = -10 +14[/tex]

⇒ [tex]2x=4[/tex]

⇒ [tex]x=2[/tex]

Putting value of [tex]x=2[/tex] in [tex]x-y = 14[/tex] :

⇒ [tex]2-y = 14[/tex]

⇒ [tex]y = -12[/tex]

Therefore, two numbers multiply into (-24) and adds up to (-10) are 2 & -12.

Answer:

12

Step-by-step explanation:

42+6=48

48/4=12

Answer:

42

Step-by-step explanation:

I think it's 42 because 42/-6 is -7

Answer:

z = 42

Step-by-step explanation:

Given -7 = z/-6

Cross multiply

-7 x -6 = z

Negative times negative gives you positive.

42 = z

z = 42

Answer:

x=0 and x=sqrt(3/2)i

Step-by-step explanation:

3x^2(2x^2+3)=0

Make into two equations due to Zero Product Property:

3x^2=0 and 2x^2+3=0

x^2=0             2x^2=-3

x=0                  x^2=-3/2

                         x=sqrt(3/2)i

You have the right equation.

p(x) = 0.586041x - 3,200,000

3200000 of course represents the deduction from the loan

0.586041 - this number represents the amount of money left after taxes (58.6041% of the total is left)

We get this by taking into account all the taxes on top of another...

35% federal tax = 65% left

35% federal tax and 8% state tax = 65% x 92% left

35% federal tax and 8% state tax and 2% local tax = 65% x 92% x 98% left = 58.6041%

To get the profit plug in the given taxable income for x.

p(6775989) = 0.586041(6775989) - 3,200,000 = $771,007.37 approx.

answer: $771,007.37 approx.

Answer: multiplies

Explain: this is because exponentially is multiplication.

The table of exponential multiplies by the same amount each time to get to the next number.

In mathematics, an exponential function is a relationship of the type y = ax, where x is an independent variable that spans the entire real number line and is expressed as the exponent of a positive number.

In another meaning, an exponential function is that function above which a variable x has imposed.

For example [tex]3^{x}[/tex] , [tex]7^{x}[/tex] like that.

Let a general exponential function [tex]a^{x}[/tex] where a is constant.

Let x = 1,2,3,4,5....

At x = 1 ⇒ a¹ = a

At x = 2 ⇒ a² = a × a = previous numebr ×  (a)

At x = 3 ⇒ a³ = a² × a = previous number × (a)

So,

It is clear that in exponential function each term multiplies the same amount each time to get to the next number.

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Answer:

40 passes

Step-by-step explanation:

we know that

Bobby catches 8 passes in 3 football games

so

using proportion

Find out how many passes does he  catch in 15 games

[tex]\frac{8}{3}=\frac{x}{15}\\\\x=8(15)/3\\\\x=40\ passes[/tex]

Answer: 40 passes

Step-by-step explanation:

Hi, to answer this we have to use proportions:

Proportion = Passes catched/ football games

Bobby catches 8 passes in 3 football games: 8/3

For 15 games: x/15

8 /3 = x/15

Solving for x

(8/3)15 =x

40 = x

He catches 40 passes in 15 games.

Feel free to ask for more if needed or if you did not understand something.

Answer:

Perimeter = 63.9 cm.

Area = 166.96 cm^2 to the nearest hundredth.

Step-by-step explanation:

The perimeter = 16+20.9+27 = 63.9 cm.

To find the area you can use Heron's Formula.

Area = √ [ s(s-a)(s-b)(s-c)]  where  s = the semi-perimeter and a, b and c are the lengths of the 3 sides.

s = 63.9 / 2 =  31.95.

Area of the triangle = √ (31.95(31.95-16)(31.95-20.9)(31.95-27)]

 = 166.96 cm^2.

Answer:

Step-by-step explanation:

So you would do x as other ages, 3 as well obviously 3.

x < 3

THE < WILL HAVE A LINE UNDER IT!

The line stands for less than or EQUAL to. In this case, you have to be 3 or younger. Do not forget the line under the <. I am unable to type it!

The question is about writing an inequality to represent the ages of children who can enter an amusement park for free. The correct mathematical expression according to the given scenario is 'age ≤ 3'.

The subject of the question deals with the practical application of inequalities in a real-world context. In this case, the inequality would represent the ages at which children could enter an amusement park for free. According to the amusement park policy, children ages 3 and under are free. In mathematical terms, this can be expressed as 'age ≤ 3'. The symbol '≤' represents 'less than or equal to', indicating that the age could be any number less than or equal to 3.

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Answer:

0.3333

Step-by-step explanation:

To convert 33.33% to decimal, simply divide 33.33 by 100.

Answer: 0.3333

Step-by-step explanation:

33.33% = 33.33 / 100 = 0.3333.

Since 100 has 2 zeros, you count the decimal point in 33.33 forward twice.

Answer:

[tex]\frac{3}{8}[/tex]

Step-by-step explanation:

since [tex]\frac{5}{8}[/tex] has been completed

the remaining would be :

[tex]\frac{8}{8} -\frac{5}{8}[/tex]

since denominators are the same

= [tex]\frac{8 - 5}{8} \\\\[/tex]

= [tex]\frac{3}{8}[/tex]

the fraction of the race that is remaining is 3/8

Answer:option c

Step-by-step explanation:

An Isosceles Right Triangle is a right triangle that consists of two equal-length legs. Since the two legs of the right triangle are equal in length, the corresponding angles would also be congruent. Thus, in an isosceles right triangle, two legs and the two acute angles are congruent.

So the correct answer is option c. It is an isosceles right triangle.

Since the two sides are equal it makes the corresponding angle congruent. Thus, in an isosceles right triangle two sides are congruent and the corresponding angles will be 45 degree each which sums to 90 degree. So the sum of three angles of the triangle will be 180 degrees.

The area of the isosceles right triangle follows the general formula of the area of a triangle that is (1/2) × Base × Height. In ∆QPR shown above with side lengths PQ = QR = x where PQ represents the height and QR represents the base, the area of isosceles right triangle formula is given by 1/2 × PQ × QR = x2/2 square units.

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Answer:

A

Step-by-step explanation:

when you plug in 2,11

11 = 3*2 +5 that is correct

13 = 3*3 +5 that is not correct

only 2,11 works

Answer:

A. only (2,11)

Step-by-step explanation:

Answer:

18 servings

Step-by-step explanation:

Because 6 divided by 1/3 is the same as 6*3, we can just do it that way so it makes more sense.

6*3= 18

And there you have your answer!

Answer:

There are 13 cards for each suit so the first fraction is 13/52 and the next one is 13/51 as there is no replacement for the first card you pulled.

Multiplying them you get: 13/52*13/51= 169/2652,

Then you divide both sides by 13 to get: 13/204

So, the answer is C.

I hope this helps!

The probability of drawing a club and then a diamond consecutively from the deck without replacement is 13/204.

Option C is the correct answer.

It is the chance of an event to occur from a total number of outcomes.

The formula for probability is given as:

Probability = Number of required events / Total number of outcomes.

We have,

Number of cards = 52

Number of clubs = 13

Number of diamonds = 13

Now,

The probability of drawing a club.

= 13/52

And,

The probability of drawing a diamond consecutively from the deck without replacement.

= 13/51

[ There will be only 51 cards in total since we are not replacing ]

Now,

The probability of drawing a club and then a diamond consecutively from the deck without replacement.

= 13/52 x 13/51

= 13/4 x 1/51

= 13/204

Thus,

13/204 is the probability of drawing a club and then a diamond consecutively from the deck without replacement.

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The right answer is Option C: 3 units

Step-by-step explanation:

Given coordinates are;

A polygon has the following coordinates: A(3,-3), B(-3,-2), C(-5,1), D(-5,4), E(-4,6), F(-2,6), G(3,2).

For finding length of CD, we will find the distance between C and D.

C(-5,1) and D(-5,4)

Here;

[tex]x_1=-5, y_1=1\\x_2=-5, y_2=4[/tex]

Distance = [tex]\sqrt{(x_2-x_1)^2+(y_2-y_1)^2[/tex]

[tex]Distance=\sqrt{(-5+5)^2+(4-1)^2}\\Distance=\sqrt{(0)^2-(3)2}\\Distance=\sqrt{(3)^2}\\Distance = 3[/tex]

Therefore;

The length of CD is  units.

The right answer is Option C: 3 units

Answer:

2

Step-by-step explanation:

Answer:

feet

Step-by-step explanation:

Answer:

f(4) = 11

Step-by-step explanation:

To evaluate f(4) substitute x = 4 into f(x)

f(4) = 3(4) - 1 = 12 - 1 = 11

Answer:

The answer is 19

Step-by-step explanation:

Answer:so easy its 19 it's right i promise you

Answer: option is C

Step-by-step explanation:

Answer: w= -9

Step-by-step explanation:

Set up an equation, 5 times a number is 5w, and 35 more, means plus 35. All of this is equal to -10, so the equation will be:

5w+35=-10

Subtract 35 from both sides

5w=-45

Divide by 5 on both sides

w= -9

Hope this helped!

Answer:y= -5

Step-by-step explanation:

-3(3)+4= -5

-3(3)= -9

-9 + 4= -5

Answer:

-5

Step-by-step explanation:

y = -3x + 4

If x = 3

Plug the value into the expression

We have

y = -3(3) + 4

= -9 + 4

= -5

Step-by-step explanation:

[tex](7 + x) + 7x \\ = 7 + x + 7x \\ = 7 + (x + 7x) \\ = 7 + 8x \\ = 8x + 7[/tex]

Answer: C

it's C) 2/3

Answer:

C! X = 2/3

Step-by-step explanation:

Next part on edge is

(C) X=1

Answer:

a=5 and b=3

Step-by-step explanation:

a+b=8

okay, so the numbers that can make 8 are 4+4, 5+3, 6+2, and 7+1

Try 5+3

so plug them in

5+3=8

5*5=25

3*3=9

25-9=16

that's your answer

Answer:

x = [tex]\frac{ln(16)}{ln(2)}[/tex]

Step-by-step explanation:

[tex]4^{2x-1} =8^{x+2}[/tex]

ln both sides like you would add the same number to both sides to keep the equation equivalent

[tex]ln4^{2x-1} = ln 8^{x+2}[/tex]

using log rules, exponents can be brought down as a constant multiplying ln

[tex](2x-1)ln(4) =(x+2)ln(8)[/tex]

use distributive property to remove parentheses

2xln(4) - ln(4) = xln(8) + 2ln(8)

isolate x

2xln(4) - xln(8) = 2ln(8) + ln(4)

rewrite the logs using log rules: ln(x) - ln(y) = ln([tex]\frac{x}{y}[/tex]) and the exponent rule stated above

xln([tex]4^{2}[/tex])-xln(8) = ln([tex]\frac{8^{2} }{4}[/tex])

factor out x

x(ln[tex]4^{2}[/tex]-ln8) = ln([tex]\frac{8^{2} }{4}[/tex])

again use log rules:  ln(x) - ln(y) = ln([tex]\frac{x}{y}[/tex])

x* [tex]ln(\frac{4^{2} }{8}[/tex][tex])[/tex]=  ln([tex]\frac{8^{2} }{4}[/tex])

now simplify the stuff inside the ln parentheses

x*ln(2) = ln(16)

x = [tex]\frac{ln(16)}{ln(2)}[/tex]

Answer: _(32)(16)=(4)/(5)

Step-by-step explanation: