What is the area of the shaded region?
21 mm
24 mm
42 mm
48mm

Answer:

Step-by-step explanation:

There are many ways to solve this:

- factorising

- formula

- perfect squaring

FACTORISING:

The first step would be to multiple the coefficient of x^2 and 6.

Then find which of the factors of 6 sum up to 5. (In this case it is 2 and 3.)

So you would rewrite the equation like this:

x2 -3x -2x + 6 = 0

Then factorise

x(x-3) - 2(x-3) = 0

Then factorise again

(x-2)(x-3) = 0

So if we were to divide each side by (x-2)

(x-3) =0

so x = 3

OR

if we were to divide each side by (x-3)

(x-2) = 0

x = 2

FORMULA:

The formula is

-b±[tex]{\sqrt{b^2 -4ac}[/tex] / 2a

where

ax^2 + bx + c = 0

The first step would be to substitute.

PERFECT SQUARING:

The first step would be to half the second term.

[tex](x - \frac{5}{2})^{2} - \frac{25}{4} - 6 = 0[/tex]

Then solve for x.

Answer:

B. 62°

Step-by-step explanation:

According to the Supplementary Angles Theorem, in this case, ∠s and 152° form a straight angle, so you use the Supplementary Angles Theorem:

-152° + 180 = 28°; 28° = m∠s

Then, use the Triangular Interior Angles Theorem to find the m∠t:

28° + 90° = 118°

↑

∠s

-118° + 180° = 62°; 62° = m∠t

I am joyous to assist you anytime.

Answer:  Option 'b' is correct.

Step-by-step explanation:

Since we have given that

Measure of exterior angle = 152°

and measure of one opposite interior angle = 90°

Measure of another opposite interior angle be 't'.

As we know that

Sum of interior angle is equal to exterior angle.

[tex]90^\circ+t=152^\circ\\\\t=152^\circ-90^\circ\\\\t=62^\circ[/tex]

Hence, the measure of t is 62°.

Therefore, Option 'b' is correct.

let's firstly convert the mixed fractions to improper fractions.

[tex]\bf \stackrel{mixed}{3\frac{1}{2}}\implies \cfrac{3\cdot 2+1}{2}\implies \stackrel{improper}{\cfrac{7}{2}}~\hfill \stackrel{mixed}{1\frac{3}{4}}\implies \cfrac{1\cdot 4+3}{4}\implies \stackrel{improper}{\cfrac{7}{4}} \\\\[-0.35em] ~\dotfill\\\\ \begin{array}{ccll} \stackrel{size}{actual~miles}&\stackrel{size}{map~inches}\\ \cline{1-2} 210&\frac{7}{2}\\\\ x&\frac{7}{4} \end{array} \implies \cfrac{210}{x}=\cfrac{~~\frac{7}{2}~~}{\frac{7}{4}}[/tex]

[tex]\bf \cfrac{210}{x}=\cfrac{~~\begin{matrix} 7 \\[-0.7em]\cline{1-1}\\[-5pt]\end{matrix}~~}{~~\begin{matrix} 2 \\[-0.7em]\cline{1-1}\\[-5pt]\end{matrix}~~}\cdot \cfrac{\stackrel{2}{~~\begin{matrix} 4\\[-0.7em]\cline{1-1}\\[-5pt]\end{matrix}~~}}{~~\begin{matrix} 7 \\[-0.7em]\cline{1-1}\\[-5pt]\end{matrix}~~} \implies \cfrac{210}{x}=2\implies 210=2x\implies \cfrac{210}{2}=x\implies 105=x[/tex]

Answer: the false one is the last one (if a number is an integer, then it is irrational)

Step-by-step explanation:

Answer:

D is the correct answer.

Answer:

9x + 36 = 10

Step-by-step explanation:

Given

[tex]\frac{3}{4}[/tex] x + 3 = [tex]\frac{5}{6}[/tex]

Multiply by the lowest common multiple of 4 and 6, that is 12

12 × [tex]\frac{3}{4}[/tex] x + 12 × 3 = 12 × [tex]\frac{5}{6}[/tex], that is

9x + 36 = 10 ← equation without fractions

Answer:

x = 30

Step-by-step explanation:

(x+20) + (x+10) +90 = 180

(2x+30) + 90 = 180

2x+120 = 180

2x = 60

x = 30

The value of x will be 30.

Rhombus is a parallelogram whose all sides are of equal lengths.

Its diagonals are perpendicular to each other and they cut each other in half( thus, they're perpendicular bisector of each other).

Its vertex angles are bisected by its diagonals.

The triangles on either side of the diagonals are isosceles and congruent.

Form the Figure abcd is a kite. we need to Find the value of x. ​

Therefore,

The sum of angle property;

(x+20) + (x+10) +90 = 180

(2x+30) + 90 = 180

2x+120 = 180

2x = 60

x = 30

Hence, the value of x will be 30.

Learn more about angles here;

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Step-by-step explanation:

3(1+5)  (distributive property)

= 1(3) + 5(3)

= 3 + 15

= 18 (answer)

Answer: -79.6°F

Formula

(-62°C × 9/5) + 32 = -79.6°F

Answer:

Step-by-step explanation:

The answer is the -558.9

Whenever you take the square root of a number you get a negative and a positive result: √ 4 = ± 2 or { − 2 , 2 } − 2 ⋅ − 2 = 4 and 2 × 2 = 4

The two square roots of 4 are 2 and -2.

The factor of a number that, when multiplied by itself, yields the original number is known as the square root of the number. Special exponents include squares and square roots. Think about the number 9. When the number 3 is multiplied by itself, the result is 9. This can be expressed as either 3² or 3 × 3.

Given:

The number is 4,

Factorize the number as shown below,

4 = 2 × 2

Calculate the value of the square root of 4 as shown below,

√4 = √(2 × 2)

√4 = ±2

√4 =  2 or -2

Check as:

-2 × -2 = 4

2 × 2 = 4

Thus, the square root of 4 is  2 and -2.

To know more about square root:

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Answer:

[tex]a=3,\text{ then } x\in(-\infty,\infty)\\ \\a\in(-\infty,3),\text{ then }x\in \left[\dfrac{-4a-8}{3-a},\infty\right)\\ \\a\in(3,\infty),\text{ then }x\in \left(-\infty, \dfrac{-4a-8}{3-a}\right][/tex]

Step-by-step explanation:

In the inequality

[tex]3x+8+2ax\ge 3ax-4a\ \ \ (1)[/tex]

a is an arbitrary real number.

Separate the terms with x into left side and the terms without x in the right side:

[tex]3x+2ax-3ax\ge -4a-8\\ \\3x-ax\ge -4a-8\\ \\(3-a)x\ge -4a-8\ \ \ (2)[/tex]

First, look at the leading coefficient at x. If this coefficient is equal to 0 (when [tex]a=3[/tex]), then the inequality is

[tex]0\ge -4a-8\\ \\0\ge -12-8\ [\text{Substituted }a=3]\\ \\0\ge -20[/tex]

This is true inequality for all x, so at [tex]a=3,[/tex] the inequality (1) has the solution [tex]x\in (-\infty,\infty)[/tex]

Now, if the leading coefficient

[tex]3-a>0\\ \\a<3,[/tex]

then we can divide the inequality (2) by this positive number [tex]3-a[/tex] and get

[tex]x\ge \dfrac{-4a-8}{3-a}[/tex]

If the leading coefficient

[tex]3-a<0\\ \\a>3,[/tex]

then we can divide the inequality (2) by this negative number [tex]3-a[/tex] and get

[tex]x\le \dfrac{-4a-8}{3-a}[/tex]

So, the answer is

[tex]a=3,\text{ then } x\in(-\infty,\infty)\\ \\a\in(-\infty,3),\text{ then }x\in \left[\dfrac{-4a-8}{3-a},\infty\right)\\ \\a\in(3,\infty),\text{ then }x\in \left(-\infty, \dfrac{-4a-8}{3-a}\right][/tex]

Answer:

Area of a square = side times side. Since each side of a square is the same, it can simply be the length of one side squared. If a square has one side of 4 inches, the area would be 4 inches times 4 inches, or 16 square inches.

Step-by-step explanation:

Answer:

You cannot add like terms like that.

Step-by-step explanation:

The terms are supposed to be added together, by combining them like that you are multiplying them together.

Answer:

A=0

Step-by-step explanation:

i think this is right if not im so sorry

Final answer:

To solve the system of equations, we determined the number of hotdogs sold as 'h' and found out that the vendor sold 57 hotdogs and 171 sodas.

Explanation:

The problem given is a system of equations question where we need to find the number of sodas and hotdogs sold by a vendor when given the total sales and the ratio of sodas to hotdogs. To solve this, we'll denote the number of hot dogs sold as 'h' and the number of sodas sold as 's'. According to the problem, the total number of items sold is 228, which gives us the equation:

s + h = 228.

It's also given that the number of sodas sold is three times the number of hot dogs sold. This is our second equation:

s = 3h.

Now we can substitute the second equation into the first, yielding:

3h + h = 228,

which simplifies to:

4h = 228.

Dividing both sides by 4 gives:

h = 57.

With the knowledge that h = 57, we use s = 3h to find that:

s = 3 × 57,

s = 171.

Therefore, the vendor sold 57 hotdogs and 171 sodas.

Answer: 3/4 (8x + 16) simplified expression is 6x + 12

                2x - 5x + 5 - 4 simplified expression is -3x + 1

                 x + x + x +3 + 5 - 2 simplified expression is 3x + 6

               6x - 7 + 3x + 5 simplified expression is 9x  - 2

                3 + 2(2x + 5) simplified expression is 4x + 13

Step-by-step explanation:

3/4 (8x + 16) in the example the 3 is multiplying and the 4 is dividing,

so you can start with multiplication, multiply the 3 for each value into the parenthesis after that you can place 4 as the divisor of this equation

(3 * 8x + 3 * 16) / 4

after we perform this equation the product is the following

(24x + 48) / 4

after this step you can divide the each value into the parenthesis between 4, this process give us separate equations.

(24x/ 4) + (48/4)

if you proceed with the division of each value we will find the last equation.

(24x/ 4) = 6x

(48/4) = 12

then the simplified expression is 6x + 12.

2x - 5x + 5 - 4, with this case you can resolve the equation with the similar values, for example, you can start with the values that has the x, and after that proceed with the simple values.

2x - 5x = -3x

5 - 4 = 1

after we resolve this, you only need placed the values with its sign in one equation then the simplified expression is  -3x + 1.

x + x + x +3 + 5 - 2, in this example you can start with the sum of x, and after that proceed with sum of the simple values.

x + x + x = 3x

3 + 5 - 2 = 6

after that we place the values in one expression , then the simplified expression is 3x + 6.

6x - 7 + 3x + 5, in this equation we can star with the similar values, the values with x and after that the simple values

6x + 3x = 9x

-7 + 5 = -2 ( as the 7 is bigger than 5 the result get value of the biggest number.

after you only need to place the values in one equation, then the simplified expression is 9x - 2.

3 + 2(2x + 5), with this example you can start with the product of 2 with the values into the parenthesis.

2 * (2x + 5) the 2 is passing to multiply each value into the parenthesis.

2 * 2x + 2 * 5

4x + 10

after that we can place the result of this product in the first equation

3 + 4x + 10

after that you only need to sum the similar values and we get that the simplified expression is 13 + 4x

Final answer:

Explanation of matching simplified expressions to problems in a math question that is option D is correct

Explanation:

Match the simplified expression with the correct problem:

3/4(8x + 16) matches with 6x - 7 + 3x + 5

2x - 5x + 5 - 4 matches with x + x + x + 3 + 5 - 2

x + x + x + 3 + 5 - 2 matches with 3 + 2(2x + 5)

Are you talking about the angles in a triangle? Your question is not clear. I'll assume you are talking about a triangle.

Angle 1 + Angle 2 + Angle 3 = 180°

4x + 15 + 2x + 16 + x = 180°

Solve for x to find Angle 3, which in this case is the value of x.

Answer:

1st Part- $41     2nd Part- 48 Tickets

Step-by-step explanation:

1st Part)

Suzie- 2($4) + 2($7)= $22

Devon- 3($4)+ 1($7)= $19

                        Total=$41

-------------------------------------------------

2nd Part)

4(6) + 8(3) = 48 Tickets

Answer:

If i understood correctly n = 4

Step-by-step explanation:

You are looking for the smallest n that gives a result to the square root so you have to try known squares.

Since you have 60+n, you have to start with 64, 81, 100, etc

First try with 64 means n equals 4

Then you go for the next expresion and replace 4:

2(4) + 28 = 36 which is 6*6

So thats your answer

Final answer:

The smallest natural number that could be the square root of (60 + n) and (2n + 28) is 4.

Explanation:

The smallest natural number that could be √(60 + n) and √(2n + 28) is 8. To find this, we need to solve the equations:

√(60 + n) = 8 and √(2n + 28) = 8.

Squaring both sides of each equation, we get:

60 + n = 64 and 2n + 28 = 64.

Solving these equations, we find:

n = 4 and n = 18.

Since we are looking for the smallest natural number, the answer is 4.

Answer:

Step-by-step explanation:

14 = (2)(7)

49 = (7)(7)

7 = (7)(1)

GCF(14, 49, 7) = 7

Answer:

6.3 kilograms

Step-by-step explanation:

Because 1 kilo is 2.2 pounds, divide 13.86 pounds by 2.2 to get 6.3 kilograms

Answer:

There are 6.3 Kilograms

Step-by-step explanation:

1 kilogram = 2.2 pounds

13.86 pounds = ? kilograms

[tex]\frac{13.86}{2.2} = 6.3[/tex]

Answer:

A. It would be less steep.

Step-by-step explanation:

took the test

Answer:

42/n-8 which equals -1. (The 3rd answer)

Step-by-step explanation:

8 less means + (-8) and the quotient of 42 and a number means 42/n. Therefore the expression can be derived as (-8)+42/n which can be rewritten as (using the commutative property) 42/n+(-8) or 42/n-8, and to solve substitute n as 6 to find:

42/6-8=7-8=-1

Answer:3rd answer choice

Step-by-step explanation:3rd answer choice

Answer:

The distance between 8,-3 is 12 and the distance between 4,-7 is 11

Step-by-step explanation:

Answer:

1.49 per necklace

Step-by-step explanation:

there are 3 necklaces sold for 4.47. if we divide the three necklaces by the overall price we get the price per necklace. 4.47 divided by 3 = 1.49

Answer:

Each necklace cost $1.49

Step-by-step explanation:

Three necklaces cost $4.47. So to see how much one necklace cost you must divide the cost of all three necklaces by 3. Then you get $1.49

88

Step-by-step explanation:

Answer:

Step-by-step explanation:

12: 88

Answer:

Step-by-step explanation:

2^5 = 32 answer A

$12870 hope this helps bebe :)

Answer:

well 5% of 16 is 0.8 soo...?

Step-by-step explanation:

Answer:

he makes 0.8 jokes a year

Answer:

12 cubic units

Step-by-step explanation:

Each square has a length of 1 unit (2units/2 squares = 1unit), therefore since the height of the prism is made up of 3 squares, its length is 3 units.

Using the equation

V = l x w x h

V = 2 x 2 x 3

V = 12 cubic units

Answer:

all work is pictured/shown