Find the area of Diameter of 8.42

Answer:

Step-by-step explanation:

You could use the 'brute force' method, which would be to simply write out all the possible subsets.  We could avoid repetition within the subsets.

{2} would be the first subset; it contains one even number.

Next would be {2, 4}, next {2, 4, 6} ... {2, 4, 6, ... 94, 96, 98, 100}.  Provided that we correctly understand what this problem is asking for, writing out and then counting all these subsets should answer the question.

Answer:

see explanation

Step-by-step explanation:

Given

x² + 10x + 14 = - 7 ( subtract 14 from both sides )

x² + 10x = - 21

To complete the square

add ( half the coefficient of the x- term )² to both sides

x² + 2(5)x + 25 = - 21 + 25

(x + 5)² = 4 ( take the square root of both sides )

x + 5 = ± 2 ( subtract 5 from both sides )

x = - 5 ± 2

x = - 5 - 2 = - 7, or x = - 5 + 2 = - 3

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

The equation can also be solved by factoring

x² + 10x + 14 = - 7 ( add 7 to both sides )

x² + 10x + 21 = 0 ← in standard form

(x + 7)(x + 3) = 0 ← in factored form

Equate each factor to zero and solve for x

x + 7 = 0 ⇒ x = - 7

x + 3 = 0 ⇒ x = - 3

Answer:

There are no real number solutions to this question.

The statement which is true for the equation[tex]\sqrt{2x-1} =-1[/tex] is option C which is that x=1.

It is a relationship between variables and it can be in the form of one variable also.

We have been given [tex]\sqrt{2x-1} =-1[/tex]

squaring both sides we get

2x-1=1

2x=1+1

2x=2

x=1

Hence the solution of the equation is x=1.

Learn more about equations at https://brainly.com/question/2972832

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Answer:

68

Step-by-step explanation:

48+2+20

Consider x as the missing number of hours, so 10x + 25(initial hour) and the total of the rental is $75

10x + 25 = $75

Answer

B

Answer:

From greatest to least is  23:24 , 11:12, 7:8

Step-by-step explanation:

Hope this helps!!!

Answer:

The correct answer is third option

The sum of any number and its opposite is 0

Step-by-step explanation:

It is given an expression,

8.29 * (-5.62 + 5.62)/5.62

To find the correct reason

Here - 5.62 + 5.62 = 0

5.62 is opposite to - 5.62

because sum of a number and its opposite is 0.

Therefore the correct answer is third option.

The sum of any number and its opposite is 0

Answer:

x= 25, y = 19

Step-by-step explanation:

Solve the following system:

{x = y + 6 | (equation 1)

9 y - 8 x = -29 | (equation 2)

Express the system in standard form:

{x - y = 6 | (equation 1)

-(8 x) + 9 y = -29 | (equation 2)

Swap equation 1 with equation 2:

{-(8 x) + 9 y = -29 | (equation 1)

x - y = 6 | (equation 2)

Add 1/8 × (equation 1) to equation 2:

{-(8 x) + 9 y = -29 | (equation 1)

0 x+y/8 = 19/8 | (equation 2)

Multiply equation 2 by 8:

{-(8 x) + 9 y = -29 | (equation 1)

0 x+y = 19 | (equation 2)

Subtract 9 × (equation 2) from equation 1:

{-(8 x)+0 y = -200 | (equation 1)

0 x+y = 19 | (equation 2)

Divide equation 1 by -8:

{x+0 y = 25 | (equation 1)

0 x+y = 19 | (equation 2)

Collect results:

Answer:  {x = 25 , y = 19

Answer: X= -29, Y= -267 over 10

Step-by-step explanation:

X= -29, substitute the value of X into the equation 6+y-8(-29)+9y an then solve for Y...

Hope this helps!

Answer:

7x-y=61

Step-by-step explanation:

The standard form is Ax+By=C.

Let's simplify the equation first.

1. Distribute: y+5=7x-56

2. Subtract 5: y=7x-61

3. Arrange into standard form: 7x-y=61

Answer

-7x+y=-61

Its the same as 7x-y=61, but in a different form

Answer:

20% of the number 40 is 8

20% x 40=800 divide 100 =8

Answer:

production cost f(x), in dollars, for x number of units produced by company 1:

f(x) = 0.05x^2 − 7x + 300

2) Table that represents the production cost g(x), in dollars, for x number of units produced by company 2:

x        g(x)

0.6     899.58

0.8     899.52

1        899.50

1.2     899.52

1.4     899.58

3) Comparison: do a table for f(x) with the same x-values of the table for g(x).

x            f(x) = 0.05x^2 − 7x + 300    g(x)

0.6         295.818                               899.58

0.8         294.432                               899.52

1            293.05                                 899.50

1.2         291.672                               899.52

1.4          290.298                              899.58

As you can see the values of f(x) are consistently lower than the values of g(x) for the same x-values.

The minimum production cost for company 2 is around 899.50 at x = 1, while the minimum production cost of company 1 is defintely lower (lower than 292.298 for sure, in fact if you find the vertex it is 55).

Answer: Based on the given information, the minimum production cost for company 2 is greater.

Step-by-step explanation:

Answer:

X= -13

Step-by-step explanation:

Your first goal is to get all the X’s to one side of the equation.

So:

3x - 5 = 9x + 8 - 5x

+5x +5x

8x - 5 = 9x + 8

-9x -9x

-1x - 5 = 8

Now that you have all the X variables simplified and on one side, you make sure all of you constant terms are on the other side.

-1x - 5 = 8

+5 +5

-1x = 13

Because you can’t have a negative X, you divide the entire equation by -1.

-1x = 13

-1

x = -13

Dividing by -1 will give you the inverse of the equation which is positive one x equals negative thirteen.

Answer:

answer is Z

Step-by-step explanation:

[tex]\bf \begin{array}{|lllllllll|ll} \cline{1-9} label&A&B&C&D&E&F&G&H\\ &&&&&&&&&\\ pennies&2^0&2^1&2^2&2^3&2^4&2^5&2^6&2^7\implies 128\\ \cline{1-9} \end{array}[/tex]

Answer: part 2: 2n-1

Step-by-step explanation:

I can answer your question if you could type in English plz

Answer:

154 adults 94kids

Step-by-step explanation:

Answer:

Both Scott and Tara have responded correctly.

Step-by-step explanation:

we know that

The area of a trapezoid is equal to

A=(1/2)[b1+b2]h

we have

b1=16 cm

b2=24 cm

h=8 cm -----> Note The height is 8 cm instead of 18 cm

substitute

A=(1/2)[16+24](8)

A=160 cm²

Verify Scott 's work

Note Scott wrote A = (1/2)(24 + 16)(8) instead of A = 2(24 + 16)(8)

Remember that the Commutative Property establishes "The order of the addends does not alter its result"

so

(24+16)=(16+24)

A = (1/2)(24 + 16)(8)=160 cm²

Verify Tara's work

Note Tara wrote A = (1/2)(16+24)(8) instead of A = (16 + 24)(8)

A = (1/2)(16+24)(8)=160 cm²

Answer:

The length of the other leg is [tex]3.21\ units[/tex]

Step-by-step explanation:

I will assume that the triangle is a right triangle

In a right triangle the legs are perpendicular

so

The area of a right triangle is equal to

[tex]A=\frac{1}{2}(a)(b)[/tex]

where

a and b are the legs of the triangle

In this problem we have

[tex]a=39.2\ units[/tex]

[tex]A=63\ units^{2}[/tex]

substitute the values

[tex]63=\frac{1}{2}(39.2)(b)[/tex]

[tex]126=(39.2)(b)[/tex]

[tex]b=126/(39.2)=3.21\ units[/tex]

For this case we have that by definition of trigonometric relations of a rectangular triangle that, the sine of an angle is given by the opposite leg to the angle on the hypotenuse of the triangle.

That is to say:

[tex]Sin (30) = \frac {IR} {14}[/tex]

We clear the length of the leg:

[tex]IR = 14 * sin (30)\\IR = 14 * \frac {1} {2}\\IR = 7 \ in[/tex]

Answer:

[tex]IR = 7 \ in[/tex]

Answer:

Step-by-step explanation:

7/8 0r 0.875

Answer:

c. y=-3x

Step-by-step explanation:

Plug in x=0 and y=0.

0=-3(0)

0=0...the origin

Answer:

1/2

Step-by-step explanation:

A die has 6 sides, in which 3 numbers (2 , 4 , 6) are even.

Simplify: 3/6 = 1/2

There is a 1/2 chance that blue is even and green is even.

~

Answer:

C

Step-by-step explanation:

Using the rules of exponents

• [tex]a^{m}[/tex] × [tex]a^{n}[/tex] ⇔ [tex]a^{(m+n)}[/tex]

• [tex]a^{-m}[/tex] ⇔ [tex]\frac{1}{a^{m} }[/tex]

Hence

[tex]7^{-5/6-7/6}[/tex] = [tex]7^{-\frac{12}{6} }[/tex] = [tex]7^{-2}[/tex], then

[tex]7^{-2}[/tex] = [tex]\frac{1}{7^{2} }[/tex] = [tex]\frac{1}{49}[/tex] → C

ANSWER

C. 1/49

EXPLANATION

The given expression is

[tex] {7}^{ - \frac{5}{6} } \times {7}^{ - \frac{7}{6} } [/tex]

Recall that:

[tex] {a}^{m} \times {a}^{n} = {a}^{m + n} [/tex]

We apply this product rule of exponents to get:

[tex] {7}^{ - \frac{5}{6} } \times {7}^{ - \frac{7}{6} } = {7}^{ - \frac{5}{6} + - \frac{7}{6} } [/tex]

This implies that:

[tex] {7}^{ - \frac{5}{6} } \times {7}^{ - \frac{7}{6} } = {7}^{ - \frac{12}{6} } [/tex]

[tex]{7}^{ - \frac{5}{6} } \times {7}^{ - \frac{7}{6} } = {7}^{ - 2} [/tex]

Recall again that:

[tex] {a}^{ - m} = \frac{1}{ {a}^{m} } [/tex]

We apply this rule to get:

[tex]{7}^{ - \frac{5}{6} } \times {7}^{ - \frac{7}{6} } = \frac{1}{ {7}^{2} } [/tex]

This simplifies to:

[tex]{7}^{ - \frac{5}{6} } \times {7}^{ - \frac{7}{6} } = \frac{1}{49} [/tex]

Answer:

See below.

Step-by-step explanation:

This is a skewed distribution so the best measure of centre is the median.

The best measure of spread  is the IQR because of the skewed distribution.

14×3×3=126. So 126 is your answer.

Answer:

14*4*3         168

Step-by-step explanat

Answer:

[tex]y=(2/3)x[/tex]

The graph in the attached figure

Step-by-step explanation:

Let

x-----> the number of pints

y----> the number of servings

For x=3 pints, y=2 servings

This is a proportional variation

A relationship between two variables, x, and y, represent a proportional variation if it can be expressed in the form [tex]y/x=k[/tex] or [tex]y=kx[/tex]

so

The linear equation is equal to

[tex]y=(2/3)x[/tex]

The graph in the attached figure

Answer:

The graph is attached below

Step-by-step explanation:

A refreshment stand makes 2 large servings of frozen yogurt from 3 pints.

Equation of the line is y=mx+b

where m is the slope and b is the y intercept

2 large serving from 3 pints

So the servings over pints is 2/3

[tex]slope = \frac{2}{3}[/tex]

The y intercept is (0,0). the value of b is 0

We got m=2/3 and b=0

The equation of the line is

[tex]y=\frac{2}{3}x+0[/tex]

[tex]y=\frac{2}{3}x[/tex]

Now make a table. Assume some number for x  and find out y

x            y

0            0

3             2

6             4

Now make a graph using points (0,0) (3,2) and (6,4)

ANSWER

See below

EXPLANATION

The given point (-3,1) lies in the second quadrant.

In this quadrant only sine is positive.

The length of the hypotenuse formed by the right angle triangle is

[tex] {h}^{2} = {3}^{2} + {1}^{2} [/tex]

[tex] {h}^{2} = 9 + 1[/tex]

[tex]{h}^{2} = 10[/tex]

[tex]h = \sqrt{10} [/tex]

The side opposite to θ, is 1 units.

The adjacent side is 3 units.

[tex] \sin( \theta) = \frac{opposite}{hypotenuse} [/tex]

[tex]\sin( \theta) = \frac{1}{ \sqrt{10} } = \frac{ \sqrt{10} }{10} [/tex]

[tex]\cos( \theta) = - \frac{adjacent}{hypotenuse} [/tex]

[tex]\cos( \theta) = - \frac{3}{ \sqrt{10} } = - \frac{3 \sqrt{10} }{10} [/tex]

[tex] \tan( \theta) = - \frac{opposite}{adjacent} [/tex]

[tex]\tan( \theta) = - \frac{1}{3} [/tex]

The values of sine, cosine and tangent of θ are; 1/√10, -3/√10 and -1/3 respectively.

From the task content, it follows from Pythagoras theorem that;

On this note;

Read more on Trigonometric identities;

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y = -5x + 24

y = 4x - 21

Since both of these equations are equal to Y, theyre equal to each other.

So we can make an equation with y = -5x + 24 in one side and y = 4x - 21 on the other.

-5x + 24 = 4x - 21

Now in order to get the value of x we need to isolate it in one side of the equation. We can do this by subtracting 24 from both sides of the equation:

-5x + 24 - 24 = 4x - 21 - 24

-5x = 4x - 45

Now we subtract 4x from both sides so the 4x shift to the other side

-5x - 4x = 4x - 4x - 45

-9x = -45

Finally divide both sides by -9 so x is by itself

(-9)÷(-9x) = -(45)÷(-9)

x = 5

Since we did all of this to BOTH sides of the equation, both sides are still equal to each other and the equation still is true.

Now apply x = 5 to either of the initial equations to find the value of Y

y = -5x + 24 or y = 4x - 21

(I'll do both but u only need one)

y = -5(5) + 24

y = -25 + 24

y = -1

y = 4(5) - 21

y = 20 - 21

y = -1

Either way, X is 5 and Y is -1

Answer (5, -1)

Final answer:

The solution to the system of equations is (5, -1), matching option b. This is found by setting both equations equal to each other, combining like terms, solving for x, and then using that value to find y.

Explanation:

To solve the system of equations, set the two equations equal to each other since they both equal y:

y = -5x + 24
y = 4x - 21

Now equate them:

-5x + 24 = 4x - 21

Add 5x to both sides:

24 = 9x - 21

Add 21 to both sides:

45 = 9x

Now divide by 9 to solve for x:

x = 5

Substitute x back into either original equation to find y:

y = -5(5) + 24
y = -25 + 24
y = -1

The solution is (5, -1), which corresponds to option b.

To check the solution, we can substitute x = 5 into both of the original equations to verify that they are true. For the first equation:

-5(5) + 24 = -25 + 24 = -1

For the second equation:

4(5) - 21 = 20 - 21 = -1

Since both substitutions lead to an identity, the solution is correct. The final answer is (5, -1), or option b.

The answer is A, Angles in an equilateral triangle are congruent.

Which fact would help you to solve for x in the diagram shown?

A) Angles in an equilateral triangle are congruent.  

Answer:

Perimeter of Rhombus = 104 inches  

Step-by-step explanation:

To find the Perimeter of Rhombus we use the formula

Perimeter of rhombus = 4*Length

We need to find the length of rhombus.

if the rhombus has diagonals, it makes four right angled triangles (as shown in figure).

Since 4 triangles are made so, each side of triangle is half of the length of the diagonal.

In our case: Length of diagonals are: 20 and 48

but the Length of sides of triangle will be: 10 and 24

To find the side of rhombus, we can use Pythgoras theorem since the triangles are right angled.

c² = a²+b²

c² = (10)² + (24)²

c² = 100 + 576

c² = 676

√c²= √676

c = 26

So, the length of side of rhombus is 26 inches

Perimeter = 4*length

                = 4*26

                = 104 inches

Perimeter of Rhombus = 104 inches.  

The length of the perimeter of the rhombus is 104 inches.

To find the perimeter of a rhombus with given diagonal lengths of 20 inches and 48 inches, we can use the properties of rhombuses:

Step 1. Relationship between diagonals in a rhombus:

The diagonals in a rhombus cut each other at right angles. Let the diagonal lengths be [tex]\( d_1 \)[/tex] and [tex]\( d_2 \)[/tex].

Step 2. Formula to find side length from diagonals:

The following formula can be used to find the side length ( s ) of a rhombus:

[tex]\[ s = \frac{1}{2} \sqrt{d_1^2 + d_2^2} \][/tex]

where [tex]\( d_1 = 20 \)[/tex] inches and [tex]\( d_2 = 48 \)[/tex] inches.

Step 3. Calculate the side length:

[tex]\[ s = \frac{1}{2} \sqrt{20^2 + 48^2} \][/tex]

[tex]\[ s = \frac{1}{2} \sqrt{400 + 2304} \][/tex]

[tex]\[ s = \frac{1}{2} \sqrt{2704} \][/tex]

[tex]\[ s = \frac{1}{2} \times 52 = 26 \text{ inches} \][/tex]

Step 4. Calculate the perimeter:

The perimeter ( P ) of a rhombus, with all sides equal, is determined by:

[tex]\[ P = 4 \times s = 4 \times 26 = 104 \text{ inches} \][/tex]

Therefore, the length of the perimeter of the rhombus is 104 inches.