Given segment AC and point B that lies on AC,
find CB if AC = 17, AB = 32 + 3x, and CB=57+6x
CB=

I give brainliest

The total number of ways the study can be selected is: 637065

Given,

Total number of women in a group= 13

Total number of men in a group = 12

Number of women chosen = 8

Number of men chosen = 8

∴ the total number of ways the study group can be selected = 13C₈ and 12C₈.

This in the form of combination factor = nCr

                                                     ∴ nCr = n!/(n₋r)! r!

13C₈ = 13!/(13 ₋ 8)! 8!

        = 13!/5!.8!

        = 1287

12C₈ = 12!/(12₋8)! 8!

        = 12!/5! 8!

        = 495

Now multiply both the combinations of men and women

= 1287 × 495

= 637065

Hence the total number of ways the study group is selected is 637065

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The non-extraneous solutions are -6 and -5.

By checking these solution values in the original equation.

[tex](x+6)^{1/2}-5=x+1\\(x+6)^{1/2}=x+6\\((x+6)^{1/2})^2=(x+6)^2\\x+6=x^2+12x+36\\0=x^2+11x+30\\(-11+(11^2-4(1)(30))^{1/2})/2\\(-11+((1)^{1/2})/2\\(-11+1)/2=-5\\(-11-1)/2=-6\\((-6)+6)^{1/2}-5=(-6)+1\\(0^{1/2})-5=-5[/tex]

Thus, -6 is non-extraneous.

[tex]((-5)+6)^{1/2}-5=(-5)+1\\(1^{1/2})-5=-4\\1-5=-4\\-4=-4[/tex]

Thus, -5 is non-extraneous.

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Answer:

4 quarts of milk

Step-by-step explanation:

4 quarts = 1 gallon

so, melissa needs to buy 4 quarts

A constant function is exactly that - constant - meaning it exhibits no change whatsoever with respect to any change in its input. If [tex]f(x) = 1[/tex], then it doesn't matter what value of [tex]x[/tex] I give you, the value of [tex]f(x)[/tex] will always be nothing other than 1.

That the derivative of such a function is zero follows immediately from the definition of the derivative. If [tex]c\in\Bbb R[/tex] and [tex]f(x) = c[/tex], then

[tex]f'(x) = \displaystyle \lim_{h\to0}\frac{f(x+h)-f(x)}h = \lim_{h\to0} \frac{1 - 1}h = \lim_{h\to0}\frac0h = 0[/tex]

The observation about the student's grade with the z score illustrated is that it's a half standard deviation above the mean of the total test score.

It should be noted that the z score is a numerical measurement which describes the relationship of a value to the mean value of the group.

In this case, the observation about the student's grade with the z score illustrated is that it's a half standard deviation above the mean of the total test score.

This is illustrated as the z score is 0.5.

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Answer:

5, 7

Step-by-step explanation:

The mode of the numbers is 5, which means that 5 should be the most common card (highest frequency). Therefore the cards should have at least one more 5 among them.

Considering that 5 is one of the hidden cards and x is the other,

• Using the equation for the mean:

[tex]mean = \frac{sum \space\ \space\ of \space\ \space\ numbers}{number \space\ \space\ of \space\ \space\ numbers}[/tex]

[tex]6 = \frac{4+5+ 9 + 5 + x}{5}[/tex]

⇒ [tex]30=23 + x[/tex]

⇒ [tex]x = 7[/tex]

This means 5 and 7 are the hidden cards.

Answer:

See attached

Step-by-step explanation:

The graph of a proportional linear relationship is a line that passes through the origin (0, 0).

From inspection of the given tables, the linear equations for each table of points is:

The only equation for which y = 0 when x = 0 is y = x/2  →  Table 2.

Given points from Table 2:

To graph the line, plot the given points and draw a line through them (see attached).

By applying the concept of composition between two functions and utilizing the information given in the two tables, we find the following results: f ° g (0) = - 2, f ° g (x) = 1.

Compositions are binary operators between two functions: f - Former function, g - Latter function.

f ° g (x)

Where the input of the former function is the output of the latter function. By a brief observation, we find the following relationships in accordance with the two tables:

Case I

f(x):

0 → 1

g(x):

1 → - 2

Case II

f(x):

1 → 0

g(x):

0 → 1

By applying the concept of composition between two functions and utilizing the information given in the two tables, we find the following results: f ° g (0) = - 2, f ° g (x) = 1.

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it's B why they need me to write something long the answer is ez B

Step-by-step explanation:

it f common sense

Step-by-step explanation:

[tex]f(x) = 3 {x}^{2} + 2x + 4[/tex]

[tex] \: [/tex]

[tex]f(2) = 3. {2}^{2} + 2.2 + 4[/tex]

[tex]f(2) = 3.4 + 4 + 4[/tex]

[tex]f(2) = 12 + 8[/tex]

[tex]f(2) = 20 \\ [/tex]

[tex] \: [/tex]

[tex]f(a + h) = 3 {(a + h)}^{2} + 2.(a + h) + 4[/tex]

[tex]f(a + h) = 3( {a}^{2} + 2ah + {h}^{2} ) + 2a + 2h[/tex]

[tex]f(a + h) = 3 {a}^{2} + 6ah + 3 {h}^{2} + 2a + 2h + 4[/tex]

[tex]f(a + h) = 3 {a}^{2} + 3 {h}^{2} + 6ah + 2a + 2h + 4[/tex]

Answer:

Step-by-step explanation:

$18. 50÷25=0. 74$

Answer: A. DC||AB

Step-by-step explanation:

Line DC is parallel to AB so the correct answer is option B.

If two objects are having the same shape then they will be termed as similar. So in mathematics, if two figures have the same shapes, lines or angles then they are called similar.

In the given image we can see that the two angles ABC and HCB are congruent to each other. So the line DC is parallel to AB.

Therefore Line DC is parallel to AB so the correct answer is option B.

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Answer: formula

AB= (-1- -3)+((3-1)

(-1+3 )^2+(3-1)^2

2^2+2^2

Sq rt of 8 is 2.83

length of AB is 2

BC= (-3- -1)^2 + (5-3)^2

-3+1 =-2^2+2^2=4+4=8

Sq rt of 8 is 2.828= 2.83

Step-by-step explanation:

The answer to the question that is modeled here is one sixth plus four sixths.

We have the following fractions

1/6 and 5/6

We are to find the fraction which when added to 1/6 would give us 5/6. Hence we have

1/6 + 4/6 = 5/6

Hence the correct answer to the question here is option a.

PLS HELP 1HOUR LEFT Select the expression that is modeled on the number line. A number line from zero to one partitioned into sixths. There are four hops beginning at one sixth and ending at five sixths one sixth plus five sixths

one sixth plus four sixths

five sixths minus one sixth

five sixths minus four sixths

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Round this however your teacher instructs.

=================================================

Work Shown:

mu = 830 = mean

sigma = 96.7 = standard deviation

x = 915 = given raw score we want to convert

z = (x - mu)/sigma

z = (915 - 830)/(96.7)

z = (85)/(96.7)

z = 0.8790072 approximately

Answer:

70/45

Step-by-step explanation:

(-10/9) divided by (-5/7)  = (-10/9) / (-5/7)

dividing two fractions is the same as multiplying the top fraction by the reciprocal of the bottom one

top fraction = -10/9

bottom fraction = -5/7

reciprocal just means switching the numerator and denominator

reciprocal of bottom fraction = 7 / -5 = -7/5

thus,

(-10/9) / (-5/7) = (-10/9) * reciprocal of (-5/7) = (-10/9) * (-7/5) = 70/45

note that to multiply two fractions, you just multiply the numerators to get your new numerator and do the same thing with the denominators

The expression that represents a complex number is the one in the second option.

[tex]\frac{2}{3} + \sqrt{-\frac{27}{28} }= \frac{2}{3} + \sqrt{\frac{27}{28} } i\\[/tex]

Remember that the complex number i is given by:

[tex]i = \sqrt{-1}[/tex]

So we have complex numbers when we have negative arguments inside of square roots.

In this particular case, the only option with a negative argument on a square root is on the second option:

[tex]\frac{2}{3} + \sqrt{-\frac{27}{28} } \\\\\frac{2}{3} + \sqrt{-1} *\sqrt{\frac{27}{28} } \\\\\frac{2}{3} + \sqrt{\frac{27}{28} } i\\[/tex]

We conclude that the correct option is the second one.

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Answer:

(2)/(3)+\sqrt(-(27)/(28))

Step-by-step explanation:

Plato/Edmentum

[tex]\huge\boxed{4x}[/tex]

Start by simplifying the power.

[tex](5x)^3=5^3x^3=125x^3[/tex]

[tex]\dfrac{500x^4}{125x^3}[/tex]

Cancel out the common factor of [tex]125[/tex].

[tex]\dfrac{4x^4}{x^3}[/tex]

Finally, cancel out the common factor of [tex]x^3[/tex].

[tex]\boxed{4x}[/tex]

Answer:

Step-by-step explanation:

F = [tex]\frac{mv^2}{r}[/tex]

mv² = Fr

m = [tex]\frac{Fr}{v^2}[/tex]

The solution to the system of equations is x = 0.5, y = 0

The system of equations is given as:

y = 2x-1

4x + y=2

Substitute y = 2x-1  in 4x + y=2

4x + 2x-1  =2

Evaluate the like terms

6x = 3

Divide by 6

x = 0.5

Substitute x = 0.5 in y = 2x-1

y = 2 * 0.5 - 1

Evaluate

y = 0

Hence, the solution to the system of equations is x = 0.5, y = 0

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Step-by-step explanation:

the area of s circle is

pi×r²

r being the radius.

so, in our case

pi×17.8² = pi×316.84 = 995.3822164... ≈ 995 m²

From the statements and reasons given below as regards the Isosceles Triangle, we have been able to prove that; ∆BAM ≅ ∆CAN

Isosceles Triangle means that two sides of the triangle are equal and also 2 angles are equal.

Now, we are told that triangle ABC is an Isosceles and as such, AB and AC are congruent.

We are given that BM and NC are congruent. Now, due to the fact that Triangle AMN is an isosceles triangle, it means that the sides AM and AN are congruent to each other.

Thus, from the proofs above and from the definition of the isosceles Triangle, we can say that triangles BAM and CAN are congruent.

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Answer & Step-by-step explanation:

To prove ∆BAM ≅ ∆CAN:

1. Given that ∆ABC is an isosceles triangle with base BC, and BM = CN, we know that AB = AC.

2. Using the Side-Angle-Side (SAS) congruence criterion, we can show that ∆ABM and ∆ACN are congruent.

3. Therefore, corresponding angles ∠BAM and ∠CAN are congruent.

4. Similarly, ∠BMA and ∠CNA are congruent.

5. By showing that corresponding angles in ∆ABM and ∆ACN are congruent, we can conclude that ∆BAM ≅ ∆CAN.

To prove ∆AMN is an isosceles triangle:

1. From the given information, we know that BM = CN.

2. By proving ∆BAM ≅ ∆CAN, we have shown that ∠BAM ≅ ∠CAN.

3. Since ∠BAM and ∠CAN are congruent, we can conclude that ∠BAN ≅ ∠CAM using the Transitive Property of Congruence.

4. By establishing that ∠BAN ≅ ∠CAM, we can conclude that ∆AMN is an isosceles triangle because it has two congruent angles.

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

Step-by-step explanation:

As the given figure is a rectangle, therefore the opposite sides should be equal. So -

3x + y = 12 – y...(eqn (i) )

and

y – x = x – 1...(eqn (ii) )

Solving eqn (ii) we get -

→ y – x = x – 1

→ y = x + x – 1

→ y = 2x – 1...eqn(iii)

Solving eqn (i) we get -

→ 3x + y = 12 – y

→ 3x = 12 – y – y

→ 3x = 12 – 2y

Substituting the value of eqn (iii)

→ 3x = 12 – 2(2x– 1)

→ 3x = 12 – 4x + 2

→ 3x + 4x = 14

→ 7x = 14

→ x = 14/7

→ x = 2

Answer:

x = 2; y = 3

Step-by-step explanation:

Since the quadrilateral has 4 right angles, it is a rectangle.

In a rectangle, opposite sides are congruent.

3x + y = 12 - y

x - 1 = y - x

We have a system of two equation is 2 variables.

Let's simplify both equations.

3x + 2y = 12

2x - y = 1

Rewrite the first equation. Multiply both sides of the second equation by 2. Add the equations.

      3x + 2y = 12

(+)   4x - 2y = 2

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

      7x        = 14

Divide both sides by 2.

x = 2

Substitute 2 for x in the second original equation and solve for y.

x - 1 = y - x

2 - 1 = y - 2

1 = y - 2

y = 3

Answer: x = 2; y = 3

Based on the calculations, Tart & Sweet's total profit from April to June is equal to -2 dollars.

A bar chart can be defined as a type of chart that is used for the graphical representation of a data set, especially by using rectangular bars or vertical columns.

In order to determine Tart & Sweet's total profit, we would simply add the amount of money (in dollars) generated from April to June as follows:

Total profit = -8 + 2 + 4

Total profit = -$2.

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The simplified expression of axaxbxb is a^2b^2

The expression is given as;

axaxbxb

Rewrite properly as:

a * a * b * b

Evaluate the product

a^2b^2

Hence, the simplified expression of axaxbxb is a^2b^2

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Answer:

0.23

Step-by-step explanation:

5y+14=27y+9

14-9=27y-5y

5=22y

dividing through by 22

y=0.23