Rewrite x² - 10x = 4 so that the left side is a perfect square trinomial.
x² - 10x -4 = 0
x² - 10x + 25 = 4
x² − 10x + 25 = 29
x². - 10x + 10 = 14

Answer:

C. 6

Step-by-step explanation:

[tex]\frac{ZY}{FE} =\frac{XY}{DE}[/tex]

[tex]\frac{12}{8} =\frac{9}{DE}[/tex]

[tex]12DE=(9)(8)[/tex]

[tex]DE=\frac{(9)(8)}{12} =\frac{72}{12} =6[/tex]

Hope this helps

Answer:

1.15 or [tex]\frac{15}{13}[/tex]

Step-by-step explanation:

1. The slope can be found with this formula: [tex]\frac{y2-y1}{x2-x1}[/tex]

2. Let's plug in the numbers: [tex]\frac{14--1}{13-0}[/tex]

4. [tex]\frac{15}{13}[/tex] ≈ 1.1538

Using the normal distribution, it is found that the operating cost for the lowest 3% of the airplanes is of at most $1,630.

The z-score of a measure X of a normally distributed variable with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex] is given by:

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

The mean and the standard deviation are given, respectively, by:

[tex]\mu = 2100, \sigma = 250[/tex].

The operating cost for the lowest 3% of the airplanes is of at most the 3rd percentile, hence at most X when Z = -1.88.

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

[tex]-1.88 = \frac{X - 2100}{250}[/tex]

X - 2100 = -1.88(250)
X = 1630.

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Answer:

2.45 units

5 units

5.99 units

5.10 units

Change in Amplitude is 2

Change in Period is π

Transforming sin(x) to [tex]3sin(\frac{2x}{3})[/tex]

y = a(sin(bx+c)) + d

Where, a is Amplitude and [tex]\frac{2}{b}[/tex]π is period

Amplitude of sin(x) =1

Period of sin(x) = 2π

Amplitude of 3sin([tex]\frac{2x}{3}[/tex]) = 3

Period of 3sin([tex]\frac{2x}{3}[/tex]) = [tex]\frac{2}{\frac{2}{3}}[/tex]*π = 3π

Change in Amplitude = 3sin([tex]\frac{2x}{3}[/tex]) - sin(x)

                                    = 3 - 1

                                    = 2

Change in Period = 3sin([tex]\frac{2x}{3}[/tex]) - sin(x)

                              = 3π - 2π

                               = π

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Answer: B

Step-by-step explanation:

The rigid transformations which will map the triangle ABC to triangle DEF is; Translate vertex A to vertex D, and then rotate△ABC around point A to align the sides and angles.

It follows from the task content that the two triangles given are △ABC to △DEF.

Hence, in a bid to map the triangle ABC to DEF, Vertex A is translated to point D which represents vertex D in△DEF. Afterwards, the triangle ABC is simply rotated about the translated vertex A until all sides and angles of both triangles align.

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By using the definition of similarity between triangles and algebraic properties, the length of the segment AB of the system is equal to 4 units.

In this problem we have two similar triangles and we need first to determine the lengths of segments AC and BC and then subtract the length of the latter from the length of the former, that is:

AC/BC = CE/CD

AC/2 = 15/5

AC = 6

AB = AC - BC

AB = 6 - 2

AB = 4

By using the definition of similarity between triangles and algebraic properties, the length of the segment AB of the system is equal to 4 units.

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The probability that the mean of a sample of 106 randomly selected humans is lower than 98.5°F is 4.85%

An equation is an expression that shows the relationship between two or more numbers and variables.

Z score is given as:

z = (raw score - mean) ÷ (standard deviation/√sample size)

Given mean of 98.6°F,  standard deviation is 0.62°F, sample size = 106

For x < 98.5:

z = (98.5 - 98.6) ÷ (0.62÷√106) = -1.66

P(z < -1.66) = 0.0485

The probability that the mean of a sample of 106 randomly selected humans is lower than 98.5°F is 4.85%

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20 girls and 30 boys

A branch of mathematics that deals usually with the nonnegative real numbers including sometimes the transfinite cardinals and with the application of the operations of addition, subtraction, multiplication, and division to them

To make the new situation:

Suppose A classroom has 50 people.

The ratio of girls to boys is 2:3, so in other words, we need to find out how many boys and girls there are, and there are 2 girls for every three boys, So ,how many boys and girls are there?

The answer would be :

Let the two parts in which we divide 50 be 2x and 3x respectively

2x+3x=50

5x=50

x= [tex]\frac{50}{5}[/tex]

x=10

Here,

2x= 2×10=20

3x =3*10=30

20 girls and 30 boys.

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Here, we are concerned about two variables from the above data set, namely, Condo or co-ops and the Unemployment rate. We use the CORREL function of Excel to calculate the correlation coefficient rate and it is = R = -0.01873.

A Weak (negative) correlation exists between the list price of condominiums and co-ops and the unemployment rate.

The correlation coefficient is a statistical measure of the strength of the connection between the relative actions of two variables. The values varied between -1.0 and 1. zero. A calculated wide variety greater than 1. zero or less than -1.zero means that there was an error within the correlation size.

The correlation coefficient is decided with the aid of dividing the covariance by way of the product of the 2 variables' popular deviations.

Correlation values above 0. eight are deemed to signify a strong tremendous linear courting between the variables. Values among zero and 0. three imply a vulnerable relationship or none.

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What is initial value?

It is given that,

The height of the palm tree at the time Myles bought it was 62 inches.

He is tracking the growth of the tree and he has observed that it has grown 6 inches per year.  

So, the initial value of the tree, here, is representing the height of the palm tree when it was bought.

As can be seen clearly, there is no input for the initial value. And, the output for the initial value is given to be 62 inches.

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Answer:

2 tons and 1824 pounds

Step-by-step explanation:

Ton= 2,000 pounds

We know that 2,000 will go into 5824 twice, resulting in 4,000. Subtract 4,000 from 5,284, and you will have an answer of 1284. 1,284 does not go into a ton, therefore you have a remainder of 1,284 pounds.

Answer: -5

Step-by-step explanation:

[tex]\frac{g(6)-g(3)}{6-3}=\frac{44-59}{3}=-5[/tex]

The area of ​​the trapezoid is x+11 cm.

Given a trapezoid has one side of (x+6) cm, the other side is 5 cm, and the height is 2 cm.

A two-dimensional quadrilateral consisting of the sum of non-adjacent parallel sides and a suitable non-parallel side is denoted as a trapezoid.

Now we will use the formula to find the area of ​​a trapezoid

Area = 1/2 × (base 1 + base 2) × height

Here base 1 = (x+6) cm, base 2 = 5cm and height = 2cm

Substituting the values ​​into the formula,  we get

Area = 1/2 × (x+6+5) × 2

Area = 1/2 × (x+11) × 2

Area = x+11

Thus, the area of ​​the given figure when one side is x+6, the other side is 5 cm and the height is 2 cm is x+11 cm.

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Answer:

2√61/19

Step-by-step explanation:

sin^2 x = 1 - cos^2 x

            =  1 - (3√13/ 19)^2

             =   1 - 117/361

              =  244/361

sin x       = √244/19

              = 2√61/19.

The following logarithmic expression can be used to approximate the given expression,

[tex]\frac{log_{b} x}{log_{b} a}[/tex]

Finding the Logarithmic Expression

It is given that for all positive numbers a, b, and x on the condition that a≠1 and b≠1.

Now, for positive values of m and n, we have the following logarithmic expression,

[tex]\frac{log_{m} x}{log_{n} a}[/tex]

Here, m, n and x are all positive numbers.

The logarithmic property imposes that m and n are not equal to 1.

So, by substituting the values m and n by a and b respectively, we get the following logarithmic expression,

[tex]\frac{log_{b} x}{log_{b} a}[/tex]

Therefore, [tex]\frac{log_{b} x}{log_{b} a}[/tex] is the required expression.

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Answer:

a=8.2

Step-by-step explanation:

Answer:

[tex]\huge\boxed{\sf (f-g)(x) = 3x\² + 4x - 14}[/tex]

Step-by-step explanation:

Subtract both functions

(f-g)(x) = 4x² - 6 - (x² - 4x - 8)

(f-g)(x) = 4x² - 6 - x² + 4x - 8

Combine like terms

(f-g)(x) = 4x² - x² + 4x - 6 - 8

(f-g)(x) = 3x² + 4x - 14

[tex]\rule[225]{225}{2}[/tex]

Given: f(x)=4x^2-6f(x)=4x2−6g(x)=x^2-4x-8g(x)=x2−4x−8

To find : (f-g)(x)

(f-g)(x)=f(x)-g(x)(f−g)(x)=f(x)−g(x)

(4x^2-6)-(x^2-4x-8)

Using Distributive property:-

4x^2-6-x^2+4x+8

4x^2-x^2+4x+8-6

Combine like term

3x^2+4x+2

(f-g)(x)=3x^2+4x+2

Hence, The composite function is (f-g)(x)=3x^2+4x+2

Answer:

Step-by-step explanation: The answer is 5/11.



Hello!

Fraction of boys = Number of boys / Total kids

Fraction of boys = [tex]\boxed {\frac{5}{11}}[/tex]

By solving a system of equations, we see that:

x = 89 and y = 98.

First, we can write:

x = a*10 + b

y = b*10 + c

Where a, b, and c are single digit numbers. You can see that b is on both numbers because we know that the numbers share a digit, but on different order.

We also know that:

x + y = 187

a + b + b + c = 34

I we rewrite the first equation, we get:

(a*10 + b) + (b*10 + c) = 187

10a + 11b + c = 187

Then we have two equations:

a + 2b + c = 34

10a + 11b + c = 187

In both equations we can isolate c:

34 -2b -a = c

10a + 11b - 187 = c

Now we have:

-a - 2b + 34  = -10a - 11b + 187

Solving that, we get:

9a + 9b = 153

a + b = 153/9 = 17

Then a and b add up to 17, we can take:

a = 8

b = 9

And:

c = -a - 2b + 34 = -8 - 9 - 9 + 34 = 8

Then the numbers are:

x = 89

y = 98

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Answer:

x = 2

Step-by-step explanation:

AB is given as 3(3x-1) multiply inside the parenthesis with 3

AB = 9x - 3

AC is given as 5(2x+2) multiply inside the parenthesis with 5

AC = 10x + 10

if B is midpoint of AC then AB = BC and AC = AB + BC if we write this equation using the given values

9x - 3 + 9x - 3 = 10x + 10 add like terms

18x - 6 = 10x + 10 transfer like terms to the same side of the equation

18x - 10x = 10 + 6

8x = 16 divide both sides by 8

x = 2 replace x with 2 in given expressions to find the value of each component

Answer:   x = 2; AB = 15; BC = 15; AC = 30

Step-by-step explanation:

AB = BC = 3(3x - 1) = 9x - 3

AC = 5(2x + 2) = 10x + 10

AB + BC = AC

(9x - 3) + (9x - 3) = 10x + 10

   9x - 3 + 9x - 3 = 10x + 10

               18x - 6 = 10x + 10

                8x - 6 = 10

                      8x = 16

                        x = 2

Plug x = 2 to find AB, BC, and AC.

AC = BC = 3(3x - 1) = 9x - 3 = 9(2) - 3 = 18 - 3 = 15

AC = 5(2x + 2) = 10x + 10 = 10(2) + 10 = 20 + 10 = 30

The graph that has been drag into the box in the image attached are the options that shows the results of that transformation.

Note that there are 4 types of function transformations which are are:

Therefore, The function above is known to have passed through the following points

(1,1) and (0,-1)

The graphs of the functions

(a) Function g(x)

The equation of the function is given as: g (x) = 2 + f (x)

This implies that f(x) is said to be translated up by 2 units.

The graph that shows this is graph (b)

(b) Function h(x) = f (x + 2)

This implies that f(x) is translated left by 2 units.

The graph that shows this is graph (e)

(c) Function k(x)  = f (x) -2

This implies that f(x) is translated down by 2 units.

The graph that shows this is graph (c)

(d) Function m(x) =  f (x - 2)

This implies that f(x) is translated right by 2 units.

The graph that depicts this is graph (f)

Therefore,  The graph that has been drag into the box in the image attached are the options that shows the results of that transformation.

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To find Y-intercept, the x-value must be 0.

In the table you can see x = 0 and y = -4

so, the y-intercept of this line is (0 -4)

Hope it helps!

Answer:

13

Step-by-step explanation:

The graph will start repeating after every 13 degrees

The period of the function is of 12 units.

The period of the function is the interval between repetitions of any function. A trigonometric function's period is the length of one whole cycle. As a starting point, we can use x = 0 for any trigonometry graph function.

The period of a function is given by the distance between it's repetitions.

Also, it is the distance between two peak value.

Looking at the graph, the distance between the repetitions is of

= 13- 1

= 12 units, which is the period of the function.

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The expansion of the given expressions are; 4x² - 5x - 5;  2x² - 13x + 15; -2x² - 5x + 3; 3x² + 6x - 1

A) x(x - 5) + 3x² - 5

Expanding this gives us;

x² - 5x + 3x² - 5

⇒ 4x² - 5x - 5

B) (2x - 3)(x - 5)

Expanding the function gives;

⇒ (2x² - 3x - 10x + 15)

⇒ 2x² - 13x + 15

C) -2x(x + 3) + x + 3

⇒ -2x² - 6x + x + 3

⇒ -2x² - 5x + 3

D) 3(x + 1)² - 4

⇒ 3(x² + 2x + 1) - 4

⇒ 3x² + 6x + 3 - 4

⇒ 3x² + 6x - 1

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Answer:

353.9 + 3.8 = 357.7 million barrels of oil

For this problem, I will be using the equal sign instead of the congruent sign for segments.

1) AC = AB, CD = DE, m∠ABC = 70°, m∠ECB = 35° (given)

2) ∠ACB is congruent to ∠ABC (base angles theorem)

3) m∠ACB = 70° (congruent angles have equal measure)

4) m∠DCE = 35° (angle subtraction postulate)

5) ∠DCE and ∠DEC are congruent (base angles theorem)

6) m∠DEC = 35° (congruent angles have equal measure)

7) ∠DEC is congruent to ∠ECB (angles with the same measure are congruent)

8) DE is parallel to BC (if two lines are cut by a transversal and the alternate interior angles are congruent, then the lines are parallel)

Answer:

y = - x + 10

Step-by-step explanation:

the equation of a line in slope- intercept form is

y = mx + c ( m is the slope and c the y- intercept )

calculate m using the slope formula

m = [tex]\frac{y_{2}-y_{1} }{x_{2}-x_{1} }[/tex]

with (x₁, y₁ ) = (6, 4 ) and (x₂, y₂ ) = (8, 2 )

m = [tex]\frac{2-4}{8-6}[/tex] = [tex]\frac{-2}{2}[/tex] = - 1 , then

y = - x + c ← is the partial equation

to find c substitute either of the 2 points into the partial equation

using (6, 4 ) , then

4 = - 6 + c ⇒ c = 4 + 6 = 10

y = - x + 10 ← equation of line

The relationship between lines KO and K’O’ is given as Line K'O' = 5 * line KO

Transformation is the movement of a point from its initial point to a new location. Types of transformation are reflection, rotation, translation and dilation.

Dilation is the increase or decrease in size of a figure by a scale factor.

The larger figure was dilated using a scale factor of 5, hence:

Line K'O' = 5 * line KO

The relationship between lines KO and K’O’ is given as Line K'O' = 5 * line KO

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