Solve the equation and show the solution set on a number line: |x+5|=x+5

Answer:

Our system of equations is:

We are looking for x

Let's express y using x

Replace x in the second equation with the result

4x²+20x+3=0 is a quadratic equation

Let Δ be our discriminant

Δ= 20²-4*4*(-3)

Δ=448 > 0 so we have two solutions for x

let x and x' be the solutions

so the solutions are:

-5.15 and 0.15

Answer:

Step-by-step explanation:

A = {2,8,10,14}

B= {6,8,20}

C={8,18,20,24}

A ∩ B --> intersection means elements that  are in both sets A & B

A ∩ B = {8}

A∩ C =  {8}

B ∩ C = {8 , 20}

A∩B ∩ C = {8}

First blue box = { 2,10, 14}

Second blue box = {18, 24}

First green box = { 8}

Second green box = { 20}

b) A ∩ B = {8}

n [ A ∩ B] = 1

Probability of the number to be a member of A∩B =  1 / 25

Answer:

see explanation

Step-by-step explanation:

Using the translation rule (x, y ) → (x - 2, y + 4 )

Subtract 2 from the original x- coordinate and add 4 to the original y- coordinate, thus

A(0, 3 ) → A'(0 - 2, 3 + 4 ) → A'(- 2, 7 )

B(- 2, - 4 ) → B'(- 2 - 2, - 4 + 4 ) → B'(- 4, 0 )

C(1, 5 ) → C'(1 - 2, 5 + 4 ) → C'(- 1, 9 )

Answer:

m∠CDE = 60°

Step-by-step explanation:

Given that the arc at the center = 2 times the arc at the circumference, we have;

Angle at the center = arc CE = 120°

Whereby the angle at the circumference is given as m∠CDE and it is opposite the circle arc CE

We note that m∠CDE is the acute angle between chord DC and DE

Therefore, we have;

Angle at the center = 120° = 2 times the arc at the circumference = 2 × m∠CDE

120° = 2 × m∠CDE

m∠CDE = 120/2 = 60°

Therefore the angle of m∠CDE is equal to 60°.

Answer:

approximately 2.46

Step-by-step explanation:

Answer:

2.4666666666

Step-by-step explanation:

To Find How Much Larger Or Smaller Any Given Number Is To Another, Do (#1)/(#2). In This Case, 74/30 Into Google Does A Quick Job Of This Question!

Answer:

the width is 17.5 feet and the length is 82.5 feet.

Step-by-step explanation:

The house has a rectangular shape and we know that the length is 5 feet less than 5 times the width.

We will call the width x, thus, the length would be represented as 5x-5 (5 less than 5 times the width).

Since Darrin is going to hang garland around the perimeter of the house, we know that the perimeter is 2 times the length plus two times the width and this equals 200.

Let's write this in algebraic form

[tex]width = x\\length= 5x-5\\Perimeter= 2width +2length=200\\200=2(x)+2(5x-5)\\200=2x+10x-10\\200=12x-10\\200+10=12x\\210=12x\\210/12=x\\x=17.5[/tex]

Therefore, the width is 17.5 feet.

Now, the length is 5x-5, thus substituting the 17.5 in this equation we have:

[tex]5x-5=5(17.5)-5=87.5-5=82.5[/tex] feet

Therefore, the width is 17.5 feet and the length is 82.5 feet.

Answer:

total rotation = 90 clockwise.

Step-by-step explanation:

Rotation from B to negative y-axis = 45 degrees because B(-3,-3)

Rotation from negative y-axis to B' = 45 degrees because B(-3,3)

Therefore total rotation = 45+45 = 90 clockwise.

Answer:

Step-by-step explanation:

The median is 4, which is the middle number. If there is no middle number, get the average of the two numbers closest to the median.

The mean is 4, which is the average of all the numbers. you add all of them up and divide by how many integers there are in the list.

The mode is 6, which is the integer that is shown the most.

Answer:

mean=4

median=4

mode=6

Step-by-step explanation:

Mean: add 0+2+2+4+4+6+6+6+6=36

36/ (the amount of numbers) 9= 4

Median: cross out the numbers left to right until you get to the middle which is 4.

Mode: 6 occurred four times, which is the most out of any of the other numbers in this sequence, so the answer is 6.

Answer:

(-2,-4)

Step-by-step explanation:

The vertex of a parabola is it's lowest (or highest, but lowest in this context) point. Your lowest point is (-2,-4), so that is your answer.

Answer:

Step-by-step explanation:

When events are independent, the probability of some sequence of them is the product of the probabilities of the individual events in that sequence.

The probability of a child having spina bifida is 16% = 0.16, so the probability that the child will not have the condition is 1 - 0.16 = 0.84. The probability that 0 of 2 children will have spina bifida is ...

  p(0 for 2) = p(0 for 1)×p(0 for 1) = 0.84×0.84 = 0.7056

__

There are two ways that 1 of 2 children can have spina bifida: either the first one does, or the second one does. These are mutually exclusive conditions, so their probabilities add:

  p(1 for 2) = p(1 for 1)×p(0 for 1) +p(0 for 1)×p(1 for 1) = 0.16×0.84 +0.84×0.16

  p(1 for 2) = 0.2688

__

There is one way both children can have spina bifida:

  p(2 for 2) = p(1 for 1)×p(1 for 1) = 0.16×0.16 = 0.0256

__

In summary, our probability distribution is ...

  p(X=0) = 0.7056

  p(X=1) = 0.2688

  p(X=2) = 0.0256

Answer: 27061

Step-by-step explanation:

given that Р = 0.5

so

1 - P = 1 - 0.5  = 0.5

ERROR OF MARGIN E = 0.01

SIGNIFICANCE LEVEL α = 1 - confidence level

α = [(1 - (99.9/100)] = 0.0010

α / 2 = 0.001 / 2 = 0.0005

Zα/2 = Z0.0005 = 3.29  (using the Z table )

therefore

Sample size n = ((Zα/2) / E)² * P * (1 - P )

Sample size  n = (3.29 / 0.01)² * 0.5 * 0.5

Sample size n = 108,241 * 0.5 * 0.5

Sample size n = 27,060.25 ≈ 27,061

Answer:

sample size should be atleast n= 27069

Step-by-step explanation:

Given that,

confident level(CI) = 99%= 0.999

desired marginal error=1%= 0.01

note: marginal error = length of CL/2

significant level α = 1 - confident level = 1 - 0.999= 0.001

critical value = Zα/2 = Z(0.001/2) = Z0.0005( value of from z table) = 3.2905267

since we don't have preliminary estimate, p' = 0.5, which is require for maximum value

n = p' × (1 - p')(critical value/desired marginal)²

n= 0.5 × 0.5(3.2905267/0.01)²

n = 27068.91

the value of n has to be an integer = 27069

Answer:

Option C.

Step-by-step explanation:

It is given that,

[tex]\overline{AB}\cong \overline {DE}[/tex]

[tex]\overline{AC}\cong \overline {DF}[/tex]

According to SAS congruence property, two triangles are congruent if they have two congruent corresponding sides and their included angles are congruent.

Angle between [tex]\overline{AB}\text{ and }\overline {AC}[/tex] is [tex]\angle A[/tex].

Angle between [tex]\overline{DE}\text{ and }\overline {DF}[/tex] is [tex]\angle D[/tex].

So, [tex]\Delta ABC\cong \Delta DE F[/tex] by SAS, if

[tex]\angle A\cong \angle D[/tex]

Therefore, the correct option is C.

Answer:

6n or 6 x n

Step-by-step explanation:

Answer:

13.33 cm

Step-by-step explanation:

Given, ratio of volumes v ÷ V = 8 ÷ 27

This ratio is applicable to heights of same containers, as the volume is directly proportional with height (V=Ah, A- base, h- height)

So we have:

and

Then,

Answer:

13.33 cm

Step-by-step explanation:

Down here.

Answer:

mMN + 150 = 180

Step-by-step explanation:

Circle O is shown. Line segment M P is a diameter. Line segment N O is a radius. Angle N O P is 150 degrees.

Given that:

NO is the radius and ∠NOP = 150°.

The angle addition postulate which states that a larger angle is formed when two smaller angles are placed side by side. If two angle x and y are small angles placed side by side, a big angle Z formed is given as:

z = x + y.

Therefore in circle O, using angle addition postulate:

mMN + ∠NOP = mMP

But mMP = 180° (angle on a straight line)

mMN +   ∠NOP = 180°

mMN + 150 = 180

Answer:

Transformed   [tex]\,\,f(x)= -3\,(x-1)^2[/tex]

Step-by-step explanation:

The process of shifting the graph of the function 1 unite to the right can be obtained by subtracting 1 to the x-coordinate in the expression of the function:

[tex]f(x)=x^2\\new\,f(x) =(x-1)^2[/tex]

The process of stretching vertically the function, would be accomplished by multiplying now the full function by "3":

[tex]new \,\,f(x)= 3\,(x-1)^2[/tex]

the reflection over the x-axis is obtained by multiplying the full function by the constant "-1":

[tex]new \,\,f(x)= -3\,(x-1)^2[/tex]

Answer:

the second one.its a parallelogram

Answer:

90000 km

Step-by-step explanation:

1 hour = 3600 sec

distance = speed x time

              = 25 km/s x 3600 s

               = 90000 km

standard form = 9 x 10⁴

Answer:

The percentage by which the booster club fell short is 33% as shown on the chart

Step-by-step explanation:

To represent the given data pictorially, a pie chart is suitable

The circumference of the pie chart will represent the amount to be raised by the booster club and a sector of the circle which is two-thirds of the circumference represents the amount raised

Given that the amount raised = 2/3×Goal = $15,000, we have;

We represent the amount raised as a sector of the circle as follows;

Sector angle = 2/3×360° = 240°

Total sector of goal amount = Entire circle = 360°

Amount club fell short = 360° - 240° = 120°

The goal amount = 3/2 × $15,000

Percentage by which the club fell short = 120/360×100 = 1/3×100 = 33.33%

Answer:

5

Step-by-step explanation:

We need to find the value of AP

First, lets compare the perimeters:

Sum of the perimeters of smaller triangles:

As BP+PC= BC we can put it as:

and

Plug in values of perimeters:

Answer is: 5

Answer:

D(-4, -3), E(-7, 4), and F(-7, -3).

Step-by-step explanation:

The current coordinates are A(4, 2), B(7, 9), and C(7, 2).

If you reflect the coordinates over the y-axis, the y-values will not be changing, but the signs of the x-values will flip. So, you will have A'(-4, 2), B'(-7, 9), and C'(-7, 2).

When you translate the resulting triangle down 5 units, the y-values will decrease by 5 units. So, the coordinates of triangle DEF will be D(-4, -3), E(-7, 4), and F(-7, -3).

Hope this helps!

Answer:

D (-4, -3)

E (-7, 4)

F (-7,-3)

Step-by-step explanation:

Well triangle ABC reflected over the y-axis to make triangle DEF looks like the image below. ↓

Then we have to translate triangle DEF 5 units down.

With the coordinates D, E, F,

D (-4,2)

E (-7,9)

F (-7,2)

To translate it 5 units down we just subtract the y coordinates by 5.

D (-4, -3)

E (-7, 4)

F (-7,-3)

Thus,

the coordinates for triangle DEF are (-4, -3) , (-7, 4) , (-7,-3).

Hope this helps :)

Answer:

-2/3

Step-by-step explanation:

We have two points ( 0,3) and ( 3,1)

We can use the slope formula

m = (y2-y1)/(x2-x1)

  = (1-3) /(3-0)

   = -2/3

Answer:

-2/3

Step-by-step explanation:

Two points are given on the graph:

(0, 3) and (3, 1)

Use slope formula.

m = rise/run

m = (y₂ - y₁)/(x₂ - x₁)

x₁ = 0

y₁ = 3

x₂ = 3

y₂ = 1

m = (1 - 3)/(3 - 0)

m = -2/3

The slope of the line is -2/3.

Researchers are observing those with mumps to see how it affects hearing loss at all. There may be strong correlation, weak correlation, or no correlation at all.

With an experiment, researchers would break the participants into two groups: control group and treatment group. Those in the control group get the placebo (fake treatment) while the treatment group gets the treatment applied to them. If we were dealing with an experiment for this context, then the treatment group would get exposed to mumps on purpose. Of course, this is unethical and dangerous so an experiment for this type of project is not a good idea. It's better to go with an observational study.

Answer:

2x - y = 3

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 )

Given

x + 2y = - 2 ( subtract x from both sides )

2y = - x - 2 ( divide all terms by 2 )

y = - [tex]\frac{1}{2}[/tex] x - 1 ← in slope- intercept form

with slope m = - [tex]\frac{1}{2}[/tex]

Given a line with slope m then the slope of a line perpendicular to it is

[tex]m_{perpendicular}[/tex] = - [tex]\frac{1}{m}[/tex] = - [tex]\frac{1}{-\frac{1}{2} }[/tex] = 2 , thus

y = 2x + c ← is the partial equation

To find c substitute (2, 1) into the partial equation

1 = 4 + c ⇒ c = 1 - 4 = - 3

y = 2x - 3 ← equation in slope- intercept form

add 3 to both sides

y + 3 = 2x ( subtract y from both sides )

3 = 2x - y, thus

2x - y = 3 ← equation in standard form

]

Answer:

x = 26, 16

Step-by-step explanation:

( x-21) ^2 = 25

Take the square root of each side

sqrt(( x-21) ^2) = ±sqrt(25)

x-21 = ±5

Add 21 to each side

x-21+21 = 21±5

x = 21±5

x = 21+5  and x = 21-5

x = 26, 16

Answer:

10

Step-by-step explanation:

8+5+15+12+10= 50 / 5 = 10

Answer:

-12p^7q^9

Step-by-step explanation

-\left(-\frac{2}{3}pq^4\right)^2\cdot \:27p^5q

-27\cdot \frac{2^2p^2q^8}{3^2}p^5q

Multiply the fractions

\frac{2^2p^2q^8\cdot \:27p^5q}{3^2}

-\frac{2^2\cdot \:27p^7q^9}{3^2}

-2^2\cdot \:3p^7q^9

Answer:

1.475

Step-by-step explanation:

Answer:

Option C. 3077.2 mm³

Step-by-step explanation:

Data obtained from the question include the following:

Diameter (d) = 17 mm

Height (h) = 60 mm

Pi (π) = 3.14

Volume =?

Next, we shall determine the radius of the cone. This is illustrated below:

Diameter (d) = 17 mm

Radius (r) =.?

Radius (r) = diameter (d)/2

r = d/2

r = 14/2

r = 7 mm.

The radius therefore, is 7 mm.

To know how much frozen water

is in the icicle, we shall calculate the volume of the icicle using the formula for calculating the volume of a cone. This is illustrated below:

Height (h) = 60 mm

Pi (π) = 3.14

Radius (r) = 7 mm

Volume =..?

V = ⅓πr²h

V = ⅓ × 3.14 × 7² × 60

V = 3.14 × 49 × 20

V = 3077.2 mm³

Therefore, the amount of frozen water in the icicle is 3077.2 mm³

Answer:

C 3,077.2 mm

Step-by-step explanation:

Answer:

For numerator

2sin(2∅)=2(2sin∅cos∅)

For Denominator

(1+cos(2∅))(1+tan²∅)

=(1+cos(2∅))(sec²∅)

=(1+cos²∅-sin²∅)(sec²∅)

Recall. 1-sin²∅=cos²∅

=2cos²∅(sec²∅)

=2.

Answer is...

2(2sin∅cos∅)/2

=2sin∅cos∅ or sin(2∅)