AE=EC and BF = FC
M EF=10
M

Answer:

The absolute value function that models the path of the ball is

[tex]f(x) = \left | -\frac{3}{4}\cdot x + 15 \right |[/tex]

The coordinates when the ball passes within 3 meters of the wall is [tex]\left (3, 12\tfrac{3}{4} \right )[/tex]

Step-by-step explanation:

Given that the ball rolls without other external influences, we have;

(y - 0) = (x - 15)

The slope, m is give by the relation;

m = (y₂ - y₁)/(x₂ - x₁)

m = (15 - 0)/(0-20) = -3/4

The equation of the path of the ball in slope and intercept form is presented as follows;

y = m·x + c

15 = -3/4 ×0 + c = 15

c = 15

The absolute value function that models the path of the ball is then;

[tex]f(x) = \left | -\frac{3}{4}\cdot x + 15 \right |[/tex]

The vale of the function when x = 3 is given by the relation

[tex]f(x) = \left | -\dfrac{3}{4}\times 3 + 15 \right | = \dfrac{51}{4}[/tex]

Therefore, we have the coordinates as  [tex]\left (3, 12\tfrac{3}{4} \right )[/tex].

Answer:

-11x+8 or 8-11x

Step-by-step explanation:

Answer:

3

[tex]d\in R,\hspace{5}d\neq 0[/tex]

Step-by-step explanation:

You can solve for any variable. From the first equation, let's solve for c :

[tex]\frac{c+1}{d} =5\\\\c+1=5d\\\\c=5d-1[/tex]

Now, replace the value of c into the other equation:

[tex]\frac{30d}{2c+2} \\\\\frac{30d}{2(5d-1)+2} \\[/tex]

Using distributive property

[tex]\frac{30d}{10d-2+2} =\frac{30d}{10d} =3[/tex]

However, keep in mind that this is true for:

[tex]d\in R,\hspace{5}d\neq 0[/tex]

Answer:

The 95% confidence interval (6.9, 8.2) they obtained means that "We are 95% confident that the population mean duration is between 6.9 and 8.2 days".

Option B from the complete Question.

Step-by-step explanation:

Confidence Interval for the population mean is basically an interval of range of values where the true population mean can be found with a certain level of confidence.

Mathematically,

Confidence Interval = (Sample mean) ± (Margin of error)

Margin of Error is the width of the confidence interval about the mean.

It is given mathematically as,

Margin of Error = (Critical value) × (standard Error of the mean)

Critical value will be obtained using the t-distribution if there is no information provided for the population standard deviation and it is obtained from the z-tables if the population standard deviation is known or the sample size is large enough that the sample properties can be approximated to be the same as the population properties.

Standard error of the mean = σₓ = (σ/√n)

σ = standard deviation of the sample

n = sample size

Confidence Interval = (Sample mean) ± [(Critical value) × (standard Error of the mean)]

So, the confidence interval (6.9, 8.2) obtained in the question means that "We are 95% confident that the population mean duration is between 6.9 and 8.2 days".

Hope this Helps!!!

Answer:

(B) There is no solution.

Step-by-step explanation:

Given the two lines A and B where:

[tex]L$ine A: x + y = 6 \implies y=6-x\\$Line B: x + y = 4 \implies y=4-x\\$Therefore:$\\6-x=4-x\\-x+x=4-6\\0=-2\\$Since, $ 0\neq -2,$ there is no solution.[/tex]

The correct option is B.

Answer:

A

Step-by-step explanation:

Just took test, can I have Brainliest.

Answer:

a = 8.

Step-by-step explanation:

a^2 + b^2 = c^2

b = 6; c = 10

a^2 + 6^2 = 10^2

a^2 + 36 = 100

a^2 = 64

a = plus or minus 8

Since side lengths can't be negative, a = 8.

Hope this helps!

Answer:

(6, -4)

Step-by-step explanation:

If ABCD is dilated by a factor of 2, you multiply the coordinates by 2. For the coordinate D', you would multiply 3 by 2 to get 6 and you would multiply -2 by 2 to get -4. Answer: (6, -4)

Answer:

A

achievements

Step-by-step explanation:

Answer:

Step-by-step explanation:

[tex]x^2-5=-2x+3\\\\x^2+2x-8=0\\\\a=1\,,\ b=2\,,\ c=-8\\\\x=\dfrac{-b\pm\sqrt{b^2-4ac}}{2a}\\\\x=\dfrac{-2\pm\sqrt{2^2-4\cdot1\cdot(-8)}}{2\cdot1}=\dfrac{-2\pm\sqrt{4+32}}{2}=\dfrac{-2\pm\sqrt{36}}{2}=\dfrac{-2\pm6}{2}\\\\x_1=\dfrac{-2-6}2=\dfrac{-8}2=-4\\\\y_1=-2x_1+3=-2(-4)+3=8+3=11\\\\(-4\,,\ 11)\\\\x_2=\dfrac{-2+6}{2}=\dfrac{4}2=2\\\\y_2=-2x_2+3=-2\cdot2+3=-4+3=-1\\\\(2\,,\ -1)[/tex]

Answer:

D. 399

Step-by-step explanation:

3x19(19-12)

57x7=399

Answer:

can I see the diagram please

Answer:

80days

Step-by-step explanation:

20m=60days

15m(will take more days)

20÷15×60 = 80 days

Answer:

El ascensor recorrió unos 39 metros

Step-by-step explanation:

Segun la pregunta cada cada piso tiene 3 metros de altura, por lo tanto para calcular los metros que recorrió el ascensor tenemos que hacer el siguiente calculo:

metros desde el primer piso al quinto piso=3 metros*4=12 metros

metros desde el quinto piso al segundo piso=3 metros*3=9 metros

metros desde el segundo piso al octavo piso=3 metros*6=18 metros

Por lo tanto los metros que recorrió el ascensor=12 metros+9 metros+18 metros

metros que recorrió el ascensor=39 metros

El ascensor recorrió unos 39 metros

Answer:

1²+3

Step-by-step explanation:

I'm not to sure I hope this helped.

Answer:

The correct option is;

ASA

Step-by-step explanation:

The given information are;

1. ∠A ≅ ∠D,                                    1. Given

2. [tex]\overline{CD}\left | \right |\overline{AB}[/tex],                                   2. Given

3. [tex]\overline{CB}\cong \overline{BC}[/tex],                                  3. refl. prop.

4. ∠ABC ≅ ∠ DCB,                        4. Alt int. ∠s are ≅

5. ΔABC ≅ ΔDCB,                         5. Angle Side Angle ASA rule of congruency        

The conditions for two triangles to be congruent includes;

1. All sides equal or SSS rule

2. Side Angle Side or SAS rule

3. Angle Side Angle or ASA rule

4. Angle Angle Side or AAS rule

5. Right angle Hypotenuse Side or RHS also known as Hypotenuse Leg, HL rule

Answer:

Option A, y=8

Step-by-step explanation:

If you graph each of the equations, you will find that y=8 is the only line that crosses through the point (-3,8)

Also,

If you notice the given point, the y-coordinate is 8 indicating that the point lies on the line that has y as 8

Hope that helps!!

Answer:

On a coordinate plane, an absolute value graph has a vertex at (negative 0, 0.5).

Step-by-step explanation:

h(x) = |x| + 0.5

Has its vertex at h(x) = 0, h(x) = |x| + 0.5

0 = |x| + 0.5

|x| = -0.5

So x = -0.5

So, the vertex is at (-0.5, 0)

The graph that represents [tex]h(x) = |x| + 0.5[/tex] is (a) on a coordinate plane, an absolute value graph has a vertex at (0, 1.5)

The function is given as:

[tex]h(x) = |x| + 0.5[/tex]

An absolute function is represented as:

[tex]h(x) = |x - h| + k[/tex]

Where:

[tex]Vertex=(h,k)[/tex]

By comparison:

[tex](h,k) = (0,0.5)[/tex]

i.e. the vertex of function h(x) is (0,0.5)

Hence, the graph that represents [tex]h(x) = |x| + 0.5[/tex] is (a)

Read more about absolute functions at:

https://brainly.com/question/7515527

Answer:

System of linear equations

[tex]\left\{\begin{matrix} 3a+c=38 \\\\ 3a+2c=52 \end{matrix}\right.[/tex]

a: adult ticket price and c: child ticket price

Step-by-step explanation:

This system of equations can be used to find the price of the adult and child tickets.

We have two equations (one for each day) and two unknowns (adult ticket price and child ticket price).

Let a: adult ticket price and c: child ticket price,

we have for the first day that 3 adult tickets and 1 child ticket adds $38:

[tex]3a+1c=38[/tex]

and for the second day we have that 2 adult tickets and 2 child tickets adds $52:

[tex]3a+2c=52[/tex]

If we write this as a system of equations, we have:

[tex]\left\{\begin{matrix} 3a+c=38 \\\\ 3a+2c=52 \end{matrix}\right.[/tex]

Answer:

Step-by-step explanation:

Let the number be x

Twice the difference of a number and 5 is written as

2( x - 5)

three times the sum of the number and 2 is written as

3( x + 2)

Equate them

We have

2(x - 5) = 3(x + 2)

Expand

2x - 10 = 3x + 6

Group like terms

2x - 3x = 16 + 10

- x = 16

Multiply through by - 1

x = - 16

Hope this helps you

Answer:

C. 6

Step-by-step explanation:

Use Order of Operations BPEMDAS to help you solve:

9 - 1/16(48)

9 - 3

6

Answer: 40, 36

Step-by-step explanation:

the first dot is 5/4

the second dot is 10/8

the second 15/12

the fourth dot is 20/16

They all are equivalent to 40,36

Answer:

25,20

Step-by-step explanation:

It’s right

Answer:

Step-by-step explanation:

Given: 4X-3Y=17

so, 4x-17 = 3Y

=> Y = (4X-17)/3

Substituting the value in second equation, we get,

=> -78 + m(4x-17)/3 = 2

=>2+78 = m(4x-17)/3

=> 80*3 = m(4x-17)

=>m= 240/(4x-17)

Hope It Helps!!

Answer:

Step-by-step explanation:

#2:  Amber is correct.  The distribution is skewed to the left.

Answer:

42.1

Explanation step-by-step:

Working out the lenght of the blue-dashed line:

SOH

47 is the Hypotenuse.

the blue line is the adjacent.

adjacent= Cos(30) x47

adjacent= 40.7

Working out x :

40.7 is the opposite this time.

x is the adjacent.

x = 40.7/ Tan(44)

x = 42.1

Answer:

24

Step-by-step explanation:

33 + 11 - 10 ÷ 2 × 4

Division is first.

33 + 11 - 5 × 4

Multiplication.

33 + 11 - 20

Add or subtract.

44 - 20

= 24

Answer:

3 cups

Step-by-step explanation:

Bill needs 5 cups of paint for his bed frame.

The store only sells in quarts and so he buys 2 quarts of paint.

Let us convert to cups to see how many he bought:

1 quart = 4 cups

2 quarts = 2 * 4 = 8 cups

Bill bought 8 cups of paint. Therefore, the number of cups he has left is:

8 - 5 = 3 cups

He will have 3 cups left.

Answer:

150 cans were thrown away

Step-by-step explanation:

If the weight of 10 aluminum cans=0.16 kilogram

Each can weighs=0.16 kilograms/10

=0.016kg per can

If the family threw away 2.4 kilogram of aluminum in a month,

How many cans did they throw away?

Total cans thrown away= Total kilogram of cans/each kilogram of cans

=2.4kg/0.016kg

=150 cans

150 cans were thrown away

Answer:

Since in option B, the bacteria are growing exponentially, B would be the correct answer to this question.

Step-by-step explanation:

[tex]P_(_A_o_r_B_)[/tex] = 1

This means that the probability of event A or event B of happening is 1 or certainly would happen.

You can set up an equation for the large triangle made up of the smaller ones by knowing that the total interior angles must sum to 180°. We also can know that angle RPN is also 78° by the geometric law of alternate interior angles. Therefore you know that the angles to sum up are 2x, 2x (which comes from x + x), and 78°.

2x + 2x + 78 = 180

4x + 78 = 180

4x = 102

x = 25.5°

*note, there are many ways to solve this