the graph of the function f(x) = (x +2)(x + 6) is shown below. On a coordinate plane, a parabola opens up. It goes through (negative 6, 0), has a vertex at (negative 4, negative 4), and goes through (negative 2, 0). What is true about the domain and range of the function? The domain is all real numbers, and the range is all real numbers greater than or equal to –4. The domain is all real numbers greater than or equal to –4, and the range is all real numbers. The domain is all real numbers such that –6 ≤ x ≤ –2, and the range is all real numbers greater than or equal to –4. The domain is all real numbers greater than or equal to –4, and the range is all real numbers such that –6 ≤ x ≤ –2.

Answer:

Step-by-step explanation:

NOTE : we have 6×6=36 possible outcome.

we can resume the set of outcomes in the table below :

Then

the probability that the sum is not divisible

by 2 and not divisible by 4 :

= 18/36

= 1/2

Using the binomial distribution, it is found that there is a 0.3438 = 34.38% probability that fewer than 3 of them are boys.

The formula is:

[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]

[tex]C_{n,x} = \frac{n!}{x!(n-x)!}[/tex]

The parameters are:

In this problem, the values of the parameters are given as follows:

n = 6, p = 0.5.

The probability that fewer than 3 of them are boys is given by:

[tex]P(X < 3) = P(X = 0) + P(X = 1) + P(X = 2)[/tex]

In which:

[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]

[tex]P(X = 0) = C_{6,0}.(0.5)^{0}.(0.5)^{6} = 0.0156[/tex]

[tex]P(X = 1) = C_{6,1}.(0.5)^{1}.(0.5)^{5} = 0.0938[/tex]

[tex]P(X = 2) = C_{6,2}.(0.5)^{2}.(0.5)^{4} = 0.2344[/tex]

Then:

[tex]P(X < 3) = P(X = 0) + P(X = 1) + P(X = 2) = 0.0156 + 0.0938 + 0.2344 = 0.3438[/tex]

0.3438 = 34.38% probability that fewer than 3 of them are boys.

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Answer: 10

Step-by-step explanation:

By the geometric mean theorem, if we let the length of the altitude to the hypotenuse be [tex]y[/tex], this means that [tex]y^{2}=84 \longrightarrow y=\sqrt{84}[/tex].

So, by the Pythagorean theorem, [tex]x=\sqrt{(\sqrt{84})^{2}+4^{2}}=\boxed{10}[/tex]

The rate of change of this simple index over 1 week is - 8.81%

The rate of change is the ratio of the difference in the value of the simple index to the original value of simple index.

Total value of the simple index at day 1 = (8000 x $4.25) + (5000 x $2.90) + (2000 x $6.40) = $61,300

Total value of the simple index at day 8 = (8000 x $3.90) + (5000 x $2.50)+(2000*6.10)  = 55900

the rate of change of this simple index over 1 week

= (55900-61300)/ 61300          * 100 %

= -8.81 %

the rate of change of this simple index over 1 week is - 8.81%

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Answer:

-204kk+3+32k/4k

Hope this helps!!

Answer:

area = 62ft

Step-by-step explanation

so you section the polygon into a big rectangle and 2 small rectangles

the area of the small rectangle will be 2ft x 3ft which will be 6 ft, and as there are 2 of them the area of it will be 12ft

the area of the big rectangle will be 10ft x 5ft, as 8ft - 3ft is 5ft so 5x10=50ft

now add the areas you got, 50+12 which is 62ft

hope this helps:)

Answer:

I think that the answer is 432.

Step-by-step explanation:

6x2y3.We have x as 6 and y as 2.So we replace them with their numbers.

We'll have 6*6*2*2*3 which will give us 432. I HOPE THIS HELPS.

Answer:

g(x) = 1/3 • |x|

Step-by-step explanation:

To stretch a parent function, you multiply by whatever you want to stretch it with. If you multiplied by 3, it would be a vertical stretch... if you multiplied by 1/3, it makes it horizontal.

Hope this helps!

Answer:

A- 17/24 sugar all together

B- yes the bowl would be big enough because when you add all the ingredients together it equals 3 5/24 and it's less than 3 1/2.

Answer:

162.5

Step-by-step explanation:

25=height

13=base

to find the area of a triangle you do (h(b)b)/2

Answer:

\begin{gathered}\\1) \: \: \underline{ \sf{ Alternate \: interior \: angles \: \: : }}\\\end{gathered}

1)

Alternateinteriorangles:

\begin{gathered} \sf \implies \: 2\: \: and \: \: 7\\\end{gathered}

⟹2and7

\begin{gathered} \sf \implies \: 6\: \: and \: \: 3\\\\\end{gathered}

⟹6and3

\begin{gathered}\\2) \: \: \underline{ \sf{ Alternate \: interior \: angles \: \: : }}\\\\\end{gathered}

2)

Alternateinteriorangles:

\begin{gathered} \sf \implies \: 1\: \: and \: \: 8\\\end{gathered}

⟹1and8

\begin{gathered} \sf \implies \: 5\: \: and \: \: 4\\\\\end{gathered}

⟹5and4

\begin{gathered}\\3) \: \: \underline{ \sf{ Corresponding \: angles \: \: : }}\\\end{gathered}

3)

Correspondingangles:

\begin{gathered} \sf \implies \: 3\: \: and \: \: 1\\\end{gathered}

⟹3and1

\begin{gathered} \sf \implies \: 5\: \: and \: \: 7\\\end{gathered}

⟹5and7

\begin{gathered} \sf \implies \: 4\: \: and \: \: 2\\\end{gathered}

⟹4and2

\begin{gathered} \sf \implies \: 6\: \: and \: \: 8\\\\\end{gathered}

⟹6and8

\begin{gathered}\\4) \: \: \underline{ \sf{ Consecutive\: Interior \: angles \: \: : }}\\\end{gathered}

4)

ConsecutiveInteriorangles:

\begin{gathered} \sf \implies \: 2\: \: and \: \: 3\\\end{gathered}

⟹2and3

\begin{gathered} \sf \implies \: 6\: \: and \: \: 7\\\\\end{gathered}

⟹6and7

\begin{gathered}\\5) \: \: \underline{ \sf{ Consecutive\: Exterior \: angles \: \: : }}\\\end{gathered}

5)

ConsecutiveExteriorangles:

\begin{gathered} \sf \implies \: 1\: \: and \: \: 4\\\end{gathered}

⟹1and4

\begin{gathered} \sf \implies \: 5\: \: and \: \: 8\\\\\end{gathered}

⟹5and8

The rule for construction of Inscribed equilateral triangle

Means if marks are from 1 to 6 then

Or

Now

Here the rest two segments are

Answer:

FB and DB

Step-by-step explanation:

got it right on the test

To Find = Diameter, Area

Solution :

Diameter = 2 × Radius

Diameter = 2 × 6cm

Diameter = 12 cm

Area = 2πr

[tex]area \: = 2 \times \frac{22}{7} \times 6cm[/tex]

[tex]area \: = \frac{264}{7} [/tex]

[tex]area \: = 37.7 \: cm[/tex]

2. Given : Diameter = 8 DM

( 1dm = 10 cm

8dm = 8 × 10 = 80cm )

To find : Radius , area

Solution :

[tex]raduis \: = \frac{1}{2} \times diameter[/tex]

[tex]radius \: = \frac{1}{2} \times 80cm[/tex]

[tex]radius \: = 40 \: cm \: or \: 4dm[/tex]

Area = 2πr

[tex]area \: = 2 \times \frac{22}{7} \times 40[/tex]

[tex]area \: = \frac{1760}{7} [/tex]

[tex]area \: = 251.4cm \: \: \: or \: 25.14dm[/tex]

3. Given : Radius = 2.5m

To find : Diameter , Area

Solution :

Diameter = 2 × radius

Diameter = 2 × 2.5m

Diameter = 5m

Area = 2πr

Area = 2 × 22/7 × 5m

Area = 220/7

Area = 31.4m

Answer:

perpendicular

Step-by-step explanation:

x = -2    is a vertical line at   x   =  -2

y is a horizontal line          the two lines are perpindicular

the lines  x=−2, y=10 are perpendicular to each other.

What is a linear equation?

It is defined as the relation between two variables, if we plot the graph of the linear equation we will get a straight line.

If in the linear equation, one variable is present, then the equation is known as the linear equation in one variable.

Here, The given equations are :

x=−2 and y=10

First, consider x = -2 equation :

equation x = -2 is a vertical line, parallel to x = 0 line and perpendicular to line y = 0.

Consider second line y = 10 :

line y = 10 is horizontal line and is parallel to line y = 0 and is perpendicular to line x = 0.

Therefore, the lines  x=−2, y=10 are perpendicular to each other.

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Answer:

2/3(cx+1/2)-1/4=5/2. CX=29/8

Based on the table, a conclusion which can be drawn about f(x) and g(x) is that: B. the functions f(x) and g(x) are reflections over the y-axis.

In Mathematics, two functions are considered to be reflections over the y-axis under the following condition:

If, f(-x) = g(x).

Evaluating the given functions, we have:

f(x) = 2ˣ

f(-x) = 2⁻ˣ = ½ˣ = g(x).

Similarly, two functions are considered to be reflections over the x-axis under the following condition:

If, -f(x) = g(x).

Evaluating the given functions, we have:

f(x) = 2ˣ

-f(x) = -2ˣ ≠ g(x).

Therefore, we can logically conclude that the two functions f(x) and g(x) are considered to be reflections over the y-axis but not the x-axis.

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Answer:

84 circular tiles are needed to make pattern number 20

4(20+1)

Step-by-step explanation:The number of circular tiles is 1 more than the pattern number on each side of the square.

circular tiles = 4(n +1)

Answer:

v = √(LT/m)

Step-by-step explanation:

Given :

Multiply both sides with L :

Divide both sides by m :

Take the square root on each side :

Answer:

[tex]v = \sqrt{ \frac{tl}{m} } [/tex]

Step-by-step explanation:

[tex]t = \frac{mv {}^{2} }{l} \\ making \: v \: the \: subject \\ t \times l = mv {}^{2} \\ dividing \: bothsides \: by \: m \\ \frac{tl}{m} = \frac{mv {}^{2} }{m} \\ v {}^{2} = \frac{tl}{m} \\ finally \\ v = \sqrt{ \frac{tl}{m} } [/tex]

Answer:

option c and d are correct

Step-by-step explanation:

if there is only one choosing option you can choose option c

Answer:

2,160 ÷ 36 = 60

Step-by-step explanation:

The division problem that this area model represents is,

2,160 ÷ 36 = 60

The approximate area that is within range of the motion sensor is 4975 square meters

The figure is not given, however the area of the range can be calculated without the figure.

The given parameters are:

Angle, ⊕ = 135°

Radius, r = 65 meters

The area of the range is calculated using the following sector area

[tex]A = \frac{\theta}{360} * \pi r^2[/tex]

This gives

[tex]A = \frac{135}{360} * 3.14 * 65^2[/tex]

Evaluate

A = 4974.9375

Approximate

A = 4975

Hence, the approximate area that is within range of the motion sensor is 4975 square meters

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Answer:

See below

Step-by-step explanation:

You will just need to use your protractor to measure the given angles..

  Here is some gross guesses  starting with top row

      45     120   100  25   90   80  135  120 °

Answer:

Step-by-step explanation:

The first shape has 6 sides. Hence, it is called a hexagon.

The second shape has 7 sides. Hence, it is called a heptagon.

The mathematical name for the given 2 polygons.

The first polygon has 6 sides with an angle sum of 720°, which means the mathematical name given for this polygon is,

[tex]\large\boxed {Hexagon}[/tex]

The second polygon has 7 sides with an angle sum of 900°, which means the mathematical name given for this polygon is,

[tex]\large\boxed {Heptagon}[/tex]

Hence, the first polygon is a hexagon and the second polygon is a heptagon.

Answer:

Total, 2 milkshakes, and 3 cokes would cost $12.50

Step-by-step explanation:

The cokes cost $11.50 and the milkshakes $10.00

The volume of the region R bounded by the x-axis is: [tex]\mathbf{\iint_R(x^2+y^2)dA = \int ^{tan^{-1}(4)}_{0} \int^{\frac{2}{cos \theta}}_{0} \ r^3 dr d\theta}[/tex]

If the axis of revolution is the boundary of the plane region and the cross-sections are parallel to the line of revolution, we may use the polar coordinate approach to calculate the volume of the solid.

From the given graph:

The given straight line passes through two points (0,0) and (2,8). Thus, the equation of the straight line becomes:

[tex]\mathbf{y-y_1 = \dfrac{y_2-y_1}{x_2-x_1}(x-x_1)}[/tex]

here:

Suppose we assign (x₁, y₁) = (0, 0) and (x₂, y₂) = (2, 8)  from the graph, we have:

[tex]\mathbf{y-0 = \dfrac{8-0}{2-0}(x-0)}[/tex]

y = 4x

Now, our region bounded by the three lines are:

Similarly, the change in polar coordinates is:

where;

Therefore;

Then:

[tex]\mathbf{\iint_R(x^2+y^2)dA = \int ^{tan^{-1}(4)}_{0} \int^{\frac{2}{cos \theta}}_{0} \ r^2 (rdr d\theta )}[/tex]

[tex]\mathbf{\iint_R(x^2+y^2)dA = \int ^{tan^{-1}(4)}_{0} \int^{\frac{2}{cos \theta}}_{0} \ r^3 dr d\theta}[/tex]

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Answer:

goto gauth maths and ask again