Math Post Q3 What inequality describes the graph?

Answer:

D

Step-by-step explanation:

[tex]\frac{5x}{20} =\frac{45}{36}[/tex]

Cross multiply:

(5x)(36)=(20)(45)

180x = 900

divide by 180.

x=5

The value of x is 5.

Δ ACE ≅ Δ BCD    (by AAA property)

Therefore

[tex]\frac{CD}{CE} = \frac{CB}{CA}[/tex]         ( Similar triangle property)

[tex]\frac{20}{36} = \frac{5x}{45}[/tex]

5x = [tex]\frac{20 * 45}{36}[/tex]

5x = 25

x = 5

Therefore, option D. 5 is the correct answer

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Answer:

6135.9m^3

Step-by-step explanation:

V=3.14r^2 h/3

step by step

1. the radius is half so half of 25 is 12.5 that's the r in your equation

2.the height in your equation is 3 times more then the radius and your radius is 12.5X3 =37.5 for your height

3. plug everything in back into the equation v=3.14(12.5)^2(37.5/3)= 6135.923 when rounded it is 6135.9m^3

1. The parabola opens upward.

2. It has a minimum value

The explanation is shown below. Also, the graph of this function  is shown below including the vertex.

Answer:

(2x+3)(2x+3)

Step-by-step explanation:

a^2+2ab+b^2

C seem reasonable to me

Answer:

The same number was not added to both sides.

Step-by-step explanation:

The same number was not added to both sides.

In line 2,  6 was added to the left side  and 78 was added to the right side.

The best that describes the error made when solving for the current temperature is that the same number was not added to both sides of the equation.

An equation is formed when two equal expressions are equated together with the help of an equal sign '='.

The given equation can be solved as shown below.

t - 6 = 78

t - 6 + 6 = 78 + 6

t = 84

Now, if we compare it with the given equation, we can find that the error made when solving for the current temperature is that the same number was not added to both sides of the equation.

Hence, the best that describes the error made when solving for the current temperature is that the same number was not added to both sides of the equation.

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Answer:

The correct answer option is D. 17/50.

Step-by-step explanation:

We are given that a jelly bean machine has 16 pink jelly beans, 34 blue jelly beans, 24 black jelly beans and 26 purple jelly beans.

We are to find the probability of getting a blue jelly bean chosen at random.

Total number of jelly beans = 16 + 34 + 24 + 26 = 100

Number of blue jelly beans = 34

P (getting a blue jelly bean) = 34/100 = 17/50

Answer:

The last graph

Step-by-step explanation:

The problem presented here is similar to a compound interest problem since we have an initial value, a growth constant and the aspect of time.

We can consider the number of television sets currently produced by the company to be our Principal amount;

P = 2000

The rate of increase in production per month can be considered as our interest rate earned;

r = 25% = 0.25

The total number of television sets y will be our Accumulated amount;

A = y

The duration x becomes our time n.

The compound interest formula is given as;

[tex]A=P(1+r)^{n}[/tex]

We simply substitute the given information into the formula;

[tex]y=2000(1.25)^{x}[/tex]

This is an exponential growth function since the base of the exponent x is greater than 1.

A graph of the function will be an exponential curve passing through ( 0, 2000) since 2000 is our initial value

Answer: the last ones

Step-by-step explanation: I put it and got it right:)

[tex]\bf ~\hspace{5em} \textit{ratio relations of two similar shapes} \\[2em] \begin{array}{ccccllll} &\stackrel{ratio~of~the}{Sides}&\stackrel{ratio~of~the}{Areas}&\stackrel{ratio~of~the}{Volumes}\\ \cline{2-4}&\\ \cfrac{\textit{similar shape}}{\textit{similar shape}}&\cfrac{s}{s}&\cfrac{s^2}{s^2}&\cfrac{s^3}{s^3} \end{array}\\\\[-0.35em] ~\dotfill[/tex]

[tex]\bf \cfrac{\textit{similar shape}}{\textit{similar shape}}\qquad \cfrac{s}{s}=\cfrac{\sqrt{s^2}}{\sqrt{s^2}}=\cfrac{\sqrt[3]{s^3}}{\sqrt[3]{s^3}} \\\\[-0.35em] \rule{34em}{0.25pt}[/tex]

[tex]\bf \cfrac{\textit{small cylinder}}{\textit{large cylinder}}\qquad \stackrel{\stackrel{\textit{ratio of the }}{\textit{sides}}}{\cfrac{3}{6}}= \stackrel{\stackrel{\textit{ratio of the }}{\textit{volumes}}}{\cfrac{\sqrt[3]{V}}{\sqrt[3]{V}}}\implies \cfrac{3}{6}=\sqrt[3]{\cfrac{1000}{V}}\implies \left( \cfrac{3}{6} \right)^3=\cfrac{1000}{V} \\\\\\ \left( \cfrac{1}{2} \right)^3=\cfrac{1000}{V}\implies \cfrac{1^3}{2^3}=\cfrac{1000}{V}\implies \cfrac{1}{8}=\cfrac{1000}{V}\implies V=8000[/tex]

The equation in point-slope form for the line through the point (-3, -7) with slope -6/5x is y - (-7) = -6/5(x - (-3)).

To write the equation of a line in point-slope form, we can use the given point and slope. The point we have is (-3, -7) and the slope is -6/5. The point-slope form of a linear equation is y - y1 = m(x - x1), where (x1, y1) is a point on the line and m is the slope. Plugging in the values, we get the equation as:

y - (-7) = -6/5(x - (-3))

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To write an equation in point-slope form, you need the coordinates of a point on the line and the slope of the line. In this case, the given point is (–3, –7) and the slope is -6/5. The equation in point-slope form is y + 7 = -6/5(x + 3).

To write an equation in point-slope form, you need the coordinates of a point on the line and the slope of the line. In this case, the given point is (–3, –7) and the slope is -6/5.

The point-slope form of the equation is y - y1 = m(x - x1).

Plugging in the values, we get y - (-7) = -6/5(x - (-3)).

Simplifying, we have y + 7 = -6/5(x + 3).

Thus, the equation in point-slope form for the line through the point (–3, –7) with a slope of -6/5x is y + 7 = -6/5(x + 3).

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Answer:

A (-4, -4), B (-2, 6), C (-1, 1), D(-3, -5)

Step-by-step explanation:

Before the rotation:

A (-4, 4), B (6, 2), C (1, 1), D(-5, 3)

270° rotation clockwise is the same as 90° counterclockwise.  To do that transformation:

(x, y) → (-y, x)

Therefore, the coordinates of the rotated figure are:

A (-4, -4), B (-2, 6), C (-1, 1), D(-3, -5)

The coordinates of the image are:

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

This question is solved applying a 270° clockwise about the origin, which has the following rule:

[tex](x,y) = (-y,x)[/tex]

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

Coordinate A:

At the Figure, coordinate A is A(-4,4). Applying the rule:

[tex](-4,4) = (-4, -4)[/tex]

So the image of A is A'(-4,-4).

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

Coordinate B:

At the Figure, coordinate B is B(6,2). Applying the rule:

[tex](6,2) = (-2, 6)[/tex]

So the image of B is B'(-2,6).

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

Coordinate C:

At the Figure, coordinate C is C(1,1). Applying the rule:

[tex](1,1) = (-1, 1)[/tex]

So the image of C is C'(-1,1).

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

Coordinate D:

At the Figure, coordinate C is D(-5,3). Applying the rule:

[tex](-5,3) = (-3,-5)[/tex]

So the image of D is D'(-3,-5).

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Answer:

a. 1/150.

b. 14.

Step-by-step explanation:

a.  That would be 2/300 = 1/150.

b.  So we expect 1 out of every 150  bikes will have 1 with defective brakes so out of 2,100 it is (1/150) * 2,100

= 14.

Step-by-step explanation:

Answer:125+220+c

if c= 20 then it would be 125+220+20=365

Step-by-step explanation:

Answer:

Option d.

±π/2 ; ±3π/2

Step-by-step explanation:

To quickly solve this problem, we can use a graphing tool or a calculator to plot the equation.

Please see the attached image below, to find more information about the graph

The equation is:

f(x)= 3*cos (x)

We can see from the graph that the zeros are

±π/2 ; ±3π/2

Correct option is d.

Answer:

x + 6 =

Step-by-step explanation:

In math sum means addition, difference is subtraction, product is multiplication, and quotient is division

ANSWER

x+6

EXPLANATION

An algebraic expression contains letters and numbers that are connected with mathematical operators or symbols.

The sum of x and 6 as an algebraic up expression is:

x+6

This expression contains a variable , a mathematical symbol and a number.

Answer:

C

Step-by-step explanation:

C:  AB is the radius of both circles.

Answer:

C. line segment AB is the radius of both circles.

Step-by-step explanation:

If point A is the center of the first circle and point B is the center of the second circle (in the figure), therefore Line segment AB is the radius of both circles and we write.

Line segment AB = line segment AC (radius of first circle ) and

line segment  AB =  line segment BC (radius of second circle).

Hence line segment AB is the radius of both circle is the correct option for AB =AC.

Answer:

The required paint for a total of [tex]1.404\ ft^{2}[/tex] is approximate 6 gallons

Step-by-step explanation:

we know that

To find how much paint would I need to buy to paint the walls of all three bedrooms, calculate the area of all three bedrooms

Master Bedroom

The area is equal to

[tex]A1=(16+16+12+2+18)*9=576\ ft^{2}[/tex]

2 Bedroom

The area is equal to

[tex]A2=(12+14+10+10)*9=414\ ft^{2}[/tex]

3 Bedroom

The area is equal to

[tex]A3=(10+10+14+10+2)*9=414\ ft^{2}[/tex]

The total area is equal to

A=A1+A2+A3

[tex]A=576+414+414=1.404\ ft^{2}[/tex]

Approximate one gallon of paint covers 250 square feet

so

[tex]1.404/250=5.6\ gal[/tex]

ANSWER

B.) 72

EXPLANATION

Recall the expansion for the factorial notation:

[tex]n! = n \times (n - 1) \times (n - 2) \times ...3 \times 2 \times 1[/tex]

We want to simplify

[tex] \frac{9!}{7!} [/tex]

Let us expand the numerator up to 7! while maintaining the denominator.

[tex] \implies \: \frac{9 \times 8 \times 7!}{7!} [/tex]

When we cancel out the common factors,we obtain:

[tex]\implies \: \frac{9 \times 8 \times 1}{1} [/tex]

This simplifies to

[tex]\implies \: \frac{72}{1} = 72[/tex]

The correct answer is B.

Answer:

Gum’s Minimum height: 6ft

Gum’s Maximum height: 8ft

2nd part

How far does the gym travel in one revolution of the bicycle wheel?

2pi

Answer:

Minimum height of gum = 6 foot.

Maximum height of gum = 8 foot.

Step-by-step explanation:

A rider is riding a bicycle on a 6 foot wall, therefore the height of the lowest point of the rear wheel is 6 foot from the ground and highest point of the rear wheel is (6+2) foot = 8 foot ( because diameter of rear wheel =2 foot ).

If a piece of gum become stuck to the rear wheel, hence the minimum height of the gum is 6 foot from the ground and maximum height of the gum is 8 foot  from the ground.

Answer:

[tex]\dfrac{11}{30}[/tex]

Step-by-step explanation:

Urn U1: 3 red and 2 yellow marbles, in total 5 marbles.

The probability to select red marble is [tex]\dfrac{3}{5}=0.6.[/tex]

Urn U2: 3 red and 7 yellow marbles, in total 10 marbles.

The probability to select red marble is [tex]\dfrac{3}{10}=0.3.[/tex]

Urn U1: 1 red and 4 yellow marbles, in total 5 marbles.

The probability to select red marble is [tex]\dfrac{1}{5}=0.2.[/tex]

The probability to choose each urn is the same and is equal to [tex]\frac{1}{3}.[/tex]

Thus, the probability that the marble is red is

[tex]\dfrac{1}{3}\cdot 0.6+\dfrac{1}{3}\cdot 0.3+\dfrac{1}{3}\cdot 0.2=\dfrac{1.1}{3}=\dfrac{11}{30}.[/tex]

10-14-19-12-14-18-10-15-15

Answer:

first 1

Step-by-step explanation:

first 1

Answer:

7/4 ÷ 1/2= 3 1/2

Step-by-step explanation:

This is the answer hope it help's :)

Answer:

Choice B is correct

Step-by-step explanation:

The given radical division can be expressed in the following form;

[tex]\frac{\sqrt{16x^{3} } }{\sqrt{8x} }[/tex]

Using the properties of radical division, the expression can be expressed in the following form;

[tex]\sqrt{\frac{16x^{3} }{8x} }=\sqrt{2x^{2} }[/tex]

Simplifying further yields;

[tex]\sqrt{2x^{2} }=\sqrt{2}*\sqrt{x^{2} }=x\sqrt{2}[/tex]

Choice B is thus the correct alternative

For this case we must simplify the following expression:

[tex]\frac {\sqrt {16x ^ 3}} {\sqrt {8x}} =[/tex]

Join the terms in a single radical:

\[tex]\sqrt {\frac {16x ^ 3} {8x}} =\\\sqrt {\frac {8 * (2x ^ 3)} {8x}} =\\\sqrt {\frac {2x ^ 3} {8x}} =\\\sqrt {2x ^ 2} =\\\sqrt [n] {a ^ m} = a ^ {\frac {m} {n}}[/tex]

So:

[tex]\sqrt {2x ^ 2} =\\x \sqrt {2}[/tex]

Answer:

Option B

Answer:

  the correct answers are marked in green below

Step-by-step explanation:

As with any right triangle, the length of the hypotenuse is equal to the root of the sum of the squares of the legs. That root is less than the sum of the leg lengths and greater than the longest leg (for non-zero leg lengths).

_____

Comment on the choices

The relationship is actually ...

  ║u+v║ ≤ ║u║ + ║v║

That makes the first selection possibly correct. It will only be correct if ║u║ or ║v║ is zero. The problem statement does not rule out that case.

Answer:

As with any right triangle, the length of the hypotenuse is equal to the root of the sum of the squares of the legs. That root is less than the sum of the leg lengths and greater than the longest leg (for non-zero leg lengths).

_____

Comment on the choices

The relationship is actually ...

 ║u+v║ ≤ ║u║ + ║v║

That makes the first selection possibly correct. It will only be correct if ║u║ or ║v║ is zero. The problem statement does not rule out that case.

Step-by-step explanation:

The depth of the lake is 1.4 kilometers after converting the result to kilometers.

To find the depth of the lake in kilometers when it is 100 centimeters less than 1401 meters, first convert the depth difference to meters.

Since 100 centimeters is equivalent to 1 meter, the actual depth of the lake in meters is 1400 meters (which is 1401 meters - 1 meter).

To convert this depth into kilometers, we divide by 1000, since there are 1000 meters in one kilometer.

Hence, the depth is 1.4 kilometers.

For this case we have a system of two equations with two unknowns:

[tex]x = -3y-13\\2x + 2y = -6[/tex]

To solve we follow the steps below:

We substitute the first equation in the second:

[tex]2 (-3y-13) + 2y = -6[/tex]

We apply distributive property to the terms of parentheses:

[tex]-6y-26 + 2y = -6[/tex]

We add 26 to both sides of the equation:

[tex]-6y + 2y = -6 + 26\\-4y = 20\\y = \frac {20} {- 4}\\y = -5[/tex]

We find the value of x:

[tex]x = -3 (-5) -13\\x = 15-13\\x = 2[/tex]

Answer:

[tex](x, y) :( 2, -5)[/tex]

For this case we have to:

[tex]cos (F) = \frac {h} {27}[/tex]

That is, the cosine of the angle F, will be equal to the adjacent leg on the hypotenuse.

So, by clearing h we have:

[tex]h = 27 * cos (54)\\h = 27 * 0.58778525\\h = 15.87020175[/tex]

Rounding out the value of h we have:

[tex]h = 15.9[/tex]

Answer:

Option B

Answer:

The correct answer is option b.   15.9

Step-by-step explanation:

Points to remember:-

Trigonometric ratio

Cos θ = adjacent side/Hypotenuse

From the figure we can see a right triangle triangle FGH.

To find the value of h

It is given that, g=27 and F=54°

Cos F =  adjacent side/Hypotenuse

Cos 54 =  adjacent side/Hypotenuse

     = FG/FH = h/g

h = g * Cos F = 27 * Cos 54 = 27 * 0.5878 = 15.87 ≈ 15.9

Therefore the correct answer is option b.  15.9

Answer:

  33% off is the better deal

Step-by-step explanation:

1.33 times as much popcorn for the same price is equivalent to 1/1.33 ≈ 0.75 times the price for the original amount of popcorn. That price is equivalent to a sale of 1 - 0.75 = 0.25 = 25% off.

The sale price of 33% off is a better deal (if you don't want the extra popcorn).

ANSWER

Period: 2π , amplitude: 4

EXPLANATION

The graphed function is

[tex]y = 4\cos(x) [/tex]

The amplitude of this function is

[tex] |4| = 4[/tex]

The period is 2π because there is no phase shift hence the period is still equal to the parent function.

Period: 2π , amplitude: 4

Answer:

The correct option is 3.

Step-by-step explanation:

The general form of a cosine function is

[tex]f(x)=A\cos (Bx+C)+D[/tex]

where, A is amplitude, 2π/B is period, C is phase sift and D is midline.

[tex]A=midline=\frac{Maximum-Minimum}{2}[/tex]

[tex]A=midline=\frac{4-(-4)}{2}[/tex]

[tex]A=midline=4[/tex]

The amplitude of the function is 4.

The given graph complete a cycle in the interval [0,2π], therefore the period of the graph is 2π.

Therefore the correct option is 3.

FED is 5/4 times bigger than CBA. So, 44×1.25 is 55. 40×1.25 is 50. The perimeter is 125