The figure consists of a quarter circle and a parallelogram. What is the area of the composite figure? Us
to the nearest whole number.
14 in.
14 in.
1 5 in.
17

Answer:

Yes, it is true that [tex]x^2+3x-1[/tex]  is a factor of [tex]x^4+3x^3-2x^2-3x+1[/tex].

Step-by-step explanation:

Let us try to factorize [tex]x^4+3x^3-2x^2-3x+1[/tex]

[tex]x^4+3x^3-2x^2-3x+1\\\Rightarrow x^4-2x^2+1-3x+3x^3[/tex]

Let us try to make a whole square of the given terms:

[tex]\Rightarrow (x^2)^2-2\times x^2 \times 1+1^2+3x^3-3x\\\Rightarrow (x^2-1)^2+3x^3-3x\\[/tex]

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

Formula used above:

[tex]a^{2} -2 \times a \times b +b^{2} = (a-b)^2[/tex]

In the above equation, we had [tex]a = x, b = 1[/tex].

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

Further solving the above equation, taking [tex]3x[/tex] common out of [tex]3x^3-3x[/tex]

[tex]\Rightarrow (x^2-1)^2+3x(x^2-1)\\[/tex]

Taking [tex](x^{2} -1)[/tex] common out of the above term:

[tex]\Rightarrow (x^2-1)((x^2-1)+3x)\\\Rightarrow (x^2-1)(x^2+3x-1)[/tex]

So, the two factors are [tex](x^2-1)\ and\ (x^2+3x-1)[/tex].

[tex]\therefore[/tex] The statement that [tex]x^2+3x-1[/tex]  is a factor of [tex]x^4+3x^3-2x^2-3x+1[/tex] is True.

Answer:

Step-by-step explanation:

In order to do this, you have to know how to use your calculator's regression equation function.  

First enter in the data. Hit "stat" then 1:Edit and enter all the x values into L1. After each value, hit enter. When you're done with the x list, arrow over to L2 and enter in all the y-values. If there are already values there you need to clear, arrow up to highlight L1, hit "clear", then "enter" and the values will disappear. Do that for both lists if you need to.

After the data is listed in L1 and L2, hit "stat" again and arrow over to "Calc". Hit 5:QuadReg. If you have a TI 83, your equation will be there for you. If you have a TI 84, you'll need to arrow down to "calculate" to get the equation. Regardless, the equation is

[tex]y=3.48x^2+1.22x+3.44[/tex], the last choice in your options.

Answer: D

Becasye I got it from him

Answer:

The pre image is a factor 2 bigger, and there fore it's endpoints a' and b' must also be a factor 2 further away from the center 2,0.

Step-by-step explanation:

This is a long explanation. I did my best to guide you through all the steps needed to answer the question, because it almost instantly happens in my mind. Writing down these "reasoning steps", hopefully can give you some insight in understanding what I am asking myself to finally solve the problem. I hope it helps you, and that you can learn from it.

The pre image is the original image, which is NOT visible. Because original image is not visible, that makes it a little tricky, because you have to "imagine" an image that is not there...

Please understand what is described:

The original was dilated at a scale factor of 1/2 from center 2,0 and that result is now visible as An, which has endpoints located at a and b.

So, the big "problem" is to understand what effect the dialated scale factor of 1/2 has, when it was applied to the ORIGINAL.

You ask yourself, was the original bigger or was the original smaller? If you CONCLUDE that the scaling factor 1/2 must result in a SMALLER image, then the original, then you can finally conclude that the original image must have been bigger to make that happen.

Ok, so the pre image was bigger...

How much bigger was the pre image, when you know a dialation scale factor of 1/2 was used to form the endpoints a and b...

Well, now you ask yourself, by what amount do you need to multiply the scale factor 1/2 to get to 2/2 (which is 1 by the way). You do this, because you want to know how big the original must have been, and the original can be "reconstructed" by "reversing" the dialation the other way around. In other words by what amount do you need to multiply the scale factor 1/2 to get to 2/2.

Since 2 * 1/2 = 1, then the original image can be formed from the given image by applying a dialation factor of 2.

So now we know that the original must have been BIGGER by a factor 2.

Finally, do not forget to mention that ORRIGINAL endpoints, a' and b', MUST also be a factor 2 further away from the center 2,0.

So now you have your answer. I hope it helps.

Answer:

R: {-7,-2,3,8}

Step-by-step explanation:

The range is the output values of the function

The values or 8,3,-2,-7

We put them in order from smallest to largest

R: {-7,-2,3,8}

Answer:

2nd option would be the answer

B

{y:y=-7,-2,3,8}

Step-by-step explanation:

Answer:

The answer is 3.

Hope it helped!

i believe the answer is 3

Answer:

I think that the required options are wrong.

Answer is given below with explanations.

mZCBD = 41 degrees

Step-by-step explanation:

[tex]from \: the \: \: above \: mentioned \: diagram \\ we \: can \: say \: that \: \\( angle \: ABD) + (angle \: DBC) = 68 \\ given \: that \: \: angle \: ABD = 2x + 5 \\ and \: \: angle \: CBD = 3x + 8 \\ on \: substituting \: the \: values \\ (2x + 5) + (3x + 8) = 68 \\ 5x + 13 = 68 \\ 5x = 68 - 13 \\ 5x = 55 \\ x = \frac{55}{5} \\ x = 11 \\ angle \: CBD = 3x + 8 \\ \: \: = 3(11) + 8 \\ \: \: = 33 + 8 \\ \: \: angle \: CBD= 41[/tex]

HAVE A NICE DAY!

THANKS FOR GIVING ME THE OPPORTUNITY TO ANSWER YOUR QUESTION.

Answer:

= 5/6x + -104/15

Step-by-step explanation:

x+2/5−6−(8+x)/6

Distribute:

=x+2/5+−6+−1/6x+−4/3

Combine Like Terms:

=x+2/5+−6+−1/6x+−4/3

=(x+−1/6x)+(2/5+−6+−4/3)

=5/6x+−104/15

Answer:

11/8 or, 1 and 3/8

Step-by-step explanation:

First, we have to make both the denominators the same. In this case, we can multiply 3/4 by 2, to make 4, the denominator, into 8. What we do to the denominator, we must do to the numerator! So, we multiply 3 by 2, and get 6!

Now we have, 5/8 + 6/8, which equals 11/8! Which can also be simplified to 1 and 3/8 (because the numerator is larger than the denominator)

Hope this helps! :)

Answer:

c

Step-by-step explanation:

1  =  3

2         6

Cross multiply:

1 * 6 = 2 * 3

Simplifying

1 * 6 = 2 * 3

Multiply 1 * 6

6 = 2 * 3

Multiply 2 * 3

6 = 6

Add '-6' to each side of the equation.

6 + -6 = 6 + -6

Combine like terms: 6 + -6 = 0

0 = 6 + -6

Combine like terms: 6 + -6 = 0

0 = 0

Solving

0 = 0

Answer:

The answer is 2.

Step-by-step explanation:

3 - 2 = 1

7 - 5 = 2

2 x 1 = 2

Answer:

D

Step-by-step explanation:

.........

Answer:

405 miles

Step-by-step explanation:

Take the miles per gallon and multiply the gallons to get the miles

22.5 * 18

405 miles

Answer:

202 1/2 miles

Step-by-step explanation:

We want to find how far she can drive on 1/2 a tank of gas.

Her tank can hold 18 gallons. Multiply 18 and 1/2, or divide 18 by 2.

18*1/2=18*0.5=9

or

18/2=9

1/2 a tank of gas is 9 gallons. Now, we need to find how far she can drive. Multiply the number of gallons in 1/2 a tank by the miles per gallon.

gallons in 1/2 tank * miles per gallon

We know she has 9 gallons in 1/2 tank, and she gets 22 1/2, or 22.5 miles per gallon.

9 gallons * 22.5 miles/gallon

9*22.5=202.5= 202 1/2

She can drive 202 1/2 miles on 1/2 a tank of gas.

Answer:

[tex] - \frac{5 + 5 \sqrt{3} }{2} [/tex]

Option A is the correct option.

Solution,

Multiply and divide by its conjugate.

[tex] \frac{5}{1 - \sqrt{3} } \times \frac{1 + \sqrt{3} }{1 + \sqrt{3} } \\ = \frac{5(1 + \sqrt{3)} }{(1 - \sqrt{3} )(1 + \sqrt{3)} } \\ = \frac{5 + 5 \sqrt{3} }{ {(1)}^{2} - { (\sqrt{3}) }^{2} } \\ = \frac{5 + 5 \sqrt{3} }{1 - 3} \\ = \frac{5 + 5 \sqrt{3} }{ - 2} \\ = - \frac{5 + 5 \sqrt{3} }{2} [/tex]

hope this helps...

Good luck on your assignment..

Answer:

see explanation

Step-by-step explanation:

Because the quantities are in proportion

When x doubles then y doubles

Answer:

f(x) > -x + 2

Step-by-step explanation:

First I found the equation of the line.

The y intercept is at 2 so I know to add 2 at the end

The slope is -1 since it is going downwards

Since the top side is shaded, that represents greater than, if it was shaded downwards, it would be less than

Putting all that together, the equation is f(x) > -x + 2

Answer:

The summands are 4 and 5. The sum is 9.

Step-by-step explanation:

In the binary system, the digits, starting at the right and moving to the left are:

1's

2's

4's

8's

etc.

100 = 0 units + 0 2's + 1 four = 0 + 0 + 4 = 4

101 = 1 unit + 0 2's + 1 4's = 1 + 0 + 4 = 5

In decimal, the addition is:

4 + 5 = 9

The summands are 4 and 5. The sum is 9.

The decimal equivalent  of the sum is 9.

It is required to write decimal equivalent of the summand and sum.

Positional numeral system employing 2 as the base and so requiring only two different symbols for its digits, 0 and 1.It is used for representing binary quantities which can be represented by any device that has only two operating states or possible conditions.

Given:

In the binary system, the digits, starting at the right and moving to the left.

The binary numeral system or base-2 numeral system which represents numeric values using two different symbols: typically 0 (zero) and 1 (one). The base-2 system is a positional notation with a radix of 2.

1's  2's  4's   8's  etc.

[tex]100\\\\0*2^{0} +0*2^{1}+1*2^{2}\\\\=0+0+4\\\\=4[/tex]

[tex]101\\\\=1*2^{0} +0*2^{1} +1*2^{2} \\\\=1+0+4\\\\=5[/tex]

In decimal, the addition is:

4 + 5 = 9

∴The summands are 4 and 5.

Therefore, the decimal equivalent  of the sum is 9.

Learn more about binary system here:

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Answer:

It's -5.3 and -6.5

I got it right on my test

-5.3 and -6.5 are located below -3.5 on the vertical number line and its pretty easy to find that out

Answer:

y = -x - 2

Step-by-step explanation:

Simplifying the equation of our line;

y - 1 = (x + 2)

y = x + 3

The slope of our line is 1

The slope of the perpendicular line(s) must be -1 (the product of slopes of two perpendicular lines = -1)

The line whose slope is -1 (from the choices) is the one whose equation is:

y = -x - 2

Answer:

[tex] \boxed{\sf \huge \boxed{ \sf ?} = 6} [/tex]

Step-by-step explanation:

[tex] \sf Solve \: for \: \boxed{ \sf ?} : \\ \sf \implies \frac{\boxed{ \sf ?}}{5} \times \frac{10}{8} = 1.5 \\ \\ \sf \implies \frac{\boxed{ \sf ?} \times 10}{5 \times 8} = 1.5 \\ \\ \sf \frac{10}{5} = \frac{ \cancel{5} \times 2}{ \cancel{5}} = 2 : \\ \sf \implies \frac{ \boxed{ \sf 2} \times \boxed{ \sf ?} }{8} = 1.5 \\ \\ \sf \frac{2}{8} = \frac{ \cancel{2}}{ \cancel{2} \times 4} = \frac{1}{4} : \\ \sf \implies \frac{\boxed{ \sf ?}}{ \boxed{ \sf 4}} = 1.5 \\ \\ \sf Multiply \: both \: sides \: of \: \frac{\boxed{ \sf ?}}{4} = 1.5 \: by \: 4 : \\ \sf \implies \frac{4 \times \boxed{ \sf ?}}{4} = 4 \times 1.5 \\ \\ \sf \frac{4 \times \boxed{ \sf ?}}{4} = \frac{ \cancel{4}}{ \cancel{4}} \times \boxed{ \sf ?} = \boxed{ \sf ?} : \\ \sf \implies \boxed{\boxed{ \sf ?}} = 4 \times 1.5 \\ \\ \sf 4 \times 1.5 = 6 : \\ \sf \implies \boxed{ \sf ?} = 6[/tex]

Answer:

4/15

Step-by-step explanation:

You add up all the balls for the bottom number(denominator), for the top number you put the amount of green balls (numerator)

Answer:

1. 25, 36

2. 125, 216

Step-by-step explanation:

in the sequence of 1.4.9.16. The next two terms are 25 and 36. This is because we are calculating the squares of the number in the term in other words, the nth term = n^2

For the sequence starting 1,8,26,64. The next terms are 125 and 216. This is because the nth term = n^3

Hope this helps

Answer:

1 pound

Step-by-step explanation:

Given the cost function of two domestic courier services.

We want to determine the weight (x) at which the costs (y) will be the same.

Since y=4x+1 and y=3x+2, then:

4x+1=3x+2

4x-3x=2-1

x=1 pound

When the weight of the parcel is 1 pound, the total cost of the parcel will be the same for the two domestic courier.

Answer:

−8, 19

1, −8

-5, 10

Step-by-step explanation:

The points that are on the perpendicular bisector of the given segment is (-5, 10)

Perpendicular bisector is defined as a line that divide an angle into  two equal parts at 90 degrees.

The standard equation of a line in point-slope form is expressed as

y-y₁ = m(x-x₁)

First, we need to get the equation of the line using the coordinates (-20, 0) and (10, 15)

Get the slope of the line

m = 15-0/10-(-20)

m = 15/30

m = 1/2

The slope of the line perpendicular to the line is -2

Using the point (-5, 10) on the line, get the equation in the point-slope form:

y - 10 = -2(x + 5)

y - 10 = -2x - 10

y + 2x = -10 + 10

y + 2x = 0

y = -2x

To check which points are on the perpendicular bisector of the given segment, hence;

For the coordinate (-8, 19)

19 = -2(-8)

19 ≠ 16 (This is not a solution)

For the coordinate (1, -8)

-8 = -2(1)

-8 ≠ -2 (This is not a solution)

For the coordinate (-5, 10)

10 = -2(-5)

10 = 10 (This is a solution)

Hence, the point that is on the perpendicular bisector of the given segment is (-5, 10)

Learn more about perpendicular bisector here:

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Answer:

20

Step-by-step explanation:

We can calculate the value of b using Euclidean theorem

b^2 = 16 × 25 ➡ b^2 = 400 and b = 20

Answer:

53.8 L

Step-by-step explanation:

We can use the ideal gas formula that relates pressure, volume and temperature:

[tex]\frac{P_1 V_1}{T_1} = \frac{P_2 V_2}{T_2}[/tex]

where P1 = initial pressure = 1.0 atm

V1 = initial volume = 45 L

T1 = initial temperature = 25°C = 25 + 273 = 298 K

P2 = final pressure = 0.78 atm

V2 = final volume

T2 = final temperature = 5.0°C = 5 + 273 = 278 K

Therefore, the final volume will be:

[tex]\frac{1 * 45}{298} = \frac{0.78 * V_2}{278}\\\\0.151 = 0.002806 V_2\\\\=> V_2 = 0.151 / 0.002806\\\\V_2 = 53.8 L[/tex]

Its volume is 53.8 L

Complete Question

Situation: A 25 gram sample of a substance used for drug research has a k-value of 0.1205. [tex]N=N_0e^-kt[/tex]

Find the substance's half-life in days, round to the nearest tenth.

Answer:

5.8 days

Step-by-step explanation:

The decay model for drugs and radioactive substances is given as

[tex]N=N_0e^{-Kt}[/tex]

The half-life of any substance is the time it takes for the substance to decay to half its initial amount. That is the period it takes for:

[tex]N(t)=\dfrac{N_0}{2}[/tex]

If we substitute this into the model, we obtain:

[tex]\dfrac{N_0}{2}=N_0e^{-Kt}\\$Dividing both sides by N_o\\\dfrac12=e^{-Kt}[/tex]

We can solve for t.

Taking the natural logarithm of both sides

[tex]\ln\dfrac12=\ln e^{-Kt}\\\implies-\ln2=-Kt\\t=\dfrac{\ln2}{k} \\$Since k=0.1205$\\t_{1/2}=\dfrac{\ln2}{0.1205}=5.8$ days (to the nearest tenth)[/tex]

Answer:

Step-by-step explanation:

In the picture above

I hope it helps :)

Answer:

g = 48 divided by 4

Step-by-step explanation:

Answer:

g=48/4

Step-by-step explanation:

this thing / mean divided