After being rearranged and simplified, which of the following equations could
be solved using the quadratic formula? Check all that apply.
A. 5x + 4 = 3x^4 - 2
B. -x^2 + 4x + 7 = -x^2 - 9
C. 9x + 3x^2 = 14 + x-1
D. 2x^2 + x^2 + x = 30

so the rainwater flows as R(x), and the decrease of the flow will be D(x), the new smaller pipe after the decrease will have water flowing at R(x) - D(x)

[tex]\bf \begin{cases} R(x)=-0.1x^3+1.4x^2-1.5x\\ D(x)=-0.04x^3+0.5x^2+x \end{cases} \\\\[-0.35em] ~\dotfill\\\\ \stackrel{R(x)}{(-0.1x^3+1.4x^2-1.5x)}-\stackrel{D(x)}{(-0.04x^3+0.5x^2+x)} \\\\\\ (-0.1x^3+1.4x^2-1.5x)+0.04x^3-0.5x^2-x \\\\\\ -0.1x^3+1.4x^2-1.5x+0.04x^3-0.5x^2-x \\\\\\ -0.10x^3+0.04x^3+1.4x^2-0.5x^2-1.5x-x\implies \stackrel{H(x)}{-0.6x^3+0.9x^2-1.6x}[/tex]

To find the rate of water flow through the smaller pipe, subtract the decrease function from the original rate function.

To find the rate at which rainwater flows through the smaller pipe, we need to subtract the decrease function from the original rate function. Let's call this new function H(x). So, H(x) = R(x) - D(x).

Substituting the given values, H(x) = (-0.1x^3 + 1.4x^2 - 1.5x) - (-0.04x^3 + 0.5x^2 + x). Simplifying, H(x) = -0.1x^3 + 1.4x^2 - 1.5x + 0.04x^3 - 0.5x^2 - x.

Combining like terms, H(x) = -0.06x^3 + 0.9x^2 - 2.5x.

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Answer:

  see below

Step-by-step explanation:

The attached printable graph paper is a scale drawing. The 1 : 100 scale means each meter will be represented by 1 cm.

Answer:

x=9

Step-by-step explanation:

I have answered ur question

Answer:

2/3

Step-by-step explanation:

These two figures are similar since they have the same shape but not the same size

Yellow figure is larger than the orange figure therefore, the yellow figure is a larger or a dilated version of the orange figure.

Scale factor = Small side

                       Large side

Scale factor = 10/15

Scale factor = 2/3

The scale factor of this dilation is 2/3. The orange figure is dilated 2/3 times to form the yellow figure.

!!

Answer:

It's 2/3

Step-by-step explanation:

Trust me

Answer:

b. 9/5

Step-by-step explanation:

Cotangent is the inverse of tangent.

tan θ = y/x

cot θ = x/y

cot θ = (-9)/(-5)

cot θ = 9/5

just to add to that great reply by @MathPhys above

[tex]\bf (\stackrel{adjacent}{-9},\stackrel{opposite}{-5})~\hfill cot(\theta )=\cfrac{\stackrel{adjacent}{-9}}{\stackrel{opposite}{-5}}\implies cot(\theta )=\cfrac{9}{5}[/tex]

bear in mind that, the value coordinate pairs we get is the (x,y) coordinates, and x = adjacent side of the triangle whilst y = opposite side of it.

Answer:

c

Step-by-step explanation:

It would be c because you would add subtract 30 - x which equals 30x then you would divided 5 / 6 which equals 0.12 then you would add y plus some number which equals 12y then you would add 12y+12=24y=24y / 2=12 thenyou have 30x,12y.

Answer:

D

Step-by-step explanation:

A might be right for the wrong linear equation type. It could be describing a y intercept slope line. So even if it is right, it is not the answer. Actually the answer to A should be y = (5/6)x - 13

The general formula for the answer you want is

Givens

y -y1 = m(x - x1)

x1 = 30

y1 = 12

m = 5/6

Solution

y - 12 = (5/6)(x - 30)

That makes the answer D

Answer:

Yes.

Step-by-step explanation:

To see if h is a factor of f, we can use the factor theorem.

h(x)=x-3 has a zero at x=3 because h(3)=3-3=0.

So we want to see if the zero of h is a zero of f.

Is x=3 a zero of f?

You can check using synthetic division or just plug in 3.

Let's do both.

If you use synthetic you are trying to see if you get a remainder of 0.

If you plug it in you are trying to see if you get 0 as the output when plugging your input 3.

Let's do synthetic first:

Since we are checking to see if x=3 is a zero, that will go on the outside:

3 |  1   -1  -1   -15

 |        3   6    15

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

     1    2   5     0

So yep the remainder is 0 so the answer is yes.

Let's plug it in:

f(3)=3^3-3^2-3-15

f(3)=27-9-3-15

f(3)=18-3-15

f(3)=15-15

f(3)=0

The result is 0 so the answer is yes.

You pick your favorite way here.

Answer:

Widow's Share = Rs 500.05

Son's share = Rs 1400.14

Step-by-step explanation:

Property = 4000.40

Widow get share = 0.125

So, Share of Widow = 0.125 * 4000.40

Widow's Share = Rs 500.05

Remaining Property = 4000.40 - 500.05

Remaining Property = 3500.35

Son's share = 0.4 * 3500.35

Son's share = Rs 1400.14

To solve this problem, we will follow these steps:
1. Calculate the widow's share of the property.
2. Determine the remainder of the property after the widow has received her share.
3. Calculate the son's share of the remainder of the property.
Step 1: Calculate the widow's share.
The widow gets 0.125 (or 12.5%) of the total property. The total property is valued at 4000.40 units (where the unit could be in rupees, dollars, etc.).
Widow's share = Total property * Widow's share percentage
              = 4000.40 * 0.125
Let's calculate that:
Widow's share = 4000.40 * 0.125
              = 500.05
So, the widow gets 500.05 units.
Step 2: Determine the remainder of the property.
Now, subtract the widow's share from the total property to find out how much is left for the son to receive his share from.
Remainder of property = Total property - Widow's share
                      = 4000.40 - 500.05
Let's calculate that:
Remainder of property = 4000.40 - 500.05
                      = 3500.35
Now we have 3500.35 units remaining after the widow has received her share.
Step 3: Calculate the son's share.
The son gets 0.4 (or 40%) of the remainder of the property.
Son's share = Remainder of property * Son's share percentage
            = 3500.35 * 0.4
Let's calculate that:
Son's share = 3500.35 * 0.4
            = 1400.14
So, the son gets 1400.14 units.
To summarize, the widow receives 500.05 units of the property, and the son receives 1400.14 units of the property after the widow has received her share.

Answer:

[tex]\large\boxed{y=\dfrac{3}{5}x-2}[/tex]

Step-by-step explanation:

The slope-intercept form of an equation of aline:

[tex]y=mx+b[/tex]

m - slope

b - y-intercept

The formula of a slope:

[tex]m=\dfraxc{y_2-y_1}{x_2-x_1}[/tex]

From the graph we have the points:

(-5, -5)

y-intercept (0, -2) → b = -2

Calculate the slope:

[tex]m=\dfrac{-2-(-5)}{0-(-5)}=\dfrac{3}{5}[/tex]

Put the value of the slope and the y-intercept to the equation of a line:

[tex]y=\dfrac{3}{5}x-2[/tex]

Answer:

90 sq. ft.

Step-by-step explanation:

To find the "volume," you will need to multiply every the LxWxH.

Length = L

Width = W

Height = H

Then the answer is 90 sq. ft.

Answer:

Surface area = 126 square ft .

Step-by-step explanation:

Given : Rectangular cuboid .

To find : Find the total area of the solid figure.

Solution : We have given Rectangular cuboid .

Length = 3 ft .

Width = 5 ft .

Height = 6 ft .

Surface area = 2 ( l*w + w*h + l *h).

Plug the values

Surface area = 2 ( 3*5 + 5*6 + 3 *6).

Surface area = 2 (15 + 30 + 18).

Surface area = 2 ( 63).

Surface area = 126 square ft .

Therefore, Surface area = 126 square ft .

Answer:

(0.78,0)

Step-by-step explanation:

I would use the quadratic formula.

[tex]a=3[/tex]

[tex]b=-8[/tex]

[tex]c=5[/tex]

[tex]\text{ The quadratic formula is } x=\frac{-b \pm \sqrt{b^2-4ac}}{2a}\\\\\text{ Let's find } b^2-4ac \text{ first}\\(-8)^2-4(2)(5)\\64-8(5)\\64-40\\24\\\\\text{ Now let's find } -b\\-b=8\\\text{ And } 2a\\2(2)=4\\\\\text{ Let's plug in this information }\\x=\frac{8 \pm \sqrt{24}}{4}\\\\\text{ We are now going to simplify }\\x=\frac{8}{4} \pm \frac{\sqrt{24}}{4} \\x=2 \pm \frac{\sqrt{4 \cdot 6}}{4}\\x=2 \pm \frac{\sqrt{4} \sqrt{6}}{4} \\x=2 \pm \frac{2 \sqrt{6}}{4}\\[/tex]

[tex] x=2 \pm \frac{\sqrt{6}}{2}[/tex]

So let's put both of these into out calculator

2 + sqrt(6)/2                  and             2-sqrt(6)/2

One of them should be approximately 3.22 as the question suggests.

3.22                                                        0.78

So the other x-intercept is approximately (0.78,0)

Answer:

9

Step-by-step explanation:

Plug the numbers in

The result for each number when plugged in order is:

121

81

0

9

49

So 9 would be the answer

Answer:

9

Step-by-step explanation:

If (x-2)^2=49 then x could be 9.

(x-2)^2 = 49

x or 9 - 2 = 7

7^2 = 49

By looking at the graph, we can visually determine that the value of y when point x = -2 is -4.

Answer:

-4

Step-by-step explanation:

The y value at x=-2 is -4 because when you go to -2 on the x-axis the function is below there.  You can only go straight up or straight down to determine the y-value that corresponds to x=-2 so we go down because the function is below the x-axis there.

We are going to go down until we get on the graph of the line.  Scroll over with eyeballs to see that the y there is -4 (use the y-axis).

So the ordered pair (-2,-4) is on our line and when x=-2, y=-4.

Another example:

y=0 when x=2

Another example:

y=2 when x=4

Another example:

y=-3 when x=-1

Answer:

AC, CE, AB, and AS

I belive those are your answers

Answer:

chords: CE and AB; secant: CE; tangent:t; diameter AB; radii: AS and SB

Step-by-step explanation:

i was a

Step-by-step explanation:

Answer:

a

Step-by-step explanation:

Answer:

See below in bold.

Step-by-step explanation:

The ratio of oil to vinegar is 5 : 1. That means that 5/6 of the mixture is oil and 1/6 is vinegar.

So to make 57 oz of the polish,  57/ 6 = 9 1/2 oz is vinegar and 5/6 * 57 =

47 1/2 oz is olive oil.

Answer:

  83 25/27 yd³

Step-by-step explanation:

Assuming a 4 ft depth of fill, the cut volume is ...

  (2 ft)(33 ft)(65 ft) = 4290 ft³

The fill volume is ...

  (23 ft)(22 ft)(4 ft) = 2024 ft³

The left over dirt occupies a volume of ...

  4290 ft³ -2024 ft³ = 2266 ft³ = (2266 ft³)(1 yd³)/(27 ft³) = 83 25/27 yd³

Answer:

Mean = 0.8

Standard Deviation = 0.8

P(x = 3) is unusual event

Step-by-step explanation:

Part A)

The probability distribution with correct formatting is shown in the table attached with:

We have to find the mean and standard deviation of this distribution. The mean of the probability distribution is calculated as summation of the products of "the variable with its respective probability".

[tex]u = \sum x P(x)[/tex]

So, for the given distribution:

Mean = 0(0.4096) + 1(0.4096)+2(0.1536)+3(0.0256)+4(0.0016)

Mean = 0.8

Standard deviation is calculated by the following formula:

[tex]\sigma=\sqrt{\sum x^{2}P(x) - u^{2}}[/tex]

[tex]x^{2}P(x)=1.28[/tex]

Substituting the values, we get:

[tex]\sigma=\sqrt{1.28-(0.8)^{2}}\\\\ \sigma=0.8[/tex]

Part B)

Since the probability of 3 defective computers is less than 0.05, this is an unusual event.

So it would be unusual to have 3 defective computers in the batch.

Using the discriminant to know about the nature of the solution of the quadratic equation x² -x = -1/4 tells us the fact as given by: Option c. one real solution

Let the quadratic equation given be of the form [tex]ax^2 + bx + c = 0[/tex], then

The quantity [tex]b^2 - 4ac[/tex] is called its discriminant.

The solution contains the term [tex]\sqrt{b^2 - 4ac}[/tex] which will be:

There are two roots of a quadratic equations always(assuming existence of complex numbers). We say that the considered quadratic equation has 2 solution if roots are distinct, and have 1 solutions when both roots are same.

For this case, the given equation is:

[tex]x^2 - x = -1/4[/tex]

Converting this to the form [tex]ax^2 + bx + c = 0[/tex], we get:

[tex]x^2 - x + 1/4= 0\\or\\4x^2 -4x + 1 = 0[/tex]

Thus, we get:

a = 4, b = -4, c = 1

Putting these values in the expression for discriminant, we get:

[tex]D = b^2 - 4ac =(-4)^2 - 4(4)(1) = 16 - 16 = 0[/tex]

The discriminant is 0, so the considered quadratic equation is going to have both roots real and equal. Or in terms of distinct solutions, it is going to have one real solution (distinct).

Thus, using the discriminant to know about the nature of the solution of the quadratic equation x² -x = -1/4 tells us the fact as given by: Option c. one real solution

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Answer:

  13 lb

Step-by-step explanation:

The horizontal component of the force is the magnitude of the force multiplied by the cosine of the angle with the horizontal.

  (16 lb)·cos(35°) ≈ 13.1 lb ≈ 13 lb

Answer:

b.13 lb

Step-by-step explanation:

We are given that  a boy pulls his sled with a rope .

The rope makes an angle with horizontal =[tex]35^{\circ}[/tex]

If a pull on the rope is needed to move the sled=16 pounds

We have to find the horizontal component of force

We know that horizontal component force=[tex]fcos\alpha[/tex]

Therefore, we have f=16 pound

Then, horizontal component of force=[tex]16cos 35^{\circ}[/tex]

Horizontal component of force=[tex]16\times 0.819=13.1lb[/tex]

Hence, horizontal component of force=13 lb

Answer:b.13 lb

Answer:

B

Step-by-step explanation:

Answer:

Its B) 60°

Step-by-step explanation:

135°=75°+CAD

135°-75°=CAD

60°=CAD

Answer:

A) (2, -1/2)

Step-by-step explanation:

Start with one equation and isolate a variable:

4x - 4y = 10

4x - 4x - 4y = 10 - 4x

-4y = 10 - 4x

-4y/-4 = 10/-4 - 4x/-4

y = -2 1/2 + x

Now plug this in for y in the other equation:

3x + 2(-2 1/2 + x) = 5

3x - 5 + 2x = 5

5x - 5 = 5

5x - 5 + 5 = 5 + 5

5x = 10

5x/5 = 10/5

x = 2

Right here we can tell your answer is A since it is the only one with 2 as the x-value

Answer:

Answer B

Step-by-step explanation:

The triangle has side lengths that are dilated by 2x in the second triangle

Answer:

2

Step-by-step explanation:

A P E X

Answer:

[tex]\sqrt{28} \approx 5.3[/tex]

Step-by-step explanation:

The Pythagorean Theorem says if you have a right triangle, then relationship between the three sides is the sum of the square of each leg is the hypotenuse squared.

So [tex]a^2+b^2=c^2[/tex]

where a and b are legs and c is the hypotenuse.

Plug in your a,b, and c. In this case it is a,6, and 8.

This means we have

[tex]a^2+6^2=8^2[/tex]

Simplify where you can before we begin the solving (the moving around of things to other sides).

[tex]a^2+36=64[/tex]

Now time for the solving. We are first going to get [tex]a^2[/tex] by itself.

To do this, we just need to subtract 36 on both sides giving us:

[tex]a^2=64-36[/tex]

[tex]a^2=28[/tex]

Now to get rid of the square on a, just square root both sides:

[tex]a=\sqrt{28}[/tex].

Answer:

B. H0: μd = 0 Ha: μd < 0

Step-by-step explanation:

Let μ1 and μ2 represent the number of correct answers during the timed condition and the unlimited time condition, respectively.

Let μd be the mean of the differences in the number of correct answers (timed − un timed) of all sixth graders.

The answer is B. H0: μd = 0 Ha: μd < 0

Here we have to check that the students will get few correct answers in the timed condition as compared to the unlimited time condition.

To know this, difference was calculated so we get the correct hypotheses as : H0: μd = 0 and Ha: μd < 0 .

Answer:

Also "H0: μ1 − μ2 = 0 Ha: μ1 − μ2 < 0" is correct

Step-by-step explanation:

Answer:

Step-by-step explanation:

The product of two identical binomial factors will be a perfect square trinomial. The appropriate answer choices are those having both factors the same.

Answer:

Step-by-step explanation:

(xy + x)(xy + x)

(16 x2)(x2 16)

(4y2 + 25)(25 + 4y2)

Answer:

The last option is correct for two independent events.

P(A and B) = P(A) P (B)

And P(B and A) = P(B) P(A) which is equal. And other three cases are false.

P(AB) = P(BA) is true.

If outcomes of an event doesn't affect the outcomes of other event, the the events are called independent events, i.e. they are independent to each other.

For two independent events,

P(AB) = P(A)P(B)

Also, P(BA) = P(B)P(A)

And,  P(A)P(B) = P(B)P(A)

Hence, we can say that P(AB) = P(BA)

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Answer:

x = 5.34

Step-by-step explanation:

The reference angle is 24 degrees.  I'm sure you are aware from the square at the other base angle that is a right triangle.  Right triangles have ratios by which we can determine missing side and angle measures.  The sin of a reference angle has a ratio that is side opposite/hypotenuse.  The cos of a reference angle has a ratio that is side adjacent/hypotenyse.  The tan of a reference angle has a ratio that is side opposite/side adjacent.

We need to decide which of these fits our needs according to the angle and sides we are given and need to find.  We have the reference angle as 24 degrees, we have the side adjacent to this angle as 12.  We are looking for x, which is the side opposite the reference angle.  Looking to what our definitions are for each ratio, the sides opposite and adjacent are defining the tan of the reference angle.  Setting up the ratio then looks like this:

[tex]tan(24)=\frac{x}{12}[/tex]

Multiply both sides by 12 to get

12 tan(24) = x

Do this on your calculator in DEGREE mode to get that

x = 5.342744224

Not sure what your teacher has you round to, but I usually have my students give me 2 decimal places

Answer:

x= 16±√-64 over 2

Step-by-step explanation:

x= -(-16)±√(-16)²-4×1×80 over 2×1

x= 16±√256-320 over 2

x= 16±√-64 over 2

can also be represented with all real numbers.

Answer:

Step-by-step explanation:

The probability of drawing a boy's name is found in:

number of boys/total number of students

Our ratio then is

16/16+18 which is

16/34 which reduces to

8/17

As a percentage, it would be about 47%

Total students = 16 + 18 = 34

16 boys

Probability of picking boy = 16/34

Which reduces to 8/17