Synthetic Division to Find Zeros (Lev 1)
May 25, 1:20:18 PM
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If ƒ(x) = x³ – 11x² + 26x — 16 and x – 1 is a factor of f(x), then find all of zeros

[tex]\\ \rm\Rrightarrow \dfrac{AB}{AD}=\dfrac{BC}{CD}[/tex]

[tex]\\ \rm\Rrightarrow \dfrac{18}{x}=\dfrac{19}{11}[/tex]

[tex]\\ \rm\Rrightarrow 19x=198[/tex]

[tex]\\ \rm\Rrightarrow x=10.4[/tex]

Answer:

x = 10.4 (nearest tenth)

Step-by-step explanation:

Angle Bisector Theorem

The angle bisector of any angle in a triangle will divide the side opposite the bisected angle in the ratio of the sides containing the angle.

Therefore:

AD : DC = BA : BC

Given:

Substituting the given values into the ratio and solving for x:

[tex]\implies \sf x : 11 = 18 : 19[/tex]

[tex]\implies \sf \dfrac{x}{11}=\dfrac{18}{19}[/tex]

[tex]\implies \sf 19x=18 \cdot 11[/tex]

[tex]\implies \sf 19x=198[/tex]

[tex]\implies \sf x=\dfrac{198}{19}[/tex]

[tex]\implies \sf x=10.4 \: (nearest\:tenth)[/tex]

Answer:

(0, 2)

Step-by-step explanation:

it right I got 100% on my quiz

And… here are others that are right in the quiz

Identify coordinate point B.

(1, 5)

Identify coordinate point D.

(7, 3)

Identify coordinate point C.

(6, 7)

Hope it helps! :)

Answer:

Find the area of the triangle side, then multiply by the length of the prism.Area of triangle = 1/2 x height x baseArea  = 1/2 x 2 x 3 = 3 square cmVolume = 3 x 4 = 12 cubic cm.Answer is A)

Step-by-step explanation:

Answer:

1456ft²

Step-by-step explanation:

A = lw

A = 60(20)

A = 1200ft²

A = 16(16)

A = 256ft²

1200 + 256 =

1456ft²

Step-by-step explanation:

it depends if you use degrees or radians as angle measure.

let's assume degrees.

arcsine is the inverse function of sine.

so, when sin(x) = 1/2, arcsin(1/2) = x

when now x = 2×arcsin(1/2), we get

x = 2×30 = 60°

Answer:

29 feet

Step-by-step explanation:

20^2 + 21^2 = 841

841sqrt = 29 feet

Solution:

[tex]x > - 1[/tex]

[tex]\huge\mathfrak\colorbox{white}{}[/tex]

Interval Notation:

x ∈ (-1,∞)

The slant height of the right circular cone will be  [tex]l=2\sqrt5}[/tex]

The formula for the slant height of the cone is given as:

[tex]l^2=r^2+h^2[/tex]

Here we have

r=2 units

h=4 units

By putting the values we will get

[tex]l=\sqrt{4^2+2^2[/tex]

[tex]l=\sqrt{16+4[/tex]

[tex]l=\sqrt{20}[/tex]

[tex]l=2\sqrt{5}[/tex]

Hence the slant height of the right circular cone will be  [tex]l=2\sqrt5}[/tex]

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Answer:

54.59

Step-by-step explanation:

carry the 10 over and 1-.41 is .59

Answer:

People can not be in fractions

Answer:

I think 24.

Step-by-step explanation:

The minimum number of sets of knives Indigo should buy is 9.

An inequality is a relation which makes a non-equal comparison between two numbers or other mathematical expressions. It is used most often to compare two numbers on the number line by their size.

Here, Let the minimum number of sets be x.  

          restaurant needs at least 430 knives

         currently restaurant have 269 knives

         each set contains 18 knives.

According to question,

           18x + 269 ≥ 430

            18x ≥ 161

              x ≥ 161/18

              x ≥ 8.94

Thus, the minimum number of sets of knives Indigo should buy is 9.

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Answer:

▪︎ Domain: all real numbers (x can be any number)

▪︎ Range: y <= 0 (y can never become greater than 0 bc the vertex of this function (highest point) is (0,0))

The quadratic regression equation of the table of values is y = 0.71x² - 5.04x + 3.76

The table of values is given as:

x: 0     1       2    3     4     5   6

y: 4.1 -0.9 -3.9 -5.1 -4.1 -4.1 -1.1

To determine the quadratic regression equation, we make use of a graphing calculator

From the graphing calculator, we have the following calculation summary:

a = 0.7, b = -5.04 and c = 3.76

A quadratic regression equation is represented as:

y = ax² + bx + c

Hence, the quadratic regression equation of the table of values is y = 0.71x² - 5.04x + 3.76

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Applying the Pythagorean theorem, the distance between the Earth's horizon and the satellite would be 5756.70 miles.

To calculate the distance from the satellite to the Earth's horizon, it is necessary to use the Pythagorean Theorem as follows:

We must identify the data we have:

To calculate the distance from the satellite to the Earth's horizon, we must first establish the distance from the center of the Earth to the satellite, for this we calculate the radius of the Earth and add the distance to the satellite:

With these data we can draw an imaginary triangle from the center of the Earth, one of its legs would be the distance between the center of the Earth and the satellite, the other leg would be the distance between the center of the Earth and the Earth's horizon (at 90° to the other leg).

Now, to identify the distance between the horizon and the satellite, we apply the Pythagorean Theorem:

According to the above, the distance between the satellite and the horizon would be 5756.70 miles.

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the mean numbers of point scored is greater than 12 points(C.)

Answer:

Below in bold.

Step-by-step explanation:

Circumference = π * diameter

= π * 7

= 20.99 cm to nearest hundredth.

Radius of the circle = 1/2 * diameter = 7/2

= 3.5cm.

Area = π r^2

= π * 3.5^2

= 38.48 cm^2 to nearest hundredth.

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

[tex]\diamond\large\blue\textsf{\textbf{\underline{\underline{Question:-}}}}\diamond[/tex]

            ◈ The diameter of a circle is 7 cm. What is its area? How about its circumference?

[tex]\diamond\large\blue\textsf{\textbf{\underline{\underline{Answer and How to Solve:-}}}}\diamond[/tex]

We're asked to find the circle's circumference, which can be found using the formula below:-

[tex]\textsf{Formula for Circumference of a Circle:- \boxed{\bold{C=\pi d}}}[/tex]

Where:-

As per provided information (d=7cm), we can easily find the circumference by substituting 7 for d:-

↬ [tex]\sf{C=\pi (7)}[/tex]

On simplification,

   ↬ [tex]\sf{C=7*3.14}[/tex]

Remember, 3.14 is pi.

On further simplification,

            ↬  C=21.98 cm.

So we conclude that the circumference of the given circle is:-

      C=21.98 cm.

Now, how about the area?

[tex]\textsf{Formula for Area of a Circle:-\boxed{\bold{A=\pi r^2}}}[/tex]

Where:-

Notice that we only have the diameter and not the radius.

We can easily find the radius by dividing the diameter by 2:-

3.5

So the radius is 3.5.

Substitute the value of r into the formula, which results in:-

         ↬ [tex]\sf{A=\pi (3.5)^2}[/tex]

On simplification,

On further simplification,

A=12.25•3.14 (3.14 is pi)

On further simplification,

A=38.465 cm²

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

[tex]\large \boxed{ \ \sf \dfrac{13}{36} \ }[/tex]

[tex]\rightarrow \sf 10 \dfrac{1}{9} - 9\dfrac{3}{4}[/tex]

[Convert to improper Fractions]

[tex]\rightarrow \sf \dfrac{91}{9} - \dfrac{39}{4}[/tex]

[Make the denominator same]

[tex]\rightarrow \sf \dfrac{4(91)}{36} - \dfrac{9(39)}{36}[/tex]

[Multiply Integers]

[tex]\rightarrow \sf \dfrac{364}{36} - \dfrac{351}{36}[/tex]

[Join both fractions]

[tex]\rightarrow \sf \dfrac{364-351}{36}[/tex]

[Subtract Integers]

[tex]\rightarrow \sf \dfrac{13}{36}[/tex]

Answer:

13/36.

Step-by-step explanation:

First convert to improper fractions:

10 1/9 = (10*9 + 1)/9 = 91/9.

9 3/4 = (9*4 + 3)/4 = 39/4.

Next find the Lowest Common Denominator of 9 and 4.

This is 9*4 = 36.

Now convert both fractions to 36th:

For 91/9 we multiply by 4/4 and for 39/9 we multiply by 9/9

91*4 / 9*4 =  364/36 and 39*9 / 9*4 =  351/36, so we have:

364/36 - 351/36

=  13/36

Answer:

hope this will help you

Step-by-step explanation:

69+420/3

first of all divide 420 by 3 which is 140

69+140

then add with 69

209

Answer:

The correct answer should be 209.

Step-by-step explanation:

Also here Is your art my good sir!

Step-by-step explanation:

1 min 4 cals

60 cals how many mins?

1min. 60cals

____. × _______ = 15 mins

4cals. ?mins

we simplify the matter by simplifying 60 with 4 and striking out cals... then we will have 15 on the top right and then we multiply 1 and 15 together at the end we add the mark of the answer which is (min).

Answer:

RT = 26

Step-by-step explanation:

Based on the figure we can say :

Scale factor :

Hence, as the proportions are the same :

The triangle ABC and RST will be similar triangles. Then the length of RT will be 26 units.

A triangle is a three-sided polygon with three angles. The angles of the triangle add up to 180 degrees.

If the two triangles are similar, the ratio of the corresponding sides will be constant.

The triangle ABC and RST will be similar triangles.

RT / 13 = 24 / 12

      RT = 26

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Answer:

See below ~

Step-by-step explanation:

Finding the x-intercepts :

Finding the vertex :

Answer/Step-by-step explanation:

Given:

A gas station offers a lucky draw to customers. Each time you spend more than $20 on gas, you can make a draw to win a prize. The probability of winning a prize is 1/12 suppose you buy gas 4 times.

To Find:

what is the probability of you winning a prize each time?

Solve:

Since, it given that you buy gas 4 times. Thus that means:

1/12 × 1/12 × 1/12 × 1/12 or  1/12⁴

Now solving it:

1/12 × 1/12 × 1/12 × 1/12 = 1/20736

Which also means (0.0048%) in decimal form since, 1 divide by 2076 equal to 0.0048%

Kavinsky

Answer:

500

-by-step explanation:

1000/2

Check the picture below.

now, we're making an assumption that, the two blue shaded region are equal in shape, and thus if that's so, that area above the 14 is 6 and below it is also 6, 14 + 6 + 6 = 26.

so hmm if we simply get the area of the trapezoid and subtract the area of the yellow triangle and the area of the cyan triangle, what's leftover is what we didn't subtract, namely the shaded region.

[tex]\textit{area of a trapezoid}\\\\ A=\cfrac{h(a+b)}{2}~~ \begin{cases} h~~=height\\ a,b=\stackrel{parallel~sides}{bases~\hfill }\\[-0.5em] \hrulefill\\ h=15\\ a=14\\ b=26 \end{cases}\implies A=\cfrac{15(14+26)}{2}\implies A=300 \\\\[-0.35em] ~\dotfill\\\\ \stackrel{\textit{\Large Areas}}{\stackrel{trapezoid}{300}~~ - ~~\stackrel{yellow~triangle}{\cfrac{1}{2}(26)(9)}~~ - ~~\stackrel{cyan~triangle}{\cfrac{1}{2}(15)(6)}} \\\\\\ 300~~ - ~~117~~ - ~~45\implies 138\qquad \textit{blue shaded area}[/tex]

Answer:

[tex]r = 2km[/tex]

Step-by-step explanation:

Area =

[tex]area = \pi {r}^{2} [/tex]

[tex]12.56 = 3.14 \times {r}^{2} [/tex]

[tex] {r}^{2} = \frac{12.56}{3.14} [/tex]

[tex] {r}^{2} = 4[/tex]

[tex]r = \sqrt{4} [/tex]

[tex]r = 2km[/tex]

Answers:

=======================================================

Part (a)

Let's find the distance from point D to point E.

In other words, this will compute the length of segment DE.

[tex]D = (x_1,y_1) = (0,-6) \text{ and } E = (x_2, y_2) = (3,1)\\\\d = \sqrt{(x_1 - x_2)^2 + (y_1 - y_2)^2}\\\\d = \sqrt{(0-3)^2 + (-6-1)^2}\\\\d = \sqrt{(-3)^2 + (-7)^2}\\\\d = \sqrt{9 + 49}\\\\d = \sqrt{58}\\\\d \approx 7.6158\\\\[/tex]

Segment DE is roughly 7.6158 units long.

Let's repeat these steps to find the length of segment EF.

[tex]E = (x_1,y_1) = (3,1) \text{ and } F = (x_2, y_2) = (-2,1)\\\\d = \sqrt{(x_1 - x_2)^2 + (y_1 - y_2)^2}\\\\d = \sqrt{(3-(-2))^2 + (1-1)^2}\\\\d = \sqrt{(3+2)^2 + (1-1)^2}\\\\d = \sqrt{(5)^2 + (0)^2}\\\\d = \sqrt{25 + 0}\\\\d = \sqrt{25}\\\\d = 5\\\\[/tex]

Segment EF is exactly 5 units long.

Lastly, we'll compute the length of segment FD.

[tex](x_1,y_1) = (-2,1) \text{ and } (x_2, y_2) = (0,-6)\\\\d = \sqrt{(x_1 - x_2)^2 + (y_1 - y_2)^2}\\\\d = \sqrt{(-2-0)^2 + (1-(-6))^2}\\\\d = \sqrt{(-2-0)^2 + (1+6)^2}\\\\d = \sqrt{(-2)^2 + (7)^2}\\\\d = \sqrt{4 + 49}\\\\d = \sqrt{53}\\\\d \approx 7.2801\\\\[/tex]

Segment FD is about 7.2801 units long.

This is close to the length of DE, but not quite.

To recap, we found these segment lengths:

As you can see, all three sides are different lengths. Therefore, triangle DEF is scalene.

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

For part (b), follow the same template as part (a).

I'll be skipping the steps.

This is what you should get for the lengths of triangle TRI

Segments TR and IT are the same length (both exactly [tex]\sqrt{37}[/tex] units long), which means triangle TRI is isosceles.

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

For part (c), I'll also be skipping steps.

Here are the lengths you should find

All three lengths are different, making this triangle scalene.

Using the z-distribution, the confidence coefficient for the 90% confidence interval is of 1.645.

In this problem, we have a 90% confidence level, hence[tex]\alpha = 0.95[/tex], and the critical value z is the value of Z that has a p-value of [tex]\frac{1+0.9}{2} = 0.95[/tex], so the critical value is z = 1.645.

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