Divide using synthetic division. ( x^4-12x^2-9)/(x+3)

x + (4 + x) = 20

2x + 4 = 20

2x = 16

x = 8

Proof

x + (4 + x) = 20

8 + 4 + 8 = 20

12 + 8 = 20

20 = 20

The numbers are 8 and 12.

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Answer:

5 lb 11⅓ oz

Step-by-step explanation:

First, convert the weight at birth from pound and ounces to just ounces.

8 lb × 16 oz/lb + 9 oz = 137 oz

The baby doubles its weight in the first six months.  That means its weight increases by 137 oz over 6 months.  To find how much weight was gained in 4 months, write a proportion.

137 / 6 = x / 4

6x = 548

x = 91 ⅓

The baby gained 91 ⅓ oz in 4 months, or 5 lb 11⅓ oz.

Surface area of cone is [tex]18 \pi[/tex] square units

Solution:

Given that cone with a slant height of 7 and a radius of 2

To find: surface area of cone

The surface area of a cone is equal to the curved surface area plus the area of the base

The surface area of cone is given by formula:

[tex]S. A=\pi r^{2}+\pi r l[/tex]

Where "r" is the radius and "l" is the slant height of cone

Substituting r = 2 and l = 7 in above formula,

[tex]\begin{array}{l}{S A=\pi\left(r^{2}+r l\right)=\pi\left(2^{2}+2(7)\right)} \\\\ {S A=\pi(4+14)=18 \pi}\end{array}[/tex]

Thus surface area of cone is [tex]18 \pi[/tex] square units

Answer:

0.5

Step-by-step explanation:

divide 2.5 and 5 since they are equal sized bottles.

Answer:.5

Step-by-step explanation:2.5 divided by 5 = 0.5

Answer:

$6900

Step-by-step explanation:

Given:

Length = 45 yards

Width = 5 yards

thickness = 1/3 yard

Volume,

= Length x Width x Thickness

= 45 x 5 x (1/3)

= 75 yards³

Costs:

1 cubic yard = $92

75 cubic yards = $92 x 75 = $6900

American airlines made a total money of $ 4263

Solution:

Given that,

Cost of 1 first class ticket = $ 53

Cost of 1 coach ticket = $ 21

There were 139 passengers total

30% of the passengers composed of the first class, Which means 30 % of 139 are first class

Number of first class passengers = 30 % of 139

[tex]\rightarrow \frac{30}{100} \times 139 = 41.7[/tex]

Thus approximately 42 passengers are from first class

Number of coach class passengers = 139 - 42 = 97

So we have,

Number of first class passengers = 42

Number of coach class passengers = 97

To find: Total money made by American airlines

We can frame a equation as:

total money = (Number of first class passengers x Cost of 1 first class ticket) + (Number of coach class passengers x Cost of 1 coach ticket)

[tex]\text{ total money } = 42 \times 53 + 97 \times 21\\\\\text{ total money } = 2226 + 2037 = 4263[/tex]

Thus american airlines made a total money of $ 4263

Answer:

(X-10y)(x+10y)

Step-by-step explanation:

Write in exponential form , calculate the product & factor !

Answer:

Step-by-step explanation:

x² - 100y² = x² -  (10y)²

                 =(x + 10y) (x - 10y)

Hint: a² - b² = (a + b) (a - b)

The true statement is : D. The boiling point decreases by 1.8 degrees as the altitude increases by 1000 feet. True statements are : A,D & E

Step-by-step explanation:

5.

The equation is given as : T(a)= -0.0018a +212 where T (a) is the boiling point of water measured in degrees at altitude a measured in feets.

From the equation , when the altitude is increased by 1000 feets, a=1000, the equation will be

T(1000) = -1.8 + 212, which means that the boiling point decreases by 1.8 degrees as the altitude increases by 1000 feet

6.

The values given can be taken as coordinates and plotted on a graph tool as shown in the attached figure.

Finding the slope of the graph'

m=Δy/Δx

Taking points (14,73) and (9,51.75) the slope of the linear graph will be;

Δy=73-51.75 = 21.25

Δx=14-9 =5

m= 21.25/5 = 4.25

The equation of the linear graph taking m=4.25 and point (14,73)

m=Δy/Δx

4.25 = y-73/x-14

4.25(x-14) = y-73

4.25x - 59.5 =y-73

4.25x - 59.5 + 73 =y

y=4.25x+13.5

From the graph,

The price in 2005 will be $77.25

The predicted average change in ticket price per year is $4.25

The y -intercept is the price of ticket in 1990

True statements are : A,D & E

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Answer:

[tex]y=2\text{cos}((\frac{2\pi}{3})t)[/tex]

Step-by-step explanation:

We have been given that an object oscillates 4 feet from its minimum height to its maximum height. The object is back at the maximum height every 3 seconds. We are asked to find the cosine function that can be used to model the height of the object.

We know that standard form of cosine function is [tex]y = A\cdot \text{cos}(Bt-C)+D[/tex], where,

|A| = Amplitude,

Period = [tex]\frac{2\pi}{|B|}[/tex],

C = Phase shift,

D = Vertical shift.

Since distance between maximum and minimum is 4, therefore, amplitude will be half of it, that is, [tex]A = 2[/tex].

Since objects gets back to its maximum value in every 3 seconds, therefore, period of the function is 3 seconds. We know that period is given by [tex]\frac{2\pi}{|B|}[/tex], therefore, we can write [tex]\frac{2\pi}{|B|}=3[/tex], therefore, [tex]B = \frac{2\pi}{3}[/tex].

We haven't been given any information about phase and mid-line, we can assume the values of C and D to be zero .

Therefore, our function required function would be [tex]y=2\text{cos}((\frac{2\pi}{3})t)[/tex].

Answer:

[tex]y=\frac{2}{3}x-\frac{16}{3}[/tex]

Step-by-step explanation:

step 1

Find the slope of the given line

The formula to calculate the slope between two points is equal to

[tex]m=\frac{y2-y1}{x2-x1}[/tex]

we have

(-2,5) and (-4,8)

substitute the values in the formula

[tex]m=\frac{8-5}{-4+2}[/tex]

[tex]m=\frac{3}{-2}[/tex]

[tex]m=-\frac{3}{2}[/tex]

step 2

Find the slope of the perpendicular line to the given line

we know that

If two lines are perpendicular, then their slopes are opposite reciprocal (the product of their slopes is equal to -1)

so

[tex]m_1*m_2=-1[/tex]

[tex]m_1=-\frac{3}{2}[/tex] ----> slope of the given line

therefore

[tex]m_2=\frac{2}{3}[/tex] ---> slope of the perpendicular line to the given line

step 2

Find the equation of the line in point slope form

[tex]y-y1=m(x-x1)[/tex]

we have

[tex]m=\frac{2}{3}[/tex]

[tex]point\ (-1,-6)[/tex]

substitute

[tex]y+6=\frac{2}{3}(x+1)[/tex]

step 3

Convert to slope intercept form

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

isolate the variable y

[tex]y+6=\frac{2}{3}x+\frac{2}{3}[/tex]

[tex]y=\frac{2}{3}x+\frac{2}{3}-6[/tex]

[tex]y=\frac{2}{3}x-\frac{16}{3}[/tex]

Answer: 2743.2

Step-by-step explanation:

A formula to try is to multiply the length value by 30.48

Answer:

The total number of codes which can be assigned is, 55440 .

Step-by-step explanation:

According to the question, the home alarm system randomly assigns a five-character code for each customer.The code will not repeat a character and there are 11 distinct characters.

So, the total number of codes that can be randomly assigned is given by,

[tex]^{11}{P}_{5}[/tex]

= [tex]\frac {11!}{6!}[/tex]

= [tex]11 \times 10 \times 9 \times 8 \times 7[/tex]

= 55440

Answer:

D. $340.91

Step-by-step explanation:

Answer:

True

Step-by-step explanation:

For $6 and 4 oranges the unit price per orange is $1.50,  and with $15 for 10 oranges the unit price per orange is also $1.50.

Answer:

I think it's 22.2%

Step-by-step explanation:

There's 9 shirts in all and there's only 2 red shirts out of the 9. And 22.2% is the percentage of 2/9

Answer:

The base is 714.436.

Step-by-step explanation:

Given:

Percentage of the base = 39%

Let the base be 'x'.

39 percent of base = 278.63

We need to find the base.

We now that Percentage of the base multiplied by the base is equal to 39 percent of base.

framing in equation form we get;

[tex]39\%x= 278.63\\\\\frac{39}{100}x=278.63\\[/tex]

Now multiplying both side by 100 we get;

[tex]\frac{39}{100}\times 100 \times x=278.63\times 100\\\\39x = 27863[/tex]

Now Dividing both side by 39 we get;

[tex]\frac{39x}{39}=\frac{27863}{39}\\\\x=714.436[/tex]

Hence the base is 714.436.

The solution is Option A.

The measure of the equation A = -2xy is A = 12

Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.

It demonstrates the equality of the relationship between the expressions printed on the left and right sides.

Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.

Given data ,

Let the equation be represented as A

Now , the value of A is

A = -2xy   be equation (1)

Now , when x = -1 and y = 6

Substituting the values of x and y in the equation , we get

A = -2 ( -1 ) ( 6 )

On simplifying the equation , we get

A = 2 ( 6 )

A = 12

Therefore , the value of A is 12

Hence , the equation is A = 12

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For this case we have that by definition, the equation of a line in the slope-intersection form is given by:

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

Where:

m: It's the slope

b: It is the cut-off point with the y axis

By definition, if two lines are parallel then their slopes are equal.

We have the following equation of the line:

[tex]3x-2y = 8[/tex]

We manipulate algebraically:

[tex]-2y = -3x + 8\\y = \frac {3} {2} x-4[/tex]

Thus, a parallel line will have an equation of the form:

[tex]y = \frac {3} {2} x + b[/tex]

Answer:

[tex]y = \frac {3} {2} x + b[/tex]

Answer: 1

Step-by-step explanation:

It will be the smallest value for f(x).

The minimum of a sinusoidal function is the lowest point on the graph that is 1.

The minimum of a sinusoidal function is the lowest point on the graph. Looking at the image you provided, the minimum point is the lowest y-coordinate the curve reaches.

Since the graph is a sine wave, it oscillates between a maximum and a minimum value. For a standard sine function, which this graph appears to resemble, these extrema occur at points where the sine of the angle is either 1 or -1.

The minimum value of sine is -1, but the actual minimum value of the function on the graph will depend on any vertical shift and amplitude changes.

To find the exact minimum value from the graph, you'd look for the lowest point on the y-axis that the graph reaches. From the image, it's not perfectly clear, but it looks like the minimum value is around -2 on the y-axis.

This would be the case if the function has no vertical shift from the standard sine wave. If there's a vertical shift, the minimum would be the standard minimum value of sine (-1) plus the vertical shift.

Answer:

3108

Step-by-step explanation:

number of 5-min segments in 1 hour

= 1 hour ÷ 5 min

= 60 min ÷ 5 min

= 12

number of 5-min segments in 7 hours

= 12 x 7

= 84

given that during each 5 min segment, jasmine decorates 37 cakes

i.e

1 (5-min) segment -----> decorates 37 cakes

84 (5-min) segments -----> decorates 37 x 84 = 3108 cakes

In this question, we're trying to find how many cakes Jasmine can decorate in 1 day.

We know that she can decorate 37 cakes everyone 5 minutes.

We also know she works 7 hours a day.

First, we need to find how much she makes it an hour.

To find this, multiply 37 by 12.

37 · 12 = 444

This means that she can decorate 444 cakes in an hour.

Now, multiply 444 by 7 to see how much she can decorate in a day.

444 · 7 = 3,108

This means that she can decorate 3,108 cakes in a day.

Answer:

3,108 cakes

Answer:

For given polynomial [tex]P(a)=a^3+2a^2-3a+5=41[/tex] and when a=3 is

[tex]P(3)=41[/tex]

Step-by-step explanation:

Given polynomial is [tex]P(x)=x^3+2x^2-3x+5[/tex]

Remainder Theorem:

To evaluate the function f(x) for a given number "a" you can divide that function by x - a and your remainder will be equal to f(a). Note that the remainder theorem only works when a function is divided by a linear polynomial, which is of the form x + number or x - number.

By using synthetic division for given polynomial [tex]P(x)=x^3+2x^2-3x+5[/tex] and factor is (x-a)    (here x-3 is a factor given)

_3|    1      2       -3         5

        0     3       15       36

      ___________________

         1      5       12      | 41

Given polynomial can be written as

[tex]P(a)=a^3+2a^2-3a+5[/tex]

To find P(a):

[tex]P(a)=a^3+2a^2-3a+5[/tex]

put a=3

[tex]P(3)=3^3+2(3)^2-3(3)+5[/tex]

[tex]P(3)=27+18-9+5[/tex]

[tex]P(3)=41[/tex]

Therefore for given polynomial [tex]P(a)=a^3+2a^2-3a+5=41[/tex] when a=3 is  [tex]P(3)=41[/tex]

Answer:

Part 3) [tex]SA=288\ cm^2[/tex]

Part 4) [tex]64\ cm^2[/tex]

Step-by-step explanation:

Part 3) Calculate the total surface area of three 4 cm cubes

we know that

The surface area of a cube is equal to the area of its six square faces

[tex]SA=6b^2[/tex]

so

The surface area of three cubes is equal to the area of its 18 square faces

[tex]SA=18b^2[/tex]

where

b is the length side of the square face

In this problem

[tex]b=4\ cm[/tex]

so

The surface area of three cubes is

[tex]SA=18b^2[/tex]

substitute the given value

[tex]SA=18(4)^2[/tex]

[tex]SA=288\ cm^2[/tex]

Part 4) How much surface area would be lost if you glued three 4-cm cubes together to make a rod that is three cubes long and one cube wide?

In this case the total surface area of the three glued 4-cm cubes is equal to the area  of  its 14 square faces

so

The surface area lost is equal to

[tex]18b^2-14b^2=4b^2[/tex]

substitute

[tex]4(4)^2=64\ cm^2[/tex]

Gluing three 4-cm cubes together to form a rod results in a loss of 64 cm²of surface area because the areas of the glued faces are no longer exposed.

Each individual cube has 6 faces, so the surface area of one cube is 6 times the area of one face. With a side length of 4 cm, the area of one face is 4 cm  imes 4 cm = 16 cm². Thus, the total surface area for one cube is 6  imes 16 cm²= 96 cm². For three separate cubes, this would be 3  imes 96 cm² = 288 cm².

When the three cubes are glued together side by side to form a rod, they share faces. Each glue contact removes two faces worth of area (one from each cube). As there are two glue contacts, a total of 4 faces are lost. Therefore, the lost surface area is 4  imes 16 cm2 = 64 cm².

The original total surface area was 288 cm², so the new surface area after gluing is 288 cm² - 64 cm² = 224 cm². Hence, gluing the cubes together results in a loss of 64 cm² of surface area.

Answer:

I m not an expert in maths but I m sure it is Option D

Final answer:

The midpoint of a segment can be found by averaging the x-coordinates and y-coordinates of the endpoints, with the formula M = ((x₁ + x₂) / 2, (y₁ + y₂) / 2) representing the midpoint's coordinates.

Explanation:

The formula for finding the midpoint of a segment involves calculating the average of the x-coordinates and the average of the y-coordinates of the two endpoints of the segment.

If we have two points, A(x₁, y₁) and B(x₂, y₂), the coordinates of the midpoint M will be calculated as follows:

Thus, the coordinates of the midpoint M will be (Mx, My). This formula is essential when dealing with problems involving geometry, coordinate systems, or finding the center point between two given locations on a line segment.

Answer:

6/10

Step-by-step explanation:

Answer:

9/15 ur welcome!

Step-by-step explanation:

Problem 1

The exterior angles sum to 360

9v+(19v-21)+45+(v+48)+7v = 360

36v+72 = 360

36v+72-72 = 360-72

36v = 288

36v/36 = 288/36

v = 8

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

Problem 2

Why is this? because TW is perpendicular to VS (the right angle marker shows this). At the same time, TW cuts VS into two equal pieces, ie VW = WS. The tickmarks indicate the segments are the same length.

Answer:

B. [tex]\frac{1}{x^2y^7}[/tex]

Step-by-step explanation:

Given:

[tex](x^3y^{-2}z)(x^{-5}y^{-5}z^{-1})[/tex]

Hence Solving the given expression we get;

By Law of Indices which states;

[tex](a^xb^yc^z)(a^pb^qc^r) = a^{x+p}b^{y+q}c^{z+r}[/tex]

Hence we get;

[tex]x^{3+(-5)}y^{(-2)+(-5)}z^{1+(-1)}\\\\x^{3-5}y^{-2-5}z^{1-1}\\\\x^{-2}y^{-7}[/tex]

Also We know that

[tex]a^{-6} =\frac{1}{a^6}[/tex]

So,

[tex]\frac{1}{x^2y^7}[/tex]

The correct answer is D. All natural numbers are integers, as natural numbers are part of the larger set of integers which includes all whole numbers both positive, negative, and zero.

Out of the options given, the true statement is: D. All natural numbers are integers. This is because natural numbers include all positive counting numbers from 1 upwards, which are also part of the integers set that includes all whole numbers both positive and negative, as well as zero.

Option A is incorrect because not all real numbers are rational. Real numbers include both rational numbers (which can be written as fractions of integers) and irrational numbers (which can't be expressed as fractions of integers).

Option B is incorrect because while all whole numbers are natural numbers, the set of whole numbers also includes 0 which is not considered a natural number.

Option C is incorrect since all integers are indeed whole numbers, but not all whole numbers are integers as integers also include negative numbers.

In addition to the answer, the commutative property of addition, which states that A+B=B+A was mentioned. This property holds true for the addition of ordinary numbers, such as 2 + 3 is the same as 3 + 2.

Answer:

150 degrees

Step-by-step explanation:

Angles FED and CEG are congruent to one another because opposite angle theorem. That makes angle CEG equal to 130. Same applies for angles DEB and AEC, making angle AEC 20 degrees.

Your variable x is a combination of these two angles, AEC + CEG. 130 + 20 = 150

Therefore x = 150 degrees.

150 degrees is the measure of the value of x from the figure.

The given diagram is a line geometry with the following parameters;

<FED = 130 degrees

<DEB = 20 degrees

Determine the measure of x

x = <FED + <DEB

Substitute the given parameters

x = 130 + 20

x = 150 degrees

Hence the measure of the value of x from the figure is 150 degrees.

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