can someone help me with this please?
could the answer be;

a.) px=-3x^3-2x²-6x-16,r(x)=-45, and q(x)=x-3
b.) px=-3x^3-2x²-6x-16,r(x)=-117, and q(x)=x-3
c.) px=-x^3+4x²+12x+16,r(x)=-117, and q(x)=x-3
d.) px=-x^3+4x²+14x+45,r(x)=-0, and q(x)=x-3

Can Someone Help Me With This Please?could The Answer Be;a.) Px=-3x^3-2x-6x-16,r(x)=-45, And Q(x)=x-3b.)

Answers

Answer 1

The simplest form of the given expression is px=-3x^3-2x²-6x-16,r(x)=-45, and q(x)=x-3.

What is polynomials?

Using variables and coefficients, polynomials are algebraic expressions. The term "indeterminates" is sometimes used to describe variables. The terms Poly and Nominal, which together signify "many" and "terms," make up the word polynomial. When exponents, constants, and variables are combined using mathematical operations like addition, subtraction, multiplication, and division, the result is a polynomial (No division operation by a variable). The expression is categorized as a monomial, binomial, or trinomial based on the number of terms it contains.

(-x^4+7x^3+2x+3)/ (x-3)

=-x² + 4x² + 12x + 38 + 117/(x - 3)

Hence the simplest form of the given expression is px=-3x^3-2x²-6x-16,r(x)=-45, and q(x)=x-3.

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Related Questions

Question 7 (5 points) Which is the area between the x-axis and y=x from x=3 to x=6

Answers

The area between the x-axis and y = x from x = 3 to x = 6 will be 13.50 square feet.

What is integration?

Integration is a way of finding the total by adding or summing the components. It's a reversal of differentiation, in which we break down functions into pieces. This approach is used to calculate the total on a large scale.

The function is given below.

y = x

Integrate the function under the limit from  x = 3 to x = 6 will be given as,

[tex]\begin{aligned} I &= \int^6_3 y dx\\\\ I &= \int^6_3x dx\\\\I &= \left [\dfrac{x^2}{2} \right ]^6_3 \\\\I &= \dfrac{6^2 - 3^2}{2} \end{aligned}[/tex]

Simplify the equation further, then we have

I = (36 - 9) / 2

I = 27 / 2

I = 13.50 square units

The area between the x-axis and y = x from x = 3 to x = 6 will be 13.50 square feet.

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The graph of function f is shown. The graph of an exponential function passes through (minus 10, minus 1), (2, 8) also intercepts the x-axis at minus 2 units and y-axis at 2 units Function g is represented by the table. x -2 -1 0 1 2 g(x) 0 2 8 26 Which statement correctly compares the two functions? A. They have the same x-intercept and the same end behavior as x approaches ∞. B. They have different x- and y-intercepts but the same end behavior as x approaches ∞. C. They have the same y-intercept and the same end behavior as x approaches ∞. D. They have the same x- and y-intercepts.

Answers

Since the graph of an exponential function passes through (minus 10, minus 1), (2, 8) also intercepts the x-axis at minus 2 units and y-axis at 2 units, a statement which correctly compares the two functions include the following: A. They have the same x-intercept and the same end behavior as x approaches ∞.

What is y-intercept?

In Mathematics, the y-intercept of any graph such as an exponential function, generally occur at the point where the value of "x" is equal to zero (x = 0).

What is the x-intercept?

In Mathematics, the x-intercept can be defined as the point at which the graph of an exponential function crosses the x-coordinate and the value of "y" is equal to zero (0).

Based on the information provided about the graph of function f, the x-intercept and y-intercept include the following:

x-intercept = (-2, 0).

y-intercept = (0, 2).

Furthermore, the x-intercept and y-intercept of function g include the following:

x-intercept = (-2, 0).

y-intercept = (0, 8).

Therefore, we can logically conclude that both functions have the same x-intercept of -2.

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What is GCF of the following rational expression?
5x(x-2)/(x-2)(x+4)

Answers

15289 because I said so and I am a genuis

Adrian grabbed a bag of mandarin oranges off the shelf and spilled them all out on the counter. He divided them into 4 piles, but there was 3 left over. He rearranged them into 5 piles but this time there were 2 left over. Then he tried putting them into six piles, but there were 3 left over. When he tried 7 piles there were 3 left over again. Finally he put them into 3 piles and he didn’t have any left over. If the number of mandarins in the bag was less than 100, how many mandarins were in the bag?

Answers

The number of mandarins in the bag is 3 * 33 + 3 = 102 mandarins.

How did we determine the values?

This is a Diophantine equation problem, which is a type of mathematical problem that looks for integers that satisfy a given equation.

We know that the number of mandarins in the bag is equal to 4n + 3, 5m + 2 and 6p + 3 and 7q + 3 for some integers n, m, p and q.

We also know that the number of mandarins in the bag is equal to 3r, where r is an integer.

From the information provided, we can set up the following equation:

4n + 3 = 5m + 2 = 6p + 3 = 7q + 3 = 3r

Now we can use the information that when he finally put them into 3 piles and he didn't have any left over, meaning that the number of mandarins in the bag is divisible by 3, we can see that the remaining number in each case is 3.

Thus the number of mandarins in the bag is 3 * (some integer) + 3.

We can then use the information that the number of mandarins in the bag was less than 100, meaning the possible value of r is less than 34.

Testing values of r starting from 1, we can see that r = 33 satisfies the equation and the number of mandarins in the bag is 3 * 33 + 3 = 102 mandarins

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What are the solutions of x² - 5x+7=0?
OA. x =
OB. x =
5+3² or x = 5-3i
2
2
5+√2 or x = 5-√2
3
3
5+i√2
2
O C. x =
O D. x = 5+√3
2
or x =
5-i√2
2
or x = 5-i√3
2

Answers

On solving the provided question, we can say that quadratic equation x² - 5x+7=0 => x = 1 , -3

What is quadratic equation?

A quadratic equation is x ax2+bx+c=0, which is a quadratic polynomial in a single variable. a 0. The Fundamental Theorem of Algebra ensures that it has at least one solution since this polynomial is of second order. Solutions may be simple or complicated. An equation that is quadratic is a quadratic equation. This indicates that it has at least one word that has to be squared. The formula "ax2 + bx + c = 0" is one of the often used solutions for quadratic equations. where are numerical coefficients or constants a, b, and c. where the variable "X" is unidentified.

x² - 5x+7=0

x(x-1) +3(x-1)

(x-1)(x+3) = 0

x = 1 , -3

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Help me solve the problem of this

Answers

In the given word problem amount does Teresa spends is $16.50.

What is word problem?

A math word problem is a question that is written as one or more sentences and asks students to use their mathematical understanding to solve an issue from "real world." In order  to understand the word problem, they must be familiar with the terminology that goes along with the mathematical symbols that they are used to.

Here,

The amount does Jayson Spends = $3.75

According to the question,

Myra spends 3times as much as Jayson . then

Amount does Myra spends = 3× 3.75 = $11.25.

Now Teresa spends $5.25 more than Myra then,

Amount does Teresa spends = 11.25+5.25 = $ 16.50.

Hence In the given word problem amount does Teresa spends is $16.50.

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Write a doubles fact you can use to find the sum. Write the sum.

2 + 3 =5

Answers

Answer:

Step-by-step explanation:

I think doubles facts are when you use a different equation to get the same sum, right?

In that case here are some doubles.

1+4=5

2+3=5

3+2=5

4+1=5

5+0=5

PLEASE HELLPPPPPPPP!!!!!!

Answers

Considering the graph of the curve shown if f(x) = 0 then the value of x is

(-1.4 0) and (1.4, 0)

How to find the value of x

The x-intercepts of the function's graph, or the zero of a function, is the location on a graph where the function's graph crosses the x-axis.

This is the solution of the graph. it also called the x intercept or the zero

Examining the graph, the points are in exact spot in both the negative and positive part of the x axis

This spot is between 1 and 2 and not up to half way while moving from 1 to 2.

The point can be estimated to be 1.4 hence the values are

(-1.4 0), (1.4, 0)

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when would the following conditional be false? If you work 20 hours a week, then you would make $125.00
a.you work 25 hours a week, and you make $125.00
b. you work 25 hours a week, nd you make $175.00
c. you work 20 hours a week, and you make $175.00
d. you work 20 hours a week, and you make $125.00

Answers

The conditional, "If you work 20 hours a week, then you would make $125.00" would be false if this holds true:

c. You work 20 hours a week, and you make $175.00

What is the wrong conclusion?

To arrive at the wrong conclusion, we need to look out for the statement that directly violates the hypothesis that working 20 hours a week will yield $125.

The answer that is in direct conflict with this statement is option C. Here, instead of making $125, the person makes $175 and this is way above the conclusion reached in the original sentence. So, the wrong conditional is C.

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Using the maxima and minima of the function, produce upper and lower estimates of the integral
I=∫∫De^5(x2+y2)dA where D is the circular disk: x^2+y^2≤4

Answers

In calculus, we can find the maximum and minimum value of any function or variable without on looking at the graph of the function.

Maxima will be the giant point on the curve within the given range and minima would be the minimum point on the curve. The combination of both is extrema.

Since 0 ≤ x^2 + y^2 ≤ 6, we have e^ (6*0) ≤ e^ (6(x^2 + y^2)) ≤ e^ (6*6) on D.

So, ∫∫ 1 dA ≤ ∫∫ e^ (6(x^2 + y^2)) dA ≤ ∫∫ e^36 dA

==> 6π ≤ ∫∫ e^ (6(x^2 + y^2)) dA ≤ 6π * e^36, since the area of D is .

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Rewrite this number in standard (decimal) notation without the use of exponents or scientific notation:
6.758 x 10^10

Answers

Therefore , the solution of the given problem of expression comes out to be sixty-seven billion five hundred eighty million.

How is expression selected?

Each variable must be replaced with a number and arithmetic operations must be performed to check an algebraic equation. Given that 6 + 6 equals 12, the answer variable in the aforementioned case is comparable to 6. We can substitute the variables values with those we know in order to evaluate the expression.

Here,

6.758 1010 in scientific notation

The scientific notation is = 6.758e10.

Engineering notation: 67.58 109 billion; prefix: giga- (G)

6.758 x 1010 standard form

10 Order of Magnitude for scientific notation and conventional forms

=>67580000000  (real number) 

=>67,580,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000  

sixty-seven billion five hundred eighty million

word form.

Therefore , the solution of the given problem of expression comes out to be sixty-seven billion five hundred eighty million.

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Write the equation of the line shown.​

Answers

Answer:

y = -2x

Step-by-step explanation:

The equation is y = mx +b

m = the slope

b = y-intercept

The slope = rise/run

Let's pick 2 points (0,0) (2,-4); we see the y decrease by 4 and the x increase by 2, so our slope is

m = -4/2 = -2

Y-intercept is when x = 0, y-intercept is located at (0,0)

So our equation is

y = -2x

Herman invests
$
6
,
400
at
5.5
% interest for
7
years compounded quarterly. Find the amount of money in the account after
7
years.

Answers

Answer:

2000 dollar and 6% impound will be your answer

Step-by-step explanation:

2) A robot vacuum cleans a dirty floor using multiple passes. During each pass, 17% of the dirt is removed. If the floor initially has 460.0 ml of dirt, how much dirt will remain after 9 passes?

Answers

86 ml of dirt will remain after 9 passes

What is an equation?

An equation is an expression showing the relationship between numbers and variables.

Let y represent the amount of dirt on the floor after x passes, hence:

y = abˣ

During each pass, 17% of the dirt is removed, therefore b = 100% - 17% = 0.83

If the floor initially has 460.0 ml of dirt, then a = 460.

The equation becomes:

y = 460(0.83)ˣ

After 9 passes:

y = 460(0.83)⁹ = 86

86 ml of dirt will remain

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What is the third angle of the triangle if the angles are 15 and 86

Answers

Answer:

79 degrees

Step-by-step explanation:

there are 180 degrees in a triangle

if you deduct the sum of 15 and 86, which is 101, the third angle must measure 79 degrees

The three angles in a triangle always add up to 180 degrees. So:
15+86+x=180
x= 180-101
x = 79
The third angle is 79 degrees

ANSWER PROPERY OR ELSE
Turn the fractions into decimals.

Answers

Answer:

a. 2/3 < 5/3

b. 2 1/2 > 9/4

c. 2/5 < 3/7

a. 5/3 > 1 1/3

b. 2 1/2 = 10/4

c. 3 5/6 < 21/4

Step-by-step explanation:

2/3 = 0.6667 (Rounded Answer)

5/3 = 1.6667 (Rounded Answer)

2 1/2 = 2.5

9/4 = 2.25

2/5 = 0.4

3/7 = 0.4286 (Rounded Answer)

5/3 = 1.6667 (Rounded Answer)

1 1/3 = 1.3334 (Rounded Answer)

2 1/2 = 2.5

10/4 = 2.5

3 5/6 = 3.8334  (Rounded Answer)

21/4 = 5.25

You are reducing a map of dimensions 2 ft by 3 ft to fit on a piece of paper 8 In by 10 in. What are the dimensions of the largest possible map
that can fit on the page?
A
2/3
in by 10 in
85 m by 10 m
Cam by 6 in
D. in by 10 in

Answers

Therefore , the solution of the given problem of area is largest map that may be utilized while still fitting on the page is 20/3 inches by 10 inches.

Area : What is it?

The term "area" refers to how much room a 2D structure or surface occupies. We use these units to measure surface in cm2 or m2. By dividing the length by the breadth of a form, you can determine its area.

Area = length times breadth and Perimeter = 2 (length + width)

Here,

Given: 2 feet by 3 feet is the size of the map.

8 by 10 inches is the size of a sheet of paper; in inches:

12 inches per foot

24 inches are equal to two feet, or two times twelve.

36 inches are equal to three feet, or three times twelve.

Scale factor is 24/36, or two-thirds.

Paper's longer side equals ten inches.

Using the scale, determine how long the shorter side is:

2/3 = x/10

the cross-multiply

3x = 2 × 10

3x = 20

x = (20 ÷ 3)

x=6.23 inches

The largest map that may be utilized while still fitting on the page is 20/3 inches by 10 inches.

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(a)
Two friends, Jeanette and Zoe, are growing out their hair. They plan to cut it off at a certain point and donate it to a charity that makes wigs for people with cancer. Jeanette's hair is already 29 centimeters long and grows at a constant rate of 1 centimeter per month. Zoe's hair is 12 centimeters and growing at a speed of 2 centimeters per month. If the girls get their hair cut on a certain day, they will have exactly the same length to donate. How long will their hair be? How long will that take?





Part A:



Using the variables y for total growth and x for rate of change answer the questions below.



Create the equation for Jeanette's hair growth:


Create the equation for Zoe's hair growth

Answers

Answer:

Step-by-step explanation:

J:  y = 29 cm + (1 cm/mo)x

Z:  y = 12 cm + (2 cm/mo)x

29 cm + (1 cm/mo)x =  12 cm + (2 cm/mo)x

Solve for x to find how many months it will take for them to have the same length of hair:

29 cm - 12 cm = (2 cm/mo)x - (1 cm/mo)x

17 cm = (1 cm/mo)x

x = (17 cm) / (1 cm/mo) = 17 months

Plug this value for x (17 months) into the equations to find how long their hair will be:

J:  y = 29 cm + (1 cm/mo)(17 mo) = 46 cm

Z:  y = 12 cm + (2 cm/mo)(17 mo) = 46 cm

This shows that it will take 17 months for each girl's hair to be 46 cm long.

Rick read half the amount of time that Rita read. Rita read one-third of the time that Larry read. Larry read twice as long as Tina. If Tina read for 3 hours, how long did Rick read?​

Answers

Answer:

Rick read for 1 hour.

Step-by-step explanation:

Tina read 3 hours, Larry read twice as long that is 6 hours, Rita read one third of Larry's so 6 times one-third is 2 hours, half that for Rick's hours and you get 1 hour

Translate to an algebraic expression: one-fifth of a number, k

Answers

The mathematical expression for the given algebraic expression is,

⇒ k / 5

What is an expression?

Mathematical expression is defined as the collection of the numbers variables and functions by using operations like addition, subtraction, multiplication, and division.

We have to given that;

The algebraic expression is,

⇒ One-fifth of a number, k

Now, We can write the mathematical expression for the given algebraic expression is,

⇒ One-fifth of a number, k

⇒ 1/5 of k

⇒ 1/5 × k

⇒ k / 5

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The sum of three consecutive numbers is ninenty- nine. What is the smallest of the three numbers?

Answers

Answer: 32

Step-by-step explanation:

32+33+34 = 99

They are consecutive numbers.

Penny reads 14 pages in 1/4 hour. What is the unit rate for hours per page

Answers

Answer:

56 pages per hour

Step-by-step explanation:

Penny reads 14 pages in 1/4 of an hour.

An hour is 4 times more than 1/4 of an hour (you could think of it as 15 minutes compared to 60 minutes)

Multiply the amount penny reads in 1/4 of an hour (14 pages) by 4 to get the rate she reads in 1 hour.

14 x 4 = 56

Now add the rate of time (per hour) to get that she reads a total of 56 pages per hour.

Hope this helps!

Rowan bought a large bag of jellybeans. She divided the jellybeans into 9 smaller bags that each contained 6 ounces. Write a division EQUATION (not answer) that could be used to find the amount of jellybeans, b, in ounces, that were in the original bag that Rowan bought.

Answers

The division equation that could be used to find the amount of jellybeans, b, in ounces, that were in the original bag that Rowan bought is given as follows:

6 = b/9.

How to obtain the division equation?

The division equation is obtained applying the proportions in the context of this problem.

The number of ounces per bean is given by the division of the total amount of jellybeans and the number of bags.

The parameters for this problem are given as follows:

6 ounces per bag.9 bags.

Hence the division equation is given as follows:

6 = b/9.

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Situation #1
The ratio of the interior angles of a hexagon is 5:5:6:7:8:9.
1a. What is the measurement of the 10 points
second-largest interior angle in this
hexagon?
Your answer:
1b. What is the measurement of the 10 points
interior angle that appears twice in
this hexagon?
Your answer:

Answers

Answer:

  a) 144°

  b) 90°

Step-by-step explanation:

You want the measures of the 2nd largest, and the smallest, of the angles in a hexagon whose ratios are 5:5:6:7:8:9.

Hexagon

The interior angles of a hexagon will have a sum of ...

  180°×(n -2) = 180°×(6 -2) = 720°

Ratio

The sum of the numbers in the given ratio is ...

  5+5+6+7+8+9 = 40

This tells us that multiplying the ratio values by 720/40 = 18 will give the angle values:

  90:90:108:126:144:162

Second largest

The second largest angle is 144°.

Repeated

The smallest angle, 90°, is the one that is repeated.

NO LINKS!!
The number of people that drink Root Beer instead of Coca-Cola in Outback, Kentuck has been declining at the rate of 6.5% per year. As of Sept. 1983, the number of people who still drink Root Beer was 5480. (NOT MULTIPLE CHOICE)

a. Write an exponential equation that will represent the number of Root Beer loyalists in Outback for any year.

b. How many Root Beer loyalists should there be as of September 2023? Show or explain how you know.

Answers

Answers in bold:Part A)     y = 5480*0.935^xPart B)     373 people

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

Explanation:

Part A

x = number of years after 1983

Example: x = 2 is the year 1985 since 1985-1983 = 2.

The number of people who drink this beverage declines by 6.5% each year. The multiplier is 1+r = 1+(-0.065) = 0.935

Meaning that if 6.5% of the people leave, then 93.5% remain. The two percentages add to 100%.

This value 0.935 is the base of the exponent portion. We have 0.935^x as the exponent portion.

Out front is the value 5480 which is the starting amount of people.

This leads to the exponential equation y = 5480*0.935^x

It is of the form y = ab^x

a = 5480 = starting population

b = 0.935 = decay factor

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

Part B

The timespan from 1983 to 2023 is 40 years (because 2023-1983 = 40).

Which means we plug x = 40 into the equation we found in part A.

y = 5480*0.935^x

y = 5480*0.935^40

y = 5480*0.06799303620922

y = 372.601838426526

y = 373

Be sure to round to the nearest whole number.

We expect or predict there will be approximately 373 people who remain loyalists to this root beer as of September 2023.

Answer:

Part (a)

[tex]y=5480(0.935)^x[/tex]

where:

x is the number of years after 1983.y is the total number of Root Beer loyalists.

Part (b)

373

Step-by-step explanation:

[tex]\boxed{\begin{minipage}{9 cm}\underline{General form of an Exponential Function}\\\\$y=ab^x$\\\\where:\\\phantom{ww}$\bullet$ $a$ is the initial value ($y$-intercept). \\ \phantom{ww}$\bullet$ $b$ is the base (growth/decay factor) in decimal form.\\\end{minipage}}[/tex]

The initial number of people who drink Root Beer (in September 1983):

a = 5480

If the number of people that drink Root Beer instead of Coca-Cola has been declining at the rate of 6.5% per year, then:

b = 100% - 6.5% = 93.5% = 0.935

Therefore, an exponential equation that represents the number of Root Beer loyalists in Outback for any year is:

[tex]y=5480(0.935)^x[/tex]

where:

x is the number of years after 1983.y is the total number of Root Beer loyalists.

The number of years between September 1983 and September 2023 is:

2023 - 1984 = 40 years

To calculate how many Root Beer loyalists should there be as of September 2023, substitute x = 40 into the equation found in part (a):

[tex]\implies y=5480(0.935)^{40}[/tex]

[tex]\implies y=5480(0.0679930362...)[/tex]

[tex]\implies y=372.601838...[/tex]

[tex]\implies y=373[/tex]

Therefore, there should be approximately 373 Root Beer loyalists as of September 2023.

H(x) = (x-1)^2 -9 plot the x intercept

Answers

Answer:

  x = -2 and 4

Step-by-step explanation:

You want a plot of the x-intercepts of H(x) = (x -1)² -9.

X-intercepts

The x-intercepts are the points where the graph crosses the x-axis, the points where H(x) = 0. Solving, we get ...

  H(x) = (x -1)² -9

  9 = (x -1)² . . . . . . . . add 9

  ±3 = x -1 . . . . . take the square root

  ±3 +1 = x = {-2, 4} . . . . . add 1

Plot

The attached graph shows the coordinates of the x-intercept points on the x-axis. The coordinates of the vertex of the parabola are also shown.

Solve this problem please

Answers

Answer:

[tex]8x-10[/tex]

Step-by-step explanation:

[tex]5x+3(x-4)+2[/tex]

Distribute:

[tex]=5x+(3)(x)+(3)(-4)+2\\=5x+3x+-12+2[/tex]

Combine Like Terms:

[tex]=5x+3x+-12+2\\=(5x+3x)+(-12+2)\\=8x+-10\\= 8x - 10[/tex]

Let W1 be the set: Determine if W1 is a basis for R3 and check the correct answer(s) below. O A. W1 is not a basis because it does not span R3. O B. W1 is a basis. O C. W1 is not a basis because it is linearly dependent.

Answers

The set W1 could be a basis for R3 if it spans R3 and is linearly independent, but without the specific elements of W1, it's not possible to determine if it meets those criteria.

The specific elements that make up the set W1. However, I can tell you that to be a basis for R3, a set of vectors must meet two criteria:

The set must span R3, meaning that any vector in R3 can be written as a linear combination of the vectors in the set.The set must be linearly independent, meaning that no vector in the set can be written as a linear combination of the other vectors in the set.

So, depending on the specific elements of W1, it could be either A, B, or C.

If the set W1 doesn't span R3, it would be A.

If the set W1 is linearly dependent, it would be C.

If both conditions are met the set is a basis, so the answer would be B.

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180.4 is what percent of 128? Rounded to the nearest tenth.

Answers

Answer:

180.4 is 140.9% of 128.

Step-by-step explanation:

180.4 is what percent of 128 Rounded to the nearest tenth?

A common way of solving these types of problems is to utilize the [tex]\frac{is}{of}[/tex] x 100% formula.This works by using the number before is as the numerator and the number after of as the denominator [tex]\frac{180.4}{128}[/tex].Once the dividend is achieved, multiply by 100 and then round the number to the nearest tenth.[tex]\frac{180.4}{128}[/tex] = 1.40931.409 x 100% = 140.93%Rounded to the nearest tenth is = 140.9%

Please answer I would really really appreciate it !

Answers

Answer:

92.5 cubic units

Choice A

Step-by-step explanation:

To approach this problem, separate out the composite solid figure into individual easily manageable components

At the bottom we have a rectangular prism which has a base length of 2a, a height of a and a width of c

Its volume = L X H X W = 2a·a·c= 2a²c

Plugging in values for a and c we get

Volume of rectangular prism

= 2 x (3.7)² x 2

= 54.76 cubic units

On top of this rectangular prism are two right-angled triangular prisms

The volume of a right-angled triangular prism =

Here height = b (confusing :)

base = a

width = c

So volume of each triangular prism
[tex]=\textrm{$\dfrac{1}{2} \times $ base x height x width}\\\\= \dfrac{1}{2} a \times b \times c\\\\ = \dfrac{1}{2} \times 3.7 \times 5.1 \times 2\\\\= 18.87[/tex]

Since there are 2 such prisms the volume of both

= 18.87 x 2 = 37.74 cubic units

Total volume of composite solid = 54.76 + 37.74 = 92.5 cubic units

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