Question 10
Divide £64 in the ratio 3:5

Answers

Answer 1

Answer:

24:40

Step-by-step explanation:

3:5

This means there are 8 divisions altogether - 8 parts to be split (3+5=8)

64 / 8 = 8

8x3 = 24

8x5 = 40

£24:£40

Hope this makes sense!


Related Questions

Find the slope of each graph by comparing the ratio of the rise over the run. (only do #3)

Find the slope of each graph by comparing the ratio of the rise over the run. (only do #3)

Answers

Answer: undefined

Step-by-step explanation:

Question 3 is undefined.

rise/0 is undefined.

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Answers

Answer: i think C correct me if i am wrong

Step-by-step explanation:

Parallel lines e and f are cut by transversal b. Horizontal and parallel lines e and f are cut by transversal b. At the intersection of lines b and e, the uppercase right angle is (2 x + 10) degrees. At the intersection of lines b and f, the bottom left angle is (3 x minus 15) degrees. What is the value of x?

Answers

Answer:

x = 25

Step-by-step explanation:

Alternate exterior angles are equal.

3x - 15 = 2x +10

3x        = 2x + 10 + 15

3x - 2x = 25

         x = 25

Answer:

c 110

Step-by-step explanation:

edge 2021

3.- Get the minimal expression for the function: xyz' + xy'z + xy'z' + x'yz + x’yz' + x'y'z. Use Boolean algebra or Karnaugh's map.

Answers

The minimal expression for the function xyz' + xy'z + xy'z' + x'yz + x'yz' + x'y'z is z'x + zxy' + x'xy'.

Karnaugh's map, also known as a K-map, is a graphical method used in Boolean algebra to simplify logical expressions and Boolean functions. It provides a systematic way to visualize and analyze the relationships between inputs and outputs in a truth table.

A Karnaugh map is represented as a grid or table, with each cell corresponding to a unique combination of input variables. The number of cells in the grid depends on the number of input variables in the Boolean function.

To minimize the expression xyz' + xy'z + xy'z' + x'yz + x'yz' + x'y'z using Boolean algebra, we can simplify it step by step using various Boolean laws and identities. Here's the process:

1. Group terms with common factors:

xyz' + xy'z + xy'z' + x'yz + x'yz' + x'y'z

= z'(xy + x'y') + z(xy' + x'y) + xyz'

= z'(x(y + y') + xy) + z(xy' + x'y) + xyz'

2. Apply the complement law: x + x' = 1

= z'(x + xy) + z(xy' + x'y) + xyz'

= z'x + z(xy' + x'y) + xyz'

3. Distribute z in the second term:

= z'x + zxy' + zx'y + xyz'

4. Group terms with common factors:

= z'x + zxy' + (zx'y + xyz')

= z'x + zxy' + (z + x')(xy')

5. Apply the distributive law: (A + B)(A + C) = A + BC

= z'x + zxy' + (z + x')(xy')

= z'x + zxy' + zxy' + x'xy'

= z'x + 2zxy' + x'xy'

6. Simplify the expression by removing the repeated terms:

= z'x + zxy' + x'xy'

Therefore, the minimal expression for the function xyz' + xy'z + xy'z' + x'yz + x'yz' + x'y'z is z'x + zxy' + x'xy'.

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The diffusion equation can be written as R2=4Dt where R is the average displacement, D is the diffusion constant, and t is the time. What can you say about the relationship between average displacement squared (R2) and time (t)? (Is it linear, exponential, etc.?)
Question 10
For the analysis, we will include a trendline on our R2 vs. t graph. The trendline equation has the form y=mx+b. Which variable from the diffusion equation corresponds to y in the trendline equation? Which variable from the diffusion equation corresponds to x in the trendline equaton?
Question 11
Given your answer to question 10, how could you solve for the diffusion constant in terms of the slope and a constant?
Question 12
Suppose your trendline equation is y=1.24x+5.63 Solve for the diffusion constant.

Answers

The fοrmula D = m/4, we can calculate the diffusiοn cοnstant 'D' as:

D = 1.24/4 = 0.31

What is a Diffusiοn?

Diffusiοn is the prοcess by which particles οf a substance mοve frοm an area οf high cοncentratiοn tο an area οf lοwer cοncentratiοn, resulting in a net mοvement οf particles dοwn their cοncentratiοn gradient.

This οccurs due tο the randοm mοtiοn οf individual particles, which leads tο a tendency fοr particles tο spread οut and becοme evenly distributed οver time.

Answer tο Questiοn 9:

The relatiοnship between average displacement squared (R²) and time (t) is linear.

Answer tο Questiοn 10:

The variable 'R2' in the diffusiοn equatiοn cοrrespοnds tο 'y' in the trendline equatiοn, and the variable 't' in the diffusiοn equatiοn cοrrespοnds tο 'x' in the trendline equatiοn.

Answer tο Questiοn 11:

We can sοlve fοr the diffusiοn cοnstant 'D' in terms οf the slοpe 'm' and a cοnstant 'c' by equating the diffusiοn equatiοn and the trendline equatiοn.

The diffusiοn equatiοn: R2 = 4Dt

The trendline equatiοn: y = mx + b

Substituting the cοrrespοnding variables, we get:

R2 = y, D = cοnstant, t = x, m = slοpe, b = cοnstant

Sο, we have:

R2 = 4Dt

y = mx + b

Equating the twο equatiοns, we get:

y = 4Dx + 0 (since b = 0)

Cοmparing this with the trendline equatiοn y = mx + b, we can see that:

m = 4D

Therefοre, we can sοlve fοr 'D' as:

D = m/4

Answer tο Questiοn 12:

Given the trendline equatiοn y = 1.24x + 5.63, we can see that the slοpe 'm' is 1.24.

Using the fοrmula D = m/4, we can calculate the diffusiοn cοnstant 'D' as:

D = 1.24/4 = 0.31

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prove that a>b and c<0, then a/c < b/c is true

Answers

We have proven that if a>b and c<0, then a/c < b/c as shown below

Proving expressions

From the question, we are to prove the given expression.

To prove that if a>b and c<0, then a/c < b/c

We will choose some numbers to represent the letters a, b, and c that satisfy the given conditions

From the given information,

a > b

Let a = 16

and b = 8

Also, from the given information

c<0

Let c = -4

Now, evaluate a/c

a/c = 16/-4

a/c = -4

Evaluating b/c

b/c = 8/-4

b/c = -2

-4 < -2

Therefore,

a/c < b/c

Hence, we have proven that if a>b and c<0, then a/c < b/c

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The table shows conversions of common units of length.

Unit of Length
Customary System Units
Metric System Units
1 inch
2.54 centimeters
1 foot
0.3048 meters
1 mile
1.61 kilometers

Approximately how many inches are in 2500 millimeters?
64 inches
98 inches
635 inches
984 inches

Answers

Answer:

98 inches

Step-by-step explanation:

30 millimeters is 1.18 inches, multiply it by 83 to get 2500 millimeters, Then you get 98

Answer:

The person above me is correct. Therefore you should make him/her brainlyest.

Step-by-step explanation:

i taking the quiz rn

what is the modular inverse of $11$, modulo $1000$? express your answer as an integer from $0$ to $999$, inclusive.

Answers

The modular inverse of 11, modulo 1000 is 901. Expressing the answer in integer form.

To find the modular inverse of 11  modulo 1000, we need to find an integer x such that \($11x\equiv1\pmod{1000}$\).

One way to find the modular inverse is to use the extended Euclidean algorithm. Using this algorithm, we can find the greatest common divisor of 11 and 1000 and express it as a linear combination of 11 and 1000.

We can then use the coefficients of this linear combination to express 1 as a linear combination of 11 and 1000.

Applying the extended Euclidean algorithm, we have:

1000= 11 *90 + 10

11 = 10 *1 + 1

Working backward, we can express 1 as a linear combination of 11 and 1000:

1 =11 - 10* 1

= 11 - (1000 - 11*90)

= 901 * 11 - 1 *1000

Therefore, the modular inverse of 11 modulo 1000 is 901, since

11*901=1 mod{1000}.

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Jessie paid $43.75 for 5 movie tickets. Each ticket cost the same amount. What was the cost of each movie ticket in dollars and cents?

Answers

If I’m not wrong each ticket was 8.75
Because 43.75 divided by 5= 8.75:)

Answer:

$8.75

Step-by-step explanation:

Divide $43.75 by 5 to get the cost of ONE movie ticket like so:

$43.75 / 5 movie tickets = $8.75 per ticket.

Therefore, ONE ticket costs $8.75.

In the first four months of the year, Noralie’s jewelry sales were declining. After April, her sales began to improve. Which of the following tables of data represents Noralie’s jewelry sales if the sales are represented by the following function?

In the first four months of the year, Noralies jewelry sales were declining. After April, her sales began

Answers

Answer:

The first one at the top is correct why?

Step-by-step explanation:

because 2 times 2 is 4 times 4 is 16 and the u divide them so that's why it is right I hope I help u understa

2. Jane bought three apples and two oranges. The total amount she paid was at most Php123.00. If x represents the cost of each apple and y represents the cost of each orange, which of the following mathematical statements represents the given situation?
a 3x + 2y 123
b. 3x + 2y < 123
c. 3x + 2y > 123
d. 3x + 2y < 123

HELP MEEEE​

Answers

Your multiple-choice selection has a typo. Notice that choice b and d is the same answer.

For at most we use the (<) symbol.

$3 per apple = 3x.

$2 per orange = 2y.

Answer: 3x + 2y < 123

Please help! Question is given below in form of image!

Please help! Question is given below in form of image!

Answers

Answer:

c

Step-by-step explanation:

Answer:

None of the choices are correct.

Step-by-step explanation:

\( 9x^3 + 9x^2 - 4x - 4 = 0 \)

The polynomial has 4 terms and no common factors. We can try factoring by grouping.

\( 9x^2(x + 1) - 4(x + 1) = 0 \)

\( (x + 1)(9x^2 - 4) = 0 \)

Now we factor the difference of squares.

\( (x + 1)(3x + 2)(3x - 2) = 0 \)

\( x + 1 = 0~~or~~3x + 2 = 0~~or~~3x - 2 = 0 \)

\(x = -1~~or~~x = -\dfrac{2}{3}~~or~~x = \dfrac{2}{3}\)

None of the choices are correct.

"Find all angles between 0 and 2π satisfying the condition cos θ = √3 / 2
Separate your answers with commas
θ=........ For the curve y = 19 cos(5πx + 9)
determine each of the following Note: Amplitude = .......
period = .....
phase shift = ....
Note : Use a negative for a shift to the left

Answers

The angles between 0 and 2π satisfying the condition cos θ = √3 / 2 are π/6 and 11π/6. For the curve y = 19 cos(5πx + 9), the amplitude is 19, the period is 2π/5, and the phase shift is π/5 to the left.

To find the angles between 0 and 2π satisfying the condition cos θ = √3 / 2, we can refer to the unit circle. At angles π/6 and 11π/6, the cosine value is √3 / 2.

For the curve y = 19 cos(5πx + 9), we can identify the properties of the cosine function. The amplitude is the absolute value of the coefficient in front of the cosine function, which in this case is 19. The period can be determined by dividing 2π by the coefficient of x, giving us a period of 2π/5. The phase shift is calculated by setting the argument of the cosine function equal to 0 and solving for x. In this case, 5πx + 9 = 0, and solving for x gives us a phase shift of -π/5, indicating a shift to the left.


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sec8.5: problem 4 previous problem problem list next problem (1 point) book problem 6 find the interval of convergence of the power series ∑n=1[infinity]n−−√3xn. the series is convergent from x = , left end

Answers

the series is convergent from x = -1 (left end) to x = 1 (right end).

To find the interval of convergence for the power series ∑n=1 to infinity of \(n^{(1/3)} * x^n\), we can use the ratio test.

The ratio test states that if the limit of the absolute value of the ratio of consecutive terms is less than 1, then the series converges. Mathematically, the ratio test can be expressed as:

lim┬(n→∞)⁡〖|(\(a_{(n+1)}/a_n)\)|〗 < 1

Let's apply the ratio test to the given series:

\(a_n = n^{(1/3)} * x^n\)

\(a_{(n+1)} = (n+1)^{(1/3)} * x^{(n+1)}\)

Taking the ratio of consecutive terms:

|a_(n+1)/a_n| = |((n+1)^(1/3) * x^(n+1)) / (n^(1/3) * x^n)|

Simplifying the expression:

\(|a_{(n+1)}/a_n| = |(n+1)^{(1/3)} * x / n^{(1/3)}|\)

Taking the limit as n approaches infinity:

lim┬(n→∞)⁡〖\(|(a_{(n+1)}/a_n)\)|〗 = lim┬(n→∞)⁡〖|\((n+1)^{(1/3)} * x / n^{(1/3)}|\)〗

Using the properties of limits, we can simplify the expression further:

lim┬(n→∞)⁡〖|(a_(n+1)/a_n)|〗 = lim┬(n→∞)⁡〖\(|(1 + 1/n)^{(1/3)} * x|\)〗

= 1 * |x|

= |x|

We know that |x| < 1 for convergence. Therefore, the interval of convergence for the given power series is -1 < x < 1.

To determine the left endpoint of the interval of convergence, we substitute x = -1 into the series:

∑n=1 to infinity of \(n^{(1/3)} * (-1)^n\)

This is an alternating series. When n is odd, the terms of the series will be positive, and when n is even, the terms will be negative. The series converges by the Alternating Series Test.

the left endpoint of the interval of convergence is x = -1.

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4. Calculate the area of the triangle.
20 mm
11 mm

Answers

I am assuming 20mm = breadth and 11mm = height

Ar of Triangle = 1/2 x b x h
= 1/2 x 20 x 11
= 110mm^2

(3,8) and (7,-7)
it’s for slope
like Y2 - Y1/X1-X2
i just don’t know what numbers go with what

Answers

Answer:-7-8/7-3

slope= -15/4

Step-by-step explanation:

(x1,y1),(x2,y2)

just plug in.

Answer:

-15/4

Step-by-step explanation:

formula for Gradient/slope=y2-y1/x2-x1

x1=3,x2=7,y1=8,y2=-7

M= -7-8/7-3

M=-15/4

i hope i helped

can someone help ill give brainliest

can someone help ill give brainliest

Answers

To find the perimeter you need to add all the sides. 7+7+6+6=26cm

A star sits at the top of a 27 foot tall christmas tree. the star is seen by a child who is standing 11 feet away from the tree.

to the nearest degree, what is the angle of elevation from the child to the star?

Answers

\(\tan x=\frac{27}{11} \\ \\ x=\tan^{-1} \left(\frac{27}{11} \right) \approx \boxed{68^{\circ}}\)

A star sits at the top of a 27 foot tall christmas tree. the star is seen by a child who is standing

The angle of elevation from the child to the star is 68°.

What is the concept of heights and distances?

The concept of heights and distances is the application of trigonometric ratios in real-life cases, to solve for the missing heights, distances, or the angle of sight from one point to the other.

How to solve the question?

In the question, we are informed that a star sits at the top of a 27-foot-tall Christmas tree, and it is seen by a child who is standing 11 feet away from the tree.

We are asked to find the angle of elevation from the child to the star.

We assume the 27-foot-tall Christmas tree to be AB, with the star at point A, C being the boy, and BC showing the distance between the boy and the tree to be 11 feet.

We are asked to find the angle of elevation from the child to the star, that is, we are asked to find angle C.

In triangle ABC,

tan C = AB/BC {tan θ = perpendicular/base},

or, tan C = 27/11,

or, C = tan⁻¹(27/11),

or, C = 67.83365417791754271396329239993‬° ≈ 68°.

Thus, the angle of elevation from the child to the star is 68°.

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A star sits at the top of a 27 foot tall christmas tree. the star is seen by a child who is standing

true or false: if you are given a graph with two shiftable lines, the correct answer will always require you to move both lines.

Answers

False. if you are given a graph with two shif table lines, the correct answer will always require you to move both lines.

In a graph with two shiftable lines, the correct answer may or may not require moving both lines. It depends on the specific scenario and the desired outcome or conditions that need to be met.

When working with shiftable lines, shifting refers to changing the position of the lines on the graph by adjusting their slope or intercept. The purpose of shifting the lines is often to satisfy certain criteria or align them with specific points or patterns on the graph.

In some cases, achieving the desired outcome may only require shifting one of the lines. This can happen when one line already aligns with the desired points or pattern, and the other line can remain fixed. Moving both lines may not be necessary or could result in an undesired configuration.

However, there are also situations where both lines need to be shifted to achieve the desired result. This can occur when the relationship between the lines or the positioning of the lines relative to the graph requires adjustments to both lines.

Ultimately, the key is to carefully analyze the graph, understand the relationship between the lines, and identify the specific criteria or conditions that need to be met. This analysis will guide the decision of whether one or both lines should be shifted to obtain the correct answer.

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$10,000 for 5 years at 4% interest

Answers

Simple interest earned on the principal amount $10,000 for 5 years at 4% interest per year will be $12,000.

As given in the question,

Simple Interest:

The simple interest is an amount that is paid for loan or borrowed money over a certain period at a fixed percentage of borrowed money.

Principal amount:

Principal amount is the money that is taken as loan or borrowed.

Formula of Simple Interest:

Simple interest = Principal amount × Rate × Time

Since,

Principal amount = $10,000

Rate = 4% per year

Time = 5 years

Then,

Simple interest = 10,000 × 4 × 5

Simple interest = $ 12000

Total value after 5 years = $ 12000

Principal amount = $ 10000

Interest Earned = (Total value) - (Principal amount)

Interest Earned = $ 12000 - $ 10000

Interest Earned = $ 2000

Therefore, simple interest earned on the principal amount $10,000 for 5 years at 4% interest per year will be $12,000.

The complete question is:

Fabian is taking out a loan in the amount of $10,000. His choices for the loan are a 5-year loan at 4% rate of interest .What is the amount of simple interest and interest earned Fabian would have to pay?

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Product of 6 1 5 x 79

Answers

Answer:

615×79=48,585

Step-by-step explanation:

hope it helps

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solve the system4x - 2y + 3z = -32x - 4y + 2z = 16x + 10z = -2enter your answer as an ordered triple

Answers

\(\begin{gathered} 4x-2y+3z=-3\ldots\ldots\text{.}(1) \\ 2x-4y+2z=1\ldots\ldots\ldots(2) \\ 6x+10z=-2\ldots\ldots\ldots..\ldots(3) \\ \text{Now, from the eqution (1) and (2) } \\ 4(\frac{1-2z+4y}{2})-2y+3z=-3 \\ 2-4z+8y-2y+3z=-3 \\ 2+3-z+6y=0 \\ 6y-z=-5 \\ z=6y+5\ldots\ldots\text{.}(4) \end{gathered}\)\(\begin{gathered} \text{Now, from equation (4) and (3) } \\ 6x=10(6y+5)-2 \\ 6x=60y+50-2 \\ 6x=60y+48 \\ x=10y+8\ldots\ldots\text{.}(5) \\ \text{Substitute all the value in the equation(1)} \\ 4(10y+8)-2y+3(6y+5)=-3 \\ 40y+32-2y+18y+15=-3 \\ 56y=50 \\ y=\frac{50}{56} \\ y=\frac{25}{28} \end{gathered}\)

Now, from equation (5)

\(\begin{gathered} x=10y+8 \\ x=10\times\frac{25}{28}+8 \\ x=16.92 \\ \text{Now, from the eqution(4)} \\ z=6y+5 \\ z=6\times\frac{25}{28}+5 \\ z=10.35 \end{gathered}\)

right trinagle xyz has legs of length xy = 12 and yz = 6. point d is chosen at randomw within the trianglexyz. what is the probability that the area of triangle xyd isd at most 12

Answers

The probability is equal to the ratio of the area of the region where the area of triangle XYD is at most 12 to the total area of triangle XYZ. The probability that the area of triangle XYD is at most 12 is 2/3 or 0.67.

Triangle XYZ has legs of length XY = 12 and YZ = 6. The area of triangle XYZ can be calculated using the formula A = (1/2) * base * height, where the base is XY and the height is YZ. Substituting the given values, we find that the area of triangle XYZ is 36 square units.

To determine the probability that the area of triangle XYD is at most 12, we need to consider the range of possible positions for point D within triangle XYZ.

The area of triangle XYD can also be calculated using the formula A = (1/2) * base * height, where the base is XY and the height is the perpendicular distance from point D to line XY. Since point D is chosen randomly within triangle XYZ, we can consider the ratio of the areas to determine the probability.

If the area of triangle XYD is at most 12, it means that the height of triangle XYD is at most (2 * 12) / XY = 2 units. Therefore, point D must lie within a region of height 2 units above line XY within triangle XYZ.

To calculate the probability, we compare the area of this region (a trapezoid shape) to the total area of triangle XYZ. The area of the trapezoid can be calculated using the formula A_trap = (1/2) * (base1 + base2) * height, where base1 and base2 are the lengths of the parallel sides of the trapezoid and height is the height of the trapezoid.

In this case, base1 = base2 = XY = 12, and the height of the trapezoid is 2. Plugging these values into the formula, we find that the area of the trapezoid is 24 square units.

Therefore, the probability that the area of triangle XYD is at most 12 is given by the ratio of the area of the trapezoid (24 square units) to the total area of triangle XYZ (36 square units), which simplifies to 24/36 = 2/3, or approximately 0.67.

In conclusion, the probability that the area of triangle XYD is at most 12 is 2/3 or approximately 0.67.

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What will be the values of x and y as a result of the following code? int x = 25, y = 8; x = y; x = 25, y = 8 x = 34, y = 8 x = 33, y = 8 x = 34, y = 9

Answers

The values of x and y as a result of the code are 8 and 8

How to determine the values of x and y as a result of the code?

The code is given as:

int x = 25, y = 8;

x = y;

At the first line, we have

x= 25 and y = 8

On the second line, where we have

x = y

This means that

x = 8 and y = 8

Hence, the values of x and y as a result of the code are 8 and 8

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Identify the slope of the following equation:
y= 5 - 3x
m=? b=?

Answers

Answer:

y = mx + b

M is slope, b is y intercept

y = -3x + 5

m = -3

b = 5

a coin is tossed 18 times. it lands on heads 12 times. what is the experimental probability of the coin landing on tails?

Answers

the experimental probability of the coin landing on tails is 1/3 or approximately 0.33 when expressed as a decimal when coin was flip 18 times and landed on heads 12times


In this case, the coin was flipped 18 times and landed on heads 12 times, so it landed on tails 6 times.

Therefore, the experimental probability of the coin landing on tails is 6/18, which simplifies to 1/3 or approximately 0.33.
. To calculate the experimental probability, follow these steps:

1. Determine the number of successful outcomes (times the coin landed on tails). In this case, the coin was tossed 18 times and landed on heads 12 times, so it must have landed on tails 6 times (18 - 12 = 6).

2. Determine the total number of trials (times the coin was tossed). In this case, it's 18.

3. Calculate the experimental probability by dividing the number of successful outcomes by the total number of trials:
Experimental probability of tails = (Number of tails) / (Total number of tosses) = 6 / 18

4. Simplify the fraction to get the experimental probability:
6 / 18 = 1 / 3

So, the experimental probability of the coin landing on tails is 1/3 or approximately 0.33 when expressed as a decimal.

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help !!!!!!!!!!!!!!!! plz

help !!!!!!!!!!!!!!!! plz

Answers

Answer:

5 > n + 10

8 x 7 < n

n/3 + 1

6 x 8 - 10 < n

n - 1 x n

n x -n + 7


\(given \: f(x) = \frac{4x - 10}{x - 2\)
determine the x and y intercept of f​

Answers

Given :-

f(x) = 4x - 10/ x -2

To Find :-

x and y intercept .

Solution :

Let ,

→ y = f(x)

So that ,

→ y = 4x - 10/ x -2

For finding x intercept , substitute y = 0 .

→ 0 = 4x - 10/x - 2

→ 4x - 10 = 0

→ 4x = 10

→ x = 10/4

→ x = 5/2

x = 2.5

For finding y intercept , put x = 0 .

→ y = 4*0 - 10 / 0 -2

→ y = -10/-2

y = 5

x intercept = (2.5,0)y intercept = (0,5)

Veronica’s favorite breakfast cereal costs $0.21 per ounce. How much would she spend on 16 ounces of cereal?​

Answers

Answer:

$3.36 for 16 ounces

Step-by-step explanation:

0.21×16=3.36

Answer:

$3.36 total

Step-by-step explanation:

0.21 * 16 = 3.36

(P.S., pls mark me brainliest, and have a nice day)

2-simplifica

1)x²-5x-16

x+2=

2)6an²-3b²n²

b4-4ab²+4a²=

3)4x²-4xy+y²

5y-10x

4)n+1-n³-n²

n³-n-2n²+2=

5)17x³y4z6

34x7y8z10=

6)12a²b³

60a³b5x6=

Answers

1.  x² - 5x - 16 can be written as (x - 8)(x + 2).

2. 6an² - 3b²n² = n²(6a - 3b²).

3. This expression represents a perfect square trinomial, which can be factored as (2x - y)².

4. Combining like terms, we get -n³ - n² + n + 1 = -(n³ + n² - n - 1).

5. 17x³y⁴z⁶ = (x²y²z³)².

6. 12a²b³ = (2a)(6b³) = 12a6b³ = 12a⁷b³x⁶.

Let's simplify the given expressions:

Simplifying x² - 5x - 16:

To factorize this quadratic expression, we look for two numbers whose product is equal to -16 and whose sum is equal to -5. The numbers are -8 and 2.

Therefore, x² - 5x - 16 can be written as (x - 8)(x + 2).

Simplifying 6an² - 3b²n²:

To simplify this expression, we can factor out the common term n² from both terms:

6an² - 3b²n² = n²(6a - 3b²).

Simplifying 4x² - 4xy + y²:

This expression represents a perfect square trinomial, which can be factored as (2x - y)².

Simplifying n + 1 - n³ - n²:

Rearranging the terms, we have -n³ - n² + n + 1.

Combining like terms, we get -n³ - n² + n + 1 = -(n³ + n² - n - 1).

Simplifying 17x³y⁴z⁶:

To simplify this expression, we can divide each exponent by 2 to simplify it as much as possible:

17x³y⁴z⁶ = (x²y²z³)².

Simplifying 12a²b³:

To simplify this expression, we can multiply the exponents of a and b with the given expression:

12a²b³ = (2a)(6b³) = 12a6b³ = 12a⁷b³x⁶.

Learn more about  expression from

https://brainly.com/question/723406

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