lateral surface for a triangular prism l=8 w=4 h=6

Answers

Answer 1

Answer:

? i need help

Step-by-step explanation:


Related Questions

Question 2 multiple choice worth 1 points)
(01.02 lc)
solve for x: 6x + 3 = 5x - 8
0-11
11
0-5
5

Answers

[tex]6x+3=5x-8[/tex] (given)

[tex]x+3=-8[/tex] (subtract 5x from both sides)

[tex]x=\boxed{-11}[/tex] (subtract 3 from both sides)

Quadrilateral ABCD was rotated 360° clockwise with the origin as the center of rotation to create a new figure. Which rule describes this transformation?

A (x, y)-(x,y)

B(x, y)(x, y)

c(x, y)-(x, y)

D (x, y)-(x, y)

Answers

The rules describes the transformation is (x, y)(x, y).

The correct option is (B)

what is Transformation?

A transformation is a general term for four specific ways to manipulate the shape and/or position of a point, a line, or geometric figure.

If the figure is rotated 360 degrees then the coordinates remains unchanged.

This is because when from where it started it stops there again.

As the 360 degree rotation is complete circle rotation.

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please help!! The dot plots below show the ages of students belonging to two groups of salsa classes:
Based on visual inspection, which group most likely has a lower mean age of salsa students? Explain your answer using two or three sentences. Make sure to use facts to support your answer.

Im thinking group A but at this point im just plain out confused

Answers

Group A I’m pretty confident with that answer

Let a population consist of the values ​cigarettes, ​cigarettes, and cigarettes smoked in a day. Show that when samples of size 2 are randomly selected with​ replacement, the samples have mean absolute deviations that do not center about the value of the mean absolute deviation of the population. What does this indicate about a sample mean absolute deviation being used as an estimator of the mean absolute deviation of a​ population?.

Answers

The "sample" with "mean absolute deviation" indicate about a sample mean absolute deviation is being used as an estimator of the mean absolute deviation of a​ population

Mean of the sample MAD=3.3Population MAD =6.4

What does this indicate about a sample mean absolute deviation used as an estimator of the mean absolute deviation of a​ population?

Generally,  The MAD measures the average dispersion around the mean of a given data collection.

[tex]1/n \sum_i-1^{n} |x_i -m(X)|[/tex]

In conclusion, for the corresponding same to mean

the sample  mean absolute deviation

7,7  ↔         0

7,21  ↔         7

7,22         ↔    7.5

21,7        ↔          7

21,21 ↔     0

21,22 ↔    0.5

22,7   ↔     7.5

Therefore

Mean of the sample MAD=3.3Population MAD =6.4

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HELP ITS ABOUT ANGLES :((((

Answers

Answer:

its D. 2 and 3

Step-by-step explanation: supplementary angles are angles that add up to 180 (or that make a straight line) the angle pairs that make a straight line are 1 and 2, 2 and 3, 3 and 4, and 4 and 1.
So D would be correct

Sara can travel 23 feet in 11 hours. Please calculate Sara's rate of speed. (round to 2 decimal places)

Answers

Answer:

12 is the answer

Step-by-step explanation:

FIRST do 23 - 11 and you will find your answer

1.1 divided by 1.54 simplified

Answers

Answer:

1•4

Step-by-step explanation:

1•54÷1•1

1•54

1•1

divide by 10 both side with can move decimal

15•4

11

=my answer is 1•4.

Answer:

The correct answer for algebraic expression 1.54÷1.1 is = 1.4.

Step-by-step explanation:

this is question based on simple algebra -

Simple Algebraic equations -  An algebraic equation can be defined as a mathematical statement in which two expressions are set equal to each other. The algebraic equation usually consists of a variable, coefficients and constants. we can apply many operations on algebraic equations like addition, subtraction, multiplication, division and raising to a power, and extraction of a root.

these equations are two algebraic expressions that are joined together using an equal to ( = ) sign. An algebraic equation is also known as a polynomial equation because both sides of the equal sign contain polynomials

so in the question algebraic operation used to solve is simple division.

therefore here in question we have to divide 1.54 with 1.1,

using the concept written above,

let the value of division be 'x'

we can write 1.54/1.1 = x

by dividing and multiplying the equation by 100 to remove the decimals.

            (1•54/ 1•1)×100/100    = x

                    154/110    =  x

now by simple division,

                      1.4   =  x  answer

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Add/Subtract the linear expression. -4(3x - 2) - 2(7x + 1)​

Answers

Answer:

10

Step-by-step explanation:

multiply -4 and 3 to get -12

multiply -12 and -2 to get 24

multiply 2 and 7 to get 14

multiply 14 and 1 to get 14

subtract 14 from 24 to get 10

If the 6th term of an arithmetic progres- sion is 11 and the first term is 1, find the common difference.​

Answers

Answer:

2

Step-by-step explanation:

An arithmetic progression with first term a and common difference d has the following first 6 terms:

a, a + d, a + 2d, a + 3d, a + 4d, a + 5d

We are given a = 1 and a + 5d = 11.

1 + 5d = 11

5d = 10

d = 2

Answer: The common difference is 2.

evaluate: (36/49)^1/2

Answers

Answer:

6/7, -6/7

Step-by-step explanation:

Given the equation y = x – 2, you substitute 5 for x. Check all true statements below.

Answers

The correct value of the given function at x = 5 is y =3.

What is Equation?

An equation is a mathematical statement with an 'equal to =' symbol between two expressions that have equal values.

Here, the given equation :

         y = x - 2

put x = 5 in the given equation, we get

        y = 5 - 2

        y = 3

Thus, the correct value of the given function at x = 5 is y =3.

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Which ordered pair is included in the solution set to the following system?

y > x2 + 1
y < x2 – x + 1


(–3, 4)
(–2, 6)
(0, 2)
(2, 4)

Answers

Inequalities help us to compare two unequal expressions. The correct option is B.

What are inequalities?

Inequalities help us to compare two unequal expressions. Also, it helps us to compare the non-equal expressions so that an equation can be formed. It is mostly denoted by the symbol <, >, ≤, and ≥.

The ordered pair which will satisfy both the inequalities will be the solution to the system of inequalities. Therefore, let's substitute each solution in the given inequalities,

A.) (–3, 4)

y > x² + 1

          4 > (-3)² + 1

Since the first inequality is not satisfied this is not a part of the solution.

B.) (–2, 6)

y > x² + 1

          6 > (-2)² + 1

          6 > 5

y < x² – x + 1

          6 < (-2)² - (-2) + 1

          6 < 7

Since both the inequalities are satisfied this is the solution to the given system of inequalities.

C.) (0, 2)

y > x² + 1

          2 > 0 + 1

          2 > 1

y < x² – x + 1

          2 < (0)² - (0) + 1

          2 < 1

Since the second inequality is not satisfied this is not a part of the solution.

B.) (2,4)

y > x² + 1

          4 > (2)² + 1

          4 > 5

Since the first inequality is not satisfied this is not a part of the solution.

Hence, the correct option is B.

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The length of a rectangle is 8 cm more than four times the width. If the perimeter of the rectangle is 46 cm, what are the dimensions? ​

Answers

Answer:

length = 20 cm

width = 3 cm

Step-by-step explanation:

If $a$ and $b$ are positive integers for which $ab - 6a + 5b = 373$, what is the minimal possible value of $|a - b|$?

Answers

Answer:

  31

Step-by-step explanation:

We can solve the given equation for 'b', then find the integer values of 'a' that make 'b' a positive integer. There are 3 such values. One of these minimizes the objective function.

__

solve for b

  ab +5b = 373 +6a . . . . . . isolate b terms by adding 6a

  b = (6a +373)/(a +5) . . . . . divide by the coefficient of b

  b = 6 +343/(a +5) . . . . . . . find quotient and remainder

integer solutions

The value of 'b' will only be an integer when (a+5) is a factor of 343. The divisors of 343 = 7³ are {1, 7, 49, 343}. so these are the possible values of a+5. Since a > 0, we must eliminate a+5=1. That leaves ...

  a = {7, 49, 343} -5 = {2, 44, 338}.

Possible values of b are ...

  b = 6 +343/{7, 49, 343} = 6 +{49, 7, 1} = {55, 13, 7}

Then possible (a, b) pairs are ...

  (a, b) = {(2, 55), (44, 13), (338, 7)}

objective function

The values of the objective function for these pairs are ...

  |a -b| = |2 -55| = 53

 |a -b| = |44 -13| = 31 . . . . . the minimum value of the objective function

  |a -b| = |338 -7| = 331

What are the first 10 digits after the decimal point (technically the hexadecimal point...) when the fraction frac17 is written in base 16?

Answers

We happen to have

[tex]\dfrac17 = \dfrac18 + \dfrac1{8^2} + \dfrac1{8^3} + \cdots[/tex]

which is to say, the base-8 representation of 1/7 is

[tex]\dfrac17 \equiv 0.111\ldots_8[/tex]

This follows from the well-known result on geometric series,

[tex]\displaystyle \sum_{n=1}^\infty ar^{n-1} = \frac a{1-r}[/tex]

if [tex]|r|<1[/tex]. With [tex]a=1[/tex] and [tex]r=\frac18[/tex], we have

[tex]\displaystyle \sum_{n=1}^\infty \frac1{8^{n-1}} = 1 + \frac18 + \frac1{8^2} + \frac1{8^3} + \cdots \\\\ \implies \frac1{1-\frac18} = 1 + \frac18 + \frac1{8^2} + \frac1{8^3} + \cdots \\\\ \implies \frac87 = 1 + \frac18 + \frac1{8^2} + \frac1{8^3} + \cdots \\\\ \implies \frac17 = \frac18 + \frac1{8^2} + \frac1{8^3} + \cdots[/tex]

Uniformly multiplying each term on the right by an appropriate power of 2, we have

[tex]\dfrac17 = \dfrac2{16} + \dfrac{2^2}{16^2} + \dfrac{2^3}{16^3} + \dfrac{2^4}{16^4} + \dfrac{2^5}{16^5} + \dfrac{2^6}{16^6} + \cdots[/tex]

Now observe that for [tex]n\ge4[/tex], each numerator on the right side side will contain a factor of 16 that can be eliminated.

[tex]\dfrac{2^n}{16^n} = \dfrac{2^4\times2^{n-4}}{16^n} = \dfrac{2^{n-4}}{16^{n-1}}[/tex]

That is,

[tex]\dfrac{2^4}{16^4} = \dfrac1{16^3}[/tex]

[tex]\dfrac{2^5}{16^5} = \dfrac2{16^4}[/tex]

[tex]\dfrac{2^6}{16^6} = \dfrac4{16^5}[/tex]

etc. so that

[tex]\dfrac17 = \dfrac2{16} + \dfrac4{16^2} + \dfrac9{16^3} + \dfrac2{16^4} + \dfrac4{16^5} + \dfrac9{16^6} + \cdots[/tex]

and thus the base-16 representation of 1/7 is

[tex]\dfrac17 \equiv 0.249249249\ldots_{16}[/tex]

and the first 10 digits after the (hexa)decimal point are {2, 4, 9, 2, 4, 9, 2, 4, 9, 2}.

The volume of a box is 5x^3 + 20x^2 + 15x cm^3. If the height of the box is 5x cm, find the width and length of the box.

Answers

Answer:

The product of the Width and Length is x^2 + 4x + 3 cm^2.

Step-by-step explanation:

The volume of a box = 5x^3 + 20x^2 + 15x cm^3.

Volume of a Box = W*L*H       [Width(W), Length(L), and Height(H)]

W*L*(5x) = 5x^3 + 20x^2 + 15x cm^3

W*L = (5x^3 + 20x^2 + 15x cm^3)/5x cm

W*L = x^2 + 4x + 3 cm^2

We know the area of the base of the box (W*L).  It is x^2 + 4x + 3 cm^2.

To find the actual width and length, we need to know one of the variables, L or W.  Without that, all we can say is that their product (W*L) is x^2 + 4x + 3 cm^2.

1. Identify your variables using let statements.

2. Determine the equations for the linear system.

3. Determine the solution to the linear system (point of intersection)

4. Explain the meaning of the solution using a therefore statement.

Chris is mixing 2 different types of fruit juice together for a summer drink. The two types of juices he is using is one that is 30% strawberry concentrate and the other is 55% lemon concentrate. If he wants 2 L that is 40% concentrate of the fruit juices, how much of each should be used to create the drink?

Answers

The meaning of the solution is; Therefore, 1.2 liters of the strawberry concentrate and 0.8 liters of the lemon concentrate.

What is the solution to the system of equations?

It follows from the task content that the variables are;

let x be the amount of 30% strawberry concentrate.

let y be the amount of 55% lemon concentrate.

The equations of the linear system according to the task content are as follows;

x + y = 20.30x + 0.55y = (2 ×0.4)

From the first equation; x = 2-y;

Hence, upon substitution; we have;

0.30(2-y) + 0.55y = 0.8

0.25y = 0.2.

y = 0.2/0.25 = 0.8L.

Hence, x = 2- 0.8 = 1.2L.

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The width of a rectangle measures (10u + 3) centimeters, and its length measures (7u - 8) centimeters. Which expression represents the perimeter, in centimeters, of the rectangle? The width of a rectangle measures ( 10u + 3 ) centimeters , and its length measures ( 7u - 8 ) centimeters . Which expression represents the perimeter , in centimeters , of the rectangle ? ​

Answers

Answer:

Perimeter of a rectangle: 2L + 2W

2(7u - 8) + 2(10u + 3)

= 14u - 16 + 20u + 6

= 34u - 10

A rectangle is a two-dimensional shape where the length and width are different.

The area of a rectangle is given as:

Area = Length x width

The perimeter of a rectangle.

P = 2 ( length + width)

The perimeter of the rectangle is represented by the expression

(34u - 10) centimeters.

What is a rectangle?

A rectangle is a two-dimensional shape where the length and width are different.

The area of a rectangle is given as:

Area = Length x width

We have,

The width of a rectangle = (10u + 3) centimeters.

The length of the rectangle =  (7u - 8) centimeters.

The perimeter of a rectangle is given as,

P = 2 ( length + width)

P = 2 ( 7u - 8 + 10u + 3)

P = 2 (17u - 5)

P = (34u - 10) centimeters.

Thus,

The perimeter of the rectangle is represented by the expression

(34u - 10) centimeters.

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The two-way table shows the estimated number of students who will enroll in three area high schools next year. a 5-column table has 4 rows. the first column has entries mount woodson high school, valley high school, riverside high school, total. the second column is labeled tenth grade with entries 110, 180, 160, 450. the third column is labeled eleventh grade with entries 120, 150, 140, 410. the fourth column is labeled twelfth grade with entries 80, 120, 200, 400. the fifth column is labeled total with entries 310, 450, 500, 1,260. in decimal form, to the nearest tenth, what is the probability that a randomly selected riverside high school student is in twelfth grade? 0.2 0.3 0.4 0.5

Answers

Answer:

A. 0.2

Step-by-step explanation:

First make the table.

                                          10-grade  11-grade  12-grade  Total

Woodson high school    |     110     |     120    |      80     |   310   |

Valley high school          |     180    |     150    |     120     | 450   |

Riverside high school     |     160    |     140    |     200    | 500   |

Total                                 |     450   |     410    |     400    | 1260 |

Question: In decimal form, to the nearest tenth, what is the probability that a randomly selected riverside high school student is in twelfth grade?

First, find 12-grade and riverside high school number. 200. Take the total lined up with total number, which is 1260, and divide 200 divided by 1260.

200/1260=0.2

The answer is 0.2.

Hope this helps!

If not, I am sorry.

Answer:

its .4

Step-by-step explanation:

i got it wrong when i tried it says it is .4 or the third option c

Use trigonometric identities to verify each expression is equal.

c) csc^2(x)-2csc(x)cot(x)+cot^2(x) = tan^2(x/2)

d) [cos(x)cos(y)][tan(x)+tan(y)] = sin(x+y)

Answers

Part (c)

[tex]\text{LHS}=\csc^{2} x-2\csc x\cot x+\cot^{2} x\\\\=(\csc x-\cot x)^{2}\\\\=\left(\frac{1}{\sin x}-\frac{\cos x}{\sin x} \right)^{2}\\\\=\left(\frac{1-\cos x}{\sin x})^{2}\\\\=\tan^{2} \left(\frac{x}{2} \right)\\\\=\text{RHS}[/tex]

Part (d)

[tex]\text{LHS}=[\cos x \cos y][\tan x+\tan y]\\\\=[\cos x\cos y]\left[\frac{\sin x}{\cos x}+\frac{\sin y}{\cos y} \right]\\\\=\sin x \cos y+\sin y \cos x\\\\=\sin(x+y)\\\\=\text{RHS}[/tex]

Which of the numbers below is greater than −7/3? Select all that apply. A) −3 B) −5.5 C) −2 D) −3/2 E) 1.25

Answers

Answer:

C, D and E

Step-by-step explanation:

The numbers which are greater than given number are : -2, -1.5, and 1.25.

What is Fraction?

A fraction represents a part of a whole or, more generally, any number of equal parts.

Here, given number: -7/3

or we can write this as -2.33

Now, Converting option fraction value into decimal

A). -3

B) -5.5

C). -2

D). -1.5

E). 1.25

On comparing options from the given value we get

the number which are greater than -2.33;   -2, -1.5, and 1.25

Thus, the numbers which are greater than given number are : -2, -1.5, and 1.25.

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A cyclist is stationary when a second cyclist passes travelling at a constant speed of 8 m s−1. The first cyclist then accelerates for 5 s at a constant rate of 2 m s−1 before continuing at constant speed until overtaking the second cyclist. By sketching both graphs, find the equations of the two straight line sections of the graphs and hence find how long it is before the first cyclist overtakes the second.

Answers

Answer:

im not too sure about that sorry!

Step-by-step explanation:

uiwgorihvncjkdnskv

It takes 15 seconds for the first cyclist to overtake the second cyclist.

How can you find how long it took before the first cyclist overtakes the second?

First, identify the two phases of the first cyclist's motion.

Phase 1: The cyclist accelerates from rest to a constant speed of 8 m/s.

Phase 2: The cyclist travels at a constant speed of 8 m/s.

Find the equations of the two straight-line sections of the graph.

The equations of the two straight-line sections of the graph are as follows:

Phase 1:

s = [tex]2t^2[/tex]

Phase 2:

s = 8t

where s is the distance traveled by the cyclist and t is the time

Set the two equations equal to each other to find the time it takes the first cyclist to overtake the second cyclist

The first cyclist overtakes the second cyclist when the first cyclist has traveled a distance of 8 m more than the second cyclist.

Let t be the time it takes the first cyclist to overtake the second cyclist.

The distance traveled by the first cyclist is then 8t, and the distance traveled by the second cyclist is 8(t - 5).

Setting these two expressions equal to each other, we get:

8t = 8(t - 5)

Solving for t, we get:

t = 15

Therefore, it takes 15 seconds for the first cyclist to overtake the second cyclist

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PLEASE HELP ME, I BEG OF YOU TO HAVE MERCY ON MY POOR SOUL

1. Calculate the slope of the trend line. (Choose two points on the line and find vertical change over horizontal change.)

2. Using the slope and y-intercept, write the equation of the trend line (y = mx + b).

3. Choose a "calories from fat" value that is not in your collected data set and that is at least 10 fat calories away from any collected value. Use the equation calculated in step to predict the number of fat grams in an item having that number of fat calories. Be sure to show your work.

4. Search for an item in a fast food menu having the same number of fat calories as the one you chose above. (If you cannot find the exact value, get as close as you can.) Compare the calculated value from step VI to this actual value. Explain why (or why not) you would have expected your prediction (calculated value) to be close to the actual value.

Answers

The answer for the following question is

1. m= 10  

2. y- intercept = 300

3. y = 10x + 300

What is Regression line?

A regression line is a graphic representation of the regression equation expressing the hypothesized relationship between an outcome or dependent variable and one or more predictors or independent variables

1.slope= rise/ run

m= 10  

2. y- intercept = 300

3. Now, the regression line:

y = 10x + 300

At, x = 1

y = 10(1) + 300

y = 310 calories

and  x = 14

y = 10(14) + 300

y = 440

We know the actual value is 330.

Hence, the value of calories is 90 and when x = 14 the value of y = 440 from the regression line, but the actual value is 330.

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The population of a small town was 3,150 last year. After a new factory opened close by, the population increased by 8%. What
is the new population of the town?

Answers

3,402

8% of 3150 is 252, 3150 + 252 = 3402.

Please find the area of the given picture. Please as fast as possible........​

Answers

Answer:

Area = 168 cm²

Step-by-step explanation:

**Please note that there is an error in the drawing of the given parallelogram.  In order for the parallelogram to have the given shape, the diagonal AC is actually 22.5 cm in length, whereas diagonal DB is 15 cm in length (see attached diagram). Therefore, I shall be using the attached diagram for my calculations.  However, please note that due of the properties of a parallelogram, the final answer will be the same, regardless of which diagonal is used.**

To calculate the area of a parallelogram, we would usually multiply the base by the perpendicular height.  As the perpendicular height is unknown in the given parallelogram, use the following formula:

[tex]\textsf{Area of parallelogram} = ab \sin (x)[/tex]

where:

a and b are the lengths of parallel sidesx is the included angle

As the diagonal of the parallelogram is given, use the cosine rule to calculate the measure of the included angle ∠DCB.

Cosine Rule (for finding angles)

  [tex]\sf \cos(C)=\dfrac{a^2+b^2-c^2}{2ab}[/tex]

where:

C is the anglea and b are the sides adjacent the anglec is the side opposite the angle

From inspection of the given diagram:

C = ∠DCBa = DC = 13 cmb = CD = 14 cmc = DB = 15 cm

Substitute the given values into the cosine rule formula and solve for ∠ABC:

[tex]\implies \sf \cos(DCB)=\dfrac{13^2+14^2-15^2}{2(13)(14)}[/tex]

[tex]\implies \sf \cos(DCB)=\dfrac{140}{364}[/tex]

[tex]\implies \sf \cos(DCB)=\dfrac{5}{13}[/tex]

[tex]\implies \sf \angle DCB=67.38013505...^{\circ}[/tex]

Substitute the found angle and the length of the parallel sides into the area formula:

[tex]\begin{aligned}\textsf{Area of parallelogram} & = ab \sin (x)\\\\\implies \textsf{Area} & = \sf (13)(14) \sin (DCB)\\& = \sf (13)(14) \left(\dfrac{12}{13}\right)\\& = \sf 168\:\:cm^2\end{aligned}[/tex]

Therefore, the area of the given parallelogram is 168 cm².

(75 POINTS PLEASE RESPOND ASAP)

Explain how to solve 4x + ^3 = 7 using the change of base formula log base b of y equals log y over log b. Include the solution for x in your answer. Round your answer to the nearest thousandth.

Answers

Answer:

1.596

Step-by-step explanation:

So you can rewrite log as: [tex]log_{b}a=x = > b^x=a[/tex] So in this case it's already in exponential form which we'll use to rewrite into logarithm form.

[tex]4^{x+3} = 7\\log_47=x+3\\\\\frac{log7}{log4}=x+3\\1.404\approx x+3\\x\approx1.596[/tex]

Answer:

x = -1.596

Explanation:

[tex]\rightarrow \sf 4^{x + 3} = 7[/tex]

take log on both sides

[tex]\rightarrow \sf log(4^{x + 3}) = log(7)[/tex]

[tex]\rightarrow \sf (x + 3)log(4) = log(7)[/tex]

[tex]\rightarrow \sf x + 3= \dfrac{log(7)}{log(4)}[/tex]

[tex]\rightarrow \sf x= \dfrac{log(7)}{log(4)} -3[/tex]

calculate

[tex]\rightarrow \sf x= -1.596322539[/tex]

[tex]\rightarrow \sf x= -1.596 \quad (rounded \ to \ nearest \ thousand)[/tex]

30 point!!!! Help me fast!!!PLS!!Question is attached!!!

Answers

Answer:

This is an extremely easy question bro!

1.

2. 3 (Base) ² (Exponent)

3. Expanded form: (9 * 1)

   Standard form: 9

Step-by-step explanation:

Well, there's none.

Please mark me as Brainliest! Thanks! :)
Detailed Answers:

1) 5^3

2) Base = 5; Exponent = 2

3) Expanded Form = 5 * 5
Standard Form = 25

Determine the intervals on which the function is (a) increasing; (b) decreasing: (c) constant.
(a) The function is increasing on the interval(s)
(Use a comma to separate answers as needed. Type your answer in interval notation.)

Answers

The intervals of the function in which it is increasing, decreasing and constant are given as follows:

a) Increasing: [tex]x \in \left[-4.5, 2\right][/tex].

b) Decreasing: [tex]x \in \left[4,6\right][/tex].

c) Constant: [tex]x \in \left[2,4\right][/tex].

When a function is increasing?

A function is increasing when the graph of the function is pointing upwards, hence this function is increasing on the interval [tex]x \in \left[-4.5, 2\right][/tex].

When a function is decreasing?

A function is increasing when the graph of the function is pointing downwards, hence this function is decreasing on the interval [tex]x \in \left[4, 6\right][/tex].

When a function is constant?

A function is constant when it is graph is a line without inclination, hence this function is constant n the interval [tex]x \in \left[2, 4\right][/tex].

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can someone please help mee (20 points and i will give brainliest!!!)

Answers

Answer:

a. y-intercept:(0,  -6), x-intercepts: (3, 0) and (-2, 0). vertex: (0.5, -6.25)

b. y-intercept: (0, 6), x-intercepts(3, 0) and (-2, 0). vertex: (0.5, 6.25)

Step-by-step explanation:

a:

 So finding the y-intercept is really easy and is simply when x=0. If you plug in 0 as x it makes [tex]y=(0)^2-0-6[/tex] which simplifies to -6, which is the y-intercept. As for the x-intercepts you can calculate that by using the quadratic equation [tex]x=\frac{-b\pm\sqrt{b^2-4ac}}{2a}\\[/tex]. In this case a=1, b=-1, c=-6. So plugging those values in you get [tex]x=\frac{-(-1)\pm\sqrt{(-1)^2-4(1)(-6)}}{2(1)}[/tex], which simplifies to [tex]x=\frac{1\pm5}{2}[/tex]. This gives you the x-intercepts 6/2 and -4/2 which are 3 and -2. The vertex can be calculated by manipulating the equation so it's in the form of [tex]y=(x-h)^2+k[/tex] where (h, k) is the vertex of the parabola. This is done by moving c to the other side and then completing the square and the isolating y. So the first step will be

Move c to the other side

[tex]y+6=x^2-x[/tex]

Complete the square by adding (b/2)^2

[tex]y+6+0.25 = x^2-x+0.25[/tex]

Rewrite as square binomial

[tex]y+6.25 = (x-0.5)^2[/tex]

Isolate y

[tex]y=(x-0.50)^2-6.25[/tex]

(h, k) = 0.50, -6.25 which is the vertex

b: To identify the y-intercept you plug in 0 as x which will only leave c which in this case is 6 which is the y-intercept. (0, 6). To identify the x-intercepts you can simplify plug in the values a, b, c into the quadratic equation which was stated in the previous answer. In this case a, b, c = -1, 1, 6. Plugging these values in gives the equation [tex]y=\frac{-(1)\pm\sqrt{1^2-4(-1)(6)}}{2(-1)}[/tex]. which simplifies to [tex]x=\frac{-1\pm5}{-2}[/tex] which gives the values -2 and 3. To find the vertex it's the same process as before

Factor out -1

[tex]y=-(x^2-x-6)[/tex]

Add 6 to both sides (on the left side add -6 since -1 was factored out).

[tex]y-6=-(x^2-x)[/tex]

Complete the square by adding (b/2)^2 to both sides (add -(b/2)^2 to left side since -1 was factored out)

[tex]y-6-0.25 = -(x^2-x+0.25)[/tex]

Rewrite as square binomial

[tex]y-6.25=-(x-0.5)^2[/tex]

Add 6.25 to both sides

[tex]y=(x-0.50)^2+6.25[/tex]

(h, k) = (0.50, 6.25)

When you graph the parabolas you'll notice there just flipped relative to the x-axis. This can be deduced by simply looking at the two equations, since the two equations have the same absolute value coefficients, the signs are just different, and more specifically they're all opposite. If you took the first equation and multiplied the entire right side by -1 you would get the same equation. And since that equation really represents the value of y (since it's equal to y) you're reflecting it across the x-axis.

Answer:

a) y-intercept (0,  -6); x-intercepts (3, 0) and (-2, 0); vertex (0.5, -6.25)

b) y-intercept (0, 6); x-intercepts (3, 0) and (-2, 0); vertex (0.5, 6.25)

Step-by-step explanation:

which expresion is equivalent to the given expresion


(3m-4)³(3m³)

Answers

The equivalent expression of [tex](3m^{-4})^3 * (3m^3)[/tex] is [tex]729m^{-9}[/tex]

How to determine the equivalent expression?

The expression is given as:

[tex](3m^{-4})^3 * (3m^3)[/tex]

Expand the brackets

[tex]27m^{-12} * 27m^3[/tex]

Apply the law of indices

[tex]729m^{-12+3}[/tex]

Evaluate the sum

[tex]729m^{-9}[/tex]

Hence, the equivalent expression of [tex](3m^{-4})^3 * (3m^3)[/tex] is [tex]729m^{-9}[/tex]

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