simplify. (write each expression without using the absolute value symbol)

|x+3| if x>2

we can solve the given equation by taking log to get answer as x = log₈(25)

what is  an equation ?

An equation is a mathematical statement that contains an equal sign, indicating that two expressions have the same value. It is a way of expressing the relationship between different variables or quantities.

In the given question,

Taking the logarithm of both sides with base 8, we get:

log₈(8ˣ) = log₈(25)

Using the logarithmic property that logₐ(b^c) = c logₐ(b), we can simplify the left-hand side to:

x log₈(8) = log₈(25)

Since log₈(8) = 1, we have:

x = log₈(25)

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To prove Triangle ACE is congruent to Triangle BDE using the ASA postulate, we need either ∠A ≅ ∠B or ∠C ≅ ∠D.

To prove two triangle congruent by angle side angle postulate, these triangle must have two sides equal or one angle from these two must be equal and identical to each other.

What are congruent triangle?

Two triangles are said to be congruent if all three corresponding sides are equal and all the three corresponding angles are equal in measure. These triangles can be slides, rotated, flipped and turned to be looked identical. If repositioned, they coincide with each other. The symbol of congruence is’ ≅’.

The meaning of congruence in Maths is when two figures are similar to each other based on their shape and size. There are basically four congruence rules that proves if two triangles are congruent.

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Answer: 112 ft²

Step-by-step explanation:

The area of a triangle can be found with the equation

[tex]A=\frac{1}{2} bh[/tex], where b is the base (bottom line of the triangle) and h is the height (the distance of the line from the peak of the triangle that forms a right angle with the base).

In this problem we are given the base and height: the base is 16 feet, and the height is 14 ft.

Therefore, the area is [tex]\frac{1}{2} *16*14[/tex], which is 112 ft²

To succeed in an i-Ready mastery check, it is essential to review the materials covered in the lessons thoroughly, actively engage in the learning process, and ask questions if anything is unclear.

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i-Ready is an online adaptive learning platform that offers personalized learning experiences for students in reading and mathematics.

Mastery checks play a crucial role in ensuring that students fully understand the concepts being taught before progressing to more advanced topics.

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Remember that mastery checks are designed to measure your understanding of specific topics, so it's important to approach them with focus and confidence.

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The correct comparison between the t-distribution and z-distribution is:

The density curve of the t-distribution is more spread out than the density curve of the z-distribution, especially for small sample sizes.

Both t-distribution and z-distribution have symmetric density curves.

However, for small sample sizes, the t-distribution curve is more spread out and has heavier tails compared to the z-distribution curve.

The area under both curves is equal to 1, as they represent probability distributions.

As the sample size increases, the t-distribution curve approaches the z-distribution curve in shape.

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The value of angle V which is ∠V is calculated as:  64.01°

The trigonometric ratios are used to find the angles and lengths of a right angle triangle.

Some of the trigonometric ratios are:

sin x = opposite/hypotenuse

cos x = adjacent/hypotenuse

tan x = opposite/adjacent

The parameters given are:

∠W = 90°

UW = 39

WV = 80

VU = 89

Thus, using trigonometric ratios, we have:

∠V = tan⁻¹(80/39)

∠V = 64.01°

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the tower leans 5.6° from the vertical, so we can draw a line perpendicular to the ground from the top of the tower to find the height. Let's call the height "h". the length of the tower is approximately  [tex]57 meters[/tex] (rounded to the nearest meter).

We know that the angle of elevation from the tourist to the top of the tower is [tex]29.2^\circ[/tex]  , so we can label that angle as 29.2°. We also know that the angle between the perpendicular line and the ground is 5.6°, so we can label that angle as 5.6°.

Using trigonometry, we can find the value of h:

[tex]tan(29.2^\circ) = h/105[/tex]

[tex]h = 105^\circ tan(29.2^\circ)[/tex]

[tex]h \approx 55.05[/tex]

So the height of the tower is approximately   [tex]55.05[/tex] meters.

To find the length of the tower, we can use the Pythagorean theorem:

[tex]h^2 + x^2 = (105/cos(5.6^\circ))^2[/tex]

[tex]x^2 = (105/cos(5.6^\circ))^2 - h^2[/tex]

[tex]x \approx 56.67[/tex]

So the length of the tower is approximately [tex]56.67[/tex] meters.

Therefore, the length of the tower is approximately [tex]57[/tex] meters (rounded to the nearest meter).

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a.(Constant of proportionality: 5)

b.(Constant of proportionality: 5)

Hi! I'm happy to help you with your question. Let's analyze each table and fill in the missing parts.

a.
X | 2
Y | 10

To find the constant of proportionality, divide Y by X:
10 / 2 = 5 (Constant of proportionality)

Now, let's fill in the missing parts for X=7 and X=1 using the constant of proportionality:
For X=7:
Y = 5 * 7 = 35

For X=1:
Y = 5 * 1 = 5

So, the completed table for (a) is:
X | 2  | 7  | 1
Y | 10 | 35 | 5
(Constant of proportionality: 5)

b.
X | 1
Y | 15

To find the constant of proportionality, divide Y by X:
15 / 1 = 15 (Constant of proportionality)

As there are no other values in table (b), we can't fill in any more parts. The constant of proportionality is 15.

Your answer:
a.
X | 2  | 7  | 1
Y | 10 | 35 | 5


b.
X | 1
Y | 15
(Constant of proportionality: 15)

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the height of the trapezoid is 8.4 kilometers. To find the height, h, of a trapezoid when given the area, A, we need to use the formula:

A = ([tex]b_{1} + b_{2}[/tex])h/2

where b1 and b2 are the lengths of the two parallel bases of the trapezoid.

Given that the area of the trapezoid is 42 square kilometers, we can write:

42 = ([tex]b_{1} + b_{2}[/tex])h/2

We can simplify this equation by multiplying both sides by 2:

84 = ([tex]b_{1} + b_{2}[/tex]) h

Now we need to find the values of b1 and b2. Unfortunately, the problem does not provide us with these values. Without them, we cannot find the exact value of h. However, we can provide an example to show how to solve the problem if we have the values of b1 and b2.

Let's say that b1 = 4 km and b2 = 6 km. We can substitute these values into the equation:

84 = (4 + 6)h

Simplifying:

84 = 10h

Dividing both sides by 10:

h = 8.4 km

So, in this example, the height of the trapezoid is 8.4 kilometers.

In general, to find the height of a trapezoid when given the area, we need to know the values of both bases. Once we have those values, we can use the formula above to solve for the height. If we are not given the values of the bases, we cannot find the exact value of the height.

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Answer: A (0.5)

Step-by-step explanation:

Determine by dividing total number of popcorn sold by the attendance. Use the plotted points to help you.

Answer:

A line graph, because it would show the association or relationship between two variables

Step-by-step explanation:

The circumference of the bottle cap is nothing but the circumference of a circle and it is 9.42 cm.

The circumference of a circle or other curved geometric form refers to the space encircling it. It is a boundary's one-dimensional linear measurement.

The diameter of the circle is given, D = 3cm

Therefore the radius of the circle, r = D/2 = 3/2 cm

Circumference of circle = 2[tex]\pi[/tex]r

                                         = 2 * 3.14 * 3/2

                                         = 3.14 * 3

                                         = 9.42 cm

Therefore the circumference of the bottle cap is 9.42 cm.

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Answer:

?=45 degrees

Step-by-step explanation:

All of the angles are congruent.

So the equation is:45+90+?=180

?=45 degrees

Answer: 45 degrees

Step-by-step explanation:

The margin of error for a 95% confidence interval for this specimen is 0.008 grams. Then the 95% confident specimen's true weight is 0.008 grams of the sample mean of 4.53 grams.

To find the margin of error for a 95% confidence interval, we need to determine the standard error of the mean. The  standard error of the mean formula can be written as:

SE = σ/√n

where:

SE = standard error of the mean,

σ = the standard deviation of the population

n = the sample size.

the standard deviation of the laboratory = 0.005

sample size = 4.

calculating the standard error of the mean:

SE = 0.005/√4

= 0.0025

Next, we need to find the critical value for a 95% confidence interval. the sample size is small (n < 30), then we need to use a t-distribution.

Critical value = 3.182.

The formula for calculating the margin of error is:

ME = t*SE

where :

ME = margin of error

t = critical value = 3.182.

SE = standard error of the mean = 0.0025

By substuting the values, we get:

ME = t*SE

= 3.182*0.0025

= 0.008 grams

Therefore, the margin of error for a 95% confidence interval for this specimen is 0.008 grams. Then the 95% confident specimen's true weight is 0.008 grams of the sample mean of 4.53 grams.

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Answer:

a = 127° , b = 12° , c = 115°

Step-by-step explanation:

a and 53° are same- side interior angles and sum to 180° , that is

a + 53° = 180° ( subtract 53° from both sides )

a = 127°

c and 115° are alternate angles and are congruent , then

c = 115°

53° , b and c lie on a straight line and sum to 180°

53° + b + c = 180°

53° + b + 115° = 180°

b + 168° = 180° ( subtract 168° from both sides )

b = 12°

then a = 127° , b = 12° , c = 115°

Answer:

a = 127; b = 12; c = 115

Step-by-step explanation:

c =115

b = 180 - 115 - 53

b = 12

a = b + c

a = 12 + 115

a = 127

The solution for the given system is x1 = (23/5s - x2)/4s, x2, where s ≠ -360/49 and x2 can be any non-zero

The values of the parameter s

for which the system has a unique solution are s ≠ -45/8. Let's understand how to find the solution and the values of s:

Given equation of the system is,5x1s + 9x2 = -3 ...(1)

5x1 + sx2 = 4 ...(2)

Now, let's solve the given system of equations using the elimination method:

Multiply equation (2) by 5, we get:25x1 + 5sx2 = 20 ...(3)

Now, we'll subtract equation (1) from equation (3) as:

25x1 + 5sx2 = 20- (5x1s + 9x2 = -3)20x1 + 5sx2 = 23 ... (4)

Let's divide equation (4) by 5s, we get:

4x1 + x2/s = 23/5s ... (5)

Multiply equation (2) by 9 and subtract equation (1) from it. We get:40x2 + 9sx2 = 39

Simplifying the above equation, we get:(49s+360)x2 = 39 ... (6)

Now, we have two equations:(5) 4x1 + x2/s = 23/5s(6) (49s+360)

x2 = 39The given system of equations will have a unique solution only if x2 ≠ 0. So, let's consider the value of x2.If x2 ≠ 0, then from equation (6)

we get,49s+360 ≠ 0 or s ≠ -360/49

This means that s ≠ -360/49 is necessary for the given system to have a unique solution.

Now, let's solve the equation (5):4x1 + x2/s = 23/5s

If we multiply both sides of the equation (5)

by s, we get:

4sx1 + x2 = 23/5If x2 ≠ 0, then we can solve this equation for x1 as:

x1 = (23/5s - x2)/4s

Therefore, the solution for the given system is x1 = (23/5s - x2)/4s, x2, where s ≠ -360/49 and x2 can be any non-zero value.

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The total number of ways to assign the guests to the rooms is 126 ways

We can solve this problem by using a combination. We have 5 friends and 5 rooms, so we can think of the friends as stars and the rooms as bars that separate them. The number of ways to assign the friends to the rooms is equal to the number of ways to arrange the 5 stars and 4 bars (since there are 4 spaces between the bars).

We can choose any 4 positions out of 9 (5 stars and 4 bars) to place the bars, so the number of ways to assign the friends to the rooms is equal to the binomial coefficient.

[tex]${9 /\choose 4} = \frac{9!}{4!5!} = 126$.[/tex]

Therefore, there are 126 ways for the innkeeper to assign the 5 friends to the 5 rooms.

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Answer:

No solution

Step-by-step explanation:

Solve for x

[tex]|x-13|+18=-4[/tex]

Subtract 18 on both sides

[tex]|x-13|=-22[/tex]

There is no solution to this problem. Absolute value cannot be less then 0.

In the proportion, Mr.Balewa needs  9 cups to makes 12 dozen cookies.

A percentage is created when two ratios are equal to one another. We write proportions to construct equivalent ratios and to resolve unclear values. a comparison of two integers and their proportions. According to the law of proportion, two sets of given numbers are said to be directly proportional to one another if they grow or shrink in the same ratio.

Here  

He uses 4 1/2 cups of flour to make six dozen cookies then to makes 12 dozen cookies the x cups of flour .

Now using proportion,

= (4 1/2) / 6 = x / 12

= (9/2) / 6 = x/12

x = (9*12)/(2*6) = 9

= 9 cups.

Hence Mr. Balewa needs  9 cups to makes 12 dozen cookies.

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Elijah incorrectly combined the constant terms 4 and 8 to get -8. The correct simplification of the expression should be 4 + 8 - 3x - 10x, which simplifies to 12 - 13x.

To simplify the expression 4 - 3x + 8 - 10x, we first combine the like terms -3x and -10x to get -13x. Then we combine the constant terms 4 and 8 to get 12. So the simplified expression is 12 - 13x.

However, Elijah made a mistake by combining the constant terms 4 and 8 as if they had opposite signs. This resulted in a term of -8 that is not present in the original expression. The rest of his simplification is correct.

Therefore, the correct simplification of the expression is 4 + 8 - 3x - 10x, which simplifies to 12 - 13x.

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Complete Question:

Elijah is simplifying the expression 4 - 3x + 8 - 10x. He arrived at the answer 4 - 8 - 3x + 10x - 4 = 7x,

where did elijah go wrong?

Using differentials to estimate the relative error in the calculated area of the disk of disk with radius 15 cm is equals to the 3.192%.

We have, a disk with radius of 15 cm.

Maximum error = 0.25

We have to determine the area of the disk. Area is a two dimensional quantity. It is defined as the space occupied by figure or any two dimensional shape. Here, formula for area of disk, A = πr² --(1)

here, r = 15 cm , dr = 0.25

Relative error is defined as the ratio of absolute error in measurement to the oringnal measurement. Differentating the equation (1) with respect to r, dA = d( πr²)

=> dA = 2πr dr

Substitutes the known values, in above formula, dA = 2× π × 15 ×0.25

=> dA = 7.50 × π = 23.55

So, absoulte error in area = 22.55

Original value of area = π(15)² = 706.5 cm²

Now, relative error % = (∆A/A)×100

= (22.55/706.5)×100

= 0.031917 × 100

= 3.1917 ~ 3.192 %

Hence, required value is 3.192%.

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Complete question:

the radius of a disk is given 15 cm as with a maximum error of 0.25 . use differentials to estimate the relative error in the calculated area of the disk. please enter your answer in decimal format with three significant digits after the decimal point.

Since the total amount of kids who participated in the survey is 150, 100% of the pie is equal to 150 kids.

We know that 46% of the 150 kids like video games so the number of kids that like video games is 0.46 * 150 = 69.

Similarly, 14 + 16 = 30% of 150 kids like reading and art so the number of kids that like reading and art is 0.3 * 150 = 45.

Your second question is quite hard to understand. But you know that 120 kids like video games and those kids make up 40% of the total so mathematically you can say,

40% * number of total students = 120

number of total students = 120/40% = 300

The answer of the given figure is ∠B = 72° and ∠C = 108°

In geometry, corresponding angles are pairs of angles that have the same relative position and the same degree of rotation, in two different geometric figures that are being compared.

More specifically, when two lines are crossed by another line, the angles on one side of the crossing line that are in the same relative position to each other (i.e., they are on the same side of the crossing line and are either both interior angles or both exterior angles), are corresponding angles.

According to question

∠CFE = 72°

In given diagram

DC ║ EF ║ AB and CB is transversal

∴ ∠CFE + ∠BFE = 180° ( Linear pair )

72° + ∠BFE = 180°

∠BFE = 180 - 72

∠BFE = 108°

∵∠DCF = ∠BFE ( Corresponding equal angle )

∠DCF = 108°

∠C = 108°

∠CFE = ∠B (  Corresponding equal angle )

72° = ∠B

∴∠B = 72°

Hence, the ∠B = 72° and ∠C = 108°

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The sample size required to estimate a population proportion with a desired level of confidence and margin of error depends on the size of the population and the confidence level desired. In this case, the population proportion is unknown and the desired confidence level is 99.5% with a margin of error of 4%.

To determine the sample size required, we can use the formula:

n = (Z² * p * q) / E²

where n is the sample size, Z is the Z-score corresponding to the desired level of confidence (which for a 99.5% confidence level is 2.81), p is the estimated population proportion (which is 0.5 as we have no reasonable estimate), q is 1-p, and E is the margin of error (which is 0.04).

Plugging in these values, we get:

n = (2.81² * 0.5 * 0.5) / 0.04² ≈ 1381

Therefore, a sample size of at least 1381 is required to estimate the population proportion with 99.5% confidence and a margin of error of 4%.

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Step-by-step explanation:

(1/6²)⁵ = 1/6¹⁰ = 6^-10

because in the case of exponent of an exponent the exponents are multiplied with each other.

and 1/n = n^-1

(6^-5)² = 6^-10

because as above the exponents are multiplied with each other.

6^-3 / 6⁷ = 6^(-3 - 7) = 6^-10

a^n × a^m = a^(n+m)

a^n / a^m = a^(n-m)

the others are not 6^-10 :

6^-5 × 6² = 6^(-5 + 2) = 6^-3

6⁵×6^-3 / 6^-8 = 6^(5 - 3 - -8) = 6^(5 ‐ 3 + 8) = 6¹⁰

Answer:

use long divison  ike this

      16

  -------

8 | 132

    8

  -----

    52

    48

  -----

     4

Step-by-step explanation:

Answer:

Step-by-step explanation:

                                         132/8 = 16 with 4 leftover

                                             32 divided by 8 is 4, 96 divided by 8 is 12, the                                                                  

                                                  extra 4 left over

Answer:

x^4 - mx^2 + n^2 = 0

Step-by-step explanation:

We can use algebraic manipulation to solve for m and n. First, we can square the equation xy = n to get:

(x^2)(y^2) = n^2

Since we also have x^2 + y^2 = m, we can substitute y^2 with m - x^2 to get:

x^2(m - x^2) = n^2

Expanding the left side of the equation, we get:

mx^2 - x^4 = n^2

Multiplying both sides by 16, we get:

16mx^2 - 16x^4 = 16n^2

Adding 32xy to both sides, we get:

16mx^2 + 32xy - 16x^4 = 16n^2 + 32xy

Substituting n for xy, we get:

16mx^2 + 32n - 16x^4 = 16n^2 + 32n

Rearranging the equation, we get:

16mx^2 - 16x^4 - 16n^2 = 0

Dividing both sides by -16, we get:

x^4 - mx^2 + n^2 = 0

Answer:

(4x+4y)²

Step-by-step explanation:

Given x²+y² = m ,xy=n.

Now 16m+32n = 16(m+2n)

= 16(x²+y²+2xy) = 4²(x+y)²[ x²+y²+2xy= (x+y)²]

(4x+4y)².