[tex]x^2=225[/tex]
Use the square root property to solve the equation. The equation has real number solutions.

The perimeter and the area of each composite figure are, respectively:

Case 1: p = 77.6 cm, A = 304 cm²

Case 2: p = 25.1 ft, A = 28 ft²

Case 3: p = 42 mi, A = 52.5 mi²

Case 4: p = 56.5 in, A = 179.424 in²

In this problem we need to determine the perimeter and the area of four composite figures, that is, figures formed by combining triangles and rectangles, whose area formulas are listed below:

Triangle

A = 0.5 · b · h

Rectangle

A = b · h

Where:

Now we find the perimeter and the area of each figure:

Case 1

p = 2 · (18.8 cm) + 2 · (20 cm)

p = 77.6 cm

A = (15.2 cm) · (20 cm)

A = 304 cm²

Case 2

p = 10 ft + 8.1 ft + 7 ft

p = 25.1 ft

A = 0.5 · (10 ft) · (5.6 ft)

A = 28 ft²

Case 3

p = 17.5 mi + 6 mi + 18.5 mi

p = 42 mi

A = 0.5 · (17.5 mi) · (6 mi)

A = 52.5 mi²

Case 4

p = 20 in + 13.9 in + 15 in + 7.6 in

p = 56.5 in

A = (7.6 in) · (13 in) + 0.5 · √[(13.9 in)² - (13 in)²] · (13 in) + 0.5 · √[(15 in)² - (13 in)²] · (13 in)

A = 98.8 in² + 31.982 in² + 48.642 in²

A = 179.424 in²

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Answer:

A

Step-by-step explanation:

(x+5)(x-1)－(x+1)(x-4)=7x-1

Answer:

Step-by-step explanation:

The rule for a triangle is that if you add the 2 shorter sides, it must be greater than the longest side (can't even be =, must be bigger.

A.  36+48>60 true yes triangle

B   6.2+5.7>9.4 yes triangle

C.  20+20 is not greater than 50 no not at triangle

D.  12+24>32 yes triangle

Vertical angles mean angles across from each other when 2 lines intersect.

So:

B, C, D  are vertical angles

Answer:

Only Carla's

Step-by-step explanation:

I believe the answer is only Carla's because even though the left side is factored, there is still an 8 on the right side. To apply the zero product property rule, the equation needs to equal 0

Meanwhile Carla's works because then the equation would be x²=9 which we can easily take the square root of

Answer:  Only Carla

Step-by-step explanation:

Only Carla

Carla said:

(x+1)(x-1)=8          FOIL

x²-1=8

x²=9

x=±3

Jordan said:

He will use 0 property rule but the factored portion must =0   It equals 8, so you can't use that property.

The number of triangle that can be formed is one, with angles m∠S and m∠T derived to be 127° and 33° using the sine rule.

The sine rule is a relationship between the size of an angle in a triangle and the opposing side.

Using the sine rule;

29/sin20° = 32°/sinT

T = (33 × sin20°)/29° {cross multiplication}

m∠T = 23 {to the nearest degree}

m∠S = 180 - (20 + 23)° {sum of interior angles of a triangle}

S = 127°

Therefore, the number of triangle that can be formed is one, with angles m∠S and m∠T derived to be 127° and 33° using the sine rule.

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Answer:

Step-by-step explanation:

The area of a parallelogram with the given base and height is 96 square units.

Given that, x=4 units, y=12 units, and h=8 units.

From the given figure,

Area of parallelogram = Base×Height

Here, b=4+12 =16 units and h=8 units

Now, area of parallelogram = 16×8

= 96 square units

Therefore, the area of a parallelogram with the given base and height is 96 square units.

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The length BC of the bisected line segment is: 11.5

Usually a line that bisects a segment usually divides that segment into two equal parts.

Now, we are told that DE bisects Line AC at point B where AB = 3a + 4.

Thus, from the idea of a bisected segment, we can easily say that:

2(3a + 4) = a + 23

6a + 8 = a + 23

6a - a = 23 - 8

6a = 15

a = 15/6

a = 5/2

a = 2.5

Thus:

AB = BC = 3(2.5) + 4

BC = 11.5

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The students' line that will be parallel to line d is the line with the same slope as d

The rules are given as

This means that the equations of the function are

Carly: y = x + 2

Ramil: y = 2x + 1

If the slope of line d is 1, Carly's line will be parallel to line d and if the slope of line d is 2, Ramil's line will be parallel to line d

This is because parallell lines have equal slopes

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a. The error is that the two factors should be 5s and 3s-7s²+1

b. The student out to multiply the two factors if the product will be 15s²-35s³+5s

Factorization or factoring consists of writing a number or another mathematical object as a product of several factors.

For example, if we are given an expression , 2x +6. The expression consist of two terms and the common factor between them is 2 . Therefore we bring the 2 out . i.e 2( x+3). This means the two factors are 2 and x+3

Similarly , 15s²-35s³+5s can be factorized by bring out the common factors between the three terms

= 5s( 3s-7s²+1)

This means that the student omitted +1 and she ought to have cross checked by multiplying the two factors back if the product will be the polynomial.

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The monomials in the expression are given as follows:

x², xy, -8y².

The simplified polynomial is given as follows:

9x² + 9xy - 72y².

With the application of the distributive property, the outer term multiplies each of the inner terms of the expression. If possible, these inner terms than can be added or subtracted combining the like terms.

The expression for this term are given as follows:

9(x² + xy - 8y²).

The inner term is a polynomial composed by the sum/subtraction of the monomials presented as follows:

x², xy, -8y².

Applying the distributive property, the simplified polynomial is given as follows:

9x² + 9xy - 72y².

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Answer: Therefore, the probability of not landing on blue when spinning the spinner once is 62.5%.

Step-by-step explanation:  There are 8 sections on the spinner, and 3 of them are blue. Therefore, the probability of landing on blue is:

P(blue) = 3/8 = 0.375

The probability of not landing on blue is the complement of the probability of landing on blue:

P(not blue) = 1 - P(blue) = 1 - 0.375 = 0.625

To convert this probability to a percentage, we can multiply by 100:

P(not blue) = 0.625 x 100% = 62.5%

The value of the length x is 2√70. Option C

To determine the value of the length of the triangle, we need to consider the different trigonometric identities, they are;

Now, using the Pythagorean theorem, we have;

17² = x² + 3²

Find the square values and substitute

289 = x² + 9

collect the like terms

x² = 289 - 9

Subtract the values

x² = 280

Find the square root of both sides

x = √280

Find the values

x = √4× 70

x = 2√70

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Answer:

angle m∠WXY intercepts the diameter WY.

Then,

m∠WXY  =  90°

(13x - 1)°  =  90°

13x - 1  =  90

Add 1 to each side.

13x  =  91

Divide each side 13.

x  =  7

Step-by-step explanation:

HOPE THIS HELPSSS

The amount that was initially deposited is obtained as $10,100.

Compound interest is the interest calculated on the initial principal and also on the accumulated interest of previous periods.

The interest earned in each subsequent period is added to the principal, and the interest is then calculated on the new, larger amount.

We have that;

A = P (1 + r/n)^nt

Then we have;

A = amount

P = principal

r = rate

n = number of times compounded

t = time in years

Then;

14,472.74 = P(1 + 0.055/12)^12 * 5

P = $10,100

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The expression [tex]V^2 (V^2_Z)[/tex] is called mean-square speed.

In Mathematics and Science, mean-square speed is sometimes referred to as root-mean-square speed and it can be defined as a measure of the average value of square-speed of particles that are found in a molecule, gas, or liquid.

Mathematically, the mean-square speed of any particle is denoted or represented by this expression [tex]V^2 (V^2_Z)[/tex].

This ultimately implies that, mean-square speed is always calculated as the square root of the average value of the squares of the speeds (velocities) of each particles in thermodynamics and kinetic theory of gases.

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Complete Question:

The expression [tex]V^2 (V^2_Z)[/tex] is called ______?

The amount of tape that Abigail will use to cover the jewelry box is given as follows:

298 in².

The surface area of a rectangular prism of height h, width w and length l is given by:

S = 2(hw + lw + lh).

This means that the area of each rectangular face of the prism is calculated, and then the surface area is given by the sum of all these areas.

The dimensions of the box are given as follows:

6 in, 12.5 in and 4 in.

Hence the amount of tape, given by the surface area, is obtained as follows:

S = 2 x (6 x 12.5 + 6 x 4 + 12.5 x 4)

S = 298 in².

The dimensions of the box are given as follows:

6 in, 12.5 in and 4 in.

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Answer:

The answer is

13)CE

14)EG

15)BD

16)BF

The correct answer is 3. Response and non-response bias.

Response bias occurs when the way that questions are asked or worded, or the context in which they are asked, influences how respondents answer them. This can lead to inaccurate or incomplete information being collected.

Non-response bias occurs when some individuals selected to participate in a survey do not respond. This can happen for various reasons, such as being unavailable, unwilling, or unable to participate. Non-response bias can skew the results of a survey because the characteristics of those who do not respond may differ from those who do respond.

In this scenario, the principal has asked all math and English teachers to rank his school leadership on a scale of 1 to 10. If some teachers do not respond to the survey or are unavailable, unwilling, or unable to participate, this could lead to non-response bias.

Additionally, if the principal has a reputation for being well-liked or well-respected, some teachers may feel pressured to give a higher rating than they otherwise would, which could lead to response bias.

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The number of bows can Sydney make are 3, we get by division.

Given that Sydney has [tex]1\frac{1}{5}[/tex] yards of ribbon to make bows

Each bow is made from a piece of ribbon that is 2/5 yard long

We have to find the number of bows can Sydney make

To find this we have to divide the total length of ribbon by 2/5

[tex]1\frac{1}{5}[/tex]/(2/5)

6/5×5/2

We get 3

Hence, the number of bows can Sydney make are 3

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m∡RST angle is 146 degrees and m∡RUT is 157 degrees are the arc measures.

Let us find angle RVT

The sum of four angles should be 360 degrees

∠RVS +∠SVU+∠UVT+∠RVT=360

64+139+75+x= 360

278+x=360

x=360-278

x=82 degrees

Arc measure m∡RST =64+82

m∡RST = 146 degrees

m∡RUT = 82+75

m∡RUT = 157 degrees

Hence, m∡RST is 146 degrees and m∡RUT is 157 degrees are the arc measures.

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The name of the shape Kimberly forms by connecting the points is a plane shape

From the question, we have the following parameters that can be used in our computation:

A shape is formed by connecting points

As a general rule; shapes formed by connecting points are referred to as plane shapes, and examples of them are:

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The outlier in this data set is the sweatshirt priced at $18 since it is significantly higher than the rest of the prices.

The mean is affected more by outliers than the median.

In the provided data, the mean is higher than the median, which suggests that there may be an outlier pulling the average up. The outlier value of $18 is causing the mean to be higher.

If we remove the outlier value of $18, the mean price would be (6+12+11+15)/4 = $11, which is lower than the original mean of $12.40.

On the other hand, the median would remain the same since it is not affected by extreme values.

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Part(A),

The value of the mean is 27.1, the value of the mode is 12 and median is 27.5.

Part(B),

Tennis players should report the median value to show they are less prepared for the tournament.

Part A:

To calculate the mean, we need to find the sum of all the data values and divide by the total number of values:

Sum of the data = 12 + 12 + 29 + 20 + 22 + 26 + 31 + 31 + 40 + 68 = 271

Number of data values = 10

Mean = sum of the data/number of data values

Mean = 271 / 10

Mean = 27.1

Therefore, the mean time spent practicing is 27.1 minutes.

To find the median, we need to arrange the data in order from smallest to largest:

12, 12, 20, 22, 26, 29, 31, 31, 40, 68

There are 10 data values, so the median is the average of the two middle values:

Median = (26 + 29) / 2

Median = 27.5

Therefore, the median time spent practicing is 27.5 minutes.

To find the mode, we need to identify the data value that occurs most frequently. In this case, there are two modes:

Mode = 12 and 31

Therefore, the modes for the time spent practicing are 12 and 31 minutes.

To find the range, we need to subtract the smallest data value from the largest data value:

Range = largest data value - smallest data value

Range = 68 - 12

Range = 56

Therefore, the range of time spent practicing is 56 minutes.

Part B:

Based on the scenario, it is more appropriate for the tennis players to report the median value to show they are less prepared for the tournament. This is because there is one outlier value of 68, which is much larger than the other data values.

The mean is affected by outliers and may not represent the typical amount of time spent practicing for the tournament. On the other hand, the median is not affected by outliers and represents the middle value of the data set, which is a more accurate measure of the typical amount of time spent practicing.

Therefore, tennis players should report the median value to show they are less prepared for the tournament.

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The graph of f(x) relate to its parent function by B. The parent function has been translated up.

Given that

f(x) = 3x +2 +4

When evaluated, we have

f(x) = 3x + 6

The parent function of the above is

f(x) = 3x

When f(x) = 3x is compared to f(x) = 3x + 6, we have

Difference = 6

This means that the parant function is translated up by 6 units

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The value of the variable k is 33

Algebraic expressions are simply described as the expressions that consist of variables, terms, coefficients, constants and factors.

These expressions also consist of certain mathematical operations, such as;

From the information given, we have that;

(1/3)k - 4=7

collect the like terns

1/3k = 7 + 4

Add the values

1/3k = 11

cross multiply the values, we have;

k = 11(3)

Multiply the values

k = 33

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A relation is called a function when each element in the domain is paired with just one element from the A. Range

From the question, we have the following parameters that can be used in our computation:

The incomplete definition of relation

A relation takes the form

Domain : x

Range : y

The values from the domain are then paired with the range

If these values are paired just once, then it is a function

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Answer:

C. 16√5

Step-by-step explanation:

Use the Pythagorean Theorem.

[tex]48^2 = 32^2 + x^2\\2304 = 1024 + x^2\\x^2 = 1280\\x = \sqrt{1280}\\[/tex]

[tex]\sqrt{1280}[/tex] is also equal to [tex]16\sqrt{5}[/tex].