Two square carpets are used in the reception area of a hotel. The sum of the areas of the carpets is 720 square feet. The difference of the areas of the carpets is 432 square feet. Find the dimensions of each carpet.

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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Answer:

g(f(4)) = 106.

Step-by-step explanation:

To find f(g(4)), we first need to find

g(4):g(4) = 5(4)^2 - 4(4) + 1 = 80 - 16 + 1 = 65

Now that we know g(4) is 65, we can find

f(g(4)):f(g(4)) = f(65) = 2(65) - 3 = 127

Therefore,

f(g(4)) = 127.

To find g(f(4)), we first need to find f(4):f(4) = 2(4) - 3 = 5

Now that we know f(4) is 5, we can find g(f(4)):

g(f(4)) = g(5) = 5(5)^2 - 4(5) + 1 = 125 - 20 + 1 = 106

Therefore, g(f(4)) = 106.

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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The volume of the figure that was created by the triangle being rotated, would be 94. 83 units ³

When a triangle is rotated about y = x, a right circular cone is created. The formula is:

= π r² h / 3

We need to find the height and radius. The coordinates for the right circular cone are:

(0,0) - (0,0)

(8,8) - (8,8)

(4,12) - (12,4)

Using this, we find that the radius is 4 units. The height can be found by using any point such as ( 12, 4).

= √ ( ( 12 - 8) ² + ( 4 - 8 ) ²)

= 5. 66 units

The volume would therefore be:

= π x 4² x 5. 66 / 3

= 94. 83 units 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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Answer:

-x³ + 4x²

Step-by-step explanation:

-x^2(x-4)

Distribute

-x³ + 4x²

So, the answer is -x³ + 4x²

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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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.

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].

The volume of the cylinder that has a diameter of 7 yards and a height of 12 yards is: 147π cubic yard.

The volume of a cylinder can be determined by applying the volume formula which is given as:

Volume (V) = πr²h,

where "r" is the radius of the cylinder

"h" is the height of the cylinder

π is a constant

Given the following:

Diameter of cylinder = 7 yards, thus, radius (r) = 7/2 = 3.5 yards

Height (h) = 12 yards

Plug in the values:

Volume of the cylinder = π * 3.5² * 12 = 147π cubic yard.

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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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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 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 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 ______?

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:

A

Step-by-step explanation:

(x+5)(x-1)－(x+1)(x-4)=7x-1

The value of R² (coefficient of determination) is 0.0214

We know that the formula for the coefficient of determination is,

R² = 1 - (SSR / SST)

where, R² is  the coefficient of determination

SST is the total sum of squares

SSR is the sum of squares of regression

Here, the total sum of squares (SST) = 11654

and the sum of squares of regression (SSR) = 11405

Using above formula,

R² = 1 - (SSR / SST)

R² = 1 - (11405 / 11654 )

R² = 1 - 0.9786

R² = 0.0214

This is the required value.

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Find the complete question below.

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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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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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:

The answer is

13)CE

14)EG

15)BD

16)BF

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 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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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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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 principal amount was £1260, and the annual interest rate is 5.5%.

Given that, Olivia gets £1606.50 and £1675.80 after 5 years and 6 years of investment in simple interest respectively.

SI = principal × rate × time / 100

So,

P + 5pr = £1606.50

P = £1606.50 - 5pr............(i)

P + 6pr = £1675.80

P = £1675.80 - 6pr.........(ii)

Therefore,

£1606.50 - 5pr = £1675.80 - 6pr

Pr = 69.3

Put the value of pr in eq(i)

P + 5(69.3) = 1606.50

P = 1606.5 - 346.5

P = 1260

Now,

(1260)r = 69.3

r = 0.055

The annual interest is 5.5%

Hence, the principal amount was £1260, and the annual interest rate is 5.5%.

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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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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:

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