50 Points! Multiple choice algebra question. Photo attached. Thank you!

By the Centroid Theorem, the lengths are given as follows:

4. GZ = 12 units.

5. OT = 14.4 units.

The Centroid Theorem states that the centroid of a triangle is located two-thirds of the total distance from each vertex to the midpoint of the opposite side.

Hence for length GZ we have that:

GZ = 2GU/3

GZ = 2 x 18/3

GZ = 12 units.

For length OT, we have that:

ZT = 1/3OT

OT = 3ZT

OT = 3 x 4.8

OT = 14.4 units.

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To solve this problem, we need to use Charles's law, which states that, at constant pressure, the volume of a sample of gas is directly proportional to its temperature.

The law can be expressed mathematically as:

[tex]\boxed{\large\displaystyle\text{$\begin{gathered}\sf \bf{ \frac{V_1}{T_1}=\frac{V_2}{T_2} } \end{gathered}$} }[/tex]

Where:

Now we obtain the data to continue solving:

Now, we will convert the temperatures to Kelvin:

[tex]\boxed{\large\displaystyle\text{$\begin{gathered}\sf \bf{T_1=220 \ ^{\circ}C+273=493 \ Kelvin} \end{gathered}$} }[/tex]

[tex]\boxed{\large\displaystyle\text{$\begin{gathered}\sf \bf{T_2=40 \ ^{\circ}C+273= 313 \ Kelvin} \end{gathered}$} }[/tex]

Now we solve for V₂:

[tex]\boxed{\large\displaystyle\text{$\begin{gathered}\sf \bf{V_2=\frac{V_1T_2}{T_1 } } \end{gathered}$} }[/tex]

Where:

Now, we substitute the values in the formula:

[tex]\boxed{\large\displaystyle\text{$\begin{gathered}\sf \bf{V_2=\frac{(0.5 \ L\times313\not{k} )}{493\not{k} } } \end{gathered}$} }[/tex]

[tex]\boxed{\boxed{\large\displaystyle\text{$\begin{gathered}\sf \bf{V_2\approx0.32 \ Liters } \end{gathered}$} }}[/tex]

The interest rate that satisfies the assumption is approximately 5.33%.

We have,

To find the interest rate that satisfies the assumption, we can use the formula for compound interest:

[tex]A = P \times (1 + r)^t[/tex]

Where:

A = Final amount

P = Principal amount (initial investment)

r = Annual interest rate (in decimal form)

t = Time (in years)

In this case, we have:

P = $400

A = $684

t = 11 years

Let's substitute these values into the formula and solve for r:

$684 = $400 x [tex](1 + r)^{11}[/tex]

Dividing both sides by $400, we get:

[tex]1.71 = (1 + r)^{11}[/tex]

Now, we need to isolate (1 + r) by taking the 11th root of both sides:

[tex](1 + r) = 1.71^{1/11}[/tex]

Using a calculator, we find:

(1 + r) ≈ 1.0533

Subtracting 1 from both sides, we get:

r ≈ 0.0533

To express the interest rate as a percentage, we multiply by 100:

r ≈ 5.33%

Therefore,

The interest rate that satisfies the assumption is approximately 5.33%.

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The sum or difference that is modeled by the algebra tiles is option D. (-x² + 2x + 3) + (-x² - 2x - 1) = -2x² + 2

Algebra tiles are physical manipulatives used to teach and visualize algebraic concepts. They consist of small, square-shaped tiles that represent different algebraic expressions or values. The tiles come in different colors to represent positive and negative numbers, variables, and constant terms.

Here are the common types of algebra tiles:

1. Unit Tiles: These tiles represent the number one. They are typically square-shaped and are often the base tiles used to build other expressions.

2. Variable Tiles: These tiles represent variables or unknowns. They are usually rectangular in shape and may have different colors to distinguish between different variables.

3. Positive and Negative Tiles: Tiles of different colors, usually red and blue, are used to represent positive and negative values. These tiles can be combined or separated to illustrate operations like addition and subtraction.

4. Area/Rectangle Tiles: These tiles are used to represent quadratic expressions or algebraic expressions involving products or factoring. They are rectangular in shape and can be arranged to model multiplication, factoring, or area representation of polynomials.

Therefore, the type of the algebra tiles in the given question is that of Positive and Negative tiles.

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Answer: [tex]\sf\$6.48[/tex]

Step-by-step explanation:

If a six-pack of cola is sold for $1.50, then the price per can is:

[tex]\sf\implies\$1.50 \div 6 = \$0.25[/tex]

A 24 pack of cola contains 24 cans, so the total cost of the 24 pack is:

[tex]\sf\implies 24 \times \$0.25 = \$6.00[/tex]

The sales tax is 8%, so the tax on the purchase is:

[tex]\sf\implies \dfrac{8}{100} \times \$6.00 = \$0.48[/tex]

Therefore, the total charge including sales tax is:

[tex]\sf\implies\$6.00 + \$0.48 = \$6.48[/tex]

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The range of the reciprocal function f(x) = -7/(3x + 11) is all real numbers except for the value x = -11/3.

The range of the reciprocal function f(x) = -7/(3x + 11), we need to determine the set of all possible values that f(x) can take.

The reciprocal of a number is obtained by taking the multiplicative inverse, which means that the reciprocal of a non-zero number a is 1/a.

We are looking for the range of the reciprocal function, so we need to consider the range of the expression (3x + 11).

The range of (3x + 11) is the set of all real numbers, except when the denominator becomes zero.

The range of the reciprocal function f(x) = -7/(3x + 11) is all real numbers except when (3x + 11) equals zero.

To find the x-value when (3x + 11) equals zero, we solve the equation:

3x + 11 = 0

Subtracting 11 from both sides, we get:

3x = -11

Dividing by 3, we find:

x = -11/3

The reciprocal function is undefined at x = -11/3, as it would result in a division by zero.

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Answer:

a)

Step-by-step explanation:

the function is 11x6=66+13=79x¹=79

hope it helps

The proof that there is no set X such that P(X) ⊂ X is below

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

There is no set X such that P(X) ⊂ X

The above means that

There is no set X such that the power set of X is a subset of set X

By definition, the power set is the set of all subsets of the a Set which includes the set itself and the null or empty set

Using the above as a guide, we have the following:

Because Y is in X, then by definition of the power set P(X), Y is a subset of X.

However, this is a contradiction because it is not possible for a set to be a proper subset of itself.

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The missing root is -24 - 5i.

To find the missing root of the polynomial function f(x) = x^3 - x^2 + 24x + 26, we can use the fact that the sum of all the roots of a polynomial equation is equal to the negation of the coefficient of the second-to-last term divided by the coefficient of the leading term.

In this case, the coefficient of the second-to-last term is 24, and the coefficient of the leading term is 1. Therefore, the sum of all the roots is -24/1 = -24.

We already know that -1 and 1 + 5i are roots, so we can subtract them from the sum to find the missing root:

Missing root = -24 - (-1) - (1 + 5i) = -24 + 1 - 1 - 5i = -24 - 5i.

Note that the missing root is a complex number, indicating that the polynomial has at least one complex root.

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Answer:

The answer is the third option

Step-by-step explanation:

When an exponent is raised to the power of another exponent, both exponents are multiplied.
Recall that a number without an exponent is thought to be raised to the power of 1.

So after multiplying the exponents of all of the variables by 4, we are left with a solution identical to the third option.

Answer:

c) y=-x^2/4 - 2x - 7

Step-by-step explanation:

Answer:

(a) The function has a minimum value

(b) The minimum value is 2

Step-by-step explanation:

(a)Currently y = x^2 + 4x + 6 is in standard form, whose general equation is

y = ax^2 + bx + c.  

We know that for our function a = 1.

Thus, y = x^2 + 4x + 6 must have a minimum value.

(b) Whenever a problem asks for the minimum value, it's asking for the y-coordinate of the minimum.

Step 1:  First we can find the x-coordinate of the minimum using the equation -b/2a from the quadratic formula.  

Plugging in 4 for b and 1 for a, we get:

x-coordinate of minimum = -4 / 2(1)

x-coordinate of minimum = -4 / 2

x-coordinate of minimum = -2

Step 2:  Now we can plug in -2 for x in the quadratic function.  The result will be our minimum value:

f(-2) = (-2)^2 + 4(-2) + 6

f(-2) = 4 - 8 + 6

f(-2) = -4 + 6

f(-2) = 2

Thus, the minimum value of the quadratic function is 2.

The measure of each missing indicated side of the triangle would be given as follows;

1.) X = 2.7

2.) X = 15.2

For question 1.)

Using the sine formula such as given below;

a/sinA = b/sin B

where ;

a = X

A = 27°

b = 6

B = 90°

That is;

X/sin27° = 6/sin90°

X = 6×0.453990499/1

= 2.7

For question 2.)

a/sinA = b/sin B

where ;

a = X

A = 47.4°

b = 14

B = 180-(47.4+90)

= 180-137.4

= 42.6

That is;

X/sin47.4° = 14/sin42.6°

X = 14×0.736097087/0.676875969

= 10.305359218/0.676875969

= 15.2

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The calculated value of x in the circle is 40

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

The circle

From the circle, we have

Center = C

Also, we have

LIne CS bisects the chord RT

Using the above as a guide, we have the following:

RS = ST

Where

ST = 40 and RS = x

So, we have

x = 40

Hence, the value of x is 40

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The correct option is b, the solutions of the quadratic equation are x = ±2

Here we want to solve the following quadratic equation:

3x² = 12

To solve this, we need to isolate the variable, so let's start by dividing both sides by 3, then we will get:

x² = 12/3

x² = 4

Now we can apply the square root in both sides:

√x² = ±√4

x = ±2

These are the two solutions, then the correct option is b.

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Answer:

1. Group B

2. Group A

3. The median.

Answer:

1. Group B has the lowest age range out of both groups. Group B has at least 18 students under 16 and Group A has ages from 5 through 30.

2. Group A has more of a variability of ages because it is more scrambled than Group B. Group B had more students that had ages that were all close to each other.

3. I think it's best to use the median because it measures the age above which is found. If we use the mean, it will only be calculated by adding all numbers together and then dividing the sum of the numbers by the number of numbers.

The value of 13.3km/L corresponds to 30.595 miles/gal

The conversion required is 13.3km/L to mile/gal

converting km to miles

1km = 0.621371 miles

13.3 km = ?

cross multiplying results to

? = 13 * 0.621371 = 8.077 miles

converting L to gallons

1 liters = 0.264172

hence we have that

= 8.077 / 0.264

= 30.595

thus, 13.3km/L is equal to 30.595 miles/gal

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Answer:

region I

Step-by-step explanation:

Based on the description given, the regions that represent A ∩ B' ∩ C' are:

Region I: Items only in group A, not in B or C. (A intersection not B intersection not C)

These regions fulfill the condition of being in group A (A) and not in group B (B') and not in group C (C') simultaneously.

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The length of the radius of the given circle whose central angle has been given would be = 7cm.

To calculate the radius of the given circle, the formula that should be used will be given below as follows:

Length of arc = 2πr×∅/360

Length of arc = 14cm

∅ = 115°

14 = 2×3.14×r ×115/360

make R the subject of formula;

r = 14/2.006

= 6.9

= 7cm

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The price for which the designer will sell the maximum number of shirts is given as follows:

$11.

As the amount sold is modeled by a concave down quadratic function, the price for which the designer will sell the maximum number of shirts is given by the x-coordinate of the vertex of the quadratic function.

The function in the context of this problem is given as follows:

S(x) = -4x² + 88x - 160.

The coefficients are given as follows:

a = -4, b = 88, c = -160.

Hence the x-coordinate of the vertex is obtained applying it's formula as follows:

x = -b/2a

x = -88/-8

x = 11. -> price of $11.

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The four iterates of the function f(z) = z² + 2 + 2t are:

To find the first four iterates of the function f(z) = z² + 2 + 2t with an initial value of z0 = -1 + 2t, we will substitute the initial value into the function repeatedly.

Substitute z0 into the function:

f(z0) = (-1 + 2t)^2 + 2 + 2t

Simplify the expression:

f(z0) = 1 - 4t + 4t² + 2 + 2t

f(z0) = 4t² - 2t + 3

This is the first iterate of the function.

Substitute the first iterate into the function:

f(f(z0)) = f(4t² - 2t + 3)

Simplify the expression:

f(f(z0)) = (4t² - 2t + 3)² + 2 + 2t

f(f(z0)) = 16t⁴ - 16t² + 40t² - 12t + 14

This is the second iterate of the function.

Repeat the process for the third and fourth iterates:

f(f(f(z0))) = (16t⁴ - 16t³ + 40t² - 12t + 14)² + 2 + 2t

f(f(f(z0))) = 256t⁸ - 512t⁷ + 768t⁶ - 768t⁵ + 560t⁴ - 288t³ + 88t² - 16t + 18

and, f(f(f(f(z0)))) = (256t⁸ - 512t⁷ + 768t⁶ - 768t⁵ + 560t⁴ - 288t³ + 88t² - 16t + 18)² + 2 + 2t

f(f(f(f(z0)))) = 65536t¹⁶ - 262144t¹⁵ + 557056t¹⁴ - 787456t¹³ + 801216t¹² - 623616t¹¹ + 378752t¹⁰ - 185536t⁹ + 72432t⁸ - 21856t⁷ + 4916t⁶ - 800t⁵ + 84t⁴ - 4t³ + 2t² + 2t + 2

These are the first four iterates of the function f(z) = z² + 2 + 2t with the initial value of z0 = -1 + 2t.

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(1) The triangles ABC and DEF are not similar

(2) The triangles JKL and JMN are similar by the SAS similarity statement

(3) The triangles ABC and XYZ are similar

(4) The triangles PQR and TSR are similar

(1) Triangle ABC and DEF

The triangles in this figure are

ABC and DEF

These triangles are not similar is because:

The triangles do not have similar corresponding sides i.e. Ratio = 30/24 ≠ Ratio = 24/18

Evaluate

Ratio = 1.25 ≠ Ratio = 1.33

(2) Triangle JKL and JMN

The triangles in this figure are

JKL and JMN

"If two sides in one triangle are proportional to two sides in another triangle and the included angle in both are congruent, then the two triangles are similar"

This means that they are similar by the SAS similarity statement

(3) Triangle ABC and XYZ

The triangles in this figure are

ABC and XYZ

These triangles are similar is because:

The triangles have similar corresponding sides i.e. Ratio = 33/22 = 45/30 = 42/28

Evaluate

Ratio = 1.5

(4) Triangle PQR and TSR

The triangles in this figure are

PQR and TSR

These triangles are similar is because:

The triangles have similar corresponding sides i.e. Ratio = 10/5 = 9/4.5

Evaluate

Ratio = 2

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The triangles ABC and CDE are similar

The width AB of the river is 172.73 ft

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

The triangles ABC and CDE

The above triangles have corresponding angles and they also have similar side lengths

This means that the triangles are similar

Here, we have the following ratio

AB : 100 = 38 : 22

So, we have

AB/100 = 38/22

This gives

AB = 100 * 38/22

Evaluate

AB = 172.73

Hence, the width AB of the river is 172.73 ft

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Answer:

Step-by-step explanation:24 ft

The measure of angle B is given as follows:

m < B = 60º.

The three trigonometric ratios are the sine, the cosine and the tangent, and they are obtained according to the rules presented as follows:

For the angle B, we have that:

Hence we apply the cosine ratio to obtain the measure of angle B as follows:

cos(B) = (x/2)/x

cos(B) = 1/2

B = arccos(1/2)

B = 60º.

The triangle is given by the image presented at the end of the answer.

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N is rounded to two decimal places so n=7.052/m = 7.052/2.8 2.52.

Take the equation set into consideration:

4x² - my = 10  --- (1)

mx² + ny = 20  --- (2)

When x = 2.1, one of the system's solutions is provided by the problem. Using this knowledge, we can change x in both equations to be 2.1. It results in:

4(2.1)2 my = 10 ---> 17.64 my = 10 ---> my = 7.64 --- (3) m(2.1)² + ny = 20 ---> 4.41m + ny = 20 --- (4)

Ascertaining n's value is necessary.

My = 7.64, as determined by equation (3).

With this number as a replacement in equation (4), we obtain:

4.41m + 7.64 = 20

(Rounded to one decimal place) 4.41m = 12.36 m = 2.8

This value of m is substituted in equation (4) to yield the following results: 2.8(2.1)2 + ny = 20, 12.948 + ny = 20.

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Hello !

student's number / total students

9)

288/360 = 0,8

⇒ it's C

10)

90/360 = 0,25

⇒ it's B

Have a good day!

The volume of the moon can be shown to be 3.07% of the volume of the planet.

First, calculate the radius of the planet and the moon.

The radius (r) of the planet is half of its diameter:

r = 27, 998 mi / 2

= 13, 999 mi

The volume of the planet is V:

= 4 / 3 π ( 13, 999 mi)³

=  11, 493, 372, 846 cubic miles

The volume of the moon is:

V = 4 / 3 π (4,059.71 mi) ³

=  352, 432, 952 cubic miles

The Percent volume :

= ( Volume of moon / Volume of planet) x 100

= ( 352, 432 ,952 cubic miles / 11, 493,372,846 cubic miles) x 100

= 3.07 %

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Step-by-step explanation:

I believe it is asking for the probability that x is greater than the mean + two standard deviations .....

  look at the mean ....count up two SD ( labelled at the bottom)  ....then see what is to the right of this point  : 2.35 % + .15 % =  2.5%  is greater

The number of terminates are 2,384.78.

An exponential function can be used to illustrate the daily growth of termites.

If "t" represents the number of days, then "N" represents the number of termites.

⇒ N = [tex]1600(1 + 0.042)^{t}[/tex]

Where 0.042 is the decimal form of 4.2%.

Using this formula,

It can be  calculate the number of termites after any number of days t.

For example,

After 10 days, the number of termites would be:

⇒ N = [tex]1600(1 + 0.042)^{10}[/tex]

⇒ N = [tex]1600(1.042)^{10}[/tex]

⇒ N ≈ 2,384.78 termites

Hence,

⇒ N =  2,384.78 termites

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