geometry unit 7 : angles of polygons & parallelograms

find the value of x

The rectangle QRST have the values for the respective angles and lengths as: m∠QRS = 90°, m∠QTR = 42°, m∠RTS = 48°, TR = 16, and QU = 8.

A rectangle has two diagonals that are the same(congruent) and they bisect each other. The rectangle have two pair of parallel sides which makes the angles formed by its diagonals alternate angles. And each interior angle of the rectangle is equal to 90°

m∠QRS = 90° {an angle of a rectangle}

m∠QTR and m∠TRS are alternate angles and are equal so;

m∠QTR = 42°

m∠RTS and m∠QTR are complementary angles are they sum up to 90° so;

m∠RTS = 90° - 42°

m∠RTS = 48°

lines TR and QS are diagonals of the rectangle and are equal so;

TR = 16

line segment TR bisect QU so;

QU = 16/2

QU = 8.

Therefore, we have the values for the respective angles and lengths of the rectangle as: m∠QRS = 90°, m∠QTR = 42°, m∠RTS = 48°, TR = 16, and QU = 8.

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For the given distribution, the Expectation, E(2X² + 3X) is 28.9

Now here we see that we have the distribution given to us

We need to find

E(2X² + 3X)

Now we know that

E(X) = ∑xp(x)

Hence we get

E(2X² + 3X) = 2[1 X 0.2  +  4 X 0.3  +  9 X 0.2  +  16 X 0.4] + 3[1 X 0.2  +         2 X 0.3  +  3 X 0.2  +  4 X 0.4]

= 2[0.2 + 1.2 + 1.8 + 6.4] + 3[0.2 + 0.6 + 0.6 + 1.6]

= 2 X 9.6  +  3 X 3

= 19.2 + 9

= 28.9

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Complete Question

(image Attached)

Answer:

I don't know ten?

Step-by-step explanation:

Maybe count how many numbers are covered by the blue line

Answer:

B, Variable

A Variable is used in place of a number

With 99% confidence that the true difference lies between 0.1316 and 0.2694.

A 99% confidence interval for the difference in average SAT scores between coached and uncoached students can be constructed using the data above.

The confidence interval is calculated as (mean of coached students - mean of uncoached students) +/- (2 * standard error of the difference in means).

The mean of coached students is (0.3098 + 0.3399 + 0.219 + 0.0798) / 4 = 0.2155, and the mean of uncoached students is (0.0046 + 0.0248) / 2 = 0.0147. The standard error of the difference in means can be calculated as the square root of ((0.2155(1-0.2155)/4) + (0.0147(1-0.0147)/2)).

The confidence interval is then (0.2155 - 0.0147) +/- (2 * 0.0347) = 0.201 +/- 0.0694, or (0.1316, 0.2694). This indicates that, on average, coached students gain 0.201 points more than uncoached students, with 99% confidence that the true difference lies between 0.1316 and 0.2694.

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The number of shorts are 22 and the number of t-shirts are 132.

In mathematics, an equation is a formula that expresses the equality of two expressions, by connecting them with the equals sign =.

Given that, Dot sells t-shirts ($3) and shorts ($4). In April, total sales were $484.

Let the number of shorts be s.

People bought 6 times as many t-shirts as shorts.

Let the number of t-shirts be 6s.

Now, the equation is 4×s+3×6s=484

4s+18s=484

22s=484

s=484/22

s=22

So, 6s =132

Therefore, the number of shorts are 22 and the number of t-shirts are 132.

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Answer: It's D

Step-by-step explanation:

Answer:

-21

Step-by-step explanation:

Just replace b by 7 and x by -2

-b + 7x = -(7) + 7(-2) = -7 + -14 = -7-14 = -21

Answer:

x = 7

Step-by-step explanation:

In a triangle(3 sides), the total number of degrees is 180 degrees.

In a quadrilateral(4 sides), the total number of degrees is 360 degrees.

^^ Now convert this into a formula

Let's say s = number of sides

d = total degrees

s:       d:

3 --> 180

4 --> 360

Hence, the relation between s and d is:

(s-2)*180

Let's test this relation:

3:

(3-2)*180 =  ==> plugin 3 for s in (s-2)*180

1*180 = 180 √

4:

(4-2)*180 =  ==> plugin 4 for s in (s-2)*180

2*180 = 360 √

Now apply this formula to an 8-sided figure:

s = 8

(s-2)*180 =

(8-2)*180 =   ==> plugin 8 for s in (s-2)*180

6*180 = 1080 total degrees in the 8-sided figure

Since all 8 sides in the 8-sided figure are equal, all 8 angles are equal as well.

Hence, the measure of each angle is:

1080 / 8 = 135 degrees

Hence:

16x + 23 = 135  ==> solve for x

16x = 112  ==> subtract 23 on both sides to isolate x

x = 7  ==> divide both sides by 16 to isolate x

Answer:

V = 31,667.8 cubic ft

Step-by-step explanation:

The volume of a right circular cone can be calculated using the formula:

V = (π * r^2 * h) / 3

Where r is the radius of the base and h is the height of the cone.

First, let's find the radius:

r = diameter / 2 = 18.7 ft / 2 = 9.35 ft

Now, we can plug in the values for r and h into the formula:

V = (π * 9.35^2 * 19) / 3 = (π * 87.5295 * 19) / 3 = (1670.20355 * 19) / 3 = 31,667.76 cubic ft

Rounding to the nearest tenth of a cubic foot, we get:

V = 31,667.8 cubic ft

The equations for price of one tire patch

4x + 1.9 = 22.2

22.2 – 4x = 1.9

Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.

It demonstrates the equality of the relationship between the expressions printed on the left and right sides. LHS = RHS is a common mathematical formula.

Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.

Given:

We have to find the Equation for  price of one tire patch.

Ryan bought 4 tire patches.

Price on gift card= $22.2

Then, according situation the equations for price of one tire patch

4x + 1.9 = 22.2

and, 22.2 – 4x = 1.9

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The smallest number of units that must be sold for the company to realize a profit will be 3,637 units.

The allocation of weights to the important variables that produce the calculation's optimum is referred to as a direct consequence.

To produce each product unit, the company spends $1.75 on material and $2.95 on labor. Its total fixed cost is $6000. Each unit sells for $6.35.

Let 'x' be the number of units. Then the equation is given as,

6.35x = 1.75x + 2.95x + 6000

Simplify the equation, then we have

6.35x = 1.75x + 2.95x + 6000

6.35x = 4.7x + 6000

1.65x = 6000

x = 3637 units

The smallest number of units that must be sold for the company to realize a profit will be 3,637 units.

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By simplifying the expression  (r − 6)(r − 2) + (r + 4)(r − 9) the value is 2r² - 13r - 24.

A mathematical expression is a finite combination of symbols that is well-formed in accordance with context-specific norms.

The operations +, -, or are used to combine a number or variable set into an expression. the difference between an algebraic expression and an arithmetic expression that just contains integers and mathematical operators.

Expression in math. A mathematical expression is the collection of mathematical symbols that results from the proper combination of numbers and variables using operations like addition, subtraction, multiplication, division, exponentiation, and other as-yet-unlearned operations and functions.

Given:

(r - 6)(r - 2) + (r + 4)(r - 9)

Expand

⇒ r² - 8r + 12 + r² - 5r - 36

Group like terms

⇒ r² + r² - 8r - 5r + 12 - 36

Add similar elements: -

2r² - 13r - 24

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Hemostasis is the process that causes a blood vessel to stop bleeding. It is a multi-step process with connected steps.

Here are the right answers in the right sequence.

Hemostatic mechanisms come in THREE varieties.

First, a VASULAR spasm tightens the blood vessel that has ruptured, limiting bleeding.

A significant amount of platelets AGGREGATE and go through degranulation during the creation of platelet plugs.

DEGRANULATION AIDS IN HEMASTASIS

Blood turns from a liquid to a gel during COAGULATION, also known as clotting, creating a blood clot. Hemostasis, the stoppage of blood loss from a damaged vessel, and repair may be the outcomes. The activation, adhesion, and aggregation of platelets, as well as the deposition and maturation of fibrin, are all components of the coagulation process.

After an injury, coagulation starts virtually right after.

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The  average rate of change over  1≤x≤5 is 6.140. The rate of change over 6≤x≤8 is -2.453. The change of rate decreases as x increases.

An expression is combination of variables, numbers and operators.

The exponential decay function to model the situation is f(x)=52(0.8)ˣ

where 52 is the initial value and 0.8 is the decay factor.

The given intervals are 1≤x≤5

f(1)=52(0.8)=41.6

f(5)=52(0.8)⁵=17.039

The average rate=17.039-41.6/5-1

=24.561/4

=6.140

Now let us find for the interval 6≤x≤8

f(6)=13.631

f(8)=8.724

Average rate=8.724-13.631/8-6

=-2.453

Hence, the  average rate of change over  1≤x≤5 is 6.140. The rate of change over 6≤x≤8 is -2.453. The change of rate decreases as x increases.

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Work Shown:

[tex](7+3)^2+(14+12\div 6)\\\\(7+3)^2+(14+2)\\\\(10)^2+(16)\\\\100+16\\\\116\\\\\text{Therefore, }(7+3)^2+(14+12\div 6) = 116[/tex]

----------

Explanation:

We use the order of operations PEMDAS.

Parenthesis go first, so we evaluate each expression separately in the two parenthesis groupings.

In the second group, we have [tex]14+12\div6[/tex]. The [tex]12\div6[/tex] portion goes before addition. This is because division ranks higher than addition in PEMDAS shown above.

So this is why [tex]14+12\div6[/tex] becomes [tex]14+2[/tex]

After that we add up the stuff in the parenthesis to end up what is shown in the third step.

Then we square the 10 to get 100. The last step is to then add 100 to 16 to get 116 as the final answer.

You can type the original expression into a calculator to confirm the answer. Your calculator should have a division button labeled [tex]\div[/tex] but if not, then look for the slash symbol. Example: [tex]12 \div 6 = 12/6 = 2[/tex]

Answer: y=1/2x+3

Step-by-step explanation: Put you ordered pairs on a graph and find your slope, once you find your slope you can finish the line then you can find the y-intercept

When taking out a loan, the borrower must provide collateral such as a car or home to reduce the risk to the lender and increase the chances of the loan being approved. This includes rent, monthly bus pass, savings, student loan payment, and other expenses.

A loan is a type of debt that is typically provided by a financial institution such as a bank, credit union, or finance company. The purpose of a loan is to provide the borrower with a large sum of money that they may not have readily available, which they must then pay back over a set period of time with interest.

There are various types of loans, including personal loans, car loans, home loans, and student loans. Personal loans are unsecured loans that can be used for a variety of purposes, such as debt consolidation or home improvement. Car loans are used specifically to purchase a vehicle, while home loans are used to purchase a home. Student loans are designed to help pay for education expenses.

When taking out a loan, the borrower is typically required to provide some form of collateral, such as a car or a home, to secure the loan. This helps to reduce the risk to the lender and increases the chances of the loan being approved.

1. Rent: 30% of $3,850 = $1,155.

2. Monthly bus pass for work: 11% of $3,850 = $423.

3. Savings: 10% of $3,850 = $385.

4. Student loan payment: 5% of $3,850 = $192.5.

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The net area of the paper needed is 4.125 square feet.

A cuboid is a three-dimensional closed figure which has volume along with surface area.

The volume of a cuboid is the product of its length, width, and height.

The total surface area of a cuboid is 2(lw + wh + wl) and the lateral surface area is 2(l + w)×h.

Given, The gift is 1.5 feet tall and one of the bases is 9 inches = 0.75 by 0.5 feet.

Therefore the total surface area is,

= 2(1.5×0.5 + 1.5×0.75 + 0.75×0.5).

= 2(0.75 + 1.125 + 0.375).

= 2(2.25).

= 4.5 square feet.

Now, She left one of the bases uncovered which have an area of 0.375 square feet.

Therefore, the net amount of paper needed is = 4.5 - 0.375.

= 4.125 square feet.

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For a triangle, the sum of the interior angles is  180°.

the sum of the exterior angles of a triangle is 360∘.

Acute triangle: The interior angles are less than 90°

If the triangle is an acute triangle then

c = 180° - (a + b) = 180° - (38° + 52°) = 90°.

Right angle triangle: one interior angle is exactly 90°

then c = 90°.

Obtuse triangle: one interior angle is greater than 90°

then c = 180° - (a + b) = 180° - (38° + 52°) = 90°.

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The complete question is-

Given that a= 38° and b= 52° find c for all type of trinagles.

Answer:

The function table for g(x) = 3x - 2 is as follows:

X Y -1 -5 0 -2 1 1 2 4 3 7 4 10 5 13

By graph, the solution of the system of equations is (- 1, - 3).

The equation of line in point-slope form passing through the points

(x₁ , y₁) and (x₂, y₂) with slope m is defined as;

⇒ y - y₁ = m (x - x₁)

Where, m = (y₂ - y₁) / (x₂ - x₁)

We have to given that;

The system of equations are,

⇒ y - 2x - 1

⇒ y = - 3x - 6

Now, We can draw the graph of given system of equations.

The red line shows the graph of y = 2x - 1 and blue line shows the graph of y = - 3x - 6.

So, By graph;

Both equations are cut into at point (- 1 , - 3).

Hence, By graph, the solution of the system of equations is (- 1, - 3).

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At the end of the year there will be 356 rabbit.

Fibonacci sequence is a sequence, in which each number is the sum of the two preceding ones. The numbers in the Fibonacci sequence is the Fibonacci numbers.

Suppose a newly-born pair of rabbits, one male and one female, are put in a field.

Let [tex]f_{1},f_{2},f_{3} ,........f_{12}[/tex] represents the number of rabbit in the month 1, month2,....month12.

i.e., [tex]f_{1} =2, f_{2} =2[/tex]

At the end of its second month a female can produce another pair of

rabbits. i.e., [tex]f_{3}=4[/tex].

At the end of third month a parent female produce one pair and the daughter female produce one pair. i.e., [tex]f_{4} = 8.[/tex]

Similarly it goes on for 12 months.

Using fibonacii sequence, the general term is,

[tex]f_{n} =f_{n-1}+f_{n-2}[/tex]

for 5th month

[tex]f_{5} =f_{4} +f_{3} =8+4=12[/tex]

[tex]f_{6} =f_{5} +f_{4} =12+8=20[/tex]

[tex]f_{7} =f_{6} +f_{5} =20+12=32[/tex]

[tex]f_{8} =f_{7} +f_{6} =32+20=52[/tex]

[tex]f_{9} =f_{8} +f_{7} =52+32=84[/tex]

[tex]f_{10} =f_{9} +f_{8} =84+52=136[/tex]

[tex]f_{11} =f_{10} +f_{9} =136+84=220[/tex]

[tex]f_{12} =f_{11} +f_{10} =220+136=356.[/tex]

Hence, at the end of the year there will be 356 rabbit.

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Frequency table is provided in image and mean=57.28, mode=63 and meadian=61.5.

What is a frequency table ?

A frequency table consists of the lists of items in a given data set and the number of times each item occurs in the data set and The number of times a particular data value occurs in a given data set is referred to as its frequency.

e.g.

A, A, A, B, B, B, B, C, C, D

Count the number of times each grade occurs in the above series. Yes, ‘A’ occurs thrice, ‘B+’ occurs four times, ‘C’ occurs twice, and ‘D’ occurs once. Now, according to the definition of frequency, we can note the frequency of each grade as follows:

Frequency of A = 3

Frequency of B = 4

Frequency of C = 2

Frequency of D = 1

Let us list the grades obtained by the students in the above example, in a frequency table. Table is in image.

Now,

For given frequency table

Mean=sum of all values/no. of terms=2864/50=57.28

Mode=63 as the frequency is highest for 63

Median=(25th+26th) terms/2=61.5.

Hence,

           mean=57.28, mode=63 and meadian=61.5.

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Answer:

AC ≅ DF

Step-by-step explanation:

1. Given
2. Given
3. The whole is greater than the part.
4. The whole is greater than the part.
5. If equals are added to equals, the wholes are equal.
6. Things which are equal to the same thing are equal to one another.
7. Equal lines are congruent

The parametric equations are therefore: x is t, y is 1/3 * t, and z is t.

Response: x = t; y = 1/3; t; z = t

Given

At t = 0, r(t) equals f(t) * I + g(t) * j + h(t) * k.

(F (t0), G (t0), and H (t0))

r(t) = ln (t - 1) + (t + 2) * j + t * ln(tk) t * t * 0 = 1 Required Information is Missing

Calculate the parametric equations.

j + t * ln + (t - 1)/(t + 2) * ln + r(t) = ln(ti) (tk)

With regard to t, differentiate (t) = 1/t * I + 3/((t + 2) 2) * j + (ln(t) + 1) Let t=1 (i.e., e * t * t * 0 = 1)

r = 1/1 for prime (1). * I + 3/((1 + 2) ^ 2) * j + (ln(1) + 1) I + 3/(3 2) * k r prime (1) * j + (0 + 1) Prime (1) = I + 3/9 * K R * j + (1) (1) Prime (1) = I + 1/3 * j + * k r (1) I + 1/3 * j + k = * k r prime (1)

To find x, y, and z.

We utilise the following methods to find x, y, and z: r(t) = f(t) (t) * j + h (t) * k + I + g (t)

This suggests that:

prime r (1) * T = xi, yj, and zk

We therefore have:

I + 1/3 * j + k) = xi + yj + zk * t

it + 1/3 * jt + kt = xi + yj + zk.

In contrast:

xi = it

Divide by I x, y, and j to get 1/3 * jt.

Divide by j y = 3/9 * t zk = kt

Divided by k, z equals t.

The parametric equations are therefore: x = t, y = 1/3 * t, and z = t.

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The volume of the solid generated will be 201 cubic units

Let's rotate it around the y-axis rather than x = 0.

(x-5)² = 4 - y → y = 4 - (x - 3)²

The parabolic section's area is A.

= 2 · int_0^2 (4 - x²) dx = 2(4x - x^3/3)|_0^2 = 32/3

At x, there is a horizontal centroid.

x = 3, so C = 2π(3) = 6π

V = A · C = 32/3 · 6π = 64π cubic units.

Cylinder method: V = 2π int_1^5 (4x - x(x-3)²)) dx = 2π int_1^5(-x^3 +6x² - 5x) dx

V = 2π(-x^4/4 + 2x^3 - 5x²/2)|_1^5 = 2π[(-625/4 + 250 -125/2) - (-¼ + 2 - 5/2)]

V = 2π(125/4 + 3/4) = 2π(32) = 64π cubic units

About 201 cubic units.

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The question would be:

What is the volume of the solid generated when the region bounded by the curve (x-5) ^2 =4-y and the x-axis is revolved around the line x=2?

Answer:

To guarantee that the two pieces you've already taken out connect, you'll need to take out at least four additional pieces. This is because the two pieces you've already taken out will each need to connect to two other pieces, so you'll need four pieces to make two connections. It's possible that fewer pieces might be required, but this is the minimum number of pieces that you need to guarantee the connection.