Which of the following could be the areas of the three squares below?

The angle relationships formed in the diagram are as follows;

When parallel lines are cut by a transversal, angle relationships can be formed such as corresponding angles, alternate interior angles, alternate exterior angles, vertically opposite angles, linear angles, etc.

Therefore, let's find the angles relationship formed in the diagram as follows:

∠1 and ∠5 are corresponding angles.

∠4 and ∠7 are corresponding angles

Corresponding angles are the angles which are formed in matching corners or corresponding corners with the transversal when two parallel lines are intersected by any other line.

∠3 and ∠5 are alternate interior angles.

Alternate interior angles are the angles formed when a transversal intersects two coplanar lines.

∠1 and ∠8 are alternate exterior angles.

∠2 and ∠7 are alternate exterior angles.

Alternate exterior angles are the pair of angles that are formed on the outer side of the parallel lines but on the opposite side of the transversal.

∠3 and ∠6 are same interior angles. Same interior angles are supplementary angles.

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Answer:

5−10g+20h

Step-by-step explanation:

To distribute the 5 to the terms inside the parentheses, we can use the distributive property:

(1−2g+4h)⋅5 = 5⋅1−5⋅2g+5⋅4h

= 5−10g+20h

This is the simplest equivalent expression we can get, as there are no more terms that can be combined.

The interval of convergence for this series is [tex]$x \in \left(-1, 1\right)$[/tex].

What is Power Series Representation for the Function ?

To find a power series representation for a function, we need to express the function as an infinite series of the form

                      [tex]$$f(x) = \sum_{n=0}^{\infty} a_n (x-x_0)^n$$[/tex]

where [tex]$x_0$[/tex] is the center of the series, and the [tex]$a_n$[/tex] are the coefficients of the series. To determine the interval of convergence for the series, we need to find the values of [tex]$x$[/tex] for which the series converges.

To find the power series representation for a given function, we can use the process of Taylor series expansion. This involves finding the derivative of the function at the point [tex]$x_0$[/tex], and using the derivative to find the coefficients of the series.

For example, suppose we want to find a power series representation for the function [tex]$f(x) = \frac{1}{1-x}$[/tex]  centered at [tex]$x_0 = 0$[/tex]. We can use the process of Taylor series expansion to find the power series representation as follows:

[tex]$$f(x) = \frac{1}{1-x} = \frac{1}{1-0} + \frac{0-1}{(1-0)^2}x + \frac{2 \cdot 0 - 1 \cdot 1}{(1-0)^3}x^2 + \dotsb$$[/tex]

Simplifying this expression, we get

[tex]$$f(x) = 1 + x + x^2 + x^3 + \dotsb$$[/tex]

This is the power series representation of [tex]$f(x)$[/tex] centered at [tex]$x_0 = 0$[/tex].

To determine the interval of convergence for this series, we can use the ratio test. If we let [tex]$a_n = 1$[/tex] for all [tex]$n$[/tex], then the series becomes

[tex]$$\sum_{n=0}^{\infty} a_n (x-x_0)^n = \sum_{n=0}^{\infty} x^n$$[/tex]

If we take the limit of the absolute value of the ratio of successive terms, we get,

[tex]$$\lim_{n \to \infty} \left| \frac{x^{n+1}}{x^n} \right| = \left| x \right|$$[/tex]

If [tex]$|x| < 1$[/tex], then the series converges. If [tex]$|x| > 1$[/tex], then the series diverges. If [tex]$|x| = 1$[/tex], then the test is inconclusive and we need to use another method to determine convergence.

Therefore, the interval of convergence for this series is [tex]$x \in \left(-1, 1\right)$[/tex].

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The longest side of the triangle has a length of 11 cm.

Given that the sum of the lengths of the triangle is equal to 30 cm, and the sides are:

(x + 6)

(x + 4)

2x

Create an equation to find the value of x:

(x + 6) + (x + 4) + 2x = 30

x + 6 + x + 4 + 2x = 30

Combine like terms

4x + 10 = 30

4x = 30 - 10

4x = 20

4x/4 = 20/4

x = 5

Find the length of each of the sides of the triangle:

(x + 6) = 5 + 6 = 11 cm

(x + 4) = 5 + 4 = 9 cm

2x = 2(5) = 10 cm

The longest side is 11 cm.

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45 years will take for 15 grams of strontium to decay to 5 grams

What is strontium?

The chemical element strontium has the atomic number 38 and the symbol Sr. Strontium is a soft, silver-white, yellowish metallic element that is an alkaline earth metal and has a strong reactivity to chemicals. When the metal is exposed to air, a thick layer of dark oxide forms.

Equation Given.

[tex]P = Po e^{-0.0244t}[/tex]

given P = 5 gram

          [tex]P_o = 15 gram[/tex]

Hence ,time taken

[tex]5 = 15 e^{-0.0244t}[/tex]

[tex]\frac{5}{15} = e^{-0.0244t}[/tex]

Taking log both side,

[tex]ln(\frac{1}{3} )=ln (e^{-0.0244t})\\\\-1.098 = -0.0244t\\\\t=\frac{1.098}{0.0244}\\\\t=45years[/tex]

Hence, 45 years will take for 15 grams of strontium to decay to 5 grams.

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Answer:

15%

Step-by-step explanation:

18/120 = 0.15

0.15*100 = 15%

...

The solution is 15 %

The percentage of discount on the normal price of the jacket is given by the equation A = 15 %

What is an Equation?

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.

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 data ,

Let the percentage of discount be represented as A

Now , the equation will be

The normal price of the jacket = $ 120

The discounted price of the jacket = $ 18

So ,

Discounted price of the jacket = A % of normal price of the jacket

Substituting the values in the equation , we get

18 = A % x 120

On simplifying the equation , we get

( A / 100 ) x 120 = 18

Divide by 120 on both sides of the equation , we get

A / 100 = 18/120

A / 100 = 0.15

Multiply by 100 on both sides of the equation , we get

A = 15 %

Therefore , the value of A is 15 %

Hence , the discounted percentage is 15 %

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Answer:

Somoeone can talk here boring

Answer:

this a quesy=tion?

Step-by-step explanation:

The value of a + b must be between 5 and 11. If the value of a 3 or 4, and b will be 4 or 5.

An unknown in mathematics is a number that we are unsure of. In algebra, where they are also known as variables and denoted by symbols like x, y, and z, they are frequently utilised.

In science, a letter from the Roman or Greek alphabet stands in for an undetermined value. They are most frequently employed in physics, where equations are used to explain how different physical qualities relate to one another.

Given that

2 < a < 5, and 3 < b < 6

a is greater than 2 and lesser than 5 , so the value will be 4 or 3.

b is greater than 3 and lesser than 6, so the value will be 4 or 5.

a + b is

3 + 4 = 7 or 4 + 5 = 9

so the product of sum will be 7 or 9, it is between 5 and 11

Therefore,  a + b must be between 5 and 11.

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Answer:  The measure of the three angles is 23, 67, and 90.

Step-by-step explanation:

The sum of three angles is equal to 180. We set the equation as:

x + 23 + 90 = 180

       x + 113 = 180

                x = 67

The measure of the three angles is 23, 67, and 90.

Given line:

Plot two points and connect.

One point is the y-intercept:

Another point with an even value of x as its slope is a fraction with denominator of 2:

Plot these two points and connect.

See below graph.

The graph of a quadratic function is called a parabola

The complete table is

x = -6, -3, 0, 3 6

y = -12  -3 0 -3 -12

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

y=-1/3 x²

From the table of values , we have the following x values

x = -6, -3, 0, 3 and 6

Substitute x = -6, -3, 0, 3 and 6 in y=-1/3 x²

So, we have the following representation

y = -1/3 (-6)² = -12

y = -1/3 (-3)² = -3

y = -1/3 (0)² = 0

y = -1/3 (3)² = -3

y = -1/3 (6)² = -12

So, the complete table of values is

x = -6, -3, 0, 3 6

y = -12  -3 0 -3 -12

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When t is that value, American men earned 2.8 more PhDs than women.

The given equation for h(t) is h(t) = f(t)/g(t), where f(t) models the number of PhDs awarded to men and g(t) models the number of PhDs awarded to women.

Since h(t) = 2.8 for some value of t, this means that the number of PhDs awarded to men is 2.8 times the number of PhDs awarded to women. Therefore, for that value of t, men in the U.S. earned 2.8 more PhDs than women.

The equation h(t) = f(t)/g(t) models the ratio of the number of PhDs awarded to men compared to women in the U.S., where f(t) models the number of PhDs awarded to men and g(t) models the number of PhDs awarded to women. Thus, if h(t) = 2.8 for some value of t, it means that the number of PhDs awarded to men is 2.8 times the number of PhDs awarded to women. In other words, for that value of t, men in the U.S. earned 2.8 more PhDs than women. This indicates that more men have received PhDs than women in the U.S. over the past few decades. The National Center for Education Statistics has kept track of this data and it is clear that men are receiving more degrees than women in the U.S.

h(t) = f(t)/g(t)

h(t) = 2.8

f(t) = 2.8g(t)

Therefore, for that value of t, men in the U.S. earned 2.8 more PhDs than women.

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The result of the addition operation of 1204.2 + 4.72613 is approximately 1208.93.

An addition operation involves two addends added together to result in a number called the sum.

The addition operation is one of the four basic mathematical operations, including subtraction, division, and multiplication.

Mathematical operations combine numbers, variables, and values with mathematical operands to solve mathematical questions.

1204.2 + 4.72613

= 1208.92613

= 1208.93

Thus, the addition of 1204 and 4.72613 yields a total of 1208.93 approximately.

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Quadratic function has minimum value which is -8.

correct option: 1

A variable with the largest power of two in a quadratic equation is called a variable. Quad, which signifies square, is the root of the term quadratic. The phrase must be two times its own strength, neither higher nor lower.

Given that they are the x values for which f(x) = 0, the roots of the function f(x) = ax² + bx + c correspond to the solutions of the quadratic equation ax² + bx + c = 0.

The term ax² is known as the quadratic term (hence the function's name), the word bx is known as the linear term, and the value c is known as the constant term.

Here, the given function,

f(x) = x² - 2x - 7 .......... (i)

now, differentiate with respect to x

d/dx {f(x)} = d/dx ( x²) - d/dx (2x) - d/dx (7)

or, f'(x) = 2x - 2 ............. (ii)

Now, put f'(x) = 0

so, 0 = 2x - 2

or, 2x - 2 = 0

or, 2x = 2

or, x = 1

From equation (ii)

f'(x) = 2x - 2

now, differentiate with respect to x

f''(x) = 2 > 0

So, it implies that, the function has minimum value at x = 1

Now, putting x = 1 in equation (i), we get -

f(1) = (1)² - 2×(1) - 7

f(1) = - 8

Function has minimum value is: - 8.

Thus, correct option is : (1)

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A horizontal line indicates that the thing is travelling steadily. A line that slopes downhill indicates that an object is slowing down.

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Answer:

True.

Step-by-step explanation:

Whether you do a rotation 180 degrees clockwise( [tex]R__(-180,O)[/tex]), or a rotation 180 degrees counterclockwise ([tex]R__(180,O)[/tex]), the image will always end up in the coordinate diagonal from the pre-image.

Answer:

A = principal +interest

P = Principal Amount

r = rate

t = time

A = P(1 + rt)

5 000 = P[(1 + 0.05(821/364.25)]

5 000 = P(1 + 0.05(2.254)

5 000 = P(1 + 0.1127)

5 000 = 1.1127P

P = 4 493.5742

Therefore, you need to deposit an amount of $4 493.5742 to have $5 000 in 821 days.

Step-by-step explanation:

Answer:you need to show the diagram in order for me to

Step-by-step explanation:

If we add a vector I{k+1} to the collection of 21, 22, ... I{k}, the collection will no longer be linearly independent and yes, we will still have a linearly independent collection of vectors if we delete a vector {say 2k}.

linearly independent vectors : In the theory of vector spaces, a set of vectors is said to be linearly dependent if there is a nontrivial linear combination of the vectors that equals the zero vector. If no such linear combination exists, then the vectors are said to be linearly independent. These concepts are central to the definition of dimension

Function : In mathematics, a function from a set X to a set Y assigns to each element of X exactly one element of Y. The set X is called the domain of the function and the set Y is called the codomain of the function

Expression : A mathematical expression is made up of terms (constants and variables) separated by mathematical operators

Equation : A mathematical equation is used to equate two expressions.

Given is a linearly independent vectors in a vector space V.

If we add a vector I{k+1} to the collection of 21, 22, ... I{k}, the collection will no longer be linearly independent.

If we delete a vector {say 2k}, from the collection, yes, we will still have a linearly independent collection of vectors

Therefore, if we add a vector I{k+1} to the collection of 21, 22, ... I{k}, the collection will no longer be linearly independent and yes, we will still have a linearly independent collection of vectors if we delete a vector {say 2k}.

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Answer:

To find the probability of no more than 2 successes in 5 trials of a binomial experiment in which the probability of success in any one trial is 18%, we can use the formula for the probability mass function of the binomial distribution:

P(X = k) = (n choose k) * p^k * (1 - p)^(n-k)

Where:

X is the number of successes in the binomial experiment

n is the number of trials

p is the probability of success in any one trial

k is the number of successes we are interested in

So, in this case, we want to find the probability of X being equal to 0, 1, or 2 successes. We can do this by summing the probabilities of each of these events:

P(X = 0) + P(X = 1) + P(X = 2)

Plugging in the values from the problem, we get:

P(X = 0) = (5 choose 0) * (0.18)^0 * (1 - 0.18)^(5-0) = 0.3199

P(X = 1) = (5 choose 1) * (0.18)^1 * (1 - 0.18)^(5-1) = 0.4199

P(X = 2) = (5 choose 2) * (0.18)^2 * (1 - 0.18)^(5-2) = 0.2082

So the probability of no more than 2 successes in 5 trials of a binomial experiment in which the probability of success in any one trial is 18% is:

0.3199 + 0.4199 + 0.2082 = 0.948

Step-by-step explanation:

Answer:

y = (1/2)x + 2

Step-by-step explanation:

Go from point (-2,1) to (0, 2).

Start at point (-2, 1). First, go up 1 unit. That is a rise of 1.

Now go 2 units right. That is a run of 2.

slope = rise/run = 1/2 = m

The graph intersects the y-axis at 2, so the y-intercept = b= 2.

y = mx + b

y = (1/2)x + 2

Answer:

[tex]\begin{array}{|c|c|}\cline{1-2} \vphantom{\dfrac12} n&A \\\cline{1-2}\vphantom{\dfrac12} 1& \$4376.10\\\vphantom{\dfrac12} 2& \$4442.10\\\vphantom{\dfrac12} 4& \$4476.86\\\vphantom{\dfrac12} 12& \$4500.73\\\vphantom{\dfrac12} 365& \$4512.49\\\vphantom{\dfrac12} \sf Continuous& \$4512.89 \\\cline{1-2} \end{array}[/tex]

Step-by-step explanation:

[tex]\boxed{\begin{minipage}{8.5 cm}\underline{Compound Interest Formula}\\\\$ A=P\left(1+\frac{r}{n}\right)^{nt}$\\\\where:\\\\ \phantom{ww}$\bullet$ $A =$ final amount \\ \phantom{ww}$\bullet$ $P =$ principal amount \\ \phantom{ww}$\bullet$ $r =$ interest rate (in decimal form) \\ \phantom{ww}$\bullet$ $n =$ number of times interest is applied per year \\ \phantom{ww}$\bullet$ $t =$ time (in years) \\ \end{minipage}}[/tex]

Given:

Substitute the given values into the formula to create an equation for A in terms of n:

[tex]\implies A=2100\left(1+\dfrac{0.085}{n}\right)^{9n}[/tex]

Substitute each value of n into the equation:

[tex]\begin{aligned}n=1 \implies A&=2100\left(1+\dfrac{0.085}{1}\right)^{9 \times 1}\\&=2100\left(1.085\right)^{9}\\&=\$4376.10\end{aligned}[/tex]

[tex]\begin{aligned}n=2 \implies A&=2100\left(1+\dfrac{0.085}{2}\right)^{9 \times 2}\\&=2100\left(1.0425\right)^{18}\\&=\$4442.10\end{aligned}[/tex]

[tex]\begin{aligned}n=4 \implies A&=2100\left(1+\dfrac{0.085}{4}\right)^{9 \times 4}\\&=2100\left(1.02125\right)^{36}\\&=\$4476.86\end{aligned}[/tex]

[tex]\begin{aligned}n=12 \implies A&=2100\left(1+\dfrac{0.085}{12}\right)^{9 \times 12}\\&=2100\left(1.00708333...\right)^{108}\\&=\$4500.73\end{aligned}[/tex]

[tex]\begin{aligned}n=365 \implies A&=2100\left(1+\dfrac{0.085}{365}\right)^{9 \times 365}\\&=2100\left(1.00023287...\right)^{3285}\\&=\$4512.49\end{aligned}[/tex]

[tex]\boxed{\begin{minipage}{8.5 cm}\underline{Continuous Compounding Formula}\\\\$ A=Pe^{rt}$\\\\where:\\\\ \phantom{ww}$\bullet$ $A =$ final amount \\\phantom{ww}$\bullet$ $P =$ principal amount \\\phantom{ww}$\bullet$ $e =$ Euler's number (constant) \\\phantom{ww}$\bullet$ $r =$ annual interest rate (in decimal form) \\\phantom{ww}$\bullet$ $t =$ time (in years) \\\end{minipage}}[/tex]

[tex]\implies A=2100e^{0.085 \times 9}[/tex]

[tex]\implies A=2100e^{0.765}[/tex]

[tex]\implies A=2100(2.14899437...)[/tex]

[tex]\implies A=\$4512.89[/tex]

Input the calculated values into the table:

[tex]\begin{array}{|c|c|}\cline{1-2} \vphantom{\dfrac12} n&A \\\cline{1-2}\vphantom{\dfrac12} 1& \$4376.10\\\vphantom{\dfrac12} 2& \$4442.10\\\vphantom{\dfrac12} 4& \$4476.86\\\vphantom{\dfrac12} 12& \$4500.73\\\vphantom{\dfrac12} 365& \$4512.49\\\vphantom{\dfrac12} \sf Continuous& \$4512.89 \\\cline{1-2} \end{array}[/tex]

The values of x that can't be equal for the expression are 0 and 5

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

(5x-2)/(x^2-5x)

This means that we set the denominator to 0

So, we have

x^2 - 5x = 0

Factorize

(x - 5)x = 0

So, we have

x - 5 = 0 and x = 0

Solve for x

x = 5 and x = 0

Hence, the solution is x = 5 and x = 0

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Answer:

10 shirts, 6 pants

Step-by-step explanation:

Let y = the number of shirts

Let x = the number of pants

y + 2 = 2x

x + y = 16

y = 2x - 2

x + (2x - 2) = 16

3x = 18

x = 6

y + 6 = 16

y =  10

Answer:

[tex]\textsf{A.} \quad \begin{cases}y=2x-2\\x+y=16\end{cases}[/tex]

[tex]\textsf{B. \quad 6 pants and 10 shirts}[/tex]

Step-by-step explanation:

Given variables:

If the number of shirts Sylvia packed was 2 fewer than twice the number of pants she packed:

[tex]\implies y=2x-2[/tex]

If the total number of pairs of pants and shirts was 16:

[tex]\implies x+y=16[/tex]

Therefore, the system of equations that represents the problem is:

[tex]\begin{cases}y=2x-2\\x+y=16\end{cases}[/tex]

System of equations:

[tex]\begin{cases}y=2x-2\\x+y=16\end{cases}[/tex]

Substitute the first equation into the second equation and solve for x:

[tex]\implies x+2x-2=16[/tex]

[tex]\implies 3x-2=16[/tex]

[tex]\implies 3x=18[/tex]

[tex]\implies x=6[/tex]

Substitute the found value of x into the first equation and solve for y:

[tex]\implies y=2(6)-2[/tex]

[tex]\implies y=12-2[/tex]

[tex]\implies y=10[/tex]

Therefore, Sylvia packed:

Answer:

106*

Step-by-step explanation:

a triangle is 180*

to find angle BCA, you do 180 - (64+42)

that =74*

a straight line is also 180* so you do 180 - BCA

180-74=106

106

Answer:

To rent a car from this company, Aaliyah will be charged a base rate of $71.87 per day, plus $0.09 for every mile she drives. In total, she plans to drive 475 miles, so she will be charged an additional $0.09 * 475 = $42.75 for the miles she drives.

The total cost of renting the car for one day will therefore be $71.87 + $42.75 = $114.62.

Aaliyah has a budget of $320, so she can afford to rent a car for a maximum of $320 / $114.62 = 2.79 days. However, since she can only rent the car for whole number of days, the maximum number of days she can afford is 2 days.

The inequality that can be used to determine the maximum number of days Aaliyah can afford to rent while staying within her budget is:

dd <= 2

Where dd is the number of days she plans to rent the car for. This inequality states that the maximum number of days Aaliyah can afford is 2.

Tables and figures must all be labelled with numbered captions that clearly identify and describe them.

x = 61

Left hand triangle containing 1 angle of 74

Label the other angle opposite the marked side also as 74

Find the third angle. Call it y.

y + 74 + 74 = 180           Combine like terms

y + 148 = 180                 Subtract 148 from both sides.

y = 180 - 148

y = 32

Now work with the triangle on the right.

label the angle making up the right angle = z

32 + z = 90                             These two angles are complementary = 90

32 - 32 + z = 90 - 32              Subtract 32 from both sides

z = 58                                      Use 58 wherever you see z

x + x + z = 180                         Substitute

2x + 58 = 180                          Subtract 58 from both sides

2x = 122                                  Divide by 2

x = 61

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Answer:

3.5

Step-by-step explanation:

The ball reaches the ground when [tex]h(t)=0[/tex].

[tex]-16t^2+54t+7=0 \\ \\ 16t^2-54t-7=0 \\ \\ (8t+1)(2t-7)=0 \\ \\ t=-1/8, t=7/2 \\ \\ t>0 \implies t=3.5[/tex]