Find the value of each variable in the following parallelogram

Considering the quadrilateral, the dimensions are as follows

The given figure is a parallelogram, and the properties will be used in finding the required dimensions

QR = PS = 19 opposite sides of a parallelogram are equal

SR = PQ = 24 opposite sides of a parallelogram are equal

PT = PR / 2 = 42 / 2 = 21 (diagonals of a parallelogram bisects each other)

SQ = 2 * TQ = 2 * 10 = 20 (diagonals of a parallelogram bisects each other)

< QRS = < QPS and < PQR = < PSR (opposite angles of a parallelogram)

< QRS + < QPS + < PQR + < PSR = 360 (sum of angles of a quadrilateral)

2 < QRS + 2< PQR = 360

2 < QRS + 2 * 106 = 360

divide through by 2

< QRS + 106 = 180

< QRS = 180 - 106

< QRS = 74

< PQS = <QSR = 49 alternate angles

< RPS + < PRS + < PSR = 180 (angles on a triangle)

< RPS + 35 + 106 = 180

< RPS + 141 = 180

< RPS = 180 - 141

< RPS = 39

<PSQ + < QSR = < PSR adjacent angles

< PSQ + 49 = 106

< PSQ = 106 - 49

< PSQ = 57

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The area of quadrilateral BEFD, by using Heron’s Formula, is 16.

To calculate the area of quadrilateral BEFD, we first need to calculate the area of the entire triangle ΔABC. This can be done by using Heron’s Formula, which states that the area of a triangle is equal to the square root of the semi-perimeter multiplied by the product of the sides of the triangle, minus the sum of the squares of the sides.

In this case, the semi-perimeter is (a + b + c)/2, where a, b, and c are the sides of the triangle. The sides of triangle ΔABC are 9, 10 and 11, respectively. Applying Heron’s Formula, we have:

Area of ΔABC = √(9 + 10 + 11)/2 * (9 * 10 * 11) - (9^2 + 10^2 + 11^2)

= √27 * 990 – 1230

= √990

= 31.6

Now, since we know the areas of the three triangles within ΔABC (4, 9, and 7), we can subtract the sum of those three from the total area of ΔABC to calculate the area of quadrilateral BEFD.

Area of BEFD = 31.6 – (4 + 9 + 7)

= 31.6 – 20

= 11.6

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The required perimeter of the given rectangle is (C) 29 4/6 ft.

A rectangle is a quadrilateral with four right angles in the Euclidean plane.

It can alternatively be described as a parallelogram with a right angle or an equiangular quadrilateral, where equiangular denotes that all of its angles are equal.

A square is a rectangle with four equally long sides.

So, the perimeter formula is:

2(l+b)

Now, calculate the perimeter as follows:

2(l+b)

2(8 1/6+ 6 2/3)

2(49/6 + 20/3)

2(89/6)

178/6

29 4/6 ft

Therefore, the required perimeter of the given rectangle is (C) 29 4/6 ft.

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Correct question:

What is the perimeter of a rectangle with a length of Eight and one-sixth feet and a width of Six and two-thirds feet?

A. 14 3/9 ft

B. 16 2/6 ft

C. 29 4/6 ft

D. 48 3/18 ft

Yes, the function y=3x2-2 exists.

The core of calculus in mathematics are functions. The unique varieties of relations are the functions. In mathematics, a function is represented as a rule that produces a distinct result for each input x.

A polynomial equation is an equation that is the sum of terms that are products of constants, a variable, and/or powers of that variable. All polynomial equations are functions.

Given that y=3x2-2 is the sum of 3x2 and -2, the equation y=3x2-2 matches this description.

both of which are derivatives of variables, constants, or powers of variables.

Consequently, since y=3x2-2 is a polynomial equation, it must be a function.

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complete question - Is y=3x²-2 a function?

Answer: Ayman has saved $25

Step-by-step explanation: It's basically just 5/6th's of 30, which is 25.

The ordered pair of (4 , 16) tells us that the 4 pounds of cheese have its cost as 16 dollars.

An ordered pair is a mathematical concept used to represent a point in a coordinate system. It is a pair of values, usually represented in the form of (x, y), where x and y are real numbers. The first value, x, represents the point's position along the horizontal (x) axis, and the second value, y, represents the point's position along the vertical (y) axis.

In the graph, what we are told is that if one purchases 4 pounds of the cheese, the amount that they would pay for the cheese would be 16 dollars.

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By solving the given equation we know that $32.7 credit is left on the phone.

The definition of an equation in algebra is a logical statement that proves two formulas are equal.

Take the equation 3x + 5 = 14, wherein 3x + 5 and 14 are two expressions that are separated by the symbol "equal."

So, we have the equation:

C(x)-35.50-0.07x

As Henry use it for 40 minutes:

Now, calculate the amount left as follows:

C(x) = 35.50 - (0.07 x 40)

C(x) = 35.50 - 2.8

C(x) = $32.7 left

Therefore, by solving the given equation we know that $32.7 credit is left on the phone.

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Complete question:

Henry purchased a prepaid phone card for $35.50. Calls cost 7 cents a minute using this card. The credit, C(in dollars), left on the card after it is used for x minutes of calls is given by the following function. C(x)-35.50-0.07x . How much credit is left on the card after Felipe uses it for 40 minutes of calls?

Answer: the answer should be D 13 m

Step-by-step explanation: hope this helps :)

Answer:

[tex]13[/tex]m is the hypotenuse of the right triangle

Step-by-step explanation:

Using the Pythagorean Theorem,

[tex]a^{2} + b^{2} = c^{2} \\7^{2}+11^{2} = c^{2} \\49 + 121 = c^{2} \\170 = c^{2} \\\sqrt{170 } = 13.04[/tex]

When we round to the nearest tenth,

[tex]13.04 = 13[/tex]

Hence , the hypotenuse of a right triangle is 13m

We have the length of CE as 18.4 cm.

Since the rectangles ABCD and DEFG are congruent, all sides of rectangle ABCD will be equal to the corresponding sides of rectangle DEFG. Since AB = 7 cm and AD = 17 cm in rectangle ABCD, we can conclude that DE = 7 cm and DF = 17 cm in rectangle DEFG.

Since CE is a diagonal of rectangle DEFG, it can be found using the Pythagorean theorem. In a rectangle, the diagonal is the hypotenuse of a right triangle formed by one side and one side's corresponding side.

Therefore, CE = √(DE² + DF²) = √(7² + 17²) = √(49 + 289) = √(338) = 18.4 cm

Therefore, the length of CE is 18.4 cm.

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The requried simplified value of the given expression is given as -a³/4b². Option B is correct.

The process in mathematics to operate and interpret the function to make the function or expression simple or more understandable is called simplifying and the process is called simplification.

Here,
Given expression,
= [-b³]⁰/[2ba⁻⁷ × -2ba⁴]
= -1 / 4b²a⁻³
= -a³/4b²

Thus, the requried simplified value of the given expression is given as -a³/4b². Option B is correct.

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An exponential function is a function of the form f(x) = a^x, where a is a positive constant (a > 0). An exponential equation is an equation that involves an exponential function.

What exactly makes a function exponential?

A mathematical function with the formula f (x) = an x is an exponential function. where an is a constant known as the function's base and x is a variable. The transcendental number e, or roughly 2.71828, is the exponential-function base that is most frequently encountered.

For example, the function f(x) = 2^x is an exponential function, because it is of the form f(x) = a^x, where a = 2. The equation y = 2^x is an exponential equation, because it involves the exponential function f(x) = 2^x.

To determine whether an equation is an exponential equation, you can look for the presence of an exponential function. If the equation is of the form f(x) = a^x, where a is a positive constant, then it is an exponential equation.

If the equation is not in this form, but it involves an exponential function, it is still an exponential equation. For example, the equation y = 2^x + 1 is an exponential equation, because it involves the exponential function f(x) = 2^x.

Note that an exponential equation does not have to involve an exponent that is a positive integer. For example, the equation y = (1/2)^x is also an exponential equation, because it involves the exponential function f(x) = (1/2)^x.

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The inequality 4/3|1/4x+3|<4 are Ox>-13 and x < -11 or Ox<-24 and x > 0

We can begin by isolating the absolute value on one side of the inequality:

4/3|1/4x+3|<4

|1/4x+3|<3/2

We can then split this inequality into two cases, one for when 1/4x+3 is positive and one for when it is negative:

1/4x+3>0: 1/4x+3>3/2, so multiplying both sides by 4, we get x>-13 and x<-11

1/4x+3<0: 1/4x+3<-3/2, so multiplying both sides by -4, we get x<-24 and x>0

So, the solution is: Ox>-13 and x < -11 or Ox<-24 and x > 0

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Step-by-step explanation:

For the first equation to make a line plot a point at negitive 5 then go up three then go one to the right

For the second equation to make a like plot a point at positive 4 then go down three then go one to the left

Answer:

the one on the left

Step-by-step explanation:

This shows a direct relationship between X and Y

The mean of the variable w will be 31 and standard deviation will be 6

Here it is given that mean of x, μₓ = 12

                    standard deviation, σₓ = 3

     Also W= 7+2x

For a linear function, we know that

if y = a+bx , then E(y)= a+b× E(x), E denotes the mean.

E(w) = E (7+2x)

       = 7+2 × E(x)

     =  7+2×12  = 31

So mean of w will be 31.

As for standard deviation, σ =√Var

  Var (w) = Var( 2x+7)

               = Var(2x) + Var(7)

As variance of a constant term =0

    Var(w) = Var(2x)

As per the equation for variance Var(ax) = a²× Var(x)

So Var(w) = 2²× Var(x)   ( Standard deviation of x= √Var(x)

                  = 4× 9 = 36

Var(w) = 36, Standard deviation =√Var = √36 = 6

So the mean is 31 and standard deviation is 6.

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The given graph is of inverse function.

A function that can change into another function in the opposite direction is known as an inverse function or anti function. In other words, the inverse of a function "f" will take y to x if any function "f" takes x to y. If a function is written as "f" or "F," the inverse function is written as "f-1" or "F-1."

The original value for which a function produced its output is returned by the inverse function. Consider the inverse relationship between the functions f and g: f(g(x)) = g(f(x)) = x. The initial value is fetched by a function that is its inverse. Therefore, the inverse of f is g(y) = (y-5)/2 = x. (x).

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The proportion of the drink that is juice is one part juice to four parts water. The proportion of the drink that is juice is 1:5. This can be written in fraction as 1/5 , in decimal as 0.25 and in percentage as 25%.

A ratio is a mathematical comparison of two or more values. It is typically written as a fraction, with the values being separated by a colon (e.g. 3:4). The values in a ratio can represent any type of quantity, such as length, weight, or time.

A proportion is a statement that two ratios are equal. For example, if the ratio of boys to girls in a class is 4:5, and the ratio of boys to the total number of students is 12:20, then the two ratios are in proportion. In contrast, a ratio is simply a comparison of two or more values without any equality statement.

An orange drink is made using one part juice to four parts water. The proportion of the drink that is juice is 1/5.The proportion of the drink that is juice is 1/5, which can be expressed as a decimal as 0.2 (1/5 = 0.2) or as a percentage as 20% (0.2 x 100 = 20).

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A obtuse triangle is a triangle in which one of the angles is greater than 90°.

An obtuse triangle can be mathematically defined as a triangle with one angle greater than 90°. The formula for calculating the angles of a triangle is known as the Law of Sines. The formula states that the ratio of the length of a side of the triangle to the sine of its opposite angle is the same for all sides. To calculate the angles of an obtuse triangle, we must first find the ratio of the sides to the opposite angle. For example, if we have a triangle with sides of length a, b and c, then the ratios of the sides to their opposite angles are a/sinA, b/sinB and c/sinC. Once we have found the ratios, we can use the Law of Sines to calculate the angles of the triangle. We can then determine if any of the angles are greater than 90°, which would indicate that the triangle is obtuse.

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The total area of the figure when divided in rectangle, triangle and half circle is 86.13 square units.

Area is the room contained by a specific shape or location. It speaks of how much room is consumed. The area and perimeter of the shape will increase in size as it gets bigger.

Given figure comprises of a rectangle, triangle, and a half circle.

The area of the figure is thus calculated by adding the value of all the figures as follows:

A = Area of triangle + Area of rectangle + Area of semi-circle

[tex]A = \frac{1}{2} (b) (h) + (l)(b) + \frac{1}{2} (\pi r^{2} )\\[/tex]

Substitute the value of length, width, height and radius:

[tex]A = \frac{1}{2} (6) (6) + (9)(6) + \frac{1}{2} (3.14 (3^{2}) )\\\\\\A = 18 + 54 + 14.13\\\\A = 86.13[/tex]

Hence, the area of the figure is 86.13 square units.

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The solution is Option C.

The functions f ( x ) and g ( x ) have the same y-intercept of ( 0 , 6 )

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 first function be represented as A

Let the second function be represented as B

Now , the value of A is

f ( x ) = 2x² + 7x + 6   be equation (1)

Now , the value of B is

g ( x ) = 2ˣ + 5   be equation (2)

Now , on simplifying the equation , we get

To find the y-intercepts of the function ,

Substitute the value of x = 0 in the equation , we get

f ( 0 ) = 2 ( 0 )² + 7 ( 0 ) + 6

On simplifying the equation , we get

y = 6

Now , g ( x ) = 2ˣ + 5

Substitute the value of x = 0 in the equation , we get

g ( 0 ) = 2⁰ + 5

g ( 0 ) = 1 + 5

g ( 0 ) = 6

Hence , the y intercepts of the functions f ( x ) and g ( x ) is ( 0, 6 )

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The equation -5y + (7/3)y = -5 - (8/3)y - 4 gives no solution

An equation is an expression that shows the relationship between variables and numbers.

A linear equation is in the form:

y = mx + b

m is the rate of change and b is the initial y value

Given the equation: negative 5 times y plus seven thirds times y equals negative 5 minus eight thirds times y minus 4. This equates to:

-5y + (7/3)y = -5 - (8/3)y - 4

multiply through by 3:

-15y + 7y = -15 - 8y - 12

-8y = -27 - 8y

0 = -27

no solution

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Answer:

1

Step-by-step explanation:

T1(a) = 1

T2(ar) = 3/2

T3(ar²) = 9/4

T4(ar³) =27/8

T5(ar⁴) = 81/16

lets look for r

by using the formula

[tex] \frac{t \\ 2}{t1} = \frac{t3}{t2} = \frac{t4}{t3} = r[/tex]

let us use T2/T1

[tex] \frac{ \\ ar}{a} = \frac{3}{2} \div 1 = \frac{3}{2} \times \frac{1}{1} = \frac{3}{2} [/tex]

[tex]r = \frac{ \\ 3}{2} [/tex]

since r > 1 we will use this formula

[tex]s10 = \frac{a \\ ( r - 1)}{r - 1} [/tex]

by substituting

[tex]s10 = \frac{ \\ 1( \frac{3}{2} - 1)}{ \frac{3}{2} - 1 } [/tex]

[tex] = \frac{ \\ \frac{3}{2} - 1}{ \frac{3}{2} - 1 } [/tex]

[tex] = \frac{ \\ \frac{1}{2} }{ \frac{1}{2} } [/tex]

[tex] \frac{1}{2 \\ } \div \frac{1}{2} [/tex]

[tex] \frac{1}{2 \\ } \times \frac{2}{1} [/tex]

[tex] \frac{2}{2 \\ } = 1[/tex]

therefore the sum of first ten term of the sequence is 1

The distance PR, representing the distance across the river, is given as follows:

PR = 294 ft.

Similar triangles are triangles that share these two features given as follows:

The two similar triangles for this problem are given as follows:

POC and PRE.

Hence the distance PR is symbolized as follows:

PR = x.

The equivalent side lengths form a proportional relationship, given as follows:

x/(x + 160) = 230/355.

Hence, applying cross multiplication, the distance PR is obtained as follows:

355x = 230(x + 160)

355x = 230x + 36800

125x = 36800

x = 36800/125

x = 294 ft.

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

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Answer: The distance across the river is 181 ft.

Step-by-step explanation:

in photo

The correct answer is 6.432 × 10 raised to the power of 6

Answer:

264000 feet/hour

Step-by-step explanation:

1 mile = 5280 feet

5280 * 50 = 264000

50 miles/hour = 264000 feet/hour

Answer: 90 sqare meters

Step-by-step explanation: you have to take 972 and divide it by 10.8 then you get your answer

Using proportions and ratios, the answer is m / 160(2/5) = 37(7/10) / 100 which is option A

Proportions are relationships between two or more related numerical values, usually expressed as fractions or ratios. They are used to compare the relative sizes of different quantities, or to assess the relationship between two different sets of data. Proportions can also be used to make predictions about future events, or to compare different sets of data.

In this problem, we can approach this as

100 pounds on Earth = 37(7/10) pounds on Mars

160(2/5) pounds on Earth = m pounds on Mars

Cross multiply both sides and solve

This will become;

m = [160(2/5) * 37(7/10)] / 100

This can be written in ratio as;

m / 160(2/5) = 37(7/10) / 100

This is option A

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The factor form of quadratic equations are listed below:

In this problem we find fifteen cases of quadratic equations of the form x² + b · x + c, where b, c are real coefficients. This kind of quadratic equation can be modified into factor form by means of the following rule:

x² - (r₁ + r₂) · x + r₁ · r₂ = (x - r₁) · (x - r₂)

- r₁ - r₂ = b

r₁ · r₂ = c

Where r₁, r₂ are roots of the polynomial.

Now we proceed to find the binomial factors:

Case 1

x² + 9 · x + 20 = (x + 4) · (x + 5)

Case 2

x² + 7 · x + 12 = (x + 3) · (x + 4)

Case 3

x² + 8 · x + 15 = (x + 3) · (x + 5)

Case 4

x² + 7 · x + 12 = (x + 3) · (x + 4)

Case 5

x² + 11 · x + 10 = (x + 10) · (x + 1)

Case 6

x² + 7 · x + 6 = (x + 6) · (x + 1)

Case 7

x² + 5 · x + 4 = (x + 5) · (x + 1)

Case 8

x² + 10 · x + 21 = (x + 7) · (x + 3)

Case 9

x² + 10 · x + 16 = (x + 8) · (x + 2)

Case 10

x² + 10 · x + 9 = (x + 10) · (x - 1)

Case 11

x² + 12 · x + 20 = (x + 10) · (x + 2)

Case 12

x² + 15 · x + 14 = (x + 14) · (x + 1)

Case 13

x² + 13 · x + 42 = (x + 6) · (x + 7)

Case 14

x² + 9 · x + 18 = (x + 6) · (x + 3)

Case 15

x² + 16 · x + 60 = (x + 10) · (x + 6)

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