One Angle In A Triangle Has A Measure That Is Three Times As Large As The Smallest Angle. Themeasure (2024)

A = π * 16^2 = π * 256 sq inches is the radius of the circle.

What is ares of circle?The area of a circle is a measure of the amount of space inside the circle, and is calculated by multiplying pi (π) by the radius of the circle squared (r^2). The formula is A = π * r^2, where A is the area and r is the radius.The area of a circle is given by the formula:A = π * r^2Where A is the area of the circle, π is a mathematical constant approximately equal to 3.14, and r is the radius of the circle.Given that the radius of the circle is 16 inches, we can plug this value into the formula:A = π * 16^2 = π * 256 sq inches.

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The distance between the two towers and the building is 50 ft.

What is trigonometry?

The branch of mathematics that sets up a relationship between the sides and the angles of the right-angle triangle is termed trigonometry.

The trigonometric functions, also known as a circular, angle, or goniometric functions in mathematics, are real functions that link the angle of a right-angled triangle to the ratios of its two side lengths.

Given that The height of a tower is 55 ft and the height of a building is 25 ft. If the angle of elevation from the top of the building to the top of the tower is 30.9°.

The distance will be calculated as,

Distance = 30 / tan(30.9)

Distance = 50 ft

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The angle x is in the quadrilateral is an alternate angle and x = 29°, y = 73°, and z = 102°.

How to evaluate for the unknown angles

Angles formed by parallel lines and a transversal as in the quadrilateral can be alternate and are said to be equal

angles x and 29° are alternate angles and

x = 29°

y + x + 78° = 180° {sum of interior angles of a triangle}

y + 29° + 78° = 180°

y + 107° = 180°

y = 180° - 107°

y = 73°

z + 78° = 180° {supplementary angles}

z = 180 - 78°

z = 102°

The measures of angles in the quadrilateral are x = 29°, y = 73°, and z = 102°.

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Answer:

15*280 = 4,200 m

Step-by-step explanation:

Since it's metric, you don't need to do much except multiply the 15 km by 280 m which is 28% of 1000 m.

The median of the list of numbers is -7.

What is Median?

Median is the middle element when the data set is arranged in an increasing or decreasing order.

Given numbers are :

-3, 12, -18, 2, -18, -9, -12, -16, -4, -5

Write the numbers in the ascending order.

-18, -18, -16, -12, -9, -5, -4, -3, 2, 12

There are 10 numbers in the list which is even.

So the median is the average of the middle two elements.

Middle elements are -9 and -5.

Median = (-9 + -5) / 2 = -7

Hence the median of the set is -7.

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The car needs 59.5 gallons of gas for 714 ​a mile trip.

What is an integer?

Zero, a positive natural number, or a negative integer denoted by a minus sign are all examples of integers. The inverse additives of the equivalent positive numbers are the negative numbers.

Here, we have

Given: A particular hybrid car travels approximately 168 miles on 4 gals of gas.

We have to find the amount of gas required for the 714 ​-mile trip.

168 × d = 14 × g

168/14d = 1 g

12d = 1 g

1 gallon will take you 12 miles.

If you are given gallons, use the first one. If you are given miles, use the second one. You are given miles, so

= 714 miles ×(1 gallon/ 12 miles)

= 59.5 gallons.

Hence, The car needs 59.5 gallons of gas for 714 ​a mile trip.

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The equation of a circle passing through the point (- 2, - 3) is -

(x)² + (y)² = 13.

What is the general equation of a circle?

The general equation of a circle is -

(x - h)² + (y - k)² = r²

where (h, k) is the center and (r) is the radius.

Given is a that circle passes through (-2, -3).

For the center at origin, we can write -

(x)² + (y)² = r²

(x)² + (y)² = (- 3 - 0)² + (- 2 - 0)²

(x)² + (y)² = 9 + 4

(x)² + (y)² = 13

Therefore, the equation of a circle passing through the point (- 2, - 3) is -

(x)² + (y)² = 13.

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935 m is the cost of fencing a rectangular field,85 m long and 55 m wide at the rate of rupees 11/m

What is Area of Rectangle?

The area of Rectangle is length times of width.

Given that there is a rectangular field.

Length of rectangular field is 85 m

Width of rectangular field is 55 m.

Perimeter=2(length+width)

=2(85+55)

=2(140)

=280 m

cost of fencing per meter is 11.

cost of fencing per 85 meter is 11×85.

935

Hence, 935 m is the cost of fencing a rectangular field,85 m long and 55 m wide at the rate of rupees 11/m

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x²⁸y²⁸ is the simplified form of the expression ( x⁻⁴ / y⁴ )⁻⁷ written in positive exponents.

What is the simplified form of the expression?

Given the expression in the question;

( x⁻⁴ / y⁴ )⁻⁷

To simplify, apply the exponent rule;

b⁻ⁿ = 1/bⁿ

( x⁻⁴ / y⁴ )⁻⁷

Replace x⁻⁴ with 1/x⁴

( 1/x⁴ / y⁴ )⁻⁷

( 1/x⁴ × 1/y⁴ )⁻⁷

( ( 1 × 1 ) / ( x⁴ × y⁴ ) )⁻⁷

( 1/x⁴ y⁴ )⁻⁷

Change the sign of the exponent by rewriting the base as its reciprocal.

( x ⁴y⁴ )⁷

Apply product rule;

( bᵃ mᵇ)ⁿ = bᵃⁿ × mᵇⁿ

( x⁴ y⁴ )⁷

x⁴ ˣ⁷ × y⁴ ˣ⁷

x²⁸ × y²⁸

x²⁸y²⁸

Therefore, the simplified form of the expression is x²⁸y²⁸.

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Answer:

y^28 x^28

Step-by-step explanation:

Simplify the following:

(1/(x^4 y^4))^(-7)

(1/(x^4 y^4))^(-7) = (y^4/x^(-4))^7:

(y^4/x^(-4))^7

Multiply each exponent in y^4/x^(-4) by 7:

(y^(7×4))/((x^(-4))^7)

7×4 = 28:

y^28/(x^(-4))^7

Multiply exponents. (x^(-4))^7 = x^(-4×7):

y^28/x^(-4×7)

-4×7 = -28:

y^28/x^(-28)

Multiply the numerator of y^28/x^(-28) by the reciprocal of the denominator. y^28/x^(-28) = y^28 x^28:

Answer: y^28 x^28

Answer: 1 is that 10 is an exponent

Step-by-step explanation: 1 times anything is 1

A quadratic function is one that has the formula f(x) = ax² + bx + c, where a, b, and c are all integers with a not equal to zero.

What is meant by quadratic regression?

To choose the parabola equation that best fits a collection of data, a statistical method known as quadratic regression is performed. To get the equation of the straight line that best fits a collection of data, this sort of regression is an extension of simple linear regression.

Using a collection of data with a parabola-like form, quadratic regression seeks the best-fitting equation. Making a scatter plot is the initial stage in regression.

A quadratic function is one that has the formula f(x) = ax² + bx + c, where a, b, and c are all integers with a not equal to zero. A parabola is the shape that makes up the graph of a quadratic function. If a parabola opens up.

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GCF of 22 and 32:

=

2 .

They are not alike in anyway

The time on the first watch reads 2:31, followed by 3:13, 3:55, and 4:37 on the following watches.

What time should the watch's fifth hand display?

The time on the first watch reads 2:31, followed by 3:13, 3:55, and 4:37 on the following watches.

Adding 42 minutes to the prior watch, which is currently showing the time 4:37, results in the final time reading of 5:19.

When x minutes have passed, let the clock hands align.

Clock hands align at 21.81 minutes after four.

Option B, 21.81 minutes, is the proper response, therefore.

They need to be 30 minutes apart for them to be moving in the opposing directions.

Minute hand will need to add 50 minute gaps as a result.

It takes 60 minutes to fill 55 minute gaps.

In light of this, 54 6/11 minutes after four is the right response.

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The period of time it will take for the element to remain 110 grams would be = 11.7mins

What is decay reaction?

A decay reaction is defined as the type of reaction whereby the a substance disintegrates to form new smaller substances.

The mass of the element = 300g

The percentage that decays per minute = 5.4% of 300g.

That is;

= 5.4/100 ×300

= 1620/100

= 16.20g

The difference between the given mass = 300 - 110 = 190g

if 1 minute = 16.20

X minutes = 190

X = 190/16.20

X = 11.7mins.

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The value of the composite function h(1) is 24

What is the value of h(1)?

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

f(x) = -5x, g(x) = x + 3 and

h(x) = -2f (x + 2) - 2g(x - 1)

The above are individual functions

This means that

h(x) = -2(-5(x + 2)) - 2(x + 3 - 1)

For h(1), we have

h(x) = -2(-5(1 + 2)) - 2(1 + 3 - 1)

Evaluate

h(x) = 24

Hence, the value of the composite function is 24

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Hope it helps.

If you have any query, feel free to ask.

Answer:

28 words Maria got right

Step-by-step explanation:

70% of total words Maria got right

Therefore:

[tex]\frac{70}{100} *40= 28[/tex]

Answer: C

Step-by-step explanation:

12/4=3

16/4=4

3*8=24

4*8=32

To simplify 12/16 to lowest terms, we can divide both the numerator and denominator by their greatest common factor, which is 4:

12/16 = 3/4

Now we need to find an equivalent fraction with a denominator of 32. To do this, we can multiply both the numerator and denominator of 3/4 by 8:

3/4 = (38)/(48) = 24/32

So the answer is C. 3/4, 24/32.

Answer:

48 pieces of jewelry (if you're writing this out be sure to add units as some teachers are sticklers for that!)

Step-by-step explanation:

20% of 40 is 8. This means she needs to sell 8 more than 40 this month. So, she must sell 48 pieces (40+8=48).

Hope this helps!

The length of the steel band that fastens the three 2-ft cylindrical drums is (6 + 2·π) ft

What is a cylinder?

A cylinder is a three dimensional solid with a horizontal circular cross-section and a vertical rectangular cross section, such that the sides of the cylinder are parallel.

Number of drums = 3 drums

The diameter of each drum = 2-ft

The cross-section of each drum = A circle

The distance between two poinrts of tangency of the steel band = 2 × The radius = The diameter of each drum

Distance between two points of tangency = 2 ft.

The number of distances between two points of tangency on the cylinders = 3

The length of the steel band that curves round each circle is found as using the formular for finding the length of an arc of a circle, as follows;

Angle made at the center of the circle = 90° + 30° = 120°
Length of the arc with angle 120° at the center is therefore;

Length of arc = (120/360)× 2 × π × 1 = (2/3)·π

The total length of the band = 3 × 2 + 3 × (2/3·π) = 6 + 2·π

The length of the steel band = (6 + 2·π) feet

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The graph of the straight line that has a slope of {-2/3} and a y-intercept of {2} is attached with the answer.

What is a 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.Functions whose domain are the non - negative integers, known as sequences, are often defined by recurrence relations.Given a function as [tex]${\displaystyle f\colon X\to Y}[/tex] its graph is, formally, the set -

[tex]${\displaystyle G=\{(x,f(x))\mid x\in X\}.}[/tex]

Given is a even function.

The function f(x) is called an even function if f(- x) = x for all real values of {x}.

Now, for the first statement -

f(1) = 5

f(- 1) = - 5

f(1) ≠ f(- 1)

It is not a even function.

For the second statement, it can be concluded that the asymptotic curves are not even.

Therefore, none of the given statements represent a even function graph.

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Answer:

bbbb

Step-by-step explanation:

The graph that represents the inequality 5y≤10 is plotted below.

What is an inequality?

In Algebra, an inequality is a mathematical statement that uses the inequality symbol to illustrate the relationship between two expressions. An inequality symbol has non-equal expressions on both sides. It indicates that the phrase on the left should be bigger or smaller than the expression on the right, or vice versa.

The given inequality is 5y≤10.

In a graph of an inequality, the symbols (<,>) are represented using a dotted line and the symbols (≤,≥) are represented using a straight line.

So, the graph of inequality 5y≤10 will have a straight line.

Now, writing the inequality 5y≤10 in slope-intercept form y = mx + b -

5y = 10

5y = 0x + 10

Substituting the values of x and y with origin (0,0) -

5(0) = 0(0) + 10

0 = 10

Putting the inequality symbol back -

0 ≤ 10

Since, 0 ≤ 10 is true hence the shaded region of graph will cover the origin.

On solving 5y = 10 -

y = 2

Hence the points of the inequality will be (0,2).

Therefore, the graph for the inequality 5y≤10 is plotted.

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The total area of the garden plots is 2.8 acres.

What is the unitary method?

The unitary method is a technique for solving a problem by first finding the value of a single unit, and then finding the necessary value by multiplying the single unit value.

Given that, Mara has 4 garden plots. Each is 0.7 acre in area.

Here, the total area is

4×0.7 acre

= 2.8 acres

Therefore, the total area of the garden plots is 2.8 acres.

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The relationship between the number of hours and cost shows a proportional relationship.

How to illustrate the proportion?

A proportion is an equation that sets two ratios at the same value. A proportion is an equation that sets two ratios at the same value. One variable in a proportional relationship is always a constant value multiplied by the other.

In this case, mechanic charges a very reasonable price per hour to work on cars. This was illustrated as the relationship between the number of hours and cost was given

For 1 hour, cost is $40, for 2 hours, the cost is $80. In this case, there's a proportional relationship. The cost per hour will be:

= $20 / 1

= $20

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Complete question

mechanic charges a very reasonable $ 40 $ 40 per hour to work on cars. For a particular repair, $ 120 $ 120 worth of parts are required. Let x x represent the number of hours that the mechanic works on the car, and let y y represent the total cost of the repair: 1 2 3 4 5 6 7 8 -1 -2 40 80 120 160 200 240 280 320 360 -40. Is the relationship proportional?

Answer: 6 ten dollar bills

Step-by-step explanation:

At the start Sasha had seven ten dollar bills and 5 one dollar bills. It then says she has 15 one dollar bills after the exchange, she exchanged one ten dollar bill for 10 one dollar bills adding up to 15 one dollar bills and six ten dollar bills.

The width of the fourth shim used by a carpenter is, 0.525 centimeter.

What is Addition?

The process of combining two or more numbers is called the Addition. The 4 main properties of addition are commutative, associative, distributive, and additive identity.

Given that;

The carpenter uses four shims to fill gap that is 1.5 centimeters wide.

And, The width of three of the shims are 0.75 centimeter, 0.125 centimeter, and 0.1 centimeter.

Now, Let the width of the fourth shim used by a carpenter = x

So, We can formulate;

⇒ x + 0.75 + 0.125 + 0.1 = 1.5

⇒ x + 0.975 = 1.5

⇒ x = 1.5 - 0.975

⇒ x = 0.525 centimeter

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The resolution was found by the 13, or 13.3% over the ensuing ten years, and The example regression function is an equation that depicts how the variables Y and X are related (s)

How do you estimate the population regression model?

[tex]$\begin{aligned} & Y_i=f\left(X_i, \beta\right)+e_i \\ Y_i & =\text { dependent variable } \\ f & =\text { function } \\ X_i & =\text { independent variable } \\ \beta & =\text { unknown parameters } \\ e_i & =\text { error terms }\end{aligned}$[/tex]

Year : 1990 1993 1996 2000 2004 2008 2012

Population : 4000 3010 2400 1950 1625 1400 1220

It is said that the population fall follows a logarithmic model, where x=1 corresponds to the year 1990, x=2 to the year 1991, and so on.

Along with the population, a table describing a tiny mining town's dwindling population is provided. The term "logarithmic model" refers to a model where x is 1 and symbolizes the year 99 on x is 1991. As we search for a solution, let's employ the regression equation.

The progression is used to project the population in 1995, and I'm going to use a calculator to do it. This wasn't a but a 1, and then this is 2, and then this is 3, and then this is 4, and then this is 5, and then this is 6, and then this is 7, and then this is 8, and then this is 9. By the.13, or 13.3% over the following ten years, the solution was found.

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Answer:

x = - 9

i have answered this question before

Answer:

x = -9

Step-by-step explanation:

Distribute them:

−5(x−3)=60

−5 + 15 =60

Now lets, subtract:

−5x+15=60

−5x + 15 − 15 = 60 − 15

Simplifying:

−5x+15−15=60−15

−5+15−15=60−15

Answer =

-9
hope it helps

Answer:

Inverse variation.

Step-by-step explanation:

I would say inverse variation because inverse variation is represent as, y=k/×. And deals with division.

While direct variation is represented with, y=kx. And deals with multiplication.