The measures of complementary angles have a sum of 90 degrees. Angle A and angle B are complementary, and their measures have a difference of 20°. What are the measures of the angles?

thanks.

Answers

Answer 1

angle A=36 degrees
angle B=54 degrees
36+54=90

Answer 2

To find the measures of complementary angles A and B with a known difference of 20 degrees, we set up a system of equations and solved them to find that angle A measures 55 degrees and angle B measures 35 degrees.

The problem involves finding the measures of two complementary angles, angle A and angle B, with a known difference in their measures. By definition, complementary angles are two angles whose sum is 90 degrees. Given the difference of 20 degrees between the angles, we can set up a system of equations to solve for their measures.

Let's denote the measure of angle A as a and angle B as b. Therefore, we have the two equations based on the problem statement:

a + b = 90 (because they are complementary)

a - b = 20 (the difference in their measures)

To find the values of a and b, we can add the two equations:

a + b = 90
a - b = 20

By adding them together, we get:

2a = 110

Dividing both sides by 2, we find a:

a = 55

To find b, we substitute a back into one of the original equations:

55 + b = 90

Subtracting 55 from both sides gives us b:

b = 35

Therefore, angle A measures 55 degrees and angle B measures 35 degrees.

Related Questions

What is the equation of a line that passes through the points (3,6) and (8,4)

Answers

first, you must find the slope. 4-6/8-3 which is -2/5.
then, plug in a point to the slope intercept formula. Y=MX+B 6=-2/5(3)+b
-2/5x3= -1 1/5
6+1 1/5=7 1/5
7 1/5=B
Your equation is y=-2/5x+7 1/5

PLEASE HELP!!! :))

In isosceles ∆DEK with base DK, EF is the angle bisector of ∠E, m∠DEF = 43°, and DK = 16cm. Find: KF, m∠DEK, m∠EFD.

Answers

we have isosceles ∆DEK

EF is the angle bisector of ∠E,
m∠DEF = 43°=  m∠FEK ( the bisector divide the angle in two equal angles)

so m∠DEK = m∠DEF +  m∠FEK = 43 + 43 = 86

∆DEK is isoceles triangle (given)
the two base angles are equal m∠EDK =  m∠DKE
and the sum of angles in a triangle = 180

so m∠DEK + m∠EDK+ m∠DKE = 180
86 + m∠EDK+ m∠DKE = 180

2 x m∠EDK = 94

m∠EDK = 94 / 2 = 47

in triangle DEF
m∠EDF + m∠E FD+m∠FED= 180

47 +m∠E FD + 4 3 = 180

m∠E FD = 180-43-47 = 90

Find: KF?
in an isoseles triangle the bisector is in the same time median so
KF= DK / 2 = 16/ 2 = 8 cm

The temperature fell from 0 degrees to 6 3/5 degrees below 0 in 2 1/5 hours. what was the temperature change per hour?

Answers

divide 6 3/5 by 2 1/5

6 3/5 = 33/5

2 1/5 = 11/5

33/5 / 11/5 = 3

the temperature dropped 3 degrees per hour

find the roots of the quadratic function x^2=100

Answers

x^2 = 100

√x² = √100

x= 10

hope this helps

x^2 = 100
Take the square root of both sides of the equation:-

x = 10, - 10 Answer

Which of the following is a radical equation?

Answers

Answer:

C. [tex]\sqrt{x}+3=13[/tex]

Step-by-step explanation:

We know that,

A radical equation is the equation in which the variable is under the radical.

According to the options, we see that,

In the equation [tex]\sqrt{x}+3=13[/tex], the variable is under the radical.

All other equations have constant number under the radical.

Thus, we get,

Equation C i.e. [tex]\sqrt{x}+3=13[/tex] is a radical equation.

[tex]\fbox{\text{Option C}}[/tex] is correct as [tex]\sqrt x+3 = 13[/tex] is radical equation because the variable is under the radical and the radicand is [tex]x[/tex].

Further explanation:

Radical can be describing as a square root, a cube root, a fourth root or higher root.

Radical equation can be defined as any equation that contains a radical on the variable is known as the radical equation.

The term under the radical symbol is known as radicand.

Option A is not correct.

Here, [tex]x\sqrt 3= 13[/tex] is not radical equation because the radical is on a constant term 3 not on the variable.

Option B is not correct.

Here, [tex]x+\sqrt 3=13[/tex] is not radical equation because the radical is on a constant term 3 not on the variable.

Option C is correct.

Here, [tex]\sqrt x+3=13[/tex] is radical equation because the variable is under the radical and the radicand is .

Option D is not correct.

Here, [tex]x+3 =\sqrt {13}[/tex] is not radical equation because the variable is not under the radical.

The equation [tex]\sqrt x+3=13[/tex] is a radical equation. Therefore [tex]\fbox{\text{Option C}}[/tex] is correct.

Learn more:

1. Learn more about functions https://brainly.com/question/2142762

2. Learn more about range of the functions https://brainly.com/question/3412497

3. Learn more about relation and function https://brainly.com/question/1691598

Answer details:

Grade: High school

Subject: Mathematics

Chapter: Number system

Keywords: functions, equation, radical equation, radical, square root, cube root, fourth root, variable, radicand, term, under, contains describe.

Is it possible for two different numbers, when squared, to give the same result? What does this result tell you about solving an equation when the variable is squared? How many solutions will an equation like this have? Will there always be the same number of solutions for any equation with a squared variable? Explain.

Answers

Let x,y be two different numbers
suppose x^2=y^2
then x^2-y^2=0
which yields (x+y)(x-y)=0
so either x=y or x=-y
In any case, x and y must be the same value
also when a vairable is squared like y=x^2
we must note that there are 2 possible solutions
x=(+/-)sqrt(y)

The temperature dropped 6c every hour for 7 hours. What was the total number of degrees the temperature changed in the 7 hours

Answers

Hello There!

You are given the unit rate:
6°C per hour
So for 7 hours, multiply the drop per hour by the number of hours:
6 x 7 = 42.
It would have dropped 42°C.

Hope This Helps You!
Good Luck :)

- Hannah ❤

True false to find the midpoint of a segment, first mark a point not on the segment and then fold the paper so that the point you marked and a point on the line are included in the fold

Answers

That is not true. To find the midpoint of a line, you must add the values of x’s together and divide by 2 and then add the values of y together and divide by 2. The formula is (x1+x2/2 , y1+y2/2)

Mt.Whitney in California is 14,492 feet tall. Mt. McKinley in Alaska is 5,826 feet taller than Mt.Whitney. How tall is Mt.Mckinley

Answers

You have to multiply 14,492 x 5,826 which equals 84,430,392

Final answer:

Mt. McKinley is 20,318 feet tall. This is found by adding Mt. Whitney's height of 14,492 feet to the additional 5,826 feet that Mt. McKinley is taller by.

Explanation:

The question asks how tall Mt. McKinley is. First, we know Mt. Whitney has a height of 14,492 feet. According to the question, Mt. McKinley is 5,826 feet taller than Mt. Whitney. To find the height of Mt. McKinley, we need to add these two measurements together.

Step 1: Write down the height of Mt. Whitney: 14,492 feet.

Step 2: Add the additional height of Mt. McKinley to Mt. Whitney's height: 14,492 feet + 5,826 feet.

Step 3: Perform the addition: 14,492 + 5,826 = 20,318 feet.

Therefore, Mt. McKinley is 20,318 feet tall.

What's the relationship between compound interest and exponential growth?

Answers

I would say that compound interest is a form of exponential growth.
the exponential functions are the family of functions that have the form a^x, where a > 1.
Compound interest is modeled as an exponentila growth problem. Another phenomenon that can be modeled as exponential growth is population growth.
In other words, compound interest is an application of exponential growth.

Final answer:

Compound interest and exponential growth both involve the concept of compounding, where growth is based on previous amounts. Compound interest refers to interest earned on past interest, causing savings to grow over time. Similarly, compound growth rates result in exponential growth.

Explanation:

The relationship between compound interest and exponential growth is that they both involve the concept of compounding, where the growth or increase is based on previous amounts. Compound interest refers to the interest earned on past interest, causing the total amount of financial savings to grow over time. Similarly, compound growth rates mean that the rate of growth is multiplied by a base that includes past growth, resulting in an exponential growth curve.

For example, if you have $1,000 in a bank account with a compound interest rate of 5% per year, the interest earned each year is added to the principal amount and becomes part of the new base for calculating future interest. As a result, the amount of money in the account grows exponentially over time. This relationship can also be seen in other areas, such as population growth or economic growth rates.

True or false.The GCF of any two odd numbers is always odd

Answers

Hello! The correct answer would be true.

This is because their multiples are odd and once their multiples are odd, the GCF will be odd as well.

I hope that helped! c:

1 cubic meter of concrete has a wight of 2400 kg. 15% of the concrete is water. The rest of the ingredients are cerment, sand and stone. The weights are in a ratio of 1:2:5. Work out the weight of cement, sand and stone in the 1 cubic meter of concrete
Help me please i have a test coming up

Answers

Answer:

Step-by-step explanation:

2400 × 0.15 = 360

2400 - 360 = 2040

2040 × 1/8 = 255 kg of Cement

2040 × 2/8 = 510 kg of Sand

2040 × 5/8 = 1275 kg of Stone

To check if it is right

255 + 510 + 1275 = 2040 kg

1 cubic meter of concrete the weight of water is 360 Kg, the weight of cement is 255 Kg, the weight of sand is 510 Kg and the weight of stone is 1275 Kg and this can be determine by forming the linear equation in one variable.

Given :

1 cubic meter of concrete has a wight of 2400 kg.15% of the concrete is water.The rest of the ingredients are cement, sand and stone. The weights are in a ratio of 1:2:5.

The weight of the water in the concrete will be:

[tex]= 2400\times \dfrac{15}{100}[/tex]

= 360 Kg

Let x be the weight in Kg. Then the combine weight of stone, cement and sand will be:

[tex]8x = 2400 - 360[/tex]

8x = 2040

x = 255 Kg

Then the weight of the cement will be = 255 Kg.

The weight of the sand will be = [tex]\rm 255\times 2 = 510\; Kg[/tex].

The weight of the stone will be = [tex]\rm 255\times 5 = 1275\; Kg[/tex].

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PLEASE HELP WILL MARK BRAINLIEST FOR CORRECT ANSWER

The coordinates of the vertices of quadrilateral ABCD are A(−1, −1) , B(−3, 3) , C(1, 5) , and D(5, 2) . Drag and drop the choices into each box to correctly complete the sentences.

Answers

The slope of AB is -2
The slope of BC is 1/2
The slope of CD is -3/4
The slope of AD is 1/2
The quadrilateral ABCD is a trapezoid because only one pair of opposite sides are parallel. YOU'RE WELCOME :D

ANSWER TO QUESTION 1

The Vertex A has coordinates [tex](-1,-1)[/tex] and the vertex B has coordinates [tex](-3,3)[/tex].

The slope of AB can be determined using the formula;

[tex]Slope_{AB}=\frac{y_2-y_1}{x_2-x_1}[/tex]

Where [tex](x_1,y_1)=A(-1,-1)[/tex] and [tex](x_2,y_2)=B(-3,3)[/tex].

Plugging these values in to the formula gives;

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

[tex]Slope_{AB}=\frac{3+1}{-3+1}[/tex]

[tex]Slope_{AB}=\frac{4}{-2}[/tex]

[tex]Slope_{AB}=-2[/tex]

ANSWER TO QUESTION 2

The Vertex B has coordinates [tex](-3,3)[/tex] and the vertex C has coordinates [tex](1,5)[/tex].

The slope of BC can be determined using the formula;

[tex]Slope_{BC}=\frac{y_2-y_1}{x_2-x_1}[/tex]

Where [tex](x_1,y_1)=B(-3,3)[/tex] and [tex](x_2,y_2)=C(1,5)[/tex].

Plugging these values in to the formula gives;

[tex]Slope_{BC}=\frac{5-3}{1--3}[/tex]

[tex]Slope_{BC}=\frac{5-3}{1+3}[/tex]

[tex]Slope_{BC}=\frac{5-3}{1+3}[/tex]

[tex]Slope_{BC}=\frac{2}{4}[/tex]

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

ANSWER TO QUESTION 3

The Vertex C has coordinates [tex](1,5)[/tex] and the vertex D has coordinates [tex](5,2)[/tex].

The slope of CD can be determined using the formula;

[tex]Slope_{CD}=\frac{y_2-y_1}{x_2-x_1}[/tex]

Where [tex](x_1,y_1)=C(1,5)[/tex] and [tex](x_2,y_2)=D(5,2)[/tex].

Plugging these values in to the formula gives;

[tex]Slope_{CD}=\frac{2-5}{5-1}[/tex]

[tex]Slope_{CD}=\frac{-3}{4}[/tex]

[tex]Slope_{CD}=-\frac{3}{4}[/tex]

ANSWER TO QUESTION 4

The Vertex A has coordinates [tex](-1,-1)[/tex] and the vertex D has coordinates [tex](5,2)[/tex].

The slope of AD can be determined using the formula;

[tex]Slope_{AD}=\frac{y_2-y_1}{x_2-x_1}[/tex]

Where [tex](x_1,y_1)=A(-1,-1)[/tex] and [tex](x_2,y_2)=D(5,2)[/tex].

Plugging these values in to the formula gives;

[tex]Slope_{AD}=\frac{2--1}{5--1}[/tex]

[tex]Slope_{AD}=\frac{2+1}{5+1}[/tex]

[tex]Slope_{AD}=\frac{3}{6}[/tex]

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

ANSWER TO QUESTION 5.

When we examine the slopes carefully we can see that

[tex]Slope_{AD}=\frac{1}{2}=Slope_{BC}[/tex].

Whenever the slopes of two straight lines are the same, it means the two lines are parallel.

Since quadrilateral ABCD has one pair of opposite sides parallel and the pair of opposite sides not parallel, the quadrilateral is a trap-ezoid.

Hence the answer is :

Quadrilateral ABCD is a trap-ezoid because only one pair of opposite side is parallel.

Use laws of sine to answer

Answers

Angle B = 86

25 / sin(86) = Line BC / sin(73)

Line BC = sin(73) * 25 / sin (86)

Line BC = 0.9563 * 25 / .99756

Line BC = 23.9075 / .99756

Line BC = 23.966

Find the time in hours and minutes from 09.40 to 13.25

Answers

3 Hours And 45 Minutes
Hope This Helps!

Which expression represents the phrase "one third the sum of 12 and a number"?
A.) 1/3+12+x
B.) 1/3(12+x)
C.) 1/3x+12
D.) 1/3(12)+x

Answers

The answer is B. 1/3(12+x).

The expression that represents the phrase 'one third the sum of 12 and a number' is B.) 1/3(12+x).

To represent the phrase "one third the sum of 12 and a number", we can break it down into two parts:

1. The sum of 12 and a number

2. One third of that sum

The expression for the sum of 12 and a number is (12 + x). Then, one third of that sum is [tex]$\frac{1}{3}(12 + x)$.[/tex]

So, the correct expression is:

[tex]B.) $\frac{1}{3}(12 + x)$[/tex]

The acceleration of an object varies directly with the force acting on it. If a force of 70 newtons causes an acceleration of 6.5 m/s2, what force will cause ann acceleration of 8m/s2? round your answer the hundredths place

Answers

Final answer:

Using Newton's Second Law of Motion, and the principle that acceleration is directly proportional to the applied force, a force of approximately 86.15 newtons will cause an acceleration of 8 m/s².

Explanation:

The question relates to the principle stated in Newton's Second Law of Motion, which states that the acceleration of an object is directly proportional to the net force acting on it and inversely proportional to its mass. In this case, we can assume the mass of the object remains unchanged.

To find the force that will cause an acceleration of 8 m/s², we can set up a direct proportion based on the given data (70 N correlates with 6.5 m/s²):

70 N / 6.5 m/s² = X N / 8 m/s²

Solving this for X gives X = (70 N * 8 m/s²) / 6.5 m/s². Round your answer to the nearest hundredth, you get approximately 86.15 N.

Learn more about Newton's Second Law of Motion here:

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3 1/3 lb of turkey for 10.50

Answers

Okay so what's your question?

It is 3.15 a pound of turkey

What are the domain restrictions of the expression h^2+3h−10/h^2−12h+20 ?

Select each correct answer.

h≠10

h≠5

h≠2

h≠−5

h≠−10

h≠−2

Answers

the denominator cannot be 0, so if h^2-12h+20=0
(h-2)(h-10)=0
h=2 or h=10
So h cannot be 2 or 10, the first and third choices are correct.

The domain restrictions of the expression (h² + 3h −10) / (h² − 12h + 20) are h≠2 and h≠10. which are the correct answers would be options (A) and (C).

What are the domain and range of the function?

The domain of the function includes all possible x values of a function, and the range includes all possible y values of the function.

The expression is given in the question as

(h² + 3h −10) / (h² − 12h + 20)

(h² + 5h - 2h−10) / (h² − 10h - 2h + 20)

(h(h + 5) - 2(h+5)) / (h(h − 10) - 2(h - 10))

(h + 5)(h - 2) / (h − 10)(h - 2)

We know that the denominator cannot be zero

Here (h-2)(h-10)=0

h= 2 or h = 10

Therefore, h cannot be 2 or 10 i.e. in the notation h≠2 and h≠10.

The domain restrictions of the expression (h² + 3h −10) / (h² − 12h + 20) are

h≠2 and h≠10.

Hence, the correct answers would be options (A) and (C).

Learn more about the domain and the range here:

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What is the inverse of the function f(x) = 2x - 10?

Answers

the answer for your question is x+10/2

Answer:

[tex]f^{-1}(x)=\frac{x+10}{2}[/tex]

Step-by-step explanation:

We ate asked to find the inverse of the given function [tex]f(x)=2x-10[/tex].

To find the inverse of function, first of all we will replace [tex]f(x)=y[/tex] and then interchange x and y values as shown below:

[tex]y=2x-10[/tex]

Inter-change x and y variables:

[tex]x=2y-10[/tex]

Solve for y using opposite operations:

[tex]x+10=2y-10+10[/tex]

[tex]x+10=2y[/tex]

Switch sides:

[tex]2y=x+10[/tex]

Divide both sides by 2:

[tex]\frac{2y}{2}=\frac{x+10}{2}[/tex]

[tex]y=\frac{x+10}{2}[/tex]

We will inverse function notation [tex]f^{-1}(x)[/tex] to write the inverse function as:

[tex]f^{-1}(x)=\frac{x+10}{2}[/tex]

Therefore, our required inverse function would be [tex]f^{-1}(x)=\frac{x+10}{2}[/tex].

Why do you flip the inequality sign when dividing by a negative number?

Answers

Assume x is 100.

-x<1
-100 is smaller than 1.

Dividing by -1,
x>-1
100 is greater than -1
If the inequality is not changed,
100<-1
100 is less than -1 which is not true

PLZ HELP!
WIL MARK AS BEST ANSWER

Answers

There are 12 units in between. You have to remember the number line is in twos. So, when you count the units in between, you have to remember to count in twos. Another way to figure it out is you can count the number of lines above the numbers or plots and multiply times two to find how many units are in between. Again, multiplying it times two is necessary in this equation because it is in units of two.

So, there are 12 units in between.
I really hope this helps and I know how I worded it is kind of confusing, but hopefully you understand. If you have any question feel free to ask. Have an awesome day:)

Jordan is three years older than four times Lily's age. The sum of their age is 68. How old is Jordan?

Answers

you have to multiply 4times 3 with gives you 12 plus 68

Create an expression, to equal 13, using any grouping of addition, subtraction, multiplication, and division. You must use all the basic operations at least once (addition, subtraction, multiplication, and division) and you must use at least one set of parentheses.

Answers

(29 - 2 + (6 * 2)) / 3 = 13

Answer:

Step-by-step explanation:

(5x2)+3

=13

This how you work the problem:

(5x2)+3 (5x2=10) 10+3=13. :)

A card is dealt from a 52-card deck. find the probability that it is not a 77. express the probability as a simplified fraction

Answers

Did you mean that it is not a 7? If so...

48/52 which, when simplified, is 12/13

I NEED ALGEBRA HELP, QUICK!! PLEASE!!!!!!!

A savings account balance can be modeled by the graph of the linear function shown on the grid.

What is the rate of change of the balance with respect to the number of deposits?
A) $100 per deposit
B) $50 per deposit
C) $0.50 per deposit
D) $2 per deposit

Answers

I believe that the answer is a

Answer:

Hey I am also taking the k12 interim right now and I also think the answer is a.

Step-by-step explanation:

The starting balance was at $50 then it gradually started to increase by $100 with each deposit. So you're answer is a.

Check it out yourself and see that the balance is increasing by $100 dollars with each deposit.

Give a thanks and a brainly!!!

What is the expression in radical form?
(3p^3q)^3/4

Answers

[tex]\bf a^{\frac{{ n}}{{ m}}} \implies \sqrt[{ m}]{a^{ n}} \qquad \qquad \sqrt[{ m}]{a^{ n}}\implies a^{\frac{{ n}}{{ m}}}\\\\ -------------------------------\\\\ (3p^3q)^{\frac{3}{4}}\implies \sqrt[4]{(3p^3q)^3}\implies \sqrt[4]{3^3p^{3\cdot 3}q^3}\implies \sqrt[4]{27p^9q^3} \\\\\\ \sqrt[4]{27p^{4+4+1}q^3}\implies \sqrt[4]{27p^4p^4p^1q^3}\implies pp\sqrt[4]{27pq^3}\implies p^2\sqrt[4]{27pq^3}[/tex]

The Expression [tex](3p^{3} q)^{\frac{3}{4} }[/tex] in radical form is [tex]p^{2} \sqrt[4]{27pq^{3} }[/tex]

What is Expression?

An expression is a combination of numbers, operator and variables.

The given expression is [tex](3p^{3} q)^{\frac{3}{4} }[/tex]

We know that

[tex]a^{\frac{p}{q} } =\sqrt[q]{a^{p} }[/tex]

So let us use same form to solve the given expression to radical form.

[tex](3p^{3} q)^{\frac{3}{4} }[/tex]=[tex]\sqrt[4]{(3p^{3} q)^{3} }[/tex]

Simplify the terms in root,

=[tex]\sqrt[4]{(3^{3}p^{3.3}q^{3} }[/tex]

=[tex]\sqrt[4]{27p^{9}q^{3} }[/tex]

[tex]\sqrt[4]{27p^{4}p^{4}pq^{3} }[/tex]

=[tex]p.p\sqrt[4]{27pq^{3} }[/tex]

=[tex]p^{2} \sqrt[4]{27pq^{3} }[/tex]

Hence the Expression [tex](3p^{3} q)^{\frac{3}{4} }[/tex] in radical form is [tex]p^{2} \sqrt[4]{27pq^{3} }[/tex]

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What compound inequality has all real numbers that are less than than -3 or greater than or equal to 5?

Answers

less than -3 and greater than 5

Answer:

less than -3 and greater than 5

Step-by-step explanation:

Complete the following theorem.
If two angles in a triangle are congruent to two angles in another triangle, then the ______________ angles are also congruent.

Answers

: If all of the angles in both triangles are congruent then the triangles are SIMILAR not necessarily congruent. They can be congruent by using a theorem called ASA, SSS, or SAS. The "S" stands for Side and the "A" stands for angle.

If two angles in a triangle are congruent to two angles in another triangle, then the third angles are also congruent.
(Third Angle Theorem)

hope this helped!
(:

Use the vertical line test to determine whether the relation is a function ((-6,-2)

Answers

There should be a graph to do the vertical line test and I don't see a graph.

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The measures of complementary angles have a sum of 90 degrees. Angle A and angle B are complementary, and their measures have a difference of 20°. What are the measures of the angles? thanks.

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The measures of complementary angles have a sum of 90 degrees. Angle A and angle B are complementary, and their measures have a difference of 20°. What are the measures of the angles?

thanks.