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.
What's the relationship between compound interest and 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.
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?
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
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
Why do you flip the inequality sign when dividing by a negative number?
The temperature dropped 6c every hour for 7 hours. What was the total number of degrees the temperature changed in the 7 hours
Find the time in hours and minutes from 09.40 to 13.25
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.
Use laws of sine to answer
Use the vertical line test to determine whether the relation is a function ((-6,-2)
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.
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.
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
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!!!
:)
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.
Answer:
Step-by-step explanation:
(5x2)+3
=13
This how you work the problem:
(5x2)+3 (5x2=10) 10+3=13. :)
Complete the following theorem.
If two angles in a triangle are congruent to two angles in another triangle, then the ______________ angles are also congruent.
PLZ HELP!
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True or false.The GCF of any two odd numbers is always odd
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
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
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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3 1/3 lb of turkey for 10.50
What is the expression in radical form?
(3p^3q)^3/4
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 is the equation of a line that passes through the points (3,6) and (8,4)
Which of the following is a radical equation?
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.
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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.
Jordan is three years older than four times Lily's age. The sum of their age is 68. How old is Jordan?
What compound inequality has all real numbers that are less than than -3 or greater than or equal to 5?
Answer:
less than -3 and greater than 5
Step-by-step explanation:
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
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).
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What is the inverse of the function f(x) = 2x - 10?
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].
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
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.
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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
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]
find the roots of the quadratic function x^2=100
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
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.