Answers
Answer:
20°,70°
Step-by-step explanation:
X+y+90=180
X+y=90
20+y=90
y=70°
2x+180-40=180
2x=40
X=20°
The measures of angles of the triangle is x = 20° and y = 70°
What is a Triangle?A triangle is a plane figure or polygon with three sides and three angles.
A Triangle has three vertices and the sum of the interior angles add up to 180°
Let the Triangle be ΔABC , such that
∠A + ∠B + ∠C = 180°
The area of the triangle = ( 1/2 ) x Length x Base
For a right angle triangle
From the Pythagoras Theorem , The hypotenuse² = base² + height²
if a² + b² = c² , it is a right triangle
if a² + b² < c² , it is an obtuse triangle
if a² + b² > c² , it is an acute triangle
Given data ,
Let the triangle be represented as ΔABC
Now , let the side be represented as BD , which cuts AC at point D
And , the measure of BD = measure of DC ( given )
And , the measure of ∠ABC = 90°
The measure of ∠BDA = 40°
So , the measure of angle ∠BDC = 140° ( angles on a straight line )
Now , the measure of angle ∠DBC = measure of ∠BCD ( given )
So , the measure of x = ( 180 - 140 ) / 2
x = 20°
And , the measure of y = 180° - 40° - 70°
y = 70°
Hence , the angles of triangle are x = 20° and y = 70°
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Related Questions
the probability that an individual without a college education earns more than $100,000 is 0.4, whereas the probability that a person with a b.s. or higher degree earns more than $100,000 is 0.6. the probability that a person chosen at random has a b.s. degree is 0.4. what is the probability that a person has at least a b.s. degree if it is known that he or she earns more than $100,000? (round your answer to four decimal places.)
Answers
The Probability that someone holds b.s. degree if it is known that he or she earns more than $100,000 is 0.75.
Considering the values given in the question,
P(earns more than $100000 without college education) = 0.2
P(earns more than $100000 with a B.S. or higher degree) = 0.6
P(Has a B.S. degree) = 0.5
P(earns more than $100000) = P(earns more than $100000 | without college education) × P(without college education) + P(earns more than $100000 | with a B.S. or higher degree) × P(has a B.S. degree)
= 0.2 × (1 - 0.5) + 0.6 × 0.5
= 0.4
P(at least a B.S. degree | earns more than $100,000) = P(earns more than $100000 | with a B.S. or higher degree) × P(has a B.S. degree) / P(earns more than $100000)
= 0.6 × 0.5 / 0.4
= 0.75
Therefore, If a person's income above $100,000 is known, there is a 0.75 probability that they have at least a b.s. degree.
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Reid's Hardware discounts all riding lawnmowers 9% to customers paying in cash. If Trey paid $1,517.74 in cash for a riding lawnmower, which of the following equations can be used to determine the original price of the lawnmower?
(Let x represent the original price of the lawnmower and y represent the discounted price.)
A.
y = 1.09x
B.
y = 0.91x
C.
y = 1.9x
D.
y = x - 9x
Answers
An equation to determine the original price of the lawnmower discounted at 9% to $1,517.74 is B. y = 0.91x.
What is an equation?An equation summarizes a mathematical statement that equates two or more mathematical expressions.
Equations operate with values, numbers, and variables, using the equation symbol (=) and mathematical operands to establish the equality of values.
Discount offered = 9%
Amount paid for a lawnmower = $1,517.74
Original price = x
Discounted price, y = 0.91x
Y = 0.91x
1,517.74 = 0.91x
x = 1,667.85
Thus, the original price of the lawnmower is determined by Equation B.
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What is the solution to the equation 1/4 ×-1/8=7/8+1/2x? X?
O x=-5
O x=-4
O x = 4
O x = 5
Answers
Answer: I think its B: x=-4
Step-by-step explanation:
Using quadratic formula x²-6x+8=0
Answers
Answer:
x = 4, 2
Step-by-step explanation:
help meeeeeeeeeee pleaseeeeeeeeeeeee!!!!!!!!!!!!!!!!!!!!!!!!
Answers
Answer:
h = 289 feet
Step-by-step explanation:
Comment
You need two givens to use in the formula to solve for the third.
Formula
v = sqrt(2*g*h)
Givens
V = 136 ft/s
g = 32 ft/s^2
h = ?
Solution
v = sqrt(2*g*h) Put the givens into the formula.
136 = sqrt(2* 32 * h) Square both sides
136^2 = sqrt(2*32*h)^2 Expand
18496 = 64* h Divide by 64
18496/64 = 64*h/64
289 feet = h
So the object must fall 289 feet before it reaches 136 m/s
What does 1.03 estimate to math
Answers
Answer:
provide context
Step-by-step explanation:
Help please, I don't know how to get QS
Answers
The complete proof using the AAS congruence postulate and CPCTC is explained below to show that QT ≅ SR.
What is the AAS Congruence Postulate?When two angles of a triangle, and one of its side that is nonincluded are congruent to corresponding two angles and a nonincluded side in the another triangle, then both triangles are congruent by the AAS congruence postulate.
If two triangles are congruent, then all its corresponding parts are also congruent to each other based on the CPCTC theorem.
Below is the two-column proof that proves that side QT is congruent to side SR.
Statement Reasons
1. ∠R ≅ ∠T, QT ≅ SR 1. Given
2. ∠TQS ≅ ∠RSQ 2. Alternate interior angles
3. QS ≅ QS 3. Reflexive property
4. ΔTQS ≅ ΔRSQ 4. AAS
5. QT ≅ SR 5. CPCTC
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Here is a correlation, does it also represent causation? Explain you answer.
The miles driven and the amount of gasoline used.
Answers
Yes the miles driven and the amount of gasoline used can be said to have a causation as well as a correlation.
What is causation in statistics?The strength and direction of a relationship between two or more variables are described by the statistical measure of correlation, which is given as a number. However, a correlation between two variables does not necessarily imply that a change in one variable is the reason for a change in the values of the other.
There is a causal relationship between the two occurrences, which means that causation shows that one event is the outcome of the occurrence of the other event. This concept is also known as cause and effect.
When the amount of gasoline is small, it would cause the miles covered to be just a few miles. Or if there is no gas, then no mile would be covered.
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Find the measures of angle PQR and angle PRQ in the triangle below.
Answers
Using the exterior angles theorem, the measures of the named angles are:
m∠PQR = 51°
m∠PRQ = 96°
What is the Exterior Angles Theorem?Based on the exterior angles theorem, the measure of the exterior angle of a triangle has an angle degree that is equal to sum of the interior angles of the triangle.
Therefore, the following equation would be set to find the value of x:
33 + 10x + 1 = 17x - 1
34 + 10x = 17x - 1
Combine like terms
34 + 1 = 17x - 10x
35 = 7x
35/7 = 7x/7
5 = x
x = 5
m∠PQR = 10x + 1 = 10(5) + 1 = 51°
m∠PRQ = 180 - (17x - 1) = 180 - (17(5) - 1) = 96°
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List all factors of the numerator and denominator. Use gcf method to simplify Creduce) each fraction. You must show work
Answers
The reduced fraction is 6/7 using GCF method.
What is GCF method?
The largest number, which is the factor of two or more number is called the Greatest Common Factor (GCF). It is the largest number (factor) that divide them resulting in a Natural number. Once all the factors of the number are found, there are few factors which are common in both. The largest number that is found in the common factors is called the greatest common factor. The GCF is also known as the Highest Common Factor (HCF)
Given,
the fraction = 24/28.
the factors of 24 = 2×2×2×3
The factors of 28 = 2×2×7
The gcf is 2 × 2 = 4
divide the denominator and numerator by 4
24 ÷ 4 = 6
28÷ 4 = 7
We get,
the fraction = 6/7.
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A fence is to be built to enclose a rectangular area of square feet. The fence along three sides is to be made of material that costs $ per foot. The material for the fourth side costs $ per foot. Find the dimensions of the rectangle that will allow for the most economical fence to be built.
Answers
The dimensions of the rectangle that will allow for the most economical fence to be built is 50 feet and 25 feet in length and width respectively.
Given in the question,
Area = 1250 ft²
The three sides cost $3 per foot, and the fourth side costs $9 per foot.
Let x and y be the length and width of the rectangle.
Because the area is 1250 ft², therefore
xy = 1250, or
y = 1250/x
Case 1: Three sides are (x,y,x) and the 4-th side is y.
The cost is
C = 3(2x +y) + 9y
= 6x + 12y
= 6x + 12(1250/x)
= 6x + 15000/x
For C to be minimum, C' = 0. That is
6 - 15000/x² = 0
x² = 15000/6
x = 50 ft, y = 1250/50 = 25 ft
C = 6(50) + 15000/(50²) = $600
Case 2: Three sides are (y,x,y) and the 4-th side is x.
The cost is
C = 3(x + 2y) + 9x
= 12x + 6y
= 12x + 6(1250/x)
= 12x + 7500/x
For C to be minimum, C' = 0.
12 - 7500/x² = 0
x² = 7500/12 = 625
x = 25 ft, y = 50ft
C = 12(25) + 7500/25 = $600
Thus, the Dimensions will be 25 feet and 50 feet.
Question:
A fence is to be built to enclose a rectangular area of 1250 square feet. the fence along three sides is to be made of material that costs $3 per foot. the material for the fourth side costs $9 per foot. find the dimensions of the rectangle that will allow for the most economical fence to be built.
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A store is instructed by corporate headquarters to put a markup of %67 on all items. An item costing $12 is displayed by the store manager at a selling price of $8
. As an employee, you notice that this selling price is incorrect. Find the correct selling price. What was the manager's likely error?
Answers
The correct selling price of the item has being solved as $20.04 The error that the manager has made is $12.04
How to solve for the markupGiven that there is a markup, the item that is being sold for 12 dollars would be affected by the percentage of the mark up.
This mark up is a 67% markup
This would be solved as
12$ + 67% of 12$
= $12 + 8.04
= $20.04
Hence the correct selling price is $20.04
Next we would have to find the likely error that the manager has made
= $20.04- $8
= $12.04
The likely error of the manager is $12.04
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Find the initial population size
Answers
The numeric values for the population function are given as follows:
Initial population: 49 individuals.Population after eight years: 292 individuals.How to find the numeric value of a function or of an expression?To obtain the numeric value of a function or of an expression, each instance of the input variable in the function or in the expression is replaced by the value at which we want to find the numeric value.
The function giving the population after t years is defined as follows:
[tex]P(t) = \frac{340}{1 + 6e^{-0.45t}}[/tex]
The initial population is the numeric value at t = 0, that is, the lone instance of t is replaced by zero, hence:
[tex]P(0) = \frac{340}{1 + 6e^{-0.45(0)}} = \frac{340}{7} = 49[/tex]
After eight years, the population is given by the numeric value at t = 8, hence:
[tex]P(8) = \frac{340}{1 + 6e^{-0.45(8)}} = 292[/tex]
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-9 ( x + 6)= -9x + 108
Answers
Answer: 0=1620=162
PLEASE GIVE BRAINLIEST THANK YOU VERY MUCH!!
39 Points, need this ASAP
If a = -9 and b = -4, what is the value of a + b ?
-5
5
13
-13
Answers
There are 15 plates in a kitchen cabinet. the diameter of each plate is either 7 inches or 12 inches. the diameter of all 15 plates combined is 140 inches. which system of equations can be used to find the number of 7-inch plates, x, and the number of 12-inch plates, y, that are in the cabinet?
Answers
The system of linear equations which is used to find number of 7 -inch plates ,x and 12- inch plates y is
x+y = 15 ---(1)
7x+12y = 144 ---(2)
In the given question we have following informations,
total number of plates in kitchen cabinet = 15
diameter of each plate either 7-inch or 12-inch.
let the number of plates in kitchen cabinet with Diameter 7-inch = x
and number of plates in kitchen cabinet with Diameter 12-inch = y
the diameter of all 15 plates combined = 144 inches
from the above details we can make a system of linear equations for two variables say x and y
x + y = 15 -----(1)
7x + 12y = 144 ---(2)
equation (1), (2) made the required system of equations.
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3.13 test: congruence and constructions
Answers
Answer:
The angle-angle-side postulate. A.A.S
Step-by-step explanation:
PLSSSS HELPPP UGRNETLY
Answers
The GCF of the number given as 45 and 27 is 9 and the factored expression is 9(5 - 3)
How to determine the GCF of the expressions?From the question, we have the following statement
The greatest common factor of 45 and 27
Rewrite the given expression as follows
This is represented using
45 and 27
Factor out 3 from the expression
So, we have the following representation
15 and 9 => Factored 3
Factor out 3 from the expression
So, we have the following representation
5 and 3 => Factored 3 * 3
So, we have
Factored = 3 * 3 = 9
This represents the GCF
So, the GCF is 9
Factor the expressionIn (a), we have
5 and 3 => Factored 3 * 3
This means that
45 - 27 = 3 * 3(5 - 3)
Evaluate the product
45 - 27 = 9(5 - 3)
Hence, the factored expression is 9(5 - 3)
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Britney operates an orange juice stand. On Monday she used 3 bags of oranges. On Tuesday
she used 1/2 as many oranges as on Monday. How many bags of oranges did Britney use on
Tuesday?
Answers
Answer:
1.5
Step-by-step explanation:
3÷2=1.5
Solve for the value of e.
Answer: e=
(9e-8)
(4e+6)
Submit Answer
posse
Answers
Answer:
Step-by-step explanation:
Expand: 36e^2+12e-48=e
Subtract e from both sides 36e^2+11e-48=0
Using the quadratic formula, e=(-11+-sqrt7033)/72
Question 2
Which set of rational numbers is arranged from least to greatest?
O
O
O
O
-3.5, 4, 2, 3
11
-3.5, 4,3,2
113
2, 3.
1
4.-3.5
11
4.3.2, -3.5
11
10 pts
Answers
Answer:
The second option.
Step-by-step explanation:
We can figure this out by going down each option and checking if it works and is arranged from least to greatest.
The first option provides the numbers -3.5, -1/4, 2, 1/3 in that order.
This does not work because 1/3 is less than 1 which is less than 2. 1/3 should come before 2.
The second option provides the numbers -3.5, -1/4, 1/3, 2.
This option does work, because -3.5 is less than -1/4, -1/4 is less than 1/3 because it is negative, and 1/3 is less than 2.
If we look at this on a number line, the numbers that are smaller will appear farther to the left on the number line.
It takes 12 minutes per pound to cook a turkey and dinner is at
3:00 pm.
How many hours and minutes is this?
Answers
Answer:
The result is 2 hours
Hope this helped!
can somone help will mark u brainliest
Answers
Solve the equation V = s³ for s.
Answer in the form s = .
Answers
[tex]{ \bold{ \sqrt[3]{V}}} [/tex]
Step-by-step explanation:
[tex]{ \green{ \sf{V = s³}}}[/tex]
Cube on both sides, then
[tex]{ \green{ \sf{s = \sqrt[3]{V}}}} [/tex]
A group of friends wants to go to the amusement park. They have no more than $110 to spend on parking and admission. Parking is $10.50, and tickets cost $23.50 per person, including tax. What is the maximum number of people who can go to the amusement park?
Answers
Considering the definition of an inequality, the maximum number of people who can go to the amusement park is 4.
Definition of inequalityAn inequality is the existing inequality between two algebraic expressions, connected through the signs:
greater than >.less than <.less than or equal to ≤.greater than or equal to ≥.An inequality contains one or more unknown values, in addition to certain known data.
Solving an inequality consists of finding all the values of the unknown for which the inequality relation holds.
Inequality in this caseIn this case, you know that:
A group of friends have no more than $110 to spend on parking and admission. Parking is $10.50, and tickets cost $23.50 per person, including tax.Being "x" the maximum number of people who can go to the amusement park, the inequality that expresses the previous relationship is
10.50 + 23.50x ≤ 110
Solving:
23.50x ≤ 110 - 10.50
23.50x ≤ 99.50
x ≤ 99.50÷ 23.50
x ≤ 4.23
Finally, the maximum number of people is 4.
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the probability that a new microwave oven will stop working in less than 2 years is 0.05. the probability that a new microwave oven is damaged during delivery and stops working in less than 2 years is 0.04. the probability that a new microwave oven is damaged during delivery is 0.10. given that a new microwave oven is damaged during delivery, what is the probability that it stops working in less than 2 years? responses 0.05 0.05 0.06 0.06 0.10 0.10 0.40 0.40 0.50
Answers
Option D is the right choice.
It is discovered through the use of conditional probability that there is a 0.4 = 40% chance that it will stop working in less than 2 years.
Conditional probability is a term used in probability theory to describe the likelihood that one event will follow another given the occurrence of another event.
Conditional Probability:
P (B / A) = P (A∩B) / P (A)
Here:
P(B / A) is the likelihood that event B will occur in the absence of event A.
P (A∩B) is the likelihood that both A and B will occur.
P(A) denotes the likelihood that A will occur.
As per the question:
Event A: Delivery was harmed.
Event B: Fails to function after less than two years.
P (A) = 0.1 due to the probability of being damaged during delivery being 0.1.
P (A∩B) = 0.04 because there is a 0.04 likelihood that it will be damaged during the delivery and stop working.
The likelihood under the condition is:
P (B / A) = P (A∩B) / P (A) = 0.04 / 0.1 = 0.4
0.4 = 40% chance that it will stop working in under two years.
Therefore, option D is correct.
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which is a reasonable estimate for the amount of kernels serena needs to make 6 cups of popcorn
Answers
Answer:
four tablespoons to make 6 cups of popcorn.
Step-by-step explanation:
1.5 is nine Equals 2.25 x. And then divide both sides by 2.25. That gives you four tablespoons to make 6 cups of popcorn.
Decide whether each equation is true for all, one, or no values of x.
Answers
1. 3x + 9 = -4.5x + 20 ; This is true for one value of x.
2. 9(x + 3) = 9x + 12 ; This is true for no values of x.
3. 4(2x + 3) = 12 + 8x ; True for any values of x.
Given,
The equations;
1. 3x + 9 = -4.5x + 20
2. 9(x + 3) = 9x + 12
3. 4(2x + 3) = 12 + 8x
We have to find whether each equation is true for all, one or no values of x.
Here,
1. 3x + 9 = -4.5x + 20
Solve for x;
3x + 4.5x = 20 - 9
7.5x = 11
x = 11/7.5
x = 1.47
Then,
This is true for one value of x.
2. 9(x + 3) = 9x + 12
Solve using distributive property;
9x + 27 = 9x + 12
9x - 9x = 12 - 27
0 = -15
This is true for no values of x.
3. 4(2x + 3) = 12 + 8x
Use distributive property and solve;
8x + 12 = 12 + 8x
8x - 8x = 12 - 12
0 = 0
True for any values of x.
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Find all the zeros of the equation.
[tex]2x^4+70x^2-72=0[/tex]
Answers
Answer:
x = 1, -1
x = 6i, -6i
Answer:
1, -1, 6i, -6i
Step-by-step explanation:
A rectangle with dimensions 60 units * 40 units is drawn on a grid paper that has a 1 unit * 1 unit grid. Each vertex of the rectangle is on a node, and each side of the rectangle is on a gridline. Then a diagonal of the rectangle is drawn. How many cells are cut into two(not necessarily equal) parts? PLEASE ANSWER ASAP!!!!!!!
Answers
The number of cells cut into two by the diagonal of the rectangle, found by using Pythagorean theorem, are approximately 51 cells
What is Pythagorean theorem?Pythagorean theorem can be expressed as the square of the hypotenuse side of a right triangle is equal to the sum of the square of the legs of the triangle.
The dimensions of the rectangle = 60 units by 40 units
The dimensions of each grid = 1 unit by 1 unit
The vertices of the rectangle are (0, 0), (60, 0), (60, 40), (0, 40)
The slope of the diagonal is therefore;
m = 40/(60) = 2/3
The equation of the line is; y - 0 = 2/3·(x - 0) = 2/3·x
y = 2/3·x
The number of cells in the diagonal is found using Pythagorean theorem as follows as follows;
Length the diagonal, l = √(60² + 40²) ≈ 72.1
Length of the diagonal of a unit = √(1 + 1) =√2
Number of units in the diagonal, n = 72.1/√(2) ≈ 51 units
The number of cells cut into two ≈ 51 cells
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