There are many methods for solving equations, but the two main methods are algebraic method and graphic method.
Algebraic methods: These methods involve using algebraic manipulation to isolate the variable on one side of the equation and find its value. This can include using operations such as addition, subtraction, multiplication, and division, as well as the use of inverse operations (e.g. undoing addition with subtraction) and properties of equality (e.g. transitive property).
Graphic methods: These methods involve using graphs to represent the equation and find the solution. This can include plotting the equation on a coordinate plane and finding the points of intersection, or using a graphing calculator or software to plot the equation and find the solution.
It's worth noting that the method used to solve an equation will depend on the complexity of the equation and the information available. Some equations can be easily solved using algebraic methods, while others may require a combination of algebraic and graphic methods or an entirely different approach.
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________ 11B. If m∠ABC = 74, then what is the measure of AB ?
Please someone help me with question a) and b). I’ve been having so much trouble with these types of questions. The booklet says that the answers are a) 134degrees and b) 14.3km. I just don’t get how to get there. Thank you!
The bearing to take is 134 degrees and the shortest distance is 14.3 km
The bearing it would takeThe attached diagram represents a labelled version of the ship movement
The angle at Q is
Q = 180 - 155 + 90 + 120 - 90
This gives
Q = 145
The distance PR is calculated as:
PR^2 =PQ^2 + QR^2 - 2 * PQ * QR * cos(Q)
This gives
PR^2 = 9^2 + 6^2 - 2 * 9 * 6 * cos(145)
Evaluate
PR^2 = 205.46
Take the square root
PR = 14.3 km
The angle at P is then calculated as:
QR/sin(P) = PR/sin(Q)
This gives
6/sin(P) = 14.3/sin(145)
Evaluate the quotient
6/sin(P) = 24.93
Make sin(P) the subject
sin(P) = 6/24.93
Divide
sin(P) = 0.2407
Take the arc sin of both sides
P = 14
The bearing is then calculated as:
Bearing = P + 120
This gives
Bearing = 14 + 120
Evaluate
Bearing = 134
Hence, the bearing to take is 134 degrees
The shortest distanceIn (a), we have
PR = 14.3 km
This represents the shortest distance
Hence, the shortest distance is 14.3 km
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Simplify the expression 3(x + 2)(x2 − x − 8). (6 points)
Answer:
3x³ + 3x² - 30x - 48
Step-by-step explanation:
3(x + 2)(x² - x - 8) ← distribute (x + 2) by 3
= (3x + 6)(x² - x - 8)
each term in the second factor is multiplied by each term in the first factor
= 3x(x² - x - 8) + 6(x² - x - 8) ← distribute both parenthesis
= 3x³ - 3x² - 24x + 6x² - 6x - 48 ← collect like terms
= 3x³ + 3x² - 30x - 48
HELP!!!!!!!!!!!!!!!!!!!! I WELL GIVE BRAINLIST AND 100 point if answered in less the 20 mins
If I have 419 assignments to do and i have pleated completed 79 how much work will I need to do every day to finish in one week
Answer:
10
Step-by-step explanation:
Answer:
You have to complete around 49 assignments everyday to finish in one week.
Step-by-step explanation:
• First, we have to calculate the number of assignments left to do:
Assignments remaining = 419 - 79
= 340
• There are 7 days in a week, which means 340 assignments need to be completed in 7 days.
7 days ⇒ 340 assignments
1 day ⇒ 340 ÷ 7
= 48.6
≅ 49 assignments
∴ You have to complete around 49 assignments everyday to finish in one week.
What are the solutions of the equation6x^2-x-1=0
Answer:
1/2
1/3
Step-by-step explanation:
x=1/2
x=-1/3
Answer:
[tex]x_{1} =-\frac{1}{3} \\x_{2} =\frac{1}{2}[/tex]
Step-by-step explanation:
[tex]6x^{2} -x-1=0[/tex]
Factoring the equation:
[tex](3x+1)(2x-1)=0[/tex]
Extract the roots:
First factor
[tex]3x+1=0\\3x=-1\\x_{1} =-\frac{1}{3}[/tex]
Second factor
[tex]2x-1=0\\2x=1\\x_{2} =\frac{1}{2}[/tex]
Hope this helps
Drag the tiles to the correct boxes to complete the pairs. Not all tiles will be used. Match each scenario with its effect on the PPC.
These are the effect on the PPC
1st pairs with a point original to PPC. and 2nd pairs with PPC shifts to the left. and 3rd pair with PPC shifts to the right.
According to the statement
we have given the some conditions and we have to match the each scenario with the effect of the PPC.
So, The given effect on the tiles are Tiles
- the PPC shifts to the right
- the PPC shifts to the left
- a point on the original PPC
- a point inside the PPC
- a point outside the PPC
And we have to join it with its pairs.
So,
First :
A manufacturing unit uses all its resources efficiently = A point on the original PPC
Second :
Andrew has 5 hours to complete his homework but uses only 3 hours, so he doesn’t complete it. = The PPC shifts to the left
Third :
A country acquires part of its neighboring country = The PPC shifts to the right
These are the conditions that satisfy the effect of PPC.
So, These are the effect on the PPC
1st pairs with a point original to PPC. and 2nd pairs with PPC shifts to the left. and 3rd pair with PPC shifts to the right.
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Disclaimer: This question was incomplete. Please find the full content below.
Question:
Match each scenario with its effect on the PPC.
Tiles
- the PPC shifts to the right
- the PPC shifts to the left
- a point on the original PPC
- a point inside the PPC
- a point outside the PPC
Pairs
- A manufacturing unit uses all its
resources efficiently.
- Andrew has 5 hours to complete his
homework but uses only 3 hours, so
he doesn’t complete it.
- A country acquires part of its neighboring
country.
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^it doesn't need to be this complicated
Marissa is painting her rectangular patio, with the exception of a bench that does not need to be painted: rectangle with a length of x plus 20 and width of x plus 10 with a rectangle in the bottom right corner labeled bench that has a length of 6 and width of 2 write an equation to determine the area, a, of the patio that will be painted. a = (x 20)(x 10) 12 a = (x 20)(x 10) − 12 a = (x 26)(x 12) a = (x 14)(x 8)
The area of the rectangular patio to be painted is: B. A = (x + 20)(x + 10) - 12.
What is a Rectangle?A rectangle, by definition, is a quadrilateral with two pairs of opposite that have the equal lengths. All four angles of a rectangle are right angles (90 degrees).
What is the Area of a Rectangle?The area of a rectangle = (length of rectangle)(width of rectangle).
Given the following parameters for the patio and the bench:
Length of rectangular patio = x + 20Width of rectangular patio = x + 10Length of rectangular bench = 6Width of rectangular bench = 2Area to be painted = area of rectangular patio - area of rectangular bench
Area of rectangular patio = (x + 20)(x + 10)
Area of rectangular bench = (6)(2) = 12
Area to be painted = (x + 20)(x + 10) - 12
The answer is: B. A = (x + 20)(x + 10) - 12.
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.
If f(x)=3x^2+x-2, then f(-2)=
) Suppose that we have a bucket of 30 red balls and 70 blue balls. If we pick 20 balls uniformly out of the bucket, what is the probability of getting exactly k red balls
Answer: 30%
Step-by-step explanation:
Use the distributive property with factoring to find the equivalent expression. 20a + 28b = ( a + 7b)
The equivalent expression after factoring 20a + 28b = ( a + 7b) using the distributive property is 19a + 21b = 0.
What is Distributive Property?According to the distributive property, an expression in the form A (B + C) can be solved as A (B + C) = AB + AC. This distributive law applies to subtraction as well and is written as A (B - C) = AB - AC. This means that operand A is shared by the other two operands.
The given equation is 20a + 28b = ( a + 7b).
20a + 28b = ( a + 7b).
Now, subtract both sides by a.
20a - a + 28b = a + 7b - a.
19a + 28b = 7b.
Now, subtracting both sides by 7b.
19a + 28b - 7b = 7b - 7b.
19a + 21b = 0.
Therefore, the equivalent expression to 20a + 28b = ( a + 7b) is 19a + 21b = 0.
1.5, 2.25, 3.0, 3.75, ...
Which recursive formula can be used to determine the total amount of time spent making hats based on the total amount of time spent previously?
f(n + 1) = f(n) + 1.5
f(n + 1) = f(n) + 0.75
f(n + 1) = one-halff(n)
f(n + 1) = three-halvesf(n)
The recursive formula can be used to determine the total amount of time spent making hats based on the total amount of time spent previously is f(n + 1) = f(n) + 0.75
Recursive functionsThe general recursive function is expressed as:
an+1 = d + an
where
r is the common difference
Given the sequence below
1.5, 2.25, 3.0, 3.75, ...
Common difference = 2.25 - 1.5 = 0.75
Substitute
f(n + 1) = f(n) + d
f(n + 1) = f(n) + 0.75
Hence the recursive formula can be used to determine the total amount of time spent making hats based on the total amount of time spent previously is f(n + 1) = f(n) + 0.75
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explanation?
please help asap
Answer:
70 degrees = a
Step-by-step explanation:
Triangle= 180 degrees.
Therefore, since a and the unmarked angle are congruent since it is an isosceles triangle, we subtract 40 from 180, with a result of 140. With 140, we divide by 2 to find the degrees for both the unmarked angle and angle a, since they are congruent. 140/2 = 70, Angle A will equal to 70 degrees
use the formulas for lowering powers to rewrite the expression in terms of the first power of cosine cos^4
The expression cos⁴ θ in terms of the first power of cosine is [ 3 + 2cos 2θ + cos 4θ]/8.
The power-reducing formula, for cosine, is,
cos² θ = (1/2)[1 + cos 2θ].
In the question, we are asked to use the formulas for lowering powers to rewrite the expression in terms of the first power of cosine cos⁴ θ.
We can do it as follows:
cos⁴ θ
= (cos² θ)²
= {(1/2)[1 + cos 2θ]}²
= (1/4)[1 + cos 2θ]²
= (1/4)(1 + 2cos 2θ + cos² 2θ] {Using (a + b)² = a² + 2ab + b²}
= 1/4 + (1/2)cos 2θ + (1/4)(cos ² 2θ)
= 1/4 + (1/2)cos 2θ + (1/4)(1/2)[1 + cos 4θ]
= 1/4 + cos 2θ/4 + 1/8 + cos 4θ/8
= 3/8 + cos 2θ/4 + cos 4θ/8
= [ 3 + 2cos 2θ + cos 4θ]/8.
Thus, the expression cos⁴ θ in terms of the first power of cosine is [ 3 + 2cos 2θ + cos 4θ]/8.
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I need help with this question, not really understanding
The measure of angle D in the inscribed triangle is as follows;
∠D = 63 degrees
How to solve circle theorem?The circle theorem can be use to find the ∠D as follows;
The triangle BCD is inscribed in the circle.
Using circle theorem,
The angle of each triangle is double the angle of the arc it create.
Therefore,
arc BC = m∠D
m∠B = 134 / 2 = 67 degrees.
Therefore, using sum of angles in a triangle.
67 + 50 + m∠D = 180
m∠D = 180 - 50 - 67
m∠D = 63 degrees.
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Consider dealing a hand of 8 cards from a well shuffled standard deck of playing cards. The expected value of the number of face cards in the hand is (Q
Answer:
2 face cards
Step-by-step explanation:
By definition, there are 12 face cards (Kings, queens, and jacks) and 36 numbered cards (2's through 10's) in a standard deck of 52 cards. Aces are not considered face cards (no face on the card).
The ratio of face cards in a full deck is (12/52) or slightly over 23%.
The likelihood of a face card in a hand of 8 cards is:
(8 cards)*(12 face cards/52 cards) = 1.85 cards. We need to round to the nearest whole card, so the expected number of face cards in a hand of 8 is 2 cards.
Bob grows tomatoes in his garden. He picked four tomatoes, and weighed every possible grouping of three tomatoes. The results are 900 grams, 1400 grams, 1600 grams, and 1800 grams. What is the weight of the biggest tomato?
Answers could be 600, 800, 900, 1000, 1200
Answer:
1000.
Step-by-step explanation:
We need 4 weights where 3 of them add up to
900, 1400, 1600 or 1800g.
Not sure of the method for doing this!
Lets assume that the answer is 1000 g.
Then the 3 that make 1800 could be
1000 500 and 300
- then to make 900 we need a 100g tomato giving:
1000 500 300 and 100 grams
So the 1400 will be the 1000, 300 and 100 tomato
and the 1600 will be 1000, 500 and 100.
That seems to fit !!
Can someone please help???
Answer:
A 0.08
Step-by-step explanation:
Find the unknown angle
60°
Xº
30°
Answer:
x = 90°
Step-by-step explanation:
Hello!
The sum of angles on a straight line is 180°.
To find the value of angle x°, we can subtract all the given angles form 180°.
Find x180° - 60° - 30° = x°180° - 90° = x°90° = x°The value of x is 90°.
Will mark Brainliest. Find x
the value of 'x' is 0. 9
How to determine the value
For the given triangle, we have the;
Adjacent side = 7Opposite side = 13 + xWe want to find the value of x
Using the tangent ratio
Tan θ = opposite/adjacent
Let's substitute the value of theta, opposite and adjacent
Tan 60 = 13 + x / 7
1. 73 = 13+ x/ 7
cross multiply
1. 73 × 7 = 13 + x
12. 1 = 13 + x
x = 13 - 12. 1
x = 0. 9
We can see that the value of x is 0. 9
Thus, the value of 'x' is 0. 9
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If the value of the sample standard deviation increases, what happens to the confidence interval?
If the value of the sample standard deviation increases, the confidence interval becomes wider and is denoted as option A.
What is Confidence interval?This term is used in statistics and refers to the probability that a population parameter will fall between two set values.
it has a direct relationship with standard deviation in which its increase will also lead to the set of values being wider thereby making it the most appropriate choice.
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The options are :
a. It becomes wider
b. It becomes more precise
c. It does not change
d. It narrows
Choose the equation for the graph.
A. Y=|x/2|-5
B. Y=2|x|+5
C. Y=2|x|-5
D. Y=|x/2|+5
E. Y= |x/5|-2
The correct equation of the given graph is; Option A: y = |x/2| - 5
How to find the equation of a graph?
From the given graph, we can see the following coordinates;
At x = 0, y = -5
At x = 1, y = -4.5
At x = -1, y = -4.5
At x = 2, y = -4
At x = -2, y = -4
Since the y-intercept is at y = -5, looking at the given options, the only one that is correct will be;
y = |x/2| - 5
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Angle 1 and Angle 2 are complementary angles. Angle 1 is 5x degrees. Angle 2 is 50 degrees. Find the value of x. Type ONLY the number.
Answer:
x = 8
Step-by-step explanation:
complementary angles sum to 90°
sum the 2 angles and equate to 90
5x + 50 = 90 ( subtract 50 from both sides )
5x = 40 ( divide both sides by 5 )
x = 8
HELP PLEASE!!!!!!
Parallel lines r and s are cut by two transversals, parallel lines t and u.
How many angles are alternate exterior angles with angle 5?
Picture below:
The number of angles that are alternate exterior with angle 5 is one, which is angle 11.
What are Alternate Exterior Angles?Alternate exterior angles are formed on the outside of the two parallel lines that are intersected by a transversal, each being located on the opposite side of the transversal.
The alternate exterior angle pairs are two angles that are supplementary. This means they add up to give a sum of 180 degrees.
Considering transversal s and parallel lines t and u, the angle that is an alternate angle to angle 5 is angle 11.
Angle 11 is the only angle that is alternate exterior angles with angle 5. therefore, we can conclude that, the number of angles that are alternate exterior with angle 5 is just 1, which is angle 11.
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Please answer hurry!
By trigonometric functions we find that the measure of angle A is approximately 0.12π radians.
How to determine the missing angle in a right triangleIn this question we have a right triangle, of which the length of two sides are known (AB, BC). We can know the measure of angle A by trigonometric functions:
[tex]\tan A = \frac{BC}{AC}[/tex]
[tex]\tan A = \frac{2}{5}[/tex]
A ≈ 0.12π radians
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[tex]x^{2} +x-12[/tex]
solve this polynomial by class 9 corse
The factored expression of the polynomial is (x - 3)(x + 4)
How to solve the polynomial?The polynomial expression is given as;
x^2 + x - 12
Expand the expression
x^2 + 4x - 3x - 12
Factorize the expression
x(x + 4) -3(x + 4)
Factor out x + 4
(x - 3)(x + 4)
Hence, the factored expression of the polynomial is (x - 3)(x + 4)
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Katie has 100 apples, and she plans on eating 2 of them every day.
True or false...the number of apples Katie has left is proportional to the number of days that pass.
Alejandro wants to determine the average shoe size of all of the male students in his school. Which sample is likely to yield the most biased results?.
The sample that is likely to yield the most biased results is; B) every member of the boys’ basketball team
How to identify a bias in sampling?The sample that is likely to yield the most biased results is; B) every member of the boys’ basketball team.
The reason option B is the most biased is because members of a basketball team are typically taller than other people. We know that taller people generally have larger feet, and larger shoe sizes, than shorter people. Thus, choosing only people from this area would lead to a biased sample.
The missing options are;
A) every tenth boy on the school’s phone list
B) every member of the boys’ basketball team
C) every boy in a randomly selected ninth-, tenth-, eleventh-, and twelfth-grade gym class
D) every fifth boy who walks through the front doors of the school in the morning
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Answer:
B)
Step-by-step explanation:
Jasmine buys a turkey every year . The first time she bought a turkey, in year 0, it cost $15.50. She notices the price is getting more expensive, at a rate of 2%
The price of the turkey based on the percentage given is $15.81.
How to illustrate the information?It was stated that the cost is $15.50 but that there was a 2% increment in price.
Therefore, the new price will be:
= $15.50 + (2% × $15.50)
= $15.50 + $0.31
= $15.81
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pls help i’ll give brainliest
Answer:
A
Step-by-step explanation:
Area of the rectangle is 15*20=300
Area of the triangle is 8*17/2=68
Total area is 300+68=368
Perimeter is 15+20+20+8+17=80
Answer:
[tex]\rm {P = 80 \space\ feet,\space\ A = 360 \space\ square \space\ feet}[/tex]
Step-by-step explanation:
The perimeter of a shape is the sum of all the sides of the shape.
• Perimeter of the polygon = 15 + 20 + 17 + 8 + 20
= 80 feet
To find the area of the polygon, we can separately find the areas of the triangle and the rectangle and then add them together.
• Area of rectangle = length × breadth
= 15 × 20
= 300 square feet
• Area of triangle = [tex]\frac{1}{2}[/tex] × base × height
As the height of the triangle is not provided, we have to calculate it.
Let the height of triangle = [tex]x[/tex]
Using Pythagoras's theorem:
[tex]x^2 + 8^2 = 17^2[/tex]
⇒ [tex]x^2 = 17^2 - 8^2[/tex]
⇒ [tex]x = \sqrt{17^2 - 8^2}[/tex]
⇒ [tex]x=\bf15[/tex]
Now using this value of height, we can find the area of the triangle:
Area of triangle = [tex]\frac{1}{2}[/tex] × 8 × 15
= 60 square feet
• Finally, we can add the areas of the triangle and rectangle together to find the area of the polygon:
Area of polygon = 300 + 60
= 360 square feet
We spend 85 minutes a day in math class. How many hours would we spend in math class in a 9 week period
Answer:
we spend maths class in a. day =85m
.:we spend in a maths class in a 9 week period=85x9x7:- 24=223.125