Answer:
x = 3
y = -1
Step-by-step explanation:
Solving system of equations:Method: substitution
x - 3y = 6 --------------(I)
x = 6 + 3y -------------(II)
2x + 2y = 4 ----------(III)
Substitute x = 6 +3y in equation (II),
2*(6+3y) + 2y = 4
Use distributive property to open the parenthesis,
2*6 + 2*3y + 2y = 4
12 + 6y + 2y = 4
Combine like terms.
12 + 8y = 4
Subtract 12 from both sides,
8y = 4 - 12
8y = -8
Divide both sides by 8,
y = -8÷ 8
[tex]\boxed{\bf y = (-1)}\\[/tex]
Substitute y = -1 in equation (II) and find the value of x.
x = 6 + 3*(-1)
= 6 - 3
[tex]\sf \boxed{\bf x = 3}[/tex]
Answer:
(3, - 1 )
Step-by-step explanation:
x - 3y = 6 ( add 3y to both sides )
x = 3y + 6 → (1)
2x + 2y = 4 → (2)
substitute x = 3y + 6 into (2)
2(3y + 6) + 2y = 4
6y + 12 + 2y = 4
8y + 12 = 4 ( subtract 12 from both sides )
8y = - 8 ( divide both sides by 8 )
y = - 1
substitute y = - 1 into (1)
x = 3(- 1) + 6 = - 3 + 6 = 3
solution is (3, - 1 )
Instructions: Find the missing probability.
P(B)=1/2P(A|B)=11/25P(AandB)=
If ΔABC is dilated from point A by a scale factor of one half, which of the following equations is true about segment D prime E prime?
segment D prime E prime = one half segment DE
segment D prime E prime = two segment DE
segment D prime E prime = segment DE
segment D prime E prime = three segment DE
An equation that is true about segment D prime E prime include the following: A. segment D prime E prime = one half segment DE
What is a dilation?In Geometry, a dilation is a type of transformation which typically changes the side lengths of a geometric object, but not its shape.
In this scenario and exercise, we would dilate the coordinates of the vertices of triangle ABC (ΔABC) by applying a scale factor of 1/2 that is centered at point A as follows:
D'E' = 1/2 × DE
In conclusion, line segment D'E' is equal to one half line segment DE.
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If the equation is an identity
The equation is an identity is discussed below.
An identity is a mathematical equation that holds true for all values of the variables involved.
In other words, it is true regardless of the specific values of the variables. When an equation is an identity, it means that both sides of the equation are equivalent and represent the same mathematical relationship.
For example, the equation 2x + 3 = 2(x + 1) is an identity because it holds true for all values of x.
When an equation is an identity, it provides a general statement or rule that is universally applicable and does not depend on specific values or conditions. Identifying an equation as an identity is important because it allows us to make general conclusions and deductions that apply in all cases.
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There are 1000 students at a college. In January, æ of these students had passed
their driving test.
Between January and April, the number of students who had passed their driving
test increased by 20%, and the number of students who had not passed
decreased by 5%. No one left or joined the college during this time.
a) Explain why the number of students who had not passed their driving test yet
was 0.95(1000 - x) in April.
b) Hence explain why 1.2x +0.95(1000-x) = 1000.
c) How many students had passed their driving test in January?
a) In April, the number of students who had not passed their driving test decreased by 5%.
b) The equation is 1.2x + 0.95(1000 - x) = 1000.
c) 200 students passed their driving test in January.
a) At the beginning, of January, x students had passed their driving test, then the remaining number of students who had not passed their driving test was (1000 - x).
In April, the number of students who had not passed their driving test decreased by 5%, which means the remaining number of students who had not passed their driving test is 0.95 times the original number (1000 - x).
b)
The number of students who had passed their driving test increased by 20%, which means the new number of students who passed their driving test is 1.2 times the original number (x).
The number of students who had not passed their driving test decreased by 5%, which means the new number of students who had not passed their driving test is 0.95 times the original number (1000 - x).
Therefore, we can write the equation 1.2x + 0.95(1000 - x) = 1000.
c) We can solve for x in the equation 1.2x + 0.95(1000 - x) = 1000.
Expanding the equation, we get:
1.2x + 950 - 0.95x = 1000
0.25x = 50
x = 200
Therefore, 200 students passed their driving test in January.
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Is the inverse of the function shown below also a
function? Explain your answer.
DONE ✔
AY
y
4
We can see here that it is true that the inverse of the function shown is also a function. This is true because the graph of the inverse of the function shown by reflecting the red graph about the line y = x.
What is a function?A function in mathematics is a unique connection between a group of inputs and their results. A function is a rule that specifically assigns one element from another set to each element in a set.
The set of inputs is referred to as the function's domain, while the set of outputs is referred to as the function's codomain.
From the given graph, we can deduce that the resulting graph is true for all x values and for all y values; it passes the vertical line test.
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ANSWER ASAP!! (GIVING BRAINLIEST IF CORRECT!!)
A basketball player guesses her team will score 54 points during the game. The player's team actually scores 60 points.
What is the percent error in the player's guess?
A: 5%
B: 10%
C: 12%
D: 15%
Answer:
6 divide by 60 into 100
Step-by-step explanation:
is 10
Be sure to round the mileage to nearest whole mile
The miles you drive must be greater than or equal to 183 miles in order for Plan B to save you money.
How to define a linear function?The slope-intercept equation for a linear function is presented as follows:
y = mx + b
In which:
m is the slope.b is the intercept.For the mileages, we have that:
The slope is the cost per mile.The intercept is the daily cost.Hence the functions are given as follows:
Plan A: A(x) = 30 + 0.14x.Plan B: B(x) = 50.Cost B is the better plan when:
A(x) > B(x)
Hence:
30 + 0.14x > 50
0.14x > 20
x > 20/0.14
x > 142.9 miles -> rounded to 143.
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Assessment
What is a brokerage account?
A. An online account used to pay expenses.
B. A deposit account at a financial institution that allows
withdrawals and deposits.
C. An interest-paying deposit account at a financial
institution that provides a modest interest rate.
D. An account used to buy investments like stocks, bonds,
and mutual funds.
5/10
Answer:
Step-by-step explanation:
A brokerage account is an investment account that allows you to buy and sell a variety of investments, such as stocks, bonds, mutual funds, and ETFs.
Therefore the answer is D
Directions: Transformations from the parent function y = x² are described
below. Write an equation to represent the function.
13, translated 2 units right
14. translated 5 units up
15. translated 3 units left and 4 units
down
17. reflected over the x-axis, then
translated 3 units down
16. translated 7 units right and 4
units up
18. reflected over the x-axis, then
translated 5 units right and 2 units
down
19. vertically compressed by a factor 20. vertically stretched by a factor
of 1/3, then translated 8 units up
of 2, reflected over the x-axis,
then translated 4 units left
The result of the transformation of the parent function y = x² are;
13. y = (x - 2)²
14. y = x² + 5
15. y = (x + 3)² - 4
16. y = (x - 7)² + 4
17. y = -(x²) - 3
18. y = -(x - 5)² - 2
19. y = (1/2)x²
20. y = (3x²) + 8
What are the results of the transformations?The transformations on the parent function y = x² can be described as;
13. Translated 2 units right:
The equation will be y = (x - 2)²
14. Translated 5 units up:
The equation will be y = x² + 5
15. Translated 3 units left and 4 units down:
The equation will be y = (x + 3)² - 4
16. Translated 7 units right and 4 units up:
The equation will be y = (x - 7)² + 4
17. Reflected over the x-axis, then translated 3 units down:
The equation will be y = -(x²) - 3
18. Reflected over the x-axis, then translated 5 units right and 2 units down:
The equation will be y = -(x - 5)² - 2
19. Vertically compressed by a factor of 2:
The equation will be y = (1/2)x²
20. Vertically stretched by a factor of 1/3, then translated 8 units up:
The equation will be y = (3x²) + 8
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Byron worked fewer than 20 days last month. Write an inequality for d, the number of days Byron worked last month.
Answer:
[tex]d < 20[/tex]
Step-by-step explanation:
The key words in this question are fewer than, which signifies the less than sign. So, the number of days that Byron worked is less than 20.
A triangle has sides with lengths of 13 meters, 18 meters, and 8 meters. Is it a right triangle?
Answer:
The Pythagorean Theorem describes the relationship among the three sides of a right triangle
[tex]a^{2} +b^{2} = c^{2} \\8^2+13^2=c^2=208 \\\sqrt{208}=14.4\\ 14.4 \neq 18[/tex]--> not a right triangle
(05.03 MC)
A regular heptagon with 7 sides is inscribed in a circle with radius 8 millimeters. What is the area of
the figure? (3 points)
O 25.019 mm.2
O 150.112 mm.2
O 175.130 mm.²
205.639 mm.2
Answer:
i think 25.019mm2 is the correct answerrrrrrrr.
Answer:
175.130 mm^2
Step-by-step explanation:
Took the test.
Eight fourths is proportional to what value?
Eight fourths is proportional to the value of 2/1
What is proportionality of values?Proportionality of values means the relationship that exists between two variables where their ratios are equivalent to each other.
A ratio that is made up of two variables is said to be proportional to another ratio when after being simplified one arrives at the same ratio.
Using the 8:4 or 8/4. This is equivalent to 2/1 and also equivalent to 16/8 as the simplification leads to 2/1
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If you flip two coins 68 times, what is the best prediction possible for the number of times both coins will land on heads?the number of times it will land on tails?
If you flip two coins 68 times, the best prediction for the number of times both coins will land on heads is 17.
If you flip two coins 68 times, the best prediction for the number of times both coins will land on tails is 17.
What is the probability of getting two heads?The possible outcomes when two coins are flipped are;
head - head = HH
tail - tail = TT
Head and tail = HT
Tail and head = TH
The probability of getting two heads = 1/4
If you flip two coins 68 times, the best prediction for the number of times both coins will land on heads is calculated as;
Expected value = (68 flips) x (1/4 probability of getting HH) = 17
The probability of getting two tails = 1/4
Expected value = 68 x 1/4 = 17
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8 cosθ-1=0 to the nearest 0.1°
Answer:
82.8°
Step-by-step explanation:
We can solve for θ by first isolating cosθ:
8 cosθ - 1 = 0
8 cosθ = 1
cosθ = 1/8
We can find the inverse cosine of 1/8:
θ = cos⁻¹(1/8) = 82.8191°
Rounding to the nearest 0.1°, we get:
θ ≈ 82.8°
find the perimeter of a triangle where one side is 2 inches, one side is 6 inches and another side is 10 inches.
(a) 2in.
(b) 9in.
(c) 36in.
(d) 18in.
Answer:
(d) 18 in.
Step-by-step explanation:
When we're given the three sides of a triangle, one formula we can use for perimeter of a triangle is:
P = s1 + s2 + s3, where
P is the perimeter,and s1, s2, and s3 are the three sides:P = 2 + 6 + 10
P = 8 + 10
P = 18
Thus, the perimeter of the triangle is 18 in.
what is the probability of spinning a blue, then green
The probability of getting Blue then Green while spinning the wheel is
3 / 32
Probability is a branch of mathematics that helps us to understand the likelihood of an event occurring. It is represented by a number between 0 and 1, where 0 means the event is impossible and 1 means the event is certain. Probability can be used to make predictions and informed decisions in real-world situations.
From the given figure we can find out the following information
The probability of getting Blue While spinning the wheel = 3/8
The probability of getting Green While spinning the Wheel = 2 / 8
The probability of getting Blue then Green while spinning the wheel
= 3/8 * 2/8
= 6/64
= 3/32
Therefore, probability of getting Blue then Green while spinning the wheel is 3 / 32
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Please help me understand this problem!
The requried solution of the given derivative has been given below.
If F(t) is an antiderivative of t⁵, then we have:
F'(t) = d/dt(F(t)) = t⁵
According to the Second Fundamental Theorem of Calculus, we have:
[tex]\int_1^x t^5 dt = F(x) - F(1)[/tex]
Using this formula, we can find [tex]d/dx(\int_1^x t^5 dt)[/tex] as follows:
[tex]d/dx(\int_1^x t^5 dt) = d/dx(F(x) - F(1)) = F'(x) - 0 = t^5[/tex]
Therefore, [tex]d/dx(\int_1^x t^5 dt) = t^5.[/tex]
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Suppose that a safety deposit box at your bank costs $45/month to rent. How much would
it cost for you to rent the box for 15 years?
What are the first five terms of the sequence a_{n} = - 11 * (1/2) ^ (n - 1)
A) -11, - 11/2 - 11/4 - 11/8 - 11/16
B) -11/2 - 11/4 - 11/16 - 11/32 - 11/8
C) -11, 5, - 9/4 - 4/3 - 7/8
D) -11, - 11/2 - 11/3 - 11/4 - 11/5
All the first five terms of sequence are,
A) -11, - 11/2 - 11/4 - 11/8 - 11/16
We have to given that;
Rule for sequence is,
⇒ a (n) = - 11 × (1/2)ⁿ⁻¹
Now, WE can find first five terms of sequence as;
⇒ a (n) = - 11 × (1/2)ⁿ⁻¹
Put n = 1;
⇒ a (1) = - 11 × (1/2)¹⁻¹
⇒ a (1) = - 11
Put n = 2;
⇒ a (n) = - 11 × (1/2)ⁿ⁻¹
⇒ a (2) = - 11 × (1/2)²⁻¹
⇒ a (2) = - 11 × (1/2)¹
⇒ a (2) = - 11 / 2
Put n = 3;
⇒ a (n) = - 11 × (1/2)ⁿ⁻¹
⇒ a (3) = - 11 × (1/2)³⁻¹
⇒ a (3) = - 11 × (1/4)
⇒ a (3) = - 11 / 4
Put n = 4;
⇒ a (n) = - 11 × (1/2)ⁿ⁻¹
⇒ a (4) = - 11 × (1/2)⁴⁻¹
⇒ a (4) = - 11 × (1/2)³
⇒ a (4) = - 11 / 8
Put n = 5;
⇒ a (n) = - 11 × (1/2)ⁿ⁻¹
⇒ a (5) = - 11 × (1/2)⁵⁻¹
⇒ a (5) = - 11 × (1/2)⁴
⇒ a (5) = - 11 / 16
Thus, All the first five terms of sequence are,
A) -11, - 11/2 - 11/4 - 11/8 - 11/16
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PLS HELP! In the figure below, m angle SUT=123 and m arc PR= 124 . Find m arc ST.
The measure of the arc of the circle is mST = 122°
Given data ,
Let the circle be represented as C
where the two chords of the circle are RT and PS
And the chords RT and PS intersect at the point U
Now , when two chords intersect inside a circle, four angles are formed. At the point of intersection, two sets of congruent vertical angles are formed in the corners of the X that appears.
On simplifying , we get
m∠SUT = ( 1/2 ) ( mPR + mST )
123° = ( 1/2 ) ( 124° + mST )
On solving for mST , we get
( 124° + mST ) = 246°
Subtracting 124° on both sides , we get
mST = 122°
Hence , the measure of arc mST = 122°
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Here is a map of an island with cities A, B and C Jeremy drives
1) The three figure bearing of B from A when B is due East of A is 090°
2) Note that Kenzi drives 60km further than Jafar.
What is bearing?A) A bearing is the angle in degrees measured clockwise from north in mathematics. Bearings are often specified in three figures. 30° clockwise from north, for example, is generally represented as 030°.
Hence in the above case of option A, The three figure bearing of B from A when B is due East of A is 090°
B) To find or compute how much further Kenzi drives than Jafar, we need to convert the distances on the map to their real-world distances using the given scale of 1cm to 200km.
So A to B for Jafar -
Distance from A to B = 2.4cm x 200km/ cm = 480km
Then for B to C for Kenzi -
Distance from B to C = (1.2cm + 1.5cm) x 200km/cm
= 2.7cm x 200km/cm
= 540km
So to determine how much further Kenzi drives compared to Jafar
Kenzi drives 540km - Distance from A to B
= 540km - 480 km = 60km
Therefore, Kenzi drives 60km further than Jafar.
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Full Question:
Although part of your question is missing, you might be referring to this full question:
See attached image.
There is a multiple choice quiz with six questions and five possible answers and only one choice is correct what is the probability you get your first and only incorrect answer on the fourth question?n
Answer:1/1875
Step-by-step explanation:
the probability of getting any one question correct is 1/5, and the probability of getting any one question incorrect is 4/5.
The probability of getting the first three questions correct and the fourth question incorrect can be calculated as follows:
(1/5) * (1/5) * (1/5) * (4/5) = 4/3125
Since there are six possible positions for the incorrect answer to occur (first, second, third, fourth, fifth, or sixth), the probability of getting the first and only incorrect answer on the fourth question is 4/3125 * 1/6 = 1/1875.
Can you guys help me with this please
Step-by-step explanation:
Using rules of logs :
9 loga x = loga x^9
Then using another rule:
loga x^9 + loga y = loga (x^9 * y )
In triunghiul ABC ,A este de 75 grade si B este de 45 grade. Daca AD perpendicular BC, D apartine BC si BE perpendicular AC, E apartine AC iar AB=12 Radical din 6 cm calculati lungimile AD si BE si Perimetrul ABC
Answer:
just start scamming
Step-by-step explanation:
A circle with circumference 72π is divided into 10 congruent sectors. Find the area of two sectors. Round to the nearest tenth
Pablo mixed 2 1/2 quarts of fruit juice with 1 gallon of seltzer. If each serving is 8 fluid ounces, how many servings did Pablo make?
A. 20
B. 26
C. 32
D. 36
Determine which set of sides measurements could be used of form a right triangle 14,5,15 3,4,5 9,14,16 5,2,7
Answer: 14,5,15 is correct
Step-by-step explanation:
(x+3)(x+7)=0
Problem answered, solution and why!
Answer:
the solution set is { - 7, - 3 }
Step-by-step explanation:
(x + 3)(x + 7) = 0 ← in factored form
equate each factor to zero and solve for x
x + 3 = 0 ( subtract 3 from both sides )
x = - 3
x + 7 = 0 ( subtract 7 from both sides )
x = - 7
solution set is { - 7, - 3 }
Which best describes the solution set for the compound inequality below?
2(x + 7) – 1 > 15 or 3(x + 2) < 2x + 7
no solution
x = 1
all real numbers except x = 1
all real numbers
The statement that best describes the solution to the inequality in this problem is given as follows:
all real numbers except x = 1.
How to solve the inequality?The inequality in the context of this problem is defined as follows:
2(x + 7) – 1 > 15 or 3(x + 2) < 2x + 7
The solution to the first inequality is given as follows:
2(x + 7) – 1 > 15
2x + 14 > 16
2x > 2
x > 1.
The solution to the second inequality is given as follows:
3(x + 2) < 2x + 7
3x + 6 < 2x + 7
x < 1.
The or operation includes the elements that belong to the solution set of at least one of the inequalities, hence the solution is given as follows:
all real numbers except x = 1.
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