Answer:
r = 3
Step-by-step explanation:
Slope-intercept form of a linear equation:
[tex]\large\boxed{y=mx+b}[/tex]
where:
m is the slope.b is the y-intercept.Given:
Slope = ⁶/₅Point = (-2, -3)Substitute the given slope and point into the formula and solve for b:
[tex]\begin{aligned}y & = mx+b\\\implies -3 & = \dfrac{6}{5}(-2)+b\\-3 & = -\dfrac{12}{5}+b\\-3 +\dfrac{12}{5} & = b\\\implies b & = -\dfrac{3}{5}\end{aligned}[/tex]
Substitute the given slope and found value of b into the formula to create an equation for the line:
[tex]\boxed{y=\dfrac{6}{5}x-\dfrac{3}{5}}[/tex]
Substitute the point (r, 3) into the equation and solve for r:
[tex]\begin{aligned}y & = \dfrac{6}{5}x-\dfrac{3}{5}\\\implies 3 & = \dfrac{6}{5}r-\dfrac{3}{5}\\5 \cdot 3& = 5 \cdot \left(\dfrac{6}{5}r-\dfrac{3}{5}\right)\\15 & = 6r-3\\15+3&=6r-3+3\\ 18 & = 6r\\\dfrac{18}{6} & = \dfrac{6r}{6}\\3 & = r\\ \implies r & =3\end{aligned}[/tex]
Solution
Therefore, the value of r is 3.
pls helppppppppppppp
Answer:
Option 2
Step-by-step explanation:
2.2 x 1.25 = 2.7510-2.75=7.25
ASAP NEED>...............
Give an example of a 2x2 matrix whose
determinant is 13.
Answer:
The method for appearing with numbers for the 2x2 matrix whose determinant is 13 is clarified.
Step-by-step explanation:
Determinant of 2×2 matrix
If we have a 2×2 matrix A of the form;
A =
\binom{a \: \: \: b}{c \: \: \: d}(
cd
ab
)
The determinant of the matrix is;
|A| = (a.d) - (b.c)
Therefore, to appear with numbers for a, b, c, and d, we must ensure; (a.d) - (b.cdeterminantse, if a = 3, d = 15, b = 2, and v = 1.
Ultimately, |A| = (3×5) - (2×1) = 13
Find the 32 nd term of each sequence. -9,-8.7,-8.4, ...........
The 32th term of the arithmetic sequence AP is estimated to be 0.3.
What is meant by arithmetic sequence AP?In math, an arithmetic progression (AP) is a list or sequence of numbers in which each term is obtained by adding a finite number to the term before it.
The fixed number is known as the arithmetic progression's common difference written by 'd'The common difference of AP is 'd': d = a2 - a1 = a3 - a2 = a4 - a3 =...... = a - an-1.nth term of an AP: an = a + (n - 1) dThe sum of n terms of an AP's is Sn = n/2(2a+(n-1)d) = n/2(a + l), where l is the final term of the AP.Now for the answer to the question;
The numbers in the given sequence are-
-9,-8.7,-8.4, ...........
There are 32 terms with in series for that we need to find the 32nd number.
Let's say the first term is 'a₁' = -9.
Let 'a₂' = -8.7 be the second term.
Let 'a₃' = -8.4 be the third term.
The common difference between two consecutive terms that are equal of an AP is 'd.'
d = a₂ - a₁
Substitute the values in the preceding equation; the 32nd term is
d = -8.7 - (-9)
d = -8.7 + 9
d = 0.3
Now calculated using the nth term formula.
nth term of an AP: an = a + (n - 1) dTotal number of terms is; n = 32First term is a = -9common difference d = 0.3Substitute all of the values in the formula now.
a₃₂ = a + (n - 1) d
a₃₂ = -9 + (32 - 1)(0.3)
a₃₂ = -9 + 9.6 - 0.3
a₃₂ = 0.3
As a result, the arithmetic sequence's 32nd term is estimated to be 0.3.
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What is the slope of a line perpendicular to the line whose equation is x+4y=16x+4y=16. Fully simplify your answer.
The slope of a line perpendicular to the line of x + 4y = 16 is 4.
What is the slope of a line perpendicular to the line of the given equation?Given the equation of line;
x + 4y = 16
First, rearrange in slope intercept form ( y = mx + b ) by solving for y
x + 4y = 16
Subtract x from both sides
x - x + 4y = 16 - x
4y = -x + 16
Divide each term by 4 and simplify
4y/4 = -x/4 + 16/4
y = -(1/4)x + 4
Using the slope intercept form ( y = mx + b ) to compare.
y = -(1/4)x + 4
Slope m = -(1/4)
Now, the equation of a perpendicular line to y = -(1/4)x + 4 must have a slope that is the negative reciprocal of the original slope.
Hence, m_perpendicular will be;
m_perpendicular = -( 1 / original slope )
m_perpendicular = -( 1 / -(1/4) )
m_perpendicular = -( -4 )
m_perpendicular = 4
Therefore, the slope of a line perpendicular to the line of x + 4y = 16 is 4.
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A major fishing company does its fishing in a local lake. The first year of the company's operations it managed to catch 175,000 fish. Due to population decreases, the number of fish the company was able to catch decreased by 8% each year. How many total fish did the company catch over the first 10 years, to the nearest whole number?
The company catches 1,237,275.5 fishes over 10 years.
Given that, a company catches 175000 fishes in a year, the population decreases, the number of fish the company was able to catch decreased by 8% each year.
So, the population in 10 year =
The second year = 175000 × 0.92 = 161000
The third year = 161000 × 0.92 = 148120
The fourth year = 148120 × 0.92 = 136,270.4
The fifth year = 136270.4 × 0.92 = 125368.8
The sixth year = 125268.8 × 0.92 = 115339.3
The seventh year = 115339.3 × 0.92 = 106112.2
The eighth year = 106112.2 × 0.92 = 97623.2
The ninth year = 97623.2 × 0.92 = 89813.3
The tenth year = 89813.3 × 0.92 = 82628.3
The total = 175,000+161000+148120+136,270.4+125368.8+115339.3+106112.2+97623.2+89813.3+82628.3 = 1,237,275.5
Hence, the company catches 1,237,275.5 fishes over 10 years.
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The table shows the number and type of books that Sarah owns. Find the probability.
A randomly chosen title is a print or audio book.
Answer:
hi
Step-by-step explanation:
Answer:
FITNESS Laura wants to go to a fitness class
tomorrow. She can choose a 5:00 or a 7:30 class and
spin or water aerobics. Represent the sample space
for the situation by making an organized list, a table,
and a tree diagram.
Step-by-step explanation:
Find the expression for h(x)
Hello,
[tex]f(x) = - {x}^{2} + 8[/tex]
[tex]h(x) = - {x}^{2} + 8 - 3 = - { {x}^{2} } + 5[/tex]
234.8−38.94 helppppp
Answer:
195.86
Step-by-step explanation:
Answer: 195.86. Yw.
Step-by-step explanation: Pls add me Brainliest >3
If p(a|b) =0.40, p(b) = 0.74, and p(a) = 0.42, are the events a and b independent?
The set of items that exist as part of both sets A and B exists at the intersection of the two sets.
If p(a|b) =0.40, p(b) = 0.74, and p(a) = 0.42, then P(A∩B) is 0.46.
What is Probability?The area of mathematics known as probability deals with numerical representations of the likelihood that an event will occur or that a statement is true.
It exists given that the Probability of two independent event A and B exists given by P(A) and P(B).
The intersection of event A and B is given by P( A∩B).
The group of items that are part of both sets A and B is the intersection of the two sets. A ∩ B represent the intersection. The symbol "∩" can be used to represent the intersection of sets.
The collection of all outcomes that are components of both sets A and B is known as the intersection of events A and B (abbreviated AB).
Given: P(a|b) = 0.40
P(A) = 1 - 0.40 = 0.6
P(B) = 1 - 0.74 = 0.26
P(A∪B) = P(A) + P(B) − P(A∩B)
substitute the values in the above equation, we get
0.40 = 0.6 + 0.26 - P(A∩B)
- P(A∩B) = 0.40 - 0.6 - 0.26
P(A∩B) = 0.46
Therefore, the independent events of A and B exists 0.46.
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-8(-10/7)=4(-10/7+5)+2(-10/7)
help pls
just like show solution
Answer:
Step-by-step explanation:
[tex]\displaystyle\\-8(-\frac{10}{7})= 4(-\frac{10}{7} +5)+2(-\frac{10}{7} )\\[/tex]
[tex]\displaystyle\\Let \ -\frac{10}{7} =t\\Hence,\\(-8)(t)=(4)(t+5)+(2)(t)\\-8t=(4)(t)+(4)(5)+2t\\-8t=4t+20+2t\\-8t=6t+20\\-8t+8t=6t+20+8t\\0=14t+20\\0-20=14t+20-20\\-20=14t\\-20=(14)(-\frac{10}{7} )\\-20=-\frac{(14)(10)}{7} \\\\-20=-\frac{(7)(2)(10)}{7} \\-20=-(2)(10)\\-20\equiv-20[/tex]
help me with this question
Thomas took a 140-mile bus trip to visit his grandparents.
His trip is outlined on the graph
Explain what might have happened in the interval
between D and E.
a. Show work (50 points). Mark the graph
Answer:
they stopped at 110 for a restroom break?
I don't think I fully understand lol srry
Thomas and his grandparents are on a trip of 140-mile. From Points D and E, there is no movement of the bus, which means they halt at the point.
What is a graph?An orderly schematic illustration or diagram of facts or quantities is known as a graph in mathematics.
Usually, the graph's examples indicate how two or more items are related to one another.
As per the graph provided in the question,
As we can see in the graph there are covering 140 miles in a bus and the graph shows distance (in miles) and time (in hours).
From the graph we can see that between point D and E only time is increasing but the distance is constant which means they stopped at some place to halt.
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Ms. Lopez is creating posters to decorate
her classroom. She uses 0.25 ounce of paint
per poster. If she has 4.05768 ounces of
paint, how many posters can she make?
Write a two-column proof. (Lesson 4-4)
Given: Δ L M N is isos. with LM ≅ NM , and MO bisects ∠L M N .
Prove: Δ M L O ≅ ΔM N O
It is proved that ΔLMN is an isosceles triangle.
What exactly do we mean by a triangle's congruency?Two triangles are said to be congruent if all three corresponding sides are equal and all three corresponding angles are equal in measure.These triangles can be moved, rotated, flipped, and turned to appear identical.If they are repositioned, they will coincide.If two triangles satisfy the five congruence conditions, they are congruent.They are side-side-side (SSS), side-angle-side (SAS), angle-side-angle (ASA), angle-angle-side (AAS), and right angle-hypotenuse-side (RHS).So,
Given:
LM ≅ NMMO bisects ∠L M NTo prove congruency:
MO = MO (Common line)LM = NM = Given∠LM0 = ∠NMO = equal angles (As MO bisects ∠LMN)Therefore, ΔM LO ≅ ΔMNO under SSA congruency.
Since the 2 sides are similar so the angles in front of them will also be similar.So we can say that ΔLMN is an isosceles triangle.Therefore, it is proved that ΔLMN is an isosceles triangle.
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Which graph represents exponential decay?
Answer:
The graph of g(x) shows exponential decay, while the graph of f(x) shows exponential growth. What you need in your answer: The graphs are reflections of each other over the y-axis. The g(x) function represents exponential decay.
A b = 8x - 7 BC = 6X + 7 what is AC
Answer:
a
Step-by-step explanation: codigo binario
What is the 2 nd term of the geometric sequence 3, II, 12, . . . . . . . ?
The second term of the given geometric sequence is: 6.
What is a geometric progression?A geometric progression, sometimes referred to as a geometric sequence in mathematics, is a series of non-zero numbers where each term following the first is obtained by multiplying the preceding one by a constant, non-zero value known as the common ratio.Given:
First term of GP = 3 (a₁).Third term of the GP = 12 (a₃).To find: Second term of the GP (a₂).
Finding:
Since the given sequence is a GP, the nth term will be given by: [tex]a_n=a_1(r^{n-1})[/tex], where r = common ratio of the GP.
Now, for n = 3, [tex]a_3=3(r^{3-1})[/tex]
=> 12 = 3 (r²)
=> 4 = r²
=> r = ±2
Since the given sequence is increasing and positive, r = 2.
Thus, a₂ = a₁ (r¹)
=> a₂ = 3 (2) = 6
Hence, The second term of the given geometric sequence is: 6.
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there are 5 more of this same question get free pounts! Rex and Samir participated in a walkathon. Rex walked for 1 2/3 hours, and Samir walked for 3 1/3 hours. complete the comparison. Samir walked _____ times ad many hours as Rex walked.
Answer:
2 times as much
Step-by-step explanation:
1 hour 2/3 = 60 + (2/3) 40 mins = 100 minutes
3 hours 1/3 = (60 ×3 ) + 20 mins = 200 mins
200 is twice as much as 100
help asap!! check screenshot
The sequence of the angles from lower to bigger will be ∠WXY < ∠YXZ < ∠WYX < ∠XZY < ∠XYZ.
What is the triangle?A triangle is a three-sided polygon with three angles. The angles of the triangle add up to 180 degrees.
In a triangle, if the angle is small then the opposite side will be short, and if the angle increases then the side also increases.
The sides of the triangle are in ascending order, then we have
WY < YZ < WX < XY < XZ
Then the sequence of the angles is given as,
∠WXY < ∠YXZ < ∠WYX < ∠XZY < ∠XYZ
The sequence of the angles from least to biggest is ∠WXY < ∠YXZ < ∠WYX < ∠XZY < ∠XYZ.
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Urijah is starting a food cart business. The cost to start the business is $20,000 and the monthly costs are $8,000. He has been earning $8,800 every month in revenue. In how many months will Urijah's business break-even and earn a profit?
He will break even on the 25th month.
How to find the number of month his business will break even?The cost to start the business is $20,000 and the monthly costs are $8,000.
He has been earning $8,800 every month in revenue.
Profit = Selling Price - Cost Price
Therefore,
let
x = number of month
Hence,
selling price = 8800x
cost price = 20000 + 8000(x) = 20,000 + 8000x
Therefore,
profit = 8800x - (20,000 + 8000x)
profit = 8800x - 20000 - 8000x
profit = 8800x - 8000x - 20000
profit = 800x - 20000
Hence,
The month when they will break even is as follows:
8800x = 20,000 + 8000x
20000 = 8800x - 8000x
20000 = 800x
x = 20000 / 800
x = 25
Therefore, he will break even on the 25th month.
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After robbing a bank in Dodge City, a robber gallops off at 14 mi/h. 30 minutes later, the marshall leaves to pursue the robber at 16 mi/h. How long (in minutes) after the marshall takes off does it take the marshall to catch up to the robber?
The number of minutes it will take the marshal to catch up to the robber in discuss is; 210.
How long will it take to catch up with the robber?Let 30minutes = 0.5 hours.
Let x represent the time for which the marshal has ran.
On this note, the robber must have galloped at; (x +0.5) hours.
Hence, it follows from the task content that if they are at the same distance from the bank; we have;
14(x+0.5) = 16(x)
14x + 7 = 16x
7 = 2x
x = 7/2 = 3.5 hours.
= 3.5 × 60minutes = 210minutes.
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HELP WITH INEQUALITY PROBLEM PLEASE!!!
Answer:
A. s+7726>=12,600
Step-by-step explanation:
s is the number of steps left to reach her goal of at least 12,600 steps.
7726 is the number of steps already taken.
12,600 is her goal.
s+7726>=12,600
Hope this helps!
Please mark as brainliest if correct!
Find the values of x and y given that 182x + 247 y = gcd(182, 247)
Answer:
Hello,
x=-4, y=3
Step-by-step explanation:
14*x+19*y=1 since gcd(182,247)=13
Here is a automatic calculus (using Bezout 's method)
All you have to do is to put in B1 and B2 the right numbers
The values of x and y given that 182x + 247 y = gcd(182, 247) would be x=-4 and y=3.
What does it mean to solve an equation?An equation represents equality of two or more mathematical expression.
To solve an equation, then the values of the unknowns for which that equation would be true (the equality between expressions should hold true for those values).
And Solutions to an equation are values of the variables involved in that equation for which the equation is true.
We have given the equation as;
182x + 247 y = gcd(182, 247)
Then we get
14*x+19*y=1
Thus, x=-4 and y=3.
since we have given gcd(182,247)
=13
Hence, The values of x and y given that 182x + 247 y = gcd(182, 247) would be x=-4 and y=3.
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Two trains leave towns 978 miles apart at the same time and travel toward each other. one train travels 21 miles per hour faster than the other. if they meet in 6 hours what is the rate of each train?
If two trains leave towns 978 miles apart at the same time and travel toward each other and one train travels 21 miles per hour faster than the other and if they meet in 6 hours, then the rate of the faster and slower train will be 92mph and 71 mph respectively.
To determine the rate or speed of each train, an algebraic expression can be used.
As one train travels 21 miles per hour faster than the other, consider x to be the speed of the train that travels slower. In this case, an algebraic expression can be given as,
6x + 6(x + 21) = 978
Here, (x + 21) represents the speed of the faster train
6x + 6x + 126 = 978
12x = 978 - 126
12x = 852
x = 852 ÷ 12
x = 71
x + 21 = 71 + 21 = 92
Hence, the rate of the faster train is 92 miles per hour and the rate of the slower train is 71 miles per hour.
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On Monday, 222 students went on a trip to then zoo. All 4 buses were filled and 6 students had to travel in cars. Write an equation where x is the number of students on each bus. How many students were on the bus
Step-by-step explanation:
222-6=216
216÷4=54
so 54 students per bus
Answer:
54 students
Step-by-step explanation:
222 - 6 (students that had to travel in cars) = 216
216 / 4 (4 buses) = x
x = number of students on each bus
216 / 4 = 54
x = 54
54 students on each bus
216 students rode the bus, 6 students rode in cars
Find the value of x if A C=4 x-3, D C=2 x+9, m∠ E C A=15 x+2, and EC is a median of ΔAED. Is EC also an altitude of Δ A E D ? Explain.
If AC = 4x - 3, DC = 2x + 9, m ∠ ECA = 15x + 2, and EC is a median of ΔAED then EC is not an altitude of ΔAED because of m ∠ ECA = 92.
What is meant by the altitude of a triangle?
In geometry, an altitude is a line that passes through two very specific points on a triangle: a triangle's vertex, or corner, and its opposite side at a right, or 90-degree, angle. The base is the opposite side. Triangles have three vertices and three opposite sides in common.
Given: AC = DC
4x - 3 = 2x + 9
4x - 2x - 3 = 2x - 2x + 9
simplifying the above equation, we get
2x - 3 = 9
2x - 3 + 3 = 9+3
2 x = 12
x = 6
Substitute the value of x in m ∠ ECA, then we get
m ∠ ECA = 15x + 2
= 15(6) + 2
m ∠ ECA = 92
EC is not an altitude of ΔAED because of m ∠ ECA = 92.
Therefore, EC is not an altitude of ΔAED.
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Write the equation of each line in slope-intercept form and identify the slope.
4 x+6 y=12
The equation of the line 4x + 6y = 12 expressed in slope-intercept form is y = -2/3 x + 2 with a slope equal to -2/3.
The equation of a line can be expressed in three different forms: standard form, slope-intercept form, and point-slope form.
The slope-intercept form of the equation of a line is given by the formula:
y = mx + b
where m is the slope of the line
b is the y- intercept
Given the equation of the line 4x + 6y = 12, which is in standard form, transform it into slope-intercept form by isolating the variable y in one side.
4x + 6y = 12
6y = -4x + 12
Dividing both sides by 6,
y = -4/6 x + 2
y = -2/3 x + 2
Hence, the equation of the line in slope-intercept form is y = -2/3 x + 2 where the slope, m, is equal to -2/3.
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#3 i
The endpoints of AB are A (-8, 5) and B (0,7). Find the coordinates of the midpoint M.
The coordinates of the midpoint M
The coordinates of the midpoint M of the segment AB is (-4,6).
What is the coordinates of the midpoint M of the segment AB?The midpoint formula is expressed as;
M = ( (x₁+x₂)/2, (y₁+y₂)/2 )
Given the data in the question;
Point A (-8, 5)
x₁ = -8y₁ = 5Point B (0,7)
x₂ = 0y₂ = 7To determine the midpoint, plug the given points into the formula above and simplify.
M = ( (x₁+x₂)/2, (y₁+y₂)/2 )
M = ( ((-8)+0)/2, (5+7)/2 )
M = ( ( -8+0 )/2, (5+7)/2 )
M = ( ( -8 )/2, (12)/2 )
M = (-4,6)
Therefore, the coordinates of the midpoint M of the segment AB is (-4,6).
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The temperature is 10 degrees below zero. The sun come out and the temperature went
up 15 degrees. What is the temperature now since the sun came out?
Answer:
5 degres
Step-by-step explanation:
0-10 is -10
-10+15 is 5
