Answer:
4 is the correct answer to your question
Write the equation in slope-intercept form of the line that is parallel to the given line and passes through the given point.
y = 2x + 1; (6, -1)
The equation of line in slope - intercept form is, y = 2x - 13.
What is slope-intercept form of the line?
Using a straight line's slope and the location of its y-axis intersection, the slope intercept equation can be used to determine the general equation of the line. y = mx + b is the equation in slope intercept form.
Consider the given equation of line y = 2x + 1.
And the point given is, (6, -1).
We have to find the equation of line parallel to the given line and passes through the point (6, -1).
First we have to find the slope of the parallel line.
Since, Slope of the parallel line is same as the slope of the given line.
Here, the slope of the line is 2.
So, the slope of the parallel line is also 2.
Now consider the point slope form of the line,
[tex]y-y_1=m(x-x_1)[/tex]
Plug [tex](x_1, y_1)=(6, -1) , m = 2[/tex]
⇒
[tex]y-(-1)=2(x-6)\\y+1=2x-12\\y=2x-12-1\\y=2x-13[/tex]
Hence, the equation of the line parallel to the given line in slope intercept form is, y = 2x - 13.
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Select all the solutions to the inequality 2(7x + 1) < -26
_
A. -2
B. 9
C. -7
D. 4
Answer:X<-2
Step-by-step explanation:
7x+1<-13
7x<-13-1
7x<-14
Answer:
Step-by-step explanation:
the answer is A: x<-2
Find the maximum value of the function =z+8x3y subject to the following constraints.
≤+xy15≤+2xy18≥x0≥y0
Note that the ALEKS graphing calculator can be used to make computations easier.
The maximum value of the function z is 120
How to determine the maximum value of the function?The objective function is given as
z = 8x + 3y
While the constraints are given as
x + y ≤ 15
2x + y ≤ 18
x ≥ 0 and y ≥ 0
To determine the feasible region, we simply plot the graphs of x + y ≤ 15 and 2x + y ≤ 18
And we subset the graph to where x ≥ 0 and y ≥ 0
From the graph, we have the feasible coordinates to be
(x, y) = (0, 18), (3, 12) and (15, 0)
Substitute (x, y) = (0, 18), (3, 12) and (15, 0) in z = 8x + 3y
z = 8(0) + 3(18) = 54
z = 8(3) + 3(12) = 60
z = 8(15) + 3(0) = 120
Hence, the maximum value is 120
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Consider the following scenario: P(E) = 0.4, P(F) = 0.5
a. Find P(E or F) if E and F are disjoint
b. Find P(E or F) if E and F are independent
Part (a)
The term "disjoint" is the same as "mutually exclusive".
If events E and F are disjoint, then we know that P(E and F) = 0. In other words, the two events have nothing in common. Therefore, it's impossible for them both to occur simultaneously.
P(E or F) = P(E) + P(F) - P(E and F)
P(E or F) = 0.4 + 0.5 - 0
P(E or F) = 0.9
Answer: 0.9====================================================
Part (b)
If events E and F are independent, then P(E and F) = P(E)*P(F).
P(E or F) = P(E) + P(F) - P(E and F)
P(E or F) = P(E) + P(F) - P(E)*P(F)
P(E or F) = 0.4 + 0.5 - 0.4*0.5
P(E or F) = 0.4 + 0.5 - 0.2
P(E or F) = 0.9 - 0.2
P(E or F) = 0.7
Answer: 0.7Josie has $47 left on her checking account. If she writes a check for $55, what will Josie's balance be?
use synthetic division to find the quotient and remainder of the following. Write your answer on the form of
Answer:
Step-by-step explanation:
1. x^2 + 4x + 5/x-1
2. x^3-3x^2 + 9x-2 + 3/x+3
3. 2x^2 - 2x+5- 14/3x+1
4.3x2^2- 4x+3 - 13/ 2x-1
5. 3x^2 + 6x + 7 + 12/2x-3
If you took out a loan for $10,000 with a 2% interest rate & it was for 18 months. How much interest would pay?
The amount of interest he would pay for a loan of $10,000 with a 2% interest rate and for 18 months is $300
Amount of money taken as a loan = $10000
The rate of interest = 2%
The time period of interest is 18 months = 1.5 year
Interst = prt/100
= 10000x 2 x 1.5/100
= 300
Therefore, the amount of interest he would pay for a loan of $10,000 with a 2% interest rate and for 18 months is $300
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For the parallelogram, if m / 2 = 4x - 20 and m /4 = 3x - 11, find m / 1. The diagram is not drawn to scale.
For a parallelogram having (∠1 and ∠3) and (∠2 and ∠4) as the two pairs of opposite angles, if [∠2 = (4x - 20)] and [∠4 = (3x - 11)], then the measure of ∠1 will be 164°.
As per the question statement, a parallelogram has (∠1 and ∠3) and (∠2 and ∠4) as the two pairs of opposite angles, and [∠2 = (4x - 20)] and [∠4 = (3x - 11)],
Then, we are required to calculate the measure of ∠1.
To solve this question, first we will need to know about two important properties of a parallelogram,
(a) The sum of all the four interior angles of a parallelogram is equal to 360°,
(b) Opposite angles of a parallelogram are equal.
Now since our concerned parallelogram has (∠1 and ∠3) and (∠2 and ∠4) as the two pairs of opposite angles,
Therefore, (∠1 = ∠3) and (∠2 = ∠4),
And [(4x - 20) = (3x - 11)]...[∵(∠2 = ∠4)]
Or, [(4x - 3x) = (20 - 11)]
Or, [x = 9]
Therefore, [∠2 = ∠4 = (4x - 20) = 16°].
Now, [(∠1 + ∠2 + ∠3 + ∠4) = 360°]
Or, [(∠1 + ∠2 + ∠1 + ∠2) = 360°]...[∵(∠1 = ∠3) and (∠2 = ∠4)]
Or, [{(∠1 + ∠1 ) + (∠2 + ∠2)} = 360°]
Or, [(2∠1 + 2∠2) = 360°]
Or, [2∠1 = {360 - (2 * 16)}°]
Or, [2∠1 = (360 - 32)°]
Or, [2∠1 = 328°]
Or, [∠1 = (328/2)°]
Or, [∠1 = 164°]
That is, for a parallelogram having (∠1 and ∠3) and (∠2 and ∠4) as the two pairs of opposite angles, if [∠2 = (4x - 20)] and [∠4 = (3x - 11)], then the measure of ∠1 will be 164°
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A sweater has an original price of $65. It is on sale for 25% off. What is the amount of the discount?
Answer:
16.25
65 x 0.25 = 16.25
If another type of question the total price would be 48.75 :)
A car rental company charges an initial fee plus an additional fee for each mile driven. The charge depends on the type of car: economy or luxury.
The charge E (in dollars) to rent an economy car is given by the function E=0.70M+11.95, where M is the number of miles driven. The charge L (in dollars)
to rent a luxury car is given by the function L-1.25M+17.30.
Let C be how much more it costs to rent a luxury car than an economy car (in dollars). Write an equation relating C to M. Simplify your answer as much as
possible.
The equation to find rent difference C from given values of E and L is 1.75M + 3.25. After adding the values of E and L.
How to calculate cost difference ?A mathematical equation is a formula that uses the equals sign to represent the equality of two expressions. The meanings of the word equation and its translations into various languages can vary slightly.
Finding the values of the variables that result in the equality is the first step in solving an equation with variables.
Let E represent Economy
Let L represent Luxury
Let M be the number of miles driven
Let C be how much it cost to rent a luxury car than economy
E = -0.70M + 11.95
L = 1.25M + 17.30
C = L - E
C =(1.25M + 17.30) - (-0.70M + 11.95)
C = 1.25M + 17.30 + 0.70M - 11.95
collect like terms
C = 1.25M + 0.70M + 18.20 - 14.95
C = 1.95M + 3.25
The rent difference between luxury car and economy car is 1.95M +3.25 .
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The longest runway at an airport has the shape of a rectangle and an area of 2,304,700 square feet. This runway is 190 feet wide. How long is the runway?
The runway is 12,130 feet long.
To find are you have to times the two sides, in this case it's 190 X 12,130. To find the length of one of these sides you must divide the area by one known side, in this case 2,304,700/190, which means the answer is 12,130 feet
Which number is an integer?
2.3
0
-3/4
pi
0 is an integer number.
A number without a decimal or fractional element is known as an integer, which encompasses both positive and negative numbers, including zero.
i.e. the set of integers is
Z = {... -7, -6, -5, -4, -3, -2, -1, 0, 1, 2, 3, ...}
The integers do not contain any fraction or rational number.
Here,
2.3 is a fraction number so it is not an integer.
And -3/4 is a rational number and rational numbers are not integers.
And pi is irrational number
So,
This three numbers are not an integer
Now,
0 is an integer as per the definition of integers.
Hence,
0 is the integer number
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Find the volume of a right circular cone-shaped building with a radius of 3cm and a height of 14 cm.
The volume of the right circular cone is, 131.95 cubic centimeter.
What is cone?
A cone is a smooth-tapering three-dimensional geometric object with a flat base and an apex or vertex. The base of a cone is made up of all the points on a plane other than the apex, and the apex is connected to all the other points on the base by a series of line segments, half-lines, or lines.
Here, the radius, r = 3 cm, and height h = 14 cm.
We have to find the volume of right circular cone.
Since,
Volume = [tex]\pi r^2\frac{h}{3}[/tex]
[tex]V = \pi (3)^3(\frac{14}{3})\\ V = \pi (3)(14)\\V = 42\pi \\V = 131.95 cm^3[/tex]
Hence, the volume of the right circular cone is, 131.95 cubic centimeter.
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Determine which set of side measurements could be used to form a right triangle.
6, 12, 60
4, 5, 7
square root of 27 comma square root of 35 comma 62
square root of 12 comma 3 comma square root of 21
Answer:
square root of 12, 3, square root of 21
Step-by-step explanation:
a
3.5 in
b
3 in
c (hypotenuse)
4.60977 in
Area
5.25
in²
The set of side measurements √12, 3, and √21 could be used to form a right triangle. which is the correct answer would be option (D).
What is Pythagoras's theorem?Pythagoras's theorem states that a right-angled triangle, the square of one side is equal to the sum of the squares of the other two sides.
We have to apply Pythagoras's theorem in all the given options to find the right triangle.
As per option (A),
6, 12, 60
6² + 12² = 60²
36 + 144 = 3600
180 = 3600
This equation is not true.
As per option (B),
4, 5, 7
4² + 5² = 7²
16 + 25 = 49
41 = 49
This equation is not true.
As per option (C),
√27, √35, 62
(√27)² + (√35)² = 62²
27 + 35 = 3844
This equation is not true.
As per option (D),
√12, 3, √21
(√12)² + (3)² = (√21)²
12 + 9 = 21
21 = 21
The above equation is true and satisfies Pythagoras's theorem which means these measurements could be used to form a right triangle.
Hence, the correct answer would be an option (D).
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Which triangle congruence postulate or theorem proves that these triangles
are congruent?
The Angle-Side-Angle Postulate (ASA) asserts that two triangles are congruent if their two angles and included sides are congruent with each other.
What is Angle-Side-Angle Postulate ?According to the definition of an angle side angle, two triangles are congruent to one another if two angles from one triangle and the side between them are, respectively, equal to two angles from another triangle and the side between them. If two triangles are congruent, thenOne triangle's three sides will be equivalent to its three sides, respectively.The three angles of one triangle will be equivalent to the three angles of the other, respectively.But we don't always need to know information about all the sides and angles of a triangle to be sure that two triangles are congruent. Let's use an example to illustrate ASA.Let's use an example to illustrate ASA. Take into account the triangles ABC and DEF:We are given that,
BC = EF
∠B = ∠E
∠C = ∠F
We say that by ASA criterion: Δ ABC ≅ ΔDEF.
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1. Corey buys a Toyota Yaris for $15,000 at 4.1% interest rate for 6 years.
How much interest will Corey pay on his Yaris?
What is the total amount that will paid?
What is his monthly payment?
Answer:
a) $4089.55
b) $19089.55
c) $56.80
Step-by-step explanation:
a) (100 + 4.1)/100 = 1.041. So, 15000 × 1.041⁶ = 19089.55. Interest that will be paid: 19089.55 - 15000 = $4089.55 (2 dp).
b) $19089.55 (with interest and principal)
c) 4089.55/72 = $56.80
What is 6/21 + 6/7? Please help with question
Answer: 8/7 Or In Mixed Number Form 1 1/7
Step-by-step explanation: Get the common denominator which is 21 because you get 6/7 and multiply the number and denominator by 3. You will get 18/21. Now you add. 18/21 + 6/21 = 24/21. Simplify them by the greatest common factor and so I divide by 3 and get 8/7.
Hoped This Helped!
Answer:
Step-by-step explanation:
6/21 + 6/7
6/21 + 18/21
24/21 = 1 1 / 7
6 x 3 18
____ = __
7 x 3 21
- You need common denominators to add fractions together!!
(6,- 8); 2x + 3y = 6
A. Write in slope intercept form
B. Write equation in the form Ax+By=C
help by the end of the week.
Answer:
1 ) Slope of the line
[tex]m = 2[/tex]
2 ) Equation of the line
[tex]y=2x-2[/tex]
3 ) Values of a and b
a = 5
b = 6
4 ) What is the y-coordinate when?
The y-coordinate is the vertical position of a point in terms of distance and direction along the y-axis.
In this graph, when x = 2 they y-coordinate is also 2 so it is 2 units from the y-axis.
Hope this helps! :)
Work out the circumference of this circle.
Take pie T to be 3.142 and give your answer to 1 decimal place.
4 cm
Answer:
25.1 cm
Step-by-step explanation:
4 * 2 * 3.142 = 25.136 = 25.1 cm
Solve the formula for t.
V=6πrt+7πr*2
t=
The unknown variable t has a value of t = (V - 7πr²)/6πr
How to determine the unknown variable?From the question, we have the following parameters that can be used in our computation:
Formula; V = 6πrt+7πr*2
Rewrite the formula properly
So, we have the following representation
V = 6πrt + 7πr²
Subtract the expression 7πr² from both sides of the equation
So, we have
V - 7πr² = 6πrt + 7πr² - 7πr²
Evaluate the difference
V - 7πr² = 6πrt
So, we have
6πrt/6πr = (V - 7πr²)/6πr
Evaluate
t = (V - 7πr²)/6πr
Hence, the value is t = (V - 7πr²)/6πr
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Answer:
[tex]t = \dfrac{V-7\pi r^2}{6\pi r}[/tex]
Step-by-step explanation:
V = 6πrt + 7πr²
Subtract the term without t from both sides.
V - 7πr² = 6πrt
Now you have a single term with t on the right side and two terms without t on the left side.
Switch sides.
6πrt = V - 7πr²
Divide both sides by 6πr.
[tex] t = \dfrac{V - 7\pi r^2}{6\pi r} [/tex]
If <1 and <2 are complementary, what are the measures of the backed when
The measures of the angles are m∠1 = 69° and m∠2 = 29°
How to find the measures of an angle?
*Triangles always have angles that add up to 180 degrees. As a result, you may find the unknown angles by taking the specified angles of a triangle and subtracting them from 180.
*Finding Unknown Measurements Using Exterior Angles
Two angles that together total 180 degrees are known as supplementary angles. These two angles combine to form a straight angle when put side by side
m∠1 = (4x-7)°
m∠2 = (x+12)°
As the two angles are complementary
4x-7+x+12=90°
5x+5=90°
5x=90-5
5x=85
x=[tex]\frac{85}{5}[/tex]
x=17
Therefore
m∠1 = 4(17)-7
m∠1 = 61°
m∠2 = 17+12
m∠2= 29°
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I need help please
In a test of a sex-selection technique, results consisted of female babies and male babies.
1. Based on this result, what is the probability of a female being born to a couple using this technique?
2. Does it appear that the technique is effective in increasing the likelihood that a baby will be a female?
The probability of a female being born to a couple using this technique is 0.923.
Yes, it is effective in increasing the likelihood that a baby will be a female.
Given:
In a test of a sex-selection technique, results consisted of 215 female babies and 18 male babies.
Total = 215+18
= 233
1.
The probability of a female being born to a couple using this technique is:
p = 215/233
p = 0.923.
hence the probability of the female being born to a couple is 0.923.
2.
Yes it is effective in increasing the likelihood that a baby will be a female because the probability of female is higher than the probability of male to be born.
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cual es la solucion de este numero entero (+4)+(+12)
Answer:
16
Step-by-step explanation:
12+1=13
13+1=14
14+1=15
15+1=16
1+1=2
2+1=3
3+1=4
---------
4+6=10
10+6=16
(6+6=12)
What would the domain and range be for a problem like this. I can’t seem to recall how to determine them
The domain and range are [−4, 1] & [−4, 5].
What are the domain and range of a graph?
Graphs can also be used to determine the domain and range of functions. Because the domain refers to the set of possible input values, the domain of a graph includes all of the input values shown on the x-axis. The range is the set of possible output values shown on the y-axis.
We have given the graph,
The domain refers to the set of possible input values, the domain of a graph consists of all the input values shown on the x-axis.
The range is the set of possible output values, which are shown on the y-axis.
We can observe that the graph extends horizontally from −4 to the right 1. so the domain of function h is [−4, 1].
The vertical extent of the graph is 0 to –4, so the range of function h is [−4, 5].
Therefore, the domain and range are [−4, 1] & [−4, 5].
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Find the slope of the line that passes through the following points: (−4, 3) and (5, 4).
Answer:
The slope would be 1/9.
Step-by-step explanation:
From 3 to 4 it would be 1. From -4 to 5 it would be 9, the equation for slope is y/x so it would be 1/9.
solution
slope M =(Y' - Y)/(x' - x)
Indicated by (-4, 3) and (5 , 4)
x = -4 , x' = 5 , y = 3 , y' = 4
M = (4 - 3)/( 5 + 4)
M = 1/9 Ans
If f is a linear function for which f(4) = −13 and f(−4) = 19, find f(5). f(5) =
The value of the function f(5) is - 17.
How to solve linear function?A linear function is a function that represents a straight line on the coordinate plane.
A linear function in slope intercept form is as follows:
y = mx + b
where
m = slopeb = y-interceptTherefore, for the linear function, f(4) = −13 and f(−4) = 19.
f(5) can be found as follows;
-13 = 4m + b
19 = -4m + b
2b = 6
b = 6 /2
b = 3
-13 - 3 = 4m
-16 = 4m
m = -4
Hence,
f(5) = -4(5) + 3
f(5) = -20 + 3
f(5) = - 17
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5. Rewrite the expression as a single logarithm. (1 point)
We can rewrite the given logarithmic expression as [tex]ln(\frac{\sqrt{x}(x-1)^3 }{\sqrt[3]({x+1})^2 })[/tex].
So option (D) is the correct answer.
What is a logarithmic expression?
A logarithmic equation is one that involves the logarithm of a variable-containing expression. To solve exponential equations, first, determine whether both sides of the equation can be written as powers of the same number.
The given logarithmic expression can be expressed as
[tex]=\frac{1}{2}\ln}\left(x\right)+3\left(\ln\left(x-1\right)-\frac{2}{9}\ln\left(x+1\right)\right)[/tex]
[tex]=\frac{\ln\left(x\right)}{2}+3\left(\ln\left(x-1\right)-\frac{2}{9}\ln\left(x+1\right)\right)[/tex]
[tex]=\frac{\ln\left(x\right)}{2}+3\ln\left(x-1\right)-\frac{2\ln\left(x+1\right)}{3}[/tex]
By using the logarithmic properties, we get
[tex]=ln(\frac{\sqrt{x}(x-1)^3 }{\sqrt[3]({x+1})^2 })[/tex]
We can rewrite the given logarithmic expression as [tex]ln(\frac{\sqrt{x}(x-1)^3 }{\sqrt[3]({x+1})^2 })[/tex].
So option (D) is the correct answer.
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please help me with this im struggling :(
The equation that best represent the relationship on the scatter plot is y = 6 / 5 x + 18 / 5.
How to find the equation of a scatter plot?The line of best fit is used to express a relationship in a scatter plot of different data points.
The line of best fit (or trendline) is an educated guess about where a linear equation might fall in a set of data plotted on a scatter plot.
Therefore, the line of best fit will pass through (2, 6)(7, 12) and (12, 18).
Therefore, the equation of the line can be represented as follows;
y = mx + b
where
m = slopeb = y-interceptTherefore,
m = 12 - 6 / 7 - 2
m = 6 / 5
Let's find y-intercept using (2, 6)
6 = 6 / 5(2) + b
6 - 12 / 5 = b
b = 18 / 5
Therefore, the equation is y = 6 / 5 x + 18 / 5
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For some particular website, the password must start with one of the letters W, X, Y, or Z. Then there must be 5 more charaters, and each of those characters may be a numeric digit or a letter of the alphabet. How many different passwords are possible?
241,864,704 many different passwords are possible.
The total characters of the password is six in which it is given that first character should start with W, X, Y or Z. So the first character can be filled in 4 ways.
For next five characters it can be any letter of the alphabet or any numeric digit so it will be 26 + 10 = 36.
So second, third, fourth, fifth and sixth space can be taken by 36 characters.
Therefore the total no. of passwords will be 4 * 36 * 36 * 36 * 36 * 36 that is equal to 241,864,704.
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