An equation of the line that passes through the point (−6,−8) and is parallel to the line x−2y=6 is y=x/2-5.
Given that, an equation of the line that passes through the point (−6,−8) and is parallel to the line x−2y=6.
What is slope of a line?The slope of the line is the ratio of the rise to the run, or rise divided by the run. It describes the steepness of line in the coordinate plane.
We know that, the slope of a line parallel to given line is m1=m2.
Here, x−2y=6
⇒ 2y=x-6
⇒ y=x/2-3
So, slope = 1/2
The slope of a line parallel to the given line = 1/2
Now, put m=1/2 and (x, y)=(-6, -8) in y=mx+c and solve for c
-8=1/2(-6)+c
⇒ c=-8+3
⇒ c=-5
Thus, y=x/2-5
Therefore, an equation of the line that passes through the point (−6,−8) and is parallel to the line x−2y=6 is y=x/2-5.
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What is the slope of the line on the graph?
Enter your answer in the box.
Which shows all the critical points for the inequality 2x+5/x-2 => x-1/x-2
x = 1, and x = 2 x = –6 and x = 2 x = –4 and x = 2 x = 2
The critical points of the given inequality are; x=-6 and x=2
What are the critical points of the Inequality?1) When the denominator is equal to zero, at that point, we will have a critical point.
We are given the inequality;
(2x + 5)/(x - 2) ≥ (x - 1)/(x - 2)
Thus, x - 2 = 0
x = 2.
Thus, x = 2 is a critical point
2) Simplify the numerator to get the expression such that p(x) ≥ 0 or p(x) ≤ 0.
Thus, at p(x) = zero, we have other critical point(s)
Multiply both sides by (x - 2) to get;
2x + 5 = x - 1
2x - x = - 1 - 5
x = - 6
Then, the two critical points are x = 2 and x = - 6.
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a ball is thrown up vertically. after t seconds, it's height (in feet) is given by the function h (t)=96t-16t^2 . after how long will it reach its maximum height
The time taken to reaches its maximum height is 3s.
In the question,
It is given that,
Height, h(t) = [tex]96t - 16t^{2}[/tex]
The maximum value of the function is obtained if the first derivative of the function h (t) = 0.
[tex]\frac{dh(t)}{dt} = 96 - 32t = 0[/tex]
⇒ [tex]t = 3[/tex]
So, time taken to reach its max height is 3 seconds.
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5 miles is 8km Convert 22.3miles to km
Answer:
13.9375
Step-by-step explanation:
this is your answer 1234
Identify the values of the variables. Give your answers in simplest radical form. HELP!
The value of the variables in the right triangle are as follows;
[tex]v = \frac{3\sqrt{2} }{2}[/tex][tex]w=\frac{3\sqrt{6} }{2}[/tex]How to find the side of a right tringle?A right triangle is a triangle that has one of its angles as 90 degrees.
The side of a right triangle can be found by using trigonometric ratios.
Therefore, let's find the variable length of the right triangle as follows;
sin 30 = opposite / hypotenuse
sin 30 = v / 3√2
1 / 2 = v / 3√2
cross multiply
3√2 = 2v
divide both sides by 2
v = 3√2 / 2
Let's find the variable w.
cos 30 = adjacent / hypotenuse
cos 30 = w / 3√2
√3 / 2 = w / 3√2
cross multiply
√3 × 3√2 = 2w
3√6 = 2w
divide both sides by 2
w = 3√6 / 2
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The heights of adult men in America are normally distributed, with a mean of 69.2 inches and a standard deviation of 2.64 inches. The heights of adult women in America are also normally distributed, but with a mean of 64.2 inches and a standard deviation of 2.53 inches.
If a man is 6 feet 2 inches tall, his z-score is equal to 1.82.
If a woman is 5 feet 10 inches tall, her z-score is equal to 2.92.
The 5 feet 10 inches American woman is relatively taller.
What is a z-score?In a normal distribution, the z-score of a given sample score can be calculated by using this formula:
Z-score = (x - μ)/σ
Where:
σ represents the standard deviation.x represents the sample score.μ represents the mean score.Next, we would convert the height in feet to inches as follows:
American man = 6 × 12 + 2 = 74 inches.
American woman = 5 × 12 + 10 = 70 inches.
For the American man's z-score, we have:
Z-score = (74 - 69.2)/2.64
Z-score = 4.8/2.64
Z-score = 1.82
For the American woman's z-score, we have:
Z-score = (70 - 64.2)/2.53
Z-score = 5.8/2.53
Z-score = 2.92
Therefore, the 5 feet 10 inches American woman is relatively taller because she has a higher z-score (2.92 > 1.82).
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Complete Question:
The heights of adult men in America are normally distributed, with a mean of 69.2 inches and a standard deviation of 2.64 inches. The heights of adult women in America are also normally distributed, but with a mean of 64.2 inches and a standard deviation of 2.53 inches.
a) If a man is 6 feet 2 inches tall, what is his z-score (to two decimal places)?
b) If a woman is 5 feet 10 inches tall, what is her z-score (to two decimal places)?
c) Who is relatively taller?
The 6 feet 2 inches American man
The 5 feet 10 inches American woman
4.5,3,1.5,0 fin the difference in the following sequence
-1.5 is the difference in the sequence
How determine the difference in a sequence?
An arithmetic sequence is a sequence of numbers where the differences between every two consecutive terms are the same.
The difference is usually called the common difference. For example, the sequence 3, 6, 9, 12 have a common difference of 3 i.e. 6-3 = 3 or 9-6 = 3
Given: the sequence 4.5,3,1.5,0
The difference = 3 - 4.5 = -1.5 or 1.5-3 = -1.5
Note: You can pick any two consecutive terms to get the difference
Therefore, the difference in the sequence is -1.5
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A room is 12 m long,10m broad and 6 m high. It has a door of size 1m×2m and a windows of size 2m × 1.5m. Calculate the cost of plastering the walls at the rate of Rs 15/m².
The cost of plastering the rectangle walls at rate of Rs.15/[tex]m^2[/tex] is Rs.5565.
What is rectangle?
With four sides, four corners, and four right angles (90°), a rectangle is a closed 2-D object. A rectangle's opposing sides are equal and parallel. Since a rectangle is a two-dimensional form, it has two dimensions: length and width. The opposite sides of a quadrilateral are equal and parallel, and all the angles are equal. Around us, there are several rectangle-shaped items. Two dimensions, the length and breadth, define each rectangle shape. The width and length of a rectangle are its longer and shorter sides, respectively.
Given,
Length of room =12m
Breadth of room =10m
Height of room =6m
So, Area of four walls =2(l+b)×h
=>area of four wall=2(12+10)×6=264[tex]m^2[/tex]
Now Area of 2 doors and 3 windows =(2×1×2+3×2×1.5)
=> area of 2 doors and 3 windows = 13[tex]m^2[/tex]
Area of ceiling =l×b=12×10=120 [tex]m^2[/tex]
Thus, total area for plastering =(264−13+120)= 371[tex]m^2[/tex]
Hence, the cost of whitewashing =Rs.(371×15)=Rs.5565.
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Write an equation in slope-intercept form for the line that passes through (3, 1) and (1,2).
The equation of the line that passes through (3, 1) and (1,2) in slope intercept form is y = - 2 / 2 x + 5 / 2.
How to find equation of a line?The equation of a line can be represented in different form such as slope intercept form, point slope form, standard form and general form.
Therefore, let's write the equation of a line that passes through (3, 1) and (1, 2).
using slope intercept form,
y = mx + b
where
m= slopeb = y-interceptTherefore, let's find slope
m = 2 - 1 / 1 - 3
m = 1 / - 2
m = - 1 / 2
Let's find y-intercept using (1, 2)
2 = - 1 / 2(1) + b
b = 2 + 1 / 2
b = 5 / 2
Therefore, the equation is y = - 2 / 2 x + 5 / 2
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Young Frankenstein has two brothers, Pugsley and Gomez. The sum of their ages is 34. Frankenstein is older than Pugsley, but Pugsley is not the youngest. Gomez is 8 years younger then Frankenstein and Pugsley and Gomez’s ages differ by 5 years. How old are the three brothers?
The age of the three brothers, based on the relationship between the ages of Frankenstein, Pugsley, Gomez, is:
Frankenstein - 15 years Pugsley - 12 years Gomez - 7 yearsHow to find the ages?Frankenstein is older than Pugsley and so is not the youngest. Pugsley is not the youngest according to the question so Gomez must be the youngest.
Assuming Gomez's age is x, the relationship between their ages is:
Gomez age + Pugsley age + Frankenstein age = 34
x + x + 5 + x + 8 = 34
3x + 13 = 34
x = (34 - 13) / 3
x = 7 years
Pugsley's age is:
= x + 5
= 7 + 5
= 12 years
Frankenstein's age is:
= x + 8
= 7 + 8
= 15 years
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If f(x) = x² - 7x + k and f(k) = -9, then the value of f(-1) is
(A) -9
(B) -3
(C) 3
(D) 11
Answer:
D.) 11
Step-by-step explanation:
-9=-k^2-7k+k Plugging in k for x
-9=k^2-6k Combine like terms
0=k^2-6k+9 Add 9 to both sides
0=(k-3)(k-3) Factor
k=3
The equation is now
f(x)=x^2-7x+3
so
f(-1)=(-1)^2-7(-1)+3
f(-1)=1+7+3
f(-1)=11
a sequence is defined by a term to term rule
iteration help please
By the sequence of term to term rule the value of : a) [tex]U_{1}[/tex]= [tex](U_{0})^{2}[/tex] + 3 =[tex]1^{2}[/tex] + 3 = 4 b). [tex]U_{2}[/tex] = [tex](U_{1})^{2}[/tex] + 3 = [tex]4^{2}[/tex] + 3 =19 c). [tex]U_{3}[/tex] = [tex](U_{2})^{2}[/tex] + 3 = [tex]19^{2}[/tex] + 3 = 364 .
What is the term to term rule like for you?
Give the first number in the sequence and then describe the pattern of the numbers to get the term-to-term rule. Three is the first number. The rule for terms to terms is "add 4." All of the terms in the series can be located once the initial term and term to
[tex]$$\mathrm{u}_0=1$$[/tex]
The difference is given by[tex]$u_{n+1}=\left(u_n\right)^2[/tex]+ 3
We have to simply put the value in their places to get the proper answer -
a). Put the [tex]$u_{n+1}=u_1$[/tex]
n+1 = 1 ⇒ n = 0
put n = 0in the formula[tex]$\mathrm{u}_{n+1}=\left(\mathrm{u}_n\right)^2[/tex] +3
we wil get
[tex]$$u_1=\left(u_0\right)^2[/tex] + 3 = [tex]1^{2}[/tex] =3 = 4
b). Put the [tex]$u_{n+1}=u_2$[/tex]
n + 1 = 2 => n = 1
put n=1 in the formula [tex]$u_{n+1}=\left(u_n\right)^2[/tex]+3
we wil get:
[tex]$$u_2=\left(u_1\right)^2[/tex]+3= [tex]4^2[/tex]+3=19
c). Put the [tex]$u_{n+1}=u_3$[/tex]
n + 1 = 3 => n = 2
Put n=2 in the formula+3
we wil get :
[tex]$$u_3=\left(u_2\right)^2[/tex] +3= [tex](19)^2[/tex] +3 =364
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4. Which statement about the lines below is true?
7x=-21 and 11y = 55
Select all that apply.
A. Line 11y = 55 is vertical.
B. Line 7x=-21 is vertical.
C. For both lines, all points on the line have an x- and a y-coordinate.
D. For either line, one of the coordinates of all of the points is always the same value.
The statements about lines that is true are
A. Line 11y = 55 is vertical.
C. For both lines, all points on the line have an x and a y-coordinate.
D. For either line, one of the coordinates of all of the points is always the same value.
Lines given to us are
1. 7x = -21
x = -3
2. 11y = 55
y = 5
Now let us check the statements.
A. Line 11y = 55 is vertical.
Yes, it is absolutely true as y = 5 will be a straight vertical line from origin of the graph (0 , 0) to (0 , 5)
B. Line 7x= -21 is vertical.
No, this statement is not true as this will be a horizontal line from (0 , 0) to (-3 , 0)
C. For both lines, all points on the line have an x- and a y-coordinate.
Yes, for both the lines there will be both x and y coordinate as every point on graph has x and y coordinates to represent them.
D. For either line, one of the coordinates of all of the points is always the same value.
Yes, this statement is true as for first line x coordinate is a constant value of 0 and for second line y is a constant value of 0.
Therefore the statements about lines that is true are A, C and D.
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(−3,y) and (x,2).
y=4x+6
orderd pair
The values of x and y are -1 and 6 respectively, this forms an ordered pair of (-3,6) and (-1,2).
What are the missing x and y values values of the given ordered pair?Given the equation and ordered pair in the question;
y = 4x + 6Point: (-3,y) Point; (x,2)Find the y-value by substituting the x-value into the equation and solving for y.
y = 4x + 6
Plug in x = -3
y = 4( -3 ) + 6
y = -12 + 6
y = 6
Find the x-value by substituting the y-value into the equation and solving for x.
y = 4x + 6
Plug in y = 2
2 = 4x + 6
2 - 6 = 4x
-4 = 4x
x = -4/4
x = -1
Therefore, the ordered pair are (-3,6) and (-1,2).
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KT's Restaurant has contracted with the Vidalia Times for
5,000 column inches in daily newspapers and 10,000
column inches in the Saturday newspaper. Daily column
inches are $27.55, and Saturday rates are $29.35 per
column inch. How much should KT's Restaurant budget for
newspaper advertising for the coming year?
The budget of KT's Restaurant for newspaper advertising for the coming year is $58,533,500
Given,
The length of advertisement of KT's Restaurant in Vidalia Times in week days = 5,000
The length of advertisement of KT's Restaurant in Vidalia Times in Saturdays = 10,000
The cost of daily column = $27.55 per column inch
The cost of Saturdays = $29.35 per column inch
We have to find the budget of KT's Restaurant for newspaper advertising for the coming year;
Here,
There are approximately 53 Saturdays in a year.
So,
365 - 53 = 312
Then,
The budget of advertisement on daily column = 312 × 5000 × 27.55 = $42,978,000
The budget of advertisement on Saturday column = 53 × 10,000 × 29.35 = $1,555,500
Therefore,
The total budget for advertisement = 42,978,000 + 1,555,500 = $58,533,500
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Please help me to solve this simple question.
I will mark your answer brainliest!
Answer:
4/3
Step-by-step explanation:
You want the limit as t→1 of (t³+t²-5t+3)/(t³-3t+2).
Simplified formThe fact that each polynomial evaluates to 0 at t=1 tells you that (t-1) is a factor of each. Factoring that out gives ...
[tex]\dfrac{t^3+t^2-5t+3}{t^3-3t+2}=\dfrac{(t-1)(t^2+2t-3)}{(t-1)(t^2+t-2)}=\dfrac{(t-1)(t-1)(t+3)}{(t-1)(t-1)(t+2)}\\\\=\dfrac{t+3}{t+2}[/tex]
The limit at t = 1 is found by direct substitution:
lim = (1 +3)/(1 +2) = 4/3
Graph the function with the given domain. Then identify the range of the function.
1) y = -6; domain: x ≥ 5
2) y = -x - 1; domain: -1 ≤ x ≤ 3
There are 40 students in class. 12 like pink best, 4 like yellow and the rest blue. What fraction of the class likes blue?
Answer: [tex]\frac{3}{5}[/tex]of the class like blue
Step-by-step explanation:
There are : 40 - 12 - 4 = 24 ( students like blue )
[tex]\frac{24}{40}[/tex]= [tex]\frac{3}{5}[/tex]
help for brainlest please???
Answer:
45
Step-by-step explanation:
the pattern adds 3 if you look at it care fully
Tammy must choose a number between 61 and 107 that is a multiple of 3,9 and 12. Write all the numbers that she could choose
Answer:
G LCM (least common multiple) of 3, 9, and 12. After doing that, find the number that is between 61 and 107.
Step-by-step explanation:
Least common multiple (lcm) is where g finds out the number that can be divided by all the numbers (3, 9, and 12 in this case) and still come out with a whole number.
The perimeter of an ICU ward, that is rectangular in shape, is 258 feet. The width is 37 feet less than the length. Find the dimensions of this ward.
Find Length(ft) and Width(ft)
The dimensions of the rectangle is 83 feet x 46 feet
What is the Perimeter of a Rectangle?
The perimeter P of a rectangle is given by the formula, P=2 ( L + W) , where L is the length and W is the width of the rectangle.
Perimeter P = 2 ( Length + Width )
Given data ,
The perimeter P of the rectangle = 258 feet
Let the length of the rectangle be = L
Let the width of the rectangle be = W
And , The width is 37 feet less than the length. ,
So , W = L - 37
Perimeter P = 2 ( Length + Width )
Substituting the values of L and W in the equation , we get
Perimeter P = 2 ( L + L - 37 )
2 ( L + L - 37 ) = 258
( L + L - 37 ) = 129
2L - 37 = 129
Adding 37 on both sides , we get
2L = 166
Divide by 2 on both sides , we get
Length L of the rectangle = 83 feet
Substituting the value of L in equation ,we get
W = L - 37
Width W of the rectangle = 46 feet
Therefore , Length = 83 feet and Width = 46 feet
Hence , the dimensions of the rectangle is 83 feet x 46 feet
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What is the size of angle x?
Write a justification for your answer.
The angle x will be 34°.
From the properties of circles we get to know that the angle at the center and the angle between two tangents are always supplementary.
Supplementary angles are those which always sum to to 180°.
For example ∠HJK is supplementary to ∠HIK the their sum will come out to be 180°.
similarly ∠ROP + ∠RQP = 180°
∠RQP = 180° - ∠ROP
∠ROP is given to us 146°
After putting it in the equation above we get ∠RQP = 34°
Therefore x comes out to be 34°.
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If the pediatric floor of the hospital has 165 beds how many rooms are there if each room holds 3 beds?
A medic's bag contains individually wrapped tongue depressors (each costing 4 cents) and Band-Aids (each costing 8 cents). If the materials are worth $12.48 and there are 184 individual packages in total, how many tongue depressors and Band-Aids are there?
# of Tongue Depressors:
# of Band-Aids:
The number of tongue depressors = 56
The number of Band-Aids = 128
What is an equation?
An equation is a mathematical statement that proves two mathematical expressions are equal in algebra, and this is how it is most commonly used. In the equation 3x + 5 = 14, for instance, the two expressions 3x + 5 and 14 are separated.
Let x be the number of tongue depressors.
Let y be the number of Band-Aids
Convert cents to dollars
1 cent = $0.01
So, 4 cents = 0.01*4 = $0.04
8 cents = 0.01* = $0.08
The materials are worth $12.48 .
This means, 0.04x+0.08y=12.48......(1)
There are 184 individual packages in total.
This means, x+y=184.......(2) => x=184-y.....(3)
Substitute (3) in (1),
0.04(184-y)+0.08y=12.48
7.36-0.04y+0.08y=12.48
=> y= 128
(3) => x=184-128=56
So, the number of tongue depressors = 56
The number of Band-Aids = 128
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What does the transformation f(x) → f(x + 3) - 7 do to the graph of f(x)? choose answer below:
translates it 7 units left and 3 units up
translates it 3 units left and 7 units up
translates it 7 units right and 3 units up
translates it 3 units left and 7 units down
Answer:
3 units left 7 units down
Step-by-step explanation:
if the sign is inside the bracket opposite sign
if the sign is outside the bracket leave it as it is
so (x+3)=0 which means x= -3 so 3 units left since it is on x axis. 7 is on y axis and since it is negative so 7 units down.
45 POINTS!!!!! WILL GOVE BRAINLYEST!!
Answer:
20 units
Step-by-step explanation:
we find the side lengths by looking at the coordinates and just counting up
Sides are 6,4,6,4
So we just add
6+4+6+4
10+10
20
Hopes this helps please mark brainliest
Answer: Your answer is 20 units, because the height is 6 units, and the length is 4 units, so we then multiply by 2 for both numbers, then add them together, having a sum of 20 units.
Hope that helps.
75 less than the product of 30 and a number is -225. What is the number?
Answer:
The Number is -5
Step-by-step explanation:
We will form the Equation and solve for the Number
Let the Number be x
Product of 30 and a Number = 30x
75 less than the Product of 30 and a Number = 30x - 75
75 less than the Product of 30 and a Number is -225
Then 30x - 75 = -225
Now solve for x (the Number)
add 75 for both sides
30x = -225 + 75 = -150
Divide both sides by 30
x = -150 / 30 = -5
Glad to Help
PLEASE HURRY I WANT TO FINISH THIS TEST PLEASE ASAP!!
Determine which integer will make the inequality x − 4 < 16 true.
The integers that would make the inequality true is the set of integers less than 20.
Solving Linear inequalitiesFrom the question we are to determine the integer that would make the given inequality true
The given inequality is
x - 4 < 16
To determine the integer that would make the inequality true, we will solve the inequality for the variable x
Solving the inequality
x - 4 < 16
Add 4 to both sides of the inequality
x - 4 + 4 < 16 + 4
x < 20
Hence, the solution to the given inequality is x < 20. All integers less than 20 will make the inequality true.
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Please help question from 4 through 12 thank you very much
The answer to the questions from 4 through 12 are below:
4. z³ + 5z² + 5z + - 35. 4d + 6c - 66. 20a - 2b - 17. 40x8. 10x + 16y + 149. a² + 8a - 1010. 15v + 22w11. 10c² + 4c12. z³ - 8z² + 5z + 23What is the perimeter of a rectangle and triangle4. z³ + 5z + 3z² + 1 - 4 - 2z²
= z³ + 5z² + 5z + - 3
5. Perimeter of the square = Addition of all the sides
= (2d - 3) + (3c) + (2d - 3) + (3c)
= 2d - 3 + 3c + 2d - 3 + 3c
= 4d + 6c - 6
6. Perimeter of the triangle = Addition of all the sides
= (4a - 2b) + (9a - 4) + (7a + 3)
= 4a - 2b + 9a - 4 + 7a + 3
= 20a - 2b - 1
7. Perimeter of a square = 4 × side length
= 4 × 10x
= 40x
8. Perimeter of a rectangle = 2(length + width)
= 2{(2x + 7) + (3x + 8y)}
= 2(2x + 7 + 3x + 8y)
= 2(5x + 8y + 7)
= 10x + 16y + 14
Simplify the following
9. 3a + a² + 5(a - 2)
= 3a + a² + 5a - 10
= a² + 8a - 10
10. 8(v + w) + 7(v + 2w)
= 8v + 8w + 7v + 14w
= 15v + 22w
11. 4c² + 6(c + c²) - 2c
= 4c² + 6c + 6c² - 2c
= 10c² + 4c
12. z³ + 5(z + 3) + 4(2 - 2z²)
= z³ + 5z + 15 + 8 - 8z²
= z³ - 8z² + 5z + 23
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Harry is paid semimonthly. His
Semimonthly salary is $2,052. What is his
annual salary?
Answer:
$12,312
Step-by-step explanation:
$2,052 * 6 = $12,312