Answer:
y = −2x + 13
Step-by-step explanation:
equation of line slope intercept form is y = mx +c
where m is slope and c is y intercept
when two lines are parallel then their slope are equal.
_______________________________________
Given line
CD
y = −2x − 2
it is in form of y = mx +c
thus, m = -2
Given that other line parallel to CD y = −2x − 2
Thus, its slope will be -2.
Let the equation of required line be
y = mx +c (as slope will be -2)
Then equation of line will be
y = -2x +c
Given that this line contains (4,5) it will satisfy the equation y = -2x+c
using x = 4 and y = 5
we have
y = -2x +c
5 = -2*4 + c
=> 5 = -8 + c
=> c = 5+8 = 13
Thus, equation of line parallel to y = −2x − 2 and containing point(4,5) is
y = −2x + 13
Answer:
A. y = −2x + 13
Step-by-step explanation:
2. Which of the following methods can't be used to find the zeros of a function?
options:
A. Substitute x = 0 in the function and solve for f(x).
B. Graph the function using a table of values.
C. Factor the function and apply the zero-product property to its factors.
D. Apply the quadratic formula.
Answer:
The correct option is;
Substitute x = 0 in the function and solve for f(x)
Step-by-step explanation:
The zeros of a function are the values of x which produces the value of 0 when substituted in the function
It is the point where the curve or line of the function crosses the x-axis
A. Substituting x = 0 will only give the point where the curve or line of the function crosses the y-axis,
Therefore, substituting x = 0 in the function can't be used to find the zero's of a function
B. Plotting a graph of the table of values of the function will indicate the zeros of the function or the point where the function crosses the x-axis
C. The zero product property when applied to the factors of the function equated to zero can be used to find the zeros of a function
d, The quadratic formula can be used to find the zeros of a function when the function is written in the form a·x² + b·x + c = 0
Answer: Substitute x = 0 in the function and solve for f(x).
Step-by-step explanation:
(99^2-98^2)/197+(98^2-97^2)/195+(97^2-96^2)/193+ ... +(2^2-1^2)/3
plz help
Answer:
99
Step-by-step explanation:
(99^2-98^2)/197+(98^2-97^2)/195+(97^2-96^2)/193+ ... +(2^2-1^2)/3
each term can be written as:
(a²- b²)/(a+b)= (a+b)(a-b)/(a+b)= a-bso the sum will look as:
99 -98+ 98- 97 + 97- 96 + ... +2- 1= 99-1= 98(all middle terms get cancelled leaving only 99 and -1 in the equation)
I need help I have been sitting for an hour trying to figured this out:(
Answer:
This is really weird. None of them seem to be right.
For the first one, it says that -7.5 is greater than or equal to -6.4, which is not true. -7.5 is less than -6.4. The next one is the only one that makes a true comparison, but I don't agree with the "or equal to" part. -7/8 cannot be equal to 7/8. The next one is false, -4 is greater than -8. Finally, the last one is incorrect as well because -4.2 is less than -3.6.
However, if I had to choose one, I'd choose the second option. It's the closest to being correct.
Pete, Chris, and Dina realized that the number of A’s they each received on their report cards were in a ratio of 4:2:5. If Pete got 14 more A’s than Chris, how many A’s did Dina get?
Answer:
[tex]Dina= 35[/tex]
Step-by-step explanation:
Given
[tex]Ratio = 4:2:5[/tex]
Peter = 14 more A's than Chris
Required
How many A’s did Dina get?
The order of the ratio is Peter: Chris: Dina
This implies that
[tex]Peter: Chris: Dina = 4:2:5[/tex]
Considering Peter and Chris
[tex]Peter: Chris = 4:2[/tex]
Let the number of Chris' A's be represented by A
This implies that:
Peter's = 14 + A
And as such;
[tex]14 + A : A = 4 : 2[/tex]
Convert ratio to division
[tex]\frac{14 + A}{ A} = \frac{4}{ 2}[/tex]
Multiply both sides by A
[tex]A * \frac{14 + A}{ A} = \frac{4}{ 2}* A[/tex]
[tex]14 + A = \frac{4}{ 2}* A[/tex]
[tex]14 + A = 2* A[/tex]
[tex]14 + A = 2 A[/tex]
Subtract A from both sides
[tex]14 + A-A = 2 A-A[/tex]
[tex]14 = A[/tex]
This means that;
Chris answered 14 while Pete answered 28 (14 + 14)
Considering Chris and Dana
[tex]Chris :Dana = 2:5[/tex]
Replace Chris with 14
[tex]14:Dana = 2:5[/tex]
Convert ratio to division
[tex]\frac{14}{ Dina} = \frac{2}{5}[/tex]
Cross Multiplication
[tex]Dina * 2 = 14 * 5[/tex]
Divide both sides by 2
[tex]\frac{Dina * 2}{2} = \frac{14 * 5}{2}[/tex]
[tex]Dina= \frac{14 * 5}{2}[/tex]
[tex]Dina= \frac{70}{2}[/tex]
[tex]Dina= 35[/tex]
Hence, Dina had 35 A's
Two vehicles, a car and a truck, leave an intersection at the same time. The car heads east at an average speed of 70 miles per hour, while the truck heads south at
an average speed of 30 miles per hour. Find an expression for their distance apart d (in miles) at the end of thours.
At the end of t hours, the two vehicles are miles apart.
(Simplify your answer. Type an exact answer, using radicals as needed.)
Step-by-step explanation:
[70,30] = 210 miles per hour
d=76.157t is the expression for two vehicles, a car and a truck which were distance apart d (in miles) at the end of t hours.
Two vehicles, a car and a truck, leave an intersection at the same time. The car heads east at an average speed of 70 miles per hour, while the truck heads south at an average speed of 30 miles per hour. we need to find expression for their distance apart d at the end of t hours
What is distance?Distance=Speed*Time
distance= speed * time.
*70t be the car traveling EAST at 60 miles per hour after t hours
*30t be the distance of the truck traveling SOUTH at 20 miles per hour after t hours.
*Use the Pythagorean Theorem to find the distance d.
The Pythagoras theorem states that sum of the squares on the legs of a right triangle is equal to the square on the hypotenuse
d^2=(70t)^2+(30t)^2
d^2=4900t^2+900t^2
d^2=5800t^2
d=76.157t
Therefore d=76.157t is the required expression for their distance apart d (in miles) at the end of t hours.
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A bridge constructed over a bayou has a supporting arch in the shape of an inverted parabola. Find the equation of the parabolic arch if the length of the road over the arch is 100 meters and the maximum height of the arch is 40 meters.
Answer:
y = (-2/125)(x - 50)² + 40
Step-by-step explanation:
The total length of the bridge is 100 meters.
Maximum height always occurs at midpoint of x.
So for x=50 meters , y = 40 meters.
As the vertex is given at the maximum height, Vertex can be defined at the point (50,40)
We know that the general equation for vertical parabola is:
y = a(x - h)² + k
Where (h,k) = Vertex = (50,40)
Substitute in the equation:
y = a(x - 50)² + 40 ⇒ Equation (i)
We know 2 more points on the parabola. We know that when x=0 , y=0 and we also know that when x=100m, y=0 meters.
Substitute any point in the above equation
Substituting (100,0) in the equation
0 = a(100 - 50)² +40
Solve the equation for a:
a = - 2/125
Substitute a in Equation (i)
y = (-2/125)(x - 50)² + 40
On a number line, the distance from zero to -8 is 8 units. Which equation demonstrates this concept? A. 82 = 64 B. |-8| = 8 C. |-8| = -8 D. 0 + 8 = 8
Answer:
Option B
Step-by-step explanation:
The absolute value of a number is how far a number is from zero. We can use ' | | ' to represent the absolute volume of a number. The distance, or absolute value, of -8 is 8.
We can represent this by writing:
|-8| = 8
Option B should be the correct answer.
Answer:
B
Step-by-step explanation:
The absolute value of a number means the distance from 0.
For example, |-2| is 2 units from 0.
|-8| = 8
-8 is 8 units from 0.
Formulate the recursive formula for the following geometric sequence. {-16, 4, -1,...}
Answer:
Step-by-step explanation:
Common ratio = 2nd term/1st term = 4/-16 = -1/4
[tex]a_{n}=a_{n-1}*r\\a_{n}=a_{n-1}*\frac{-1}{4}\\\\a_{n}=\frac{-1}{4}a_{n-1}[/tex]
Answer:
Common ratio = 2nd term/1st term = 4/-16 = -1/4
Step-by-step explanation:
Line j is a straight line. Line j is a straight line. 2 lines come out of the line to form 4 angles. From top left, clockwise, the angles are: x, y, z, w. Which equation represents the relationship between the measures of Angle w and Angle z? Measure of angle w = measure of angle z Measure of angle w + measure of angle z = 90 degrees Measure of angle w + measure of angle z = 100 degrees Measure of angle w + measure of angle z = 180 degrees
Answer:
c
Step-by-step explanation:
In the given line the relationship between angle w and z is Measure of angle w + measure of angle z = 180 degrees.
What is a supplementary angle?This is the type of angle that when measured, two of the angles would sum up to 180 degrees.
The supplementary angle is the sum of angle w + angle z = 180 degrees. Hence c is correct.
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(1−cos^2 x )·(1+tan^2 x)
Answer:
[tex](1-cos^2 x ).(1+tan^2 x) = tan^2x[/tex]
Step-by-step explanation:
Given
[tex](1-cos^2 x ).(1+tan^2 x)[/tex]
Required
Solve
[tex](1-cos^2 x ).(1+tan^2 x)[/tex]
In trigonometry;
[tex]1 - cos^2x = sin^2x[/tex]
So, make substitution
[tex](1-cos^2 x ).(1+tan^2 x)[/tex] becomes
[tex](1-cos^2 x ).(1+tan^2 x) = (sin^2 x ).(1+tan^2 x)[/tex]
Also; in trigonometry:
[tex]1 + tan^2x = sec^2x[/tex]
Make another substitution
[tex](1-cos^2 x ).(1+tan^2 x) = (sin^2 x ).(sec^2 x)[/tex]
Recall that [tex]secx = \frac{1}{cosx}[/tex]
So;
[tex](1-cos^2 x ).(1+tan^2 x) = (sin^2 x ).(sec^2 x)[/tex] becomes
[tex](1-cos^2 x ).(1+tan^2 x) = (sin^2 x ).(\frac{1}{cos^2 x})[/tex]
[tex](1-cos^2 x ).(1+tan^2 x) = \frac{sin^2 x }{cos^2 x}[/tex]
[tex](1-cos^2 x ).(1+tan^2 x) = (\frac{sin x }{cosx})^2[/tex]
In trigonometry;
[tex]tan x = \frac{sin x}{cos x}[/tex]
[tex](1-cos^2 x ).(1+tan^2 x) = tan^2x[/tex]
The expression cannot be further simplified
Susan wants to make 2 square flags to
sell at a crafts fair. The fabric she wants
to buy is 5 meters wide. She doesn't
want any fabric left over. What's the
least amount of fabric she should buy?
Answer:
10 meters
Step-by-step explanation:because they are square and they would have to be 5 meters long and she dose not want any left over so...
Determine the possible side lengths of the third side of a triangle with known side lengths of 5 and 8.
Answer:
Answer:
3 < c < 13
Step-by-step explanation:
A triangle is known to have 3 sides: Side a, Side b and Side c.
For a triangle, one of the three sides is longer than the other two sides. (The only exception is when we are told specifically that a triangle is an equilateral triangle, where all the 3 sides are equal to each other).
To solve the above question, we would be using the Triangle Inequality Theorem.
The Triangle Inequality Theorem states that the summation or addition of the lengths of any two sides of a triangle is greater than the length of the third side.
Side a + Side b > Side c
Side a + Side c > Side b
Side b + Side c > Side a
For the above question, we have 2 possible side lengths for the third side of the triangle. We are given in the above question,
side (a) = 5
side (b) = 8
Let's represent the third side as c
To solve for the above question,we would be having the following Inequality.
= b - a < c < b + a
= 8 - 5 < c < 8 + 5
= 3 < c < 13
Use the interactive to graph a line with the given points: (–1,7) and (1,–1) The coordinates of the y-intercept of the line are.
Answer:
The y-intercept would be 6.25
Step-by-step explanation:
I found this by taking the two points and making it into a y = mx + b line.
Answer:
(0,3)
Step-by-step explanation:
We can use the slope-intercept form to find the y-intercept.
First, we need to find the slope of the line.
We are given the points (-1,7) and (1,-1).
[tex]m=\frac{rise}{run}=\frac{-1-7}{1+1}=\frac{-8}{2}=-4[/tex]
The slope is -4.
Slope-intercept is [tex]y=mx+b[/tex].
We can replace 'y' and 'x' with one of the points given, 'm' with the slope, and solve for 'b'. "B" would be the y-intercept.
I will use (-1,7):
[tex]7=-4(-1)+b\\\\7=4+b\\\\7-4=4-4+b\\\\\boxed{3=b}[/tex]
The line's equation is [tex]y=-4x+3[/tex].
Therefore, the y-intercept is '3'. The coordinates of the y-intercept is (0,3).
Marco has a sandbox that is 3 feet long, 5 feet wide, and
foot deep. How many cubic feet of sand does he need to fill the
sandbox completely?
Answer:
Choice D
Step-by-step explanation:
[tex]3\dfrac{1}{2}\cdot 5 \cdot \dfrac{1}{2}= 3.5\cdot 5\cdot 0.5=8.75 = 8\dfrac{3}{4}[/tex]
Hope this helps!
Cubic feet would be volume.
Volume = length x width x height
Volume = 3 1/2 x 5 x 1/2 = 8 3/4 cubic feet.
2x-3y=21 -6x+2y=7 I also need to be shown how to solve this
Answer:
(-9/2 , -10)
Step-by-step explanation:
2x-3y=21
-6x+2y=7
Multiply the first equation by 3
3(2x-3y)=21*3
6x - 9y = 63
Add this to the second equation to eliminate x
6x - 9y = 63
-6x+2y=7
------------------
0x -7y = 70
Divide by -7
-7y/-7 = 70/-7
y = -10
Now find x
2x- 3y = 21
2x -3(-10) = 21
2x +30 =21
subtract 30 from each side
2x = 21-30
2x= -9
Divide by 2
x = -9/2
(-9/2 , -10)
Now lets solve it by elemination method !
[tex]:\implies\sf 2x-3y=21--------(1)\\ \\ \\ :\implies\sf -6x+2y=7-------(2)\\ \\ \\ \sf Eleminate\ (x) \\ \\ \\ \it Multiply\ first \ equation \ with \ 3\ \ \ and \ 2nd \ \ with \ 1 \\ \\ \\ :\implies\sf (2x-3y=21)\times 3 \\ \\ \\ :\implies\sf (-6x+2y=7)\times 1\\ \\ \\ :\implies\sf 6x-9y=63------(3) \\ \\ \\ :\implies\sf -6x+2y=7-----(4)\\ \\ \\ \it\ \ Add \ equation\ 3\ \ and \ 4\\ \\ \\ :\implies\sf 6x-9y=63+ (-6x+2y= 7)\\ \\ \\ :\implies\sf (6x-6x)+(-9y+2y) = 63+7\\ \\ \\ :\implies\sf 0-7y=70\\ \\ \\ :\implies\sf y= \cancel{\dfrac{70}{-7}}= - 10\\ \\ \\ :\implies\sf y= -10 [/tex]
★ Now find the value of x
let's substitute the value of y in equation 4
[tex]:\implies\sf -6x+2y=7\ \ \ \ \ \ (y= -10)\\ \\ \\ :\implies\sf -6x+2\times (-10)=7\\ \\ \\ :\implies\sf -6x-20= 7\\ \\ \\ :\implies\sf -6x = 7+20 \\ \\ \\ :\implies\sf x= \cancel{\dfrac{27}{-6}}= \dfrac{-9}{2}[/tex]
[tex]\underline{\textit{ \ \ So, \ the \ value \ of \ x\ and \ y }}[/tex]
[tex]\bigstar{\boxed{\sf x= \dfrac{-9}{2}}}[/tex]
[tex]\bigstar{\boxed{\sf\ y= (-10)}}[/tex]
Plz plz plz help me Plz tell me the correct answer
Answer:
Question 1:
The smallest 5-digit no. is 10,000
The product of its prime factors is:
=> 10,000 = 2 × 2 × 2 × 2 × 5 × 5 × 5 × 5
Question 2:
The prime factors of 1729 are:
=> 1729 = 7 × 13 × 19
The relation between their 2 consecutive prime factor is that when they both are subtracted, they give the result 6
Such as :
=> 13-7 = 6
=> 19-13 = 6
Hope this helps!
Don't hesitate asking anything regarding this question!
Answer:
1. The smallest 5-digit number is: 10000
10000= 2 × 2 × 2 × 2 × 5 × 5 × 5 × 5
2. 1729= 7 × 13 × 19
7= 6+1
13= 6*2+1
19= 6*3+1
Which system of inequalities has a solution set that is a line?
[x+y23
[x+y s3
[x+y2-3
Extysa
0
[x+y>3
(x + y <3
(x+y> -3
(x+y<3
Answer:
x + y ≥ 3
x + y ≤ 3
Step-by-step explanation:
In the picture attached, the problem is shown.
The solution to the system:
x + y ≥ 3
x + y ≤ 3
is the line x + y = 3
In order to get a solution to a system of inequalities that is a line, we need the same equation on the left (here, x + y), the same constant on the right (here, 3), and the ≥ sign in one inequality and the sign ≤ in the other one.
Asher has about a probability of winning then Ethan has which could be the outcome that Ashlee needs to win the game select three options
Answer:
There are 36 total possible outcomes.
Rolling a sum of 11 or higher, there are 3 possible rolls, to make a 3/36 = 1/12 probability.
Rolling a sum of 4 there are also 3 possibilities, so the chance would be the same.
Rolling a sum of 9, there are 4 possibilities, which is a better chance.
Rolling a sum less than 5, there is 6 possibilities, which is a better chance.
Rolling greater than 5 but less than 7 means rolling a sum of 6, there are 5 chances, which is a better chance.
Rolling greater than 9 but less than 11, means rolling a 10, there are 3 possibilities, which is the same.
Rolling greater than 2 and less than 4 means rolling a 3, there are 2 possibilities, which is less.
The answers would be:
Rolling a sum of 9,
Rolling a sum less than 5
Rolling greater than 5 but less than 7
Answer:
There are 36 total
Step-by-step explanation:
In one city, customers must pay 6% on all items purchased. The video game controllers cost $18.50 each. If a customer purchases 2 controllers, how much tax will she pay? A. $1.11 B. $2.22 C. $19.61 D. $39.22
Answer: B $2.22
Step-by-step explanation:
2 controllers will cost
= 2 x 18.50 = 37
6% tax = 37 x 0.06 = 2.22
Answer:
B
Step-by-step explanation:
i took the test
Determine the vertical asymptote for the rational function f(x) = x-4 over 3x +2
Answer: (b) x = -2/3
Step-by-step explanation:
The vertical asymptote is the restriction on x.
The denominator cannot be equal to zero so that it the restriction.
Set the denominator equal to zero and solve for x to find the asymptote.
3x + 2 = 0
3x = -2
x = -2/3
How much pure water must be mixed with 10 liters of a 25% acid solution to reduce it to a 10% acid solution? 11 L 15 L 25 L
10 L of a 25% acid solution contains 0.25 * (10 L) = 2.5 L of acid.
Adding x L of pure water dilutes the solution to a concentration of 10%, such that
(2.5 L)/(10 L + x L) = 0.10
Solve for x :
2.5 = 0.10 * (10 + x)
2.5 = 1 + 0.10x
1.5 = 0.10x
15 = x
so 15 L of pure water are needed.
ΔABC has been translated right to create triangle ΔXYZ. Based on this information, which of the following is a true statement? answers: A) ≅ B) ≅ C) ∠A ≅ ∠C D) ∠B ≅ ∠X
Answer:
None. (or B)
Step-by-step explanation:
A) AC≅ZY
B) AZ≅
C) ∠A ≅ ∠C
D) ∠B ≅ ∠X
Options C and D are not true and Options A is wrong and B is incomplete but using process of elimination, the answer is probably B.
The resulting information will be ∠ A ≅ ∠ X, ∠ B ≅ ∠ Y and ∠ C ≅ ∠ Z and AB ≅ XY, BC ≅ YZ and AC ≅ XZ
What is translation transformation?A translation is a type of transformation that takes each point in a figure and slides it the same distance in the same direction.
Given that, Δ ABC has been translated right to create triangle Δ XYZ
We know that in translation transformation, in translation, only the position of the object changes, its size remains the same.
That means Δ ABC ≅ Δ XYZ Therefore, we get,
Congruent parts are;
Angles:-
∠ A ≅ ∠ X,
∠ B ≅ ∠ Y and
∠ C ≅ ∠ Z
Side:-
AB ≅ XY,
BC ≅ YZ and
AC ≅ XZ
Hence, The resulting information will be ∠ A ≅ ∠ X, ∠ B ≅ ∠ Y and ∠ C ≅ ∠ Z and AB ≅ XY, BC ≅ YZ and AC ≅ XZ
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A car travels 3 hours at 50mph; then travels 40mph for 7 hours. How many miles does it travel during the 10 hours?
Answer: 430 miles
Step-by-step explanation:
Distance = speed x time
1) D = 50 x 3 = 150
2) D = 40 x 7 = 280
Total distance travelled = 150+280 = 430
Problem 1 Given: HJ=4x+9, JK=3x+3, and KH=33 Find: x, HJ, and JK x= Answer HJ= Answer JK= Answer
Answer:
Step-by-step explanation:
PLEASEEEEEE HELP ME 40 POINTS :((((((!!!!!!!!!!!!!!!!!!!!!!!!!
Answer:
hi
Step-by-step explanation:
Simon is trying to figure out how much it will cost to buy 30 cases of water for a school picnic. How much will Simon pay for 30
cases of water?
Water Prices by the Case
Number of cases
Price in dollars
15
66.00
20
88.00
35
154.00
$99.00
$119.00
$121.00
$132.00
Answer:
132 dollars, I think
Step-by-step explanation:
15*2=30
66*2=132
Answer:
D
Step-by-step explanation:since 15 cases is $66 multiply 66 by 2 to get $132
Find the value of y.
Answer:
y = [tex]\frac{4\sqrt{3} }{3}[/tex]
Step-by-step explanation:
We are working with 30-60-90 triangles, and to solve for y we need to know the hypotenuse of the smaller triangle.
You can get that by finding the smaller value of the larger triangle.
[tex]\frac{8}{\sqrt{3} } =\frac{x}{1}[/tex]
x[tex]\sqrt{3}[/tex] = 8
x = [tex]\frac{8}{\sqrt{3} }[/tex]
x = [tex]\frac{8\sqrt{3} }{3}[/tex]
That is the hypotenuse of the smaller triangle. To find y...
[tex]\frac{(\frac{8\sqrt{3} }{3}) }{2} =\frac{y}{1}[/tex]
2y = [tex]\frac{8\sqrt{3} }{3}[/tex]
y = [tex]\frac{4\sqrt{3} }{3}[/tex]
Hope this helps!
(a) The perimeter of a rectangular parking lot is 332 m.
If the width of the parking lot is 75 m, what is its length?
Length of the parking lot:
m
Answer:
Step-by-step explanation:
Perimeter of the rectangle = 332m
Perimeter of a rectangle = 2(L+b)
Breadth = 75m
= 2 ( L + 75) = 332
2L + 150 = 332
2L = 332-150
L = 182/2
L= 91m
What is the end behavior of the function f(x)=54x2? As x→∞, f(x)→−∞ As x→−∞, f(x)→−∞ As x→∞, f(x)→∞ As x→−∞, f(x)→∞ As x→∞, f(x)→∞ As x→−∞, f(x)→−∞ As x→∞, f(x)→−∞ As x→−∞, f(x)→∞
Answer:
3f(x)
3x^2
12
-x+6
0
Step-by-step explanation:
Fashoo
Pls help summer homework :D C:
Answer:
C) None of the above
Step-by-step explanation:
Reason is V is a shorter distance and q is longer they need to be subtraction but the other way round to enable the correct subtraction we can show (q-V) which means the longer distance minus the shorter distance.