what equation defines a line that intersects the graph of 6x-2y=10 exactly once?
Any line with a slope different than 3 will intercept the given line only once.
What equation defines a line that intersects the graph?The answer will be any line that is not parallel (nor the same) to the given line.
Remember two lines are parallel if the lines have the same slope and different y-intercept
In this case, the given linear equation is:
6x - 2y = 10
y = 3x - 5
So the slope is 3 and the y-intercept is -5.
Then, any line with a slope different than 3 will intercept this line only once.
An example can be:
y = 314*x
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Solve for x. Round to the nearest tenth, if necessary.
Answer:
x = 3.4
Step-by-step explanation:
Use the sin formula, due to the fact of the hypotenuse being known, and the variable being across 70.
Sin(70) = x / 3.6
Sin(70) * 3.6 = x
3.3828934 = x
Round to nearest tenth, as question asked
3.4 = x
-- Gage Millar, Algebra 1/2 Tutor (Pending Pre-Calc Tutor)
You plan to build a house that is 1 ½ times as long as it is wide. You want the land around the house to be 20 feet wider than the width of the house, and twice as long as the length of the house, as shown at the right.
The total area with land based on the information given is 3x² + 60x.
How to find the area?Let the width = x
Let the length = (1.5 × x) = 1.5x
Area = 1.5x × x = 1.5x²
The area along with land:
Width = x + 20
Length = 3 × x = 3x
The total area with land:
= Length × Width
= 3x(x + 20)
= 3x² + 60x.
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A rubber bouncy ball is dropped from a
height of 101.00 inches onto a hard flat
floor. After each bounce, the ball returns
to a height that is 19% less than the
previous maximum height. What is the
maximum height reached after the 5th
bounce?
Using a geometric sequence, it is found that the maximum height reached after the 5th bounce is of 43.48 feet.
What is a geometric sequence?A geometric sequence is a sequence in which the result of the division of consecutive terms is always the same, called common ratio q.
The nth term of a geometric sequence is given by:
[tex]a_n = a_1q^{n-1}[/tex]
In which [tex]a_1[/tex] is the first term.
In this problem, the ball is dropped from a height of 101.00 inches onto a hard flat floor, and after each bounce, the height is 19% less, that is, 81% of the previous height, hence the first term and the common ratio are given by:
[tex]a_1 = 101, q = 0.81[/tex]
Then, the height of the nth bounce is given by:
[tex]a_n = 101(0.81)^{n-1}[/tex]
And the height of the 5th bounce is:
[tex]a_5 = 101(0.81)^{5-1} = 43.48[/tex]
The maximum height reached after the 5th bounce is of 43.48 feet.
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Wendy winholtz 8 year savings certificate pays an annual interest rate of 5.3% at the end of 5 years she cashed out the 6,000 CD and paid a penalty of 12 month simple interest. What penalty did she pay
Answer:
318
Step-by-step explanation:
The rate of 5.3% is an annual rate, and specifies the amount of interest earned in a 12-month period by the principal amount of the CD. The interest amount is found by multiplying the interest rate by the principal amount.
__
penaltyThe amount of the penalty is 5.3% of 6000:
0.053 × 6000 = 318
Wendy paid a penalty of 318 for her early withdrawal.
What is the value of 9+n/3when n equals 12
Answer:
13
Step-by-step explanation:
Divide 12 by 3 first because of (PEMDAS) you get 4 tge add that to the 9 the you get 13.
P = parentheses
E = exponent
M = multiplication
D = division
A = addition
S = subtraction
A copy machine makes 36 coples per minute. How many coples does it make in 4 minutes and 45 seconds?
A certain city in Washington has a population of 46,400 people.
If the city is 580 sq mi in area, approximately how many people live in each square mile?
Step-by-step explanation:
please can you divide it will give you the answer
solving separable differential equation DY over DX equals xy+3x-y-3/xy-2x+4y-8
It looks like the differential equation is
[tex]\dfrac{dy}{dx} = \dfrac{xy + 3x - y - 3}{xy - 2x + 4y - 8}[/tex]
Factorize the right side by grouping.
[tex]xy + 3x - y - 3 = x (y + 3) - (y + 3) = (x - 1) (y + 3)[/tex]
[tex]xy - 2x + 4y - 8 = x (y - 2) + 4 (y - 2) = (x + 4) (y - 2)[/tex]
Now we can separate variables as
[tex]\dfrac{dy}{dx} = \dfrac{(x-1)(y+3)}{(x+4)(y-2)} \implies \dfrac{y-2}{y+3} \, dy = \dfrac{x-1}{x+4} \, dx[/tex]
Integrate both sides.
[tex]\displaystyle \int \frac{y-2}{y+3} \, dy = \int \frac{x-1}{x+4} \, dx[/tex]
[tex]\displaystyle \int \left(1 - \frac5{y+3}\right) \, dy = \int \left(1 - \frac5{x + 4}\right) \, dx[/tex]
[tex]\implies \boxed{y - 5 \ln|y + 3| = x - 5 \ln|x + 4| + C}[/tex]
You could go on to solve for [tex]y[/tex] explicitly as a function of [tex]x[/tex], but that involves a special function called the "product logarithm" or "Lambert W" function, which is probably beyond your scope.
simplify 2 2/3-1.25+5/6
Answer:
2.25or21/4
Step-by-step explanation:
hope it helps
Answer:
2 1/4 or 2.25Step-by-step explanation:
GivenExpression:
2 2/3 - 1.25 + 5/6SolutionSimplify it in below steps:
2 2/3 - 1.25 + 5/6 = 2 + 2/3 - 1 - 0.25 + 5/6 = 1 + 4/6 + 5/6 - 1/4 =1 + 9/6 - 1/4 =1 + 1 + 3/6 - 1/4 = 2 + 2/4 - 1/4 = 2 + 1/4 = 2 1/4 or 2.25
Estimate the solution to the following system of equations by graphing.
3x + 5y = 14
6x - 4y = 9
Answer:
(2.405, 1.537)
Step-by-step explanation:
When you graph these, they intersect at (2.405, 1.537).
You can use desmos as a graphing calculator, it is extremely helpful.
Hope this helps!
Classify the following triangle as acute, obtuse, or right.
A. Obtuse
B. Acute
C. Right
D. None of these
Answer:
Acute Triangle.
Explanation:
The figure shows an equilateral triangle which has all the angles equal.
Acute Triangles are those who has angles less than 90°
Hence, an equilateral triangle is always an acute triangle.
Additional,
A right angle triangle has 90° angle.
An obtuse triangle has greater than 90° angle.
There are 35 students on the Step Team to raise a total of 3,500 for uniforms. So far they have raised a total of 1,800. How much more money in dollars, does each member of the Step Team need to raise
Answer:
48.57 USD
Step-by-step explanation:
Just subtract 3500 from 1800 you get 1700
then
1700 divided by 35
Jessica and Callista go the local burger joint. They both want to buy the meal deal. Jessica has 34 of the money needed to buy the meal deal and Callista has half of the money needed to buy the meal deal. If the meal deal was $3 cheaper, then together they would have exactly enough money to buy two of the meal deals.
What is the original price of the meal deal? Show or explain how you got your answer.
The original price of the meal deal if they would have exactly enough money to buy two of the meal deal is $4
How to write and solve equation?let
x = cost of the meal
Both = 2x - 3
Jessica = 3/4xCallista = 1/2x3/4x + 1/2x = 2x - 3
(3+2)x / 4 = 2x - 3
5/4x = 2x - 3
5/4x - 2x = - 3
(5-8)x/ 4 = -3
-3/4x = -3
x = -3 ÷ -3/4
= -3 × -4/3
= 12/3
x = $4
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ƒ(1) = −6
f(2)=-4
f(n) = f(n-2) + f(n-1)
f(3) =
Answer:
-10
Step-by-step explanation:
if we put f(n)=3 , Then
f(3)=f(3-2) + f(3-1)
= f(1) + f(2)
= -6+(-4). [since f(1)= -6 and f(2) = -4)
= -6-4
= -10
5 more than n is the quotient of n and 4
Answer:
3
Step-by-step explanation:
Complete the table of values for the equation, 16x + 4y = 12.
x y
-2
-1
0
1
2
The x-y coordinates for the given equation are: (-2,11),(-1,7),(0,3), (1,-1) and (2,-5).
Linear FunctionA linear function can be represented by a line. The standard form for this equation is: ax+b , for example, y=2x+7. Where:
a= the slope;b=the constant term that represents the y-intercept.The given equation is 16x + 4y = 12. For solving this question, you should replace the given values of x for finding the values of y.
Thus,
For x= -2, the value of y will be:16*(-2)+4y=12
-32+4y=12
4y=12+32
4y=44
y=11
For x= -1, the value of y will be:
16*(-1)+4y=12
-16+4y=124y=12+164y=28y=7For x= 0, the value of y will be:16*(0)+4y=12
0+4y=124y=124y=12y=3For x= 1, the value of y will be:16*(1)+4y=12
16+4y=124y=12-164y=-4y= -1For x= 2, the value of y will be:16*(2)+4y=12
32+4y=124y=12-324y=-20y= -5Read more about the linear equation here:
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Q5. Find each value.
Answer:
[tex]a. {( \sqrt{36} )}^{2} = 36[/tex]
[tex]b. ({ \sqrt{ \frac{25}{81} } })^{2} = \frac{25}{81} = 0.3086[/tex]
[tex]c. {( \sqrt{1.99} )}^{2} = 1.99[/tex]
[tex]d. {( \sqrt{x} })^{2} = x[/tex]
The square exponent is removed with the root .
A line intersects the points (-5, 1) and (-2,7). What is the slope of the line in simplest form? m=[?}
Step-by-step explanation:
To find slope : y2- y1 / x2 - x1
we have ( -5 , 1 ) which is ( x1 , y1 )
and ( -2 , 7 ) is ( x2 , y2 )
so; 7 - 1 / -2 - (-5)
6/3
= 2
100 points
1942 divded by 2^4
Answer: 121.375
Step-by-step explanation:
[tex]2^4=16[/tex]
[tex]\frac{1942}{2^4}[/tex]
[tex]\frac{1942}{16}=121.375[/tex]
this shape is a triangular Pyramid the 3 sides slant height is 14 the base width is 8 and the base height is 6.9
The surface area of a triangular prism with the 3 sides slant height as 14 the base width as 8 and the base height as 6.9 is 155. 705 in²
What is the surface area of a triangular prism?
The surface area of a triangular pyramid is the total area of all it's faces.
The properties of a triangular prism are;
It has a triangular base It is bounded y three lateral triangular faces meeting at one vertex. It has all its faces as trianglesHow to determine the surface area
Surface area = Base Area + 1÷2 (perimeter × base height)
But base area = 1÷2 (base side × height)
Base area = 1÷ 2 (8 × 14) = 0.5 × 112 = 56 in²
Perimeter = sum of all the sides = 14 + 8 + 6.9 = 28. 9 in
Base height = 6. 9in
Surface area = 56 + 1 ÷ 2 ( 28.9× 6. 9) = 56 + 0.5 × 199.41 = 56 + 99. 705 = 155. 705 in²
Surface area = 155. 705 in²
Therefore, the surface area of the triangular prism is 155. 705 in²
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The distance between two cities is 13 kilometers. There are approximately 1.6 kilometers in 1 mile. What is the number of miles between the two cities?
The number of miles between the two cities is 8.13 miles.
What is the number of miles between the two cities?In order to determine the number of miles between the two cities, we would have to divide 13 kilometers by 1.6 miles. Division is when a number is grouped into equal numbers using another number.
Number of miles = 13 / 1.6 = 8.13 miles
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19) Florence has a strip of clothing that is 8 feet long. About how many 2 feet strips can she cut from the 8-foot strip?
I really need help with this
Answer:
4
Step-by-step explanation:
8/2 is 4
In ΔABC, m∠A = 2m∠B and m∠B = 3m∠C.
What is m∠C?
A triangle is a three-edged polygon with three vertices. The measure of ∠C is 18°.
What is a triangle?A triangle is a three-edged polygon with three vertices. It is a fundamental form in geometry. The sum of all the angles of a triangle is always equal to 180°.
Let the measure of ∠C be represented by x. Given the measure of ∠A= 2(∠B), while the measure of ∠B=3(∠C). Therefore, the measure of angles can be written as,
∠A = 2(∠B) = 2[3(∠C)] = 6x
∠B = 3x
∠C = x
Now, since the sum of all the angles of a triangle is 180°. Therefore,
∠A + ∠B + ∠C = 180°
6x + 3x + x = 180°
10x = 180°
x = 18°
Hence, the measure of ∠C is 18°.
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Simplify the following: 9 – 2(x - 5) = x + 10
Answer:
x = 3
Step-by-step explanation:
Hello!
We can distribute the parenthesis and solve for x.
Solve9 - 2(x - 5) = x + 109 - 2x + 10 = x + 1019 - 10 = 3x9 = 3xx = 3The value of x is 3.
We can plug it back in to check if it works.
Check9 - 2(x - 5) = x + 109 - 2(3 - 5) = 3 + 109 - 2(-2) = 3 + 109 + 4 = 3 + 1013 = 13Correct!
Answer:
[tex]\huge\boxed{\sf x = 3}[/tex]
Step-by-step explanation:
Given equation:9 - 2(x - 5) = x + 10
Distribute
9 - 2x + 10 = x + 10
Subtract 10 to both sides
9 - 2x = x
Add 2x to both sides
9 = x + 2x
9 = 3x
Divide 3 to both sides
9/3 = 3x/3
3 = x
OR
x = 3[tex]\rule[225]{225}{2}[/tex]
solve the equation
x + 10 = 20
Which expression represents the perimeter of the triangle?
8x + 2
18x
8x
Answer:
8x
Step-by-step explanation:
We can add all of the side lengths of the triangle to figure out the perimeter. 3x-1+3x+1=6x+2x=8x
The constant is four
x=4
Step-by-step explanation:
4x=16y
x=16divide4
x=4
Answer:
y = 4x
Step-by-step explanation:
Take a pair of coordinates, like
(8,32) ; (4,16)
m = (Δy):(Δx)
= (32-16) : (8 - 4) = 4
y = mx + c
= 4x +c
Now substitute the values from one of the 2 coordinates' pair.
16 = 16 + c
c = 0
Therefore,
y = 4x
Simplify
Inx + lny + ln3
Step-by-step explanation:
[tex] ln(x) + ln(y) + ln(3) [/tex]
[tex] ln(3xy) [/tex]
Statistics
Assume there are 20 advanced English level students, 8 intermediate English
level students and 15 beginner English level students at statistics class. What
is the probability of selecting 10 advanced English level students and 10
non_ advanced English level students?
Answer:
no thank you sorry 4h he'll be a great day of school and I have been a while ago but it's a good time 44
Answer:
o
Step-by-step explanation: