To write the equation of a line that goes through the point (3,2) and has a y-intercept of 1, we can use the point-slope form of a line. The point-slope form is:
y - y1 = m(x - x1)
Where (x1, y1) is a point on the line, and m is the slope of the line. The slope is a measure of the steepness of the line, and it is calculated as the rise (the change in y) over the run (the change in x).
To find the slope of the line, we can use the two points (3,2) and (3,1). The rise is 1 - 2 = -1 and the run is 3 - 3 = 0, so the slope is -1/0, which is undefined. This means that the line is a vertical line and does not have a slope.
Since the line is a vertical line, we cannot use the point-slope form to write its equation. Instead, we can use the slope-intercept form, which is:
y = mx + b
Where m is the slope of the line and b is the y-intercept. In this case, the slope is 0 (since the line is vertical), and the y-intercept is 1, so the equation of the line is:
y = 0x + 1
To write the equation of a line that is perpendicular to line a and goes through the point (-4,2), we need to find the slope of line a. Since line a is a vertical line, its slope is undefined. However, we know that the slope of a line perpendicular to it must be 0.
Using the point-slope form, the equation of line b is:
y - 2 = 0(x - (-4))
Simplifying, we get:
y = 0x + 2
So, the equation of line b is:
y = 0x + 2
Help real answers only
draw a small table with x and y
whenever x is 1 y becomes 14
using y=mx + c
y= 12(1) + 2
12×1=12
12+2=14
therefore x is 1
NEED HELP ASAP DUE TMR
1. The length of the altitude is 15 units.
2. The perimeter of trapezoid ABCD is 132 units.
Perimeter of a trapezoid.An altitude is the vertical height of a given object from the sea level. This is majorly a height reached by an object to the sea level as a reference.
The perimeter of a trapezoid is the sum of all its sides.
From the question;
1. To determine AE,
DE = (DG - EF)/ 2
= (22 - 6)/ 2 (since AB = EF = 6)
= 8
DE = 8 units
The altitude AE can be determined by applying the Pythagorean theorem to triangle ADE. So that;
/hyp/^2 = /opp/^2 + /adj/^2
AD^2 = DE^" + AE^2
17^2 = 8^2 + AE^2
289 = 64 + AE^2
AE^2 = 225
AE = 15
Thus the length of the altitude is 15 units.
2. To determine the perimeter of the trapezoid, we have;
AE = (AD - EF)/ 2
= (58 - 16)/ 2 (since BC = EF = 16)
= 21
AE = 21 units
So that from triangle ABE, applying the Pythagorean theorem to determine the value of AB, we have;
/hyp/^2 = /opp/^2 + /adj/^2
AB^2 = BE^2 + AE^2
= 20^2 + 21^2
AB = 841^1/2
AB = 29
Perimeter of the trapezoid = 29 + 16 + 29 + 58
= 132 units
Thus, the perimeter of the trapezoid is 132 units.
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Please help me, I need help asap !! I can’t figure it out
Help answer this pls if really appreciate it!! Also if you could explain a little I’d appreciate it extra since I’m a little lost. Thank you!!!
According to the question the angle between right angle triangle hence the M∠1 = [tex]90^{0}[/tex] .
What does a triangle's right angle look like?90 degrees or a straight angle is always one angle. The hypotenuse is the side that has an angle of 90° on it. Always, the hypotenuse is the longest side. The remaining two inner angles add up to a total of 90°.
Which three angles make up a right triangle?Right triangles are triangles with one of the internal angles at a right angle of 90 degrees. Since a triangle's three interior angles sum up to 180 degrees, a right triangle's three interior angles must always add up to 90 degrees since one of them is always 90 degrees (they are complementary).
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3. Kyle has a notebook for each of his 13 classes. He puts 5 stickers on
each notebook. There are 10 stickers on each sheet. How many
sheets of stickers will Kyle need? Write an equation to solve. Use a
variable for the unknown.
The number of sheets of stickers that Kyle needs will be 7 sheets.
How to explain the equation?The equation simply has to do with the statement that illustrates the variables given. In this case, it is vital to note that two or more components are considered in order to be able to describe the scenario.
From the information, Kyle has a notebook for each of his 13 classes. He puts 5 stickers on
each notebook and there are 10 stickers on each sheet.
The number of sheets of stickers that Kyle needs will be:
= (13 × 5) / 10
= 65 / 10.
= 6.5
= 7 approximately
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There a bag containing 10 red, 10 blue, and 10 yellow pieces of paper. Each paper color is numbered from to 10. How would you express the probability that you select a blue piece of paper given that it has a number 10 on it? 10) Pblue ) P(10)
Answer:
D. P(10|blue)
Step-by-step explanation:
Answer:
P(blue|10)
Step-by-step explanation:
Let A = "number is 10" and let B = "blue paper."
Marlowe earned $5,000 over the summer.
• He spent $800 of his earnings.
He invested the remainder into an account that pays 3.5% interest compounded annually.
.
Which equation represents the value of the account, V, after x years?
A. V = 4,200(1.35)*
OB V = 4,200(1.035)*
OC V = 5,000(1.35)
.
D. V = 5,000(1.035)*
Answer:
The answer is D
Step-by-step explanation:
V= 5,000(1.035)*
16^x^2
= 8⁰
I’ll put a picture of it so you can better understand it. Also I’ll give you 30 points, so one of you better answer by 10:00 tomorrow.
Answer:
x=0
Step-by-step explanation:
[tex]16^{x^2}=8^0\\\\16^{x^2}=1\\\\x^2\ln(16)=0\\\\x^2=0\\\\x=0[/tex]
The total cost (t) after 8% sales tax is added to an item's price (p): 1.08p= t
The total cost of the item after the sales tax of 8 % is given by the equation t = 1.08p , where p is the initial price of the item
What is an Equation?Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.
It demonstrates the equality of the relationship between the expressions printed on the left and right sides.
Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.
Given data ,
Let the total cost price of the item be represented as t
Let the initial cost price of the item be represented as p
Now , the sales tax percentage = 8 %
So , the equation will be
The total cost price of the item t = sales tax percentage ( initial cost price of the item ) + initial cost price of the item
Substituting the values in the equation , we get
The total cost price of the item t = 8 % ( p ) + p
On simplifying the equation , we get
The total cost price of the item t = ( 8/100 ) p + p
The total cost price of the item t = 0.08p + p
The total cost price of the item t = 1.08p
Hence , the equation is t = 1.08p , where p is the initial price of the item
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Help me
Like just draw on it
Answer:
Step-by-step explanation:
let there be 800 people at school. prove that 3 of them do share a birthday. how can we prove it according to the pigeonhole principle?
Find the slope of the line passing through the points (3, 4) and (8, -3).
Answer: -7/5
Step-by-step explanation:
Which expressions are solutions to the equation 3/4 x = 15?
a
15/3/4
b
15/4/3
С
4/3.15
d
3/4.15
e
15-3/4
hi
A square photograph is printed on a larger rectangular sheet of paper leaving a border around the
photograph of 2 centimeters on the top and 3 centimeters on each of the remaining sides. The sheet of paper
has an area of 72 square centimeters. If x is the length of a side of the photograph measured in centimeters,
which of the following equations could be used to find x ?
The area of a shape is the amount of space, the shape can occupy. The equation to calculate the value of x is: [tex](e)\ x^2 + 11x -42= 0[/tex]
The space on the border is given as:
[tex]Top = 2[/tex]
[tex]Others = 3[/tex]
So, the dimension of the sheet of paper is:
[tex]Length = x + 2 + 3[/tex]
[tex]Length = x + 5[/tex]
[tex]Width = x + 3 + 3[/tex]
[tex]Width = x + 6[/tex]
The area of the sheet is then calculated as follows:
[tex]Area= Length \times Width[/tex]
[tex]Area= (x + 5) \times (x + 6)[/tex]
Open brackets
[tex]Area= x^2 + 5x + 6x + 30[/tex]
[tex]Area= x^2 + 11x + 30[/tex]
From the question, we understand that the area of the sheet is [tex]72cm^2[/tex]
So, the equation becomes
[tex]x^2 + 11x + 30 = 72[/tex]
Subtract 72 from both sides
[tex]x^2 + 11x + 30 -72= 0[/tex]
[tex]x^2 + 11x -42= 0[/tex]
Hence,
[tex](e)\ x^2 + 11x -42= 0[/tex] can be used to calculate the value of x
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The value of
Arc sin(1/2) + Arc tan(1) is
Answer:
75°Step-by-step explanation:
We know that:
sin 30° = 1/2, therefore arcsin (1/2) = 30°tan 45° = 1, therefore arctan (1) = 45°So the value of the expression is:
arcsin (1/2) + arctan (1) = 30° + 45° = 75°Answer:
75°
Step-by-step explanation:
Recall the common trigonometric angles:
[tex]\sin 30^{\circ}=\dfrac{1}{2}[/tex]
[tex]\tan 45^{\circ}=1[/tex]
Arcsin is the inverse of sin.
Arctan is the inverse of tan.
[tex]\implies \arcsin \left(\dfrac{1}{2}\right)=30^{\circ}[/tex]
[tex]\implies \arctan (1) = 45^{\circ}[/tex]
Therefore:
[tex]\implies \arcsin \left(\dfrac{1}{2}\right)+\arctan (1) = 30^{\circ}+ 45^{\circ}=75^{\circ}[/tex]
Complete the equation describing how X and Y are related, only answer if you’re sure. Need full equation, not just the box. Will give Brainly.
Answer:
? = -1/2 dark gray box = - 1
y = -1/2 x - 1 or
y = -0.5x - 1
Step-by-step explanation:
The place to start is at 0.
When x = 0 then y = - 1
That means that the second box (the dark gray one) is - 1
So far what you know about the equation is
y = ?x - 1
We need to check two more points.
x = 4
y = - 3
- 3 = ? 4 - 1 Add 1 to both sides
-3 +1 = ?4 - 1 + 1 Combine The -1 and + 1 Cancel
-2 = ?4 Divide by 4
-2/4 = ?
? = -1/2 or - 0.5
Now we need 1 more point to check the result
Let x = 2. Do we get - 2 for y
y = -1/2 * 2 - 1
y = -1 - 1
y = - 2 just as it should
An astronaut was exploring the moon of a distant planet, and found some glowing goo at the bottom of a very deep crater. She brought a 10-gram sample of the goo to her laboratory. She found that when the goo was exposed to light, the total amount of goo increased by 100% every hour.
How much goo will she have after 1 hour? After 2 hours? After 3 hours? After n hours?
When she put the goo in the dark, it shrank by 75% every hour. How many hours will it take for the goo that was exposed to light for n hours to return to the original size?
The amounts of goo after each hour are given as follows:
1 hour: 20 grams.2 hours: 40 grams.3 hours: 80 grams.n hours: 10(2)^n.The time that it takes for the goo to return to original size is given as follows:
n hours, for which:
[tex](2)^n(0.25)^n = 1[/tex]
How to model the situation?An increasing exponential function is defined as follows:
y = a(1 + r)^x.
For which the parameters are given as follows:
a is the initial value.r is the growth rate, as a decimal.Her sample is of 10 grams, and the amopunt of goo increases by 100%, hence the parameter values' are given as follows:
a = 10, r = 1.
Thus the exponential function is defined as follows:
y = 10(2)^n.
Then the amounts are given as follows:
One hour: y = 10 x 2 = 20 grams.Two hours: y = 10 x 2² = 40 grams.Three hours: y = 10 x 2³ = 80 grams.A decreasing exponential function is given as follows:
y = a(1 - r)^x.
The goo shrinks by 75% every hour, hence:
r = 0.75.
The amount after n hours is of 10(2)^n, hence the shrinking function is given as follows:
[tex]y = 10(2)^n(0.25)^n[/tex]
It returns to the original amount when:
y = 10.
Hence:
[tex]10 = 10(2)^n(0.25)^n[/tex]
[tex](2)^n(0.25)^n = 1[/tex]
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What is the following sum?
Answer:
The 4th one
Step-by-step explanation:
Right on edge!
If the dimensions of the following cylinder are doubled, what factor will the surface area change by? 8 in 0.5 ft answers 2 8 4 6
Question: If the dimensions of the following cylinder are doubled, what factor will the surface area change by?
8
6
4
2
Answer: i think it is 8 but i will update it if not i am on the test
If the dimensions of the cylinder are doubled, then by 4 factor the surface area changed
What is Three dimensional shape?a three dimensional shape can be defined as a solid figure or an object or shape that has three dimensions—length, width, and height.
A cylinder is a three-dimensional shape consisting of two parallel circular bases, joined by a curved surface.
The radius of cylinder is r=8 inches
Height is 0.5 feet.
Surface area of cylinder=2πr(r+h)
We know that 0.5feet=6 inches
Suface area of original cylinder=2πr(r+h)
=2×π×8(8+6)
=224π
Now the dimensions are doubled ,so r=16 inches , h=12 inches
Suface area of changed cylinder=2πr(r+h)
=2π×16(16+12)
=32π×(28)
=896π
=4(224π)
Hence by 4 factor the surface area is changed.
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Peter works in the Spring Roll restaurant. He earns $15.50 per hour plus tips of 15% of food sales. If Peter works 35 hours this week and has $4000 of food sales, how much does he earn in total?
Base salary =
Tips =
Total earnings =
Find the inverse of the function.
y = x + 2
Write your answer in the form ax + b. Simplify any fractions.
y =
Given:
The function is:
[tex]y=x+2[/tex]
To find:
The inverse of the given function.
[tex]y=x+2[/tex]
Solution:
We have,
[tex]y=x+2[/tex]
Step 1: Interchange x and y.
[tex]x=y+2[/tex]
Step 2: Solve to y.
[tex]x-2=y[/tex]
[tex]y=x-2[/tex]
Therefore, the inverse of the given function is [tex]y=x-2[/tex].
Can someone please help me with number 9.
9614 1404 393
Answer:
31.5 ft
Step-by-step explanation:
The length of the arc is the product of the radius of the circle, 11 ft, and the angle measure in radians. Arc PS has radian measure ...
(180° -16°)/180°×π = 41π/45
So, the length of arc PS is ...
s = rθ
s = (11 ft)(41π/45) = 451π/45 ft
s ≈ 31.5 ft
I just need help with question A
Suppose your cousin missed class and asks you, “Why do we plug in 0 for x to find y-intercepts and 0 for y to find x-intercepts? That doesn’t make sense to me.” Explain to your cousin WHY this process works. Use the line
5x+4y=14 as an example.
A) A description in words why this works
The reason why the cousin's procedure for getting the x and y intercepts work is because they represent the definition of those points on a graph.
How to find the x and y intercepts?The x-intercept of a graph or function simply refers to the point at which the graph crosses the graph crosses the x-axis or the point at which y = 0. In a similar manner, the y-intercept simply refers to the point at which the graph crosses the y-axis or simply the point at which x = 0.
Now, we are given the equation of the line as;
5x + 4y = 14
The general form of equation of a line in slope intercept form is;
y = mx + c
where;
m is slope
c is y-intercept
Rewriting the equation of the line in slope intercept form is;
y = -⁵/₄x + ⁷/₂
Now, the reason why we plug in 0 for x to get the y-intercept is because when x = 0, that is only where we can get the y-intercept as the corresponding value of x will be traced to 0.
Similarly, the reason why we plug in 0 for y to get the x-intercept is because when y = 0, that is only where we can get the x-intercept as the corresponding value of y will be traced to 0.
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Find x.
Round to the nearest tenth.
7cm
7cm
10 cm
x = [? ]cm
Answer:
x = 4.9
Step-by-step explanation:
We can use the intersecting chords formula:
(segment piece) x (segment piece) = (segment piece) x (segment piece)
7*7 = 10x
49 = 10x
Divide each side by 10
49/10=10x/10
4.9 = x
Please like and give me Branlist and rate Thank you!
In this figure please see attached
Answer:
Step-by-step explanation:
Formula
t = 1.06 * p
Givens
p = 8.5
Solution
t = 1.06 * 8.5
t = 9.01
If you cannot see my apologies, but you can zoom in!
DO NOT ANSWER IF YOU DO NOT KNOW THE ANSWER!! Whoever answers correctly will get Brainliest! :)
Answer:
C
Step-by-step explanation:
The sum of the angles is 90
2x + x = 90
3x = 90
x = 30
the angle ABC is 2x, so it means that is the double of x, so it is 60 degrees
Which integer in the set has the greatest value (7, -7, -3, 3)?
A. -7
B. -3
C. 3
D. 7
Answer:
-3
Step-by-step explanation:
i hope this helps
Read the scenarios and decide which type of interaction (absorption or transmission) took place between the wave
and the object.
People are able to hear footsteps because the sound made by a foot hitting the floor travels through the air to reach
their ears.
When light from the sun hits the sidewalk, the sidewalk becomes warmer.
Answer:
transmission absorption
Step-by-step explanation:
This is because the sound of the foot striking the floor is being transmitted through the air. The sun's light is absorbed when it strikes the sidewalk.
What is absorption and transmission?
Absorption is the process or action by which one thing absorbs or is absorbed by another.
The act of sending something, such as a cold or a message, or the component of a machine that transfers power from the engine to the moving parts is known as transmission.
Which process is represented by the given statements?Because of the air pressure, people can hear when their foot strikes the ground. In a similar manner, when sunlight strikes a sidewalk, it warms up as a result of absorbing the heat.
Therefore, the first statement is transmission and second statement is absorption.
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Can someone pls tell me how to do this?
Simplify (5y)³
Answer: 125y³
To rise a product to a power, rise each factor to that power:
(5y)³ = 5³y³ = 125y³
•50 POINTS HELP• guessers will be reported.
If P=(4,7), Find: D2 (p)
The answer is distance from P to l. is equal to square root of 2
Find the distance from P to l ?Line I contains points (0, -3) and (7,4). Point P has coordinates (4,3)
Find the slope of line l we have the points (0, -3) and (7,4)
m=(4+3)/(7-0) m=7/7 m=1
Find the equation of the line perpendicular to the line l that passes through the point P
Remember that
If two lines are perpendicular, then the product of their slopes is equal to -1, the slope of the perpendicular line is
m=-1 .Find the equation in point slope form
y-y1=m(x-x1)
(x1,y1)=P(4,3)
substitute
y-3=-1(x-4)
y-3=-x+4
y=-x+7
m=1 (see the step 1)
and we have the point (0,-3) -----> y-intercept
so the equation of the line l is
y=x-3
Find the intersection point line l and its perpendicular line
y=x-3 ------> equation A
y=-x+7 -----> equation B
solve the system of equations
Adds equation A and equation B
2y=-3+7
2y=4
y=2
substitute in equation A
2=x-3 x=2+3 x=5
the intersection point is (5,2)
Find the distance between point (5,2) and point P(4,3)
Remember that, this distance is the distance from P to l.
the formula to calculate the distance between two points is equal to
we have
(x1,y1)=(5,2)
(x2,y2)=(4,3)
substitute in the formula
therefore
The answer is distance from P to l. is equal to square root of 2
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