The y-intercept of the equation of a line in general form is:(0, -c/b) or -c/b
The y-intercept is the point where the graph intersects the y-axis. To graph, any function that is of the form y = f(x) finding the intercepts is really important. There are two types of intercepts that a function can have. They are the x-intercept and the y-intercept. An intercept of a function is a point where the graph of the function cuts the axis.
The y-intercept of a function is a point where its graph would meet the y-axis. The x-coordinate of any point on the y-axis is 0 and we use this fact to derive the formula to find the y-intercept. i.e., the y-intercept of a function is of the form (0, y).
The equation of a straight line in general form is ax+by+c=0. For the y-intercept, we substitute x=0 and solve it for y.
a(0)+ by + c =0
by + c =0
y = - c/b
Thus, the y-intercept of the equation of a line in general form is:(0, -c/b) or -c/b
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Find the sum of each finite arithmetic series. 8+9+10+. . . . . . +15
The sum of finite arithmetic series 8+9+10+. . . . . . +15 is 92
Suppose we are given an arithmetic series:
a(1) + a(2) + ... + a(n)
Then the sum is:
S(n) = n/2 (a(1) + a(n))
Where: a(1) = first term
a(n) = nth term
The given series is:
8+9+10+. . . . . . +15
We need to find n such that a(n) = 15.
Recall that in an arithmetic sequence:
a(n) = a(1) + (n -1) . d
where d = difference between 2 consecutive terms.
Substituting a(1) = 8, and d = 9 - 8 =1 into the formula:
a(n) = 8 + (n -1) . 1
15 = 7 + n
n = 8
Substitute n = 8 into the sum formula:
S(n) = n/2 (a(1) + a(n))
S(8) = 8/2 . (8 + 15)
= 4 . 23 = 92
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|x| means “distance between_ and _
Answer:|x| means “distance between a number and zero
Step-by-step explanation:
Also known as absolute value
ex l5l=5 & l5l=-5
A lawn is 4m longer than it is wide. The total area of the lawn is 30 metres squared. What is its perimeter? Give your answer to 2 d.p.
Answer:
7.5
Step-by-step explanation:simply divide 30 and 4 and the answer is 7.5
I need help with this problem...please response and show the process
The equation that represents the linear relationship between the x- values and y-values in the table is y = 6x - 5 .
What is a linear equation?
An algebraic equation of the form y=mx+b is referred to as a linear equation. m is the slope, and b is the y-intercept, and all that is involved is a constant and a first-order (linear) term. The variables in the preceding equation are y and x, and it is occasionally referred to as a "linear equation of two variables."
The equation y = 6x - 5 can represent the linear relationship between the x- values and y-values because it satisfies all the given values for x and y.
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Write an equation for each transformation of y=x .
Vertical compression by a factor of 1/2.
Vertically Stretching and Compressing
It multiplies a function by a positive constant that yields a position whose graph is vertically stretched or compressed relative to the original function's graph. If the constant is greater than 1, it will stretch vertically. If the constant is between 0 and 1, vertical compression is done and you will get vertical compression.
Vertical compression occurs when you multiply the function by a rational scaling factor. The base of the function graph remains the same even when the graph is compressed vertically. Only initial values are affected.
Solution
Y=x
Multiplying the right side by ½
Y= (1/2) *X
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Drag each length to the correct location on the image. Each length can be used more than once, but not all lengths will be used.
What are the missing segment lengths in the image?
12√3
24
12√2
12
45
E
45°
12
24√3 24√2
45°
45°
Answer:
DF=12√2
FG=12√2
DG=24
Step-by-step explanation:
Ratio of special Right Triangle (45:45:90): x:x:x√2
Triangle DEF: x:x:x√2
x=12
12: 12: 12√2
So, DF= 12√2
Opposite (if q, then p) Base angle theorem. So, FD≅FG.
FD=12√2
FG=12√2
Ratio of 45:45:90 Triangle: x:x::x√2
x in triangle FDG= 12√2
12√2:12√2:12√2(√2)
12√2*√2=24
=12√2: 12√2: 24
DG=24
2x^2+7x+2 greater than or equal to 0
Answer:
Greater than
Step-by-step explanation:
2x2+7x+2
----------
a. Measures less than m ∠ 1 .
A triangle's exterior angle is always greater than its two remote interior angles. The exterior angle ∠1 is greater than ∠3, ∠5, ∠7, and ∠8.
What is meant by Exterior Angle Inequality Theorem?
According to the exterior angle inequality theorem, the measure of any exterior angle of a triangle is greater than the measure of either of the opposite interior angles. The adjacent interior angle and the exterior angle are supplementary. A triangle's exterior angles add up to 360º.
A triangle's exterior angle is always greater than its two remote interior angles.
Since, angle 1 is an exterior angle of Δ ABE,
m∠1 > m∠3 and m∠4
Since, angle 1 is an exterior angle of Δ ABD,
m∠1 > m∠5
Since, angle 1 is an exterior angle of Δ ABC,
m∠1 > m∠7 and m∠8
Therefore, ∠1 is greater than ∠3, ∠5, ∠7, and ∠8.
The complete question is:
Use the Exterior Angle Inequality Theorem to list all of the angles that satisfy the stated condition.
a. Measures less than m ∠ 1 .
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Write a function g whose graph represents the indicated transformation of the graph of f. f(x)= | 4x+3| + 2 translated 2 units down is g (x)
Answer:
g(x) = |4x+3|
Step-by-step explanation:
g(x) = f(x) - 2
=|4x+3|
Can someone please help me? It’s due tmrw.
For Exercises 1-3 use the following information. Then estimate to find the distance sound travels through each material in each given time.
Problem: Sound travels through different materials at different speeds. For example, the graph shows that in one second, sound travels 5,971 meters through stone.
However, it travels only 346 meters through air in one second.
1. air, 20 seconds
Answer:??
2. Stone, 12 seconds
Answer:??
3. Estimate how much farther sound travels through stone in 17 seconds than through aluminum in the same time.
Answer:??
Thanks! :)
Chart
|
|
|
|
|
|
\/
Answer:
Step-by-step explanation:
1. We know it travels 346 meters in a second, we now need to multiply 346 by 20. This equals 6920
2. Sound travels 5971 meters per second. We need to multiply this by 12 to find the distance it travels in 12 seconds. 71652 meters
3. We know sound travels 5971 meters per second in stone and 5000 meters per second from the chart. We need to find the difference between these and multiply that by 17 to find the distance covered in 17 seconds.
5971-5000=971
971*17=16507
Sound travels 16507 more meters in 17 seconds through stone than it would travel in aluminum
Solve each equation. Check each solution. 11/3x - 1/3 = -4/x²
The solutions of the given equation 11/3x - 1/3 = -4/x² are x = -1 and x = 12
In this question, we have been given an equation.
11/3x - 1/3 = -4/x²
We need to solve given equation.
⇒ 11/3x - 1/3 = -4/x²
⇒ (33 - 3x)/9x = -4/x²
⇒(33 - 3x)/9 = -4/x
⇒ x(33 - 3x) = -36
⇒ -3x² + 33x + 36 = 0
⇒ x² - 11x - 12 = 0
⇒ x² - 12x + x - 12 = 0
⇒ x(x - 12) + 1(x - 12) = 0
⇒ (x - 12)(x + 1) = 0
⇒ x - 12 = 0 or x + 1 = 0
⇒ x = 12 or x = -1
Now we need to check above solutions.
Substitute x = 12 in given equation.
⇒ 11/3(12) - 1/3 = -4/(12)²
⇒ 1/3 (11/12 - 1) = 1/3(-4/48)
⇒ -1/12 = -1/12
⇒ LHS = RHS
Now substitute x = -1 in given equation.
⇒ 11/3(-1) - 1/3 = -4/(-1)²
⇒ -12/3 = -4/1
⇒ -4 = -4
⇒ LHS = RHS
Therefore, the solutions of the given equation 11/3x - 1/3 = -4/x² are x = -1 and x = 12
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Edgar is a high school senior who has great grades and is at the top of his class. he just received a notification that he was awarded a few scholarships in the amounts of $4,500, $7,500, and $750. if his expected tuition with books and fees is $25,000, how much money will edgar need to pay for the rest of his education bill? show your work.
If Edgar is a high school senior who has great grades and just received a notification that he was awarded a few scholarships in the amounts of $4,500, $7,500, and $750 while his expected tuition with books and fees is $25,000, then the amount of money Edgar will need to pay for the rest of his education bill is equal to $12,250.
The amount of money Edgar will need to pay can be determined by the subtraction of the total tuition with books and fees from the total amount of scholarships awarded to Edgar.
The total amount of scholarships awarded to Edgar can be determined by the sum of all of the scholarships.
Total amount of scholarships = 4500 + 7500 + 750
Total amount of scholarships = $12,750
Now the amount that Edgar will need to pay for the rest of his education bill can be determined by subtraction.
Amount to be paid by Edgar = Tuition with books and fees - Total amount of scholarships
Amount to be paid by Edgar = 25,000 - 12750
Amount to be paid by Edgar = $12,250
Hence, the amount of money Edgar will need to pay for the rest of his education bill is calculated to be $12,250.
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13+(2^2xx7)-10 i need help with this i dont get it
The value of the expression 13 + (2^2 x 7) - 10 is 31
How to evaluate the expression?The expression is given as
13 + (2^2 x 7) - 10
Evaluate the exponent
So, we have
13 + (2^2 x 7) - 10 = 13 + (4 x 7) - 10
Evaluate the product
So, we have
13 + (2^2 x 7) - 10 = 13 + 28 - 10
Evaluate the sum
So, we have
13 + (2^2 x 7) - 10 = 41 - 10
Evaluate the difference
So, we have
13 + (2^2 x 7) - 10 = 31
Hence, the value of the expression 13 + (2^2 x 7) - 10 is 31
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the radius of Jupiter at its equator is approximately 2 * 5^2 * 11 * 79 miles. Use the formula A = 3.14r^2 to find the area of the cross section of the planet at the equator.
PLEASSEEE I NEED HELLPPP!!!!
The area of the cross section of the planet at the equator is 5. 92 × 10^9 square miles
How to determine the areaFrom the information given, we have the formula for area to be;
A = 3.14r²
Where 'r' is the radius of the shape
The radius of Jupiter = 2 * 5^2 * 11 * 79
This is simplified to = 2 × 25 × 11 × 79 = 43, 450
Substitute into the formula
Area = 3. 14 × (43, 450)²
Area = 3. 14 × 1. 89 × 10^9
Area = 5. 92 × 10^9 square miles
Thus, the area of the cross section of the planet at the equator is 5. 92 × 10^9 square miles
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Answer:
5,928,013,850
Look at this graph.
What is the equation of the line in slope-intercept form?
Answer: y = -4x + 3
Step-by-step explanation:
Line touches at point 3 on the y axis
Goes up 4 and left by 1
Determine whether the following statement is sometimes, always, or never true. Explain.
The distance between a line and a plane can be found.
The statement "The distance between a line and a plane can be found" is sometimes true.
Given,
The statement "The distance between a line and a plane can be found".
The distance between the point and the plane can be found by the taking a point on the line and finding the perpendicular distance from line to the plane.
But we can't apply this method in every case. We can only apply when either the line is parallel to the plane or the line intersects the plane.
Hence, the statement "The distance between a line and a plane can be found" is sometimes true.
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A bookstore has 45 copies of a bestseller available on Saturday morning. Twenty-one customers purchase the book that day. On Monday, a shipment of 25 books arrives and 14 copies are sold. Which statements are correct?
A The integer −21 represents the sale of 21 books.The integer −21 represents the sale of 21 books.
B After Monday's sales, 26 copies are available.After Monday's sales, 26 copies are available.
C The integer 25 represents the new shipment.The integer 25 represents the new shipment.
D After Monday's sales, 35 copies are available.After Monday's sales, 35 copies are available.
E The integer 14 represents the sale of 14 books.
(P.S it can have multiple answers)
The correct statements are:
The integer −21 represents the sale of 21 books.The integer 25 represents the new shipmentAfter Monday's sales, 35 copies are available.IntegersBooks available on Saturday morning = 45 copiesBooks purchased on Saturday = 21 copiesShipment of books on Monday = 25 copiesBooks sold on Monday = 14 copiesCheck all that applies:
A The integer −21 represents the sale of 21 books.
True
B After Monday's sales, 26 copies are available.
False
Saturday = 45 - 21
= 24 books available
Monday = 25 - 14
= 11 books available
Total books available = 24 + 11
= 35 copies available
C The integer 25 represents the new shipment.
True
D After Monday's sales, 35 copies are available.
True
E The integer 14 represents the sale of 14 books.
False
Therefore, option A, C and D are the correct statements.
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All the data collected in a particular study are referred to as the? inference data set variable population
A variable is any property, number, or quantity that can be measured or counted. Variables can also be referenced as data items.
Inference: Inference uses selected samples from a population to estimate the properties of unknown people.
A record (or record) is a collection of data. For tabular data, a record corresponds to one or more database tables, each table column represents a specific variable, and each row corresponds to a particular record in that data set.
Therefore:
All the data collected in particular is referred to as Data Set.
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The length of the roller coaster track from the top of a hill to the bottom of the hill is 125 feet at a 53°C angle with the vertical. If the position at the top of the hill is (x, y) , use function notation to describe the translation to the bottom of the hill. Round to the nearest foot.
(x + 100, y - 75) is the function notation used to characterise the translation to a bottom of the hill.
What is defined as Pythagorean Theorem?The Pythagorean theorem states that the sum of a squares on a legs of a right triangle equals the square on hypotenuse (this same side opposite this same right angle)—or, in recognizable algebraic notation, a² + b² = c².
Now, as per the given question;
From the shown diagram,
AC = b
Ab = c
We must find the coordinates of a point B. If C(x,y), then the coordinates of points A and B are:
A(x, y−b) and B(x+c, y−b)
We need to figure out b and c. To find c, we should use sine function.
sinC = perpendicular/hypotenuses
sinC = c/BC
Thus, c = BC sinC
c = 125sin53°
=125⋅0.79863551
c ≈100
To find b, we are using the Pythagorean Theorem.
BC² = AC² + AB²
125² = b² + 100²
b² = 125² - 100²
b = √5625
b = 75
The coordinates of a point B are as follows:
B(x+c, y−b)
B(x+100, y−75).
Therefore, the translation to the bottom of the hill defined by the function notation is B(x+100, y−75).
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Apply the order of operations to simplify each
expression
4.24-8×2÷4=
0
12
16
4
Answer:
4.24-(8*2)/4)=
4.24- 4= 0.24
Marcel made an error when he used the distributive property to write an equivalent expression.
Which sentence describes the error?) A) Both terms aren’t multiplied by 8x, so 8x can’t go in front of the parentheses.
b) 32x does not equal 8x⋅4.
c) 8x(2) does not equal 16x.
d) 32x and 16 have no factors in common.
The sentence describes the error is that A) Both terms aren’t multiplied by 8x, so 8x can’t go in front of the parentheses.
How to illustrate the information?It should be noted that the expression given is illustrated as 32x and 16.
In this case, it should be noted that the common factor between the expression is 8.
Therefore, the sentence describes the error is that both terms aren’t multiplied by 8x, so 8x can’t go in front of the parentheses.
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Answer: Therefore, the sentence describes the error in that both terms aren’t multiplied by 8x, so 8x can’t go in front of the parentheses.
Step-by-step explanation:
Ricardo went jet skiing while on vacation. The jet ski rental cost a flat rate of $25, plus $17.75 per hour. Ricardo had $102.17. How much did he have left after 3 hours of jet ski riding?
$23.92
$48.92
$53.25
$78.25
Ricardo will be left with $23.92 after 3 hours of Jet ski riding
How to calculate the amount left ?Ricardo is on vacation so he went jet skiing
The Jet ski has a rental flat rate of $25
They also charge $17.75 per hour
Ricardo had $102.17
The amount spent in 3 hours is
17.75(3) + 25
= 53.25 + 25
= 78.25
The amount left is
= 102.17 - 78.25
= 23.92
Hence Ricardo has $23.92 left after the Jet ski ride
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Solve for d. -19= d/7- 21
suppose that Angle Hik and Angle LIJ are verticle angles. find their measures if the following conditions apply. see picture
10. m∠HIK (2x+15)°, m∠LIJ = (5x-27)°, m∠HIK =
if they are vertice angles then they are equal to each other or
they both add up to 180°
A.
2x+15=5x-27
3x=42
x=14
B.
(2x+15)° + (5x-27)° = 7x-12
7x-12 = 180
7x=192
x = 27 3/7 or 27.43
The population of a city has increased by 28 since it was last measured. if the current population is 80000, what was the previous population?
According to the given statement The preceding population was = 62,500.
In mathematics, what is a percentage?A % is a relative figure that represents the hundredth part of any amount. One percent (symbolized 1%) is a one-hundred part; consequently, 100 percent denotes the complete amount and 200 percent defines twice the supplied amount.
What is the significance of the term "percentage"?Percent originated from the Latin adverbial phrase per centum, which means "by the hundred." The Latin phrase made its way into English in the 16th century. Later, it was abbreviated to % with a period. The period was eventually eliminated, and the two components amalgamated to form the contemporary one-word form %.
According to the given data:The current population of a city = 80000
A city's population has grown by 28% since the last census.
measured.
We have to calculate the previous population before increasing 28%.
Let the previous population be p
p +(28% × p) = 80000
p + 0.28p = 80000
1.28p = 80000
p = 80000/1.28
p = 62,500
The preceding population was = 62,500.
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Question 1
A pair of running shoes is on sale for $125.99. If the sale price is discounted 9% from the original price, what is the
original price?
Answer:
$138.45
Step-by-step explanation:
The original price was 100% of the original price since 100% is the whole thing.
The price was discounted by 9%.
100% - 9% = 91%
That means the discounted price is 91% of the original price.
Let x = original price.
91% of x = $125.99
0.91x = 125.99
x = 125.99/0.91
x = 138.45
Answer: $138.45
What is 1+10-70
Please help
Answer:
-59
Step-by-step explanation:
use pemdas
1+10-70
11-70
-59
write the point slope form of the equation of the line described question 17
Answer:
[tex]y - 2 = -\frac34(x - 4)[/tex]
Step-by-step explanation:
Hello!
The equation in #17 is written in Slope-Intercept Form: [tex]y=mx+b[/tex]
y = outputm = slopex = inputb = y-interceptPoint Slope form is the equation given slope and a point: [tex]y - y_1 = m(x - x_1)[/tex]
y = y - value of second pointy1 = y - value of first pointm = slopex = x - value of second pointx1 = x - value of first point.The point given to us is (4,-2), which we can use as x1 and y1.
The slope is given in the slope-intercept form equation: -3/4
Plug in the values to find the equation:
[tex]y - y_1 = m(x - x_1), (4,2), -\frac34[/tex][tex]y - 2 = -\frac34(x - 4)[/tex]The equation is [tex]y - 2 = -\frac34(x - 4)[/tex].
Answer questions 7 and 8 and I'll give brainliest (20 points)
7 - The geocentric model says that the earth is at the center of the cosmos or universe, and the planets, the sun and the moon, and the stars circles around it. The early heliocentric models consider the sun as the center, and the planets revolve around the sun.
8 - Modele A is the most accurate cause the sun, earth, & moon are in a straight line & in the time and space all the planets are in one straight line.
Hope this helps!
2xy; when x = 5 and y = 3x
30x is the value of the given equation .
WHAT IS MULTIPLICATION OF ALGEBRA ?Algebraic expression multiplication is the operation of multiplying two given expressions made up of variables and constants. An algebraic expression is one that incorporates variables and integer constants.
CALCULATIONx = 5
y = 3x
2xy = 2 * 5 * 3x ( plugging in the value )
= 30x
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