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Answer: [tex]\textsf{y = 4x - 12}[/tex]
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Given: [tex]\textsf{Slope = 4, Point = (2, -4)}[/tex]
Find: [tex]\textsf{The equation in slope-intercept form}[/tex]
Solution: We need to plug in the values into point-slope form and after simplifying, distributing, and solving for y we will have our equation in slope-intercept form.
Plug in the values
[tex]\textsf{y - y}_1\textsf{ = m(x - x}_1\textsf{)}[/tex][tex]\textsf{y - (-4) = 4(x - 2)}[/tex]Distribute and simplify
[tex]\textsf{y + 4 = 4(x - 2)}[/tex][tex]\textsf{y + 4 = (4 * x) + (4 * -2)}[/tex][tex]\textsf{y + 4 = 4x + (-8)}[/tex][tex]\textsf{y + 4 = 4x - 8}[/tex]Subtract 4 from both sides
[tex]\textsf{y + 4 - 4 = 4x - 8 - 4}[/tex][tex]\textsf{y = 4x - 8 - 4}[/tex][tex]\textsf{y = 4x - 12}[/tex]Using the information that was provided in the problem statement we were able to determine that the equation in slope-intercept form was y = 4x - 12.
Answer:
y = 4x - 12
Step-by-step explanation:
Given:
slope of 4, and point (2, -4)
Here, we're being asked to write the equation in Slope-Intercept Form. As we have been given the slope and a point on the line, we can use the Point-Slope Form to be able to find that equation.
First, know the two forms:
⇒ Point-Slope Form: y - y₁ = m(x - x₁)
where: m is the slope, and (x₁, y₁) is the given point
⇒ Slope-Intercept Form: y = mx + b
where: m is the slope, and b is the y-intercept
Now, substitute the given values into the Point-Slope Form:
⇒ y - y₁ = m(x - x₁)
⇒ y - (-4) = 4(x - 2) [simplify]
⇒ y + 4 = 4x - 8
Change to the Slope-Intercept Form:
⇒ y + 4 = 4x - 8 [subtract 4 from both sides]
⇒ y + 4 - 4 = 4x - 8 - 4
⇒ y = 4x - 12
Therefore, the equation of the line in slope-intercept form is: y = 4x - 12
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Solve equation
-15+n=-9
Convert scientific notation to decimal format.
9.8*10^-9
Answer:
- 9,800,000,000
Step-by-step explanation:
9.8 * [tex]10^{-9}[/tex]
Simplify 10 with exponent
[tex]{10}^{-9}[/tex] = -10 with 9 zeroes
Rewrite
[tex]{10}^{-9}[/tex] = -1,000,000,000
Place back into expression
9.8 * -1,000,000,000
Simplify by multiplying
- 9,800,000,000
Let me know if you have any questions!
I need help with a question
Answer:
y = 3
x = -15
Step-by-step explanation:
When substituting, we want to get rid of one of the variables. (It's easiest ot find the variable in terms of other variable)
so, we know that...
x + 5y = 0
- 5y - 5y
x = -5y
We can plug this x-value into the second equation to find our y-value:
3y + 2x = -21
3y + 2(-5y) = -21
3y - 10y = -21
-7y = -21
÷ -7 ÷ -7
y = 3
So, if x = -5y,
x = -5y
x = -5(3)
x = -15
(we can test these values in one of the original equations):
x + 5y = 0
(-15) + 5(3)= 0
-15 + 15 = 0
{true}
so, y = 3 ; and x = -15
hope this helps!! :)
En una tienda comercial anuncia descuentos sucecivos del 30% y 20% en todos los electrodomésticos, ¿Que descuento único equivale?
Answer:
0
Step-by-step explanation:
Solve the compound inequality for x and identify the graph of its solution.
x+7>3 and x-5≤-1
O A. Solution: x<-4 or x ≥ 4
-5-4-3 -2 -1 0 1 2 3 4 5
OB. Solution: x>-4 and x≤ 4
-5-4-3 -2 -1 0 1 2 3 4 5
O C. Solution: x>-4 and x≤ 4
-5 -4 -3 -2 -1 0 1 2 3 4 5
OD. Solution: x²-4 and x < 4
Answer:
C is the answers for the question
Step-by-step explanation:
please mark me as brainlest
select the most appropriate measurement for each of the following
Answer:The following what
Step-by-step explanation:
what is the following and there is no questions.
2/6+5/6 as a whole number
Answer: 2/6+5/6 + 1.167
Answer:
1.16
Step-by-step explanation:
Divide: 1,485 ÷ 0.09
1,485 ÷ 0.09
Answer:
16500
Step-by-step explanation:
PLEASE HELP ME!!! I'M ON A SERIOUS TIME CRUNCH!!!
Given the graph of trapezoid FOUR and its reflection. Use the coordinates of the images’ vertices, U and U' to to algebraically find the line of reflection.
x = -1
y = 1
x = 1
y = -1
Answer:
y = -1
Step-by-step explanation:
Because the coordinate of U and U' is (5, 0) and (5, -2), the line that is right in the middle would be y = -1.
Or you can compare two of the coordinates to create the line of reflection.
For example: R (0,0), R'(0, -2)
U(5, 0), U'(5, -2)
The middle points are (0, -1) (5, -1).
In this case, y = -1.
A portion of John Locke's time card is shown below. How many hours did he work for the week?
PLS PLS HELP IVE BEEN STUCK ON THIS FOR A VERY LONG TIME AND PLS IF YOU DONT KNOW THE ANSWER DONT ANSWER!!!!!
Answer:
40
Step-by-step explanation:
it's 8+8+8+7+9 so it's gonna be 40
choose the system of equations!!
Answer:
It is the FOURTH OPTIONor D
Rosa has $12.29 and spends $4.85. To the nearest dollar, about how much does she have left?
A $3
B $5
C $7
D $9
The perimeter of a triangle is 84 cm and it's area is 336cm².If one of it's sides is 30 cm find the length of other two sides.
Answer:
26,28
Step-by-step explanation:
We can make a system of equations based on the information given
first we can make one for the perimeter
and one for the area using herons formula
(x and y are the two unknown sides)
[tex]84=30+x+y[/tex]
[tex]336=\sqrt{42(12)(42-x)(42-y)}[/tex]
Now solve for x and y or you can find it by graphing
x and y = 26 and 28, the order does not matter since they are both unkown
so the two sides are 26 and 28
Solve for x in the diagram below.
Answer:
x = 20°
Step-by-step explanation:
x° + 2x°+ (x+10)° = 90°
4x° + 10° = 90°
4x° = (90 -10)°
x° = (80/4)°
x = 20°
Hope this helps
Answer:
x = 20
Step-by-step explanation:
Key points:
understanding diagram notationunderstanding the Angle Addition PostulateDiagram notation
In the diagram, there are three angles, each with an expression representing the measure of their angle (in degrees). Angles are adjacent (next to each other with the same vertex) such that collectively they form one large angle.
The small square in the lower left corner means that the large angle is a right angle. All right angles are 90°.
Note: The expressions for each angle all have a degree marking, so each angle is measured in degrees. The unknown value x, is a number without any units, the expression is simplified, and then the units "degrees" are applied. So in the end, the answer for "x" will not have units; "x" will just be a number.
Angle Addition Postulate
The Angle Addition Postulate states that the sum of the measures of two adjacent angles is equal to the measure of the large angle formed by those adjacent angles.
[tex](\text{measure of first angle})+(\text{measure of second angle})=(\text{measure of the combined angle})[/tex]
Solving the given problem
By applying the Angle Addition Postulate a couple times, the sum of the measures of all three angles in the diagram is equal to the measure of the large angle formed by those three angles.
[tex](\text{measure of first angle})+(\text{measure of second angle})+(\text{measure of third angle})=(\text{measure of the large right angle})[/tex]
or
[tex](x)+(2x)+(x+10)=(90)[/tex]
From here, to solve for x, we'll need to combine like terms, isolate x, and simplify.
Start with the Associative Property of Addition to combine like terms:
[tex](x+2x+x)+10=90\\4x+10=90[/tex]
To isolate x, subtract 10 from both sides and simplify...
[tex](4x+10)-10=(90)-10\\4x=80[/tex]
... then divide by 4 on both sides and simplify.
[tex]\dfrac {4x}{4}=\dfrac {80}{4}\\x=20[/tex]
So, x=20
3 *(x-7)*(x+7)-(x-1)*(3x+2)=13
The value of x will be 158. The value of x is obtained by simplifying the equation.
What is the equation?A mathematical statement consisting of an equal symbol between two algebraic expressions with the same value is known as an equation.
Identity used;
(x+a)(x-a) = x² - a²
Given expression;
3(x-7)(x+7) - (x-1)(3x+2) = 13
Solving the equation step by step;
[tex]\rm 3(x^2 - 7^2 ) - [x(3x+2)-1(3x+2) ]= 13\\\\ 3x^ 2 -147 -[3x^2 +2x -3x-2] = 13 \\\\ 3x^2 -147 -[3x^2 -x-2] = 13\\\\ 3x^2-147-3x^2 +x+2 = 13 \\\\ x= 13+145 \\\\ x= 158[/tex]
Hence, the value of x will be 158.
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Mary is running a marathon which is a total of 26 miles. She is running at a pace of 7.5 miles per hour and
has already run 8 miles. If she stays at the same pace, how much time in hours does she have left? (Round your answer to the nearest tenth)
===================================================
Explanation:
She has already ran 8 miles, so she has 26-8 = 18 miles left to go.
She runs at a pace of 7.5 mph, which means she has 18/(7.5) = 2.4 hours left to go.
I used the equation distance = rate*time, and solved for time to get time = distance/rate.
--------------------
Another approach:
Here's how you can use algebra.
x = time she has left in hours
7.5x = distance covered in those x hours
7.5x+8 = total distance
7.5x+8 = 26
7.5x = 26-8
7.5x = 18
x = 18/(7.5)
x = 2.4
Each statement describes a transformation of the graph of y= x. Which statement correctly describes the graph of y= x+ 9.5?
a. it is the graph of y= x where the slope is increased by 9.5 .
b. it is the graph of y= x translated 9.5 units to the right.
c. it is the graph of y= x translated 9.5 units up.
d. it I'd the graph of y= x translated 9.5 units down.
Answer: C
Step-by-step explanation: The graph is going to go up because the +9.5 isn't in any parentheses. If it was, that would mean it would move horizontally. I hope this helps!
The correct statement:
It is the graph of y = x translated 9.5 units up.
The correct option is c.
The equation y = x represents a straight line passing through the origin with a slope of 1. When we have the equation y = x + 9.5, it means that for every x-value, the corresponding y-value is obtained by adding 9.5 to the original x-value. This translation in the y-direction shifts the entire graph upward by 9.5 units.
To visualize this, imagine the original line y = x. Each point on this line has an x-coordinate and a corresponding y-coordinate, which are the same due to the equation y = x. When we add 9.5 to each y-coordinate, the line shifts vertically by 9.5 units without any change in slope or horizontal position.
The other options can be eliminated because the statement does not mention changing the slope or the horizontal position of the graph. Instead, it specifically describes a vertical translation, indicating a movement in the y-direction. Therefore, the correct answer is c.
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Timothy has a savings account that he started five years ago to begin saving for college. The
savings account has an interest rate of 3% and has earned $225 in interest since he began the
account. How much money did Timothy start the account with when he originally opened the
savings account?
A. $1500.00
B. $33.75
C. $7500.00
D. $3375.00
of $18
Answer:
A. $1500.00
Step-by-step explanation:
Assuming this is a simple interest savings account.
Simple interest formula
I = Prt
where:
I = total interestP = principal amountr = interest rate (in decimal form)t = time (in years)Given:
I = $225r = 3% = 0.03t = 5 yearsSubstitute the given values into the formula and solve for P:
⇒ I = Prt
⇒ 225 = P(0.03 ×5)
⇒ 225 = P(0.15)
⇒ P = 225 ÷ 0.15
⇒ P = 1500
Therefore, Timothy started the account with $1500.00.
Given ST|UV and SU || TV, find the measure of each angle below.
Find the angle of STU
Find the angle of TVW
Answer: [tex]\angle STU=34^{\circ}, \angle TVW=116^{\circ}[/tex]
Step-by-step explanation:
By the alternate interior angles theorem,
[tex]3x+4=2x+14\\\\x+4=14\\\\x=10\\\\\implies \angle STU=3(10)+4=\boxed{34^{\circ}}[/tex]
By the alternate interior angles theorem, [tex]\angle UTV=82^{\circ}[/tex], and we also know that [tex]\angle TUV=34^{\circ}[/tex].
Thus, by the exterior angle theorem,
[tex]\angle TVW=82+34=\boxed{116^{\circ}}[/tex]
Squares are cut out of the corners of a piece of 18*18 graph paper so that the sides can be folded to make an open box. What is the largest possible number of cubic units in the volume of the box if we require that the length of each edge is a whole number?
Answer:
432 mm²
Step-by-step explanation:
We need to cut out 3x3 squares from corners and make an open box. It's height will be 3mm(see the plan). So volume will be:
V = 12 * 12 * 3 = 432mm²
Teresa is factoring this polynomial by grouping. Which common factors should be used in the next step of factoring?
10x3+3x2−20x−6
(10x3+3x2)+(−20x−6)
x2 and −2x
2x2 and −2x
x2 and −2
2x2 and −2
Answer: [tex]x^2[/tex] and [tex]-2[/tex]
Step-by-step explanation:
original :
[tex](10x^3+3x^2)+(-20x-6)[/tex]
factored :
[tex]x^2(10x+3)+-2(10x+3)[/tex]
Answer :
[tex]x^2[/tex] and [tex]-2[/tex]
√2/√2+√3-√5 rationalise the denominater
Answer:
Multiply the denominator and numerator with root 2 to get a fair denominator and simplify if needed. Hope it helps
Answer:
1 + √3 - √5
Step-by-step explanation:
The given √2/√2 equals 1, and so we now have 1 + √3 - √5, whose denominator is the integer 1. There's nothing left to rationalize.
the scale on a map is 1 cm to 2 cm what is the actual distance between two town if the distance on the map is 5.5
If the distance on the map is 5.5 cm. Then the actual distance between two town will be 11 miles.
The complete question is given below.
The scale on a map is 1 cm to 2 miles. What is the actual distance between two town if the distance on the map is 5.5 cm.
What is dilation?Dilation is the process of increasing the size of an item without affecting its form. Depending on the scale factor, the object's size can be raised or lowered.
The scale on a map is 1 cm to 2 miles.
If the distance on the map is 5.5 cm.
Then the actual distance between two town will be
⇒ 5.5 cm = 5.5 × 2 miles
⇒ 5.5 cm = 11 miles
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graph of an equation is shown below:
Based on the graph, which of the following represents a solution to the equation?
O(-2,-3)
O (3, 1)
O (1,3)
(3,2)
Answer:
Coordinates follow (x,y) so to find a solution to the line you want to find a point in (x,y) form which is on the line.
This means (1,3) is a solution because at x=1 and y=3 it is on the line.
C | (1,3)
What is the greatest common factor of 10 and 3? i dont get this i have a math touter that wont really help and i still dont understand. by the way i was not using brainly touter.
if u have the time to help please answer
Answer:
1
Step-by-step explanation:
listing the factors of both numbers
factors of 10 are 1, 2, ,5, 10
factors of 3 are 1, 3
the only common factor to both is 1
the greatest common factor is 1
Lindsey is a member of the swim team at a local university. She has been working hard to perfect her dive for an upcoming swim meet. Lindsey's dive can be modeled by the quadratic equation y = – 16x2 + 33x + 45, where x is time in seconds, and y is Lindsey's height in the air in feet.
1. At what time will Lindsey be 30 feet in the air?
2. How high is the diving board? Explain your thinking.
Answer:
1. [tex]x = 2.45s[/tex]
2. The diving board is 45 ft high.
Step-by-step explanation:
• When Lindsey is 30 feet in the air, y = 30.
[tex]30 = -16x^2 + 33x +45\\\\-16x^2 + 33x +15 = 0\\\\16x^2 - 33x -15 = 0\\[/tex]
Using quadratic formula, solve for x:
[tex]x = \frac{33 + \sqrt[]{(-33)^2 - 4(16)(-15)} }{2(16)}[/tex]
[tex]x = 2.45s[/tex]
• If we calculate the height of Lindsey in the air when she is standing on the diving board, we can find the height of the diving board above the ground.
When she is standing on the board, x = 0 as no time has passed after jumping.
[tex]y = -16(0)^2 + 33(0) +45\\\\y = 45 ft[/tex]
Helppppppppp plssssss
The swimming pool at Spring Valley High School is a rectangle with a width of 70 meters and a length of 30 meters. Around the perimeter of the pool is a tiled floor that extends w meters from the pool on all sides. Find an expression for the area of the tiled floor.
The expression for the area of the rectangular swimming pool is given as follows:
A = w² + 100w + 2100.
What is the area of a rectangle?The area of a rectangle of length l and width w is given by the multiplication of these measures, that is:
A = lw.
In this problem, considering the width of 70 meters and a length of 30 meters, plus the floor of w meters, we have that:
l = 30 + w.wi = 70 + w.Hence the area is given as follows:
A = l x wi = (30 + w)(70 + w) = w² + 100w + 2100.
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Which distance measures 7 units? L 50+5 7 -8 -7 -6 5 4 3 -2 -1 0 1 2 O the distance between points L and M O the distance between points L and N O the distance between points M and N the distance between points M and P 3 4 OL 5 6 s 8
The distance that measures 7 units is the distance between points M and P
How to determine the distance?The complete question is in the attached image
The points are given as:
L= -7
M = -1
N = 2
P = 6
The distance between any points A and B is calculated using:
AB = |B - A|
Using the above formula, we have:
MP = |6 -(-1)|
Evaluate the difference
MP = |7|
Remove absolute bracket
MP = 7 units
Hence, the distance that measures 7 units is the distance between points M and P
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How many solutions does the following system of equations have?
Answer:
1
Step-by-step explanation:
Solutions to a systems of equations are when the (x, y) of two equations are equal with both equations remaining true or in other words when both equations intersect. So by looking at the graph, both equations seem to be linear so there should only be 0, 1, or infinitely many solutions. Since they do have one intersection there is only 1.
Answer:
The system of equations only has 1 solution.
Explanation:
This can be seen by looking at the graph and seeing where the lines were to intersect. For example, if the lines were parallel and never intersected, then there would be 0 solutions. On the other hand, if the lines were essentially the same and overlapped at every point, then there would be infinitely many solutions.
