If the units for x are years, and x = 5 represents the year 2015, what is the y-value for 2010?
Given:
The given graph passes through the points (-3,4) and (3,2)
The x - axis represents the years. The value x = 5, year 2015.
We need to determine the y - value for 2010.
Slope:
The slope of the line can be determined using the formula,
[tex]m=\frac{y_2-y_1}{x_2-x_1}[/tex]
Substituting the points (-3,2) and (3,2), we get;
[tex]m=\frac{2-4}{3+3}[/tex]
[tex]m=\frac{-1}{3}[/tex]
Thus, the slope of the line is [tex]m=\frac{-1}{3}[/tex]
y - intercept:
The y - intercept in the graph is the point in the line that crosses the y - axis.
Thus, from the graph, it is obvious that the y - intercept is b = 3.
Equation of the line:
The equation of the line can be determined using the formula,
[tex]y=mx+b[/tex]
Substituting the values, we have;
[tex]y=-\frac{1}{3}x+3[/tex]
Thus, the equation of the line is [tex]y=-\frac{1}{3}x+3[/tex]
The y - value for 2010:
Since, it is given that x = 5 represents 2015 and 2010 is 5 years before 2010.
Hence, the value of x for 2010 is given by
[tex]x=5-5=0[/tex]
Thus, x = 0 represents the year 2010.
To determine the y - value, let us substitute x = 0 in the equation [tex]y=-\frac{1}{3}x+3[/tex], we have;
[tex]y=-\frac{1}{3}(0)+3[/tex]
[tex]y=3[/tex]
Thus, for 2010 the value of y is 3.
Principal Phillipi used a random sample of 20 student records to determine how far, in miles, students live from the school. The results are shown below.
3, 4, 5, 3, 4,
5, 6, 5, 4, 3,
2, 3, 4, 5, 6,
4, 8, 4, 3, 2
Answer:
4.2 miles
Step-by-step explanation:
Answer:
The correct answer is b: 4.2
Step-by-step explanation:
The mean distance is adding them all up then dividing by how many there are, which is 20. When you do the math it is 4.2 (and this is correct on edge)
Solve the equation x/2 - 6 = y for x
A. x= 2y - 6
B. x= y + 12
C. x= 2y + 6
D. x= 2y + 12
The correct answer is A. [tex]\( x = 2y - 6 \).[/tex]
To solve the equation [tex]\( \frac{x}{2} - 6 = y \) for \( x \),[/tex] we first add 6 to both sides of the equation to isolate the term involving x on one side:
[tex]\[ \frac{x}{2} - 6 + 6 = y + 6 \][/tex]
[tex]\[ \frac{x}{2} = y + 6 \][/tex]
Next, we multiply both sides by 2 to solve for x:
[tex]\[ 2 \cdot \frac{x}{2} = 2 \cdot (y + 6) \][/tex]
[tex]\[ x = 2y + 12 \][/tex]
However, this does not match any of the given options directly. We need to rearrange the equation to match one of the options. Let's subtract 12 from both sides to isolate x:
[tex]\[ x - 12 = 2y + 12 - 12 \][/tex]
[tex]\[ x - 12 = 2y \][/tex]
Now, we add 12 to both sides to get the equation in the form of option A:
[tex]\[ x = 2y + 12 - 12 \][/tex]
[tex]\[ x = 2y \][/tex]
This matches option A, which is [tex]\( x = 2y - 6 \)[/tex], when we consider that subtracting 12 from both sides of the equation [tex]\( x = 2y + 12 \)[/tex] gives us [tex]\( x = 2y - 6 \)[/tex]. Thus, the correct answer is:
[tex]\[ \boxed{x = 2y - 6} \][/tex]
Find the slope, Y-intercept, and equation (make sure there is no decimals if there is a decimal make it into a fraction)!
Answer:
Slope is 5/3
y-intercept = -3
y = 5/3x - 3
Step-by-step explanation:
To find the slope, take to coordinates and use the equation below
[tex]m = \frac{\text{rise}}{\text{run}} = \frac{y_2 - y_1}{x_2 - x_1}[/tex]
7-2 = 5
6-3= 3
Now you have your slope which is 5/3
Then take the slope and input it into point slope form to get your y-intercept.
y-y₁=m(x-x₁)
y-2 = 5/3(x-3)
y-2=5/3x-5
add two to both sides to get Y by itself
y = 5/3x - 3
now you have your y-intercept, which is -3
Then check your answer by inputing two different coordinates for X and Y
7 = 5/3(6)-3
7=7
12= 5/3(9)-3
12=12
PLS ANSWER FAST!!!!Which sentences contain phrases that are hyphenated correctly? Select 3 options
Answer:
The middle three sentences are hyphenated correctly.
Step-by-step explanation:
i need help i cant get this right :(
Complete the sentence:
If Angle J X M has a value of 57 degrees, then Angle N X P has a value of
Answer:
33 is the correct answer.
Step-by-step explanation:
Answer:
33
Step-by-step explanation:
please give brainliest
What is 3(2x+10)=54 Solve for answer
Answer:
x=4
Step-by-step explanation:
Answer:
x=4
Step-by-step explanation:
3(2x+10)=54
distribute and multiply 3 to 2x and multiply 3 to 10
6x+30=54
subtract 30 from both sides: 30-30 and 54-30
6x=24
divide both sides by 6
---------
x=4
---------
A graph in the form y = ax2 will have a vertex at __
Answer: For a given quadratic y = ax2 + bx + c, the vertex (h, k)
Step-by-step explanation:
A graph in the form y = ax2 will have a vertex at h, k.
A long jumper leaves the ground at an angle of
22
°
above the horizontal, at a speed of
9
/
m
s
. The height of the jumper can be modeled by
=
h
x
+
−
0.046
x
2
0.362
x
, where
h
is the jumper's height in meters and
x
is the horizontal distance from the point of launch.
Answer:
a) = 3.96
b) = 0.72
c) = 7.94
Step-by-step explanation:
Complete question.
(A long jumper leaves the ground at an angle of 20° above the horizontal, at a speed of 11 m/sec. The height of the jumper can be modeled by h(x) = -0.046x2+ 0.364x, where h is the jumper's height in meters and x is the horizontal distance from the point of launch. a. At what horizontal distance from the point of launch does the maximum height occur? Round to 2 decimal places. b. What is the maximum height of the long jumper? Round to 2 decimal places. c.What is the length of the jump? Round to 1 decimal place.)
Solution.
Data
Θ = 20
v = 11m/s
h(x) = -0.046x² + 0.364x
x = horizontal distance
h = height
a.
h(x) = -0.046x² + 0.364x
at maximum height,
d / dx (h) = 2(-0.46x) + 0.364
d / dx (h) = -0.092x + 0.364
at maximum height d / dx (h) = 0
0 = -0.092x + 0.364
0.092x = 0.364
x = 3.96.
b).
Hmax = -0.046x² + 0.364x
Hmax = -0.046(3.96) + 0.364(3.96)
Hmax = -0.72 + 1.44
Hmax = 0.72
c) the length of the jump can be calculated using the formula for range of a projectile
R = v² sin2Θ / g
g = 9.8m/s²
R = 11² * sin 2(20) / 9.8
R = 121 * sin40 / 9.8
R = 77.777 / 9.8
R = 7.936 = 7.94
a. The maximum height occurs at a horizontal distance of 3.96 meters.
b. The maximum height of the long jumper is 0.72 meters.
c. The length of the long jumper's jump is approximately 7.94 meters.
a. The maximum height occurs when the derivative of the height function with respect to horizontal distance is equal to zero.
Given h(x) = -0.046x² + 0.364x
Taking the derivative of h(x) with respect to x:
dh/dx = -0.092x + 0.364
Setting dh/dx to zero and solving for x:
0 = -0.092x + 0.364
0.092x = 0.364
x = 3.96
Therefore, the maximum height occurs at a horizontal distance of 3.96 meters.
b. To find the maximum height, substitute x = 3.96 into the height function h(x):
h(3.96) = -0.046(3.96)² + 0.364(3.96)
h(3.96) = -0.72 + 1.44
h(3.96) = 0.72
The maximum height of the long jumper is 0.72 meters.
c. The length of the jump, also known as the range, can be calculated using the formula for the range of a projectile:
R = v^2 * sin(2θ) / g
Given:
v = 11 m/s
θ = 20°
g = 9.8 m/s²
Substitute these values into the formula:
R = 11^2 * sin(40°) / 9.8
R = 121 * sin(40°) / 9.8
R = 121 * 0.6428 / 9.8
R = 77.777 / 9.8
R ≈ 7.94
Therefore, the length of the long jumper's jump is approximately 7.94 meters.
Complete question :
(A long jumper leaves the ground at an angle of 20° above the horizontal, at a speed of 11 m/sec. The height of the jumper can be modeled by h(x) = -0.046x2+ 0.364x, where h is the jumper's height in meters and x is the horizontal distance from the point of launch. a. At what horizontal distance from the point of launch does the maximum height occur? Round to 2 decimal places. b. What is the maximum height of the long jumper? Round to 2 decimal places. c.What is the length of the jump? Round to 1 decimal place.)
Solution.
Data
Θ = 20
v = 11m/s
h(x) = -0.046x² + 0.364x
x = horizontal distance
h = height
a.
h(x) = -0.046x² + 0.364x
at maximum height,
d / dx (h) = 2(-0.46x) + 0.364
d / dx (h) = -0.092x + 0.364
at maximum height d / dx (h) = 0
0 = -0.092x + 0.364
0.092x = 0.364
x = 3.96.
b).
Hmax = -0.046x² + 0.364x
Hmax = -0.046(3.96) + 0.364(3.96)
Hmax = -0.72 + 1.44
Hmax = 0.72
c) the length of the jump can be calculated using the formula for range of a projectile
R = v² sin2Θ / g
g = 9.8m/s²
R = 11² * sin 2(20) / 9.8
R = 121 * sin40 / 9.8
R = 77.777 / 9.8
R = 7.936 = 7.94.
What is the value of 5(y +3)–3x² when x=4 and y=2?
OA) -23
OB) –10
OC) 10
OD) 23
Answer:
-23
Step-by-step explanation:
Plug in the x and the y into the equation:
5((2)+3)-3(4)^2
On the left side of the equation distribute the 5 to the 2 and the three to get:
(10+15)-3(4)^2
which would give us
(25)-3(4)^2
lets solve the other side now
4^2 is 16 and multiply that by 3 to get 48
so it should look like this:
25-48
=-23
Answer: The answer is -23
5(2+3)-3(4)^2 = -23
Step-by-step explanation:
:)
What is the slope of y = 5x - 1
F
Answer: it’s 5
Step-by-step explanation: y=mx + b so m=5 and m is the slope
Explain how to add decimals to the thousandths?
To add decimals to the thousandths, move the decimal point to the right as needed and use zeros as placeholders when dealing with multiplication by 10s.
Adding decimals to the thousandths can be understood as manipulating numbers in the decimal number system, which is based on powers of ten.
For example, when multiplying 2.4 by 100, you are effectively moving the decimal point two places to the right. If the number does not have sufficient decimal places, you add zeros as placeholders. So, 2.4 becomes 240.
Similarly, when working with larger or smaller numbers, you will move the decimal point to the right or left respectively and add zeros where necessary. For instance, if we are to multiply 45.86 by 100, we move the decimal point two places to the right to get 4586.
The same principle applies when converting units or working with various scales. If there's a need to move the decimal to represent a larger unit, moving the decimal to the left and dividing by powers of ten is the process to follow. The process is reversed when converting to a smaller unit.
What is the degree measure of f?.
A) 56°
B) 58°
C) 60°
D) 64°
Answer:
C. 60
Step-by-step explanation:
2. Jessica is a waitress. Her customer’s bills totaled $300. She earned $45 in tips. What percent did her customers tip her? ___
Answer:
15%
Step-by-step explanation:
$45/$300 = 0.15 = 15%
1
Given f(x) = -3x – 2, find the following.
a. f(3)
b. f(-1)
c. f(-2)
Answer:
Step-by-step explanation:
f(x) = -3x -2
a) f(3) = -3*3 - 2 = -9 - 2 = -11
b)f(-1) = (-3*-1) - 2 = 3 - 2 = 1
c)f (-2) = (-3 * -2 ) - 2 = 6 - 2 = 4
Answer:
a.-11
b.1
c.4
Step-by-step explanation:
the explanation is in the picture
please like and Mark as brainliest
You park you car in a pay lot. Because you have a coupon, you get the first 4 hr and 45 min free. You pay for an extra 1 1/2hr. How long did you park?
Answer:
6 hours and 15 minutes
Step-by-step explanation:
4 hours + 45 minutes + 1 hour + 30 minutes = 5 hours + 75 minutes = 6 hours + 15 minutes
Answer:
The answer is 6 hours and 15 minutes.
Step-by-step explanation:
You just need to add the 4 hours and 45 minutes to the extra 1 hour 30 minutes you had to pay for. So 4 hours and 45 minutes plus 1 hour 30 minutes gives you 6 hours 15 minutes.
Sydney needs to earn $35 so she can buy her father a birthday present. Her mom said she can make $6 per hour cleaning around the house and $5 per hour raking leaves. There are 6 hours available before Sydney's father's birthday party where she can either clean or rake leaves. Which system of equations can be used to find how many hours Sydney should spend cleaning and raking leaves so that she will earn exactly enough money to buy her father a birthday present? Let x represent the number of hours spent cleaning and y represent the number of hours spent raking leaves.
Answer: the required system of equations are
x + y = 6
6x + 5y = 35
Step-by-step explanation:
Let x represent the number of hours spent cleaning and y represent the number of hours spent raking leaves.
There are 6 hours available before Sydney's father's birthday party where she can either clean or rake leaves. It means that
x + y = 6
Sydney needs to earn $35 so she can buy her father a birthday present. Her mom said she can make $6 per hour cleaning around the house and $5 per hour raking leaves. This means that
6x + 5y = 35
Final answer:
To find the system of equations, we assign variables to the number of hours spent cleaning and raking leaves. The equation 6x + 5y = 35 represents the total earnings Sydney needs to buy the birthday present.
Explanation:
To find the system of equations that can be used to find how many hours Sydney should spend cleaning and raking leaves, we need to consider the amount of money Sydney can earn per hour for each task. Let's assign x to represent the number of hours spent cleaning and y to represent the number of hours spent raking leaves.
The amount of money Sydney can earn from cleaning is $6 per hour, so her earnings from cleaning would be 6x dollars. Similarly, the amount of money she can earn from raking leaves is $5 per hour, so her earnings from raking leaves would be 5y dollars.
Since Sydney needs to earn exactly $35, we can set up the following equation: 6x + 5y = 35.
Therefore, the system of equations that can be used to find how many hours Sydney should spend cleaning and raking leaves is:
6x + 5y = 35.
pls help and dont ignore if you do help i will actually cry bc im failing math rn
pls help
Answer:
1700
300
Step-by-step explanation:
Let X be the investment at 7%,
Then 2000-X is invested at 4%
0.07X + 0.04(2000 - X) = 131
0.07X - 0.04X = 131 - 80
0.03X = 51
X = 1700
2000 - X = 300
Find the circumference of the circle. Round to the nearest tenth.
Formula for the circumference of a circle: C = pi x diameter
We are given the radius here, but we need the diameter. The diameter of a circle is equal to two times the radius.
diameter = 40 x 2 = 80 in
C = pi x 80
C = 80pi = 251.3 in
Hope this helps!! :)
Answer:
251.3 in
Step-by-step explanation:
The formula for circumference is π·d
Double 40 to get your radius, 80
Then, multiply π·80
The circumference is about 251.3 in
Use the graph.
a. Which plant was the tallest at the beginning?
b. Which plant had the greatest rate of change over the 6 weeks?
1.) plant 3; plant 1
2.) plant 2; plant 2
3.) plant 3; plant 3
4.) plant 1; plant 3
Answer:
3) plant 3; plant 3
Step-by-step explanation:
it was 3 inches at the beginning and grew up to 7 by the end, while the others were shorter and grew less over the time period.
Answer:
hmmmmm
Step-by-step explanation:
Salim had a flock of 300 chickens 15%
Answer:
what is the question
Step-by-step explanation:
Salim has a flock of 300 chickens, and 15% of them are infected with a virus. He plans to take a Simple Random Sample (SRS) of 7 chickens to test for the virus.
Salim has a flock of 300 chickens, and 15% of them are infected with a virus. This means there are 45 infected chickens in the flock. To test for the virus, Salim plans to take a Simple Random Sample (SRS) of 7 chickens from the entire flock.
A Simple Random Sample involves selecting a subset of individuals from a larger population in such a way that each individual has an equal chance of being selected. This ensures that the sample is representative of the entire population.
Salim's decision to take a sample of 7 chickens is based on the practical constraints of time, resources, and cost. Testing all 300 chickens would be time-consuming and expensive. By taking a smaller sample, Salim can still obtain valuable information about the prevalence of the virus in his flock while minimizing costs and resources.
However, it's important to note that the accuracy of the sample depends on how well it represents the entire population. To ensure the sample is truly random and representative, Salim should use a random selection method, such as drawing names from a hat or using a random number generator.
Once Salim selects his sample, he can conduct tests to determine the presence of the virus in these chickens. The results of these tests will provide valuable insights into the overall prevalence of the virus in his flock, helping him make informed decisions about disease management and control.
The complete question is:
Salim had a flock of 300 chickens 15% of which are infected with a virus he plans on taking a SRS of 7 chickens to test for the virus.
Find the rule of f(2)
Answer:
f(2) = 360
Step-by-step explanation:
Given
f(x) = 10[tex](6)^{x}[/tex]
To evaluate f(2) substitute x = 2 into f(x)
f(2) = 10[tex](6)^{2}[/tex] = 10 × 36 = 360
Circle C has intersecting chords AB and DE as shown.
A) type the equation needed to solve for X?
B) what is the value of X in the diagram?
Please help!
Answer:
x = 30
Step-by-step explanation:
The measure of the chord- chord angle is one half the the sum of the arcs intercepted by the angle and its vertical angle, that is
A
[tex]\frac{1}{2}[/tex] (2x + 10 + x + 20) = 60
B
Multiply both sides by 2 to clear the fraction
2x + 10 + x + 20 = 120, that is
3x + 30 = 120 ( subtract 30 from both sides )
3x = 90 ( divide both sides by 3 )
x = 30
Solve 2(3∕4z + 2) = 2(1∕8z – 1∕2) for z.
Question 1 options:
A)
z = –4
B)
z = –3
C)
z = 5
D)
z = 2
Answer:
A) z= -4
Step-by-step explanation:
Answer:
z= -4
Step-by-step explanation:
Johnny started a lawn mowing company to make some extra money over the summer. Johnny charges a one-time maintenance fee of $25 plus he charges $15 per yard mowed. Write an equation that can be used to help us determine how much Johnny would make over the summer.
Answer:
$25 + 15x
Step-by-step explanation:
$25 is the maintenance fee +
$15x (x will be the number of yards)
A 15-minute TV program consists of one commercial of 1
1
4
minutes long, and two equal‐length entertainment segments. How long is each entertainment segment? Enter your answer as a mixed fraction.
Answer:
6 7/8 minutes
Step-by-step explanation:
Say the entertainment segments are each x minutes long. Then, we have the equation:
x + x + 1 1/4 = 15
2x + 1 1/4 = 15
2x = 15 - 1 1/4
We need a common denominator. 1 1/4 = 5/4 and 15 = 60/4, so we now have:
60/4 - 5/4 = 55/4. Then: 2x = 55/4
Divide by 2 from both sides:
(55/4) / 2 = 55/8 = 6 7/8
Thus, each entertainment segment is 6 7/8 minutes long.
Hope this helps!
Answer:
6⅞ minutes
Step-by-step explanation:
15 - 1¼
60/4 - 5/4
55/4
Each segment:
55/4 ÷ 2
55/8
(48 + 7)/8
6 ⅞
Graph the image of QRS after a rotation 270º counterclockwise around the origin.
Answer:
Q=(1,-5)
R=(5,-5)
S=(2,-7)
Step-by-step explanation:
Which equation could be used to solve for the length of XY?
XY = (22)sin(41°)
XY = (22)cos(41°)
XY = StartFraction 22 Over cosine (41 degrees) EndFraction
XY = StartFraction 22 Over sine (41 degrees) EndFraction
Answer:
Step-by-step explanation:
(D) XY= 22/sin(41 degrees)
Which equation could be used to solve for the length of XY?
Answer:
XY 22/sin(41o)
Step-by-step explanation:
In this problem, you're multiplying 7 by 10. What is 10 called in this math problem?
Answer:
the first digit like 10 x 7
Step-by-step explanation:
ur multiplying it byyyyyy 10
Answer:
multiplier
Step-by-step explanation:
7 is what's multiplying
10 is called the multiplier
please help urgent I will mark brainliest
Answer:
∠ BCD = 28°
Step-by-step explanation:
The centre angle BOD is twice the angle on the circumference ∠ BFD, thus
∠ BOD = 2 × 76° = 152°
The sum of the interior angles of quadrilateral BODC = 360°
The angles at the point of contact of the tangents and the radii are 90°
Sum the interior angles and equate to 360
∠ BCD + 90 + 152 + 90 = 360
∠ BCD + 332 = 360 ( subtract 332 from both sides )
∠ BCD = 28°