Answer:
y = 5x + 3
Step-by-step explanation:
The equation of a line in slope- intercept form is
y = mx + c ( m is the slope and c the y- intercept )
here m = 5, hence
y = 5x + c
The line passes through the y- axis at (0, 3) ⇒ c = 3
y = 5x + 3 ← equation of line
Please help fast I'll let you know if u got it right:)
Answer:
the answer is 15 to the nearest tenth
Answer:
add all the points together like
1+3+4+6+6+7+7+7+8+8+8+8+9+9+9+15= 115
the divide by the total number of elements we have. as so
115÷16= 7.18
rounding that to the nearest tenth is going to 7.2
Step-by-step explanation:
hope this helps
correct me if I'm wrong
The height (in feet) of a rocket launched from the ground is given by the function f(t) = -16t2 + 160t. Match each value of time elapsed (in seconds) after the rocket’s launch to the rocket's corresponding instantaneous velocity (in feet/second).
t = 2 96 t = 3 -64 t = 4 32 t = 5 0 t = 6 -128 t = 7 -32 t = 8 t = 9
Answer:
t = 2 s= 96
t = 3 s = 64
t = 4 s= 32
t= 5 s = 0
t= 6 s = -32
t = 7 s = -64
t = 8 s = -96
t= 9 s = -128
Step-by-step explanation:
We have the equation of the position of the rocket as a function of time t.
[tex]f(t) = -16t^2 + 160t[/tex]
The instantaneous velocity of the rocket as a function of time is given by the derivation of the position with respect to time.
So
[tex]S(t)=\frac{df(t)}{dt} = -2*16t + 160\\\\S(t) = -32t+160[/tex]
[tex]s(1) = -32(1)+160=128\ ft/s\\\\s(2) = -32(2)+160=96\ ft/s\\\\s(3) = -32(3)+160=64\ m/s\\\\s(4) = -32(4)+160=32\ m/s\\\\s(5) = -32(5)+160=0\ m/s\\\\s(6) = -32(6)+160=-32\ m/s\\\\s(7) = -32(7)+160=-64\ m/s\\\\s(8) = -32(8)+160=-96\ m/s\\\\s(9) = -32(9)+160=-128\ m/s[/tex]
So
t = 2 s= 96
t = 3 s = 64
t = 4 s= 32
t= 5 s = 0
t= 6 s = -32
t = 7 s = -64
t = 8 s = -96
t= 9 s = -128
Final answer:
To match time values with the rocket's velocity after launch, we take the derivative of the position function f(t) to obtain the velocity function v(t) = -32t + 160. The corresponding velocity for each time value can be calculated by plugging the time into the velocity function.
Explanation:
The height of a rocket as a function of time after launch is given by f(t) = -16t2 + 160t, and we are asked to match each value of time elapsed with the rocket's corresponding instantaneous velocity. To find the instantaneous velocity, we need to take the derivative of the position function with respect to t, which represents time in seconds. The derivative of f(t) with respect to t is f'(t) = -32t + 160. This is the velocity function v(t), which gives the instantaneous velocity at any given time t.
At t = 2, the velocity v(2) = -32(2) + 160 = 96 feet/second.
At t = 3, the velocity v(3) = -32(3) + 160 = 64 feet/second.
At t = 4, the velocity v(4) = -32(4) + 160 = 32 feet/second.
At t = 5, the velocity v(5) = -32(5) + 160 = 0 feet/second. (This is the point at which the rocket reaches its peak and starts descending.)
At t = 6, the velocity v(6) = -32(6) + 160 = -32 feet/second (indicating the rocket is now falling back to the ground).
The values for t = 7, t = 8, and t = 9 can be calculated in a similar manner using the velocity function v(t).
The axis of symmetry for the function f(x) = −x2 − 10x + 16 is x = −5. What are the coordinates of the vertex of the graph?
Answer:
The coordinates of the vertex are (-5, 41)
Step-by-step explanation:
For a quadratic function of the form
[tex]f(x) = ax ^ 2 + bx + c[/tex]
Where a, b and c are constants and represent the coefficients of the function, then the symmetry of the parabola always passes through its vertex.
In this case we have the following parabola
[tex]f (x) = -x2 - 10x + 16[/tex]
And we know that its axis of symmetry is the line [tex]x = -5[/tex]
Then we know that this axis of symmetry passes through the vertex of the parabola.
Therefore, the x coordinate of the vertex is -5.
To find the coordinate in y of the vertex, we substitute x = -5 in the function.
[tex]f (-5) = -(- 5) ^ 2 -10 (-5) +16\\\\f (-5) = 41[/tex]
Finally, the vertices are in the point (-5, 41).
Write an equation of the lines that passes through (-1,6) and (4,1)
[tex]\bf (\stackrel{x_1}{-1}~,~\stackrel{y_1}{6})\qquad (\stackrel{x_2}{4}~,~\stackrel{y_2}{1}) \\\\\\ slope = m\implies \cfrac{\stackrel{rise}{ y_2- y_1}}{\stackrel{run}{ x_2- x_1}}\implies \cfrac{1-6}{4-(-1)}\implies \cfrac{1-6}{4+1}\implies \cfrac{-5}{5}\implies -1 \\\\\\ \begin{array}{|c|ll} \cline{1-1} \textit{point-slope form}\\ \cline{1-1} \\ y-y_1=m(x-x_1) \\\\ \cline{1-1} \end{array}\implies y-6=-1[x-(-1)]\implies y-6=-1(x+1) \\\\\\ y-6=-x-1\implies y=-x+5[/tex]
How much of a radioactive kind of ruthenium will be left after 6 days if the half-life is 3 days and you start with 80 grams?
After 6 days, 20 grams will be left from the original 80 grams.
The half-life is the time it takes for half of the radioactive substance to decay. In this case, the half-life of ruthenium is given as 3 days. Starting with an initial quantity of 80 grams, we can calculate the remaining quantity after each half-life period.
After the first 3 days, one half-life will have passed, and half of the 80 grams will have decayed:
80 g / 2 = 40 g remaining.
After the second 3 days, another half-life will have passed, so another half of the remaining 40 grams will have decayed:
40 g / 2 = 20 g remaining.
Therefore, after 6 days, which corresponds to two half-life periods, 20 grams of the radioactive isotope of ruthenium will be left.
The value of x is..............???
Answer:
x = 3
Step-by-step explanation:
There are two ways to do this. The simplest way is to realize that the exterior angle (45x) = the sum of the two remote interior angles.
25x and 57 + x
45x = 25x + 57 + x Subtract 26x from both sides.
45x - 26x = 25x - 25x + 57 Combine
19x = 57 Divide by 20
19x/19 = 57/19 Do the division
x = 3
===================================
Second method.
The supplement of the 45x angle is 180 - 45x
Now add the three angles together.
180 - 45x + x + 57 + 25x = 180 Combine like terms.
180 + 57 - 45x + x + 25x = 180
237 - 19x = 180 Subtract 237 from both sides.
- 19 x = 180 - 237 Combine the right side
- 19x = -57
x = 3
Good thing you made me redo it. Sorry!! I made an error. I lost 1 of the xs.
there are 3/7 as many girls as ther are boys in a field.thereare 64 more boys than girls in how many children are in the field.
Answer:
160 children, 112 boys and 48 girls.
Step-by-step explanation:
You can translate this into two equations:
g = 3/7 * b
g+64 = b
Then fill in one in the other and simplify:
3/7 b + 64 = b =>
4/7 b = 64
b = 64 * 7/4 = 112
g = 112 * 3/7 = 48
Final answer:
By setting up equations with the given proportions and difference in numbers, we can calculate that there are 112 boys and 48 girls in the field, totaling 160 children.
Explanation:
To solve the problem of how many children are in the field, we need to set up an equation based on the information given. It states that there are 3/7 girls there are boys, and that there are 64 more boys than girls. Let's define the number of boys as B and the number of girls as G. According to the problem, B = G + 64 and G = (3/7) * B.
To find the solution, we need to substitute G from the second equation into the first to get B = (3/7) * B + 64. Simplifying this equation, we multiply both sides by 7 to get rid of the fraction 7B = 3B + 448. Then we subtract 3B from both sides yielding 4B = 448. Dividing both sides by 4 gives us B = 112. Now that we have the number of boys, we can find the number of girls using the second equation: G = (3/7) * 112 = 48. Finally, we add the number of girls and boys to find the total number of children in the field 112 + 48 = 160.
What is the value of x in the equation 2(x+3)=4(x-1)
Step 1: Distribute the 2 to numbers and variables inside parentheses
(2 × x) + (2 × 3) = 4 (x - 1)
2x + 6 = 4 (x - 1)
Step 2: Distribute the 4 to numbers and variables inside parentheses
2x + 6 = (4 × x) + ( 4 × - 1)
2x + 6 = 4x+ (-4)
2x + 6 = 4x- 4
Step 3: Combine like terms (x's go with x's) by subtracting 2x to both sides
(2x - 2x) + 6 = (4x - 2x) - 4
6 = 2x - 4
Step 4: Combine like terms by adding 4 to both sides
6 + 4 = 2x - 4 + 4
10 = 2x
Step 5: Isolate x by dividing 2 to both sides
10 ÷ 2 = 2x ÷2
5 = x
x = 5
To check: plug 5 into all the x's of the equation
2(x+3)=4(x-1)
2(5+3)=4(5-1)
2(8) = 4(4)
16 = 16
Hope this helped!
Answer:5
Step-by-step explanation:
b) Work out (6 * 10^2) /(3 x 10^-5)
Give your answer in standard form.
The result of the calculation (6 * 10^2) / (3 x 10^-5) is 2 x 10^7, when written in standard form.
Explanation:To solve the equation (6 * 10^2) / (3 * 10^-5), we first simplify both sides. 6 * 10^2 equates to 600, and 3 x 10^-5 equates to 0.00003. Therefore, we are left with the simple division: 600 / 0.00003.
To divide these two numbers, you would get a result of 20000000. However, the problem asks for the answer in standard form. Standard form is a way of writing numbers that are too large or too small to be conveniently written in decimal form. In standard form, 20000000 is represented as 2 x 10^7.
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math algebra Please help pick the best answer please
[tex]\bf \cfrac{4}{~~\frac{1}{4}-\frac{5}{2}~~}\implies \cfrac{\frac{4}{1}}{~~\frac{1}{4}-\frac{5}{2}~~}\implies \cfrac{\frac{4}{1}}{~~\frac{(1)1-(2)5}{4}~~}\implies \cfrac{\frac{4}{1}}{~~\frac{1-10}{4}~~}\implies \cfrac{\frac{4}{1}}{~~\frac{-9}{4}~~} \\\\\\ \cfrac{4}{1}\cdot \cfrac{4}{-9}\implies \cfrac{-16}{9}[/tex]
What is on a graphY<7
in short, we simply graph her countertpart of y = 7, and then we test a point for "true" or "false" for that region.
say for example the point ( 3, 5 ), meaning x = 3, y = 5
y < 7
5 < 7
is that really true? 5 smaller than 7? yeap, so that region is the "true" region, and is the region we shade.
the line in the graph is a dashed one, because it does NOT include the points at the border, y < 7, "y" is less, not equals to, but less than 7.
Check the picture below.
I'm sorry but there is no graph, If you could put up the graph I can answer. Thank You!
Landon is saving up to buy a new jacket. He already has $70 and can save an additional $7 per week using money from his after school job. How much total money would Landon have after 5 weeks of saving? Also, write an expression that represents the amount of money Landon would have saved in ww weeks.
Savings after 5 weeks:
Savings after ww weeks:
For this case we have to:
Let "w" be the variable that represents the number of savings weeks.
We have that Landon's initial amount is $ 70.
We want to know how much money you have after 5 weeks, knowing that you save $ 7 each week, so be "y" the amount of money after "W" weeks:
[tex]y = 70 + 7w[/tex]
After 5 weeks:
[tex]y = 70 + 7 (5)\\y = 70 + 35\\y = 105\[/tex]
Answer[tex]y = 70 + 7w\\y = 105[/tex]
Is the following number rational or irrational?
\sqrt{99}
(Choice A)
Rational
(Choice B)
Irrational
Answer:
B. Irrational.
Step-by-step explanation:
√99 is irrational.
Its value just below 10 as √100 = 10.
What is the domain and range of f(x)= x^2 + 4x - 21
Answer:
The domain is all real numbers.
The range is y ≥ −25
Step-by-step explanation:
The equation has no domain restrictions.
If volume is 325m to the power of 3,
Find x
Answer:
13/6
Step-by-step explanation:
volume=length*width*height
so
325m^3=10*15*x
325=150x
x=2.16666666 or 325/150
I don’t understand this question someone plz help!
Express the area of a rectangle with length 5 m4 and width 6m2 as a monomial.
[tex]A=5m^4\times6m^2=\boxed{30m^6}[/tex]
What is the MAD for 4,5,6,1? Please help I am really confused!
Answer:
MAD = 1.5.
Step-by-step explanation:
MAD is the Mean Absolute Deviation.
The MAD is a measure of the spread of the data.
The mean of these numbers is (1 + 4 + 5 + 6) / 4
= 16/4 = 4.
Now you subtract this from the individual values and take the absolute values:
1 - 4 = -3 (absolute value = 3).
4-4 = 0
5-4 = 1
6-4 = 2.
Adding 0+1+2+3 = 6.
The MAD = 6 / 4 = 1.5.
Answer:
Step-by-step explanation: The mad is 1.5
the sum of three consecutive natural numbers is 1086
Answer:
361. 362,363
Step-by-step explanation:
Here we will use algebra to find three consecutive integers whose sum is 1086.
We assign X to the first integer. Since they are consecutive, it means that the 2nd number will be X+1 and the third number will be X+2 and they should all add up to 1086. Therefore, you can write the equation as follows:
X + X + 1 + X + 2 = 1086
To solve for X, you first add the integers together and the X variables together. Then you subtract 3 from each side, followed by dividing by 3 on each side. Here is the work to show our math:
X + X + 1 + X + 2 = 1086
3X + 3 = 1086
3X + 3 - 3 = 1086 - 3
3X = 1083
3X/3 = 1083/3
X = 361
Which means that the first number is 361, the second number is 361+1 and third number is 361+2. Therefore, three consecutive integers that add up to 1086 are:
361
362
363
Follow below steps;
The question asks to find three consecutive natural numbers that add up to 1086. Let's denote the smallest of these three numbers as n. Then, the next two numbers can be represented as n + 1 and n + 2. The sum of these three numbers is:
n + (n + 1) + (n + 2) = 1086
Combining like terms, we get:
3n + 3 = 1086
Subtracting 3 from both sides, we get:
3n = 1083
Dividing both sides by 3, we find:
n = 361
So the three consecutive numbers are 361, 362, and 363, and they indeed sum up to 1086:
361 + 362 + 363 = 1086
These figures are similar. The
area of one is given. Find the
area of the other.
Answer:
The Area of the first figure is 18[tex]in^{2}[/tex]
Step-by-step explanation:
Since the question states that both of the figures are similar we can use the information from figure 2 in order to find the area of figure 1. We do this by using the simple rule of three.
8[tex]in[/tex] ----> x
12[tex]in[/tex] ---> 27[tex]in^{2}[/tex]
Since the ratios (figures) are stated to be similar we just solve the rule of three as shown above.
[tex]\frac{(8in)(27in^{2} )}{12in} = x[/tex]
[tex]\frac{216in^{3} }{12in } = x[/tex]
[tex]18in^{2} = x[/tex]
Therefore the Area of figure 1 is 18[tex]in^{2}[/tex]
I hope this answered your question. If you have any more questions feel free to ask away at Brainly.
Answer: 12
Step-by-step explanation: I know this website, this is the answer there
The following box plot shows the number of years during which 24 schools have participated in an interschool swimming meet:
A box and whisker plot is drawn using a number line from 0 to 10 with primary markings and labels at 0, 5, 10. In between two primary markings are 4 secondary markings. The box extends from 1 to 6 on the number line. There is a vertical line at 3.5. The whiskers end at 0 and 8. Above the plot is written Duration of Participation. Below the plot is written Years.
At least how many schools have participated for 1 year or less?
6 schools
8 schools
12 schools
14 schools
Please explain, best answer and explanation gets brainliest
Answer:
The answer is 6 schools.
In a box and whisker plot, every piece of whisker or box represents 25% of the whole number of schools.
The schools participated 1 year or less are represented by the left part of the whisker. Which stands for 25%.
BOOM
Step-by-step explanation:
On analyzing the boxplot, we find that 6 schools have participated for 1 year or less.
What is a boxplot?A boxplot is a standardized way of displaying the distribution of data based on a five number summary (minimum, first quartile (Q1), median, third quartile (Q3), and maximum).
The box extends from 1 to 6 on the number line. This implies first quartile (Q1) = 1 and third quartile (Q3) = 6.
There is a vertical line at 3.5, median = 3.5.
The whiskers end at 0 and 8, i.e., minimum = 0 and maximum = 8.
Since, Q1 = 1, this implies 25% of the schools participated for 1 year or less.
(First quartile (Q1) is the value under which 25% of data points are found when they are arranged in increasing order.)
Number of schools that have participated for 1 year or less = 25% of 24 = [tex]\frac{25}{100} * 24 = 6[/tex]
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thirty-five maths majors, 33 music majors, and 45 history majors are randomly selected from 251 math majors, 518 music majors 332 history majors at the state university
identify the type of sampling (simple random sample, cluster, stratified, convenience, systematic
The scenarios provided represent different types of sampling methods, such as stratified, cluster, simple random, and systematic, based on how the samples are selected from the population.
Explanation:The type of sampling can be determined based on how the samples are chosen from the population. Here, we discuss different sampling methods using the provided scenarios.
Stratified sampling is used when the soccer coach selects players from different age groups to form a team. Each age group is a stratum.Cluster sampling takes place when a pollster interviews all human resource personnel in a few high tech companies. Each company is a cluster.When a high school educational researcher interviews an equal number of female and male teachers, this is an example of stratified sampling as well.The high school principal who polls an equal number of students from each grade level utilizes stratified sampling.A sample of high school students chosen by first organizing by class and then selecting an equal number from each also exemplifies stratified sampling.If a completely random method is used to select students giving each one the same chance of being chosen, this represents simple random sampling.When selecting a sample proportionate to class standings in a college, and drawing from each class based on their representation in the total population, stratified sampling is again used.Using a random number generator to select every 50th student from an alphabetical list represents systematic sampling.Rewrite the following expression 15+21 using the GCF and the distribution property?
Factors:
15 = 1, 3, 5, 15
21 = 1, 3, 7, 21
The GCF is 3
That means that you can take three out of 15 and 21
15/3 = 5
21/3 = 7
so...
3 (5 + 7)
Hope this helped!
~Just a girl in love with Shawn Mendes
Function f is represented by the equation shown.
f(x)=x^2-4x+3
Function g has a vertex at (1,3) and the parabola opens downwards.
Which statement is true?
A.
The y-intercept of function f is greater than the y-intercept of function g.
B.
The y-intercept of function f is less than the y-intercept of function g.
C.
The minimum of function f is at (-4,3).
D.
The minimum of function g is at (1,3).
Answer:
[tex]\boxed{\text{A. The y-intercept of function f is greater than the y-intercept of function g}}[/tex]
Step-by-step explanation:
A. y-Intercept of ƒ(x)
ƒ(x) = x² - 4x + 3
f(0) = 0² - 4(0) + 3 = 0 – 0 + 3 = 3
The y-intercept of ƒ(x) is (0, 3).
If g(x) opens downwards and has a maximum at y = 3, it's y-intercept is less than (0, 3).
Statement A is TRUE.
B. y-Intercept of g(x)
Statement B is FALSE.
C. Minimum of ƒ(x)
ƒ(x) = x² - 4x + 3
a = 1; b = -4; c = 3
The vertex form of a parabola is
y = a(x - h)² + k
where (h, k) is the vertex of the parabola.
h = -b/(2a) and k = f(h)
h = -b/2a = -(-4)/(2×1 = 2
k = f(2) = 2² - 4×2 + 3 =4 – 8 +3 = -1
The minimum of ƒ(x) is -1. The minimum of ƒ(x) is at (2, -1).
Statement C is FALSE.
D. Minimum of g(x)
g(x) is a downward-opening parabola. It has no minimum.
Statement D is FALSE
35 POINTS PLEASE HELP
Find the Least Common Multiple (LCM) of the denominator in order to find the Least Common Denominator (LCD).
LCM = 6/5 * (x^2y^2)
Answer = B. 10x^2y^2
Answer:
Your answer is option B. 10x^2y^2
Step-by-step explanation:
Firstly, Find the Least Common Multiple of the denominator.
Then you'll get your Least Common Denominator.
You'll get LCM as :
LCM = 6/5 * ( x^ 2y ^2 )
Your answer you'll get is 10x^2y^2
find the value of an investment of $5000 at 7% compounded continuously for 6 years
1. 7503.65
2. 7709.81
3. 7100.00
4. 7609.81
Answer:
Option 4 is correct
Step-by-step explanation:
If the rate is compounded continuously, the formula used to find the future value is:
A= Pe^rt
Where A = Future Value
P= Principal amount
r = interest rate in decimal
t = time
For the given data:
A=?
P = $5000
r = 7% or 0.07
t = 6
Putting values in the above formula
A= 5000e^(0.07 *6)
A = 7609.81
So, Option 4 is correct.
Evaluate if x = 3, y = 2, and z = 5.
4xyz
z2 - x2
Answer:
120
16
Step-by-step explanation:
Givens
x = 3y = 2z = 5Solution
4xyz = 4(3)(2)(5)
4xyz = 30 * 4
4xyz = 120
======================
z^2 - x^2
5^2 - 3^2
25 - 9
16
Simplify the following algebraic expression 3/4(1/2x-12)+4/5
ANSWER
[tex] \frac{15x - 328}{40} [/tex]
EXPLANATION
The given expression is
[tex] \frac{3}{4} ( \frac{1}{2} x - 12) + \frac{4}{5} [/tex]
We expand to obtain;
[tex] \frac{3}{8} x - 9+ \frac{4}{5}[/tex]
The least common denominator is 40
[tex] \frac{15x - 360 + 32}{40} [/tex]
This simplifies to:
[tex] \frac{15x - 328}{40} [/tex]
Answer:
That’s wrong
Step-by-step explanation:
Ms. Williams wants to analyze the scores for the first unit test of her NC Math 1 class
The scores for the class are below.
Scores:
82, 100, 94, 68, 34, 72, 70, 96, 99,92,
90, 85, 70, 46, 71, 71, 77, 78, 95, 82,
80, 100, 99,72,69,74,84,87
Calculate the the following for the class. Round answers to the nearest whole number.
mean =
median =
standard deviation =
interquartile range =
Answer:
Mean:79
Median:81
Standard deviation:15
Interquartile range:22
Mean (aka average)-79.8928
add all the numbers together and divide by how many numbers there are
sum of terms-2237
number of terms-28
Median- 81
I do it this way-
order the numbers from least to greatest
cross off the front number and back number until you are left with a middle
in this case there were 2
80 and 82
the average of those two is 81
Standard Deviation-15.37237
Interquartile Range-22.5
25th percentile-71
50th percentile-81
75th percentile-93
Consider that x = -5 and y = -4. Which statement is true about x+y
A) The sum of x and is a rational number
B) The sum of x and y is an imaginary number
C) The sum of x and y is an irrational number
D) The sum of x and y is neither rational or irrational
Answer:
The answer is A.
Step-by-step explanation:
Rational numbers are any real numbers (including negatives) and -5 + -4 = -9 which is a real number, so it is rational.
i need help pleaseeeeeeeeee
Answer:
4 4/2
Step-by-step explanation:
What you do is you have to do 8-4=4 5-1=4 6-4=2 so there for the answer is 4 4/2
Hello There!
We are given the problem 8 5/6 - 4 1/4
Your answer would be 4 7/12
First, we subtract 4 from 8 and get a difference of 4.
Then we have to subtract 1/4 from 5/6.
We have to find a common denominator.
We can get 10/12-3/12=7/12
Then, we add 4+7/12 and we get 4 7/12.