Answer:
y = 0.1x - 4
Step-by-step explanation:
Given the following data;
Points on the x-axis (x1, x2) = (-3, 7)
Points on the y-axis (y1, y2) = (-7, -6)
First of all, we would find the slope;
Mathematically, slope is given by the formula;
[tex] Slope = \frac{Change \; in \; y \; axis}{Change \; in \; x \; axis} [/tex]
[tex] Slope, m = \frac {y_{2} - y_{1}}{x_{2} - x_{1}} [/tex]
Substituting into the equation, we have;
Slope = (-6 - (-7))/(7 - (-3))
Slope = (-6 + 7)/(7 + 3)
Slope = 1/10
Slope = 0.1
Next, we would write the equation using the formula;
y - y1 = m(x - x1)
y - (-7) = 0.1(x - (-3))
y + 7 = 0.1(x + 3)
y + 7 = 0.1x + 3
y = 0.1x + 3 - 7
y = 0.1x - 4
6 triangles and 10 squares what is the simplest ratio of triangles to squares?
Answer:
3:5
Step-by-step explanation:
To find the simplest ratio, divide each number by 2:
6/2
= 3
10/2
= 5
So, the simplest ratio of triangles to squares is 3:5
mathhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhh
Answer:
interior
Step-by-step explanation:
exterior would be located outside the triangle.(10)
vertex is the point of the connected lines (12)
What is the value of a?
Answer:
your answer will be option B
Step-by-step explanation:
[tex]\frac{10}{12} =\frac{a}{38} \\\\a=\frac{(10) (38)}{12} \\\\=31.6[/tex]
Mary and Lewis each open a savings account at the same time. Mary invests $3,700 in an account yielding 3.2% simple interest, and Lewis invests $3,000 in an account yielding 5.9% simple interest. After fifteen years, who has the greater total amount of money, and how much greater is it?
a.
Lewis has $879 more than Mary.
b.
Lewis has $179 more than Mary.
c.
Mary has $776 more than Lewis.
d.
Mary has $345 more than Lewis.
Answer:
lewis has $179 more than mary
Lewis has the greater total amount of money than Mary by $879
Given the following data:
Mary's principal = $3,700Mary's interest = 3.2% = 0.032Lewis's principal = $3,000Lewis's interest = 5.9% = 0.059Time = 15 years.To determine who has the greater total amount of money and by how much greater is it:
The formula for simple interest.Mathematically, simple interest is given by the formula:
[tex]S.I = PRT[/tex]
Where:
S.I is the simple interest.P is the principal or starting amount.R is the interest rate.T is the time measured in years.For Mary:[tex]S.I = 3700 \times 0.032 \times 15[/tex]
S.I = $1,776
For Lewis:[tex]S.I = 3000 \times 0.059 \times 15[/tex]
S.I = $2,655
Therefore, Lewis has the greater total amount of money.
Next, we would find the difference in their simple interest:
[tex]Difference = 2655-1776[/tex]
Difference = $879
Read more on simple interest here: https://brainly.com/question/24341207
Given AFGH ~ ALMN, select all the statements that are true.
Answer:
1st, 3rd, and 4th options are true
Step-by-step explanation:
Keiko, Dale, and Tony sent a total of 95 text messages during the weekend. Dale sent 7 fewer messages than Kelko. Tony sent 4 times as many messages as
Keiko. How many messages did they each send?
Answer:
Keiko sent 17 messages, Dale sent 10 messages, and Tony sent 68 messages
Step-by-step explanation:
Let x represent the number of messages that Keiko sent.
Since Dale sent 7 less than Keiko, his number can be represented by x - 7
Since Tony sent 4 times as many as Keiko, his number can be represented by 4x
Using these variables, create an equation:
(x) + (x - 7) + (4x) = 95
Add like terms and solve for x:
6x - 7 = 95
6x = 102
x = 17
So, Keiko sent 17 messages.
Subtract 7 from this to find how many Dale sent:
17 - 7
= 10
Multiply it by 4 to find how many Tony sent:
17(4)
= 68
So, Keiko sent 17 messages, Dale sent 10 messages, and Tony sent 68 messages
Victoria is going to a carnival that has games and rides. Each game costs $2 and each ride costs $4. Victoria spent $16 altogether on 6 games and rides. Graphically solve a system of equations in order to determine the number of games Victoria played, x,x, and the number of rides Victoria went on, yy.
Answer:
2 rides & 4 games
Step-by-step explanation:
2 rides=$8
4 games=$8
8+8=$16
Point (4,2), represents that Victoria played 4 games (x = 4) and went on 2 rides (y = 2).
What is a graph?A graph can be defined as a pictorial representation or a diagram that represents data or values.
The number of games Victoria played, x, and the number of rides Victoria went on, y.
Each game costs $2 and each ride costs $4, so we can set up the following system of equations:
2x + 4y = 16
x + y = 6
To graphically solve this system of equations, we can plot the equations on the same coordinate plane and find the point where they intersect. This point will represent the values of x and y that satisfy both equations.
To plot the equations, we can first graph the equation 2x + 4y = 16.
The slope is 2 and the y-intercept is 4, so we can plot the line by starting at the point (0,4) and moving 2 units up and 1 unit to the right to find the next point on the line.
We can then connect this point to the first point with a straight line to complete the graph of the equation.
Next, we can graph the equation x + y = 6 similarly.
The point will represent the values of x and y that satisfy both equations.
In this case, we can see that the lines intersect at point (4,2), which means that Victoria played 4 games (x = 4) and went on 2 rides (y = 2).
Learn more about the graphs here:
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WILL GIVE BRAINLST
HAVE A GOOD DAY
Answer:
6.633249581 and I would say it's irrational
Step-by-step explanation:
:)
kennedy has 12 apple. togethe, she and Ariana have 42 apple. which diagram represents best represents the situation where A is the amount of apples that Ariana has?
Uhm... I’m sorry I don’t really know the answer to your question I’m just answering it for points....
9x-6y=-12 and -2x+3y=-4 by elimination
Answer:
x = 4, y = 4 or you can say (4, 4)
Drag the values to the correct locations on the image. Not all values will be used.
Susan is conducting a survey about the electric bills of households in her city. From the electric company, she found that the population mean is
$98.75 with a standard deviation of $10.45. Susan has a sample size of 60.
Complete the equation that Susan can use to find the interval in which she can be 68% sure that the sample mean will lie.
98.75
109.2
88.3
7.75
60
10.45
C
+
r
Answer:
[tex]x\\[/tex] ± [tex]\frac{s}{\sqrt{n}}[/tex] = [tex]9.78[/tex] ± [tex]\frac{10.45}{\sqrt{60}}[/tex]
Step-by-step explanation:
x is the value of our population/sample mean. Given that it's 98.75, we substitute x for 98.75.
We follow this pattern for s and n, which are the standard deviation and sample size respectively, to fill out the rest of our equation. This means that s is 10.45 and n is 60
Since we know the formula is [tex]x\\[/tex] ± [tex]\frac{s}{\sqrt{n}}[/tex], we can input our new values.
This gives us our answer of [tex]9.78[/tex] ± [tex]\frac{10.45}{\sqrt{60}}[/tex]
TL;DR
I took the test and the answer was right
The interval in which the population mean $98.75 with standard deviation of $10.45 with a sample size of 60 is given by its lower and upper limit as given by: 98.75 ± 10.45/(√(60))
What is empirical rule?According to the empirical rule, also known as 68-95-99.7 rule, the percentage of values that lie within an interval with 68%, 95% and 99.7% of the values lies within one, two or three standard deviations of the mean of the distribution.
[tex]P(\mu - \sigma < X < \mu + \sigma) \approx 68\%\\P(\mu - 2\sigma < X < \mu + 2\sigma) \approx 95\%\\P(\mu - 3\sigma < X < \mu + 3\sigma) \approx 99.7\%[/tex]
where we had where mean of distribution of X is [tex]\mu[/tex] and standard deviation from mean of distribution of X is [tex]\sigma[/tex] (assuming X is normally distributed).
What is the distribution of sample mean for large samples?Suppose X has has a distribution with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], then, the distribution of the mean of samples of size n, drawn from the values of X, is normally distributed with mean equal to the mean of X, and standard deviation equal to [tex]\sigma/\sqrt{n}[/tex]
Symbolically, we write it as:
[tex]X \sim N(\mu, \sigma) \implies \overline{X} \sim N(\mu,\sigma/\sqrt{n} )[/tex]
(for large enough samples, n > 30)
For this case, we're specified that:
Population mean = [tex]\mu = $98.75[/tex] (dollars)Population standard deviation = [tex]\sigma = 10.45[/tex] (dollars)sample size = n = 60Then, the distribution of the sample mean is approximately normal distribution with mean $98.75 and standard deviation approximately [tex]10.45/\sqrt{60}[/tex]
Symbolically, we get:
[tex]X \sim N(98.75, 10.45/\sqrt{60})[/tex]
Then, using empirical rule, we find the limits for sample mean for which we're 68% sure that the sample mean will lie in that interval as one standard deviation (of the sample mean) away from its mean.
[tex]P\left( 98.75 - 10.45/\sqrt{60} < \overline{X} < 98.75 + 10.45/\sqrt{60}\right) \approx 68\%[/tex]
So, limits are:
[tex]98.75 \pm \dfrac{10.45}{\sqrt{60}}[/tex]
Thus, the interval in which the population mean $98.75 with standard deviation of $10.45 with a sample size of 60 is given by its lower and upper limit as given by: 98.75 ± 10.45/(√(60))
Learn more about empirical rule here:
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HELP!! i will vote brainlest answer
Answer:
D. 18
Step-by-step explanation:
The polygon given is a 5-sided polygon (pentagon). Sum of all interior angles of a 5-sided polygon = (n - 2) * 180°
= (5 - 2) * 180 = 540°
Therefore:
95° + (7x - 4)° + (3x + 23)° + (9x - 6)° + 90° = 540°
Solve for x
95 + 7x - 4 + 3x + 23 + 9x - 6 + 90 = 540
Add like terms
198 + 19x = 540
19x = 540 - 198
19x = 342
x = 342/19
x = 18
What is the value of the expression 12.25 + (-17.75)?
Answer:
-5.5
Step-by-step explanation:
Carlotta has 2/3 of a bag of dog food. She gives her dog 2/9 of the bag at each feeding. How many times can she feed her dog with what is left in this bag of dog food?
A. 3
B. 4
C. 18
D. 27
Answer:
27
Step-by-step explanation:
Carlotta can feed 3 times her dog with leftover in this bag of dog food
What is the unitary method?
The unitary method is a method for solving a problem by the first value of a single unit and then finding the value by multiplying the single value. If an event can occur in m different ways and if following it, a second event can occur in n different ways, then the two events in succession can occur in m × n different ways.
WE have been given that Carlotta has 2/3 of a bag of dog food and She gives her dog 2/9 of the bag at each feeding.
The bag of dog food = 2/3
Let she feed her dog with leftover in this bag of dog food = X
Therefore, X = 2/3 × 9/2
X = 18 / 6
X = 3
Hence, Carlotta can feed 3 times her dog with leftover in this bag of dog food
Learn more about the unitary method, please visit the link given below;
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Find the value of the variable 7x + 19 11x -89 60°
Step-by-step explanation:
let third angle be x
60° + 60° + x = 180° (Δ sum property)
x = 60°
so, this is a equilateral triangle (all Δ equal)
-----------------------------------------in equilateral triangle --> all sides are equal
so, therefore =>>
7x + 19 = 11x - 89
19 + 89 = 11x - 7x
108 = 4x
108 ÷ 4 = x
27 = x
x = 27-----------------------------------------so variable
1.) 7x + 19
= 7(27) + 19
= 189 + 19
= 208
2.) 11x - 89
= 11(27) - 89
= 297 - 89
= 208
A person on a moving sidewalk travels 6 feet in 3 seconds. The moving sidewalk has a length of 60 feet. How long will it take to move from one end of the sidewalk to the other?
Answer:
Speed = distance / time
= 6/3 =2 ft/sec
Time = distance / speed
= 60/2
= 30 seconds
Volume of a cone is 48 pi and have a radius of 8 what is the height
Answer:
Step-by-step explanation:
the answer is in the pic open it
hope it help mark me as a brill please
Help pls and explain how you got your answer pls!!!
You need 25 pounds of potatoes. If each potato weighs 5 ounces, how many potatoes will you need?
Answer:
80 potatoes
Step-by-step explanation:
How to do this here
Answer:
Step-by-step explanation:
Jordan typed 40 words a minute and he spends 1 minute typing a ending how many minute did it take him to write a sentence
i also heard that you can get points for answering questions.
Answer:
02920
Step-by-step explanation:
92823
Is this correct hehevdhegged
Answer:
b is the correct answer
Step-by-step explanation:
btw can i have brainliest please
...........................................................
Answer:
Top is A bottom is B. ........
25 POINTS!!!!!!!!!!!
I WILL GIVE BRAINLEIST
I need the answers for
15.
16.
17
would this be a cone??
no that would NOT be a cone
That would not be a cone.
will give the BRAINLIEST pls helpppppp
Answer:
pretty sure youre right kiddo
Guys please help me out ASAP, Due today. I
In an arithmetic sequence Sn = n² - 2n.
Use your formula in 2c to determine the value of
(a) T7 =
(b) Tn=
The formula in 2c : Sn - Sn-1 =Tn
Answer:
[tex]T_7 = 11[/tex]
[tex]T_n = 2n- 3[/tex]
Step-by-step explanation:
Given
[tex]S_n = n^2 -2n[/tex]
[tex]T_n = S_n - S_{n-1}[/tex]
Solving (a): T7
Substitute 7 for n in [tex]T_n = S_n - S_{n-1}[/tex]
[tex]T_7 = S_7 - S_{7-1}[/tex]
[tex]T_7 = S_7 - S_6[/tex]
Calculate S7 and S6
[tex]S_n = n^2 -2n[/tex]
[tex]S_7 = 7^2 - 2 * 7 = 35[/tex]
[tex]S_6 = 6^2 - 2 * 6 = 24[/tex]
So:
[tex]T_7 = 35 -24[/tex]
[tex]T_7 = 11[/tex]
Solving (b): Tn
[tex]T_n = S_n - S_{n-1}[/tex]
Where [tex]S_n = n^2 -2n[/tex]
Calculate[tex]S_{n-1}[/tex]
We have:
[tex]S_{n-1} =(n-1)^2 - 2(n-1)[/tex]
Open brackets
[tex]S_{n-1} = n^2 -2n + 1 -2n +2[/tex]
[tex]S_{n-1} = n^2 -2n-2n + 1 +2[/tex]
[tex]S_{n-1} = n^2 -4n + 3[/tex]
So:
[tex]T_n = S_n - S_{n-1}[/tex]
[tex]T_n = n^2 - 2n - (n^2 -4n + 3)[/tex]
[tex]T_n = n^2 - 2n - n^2 +4n - 3[/tex]
Collect Like Terms
[tex]T_n = n^2 - n^2- 2n +4n - 3[/tex]
[tex]T_n = 2n- 3[/tex]
7
T
S
U
The triangle STU has been drawn on to a centimetre grid.
Calculate the area of triangle STU *
(2 Points)
Enter your answer
Answer:
12 square units
Step-by-step explanation:
The area of a given figure is the measure of space occupied by the figure on a 2 dimensional plane.
Area of a triangle = [tex]\frac{1}{2}[/tex] x base x height
From the given grid, the following can be observed for triangle STU.
base SU = 6 units
height = 4 units
Thus,
area of triangle STU = [tex]\frac{1}{2}[/tex] x base x height
= [tex]\frac{1}{2}[/tex] x 6 x 4
= 3 x 4
area of triangle STU = 12 square units
The required area of triangle STU is 12 square units.
A triangle has vertices X(2, 1), Y(5, 4), and Z(5, 1). What is the area of the triangle?
Answer:
Step-by-step explanation:
They gave you an easy triangle. You can tell by the coordinates that X and Z are horizontally aligned, and Y and Z are vertically aligned, so Z is a right angle.
Area = 0.5(XZ)(YZ) = 0.5(3)(3) = 4.5 square units.
Find the point on the line 2x+6y+1=0 which is closest to the point (-5,-3)
Answer:
(-1.875, -1.625)
Step-by-step explanation:
We want to find the point on the equation 2*x + 6*y + 1 = 0 which is closest to the point (-5, -3)
Remember that the distance between two points (a, b) and (c, d) is:
D = √( (a - c)^2 + (b - d)^2)
First we can write our equation as a line in the slope intercept form:
y = -(2/6)*x - 1
Now we could minimize the equation:
D = √( (x - (-5))^2 + (y - (-3))^2) = √( (x + 5)^2 + (y + 3)^2)
D = √( ( x + 5)^2 + ( -(2/6)*x - 1 + 3) ^2)
Then we can minimize:
D^2 = (x + 5)^2 + ( -(2/6)*x + 2)^2
= x^2 + 10*x + 25 + (4/36)*x^2 - (8/6)*x + 4
= (1 + 4/36)*x^2 + (10 - 8/6)*x + 29
= (40/36)*x^2 + (52/6)*x + 29
This is a quadratic equation whose leading coefficient is positive, then the minimum of this equation is at the vertex.
The vertex is at the x-value such that (D^2)' = 0
Then:
(D^2)' = 2*(40/36)*x + (52/6)
This needs to be zero then:
0 = 2*(40/36)*x + (52/6)
-52/6 = (80/36)*x
(-52/6)*(36/80) = x
-1.875 = x
And the y-value when x = -1.875 is:
y = -(2/6)*-1.875 - 1
y = -1.625
Then the point on the line 2x+6y+1=0 that is closest to (-5,-3) is the point (-1.875, -1.625)