well, let's find the equation of the line through those points then, and let's see
[tex](\stackrel{x_1}{-2}~,~\stackrel{y_1}{0})\qquad (\stackrel{x_2}{0}~,~\stackrel{y_2}{-6}) \\\\\\ \stackrel{slope}{m}\implies \cfrac{\stackrel{\textit{\large rise}} {\stackrel{y_2}{-6}-\stackrel{y1}{0}}}{\underset{\textit{\large run}} {\underset{x_2}{0}-\underset{x_1}{(-2)}}} \implies \cfrac{-6 }{0 +2} \implies \cfrac{ -6 }{ 2 } \implies - 3[/tex]
[tex]\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-\stackrel{y_1}{0}=\stackrel{m}{- 3}(x-\stackrel{x_1}{(-2)}) \implies y = - 3 ( x +2) \\\\\\ y=-3x-6\implies \boxed{3x+y=-6} ~~ \ne ~~ 3x-y = 6[/tex]
x+2x-15 somebody solve this right now and quickly please
Answer:
3(x-5)
Step-by-step explanation:
Answer:
3(x - 5)
Step-by-step explanation:
Make terms..
x + 2x - 15 =
3x - 15
Now lets find a common factor of them..
3x - 15
3(x - 5)
Thus,
3(x - 5), Is your answer
Antonio's toy boat is bobbing in the water under a dock. The vertical distance
�
HH (in
cm
cmstart text, c, m, end text) between the dock and the top of the boat's mast
�
tt seconds after its first peak is modeled by the following function. Here,
�
tt is entered in radians.
�
(
�
)
=
5
cos
(
2
�
3
�
)
−
35.5
H(t)=5cos(
3
2π
t)−35.5H, left parenthesis, t, right parenthesis, equals, 5, cosine, left parenthesis, start fraction, 2, pi, divided by, 3, end fraction, t, right parenthesis, minus, 35, point, 5
How long does it take the toy boat to bob down from its peak to a height of
−
35
cm
−35 cmminus, 35, start text, space, c, m, end text?
Answer: To find the time it takes for the toy boat to bob down from its peak to a height of -35 cm, we need to find the value of t when H(t) = -35.
So, we can substitute -35 for H(t) in the given equation:
5 cos (2π/3t) - 35.5 = -35
Now we can solve for t by isolating it on one side of the equation:
5 cos (2π/3t) = 0.5
cos (2π/3t) = 0.1
2π/3t = cos^-1(0.1)
3t = 2π * cos^-1(0.1)/π
t = 2 * cos^-1(0.1)
The time it takes for the toy boat to bob down from its peak to a height of -35 cm is approximately 2 * cos^-1(0.1) seconds.
Step-by-step explanation:
Gilowing 50 Hz. A, B, C and D are points on the wave A Direction of wave motion 10 m B 3 m Calculate the time that the wave takes to travel the distance AB. Calcuplate the wavelength of this wave. Calculate the amplitude of this wave. Are points A and B on the wave in phase? Explain your answer
The time it takes for the wave to travel from point A to point B is 0.0086 seconds.
How to find the time of wave to travel from point A to point B?Assuming the question is referring to a sinusoidal wave with a frequency of 50 Hz, we can use the wave speed formula to calculate the time it takes for the wave to travel from point A to point B.
Wave speed (v) = frequency (f) x wavelength (λ)
Since the frequency is given as 50 Hz, we need to determine the wavelength to find the wave speed.
To calculate the wavelength, we can use the distance between two consecutive points on the wave that is in phase, such as points A and D or B and C. From the given information, we know that the distance between A and D or B and C is one wavelength. Therefore, we can calculate the wavelength as follows:
wavelength (λ) = distance between A and D or B and C = 10 m - 3 m = 7 m
Using the wave speed formula and the calculated wavelength, we can find the wave speed:
v = f x λ = 50 Hz x 7 m = 350 m/s
Now we can use the wave speed formula to find the time it takes for the wave to travel from point A to point B:
v = d / t
where d is the distance between A and B (which is 3 m) and t is the time it takes for the wave to travel that distance.
Rearranging the formula, we get:
t = d / v = 3 m / 350 m/s = 0.0086 s
Therefore, the time it takes for the wave to travel from point A to point B is 0.0086 seconds.
To find the amplitude of the wave, we would need additional information, as the amplitude is the maximum displacement of the wave from its equilibrium position.
As for whether points A and B are in phase, we need to compare the phase difference between the two points to the wave period. The period of a wave is the time it takes for one complete oscillation, and it is given by:
period (T) = 1 / frequency (f) = 1 / 50 Hz = 0.02 s
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Question 3 (2 points)
Lauren deposited $300 to start her savings account. After one year, she had $312 in
her account. If she did not deposit or withdraw any money that year, how much
interest did she earn?
A
She earned $12 at 4% interest rate. The solution has been obtained by using simple interest.
What is simple interest?
Simple interest is the cost of borrowing that is computed using the original principal amount alone and a constant interest rate.
We are given that Lauren deposited $300 to start her savings account and after one year, she had $312 in her account.
This means that the difference between both the amounts is the interest because it is mentioned that she did not deposit or withdraw any money that year.
So, the interest is $12.
The rate of interest is found using simple interest
⇒S = p*r*t
⇒12 = 300*r*1
⇒0.04 = r
This means that interest rate is 4%.
Hence, she earned $12 at 4% interest rate.
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I just need the answer to UV
Answer:
In a rhombus, all sides are equal. Therefore, you can set WV (s+12) and UV (3s) equal to each other.
s+12 = 3s
Subtract s from both sides, so the variables are all on one side.
12 = 2s
Divide both sides by 2 to isolate the variable.
6 = s
UV = 3s
UV = 3(6)
UV = 18
Pls help I’m so stuck
By evaluating the given equation, we will see that they made 1,524 dollars by selling tickets.
What was the total ticket sales?We know that each adult ticket costs $12 and each student ticket costs $9, then the expression for the total cost is:
c(a, b) = 12a + 9s
Where a is the number of adults and s is the number of students.
Here we know that there where 64 adults and 84 students, so the total cost will be:
c(64, 84) = 12*64 + 9*84 = 1,524
They made $1,524 by selling tickets.
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Triangle ABC has vertices A(-1, 10), B(2, 1),
and C(-4, 1). What are the coordinates of
the centroid of the triangle?
The coordinates of the centroid of triangle ABC are given as follows:
(-1, 4).
How to obtain the coordinates of the centroid of the triangle?The coordinates of the centroid of a triangle are obtained finding the mean of the coordinates of the three vertices of the triangle.
This means that the x-coordinate of the centroid of triangle ABC is given as follows:
(-1 + 2 - 4)/3 = -1.
(mean of the x-coordinates of each of the three vertices).
The y-coordinate of the centroid of triangle ABC is given as follows:
(10 + 1 + 1)/2 = 4.
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the population of algae in an experiment increases by %5 each day. if there were 50 algae at the beginning, predict the number of algae after 7 days.
The number of algae after 7 days is approximately 70.
What is Percentage?Percentage is defined as the parts of a number per fraction of 100. We have to divide a number with it's whole and then multiply with 100 to calculate the percentage of any number.
Given that,
Initial population of algae = 50
Percentage increase = 5%
To calculate the number of algae at any day, we need to find a formula.
Initial population = 50
After 1 day, population = 50 + (5% × 50) = 50 + (0.05 × 50) = 50 (1 + 0.05)
After 2 days, population = 50 (1 + 0.05)²
So, population after n days = 50 (1 + 0.05)ⁿ
Population of algae after 7 days = 50 (1 + 0.05)⁷
= 50 (1.05)⁷
= 70.355 ≈ 70
Hence there will be approximately 70 algae after 7 days.
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what is 7x-21=11x-73
Answer:
[tex]7x - 21 = 11x - 73 \\ \dashrightarrow \: 11x - 7x = 73 - 21 \\ \dashrightarrow \: 4x = 52 \\ \ \: \: \: \: dividing \: both \: sides \: by \: 4 \\ \dashrightarrow \: \cancel \frac{4x}{4} = \cancel \frac{52}{4} \\ \\ \dashrightarrow \: \: \boxed{ x = 13}[/tex]
hope helpful :)
can some1 help me with this pls
Answer:
b
Step-by-step explanation:
Open up the second bracket by changing all signs to the opposite
2a²-3ab+5b² -a²+2ab-3b²
=a²-ab+2b²
1+1=??????
Help me I am stuck
Determine whether the following graph represents y as a function of x. If it does, explain why and estimate the domain and range. If it does not, explain why, describe a portion of the graph that could be removed to turn it into a function, and estimate the domain and range of the result.
The graph does not represent y as a function of x, as each value of x is mapped to two outputs.
The portion that could be removed to make it a function is given as follows:
y < 0.
Hence the domain and the range are given as follows:
-3 ≤ x ≤ 3.0 ≤ y ≤ 3.When does a relation represents a function?A relation represents a function when each input value is mapped to a single output value.
On the circle, a vertical line through the circle would cross the line twice, meaning that each input is mapped to two outputs, hence the relation is not a function.
We have to remove one of the outputs for the relation to be a function, hence, removing y < 0, the domain and the range are given as follows:
-3 ≤ x ≤ 3. -> values of x.0 ≤ y ≤ 3. -> values of y.More can be learned about relations and functions at brainly.com/question/10283950
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Provide numerical measures of individuals. The values of a quantitative variable can be added or subtracted and provide meaningful results?
Quantitative variables provide numerical measures that can be added/subtracted with meaningful results.
Discrete variables are quantitative and have a finite or countable number of positive values.
Continuous variables are quantitative and have an infinite number of possible values that are not countable and also measure with some sort of scale that uses numbers.
Qualitative variables allow for the classification of individuals based on some attribute or characteristic and also provide numerical measures of individuals.
Arithmetic operations such as addition and subtraction can be performed on the values of a quantitative variable and will provide meaningful results.
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Mark charged a battery . Each minute , the percentage of battery’s capacity that was charged increased by 2.5 percent after 17 minutes of charging the battery was 61.5 percent full
how full was the battery when the charging began ??
percent
how long from the time that mark started charging did it take the battery to be fully charged ?
minutes
The initial battery charge was of:
19%.
The time it takes for the battery to be full is of:
32.4 minutes.
What is a linear function?The linear function in slope-intercept format is given as follows:
y = mx + b
In which:
m is the slope, representing the rate of change of the battery change.b is the intercept, representing the initial battery charge.Each minute , the percentage of battery’s capacity that was charged increased by 2.5 percent, hence the slope m is given as follows:
m = 2.5.
Hence:
y = 2.5x + b.
After 17 minutes of charging the battery was 61.5 percent full, hence when x = 17, y = 61.5, and the intercept b is obtained as follows:
61.5 = 2.5(17) + b
b = 61.5 - 2.5 x 17
b = 19.
The battery is fully charged when y = 100, hence the time is obtained as follows:
2.5x + 19 = 100
2.5x = 81
x = 81/2.5
x = 32.4 minutes.
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Please answer these questions step-by-step
Which of the following represents "36 is 18 times as many as 2"?
Answer:
36 = 2 x 18
Step-by-step explanation:
How many solutions does the equation 6x + 12 = 2(3x + 6) have? Explain.
Answer: No solution
Step-by-step explanation:
6x + 12 = 2(3x + 6)
Expand the right side:
6x + 12 = 6x + 6
Subtract 6x from both sides:
12 = 6
This is obviously not true, so there are no solutions to this equation :>
Solve the system of equations using elimination.The graph shows the solution to a system of inequalities:
Solid line joining ordered pairs 0, 3 and 7, 0. Shade the portion of the graph below the line in the first and fourth quadrants.
Which of the following inequalities is modeled by the graph?
2x + 5y ≥ 14; x ≥ 0
2x + 5y ≤ 14; x ≥ 0
2x − 5y ≤ 14; x ≥ 0
−2x − 5y ≤ 14; x ≥ 0
The inequality that is modeled by the graph is 2x + 5y ≥ 14; x ≥ 0
This inequality corresponds to the solid line that passes through the ordered pairs (0,3) and (7,0). The line has a slope of -2/5, and it can be written in the form y = (-2/5)x + b, where b is the y-intercept, and it can be calculated as b = (5/2)x + 14. The shading is below the line and in the first and fourth quadrants, which corresponds to the inequality 2x + 5y ≥ 14; x ≥ 0.
The other inequalities provided in the options do not correspond to the graph:
2x + 5y ≤ 14; x ≥ 0, the shading is above the line
2x − 5y ≤ 14; x ≥ 0, the slope is positive and the shading is above the line
−2x − 5y ≤ 14; x ≥ 0, the slope is positive and the shading is above the line
So, the inequality that is modeled by the graph is 2x + 5y ≥ 14; x ≥ 0
Diana say that the qadrillatral in the right is a rhombus Melissa says the qadrillatral left is a rhombus
Diana and Melissa are correct based on the description of the rhombus's appearance. Option C. is correct.
Moving from the details to the fact to make judgements is known as inductive reasoning. Inferential reasoning, which involves moving from known facts to precise conclusions, is typically used to determine it.
A parallelogram's special case is the rhombus.
In a rhombus, the opposing sides and angles are parallel and equal.
The sides of a rhombus are all the same length, while the diagonals are split at right angles. The rhombus is frequently referred to as a diamond or rhombus.
It can be inferred that Melissa and Diana are correct to claim that the image is a rhombus from the description of rhombus attributes.
The given question is incomplete. The complete question is 'Who is correct?
An image shows two quadrilaterals. They are facing different directions, but each of them has two pairs of opposite sides that are parallel and equal in length.
A. Diana is correct. Only the quadrilateral on the right has two pairs of parallel sides and all sides the same length.
B. Melissa is correct. Only the quadrilateral on the left has two pairs of parallel sides and all sides the same length.
C. Both are correct. Both quadrilaterals have two pairs of parallel sides and all sides the same length.
D. Neither is correct. Neither figure has all sides the same length.'
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HELPPPPPPPPPPPPPPPPPPPPP!!!!!!!!!!!!!!!!!!!!!!
YALL AMAZING :)
Answer:
11 and 12
Step-by-step explanation:
Solving this would be the case of finding that square root of 131, then rounding both up and down.
First, to solve
The square root of 131 is 11.45
Now we take that 11.45 and round both up and down
Rounding down is 11 and rounding up is 12.
11 and 12 are next to each other, making them consecutive.
Answer:
I think its 11 and 12
Step-by-step explanation:
1 A line passes through (8, -2) and has a slope of ¼.
a. Write an equation for the line in point-slope form.
[tex](\stackrel{x_1}{8}~,~\stackrel{y_1}{-2})\hspace{10em} \stackrel{slope}{m} ~=~ \cfrac{1}{4} \\\\\\ \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-\stackrel{y_1}{(-2)}=\stackrel{m}{ \cfrac{1}{4}}(x-\stackrel{x_1}{8}) \implies {\large \begin{array}{llll} y +2= \cfrac{1}{4} (x -8) \end{array}}[/tex]
Mr. Chi wants to sell his house. The state he lives in charges a 3.5% sales tax on the sale of a house. The county charges a 3.4% sales tax, and the city charges a 1.1% sales tax. If Mr. Chi sells his home for $313,800, what is his total tax bill?
Answer: 32082.2
Step-by-step explanation:
Based on the given conditions, formulate:: 341300 * (2.3% + 4.4% + 2.7%)
Calculate the sum or difference: 341300 * 0.094
Calculate the product or quotient: 32082.2
Step-by-step explanation:
help thank you :)
You are beautiful. Don't let anyone tell you different<3
Answer:
11/20
Step-by-step explanation:
Add 1/5 and 1/4. You get 9/20.
Subtract that from 1 and you get 11/20 :)
Answer:
11/20
Step-by-step explanation:
1/5+1/4
4/20+5/20= 9/20
20/20-9/20=11/20
What is 2 to the 43000000th power
Step-by-step explanation:
so much sorry about that
Answer: 2^43000000 (the answer is impossibly large)
A triangle has an area of 100 square feet and a height of 5 feet. What is the length of the base of the triangle? Responses 10 ft 10 ft 20 ft 20 ft 40 ft 40 ft 160 ft
The length of the base of the triangle is 40ft
How to find the length of the base?A triangle is a polygon with three sides, three angles, three vertices, and sum of angles is s 180 degrees
The given parameters that will help us to solve the problem are
the triangle has area of 100height of the triangle is 5ftthe length of the base is = xThe area of the triangle is given as
Area = 1/2 *b*h
Area = 1/2*b*5 = 100
Area = 5b/2 = 100
Area = 5b = 200
Making b the subject of the relation
b= 200/5 =40 ft
Therefore the response for 40 ft is correct
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the back of dante's property is a creek. dante would like to enclose a rectangular area, using the creek as one side and fencing for the other three sides, to create a corral. if there is 200 feet of fencing available, what is the maximum possible area of the corral?
If there is 200 feet of fencing available, the maximum possible area of the corral is 5000 Feet.
In the question, if there is 200 feet of fencing available, then we have to find the maximum possible area of the corral.
The formula of area of rectangle is:
A = L × B, where L is the length of the rectangle and B is the breadth of the rectangle.
The A = 200 feet and rectangular area is enclosed using the creek as one side and fencing for the other three sides, to create a corral.
So, L + 2B = 200
Subtract L on both side, we get
2B = 200 - L
Divide by 2 on both side, we get
B = 100 - L/2
A = f(L)
A = L·(100 - L/2)
A = 100L - [tex]L^2[/tex]/2
Now finding the derivative.
A' = [tex]\frac{df(L)}{dL}[/tex]
A' = -L + 100
Let A' = 0
-L + 100 = 0
Subtract 100 on both side, we get
-L = -100
L = 100 feet
Now putting the value of L in B = 100 - L/2.
B = 100 - 100/2
B = 100 - 50
B = 50 feet
The maximum possible area of the corral = 100 × 50
The maximum possible area of the corral = 5000 Feet
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A triangle was dilated by a scale factor of 6. if sin a° = four fifths and segment de measures 30 units, how long is segment ef? triangle def in which angle f is a right angle, angle d measures a degrees, and angle e measures b degrees segment ef = 15.5 units segment ef = 24 units segment ef = 30 units segment ef = 37.5 units
The triangle DEF's section EF measures 24 units in length.
As per the data given in the above question are as bellow,
The provided details are as follow,
Procedure: Calculating the length that results from distorting a triangle by a scale factor
The triangle mentioned in the previous sentence is summarised in the diagram below. Using a trigonometric relationship, we discover that the following formula best describes the length of the section EF:
[tex]$\sin a^{\circ}=\frac{E F}{D E}$[/tex]
If we know that DE=30 and [tex]$\sin a^{\circ}=\frac{4}{5}$[/tex], then the length of the segment EF is:
[tex]E F=D E \cdot \sin a^{\circ} \\& E F=30 \cdot\left(\frac{4}{5}\right) \\[/tex]
EF=24
Sine (sin), cosine (cos), and tangent (tan), which are defined in terms of the ratios of the sides of a right triangle, are the fundamental trigonometric functions.
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Note: The correct question would be as bellow,
A triangle was dilated by a scale factor of 6. If sin a° = four fifths and segment DE measures 30 units, how long is segment EF?triangle DEF in which angle F is a right angle, angle D measures a degrees, and angle E measures b degrees
15.5 units
24 units
30 units
37.5 units
the numberline shows the temperatures at 2:00 AM. and 2:00 P.M. in the Gobi Desert. Find and interpret the distance between the points?
2:00am -13F 2:00pm 38F
Answer:
There is a difference of 51 degrees
Step-by-step explanation:
-13 to zero is 13 degrees
zero to 38 degrees is 38 degrees
13 + 38 is an increase of 51 degrees
In a right triangle, sin (8x - 9)° = cos (x+6)°. Solve for x. Round your answer to the nearest hundredth if necessary.
To solve the triangle, or identify unknown portions in terms of known portions, we can apply the Pythagorean theorem and the properties of sines, cosines, and tangents. The x is 8 .
Find value of x ?To solve the triangle, or identify unknown portions in terms of known portions, we can apply the Pythagorean theorem and the properties of sines, cosines, and tangents.
Pythagorean theorem: a2 + b2 = c2.
Sine: sin A=a/c, sin B=b/c.
Cosines: cos A = b/c, cos B = a/c.
Identity based on trigonometry
cos x sin (90-x)
therefore, if we have
(4x plus 10) o = Cos (6x)
(4x plus 10) o = Sin (90- 6x)
4x + 10 = 90 - 6x
4x+6x = 90 - 10
10x = 80
x = 80/10
x = 8
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Simplify the square root of 3/8