Answers
Answer:
Step-by-step explanation:
The correct domain for the function y = √x is 0 ≤ x < ∞. The square root function is defined for non-negative real numbers, so x must be greater than or equal to 0 (0 ≤ x) to have a real value for the square root. The domain does not include negative values since the square root of a negative number is not a real number. The notation 0 ≤ x < ∞ represents all values of x that are greater than or equal to 0 and less than positive infinity.
Related Questions
the population of a certain state can be estimated by the equation p=80.7t+18,312.3, where p represents the population of the state in thousands of people t years since 2010
Answers
The estimated population of the state in the year 2022 is 19,280,700 people.
The given equation represents the population of a certain state as a function of time, where p is the population in thousands of people and t is the number of years since 2010.
The equation is given as p = 80.7t + 18,312.3.
To estimate the population of the state, we substitute the value of t into the equation. For example, if we want to estimate the population in the year 2022 (12 years since 2010), we substitute t = 12 into the equation:
p = 80.7(12) + 18,312.3
= 968.4 + 18,312.3
= 19,280.7.
The estimated population of the state in the year 2022 is 19,280,700 people.
We can estimate the population for any given year by substituting the corresponding value of t into the equation.
It's important to note that the population is given in thousands of people, so we multiply the final result by 1,000 to obtain the population in actual numbers.
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3.
Your family is planning a road trip stretching from coast to coast for this summer. The route and the time frame are nearly set; now you need to plan out the finances. Your parents have decided that rental of an RV will be cheaper than staying in hotels, but they would like an estimate on the total cost. Can you help them?
a. To rent an RV, the following costs apply: $125 per day, plus 32 cents per mile. Additionally, to drop off the RV on the other side of the country, there is an extra fee of $2,500. Write an equation to describe the total cost of RV rental.
b. Your parents have two options for their road trip plans. The first option stretches over 3500 miles and includes fewer stops but more beautiful scenery. It will take about a week and a half (11 days). The second option stretches over just 3000 miles, but it includes more overnight stops and will therefore take two weeks (14 days). Which of these two options is cheaper?
c. Your little sister really wants to take the two-week trip, but your parents really want to keep the RV rental cost under $5,000. You can compromise by either taking a more direct route (lessening the miles) or by stopping for less overnight stays (lessening the days of the rental). What would the domains be for these two compromises? Justify why you think your domains are correct.
d. Write and solve equations to find how many miles or how many days you would have to eliminate in order to stay under the $5,000 budget. Explain each step as you solve your equations. Finally, make a recommendation to your parents about which compromise you think is best.
Answers
a. An equation to describe the total cost of RV rental:
Cost = (125 * d) + (0.32 * m) + 2500
b. Comparing the two costs will determine which option is cheaper.
c. For the more direct route: m ≤ 3500
For fewer overnight stays: d ≤ 14
These domains ensure that we don't exceed the original values for miles and days.
d. I recommend compromising by lessening the number of days of the rental. By reducing the rental period to 11 days, you can stay within the $5,000 budget while still allowing your little sister to take the two-week trip.
a. To write an equation for the total cost of RV rental, we can use the given information. The cost per day is $125, and there is an additional charge of 32 cents per mile. Let's denote the number of days as d and the number of miles as m. The equation for the total cost of RV rental can be written as:
Cost = (125 * d) + (0.32 * m) + 2500
b. To compare the costs of the two options, we need to calculate the total cost for each. Option 1 has 3500 miles and takes 11 days, while option 2 has 3000 miles and takes 14 days. We can substitute these values into the equation from part a to find the total costs for each option. Comparing the two costs will determine which option is cheaper.
c. To compromise and stay within a budget of $5,000, we can adjust either the number of miles or the number of days. For the more direct route, we can reduce the number of miles, and for fewer overnight stays, we can reduce the number of days. The domains for these compromises would be:
For the more direct route: m ≤ 3500
For fewer overnight stays: d ≤ 14
These domains ensure that we don't exceed the original values for miles and days.
d. To find the number of miles or days to eliminate in order to stay under the $5,000 budget, we can set up equations using the total cost equation from part a. Let's denote the reduced number of miles as m' and the reduced number of days as d'. We need to solve the following equation for each compromise:
(125 * d') + (0.32 * m') + 2500 ≤ 5000
By substituting the appropriate values into the equation and solving for m' or d', we can determine how many miles or days need to be eliminated.
Based on the given information, I recommend compromising by lessening the number of days of the rental. By reducing the rental period to 11 days, you can stay within the $5,000 budget while still allowing your little sister to take the two-week trip. This compromise ensures that you don't have to sacrifice too much scenic beauty or make drastic changes to the route.
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The graphs of the functions f(x)
Answers
If the graph of [tex]f(x) = 4e^{0.1x}[/tex] is blue, then the graph of [tex]f(x) = 4(1 + \frac{0.1}{0.5} )e^{0.5x}[/tex] is green.
How to write an exponential function to represent the situation?In Mathematics and Geometry, an exponential function can be modeled by using this mathematical equation:
[tex]f(x)=a(b)^x[/tex]
Where:
a represents the initial value or y-intercept.x represents x-variable.b represents the rate of change or common ratio.Assuming x = 10, the output value of [tex]f(x) = 4e^{0.1x}[/tex] is given by;
[tex]f(x) = 4e^{0.1x}\\\\f(10) = 4e^{0.1\times 10}[/tex]
f(10) = 10.872
[tex]f(x) = 4(1 + \frac{0.1}{0.5} )e^{0.5x}\\\\f(10) = 4(1 + \frac{0.1}{0.5} )e^{0.5 \times 10}[/tex]
f(10) = 9.9533
Therefore, the green graph most likely represents [tex]f(x) = 4(1 + \frac{0.1}{0.5} )e^{0.5x}[/tex] .
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NEED HELP FASTT PLEASE
Answers
Answer:
x=8
Step-by-step explanation:
This is a triangle, all 3 angles should add up to 180 degrees. Since we already have an angle at 69 degrees (nice), and we know that this is an isosceles triangle, we can put it as 9y-3 = 69
9y = 72, y=8
Now, you know that two angles both have angles of 69, add it up and subtract it from 180. This gives a 42-degree angle of angle B. Make its equation equal to 42 degrees.
42 = 5x+2
40 = 5x
x=8
Hope this helps!
The physician’s order reads to administer Lasix 80 mg PO STAT. You have Lasix 20 mg tablets on hand. How many tablets will you administer to the patient ?
Answers
The nurse should administer 4 Lasix 20 mg tablets to the patient to achieve the prescribed dose of 80 mg.
To determine the number of Lasix 20 mg tablets that should be administered to the patient, we need to calculate how many tablets are equivalent to the prescribed dose of 80 mg.
Given that each Lasix tablet contains 20 mg of the medication, we can divide the prescribed dose (80 mg) by the dosage strength of each tablet (20 mg) to find the number of tablets needed.
Number of tablets = Prescribed dose / Dosage strength per tablet
Number of tablets = 80 mg / 20 mg
Number of tablets = 4 tablets
Therefore, the nurse should administer 4 Lasix 20 mg tablets to the patient to achieve the prescribed dose of 80 mg.
It is important to note that this calculation assumes that the Lasix tablets can be divided or split if necessary. However, it is crucial to follow the specific instructions provided by the prescribing physician or consult with a pharmacist if there are any concerns about the appropriate administration of the medication.
Additionally, it is important to consider any additional instructions, such as the frequency and timing of administration, as specified by the physician's order.
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I can’t figure this out. Please help
Answers
Answer:
Relative maximum at x=0; Relative minimum at x=8/3
Step-by-step explanation:
To find the relative maximums and the relative minimums, you must first find the first derivative of the function. The first derivative of this function is 6x^2-16x. Simply it and you get 2x(3x-8). X would be equal to 0 and 8/3. Next, make a number line where you put 0 and 8/3 have a value of zero.
+ - +
-------------------0----------------------------8/3-----------------------
Plug in a value of x<0 to get the region left of 0. Say we use -1, we get -2(-3-8), which is positive, meaning that it is increasing there. From 0 to 8/3, if we use 1, we get 2(3-8), which is decreasing. If we use 3, we get 6(9-8), which is increasing. From this, we can see that when x=0, the graph has a relative maximum. When x=8/3, the graph has a relative minimum.
which number best represents the slope of the graphed line?
A. -5
B. -1/5
C. 1/5
D. 5
Answers
Answer:
The slope of the graphed line is A. -5
Step-by-step explanation:
Since when we move one step in x direction, we move 5 steps downwards in y direction, so, the slope is,
m = y/x
m = -5/1
m = -5
Solve each equation for the angle in standard position, for 0° ≤ 0 < 360° (nearest tenth, if necessary).
a) tan 0 = 1 / √3
b) 2cos 0= √3
Answers
Answer:
Step-by-step explanation:
a) To solve the equation tan θ = 1/√3, we can find the angle whose tangent is 1/√3 by taking the inverse tangent (arctan) of 1/√3.
θ = arctan(1/√3)
θ ≈ 30.0°
Therefore, the angle in standard position that satisfies tan θ = 1/√3 is approximately 30.0°.
b) To solve the equation 2cos θ = √3, we can isolate the cosine term by dividing both sides of the equation by 2.
cos θ = √3 / 2
Now, we can find the angle whose cosine is √3/2 by taking the inverse cosine (arccos) of √3/2.
θ = arccos(√3/2)
θ ≈ 30.0°
Therefore, the angle in standard position that satisfies 2cos θ = √3 is approximately 30.0°.
If f(x)=x+3 and g(x)=x^2-2, find the following.
a. f(g(0))
b. g(f(0))
c. f(g(x))
d. g(f(x))
e. f(f(-2))
f. g(g(4))
g. f(f(x))
h. g(g(x))
Answers
Step-by-step explanation:
a. f(g(0)) = f(0^2 - 2) = f(-2) = -2 + 3 = 1
b. g(f(0)) = g(0+3) = g(3) = 3^2 - 2 = 7
c. f(g(x)) = g(x) + 3 = x^2 - 2 + 3 = x^2 + 1
d. g(f(x)) = f(x)^2 - 2 = (x+3)^2 - 2 = x^2 + 6x + 7
e. f(f(-2)) = f(-2+3) = f(1) = 1+3 = 4
f. g(g(4)) = g(4^2 - 2) = g(14) = 14^2 - 2 = 194
g. f(f(x)) = f(x+3) = (x+3)+3 = x+6
h. g(g(x)) = g(x^2 - 2) = (x^2 - 2)^2 -2 = x^4 - 4x^2 + 2
Write the inequality and solve.
Negative nine times one more than a number is not as much as twelve times that number plus nine.
Answers
Answer:
-9(x+1) < 12x+9
if you need me to solve it here it is:
-9x - 9 < 12x + 9
+ 9 +9
-9x < 12x + 18
-12x -12x
-18x < 18
(divide by -18 on both sides)
x < - 1
Therefore, any number is that is greater than -1 will work for this inequality.
Hope this helps!
Analyzing Wages-Plus-Commission Pay
Maybelle works in the shoe department for a high-end
store. She earns $15 per hour for at least 40 hours per
week. On top of that, she earns 10% commission for each
pair of shoes she sells. She is expected to sell $2,500
worth of shoes every week.
What will Maybelle earn in wages in a typical week?
How much commission will Maybelle earn if she sells
$3,000 of shoes in one week?
v
The next week, customers return $1,000 worth of
shoes. How much money will be deducted from
Maybelle's paycheck?
With an economic downturn, sales slump. As a result,
Maybelle will likely
Answers
a)In a typical week, Maybelle will earn a total of: $600 + $250 = $850
b) Her total earnings for the week would be: $600 + $300 = $900
c) Her paycheck will be reduced by $100.
d) Her wage earnings should remain the same assuming she still works at least 40 hours per week.
To calculate Maybelle's earnings in a typical week, we first need to determine the minimum number of hours she works. Since she earns $15 per hour for at least 40 hours per week, her minimum wage earnings are:
$15 x 40 = $600
In addition to her wage earnings, Maybelle earns a commission of 10% for each pair of shoes she sells. Since she is expected to sell $2,500 worth of shoes every week, her commission earnings are:
$2,500 x 0.10 = $250
b) If Maybelle sells $3,000 worth of shoes in one week, her commission earnings would be:
$3,000 x 0.10 = $300
On top of her wage earnings of $600 (based on working at least 40 hours at $15 per hour)
c) If customers return $1,000 worth of shoes the next week, Maybelle's commission earnings will not be affected. However, her wage earnings will be reduced by the amount of the returned shoes, which is $1,000 x 0.10 = $100.
d) With an economic downturn and sales slump, Maybelle's earnings from commission will likely decrease since she will sell fewer shoes. However, her total earnings will likely decrease due to the decrease in commission earnings.
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Question 1 (11 point) What are the x-intercepts of the function y=(x-5Xx+3)? ( Blank 1- .0) ( 0)
Answers
The x-intercepts of the function y = (x-5)(x+3) are 5 and -3.
To find the x-intercepts of the function y = (x-5)(x+3), we need to set y equal to zero and solve for x.
The x-intercepts are the values of x where the graph of the function intersects or crosses the x-axis.
Set y = 0:
0 = (x-5)(x+3)
Apply the zero-product property:
The product of two factors is equal to zero if and only if at least one of the factors is equal to zero.
Therefore, we can set each factor equal to zero and solve for x.
Setting x-5 = 0:
x - 5 = 0
x = 5
Setting x+3 = 0:
x + 3 = 0
x = -3.
The x-intercepts of the function y = (x-5)(x+3) are x = 5 and x = -3.
These are the values of x where the graph of the function crosses the x-axis.
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Movimiento en linea recta
Answers
El movimiento en línea recta se refiere al desplazamiento de un objeto en una trayectoria rectilínea, es decir, sin cambios de dirección.
En este tipo de movimiento, la velocidad y la aceleración del objeto pueden variar, pero su dirección se mantiene constante a lo largo del recorrido.
El movimiento en línea recta puede ser uniforme o no uniforme. En el caso del movimiento uniforme, la velocidad del objeto es constante, lo que implica que el desplazamiento realizado en intervalos iguales de tiempo es también constante.
Por otro lado, en el movimiento no uniforme, la velocidad cambia a lo largo del tiempo, resultando en diferentes desplazamientos en intervalos de tiempo iguales.
La descripción matemática del movimiento en línea recta se basa en conceptos como la posición, la velocidad y la aceleración. La posición se refiere a la ubicación del objeto en relación a un punto de referencia, la velocidad representa la tasa de cambio de la posición y la aceleración indica la tasa de cambio de la velocidad.
El estudio del movimiento en línea recta es fundamental en la física y tiene aplicaciones en diversas áreas, como la mecánica, la cinemática, la dinámica y la física de partículas.
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Which of the following are necessary when proving that the opposite sides of
a parallelogram are congruent? Check all that apply.
A. Opposite sides are parallel.
B. Corresponding parts of congruent triangles are congruent.
C. Opposite sides are perpendicular.
D. Corresponding parts of similar triangles are similar.
SUBMIT
Answers
Answer:
It's A and B: Opposite sides are parallel and Corresponding parts of congruent triangles are congruent.
Step-by-step explanation:
What is the mean and median reasoning, As the last one is incorrect
Answers
The best measure of center of the data is (a) mean; because the data are close together
How to determine the best measure of center of the dataFrom the question, we have the following parameters that can be used in our computation:
The dataset of 10 values
Where we can see that there are no outliers present in the dataset
By definition, outliers are extreme values.
Since there are no outliers, it means that the mean is the best measure of center
This is because the mean is affected by the presence of outliers and since no outlier is present, we use the mean
From the list of options, we have the mean value to be 42.536
Hence, the true statement is (a)
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what is the percentage of profit of $350 on a $1200 investment
Answers
The percentage of profit on a $1200 investment resulting in a $350 profit is 29.17%.
The percentage of profit on a $1200 investment that results in a $350 profit can be calculated using the formula:
Percentage of profit = (Profit / Investment) x 100
In this case, the profit is $350 and the investment is $1200. Plugging these values into the formula:
PercThe percentage of profit on a $1200 investment that results in a $350 profit can be calculated using the formula:
Percentage of profit = (Profit / Investment) x 100
In this case, the profit is $350 and the investment is $1200. Plugging these values into the formula:
Percentage of profit = (350 / 1200) x 100
Calculating this expression gives us:
Percentage of profit = 0.2917 x 100 = 29.17%
Therefore, the percentage of profit on a $1200 investment resulting in a $350 profit is 29.17%.
To calculate the percentage of profit, we divide the profit by the investment and then multiply by 100 to express it as a percentage. In this case, the profit is $350 and the investment is $1200. Dividing $350 by $1200 gives us 0.2917. Multiplying this by 100 gives us 29.17%. This means that the profit of $350 represents 29.17% of the initial investment of $1200.entage of profit = (350 / 1200) x 100
Calculating this expression gives us:
Percentage of profit = 0.2917 x 100 = 29.17%
Therefore, the percentage of profit on a $1200 investment resulting in a $350 profit is 29.17%.
To calculate the percentage of profit, we divide the profit by the investment and then multiply by 100 to express it as a percentage. In this case, the profit is $350 and the investment is $1200. Dividing $350 by $1200 gives us 0.2917.
Multiplying this by 100 gives us 29.17%. This means that the profit of $350 represents 29.17% of the initial investment of $1200.
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Which system has the same solution as the system of equations shown?
3x + 2y = -5
2x + 3y = 5
Answers
Step-by-step explanation:
To find a system with the same solution as the given system, we can multiply both sides of both equations by a nonzero constant, which will result in a system that is equivalent to the original one.
For example, let's multiply the first equation by 2 and the second equation by 3:
First equation (multiplied by 2):
6x + 4y = -10
Second equation (multiplied by 3):
6x + 9y = 15
The new system of equations is:
6x + 4y = -10
6x + 9y = 15
This system has the same solution as the original system because it's just a scalar multiple of the original system.
Question
Determine whether it is possible to construct one, many or no triangle(s) with two side lengths of 3 inches that meet at a 20 degree angle.
one triangle
many triangles
no triangles
Answers
Answer:
We can construct only one triangle with the given description(this triangle is unique).
It is isosceles so the two sides are congruent(
4
4 cm) each. The angle they form is specified
80
°
80° so there is no way to construct one more with the same characteristics(we will have to change the angle or the length of the two sides).
Step-by-step explanation:
Answer:
One triangle
Step-by-step explanation:
By the Law of Cosines, given two side lengths of 3 inches and an included angle of 20°, then we are able to get the length of the third side using the formula [tex]a^2=b^2+c^2+2bc\cos(A)[/tex]
Hence, you can construct only one triangle because of SAS Theorem.
If FE =14 find the length of BC
Please give a very in-depth explanation and I will mark Brainliest!!
Answers
HI Your answer is 42
I have calculated it you can trust me
Well you have marked right in the pic
PLEASE MARK AS BRAINLIEST
21. Find the surface area of the figure below.
20 mm
17.mm
A. 969 mm²
B. 984 mm²
17 mm
C. 1,040 mm²
D. 1,105 mm²
Answers
Answer:
Step-by-step explanation:
What is 1,0000 ÷ 2,0000
Answers
How can you use the transformations to prove 2 triangles are congruent
Answers
Answer:
There are three main ways to prove that two triangles are congruent using transformations:
1. Congruence by translation: If there is a translation that maps one triangle onto the other, then the triangles are congruent.
2. Congruence by reflection: If there is a line of reflection that maps one triangle onto the other, then the triangles are congruent.
3. Congruence by rotation: If there is a rotation that maps one triangle onto the other, then the triangles are congruent.
In order to use these transformations to prove congruence, you need to show that all corresponding parts (angles and sides) are congruent after the transformation is applied. This can be done either algebraically, using coordinate geometry, or by providing a clear visual representation of the transformations that are applied.
For example, if you want to prove that two triangles, ABC and DEF, are congruent by translation, you need to show that there is a vector that, when added to the coordinates of any point on triangle ABC, produces the coordinates of the corresponding point on triangle DEF. Once you have shown that all three sides and angles are congruent after the translation, you can conclude that the triangles are congruent.
Identify the transformations needed to map one triangle onto the other. These transformations can include translations, rotations, and reflections.
Perform the transformations on one of the triangles.
If the transformed triangle coincides exactly with the other triangle, then the two triangles are congruent.
For example, to prove that two triangles are congruent using the side-side-side (SSS) criterion, we can use translations and rotations to map one triangle onto the other. We can also use reflections to map one triangle onto the other if we are using the side-angle-side (SAS) or angle-side-angle (ASA) criteria. The steps for each criterion may vary slightly, but the general idea is the same.
It's important to note that the transformations used must be rigid motions, meaning that they preserve the size and shape of the triangle. If a transformation changes the size or shape of the triangle, then the triangles are not congruent.
Overall, using transformations to prove triangle congruence is a useful method that can be used in conjunction with other methods such as the SSS, SAS, ASA, AAS, and HL criteria.
in a right triangle the hypotenuse is 17 and an adjacent side is 9. What is the measure of the angle opposite the adjacent sied?
Answers
★ Apply Phythagoras Theorem:-
[tex] \sf \longrightarrow \: {(adjacent \: side)}^{2} + {(opposite \: side)}^{2} = {(hypotenuse)}^{2} [/tex]
[tex] \sf \longrightarrow \: {(9)}^{2} + {(opposite \: side)}^{2} = {(17)}^{2} [/tex]
[tex] \sf \longrightarrow \: 81 + {(opposite \: side)}^{2} = {(17)}^{2} [/tex]
[tex] \sf \longrightarrow \: 81 + {(opposite \: side)}^{2} = 289[/tex]
[tex] \sf \longrightarrow \: {(opposite \: side)}^{2} = 289 - 81[/tex]
[tex] \sf \longrightarrow \: {(opposite \: side)}^{2} = 208[/tex]
[tex] \sf \longrightarrow \: opposite \: side= \sqrt{ 208}[/tex]
[tex] \sf \longrightarrow \: opposite \: side=14.422[/tex]
Show that y₁(t) = e^ãt cos(μt) and
y₂(t) = e^ãt sin(μt)
are a fundamental set of solutions and state the general solution.
Answers
The functions y₁(t) = e^ãt cos(μt) and y₂(t) = e^ãt sin(μt) are a fundamental set of solutions because they are linearly independent and satisfy the given homogeneous linear differential equation, allowing for the formation of the general solution.
To show that y₁(t) = e^ãt cos(μt) and y₂(t) = e^ãt sin(μt) are a fundamental set of solutions, we need to demonstrate two things: linear independence and satisfaction of the given homogeneous linear differential equation.
First, let's consider linear independence. We can prove it by showing that there is no constant c₁ and c₂, not both zero, such that c₁y₁(t) + c₂y₂(t) = 0 for all t.
Now, let's verify that y₁(t) and y₂(t) satisfy the homogeneous linear differential equation. If the given differential equation is of the form ay''(t) + by'(t) + cy(t) = 0, we can substitute y₁(t) and y₂(t) into the equation and verify that it holds true.
Once we have established linear independence and satisfaction of the differential equation, we can state that the general solution to the homogeneous linear differential equation is given by y(t) = c₁y₁(t) + c₂y₂(t), where c₁ and c₂ are arbitrary constants. This general solution represents the linear combination of the fundamental set of solutions.
In summary, y₁(t) = e^ãt cos(μt) and y₂(t) = e^ãt sin(μt) form a fundamental set of solutions for the given differential equation, and the general solution is given by y(t) = c₁y₁(t) + c₂y₂(t).
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which graph represents this function
f(x)=1/2x-5
help would be appreciated
Answers
The graph of the equation f(x) = 1/2x - 5 is the graph (b)
How to determine the graph of the equationFrom the question, we have the following parameters that can be used in our computation:
f(x) = 1/2x - 5
The above expression is a linear equation that implies that
Slope = 1/2
y-intercept = -5
Next, we determine the graph
The graph that has a slope of 1/2 and y-intercept of -5 is (b)
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Solve the system of equations using the substitution or elimination method.
y = 4x - 7
4x + 2y = -2
.
Show your work
Correct x and y
Answers
The solution to the system of equations is x = 1 and y = -3.
To solve the system of equations using the substitution or elimination method, let's start with the substitution method.
Given equations:
y = 4x - 7
4x + 2y = -2
We'll solve equation 1) for y and substitute it into equation 2):
Substituting y from equation 1) into equation 2):
4x + 2(4x - 7) = -2
4x + 8x - 14 = -2
12x - 14 = -2
Now, we'll solve this equation for x:
12x = -2 + 14
12x = 12
x = 12/12
x = 1
Now that we have the value of x, we can substitute it back into equation 1) to find y:
y = 4(1) - 7
y = 4 - 7
y = -3
Therefore, the solution to the system of equations is x = 1 and y = -3.
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Please explain how to do this and what the answer is. The answer with best explaination gets Brainliest
Answers
Answer:
102
Step-by-step explanation:
we substitute x by 7
7^2+9(7)-10
49+63-10
=102
Consider the transformation.
2 trapezoids have identical angle measures but different side lengths. The first trapezoid has side lengths of 4, 2, 6, 2 and the second trapezoid has side lengths of 8, 4, 12, 4.
Which statement about the transformation is true?
Answers
The true statement about the transformation is that the second trapezoid is a dilation of the first trapezoid with a scale factor of 2.
The given transformation involves two trapezoids with identical angle measures but different side lengths. Let's analyze the two trapezoids and determine the statement that is true about the transformation.
First Trapezoid:
Side lengths: 4, 2, 6, 2
Second Trapezoid:
Side lengths: 8, 4, 12, 4
To determine the relationship between the side lengths of the two trapezoids, we can compare the corresponding sides.
Comparing the corresponding sides:
4 / 8 = 2 / 4 = 6 / 12 = 2 / 4
We can observe that the corresponding sides of the two trapezoids have the same ratio. This indicates that the side lengths of the second trapezoid are twice the lengths of the corresponding sides of the first trapezoid. Therefore, the statement that is true about the transformation is:
The second trapezoid is a dilation of the first trapezoid with a scale factor of 2.
A dilation is a type of transformation that produces an image that is the same shape as the original figure but a different size. In this case, the second trapezoid is obtained by scaling up the first trapezoid by a factor of 2 in all directions.
This transformation preserves the shape and angle measures of the trapezoid but changes its size. The corresponding sides of the second trapezoid are twice as long as the corresponding sides of the first trapezoid.
For more such questions on trapezoid visit:
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Guys i need help!! Im not understanding at all.
Answers
Answer:
H= [4 -1
4 0]
Step-by-step explanation:
A comet follows a hyperbolic path in which the sun is located at one of its foci. If the equation... 100 pts
Answers
Answer:
164 million km
Step-by-step explanation:
If the hyperbola models the comet's path, and the sun is located at one of its foci, the closest distance the comet reaches to the sun is the distance between a vertex and its corresponding focus.
Therefore, we need to find the vertices and foci of the given hyperbola.
Given equation:
[tex]\dfrac{x^2}{60516}-\dfrac{y^2}{107584}=1[/tex]
As the x²-term of the given equation is positive, the hyperbola is horizontal (opening left and right).
The general formula for a horizontal hyperbola (opening left and right) is:
[tex]\boxed{\begin{minipage}{7.4 cm}\underline{Standard equation of a horizontal hyperbola}\\\\$\dfrac{(x-h)^2}{a^2}-\dfrac{(y-k)^2}{b^2}=1$\\\\where:\\\phantom{ww}$\bullet$ $(h,k)$ is the center.\\ \phantom{ww}$\bullet$ $(h\pm a, k)$ are the vertices.\\\phantom{ww}$\bullet$ $(h\pm c, k)$ are the foci where $c^2=a^2+b^2.$\\\phantom{ww}$\bullet$ $y=\pm \dfrac{b}{a}(x-h)+k$ are the asymptotes.\\\end{minipage}}[/tex]
Comparing the given equation with the standard equation:
h = 0k = ka² = 60516 ⇒ a = 246b² = 107584 ⇒ b = 328To find the loci, we first need to find the value of c:
[tex]\begin{aligned}c^2&=a^2+b^2\\c^2&=60516 +107584\\c^2&=168100\\c&=410\end{aligned}[/tex]
The formula for the loci is (h±c, k). Therefore:
[tex]\begin{aligned}\textsf{Loci}&=(h \pm c, k)\\&=(0 \pm 410, 0)\\&=(-410,0)\;\;\textsf{and}\;\;(410,0)\end{aligned}[/tex]
The formula for the vertices is (h±a, k). Therefore:
[tex]\begin{aligned}\textsf{Vertices}&=(h \pm a, k)\\&=(0 \pm 246, 0)\\&=(-246,0)\;\;\textsf{and}\;\;(246,0)\end{aligned}[/tex]
From the given diagram, the vertex and focus have positive x-values. Therefore, the vertex is (246, 0) and the focus is (410, 0).
We need to find the distance between (246, 0) and (410, 0). To do this, simply subtract the x-value of the vertex from the x-value of the focus:
[tex]410-246=164[/tex]
Therefore, the closest distance the comet reaches to the sun is 164 million km.
