[tex]\left\{\begin{array}{ccc}\dfrac{s}{2}-3t=-1&\text{multiply both sides by 4}\\3t-2s=3\end{array}\right\\\underline{+\left\{\begin{array}{ccc}2s-12t=-4\\3t-2s=3\end{array}\right}\qquad\text{add both sides of the equations}\\.\qquad\qquad -9t=-1\qquad\text{divide both sides by (-9)}\\.\qqud\qquad\boxed{t=\dfrac{1}{9}}\\\\\text{Put the value of t to the second equation}\\\\3\left(\dfrac{1}{9}\right)-2s=3\\\\\dfrac{1}{3}-2s=3\qquad\text{subtract}\ \dfrac{1}{3}\ \text{from both sides}[/tex]
[tex]-2s=2\dfrac{2}{3}\qquad\text{divide both sides by (-2)}\\\\s=\dfrac{8}{3}\cdot\left(-\dfrac{1}{2}\right)\\\\\boxed{s=-\dfrac{4}{3}}\\\\Answer:\ \boxed{\left(-\dfrac{4}{3},\ \dfrac{1}{9}\right)}[/tex]
By simplifying and rearranging the given system of equations, we find that the ordered pair (s, t) that satisfies the system is (2, 1 + 2/3).
Explanation:The system of equations given in the question is:
s/2 - 3t = -1
3t - 2s = 3.
We can begin solving this system by first multiplying the first equation by 2 to eliminate the fraction, giving us:
s - 6t = -2.
Next, we rearrange the second equation to be in terms of 's':
2s = 3t + 3.
We then substitute this into the first equation and solve for 't':
(3t + 3) - 6t = -2,
simplifying to:
-3t + 3 = -2,
leading us to t = 1 + 2/3.
Substituting 't' into the second equation to find 's', we get:
2s = 3(1 + 2/3) + 3, which simplifies to s = 2. Therefore the ordered pair (s,t) that satisfies the system of equations is (2, 1 + 2/3).
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the density of an object has the equation d= m/v. if an object has a mass of 20 g and a volume of 3.5 cm3, what is it's density?
A.0.175 G/CM3
B.70 G/CM3
C.5.71 G/CM3
D.23.5 G/CM3
[tex]\mathsf{We\;know\;that : Density = \frac{Mass\;of\;the\;Object}{Volume\;of\;the\;Object}}[/tex]
[tex]\mathsf{Given : Mass\;of\;the\;Object = 20\;Grams}[/tex]
[tex]\mathsf{Given : Volume\;of\;the\;Object = 3.5\;cm^3}[/tex]
[tex]\mathsf{\implies Density = \frac{20}{3.5}(\frac{g}{cm^3})}[/tex]
[tex]\mathsf{\implies Density = 5.71\;(\frac{g}{cm^3})}[/tex]
To find the density of an object, we will use the formula for density which is \( d = \frac{m}{v} \), where:
- \(d\) represents the density of the object,
- \(m\) is the mass of the object, and
- \(v\) is the volume of the object.
Substituting the given values into the formula:
\(m = 20 \, \text{g}\) (mass of the object),
\(v = 3.5 \, \text{cm}^3\) (volume of the object),
we get:
\(d = \frac{20 \, \text{g}}{3.5 \, \text{cm}^3}\).
Dividing 20 grams by 3.5 cubic centimeters, we obtain:
\(d ≈ 5.71 \, \text{g/cm}^3\).
Therefore, the correct answer is:
C.5.71 G/CM3
check my answer?
What is the recursive rule for this geometric sequence?
−64,−16,−4,−1,...
Enter your answers in the boxes.
a n =
a 1 =
i think it is
an = a n + 1 * an-1
and
a1=-64
am i right?
A recursive rule for a geometric sequence
[tex]a_1\\\\a_n=r\cdot a_{n-1}[/tex]
---------------------------------------------------------------
[tex]a_1=-64;\ a_2=-16;\ a_3=-4;\ a_4=-1;\ ...\\\\r=\dfrac{a_{n+1}}{a_n}\to r=\dfrac{a_2}{a_1}=\dfrac{a_3}{a_2}=\dfrac{a_4}{a_3}\\\\r=\dfrac{-16}{-64}=\dfrac{1}{4}\\\\\boxed{a_1=-64;\qquad a_n=\dfrac{1}{4}\cdot a_{n-1}}[/tex]
Wind farms are a source of renewable energy found around the world. The power P (in kilowatts) generated by a wind turbine varies directly as the cube of the wind speed v (in meters per second). If a turbine generates 500kW in a 10m/s wind, how much power does it generate in a 12 m/s wind?
Show all your step please.
Answer:
600kW
Step-by-step explanation:
Referring to the fact that 10m/s of wind is 500kW so divide 500 by 10.
500/10=50
So there is 50 kW is 1m/s of wind. Now multiply 12 by 50
12x50=600
So for 12m/s of wind there is 600kW
At 12 m/s, the turbine generates 864 kW.
We can express the given relationship as P = k * v^3, where k is a constant of proportionality.
Given that a turbine generates 500 kW at a wind speed of 10 m/s, we can find k using the equation:
500 = k * 10^3
k = 500 / 1000
k = 0.5.
Now, to find out how much power the turbine would generate at 12 m/s. The calculation is :
P = 0.5 * 12^3
P = 0.5 * 1728
P = 864 kW.
The wind turbine generates 864 kW in a 12 m/s wind.
In the diagram shown, ∠7 measures 92 degrees. What is the measure of ∠8?
8 degrees
88 degrees
92 degrees
180 degrees
∠8=180°-92°=88°
===================
Answer:
Step-by-step explanation:
The answer is 88 degrees i got that question right.
what is 78,045 rounded to the nearest thousand?
Final answer:
78,045 rounded to the nearest thousand is 78,000. You round down because the hundreds digit (0) is less than 5. This approach to rounding applies in various arithmetic contexts.
Explanation:
To round 78,045 to the nearest thousand, we need to consider the hundreds digit, which is 0. In rounding, if the hundreds digit is 5 or greater, we would round up. However, because it is 0, we keep the thousands digit the same and replace all subsequent digits with zeros. Thus, 78,045 rounded to the nearest thousand is 78,000.
When dealing with whole numbers and rounding to a certain place value, it is crucial to look at the number to the immediate right of the place value you are rounding to. If this number is 5 or higher, you round up. Otherwise, you round down. This principle is true regardless of whether you are serving a subtraction operation, like 78,500 m - 362 m which rounds to 78,100 m, or if you're dealing with large numbers in scientific notation, such as 79,345 which can be represented as 7.9345 × 104.
what is the slope of the line on this graph?
Answer: 3
Step-by-step explanation:
The slope of a line passing through two points (a,b) and (c,d) is given by :-
[tex]\text{Slope}=\dfrac{d-b}{c-a}[/tex]
In the given graph , the line is passing through (0,0) and (1,3) .\
Then the slope of line passing through (0,0) and (1,3) will be :-
[tex]\text{Slope}=\dfrac{3-0}{1-0}\\\\\Rightarrow\ \text{Slope}=3[/tex]
Hence, the slope of the given line= 3
Which choice describes whether x = 19 is the solution of the equation 42 = 3x – 15? CLEAR CHECK x = 19 is not the solution because 3 • 19 – 15 = 3 • 4 = 12, not 42. x = 19 is the solution because 3 • 19 – 15 = 3 • 4 = 12. x = 19 is the solution because 3 • 19 – 15 = 57 – 15 = 42. x = 19 is not the solution because 3 • 19 – 15 = 57 – 15 = 42.
The choice that describes whether x = 19 is the solution of the equation 42 = 3x - 15 is that x = 19 is the solution because 3 * 19 - 15 = 57 - 15 = 42.
Explanation:The choice that describes whether x = 19 is the solution of the equation 42 = 3x - 15 is the option: x = 19 is not the solution because 3 * 19 - 15 = 3 * 4 = 12, not 42.
To check if a value is the solution to an equation, we substitute the value into the equation and perform the necessary calculations. In this case, substituting x = 19 into the equation 42 = 3x - 15 gives us 42 = 3 * 19 - 15 = 57 - 15 = 42. Since both sides of the equation are equal, x = 19 is indeed the solution.
The question is asking to determine if x = 19 is the solution for the equation 42 = 3x – 15. To verify this, we need to substitute x = 19 into the equation. So, we have 42 = 3(19) - 15 which simplifies to 42 = 57 - 15. After subtraction on the right side, we get 42 = 42, which is a true statement. Hence, x = 19 is indeed the solution to the equation 42 = 3x – 15.
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Tammi deposited $520.00 into a bank account that earned simple interest each year. After 5 years she had earned $156 in interest what was the annual interest rate
Answer:
R=6%
Step-by-step explanation:
Given:
Total money deposited = $ 520
Total years = 5
Total earned = $156
Simple interest
To Find:
interest rate=R=?
Solution:
We know the formula for calculating total amount earned by a simple interest rate and formula for it is
I = P(rT) ..................(i)
where I is total amount earned
P is total money invested
r is rate
and t is time
putting the values gives us
156 = 520 (r)(5)
156 = 2600 r
dividing both sides by 2600
r = [tex]\frac{156}{2600}[/tex]
r= 0.06
We have to find R
Now from simple rules of
we know that
R = r* 100 %
so putting the value of r
R = 0.06 * 100 %
R = 6%
which is the rate at which money was invested
The gas gauge in a car shows it has 40% of a tank of gas. If the car has about 5 gallons, approximately how many gallons can the tank hold when it is full?
Answer:
the tank can hold 12.5 gallons when it is full
Step-by-step explanation:
Let's assume
tank can hold 'x' gallons when it is full
we are given
The gas gauge in a car shows it has 40% of a tank of gas
So, gas in car is
[tex]=\frac{40}{100}\times x[/tex]
and we have
the car has about 5 gallons
so, we can set it equal
and then we can solve for x
[tex]5=\frac{40}{100}\times x[/tex]
[tex]5=\frac{4}{10}\times x[/tex]
[tex]5=\frac{2}{5}\times x[/tex]
Multiply both sides 5
[tex]5\times 5=5\times \frac{2}{5}\times x[/tex]
[tex]5\times 5=2x[/tex]
[tex]25=2x[/tex]
we get
[tex]x=12.5[/tex]
So, the tank can hold 12.5 gallons when it is full
Answer:
B
Step-by-step explanation:
Question is 15 points
Answer:
sec theta = r/v
Step-by-step explanation:
sec theta = 1 / sin theta
We know that sin theta = opp/ hypotenuse
1 / sin theta = hypotenuse / opp
sec theta = hypotenuse / opp
sec theta = r/v
A car company offers financing to its customers. For the newest model, customers can pay $2000 down and then $250 a month. Write an equation for this situation. What does the independent variable represent? What does the dependent variable represent?
Answer: C: y = 250x + 2000; the independent variable, x, represents the number of months after buying the car and the dependent variable, y, represents the amount of money paid on the car.
Step-by-step explanation:
The equation representing the total cost of the car over time is C(t) = 2000 + 250t, where 't' (the number of months) is the independent variable and 'C(t)' (the total cost) is the dependent variable.
To write an equation for the financing offer of a car company where customers pay a $2000 down payment and then $250 a month, we use a linear equation to represent the total cost of the car (C) over time (t):
C(t) = 2000 + 250t
Here, the independent variable 't' represents the number of months, and the dependent variable 'C(t)' represents the total cost of the car at a particular time. The independent variable is the one we have control over or choose values for, and the dependent variable is the one that changes in response to the independent variable.
he points (-3,4) and (5,-2) are on the graph of function f. If function g is the inverse of function f, what pair of points are on function g? Type the point with the lower x-value first. ( , ) and ( , )
Answer:
(4,-3) and (-2,5)
Step-by-step explanation:
The inverse of a function, is the function or rule formed by reflecting the line over y=x. This means essentially that all (x,y) values from the original function switch to (y,x).
(x,y)--->(y,x) in the new function.
If the function has points (-3,4) and (5,-2) then the inverse has points (4,-3) and (-2, 5).
Answer:
PLATO users, use this order:
(-2,5) and (4,-3)
Step-by-step explanation:
A scale drawing of a house uses a scale of 0.5 inches = 2 feet. What is the length, in inches, of a line on the scale drawing that represent an actual length of 5 feet?
Final answer:
To find the scaled length of a line representing 5 feet on a scale drawing with a scale of 0.5 inches = 2 feet, set up a proportion and solve for x. The answer is 1.25 inches.
Explanation:
To calculate the length of a line on a scale drawing, you must use the scale provided and set up a proportion based on that scale. In this case, the scale is 0.5 inches = 2 feet. To find out what 5 feet would be on the drawing, we can set up a proportion where 0.5 inches/2 feet equals x inches/5 feet. Solving for x gives us:
0.5 inches / 2 feet = x inches / 5 feet
To keep the units consistent, we use cross-multiplication:
(0.5 inches) * 5 feet = 2 feet * x inches
2.5 inches = 2 feet * x inches
Now, divide both sides by 2 feet to solve for x:
x = 2.5 inches / 2 feet
x = 1.25 inches
Therefore, a line that represents an actual length of 5 feet would be 1.25 inches long on the scale drawing.
help me with this math please
Answer:
There would be no solution im pretty sure but not 100%
Step-by-step explanation:
What is the metric system prefix for the quantity 0.000001?
Answer:
Prefix Symbol Multiplier
deci d 0.1
centi c 0.01
milli m 0.001
micro µ 0.000001
Step-by-step explanation:
Julian used these steps to solve the equation 9x=?6+3(3x+2) 9 x = - 6 + 3 ( 3 x + 2 ) . Which choice describes the meaning of his result, 0=0 ?
Answer:
see explanation
Step-by-step explanation:
the result 0 = 0
means the equation has an infinite number of solutions
Answer:
All values of x make the equation true... THIS IS THE CORRECT ANSWER!
Step-by-step explanation:
a line in the standard (x,y) coordinate plane contains the points M(-2,4) and N(8,10) What is the midpoint of MN
Answer:
(3, 7)
Step-by-step explanation:
The midpoint of a line joining the points (x1, y1) and (x2, y2) has midpoint
[(x1 + x2)/ 2]. (y1 + y2)/2 ]
Substituting the given points:-
Midpoint of MN = (-2 + 8)/2 , (4 + 10)/2
= 6/2 , 14/2
= (3, 7) (answer)
Solve for X
Thank you
Answer:
answer is 8
8+14x+6x+12=180
Step-by-step explanation:
at the production Stars you stores you can buy four bags of bananas for 2084 how much would it cost if you were three bags
Poppy's Pizza is buying square boxes to put their pizzas in. The large box has an area of 196 square inches. What is the area of the largest possible pizza that could be placed into the box?
Answer:
154 square inches
Step-by-step explanation:
Watch the attached figure of the square pizza box and the largest pizza that can fit into it.
Let the each side of the square pizza box be a inches.
Radius of the largest pizza that can fit into it = Half of the side of the pizza box = [tex]\frac{a}{2}[/tex]
So, area of the square box = Side * Side
= a * a
= a² square inches
It has also been given that the large box has an area of 196 square inches.
So,
Area of the box = a²
=> 196 = a²
Flipping the sides of the equation, we get
=> a² = 196
Taking square root on both the sides,
√a² = √196
a = 14 inches
So,
Side of square box = 14 inches
Radius of the largest pizza that can fit into it = [tex]\frac{a}{2}[/tex]
= [tex]\frac{14}{2}[/tex]
= 7 inches
Area of the largest possible pizza that could be placed into the box
= π *radius² [since pizza is circular in shape]
= [tex]\frac{22}{7}[/tex] * 7²
= [tex]\frac{22}{7}[/tex] * 7 * 7
Cancelling out a pair of 7's from the top and bottom, we have
= 22 * 7
= 154 square inches
HEEEEEEEEEELPPPPPPPPPPP PLEASE GIVING BRAILIENST TO WHOEVER HELPS ME
Answer:
Same side: 4, 1.5, 5/3, 0.2
Opposite side: -5, -1/4
Step-by-step explanation:
We know that dilation caused by a positive factor leads to the object being on the same side and dilation caused by a negative factor leads to the object being on the opposite side. Therefore, the dilation caused by positive numbers 4, 1.5, 5/3, 0.2 will lead to object being on the same side. And dilation caused by a negative numbers -5 and -1/4 will lead to object being reflected to the opposite side
Which of the following shows 18/12 as a mixed number and 1 7/8 as an improper fraction
18/12= [tex]1\frac{1}{2}[/tex] and [tex]1\frac{7}{8}[/tex] = 15/8 is the correct option, [tex]1\frac{1}{2}[/tex] is mixed fraction of 18/12 and 15/8 is improper fraction of [tex]1\frac{7}{8}[/tex].
What is Fraction?
A fraction represents a part of a whole.
If a fraction has a numerator that is less than the denominator then the fraction is proper.
An improper fraction has a numerator that is greater than the denominator.
A mixed number is an integer written with a fraction.
18/12 is a improper fraction, let us simplify it by dividing numerator and denominator by 6
18/12 is 3/2.
The mixed fraction of 3/2 is [tex]1\frac{1}{2}[/tex]
Now the given mixed fraction is [tex]1\frac{7}{8}[/tex]
When we convert to improper we get (8×1)+7/8 , which is 15/8
Hence, 18/12= [tex]1\frac{1}{2}[/tex] and [tex]1\frac{7}{8}[/tex] = 15/8 is the correct option, [tex]1\frac{1}{2}[/tex] is mixed fraction of 18/12 and 15/8 is improper fraction of [tex]1\frac{7}{8}[/tex].
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PLease help! 20 points!!
Use graphs and tables to find the limit and identify any vertical asymptotes of limit of 1 divided by the quantity x minus 4 as x approaches 4 from the left.
Answer: Negative infinity
note: if your teacher won't allow negative infinity, then try DNE for "does not exist"
=======================================================
Explanation:
As x gets closer to x = 4 from the left side of this value, then x starts at something like x = 3 and moves to x = 3.5, then to x = 3.9, then to x = 3.99, then to x = 3.999, etc
We get closer to x = 4 but never actually get there. If you look at the table attached, then f(x) = 1/(x-4) will keep getting more negative with larger and larger negative values. This growth goes on forever without any bound. So the limit is equal to negative infinity.
As you can see on the graph below, the curve heads downward as you approach x = 4 from the left hand side. Imagine you are a point on the curve, or this point is on a rollercoaster (the curve being the track itself). As you get closer to 4 from the left side, you go downhill. There is on limit to how far downhill you can go.
note: the graph and table in the attachment below were made by the free graphing calculator program GeoGebra
Answer with explanation:
The given rational function is
[tex]y= \lim_{x \to 4^{-}} \frac{1}{x-4}[/tex]
To find the vertical Asymptotes , put
→ Denominator =0
→ x-4=0
→x=4, is the Vertical Asymptote.
Emery borrowed money from her brother to buy a new phone, and is paying off a fixed amount each week. After 2 weeks, she will owe $456, and after 5 weeks , she will owe .
Emery initially borrowed $608. Each week, she paid off $76. After 2 weeks she had $456 left to pay and after 5 weeks she owed $228.
Explanation:To find out the original amount borrowed, we need to determine how much Emery is paying off each week. If we look at the information given, after 2 weeks Emery still owes $456, and after 5 weeks, she owes $228. That's a difference of $228 over the span of 3 weeks, which means she is paying off $76 each week ($228 / 3 weeks = $76 per week).
Knowing this, we can figure out that she owed $608 before she started making payments (that is, $456 + $76*2 weeks = $608). Therefore, the original amount Emery borrowed from her brother was $608.
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the complete Question is given below
Emery borrowed money from her brother to buy a new phone and is paying off a fixed amount each week. After 2 weeks, she will owe $456, and after 5 weeks, she will owe $228. a. What was the original amount Emery borrowediginal amount borrowed?
63÷10 63÷10^2 63÷10^3. Please answer these equation and type the answer in the space below in the comment section THX and have a awesome day:)
Answer:
The answer is 63/10, 63/100, 63/1000
Someone plz help me on this!!!
Answer:
(-4,1)
Step-by-step explanation:
Answer:
A
Step-by-step explanation:
A standardized test was given to a set of high school juniors and the distribution of the data is bell shaped. The mean score is 800 and the standard deviation is 120.
To qualify for a special summer camp for accelerated students, a student must score within the top 16% of all scores on the test. What score must a student make to qualify for summer camp?
To qualify for the special summer camp for accelerated students, a student must score at least approximately 978 on the standardized test, considering a score within the top 16% of all scores, given a mean score of 800 and a standard deviation of 120.
Explanation:In a bell-shaped or normal distribution, the mean [tex]\(\mu\)[/tex] represents the central tendency of the data, and the standard deviation [tex]\(\sigma\)[/tex] measures the dispersion or spread of the scores. To find the score required to qualify for the top 16%, we use the z-score formula: [tex]\(z = \frac{X - \mu}{\sigma}\)[/tex], where X is the score, [tex]\(\mu\)[/tex] is the mean, and [tex]\(\sigma\)[/tex] is the standard deviation.
Given the mean score [tex]\(\mu = 800\)[/tex] and standard deviation [tex]\(\sigma = 120\)[/tex], the z-score corresponding to the top 16% is found using a standard normal distribution table or statistical software. The z-score associated with the top 16% is approximately z = 1.04.
Next, use the z-score formula to solve for the score X required to be in the top 16%: [tex]\(z = \frac{X - \mu}{\sigma}\)\\[/tex]. Rearranging the formula to solve for X gives us [tex]\(X = z \cdot \sigma + \mu\)[/tex]. Substituting the z-score value and the given mean and standard deviation into the equation yields [tex]\(X = 1.04 \cdot 120 + 800 = 978\)[/tex]. Hence, a student needs to score at least approximately 978 to qualify for the special summer camp for accelerated students, given the distribution of scores on the standardized test.
By which rule are these triangles congruent? A) AAS B) ASA C) SAS D) SSS
Answer:
it would be SSS...
Step-by-step explanation:
Its meaning is "side side side''... so you see how the triangle, ABD has the dashed (same number of lines) through the lines of the triangle, it means the sides are all congruent meaning that the sides are the same
Answer:
The triangles are not congruent.
Step-by-step explanation:
The triangle ABD is an equilateral triangle, then all their sides are equal and all the angles are equal to 60º. Then x=60º and y=30º (because the sum of the internal angles of a triangle have to be 180º)
Then we can conclude that the triangles are not congruent because they share two sides, but does no have any angle in common, as we can see in the next list of the angles.
Triangle ABDangle ADB= angle ABD= angle DAB=60º
TriangleBCDangle BDC=30º
angle DCB=30º
angle CBD=120º
Identify y = sec(x)
Answer:
D)
Step-by-step explanation:
sec(x) = 1/cos(x)
You know cos(x) = 1 for x=0, so sec(0) = 1.
You also know that sec(x) has vertical asymptotes where cos(x) = 0, at odd multiples of π/2. Only selection D matchest these characteristics.
Mira has breakfast at a restaurant. She leaves 20% tip of 1.80 . What is the price of mira breakfast before tip
Answer:
9.00
Step-by-step explanation:
Use proportion:-
20% is equivalent to 1.80
1% is equivalent to 1.80 / 20
100% is equivalent to (1.80 / 20 ) * 100
= 180 / 20
= 9
= 9.00