Solving the Question
When both sides of the equal sign are equal, there are infinite solutions.
When you are able to isolate the variable, there is only one solution.
When the equation states an untrue expression, there is no solution.
1=3 is an untrue fact. Therefore, there would be no solutions to the system.
AnswerThere is no solution
What is a solution to the system of equations that includes quadratic function f(x) and linear function g(x)? f(x) = 2x2 x 4 x g(x) –2 1 –1 3 0 5 1 7 2 9 (-2, 10) (–1, 7) (0, 5) (1, 7)
The solution to the system of equations that includes functions f(x) and g(x) is given by: (1,7).
What is a linear function?A linear function is modeled by:
y = mx + b
In which:
m is the slope, which is the rate of change, that is, by how much y changes when x changes by 1.b is the y-intercept, which is the value of y when x = 0, and can also be interpreted as the initial value of the function.The linear function g(x) goes through point (0,5), hence the y-intercept is of 5. The function also goes through point (1,7), hence the slope is of 2 and the function is:
g(x) = 5 + 2x.
The solution to the system of equations is found as follows:
f(x) = g(x)
2x² + x + 4 = 5 + 2x
2x² - x - 1 = 0
Which is a quadratic equation with coefficient a = 2, b = -1, c = -1, hence:
[tex]\Delta = b^2 - 4ac = (-1)^2 - 4(2)(-1) = 9[/tex][tex]x_1 = \frac{-b + \sqrt{\Delta}}{2a} = \frac{1 + \sqrt{9}}{4} = 1[/tex][tex]x_2 = \frac{-b - \sqrt{\Delta}}{2a} = \frac{1 - \sqrt{9}}{4} = -0.5[/tex]When x = 1, f(x) = g(x) = 7, hence the solution of the system is of (1,7).
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Answer:
D. (1,7)
Step-by-step explanation:
I took the exam
A con is tossed n times. How many difference sequences of head and tails can you get?
Answer:
2^n
Step-by-step explanation:
So whenever you flip a coin, you can see it as 2 nodes branching off of each existing node. so for example when you flip a coin once you're going to have 2 sequences initially H and T, now when you flip a coin again for each of those 2 sequences 2 are going to branch off of that, making the total sequences 4, and the next flip 2 sequences are going to branch off each of the 4 sequences and so on. this can generally be described as: 2^n
I attached an image describing this a bit better but the bottom line is that for each 'end node'/sequence you're going to have 2 branch off of it, thus for each coin flip the number of sequences multiplies by 2
Answer:
2^n
Step-by-step explanation:
dont worry bout it ur welcome
Given f(x) = 3 and g(x) = cos(x). what is limit of left-bracket f (x) minus g (x) right-bracket as x approaches negative pi? 2 3 4 dne
Answer:
3
Step-by-step explanation:
f(x)-g(x)=3-cos(x)
when u limit it
u have
3-cos180
which is 3-0
3
(2x+1)/(x²-3) simplified
The simplified expression of (2x+1)/(x²-3) is 2x/(x²-3) + 1/(x²-3)
How to simplify the expression?The expression is given as:
(2x+1)/(x²-3)
The above expression is a fraction and the numerator has 2 terms
For a fraction
A + B)/x
The fraction can be split as
A/x + B/x
Using the above as a guide, we have:
(2x+1)/(x²-3) = 2x/(x²-3) + 1/(x²-3)
Hence, the simplified expression of (2x+1)/(x²-3) is 2x/(x²-3) + 1/(x²-3)
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Use the scatter plot and line of best fit to predict the value of y when x equals 1910.
I'll go for 40.
To find the value of y,
draw a line up from the x - axis at 1910,
all the way up to cross the blue line;
then, draw a horizontal line from the point where the recent line meets the blue one.
Now read of the value you get for y.
Hope this helps!
5. On the way to the museum, 50% of the students rode on the first bus.
What fraction of the students rode on the second bus? Show your work
in the space below. Remember to check your solution.
Answer:
1/2
Step-by-step explanation:
50% = 50/100 = 1/2
1/2 of the students rode the first bus.
1 - 1/2 = 1/2
1/2 of the students rode the second bus.
I need help with trigonometry
Again..
Answer: C. - √2
Step-by-step explanation:
Given requirements from the question
Find the exact value of sec 135°
Convert into common trigonometric expression
sec = secant
secx = 1 / cosx
Therefore, sec 135° = 1 / (cos 135°)
Find the reference angle
135° is quite a complicated angle, but it is possible to simplify it by finding its reference angle.
Since 135° is in the second quadrant, its reference angle will be
180° - 135° = 45°
However, we need to consider the positive and negative.
In a coordinate plane, the clue is (A S T C), which corresponds to the positive values in each quadrant. In the QI, "All" are positive. In the QII, sine is positive. In the QIII, the tangent is positive. In QIV, cosine is positive.
Therefore, when the value of cosine is in QII, it is negative.
The reference angle = - (1 / cos 45°)
Determine the final value
Given that the reference angle = - (1 / cos 45°)
cos 45° = 1 / √2
Therefore:
sec 135° = - (1 / cos 45°) = - (1 / (1 / √2)) = [tex]\boxed{-\sqrt{2} }[/tex]
Hope this helps!! :)
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Solve the system of equations
ax+y=2a
x+ay=1+a^2
Answer:
x = 1; y = a
Step-by-step explanation:
ax+y=2a
x+ay=1+a^2
-a²x-ay=-2a²
x+ay=1+a^2
(1 - a²)x = 1 - a²
x = (1 - a²)/(1 - a²)
x = 1
a + y = 2a
1 + ay = 1 + a²
a = y
x = 1; y = a
Instructions: Find the circumference of the circle and round to the nearest tenth.
Circumference = 43
4 yd.
Answer:
8 pi yd.
Step-by-step explanation:
The circumference of a circle can be calculated as follows:
c = [tex]2 \cdot \pi \cdot r[/tex]
Where r is the radius of the circumference.
So in our case:
c = [tex]2 \cdot \pi \cdot 4yd = 8\cdot \pi[/tex] yd.
The circumference of the circle, in the attached image is approximately 25.1 yards.
How to calculate the circumference of the circleTo find the circumference of a circle, you can use the formula:
Circumference = 2 * π * radius
where π = 3.14159.
Given the radius of the circle is 4 yards, the circumference can be calculated as follows:
Circumference = 2 * 3.14159 * 4 yards ≈ 25.13272 yards
Now, rounding to the nearest tenth, the circumference of the circle is approximately 25.1 yards.
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The ______ a system of linear equations that has at least one solution is ---select--- , whereas a system of linear equations that has no solution is ---select--- . need help?
The system of linear equations has at least one solution is consistent , whereas a system of linear equations that has no solution is inconsistent
What is a system of linear equations?
A collection of one or more linear equations involving the same variables is known as a system of linear equations (or linear system) in mathematics.
The subject of linear algebra, which is employed in most areas of contemporary mathematics, is based on the theory of linear systems. Numerical linear algebra includes computational strategies for obtaining the solutions, which are crucial to the fields of engineering, physics, chemistry, computer science, and economics. A helpful strategy when creating a mathematical model or computer simulation of a relatively complex system is to approximate a system of non-linear equations by a linear system (see linearization).
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.
An unbiased number cube is rolled 24 times and lands on an even number 10 times. What is the approximate difference between the
theoretical and experimental probabilities for rolling an even number?
12%
17%
8%
2%
Answer:
8%
Step-by-step explanation:
The approximate difference between the theoretical and experimental probabilities for rolling an even number is 8%
Theoretical probability is what we expect to happen, whereas experimental probability is what actually happens when we try it out. The probability is still calculated the same way, using the number of possible ways an outcome can occur divided by the total number of outcomes. As more trials are conducted, the experimental probability generally gets closer to the theoretical probability.
Theoretical probability of rolling a cube and getting a even number is 1/2 or 50% as number of odd numbers and number of even numbers are equal.
Experimental probability = Favorable outcomes/Total outcomes
Experimental probability = 10/24 = 5/12 ≅ 42%
Thus approximate difference between these two equals 50% - 42% = 8%
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Are 14, 6 + 8, and (6 + 8) equivalent expressions? Explain your reasoning.
The expressions 14, 6 + 8, and (6 + 8) are equivalent because they are all equal to 1
Equivalent expression14
6 + 8
= 14
(6 + 8)
= 14
The coefficient of (6 + 8) is 1, so, the expression remains the same.
What is equivalent expression?Equivalent expressions refers to those expressions that work the same even though they look different.
The importance or significance of equivalent expression is that its makes expressions easier to work with and solve.
Therefore, the expressions 14, 6 + 8, and (6 + 8) are all equivalent to 14.
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How do you solve this geometry question?
The statement that <A > <C and <B > <D has been proved
How to prove that <A > <C and <B > <D?In geometry, the side length opposite the largest angle is the longest side.
Similarly, the side length opposite the smallest angle is the shortest side.
From the given figure of quadrilateral, we have the following sides in increasing order:
Side length ABSide length BCSide length ADSide length CDThe angles opposite the side lengths are:
Angle DAngle BAngle CAngle AThis means that:
<A > <C and <B > <D
Hence, the statement that <A > <C and <B > <D has been proved
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ANSWER MY QUESTION AND I WILL MARK YOU BRAINLYIST
The following are the distances (in miles) to the nearest airport for 11 families. 9, 11, 11, 16, 16, 24, 28, 30, 34, 42, 45 Notice that the numbers are ordered from least to greatest. Give the five-number summary and the interquartile range for the data set. Five-number summary
Minimum:
Lower quartile:
Median:
Upper quartile:
Maximum:
Interquartile range:
Here is the five-number summary:
Minimum: 9
Lower quartile: 11
Median: 24
Upper quartile: 34
Maximum: 45
Interquartile range: 23
What is the five-number summary?The minimum number is the smallest number in the dataset. The minimum number is 9. The maximum number is the largest number in the dataset. The maximum number is 45.
The first quartile, third quartile and the interquartile range are used to measure dispersion.
The first quartile : 1/4(n + 1)
1/4 x (12) = 3rd term = 11
The third quartile : 3/4 x (n + 1)
3/4 x (12) = 9th term = 34
Interquartile range = third quartile - first quartile
34 - 11 = 23
Median can be described as the number that occurs in the middle of a set of numbers that are arranged either in ascending or descending order
Median = 25
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In the circle below, if < B = 39 °, what is the measure of arc AB?
From my analysis, the answer is likely to be D. I don't have a formula to prove it though.
Answer: 78 degrees.
Step-by-step explanation:
The other guy is wrong don't listen to him.
an object moves at a speed of 3/16 feet per second. what is the speed, in yards per second? (3 feet= 1 yard)
4y^5-6y+8y^2-1 for y = -1
Answer:9
Step-by-step explanation:
The x component of vector is 5.3 units, and its y component is -2.3 units. The angle that vector makes with the x-axis is closest to?
The angle that vector makes with the x-axis is closest to [tex]340^\circ[/tex].
What is a vector?
An item with both magnitude and direction is referred to be a vector. A vector can be visualized geometrically as a directed line segment, with an arrow pointing in the direction and a length equal to the magnitude of the vector. The vector points in a direction from its tail to its head.
If the magnitude and direction of two vectors match, they are the same vector. This indicates that if we take a vector and move it to a different point (without rotating it), the vector we finish up with is the same vector we started with.
Given,
[tex]x[/tex]-component of vector = 5.3
[tex]y[/tex]-component of vector = -2.3
angle = [tex]tan^{-1}(\frac{y}{x})[/tex]
angle = [tex]tan^{-1}(\frac{-2.3}{5.3} )[/tex]
angle = [tex]340^\circ[/tex]
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In a diagram showing two parallel lines cut by a trasversal, the measures of two same side interior angles are both given as 3x. Without writing and solving an equation, can you determine the measures of both angles? Explain. Then write and solve an equation to find the measures
Answer:
90 degrees
Step-by-step explanation:
Same side interior angles, or consecutive angles, are supplementary (angle measures add up to 180 degrees). Since both angles have measures 3x degrees, the angles are congruent (same angle measure). In Geometry, when two angles are congruent and supplementary, the two angles are right angles (angles measuring 90 degrees). Therefore the angle measures of the two angles are 90 degrees and 90 degrees.
Or, to solve this algebraically, add 3x and 3x, let it equal to 180 degrees, solve for x, and find the angle measures by substituting x into the expression.
3x + 3x = 180
6x = 180
x = 30
3x = 3*30 = 90
Solve the equation in the image (yr 8 math, 40pt)
Answer:
a = 3
Step-by-step explanation:
4(2a - 3) = -2(a - 9)
8a - 12 = -2a + 18
10a = 30
a = 3
Let's check if we got it correct by substituting 3 for a in the original equation.
4(2*3 - 3) = -2(3 - 9)
4(6 - 3) = -2(-6)
4(3) = 12
12 = 12
3 cm ▼ 2 cm The diagram shows a prism. Work out the volume of the prism. 4 cm 1 cm 12 cm
What order will result in a final output of - 31 when the initial input is 0?? Someone please please helpoo
The order that will result in a final output of -31 when the first input is 0 is as follows; Third → Second → Fourth → First
How to find the order?First gives;
y = -2·x + 34 = 18
Second gives;
y = -x/3 - 10 = -38/3
Third gives;
= -24
Fourth gives;
y = (x - 2)² = 36
We have after several iterations;
Third gives,
= -24
Next we input into the second to get,
y = -(-24)/3 - 10 = 24/3 - 10 = 8 - 10 = -2
Next we input into the fourth to get,
y = ((-2) - 2)² = (-4)² = 16
Next we input into the first to get,
y = -2×16 + 34 = -32 + 34 = 2
Which gives the order as follows;
Third → Second → Fourth → First
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PLS HELP ME WITH THIS
Using it's concept, the experimental probability of getting an odd number and a number greater than 6 is given by:
1/5.
What is a probability?A probability is given by the number of desired outcomes divided by the number of total outcomes. An experimental probability is calculated considering the results of previous trials.
In this problem, there are 10 trials, and of those, 2 of them, trial 8 and trial 10, resulted in an odd number and a number greater than 6, hence the probability is:
p = 2/10 = 1/5.
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5x(3x-10) + (2x-6)(3x+8)
Answer: 21[tex]x^{2}[/tex] - 52x - 48
Step-by-step explanation:
Using the expanding rule we get
5x * 3x - 5x * 10 + (6[tex]x^{2}[/tex] - 18x + 16x -48)
15[tex]x^{2}[/tex] - 50x + 6[tex]x^{2}[/tex] - 2x - 48
21[tex]x^{2}[/tex] - 52x - 48
Answer:
21x^2-52x-48
Step-by-step explanation:
5x(3x-10) + (2x-6)(3x+8)
Distribute
5x^2 -50x+6x^2-2x-48
Combine like terms
21x^2-50x-2x-48
21x^2-52x-48
What would cause an Inequality sign in an equation to flip?
a.) When dividing both sides by a negative.
b.) When adding a negative to both sides.
c.) When multiplying a fraction by both sides.
d.) When subtracting a negative to both sides.
Answer:
When dividing both sides by a negative.
Step-by-step explanation:
When dividing OR multiplying both sides by a negative, we need to flip the inequality signs.
A trapezoid is shown. The lengths of the bases K L and J M are 10 feet and 5 feet. The length of side L M is 6 feet. An altitude is drawn from point K to a point on side J M.
A plot of land has an area of 33.75 square feet. Jackson wants to put a 4-foot by 4-foot shed on the land. He can only do this if the height of the trapezoid is at least 4.5 feet. What is the height of the trapezoid?
feet
The given height of this trapezoid is given to be 4.5m
How to solve for the height of the trapezoidWe have to solve for this by making use of the height of a trapezoid. The height is given as
A = (1/2) h (b1 + b2)
The variables here are
h = height
b1 = lenght at base 1
b2 = length at base 2
If the trapezoid that we have is a isosceles triangle, then base 1 is going to be the same length as that of the first base
b1 = 4 ft is the area. Given that the height has to be at least 4.5feet, then this would ensure that the trapezoid would be able to hold the shed.
Hence the height would begiven as 4.5 ft
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Answer: 4.5
Step-by-step explanation:
Anna wanted to buy a camera. The first discount store sold her favorite camera for $95. The second store sold the same camera for $115, but it was on sale for 20% off. The third store carried the camera for $105 but offered it at 10% off with a coupon. which store had the better buy?
Answer: third store
Step-by-step explanation:
1
First store: 95
Second store: 0.8*115=92
Third store: 0.9*105=94.5
Please help with number 5 I tried it but I’m very confused :(
Answer: [tex]\Large\boxed{15~dimes~;~9~nickels}[/tex]
Step-by-step explanation:
Given information
Number of coins = 24 coins
Total amount = $1.95
Dime = 10 cents = $0.1
Nickel = 5 cents = $0.05
Set variables
Let d be the number of dimes
Let n be the number of nickels
Set a system of equation
1) d + n = 24
2) 0.1d + 0.05n = 1.95
Multiply 10 on both sides of 2) equation
0.1d · 10 + 0.05n · 10 = 1.95 · 10
d + 0.5n = 19.5
Current system
1) d + n = 24
2) d + 0.5n = 19.5
Subtract 2) equation from the 1) equation
(d + n) - (d + 0.5n) = (24) - (19.5)
Expand the parenthesis
d + n - d - 0.5n = 24 - 19.5
Combine like terms
d - d + n - 0.5n = 4.5
0.5n = 4.5
Divide 0.5 on both sides
0.5n / 0.5 = 4.5 / 0.5
[tex]\Large\boxed{n=9}[/tex]
Substitute the n value into one of the equations to find the d value
d + n = 24
d + (9) = 24
d = 24 - 9
[tex]\Large\boxed{d=15}[/tex]
Hope this helps!! :)
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Need help with my work please
2x+3≥7 OR 2x+9>1
Please help me
Answer:
x > -4
Step-by-step explanation:
[tex]2x+3 \geq 7 \\ \\
2x \geq 4 \\ \\
x \geq 2[/tex]
[tex]2x+9>1 \\ \\ 2x>-8 \\ \\ x>-4[/tex]
So, the union of these solutions is x > -4.