I’m not sure how to answer this in a Graph, Diagram, and Algebra(algebraic reasoning too) for a,b,c, and d. Can someone please help me?
Answers
The outline that that illustrate how k values change so that the solutions are the ones in the question are as follows
(a) The number line solution contains zero
Using algebra, we have;
The given quadratic inequality is; -x² + 4 ≥ x + k
The number line solution is the expression of the solution on the number line.
We have;
-x² + 4 ≥ x + k
-x² - x + 4 - k ≥ 0
Dividing by (-1), we get;
x² + x - 4 + k ≤ 0
When - 4 + k = -2
k = 2, we get;
x² + x - 4 + 2 ≤ 0
x² + x - 2 ≤ 0
(x - 1)·(x + 2) ≤ 0
Given that the result of the product is less than zero, we have;
((-3) - 1)·((-3) + 2) > 0
Therefore, the solution are;
x ≤ 1, or x ≥ -2
Which gives
-2 ≤ x ≤ 1
Using diagram;The solution of the above inequality includes 0 as shown in the attached number line
Graphically;The graph of the inequality is plotted using MS Excel, showing the solution set, of -2 ≤ x ≤ 1
(b) There are no solution to the inequality
In the present case, we have;
((-1)² - 4×(-1) × (4 - k) < 0
17 - 4·k < 0
[tex]k > \dfrac{17}{4}[/tex]
Let k = 5, we have;
-x² + 4 ≥ x + k
-x² - x + 4 - 5 ≥ 0
-x² - x -1 ≥ 0
The discriminant, is (1² - 4×(-1)×(-1)) = -3 < 0, therefore, there are no real
roots to inequality, and -x² - x -1 is not equal to zero.
GraphicallyPlease find attached the graph of the function, which does not intersect with the x-axis, and therefore, has no values at which y = 0
(c) The solution is a single number
-x² + 4 ≥ x + k
When k = x + 5, we have;
0 ≥ x² + 2·x + 1
0 ≥ (x + 1)²
Therefore;
The only solution is; x = -1
Using diagrams:
Please find attached the solution of the function on the number line
GraphicallyThe graph of the function showing only one intercept is attached
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Related Questions
i really need help i don’t get this at ALL. :(
Answers
Step-by-step explanation:
You have to go to Y axis first then to X. For example : (4,5) go up 4 and go to x axis and when u get to 5 you put a dot. The same thing if is (-4,-5) go down 4 and to the left 5 and mark a dot. When you mark the dot put (_,_).
Hope you understand. Let me know if you don't.
What is a slope in math.
Answers
Answer:
A slope in math is basically rise/run on a coordinate plane. If you have the trend line given and a few values given on the 'x' coordinate and the 'y' coordinate, you can find the slope using rise/run.
Hoped this helped.
What’s the range of = 1 2 ⋅ 2 + 6 + 6
Answers
Answer: the range of 12 * 2 + 6 + 6 is 36
Step-by-step explanation:
Which product is negative?
−2⋅(−4)⋅8⋅(−1)
−7⋅(−3)⋅(−5)⋅(−8)
−3⋅(−4)⋅(−9)⋅0
6⋅(−2)⋅(−3)⋅1
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[tex]-2(-4)\cdot 8 (-1)\\\\=8 \cdot (-8)\\\\=-64\\\\\text{This one is negative.}[/tex]
100 POINTS IF U GET THIS RIGHT!
Answers
Answer:
9/8Step-by-step explanation:
Slope- intercept form:
y = mx + b, where m is the slopeThe line given:
y = 9/8x + 1/8This includes the slope, which is:
m = 9/8HELP PLS! Suppose the year of car accidents per day in Wilmington NC has been recorded for the past year. The table below is a probability distribution table representing the data collected.
1) what is the probability that on a randomly selected day there were no accidents?
2) find the probability there will be at least 2 accidents
3) on any given day how many accidents should the Wilmington police expect to have.
Answers
According to the discrete distribution given:
1) There is a 0.18 = 18% probability that on a randomly selected day there were no accidents.
2) There is a 0.7 = 70% probability that there will be at least 2 accidents.
3) On any given day, the Wilmington police should expect to have 2.03 accidents.
The distribution is:
[tex]P(X = 0) = x[/tex]
[tex]P(X = 1) = 0.12[/tex]
[tex]P(X = 2) = 0.32[/tex]
[tex]P(X = 3) = 0.25[/tex]
[tex]P(X = 4) = 0.13[/tex]
Item 1:
The sum of the probabilities has to be 100% = 1, hence:
[tex]x + 0.12 + 0.32 + 0.25 + 0.13 = 1[/tex]
[tex]x + 0.82 = 1[/tex]
[tex]x = 0.18[/tex]
0.18 = 18% probability that on a randomly selected day there were no accidents.
Item 2:
This probability is:
[tex]P(X \geq 2) = P(X = 2) + P(X = 3) + P(X = 4) = 0.32 + 0.25 + 0.13 = 0.7[/tex]
0.7 = 70% probability that there will be at least 2 accidents.
Item 3:
The expected value is the sum of each outcome multiplied by it's respective probability, hence:
[tex]E(X) = 0.18(0) + 0.12(1) + 0.32(2) + 0.25(3) + 0.13(4) = 2.03[/tex]
On any given day, the Wilmington police should expect to have 2.03 accidents.
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The results of a survey about favorite lunch choices are shown.
Which lunch was chosen most often? : Please help!! here’s the chart btw —>
Answers
Answer:
Grilled cheese 1/10
Step-by-step explanation:
If you divide the rest of the fractions you get decimals and since 1/10 is still 10 grilled cheese is the favour lunch
which number sentence can be used to find 42 divied by 7
Answers
Answer: isn't it 42÷7=6?
Answer:
42 / 7 = 6
Step-by-step explanation:
Just use a multiplication table.
Please simplify
(6-√-16)+(-4+√-25)
Answers
Answer:
2+i
Step-by-step explanation:
Help me out I need it
Answers
Answer:
27 Chairs (See below)
Step-by-step explanation:
A: You will put 9 chairs in each row, and have 3 rows.
For a visual example I will use the symbol "O" for the number of chairs.
OOOOOOOOO
OOOOOOOOO
OOOOOOOOO
B: The multiplication problem, using the information 3 Rows, and 9 Chairs in each row, is 9x3
C: The factors are the numbers you are multiplying with, and the product, is your outcome when you multiply the two factors, 9, and 3.
So your answer is 27.
Hope this helps!
help im not good in math
Answers
Answer:
4
Step-by-step explanation:
yeah 4/8 is the answer. yeah-ya
△RQP≅△ONM. Find the value of x. ( I WILL GIVE BRAINLIEST! PLS HELP!)
refer to attachment
Answers
[tex]\\ \sf\longmapsto 3x-5=70[/tex]
[tex]\\ \sf\longmapsto 3x=70+5[/tex]
[tex]\\ \sf\longmapsto 3x=75[/tex]
[tex]\\ \sf\longmapsto x=75/5[/tex]
[tex]\\ \sf\longmapsto x=15[/tex]
How would you find the intercept for the equation y^2=2-3x-2x^2? I need the steps to understand
Answers
9514 1404 393
Answer:
x-intercepts: -2, +1/2y-intercepts: ±√2Step-by-step explanation:
You always find the intercepts by setting the known coordinate to its known value and solving for the value of the unknown coordinate.
An x-intercept is always found on the line y=0. Setting y=0 and solving for x, we find ...
0 = 2 -3x -2x^2
x^2 +3/2x -1 = 0 . . . . . . . . . . . . . . . . divide by -2
(x2^2 +3/2x +(3/4)^2) -1 -(3/4)^2 = 0 . . . . . complete the square
(x +3/4)^2 = 25/16 . . . . . add 25/16 and write as a square
x +3/4 = ±5/4 . . . . . . . take the square root
x = -3/4 ±5/4 = -8/4, +2/4
The x-intercepts are -2 and +1/2.
__
A y-intercept is always found on the line x=0. Setting x=0 and solving for y, we find ...
y^2 = 2 -0 -0
y = ±√2
The y-intercepts are -√2 and +√2.
_____
A graphing calculator can give you a good idea of what the intercepts are.
The second rate superhero and is Arch Enemy Melvin the minor menace started 700 miles apart and fleet street toward each other in their jet propulsion packs it took 5 hours for the two to meet if the superheroes speed was 10 mph slower than a minute what was the menaces speed
Answers
Answer:75 mph
Step-by-step explanation:
Find two integers whose sum is -12 and product is 35
Answers
Answer:
-5;-7
Step-by-step explanation:
Start with the product. 35 is either 35x1, 7x5, or the product of their opposites. 35 and 1 doesn't work for the sum, neither does 7 and 5. Let's go negative. -35 and -1 gives -36, so it has to be -7 and -5, which is indeed, correct.
Angela has 3 gallons of milk.how many quarts of milk dose she have
Answers
Answer:
12
Step-by-step explanation:
4 quest make 1 gallon so 4*3=12
To form a hyperbola what is the relationship between the base of the cone and the angle of the plane that intersects the cone
A. The plane is a parallel to the base of the cone
B. The plane may be perpendicular to the base of the cone
C. the plane must be at a 45 degree angle to the base of the cone
D. The plane is at an angle that is neither parallel nor perpendicular to the base of the cone
Answers
BRAINLIEST
Please solve at least one of these problems. I would love it if you could do all of them but I know you probably won’t have time for it. Ty!
Answers
Answer:
Step-by-step explanation:
Angles of a triangle worksheet
I got most of it but still confused on the rest… anyone got answers ASAP!
Answers
Answer:
I wish a could help u,
Step-by-step explanation:
I dont know what is that:)
Simplfy the answer t-4t2/t2
Answers
Answer:
t - 16
Step-by-step explanation:
Hope this helps!! :))
+
What is the quotient when (16x4 + 40x3 - 24x2) is divided by 8x??
OA.
2x + 5x-3
OB. 2x + 3x-5
OC. 2x - 5x+5
D. 2x3 + 5X-3
+
Relat
Next
Answers
Answer: [tex]2x^{2} + 5x -3[/tex]
Step-by-step explanation:
Find the quotient of [tex]\frac{16x^4+40x^3-24x^2}{8x^2}[/tex]
Step 1: Break down the polynomial equation
[tex]\frac{16x^4}{8x^2}[/tex] + [tex]\frac{40x^3}{8x^2}[/tex] - [tex]\frac{24x^2}{8x^2}[/tex]
Step 2: Divide each piece by dividing the coeffients and subtracting the variables.
16 ÷ 8 = 2
[tex]x^{4}[/tex] - [tex]x^{2}[/tex] = [tex]x^{2}[/tex] → 2[tex]x^{2}[/tex]
40 ÷ 8 = 5
[tex]x^{3}[/tex] - [tex]x^{2}[/tex] = [tex]x[/tex] → 5[tex]x[/tex]
- 24 ÷ 8 = - 3
[tex]x^{2}[/tex] - [tex]x^{2}[/tex] = 1 → - 3
Step 3: Put the polynomial together
2[tex]x^{2}[/tex] + 5[tex]x[/tex] - 3
Han and Priya were making a kite. Han cut out a piece of fabric so
that there were 2 short sides of the same length on top and
2 long sides of the same length on the bottom. Priya cut 2 pieces
of wood to go across the diagonals of the kite. They attached the
wood like this:
Han asked Priya to measure the angle to make sure the pieces of
wood were perpendicular. Priya said, "If we were careful about
the lengths of the sides of the fabric, we don't need to measure
the angle. It has to be a right angle."
Complete Priya's explanation to Han.
Answers
A kite is a quadrilateral which has two equal adjacent sides. Therefore measuring the lengths accurately would make the pieces of wood perpendicular. Since the diagonals of a kite are at right angle to each other.
Quadrilaterals are shapes which has four straight sides. Examples are; square, trapezium, kite, rectangle etc.
A kite is a shape which has adjacent sides to have equal lengths. It has two diagonals, and one line of symmetry.
The lengths of the sides of the fabric being exact imply that the pieces of wood would be perpendicular as suggested by Priya when fixed appropriately to the piece of fabric. This is because the diagonals of a kite are always perpendicular. Thus measuring the angles as suggested by Han is not necessary.
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The 2 pieces of wood intersect at right angles if the length of sides of the fabric are measured correctly.
Since Priya said to Han that "If we were careful about the lengths of the sides of the fabric, we don't need to measure the angle. It has to be a right angle."
Priya used the properties of a kite.
Since from the properties of a kite, two pairs of sides are equal. Also, since thes two pairs of sides are equal, the diagonals from the vertices of the kite intersect at right-angles.
So, as Priya said to Han, the angle made by the 2 pieces of wood have to be right angles if the sides are measured correctly, since the diagonals intersect at right angles.
So, the 2 pieces of wood intersect at right angles if the length of sides of the fabric are measured correctly.
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The pie chart shows information about the voters in an election 2800 more women voted than men work out the total number of voters
Answers
The angle subtended by the women voters are 100° more than the angle subtended by the men voters.
The total number of voters are 10080 votersReasons:
The angle subtended by the men on the pie chart = 130°
The number of women = 2800 + The number of men
Therefore;
Angle subtended by the women voters on the pie chart = 360° - 130° = 230°
The difference between the angle representing women and the angle
representing men = 230° - 130° = 100°
Therefore;
100° = 2800
Which by common ratios gives;
[tex]\dfrac{100^{\circ}}{360^{\circ}} = \dfrac{2800}{Total \ number \ of \ voters }[/tex]
100 × Total number of voters = 2800 × 360
[tex]The \ total \ number \ of \ voters = \dfrac{2800 \times 360}{100} = 10080[/tex]
The total number of voters = 10080
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Answer:
The angle subtended by the women voters are 100° more than the angle subtended by the men voters.
The total number of voters are 10080 voters
Reasons:
The angle subtended by the men on the pie chart = 130°
The number of women = 2800 + The number of men
Therefore;
Angle subtended by the women voters on the pie chart = 360° - 130° = 230°
The difference between the angle representing women and the angle
representing men = 230° - 130° = 100°
Therefore;
100° = 2800
Which by common ratios gives;
100 × Total number of voters = 2800 × 360
The total number of voters = 10080
a line has a slope of m=-2 and the point (3, -1) lies on the line.what is the represent the equation of the line in point slope form
Answers
Answer:
Step-by-step explanation:
To find out if a point (x, y) is on the graph of a line, we plug in the values and see if we get a true statement, such as 10 = 10.
3/8 rounded to the nearest thousand
Answers
Answer:
0.38
Step-by-step explanation:
First, we convert the fraction to a decimal number by dividing the numerator by the denominator:
3 / 8 = 0.375
There are two parts to the decimal number above:
Integer Part: 0
Fractional Part: 375
Now, we will make the Fractional Part just two digits (nearest hundredth) by using our rounding rules.*
In this case, Rule II applies, so 3/8 (or 0.375) rounded to the nearest hundredth in decimal format is:
0.38
Answer:
.375
Step-by-step explanation:
3/8=.375
A book has 12 chapters. The mean length of the chapters is 38 pages. How many total pages are there in the 12 chapters
Answers
The decimal approximation for cot(235°36') is approximately -0.9503.
To find the decimal approximation for cot(235°36'), we first need to convert the angle to degrees.
The given angle is 235°36'. We can convert this to decimal degrees by adding the fraction of minutes to the degree value. There are 60 minutes in a degree, so we divide 36 by 60 to convert it to a fraction of a degree:
36 / 60 = 0.6 degrees
Now, we can add this fraction to the degree value:
235 + 0.6 = 235.6 degrees
The cotangent function is the reciprocal of the tangent function. To find the cotangent of an angle, we can use the following formula:
cot(x) = 1 / tan(x)
Since we want to find cot(235.6°), we can find tan(235.6°) first and then take the reciprocal.
Using a scientific calculator or software, we can find
tan(235.6°) ≈ -1.0529
Now, we can take the reciprocal to find cot(235.6°):
cot(235.6°) ≈ 1 / (-1.0529) ≈ -0.9503
Therefore, the decimal approximation for cot(235°36') is approximately -0.9503.
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Find the quotient. 4/12÷4/12=
Answers
Answer:
1
Step-by-step explanation:
Factor the numerator and denominator and cancel the common factors.
im not sure on how to do this If one angle of a triangle is 30° more than twice another angle, and the third angle is equal to the sum of the first two angles, find the measure of each angle.
Answers
Answer:
Step-by-step explanation: How do you find the 3rd angle of a triangle?
Image result for im not sure on how to do this If one angle of a triangle is 30° more than twice another angle, and the third angle is equal to the sum of the first two angles, find the measure of each angle.
The three angles of any triangle add up to 180 degrees. Since you know two angles (35 and 40), add them together, then subtract the total from 180 to determine the degree of the third angle.
The product of two positive numbers is 9. The reciprocal of one of these numbers is 4 times the reciprocal of the other number. What is the sum of the two numbers?
Answers
Answer:
7 and 1 / 2
Step-by-step explanation:
xy = 9
( 1 / x ) = 4 ( 1 / y )
y = 4x
x ( 4x ) = 9
4x^2 = 9
x = 3 / 2
( 3 / 2 ) y = 9
y = 6
6 + ( 3 / 2 ) = 7 and 1 / 2
The two numbers are 3/2 and 6.
What are reciprocal numbers?The reciprocal of a number is this fraction flipped upside down.
Given that, The product of two positive numbers is 9. The reciprocal of one of these numbers is 4 times the reciprocal of the other number.
Let the numbers be a and b.
ab = 9.......(i)
1/a = 4/b
a = 4b..........(ii)
Using (i) in (ii)
4b×b = 9
b² = 9/4
b = 3/2
a×3/2 = 9
a = 6
Hence, The two numbers are 3/2 and 6.
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What is the answer to the question below, I have been working on it for a while. Plz help!
The quotient of 10 times m and 7
Answers
Answer:
10m / 7
Step-by-step explanation:
times = multiplication of 10 and variable m
quotient of = division of 7
