By using the definition of second order polynomials and the discriminant from quadratic formula, we conclude that the values of k must be less than 1/4.
How to determine the value of k such that a line intersects a quadratic equation
In this question we must determine the set of values of k such that the function g(x), a linear function, intersects a quadratic function f(x) at two points. In this case, we must solve the following second order polynomial:
k · x² + 4 · x - 3 - g(x) = 0
k · x² + 4 · x - 3 - 2 · x + 7 = 0
k · x² + 2 · x + 4 = 0
In this case, the discriminant of the equation described above must be positive:
2² - 4 · k · 4 > 0
4 - 16 · k > 0
4 > 16 · k
16 · k < 4
k < 1/4
By using the definition of second order polynomials and the discriminant from quadratic formula, we conclude that the values of k must be less than 1/4.
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The graph of the piecewise function f(x) is shown.
On a coordinate plane, a piecewise function has 2 lines that connect. The first line is horizontal to the y-axis at y = 4 and goes to (0, 4). The second line goes from (0, 4) through (4, 0).
What is the range of f(x)?
The range of the function is f(x) <= 4
How to determine the range?The attached graph is the missing piece in the question
The function f(x) is given as:
2 lines connectedHorizontal line y = 4 to (0, 4)Another line from (0, 4) through (4, 0)The above means that, the value of the function do not exceed y = 4
Hence, the range of the function is f(x) <= 4
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10. The cost of manufacturing a kitchen cabinet consists of the cost of materials at $250, labour cost at $120 and warehousing cost at $60. After a change of management, the cost of materials and labour cost are increased by 10% and 8% respectively, and warehousing cost is decreased by 18%. Calculate the percentage change in the cost of manufacturing the kitchen cabinet. State whether it is an increase or a decrease.
Using proportions, the percentage change in the cost of manufacturing the kitchen cabinet was a increase of 5.5%.
What is a proportion?A proportion is a fraction of a total amount, and the measures are related using a rule of three.
The standard cost is given as follows:
S = 250 + 120 + 60 = $430.
After the increases, the price will be given as follows:
S = 250 x 1.1 + 120 x 1.08 + 60 x 0.82 = $453.8.
The price increased. The percent change, given by the change divided by the initial value, is:
P = 23.8/430 x 100% = 5.5%.
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The tree diagram represents an experiment consisting of two trials P(A andC)=
The value of P(A and C) is 0.18
How to determine the probability?From the tree diagram, we have the following probability values:
P(A) = 0.6
P(C) = 0.3
The probability P(A and C) is then calculated as:
P(A and C) = 0.6 * 0.3
Evaluate
P(A and C) = 0.18
Hence, the value of P(A and C) is 0.18
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A new washing machine is purchased for $300. it's value depreciates 20% every year for the first 6 years of its life
The value of the washing machine after 6 years with 20% depreciation every year is $78.64.
What is depreciation?Depreciation is the practice of subtracting a business asset's cost over a number of years as opposed to just one.
Depreciation is used to adjust the cost of a productive asset with a longer-than-year-long useful life to the income generated by operating the asset. The expense of the asset is typically dispersed across the years that it is utilized.
Calculation for the asset value after depreciation of 20% every year.
The purchasing cost of washing machine is $300.
The rate after 6 years is-
Rate = purchased price×[tex](1-r)^{t}[/tex]
= 300×[tex](1-0.2)^{6}[/tex]
= 300×[tex]0.8^{6}[/tex]
= 78.64
The cost of washing machine after 6 years will be $78.64.
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The sum of 5 consecutive even integers is 4 less than the sum of the first 8 consecutive odd counting numbers. What is the smallest of the even integers
The smallest of the even integers is 8.
It is a well-known fact that the sum of the first n odd numbers is n^2. This makes the sum of the first 8 odd numbers equal to 64.
Let n be equal to the smallest of the 5 even integers. Then (n+2) is the next highest, (n+4) even higher, and so on.
This sets up the equation n+(n+2)+(n+4)+(n+6)+(n+8)+4=64
Now we solve:
5n+24 = 64
5n = 40
n = 8
The smallest of the even integers is 8.
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Im really bad at geometry. Can someone please help me out
Answer:
x = 4
Step-by-step explanation:
Since they are parallel, we use the formula
[tex]\frac{part}{part} = \frac{part}{part}[/tex]
[tex]\frac{14}{x} =\frac{7}{2}[/tex]
7x = 28
x = 4
Milo's car can be driven an average of 21.6 miles on each gallon of gasoline. How far can his car be driven on 9.8 gallons of gasoline?
Answer:
211.68 miles
Step-by-step explanation:
21.6 x 9.8
What is the difference?
X
3
x²-16 X-4
2(x+6)
O (x+4)(x-4)
O
-2(x+6)
(x+4)(x-4)
X-3
(x+5)(x-4)
-2(x-6)
(x+4)(x-4)
Answer:
your question is wrong, it's not an expression but a quadratic equation. if so your answer will be x=8±2√7
Step-by-step explanation:
by using, completing the square method
x²-16x-4=0
x²-16x=4
x²-16x+(-16×0.5)²=4+(16×0.5)²
x²-16x-8²=4+8²
(x-8)²=68
x-8=√68
x-8=±2√7
so x=8±2√7
please next time write the correct question
You have several numbers in a data set: 5, 7, 9, 11, 13, 15, 17. What is the z Score for the number 7
The z score for the number 7 is -0.92.
The standard deviation is 4.32
X is the score that is 7 given.
We have to calculate the z score for doing so we need the mean also.
Mean is obtained by dividing the sum of numbers / total frequency.
Mean = Summation of numbers / total numbers
= 5, 7, 9, 11, 13, 15, 17 / 7
= 77/7
= 11
Formula of z-score, Z= x - mean /S.D.
x is the number that is 7.
S D is the standard deviation.
Z= 7-11 / 4.32
= -4/4.32
Z score = -0.92
In data, the standard deviation is a degree of the quantity of version or dispersion of a fixed of values. A low fashionable deviation suggests that the values have a tendency to be near the suggest of the set, while a high widespread deviation shows that the values are spread out over a much broader range.
Standard deviation is vital because it is able to assist users check chance. Bear in mind a funding option with a median annual return of 10% in line with the year. However, this average changed into derived from the past three-year returns of 50%, -15%, and -5%. with the aid of calculating the same old deviation and understanding your low likelihood of really averaging 10% in any single given 12 months, you're better armed to make knowledgeable decisions and apprehend underlying risk.
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Can y’all help this is for Plato !!!!!! PLEASEEE HELP ME
The two real values that are not in the domain of the composition are x = 2 and x = -2.
What two numbers are not in the domain of f°g?
Here we have:
f(x) = 1/x
g(x) = x^2 - 4
The composition is:
f°g = f(g(x)) = 1/(x^2 - 4)
The two values that are not in the domain are the values of x such that g(x) = 0, because we can't divide by zero.
g(x) = 0 = x^2 - 4
4 = x^2
±√4 = x
±2 = x
So g(x) = 0 when x = 2 or x = -2, so these are the two real values that are not in the domain of f°g.
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If Jamari pays $25 at the beginning of the month, he will pay only $5 per hour for using Vic Sporting facility. The information is recorded in the table on the image inserted. Write an equation for y, the cost of spending x hours at the sporting facility each month.
Answer:
Y = 5x + 25
Step-by-step explanation:
$25 is the constant, meaning regardless of the time he spends, he will not pay more or less.
However, he pays 5 dollars for every hours (x) = 5x
send help lol confused
Answer:
C. 0≤x≤7
Step-by-step explanation:
It is not choice D. because it has y instead of x. It is supposed to be x because it is asking for domain.
Hope this helps!
Solve the triangle.
Round your answers to the nearest tenth.
If there is more than one solution, use the button labeled "or".
The value of the side b and c will be 58.57 units and 36.86 units, and angle ∠B will be 107°.
What is law of sines?Let the triangle ABC, with side measures |BC| = a. |AC| = b. |AB| = c.
Then by the sine law, we have
[tex]\rm \dfrac{\sin\angle A}{a} = \dfrac{\sin\angle B}{b} = \dfrac{\sin\angle C}{c}[/tex]
The sum of angles of triangle is 180°.
∠A + ∠B + ∠C = 180°
36° + ∠B + 37° = 180°
∠B = 107°
Then the side b will be
sin 36° / 36 = sin 107° / b
b = 58.57 units
Then the side c will be
sin 36° / 36 = sin 37° / c
c = 36.86 units
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10
TIME REMAINING
59:02
Which is the graph of the linear inequality 2x – 3y < 12?
On a coordinate plane, a solid straight line has a positive slope and goes through (0, negative 4) and (3, negative 2). Everything to the right of the line is shaded.
On a coordinate plane, a dashed straight line has a positive slope and goes through (0, negative 4) and (3, negative 2). Everything to the right of the line is shaded.
On a coordinate plane, a dashed straight line has a positive slope and goes through (0, negative 4) and (3, negative 2). Everything to the left of the line is shaded.
On a coordinate plane, a solid straight line has a positive slope and goes through (0, negative 4) and (3, negative 2). Everything to the left of the line is shaded.
The graph of the inequality will be B. on a coordinate plane, a dashed straight line has a positive slope and goes through (0, negative 4) and (3, negative 2). Everything to the right of the line is shaded.
How to get the graph?It can be deduced that the coordinates satisfy the equation of the line.
3y = 2x - 12
Divide through by 3.
y = 2/3x - 4.
The slope is 2/3.
In conclusion, the correct option is B.
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Answer:
b
Step-by-step explanation:
What is DF=
Help me please thank you :)
The value of DF = 20.
What is similarity?Two objects are similar if they have the same shape, or one has the same shape as the mirror image of the other.
Given:
Using theorem
If two triangles are similar, then the ratio of the area of both triangles is proportional to the square of the ratio of their corresponding sides.
ΔSDF/Δ RTY = (SD/RT)= (DF/TY)= (FS/ YR)
ar ΔSDF² / ar ΔRTY² = 16/81
SD/ RT = 4/9
SD = 4x, RT= 9x
SD= 8
4x = 8
x = 2
So,
RT= 9*2 = 18
SF = RT -2
SF = 16
(SD/RT)= (FS/ YR)
8 / 18 = 16/ YR
YR= 36
TY= 9 +RY = 45
(DF/TY)= (FS/ YR)
DF / 45= 16/ 36
DF=20
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The quadratic equation 5x2 45x 24 = 0 was solved using the quadratic formula, x equals negative b plus or minus the square root of b squared minus 4 times a times c, all over 2 times a. one solution is −8.43. what is the other solution? round to the hundredths place. 8.43 0.05 −0.57 −1.14
Answer:
Please review the equation format. I made an assumption (below) for this answer.
-0.57
Step-by-step explanation:
5x2 45x 24 = 0 is not a quadratic formula,
5x^2 + 45x + 24 = 0 is, however. Also, it gives -.8.43 as one solution. The other is −0.569351, or -0.57 to the nearest hundredth.
The other solution of the given quadratic equation would be -0.57
Quadratic Equation
An algebraic equation of the second degree in x is known as a quadratic equation. The quadratic equation is written as ax² + bx + c = 0, where x is the variable, a and b are the coefficients, and c is the constant term.
The given quadratic equation is,
5x² + 45x + 24 = 0
Here,
a = 5
b = 45
c = 24
Applying the Quadratic Formula
The quadratic formula for the two roots of a quadratic equation is given as,
[tex]x=\frac{-b+\sqrt{b^{2}-4ac } }{2a}[/tex] ........... (1)
and [tex]x=\frac{-b+\sqrt{b^{2}+4ac } }{2a}[/tex] ............ (2)
Substituting the values of a, b, and c in equation (1), we get,
x = -8.43
Calculating the Second Root
Now, the other solution can be found by substituting the values of a, b, and c in the equation (2),
[tex]x=\frac{-45+\sqrt{45^{2}+4(5)(24) } }{2(5)}[/tex]
[tex]x=\frac{-45+\sqrt{(2505) } }{10}[/tex]
[tex]x=-0.57[/tex]
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I need help plsssssssss
Answer:
x = 1
y = -2
Step-by-step explanation:
x = 19 + 9y
3x- 3y = 9
________
3(19+9y)-3y=9
y=-2
x=19+9(-2)
x=1
(1,-2)
Answer:
[tex] - x = - 1 - 9y \\ \frac{ - x}{ - 1} = \frac{ - 1}{ - 1} - \frac{9}{ - 1} \\ x = 1 + 9y...(3) \\ 3(1 + 9y) - 3y = 9 \\ 3 + 27y - 3y = 9 \\ 3 + 24y = 9 \\ 24y = 9 - 3 \\ 24y = 6 \\ \frac{24y}{24} = \frac{6}{24} \\ y = \frac{1}{4} \\ \\ \\ \\ x = 9( \frac{1}{4} ) + 1 \\ x = \frac{9}{4} + 1 \\ x = \frac{13}{4} [/tex]
Step-by-step explanation:
ATTACHED IS THE SOLUTION!
which function is increasingnon the interval (negative infinity, positive infinity)
HELP 25 POINTS WILL MARK BRAINLIEST!
Answer:
h(x) = 2^(x) - 1.
Step-by-step explanation:
Let's look at each equation:
f(x) = -3x +7, Well as x increases, since it's multiplication, there are "going to be more" -3's, so it's going to be decreasing.
g(x) = -4(2^x). While 2^x is increasing, because "there are going to be more 2's multiplied by each other" as x increases, it's being multiplied by a negative number, so it's actually going to be decrasing
h(x) = 2^(x) - 1. Here's it's going to be increases as x goes towards infinity because "there are going to be more 2's multiplied by each other", and there isn't any negative sign, while there is a negative 1, it's constant, so the overall value will be increasing
The diameter of a sphere is 16.4 mm Calculate the sphere's volume
Use the value 3.14 for pi , and round your answer to the nearest tenth. (Do not round any intermediate computations.)
The volume of the sphere is 2308.4 mm³
Calculating the volume of a SphereFrom the question, we are to determine the volume of the sphere
The volume of a sphere is given by the formula
[tex]V=\frac{4}{3}\pi r^{3}[/tex]
Where V is the volume
and r is the radius
From the given information,
Diameter, d, of the sphere = 16.4 mm
r = 16.4/2
r = 8.2 mm
∴ [tex]V=\frac{4}{3}\times 3.14 \times 8.2^{3}[/tex]
V = 2308.394
V ≅ 2308.4 mm³
Hence, the volume of the sphere is 2308.4 mm³
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PLEASE HELP!!!!!!!!!!!!!!ASAP, I MEAN THAT AS NICE AS POSSIBLE, THANKS!!!!!!!!!!!!
ASAP PLS HELP
Which function is the inverse of f(x)=12x+5?
f−1(x)=2x+10
f−1(x)=2x−5
f−1(x)=2x−10
f−1(x)=2x+5
Answer:
Step-by-step explanation:
PQ¯¯¯¯¯ and PR¯¯¯¯¯ are tangent to ⊙ S. Identify PQ.
pls help 30 points
Answer:
9
Step-by-step explanation:
Because line PQ and line PR are both tangent to circle S, it would result in them being equal. So first to find PQ, you would have to find the value of variable x. To do this you would set both equations equal to each other and solve
6x - 9 = 2x + 3
-2x -2x
4x - 9 = 3
+9 +9
4x = 12
x = 3
Now you have to substitute 3 back into the equation for PQ:
6(3) - 9
18 - 9
= 9
Resulting in PQ = 9, to check your answer, take the value of x (3) and substitute it into PR and you should also get 9
2(3) + 3
6 + 3
= 9
The quadratic $x^2 1300x 1300$ can be written in the form $(x b)^2 c$, where $b$ and $c$ are constants. What is $\frac{c}{b}$
The value of c/b when the quadratic equation x² + 1300x + 1300 is written in the form (x + b)² + c, b and c being constants is -648.
The given quadratic expression needs to be expressed using the perfect square method to be of the form (x + b)² + c.
We express the quadratic expression x² + 1300x + 1300 using the perfect square method following these steps:
x² + 1300x + 1300
= x² + 2x(1300/2) + (1300/2)² + 1300 - (1300/2)²
= x² + 2x(650) + (650)² + 1300 - (650)²
= (x + 650)² + 1300 - 422500
= (x + 650)² - 421200.
Comparing this to (x + b)² + c, we get:
b = 650, and c = -421200.
Therefore, the value of c/b = (-421200)/650 = -648.
Therefore, the value of c/b when the quadratic equation x² + 1300x + 1300 is written in the form (x + b)² + c, b and c being constants is -648.
The question seems improper. The proper question is:
" The quadratic x^2+1300x+1300 can be written in the form (x + b)^2+c, where b and c are constants. What is c/b?"
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Which function has a range of fyly ≤ 5}?
O f(x) = (x-4)² +5
Of(x) = -(x-4)² +5
O f(x) = (x - 5)² + 4
O f(x) = -(x - 5)² + 4
Answer: Option 2
Step-by-step explanation:
The vertex must have a y-coordinate of 5, so eliminate options 3 and 4.
Also, since there must be a maximum, the coefficient of [tex]x^2[/tex] must be negative. So, eliminate option 1.
This leaves us with option 2.
Let X = the number of heads in 4 flips of a fair coin. Use the probability distribution of X found here to calculate the
probability of each event.
at least 2 heads
exactly 2 heads
not all heads
more than 2 heads
0.3125
0.9375
0.6875
0.375
Find the surface area of the composite figure.
The surface area of the composite figure shown in the image is 952 ft²
What is an equation?An equation is an expression that shows the relationship between two or more variables and numbers.
Surface area of composite is the sum of the individual areas of the surface.
Hence:
Surface area of composite = 2(14 * 9) + 2(0.5 * 10 * 8) + 2(10 * 10) + 2(10 * 14) + (10 * 14) = 952 ft²
The surface area of the composite figure shown in the image is 952 ft²
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Carmen is planning rail lines for a new train station. Help her find
. Explain how you found that solution.
The angle based on the information given about the rail is 163°.
How to illustrate the information?From the information given, the value of angle 2 will be:
17° + x = 180° (angle on a straight line)
Collect like terms
x = 180° - 17°
x = 163°
In this case, it should be noted that angle 1 and 2 are alternate angles. Therefore, angle 1 will be 163°.
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The volume of a cone is 1782 cm³ a cylinder has the same radius and height as the cone what is the volume of the cylinder
Answer:
A
Step-by-step explanation:
cone volume equals
V=π/3r²h
(1782=π/3r²h) multiplied by 3 to get rid of the denominator
5346=πr²h
cylinder v=πr²h by substitution the volume would be the same as cone 5346
How many five digit numbers can be created? pls help will mark brainliest
There are 120 five digit numbers that can be created
How to determine the number of digits?The digits are given as:
2, 3, 5, 7 and 8
Since there are no conditions, and the digits cannot be repeated.
Then the number of digits is:
Digits = 5!
Expand
Digits = 5 * 4 * 3 * 2 * 1
Evaluate
Digits = 120
Hence, there are 120 five digit numbers that can be created
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Hey i need help with this problem i cant figure it out
Answer:
inverse variation: xy=20
Step-by-step explanation:
Direct Variation is when y increases as x increases and is linear
Inverse Variation is when y decreases as x increases although it's not linear and the x and y has a constant product.
By observing the table, you'll see as x increases, y decreases. You'll also notice a constant product of 20 between x and y. (2 * 10) = 20. (4 * 5) = 20. ( (8 / 1) * (5 / 2) = 40/2 = 20))... and so on. So the function can be represented as xy = 20