The value of the discriminant is zero and therefore the equation has two equal and real roots.
What is discriminant ?For a quadratic Equation ax²+bx+c = 0 , the discriminant is D = b²-4ac
The given quadratic equation is -2x² = -8x+8
comparing with the standard equation
a = 1
b = -4
c = 4
Simplifying the equation given
[tex]\rm -2x^2+8x-8 = 0\\\\ -2(x^2-4x+4) = 0\\\\x^2-4x+4 = 0[/tex]
The discriminant is given by
D = (-4)²-4 * 1 *4
D = 16-16
D = 0
If D = 0 ,the equation has two equal and real roots.
Therefore, The value of the discriminant is zero.
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Which statements about the local maximums and minimums for the given function are true? Choose three options.
Over the interval [1, 3], the local minimum is 0
Over the interval [2, 4], the local minimum is –8.
Over the interval [3, 5], the local minimum is –8.
Over the interval [1, 4], the local maximum is 0.
Over the interval [3, 5], the local maximum is 0.
The statements about the local maximums and minimums for the given function which are true include:
Over the interval [2, 4], the local minimum is –8.Over the interval [3, 5], the local minimum is –8.Over the interval [1, 4], the local maximum is 0.What is Function?This is defined as the mathematical entities which assign unique outputs to given inputs and defines a relationship between the two variables.
According the the graph: over the interval [2, 4], the local minimum is –8 because the given minimum point is (3.4, -8) and over the interval [3, 5], the local minimum is –8.
Over the interval [1, 4], the local maximum is 0 and over the interval [3, 5], there is no maximum point hence why it is false.
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NEED HELP ASAP!!!!!!!!
PLEASE
For which set of data are the median and mode the same number?
(A) 4, 5, 7, 8, 9, 9
(B) 4, 5, 7, 7, 8, 10
(C) 3, 5, 6, 8, 8, 9
(D) 5, 5, 6, 8, 9, 10
Answer:
b
Step-by-step explanation:
A pen and a ruler cost $2.10. 2 such pens and 3 such rulers cost $4.90. Find the cost of one ruler.
The cost of one ruler is $0.70
Applications of simultaneous equationsFrom the question, we are to determine the cost of one ruler
Let x represent the cost of a ruler
and
y represent the cost of a pen
From the given information, we can write that
y + x = $2.10 ----------- (1)
2y + 3x = $4.90 ----- (2)
From equation (1),
y + x = $2.10
Then,
y = $2.10 - x
Substitute this into equation (2)
2y + 3x = $4.90
2($2.10 - x) + 3x = $4.90
$4.20 - 2x + 3x = $4.90
$4.20 +x = $4.90
x = $4.90 - $4.20
x = $0.70
Hence, the cost of one ruler is $0.70
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Which could be used to evaluate the expression negative 6 (4 and two-thirds)? (negative 6) (4) (negative 6) (two-thirds) (negative 6) (4) times (negative 6) (two-thirds) (negative 6 4) (negative 6 two-thirds) (negative 6 4) times (negative 6 two-thirds)
Hence, the required expression is (Negative 6) (4) + (negative 6) (two-thirds).
What is an expression?expression is a combination of numbers, variables, and functions (such as addition, subtraction, multiplication or division etc.). This math operation can be addition, subtraction, multiplication, or division. The structure of an expression is: Expression is (Number/Variable, Math Operator, Number/Variable)
How to solve?LHS,
(-6)([tex]\frac{14}{3}[/tex]) = -28
RHS,
(-6)()[tex]4+\frac{2}{3}[/tex]) = -28
LHS=RHS
Hence, the required expression is (Negative 6) (4) + (negative 6) (two-thirds).
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If the expression (2+ 3+ 2i) is a factor of a polynomial, which expression below
must also be a factor?
A: -(x+3+2i)
B: (x-3-2i)
C:(x-3+2i)
D:(x+3-2i)
Step-by-step explanation:
180 250 300 H.C.F by division method
For the following exercises, find (f ∘ g)(x) and (g ∘ f)(x) for each pair of functions.
35. f(x) = 3x + 2, g(x) = 5 − 6x
Answer:
The value of [tex]$(f \circ g)(x)$[/tex] is 17-18x and [tex]$(g \circ f)(x)$[/tex] is -7-18x.
Step-by-step explanation:
It is given in the question functions f(x) as 3x+2 and g(x)=5-6x.
It is required to find [tex]$(f \circ g)(x)$[/tex] and [tex]$(g \circ f)(x)$[/tex].
To find [tex]$(f \circ g)(x)$[/tex], substitute g(x) for x in f(x) and simplify the expression.
To find [tex]$(g \circ f)(x)$[/tex], substitute f(x) for x in g(x) and simplify the expression.
Step 1 of 2
Substitute g(x) for x in f(x) and simplify the expression.
[tex]$$\begin{aligned}&(f \circ g)(x)=f(5-6 x) \\&(f \circ g)(x)=3(5-6 x)+2 \\&(f \circ g)(x)=15-18 x+2 \\&(f \circ g)(x)=17-18 x\end{aligned}$$[/tex]
Step 2 of 2
Substitute f(x) for x in g(x) and simplify the expression.
[tex]$$\begin{aligned}&(g \circ f)(x)=g(3 x+2) \\&(g \circ f)(x)=5-6(3 x+2) \\&(g \circ f)(x)=5-18 x-12 \\&(g \circ f)(x)=-7-18 x\end{aligned}$$[/tex]
2 dogs, 4 horses 1 giraffe and a duck are lying on the bed. 3 chickens are flying over a chair. How many legs are on the ground?.
Answer:
8+16+2= 24 legs on ground
Step-by-step explanation:
Eric was rock climbing. At one point, he stopped and climbed straight down 2\dfrac{1}{2}2
2
1
2, start fraction, 1, divided by, 2, end fraction meters. Then he climbed straight up 6\dfrac{3}{4}6
4
3
6, start fraction, 3, divided by, 4, end fraction meters. Eric was wondering what his change in elevation was after these two moves.
Which of the following equations matches the situation above?
The equation that matches the given situation is [tex]-2\frac{1}{2}+6\frac{3}{4}=?[/tex] . So, after two moves, Eric's elevation changed [tex]4\frac{1}{4}[/tex] meters above.
We know that in mathematics, subtraction means removing something from a group or a number of things. What is left in the group gets smaller when we subtract. The minuend is the first element we use. The subtrahend is the part that is being removed. The difference is the portion that remains after subtraction.
Assume that "negative" means climbing down and "positive" means climbing up. We must locate the elevation change in this area.
Given that Eric climbed straight down [tex]2\frac{1}{2}[/tex] meters. So we can write [tex]-2\frac{1}{2}[/tex].
Again Eric climbed straight up [tex]6\frac{3}{4}[/tex] meters. So, we can write [tex]6\frac{3}{4}[/tex].
Then the change = [tex]-2\frac{1}{2}+6\frac{3}{4}[/tex]
=[tex]-\frac{(2*2+1)}{2}+\frac{6*4+3}{4}[/tex]
=[tex]-\frac{5}{2} +\frac{27}{4}[/tex]
=[tex]\frac{-(5*2)+27}{4}[/tex]
=[tex]\frac{-10+27}{4}[/tex]
=[tex]\frac{17}{4}[/tex]
=[tex]\frac{4*4+1}{4}[/tex]
=[tex]4\frac{1}{4}[/tex]
Therefore, the equation that matches the given situation is [tex]-2\frac{1}{2}+6\frac{3}{4}=?[/tex] . So, after two moves, Eric's elevation changed [tex]4\frac{1}{4}[/tex] meters above.
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Calculate the area of triangle OPQ.
Thus, we need information about the sides OQ and PQ to solve the triangle and find the area. The information given is not enough to determine the area of the triangle.
Is this triangle solvable?
In this question we must analyze if the area of the triangle OPQ can be found by all information given. By the law of the cosines we understand that lengths of two sides and the measure of an angle should be known to construct a triangle and by the law of the sines we understand that either two angles and a side or two sides and an angle must be known.
Thus, we need information about the sides OQ and PQ to solve the triangle and find the area. The information given is not enough to determine the area of the triangle.
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Consider parallelogram PQRS, where PQ ≅ RS and QR ≅ PS. Construct diagonal PR and diagonal QS. By the SSS criterion, ΔPQR ≅ ΔRSP and ΔPQS ≅ ΔRSQ. Therefore, ∠QPS ≅ ∠SRQ and ∠PQR ≅ ∠RSP since corresponding angles of congruent triangles are congruent.
What statement is proven by the given steps?
A.
A quadrilateral with congruent consecutive angles is a parallelogram.
B.
Consecutive angles of a parallelogram are congruent.
C.
Opposite angles of a parallelogram are congruent.
D.
A quadrilateral with congruent opposite angles is a parallelogram.
The correct answer would be option(C) opposite angles of a parallelogram are congruent.
What is Parallelogram?A parallelogram defined as a special type of quadrilateral which has both pairs of opposite sides parallel and equal.
Given that PQRS is a parallelogram.
PQ ≅ RS
QR ≅ PS
By the SSS criterion, ΔPQR ≅ ΔRSP and ΔPQS ≅ ΔRSQ.
Therefore, ∠QPS ≅ ∠SRQ and ∠PQR ≅ ∠RSP since corresponding angles of congruent triangles are congruent.
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Answer:
"B"
Step-by-step explanation:
A measure of the strength of the relationship between two variables is referred to as the.
A statistical indicator of the strength of the association between the relative movements of two variables is the correlation coefficient.
To gauge how strongly two variables are related to one another, correlation coefficients are used.
A statistical indicator of the strength of the association between the relative movements of two variables is the correlation coefficient. The values are in the -1.0 to 1.0 range. There was a measurement error in the correlation if the estimated value was larger than 1.0 or lower than -1.0. Perfect negative correlation is shown by a correlation of -1.0, and perfect positive correlation is shown by a correlation of 1.0. A correlation of 0.0 indicates that there is no linear link between the two variables' movements. Finance and investing can benefit from the usage of correlation statistics.
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Compared to continental crust, oceanic crust is:
A. mostly granite
B. more dense
C. All of these
D. thicker
Answer:
B. more dense
The______is the set of inputs For a fraction
The set of all input values of a function is the domain of the function
What is a function?A function relates an input to an output.
A function defines a relationship between one variable (the independent variable) and another variable.
The set of all input values of a function is the domain of the function.
The domain of a function are also called independent variables.
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The circumference of a sphere was measured to be 76 cm with a possible error of 0.5 cm. (a) Use differentials to estimate the maximum error in the calculated surface area. (Round your answer to the nearest integer.) cm2 What is the relative error
The maximum error in the calculated surface area is 24.19cm² and the relative error is 0.0132.
Given that the circumference of a sphere is 76cm and error is 0.5cm.
The formula of the surface area of a sphere is A=4πr².
Differentiate both sides with respect to r and get
dA÷dr=2×4πr
dA÷dr=8πr
dA=8πr×dr
The circumference of a sphere is C=2πr.
From above the find the value of r is
r=C÷(2π)
By using the error in circumference relation to error in radius by:
Differentiate both sides with respect to r as
dr÷dr=dC÷(2πdr)
1=dC÷(2πdr)
dr=dC÷(2π)
The maximum error in surface area is simplified as:
Substitute the value of dr in dA as
dA=8πr×(dC÷(2π))
Cancel π from both numerator and denominator and simplify it
dA=4rdC
Substitute the value of r=C÷(2π) in above and get
dA=4dC×(C÷2π)
dA=(2CdC)÷π
Here, C=76cm and dC=0.5cm.
Substitute this in above as
dA=(2×76×0.5)÷π
dA=76÷π
dA=24.19cm².
Find relative error as the relative error is between the value of the Area and the maximum error, therefore:
[tex]\begin{aligned}\frac{dA}{A}&=\frac{8\pi rdr}{4\pi r^2}\\ \frac{dA}{A}&=\frac{2dr}{r}\end[/tex]
As above its found that r=C÷(2π) and r=dC÷(2π).
Substitute this in the above
[tex]\begin{aligned}\frac{dA}{A}&=\frac{\frac{2dC}{2\pi}}{\frac{C}{2\pi}}\\ &=\frac{2dC}{C}\\ &=\frac{2\times 0.5}{76}\\ &=0.0132\end[/tex]
Hence, the maximum error in the calculated surface area with the circumference of a sphere was measured to be 76 cm with a possible error of 0.5 cm is 24.19cm² and the relative error is 0.0132.
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The question is already stated on the picture.
The central angle is 77 degrees mate.
Pauley graphs the change in temperature of a glass of hot tea over time. he sees that the function appears to decrease quickly at first, then decrease more slowly as time passes. which best describes this function?
Non-linear graph best describes this function.
Why nonlinear?
As described in the question, Pauley graphs the change in temperature of a glass of hot tea over time. He sees that the function appears to decrease quickly at first, then decrease more slowly as time passes. It is linear because the graph decreases over time. It is linear because there is both an independent and a dependent variable but it doesn't satisfies one condition of being linear. Thus, It's Nonlinear because linear functions are increasing functions. It is nonlinear because linear functions increase or decrease at the same rate.
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Answer:
B
Step-by-step explanation:
Evaluate 43 – 3m for m = 6.
Answer:
= 43 - 3×6= 43 - 18Therefore , 25 ans.
MN= cm
Help me please!! Stuck on this thanks:)
Answer:
3π
Step-by-step explanation:
arc length = radius x central angle in radians
π = radius x π/3
radius = 3π
since OMN is an equilateral triangle, radius = MN
thus MN = 3π
Give the outcomes for each of the following events.
Pina has two equations that she found to be valuable models for her research. She thinks that if she can find the solution of the two graphs, she will be able to identify a key point to her studies. What can Pina expect in terms of solutions of these two graphs?
-3x + y = 10
y = 3x − 6
parallel lines
infinite solutions
both parallel lines and no solution
no solution
In the falcon's nest ice cream cost 20 cents. if the school pays 15 cents, what percent mark-up is it?
Answer: 25% off
Step-by-step explanation:
1= 0.25 + 0.75
25% is off is the equivalency of multiplying the value of the original cost with 0.75.
20*0.75=15
In a large population, 76% of the households have cable tv. A simple random sample of 225 households is to be contacted and the sample proportion computed. What is the mean and standard deviation of the sampling distribution of the sample proportions
0.017559
It is given that:
Probability of Households Having cable TV, p₀ = 76% = 0.76
Therefore,
The probability that the Households not having cable TV = 1 - 0.76 = 0.24
Sample size, n = 225 households
sample proportions is less than 82% i.e p = 0.82
Now,
The standard error, SE = [tex]\sqrt{} \frac{0.76(1-0.76)}{225}[/tex]
= 0.02847
Z = [tex]\frac{0.82-0.76}{0.02847}[/tex]
Z = 2.107
therefore, P(sample porportions < 0.82) = P(Z < 2.107)
now from the p value from the Z table we get P(sample porportions < 0.82) = 0.017559
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change the unit of weight 1,000 lb =___ t ?
Answer:
0.5 t
Step-by-step explanation:
Since we know that 2,000lbs=1 t
1,000lbs is half a ton, which makes it 0.5 tons
Try it
Which graph represents the function h(x) = 5.5|x]?
LIV
-2
2 4
-4-2
Intro
2
-4-2
O
2 4
-4-2
2
[tex]take \: some \: values \\ h(1) = 5.5 \times |1| = 5.5 \times 1 = 5.5 \\h(2) = 5.5 \times |2| = 5.5 \times 2 = 11 \\ h(4) = 5.5 \times |4| = 5.5 \times 4= 22[/tex]
It's clearly the second option since the other ones aren't steep enough.Question is on the picture:)
Answer:
Z = 90 degrees
Step-by-step explanation:
Reason is a diameter subtends angle of 90 degrees on the circumference
Find the length of the midsegment .
A.15
B.44
C.22
D.13
Answer: 22
Step-by-step explanation:
Using the triangle midsegment theorem,
[tex]2(5x+2)=3x+32\\\\10x+4=3x+32\\\\7x+4=32\\\\7x=28\\\\x=4[/tex]
So, the length of the midsegment is 5(4) + 2 = 22
Given the following linear function sketch the graph of the function and find the domain and range. f( x ) = 2/7 x− 2
Answer:
Domain: All Real Numbers Range: All Real Numbers
Step-by-step explanation:
The domain and range is going to be infinite. The linear function will be using the x and y- axis in order to continue being a function. The y-intercept will be -2 on the y-axis. I recommend using the rise-over-run method for your slope value. from the point (0, -2) on the y-axis. Go up two on the y-axis, and right 7 on the x-axis.
Sorry, it may be difficult to explain through words.
I need answer fast!!
3. Write the rule that describes the second transformation. (5 points)
The rule that describes the second transformation is; Rotated at 90° clockwise
How to Interpret Transformations?From the given diagram we can see that;
The transformation from Rectangle ABCD to A'B'C'D' follows the transformation sequence of;
Shift 1 unit downwards then translate 5 units to the right.
However, for the transformation of A'B'C'D' to A"B"C"D", we see that the transformation is; Rotated at 90° clockwise
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In which year did Eugene, Oregon have the greatest difference between high and low temperatures in November?
A)November 2009
B)November 2010
C)November 2011
D)November 2008
Joe ordered a large cake for his brothers. He gave 1 out of 12 of the cake to David, 5 out of 12 of the cake to John, and 2 out of 12 of the cake to Ali. He ate the remaining cake himself. What fraction of the whole cake did Joe eat?
Answer: 4/12 or 1/3
Step-by-step explanation:
A whole cake is 12/12.
He gave away 1/12, 5/12, and 2/12s of the cake
1+5+2 = 8
So he gave out 8/12s of the cake, which means he has 4/12 left, or 1/3 if you want simplest form.
Hope this helps.