The correct option B.
The value of the zeros of function g is -6 and 7
What is Quadratic equation?Any equation that can be rewritten in standard form as where x represents an unknown, a, b, and c represent known numbers, and where a 0 is true is a quadratic equation. As there is no ax2 term when a = 0, the equation is linear rather than quadratic.
According to the given information:The factors are (x − 7) and (x + 6)
On simplifying the we get:
x²+ 6x -7x -42 = 0
x² - x - 42 = 0
The factorizing these equation we get.
So the zeros are -6 and 7 , so option b is correct.
[tex]x_{1,2}=\frac{-(-1) \pm \sqrt{(-1)^{2}-4 \cdot 1 \cdot(-42)}}{2 \cdot 1}[/tex]
[tex]$$x_{1,2}=\frac{-(-1) \pm 13}{2 \cdot 1}\\[/tex]
[tex]x_1,_2[/tex] = ((1) ± 13)/2.1
[tex]x_1[/tex] = (1+13)/2.1
[tex]x_2[/tex] = (1 - 13)/2.1
[tex]X_1\\[/tex] = 7 , [tex]X_2[/tex] = -6
The Zeros of the function are: (7 , -6)
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4 pounds of oranges cost $12. what is the unit price per pound ?
$ 1 per 3 pounds
$ 3 per 1 pound
$6 per 2 pounds
$12 per 4 pounds
the unit price is $3 per pound, the correct option is the second one.
How to get the unit price of the oranges?
The unit price for the oranges is just the price for one pound of oranges.
Here we know that the price of 4 lb of oranges is $12, with that we want to get the cost of a single lb of oranges, so we can write:
4lb = $12
If we divide both sides by 4, then we get:
4lb/4 = $12/4
1lb = $3
This means that the price of 1 pound of oranges is $3, then the unit price is $3 per pound, the correct option is the second one.
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An amusement park rounds its total attendance for last year to 120,000 people.
Which could have been the attendance at the amusement park if it was rounded to the nearest ten thousand?
Choose 1 answer:
A
126,458
B
116,390
(Choice C)
125,007
Answer:
B
Step-by-step explanation:
B Rounded to nearest ten thousand
The attendance that aligns with rounding to 120,000 is B) 116,390.
To determine the possible attendance at the amusement park if it was rounded to the nearest ten thousand, we need to consider the rounding process.
When rounding to the nearest ten thousand, we look at the digit in the ten thousand place. If this digit is 5 or greater, we round up to the next ten thousand. If it is less than 5, we round down to the previous ten thousand.
In this case, the attendance was rounded to 120,000. To round to the nearest ten thousand, we look at the digit in the ten thousand place, which is 2. Since 2 is less than 5, we round down.
Therefore, the attendance at the amusement park could have been rounded to 120,000 people if it was rounded to the nearest ten thousand.
Among the given options, the attendance that aligns with rounding to 120,000 is B) 116,390.
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Find the value of x in the given figure
Answer:
X=36
Step-by-step explanation:
2x + 3x=5x
if given figure is 180 then
5x=180
X=180/5
X=36
1/2 to the 2nd power in fraction form
Answer: [tex]\frac{1}{4}[/tex]
Work Shown:
[tex]\left(\frac{1}{2}\right)^2 = \left(\frac{1}{2}\right)*\left(\frac{1}{2}\right) = \frac{1*1}{2*2} = \frac{1}{4}[/tex]
The system of equations below has no solution.
StartLayout enlarged left-brace 1st row two-thirds x + five-halves y = 15 2nd row 4 x + 15 y = 12
Which equation could represent a linear combination of the system?
The equation that could represent a linear combination of the system 2/3x + 5/2y = 15 and 4x + 15y = 12 is 0 = 26
What are linear equations?Linear equations are equations that have constant average rates of change, slope or gradient
How to determine the linear combination to the system?A system of linear equations is a collection of at least two linear equations.
In this case, the system of equations is given as
2/3x + 5/2y = 15
4x + 15y = 12
Multiply the first equation by 6, to eliminate the fractions.
6 * (2/3x + 5/2y = 15)
This gives
4x + 15y = 90
Subtract the equation 4x + 15y = 90 from 4x + 15y = 12
4x - 4x + 15y - 15y = 12 - 90
Evaluate the difference
0 + 0 = -78
Evaluate the sum
0 = -78
The above equation is the same equation as option (b) 0 = 26
This is so because they both represent that the system of equations have no solution
Hence, the equation that could represent a linear combination of the system is 0 = 26
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If the vertex of a parabola is at the point (-2, 5), then the equation for the axis of symmetry for the parabola is x = -2. True or false?
Answer:
true
Step-by-step explanation:
thats really it i believe its true
y = x - 4
2x + y = 5
solve for x and y
Answer:
X = 2
Y = 1
Step-by-step explanation:
Solve by substitution
[tex]y = x - 4 \\ 2x + y = 5 \\ \\ y = x - 4 \\ 2x - 5 = - y \\ \\ y = x - 4 \\ - y = 2x - 5 \\ \\ add \: the \: two \: equations \\ \\ 0 = 3x - 9 \\ 9 = 3x \\ \frac{9}{3} = \frac{3x}{x} \\ x =3 \\ \\ substitute \: 3 \: for \: x \: in \: one \: of \: the \: equations \: to \: find \: y \\ \\ y = x - 4 \\ y = 3 - 4 \\ y = - 1 \\ \\ solution \: (3. - 1)[/tex]
What is the slope of the line that passes through the points (10, 3) and
(7,0)? Write your answer in simplest form.
Answer:
slope = 1
Step-by-step explanation:
calculate the slope m using the slope formula
m = [tex]\frac{y_{2}-y_{1} }{x_{2}-x_{1} }[/tex]
with (x₁, y₁ ) = (10, 3 ) and (x₂, y₂ ) = (7, 0 )
m = [tex]\frac{0-3}{7-10}[/tex] = [tex]\frac{-3}{-3}[/tex] = 1
Given: Circle M with inscribed Angle K J L and congruent radii JM and ML
Prove: mAngle M J L = One-half (measure of arc K L)
Circle M is shown. Line segment J K is a diameter. Line segment J L is a secant. A line is drawn from point L to point M.
What is the missing reason in step 8?
Statements
Reasons
1. circle M with inscribed ∠KJL and congruent radii JM and ML 1. given
2. △JML is isosceles 2. isos. △s have two congruent sides
3. m∠MJL = m∠MLJ 3.
base ∠s of isos. △are ≅ and have = measures
4. m∠MJL + m∠MLJ = 2(m∠MJL) 4. substitution property
5. m∠KML = m∠MJL + m∠MLJ 5. measure of ext. ∠ equals sum of measures of remote int. ∠s of a △
6. m∠KML =2(m∠MJL) 6. substitution property
7. Measure of arc K L = measure of angle K M L 7. central ∠ of △ and intercepted arc have same measure
8.
Measure of arc K L = 2 (measure of angle M J L)
8. ?
9.
One-half (measure of arc K L) = measure of angle M J L
9. multiplication property of equality
reflexive property
substitution property
base angles theorem
second corollary to the inscribed angles theorem
The missing reason in step 8 is the substitution property.
What is substitution property?It should be noted that according to substitution property, if x = y, then x can be substituted for y in any equation.
When a variable is equal to another variable, then the variables can be interchangeable.
In this case, the missing reason in step 8 is the substitution property.
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James covers a distance of 8 meters in the first second of a 100 meter race. then, he sprints at a speed of 9 meters per second. how far is james from the finish line 9 seconds after the race has started? a. 11 c. 28 b. 20 d. 80 please select the best answer from the choices provided a b c d
James is (B) 20 meters far from the finish line 9 seconds after the race has started.
What is the distance?Distance is a numerical measurement of the distance between two objects or places. The distance can refer to a physical length or an estimate based on other criteria in physics or common usage. The distance between two points A and B is commonly expressed as |AB|.To find the distance:
James covers 8 meters in the opening second of the 100-meter race.Then he sprints at a 9-meter-per-second pace.We need to figure out how far James is from the finish line 9 seconds after the race begins.James travels 8 meters in the first second.After running 8 meters, the time remaining in 9 seconds is 9 - 1 = 8 seconds.James completes the distance = speed time = 9 8 = 72 meters in another 8 seconds.The total distance traveled in 9 seconds is equal to 8 + 72 = 80 meters.After 9 seconds, the distance remaining in a 100-meter race is 100 - 80 = 20 meters.9 seconds into the race, James is 20 meters from the finish line.Therefore, James is (B) 20 meters far from the finish line 9 seconds after the race has started.
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The complete question is given below:
James covers a distance of 8 meters in the first second of a 100-meter race. Then, he sprints at a speed of 9 meters per second. How far is James from the finish line 9 seconds after the race has started?
a. 11
b. 20
c. 28
d. 80
Convert the cartesian coordinate (-6,-1) to polar coordinates, 0 ≤ θ < 2 π , r > 0 0≤θ<2π, r>0
The polar coordinate of given cartesian coordinate (-6, -1) is
(6.08, 0.0523π)
In this question,
We have been given the cartesian coordinate (-6, -1)
We need to convert given cartesian coordinate to polar coordinates.
We know that the polar coordinates is of the form (r, θ)
where, r is the magnitude with r = [tex]\sqrt{x^{2}+ y^{2} }[/tex]
and θ is the angle associated with the coordinates which is given by θ = [tex]tan^{-1}(\frac{y}{x} )[/tex]
The magnitude of the given polar coordinate is,
⇒ r = [tex]\sqrt{x^{2}+ y^{2} }[/tex]
⇒ r = [tex]\sqrt{(-6)^{2}+ (-1)^{2} }[/tex]
⇒ r = [tex]\sqrt{36+ 1}[/tex]
⇒ r = [tex]\sqrt{37}[/tex]
⇒ r = 6.08
And the angle associated with the coordinate is,
⇒ θ = [tex]tan^{-1}(\frac{-1}{-6} )[/tex]
⇒ θ = [tex]tan^{-1}(0.167 )[/tex]
⇒ θ = 9.48°
⇒ θ = 0.0523π
So, the polar coordinate is (6.08, 0.0523π)
Therefore, the polar coordinate of given cartesian coordinate (-6, -1) is
(6.08, 0.0523π)
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PLEASE HELP IM STUCK
Answer:
6x + 4y = 16
Step-by-step explanation:
2(3x + 2y = 8)
2(3x + 2y) = 2(8)
6x + 4y = 16
Answer:
6x+4y=16
Step-by-step explanation:
2 (3x+2y=8)
2×3x+2×2y=2×8
=6x+4y=16 ans.
What is the conditional probability that exactly four heads appear when a fair coin is flipped five times, given that the first flip came up tails?
Answer:
give it a try
Step-by-step explanation:
Okay. I'm gonna flip five coins, but I'm told the first coin is Tell there's no choice there at all. It is certain the first coin shows a tail and then I want to have four heads in a row. Okay, so one for tell which means certain getting ahead is a half chance. Again a half chance again a half and again a half So that you work out and it's 1/16. That's the answer. There's no choice about the foreheads. It just has to be head every time I said.
( a^5 ⋅ 2^3 )^3 = ?
Please help and explain.
Answer: [tex]512a^{15}[/tex]
Step-by-step explanation:
[tex](a^5*2^3)^3[/tex]
First, lets solve the inside of the parenthesis
[tex](a^5*8)^3[/tex]
Now, distribute the power of 3 to both terms. Remember taking a power of an exponent is like multiplying them (in this case [tex](a^5)^3=a^{15}[/tex]
[tex]a^{15}*512[/tex]
Simplify
[tex]512a^{15}[/tex]
if csc(θ)=2 and tan (θ)<0, determine the exact value of cos(θ)
By trigonometric functions and formulae, we find that the exact value of the cosine function is -√3 / 2.
What is the exact value of a trigonometric function?
In this question we have hints from two trigonometric functions necessary to find the exact value of the cosine function. In accordance with trigonometry, cosecant function is positive and tangent function is negative in the third quadrant of Cartesian plane and therefore the cosine function must be a negative number. Therefore, we can derive the value of the latter function by trigonometric formulas:
cos θ = - √[1 - (1 / csc θ)²]
If we know that csc θ = 2, then the exact of the cosine function is:
cos θ = -√[1 - (1 / 2)²]
cos θ = -√(3 / 4)
cos θ = -√3 / 2
By trigonometric functions and formulae, we find that the exact value of the cosine function is -√3 / 2.
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What is the measure of ∠w, rounded to the nearest degree? 19° 19° 32° 32° 56° 56° 71° 71° a horizontally-aligned scalene triangle u v w. side u v is labeled as 35 meters. side v w is labeled as 30 meters. side u w is labeled as 30 meters.
Answer:
(d) 71°
Step-by-step explanation:
The desired angle in the given isosceles triangle can be found a couple of ways. The Law of Cosines can be used, or the definition of the sine of an angle can be used.
SineSince the triangle is isosceles, the bisector of angle W is an altitude of the triangle. The hypotenuse and opposite side with respect to the divided angle are given, so we can use the sine relation.
sin(W/2) = Opposite/Hypotenuse
sin(W/2) = (35/2)/(30) = 7/12
Using the inverse sine function, we find ...
W/2 = arcsin(7/12) ≈ 35.685°
W = 2×36.684° = 71.37°
W ≈ 71°
Law of cosinesThe law of cosines tells you ...
w² = u² +v² -2uv·cos(W)
Solving for W gives ...
W = arccos((u² +v² -w²)/(2uv))
W = arccos((30² +30² -35²)/(2·30·30)) = arccos(575/1800) ≈ 71.37°
W ≈ 71°
What is the maximum number of pants per employee that can be washed each week? (2 points)
6. What is the maximum number of chef coats per employee that can be washed
each week? (2 points)
7. What is the maximum total number of items per employee that can be washed in a week? (2 points)
The computation shows that the maximum number of pants per employee that can be washed each week is 6.
How to compute the values?The maximum number of pants per employee that can be washed each week will be:
7 + 4.5x + 12 <= 46
4.5x <= 27
x <= 6
The maximum number is 6.
The maximum number of chef coats per employee that can be washed each week will be:
= 6 + 8
= 14
The maximum total number of items per employee that can be washed in a week will be:
= 6 + 14 = 20
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Determine whether the given correlation coefficient is statistically significant at the specified level of significance and sample size. r=0. 835, α=0. 01, n=4
Yes, the correlation coefficient is statistically significance
The precise metric used in a correlation analysis to quantify the strength of the linear relationship between two variables is the correlation coefficient. In a correlation report, the r stands for the coefficient.
Given,
Sample size, n = 4
Where ρ is the population correlation.
Then the number of degrees of freedom is, df = n-2 = 4-2 = 2
The corresponding critical correlation value re for a significance level of a 0.01, for a two-tailed test is た= 0.254
Here,
The null hypothesis, [tex]H_{0}[/tex] = ρ - 0 is rejected
Suppose lr> re 0.254
Because on the sample correlation provided, we know that lrl = 0.835>=0.254.
Here, it is clear that the null hypothesis is rejected.
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Find the extremum of f(x,y) subject to the given constraint, and state whether it is a maximum or a minimum. f(x,y)=xy; 6x y=
There is a maximum value of 6 located at (x, y) = (1, 6).
The function given to us is f(x, y) = xy.
The constraint given to us is 6x + y = 12.
Rearranging the constraint, we get:
6x + y = 12,
or, y = 12 - 6x.
Substituting this in the function, we get:
f(x, y) = xy,
or, f(x) = x(12 - 6x) = 12x - 6x².
To find the extremum, we differentiate this, with respect to x, and equate that to 0.
f'(x) = 12 - 12x ... (i)
Equating to 0, we get:
12 - 12x = 0,
or, 12x = 12,
or, x = 1.
Differentiating (i), with respect to x again, we get:
f''(x) = -12, which is less than 0, showing f(x) is maximum at x = 1.
The value of y, when x = 1 is,
y = 12 - 6x,
or, y = 12 - 6*1 = 6.
The value of f(x, y) when (x, y) = (1, 6) is,
f(x, y) = xy,
or, f(x, y) = 1*6 = 6.
Thus, there is a maximum value of 6 located at (x, y) = (1, 6).
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The provided question is incomplete. The complete question is:
"Find the extremum of f(x, y) subject to the given constraint, and state whether it is a maximum or a minimum. f(x, y)=xy; 6x+y=12.
Determine the simplified expression for the area of the shaded region below
Answer:
shaded area = 9x² +10x +4
Step-by-step explanation:
The area of the shaded region is the difference between the areas of the overall rectangle and the unshaded one it contains. Each area is the product of length and width.
Rectangle areasOverall rectangle
A = LW
A = (5x)(3x) = 15x² . . . . . using given dimensions
Unshaded interior rectangle
A = (3x +1)(2x -4) = 3x(2x -4) +1(2x -4) . . . . . using given dimensions
A = 6x² -12x +2x -4 = 6x² -10x -4
Difference of areasThe shaded area is the difference between the area of the overall rectangle and the area of the unshaded included rectangle.
shaded area = (15x²) -(6x² -10x -4)
shaded area = 9x² +10x +4
PLEASE HELP ME QUICKLY!! IM BEING TIMED
The sum of 2 numbers is 36. The first number is twice the second number. Find the second number
Answer: 24+12=36
Step-by-step explanation:
36= _+_
2x(2 times)
x
X+2x=36
3x=36
12
12+2(12)=36
12+24=36
Answer:
The value of the second number is 24 and the first no 12.Step-by-step explanation:
Greetings !From, the given word explanation try to create your own equation like
x + y = 36... (1) let the two numbers be x and y respectively.2x = y ....(2) let x be the first no and it's twice that of the second number.From, equation (1) solve for x
x + y = 36x = 36-y... (3)Substitute, equation (3) to equation (2).
2(36-y) =y72 - 2y =y72 = y + 2y.... solve for y72 = 3y.... divide both sides by 372/3 = y..y=24 ...simplifiedWrite an equation for the
function graphed above
Answer:
g(x) = (x + 1)² + 1
Step-by-step explanation:
the original function
f(x) = x²
for the new function g(x)
it is shifted 1 unit to the left and 1 unit up.
the shift to the left is done by adding these units to the input variable x :
g(x) = f(x+1) = (x+1)²
that way we get the function value for x+1 already at x :
1 unit "earlier" than in the original.
and the shift up is easy.
whatever the function calculates, we simply add 1 to everything.
the whole curve stays as it is, just one unit higher. g
so, the final g(x) = f(x+1) + 1 = (x + 1)² + 1
Describe the end behavior of the following function:
F(x)=x^5-x^3+x²
A. The graph of the function starts high and ends high.
B. The graph of the function starts low and ends low.
C. The graph of the function starts high and ends low.
D. The graph of the function starts low and ends high.
A boat took 4 hours to make a downstream
trip with a current of 6 km/h. The return trip
against the same current took 6 hours. Find
the speed of the boat in still water.
Answer:
30 km/h
Step-by-step explanation:
Let X km/h be the speed of the boat in still water
Let the distance covered each way be D km
Relative speed of boat downstream = X + 6
Relative speed of boat upstream = X - 6
Distance covered by boat when going downstream
D = 4(X + 6) = 4X + 24
Distance covered by boat upstream is the same as distance covered downstream
D = 6(X-6) = 6X -36
Setting the two X equations equal to each other gives us
6X - 36 = 4X + 24
Collecting like terms
6X - 4X = 24-(-36)
2X = 60
X = 30 km/hr which is the speed of boat in still water
Check
Downstream speed is 30+6 = 36 km/h and distance traveled downstream in 4 hours = 36 x 4 = 144km
Upstream speed is 30-6 = 24 km/h and it travels for 6 hours. Distance covered = 24 x 6 = 144 miles
So distance covered is same and hence check succeeds
Jacy has a collection of 140 coins worth $19.00. she has only nickels, dimes, and quarters. the difference in the number of dimes and the number of quarters is 10. using matrices, how many nickels are in jacy’s collection?
She has 38 nickels
N as the number of nickels, D as the number of dimes, and Q as the number of quarters.
She has 140 coins in total, so we can writen:
N + D + Q = 140.
And the total value is $19.00
Then we have:
N*0.05 + D*0.10 + Q*0.25 = 19
And "The difference in the number of dimes and the number of quarters is 10."
D - Q = 10.
So we have a system of 3 equations and 3 variables:
N + D + Q = 140
N*0.05 + D*0.10 + Q*0.25 = 19
D - Q = 10.
First, let's isolate one of the variables in the third equation, i will isolate D.
D = 10 + Q.
Now we can replace this in the other two equations:
N + (10 + Q) + Q = 140
N*0.05 + (10 + Q)*0.10 + Q*0.25 = 19.
Now we can isolate Q in the first equation:
N + 10 + 2*Q = 140
2*Q = 140 - 10 - N
Q = 130/2 - N/2. = 65 - N/2
Now we can replace this in the other equation:
N*0.05 + 10*0.10 + Q*(0.10 + 0.25) = 19
N*0.05 + 10*0.10 + (65 - N/2)*( 0.35) = 19
Now we can find the number of nickels.
N*0.05 + 1 + 22.75 - N*0.175 = 19
23.75 - N*(0.175 - 0.05) = 19
23.75 - 19 = N*0.125
4.75/0.125 = N
38 = N
She has 38 nickels
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Marcus needs to add a query for multiple tables in his database. he is using access 2016. which tab should he use to add the query? home external data create database tools
He is using Access 2016 Database tools are the tab that should he use for the add a query for multiple tables in his database.
What is In databases?Databases and a desk is hard and fast of records elements (values) the usage of a version of vertical columns (identifiable with the aid of using the name) and horizontal rows, the cell being the unit wherein a row and column intersect.
Tables are database gadgets that incorporate all of the records in a database. In tables, records is logically prepared in a row-and-column layout much like a spreadsheet.
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The above question is incomplete:
Marcus needs to add a query for multiple tables in his database. He is using Access 2016. Which tab should he use
to add the query?
Home
External data
Create
Database tools
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4√2/9+√2+√1/18. 1/√3-1-1/√3+1
Answer:
Exact form: 78√2 - 17√3 / 54
Decimal form: 1.49747766
Step-by-step explanation:
Rationalize and simplify the expression.
Haley conducted a study which found that a cup of coffee contains 150 milligrams of caffeine. the amount of caffeine in the body each hour after consumption of one cup is 9% less than the previous hour. if haley conducted her study for a total of 10 hours, which inequality represents the range of the exponential function that models this situation?
[tex]58.41 < f(x) < 150[/tex] inequality represents the range of the exponential function that models this situation
The exponential decay function is as follows:
[tex]y = a(1-r)^t[/tex]
Here,
y = final value
a = initial value
r = decay rate
t = time taken
Given that:
a = 150 mg
r = 9% = 0.09
Then the next hour the amount of caffeine in the body will be:
[tex]y = a (1-r)^t\\y = 150 \times (1-0.09)^2[/tex] = 136.5
Similarly, after 10 hours the amount of caffeine in the body will be:
[tex]y = 150 \times (1- 0.09)^{10} = 58.41[/tex]
Then the inequality representing the range of the exponential function that models this situation is:
58.41 < f(x) < 150
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Explain type i error and give an example. explain type ii error and give an example. what is the best way to reduce both kinds of error? find a current scenario that has a type i error and a type ii error. is this scenario an example of an inverse relationship? why or why not?
Type I error says that we suppose that the null hypothesis exists rejected when in reality the null hypothesis was actually true.
Type II error says that we suppose that the null hypothesis exists taken when in fact the null hypothesis stood actually false.
What is Type I error and Type II error?In statistics, a Type I error exists as a false positive conclusion, while a Type II error exists as a false negative conclusion.
Making a statistical conclusion still applies uncertainties, so the risks of creating these errors exist unavoidable in hypothesis testing.
The probability of creating a Type I error exists at the significance level, or alpha (α), while the probability of making a Type II error exists at beta (β). These risks can be minimized through careful planning in your analysis design.
Examples of Type I and Type II error
Type I error (false positive): the testing effect says you have coronavirus, but you actually don’t.Type II error (false negative): the test outcome says you don’t have coronavirus, but you actually do.To learn more about Type I and Type II error refer to:
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2. A football team plays 28 games and wins 4 out of every 7 games played. No match ended in a draw. 20 (a) How many times has this football team lost?