Answer:
9=0
Step-by-step explanation:
9=0
The roots of x in the equation -10x² + 12x - 9 = 0 are:
x = (3/5) + (3/5)√(6)i
x = (3/5) - (3/5)√(6)i
What is a quadratic equation?For variable x : ax² + bx + c = 0, where a≠0 is a standard quadratic equation, which is a second-order polynomial equation in a single variable. It has at least one solution since it is a second-order polynomial equation, which is guaranteed by the algebraic basic theorem.
To find the roots of x in the equation -10x² + 12x - 9 = 0, we can use the quadratic formula:
x = (-b ± √(b² - 4ac)) / 2a
where a, b, and c are the coefficients of the quadratic equation in standard form (ax² + bx + c).
In this case, a = -10, b = 12, and c = -9. Substituting these values into the quadratic formula, we get:
x = (-12 ± √(12² - 4(-10)(-9))) / 2(-10)
x = (-12 ± √(144 - 360)) / (-20)
x = (-12 ± √(-216)) / (-20)
Substituting this into the expression for x, we get:
x = (-12 ± 6√(6)i) / (-20)
Simplifying the expression further, we get:
x = (3/5) ± (3/5)√(6)i
Therefore, the roots of x in the equation -10x² + 12x - 9 = 0 are:
x = (3/5) + (3/5)√(6)i
x = (3/5) - (3/5)√(6)i
These roots are complex conjugates of each other.
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PLS HELP!!
The tables show functions representing the growth of two types of bacteria on certain days within an experiment that lasted a total of 10 days.
How do the functions in the table compare?
Since x-intercepts indicate the amount of each
bacteria at the start of the experiment, there was
more of bacteria B than bacteria A at the start.
O Since y-intercepts indicate the amount of each
bacteria at the start of the experiment, there was
more of bacteria B than bacteria A at the start.
O Since the maximum value in the table for bacteria A
is greater than the maximum value in the table for
bacteria B, bacteria A has a faster growth rate than
bacteria B.
O Since the minimum value in the table for bacteria A
is less than the minimum value in the table for
bacteria B, bacteria A has a slower growth rate than
bacteria B
The correct answer are as follows:
A. False
B. True
C. False
D. False
What is Function?The functions are the special types of relations. A function in math is visualized as a rule, which gives a unique output for every input x.
A. Since x-intercepts indicate the amount of each bacteria at the start of the experiment, there was more of bacteria B than bacteria A at the start.
False, it is the y-intercept of the function that indicates the amount at the start of the experiment.
B. Since y-intercepts indicate the amount of each bacteria at the start of the experiment, there was more of bacteria B than bacteria A at the start.
True, the y-intercept is given when x = 0, indicating the initial value of the function.
C. Since the maximum value in the table for bacteria A is greater than the maximum value in the table for bacteria B, bacteria A has a faster growth rate than bacteria B.
False, because the maximum value of each table is given in different times, and also the initial value of each table is different.
D. Since the minimum value in the table for bacteria A is less than the minimum value in the table for bacteria B, bacteria A has a slower growth rate than bacteria B.
False, the growth rate is not given by the initial value. If we model both tables with an exponential function, the count of bacteria A quadruped in two days, and the count of bacteria B doubled in one day, so they have the same growth rate.
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Suppose the only measuring cup you own is a one-third measuring cup. Using this measuring cup how many scoops will you need to have 3 2/3 cups of sugar
Answer:
11
Step-by-step explanation:
for each full cup of sugar, you need 3 one-third measuring cups.
we have 3 full cups so 3×3=9
and another 2 for the 2/3, 9+2=11
so a total of 11 scoops
For each relation decide whether or not it is a function
Answer:
Relation 1: FunctionRelation 2: FunctionRelation 3: Not a functionRelation 4: functionStep-by-step explanation:
A function is defined so that for each input, there is no more than one output.
Find the perimeter of the following polygon. Be sure to include the correct unit in your answer. 19 cm 15 cm 14 cm 9 cm
Suppose there is a big drop in interest rates in Mexico and a small drop in U.S. interest rates. Everything else equal, what is likely to happen to value of the MXN?
If we suppose that there is a big drop in the interest rates in Mexico and a small drop in the interest rates in the U.S.A, with everything else equal, the value of MXN will decrease.
The foreign exchange market works according to the principles of firms, households, and investors:
These three constituent factors of the foreign exchange market determine the demand and supply patterns in the market. Demand for a foreign currency might increase in the foreign exchange market is linked to the expectation of an increase in the value of a foreign currency. Supply of a foreign currency in the foreign exchange market is linked to an inverse principle, where the expectation of a decrease in the value of foreign currency pushes supply upwards. If we are to suppose that there is a big drop in the interest rates in Mexico and a small drop in the interest rates in the U.S.A., then the value of the MXN will decrease, with everything being equal. A higher interest rate leads to the appreciation of a foreign currency relative to other currencies in the foreign exchange market. A lower interest rate leads to the depreciation of a foreign currency relative to other currencies in the foreign exchange market.Therefore, if we suppose that there is a big drop in the interest rates in Mexico and a small drop in the interest rates in the U.S.A, with everything else equal, the value of MXN will decrease.
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A business student is interested in estimating the 95% confidence interval for the proportion of students who bring laptops to campus.
He wishes a precise estimate and is willing to draw a large sample that will keep the sample proportion within five percentage points
of the population proportion. What is the minimum sample size required by this student, given that no prior estimate of the population
proportion is available?
(You may find it useful to reference the z table. Round intermediate calculations to at least 4 decimal places
and "2" value to 3 decimal places. Round up your answer to the nearest whole number.)
Using the z-distribution, the minimum sample size required by this student is of 385.
What is a confidence interval of proportions?A confidence interval of proportions is given by:
[tex]\pi \pm z\sqrt{\frac{\pi(1-\pi)}{n}}[/tex]
The margin of error is:
[tex]M = z\sqrt{\frac{\pi(1-\pi)}{n}}[/tex]
In which:
[tex]\pi[/tex] is the sample proportion.z is the critical value.n is the sample size.In this problem, we have a 95% confidence level, hence[tex]\alpha = 0.95[/tex], z is the value of Z that has a p-value of [tex]\frac{1+0.95}{2} = 0.975[/tex], so the critical value is z = 1.96.
We want a margin of error of M = 0.05, with no prior estimate, hence [tex]\pi = 0.5[/tex], then we have to solve for n to find the minimum sample size.
[tex]M = z\sqrt{\frac{\pi(1-\pi)}{n}}[/tex]
[tex]0.05 = 1.96\sqrt{\frac{0.5(0.5)}{n}}[/tex]
[tex]0.05\sqrt{n} = 1.96(0.5)[/tex]
[tex]\sqrt{n} = 1.96 \times 10[/tex]
[tex](\sqrt{n})^2 = (1.96 \times 10)^2[/tex]
n = 384.16
Rounding up, the minimum sample size is of 385.
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Consider the following data concerning the demand (y) and price (x) of a consumer product the least squares line is found to be y= 306,619-27.71.x
A) Interpret b1
B) find a point prediction of the demand corresponding to be price 2.10
C) Find %95 confidence interval for b1 and interpret it
The value of B1 shows a fall in demand as price rises by a unit. The point prediction is given as y = 306,560.8
How to solve the question using the interceptThe regression equation shows that y= 306,619-27.71.x
b1 = -27.71
The interpretation for b1 is that if the price of this good is increased by 1, then the demand for the good would fall by about 27.71.
The point prediction for demandThe regression line equation is given as
y= 306,619-27.71.x
when x which is price is = 2.10
Then the value of y would be:
y = 306,619 - 27.71*2.10
y = 306,560.8
c. a 95% C1 for B1 is given as:
1.96 * 27.71.
= 54.31
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THE LENGTH OF A PAINTING OF A TREE IS 2/9 OF THE LENGTH OF THE ACTUAL TREE. IF THE LENGTH OF THE PAINTING OF THE TREE IS 16 INCHES, WHAT IS THE LENGTH IN INCHES OF THE ACTUAL TREE
The length of the actual tree will be 72 inches.
Fraction is the portion of a total amount where the above part of the fraction is the denominator and the bottom part of the fraction is called the numerator.
The equation whose highest degree of the variable is 1 is called a linear equation.
Here given that the length of a painting of the tree is 2/9 of the actual length of the tree.
So mathematically the length of a painting= (2/9)*the length of actual tree
Let the length of the actual tree is x
then from above it is clear that the length of a painting of the tree= (2/9)x
Given the length of the painting is 16 inches.
So the linear equation will be (2/9)x= 16
⇒ x= 16/(2/9)
⇒x= 16*9/2
⇒x=72 inches
Therefore the length of the actual tree will be 72 inches.
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what is the measure of 4?
Answer:
∠ 4 = 80°
Step-by-step explanation:
∠ 5 and 100° are vertical angles and are congruent , so
∠ 5 = 100°
∠ 4 and ∠ 5 are same- side interior angles and sum to 180° , that is
∠ 4 + ∠ 5 = 180°
∠ 4 + 100° = 180° ( subtract 100° from both sides )
∠ 4 = 80°
If f(x) = 4x² + 1 and g(x)=x²-5, find (f+ g)(x). ( x ) = 4x² + 1 and g ( x ) = x² - 5 , find ( f + g ) ( x ) .
Answer: [tex]5x^{2}-4[/tex]
Step-by-step explanation:
[tex](f+g)(x)=f(x)+g(x)=4x^{2}+1+x^{2}-5=\boxed{5x^{2}-4}[/tex]
Which expression is equivalent to 4^-5 * 4^8
A 4^-2/4^-1
B (4^3)^-1
C 4^2/4^-1
D (4^-1)^3
Answer: C
Step-by-step explanation:
[tex]a^{b} \times a^{c}=a^{b+c}[/tex], so [tex]4^{-5} \times 4^{8}=4^{-5+8}=4^{3}[/tex].
The only option that is equal to this is C
A student has a test scores of 87, 89, 94 points. What must he score on the fourth exam to have an average of at least 92 points?
Answer: He must have atleast 98 points on the next exam in order to get an average of 92 points.
Step-by-step explanation: To calculate average, you need to add all the numbers given, and divide the sum by how many numbers there are. 87 + 89 + 94 + 98 (equals 368), and divide 368 by 4. You will get the average of 92 as its result.
the segments ab and cd are graphed on a coordinate plane. The endpoints of ab are at (9,4) and (9,20). CD is parallel to the x-axis, and one of its endpoints is at (5,8). if ab=cd and cd is entirely in the first quadrant, what is the other endpoint of cd
Answer:
21, 8
Step-by-step explanation:
The second endpoint is of the form (X, 8) since it's parallel to the x axis.
Given the congruence of the two segments, we can tell that its length is 16 units (since [tex]|4-20| = |-16|= 16[/tex])
At this point the two possible endpoints for the segment are [tex](5-16; 8)[/tex] or [tex](5+16, 8)[/tex]. The fact that the segment has to sit in the first quadrant rules out the first option (it's endpoint will be at (-11, 8) which will set most of it in the second quadrant) and we're left with (21, 8)
Larry Mitchell invested part of his $11,000 advance at 3% annual simple interest and the rest at 9% annual simple interest. If his total yearly interest from both accounts was $750,
find the amount invested at each rate
The amount invested at 3% is $
The amount invested at 9% is $
Answer:
at 3%: $4000at 9%: $7000Step-by-step explanation:
The answer to this problem can be found by writing an equation for the total interest in terms of the amounts invested at each rate.
__
setupLet x represent the amount invested at 9% (the higher rate). Then (11000-x) is the amount invested at 3%, and the total interest earned is ...
0.09x +0.03(11000 -x) = 750
solution0.06x = 420 . . . . . . . subtract 330 and simplify
x = 7000 . . . . . . . divide by 0.06 . . . amount invested at 9%
11000 -7000 = 4000 . . . amount invested at 3%
Larry invested $4000 at 3%, and $7000 at 9%.
_____
Additional comment
In "mixture" problems of this type, it generally works well to let the variable represent the amount of the highest-value contributor. That way, the equations end up with positive coefficients, tending to reduce errors.
[tex] \displaystyle \sum_{n = 1}^{ \infty } {4}^{ - n} [/tex]
evaluation of the sum above
Answer:
[tex]\dfrac{1}{3}[/tex]
Step-by-step explanation:
Given:
[tex]\displaystyle \sum^{\infty}_{n=1} 4^{-n}[/tex]
The sigma notation means to find the sum of the given geometric series where the first term is when n = 1 and the last term is when n = ∞.
To find the first term in the series, substitute n = 1 into the expression:
[tex]\implies a_1=4^{-1}=\dfrac{1}{4}[/tex]
The common ratio of the geometric series can be found by dividing one term by the previous term:
[tex]\implies r=\dfrac{a_2}{a_1}=\dfrac{4^{-2}}{4^{-1}}=\dfrac{1}{4}[/tex]
As | r | < 1 the series is convergent.
When a series is convergent, we can find its sum to infinity (the limit of the series).
Sum to infinity formula:
[tex]S_{\infty}=\dfrac{a}{1-r}[/tex]
where:
a is the first term in the seriesr is the common ratioSubstitute the found values of a and r into the formula:
[tex]S_{\infty}=\dfrac{\frac{1}{4}}{1-\frac{1}{4}}=\dfrac{1}{3}[/tex]
Therefore:
[tex]\displaystyle \sum^{\infty}_{n=1} 4^{-n}=\dfrac{1}{3}[/tex]
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18 / 48 hrs left
Divide and answer the question.
Answer: I don’t understand
Step-by-step explanation:
Which linear function represents the line given by the point-slope equationy-2=4x-3)?
O fx)=6x-1
Of(x)=8x-6
Of(x)=4x-14
Of(x)=4x-10
Input 1,2,3,4,5, n output 2,-1,-4,-7, ?please help me find the linear function!
Answer:
f(x) = -3x + 5
Step-by-step explanation:
The slope of the function is -3 as the outputs decrease by three for each iteration.
The constant is 5 and can be determined if you plug in 1 as an x value and solve for c in an equation like this: -3(1) + c = 2
If a line has a slope of 4 and goes through the point open parentheses short dash 1 comma 1 close parentheses, then the equation for the line in slope-intercept form is ______________.
a.)
y equals short dash 4 x minus 3
b.)
y equals 4 x plus 3
c.)
y equals 4 x plus 5
d.)
y equals short dash 4 x minus 5
You are given the slope = 4 and a point is (-1,1)
The equation of a line is written as y - mx + b where m is the slope and b is the y intercept
Using the slope you now have y = 4x + b
Solve for b by replacing x and y with the values of the point:
1 = 4(-1) + b
Simplify:
1 = -4 + b
Add 4 to both sides:
b = 5
The equation of the line is C.) y = 4x + 5
The equation for free fall at the surface of some planet (s in meters, t in seconds) is s=2.86t^2. How long does it take a rock falling from rest to reach a velocity of 25.1 m/s on this planet?
The time taken by the rock will be 8.77 seconds.
What is speed?Speed is defined as the ratio of the time distance traveled by the body to the time taken by the body to cover the distance.
Given that:-
The equation for free fall at the surface of some planet (s in meters, t in seconds) is s = 2.86t²
The time will be calculated by using the speed formula.
Speed = Distance \ Time
25.1 = 2.86t² \ t
t = 25.1 / 2.86
t = 8.77 seconds
Therefore the time taken by the rock will be 8.77 seconds.
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9. The regular admission price at a museum is
$4.50 per adult and $2.75 per child. This week,
there is a special offer that allows 1 child to get
in for half price with each paying adult. How
much would the total admission price be for
3 children and 2 adults?
Answer:
$14.4
Step-by-step explanation:
there are 2 adults so 2 children will get the discount
4.50 + 4.50 + 1.375 + 1.375 + 2.75 = $14.5
Answer:
Step-by-step explanation:
What is the function that defines the following sequence? 10, 12, 14, 16, 18…
The sequence shown is defined by a function that generates even numbers equal or greater than 10, defined by the function s = 10 + 2 · (n - 1).
How to define the function behind a sequence
Sequences are sets of elements characterized by at least a rule. In this case, the sequence shown is characterized by a function that generates even numbers equal or greater than 10. The function behind the sequence is shown below:
s = 10 + 2 · (n - 1) (1)
Where n is the element index.
The sequence shown is defined by a function that generates even numbers equal or greater than 10, defined by the function s = 10 + 2 · (n - 1).
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Gabriel quiere comprar un carro que cuesta 286,000. La agencia le ofrece un crédito a una tasa de 9% anual, con pagos trimestrales durante un año. Elabora la tabla de amortización del crédito
Jimmy Page puts $30 into a savings account that promises 1% interest
compounded quarterly. Which formula would you use to determine the
account balance in 25 years?
In 25 years the account balance will be $38.51 if Jimmy Page puts $30 into a savings account that promises 1% interest compounded quarterly.
What is compound interest?It is defined as the interest on the principal value or deposit and the interest which is gained on the principal value in the previous year.
We can calculate the compound interest using the below formula:
[tex]\rm A = P(1+\dfrac{r}{n})^{nt}[/tex]
Where A = Final amount
P = Principal amount
r = annual rate of interest
n = how many times interest is compounded per year
t = How long the money is deposited or borrowed (in years)
P = $30
r = 1% = 0.01
n = 4
[tex]\rm A = 30(1+\dfrac{0.01}{4})^{4\times25}[/tex]
After calculating:
A = $38.51
Thus, in 25 years the account balance will be $38.51 if Jimmy Page puts $30 into a savings account that promises 1% interest compounded quarterly.
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find the distance around one-fifth of a circle with diameter of 14 inches
To solve this problem, you will need to know the formula to find the circumference of a circle given the diameter of a circle. After calculating the circumference, you will then divide this result by 5 to obtain the final answer needed for this problem.
Find the CircumferenceThe circumference of a circle is found using the formula C = 2πr.
[tex]C = 2\pi r[/tex]
We are given the diameter. The radius can be found using r = D/2.
[tex]\displaystyle r=\frac{D}{2}[/tex]
[tex]\displaystyle r=\frac{14}{2}[/tex]
[tex]r=7[/tex]
Plug in the radius to the formula for a circle's circumference: C = 2πr.
[tex]C = 2 \pi (7)[/tex]
Rearrange the equation to distribute the 7 into the 2π.
[tex]C = 7(2\pi)[/tex]
Distribute the 7.
[tex]C=14\pi[/tex]
Find One-Fifth of the DistanceTo find one-fifth of the distance (formally termed the circumference) around the circle, divide the circumference by 5.
[tex]\displaystyle \frac{14\pi}{5}[/tex]
If you are looking for a simplified answer in terms of π, this will suffice. If you need an exact answer that does not reference π, continue reading.
For a solution not in terms of π, first, multiply 14 by π.
[tex]14\times\pi = 43.98229715[/tex]
Divide this value by 5.
[tex]\displaystyle \frac{43.98229715}{5} = 8.7964594[/tex]
To make this easier to present, round to the hundredths place.
[tex]8.7964594 \approx 8.80[/tex]
The final answer, dependent on the value you are asked to provide, is:
[tex]{\boxed{\displaystyle \frac{14\pi}{5} \ \text{inches}}[/tex]
[tex]\boxed{\text{approximately} \ 8.8 \ \text{inches}}[/tex]
How do you find the median and standard deviation for 3,3,3,3,4,4,4,4,4,5,5,5,5,5,5,5,6,6,6,6,6,6,6,6,6,6,7,7,7,7,7,7,8,8,8,8,8,9,9,9,9,10,10,10,10,10,11,11, 11,11,11
Answer:
Median is 6
standard deviation is 2.39
Step-by-step explanation:
the median is the mid number in the data set
The median formula is {(n + 1) ÷ 2}th, where “n” is the number of items in the set and “th” just means the (n)th number.
There are 51 data points in this set (n = 51)
so 51 / 2 = 25.5, the. number in the 25th slot is our median
3, 3, 3, 3, 4, 4, 4, 4, 4, 5, 5, 5, 5, 5, 5, 5, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 7, 7, 7, 7, 7, 7, 8, 8, 8, 8, 8, 9, 9, 9, 9, 10, 10, 10, 10, 10, 11, 11, 11, 11, 11
the standard deviation is a measure of how dispersed the data is in relation to the mean. Low standard deviation means data are clustered around the mean, and high standard deviation indicates data are more spread out.
please help with this question
Find DG.
DE
2x+17
EF
8
FG
2
x + 20
The value of DG is 4x + 45
Determine the length of a line segmentFrom the question, we are to determine the value of DG
From the given information,
DE = 2x + 17
EF = 8
FG = 2x + 20
Then,
DG = DE + EF + FG
DG = 2x + 17 + 8 + 2x + 20
DG = 4x + 45
Hence, the value of DG is 4x + 45
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Solve the system of equations by finding the reduced row-echelon form of the augmented matrix for the system of equations.
3x-4y-5z=-27
5x+2y-2z=11
5x-4y+4z=-7
a. (1,5,51)
b. ( 10, 5, 51)
c. (10, 51, 23)
d. ( 1, 5, 2)
The value of x, y and z will be 1, 5 and 2 respectively
An augmented matrix in linear algebra is a matrix created by joining the columns of two supplied matrices, often so that the same basic row operations may be applied to each of the given matrices individually.
Lets write the augmented matrix by writing the coefficients of all the variables:
3 -4 -5 -27 Row 1
5 2 -2 11 Row 2
5 -4 4 -7 Row 3
We need to get
1 0 0
0 1 0
0 0 1
then the values of x, y, and z will be in the last column.
The row operation (R1=R1/3) is used to get the identity matrix.
1 -4/3 -5/3 -9 Row 1
5 2 -2 11 Row 2
5 -4 4 -7 Row 3
Add row 2 to row 1 and multiply by 5 (R2=R2(5)R1).
1 -4/3 -5/3 -9 Row 1
0 26/3 19/3 56 Row 2
5 -4 4 -7 Row 3
Add row 3 to row 1 and multiply by 5 (R3=R3(5)R1).
1 -4/3 -5/3 -9 Row 1
0 26/3 19/3 56 Row 2
0 8/3 37/3 38 Row 3
Multiply row 2 by 326 (R2=(3/26)R2)
1 -4/3 -5/3 -9 Row 1
0 1 19/26 84/13 Row 2
0 8/3 37/3 38 Row 3
Add row 2 multiplied by 4/3 to row 1 (R1=R1+(4/3)R2)
1 0 -9/13 -5/13 Row 1
0 1 19/26 84/13 Row 2
0 8/3 37/3 38 Row 3
Add row 3 to row 2 and multiply the result by 8/3 (R3=R3(8/3)R2).
1 0 -9/13 -5/13 Row 1
0 1 19/26 84/13 Row 2
0 0 135/13 270/13 Row 3
Multiply row 3 by 13/135 (R3=(13/135)R3)
1 0 -9/13 -5/13 Row 1
0 1 19/26 84/13 Row 2
0 0 1 2 Row 3
Add row 3 multiplied by 9/13 to row 1 (R1=R1+(9/13)R3)
1 0 0 1 Row 1
0 1 19/26 84/13 Row 2
0 0 1 2 Row 3
Row 2 is reduced by row 3 multiplied by 19/26 (R2=R2(19/26)R3).
1 0 0 1 Row 1
0 1 0 5 Row 2
0 0 1 2 Row 3
Hence the value of x, y and z will be 1, 5 and 2 respectively
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Consider the line 4x-8y= -6.
What is the slope of a line perpendicular to this line?
What is the slope of a line parallel to this line
Answer:
Perpendicular slope = -2Parallel slope = 1/2======================================================
Explanation:
Let's solve for y to get the equation into y = mx+b form, aka slope intercept form.
4x-8y= -6
-8y= -6-4x
y = (-6-4x)/(-8)
y = -6/(-8) + (-4x)/(-8)
y = 3/4 + (1/2)x
y = (1/2)x + 3/4
This is now in y = mx+b form
m = 1/2 = slope
b = 3/4 = y intercept
We'll ignore the y intercept and focus on the slope only.
-----------------
Rule: If the slope of a line is a/b, then the perpendicular slope is -b/a
Flip the fraction and flip the sign.
In this case, the original slope 1/2 has a perpendicular slope of -2/1 or simply -2.
The original slope multiplied with the perpendicular slope yields -1. So (1/2)*(-2/1) = -1
-----------------
Another rule: Two parallel lines always have equal slopes, but different y intercepts.
The original slope is 1/2, so the parallel slope is also 1/2.
