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Related Questions
I NEED HELP WITH QUESTION 6!
URGENT!
DUE TODAY!!
90PTS!!!!!! WHOEVER WANTS THEM
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How to solve completing the square with the formula a (X+h)2 + k
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The solutions of the given quadratic equation are
[tex]x = 3 \ or \ x = -\frac{1}{4}[/tex]
What is quadratic equation?
Equation shows the equality between two algebraic expressions by connecting the two algebraic expressions by an equal to sign.
A two degree equation is known as Quadratic equation.
The given quadratic equation is
[tex]4x^2 - 11x - 3[/tex]
Now,
[tex]4x^2 - 11x - 3 = 0\\\\(2x)^2 - 2 \times 2x \times \frac{11}{4} + (\frac{11}{4})^2 - (\frac{11}{4})^2 -3 = 0\\\\(2x - \frac{11}{4})^2 = \frac{121}{16} + 3\\\\(2x - \frac{11}{4})^2 = \frac{121+48}{16}\\\\(2x - \frac{11}{4})^2 = \frac{169}{16}\\\\2x - \frac{11}{4} = \sqrt{\frac{169}{16}}\\\\2x - \frac{11}{4} = \pm\frac{13}{4}\\\\2x - \frac{11}{4} = \frac{13}{4} \ or \ 2x - \frac{11}{4} = -\frac{13}{4}\\\\2x = \frac{13}{4} + \frac{11}{4} \ or \ 2x = \frac{11}{4} - \frac{13}{4}\\\\[/tex]
[tex]2x = 6 \ or \ 2x = -\frac{1}{2}\\x = 3 \ or \ x = -\frac{1}{4}[/tex]
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For which equation will f(-2) = -6?
f(x) = x³ + x
f(x)=x² - 5x
f(x) = 4x³ + 6x² − x
f(x) = -3x³-4x² + 4x
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The correct equation is f(x) = 4x³ + 6x² − x . A function in mathematics from a set X to a set Y allocates exactly one element of Y to each element of X. The sets X and Y are collectively referred to as the function's domain and codomain, respectively.
What is Function ?A function, according to a technical definition, is a relationship between a set of inputs and a set of potential outputs, where each input is connected to precisely one output.
The value of the function is f(x). The slope of the line is m. b is either the function's value at x=0 or the position at which the line in the coordinate plane crosses the y-axis. x is the x-value. This form is called the slope-intercept form.
The slope of a linear function is calculated by rearranging the equation to its general form, f(x) = mx + c; where m is the slope.
in question f(-2) = - 6
so x= -2
In function f(x) = 4x³ + 6x² - x
F(-2) = 4(-2)³ + 6 (-2)² - (-2) = - 6
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Write2 1/4 as an improper fraction in its simplest form
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Answer:
9/4
Step-by-step explanation:
an ant walks along a straight path. After traveling for 1 meter it stops, turns through an angle of 90 degrees in an anticlockwise direction and sets off in a straight line covering a distance of half a meter. Again, the ant turns through an angle of 90 degrees in an anticlockwise direction and sets off in a straight line covering a quarter of a meter. The ant continues in this manner indefinitely.
a) How many turns will the ant have made after covering a distance of 63/32 meters?
b)How far will the ant "eventually" travel?
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The description of the motion of the ant which is a geometric series is as follows;
a) After covering 63/32 meters, the ant will have made 6 turns
b) The distance the ant will eventually travel is 2 meters
What is a geometric series?Geometric series is an infinite sum of terms in which the ratio between consecutive terms is a constant.
The distances traveled by the ant is a geometric progression of the form;
aₙ = a·rⁿ⁻¹The sum of the distance is given by the sum of the geometric progression as follow;
[tex]S_n = \dfrac{a\cdot \left(1 - r^n \right)}{(1 - r)}[/tex]
Where;
aₙ = The distance traveled in the nth turn
Sₙ = The sum of the distances
a = The first term = 1 meter
r = The value of the common ratio = 0.5 meter ÷ 1 meter = 0.5
a) The number of turns the ant will have made after covering a distance of 63/32 meters is therefore;
[tex]S_n =\dfrac{63}{32} = \dfrac{1\times \left(1 - 0.5^n \right)}{(1 - 0.5)}[/tex]
31.5 = 32 × (1 - 0.5ⁿ)
32 × 0.5ⁿ = 32 - 31.5 = 0.5
0.5ⁿ = 0.5 ÷ 32
n = ln(0.5 ÷ 32) ÷ ln(0.5) = 6
After covering a distance of 63/62 meters, the ant will have made 6 turnsb) The distance the ant travels eventually is given by the formula for the sum to infinity of a geometric progression as follows;
[tex]S_{\infty} = \dfrac{a}{1-r}[/tex]
Which gives;
[tex]S_{\infty} = \dfrac{1}{1-0.5} = 2[/tex]
The distance the ant eventually travels is 2 meters
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a sanitation supervisor is interested in testing to see if the mean amount of garbage per bin is different from 50. in a random sample of 36 bins, the sample mean amount was 50.67 pounds and the sample standard deviation was 3.9 pounds. conduct the appropriate hypothesis test using a 0.01 level of significance. a) what are the appropriate null and alternative hypotheses?
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We accept the null hypothesis, according to which the average amount of trash per bin is equal to 50.
Hypothesis.Though there is not so much information, but the fact that $700 is an average. We can work with two hypothesis at first, he first Hypothesis before the downturn the rent are over $700. And the second one, the bedroom rent are under $700.Graphically, the shaded area before the downturn, represents the set of values for Rents greater than $700. So, rent (y) > 700) Graphically, the shaded area after the downturn, represents the set of values for Rents lesser than $700. So, rent 700 <y<0A hypothesis is an educated prediction regarding the solution to a scientific question that is supported by sound reasoning. It is the expected result of the experiment, however it is not proof in an experiment.Depending on the information received, it might be supported or might not be supported at all.acc to our question-
A sanitation supervisor is interested in testing o see if the mean amount of garbage per bin is different from 50.This means that the null hypothesis is:And the alternate hypothesis is:The test statistic is:In which X is the sample mean, is the value tested at the null hypothesis, is the standard deviation and n is the size of the sample.50 tested at the null hypothesis:This means that In a random sample of 36 bins, the sample mean amount was 50.67 pounds and the sample standard deviation was 3.9 pounds.This means that Value of the test statistic:p-value:Since we are testing if the mean is differente from a value and the z-score is positive, the pvalue is 2 multipled by 1 subtracted by the pvalue of z = 1.03z = 1.03 has a pvalue of 0.84851 - 0.8485 = 0.15152*0.1515 = 0.30300.3030 > 0.01, which means that we accept the null hypothesis, that is, the the mean amount of garbage per bin is not different from 50.learn more about hypothesis click here:
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Against the Wind a small plane flew 858 miles in 2 hours and 10 minutes the return trip only took 1 hour and 50 minutes what was the speed of the wind?what was the speed of the plane in still air?
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Let the speed of the small plane be 'R'.
Let the speed of the wind be 'S'.
Plane's time against wind = 2 hours and 10 minutes = 13/6 hours.
Plane's time with wind = 1 hour and 50 minutes = 11/6 hours
Use formula;
Distance = speed x time
Against the wind:
858 = (13/6) (R-S) = (13/6) R - (13/6)S
With wind:
858 = (11/6)(R + S) = (11/6)R + (11/6)S
Multiplies each by 6.
5148 = 13R - 13S
5148 = 11R + 11S
Use elimination method
56628 = 143R - 143S (multiplies by 11)
66924 = 143R + 143S (multiplies by 13)
Further solving;
123552 = 276R
R = 432 miles/ hr. (speed of small plane )
And, S = 36 miles/ hr. (speed of wind)
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please help me
this is algebra
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Answer:
The answer is 3.
Step-by-step explanation:
The highest coefficient is 3 (5x^3), the second one is 2 (4x), and the other two without coefficient are considered 1.
HOW Does 1/6, -3, square root 7, -6/5 or 45 come first when the numbers are listed from lest to greatest. explain PLEASE EXPLAIN ME!!!!!!!!!!!!!!!! :C(
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Answer:
- 3 comes first and the order is - 3, - 6/5, 1/6, √7, 45==========================
Given numbers1/6, - 3, √7, - 6/5, 45.Put these numbers in the ascending orderFirst, compare the negative numbers as they are smaller than positives since negatives are to the left from zero on the number line and positives are to the right.
- 3 vs - 6/5- 3*5/ 5 vs - 6/5- 15/5 vs - 6/5Since - 15 is smaller than - 6, the least number is - 3:
- 15/5 < - 6/5 ⇒ - 3 < - 6/5Now compare the positives.
1/6 is smaller than 1 as it is a fraction.√4 < √7 < √9 ⇒ 2 < √7 < 3, so √7 is between 2 and 3, hence greater than 1, therefore 1/6 < √7.And the greatest number is 45 as it is greater than 3.Therefore:
1/6 < √7 < 45The complete order is:
- 3, - 6/5, 1/6, √7, 45Answer:
-3 < -6/5 < 1/6 < √7 < 45
Step-by-step explanation:
Now the values will be,
→ 1/6 = 0.17
→ -3 = -3
→ √7 = 2.65
→ -6/5 = -1.2
→ 45 = 45
Let's arrange in ascending order,
→ -3, -1.2, 0.17, 2.65, 45
→ -3, -6/5, 1/6, √7, 45
Hence, number -3 comes first.
$.
(b) (i) Annie invests $330 at a rate of 1.5% per year compound interest.
Calculate the amount that Annie has after 8 years.
Give your answer correct to the nearest dollar.
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Answer: $372
Step-by-step explanation:
330 + (1.5% of 330) = 334.95
334.95 + (1.5% of 334.95) = 339.97425
339.97425 + (1.5% of 339.97425) = 345.073864
345.073864 + (1.5% of 345.073864) = 350.249972
350.249972 + (1.5% of 350.249972) = 355.503772
355.503772 + (1.5% of 355.503772) = 360.836392
360.836392 + (1.5% of 360.836392) = 366.248398
366.248398 + (1.5% of 366.248398) = 371.742124
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What is the y-intercept for x^3+8x^2+11x-20? How many zeros are their in the graph?
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for a lower tail test, the test statistic z is determined to be zero. what is the p-value for this test?
Answers
0.5 is the p-value for this Z -test .
What is the Z test's p-value?
For each test, the p-value is the likelihood that the null hypothesis will be correct, which is expressed as the probability of receiving a z-value . an absolute value at least as great as the one we actually observed in the sample data.P-value, or probability value, is the likelihood that a statistic will be at least this distant from the mean if the null hypothesis is assumed to be true. So it can be thought of as a conditional probability, to put it another way.For a lower tail test, the test statistic z is determined to be zero that means
P(z<0)
Then p-value is
p-value = P(z<0) = 0.5 (From z score table )
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The image of the point (9, -3)(9,−3) under a translation is (4, 1)(4,1). Find the coordinates of the image of the point (0, 2)(0,2) under the same translation.
Answers
(-5, 6)
Explanation
Image = where the point would be after a translation
translation = how a point’s position is moved
to find out how to translate a point, look at how it moved and apply the same movements to the other point
(9, -3) + (-5, 4) = (4, 1)
the translation is -5 along (on the x axis) and 4 up (on the y axis). Now we have to apply this to the other point (0, 2)
0 - 5 = -5
2 + 4 = 6
(0,2) + (-5, 4) = (-5, 6)
Simplify the expression:
(–5.5 + 2p)(–2) =
Answers
The expression, (–5.5 + 2p)(–2), after simplification is 11-4p.
According to the question,
We have the following expression:
(–5.5 + 2p)(–2)
Now, in order to simplify this expression, we will multiply -2 into the bracket:
(Note that when a number or a variable is multiplied into the bracket then it is multiplied into every number or term within the bracket.)
-5.5*-2+2p*(-2)
We know that when two negative integers are multiplied then the result is positive and when one negative and one positive integer is multiplied then the result is negative.
11-4p
Hence, the expression, (–5.5 + 2p)(–2), after simplification is 11-4p.
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which combination of factors is most likely to produce a significant value for an independent-measures t statistic? group of answer choices small samples and small variance small samples and large variance large samples and small variance large samples and large variance
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large samples and small variance are combination of factors is most likely to produce a significant value in standard deviation .
What is standard deviation?
The term "standard deviation" refers to the degree of dispersion of the data from the mean. Data are grouped around the mean when the standard deviation is low, and are more dispersed when the standard deviation is high.The standard deviation calculates how much the data vary from the mean value. The mean of the following two numbers, for instance, is the same: 15, 15, 15, 14, 16 and 2, 7, 14, 22, 30. The second, though, is obviously more dispersed.t = x - μ/s/√n
t = √n( x- μ)/s
t will be significant when its value will be higher .
so, the answer is large samples and small variance .
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A football team loses 4 yards on each of 9 consecutive plays. Find the total change in yards from where the team started.
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The total change in yards where the team started is 36 yards
How to determine the total change in yards?The given parameters in the question are:
Yards per play = 4 yards
Number of plays = 9 consecutive plays
The total change in yards is the amount of yard per play multiplied by the number of plays
This is represented as
Total change = Yards per play * Number of plays
Substitute the known values in the above equation So, we have the following equation
Total change = 4 * 9
Evaluate
Total change = 36
Hence, the total change is 36 yards
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A cartographer graphed the locations of a light house and all of the islands in the vicinity. He positioned the light house at (-7,9) and the farthest island at (61,9). If each
unit on the graph represents 1 mile, then how far away from the light house is the farthest island?
miles
Answers
The distance between the light house and the farthest island is 68 miles
The distance between the light house and the farthest island can be calculated by using the distance formula
The distance formula is d=√((x2 – x1)² + (y2 – y1)²).
d=√((61 – (-7))² + (9 – 9)²)
d = √(61 +7)²
d = 68
If each unit on the graph represents 1 mile
There are 68 units in the graph, so the light house is 68 miles away the farthest island
Therefore, The distance between the light house and the farthest island is 68 miles
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Pls. Help. Lots of points plus Brainliest!
What is 12*12/2+13?
Answers
Step-by-step explanation:
[tex]\sf 12 \times \cfrac{12}{2} + 13[/tex]
First, let's divide 12 by 2:-
[tex]\sf 12 \times 6 + 13[/tex]Multiply 12 × 6 :-
[tex]\sf 72 + 13[/tex]Add 72 + 13:-
[tex]\sf 85[/tex]Therefore, your answer is 85!!
____________________
Hope this helps!
Have a great day!!
12*12=144
144/2=72
72+13=85
(Using BIDMAS)
is
In 5-8, apply Laws of Exponents to write
expressions.
5, efo
e²f
7.3j4k-2.7j5k9
uiva
-3
6. (2x)-3. (y)-³
8. aº.b6.b-3
Answers
By using the concept of law of exponents,the required answers are: 5) [tex]e^{-1} f^{-1}[/tex] and 8) [tex]b^{3}[/tex]
What is the law of exponents?According to this law of exponents, exponents of numbers are added, subtracted, multiplied, and divided when numbers get multiply, divide, and number raised by another exponents.
What are exponents?Exponents are the power of numbers, which tells us how many time a number multiply by itself.
we have,
5) [tex]\frac{ef^0}{e^2f}[/tex]
⇒ [tex]e^{1-2}f^{0-1}[/tex]
⇒ [tex]e^{-1} f^{-1}[/tex]
8) [tex]a^{0}b^{6} b^{-3}[/tex] ( [tex]a^{0}[/tex]=1 )
⇒ [tex]b^{6-3}[/tex]
⇒ [tex]b^{3}[/tex]
Hence, final answer are [tex]e^{-1} f^{-1}[/tex] and [tex]b^{3}[/tex]
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One leg of a right triangle is 7 units long, and its hypotenuse is 16 units long. What is the length of the other leg? Round to the nearest whole number.
Answers
Answer:
7^{2} + x^{2} = 16^{2}
49+x^2=256
x^2=207
x=14.387=14
Answer:
14 units
Step-by-step explanation:
To find the length of the other leg of a right triangle, where one leg is 7 units long and the hypotenuse is 16 units long, use Pythagoras Theorem.
Pythagoras Theorem states that in a right triangle, the square of the length of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the lengths of the legs.
Let the legs of the right triangle be "a" and "b", and the hypotenuse be "c". Therefore:
[tex]\begin{aligned}a^2+b^2&=c^2\\a^2+7^2&=16^2\\a^2+49&=256\\a^2+49-49&=256-49\\a^2&=207\\\sqrt{a^2}&=\sqrt{207}\\a&=14.3874945...\\a&=14\;\sf(nearest\;whole\;number)\end{aligned}[/tex]
Therefore, the length of the other leg is 14 units (rounded to the nearest whole number).
Please help!! I don't get this
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5. Based on arc and central angle relationship, m∠BCD is: B. 108°.
6. The length of arc PQ is: H. 3.14 m
7. Length of CF is: A. 6 cm.
What is the Formula for the Length of an Arc?To find the length of an arc, the formula to use is:
Arc length = ∅/360 × 2πr
5. Measure of arc AB = 72°
Measure of arc BD = 180 - measure of arc AB
Measure of arc BD = 180 - 72
Measure of arc BD = 108°
Measure of angle BCD = measure of arc BD [central angle theorem]
Measure of angle BCD = 108°
The answer is: B. 108°
6. ∅ = 60°
r = 3 m
Arc length = 60/360 × 2 × π × 3
Arc length = 3.14 m
The answer is: H. 3.14 m
7. Since the distance between the two chords, AB and CD are equal, therefore, AB = CD.
AB = CD = 12 cm
CF = 1/2(CD)
CF = 1/2(12)
CF = 6 cm.
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Standing on top of a 200 m building with the estimation angle of depression from the top of the building to a park bench on the ground to be 54°
How far is the park bench is from the foot of the building
Answers
Distance of Park bench from building is 275 m when angle of depression top of the building to a park bench on the ground.
What is the elevation and depression angle?
The angle between the horizontal and an item is referred to as its elevation. The line of sight of an observer would be upward. Angle of depression refers to the downward angle from the horizontal to an item.Angle of depression, θ = 54°
The height, h = 200
The distance of park bench from the building, d is given by
Tan θ = opposite / Adjacent
Tan 54 = d / 200
d = 200 * Tan 54
d = 200 * 1.3764
d = 275.28
D = 275 M
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A sample of a radioactive isotope had an initial mass of 110 mg in the year 1990 and decays exponentially over time. A measurement in the year 1993 found that the sample's mass had decayed to 90 mg. What would be the expected mass of the sample in the year 2002, to the nearest whole number?
Answers
50 mg be the expected mass of the sample in the year 2002, to the nearest whole number
In 1990, a sample of a radioactive isotope had an initial mass of 110 mg and decayed exponentially over time.
A measurement in 1993 revealed that the sample's mass had decayed to 90
110 mg - 90 mg = 20 mg (amount decayed in the 3 total years)
20 mg ÷ 3 years = 6.6 mg decayed per year
6.6 × 9 years (years between 1993 and 2002) = 60 mg
110 mg - 60 mg = 50 mg, rounded to 50 mg
50 mg be the expected mass of the sample in the year 2002, to the nearest whole number
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can you please help me find the measure of an exterior angle of a regular hexagon?
thanks
Answers
The measure of each exterior angles of a regular hexagon is 60 degrees
The interior angle of the regular polygon is
d = 180(n - 2) / n
Where d is the measure of interior angle
n is the number of sides
The number of sides in a regular hexagon
d = 180(6 - 2) / 6
= 180×4 / 6
= 720 / 6
=120 degrees
The each interior angle of the regular hexagon is 120 degrees
The measure of exterior angle = 180 - The measure of interior angle
= 180 - 120
= 60 degrees
Hence, the measure of each exterior angles of a regular hexagon is 60 degrees
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The values in the table represent a linear function. x 1 2 3 4 f(x) 1 4 7 10 What is the function rule? Write the rule in function notation, using the slope-intercept form of a line. Enter your answer in the box.
Answers
The rule in expressed in function notation and slope-intercept form of a line is f(x) = 3x -2
How to express the rule in function notation using the slope-intercept form of a line?The equation of line is an algebraic form of representing the set of points, which together form a line in a coordinate system
The equation of a line in slope-intercept form is y = mx + c.
Where m is the slope and c is the intercept
In order to obtain the equation of the line, we are going to pick any two convenient values of x and y from the table. Let's pick the first and last point. Thus:
point1: x₁ = 1, y₁ = 1
point2: x₂ = 4, y₂ = 10
Using the equation for 2 points:
y-y₁ / y₂-y₁ = x-x₁ / x₂-x₁
y-1 / 10-1 = x-1 / 4-1
y-1 / 9 = x-1 /3
3(y-1) = 9(x-1)
y-1 = 3(x-1)
y-1 = 3x -3
y = 3x -3+1
y = 3x - 2
Thus, f(x) = 3x -2
Therefore, the rule in function notation, using the slope-intercept form of a line is f(x) = 3x -2
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The diagram Shows a square of side 8 cm and four congruent triangles of height Calculate the areanof one triangle.
Answers
The area of one triangle is 28 cm².
From the question, we have
area = 1/2*base*height
= 1/2*8*7
=28 cm².
Multiplication:
In mathematics, multiplying the numbers is used to find the product of two or more numbers. We carry out one of the basic mathematical operations on a regular basis. The main application that is obvious is using multiplication tables. Mathematicians use the multiplication of two integers to express the repeated addition of one number to another. These numbers can be natural numbers, fractions, integers, whole numbers, etc. M is either added to itself 'n' times or subtracted from itself when m is multiplied by n.
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what 5x5(45x5)x3(56x34)
Answers
Answer: 32130000
Step-by-step explanation:
Multiply all of your numbers
Solve the equation for w.
4w + 2 + 0.6w = −3.4w − 6
No solution
w = 0
w = 1
w = −1
Please help
Answers
Answer:
The answer is w= -1
Step-by-step explanation:
4w + 2 + 0.6w = -3.4w - 6
4.6w + 2 = -3.4w - 6
8w + 2 = -6
8w = -8
w = -1
Help please I will give brainliest this is due in an hour!!!
Answers
Answer:
yes for helena: not sure for edwin
Step-by-step explanation:
for helena, it would be a 270 cc rotation and then scale
for edwin, again im not sure, but it could be a refection and then scale
are these expressions equivalent
4(2a+7) and 8a +7
7y + 2y+y and 10y
8m-4m+4m and 8m
9e+2(e+5 and 11 +5
Answers
The equivalent expressions are 7y + 2y+y and 10y & 8m-4m+4m and 8m.
Other expressions are not equivalent
How to determine the equivalent expressions?Expressions 1
The expressions are given as
4(2a+7) and 8a +7
Open the brackets
8a+28 and 8a +7
The above expressions are not equal
Expressions 2
Here, we have
7y + 2y+y and 10y
Evaluate the like terms
10y and 10y
The above expressions are equal
Expressions 3
Here, we have
8m-4m+4m and 8m
Evaluate the like terms
8m and 8m
The above expressions are equal
Expressions 4
Here, we have
9e+2(e+5) and 11 +5
Open the brackets
9e+2e+10 and 11 +5
Evaluate the like terms
11e + 10 and 11 + 5
The above expressions are not equal
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