Answers
12/x = 10/5
12*5 = 10x
60 = 10x
x = 6
Check
12/6 = 10/5
2 = 2
Related Questions
Match each quadratic function given in factored form with its equivalent standard form listed on the left. f(x) = (x 2)(x – 6) f(x) = (x – 4)(x 3) f(x) = (x – 12)(x 1) f(x) = (x – 3)(x 4)
Answers
standard form of the given equation are
-f(*) = (x + 2)(x - 6) = x² - 4x - 12
f(x) = (x - 4)(x + 3) = x² - x - 12
f(x) = (x - 12)(x + 1) = x² - 11x - 12
f(x) = (x -3)(x + 4) = x² + x - 12
What is quadratic function?A polynomial function with one or more variables in which the second-degree term is the highest degree is known as a quadratic function, quadratic polynomial, polynomial of degree 2, or simply a quadratic, in algebra.
What is standard form of a quadratic function?As long as an is not equal to zero, the quadratic function f(x) = a(x - h)2 + k is considered to be in standard form. The graph starts out in either an upward or a downward direction depending on the value of a. The point at the vertex of the symmetry is represented by the vertical line x = h. (h,k).
According to the given information:The standard form list.
1 . (x + 2)(x - 6)
= x² - 6x + 2x - 12
= x² - 4x -12
2. (x - 4)(x + 3)
= x² + 3x - 4x - 12
= x² - x - 12
3. (x - 12)(x + 1)
= x² + 1x - 12x - 12
= x² - 11x - 12
4. (x -3)(x + 4)
= x² + 4x - 3x - 12
= x² + x - 12
So the equivalent standard form of the give values are :
-f(*) = (x + 2)(x - 6) = x² - 4x - 12
f(x) = (x - 4)(x + 3) = x² - x - 12
f(x) = (x - 12)(x + 1) = x² - 11x - 12
f(x) = (x -3)(x + 4) = x² + x - 12
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I understand that the question you are looking for is:
Match each quadratic function given in factored form
with its equivalent standard form listed on the left.
f(x) = (x + 2)(x – 6)
f(x) = (x – 4)(x+3)
f(x) = (x – 12)(x+1)
f(x) = (x – 3)(x +4)
Consider a situation in which p(x) = and p(y) = . if p(x and y) is = , which best describes the events?
Answers
The correct option is (A) P(X) × P(Y) = P(X ∩ Y)
What is probability and example?
Probability = the number of ways of achieving success. the total number of possible outcomes. For example, the probability of flipping a coin and it being heads is ½, because there is 1 way of getting a head and the total number of possible outcomes is 2 (a head or tail). We write P(heads) = ½ .We are given to consider a situation in which X and Y are two events such that
P(X) = 4/5, P(Y) = 1/4, P(X ∩ Y) = 1/5
We are to select the statement that best describes the events X and Y
We know that
any two events A and B are said to be independent if
P(A) × P(B) = P (A ∩ B)
We have, for events X and Y,
P(X) × P(Y) = 4/5 × 1/4 = 1/5 = P (X ∩ Y)
P(X) × P(Y) = P(X ∩ Y)
Thus, X and Y are independent because P(X) × P(Y) = P(X ∩ Y)
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The complete question is -
Consider a situation in which P(X) = 4/5 and P(Y) = 1/4. If P(X and Y) is = 1/5, which best describes the events?
They are independent because P(X) x P(Y) = P(X and Y).
They are independent because P(X) + P(Y) = P(X and Y).
They are dependent because P(X) x P(Y) = P(X and Y).
They are dependent because P(X) + P(Y) = P(X and Y).
Answer: a
Step-by-step explanation:
just took the test
Bob's favorite restaurant were salmon filet and filet mignon. The restaurant served 70 specials in all, 80% of which were salmon filets. How many salmon filets did the restaurant serve?
Answers
By working with percentages, we will see that they served 56 salmon filets.
How many salmon filets did the restaurant serve?
Here we know that the restaurant served 70 specials in total, such that 80% of these were salmon filets.
So we just need to calculate what is the 80% of 70.
This is just given by:
70*(80%/100%) = 70*0.8 = 56
This means that they served 56 salmons filet.
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What is the value of x?
90 degrees
170 degrees
X
Z
Answers
Answer:
x = 45 degrees.
Step-by-step explanation:
The arc of 90 degrees an angle of 1/2 its value on the circumference.
1/2 * 90
= 45 degrees.
Which of the following inequalities is graphed on the coordinate plane? A. y>-2x+1 B. y>-2x+1 C. y<-2x+1 D. y<-2x+1
Answers
The correct equation that has been shown by the graph is y<-2x+1. Option D
What is inequality?The term inequality refers to a mathematical statement that contains the inequality sign rather than the equality sign. Looking at the inequality sign, we know that the sign ought to be less than.
Thus, the correct equation that has been shown by the graph is y<-2x+1. Option D
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Answer: The correct equation that has been shown by the graph is y<-2x+1. Option D
What is inequality?
The term inequality refers to a mathematical statement that contains the inequality sign rather than the equality sign. Looking at the inequality sign, we know that the sign ought to be less than.
Thus, the correct equation that has been shown by the graph is y<-2x+1. Option D
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Step-by-step explanation:
Find the area of the irregular figure.
6 in.
13 in.
12 in.
5 in.
4 in.
4 in.
A = [? ]in.² please explain why or how you got the answer for future questions I only have so many points
Answers
Answer:
153 in²
Step-by-step explanation:
Area of irregular figure[tex]\sf \boxed{\text{\bf Area of rectangle = length * width}}[/tex]
[tex]\sf \boxed{\text{\bf Area of square = side *side}}[/tex]
Figure I:
length = 12 in
width = 6 in
Area of figure I = 12 * 6
= 72 in²
Figure II:
length = 13 in
width = 5 in
Area of figure II = 13 * 5
= 65 in²
Figure III:
side = 4 in
Area of figure III = 4 * 4
= 16 in²
Area of irregular shape = 72 + 65 + 16
= 153 in²
What is a solution to the system of equations that includes quadratic function f(x) and linear function g(x)? f(x) = 2x2 x 4 x g(x) –2 1 –1 3 0 5 1 7 2 9 (-2, 10) (–1, 7) (0, 5) (1, 7)
Answers
The solution to the system of equations that includes functions f(x) and g(x) is given by: (1,7).
What is a linear function?A linear function is modeled by:
y = mx + b
In which:
m is the slope, which is the rate of change, that is, by how much y changes when x changes by 1.b is the y-intercept, which is the value of y when x = 0, and can also be interpreted as the initial value of the function.The linear function g(x) goes through point (0,5), hence the y-intercept is of 5. The function also goes through point (1,7), hence the slope is of 2 and the function is:
g(x) = 5 + 2x.
The solution to the system of equations is found as follows:
f(x) = g(x)
2x² + x + 4 = 5 + 2x
2x² - x - 1 = 0
Which is a quadratic equation with coefficient a = 2, b = -1, c = -1, hence:
[tex]\Delta = b^2 - 4ac = (-1)^2 - 4(2)(-1) = 9[/tex][tex]x_1 = \frac{-b + \sqrt{\Delta}}{2a} = \frac{1 + \sqrt{9}}{4} = 1[/tex][tex]x_2 = \frac{-b - \sqrt{\Delta}}{2a} = \frac{1 - \sqrt{9}}{4} = -0.5[/tex]When x = 1, f(x) = g(x) = 7, hence the solution of the system is of (1,7).
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Answer:
D. (1,7)
Step-by-step explanation:
I took the exam
Using data from a study, we find a significant difference in the proportion of fruit flies surviving after 13 days between those eating organic potatoes and those eating conventional (not organic) potatoes. This exercise asks you to conduct a hypothesis test using additional data from this study.1 In this case, we are testing
H0:po=pcHa:po>pc
where po and pc represent the proportion of fruit flies alive at the end of the given time frame of those eating organic food and those eating conventional food, respectively. We have n1=n2=500. Show all remaining details in the test, using a 5% significance level.
Effect of Organic Raisins After 15 Days
After 15 days, 320 of the 500 fruit flies eating organic raisins are still alive, while 300 of the 500 eating conventional raisins are still alive.
Give the test statistic and the p-value.
Round your answers to three decimal places.
What is the conclusion?
Do we have evidence that the proportion surviving after eating organic is higher?
Answers
The hypothesis shows that we have evidence that the proportion surviving after eating organic is higher.
How to illustrate the information?The following can be deduced from the information:
x1 = 275
x2 = 170
n1 = 500
n2 = 500
The sample proportion will be:
p1 = 275/500 = 0.55
p2 = 170/500 = 0.34
The pooled proportion will be:
= (275 + 170)/(500 + 500)
= 0.44
The test statistic is 6.681. It should be noted that the test statistics is a number that's calculated by a statistical test. It shows how the observed data are far from the null hypothesis.
The p value in this scenario is extremely small. The p value is a measurement used to validate a hypothesis against the observed data. Therefore, we have to reject the null hypothesis.
In this case, the hypothesis shows that we have evidence that the proportion surviving after eating organic is higher.
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20 pts !!! Please give a detailed answer thanks :)
How do you construct the inscribed and circumscribed circles of a triangle?
Answers
Answer:
inscribed: centered at the intersection of angle bisectors, radius = distance to one sidecircumscribed: centered at the intersection of perpendicular bisectors, radius = distance to one vertexStep-by-step explanation:
The steps to constructing either circle start with finding the relevant center and radius. The required construction techniques are ...
bisect an angleperpendicular to a line through an external pointperpendicular bisectorInscribed circleSummaryThe incenter (center of the inscribed circle) is located at the coincidence of the angle bisectors. The radius is the perpendicular distance to any side, so will lie on the line through the incenter and perpendicular to one side.
Angle bisectorsReference the first attachment. We have elected to bisect the largest two angles of triangle ABC. In each case, we used these steps:
Centered at a vertex (B for example), draw an arc through the two sides of that angle (arc HI for example).Centered at the points of intersection with the sides, draw two intersecting arcs with the same radius (arcs HQ and IQ).Draw the angle bisector through this point of intersection and the original vertex (green line BQ).After this process is repeated for another angle, the point of intersection of the two angle bisectors is the incenter (R).
RadiusFinding the radius requires finding the perpendicular distance to one side of the triangle. That is done by constructing a perpendicular to the side through the incenter.
Centered at the incenter (R), draw an arc that intersects one side in two places (arc UV).Centered at the points of intersection with the side, draw two intersecting arcs with the same radius (arcs UZ and VZ. Z is the unlabeled point at upper right).Draw perpendicular RZ intersecting the midpoint of UV at X.IncircleThe inscribed circle is centered at R and has radius RX.
__
Circumscribed CircleSummaryThe circumcenter (center of the circumscribed circle) is located at the coincidence of the bisectors of the sides of the triangle. The radius is the distance from the circumcenter to any vertex.
Perpendicular bisectorReference the second attachment. We have elected to bisect the longest and shortest of the triangle's sides. The purpose of this choice is to make the perpendicular bisectors intersect at a large angle, so the point is as accurately located as possible.
Choose one side of the triangle and set the radius to more than half its length.Using that radius, draw intersecting arcs using each end of the side as a center (side AB and arcs FG, for example).Draw the perpendicular bisector through the points where the arcs intersect (line FG).Repeat this process for another side (BC to create bisector JK). The intersection of the two bisectors (L) is the circumcenter.
CircumcircleThe circumscribed circle is centered at L and has radius LA.
__
Additional comments
In general, arcs that are required to intersect each other will be drawn with the same radius. An arc that is required to intersect two lines, or one line in two places, may have any convenient radius.
As with any geometric construction, the tools required are a marking tool, a compass, and a straightedge. Usually, the preferred marking tool is a sharp pencil.
If the triangle is obtuse, the circumcenter will be outside the triangle (adjacent to the long side). If the triangle is a right triangle, the circumcenter is the midpoint of the hypotenuse.
The student’s t distribution will approach the standard normal distribution as the number of the degrees of freedom goes up.
a. True
b. False
Answers
Answer:
True student distribution will approach the standard
Find the missing side. Round your answer to the nearest tenth.
What are the steps to finding missing sides
Answers
Answer:
23.6
Step-by-step explanation:
→ Identify length not given
Opposite
→ Find a formula without opposite
Cos = Adjacent ÷ Hypotenuse
→ Rearrange
Adjacent = Cos × Hypotenuse
→ Substitute
cos 38 × 30 = 23.6
Answer:
[tex]x = 23.6[/tex]
Step-by-step explanation:
To find the missing side of a right-angled triangle, first look at the given angle, and notice its relationships with the given and required sides.
In this case:
• The side adjacent to the given 38° angle is [tex]x[/tex] (required).
• The hypotenuse is 30 units.
The trigonometric ratio that relates the adjacent side and hypotenuse of a triangle is cosine (cos), where:
[tex]\boxed{cos \space\ \theta = \frac{adjacent}{hypotenuse}}[/tex].
Substituting into the formula:
[tex]cos (38^{\circ}) = \frac{x}{30}[/tex]
⇒ [tex]x = cos(38^{\circ}) \times 30[/tex]
⇒ [tex]x = 23.6[/tex]
An acute triangle has sides measuring 10 cm and 16 cm. The length of the third side is unknown.
Which best describes the range of possible values for the third side of the triangle?
x < 12.5, x > 18.9
12.5 < x < 18.9
x < 6, x > 26
6 < x < 26
Answers
Answer:
12.5< × < 18.9
Step-by-step explanation:
because you would use the pythagoras theorem which a² + b² = c² in this case c is the third side the unknown so to work this out do square root of ( 10² + 16²) which is 100 + 256 = 356 and the square root of 356 is 18.86 which rounds to 18.9 so the second answer is correct :)
i hope this helps pls ask if you need any more help :)
True or false? the patient should be given a receipt for payments on account even if the account is not paid in full.
Answers
Answer:
Step-by-step explanation:
true
Answer:
False because the account isn't full
Im so confused please help!!
Answers
The factored form of the expression is (2x-1)(2x+5) and the x-intercept of the function is 1/4 and -5/2 respectively
Solving quadratic equationQuadratic equations are equations that has a leading degree of 2. Given the quadratic equation below;
y = 4x^2 + 8x -5
The x-intercept is the point where the value of y is zero.
Factorize the resulting expression
y = 4x^2 + 8x -5
y = 4x^2 - 2x + 10x -5
y = 2x(2x-1)+5(2x -1)
y = (2x-1)(2x+5)
The factored form of the expression is (2x-1)(2x+5)
Equate the given factors to zero
(2x-1)(2x+5) = 0
Equate the factors to zero
2x - 1 = 0
2x = 1
x = 1/4
Similarly
2x + 5 = 0
2x = -5
x = -5/2
Hence the x-intercept of the function is 1/4 and -5/2 respectively
C) For the end behavior, as the value of x tends to infinity, hence the y-values tends to infinity
D) In order to plot the graph, the x-intercepts of the will be plotted on the graph and then curve will be created.
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An unfair coin is flipped. if a head turns up you win $1. the probability of a head is. 54 and the probability of a tail is 0. 46. what is the expected value of the game?
Answers
Answer:
if you end up landing on a heads you should walk away with a $1.46
find the maximum value of c=4x+2y subject to the fallowing constraints x≥0 y≥0 2x+2y≤10 3x+y≤9
Answers
The maximum value of c=4x+2y subject to the constraints is 14
How to determine the maximum value?The objective function is given as:
c = 4x+2y
The constraints are given as:
x≥0 y≥0
2x+2y≤10
3x+y≤9
Rewrite 2x+2y≤10 and 3x+y≤9 as equations
2x+2y = 10
3x+y = 9
Divide 2x+2y = 10 through by 2
x+y = 5
Subtract x+y = 5 from 3x+y = 9
3x - x + y - y = 9 - 5
Evaluate the difference
2x = 4
Divide by 2
x = 2
Substitute x = 2 in x+y = 5
2+y = 5
Solve for y
y = 3
So, we have
(x, y) = (2, 3)
Substitute (x, y) = (2, 3) in c = 4x+2y
c = 4 * 2 + 2 * 3
Evaluate
c = 14
Hence, the maximum value of c=4x+2y subject to the constraints is 14
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find the size of each of the angles marked with letter
Answers
Answer:
f = 78 , g = 32 , h = 74
Step-by-step explanation:
f and 78° are alternate angles and are congruent , then
f = 78
---------------------------
h and 74° are alternate angles and are congruent , so
h = 74
--------------------------
the sum of the 3 angles in the triangle = 180°
sum the 3 angles and equate to 180
78 + g + h = 180
78 + g + 74 = 180
152 + g = 180 ( subtract 152 from both sides )
g = 28
Simplify the expression 120x^3/18xy
Answers
x^3 / xy = x^2 / y
20x^2 / 3y
Find the length of an arc of 40° in a circle with an 8 inch radius.
877
9inches
O 167
9inches
0
647
9inches
Answers
Answer:
16 pi/ 9 inches should be the right one.
PLEASE HELP ITS MATH PLEASE
Answers
Answer:
y=[4]x + [12]
Step-by-step explanation:
Remember that parallel lines have identical slopes; and to make a line which passes through a point we will use point-slope form.
Familiarize yourself with point-slope form:
[tex]y-y1=m(x-x1)[/tex]
If the line is parallel to [tex]y=4x+11[/tex] the slope must be 4.
[tex]y-y1=4(x-x1)[/tex]
And we know the point it must pass through is (-2,4), so we can fill those values in too.
[tex]y-4=4(x+2)[/tex]
Now all we have to do is solve for y:
[tex]y-4=4(x+2)\\y-4=4x+8\\y=4x+12[/tex]
Answer:
[tex]y = 4x + 12[/tex]
Step-by-step explanation:
The solution is in the attached image
"i see that your new product is available for $412.50 on the website. how much is it if i buy it in the store?" employee: "buying through the website gets you a 25% discount. if you buy the product in the store, it will cost you __________."
Answers
412.50 / 0.75 = $550
Check
550 * 0.75 = $412.50
The cost of new product on the website is $309.375.
Given that, the cost of product = $412.50 and discount percentage = 25%.
What is discount?A discount is the reduction of either the monetary amount or a percentage of the normal selling price of a product or service.
Discount = 25% of 412.50
= 25/100 × 412.50
= 0.25 × 412.50
= 103.125
So, cost = 412.50-103.125
= $309.375
Therefore, the cost of new product on the website is $309.375.
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What number has to fill in the blank to make this a perfect square trinomial: 9x^2 + ___+ 144
Answers
The number that has to fill the blank to make the trinomial a perfect square is 72x
Perfect square trinomialFrom the question, we are to determine the number that makes the given trinomial a perfect square
The given trinomial is
9x² + ___+ 144
For any given trinomial ax² + bx + c, the trinomial is a perfect square if
b² = 4ac
In given trinomial,
a = 9, c = 144, b = ?
Now, we will determine the value of b
Putting the values into the equation,
b² = 4ac
b² = 4×9×144
b² = 5184
b = √5184
b = 72
Thus,
The trinomial will become 9x² + 72x+ 144
Hence, the number that has to fill the blank to make the trinomial a perfect square is 72x
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Use the figure to the right to list all of the pairs of angles that fit each description.
Answers
The pairs of angles that fit the description are
1. alternate exterior angles S and Z; T and Y
2. alternate interior angles U and X; V and W
3. consecutive interior angles U and W; V and X
4. corresponding angles S and W; T and X; U and Y; V and Z
5. vertical angles S and V; U and T; W and Z; Y and X
6. adjacent angles S and T; Y and Z
Angle DescriptionFrom the question, we are to list the angles that fit the given descriptions
1. alternate exterior angles S and Z; T and Y
2. alternate interior angles U and X; V and W;
3. consecutive interior angles U and W; V and X
4. corresponding angles S and W; T and X; U and Y; V and Z
5. vertical angles S and V; U and T; W and Z; Y and X
6. adjacent angles S and T; Y and Z
Hence, the pairs of angles that fit the description are
1. alternate exterior angles S and Z; T and Y
2. alternate interior angles U and X; V and W
3. consecutive interior angles U and W; V and X
4. corresponding angles S and W; T and X; U and Y; V and Z
5. vertical angles S and V; U and T; W and Z; Y and X
6. adjacent angles S and T; Y and Z
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A circle is shown. Points Q, U, A, D are on the circle. Lines connect the points to form a quadrilateral. Angle Q U A is 111 degrees. Arc Q U is 88 degrees.
What is the measure of Arc A U?
44°
50°
64°
92°
Answers
The measure of Arc AU of the given Circle Geometry is; 50°
How to find the measure of arc angle?The circle theorem we will apply to solve for the arc measure states that “Measure of angles subtended to any point on the circumference of the circle from the same arc is equal to half of the angle subtended at the center by the same arc.”
We can express the above theorem as;
Angle at the center = 2 × Angle at the circumference
From the attached image below and from the given statement in the question, we are given that; ∠QUA = 111°
Therefore, applying the circle theorem earlier quoted, we can say that; m∠QDA = 2 × ∠QUA
m∠QDA = 2 × 111° = 222°
Which gives;
∠QOA = = 360° - 222° = 138°
∠QOA = ∠QOU + ∠UOA (by angle addition property)
Thus;
∠QOA = 138° = 88° + ∠UOA
∠UOA = 138° - 88° = 50°
Thus, the measure of Arc AU is;
Arc AU = ∠UOA = 50°
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Answer: b
Step-by-step explanation:
Answers are needed urgently..ty
Answers
Angle <QAB is =15° because the opposite angles of an isosceles triangle are equal.
The length of the straight line AB = 80cm
Calculation of angle of a triangleThe angle at a point = 360°
Angle AQB= 360 - 210° = 150
But the angle that makes up a triangle= 180°
180-150= 30°
But <QAB = <QBA because triangle AQB is an isosceles triangle.
30/2 = 15°
To calculate the length of the straight line the following is carried out using the sine laws.
a/ sina, = b sinb
a= 8cm, sin a { sin 15)
b= ? , sin B = 150
make b the subject formula;
8/sin15= b/sin 150
b= 8 × sin 150/sin 15
b= 80cm
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1.Name 4 other angles whose cosine is the same as cos pi/3 . Explain using mathematical language how you know this is true.
2.Is this statement true or false? Explain your answer.
All angles that have the same cosine will have the same sine.
Answers
The trigonometry illustrates that the four angles whose cosine is the same as cos pi/3 will be 7∏/3, 13∏/3, 19∏/3, and 31∏/3
How to illustrate the information?From the information, given cos (x), the value that is similar to cos x will be the sum of the angle and multiple of 360.
Therefore, for the angle cos(∏/3), the angles that are similar to this angle will be expressed as Cos(2∏n + ∏/3) where n is any positive integer.
Then the other four angles will be 7∏/3, 13∏/3, 19∏/3, and 31∏/3. Also, the statement that all angles that have the same cosine will have the same sine is false. The sine of an angle is simply equal to the cosine of the complementary angle.
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If f(x) = 3x + 1 and f^-1 = x-1/3 , then the ordered pair of f(3) =
Answers
Answer:
10
Step-by-step explanation:
f(x) = 3x + 1
f^-1 = x-1/3 , it is known as inverse function.
f(3)= 3*3 +1
=9+1
=10
To find inverse,
x=3x + 1
y=3x+1
Exchanging the position or x and y
x=3y+1
x-1=3y
.•. y=x-1/3
Can anyone help me with this?
Putting the question into an online calculator gives me 4 Rad x. but what are the steps to solve it?
Simplify the following expression:
(x^0 y^2/3 z^-2y^)^2/3 divided by (x^2 z^1/2)^-6
Show all work to recive full credit.
Answers
The simplified expression of (x^0 y^2/3 z^-2y^)^2/3 divided by (x^2 z^1/2)^-6 is x^(12) y^(10/9) z^(-1/3)
How to simplify the expression?The algebraic statement is given as:
(x^0 y^2/3 z^-2y^)^2/3 divided by (x^2 z^1/2)^-6
Rewrite the algebraic statement as:
[(x^0 y^2/3 z^-2y)^2/3]/[(x^2 z^1/2)^-6]
Evaluate the like factors
[(x^0 y^(2/3+1) z^-2)^2/3]/[(x^2 z^1/2)^-6]
Evaluate the sum
[(x^0 y^5/3 z^-2)^2/3]/[(x^2 z^1/2)^-6]
Expand the exponents
[(x^(0*2/3) y^(5/3 * 2/3)z^(-2*2/3)]/[(x^(2*-6) z^(1/2*-6)]
Evaluate the products
[(x^0 y^(10/9) z^(-4/3)]/[(x^(-12) z^(-3)]
Apply the quotient law of indices
x^(0+12) y^(10/9) z^(-4/3+3)
Evaluate the sum of exponents
x^(12) y^(10/9) z^(-1/3)
Hence, the simplified expression of (x^0 y^2/3 z^-2y^)^2/3 divided by (x^2 z^1/2)^-6 is x^(12) y^(10/9) z^(-1/3)
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Haley and tyler are on the cross country team. tyler can run 1 mile (ata constant speed) in 8 minutes and 20 seconds. haley's distances and times for a training run are given by the equation y=8x where x represent distanse and times in miles and y represents time in minutes. who ran farther in 10 minutes how much farther
Answers
Haler ran farther than Tyler in 10 minutes. She covered an extra 0.05 miles compared to Tyler.
What is an equation?An equation is an expression that shows the relationship between two numbers and variables.
An independent variable is a variable that does not depend on any other variable for its value whereas a dependent variable is a variable that depend on any other variable for its value.
Tyler can run 1 mile in 8 minutes and 20 seconds.
Time taken = 8 mins + 20 sec (0.33 min) = 8.33 minutes
Speed = distance / time = 1 mile / 8.33 = 0.12 mile per min
In 10 minutes, distance = 0.12 mile per min * 10 min = 1.2 mile
Haler is given by:
y = 8x; where y is time and x is distance.
In 10 minutes, distance = y/8 = 10/8 = 1.25 miles
Haler ran farther than Tyler in 10 minutes. She covered an extra 0.05 miles compared to Tyler.
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If a=3x^3, b=4x^4, and c=ab^2, then what is the value of bc?
Answers
[tex]a=3x^3\hspace{5em}b=4x^4 \\\\[-0.35em] ~\dotfill\\\\ c=ab^2\implies c=(\underset{a}{3x^3})(\underset{b}{4x^4})^2\implies c=(3x^3)(4^2x^{4\cdot 2}) \\\\\\ c=3x^3\cdot 16x^8\implies c=(3\cdot 16)x^{3+8}\implies c=48x^{11} \\\\[-0.35em] ~\dotfill\\\\ \boxed{bc}\implies (\underset{b}{4x^4})(\underset{c}{48x^{11}})\implies (4\cdot 48)x^{4+11}\implies \boxed{192x^{15}}[/tex]
Answer:
bc = 192x^15
Step-by-step explanation:
Perform substitution as required, then simplify.
Evaluationbc = b(ab^2) = ab^3 = (3x^3)(4x^4)^3 = (3·4^3)(x^3)(x^(4·3))
= 192x^(3+12)
bc = 192x^15
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Additional comment
The relevant rules of exponents are ...
(ab)^c = (a^c)(b^c)
(a^b)^c = a^(bc)
(a^b)(a^c) = a^(b+c)
