Answer:
A
Step-by-step explanation:
because me smart
Determine the equation of the parabola with focus
(
2
,
5
)
(2,5) and directrix
�
=
18
x=18.
The equation of the parabola with focus (2,5) and directrix x=18 is (x - 18)² + (y - 5)² = (y - (5 + (18 - 2) / 2))².
A parabola is a conic section, the intersection of a right circular conical surface and a plane parallel to a generating
straight line of that surface.
The focus of a parabola is a fixed point on the interior of a parabola used in the formal definition of the curve.
The directrix is a straight line perpendicular to the axis of symmetry and placed symmetrically with respect to the focus.
The axis of symmetry is the line through the focus and perpendicular to the directrix.
The vertex of a parabola is the point where its axis of symmetry intersects the curve. It is the point where the parabola changes direction or "opens
up" or "opens down.
The directrix is a fixed straight line used in the definition of a
parabola. It is placed such that it is perpendicular to the axis of symmetry and at a distance from the vertex equal to the
distance between the vertex and focus. It is the line that is equidistant to the focus and every point on the curve.Here's
the solution to the given problem:
The distance between the directrix and the focus is equal to p = 16 (since the directrix is x = 18, the parabola opens to the left, so the distance is measured horizontally)
The vertex is (h,k) = ((18+2)/2,5) = (10,5)
Then we can use the following formula: (x - h)² = 4p(y - k)
Substitute the vertex and the value of p. (x - 10)² = 64(y - 5)
Expand and simplify. (x - 10)² + (y - 5)² = 64(y - 5)
The equation of the parabola is (x - 10)² + (y - 5)² = 64(y - 5).
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PLEASE HELPP!! i’ve been struggling with this problem for the past 30 min.. lessons about polynomials.
Answer:
39.77 -> 39 or 40, depending on rounding
Step-by-step explanation:
Since 2002-1992 is 10. T would equal 10. At that point, it would be a gesture of plugging in 10 whereever you see a "t" and solve for both
what is y
27 y + 5 = -9
Answer:
y = \(\frac{-14}{27}\)
Step-by-step explanation:
27y + 5 = -9 -> subtract -9 and 5
(-9) - 5 = -14
27y = -14 divide 27 and -14
(-14)/27
You are then left with
y = \(\frac{-14}{27}\)
Prove that if a=n m with (n, m)=1 , then (a, b)=(b, n) \cdot(b, m) .
We have shown that (a, b) is a multiple of (b, n) * (b, m), and vice versa, we can conclude that (a, b) = (b, n) * (b, m).
To prove that (a, b) = (b, n) * (b, m) when a = nm and (n,m) = 1, we need to show that both sides of the equation are equal.
Let d = (a, b), so d divides both a and b. Then we can write a = dp and b = dq for some integers p and q. Substituting these values into a = nm, we get:
dp = nmq
Since (n, m) = 1, we know that n and m are coprime, which means they have no common factors other than 1. Therefore, n divides q, and m divides p. We can write q = nr and p = ms for some integers r and s. Substituting these values back into b = dq, we get:
b = dp = nmq = nmsr
Therefore, (b, n) divides b and n, and (b, m) divides b and m. This means that their product, (b, n) * (b, m), divides both b and nm.
Now let's show that (b, n) * (b, m) also divides d. Since n divides q, we have:
d = ap + bq = nmp + (bq - nmsr)p = n(bq') + m(bp)
where q' = q - msr is an integer. Therefore, both n and m divide d, which means that (b, n) * (b, m) also divides d.
Since (b, n) * (b, m) divides both b and d, and d divides both a and b, we know that (b, n) * (b, m) must divide a. Therefore, (a, b) is a multiple of (b, n) * (b, m).
On the other hand, we can also write:
a = nms
This means that both n and m divide a, so (n, m) divides a. Therefore, (b, n) * (b, m) is a multiple of (a, b).
Since we have shown that (a, b) is a multiple of (b, n) * (b, m), and vice versa, we can conclude that (a, b) = (b, n) * (b, m).
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The pread of a flu viru through a certain population i modeled by y=500/1990e^-. 5(t) where y i the total number of people infected after t day. In how many day will 125 people be infected with the viru?
ln t = 145.69 days day will 125 people be infected with the virus (500/125)/-.005 = t
How many days will it take for 125 people to contract the virus?This question uses the theory of exponential growth and decay.
The equation y=500/1990e^-. 5(t) models the spread of a flu virus through a population, where y is the total number of people infected after t days.
The equation follows an exponential decay curve, where the number of people infected decreases with each passing day. In this case, the rate of decay is -.005.
given below
Step 1: Rearrange the equation to isolate t.
y = 500/1990e^-.005(t)
500/y = 1990e^-.005(t)
500/y = e^-.005(t)
ln(500/y) = -.005(t)
Step 2: Substitute the given values of y (125) and solve for t.
ln(500/125) = -.005(t)
ln(500/125)/-.005 = t
t = 145.69 days
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Plz help! Question on picture :)
Answer:
125 students participated
Step-by-step explanation:
66% + 30% = 96%
100% - 96% = 4%
4% = 5 students
100% ÷ 4% = 25
25 × 5 = 125
125 students participated
Answer:
125 students
Step-by-step explanation:
30+66=96
100-96=4
5 students make up 4%.
100/4=25
25x5=125 students
Solve the real-world situation by using the substitution method.
The number of DVDs sold at a store in a month was 923 and the number of DVDs sold decreased by 12
per month. The number of Blu-ray Discs sold in the same store in the same month was 505 and the
number of Blu-ray discs sold increased by 26 per month. Let d represent the number of discs sold and t
represent the time in months.
The system of equations
{d=923-12t
{d=505+26t
can be used to represent this situation.
If this trend continues, how many months will the number of DVDs sold equal the number of Blu-ray discs
sold? How many of each is sold in that month?
There will be ____ DVDs and Blu-Ray discs sold per month in ____ months.
Answer:
In 11 months, the number of DVDs sold and Blue-Ray discs sold will be same, 791 of each.
Step-by-step explanation:
In the equation d = 923-12t, substitute 505+26t (from the second equation) for 'd'. We get
505 + 26t = 923 - 12t
-505 + 12t -505 + 12t
38t = 418
t=11
d = 923-12(11) = 791
d = 505+26(11) = 791
After 11 months, selling 791 of each.
Hope this helps.
Answer:
791
Step-by-step explanation:
of the 180 students in a college course, I of the students earned an A for the course, ſ of the students earned a B for the course, and the rest of the students
earned a C for the course. How many of the students earned a C for the course?
A
75
Answer:
179
Step-by-step explanation:
180- 2=189 this is because 2 of the students the 180 received a or b
The given question is incorrect. The correct question is:
Of the 180 students in a college course, 1/4 of the students earned an A for the course, 1/3 of the students earned a B for the course, and the rest of the students earned a C for the course. How many of the students earned a C for the course?
A. 75
B. 90
C. 105
D. 120
E. 135
The number of students who earned a C for the course can be represented by the fraction of 5/12 of the total number of students and is equal to 75. Hence, option A is the right choice.
What do we mean by a fraction?A fraction in general means a part of. We represent a part of the whole using fractions. The total number of parts is taken as the denominator, while the parts used are taken as the numerator.
Fraction = Numerator/Denominator.
How do we solve the given question?We are given that there are 180 students in a college course. 1/4 of them get an A for the course while 1/3 get a B. Rest of the students to get a C for the course.
We need to find the number of students who get a C.
Let the fraction of students getting a C be x.
We know that a whole fraction is always = 1.
∴ Fraction of students getting an A + Fraction of students getting a B + Fraction of students getting a C = Whole fraction.
or, 1/4 + 1/3 + x = 1
or, x = 1 - 1/4 - 1/3 = (12 - 3 - 4)/12 = 5/12
∴ 5/12 of the students get a C for the course.
Number of Students who get a C for the course = 5/12 of 180 = 5*15 = 75.
∴ The number of students who earned a C for the course can be represented by the fraction of 5/12 of the total number of students and is equal to 75. Hence, option A is the right choice.
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It is given that ∠ABC and ∠CBD are Response area. So, m∠ABC+m∠CBD=90° using the Response area. It is also given that m∠ABC=35°. Using the Response area, you have 35° + m∠CBD=90°. Therefore, using the subtraction property of equality, m∠CBD=55°
THE QUESTION CAN BE WRITTEN AS THIS;
It is given that ∠ABC and ∠CBD are a____________ So, m∠ABC+m∠CBD=90° using the b____________. It is also given that m∠ABC=35°. Using the substitution property of equality, you have c________+ m∠CBD=90°. Therefore, using the subtraction property of equality, m∠CBD=55°
Answer:
a)COMPLIMENTARY ANGLE
b)DEFINITION OF COMPLEMENTARY ANGLES
c)35°+ m<CBD = 90 degrees.
Step by step Explanation:
a)It's given that <ABC and <CBD are (COMPLIMENTARY ANGLE)
We know that the Sum of Complementary angles equal to 90 degrees.Those angles don't have to be next to each other, just so long as the total is 90 degrees. That's why the Sum of m<ABC and m<CBD equals 90 degrees that is m<ABC + m<CBD = 90 degrees
b)using the (DEFINITION OF COMPLEMENTARY ANGLES) It is also given that m<ABC = 35 degrees.
c)Using substitution property of equality, you have (35°+ m<CBD = 90 degrees.)
If we subtract 35 from both sides, we get 35-35+ m<CBD = 90-35.
Therefore, m<CBD = 55 degrees.
PLEASE CHECK THE ATTACHED FIGURE TO SEE HOW THE QUESTION LOOKS LIKE
Answer:
Step-by-step explanation:
The correct response since I just took this test is:
It is given that ∠ABC and ∠CBD are complementary angles. So, m∠ABC+m∠CBD=90° using the definition of complementary angles. It is also given that m∠ABC=35°. Using the substitution property, you have 35° + m∠CBD=90°. Therefore, using the subtraction property of equality, m∠CBD=55°
Given f1(x), f2(x), f3(x),f4(x) which make up a set. Which of the following describes the set being linearly dependent?
A. f2(x)=c1 f1(x)+c2 f3(x)+c3 f4(x)
B. f(x)=f1(x)+2f2(x)−3f3(x)+f4(x)
C. the Wonskian is not equal to zero D. The functions are not multiples of each other
The correct option that describes the set being linearly dependent is option A: f2(x) = c1 f1(x) + c2 f3(x) + c3 f4(x).
If one of the functions in the set can be expressed as a linear combination of the other functions, it implies that the set is linearly dependent. In option A, f2(x) can be written as a linear combination of f1(x), f3(x), and f4(x), indicating that the set is linearly dependent.
Option B does not necessarily imply linear dependence, as it represents a specific linear combination of the functions rather than one function being a linear combination of the others.
Option C refers to the Wronskian, which is a concept used to test linear independence of functions, but its value not being zero does not necessarily imply linear dependence.
Option D, stating that the functions are not multiples of each other, does not provide enough information to determine linear dependence or independence.
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1. Which pay is equivalent to a rate of $16 per hour?
$78 for 3 hours
$96 for 6 hours
$160 for 16 hours
$60 for 5 hours
Liz is making cookies for the annual bake sale at her
school. Each batch of cookies takes 2 3/4 cups of flour. If Liz
needs to makes 6 batches, how many cups of flour will
she need for all six batches?
Answer:
9
Step-by-step explanation:
It is very simple, 3/4 * 2 = 1.5
If we take 1.5 and multiply it by the amount of batches being made (6), we will have our answer.
1.5*6 = 9, so there we have our answer.
Hope this helps!
Graph the exponential function.
f(x)=3/2(2)^x
Plot five points on the graph of the function. Then click on the graph-a-function button.
\( \bf \: f(x) = \frac{3}{2} \times {2}^{x} \\ \\ = > \bf \: f(0) = \frac{3}{2} \times {2}^{0} = \frac{3}{2} \times 1 = \frac{3}{2} = 1.5 \\ \\ = > \bf \: f(1) = \frac{3}{2} \times {2}^{1} = 3 \\ \\ = > \bf \: f(2) = \frac{3}{2} \times {2}^{2} = 6 \\ \\ = > \bf \: f( - 1) = \frac{3}{2} \times {2}^{ - 1} = \frac{3}{2} \times \frac{1}{2} = \frac{3}{4} = 0.75 \\ \\ = > \bf \: f( - 2) = \frac{3}{2} \times {2}^{ - 2} = \frac{3}{2} \times \frac{1}{4} = \frac{3}{8} = 0.375\)
Assignment The exact diameter of a circle 188cm. A student Measures it as 8.2cm, calculate the percentage error in in the circumference of a circle in the area of a circle
The percentage error for the circumference ≈ -95.53% and the percentage error for the area ≈ -98.23%
Provided:
Exact diameter = 188 cm
Measured diameter = 8.2 cm
To calculate the percentage error in the circumference of a circle, we'll use the formula:
\(\[\text{{Percentage Error in Circumference}} = \left( \frac{{\text{{Measured Circumference}} - \text{{Exact Circumference}}}}{{\text{{Exact Circumference}}}} \right) \times 100\]\)
Exact Circumference = π * Exact Diameter = π * 188 cm
Measured Circumference = π * Measured Diameter = π * 8.2 cm
\(\[\text{Percentage Error in Circumference} = \left(\frac{\pi \cdot 8.2 \, \text{cm} - \pi \cdot 188 \, \text{cm}}{\pi \cdot 188 \, \text{cm}}\right) \times 100\]\)
\(\[=\frac{{8.2 \, \text{cm} - 188 \, \text{cm}}}{{188 \, \text{cm}}} \times 100 \\\\= \frac{{-179.8 \, \text{cm}}}{{188 \, \text{cm}}} \times 100\]\)
≈ -95.53%
Next, to calculate the percentage error in the area of a circle, we'll use the formula:
Percentage Error in Area = \(\(\left(\frac{{\text{{Measured Area}} - \text{{Exact Area}}}}{{\text{{Exact Area}}}}\right) \times 100\)\)
Exact Area = π * (Exact Radius)²
Exact Radius = \(\frac{Exact Diameter}{2}\)
Substituting the values:
Exact Radius = \(\frac{ 188 cm}{2}\)
Measured Radius = \(\frac{8.2 cm}{2}\)
Measured Area = π * (Measured Radius)²
Measured Radius = \(\frac{Measured Diameter}{2}\)
Substituting the values:
Exact Area = π * \((\frac{188 cm}{2} )^2\)
Measured Area = π * \((\frac{8.2 cm}{2} )^2\)
∴ Percentage Error in Area \(=$\left(\frac{\pi \left(\frac{8.2 \text{ cm}}{2}\right)^2 - \pi \left(\frac{188 \text{ cm}}{2}\right)^2}{\pi \left(\frac{188 \text{ cm}}{2}\right)^2}\right) \times 100$\)
\(= \[\frac{{\left(\frac{{8.2 \, \text{cm}}}{2}\right)^2 - \left(\frac{{188 \, \text{cm}}}{2}\right)^2}}{{\left(\frac{{188 \, \text{cm}}}{2}\right)^2}} \times 100\]\)
\(= \[\frac{{(2.05 \, \text{cm})^2 - (47 \, \text{cm})^2}}{{(47 \, \text{cm})^2}} \times 100\]\)
≈ -98.23%
Therefore, the calculated percentage errors are approximately -95.53% for the circumference and -98.23% for the area.
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Nathan and Jorge are working on a decimal division problem in
math class. After finishing the problem, it looked like this: 4.76 ÷
2.5 = 0.19. Nathan said that the decimal is incorrectly placed in the
quotient, and Jorge disagrees. Who is right? Explain your answer
Answer:
Nathan
Step-by-step explanation:
4.76 / 2.5
= (476/100) / (25/10)
= (476/100) * (10/25)
= 238/125
= 1.904
Thus, Nathan is right in saying that the decimal is incorrectly placed in the quotient of the given answer 0.19
a is 60 miles from b. a starts for b at 20 mph, and b starts for a at 25 mph. when will a and b meet?
The problem describes a scenario in which two objects, A and B, start moving towards each other from different locations and speeds. Object A starts from point A, which is 60 miles away from object B, at a speed of 20 mph, while object B starts from point B at a speed of 25 mph.
To solve this problem, we can use the formula Distance = Speed x Time. We know that the total distance between A and B is 60 miles and we want to find the time at which they meet. Let's call that time "t". Let's also assume that they meet at some point "x" miles away from A. Then, the distance that A travels is 60 - x and the distance that B travels is x. Using the formula, we can set up an equation:
Distance A + Distance B = Total Distance
(60 - x) + x = 60
Simplifying this equation, we get:
60 - x + x = 60
60 = 60
This equation is always true, so it doesn't give us any information about when A and B will meet. However, we can use the formula Distance = Speed x Time to set up another equation that relates the distance and speeds of A and B to the time they travel before meeting:
Distance A = Speed A x Time
Distance B = Speed B x Time
Substituting the distances and speeds we know, we get:
(60 - x) = 20t
x = 25t
We can use either equation to solve for t, but let's use the second equation. Substituting x = 25t, we get:
(60 - 25t) = 20t
Simplifying and solving for t, we get:
60 = 45t
t = 4/3
Therefore, A and B will meet after traveling for 4/3 hours, or 1 hour and 20 minutes.
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PLEASE HELP ME SOLVE THE FOLLOWING WITH DETAILED EXPLAINATIONS .GOD BLESS YOU .
1.Find the value of y:
3(2raised to the power -y) all over 16 - 1 =1/2
2.A train passes through a station at a speed of 108km/h.
The length of the station is 120km.
The train takes 7 seconds to completely pass through the station .
Work out the length of the train.
3.Xavier's salary increases by 2% each year.
In 2010 , his salary was £40,100
i) Calculate his salary in 2015 and give your answer to the nearest pound.
ii) In which year did Xavier's salary first greater than £47,500
The value of y is 0.26 and the length of the train is 45m
\(3( 2^-^y) / (16 - 1) )= 1/2\)
\(2^(^-^y^) = 5/6\)
After applying log on both sides we get
-y × log(2) = log(5/6)
Divide both sides by log 2
y = -log(5/6) / log(2)
We get the value of y
y =- 0.2630344
Speed of train = 108 km/h
= (108×1000) m / (60 × 60) s
= 30 m/s
Length of station = 120 km = 120000 m
Let's assume that the length of the train is L
L/30 + (L + 120)/30 = 7
2L/30 + 4 = 7
2L/30 = 3
L = 45
Hence, the length of train is 45 m
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PLEASE HELP ME!!! Brainliest + Rate + 10 Points
Answer:
The first one!
Step-by-step explanation:
A shop sold packets of corn for $1.40 each. During a sale, the shop offered 3 packets of corn for $3.60. Mrs Muthu wanted to buy 7 packs of corn. What was the least amount that Mrs Muthu had to pay?
(REPOST) STATION 3 ! 40 POINTS
Answer:
Great valley
Mercury
Liberty
Delta
International
Step-by-step explanation:
Liberty Express: 128.333
Mercury speed: 130
International speed: 122.666666
Delta Eagle speed: 125
Great Vally speed: 130.5
distance/time=speed
Order:
Great valley
Mercury
Liberty
Delta
International
Edith ordered 588 tomatoes for the produce section. if there are 84 per crate, how many crates will she receive?
Answer:
7 crates of tomatoes
Step-by-step explanation:
588÷84=7
Answer:
7 Crates of tomatoesStep-by-step explanation:
This is a simple division problem. To find out the number of crates, we need to divide 588 by 84.
588/84 = 7
7 Crates of tomatoes___________________________________________________I AM ALWAYS HAPPY TO HELP :)3. Draw and label all three sides of a right triangle that has a 35 degree angle and a hypothenuse of 12 cm.
The missing sides are 6.9 cm and 9.8 cm
What is a right angle triangle?A right triangle, also known as a right-angled triangle, is a triangle that has one angle measuring 90 degrees, which is known as a right angle. The side opposite the right angle is called the hypotenuse, while the other two sides are called the legs or the adjacent and opposite sides.
We know that;
Sin 35 = opposite/12
Opposite = 12 sin 35
= 6.9 cm
Cos 35 = adjacent/12
adjacent = 12 cos 35
adjacent = 9.8 cm
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Draw triangle GMT
PLS CREATE DRAWING!! refer to attachment
The angle between sides GM and MT is ∠M.
The 2 sides that include ∠T are MT and GT.
The angle between sides GT and MG is ∠G.
There's not much to say about this, but I can answer questions if you have any.
The box has a length of L=89.5 cm, a width of w=56.1 cm, and a height of h=13.6 cm. The electric field has the following magnitudes at different locations in space: - At the right side of the box, the field has a magnitude of E
1
=1156 N/C - At the top, bottom, front, and back sides of the box, the field has a magnitude of E
2
=2842 N/C - At the left side of the box, the field has a magnitude of E
3
=4484 N/C What is the electric flux through the right side of the box? Nm
2
/C What is the electric flux through the top side of the box? Nm
2
/C What is the electric flux through the bottom side of the box? Nm
2
/C What is the electric flux through the front side of the box? Nm
2
/C What is the electric flux through the back side of the box? Nm
2
/C What is the electric flux through the left side of the box? Nm
2
/C What is the total charge enclosed by the Gaussian box?
To calculate the electric flux through each side of the box, we need to use Gauss's Law, which states that the electric flux through a closed surface is proportional to the total charge enclosed by that surface.
Given the magnitudes of the electric field on each side of the box, we can calculate the electric flux through each side using the formula:
Electric Flux = Electric Field * Area * Cos(θ)
where:
Electric Field is the magnitude of the electric field on a particular side of the box
Area is the area of that side of the box
θ is the angle between the electric field vector and the surface normal (which is 0 degrees for a perpendicular field)
Given the dimensions of the box, we can calculate the areas of each side:
Area of the right side = w * h
Area of the top and bottom sides = L * w
Area of the front and back sides = L * h
Area of the left side = w * h
Now, we can calculate the electric flux through each side:
Electric Flux through the right side = E₁ * Area of the right side * Cos(0°)
Electric Flux through the top side = E₂ * Area of the top side * Cos(0°)
Electric Flux through the bottom side = E₂ * Area of the bottom side * Cos(0°)
Electric Flux through the front side = E₂ * Area of the front side * Cos(0°)
Electric Flux through the back side = E₂ * Area of the back side * Cos(0°)
Electric Flux through the left side = E₃ * Area of the left side * Cos(0°)
To calculate the total charge enclosed by the Gaussian box, we use the formula:
Total Charge Enclosed = Electric Flux through the right side + Electric Flux through the left side
Now, let's calculate the values:
Area of the right side = w * h = 56.1 cm * 13.6 cm = 763.96 cm²
Electric Flux through the right side = 1156 N/C * 763.96 cm² * Cos(0°)
Area of the top and bottom sides = L * w = 89.5 cm * 56.1 cm = 5023.95 cm²
Electric Flux through the top side = 2842 N/C * 5023.95 cm² * Cos(0°)
Electric Flux through the bottom side = 2842 N/C * 5023.95 cm² * Cos(0°)
Area of the front and back sides = L * h = 89.5 cm * 13.6 cm = 1216.2 cm²
Electric Flux through the front side = 2842 N/C * 1216.2 cm² * Cos(0°)
Electric Flux through the back side = 2842 N/C * 1216.2 cm² * Cos(0°)
Area of the left side = w * h = 56.1 cm * 13.6 cm = 763.96 cm²
Electric Flux through the left side = 4484 N/C * 763.96 cm² * Cos(0°)
Total Charge Enclosed = Electric Flux through the right side + Electric Flux through the left side
Now, you can plug in the values and calculate the electric flux and total charge enclosed using the given magnitudes of the electric fields.
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The average new car sells for 23,000 but loses value about 20% each year for the next 5 years
Answer:
I think It would be $18,400
Step-by-step explanation:
You would take 23,000 then divide it by 100 to get 230 then multiply that by 20 finally you would delete 23,000 by 4600 to get what do you know 18,400.
What is the slope of the line that passes through the points (1, -1)(1,−1) and (-8, -7)(−8,−7)? Write your answer in simplest form.
The slope of the line that passes through the given points (1, -1) and (-8, -7) as required is; 2 / 3.
What is the slope of the line that passes through the given points?It follows from the task content that the slope of the line which passes through the given points is to be determined.
Since the slope formula, m = (y2 - y1) / (x2 - x1)
Therefore, the slope of the line in discuss is;
Slope, m = (-7 -(-1)) / ( -8 -1)
m = -6 / -9
m = 2 / 3.
Hence, the slope of the line that passes through the points in discuss is; 2 / 3.
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Exercise 2: D) A truck travels at an average speed of 70km/h. If the truck travels a distance of 420km from Johannesburg to Pietermaritzburg, how long will the journey take?
The distance between Johannesburg to Pietermaritzburg is 420 km. The journey will take 6 hours.
What is the meaning of average speed?
The total distance traveled by the object in a given time interval is the average speed. A scalar quantity is average speed. It is represented by magnitude and lacks direction.
Given that the average speed of a truck is 70km/h.
The distance that truck travels a distance of 420km.
The formula of speed is:
Average speed = Distance/time
Rewrite the formula:
Time = Distance/Average speed
Now putting average speed = 70km/h and Distance = 420 km:
Time = 420 km/ (70km/h)
Time = 6 hours
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what is the solution if any?
Answer:
I might be wrong, But it's 0 I think
A red bird is flying at an elevation of 17 1/9 meters. A blue bird was flying at an elevation of 10 3/5
Answer:
The red bird is flying at 6 23/45 meters higher than the blue bird. But I'm not sure what you want me to solve here.
Answer:
1. 17 1/9 and 2. The red bird is flying at a higher elevation than the blue bird.
Step-by-step explanation:
In Exercises 9-12, match the expression with the
logarithm that has the same value. Justify your answer
9. log3 6 log3 2
A. log3 64
10.
2 log36
11. 6 log32
12. log3 6+ log3 2
B.
log3 3
C.
log3 12
D. log3 36
9. Expression matches with option C: log3 12.
10. Expression matches with option D: log3 36.
11. Expression matches with option A: log3 64.
12. Expression matches with option C: log3 12.
To match the expression with the logarithm that has the same value, we need to simplify each expression and rewrite it
in the form of log3 x.
9. log3 6 + log3 2 = log3 (6 × 2) = log3 12.
Therefore, the expression matches with option C: log3 12.
10. \(2 log36 = log36^2 = log3 (6^2)^2 = log3 36.\)
Therefore, the expression matches with option D: log3 36.
11. \(6 log32 = log32^6 = log3 (2^5)^6 = log3 2^30.\)
Therefore, the expression matches with option A: log3 64.
12. log3 6 + log3 2 = log3 (6 × 2) = log3 12.
Therefore, the expression matches with option C: log3 12.
In summary:
9. Expression matches with option C: log3 12.
10. Expression matches with option D: log3 36.
11. Expression matches with option A: log3 64.
12. Expression matches with option C: log3 12.
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