Answer:
10/3 mph
Step-by-step explanation:
Obviously, (time going) + (time returning) = (total time spent en route) = 54 min. Since time = distance / rate,
3 miles 3 miles
----------------------- + --------------------- = 54 min
downhill speed uphill speed
Let u = uphill speed and d = downhill speed; then d = u + 5 (all in mph)
Then we have:
3 miles 3 miles
----------------------- + --------------------- = 54 min
u + 5 u
and our task here is to determine the uphill speed, u.
The LCD is u(u + 5). Thus we have:
3u 3(u + 5) miles
----------------------- + ----------------------- = 54 min = 0.9 hr
u(u + 5) u(u + 5)
so that:
6u + 15
----------------------- = 0.9 hr or 6u + 15 = 0.9(u)(u + 5), or
u(u + 5)
6u + 15 = 0.9u² + 4.5u
Combining the u terms, we get:
15 = 0.9u² + 4.5u, or 0.9u² + 1.5u - 15 = 0
Eliminating the fractions, we get 9u² + 15u - 150, or
3u^2 + 5u - 50 = 0
This factors into (3u - 10)(u + 5) = 0. The only positive root is u = 10/3.
Your average rate on the return trip (uphill) is 10/3 mph (3 1/3 mph).
R is approximately 6 mph.
Let's denote the average rate (speed) on the return trip as
r (in miles per hour, mph). Since it is given that the speed going to campus is 5 mph faster, the speed while going downhill would be r + 5 mph. We need to find the values of r.
The total distance for the round trip is 3 miles to campus and 3 miles back, adding up to 6 miles. The total time for the trip is given as 54 minutes, which we will convert to hours by dividing by 60, giving us 0.9 hours.
The time taken to go to campus is the distance divided by the speed, which is 3 / (r + 5) hours. The time taken for the return trip is 3 / r hours. Since both times add up to 0.9 hours, we can write the equation:
3 / (r + 5) + 3 / r = 0.9
Now we need to solve this equation for r. We find a common denominator and solve:
r(r + 5)(3 / (r + 5) + 3 / r) = r(r + 5)(0.9)
3r + 3(r + 5) = 0.9r(r + 5)
3r + 3r + 15 = 0.9r^2 + 4.5r
6r + 15 = 0.9r^2 + 4.5r
0.9r^2 - 1.5r - 15 = 0
Using the quadratic formula or factoring, we can find the root for r. The root that makes sense in this context (positive speed) gives us the average rate on the return trip.
After solving, we find that r is approximately 6 mph, which is the average speed of the student on their return trip.
Which system could be used to solve the following:
A manager is comparing two companies.
Company A charges $50 plus $7 per item.
Company B charges $30 plus $9 per item.
For what number of items will the cost be the same at both companies?
(A) y=7+50x
y=30+9x
(B) y=50+7x
y=30x+9
(C) y=50+7x
y=30+9x
(D) y=50x+7
y=30x+9
Answer:
(C)
10
Step-by-step explanation:
Let y = cost of items
Let x = number of items
Total cost = fixed charge + (cost per item x number of items)
Given:
company A fixed charge = $50 , cost per item = $7
company B fixed charge = $30 , cost per item = $9
For company A,
Total Cost = $50 + ($7 x number of items),
or
y = 50 + 7x
Similarly for company B,
Total Cost = $30 + ($9 x number of items),
or
y = 30 + 9x
Hence (C) is the correct answer.
For the cost to be the same, Total cost for A = total cost for B
i.e 50 + 7x = 30 + 9x
x = 10 items (Answer)
The correct system to solve the problem is y=50+7x and y=30+9x. The cost will be the same at both companies when there are 10 items.
Explanation:The correct system that could be used to solve the problem is (C) y=50+7x and y=30+9x.
To find the number of items where the cost will be the same at both companies, we need to set the two equations equal to each other and solve for x.
50+7x = 30+9x
20 = 2x
x = 10
Therefore, the cost will be the same at both companies when there are 10 items.
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Carl's Candies has determined that a candy bar measuring 3 inches long has a z-score of +1 and a candy bar measuring 3.75 inches long has a z-score of +2. What is the standard deviation of the length of candy bars produced at Carl's Candies?
Answer:
0.75 inches
Step-by-step explanation:
The value that has z=2 is 2 standard deviations from the mean. The value that has z=1 is 1 standard deviation from the mean. The difference between these two values is 1 standard deviation:
1 standard deviation = 3.75 in - 3 in = 0.75 in
Answer:
0.75
Step-by-step explanation:
PLS HELP BRAINLIET WILL BE GIVEN :D
b)
A - wins at both games
[tex]P(A)=0.3\cdot0.4=0.12[/tex]
c)
A - wins at just one of the games
[tex]P(A)=0.3\cdot0.6+0.7\cdot0.4=0.18+0.28=0.46[/tex]
A new unit has been formed in the army . In this until, 1 member is a staff sergeant , 3 are sergeants,21 are PFC's and 35 are PVT's . What percent of the soldiers are in the army
Answer:
93%
Step-by-step explanation:
1 + 3 + 21 + 35 = 60 = 100%
21 + 35 = 56 = x%
60 = 100%
56 = x%
60x = 56 * 100
x = 56* 100 / 60
x = 2*23*2*2*5*5 / 2*2*3*5
x = 23*2*5/3
x = 93%
To find the percent of soldiers in the new army unit, you divide the number of soldiers in the unit by the total number of soldiers in the army and multiply by 100. However, the question doesn't provide the total number of soldiers in the army, making it impossible to calculate this percentage.
Explanation:The question is asking what percent of the soldiers in the newly formed army unit consists of the total personnels. The total number of soldiers in the unit is the sum of staff sergeants, sergeants, PFCs, and PVTs which is 1 + 3 + 21 + 35 = 60 soldiers. The percent of soldiers in the army is the number of soldiers in the unit divided by the total number of soldiers in the army multiplied by 100. However, without the context of the total number of soldiers in the army, it is impossible to calculate this percentage. For example, if the total army size is 600, then the percent of soldiers in this unit would be (60/600)*100 = 10%. The keywords here are
percent
,
total soldiers
, and
army unit
.
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The density of granite is about 2.75 grams per cubic centimeter. Suppose you have a granite countertop for a kitchen that is 1 meter wide, 3 meters long, and 4 centimeters thick. Which of the following equations will give you its mass, in kilograms? View Available Hint(s) The density of granite is about 2.75 grams per cubic centimeter. Suppose you have a granite countertop for a kitchen that is 1 meter wide, 3 meters long, and 4 centimeters thick. Which of the following equations will give you its mass, in kilograms? 2.75 gcm3×1 m×3 m×4 cm×1000 g1 kg 2.75 gcm3×1 m×3 m×(100 cm1 m)2×4 cm×1 kg1000 g 2.75 gcm3×1 m×3 m×4 cm×1 m100 cm×1 kg1000 g 2.75 gcm3×1 m×3 m×4 cm×1 kg1000 g 2.75 g3cm3×1 m×3 m×(100 cm1 m)2×4 cm×(1 kg1000 g)3 2.75 gcm3×1 m×3 m×(1 m100 cm)2×4 cm×1 kg1000 g
Answer:
[tex]330\ kg[/tex]
Step-by-step explanation:
Remember that
1 kg=1,000 g
1 m= 100 cm
The volume of the granite countertop in cubic centimeters is equal to
[tex]V=(100)(300)(4)\ cm^{3}[/tex]
The density in kg per cubic centimeter is equal to
[tex]D=2.75(\frac{1}{1,000}) \frac{kg}{cm^{3}}[/tex]
Multiply the density by the volume
[tex]2.75(\frac{1}{1,000})(100)(300)(4)[/tex]
[tex]2.75(120)=330\ kg[/tex]
Please help me find the area of this polygon
Answer:
The area of the polygon = 216.4 mm²
Step-by-step explanation:
* Lets talk about the regular polygon
- In the regular polygon all sides are equal in length
- In the regular polygon all interior angles are equal in measures
- When the center of the polygon joining with its vertices, all the
triangle formed are congruent
- The measure of each vertex angle in each triangle is 360°/n ,
where n is the number of its sides
* Lets solve the problem
- The polygon has 9 sides
- We can divide it into 9 isosceles triangles all of them congruent,
if we join its center by all vertices
- The two equal sides in each triangle is 8.65 mm
∵ The measure of the vertex angle of the triangle = 360°/n
∵ n = 9
∴ The measure of the vertex angle = 360/9 = 40°
- We can use the area of the triangle by using the sine rule
∵ Area of the triangle = 1/2 (side) × (side) × sin (the including angle)
∵ Side = 8.65 mm
∵ The including angle is 40°
∴ The area of each triangle = 1/2 (8.65) × (8.65) × sin (40)°
∴ The area of each triangle = 24.04748 mm²
- To find the area of the polygon multiply the area of one triangle
by the number of the triangles
∵ The polygon consists of 9 congruent triangles
- Congruent triangles have equal areas
∵ Area of the 9 triangles are equal
∴ The area of the polygon = 9 × area of one triangle
∵ Area of one triangle = 24.04748 mm²
∴ The area of the polygon = 9 × 24.04748 = 216.42739 mm²
* The area of the polygon = 216.4 mm²
Answer
[tex]216.4 {mm}^{2} [/tex]
Explanation
The regular polygon has 9 sides.
Each central angle is
[tex] \frac{360}{n} = \frac{360}{9} = 40 \degree[/tex]
The area of each isosceles triangle is
[tex] \frac{1}{2} {r}^{2} \sin( \theta) [/tex]
We substitute the radius and the central angle to get:
[tex] \frac{1}{2} \times {8.65}^{2} \times \sin(40) = 24.05 {mm}^{2} [/tex]
We multiply by 9 to get the area of the regular polygon
[tex]9 \times 24.05 = 216.4 {mm}^{2} [/tex]
The distance a car travels at a rate of 65 mph is a function of the time, t, the car travels. Express this function and evaluate it for f(3.5).
Distance = rate * time
Replace D with f. Instead of writing D(t), write f(t).
f(t) = 65t
Let t = 3.5
f(3.5) = 65(3.5)
f(3.5) = 227.5
Did you follow?
Final answer:
The distance a car travels at 65 mph is a function of time, expressed as f(t) = 65t. Evaluating it for 3.5 hours, the car would travel 227.5 miles.
Explanation:
The distance a car travels at a rate of 65 mph is a function of the time, t, the car travels. This can be expressed mathematically as f(t) = 65t, where f(t) is the distance in miles and t is the time in hours. To evaluate this function for f(3.5), we multiply 65 miles/hour by 3.5 hours.
f(3.5) = 65 miles/hour × 3.5 hours = 227.5 miles
Therefore, a car traveling at a constant speed of 65 mph for 3.5 hours will have traveled 227.5 miles.
Which postulate can be used to prove that the triangles are congruent?
A. SAS
B. SSS
C. ASA
D. not congruent
Answer:
D. not congruent
Step-by-step explanation:
Only two pairs of congruent sides are given to us, when we need either 3 pairs of congruent sides (SSS) or two pairs of congruent sides & 1 pair of congruent angles (SAS), or two pairs of congruent angles & one pair of congruent sides (ASA).
~
What is the value of n?
-4n = 696
A)
n = -2,784
B)
n = -174
C)
n = 174
D)
n = 2,784
Answer:
n = -174
Step-by-step explanation:
What I did was 696 divided by -4 and got B) n = -174.
Please mark brainliest and have a great day!
Can someone please help me? Will give the brainlest!!
Step-by-step explanation:
The ratio of the perimeters = the scale
P₂ / P₁ = 6 / 4 = 3 / 2
The ratio of the areas = the square of the scale
A₂ / A₁ = (6 / 4)² = (3 / 2)² = 9 / 4
Same for the triangles:
P₂ / P₁ = 6 / 3 = 2
A₂ / A₁ = (6 / 3)² = (2)² = 4
An election was contested by 3 candidates.A got 345983 votes. His nearest rival, Candidate B won elections by 15967 votes. Candidate C got 279845 votes and 39823 votes were declared invalid. Find total number of votes polled.
Final answer:
To find the total number of votes polled in the election with three candidates and invalid votes, the sum of votes received by each candidate and the invalid votes is calculated. The total number of votes polled is 1,027,601.
Explanation:
The question pertains to vote totals and calculating the overall number of votes polled in an election with three candidates. To solve this, we will perform simple addition of the votes received by each candidate and also include votes that were declared invalid.
Candidate A received 345,983 votes. Candidate B won the election by a margin of 15,967 votes more than Candidate A, which means Candidate B received 345,983 + 15,967 = 361,950 votes. Candidate C received 279,845 votes, and there were 39,823 invalid votes.
To find the total number of votes polled, add together all the votes:
Votes for Candidate A: 345,983
Votes for Candidate B: 361,950 (since Candidate B won by 15,967 votes more than Candidate A)
Votes for Candidate C: 279,845
Invalid votes: 39,823
Adding these together:
345,983 + 361,950 + 279,845 + 39,823 = 1,027,601
Therefore, the total number of votes polled in the election is 1,027,601.
If there are 25 questions in a test, and I got an 84% grade, how many questions did I get wrong? Please explain!
-sunny
Answer:
4 wrong
Step-by-step explanation:
Just do .84 times 25.
.84(25)=21
That means you got 21 questions right.
Answer:
You missed 4 questions.
Step-by-step explanation:
If you have a 100 questions test with 1 point each and you get and 84% that means you missed 16 questions. Since there was 25 questions on this test that is 1 quarter of 100. Divide the number of questions missed on a 100 questions test by the fraction of the actual test. So by 4. 16 divided by 4 = 4
A commercial aircraft gets the best fuel efficiency if it operates at a minimum altitude of 29,000 feet and a maximum altitude of 41,000 feet. Model the most fuel-efficient altitudes using a compound inequality.
x ≥ 29,000 and x ≤ 41,000
x ≤ 29,000 and x ≥ 41,000
x ≥ 41,000 and x ≥ 29,000
x ≤ 41,000 and x ≤ 29,000
Answer:
[tex]x\geq 29,000[/tex] and [tex]x\leq 41,000[/tex]
Step-by-step explanation:
Let
x -----> the altitude of a commercial aircraft
we know that
The expression " A minimum altitude of 29,000 feet" is equal to
[tex]x\geq 29,000[/tex]
All real numbers greater than or equal to 29,000 ft
The expression " A maximum altitude of 41,000 feet" is equal to
[tex]x\leq 41,000[/tex]
All real numbers less than or equal to 41,000 ft
therefore
The compound inequality is equal to
[tex]x\geq 29,000[/tex] and [tex]x\leq 41,000[/tex]
All real numbers greater than or equal to 29,000 ft and less than or equal to 41,000 ft
The solution is the interval ------> [29,000,41,000]
Answer:
A
Step-by-step explanation:
What integer is equal to 8^ 2/3 ?
Simplifying it, convert it to a radical form, and evaluate it.. Either way it all equals to a simple whole number, which is '4',
well, except when you convert the expression to radical form using the formula 'a^x/n=n√a^x' then it'll be '^3√8^2'.
____
I hope this helps, as always. I wish you the best of luck and have a nice day, friend..
Answer:
4
Step-by-step explanation:
8 ^ (2/3)
The 2 means squared and the 3 means root
8^2 ^ (1/3)
Rewriting 8 as 2^3
2^3 ^ (2/3)
We know a^ b^c = a^ (b*c)
2 ^ (3*2/3)
2^ 2
4
OR
8 ^ (2/3)
The 2 means squared and the 3 means root
8^2 ^ (1/3)
64 ^ 1/3
We know 4*4*4 = 64
(4*4*4)^ 1/3
4
The height of a kicked football can be represented by the polynomial –16t2 + 32t + 3 where t is the time in seconds. Find the height (in feet) of the football after 1.2 seconds. A. 18.75 feet B. 18.25 feet C. 18.36 feet D. 18.05 feet
To find the height of the football after 1.2 seconds, we substitute t with 1.2 in the polynomial −16t2 + 32t + 3, simplifying to 18.36 feet, which corresponds to answer option C.
Explanation:The student asked to find the height of a kicked football after 1.2 seconds, with the height given by the polynomial −16t2 + 32t + 3, where t is the time in seconds. To solve for the height after 1.2 seconds, we substitute t with 1.2 in the polynomial, which gives us:
−16(1.2)2 + 32(1.2) + 3
Calculating this gives:
−16(1.44) + 38.4 + 3
−23.04 + 38.4 + 3
15.36 + 3
18.36 feet.
Therefore, after 1.2 seconds, the height of the football is 18.36 feet, making the correct answer option C.
Need help with a math question
Answer:
27%
Step-by-step explanation:
take the number of times it is at 2 cars (16) and divide by the number of surveyed times in total (60). multiply by 100 to show answer as a percent
Answer:
27%
Step-by-step explanation:
We are given the results of survey of one thousand families to determine the distribution of families by their size.
We are to find the probability (to the near percent) that a line has exactly 2 cars in it.
Frequency of 2 cars in a line = 16
Total frequency = 2 + 9 + 16 + 12 + 8 + 6 + 4 + 2 + 1 = 60
P (2 cars in line) = (16 / 60) × 100 = 26.6% ≈ 27%
Which shows the correct substitution of the values a, b, and c from the equation 0 = – 3x2 – 2x + 6 into the quadratic formula? Quadratic formula: x =
Answer:
[tex]x=\frac{-(-2)\pm \sqrt{(-2)^2-4(-3)(6)}}{2(-3)}[/tex]
Step-by-step explanation:
The given quadratic equation is
[tex]-3x^2-2x+6=0[/tex] .... (1)
If a quadratic equation is defined as
[tex]ax^2+bx+c=0[/tex] .... (2)
then the quadratic formula is
[tex]x=\frac{-b\pm \sqrt{b^2-4ac}}{2a}[/tex]
On comparing (1) and (2), we get
[tex]a=-3,b=-2,c=6[/tex]
Substitute [tex]a=-3,b=-2,c=6[/tex] in the above formula.
[tex]x=\frac{-(-2)\pm \sqrt{(-2)^2-4(-3)(6)}}{2(-3)}[/tex]
Therefore, the correct substitution of the values a, b, and c in the quadratic formula is [tex]x=\frac{-(-2)\pm \sqrt{(-2)^2-4(-3)(6)}}{2(-3)}[/tex].
Which is greater, 7 P 5 or 7 C 5? 7P5 7C5
[tex]_7P_5=\dfrac{7!}{(7-5)!}=\dfrac{7!}{2!}=3\cdot4\cdot5\cdot6\cdot7=2520\\_7C_5=\dfrac{7!}{5!2!}=\dfrac{6\cdot7}{2}=21\\\\\\_7P_5> {_7C_5}[/tex]
--------------------------------------------
[tex]_nP_k[/tex] is always greater than [tex]_nC_k[/tex]. And it's greater [tex]k![/tex] times.
[tex]\dfrac{_nP_k}{_nC_k}=\dfrac{\dfrac{n!}{(n-k)!}}{\dfrac{n!}{k!(n-k)!}}=\dfrac{n!}{(n-k)!}\cdot \dfrac{k!(n-k)!}{n!}=k![/tex]
How are the graphs of the functions f(x) = /16x and g(x) = 3/64x related
Answer:
the functions f(x) and g(x) are equivalent
Step-by-step explanation:
Your full question is attached below
The equations of your problem are
f(x) = √(16^x)
f(x) = √(4^(2x))
f(x) = √(4^(2x)) = √(4^x.4^x)
f(x) = 4^(x)
and
g(x) = ∛64^x
g(x) = ∛4^(3x)
g(x) = ∛4^(3x) = ∛4^(x) .4^(x) .4^(x)
g(x) = 4^(x)
Thus, the functions f(x) and g(x) are equivalent
can anyone help with problems 6 and 8 those are the only ones I cannot figure out
Answer:
[tex](f + g) (x)=x^2 +x +3[/tex]
[tex](f - g) (x)=-x^2 +5x +1[/tex]
Step-by-step explanation:
We have the following functions:
[tex]f(x)=3x +2\\[/tex] and [tex]g(x) = x^2 -2x +1[/tex]
First we find [tex](f + g) (x)[/tex]
To find [tex](f + g) (x)[/tex] we must add the function f(x) with the function g(x)
[tex](f + g) (x)=3x +2 + x^2 -2x +1[/tex]
[tex](f + g) (x)=x^2 +x +3[/tex]
Now we find [tex](f - g) (x)[/tex]
To find [tex](f - g) (x)[/tex] we must subtract the function f(x) with the function g(x)
[tex](f - g) (x)=3x +2 - (x^2 -2x +1)[/tex]
[tex](f - g) (x)=3x +2 - x^2 +2x -1[/tex]
[tex](f - g) (x)=-x^2 +5x +1[/tex]
Which is correct regarding the statement: "If x is an odd integer, then the median of x, x + 2, x + 6, and x + 10 is an odd number" the statement is always false the statement is always true the statement is sometimes true there is not enough information provided to answer the question
Answer:
I believe it's the statement is always true.
Step-by-step explanation:
test it by substituting x = an odd number:
x=1
so
x = 1 odd number
x + 2 = 1+2 = 3 odd
x + 6 = 1 + 6 = 7 odd
x + 10 = 1+10=11 odd
Answer:
the statement is always true.
Solve for the zeros
x^2+10x+21
(x+3)(x+7)= 0
x^2+7x+3x+21= x^2+10x+21
x+3-3= 0-3
x+7-7= 0-7
Answers are :
x= -3 , x= -7
Answer:
x=-7,-3
Step-by-step explanation:
Since BC is parallel to DE, triangles ABC and ADE are similar. What are the lengths of the unknown sides?
A. AC = 6 in.; CE = 18 in.
B. AC = 15 in.; CE = 5 in.
C. AC = 18 in.; CE = 6 in.
D. AC = 5 in.; CE = 15 in.
Answer:
Since we have BC ║ DE, we know that:
AB/AD = BC/DE
12/(12 + 4) = BC/12
12/16 = BC/12
BC = (12 · 12)/16 = 9 (in)
Applying the pythagorean, we have:
AB² + BC² = AC²
12² + 9² = AC²
225 = AC²
AC = √225 = 15 (in)
Using the information about the parallel lines again, we have:
AC/CE = AB/BD
15/CE = 12/4
CE = (15 · 4)/12 = 5 (in)
So the answer is B
Help please. Select all correct answers
We're given pairs (A,B) and asked if we have
enough calcium,
5A + 4B >= 24
enough iron
4A + 6B >= 15
and enough vitamins
7A + 4B >= 15
We check each constraint on each pair; if we find any false we can stop for that pair.
(A,B)=(1,4)
5(1)+4(4)=21 under 24, NO CHECK
(A,B)=(1,5)
5(1) + 4(5) = 25, bigger than 24, good
4(1) + 6(5) = 34, bigger than 15, good
7(1) + 4(5) = 27, bigger than 15, good CHECK
(A,B)=(2,3)
5(2)+4(3)=22, NO CHECK
(A,B)=(3,2)
5(3)+4(2)=23, NO CHECK
(A,B)=(4,1)
5(4) + 4(1) = 24, ok
4(4) + 6(1) = 22, ok
7(4) + 4(1) = 32, ok, CHECK
Answer:
(1,5), (4,1)
Step-by-step explanation:
Let's check the possible answers and see if they will Steve to meet his requirements:
We'll start by looking if each answer (dose) will provide enough calcium first. If it does, we'll get iron and vitamins if needed.
a) (1,4)
Calcium, at least 24 mg
24 ≤ 5x + 4y
24 ≤ 5 (1) + 4 (4)
24 ≤ 5 + 16
24 ≤ 21
NO!
b) (1,5)
Calcium, at least 24 mg
24 ≤ 5x + 4y
24 ≤ 5 (1) + 4 (5)
24 ≤ 25 YES!
Iron, at least 15 mg
15 ≤ 4x + 6y
15 ≤ 4(1) + 6(5)
15 ≤ 34 YES!
Vitamins, at least 16 mg
16 ≤ 7x + 4y
16 ≤ 7 (1) + 4 (5)
16 ≤ 27 YES
YES, YES, YES...
c) (2,3)
Calcium, at least 24 mg
24 ≤ 5x + 4y
24 ≤ 5 (2) + 4 (3)
24 ≤ 22 NO!
d) (3,2)
Calcium, at least 24 mg
24 ≤ 5x + 4y
24 ≤ 5 (3) + 4 (2)
24 ≤ 23 NO!
e) (4,1)
Calcium, at least 24 mg
24 ≤ 5x + 4y
24 ≤ 5 (4) + 4 (1)
24 ≤ 24 YES!
Iron, at least 15 mg
15 ≤ 4x + 6y
15 ≤ 4(4) + 6(1)
15 ≤ 22 YES!
Vitamins, at least 16 mg
16 ≤ 7x + 4y
16 ≤ 7 (4) + 4 (1)
16 ≤ 32 YES
YES, YES, YES...
Given the statement "If a line is horizontal, then it has slope equal to zero," what is its contrapositive?
Answer:
if a line has a slope equal to zero, then it is horizontal
Step-by-step explanation:
Answer:
If a line does not have zero slope, then it is not a horizontal line.
Step-by-step explanation:
edg
The legs of a right triangle have lengths of 28 and 16. What's the length of the hypotenuse, rounded to the nearest hundredth? A. 32.25 B. 32.45 C. 22.98 D. 22.94
Answer:
h = 32.25.
Step-by-step explanation:
h^2 = 28^2 + 16^2 (Pythagoras theorem).
h = √1040
h = 32.25.
Using the Pythagorean theorem, the length of the hypotenuse in a right triangle with legs of lengths 28 and 16, rounded to the nearest hundredth, is 32.25.
The question asks for the length of the hypotenuse in a right triangle with legs of lengths 28 and 16. To find this, we use the Pythagorean theorem, which states that in a right triangle, the square of the length of the hypotenuse (c) is equal to the sum of the squares of the lengths of the two legs (a and b). Thus, according to the equation a² + b² = c², we substitute the given values to find the hypotenuse length.
Using the given lengths:
a = 28
b = 16
We calculate:
c = √(28² + 16²)
c = √(784 + 256)
c = √(1040)
c = 32.249
Rounded to the nearest hundredth, the length of the hypotenuse is therefore 32.25.
98 POINTS!!!!!!!!!!!!!!!!!!
Answer:
a = 13 and b = 12-5i
Step-by-step explanation:
We need a common denominator
3+2i 5-i
---------- + ---------
3-2i 2+3i
(3+2i) (2+3i) (5-i)(3-2i)
------------------ + --------------------
(3-2i) (2+3i) (2+3i) (3-2i)
Foil the numerators
6 +4i+9i+6i^2 +15-3i-10i+2i^2
------------------ --------------------
(2+3i) (3-2i)
Combine like terms
21 +8i^2
------------------
(2+3i) (3-2i)
We know that i^2 = -1
21 +8(-1)
------------------
(2+3i) (3-2i)
21 -8
------------------
(2+3i) (3-2i)
13
------------------
(2+3i) (3-2i)
Foil the denominator
13
---------------
6 +9i -4i -6i^2
Combine like terms
13
----------------
6+ 5i -6(-1)
13
----------
12 +5i
We know have
13
-------------
12 + 5i
Multiply by the conjugate
13 ( 12-5i)
------------- * -------------
12 + 5i 12 -5i
13 (12-5i)
--------------
144 +25
13(12-5i)
-------------
169
12-5i
------------
13
The parentheses are (12-5i)/13
We need the reciprocal to make the equation become 1
which is 13/ 12-5i
a = 13 and b = 12-5i
Answer:
a = 13
b= 12-5i
Step-by-step explanation:
Simplify the values and i squared will be -1
PLZ HELP ME!!! I NEED THIS DONE BY TONIGHT!!!
1. This kite has a 90 degree angle, which is equivalent to angle B.
2. Distance RB is 2.
3. Distance SB is 1.
4. The kite forms a right triangle.
5. Distance RS is the hypotenuse which has not been given. We can call RS by any variable of choice.
Solve for x: √3-x+13=1
Answer:
√3 + 12 = x
Step-by-step explanation:
Simplify both sides of the equation, isolating the variable.
Answer the following questions.
1. How many favorable outcomes are expressed in the probability 7/9 ?
2. How many possible outcomes are expressed in the probability 14/25 ?
3. What fraction correctly shows the probability of 14 favorable outcomes out of 21 possible outcomes?
(Enter
as a reduced fraction using / for the fraction bar. Do not use any spaces in your answer.. Example: 1/2 is 1/2
4. Which probability is least likely; 17/35, 5/13, 132/425, 1/2?
Answer:
1. 7
2. 25
3. 2/3
4. 132/425
Step-by-step explanation:
Probability is the likelihood of an event occurring and it can be computed by:
[tex]Probability=\dfrac{favorable\hspace{1mm}outcomes}{all\hspace{1mm}possible\hspace{1mm}outcomes}[/tex]
1. So when you are given a probability of 7/9:
[tex]Probability=\dfrac{favorable\hspace{1mm}outcomes}{all\hspace{1mm}possible\hspace{1mm}outcomes}=\dfrac{7}{9}[/tex]
So the answer is 7.
2. Given the probability is 14/25:
[tex]Probability=\dfrac{favorable\hspace{1mm}outcomes}{all\hspace{1mm}possible\hspace{1mm}outcomes}=\dfrac{14}{25}[/tex]
The number of possible outcomes is 25.
3. You have 14 favorable outcomes out of 21 possible outcomes.
[tex]Probability=\dfrac{favorable\hspace{1mm}outcomes}{all\hspace{1mm}possible\hspace{1mm}outcomes}=\dfrac{14}{21}\div \dfrac{7}{7}=\dfrac{2}{3}[/tex]
The answer is 2/3.
The least likely even would be the smallest fraction. If you want to do this the easy way, just change them all to decimal and find the value with the least.
17/35 = 0.49
5/13 = 0.38
132/425 = 0.31
1/2 = 0.5
Since 132/425 = 0.31 is the smallest, then it is the least likely probability.