Step-by-step explanation:
[tex]10x^2+2x-8\\2(5x^2+x-4)\\2(5x-4)(x+1)[/tex]
Answer:
[tex]2(5x-4)(x+1)[/tex]
You can check the answer by re-distributing the 2 and using the foil method :)
(1). An Aeroplane leaves an airport, flies due North for 2 hrs at 500km/h. It then flies on a bearing of 053 degree at 300km/h for 90 mins. How far is the plane from the airport correct to 1 dp *(2). Find the bearing of the plane from the Airport correct to 1 dp. *(3). If it takes the Aeroplane 150 mins to fly back to the airport. Find the average speed of the aeroplane for the whole flight correct to 1dp. *
Answer:
1. 1320.7 km
2. 015.8 degrees.
3. 461.8 km/h.
Step-by-step explanation:
(1) the distance from the airport is approximately 1096.5 km.
(2) the bearing of the plane from the airport is approximately 24.4 degrees.
(3) the average speed of the airplane for the whole flight is approximately 580 km/h.
(1) To find the distance the plane is from the airport, we can break down the two legs of the journey into their respective distances and use the Pythagorean theorem.
For the first leg of the journey, the plane flies due North for 2 hours at a speed of 500 km/h. Therefore, the distance covered is:
Distance = Speed * Time = 500 km/h * 2 h = 1000 km
For the second leg of the journey, the plane flies at a bearing of 053 degrees at a speed of 300 km/h for 90 minutes (1.5 hours). We can calculate the distance covered using the formula:
Distance = Speed * Time = 300 km/h * 1.5 h = 450 km
Using the Pythagorean theorem, the distance from the airport is the hypotenuse of a right triangle with sides of 1000 km and 450 km:
Distance from the airport = √(1000² + 450²) ≈ 1096.5 km (rounded to 1 decimal place)
Therefore, the distance from the airport is approximately 1096.5 km.
(2) To find the bearing of the plane from the airport, we need to determine the angle between the plane's position and the north direction. We can use the inverse tangent function (arctan) to find this angle.
The angle can be calculated as:
Angle = arctan(opposite/adjacent) = arctan(450/1000) ≈ 24.4 degrees (rounded to 1 decimal place)
Therefore, the bearing of the plane from the airport is approximately 24.4 degrees.
(3) To find the average speed of the airplane for the whole flight, we can calculate the total distance traveled divided by the total time taken.
The total distance traveled is the sum of the distances from the first and second legs of the journey:
Total Distance = 1000 km + 450 km = 1450 km
The total time taken is the sum of the time taken for each leg:
Total Time = 2 hours + 1.5 hours + 2.5 hours (150 minutes is equal to 2.5 hours)
Average Speed = Total Distance / Total Time = 1450 km / 2.5 h ≈ 580 km/h (rounded to 1 decimal place)
Therefore, the average speed of the airplane for the whole flight is approximately 580 km/h.
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Five state officials are listed to the right. a. List the 10 possible samples (without replacement) of size 3 that can be obtained from the population of five officials. Governor (Upper G) Lieutenant Governor (Upper L) Secretary of State (Upper S) Representative (Upper R) Press Secretary (Upper P) b. If a simple random sampling procedure is used to obtain a sample of three officials, what are the chances that it is the first sample on your list in part (a)? the second sample? the tenth sample? a. List all 10 possible samples (without replacement) of size 3. Use the letter abbreviation for each official.
Answer:
All possible are:
(G,L,S)
(G,L,R)
(G,L,P)
(G,S,R)
(G,S,P)
(G,R,P)
(L,S,R)
(L,S,P)
(S,R,P)
{L,R,P)
Probability of 1st/2nd/10th sample = 1/10
Step-by-step explanation:
All the possible combinations of the 3 size samples from a 5 size population have been listed without repetition.
Total Numbers of Samples = 10
To find the probability of finding the first sample from random sampling procedure,
Probability = Number of desired outcomes/ Total number of outcomes
Where Number of desired outcome is 1 and total number of outcomes is 10.
Probability = 1/10
Similarly, to find 2nd sample or 10th sample, the number of desired outcomes is same i.e 1, hecne the probability remains the same i.e 1/10
Possible samples:
(G,L), (G,S), (G,A), (G,P), (L,S), (S,A), (A,P), (L,P), (S,P), (A,L).
a) Given:
Population size [tex]N=5[/tex].
Sample size [tex]n=2[/tex]
Possible sample (without replacement)
[tex]\Rightarrow 5C_{2}=\frac{5!}{2!\times 3!}[/tex]
[tex]=\frac{5\times 4}{2}[/tex]
[tex]=10[/tex]
[tex]10 samples:-[/tex]
Governor, Lieutenant Governor, secretary of state, Attorney General, Press (P)
Possible samples:
(G,L), (G,S), (G,A), (G,P), (L,S), (S,A), (A,P), (L,P), (S,P), (A,L).
b) Event: [tex]E\to[/tex]choosing sample second and tenth.
[tex]E=\left\{\left ( G,S \right ),\left ( A,L \right ) \right\}\\n\left ( E \right )=2\\n(S) =10[/tex]
The Probability of that it is the first sample.
Second and tenth sample[tex]=\frac{n\left ( E \right )}{n(S)}[/tex]
[tex]=\frac{2}{10}[/tex]
[tex]=\frac{1}{5}[/tex]
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Given the following functions, find each: f(x)=x2+5x−14 g(x)=x−2 (f+g)(x)= (f−g)(x)=
Answer:
(f+g)(x) = x²+5x-14 + (x-2)
= x²+5x-14+x-2 = x²+6x-16
(f-g)(x) = x²+5x-14 - (x-2)
= x²+5x-14 - x+2
= x²+5x-14-x+2 = x²+4x-12
HELP PLEASE !! NEED HELP ASAPPP !! Will give brainliest !!!
1. what is the measure of angle B? (image included below)
2. What is the value of x? (image included below)
Answer:
1. 47 2. 49
Step-by-step explanation:
1st is complementary and second is supplementary
Answer:
Step-by-step explanation:
b+43˚=90˚
subtract 43˚ from both sides of the equation
b=47˚
3x+33˚=180˚ (because it's a straight angle)
subtract 33˚ from both sides
3x=147˚
divide both sides by 3
x= 49˚
Which of these triangles appears not to be congruent to any others shown
here? Check all that apply.
A
B
C
D
E
F A. Triangle A
B. Triangle B
C. Triangle C
D. Triangle D
E Triangle E
F. Triangle F
Answer:
Options (B) and (D)
Step-by-step explanation:
If two triangles have the same size and shape they are said to be congruent triangles.
Triangles given in the attachment,
Triangles A and E appear to be congruent.
And triangles C and F appear to be congruent.
[Since corresponding sides of these triangles don't appear to be the same in measure]
Remaining triangles B and D do not appear to be congruent.
Therefore, Options (B) and (D) will be the answer.
i need help pls, asap pls !!
Answer:
B
Step-by-step explanation:
How many times does 2 go into 5?
Answer:
answer is 2.5 times....
There are 2.5 times does 2 go into 5.
Since, Division method is used to distributing a group of things into equal parts. Division is just opposite of multiplications.
For example, dividing 20 by 2 means splitting 20 into 2 equal groups of 10.
We have to given that,
To find what times does 2 go into 5.
Now, We can solve as by divide 5 by 2,
⇒ 5 / 2
⇒ 2.5
Thus, A number 5 is 2.5 times 2.
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NEED HELP ASAP PLEASE!!!!!!!!!!!!!!!!
Consider the triangles
What can be concluded about these triangles? Check
all that apply
O The corresponding angles are proportional
The ratios of the corresponding sides are
equivalent
The corresponding sides are congruent.
O The corresponding angles have the same measure
DE corresponds to IH
The corresponding angles have the same measure and the ratios of the corresponding sides are equivalent.
What are similar figures?Similar figures are figures that have the same shape and the ratio of their corresponding sides are proportional. Also, they have the same corresponding angles.
From the triangles, the corresponding angles have the same measure. Hence, they are similar and the ratios of the corresponding sides are equivalent.
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Answer:
hi im sorry im late, the answers would be:
1. The ratios of the corresponding sides are equivalent.
2. The corresponding angles have the same measure
3. DE corresponds to IH.
Step-by-step explanation: here's proof :)
have a good day!!
This formula v = u + at, links:
initial velocity (u)
final velocity (v)
acceleration (a)
time (t)
What is the value of v if u = 5, a = 10 and t = 2?
Answer:
[tex]v=u+at[/tex]
[tex]v= 5+(10)\times2\\v=25[/tex]
I WILL MARK YOU BRAINLIEST!!!
Answer:
A
Step-by-step explanation:
7th grade math I need some help
Answer:
Step-by-step explanation:
[tex](-14+\frac{3}{2}b)-(1+\frac{8}{2}b)=-14-1+\frac{3}{2}b-4b[/tex]
= ([tex]-15-\frac{5}{2}b[/tex])
[tex](5+2b)+(2b+\frac{3}{2})=(5+\frac{3}{2})+(2b+2b)[/tex]
= [tex](4b+\frac{13}{2})[/tex]
[tex](\frac{7}{2}b-3)-(8+6b)[/tex] = [tex](\frac{7}{2}b-6b)-(3+8)[/tex]
= ([tex]-\frac{5}{2}b-11[/tex])
[tex](-10+b)+(7b-5)=(-10-5)+(b+7b)[/tex]
= [tex](8b-15)[/tex]
It is a Saturday morning, and Jeremy has discovered he has a leak coming from the water heater in his attic. Since plumbers charge extra to come out on weekends, Jeremy is planning to use buckets to catch the dripping water. He places a bucket under the drip and steps outside to walk the dog. In half an hour, the bucket is 3/5 of the way full. What is the rate at which the water is leaking per hour?
Answer:
Rate = 3/5 bucket / 1/2 hour
= 6/5 or 1 1/5 buckets per hour
PLs help me find the surface area of the box thxsssss
Answer:
290 in^2
Step-by-step explanation:
front side x 2 = 176
top + bottom = 48
sides x 2 = 66
Sum = 290
Answer:
Total surface area S_tot = 290 in² thus c. is your answer
Step-by-step explanation:
length l = 8 in
width w = 3 in
height h = 11 in
diagonal d = 13.9283883 in
total surface area S_tot = 290 in²
lateral surface area S_lat = 242 in²
top surface area S_top = 24 in²
bottom surface area S_bot = 24 in²
volume V = 264 in³
Formula and Agenda:
Formulas for a rectangular prism:
Volume of Rectangular Prism:
V = lwh
Surface Area of Rectangular Prism:
S = 2(lw + lh + wh)
l = length
w = width
h = height
d = diagonal
S_tot = total surface area
S_lat = lateral surface area
S_top = top surface area
S_bot = bottom surface area
V = volume
i need help!How would i find the value of X?
24. John buys 20 bunches of bananas
For N5. He sells them all for N6.50.
What is his percentage profit?
(a) 3/12%
(b) 20%
(c) 30%
(d) 762/13%
(e) 77%
Answer:
30%
Step-by-step explanation:
Profit(Gain)% = [tex]\frac{Selling price - Cost price}{Cost price} * 100%[/tex]
Selling price = N6.50
Cost price = N5
∴ Profit% = [tex]\frac{N6.50 - N5 }{N5} * \frac{100}{1}[/tex]
= [tex]\frac{1.5}{5} * \frac{100}{1}[/tex]
= (1.5 * 20)%
= 30%
Hope this helps!!!
A card is drawn at random from a standard pack of 52 playing cards. What is the probability of drawing a number greater than 5
Answer:36/52, simplified to 9/13 or 69.23%
Step-by-step explanation:
Need to pick 6, 7, 8, 9, 10, J, Q, K, A (9 cards per suit)
4 suits x 9 cards
36 cards
Answer:
uhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhh sorry needed the points lol
Solve the equation A = bh for b.
Answer:
You have to divide both sides by h, in order to make b the subject :
[tex]A = bh[/tex]
[tex]A \div h = bh \div h[/tex]
[tex] \frac{A}{h} = bh \times \frac{1}{h} [/tex]
[tex] \frac{A}{h} = b[/tex]
[tex]b = \frac{A}{h} [/tex]
Answer:
b=a/h
Step-by-step explanation:
Rewrite the equation as bh=a
Divide each term by h and simplify
b=a/h
The measure of angle JKL can be represented using the expression 3x + 5. Point K has three lines extending from it. One line extends to point J, another to point M, and the other to point L. Angle J K M is 45 degrees. Angle M K L is x degrees. What is the degree measure of AngleJKL? °
Answer:
its 65
Step-by-step explanation:
The measure of ∠JKL = 3 x 20 + 5 = 65 degrees.
We have three lines extending from point K such that one line extends to point J, another to point M, and the other to point L.
We have to determine the degree measure of ∠JKL .
Define Angle.An angle is formed when two straight lines or rays meet at a common endpoint. The common point of contact is called the vertex of an angle.
According to the question, we have -
Measure of ∠JKL = 3x + 5
Measure of ∠JKM = 45 degrees
Measure of ∠MKL = x degrees
Refer to the image attached for more clarity. It can be seen from the image that -
∠JKL = ∠JKM + ∠MKL
3x + 5 = 45 + x
3x - x = 45 - 5
2x = 40
x = 20
Therefore, the measure of ∠JKL = 3 x 20 + 5 = 65 degrees.
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Find m∠UTS, if m∠UTV=x+15, m∠VTS=140∘, and m∠UTS=15x+15.
Answer:
165
Step-by-step explanation:
First, m<UTS=m<UTV+m<VTS by Angle Addition Postulate. Then, you substitute all the values that you provided for the angles. 15x+15=x+15+140. You then solve for x.
15x+15=x+155
14x=140
x=10
You then plug back in 10 for X in the value of m<UTS. 15(10)+15=165
What is the formula for the circumference of a circle in terms of r?
Answer:
2 x pi x r
Step-by-step explanation:
i just copy n pasted this on google
Step-by-step explanation:
c= 2πr
What is the answer? Pls help
Answer:
D
Step-by-step explanation:
Plug in 6 as x in the function
h(6) = 3(6) - 4
h(6) = 18 - 4
h(6) = 14
Answer:
The answer is 14 because 3 x 6 is 18 and 18 - 4 is 14
Step-by-step explanation:
Two opposite sides of a parallelogram are 3x-8 and 10x+13. Find the measure of all sides
Answer:
Step-by-step explanation:
Using the parallelogram theorem
3x-8 = 10x+13
-7x = 21
x = -3
Substitute
3(-3) - 8
-17
10(-3) + 13
-17
The function f(x) is shown in the graph above
The function g(x) = -2x - 5
compare the slopes
A. The slope of f(x) is undefined and the slope of g(x) is negative
B. the slope of f(x) is the same as the slope of g(x)
C. The slope of f(x) is less than the slope of g(x)
D. The slope of f(x) is greater than the slope of g(x)
Answer:
B. the slope of f(x) is the same as the slope of g(x)
Step-by-step explanation:
B. the slope of f(x) is the same as the slope of g(x); that slope is m = -2.
Answer:
D ye
Step-by-step explanation:
If the first term of an AP is 'a' and the common difference is 'd', then the sum of n terms of an AP is _______
If the first term of an AP is 'a' and the common difference is 'd', then the sum of n terms of an AP is
[tex] \frac{n}{2} \times 2a + (n - 1)d[/tex]
There are only red counters and blue counters in a bag the ratio of the number of red counters to the number of blue counters is 4:6 write the ratio in the simplest form
solve using eliminates method 3x-4y=15 2x-2y=8
Answer:
Step-by-step explanation:
what is the surface area of cylinder with base radius 4 and height 7? either enter an exact answer in term of pi or use for 3.14 for pi and enter your answer as a decimal
Answer:
Step-by-step explanation:
The surface area of the sides of the cylinder is A = 2πrh, where r is the radius and h is the height.
Here this comes out to A = 2π(4)(7) = 56 π units^2
If you also want the combined area of the two ends (top and bottom of the cylinder), here's the calculation:
A = 2πr² = 2π(4 units)² = 32π units²
Answer:
its 88 pi
Step-by-step explanation:
i did it on khan
Help me please on this question
Answer:
Step-by-step explanation:
Given : QP║RT and QR║US
To prove: ∠1 ≅ ∠5
Statements Reasons
1). QP║RT 1). Given
2). QR║US 2). Given
3). ∠1 ≅ ∠2 3). Alternate angles
∠2 ≅ ∠5
4). ∠1 ≅ ∠5 4). Transitive property
Reasons for third step,
PQ║RT and QR is a transverse therefore, ∠1 and ∠2 will be alternate angles.
Similarly, QR║US and RT is a transverse therefore, ∠2 and ∠5 will be the alternate angles.
Richard's Rental Car charges a $55 rental fee and $0.25 per mile. Freddy's Rental Car charges a
$45 rental fee and $0.35 per mile. For how many miles, X, will the total charge of Richard's
Rental Car be no more than the total charge of Freddy's Rental Car?
2 < 10
> 10
> 100
2 < 100
Answer:
Correct option: third one -> X > 100
Step-by-step explanation:
The equation for the price of Richard's Rental Car is:
P1 = 55 + 0.25*X
The equation for the price of Freddy's Rental Car is:
P2 = 45 + 0.35*X
To find for how many miles will the total charge of Richard be less than Freddy, we have that P1 < P2, so:
55 + 0.25*X < 45 + 0.35*X
0.25*X - 0.35*X < 45 - 55
-0.1*X < -10
0.1*X > 10
X > 100
Correct option: third one
What is the quotient?
StartFraction (negative 3) Superscript 0 Over (negative 3) squared EndFraction
Answer:
1/9
Step-by-step explanation:
Where my coins at bruh and yo number jhit
The value of the expression {(-3)⁰}/{(-3)²} is 1/9.
What is an exponent?Exponentiation is one of the mathematics operations.
Let mᵃ, where m and a are the real numbers.
And m is multiplied by a times to itself.
So, a is the exponent of m.
Given:
Start Fraction (negative 3) Superscript 0 Over (negative 3) squared End Fraction
In numerator form:
{(-3)⁰}/{(-3)²}
= 1/9
Therefore, 1/9 is the value.
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