Answer:
Step-by-step explanation:
To begin, get everything but the x terms on one side of the equation by subtracting the 62. That gives us
[tex]x^2+16x=-55[/tex]
Next, take half the linear term, square it, and add it to both sides. Our linear term is 16. Half of 16 is 8, and 8 squared is 6, so add 64 to both sides:
[tex]x^2+16x+64=9[/tex]
The reason we do this is to get a perfect square binomial on the left, which looks like this:
[tex](x+8)^2=9[/tex]. Undo the squaring on the left by taking the square root of both sides. Doing this leaves x + 8 on the left, but + or - 3 on the right:
x + 8 = 3 and x + 8 = -3. Solving each of these equations gives you your 2 solutions:
x = -5 and x = -11
How many different 4-digit PIN codes are there that only include the digits 5, 9, 6 and 2?
Answer:
256
Step-by-step explanation:
The digits can only be one of four numbers.
4*4*4*4 = 4^4 = 256
Here are five number cards.
2
5
7
8.
CO
One of the cards is removed and the mean average
of the remaining four number cards is 6
+
Which card was removed?
You must show your working.
+
Note: Please make sure your final answer says card ...
EC
brate Geb
Answer:
um I think that it could be 7 are 2
How to show 12.8 x 1/4
Answer:
12.8 × 1/4
=128/10×1/4
= 128 × 1
10 × 4
= 128/40
= 128 ÷ 8
40 ÷ 8
= 16/5= 3 1/5
16/5
Step-by-step explanation:
Answer:
Step by step on...How to multiply 12.8 x 1/4
Step-by-step explanation:
First off...1/4 is the same to... .25
so
1. 12.8 x .25 to 12.80
x .25
multiply 5 with zero which is zero
12.80
x .25
0
2. multiply 5 with 8 which is 40 ...put 4 above 2
4
12.80
x .25
00
3. multiply 5 with 2 which is 10 then add 4, which 14. Leave the four and put 1 on top of 1
1
12.80
x .25
4 00
_____________________________________
4. Then multiply 5 with 1 which is still 5 then add one which is 6
12.80
x .25
64 00
_______________________________-
5. then put underneath whatever we have a zero under
12.80
x .25
64 00
0
______________________________________________
6. multiply 2 with 0 which is 0 then 2 with 8 which is 16...put down 6 and put up the number 1 above 2
1
12.80
x .25
64 00
600
____________________________________
7 . multiply 2 with 2 which is 4 then add 1 which is 5 put down 5 and multiply 2 with 1 soo
12.80
x .25
64 00
25600
______________________________
8. then add them up.
12.80
x .25
64 .00
256.00
32000
then move the decimal 4 times to the left
12.80
x .25
3 . -2-0-0-0
-FINAL!
12.80
x .25
3.2
If point A, having
coordinates (p, 3) and
point B, with coordinates
(6, p) lie on a line having
a slope of 2, what is the
value of p?
gradient or slope=y2 -y1
x2 - x1
so for A, p is x1 and 3 is y1..
For B, 6 is x2 and p is y2
2= p - 3
6 - p
2 ( 6 - p) = p - 3
12 - 2p = p - 3
-2p + p = -3 - 12
-p = - 15
p = 15
A ball is thrown from an initial height of 4 feet with an initial upward velocity of 23 f/s. The ball's height h (in feet) after t seconds is given by the following. Find all values of t for which the ball's height is 12 feet.
Answer:
Time taken = 0.85 and 0.59 (Approx.)
Step-by-step explanation:
Given:
Initial height = 4 feet
Initial upward velocity = 23 f/s
Equation;
h = 4 + 23t - 16t² for h = 12 feet
Find:
Time taken
Computation:
h = 4 + 23t - 16t² for h = 12 feet
12 = 4 + 23t - 16t²
16t² -23t + 8 = 0
t = [-b±√b²-4ac] / 2a
t = [23±√23²-(4)(16)(8)] / 2(16)
t = [23±√529-512] / 32
t = [23±4.12]/32
Time taken = 0.85 and 0.59 (Approx.)
(3x+6)(4x-8)=0
Find for x
Answer:
2
Step-by-step explanation:
( 3x + 6 ) ( 4x - 8 ) = 0
( 3x + 6 ) = 0 / ( 4x - 8 )
3x + 6 = 0
3x = 6
x = 6 / 3
x = 2
what is sqare root of 64
Answer:
square root of 64
√64 =8,,
Answer:
Hi Mate.,
Step-by-step explanation:
8*8=64
So 8 is the sq root.
thanks!
Which of the following is equal to tan θ using coordinates on the unit circle? Question 18 options: A) x∕y B) y C) y∕x D) x
Step-by-step explanation:
tan 0 = y/x (as a drawing attached)
The requried, y/x is equal to tan θ using coordinates on the unit circle. Option C is correct.
What is a circle?The circle is the locus of a point whose distance from a fixed point is constant i.e center (h, k). The equation of the circle is given by
(x - h)² + (y - k)² = r²
where h, k is the coordinate of the center of the circle on a coordinate plane and r is the radius of the circle.
Here,
In a unit circle, the coordinates of a point on the circle are (cos θ, sin θ), where θ is the angle formed by the radius of the circle and the positive x-axis. Therefore, the tangent of θ is given by the ratio of sin θ to cos θ, which is (sin θ)/(cos θ) = y/x. Simplifying this expression, we get tan θ = y/x.
Therefore, the answer is option C) y/x.
Learn more about Circle here:
brainly.com/question/11833983
#SPJ3
What is the common ratio of the sequence −8, 12,−18, 27, ...
Answer:
-3/2
Step-by-step explanation: Divide 12 by 8 and you get 3/2. Since the sign alters, the ratio is negative.
Alice and her friend Emma leave on different flights from the same airport. Alice's flight flies 100 miles due south, then turns 70° toward west and flies 50 miles. Emma's flight flies 100 miles due north, then turns 50° toward east and flies 50 miles. Which fight among you is farther from the airport? Explan your rreasoning
don't spam!
9514 1404 393
Answer:
Emma's flight is farther from the airport
Step-by-step explanation:
Even without doing any detailed calculation, you can see on a graph that the larger turn Alice's flight makes keeps it closer to the airport.
Emma's flight is farther from the airport.
__
The distance can be calculated using the Law of Cosines. The angle of interest is the supplement of the turn angle. Since the leg distances are the same in each case, the only variable affecting the distance from the airport is the angle measure. Again, the larger the turn, the shorter the distance from the airport. If T is the turn angle, the distance is ...
d² = 100² +50² -2·100·50·cos(180° -T)
d² = 12500 +10000·cos(T) . . . . . . . using cos(180°-T) = -cos(T)
d = 100√(1.25+cos(T))
For Alice's 70° turn, the distance is ...
d = 100√(1.25+0.342) ≈ 126.18 mi
For Emma's 50° turn, the distance is ...
d = 100√(1.25 +0.643) ≈ 137.58 mi
Emma's flight is farther from the airport.
_____
The law of cosines formula is ...
c² = a² +b² -2ab·cos(C)
where triangle sides are lengths a, b, c and angle C is opposite side c.
What is the percent of change from
82 to 67?
Answer:
-18.29
Step-by-step explanation:
Cost of dinner = $30 Tip = 20% Total paid _?
Answer:
36$
Step-by-step explanation:
20 percent of 30 is 6
30+6=36
Allowing 20% discount on the marked price. of 아 a watch, the value of the watch will be Rs. 2378. If the VAT of 10% is added, find it's M.P.
Answer:
The marked price of the watch is $2,702.27.
Step-by-step explanation:
Since allowing 20% discount on the marked price of a watch, the value of the watch will be Rs. 2378, to determine, if the VAT of 10% is added, it's marked price, the following calculation must be performed:
1 - 0.2 = 0.8
0.8 x 1.1 = 2378
0.88 = 2378
0.88 = 2378
0.8 = X
0.8 x 2378 / 0.88 = X
1,902.4 / 0.88 = X
2,161.81 = X
0.8 = 2,161.81
1 = X
2,161.81 / 0.8 = X
2,702.27 = X
Therefore, the marked price of the watch is 2,702.27.
Suppose the speeds of cars along a stretch of I-40 is normally distributed with a mean of 70 mph and standard deviation of 5 mph. Use the 68-95-99.7 rule to answer the following questions.
(a) Approximately what percent of cars are travelling between 65 and 75 mph? percent
(b) If the speed limit on this stretch of highway is 65 mph, approximately what percent of cars are traveling faster than the speed limit? percent
(c) What percent of cars are traveling at a speed greater than or equal to 80 mph? (Answer to one decimal place.)
(d) What percent of cars are traveling at a speed greater than 80 mph? (Answer to one decimal place.) percent
(e) 95% of cars are traveling between what two speeds? (Answer to two decimal places) Between mph and mph
Answer:
a) 68%.
b) 84%.
c) Approximately 2.5% of cars are traveling at a speed greater than or equal to 80 mph.
d) Approximately 2.5% of cars are traveling at a speed greater than or equal to 80 mph.
e) Between 60 mph and 80 mph.
Step-by-step explanation:
The Empirical Rule states that, for a normally distributed random variable:
Approximately 68% of the measures are within 1 standard deviation of the mean.
Approximately 95% of the measures are within 2 standard deviations of the mean.
Approximately 99.7% of the measures are within 3 standard deviations of the mean.
In this problem, we have that:
Mean of 70 mph, standard deviation of 5 mph.
(a) Approximately what percent of cars are travelling between 65 and 75 mph?
70 - 5 = 65
70 + 5 = 75
Within 1 standard deviation, so approximately 68%.
(b) If the speed limit on this stretch of highway is 65 mph, approximately what percent of cars are traveling faster than the speed limit?
The normal distribution is symmetric, which means that 50% of the measures are below the mean, and 50% are above.
65 is one standard deviation below the mean, so of the cars below the mean, 68% are above 65 mph.
0.68*50% + 50% = 34% + 50% = 84%.
84%.
(c) What percent of cars are traveling at a speed greater than or equal to 80 mph?
80 = 70 + 2*10
2 standard deviations above the mean.
Approximately 95% of the measures are within 2 standard deviations of the mean. Due to the symmetry of the normal distribution, of the other 5%, 2.5% is at least 2 standard deviations below the mean and 2.5% is at least 2 standard deviations above the mean. Then:
Approximately 2.5% of cars are traveling at a speed greater than or equal to 80 mph.
(d) What percent of cars are traveling at a speed greater than 80 mph?
Same as item c, as in the normal distribution, the probability of an exact value is considered to be 0.
(e) 95% of cars are traveling between what two speeds?
Within two standard deviations of the mean.
70 - 2*5 = 60 mph
70 + 2*5 = 80 mph.
Between 60 mph and 80 mph.
Solve 3/4w≤24 Graph the solution
Answer:
w<32
Step-by-step explanation:
In triangle RST, mZR> m_S+ m2T. Which must be true of triangle RST? Check all that apply.
O mzR > 90°
OmZS + m2T < 90°
Om S = m_T
mZR>m_T
mZR > m_S
mzS>m_T
Answer:
m∠R > 90°
m∠S + m∠T < 90°
m∠R > m∠T
m∠R > m∠S
Step-by-step explanation:
Here, RST is a triangle
Therefore, m∠R+m∠S+m∠T = 180° ⇒ m∠S+m∠T = 180° - m∠R
Given: m∠R > m∠S + m∠T
⇒ - m∠R < - (m∠S + m∠T) (by multiplying -1 on both sides)
⇒ 180° - m∠R < 180° - (m∠S + m∠T) (by adding 180° on both sides)
⇒ m∠S+m∠T < 180° - (m∠S + m∠T)
⇒ m∠S+m∠T+m∠S+m∠T < 180° (by adding m∠S + m∠T on both sides)
⇒ 2(m∠S+m∠T) < 180°
⇒ m∠S+m∠T < 90°
⇒ m∠R > 90° ( because m∠R+m∠S+m∠T=180° )
Again, m∠R > m∠S + m∠T
⇒ m∠R > m∠S and m∠R > m∠T
Thus, Option first, second, fourth and fifth are correct.
anyone know this? the box is just there when I have the answer so it's okay but I dont understand this anyone can help?
9514 1404 393
Answer:
1/10
Step-by-step explanation:
The product of fractions is the product of the numerators, divided by the product of the denominators.
[tex]\dfrac{1}{2}\text{ of }\dfrac{1}{5}=\dfrac{1}{2}\times\dfrac{1}{5}=\dfrac{1\times1}{2\times5}=\boxed{\dfrac{1}{10}}[/tex]
__
Additional comment
When working with fractions and percentages, you will find that "of" often means "times."
Which is a net for a cube
Answer:
wy m by that??!???? im confused
Chase is 7 years older than Zoe. In 4 years the sum of their ages will be 41. How old is chase now?
Answer:
Chase would be 24 years old
Simplify the expression:
7y+9+7–2y
Answer:
5y+16
Step-by-step explanation:
see image below:)
Answer:
5y+16
Step-by-step explanation:
like terms y and y
7y-2y
9+7
5y+16
Question 1 Simplify: 5!
Group of answer choices
5 120 80 20
Question 2 Simplify: 6!/3!
Group of answer choices
24 90 30 120
Question 3 Simplify: 12!/10! Group of answer choices 132 120 1320 12 Question 4 Simplify: {6! \times 5!}{4! \times 3!} 6!×5!4!×3!
Group of answer choices
60 55 600 5.5
Answer:
6535
Step-by-step explanation:
collect your own thinikng
Answer:
1. 120
2. 120
3. 132
4. 600
Rachel is solving the system of equations below by using the elimination method. Which of the following steps could she use? 7x-21y=14. 2x+3y=11
Answer:
[tex]7x - 21y = 14 - - - (a) \\ 2x + 3y = 11 - - - (b) \\ (a) + 7 \times (b) : \\ 21x + 0y = 91 \\ x = 4.33 \\ (2 \times 4.33) + 3y = 11 \\ 3y = 2.34 \\ y = 0.78 \\ { \boxed{x = 4.33}} \\ { \boxed{y = 0.78}}[/tex]
In square inches, what is the area of the composite shape?
**DO NOT INCLUDE LABELS IN YOUR ANSWER!
8 in.
X
8 in.
Answer:
40[tex]\pi[/tex]
or 125.66 rounded
Step-by-step explanation:
area of triangle:
1/2(b*h)
1/2(8*8)
1/2(64)
=32
area of half circle:
[tex]\pi r^{2}[/tex]/2
[tex]\pi r^{2}[/tex]/2
[tex]\pi 4^{2}[/tex]/2
[tex]\pi16[/tex]/2
[tex]\pi8[/tex] or 8[tex]\pi[/tex]
So, 8[tex]\pi[/tex] + 32=40[tex]\pi[/tex]
Question 21 of 25
Scientists release 10 frogs into a pond in year 0. Each year, there are 4 times
as many frogs as the year before. How many frogs are in the pond after x
years? Write a function to represent this scenario.
A. f() = 4(x) 10
B. f(x) = 10(2)
c. f(x) = 4(10)*
D. f(x) = 10(4)
SUBMIT
Step-by-step explanation:
answer is = D
D = f(x) = 10 (4)
What is the radius of C?
A planet rotates through one complete revolution every 26 hours. Since the axis of rotation is perpendicular to the equator, you can think of a person standing on the equator as standing on the edge of a disc that is rotating through one complete revolution every 26 hours. Find the angular velocity of a person standing on the equator.
Answer:
23.5 degree stands tap of the floor
Eight less than the product of three and a number is twenty two
Answer:
let x represent the missing number
3x-8=22
3x=22+8
3x=30
3x/3=30/3
x=10
Step-by-step explanation:
hope this is helpful
Answer:
3x - 8 = 22
Step-by-step explanation:
always use x as "the number"
remember product means multiply!
8 less than the product of three and a number
3x - 8
lastly, "is 22"
"is" means equals
3x - 8 = 22
I hope this helps!!
what is the slope of a line between (-4,14) and (-16,8)
Answer:
[tex] \frac{1}{2} [/tex]
Step-by-step explanation:
slope :
[tex]slope \: = \: \frac{y2 - y1}{x2 - x1} = \frac{8 - 14}{ - 16 - - 4} = \frac{ - 6}{ - 12} = \frac{1}{2} [/tex] = 0.5
What value of x is in the solution set of 8x -
- 6 > 12 + 2x?
Answer:
x>2 (x=any number greater than 2)
Step-by-step explanation:
8x-6>12+2x
-2x -2x
6x-6>12
+6 +6
6x>12
/6 /6
x>2
:) ur welcome
(08.02 MC)
A pair of equations is shown below:
y = 2x − 1
y = 4x − 5
Part A: In your own words, explain how you can solve the pair of equations graphically. Write the slope and y-intercept for each equation that you will plot on the graph to solve the equations. (6 points)
Part B: What is the solution to the pair of equations? (4 points)
Answer:
Complete y = Mx + b
Step-by-step explanation:
