Answer:
a. f(-2) = -6
b. f(0) = 6
c. f(2) = 10
Step-by-step explanation:
The function is given as:
f(x) = 5x + 4 if x < 0
f(x) = 2x + 6 if x ≥ 0
(a) f(-2)
x < 0:
=> f(-2) = 5(-2) + 4
f(-2) = -10 + 4
f(-2) = -6
(b) f(0)
x ≥ 0:
=> f(0) = 2(0) + 6
f(0) = 6
(c) f(2)
x ≥ 0:
=> f(2) = 2(2) + 6
f(2) = 4 + 6
f(2) = 10
Find the total surface area of this cylinder. Give your answer to one decimal place PLEASE HELP THANK YOUUUU
Answer:
Step-by-step explanation:
surface area of cylinder=2 πr²+2πrh
=2πr(r+h)
=2π×12(12+18)
=24π×30
=720π
≈2261.9 cm²
Which of the following is the correct factored form of the given equation? 6x^2 -13x - 8 = 0
Answer:
the 2nd
Step-by-step explanation:
Consider the graph with four lines below. On a coordinate plane, line a has a positive slope and goes through points (negative 1, 0) and (1, 2), line b has a negative slope and goes through (negative 2, 2) and (negative 1, negative 1), line c has a negative slope and goes through (0, 3) and (1, 0), and line d is horizontal at y = 1. By inspection, which system would have no solution? line a and line b line a and line c line b and line c line b and line d
Answer:
C) line b and line c
Step-by-step explanation:
On edge
A line is a one-dimensional shape that is straight, has no thickness, and extends in both directions indefinitely. The system of equations that do not have any solution is line b and line c. Hence, the correct option is C.
What is the equation of a line?A line is a one-dimensional shape that is straight, has no thickness, and extends in both directions indefinitely. The equation of a line is given by,
y =mx + c
where,
x is the coordinate of the x-axis,
y is the coordinate of the y-axis,
m is the slope of the line, and
c is the y-intercept.
The equation of line a passing through (-1,0) and (1,2) are,
m = (0-2)/(-1-1) = -2/-2 = 1
y= x + c
0 = -1 + c
c = 1
Equation of line 1, y=x+1
The equation of line b passing through (-2,2) and (-1,-1) are,
m = (2+1)/(-2+1) = 3/-1 = -3
y= -3x + c
-1 = -3(-1) + c
c = -4
Equation of line 1, y=-3x-4
The equation of line c passing through (0,3) and (1,0) are,
m = (3-0)/(0-1) = 3/-1 = -3
y= -3x + c
3 = -3(0) + c
c = 3
Equation of line 1, y=-3x+3
Also, the equation of line d is y=1
The solution of two-equation is the point at which the two equations are not intersecting. Therefore, the system of equations that do not have any solution is line b and line c.
Hence, the correct option is C.
Learn more about Equation of Line:
https://brainly.com/question/21511618
#SPJ2
x is partly constant and partly varies with y. When y=3, x = 7 and when y = 6, x = 9. Find x when y = 4
Answer:
x=23/3
Step-by-step explanation:
x=c+ay
7=c+3a | *(-1)
9=c+6a
-7=-c-3a
9=c+6a
------------
9-7=c-c+6a-3a
2=3a
a=2/3
7=c+3*2/3
7=c+2
-2 -2
5=c
so x=5+2/3*y
when y=4 then x=5+2/3*4=5+8/3
x=15/3+8/3
x=23/3
what is the equation of the graph below
Answer:
y = csc (x) + 2
Step-by-step explanation:
From the graph, we can derive the parent function y = csc(x). Notice how there are asymptotes at x = 2πk and x = π + 2πk, which is where csc(x) is undefined.
Finally, we can see a vertical shift of 2 which we can see from the mid-line of the graph which is at y = 3.
Answer:
c
Step-by-step explanation:
edg 2021
Which measurements could represent the side lengths of a right triangle?
4 m, 6 m, 10 m
5 ft, 8 ft, 9 ft
O 16 cm, 30 cm, 34 cm
o 18 in., 24 in., 42 in.
Answer:
16 cm, 30 cm, 34 cm
Step-by-step explanation:
I got this answer simply by plugging each number into my calculator with the following equation:
[tex]\sqrt{x^{2} +y^{2} }[/tex]
When you the lower numbers into the equation, if the lengths really do give you a triangle, then you should get the largest number as your output. This can help you with any of the other questions that you may have to answer.
Only the measurements of 16 cm, 30 cm, and 34 cm could represent the side lengths of a right triangle.
What are Pythagorean triplets?In a right-angled triangle, its sides, such as hypotenuse, and perpendicular, and the base is Pythagorean triplets.
Here,
The side lengths of a right triangle must satisfy the Pythagorean theorem, which states that the sum of the squares of the two shorter sides (the legs) is equal to the square of the longest side (the hypotenuse). Therefore, we need to check which sets of measurements satisfy this condition.
Only the measurements of 16 cm, 30 cm, and 34 cm could represent the side lengths of a right triangle.
For the first set of measurements, we have:
a = 16 cm, b = 30 cm, c = 34 cm
a² + b² = 256 + 900 = 1156
c² = 1156
Since a² + b² = c², these measurements do represent the side lengths of a right triangle.
Learn more about Pythagorean triplets here:
brainly.com/question/22160915
#SPJ5
Please answer this....
Answer:
c) [tex]2\frac{23}{30}[/tex] d)[tex]1\frac{23}{24}[/tex]
7) a. [tex]6\frac{3}{11}[/tex] kg b. [tex]6 \frac{2}{3}[/tex] cm c. 20 cm
d. [tex]9\frac{9}{10}[/tex] kg e. 10 g f. [tex]23 \frac{1}{4}[/tex] kg
Step-by-step explanation:
c) [tex]8\frac{2}{3}[/tex] - [tex]5\frac{9}{10}[/tex]
First we will change to improper fraction and then solve
[tex]\frac{26}{3} - \frac{59}{10}[/tex]
= [tex]\frac{260 - 177}{30}[/tex]
= [tex]\frac{83}{30}[/tex]
we will now change to mixed number
= [tex]2\frac{23}{30}[/tex]
d) [tex]8\frac{1}{8} - 6\frac{1}{6}[/tex]
we will first change it to improper fraction and then solve
= [tex]\frac{65}{8} - \frac{37}{6}[/tex]
= [tex]\frac{390 - 296}{48}[/tex]
= [tex]\frac{94}{48}[/tex]
we can reduce the fraction
=[tex]\frac{47}{24}[/tex]
we will change it mixed number
=[tex]1\frac{23}{24}[/tex]
7)
a. [tex]\frac{3}{11}[/tex] of 23
= [tex]\frac{3}{11}[/tex] × 23
= [tex]\frac{69}{11}[/tex]
=[tex]6\frac{3}{11}[/tex] kg
b. [tex]\frac{2}{3}[/tex] of 10 cm
= [tex]\frac{2}{3}[/tex] × 10 cm
= [tex]\frac{20}{3}[/tex] cm
=[tex]6 \frac{2}{3}[/tex] cm
c. [tex]\frac{5}{6}[/tex] of 24cm
= [tex]\frac{5}{6}[/tex] × 24 cm
6 will divide 24
=5 × 4 cm
= 20 cm
d. [tex]\frac{3}{10}[/tex] of 33 kg
= [tex]\frac{3}{10}[/tex] × 33 kg
=[tex]\frac{99}{10}[/tex] kg
=[tex]9\frac{9}{10}[/tex] kg
e. [tex]\frac{2}{7}[/tex] of 35 g
= [tex]\frac{2}{7}[/tex] × 35 g
7 will go into 35
=2×5 g
=10 g
f. [tex]\frac{3}{4}[/tex] of 31 kg
= [tex]\frac{3}{4}[/tex] × 31 kg
=[tex]\frac{93}{4}[/tex] kg
=[tex]23 \frac{1}{4}[/tex] kg
20 PTS, BRAINLIEST AND EXCELLENT VOTE!!
Answer:
Median: 15
Range: 9
25th: 14
75th: 17
IQR: 3
Shannon rolls 2 fair dice and adds the results from each. Work out the probability of getting a total of 13.
Answer:
0.
Step-by-step explanation:
Fair dice are dice that have 6 sides, and the probability of rolling a side is the same as rolling another.
Since each die has 6 sides, the most you can get from the two dice are 6 + 6 = 12. Therefore, getting a 13 is impossible. So, there is a probability of 0.
Hope this helps!
Steve works at an apple orchard and is paid by the bushel for the apples he harvests each day. If Steve harvests 42 bushels or less per day, he is paid y dollars per bushel. If Steve harvests more than 42 bushels per day, he receives y dollars per bushel for the first 42 bushels and is paid 1.5 times that amount for each additional bushel. How many bushels of apples did Steve harvest yesterday
Answer:
The information given in the question to solve it is insufficient.
The complete question related to this found at GMAT club forum is stated below:
Steve works at an apple orchard and is paid by the bushel for the apples he harvests each day. For the first 42 bushels Steve harvests each day, he is paid y dollars per bushel. For each additional bushel over 42, he is paid 1.5y. How many bushels of apples did Steve harvest yesterday?
1. Yesterday, Steve was paid $180 for the apples he harvested.
2. Today, Steve was paid $240, and he harvested 10 more bushels of apples than he harvested yesterday.
Step-by-step explanation:
1st 42 bushels Steve harvests each day:
Payment of 1 bushel = y dollar
Payment of ≤ 42 bushel = 42× y = $42y
Payment for Additional bushel after the 1st 42 bushels = 1.5y per bushel
Yesterday's Payment = $180
Today's payment = $240
Let the total number Steve harvested yesterday = p
Today he harvested 10 more bushels than he did yesterday
Total number Steve harvested today = p + 10
Now looking at the information in the question:
First statement did not tell us the amount he harvested that got him that pay, so it's insufficient. Second statement alone two is not sufficient to determine yesterdays pay.
In both statement, we were not told if he harvested more or less than 42 yesterday. Neither were we told if the additional 10 bushels was after he had harvested more than 42 bushels.
Let's assume the additional 10 bushels was after he had harvested more than 42 bushels (that is he harvested 42 yesterday) .
Difference in payment = 240-180 = 60
For the additional 10bushels, he was paid $60
10(1.5y) = 60
15y = 60
y = 60/15 = 4
If y = $4 per bushel and he was paid $180, the number he harvested will be:
4 × number of bushels = $180
4p = 180
p = 180/4 = 45 bushels
p = 45bushels isn't possible because the amount for the first bushels should either be less than or equal to 42
If we make another assumption, let's say he harvested more than 42 yesterday (42 + an additional number), we would get a different answer.
Thus the information given in the question to solve it is insufficient.
Translate into an algebraic expressions: b is decreased by 40% and decreased again by 40% . What is the result ?
Answer:
b-4/5b
Step-by-step explanation:
b is decreased by 80%
dat is 80/100×b
= b-80/100b
b-4/5b
Can someone please help me I really need help please help me
Answer:
1080
Step-by-step explanation:
What is the nth term rule of the quadratic sequence below? 7, 14, 23, 34, 47, 62, 79 Please could someone help me and write a step by step explanation? Thanks :D
Step-by-step explanation:
The first differences are 7,9,11,13,15,17 and the second differences are 2.
This means that the first term of the sequence is n^2.
Subtracting n^2 from the sequence gives 6,10,14,18,22,26, which has nth term of 4n + 2.
So putting these together gives a nth term of the quadratic sequence of n^2 + 4n + 2.
Hope it helped and tell me if I went wrong :)
A car is traveling at x feet per second. The driver sees a red light ahead, and
after 1,5 seconds reaction time, the driver applies the brake. After the brake is
applied, the car takes seconds to stop, during which time the average speed
24
of the car is feet per second. If the car travels 165 feet from the time the
driver saw the red light to the time it comes to a complete stop, which of the
following equations can be used to find the value of x?
A) x2 + 48x - 3,960 = 0
B) x2 + 48x - 7,920 = 0
C) x2 + 72x - 3,960 = 0
D) x2 + 72x - 7,920 = 0
Answer:
The correct option is;
D) x² + 72·x - 7920 = 0
Step-by-step explanation:
The time it takes the car to stop = x/24 seconds
the average speed during stopping = x/2 feet per second
Given that the car was initially travelling at x feet per second and it takes the car 165 feet to stop after the driver takes 1.5 seconds at the initial speed x before the break is applied, we have;
Total distance traveled = (x/24)×(x/2) + x×1.5 = 165
= x²/48 + 1.5·x = 165
Multiply through by 48, we have;
x² + 72·x = 7920
Which gives the equation as follows;
x² + 72·x - 7920 = 0.
Find the first three terms of the sequence below. Tn = 2n² - 3n - 6 Brainliest to the first correct answer!
Answer:
-7, -4, 3
Step-by-step explanation:
Tn = 2n² - 3n - 6
T1= 2*1²- 3*1- 6= 2- 9= - 7T2= 2*2²- 3*2- 6= 8- 12= - 4T3= 2*3²- 3*3- 6= 18- 15= 3WILL GIVE BRAINLEST ANSWER IF DONE IN 24 HRS Two forces with magnitudes of 150 and 100 pounds act on an object at angles of 40° and 170°, respectively. Find the direction and magnitude of the resultant force. Round to two decimal places in all intermediate steps and in your final answer. (pls show work)
Answer:
114.96 pounds at angle 81.76°
Step-by-step explanation:
Let i be the component along x-axis and j be the component along y-axis.
First force that is given is 150 acting at angle 40; [tex]F1 = 150cos170i + 150sin40j = 114.91i +96.42j[/tex]
The second force 100 is acting at angle 170;
[tex]F2 = 100cos170i + 100sin170j = -98.48i + 17.36j[/tex]
We now have the resultant force, which is: [tex]114.91i + 96.42j + (-98.48i + 17.36j) = 16.43i + 113.78j[/tex]
Magnitude of resultant:
[tex]\sqrt{16.43^{2} + 113.78^{2} }[/tex] = 114.96 pounds
Angle it makes with horizontal; inverse tangent of [tex]\frac{(113.78)}{(16.43)}[/tex] = 81.76 degrees
Hope this helps; Brainliest appreciated!
Find the missing length.
Answer:
X = 25
Step-by-step explanation:
We can calculate the value of x using Euclidean theorem
15^2 = 9 × x
225 = 9x divide both sides by 9
25 = x
What is the 5th equivalent fraction to 1/11 ?
Answer: 5/55
Step-by-step explanation:
1/11 x 5 = 5/55
So, the fifth equivalent fraction to 1/11 is 5/55.
The 5th equivalent fraction should be [tex]5\div 55[/tex]
Calculation of the equivalent fraction:Since the fraction is [tex]1\div 11[/tex]
So here the 5th equivalent should be
[tex]= 1\div 11 \times 5\div 5[/tex]
= [tex]5\div 55[/tex]
Here 5 represent the numerator and 55 represent the denominator.
Therefore, we can concluded that The 5th equivalent fraction should be [tex]5\div 55[/tex]
Learn more about fraction here: https://brainly.com/question/1786648
SHOW YOUR WORK!!!!! Best answer gets brianliest :))
Answer:
6) g = 11p
7) This equation is an example of direct variaction because it is proportional because can make a slanted line with the equation C = 6g + 15
Step-by-step explanation:
Well to find g we seperate g and combine like terms,
[tex]81 = 6g + 15[/tex]
So we subtract 15 from both sides 66 = 6g,
66/6 = 11.
So g = 11.
A sandbag is released from a hot air balloon that is 400 ft above the ground. Using the falling object model, h = −16t^2 + s, where h = height in feet, t = time in seconds, and s = initial height in feet, how long will it take for the sandbag to hit the ground? A. 4 seconds B. 5 seconds C. 20 seconds D. 25 seconds
Answer:
B. 5 seconds
Step-by-step explanation:
A graphing calculator shows the answer easily.
__
h(t) = 0 = -16t^2 +400
t = √(400/16) = 5
It will take 5 seconds for the sandbag to hit the ground.
EXCELLENT VOTE!! (only if u give the CORRECT answer)
Answer:
Option C
Step-by-step explanation:
Answer:
B.
You need to subtract 1 term because you don't include the starting 5
4^10 - 1 = 4^9
You multiply 5 by 4 each time for 9 times so it is 5 x 4^9
Hope this helps
Step-by-step explanation:
Pls ppl answer dis question PLS PLS PLS No scaming pls
4√3 x^2+5x-2√3
Answer:
\the zeroes are (2√3)/ 3, (√3)/4,
or -1.15, 0.43 to the nearest hundredth.
Step-by-step explanation:
I am assuming you want to find the zeroes of this function:
4√3 x^2+5x-2√3 = 0
Using the quadratic formula:
x = [ -5 +/- √((5)^2 - 4 * 4√3 * -2√3) ] / (2 * 4√3 )
= ( - 5 +/- √(25 - (-32*3)) / 8√3
= (-5 +/- √ 121) / 8√3
= (-5 - 11) / 8√3 or (-5 + 11) / 8√3
= -16/8√3 or 6/8√3
= -16√3/ 24 or 6√3 / 24
= -2√3/ 3 or √3/4.
Express 1/10 cm as a fraction of 3 metres
Answer:
1/3000
Step-by-step explanation:
3 meters to centimeters:
3 × 100 = 300
= 1/10 ÷ 300
= 1/10/300
= 1/(10×300)
= 1/3000
What number : Decreased by 95% is 81 ?
Answer:
1620
Step-by-step explanation:
If a number decreased by 95% is 81, then
5% is 81.
So, the number = 100/5 x 81= 20 x 81 = 1620
Hope this helps
Answer:
the answer is 1620
Step-by-step explanation:
What is the solution to……………………ASAP
Answer:
first option
Step-by-step explanation:
Using the rules of logarithms
log x - log y = log ([tex]\frac{x}{y}[/tex] )
log[tex]x^{n}[/tex] ⇔ n log x
ln e = 1
Given
4 + 5[tex]e^{x+2}[/tex] = 11 ( subtract 4 from both sides )
5[tex]e^{x+2}[/tex] = 7 ( divide both sides by 5 )
[tex]e^{x+2}[/tex] = [tex]\frac{7}{5}[/tex] ( take ln of both sides )
ln [tex]e^{x+2}[/tex] = ln ([tex]\frac{7}{5}[/tex] )
(x + 2) lne = ln ([tex]\frac{7}{5}[/tex] )
x + 2 = ln ([tex]\frac{7}{5}[/tex] ) ( subtract 2 from both sides )
x = ln([tex]\frac{7}{5}[/tex] ) - 2
which is the correct answer ? please help !
simplify to create an equivalent expression 2(-3k-5)
a) -6k - 10
b) 16k + 10
c) 6k + 10
d) 3k + 7
Answer: A
Step-by-step explanation: 2(−3k−5) = (2)(−3k+−5) = (2)(−3k)+(2)(−5) = −6k−10
There is a bag filled with 5 blue, 6 red and 2 green marbles. A marble is taken at random from the bag, the colour is noted and then it is not replaced. Another marble is taken at random. What is the probability of getting 2 blues?
Answer:
Step-by-step explanation:
Total marbles = 5 + 6 + 2 = 13
P( getting blue ball from first draw) = 5/13
The marble is not replaced. So, Now total marbles will be 12 & number blue marbles will be 4
P( getting blue ball from second draw) = 4/12 = 1/3
P(getting two blues) = [tex]\frac{5}{13}*\frac{1}{3}\\[/tex]
= 5/39
The sum of all digits in the numbers 44, 45 and 46 is 27 because (4+4)+(4+5)+(4+6)=27. Find the sum of digits in the first 25 counting numbers: 1, 2, 3, …, 25. NEED HELP PLEASE!!!!!!!!!!!!!!!!!!!!
Answer:
Total um of the digits of the first 25 numbers is 127
Step-by-step explanation:
Notice that:
The sum of the digits:
0+1+2+3+4+5+6+7+8+9 = 45
Also notice that the addition of:
10+11+12+13+14+15+16+17+18+19=0+1+2+3+4+5+6+7+8+9 + 10*1 = 45 + 10 = 55
And for the last 6 numbers:
20+21+22+23+24+25 = 0+1+2+3+4+5 + 2 * 6 = 15 + 12 = 27
So the total sum of all this is: 45 + 55 +27 = 127
what is the value of x? PLZ LMK ASAP!
Answer:
m∠x = 98°
Step-by-step explanation:
Step 1: Find the supplementary angle in the triangle
180 - (53 + 45) = 82
Step 2: Use Supplementary Angles to solve for x
180 - 82 = 98°
The equation of a linear function in point-slope form is y – y1 = m(x – x1). Harold correctly wrote the equation y = 3(x – 7) using a point and the slope. Which point did Harold use?
Answer:
Point used by Harold was:
(7, 0)
Step-by-step explanation:
Given that
Equation of linear function used by Harold:
[tex]y = 3(x - 7)[/tex]
We know that linear equation in point slope form can be represented as:
[tex]y - y_1 = m(x - x_1)[/tex]
Where [tex](x_1,y_1)[/tex] are the coordinates of a given point.
[tex]m[/tex] is the slope of line.
Formula for Slope, m is given as:
[tex]m = \dfrac{y_2-y_1}{x_2-x_1}[/tex]
Where [tex](x_1,y_1)[/tex] and [tex](x_2,y_2)[/tex] are the two points on the line.
If slope and a point with coordinates [tex](x_1,y_1)[/tex] is know, the equation of a line can be represented in linear form as:
[tex]y - y_1 = m(x - x_1)[/tex] ....... (1)
Now, the given equation is:
[tex]y = 3(x - 7)[/tex]
Re-writing the equation with a slight modification:
[tex]y-0 = 3(x - 7)[/tex]
Now, comparing the above equation with equation (1):
We get that:
[tex]x_1=7\\y_1=0[/tex]
So, the point used by Harold is (7, 0).
Answer:
(7,0)
Step-by-step explanation: