Answer:
Let's define the high temperature as T.
We know that:
"four times T, was more than 2*T plus 66°C"
(i assume that the temperature is in °C)
We can write this inequality as:
4*T > 2*T + 66°C
Now we just need to solve this for T.
subtracting 2*T in both sides, we get:
4*T - 2*T > 2*T + 66°C - 2*T
2*T > 66°C
Now we can divide both sides by 2:
2*T/2 > 66°C/2
T > 33°C
So T was larger than 33°C
Notice that T = 33°C is not a solution of the inequality, then we should use the symbol ( for the set notation.
Then the range of possible temperatures is:
(33°C, ...)
Where we do not have an upper limit, so we could write this as:
(33°C, ∞°C)
(ignoring the fact that ∞°C is something impossible because it means infinite energy, but for the given problem it works)
Derek walks to his best friends house at a rate of 1 block per minute, then turns around and walks home. The graph shows the distance Derek walks in the given amount of time. Write an equation for the graph.
In this question, we have to find an equation for two lines, depending on the input x, which creates the following piecewise function for this graph:
[tex]y = t, 0 \leq t \leq 10, -t + 20, 10 \leq t \leq 20[/tex]
Equation of a line:
The equation of a line is given by:
[tex]y = mt + b[/tex]
In which m is the slope and b is the y-intercept(value of y when x = 0).
This situation:
One line for x between 0 and 10;Another for x between 10 and 20;x between 0 and 10:
From here, we can take two points (t,y). I will take (0,0) and (10,10).
From point (0,0), we get that when [tex]x = 0, y = 0[/tex], which means that the y-intercept is [tex]b = 0[/tex], thus:
[tex]y_1 = mt[/tex]
To find the slope, when we have two points, it is given by change in y divided by change in t, so:
Change in t: 10 - 0 = 10
Change in y: 10 - 0 = 10
Slope: [tex]m = \frac{10}{10} = 1[/tex]
Thus, the first definition is:
[tex]y_1 = t, 0 \leq t < 10[/tex]
x between 10 and 20:
I will take the points (10,10) and (20,0).
First, we find the slope:
Change in t: 20 - 10 = 10
Change in y: 0 - 10 = -10
Slope: [tex]m = \frac{-10}{10} = -1[/tex]
Thus:
[tex]y_2 = -t + b[/tex]
For the intercept, we have point (20,0), which means that when [tex]t = 20, y = 0[/tex]. So
[tex]0 = -20 + b[/tex]
[tex]b = 20[/tex]
Thus, the second definition is:
[tex]y_2 = -t + 20, 10 \leq t \leq 20[/tex]
Write an equation for the graph.
We use the two definitions, that is:
[tex]y = y_1, 0 \leq t \leq 10, y_2, 10 \leq t \leq 20[/tex]
So
[tex]y = t, 0 \leq t \leq 10, -t + 20, 10 \leq t \leq 20[/tex]
A similar question can be found at https://brainly.com/question/16024991
pls help me with this question and reply answer
Step-by-step explanation:
From both the cases we can say that √n is either a natural number or an irrational number. Hence the correct option is (d)Either a natural number or an irrational number. Note: Before solving this type of question we should have proper knowledge of natural numbers, rational numbers and irrational numbers.
please prove it
(full steps required)
(No spam answers)
Answer:
Step-by-step explanation:
It's given in the question,
[tex]2^x=3^y=12^z[/tex]
[tex]2^x=12^z[/tex]
[tex]\text{log}2^x}=\text{log}12^z}[/tex]
[tex]x\text{log2}=z\text{log12}[/tex]
[tex]x=\frac{z\text{log}12}{\text{log2}}[/tex]
[tex]3^y=12^z[/tex]
[tex]\text{log}3^y}=\text{log}12^z}[/tex]
[tex]y\text{log}3}=z\text{log}12}[/tex]
[tex]y=\frac{z\text{log12}}{\text{log}3}[/tex]
Now substitute the values in the equation,
[tex]\frac{1}{y}+\frac{2}{y} =\frac{1}{\frac{z\text{log12}}{\text{log}3}}+\frac{2}{\frac{z\text{log}12}{\text{log2}}}[/tex]
[tex]=\frac{\text{log}3}{z\text{log}12}+\frac{2\text{log}2}{z\text{log}12}[/tex]
[tex]=\frac{\text{log}3+\text{log}2^2}{z\text{log}12}[/tex]
[tex]=\frac{\text{log}(3\times 2^2)}{z\text{log}12}[/tex]
[tex]=\frac{\text{log}(12)}{z\text{log}12}[/tex]
[tex]=\frac{1}{z}[/tex]
Hence proved.
URGENT‼️NEED HELP ASAP
What is the distance between the vertical asymptotes of the two graphs f(x) and g(x)?
A steep mountain is inclined 75 degree to the horizontal and rises 3900 ft above the surrounding plain. A cable car is to be installed by connecting a cable from the top of the mountain to a spot on the plain that is 910 ft from the base of the mountain. Find the shortest length of cable needed.
Answer: [tex]4004.76\ ft[/tex]
Step-by-step explanation:
Given
inclination is [tex]\theta=75^{\circ}[/tex]
Mountain is [tex]h=3900\ ft[/tex] high
Cable is tied [tex]x=910\ ft[/tex] from the base of the mountain
From the figure, length of the shortest path is [tex]l[/tex]
It is given by using Pythagoras theorem
[tex]\Rightarrow l^2=3900^2+910^2\\\Rightarrow l=\sqrt{(3900)^2+(910)^2}\\\Rightarrow l=4004.76\ ft[/tex]
Please help me anyone
Replace x with -11 and solve:
Y = (-11)^2 + 11
(-11)^2 = 121
Y = 121 + 11
Y = 132
Answer: 132
Answer:
132
Step-by-step explanation:
y = x^2 +11
Let x = -11
y = (-11)^2 +11
= 121+11
= 132
In the equation $\frac{1}{j} + \frac{1}{k} = \frac{1}{3}$, both $j$ and $k$ are positive integers. What is the sum of all possible values for $k$?
Answer:
Hello,
answer 22
Step-by-step explanation:
[tex]\dfrac{1}{j} +\dfrac{1}{k} =\dfrac{1}{3} \\\\\dfrac{k+j}{j*k} =\dfrac{1}{3} \\\\\\3k+3j=j*k\\\\k(3-j)=-3j\\\\k=\dfrac{3j}{j-3} \\\\k=\dfrac{3j-9+9}{j-3} \\\\k=3+\dfrac{9}{j-3} \\\\\\j-3\ must\ be \ a divisor\ of\ 9 ==> 1,3,9\\\\j-3=1 ==> j=4 , k=3+\dfrac{9}{1} =12\\\\j-3=3 ==> j=6 , k=3+\dfrac{9}{3} =6\\\\j-3=9 ==> j=12 , k=3+\dfrac{9}{9} =4\\\\\sum\ k=12+6+4=22\\[/tex]
The sum of all possible values for k is 22.
What is fraction?The fractional bar is a horizontal bar that divides the numerator and denominator of every fraction into these two halves.
The number of parts into which the whole has been divided is shown by the denominator. It is positioned in the fraction's lower portion, below the fractional bar.How many sections of the fraction are displayed or chosen is shown in the numerator. It is positioned above the fractional bar in the upper portion of the fraction.Given:
1/j + 1/k= 1/3
Simplifying the fraction
(k+ j)/ kj= 1/3
3k + 3j = kj
k(3- j) = -3j
k = -3j/ (3- j)
k= 3j/ (j-3)
k = 3j + 9 - 9 / (j-3)
k = 3 + 9/ (j-3)
Since (j-3) must be divisor of 9.
j- 3 = 1---> j=4, k= 3 +9 = 12
j- 3 = 3---> j=6, k= 3 +9/3 = 6
j- 3 = 9---> j=12, k= 3 +9/9 = 4
So, The sum is = 12+ 6 + 4 = 22
Learn more about Fraction here:
https://brainly.com/question/10354322
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a teacher bought sweets for her 40 students . if she gave each student 3 sweets , she would have 5 sweets left . How many sweets did she buy?
Answer:
125 sweets
Step-by-step explanation:
Let the total # of sweets the teacher bought be the variable, x.
We can set up this equation to find the # of sweets she bought:
40 · 3 + 5 = x
Because she gave 3 sweets each to her 40 students, we have to multiply these two numbers to get the # of sweets the teacher gave out.
120 + 5 = x
Then, since there's 5 extra sweets left, we can add it to the # of sweets the teacher gave out to get the total amount of sweets she bought.
125 = x
x = 125
125 sweets
Answer:
Total sweets = 125
Step-by-step explanation:
Number of sweets given to each student = 3
Number of sweets given to 40 students = 40*3 = 120
Number of sweets left with the teacher = 5
Total sweets = 120 + 5 = 125
Which of the following lists of ordered pairs is a function? A. (2,5), (3, 6), (6, 9) B. (-1,2), (2, 3), (3, 1), (2,5) C. (1,2), (4,0), (3,5),(4,3) D. (2,5), (3, 6), (2, 1)
Answer:
A. (2,5), (3,6), (6,9)
Step-by-step explanation:
In order to be a function, all inputs (x values) must go to only one output (y value). List A is the only list that obeys this rule. Therefore, List A is a function.
Find a pattern for the sequence. Use the pattern to show the next two terms.
AL, AK, AZ, AR, CA, ...
Choose the correct answer below.
СT, CO
CO, DE
CO, CT
DE, FL
============================================
Explanation:
These are state abbreviations
AL = AlabamaAK = AlaskaAZ = ArizonaAR = ArkansasCA = CaliforniaCO = ColoradoCT = ConnecticutDE = DelawareFL = FloridaSince the given sequence is "AL, AK, AZ, AR, CA", and the states are listed alphabetically so far (in terms of the two letter abbreviations), then the next two would be CO and CT in that order.
Find the first three terms of the sequence below. 3n^2+5n−2
Answer:
-2, 6, 20 ,...
Step-by-step explanation:
3n² +5n -2
if n=0 , then 3*0² +5*0 -2= -2
if n=1, then 3*1² +5*1 -2 = 3+5-2 = 6
if nu 2, then 3*2² +5*2 -2 = 12 +10 -2 = 20
How to muilti step equation this problem
answer the question
(v^3)(w^-3) / (-v^-6)(w^3)
(-v^9)(w^-3) / (w^3)
(-v^9)(w^-6)
ANSWER: Option 4
Hope this helps!
Margaret bought a video game, her father gave her 0.2 of the money, her aunt gave 0.5 of the money and she saved the rest. She saved $168 so what amt of money did her father give
Answer:
if Im correct it should be $8.40
Step-by-step explanation:
why well if you think of breaking down by say 1/4 of 168 all you do is divide 4 which is the whole amount by 0.2 which is the amount the father gave her so 4/0.2= 20 the you take your whole 168 and divide by 20 which the whole number for 0.2 the your answer should be this 168/20= 8.4 which then i assumed it was $8.40 hopefully that is correct hehe
If you buy 12 pounds of lettuce for $96 what is the rate which one pound of lettuce costs
Answer:
$8
Step-by-step explanation:
$96 divided by 12
HELP FAST 100 POINTS
MUCH SHOW WORK
Answer:
x is 7 and m<1 is 99°
Step-by-step explanation:
m<NMQ + m<MQN + m<QNM = 180°
[tex]{ \sf{(5x + 19) + (8x - 11) + (11x + 4) = 180}} \\ { \sf{24x + 12 = 180}} \\ { \sf{24x = 168}} \\ { \sf{x = \frac{168}{24} }} \\ \\ { \sf{x = 7}}[/tex]
m<1 = 180° - (11x + 4)
m<1 = 180° - 81°
m<1 = 99°
Using angle sum property
[tex]\\ \sf\longmapsto 5x+19+8x-11+11x+4=180[/tex]
[tex]\\ \sf\longmapsto 24x12=180[/tex]
[tex]\\ \sf\longmapsto 24x=180-12=168[/tex]
[tex]\\ \sf\longmapsto x=\dfrac{168}{24}[/tex]
[tex]\\ \sf\longmapsto x=7[/tex]
<1=11(7)+4=77+4=81[/tex]HAI HELP ME ASAP PLEASE
Answer:
Y/X = 2/3 x^2 + 16/3
Y= 2/3 x^3 + 16/3 x
Just replace y with y/X and X with x^2
A swimming pool has 143 gallons of water in it. The swimming pool drains at a rate of 8 gallons per minute. How much water is in the swimming pool after 11 minutes?
How much water does the swimming pool have after 11 minutes? Solve on paper, then enter your answer on Zearn.
The swimming pool has
gallons of water after 11 minutes.
Answer:
55 Gallons
Step-by-step explanation:
143 - (8)(11)
143 - 88
143 - 88
55 gallons
La señora Angélica fue al mercado y compró 2 visores protectores y 1 mascarilla, pagó $55.00, en total. En el mismo puesto, la señora Silvia compró 1 visor protector y 2 mascarillas y pagó $50.00. ¿Cuál es el precio de una mascarilla? ¿Cuáles el precio de un visor protector?
Answer:
Cost of 1 goggles = $20
Cost of 1 mask = 15
Step-by-step explanation:
Given:
Cost of 2 goggles and 1 mask = $55
Cost of 1 goggles and 2 mask = $50
Find:
Cost of each goggles and mask
Computation:
Assume;
Cost of 1 goggles = a
Cost of 1 mask = b
So,
2a + b = 55.....EQ1
a + 2b = 50.......EQ2
EQ1 x 2
4a + 2b = 110 ......EQ3
EQ3 - EQ2
3a = 60
a = 20
Cost of 1 goggles = $20
a + 2a = 50
20 + 2b = 50
2b = 30
b = 15
Cost of 1 mask = 15
.
In a mid-size company, the distribution of the number of phone calls answered each day by each of the 12 receptionists is bell-shaped and has a mean of 43 and a standard deviation of 8. Using the empirical rule (as presented in the book), what is the approximate percentage of daily phone calls numbering between 19 and 67
Answer:
Step-by-step explanation:
If you drew out the bell curve and put the values where they go, this would be a no-brainer that doesn't even need math to solve. However, we will use the formula and then the table for z-scores to find this answer.
We are looking for the probability that the number of calls falls between 19 and 67. The standard deviation is 8 and the mean is 43. The probability we are looking for is P(19 < x < 67), therefore we look for the probability first that number of calls is greater than 19:
[tex]z=\frac{19-43}{8}=-3[/tex] and from the table and to the right of the z-score, the probability that the number of calls is greater than 19 is .99865 (or 99.8%). Likewise,
[tex]z=\frac{67-43}{8}=3[/tex] and from the table and to the right of the z-score, the probability that the number of calls is greater than 67 is .00315.
Take the difference of these to get the probability that the number of calls falls between these 2:
.99865 - .00135 = .9973 or 99.7%
Use the product of powers property to simplify the expression -2x^3y4x^2y^3
Answer:
= -8x^5 y^4
Step-by-step explanation:
Multiply the numbers: -2 . 4 = -8
-2x^3 yx^2 y^3
Simplify x^3 x^2 : x^5
= -8x^5yy^3
Simplify yy^3 : y^4
= -8x^5 y^4
PLEASE HELP ASAP!!! I dont understand
Answer:
15
Step-by-step explanation:
(3x-1+2x+1)(3) -> 3 is the plug-in for x
3x-1+2x+1=5x
5*3=15
15
Answer:
15
Step-by-step explanation:
f(x) = 3x -1
g(x) = 2x+1
(f+g)(3)
find g(3) = 2(3)+1 = 6+1 = 7
Then find f(3) = 3(3) -1 = 8
f(3) + g(3) = 7+8 = 15
lcm of 12x² and 48xy
Answer:
576xxxycm
Step-by-step explanation:
1cm×12x×x+48xy=576xxxycm
Can someone please help me on these 3 equations please HELP ME !!!
please mark this answer as brainlist
If p(x)= x⁵ + 3, then find the value of x
The formula is N×x power n-1
5x⁴+0
5x⁴
This is for geometry, please help ASAP
Answer:
Option C,
y² = 18x, since the graph opens right
Answered by GAUTHMATH
The scale on a map is 1 inch = 10 miles.
What is the distance, in inches, on the map
between two towns that are m miles apart?
F.
m/10
G. M/5
H.5m
J.10m
K.m+10
Answer:
F. m/10.
Step-by-step explanation:
10 miles = 1 inch
1 mile = 1/10 of an inch so
m miles = m/10 inches.
PLEASE HELP !!! 25 POINTS!Perform the following conversion.
0.09 km to dam
0.000 009 dam
0.000 009 dam
900 dam
900 dam
90 000 dam
90 000 dam
9 dam
9 dam
Answer:
9 dam
Step-by-step explanation:
1 km = 100 dam
0.09 km = 0.09 × 100
= 9 dam
∴ 0.09 km = 9 dam
find to consecutivephone number such that five times the smaller number plus 3 times the greater number make 59 hint let the number be x and x + 1
Answer:
x = 7 is the answer for the smaller number
7 + 1 = 8 is the answer for the larger number
Step-by-step explanation:
LET x and x+1 be the two numbers here, as your hint suggests.
5x + 3(x+1) = 59
5x + 3x+3 = 59
8x = 59-3
8x = 56
/8 /8
--------------------------
x = 56/8 ---> x = 7
x = 7 is the answer for the smaller number
7 + 1 = 8 is the answer for the larger number
Check:
5 * 7 + 3 * 8 = 59
35 + 24 = 59
59 = 59 CORRECT
Find the missing side of the triangle
Answer:
missing side is √193
= 13.892443989449
