Answer:
Length = 17m
Width = 11m
Step-by-step explanation:
Expression for the area of the rectangle = 6x² + 19x + 15
Factorising the quadratic expression
6x² + 19x + 15 = (6x² + 9x) + (10x + 15) = 3x(2x + 3) +5(2x + 3) = (3x + 5)(2x + 3)
x = 4m
Length = 3x + 5 = 3(4) + 5 = 12 + 5 = 17m
Width = 2x + 3 = 2(4) + 3 = 8 + 3 = 11m
(iii) n(U) = 25, n(A) = 16 and n (B) = 2 n(AUB)=?
Answer:
n(AuB)=n(A)+n(B)=18
This is the answer
what is value of y if 2x+3y=4
Answer:
y=(4-2x)/3
Step-by-step explanation:
3y= 4-2x
y= (4-2x)/3
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
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.
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.
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
PLEASE HELP!!!!!!!!!!!!!!!!!!!!!!!!!! ANYONE PLEASE I'M DESPERATE A.F
Describe the transformation that takes place with the following rule:
(x - 2, y + 4)
A. Translates 2 units left AND 4 units up.
B. Translates 2 units down AND 4 units right.
C. Translates 2 units up AND 4 units down.
D. Translates 2 units right AND 4 units up.
Answer:
C. TRANSLATE 2 UNITS UP AND 4 UNITS DOWN
Step-by-step explanation:
The transformation that takes place with the following rule (x - 2, y + 4) is translates 2 units left AND 4 units up, the correct option is A.
How does transformation of a function happens?The transformation of a function may involve any change.
Usually, these can be shift horizontally (by transforming inputs) or vertically (by transforming output), stretching (multiplying outputs or inputs) etc.
If the original function is y = f(x), assuming horizontal axis is input axis and vertical is for outputs, then:
Horizontal shift (also called phase shift):
Left shift by c units:
y=f(x+c) (same output, but c units earlier)
Right shift by c units:
y=f(x-c)(same output, but c units late)
Vertical shift:
Up by d units: y = f(x) + d
Down by d units: y = f(x) - d
Stretching:
Vertical stretch by a factor k: y = [tex]k \times f(x)[/tex]
Horizontal stretch by a factor k: y =[tex]f\left(\dfrac{x}{k}\right)[/tex]
We are given that;
The points (x - 2, y + 4)
Now,
The rule (x - 2, y + 4) means that every point (x,y) of the original figure is moved to a new point (x - 2, y + 4) by subtracting 2 from the x-coordinate and adding 4 to the y-coordinate.
The x-axis is horizontal and positive to the right. Subtracting from the x-coordinate means moving left and adding to the x-coordinate means moving right.
The y-axis is vertical and positive upwards. Subtracting from the y-coordinate means moving down and adding to the y-coordinate means moving up.
Subtracting 2 from the x-coordinate means moving 2 units left and adding 4 to the y-coordinate means moving 4 units up.
Therefore, by transforming functions the answer will be translates 2 units left AND 4 units up.
Learn more about transforming functions here:
https://brainly.com/question/17006186
#SPJ2
Solve by substitution:
y=x-12
8x+8y=-16
Answer:
[tex](x,y) = ( 5 , - 7)[/tex]
Step-by-step explanation:
we would like to solve the following system of linear equation by substitution:
[tex] \displaystyle \begin{cases} y = x - 12\\ 8x + 8y = - 16\end{cases}[/tex]
notice that, we're already given the value of y therefore simply substitute it to the II equation
[tex]8x + 8(x - 12) = - 16[/tex]
distribute:
[tex]8x + 8x - 96= - 16[/tex]
simplify addition:
[tex]16 x- 96= - 16[/tex]
isolate -96 to left hand side and change its sign:
[tex]16 x= - 16 + 96[/tex]
simplify addition:
[tex]16 x= 80[/tex]
divide both sides by 16 and that yields:
[tex] \boxed{x= 5}[/tex]
now substitute the got value of x to the first equation:
[tex]y = 5- 12[/tex]
simplify subtraction:
[tex]y = - 7[/tex]
hence,
the solution is (x,y)=(5,-7)
Solve by substitution :
y = x - 12
8x + 8y = -16
S O L U T I O N :y = x - 12 ------- eq(1)
8x + 8y = -16 ------- eq(2)
Finding x ⤵
Putting y = x - 12 in eq(2) we get
8x + 8(x - 12) = -168x + 8x - 96 = -1616x = 96 - 1616x = 80x = 80/16x = 5Finding y ⤵
Putting x = 5 in eq(1) we get
y = x - 12y = 5 - 12y = -7Hence, x is 5 and y is -7
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
Find the missing side of the triangle
Answer:
missing side is √193
= 13.892443989449
Can someone pls help with this
here it is :)
do check properly, I have given step by step instructions:)
do give feedback on my answer, would appreciate it!
Answer:
900000
Step-by-step explanation:
[tex]30*10^{4}[/tex]
=3*10000
=30000
=30*30000
=900000
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
If A = {a,b} and B = {1, 2, 3} then, find A×B and B×A and show them by a mapping diagram.
A × B = {a, b} × {1, 2, 3} = {{a, 1}, {a, 2}, {a, 3}, {b, 1}, {b, 2}, {b, 3}}
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]
This is for geometry, please help ASAP
Answer:
Option C,
y² = 18x, since the graph opens right
Answered by GAUTHMATH
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
Kent guessed that there were
2,473 candies in the jar.
What is the value of the 2?
Answer:
The value of the 2 is two-thousand
Step-by-step explanation:
Answer:
thousands
Step-by-step explanation:
thousands, hundreds tens ones
2 4 7 3
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
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
Wrapping a Package It takes 70 inches of ribbon to make a bow and wrap the ribbon
round a box. The bow takes 32 inches of ribbon. The width of the box is 14 inches. What
the height of the box?
-14 in. -
First subtract the amount the bow takes from the total:
70 - 32 = 38 inches
The width is 14 on top and bottom so subtract 14 x 2 = 28 from 38:
38-28 = 10
Divide 10 by the 2 sides:
10/2 = 5
The height is 5 inches.
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
URGENT‼️NEED HELP ASAP
What is the distance between the vertical asymptotes of the two graphs f(x) and g(x)?
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
If p(x)= x⁵ + 3, then find the value of x
The formula is N×x power n-1
5x⁴+0
5x⁴
The width of a rectangle is 9
inches less than the length. The
perimeter is 86 inches
Answer:
Below.
Step-by-step explanation:
If the length is x then the width is x-9 inches.
Perimeter
= 2L + 2W = 86
2x + 2(x - 9) = 86
4x - 18 = 86
4x = 104
x = 26
So the length is 26 inches and the width is 17 inches.
If the right angle triangle LMN.
L=30°, MN = 4cm and diagonal LM.
Find the LM and LN.
How to muilti step equation this problem