Answer:
(-12, -2)
Step-by-step explanation:
Rearrange the equation --> x^2 + 14x + 24 = 0
Split 14x into 12x + 2x --> x^2 + 12x + 2x + 24 = 0
Group --> x(x + 12) + 2(x + 12) = 0, (x + 12)(x + 2) = 0
Find roots:
x + 12 = 0, x = -12
x + 2 = 0, x = -2
The solution of the given expression [tex]\rm x^{2} +14x = -24\\[/tex] by completing the square method is 12 and -2.
The given expression is
[tex]\rm x^{2} +14x = -24\\[/tex]
What is completing the square method?In completing the square, we take half of the coefficient of the middle term and then square it. Then we add it to both sides of the equation
Here coefficient of middle term x is +14.
So, 14/2 = 7
square of 7 is 49
[tex]\rm x^{2} +14x +49= -24+49\\\rm (x+7) (x+7)=25\\\rm (x+7)^{2} =5^{2} \\\rm x+7 =5[/tex]
x+7 = 5 and x+7 = -5
Solve for x by subtracting 7 on both sides
x = -2 and x= -12
Solution set is {-12, -2}
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Factor using the greatest common factor
25n ² - 5n
32n ² + 28n - 20
Answer:
this is my answer
5n (5n - 1)
4n (8 + 7) - 20
PLSS I NEED HELP!!
1). To make a full rotation, 59 days, 19 h, and 45 min goes by for Mercury. It only takes Earth 1 day! How many hours does it take Mercury to complete a full rotation? Show your work using the correct conversion factors.
2). Some plants grow quickly. An invasive weed species can grow quickly. One variety grows up to 0.89 ft per day. How fast in inches per hour can this weed grow? Show your work using the correct conversion factors.
3). David’s watch broke. He decides to get it fixed instead of replacing it. The total cost to repair the watch can be represented by 0.07(45h) + 45h, where h represents the number of hours it takes to repair the watch.
a). What part of the expression represents the cost of the repair before tax?
b) Explain what your answer in Part A means in the context of the problem.
1) It takes 1435.75 hours for Mercury to complete a full rotation.
2) The weed can grow at 0.445 inches per hour.
Time calculation1) Given that to make a full rotation, 59 days, 19 h, and 45 min goes by for Mercury, to determine how many hours does it take Mercury to complete a full rotation, the following calculation must be performed:
59 x 24 + 19 + 0.75 = X1416 + 19.75 = X1435.75 = X2) Given that a plant grows up to 0.89 ft per day, to determine how fast in inches per hour can this weed grow, the following calculation must be performed:
0.89 / 24 = ft per hour0.037 = ft per hour1 ft = 12 inches0.037 x 12 = 0.445Learn more about time calculation in https://brainly.com/question/14695611
Answer:
1) It takes 1435.75 hours for Mercury to complete a full rotation.
2) The weed can grow at 0.445 inches per hour.
Step-by-step explanation:
7/6 x 4/5 = in simplest form
Answer:
heyy do you still need help
Step-by-step explanation:
Solve the picture for n
The two angles shown are vertical angles which men they equal each other:
9n = 8n + 8
Subtract 8n from both sides:
N = 8
->Solution
i) 9n = 8n+8 [ V.O.A. vertically opposite angles ]
or, 9n - 8n = 8
or, n = 8
therefore, value of n is 8
Now,
ii) 9n = 9 X n = 9 X 8 = 72 degrees
iii) 8n + 8 = 8 X 8 + 8 = 64 + 8 = 72 degrees
Une bouteille cylindrique de 12 cm de hauteur a une capacité de 1 L quel est le rayon de sa base
Answer:
≈5.15 [cm].
Step-by-step explanation (English version):
1) Capacity - V - 1000 cm³;
height - h - 12 cm;
radius - r - ?
2) the initial formula is:
V=π*r²*h, where π=3.1415;
then final formula of the required r is:
[tex]r=\sqrt{\frac{V}{\pi *h}};[/tex]
3) [tex]r=\sqrt{\frac{1000}{3.1415*12}} =\sqrt{26.5266} =5.15[cm].[/tex]
Ms. Pearson kept track of student absences versus final average grades in her math dass for one semester, The
data is shown in the table below
The correct statement about the data collected by Ms. Pearson is that there is no association between a student's absences and the final average grades.
When do variables have a linear relationship?The equation that represents a linear relationship is: a + bx
Where x represents the rate of increase. Thus, for linear equations, the functiion increases by a constant term.
Looking at the table, the average final grade does not increase by a constant term.
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for the following question, true or false.
Answer:
False
Step-by-step explanation:
You can't add without first doing the terms of 2^3---(PENDAS)
What number is one hundred thousand less than one hundred
million?
Answer:
900,000
Explanation:
1 million is 10*100,000, so subtracting 100,000 from it is just like subtracting 1 from 10-- just much much larger numbers.
Answer:
99,900,000
Step-by-step explanation:
Less than ⇒ subtraction⇒ Subtract 100,000 from 100,000,000⇒ 100,000,000 - 100,000⇒ 99,900,000Enter the correct answer in the box. Write your answer in the form y = mx + b, using the appropriate inequality symbol in place of the equal sign.
What inequality is shown in the graph?
Answer:
y ≥ -x - 4
Step-by-step explanation:
[tex]\sf let (x_1,y_1)=(-4,0)\\\\let (x_2,y_2)=(0,-4)[/tex]
[tex]\sf slope \ (m)=\dfrac{y_2-y_1}{x_2-x_1}=\dfrac{-4-0}{0-(-4)}=-1[/tex]
Slope-point form of linear equation:
[tex]\sf \implies y-y_1=m(x-x_1)[/tex]
[tex]\sf \implies y-0=-1(x-(-4))[/tex]
[tex]\sf \implies y=-x-4[/tex]
For ≤ or ≥ graph a solid line
For < or > graph a dashed line
For shading above the line: y ≥ or y >
For shading below the line: y ≤ or y <
Therefore, as the line is solid and shading is above the line:
[tex]\sf y\geq -x-4[/tex]
Answer: y ≥ -x - 4
Step-by-step explanation:
Assume that we want to construct a confidence interval. Do one of the following, as appropriate: (a) find the critical value tα/2, (b) find the critical value zα/2, or (c) state that neither the normal distribution nor the t distribution applies.
The confidence level is 99%, σ is not known, and the histogram of 56 player salaries (in thousands of dollars) of football players on a team is as shown.
Considering that we have the standard deviation for the sample, the t-distribution will be used, and the critical value is t = 2.6682.
When should the t-distribution and the z-distribution be used?If we have the standard deviation for the sample, the t-distribution should be used.If we have the standard deviation for the population, the z-distribution should be used.In this problem, σ is not known, hence we get the standard deviation of the sample from the histogram and the t-distribution is used.
Using a t-distribution calculator, considering a confidence level of 99% and 56 - 1 = 55 df, the critical value is t = 2.6682.
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If ABCD is dilated by a factor of 1/2, the coordinate of D' would be:
Answer:
D'=(1,-1)
Step-by-step explanation:
If you dialate by 1/2 then all you have to do, is find half of point D. so point D sits at (2,-2) and half of 2 would be (1,-1).
The dilated coordinates of D(2,-2) = D'(1,-1).
What is dilation?Resizing an item uses a transformation called dilation. Dilation is used to enlarge or shorten the structures. The result of this transformation is an image with the same shape as the original. However, there is a variation in the shape's size. The initial form should be stretched or contracted during a dilatation.
From the graph,
we interpreted the coordinates of D (2,-2).
Coordinates are a pair of integers (Cartesian coordinates), or occasionally a letter and a number, that identify a certain place on a grid, often referred to as a coordinate plane.
To find the dilation of transformation
The basic formula to find the scale factor of a dilated figure is:
Scale factor = coordinates of the new shape ÷ coordinates of the original shape.
That means,
multiply the factor to the coordinates.
D' = (2 x 1/2, -2 x 1/2)
D' = (1, -1)
Therefore, the coordinates after the dilation D' (1,-1).
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Please help!!!!!!!!!!!!!!!!1
Answer:
The correct answer is C: [tex]t\leq 58[/tex]
Step-by-step explanation:
In order to solve this problem, start by first creating an inequality to represent the situation above. The price of the hours and the supply fee can't go over $1,500, so you can set the representative inequality as [tex]25t+50\leq 1500[/tex]. Now solve the inequality, and you will get [tex]25t+50\leq 1500[/tex] => [tex]25t\leq 1450[/tex] => [tex]t\leq 58[/tex] hrs. So C is the correct answer.
Answer:
The answer is C.t is less than or equal to 58.
Step-by-step explanation:
Let x = Number of tutoring sessions
Supplies + tutoring cost = total cost
50 + 25x = 1500
Now need to solve:
Subtract 50 from both sides and simplify
50/ + 25x - 50 = 1500 - 50
25x = 1450
Divide both sides by 25 and simplify
25x/25 = 1450/25
Therefore,
[tex]x\leq 58[/tex]
helpppppp meeeee pleaseeeeeeeee thanksssssss :)))))))
Answer:
815.76 is your answer
Step-by-step explanation:
the diameter of a circle is 12 kilometers. What is the length of a 60 degree arc?
Answer:
Step-by-step explanation:
Write an equation in slope intercept for for the like with slope -3/5 and
y-intercept -3
Answer:
An equation for the slope and y-intercept would be y=-3/5x-3
Step-by-step explanation:
Remember the formula for this, y=mx+b, in which the m stands for the slope and the x would be next to the slope always because the slope is ever changing, and the b stands for the y-intercept or in other words, where the line crosses the y-axis not the x-axis.
Answer:
y = -3/5x - 3
Explanation:
The format of slope-intercept is:
[tex]\sf{y = mx + b}[/tex]
Where:
m = slopeb = y-interceptSo to write the equation, I just plug the data into y = mx + b:
[tex]\sf{y=-\dfrac{3}{5}x+(-3)}\\\\\sf{y=-\dfrac{3}{5}x-3}[/tex]
Hence, the equation is y = -3/5x - 3.
The area of a rectangle is 5 x cubed + 19 x squared + 6 x minus 18 with length x + 3. using synthetic division, what is the width of the rectangle?
5 x squared + 4 x minus 6
5 x squared + 34 x + 108 + startfraction 306 over x + 3 endfraction
5 x cubed + 4 x squared minus 6 x
5 x squared + 34 x + 108 + startfraction 306 over x minus 3 endfraction
A rectangle is a 2-dimensional shape having 4 sides. The width of the rectangle is 5x^2 + 4x - 6
How to find the quotient of a function using synthetic division?A rectangle is a 2-dimensional shape having 4 sides
The formula for calculating the area of the rectangle is given as:
A = lw
Given the following
Area = 5x^3+19x^2+6x-18
Length = x + 3
Using the synthetic division:
5x^2 + 4x - 6
x + 3 | 5x^3+19x^2+6x-18
5x^3 + 15x^2
________________________
4x^2 + 6x
4x^2 + 12x
__________________________
-6x - 18
-6x - 18
Hence the width of the rectangle is 5x^2 + 4x - 6
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Answer:
A
Step-by-step explanation:
Can anyone help me on this?
Answer:
Out of the two sums, B is the closest to the value to 1/2.
Steps for A:
Change 1/3 to 5/15
2+5/15
= 7/15
7/15 as a decimal: 0.46
0.50 - 0.46 = 0.04
Steps for B:
Change 6/7 to 18/21
Change 1/3 to 7/21
18-7/21
= 11/21
11/21 as a decimal: 0.52
0.52 - 0.50 = 0.02
You deposit 2,000$ in a savings account earning 5% simple interest. How long will it take for ythe balance of the account to be 3,800$
Answer:
1 year and a half or 18 months
Step-by-step explanation:
Helppp plssssss!!!!!!
I need answers NOW!
BRAINLIEST FOR WHO CAN ANSWER!
When planning space exploration, scientists face many
challenges. One issue is the weight of the items being
transported. They can use the engineering design process
to help minimize the weight of materials on board a
spacecraft.
The engineering design process starts with a statement of the problem to be
solved. Which sentence best states the problem described above?
O A. Metal is stronger than plastic, but it is also much heavier.
OB. Space vessels must carry heavy equipment but also minimize
weight.
O C. The longer a space flight will last, the more equipment must be
carried
D. Lower gravity on the Moon means that objects weigh less on the
Moon than on Earth.
Answer: Space vessels must carry heavy equipment but also minimize weight.
Step-by-step explanation:
i got it right on a p e x
select exponential growth or decay for each function:
PLEASE HELP, 24 BRAINLY POINTS REWARD
Answer:
1. growth
2. decay
3. growth
4. decay
Answer:
Step-by-step explanation:
Growth: anything in the parenthesis that is greater than 100% or 1 | > 1
Decay: anything in the parenthesis that is less than 100% or 1 | < 1
(1 + r) = growth
(1 - r) = decay
r = rate of growth
[tex]f(x)=485(1.98)^t < ==|(1+0.98=1.98)| > 1= > growth\\[/tex]
[tex]f(x)=\frac{1}{4}(0.18)^t < ==|(1-0.82=0.18)| < 1= > decay[/tex]
[tex]f(x)=46(1.001)^t < ==|(1+0.001=1.001)| > 1= > growth[/tex]
[tex]f(x)=0.08(0.34)^t < ==|(1-0.66=0.34)| < 1= > decay\\[/tex]
Hope this helps!
Dogs lap water to drink it. Every 3 minutes a dog laps water, it gets 30 ounces. If a dog needs 155 ounces per day, predict how many minutes the dog will lap water.
Answer:
15 minutes and 51 seconds
Step-by-step explanation:
155/30 = 5.17
5.17 x 3 = 15.51
It will take the dog approximately 15.5 minutes to lap enough water to consume 155 ounces.
Here, we have to predict how many minutes a dog will lap water to consume 155 ounces per day, we can set up a proportion based on the given information:
1 dog laps water every 3 minutes and gets 30 ounces.
Therefore, in 1 minute, a dog laps 30/3 = 10 ounces.
Now, we want to find out how many minutes it takes for the dog to consume 155 ounces:
Let x be the number of minutes the dog laps water to consume 155 ounces.
Proportion:
(Ounces lapped in x minutes) / (Ounces lapped in 1 minute) = (Total ounces needed) / (Ounces lapped in 1 minute)
(10x) / 10 = 155 / 1
Simplify the equation:
10x = 155
Now, solve for x:
x = 155 / 10
x = 15.5
So, it will take the dog approximately 15.5 minutes to lap enough water to consume 155 ounces.
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what type of line is this
~Denki Kaminari here~
Answer:
its a best fit line
Step-by-step explanation:
because it is in-between the blue and yellow points, that is what i assume the answer is.
hope this helps :D
Answer:
oblique line.
Step-by-step explanation:
hops this helps
Which rule dilates a figure in the coordinate plane by a scale factor of 5?
Dilation involves changing the size of a figure
The dilation rule of a figure in the coordinate plane by a scale factor of 5 is (b) (x,y) [tex]\to[/tex] (5x,5y)
How to determine the dilation rule?The scale factor (k) is given as:
k = 5
Assume the coordinates of the figure is (x,y)
The dilation rule would be:
(x,y) [tex]\to[/tex] k(x,y)
Substitute 5 for k
(x,y) [tex]\to[/tex] 5(x,y)
Expand
(x,y) [tex]\to[/tex] (5x,5y)
Hence, the dilation rule is (b) (x,y) [tex]\to[/tex] (5x,5y)
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If the coordinate plane is dilated by a scale factor of 5, hence the resulting coordinate of the preimage will be (5x, 5y)
Dilation of coordinateDilation is a transformation technique that changes the size and shape of an object in an xy plane
If the coordinate point (x, y) is dilated by a factor of "k", the resulting coordinate of the preimage will be (kx, ky)
If the coordinate plane is dilated by a scale factor of 5, hence the resulting coordinate of the preimage will be (5x, 5y)
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What is the reason for statement 3 in the proof below?
Given: ABCD is a parallelogram
Prove:
Answer: Alternate interior angles theorem
Step-by-step explanation:
59+55+854+456+456+7894
Answer :
59+55+854+456+456+7894=9,774
Multiplying a number by 3 is equal to sum of the number and 5.
Answer:
this makes no sense
Step-by-step explanation:
The number that when multiplied by 3, equals the sum of the number and 5 is 2.5.
How can we solve for 2.5?First assume that the number we are looking for is x.
One side of the equation will be:
= 3 × x
= 3x
The other side of the equation would be:
= 5 + x
Equating these numbers gives:
3x = 5+ x
3x - x = 5
2x = 5
x = 5/ 2
x = 2.5
In conclusion, the number is 2.5.
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6+8 divided by 2 simplify the expression
Answer:
6+8 is 14 and 14/2 is 7.
Step-by-step explanation:
the answer is 7
The 25th term of an arithmetic series is 44.5
The sum of the first 30 terms of this arithmetic series is 765
Find the 16th term of the arithmetic series.
Show your working clearly.
Answer:
[tex]a_{16}=26.5[/tex]
Step-by-step explanation:
Arithmetic series: [tex]a_n=a+(n-1)d[/tex]
Sum of arithmetic series: [tex]S_n=\dfrac{n}{2}[2a+(n-1)d][/tex]
(where a is the first term and d is the common difference)
Given:
[tex]a_{25}=44.5[/tex][tex]S_{30}=765[/tex][tex]\implies a_{25}=44.5[/tex]
[tex]\implies a+(25-1)d=44.5[/tex]
[tex]\implies a+24d=44.5[/tex]
[tex]\implies S_{30}=765[/tex]
[tex]\implies \dfrac{30}{2}[2a+(30-1)d]=765[/tex]
[tex]\implies 30a+435d=765[/tex]
Rewrite [tex]a+24d=44.5[/tex] to make a the subject:
[tex]\implies a=44.5-24d[/tex]
Substitute found expression for a into [tex]30a+435d=765[/tex] and solve for d:
[tex]\implies 30(44.5-24d)+435d=765[/tex]
[tex]\implies 1335-285d=765[/tex]
[tex]\implies 285d=570[/tex]
[tex]\implies d=2[/tex]
Substitute found value of d into [tex]a=44.5-24d[/tex] and solve for a:
[tex]\implies a=44.5-24(2)=-3.5[/tex]
Therefore:
[tex]\implies a_{16}=-3.5+(16-1)2=26.5[/tex]