To solve the given quadratic equation, a² - 5 = -2, the first step we need to do is to represent it in the standard form by adding 2 to both sides.
A quadratic equation is solved using the quadratic formula, [tex]x = \frac{-b\pm \sqrt{b^2-4ac} }{2a}[/tex], when the equation is in the standard form, ax² + bx + c = 0, where, a, b, and c, are real numbers.
In the question, we are asked for the first step in solving a² - 5 = -2.
We can see that the provided equation is quadratic in the variable a.
To solve, the equation, we first need to represent the given equation in the standard form, ax² + bx + c = 0, where, a, b, and c, are real numbers.
To represent it in the standard form, we add 2 to both sides of the equation, to get a² - 5 + 2 = -2 + 2, or, a² - 3 = 0, which is a standard quadratic equation in the variable a.
Thus, to solve the given quadratic equation, a² - 5 = -2, the first step we need to do is to represent it in the standard form by adding 2 to both sides.
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Troy travels 100 miles in 2 hours. Find the unit rate of speed by filling in the missing number.
100 miles/ 2hours = ? miles/ 1 hour = ? miles/hour
Answer:
50 miles/1 hour = 50 miles/hour
Step-by-step explanation:
The fraction is reduced by dividing numerator and denominator by their common factor of 2.
100 miles / (2 hours) = 50 miles/ (1 hour) = 50 miles/hour
Which statements are true for the functions g(x) = x2 and h(x) = –x2 ? Check all that apply.
For any value of x, g(x) will always be greater than h(x).
For any value of x, h(x) will always be greater than g(x).
g(x) > h(x) for x = -1.
g(x) < h(x) for x = 3.
For positive values of x, g(x) > h(x).
For negative values of x, g(x) > h(x).
The answer choice which is correct regarding the two functions is; For any value of x, g(x) will always be greater than h(x).
Which statement is true for the functions?It follows from the task content that the functions given are; g(x) = x² and h(x) = –x².
On this note, since all values of x return a positive value for g(x) due to the square, it follows that the corresponding value of h(x) is always lesser.
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For a standard normal curve, find the z-score that separates the bottom 70% from the top 30%.
Using the normal distribution, the z-score that separates the bottom 70% from the top 30% is z = 0.525.
Normal Probability DistributionThe z-score of a measure X of a normally distributed variable with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex] is given by:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
The z-score measures how many standard deviations the measure is above or below the mean. Looking at the z-score table, the p-value associated with this z-score is found, which is the percentile of X.The z-score that separates the bottom 70% from the top 30% is z with a p-value of 0.7, hence z = 0.525.
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What's the total surface area of a covered box with a length of 4 ft, a width of 3 ft, and a height of 6 ft?
Answer: 108 square feet
===============================================
Work Shown:
L = 4 = length
W = 3 = width
H = 6 = height
SA = surface area of the box
SA = 2*(LW + LH + WH)
SA = 2*(4*3 + 4*6 + 3*6)
SA = 108
b)Find z
: (√z+√22)(√z-√22) = 35
Answer: [tex]\Large\boxed{z=57}[/tex]
Concept:
Here, we need to know how to expand expressions like (a - b)(a + b).
For expressions like (a - b)(a + b), the expanded form must be:
a² - b²
For checking whether it is true:
(a - b)(a + b)
= a² - ab + ba - b²
= a² - b²
Solve:
Given equation
[tex](\sqrt{z}+\sqrt{22})(\sqrt{z}-\sqrt22)}=35[/tex]
Expand the parenthesis by the concept
[tex](\sqrt{z})^2-\sqrt{22}^2=35[/tex]
Simplify the exponents
[tex]z-22=35[/tex]
Add 22 on both sides
[tex]z-22+22=35+22[/tex]
[tex]\Large\boxed{z=57}[/tex]
Hope this helps!! :)
Please let me know if you have any questions
Annel sells a phone which costs $180 and earns $9 commission. If he sells $640
worth of phones the following day, how much will he earn on commission?
Answer:
he will earn 32$ worth of commision
Step-by-step explanation:
so if the commission is 9$ and 9 is 5% of 180$ then commission percentage is 5% so to find how much commission he got selling 640$ worth of phones we just have to find 5% of 640$ which is 32$
If amelia wants to make the maximum amount of money working only 22 hours per week, which company should she work for? explain your answer.
C) Company B: Using linear regression models from both data sets, she determines that it pays about $10 more.
What is linear regression?
Linear regression analysis is used to predict the value of a variable based on the value of another variable.
The variable you want to predict is called the dependent variable.
The variable you are using to predict the other variable's value is called the independent variable.
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Amelia should work for (C) company B: using linear regression models from both data sets, she determines that it pays about $10 more.
What is a linear model?The word linear model is used differently in statistics depending on the context. The most common usage is in relation to regression models, and the phrase is frequently used interchangeably with linear regression models. However, the phrase is also used with a different connotation in time series analysis.Linear regression analysis predicts the value of one variable depending on the value of another.The variable you wish to forecast is referred to as the dependent variable.The variable you are using to forecast the value of the other variable is known as the independent variable.Therefore, Amelia should work for (C) company B: using linear regression models from both data sets, she determines that it pays about $10 more.
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The complete question is given below:
If Amelia wants to make the maximum amount of money working only 22 hours per week, which company should she work for? explain your answer.
A) Company A: Using linear regression models from both data sets, she determines that it pays about $14 more.
B) Company A: Using quadratic regression models from both data sets, she determines that it pays about $5 more.
C) Company B: Using linear regression models from both data sets, she determines that it pays about $10 more.
D) Company B: Using exponential regression models from both data sets, she determines that it pays about $8 more.
Choose the most appropriate translation of the english sentence. the amount of time spent spent driving is 5 hours
The most appropriate translation of the English sentence. the amount of time spent driving (which depends on the speed of the car) is 5 hours. is time(speed) = 5, making option C the right choice.
The time spent by a body covering a certain distance at a certain speed is given as time = distance/speed.
In the question, we are asked to translate the English sentence, :"the amount of time spent driving (which depends on the speed of the car) is 5 hours".
In the given sentence, the time spent driving is given to be 5 hours, depending on the speed of the car.
Thus, the time can be shown as a function of speed with a value of 5.
Thus, the translation can be, time(speed) = 5.
Thus, the most appropriate translation of the English sentence. the amount of time spent driving (which depends on the speed of the car) is 5 hours. is time(speed) = 5, making option C the right choice.
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The provided question is incomplete. The complete question is:
"Choose the most appropriate translation of the English sentence. the amount of time spent driving (which depends on the speed of the car) is 5 hours.
a. speed(time) = 5
b. time(5) = 50 mph
c. time(speed) = 5
d. time(speed) > 0"
tan 45- cos ~ 60° = x. Sin 45. ta
The trigonometric values we require :
[tex]\begin{tabular}{c | l}trigonometric value & numerical value \\\cline{1-2}tan 45^{o}& 1 \\cos 60^{o} & 0.5 \\sin 45^{o} & 1 \div \sqrt{2}\end{tabular}[/tex]
Now, let's solve for x.
tan 45° - cos 60° = x (sin 45°)
[tex]\mathrm {1 - \frac{1}{2} = x (\frac{1}{\sqrt{2}})}[/tex]
[tex]\mathrm {\frac{1}{2} = \frac{x}{\sqrt{2}}}[/tex]
[tex]\mathrm {x = \frac{\sqrt{2}}{2}}[/tex]
[tex]\mathrm {x = \frac{1}{\sqrt{2}}}[/tex]
The value of x is 1/√2.
I hope it helped you solve the problem
Good luck on your studies!
7
of the trains are arriving late due to a train strike.
Write down the ratio of on-time trains to late trains.
15
Answer:
15:7
Step-by-step explanation:
you put the numbers in order first the number of on time trains to off time trains
solve this if u can pls!
using the numbers 5, 7, and 8 only once each, fill in the boxes to make the statement true.
Answer:
its log 5 7/8
Step-by-step explanation:
Sierra found that 15 meters is equivalent to 49.2 feet. Which of the following is an equivalent ratio?
3 to 8.84
5 to 18.22
7 to 22.96
9 to 25.32
Answer:
7 to 22.96
Step-by-step explanation:
Hello!
We can represent each ratio as a fraction:
Original: 15 to 49.2 = [tex]\frac{15}{49.2}[/tex]3 to 8.84 = [tex]\frac{3}{8.84}[/tex]5 to 18.22 = [tex]\frac{5}{18.22}[/tex]7 to 22.96 = [tex]\frac{7}{22.96}[/tex]9 to 25.32 = [tex]\frac{9}{25.32}[/tex]To find equivalent values, we can convert each fraction into a decimal by dividing them.
ConvertOriginal: [tex]\frac{15}{49.2} = 0.304878048780488[/tex][tex]\frac{3}{8.84} = 0.339366515837104[/tex][tex]\frac{5}{18.22} = 0.274423710208562[/tex][tex]\frac{7}{22.96} = 0.304878048780488[/tex][tex]\frac{9}{25.32} = 0.355450236966825[/tex]The ratio of 7 to 22.96 is equivalent to the ratio of 15 to 49.2.
Are the two triangles similar?
Answer:
Yes
Step-by-step explanation:
The missing angle in triangle DER is 42 (as angles in a triangle add up to 180) and the missing angle in TVA (LOKI lol ) is 110 (as angles in a triangle add up to 180) .
Since all angles are equal the triangles must be similar .
Hope this helped and have a good day
What are the domain and range of g of x equals negative 3 times the square root of the quantity x minus 1? d: (1, [infinity]) and r: (0, [infinity]) d: [–3, [infinity]) and r: [0, [infinity]) d: (–3, [infinity]) and r: (–[infinity], 0) d: [1, [infinity]) and r: (–[infinity], 0]
Answer:
d: d [1, infinity) and r (-infinity, 0)
Step-by-step explanation:
right on the test :3 good luck dear!!
subtract the sum of -5/6 and -1 3/5 from the sum of 2 2/3 and -6 2/5
- 1.3 is the number we get when we subtract the sum of -5/6 and -1 3/5 from the sum of 2 2/3 and -6 2/5. This can be obtained by finding sum separately and then subtracting them.
What is the required number:Here in the question it is given that,
subtract the sum of -5/6 and -1 3/5 from the sum of 2 2/3 and -6 2/5
By separating them as two parts
sum of -5/6 and -1 3/5 sum of 2 2/3 and -6 2/5⇒ sum of -5/6 and -1 3/5
- 5/6 + - 1 3/5 = - 5/6 + - 8/5 (∵ a b/c = (ac+b)/c(5+3)/5 = 8/5)
= (- 25 - 48)/30 (LCM = 30)
= - 73/30
⇒ sum of 2 2/3 and -6 2/5
2 2/3 + -6 2/5 = 8/3 + -32/5
= (40 - 96)/15 (LCM = 15)
= - 56/15
subtract the sum of -5/6 and -1 3/5 from the sum of 2 2/3 and -6 2/5
= (sum of 2 2/3 and -6 2/5) - (sum of -5/6 and -1 3/5)
= (- 56/15) - (- 73/30 )
= - 56/15 + 73/30
= - 112/30 + 73/30 (LCM = 30)
= - 39/30
= - 13/10
= - 1.3
Hence - 1.3 is the number we get when we subtract the sum of -5/6 and -1 3/5 from the sum of 2 2/3 and -6 2/5.
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Rose and Tyler divided their 1.5kg of pizza
dough in the ratio 2:3.
How much did Rose receive?
Answer:
0.6kg
Step-by-step explanation:
first roses share becomes 2:5
then you change the kilograms into grams for an easier working
then you multiply 2:5 by 1500g to get roses share
From the figure below, identify all pairs of alternate interior and alternate exterior angles
A.
alternate exterior
exterior means outside
like a front entrance to a home
1. o & t
2. n & u
B.
alternate interior
interior means inside
like as if its inside a house
1. p & s
2. q & r
( p & s ) AND ( q & r ) both look like the letter Z
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PLEASE HELP ITS MATH PLEASE
Answer:
y=3x-5
Step-by-step explanation:
they are parallel meaning that only the constant is changing
-2 = 3(1) - (something)
-2 = 3 - (something)
something = 5. - > that was 3+2
so y=3x+(-5)
1. If R = 32 - 11 (OC+2y). then find R when: x=2 and y=4
The correct equation says to find R = 32 - 11 (X+2y). This gives us the value of -78.
How to solve for the equation belowWe have this
R = 32 - 11 (X+2y)
we have the following values for x and y as 2 and 4 respectively.
What we have to do would be to find the value of R after we have put in these values in the equation.
To do this, we would then have:
R = 32 - 11(2 + 2*4)
R = 32 -11(2+8)
R = 32 - 11 * 10
R = 32 - 110
This would give us the value that says
R = -78
Hence the value of R is given as -78
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Helppp!! pleasee i put a ss!
Answer:
-20
Step-by-step explanation:
He went back 20 and not forward 20. Everyone would want a penalty if you got to go forward.
Use the elimination method to slice the system of equations Choose the correct ordered pair 6x+2y=8 12x+y=22
Answer:
x=2 and y=-2
Step-by-step explanation:
Solution Given:
6x+2y=8....................................................[1]
12x+y=22....................................................[2]
Multiplying equation in 1 by 2 and subtracting equation 1 by 2 we get
equation 1 becomes 12x+4y=16
and subtracting by equation 2 we get
12x+4y=16
-12x-y=-22[Note: while subtracting we must change sigh)
__________________
0x+3y= -6 [note: while subtracting we must keep the sigh which have greater value]
3y=-6
dividing both side by 3, we get
3y/3=-6/3
we get y=-2
Again similarly
Multiplying equation in 2 by 2 and subtracting equation 2 by 1 we get
equation 2 becomes 24x+2y=44
and subtracting by equation 1 we get
24x+2y=44
-6x-2y=-8
_____________________
18x-0y=36
18x=36
dividing both side by 18, we get
18x/18=36/18
x=2
please help
the line ABC is tangent to a circle at B centre O with diameter EB the angle DAB = 28
(a) ABE=
(b) EDB=
(c) AOB=
(d) BOD=
(e) OBD=
(f)DBC=
Answer:
A 90°
B 90°
C 62°
D 118°
Hopefully this helps u
(d) The perimeter of the figure below is equal to 150 cm.
X
x+6
x+5
x+1
x+8
X+4
What is the length of the longest side of the polygon?
Use mathematics to explain how you determined your answer.
Use words, symbols, or both in your explanation.
Based on the given perimeter of the polygon and the length of each side; the length of the longest side of the polygon is 29 cm
Perimeter of a polygonPerimeter = 150 cmPerimeter of the polygon = x + (x + 6) + (x + 5) + (x + 1) + (x + 8) + (x + 4)
150 = x + x + 6 + x + 5 + x + 1 + x + 8 + x + 4
150 = 6x + 24
150 - 24 = 6x
126 = 6x
x = 126/6
x = 21
The longest side of the polygon is (x + 8)
= 21 + 8
= 29 cm
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what value ofx is in the solution set of 3(x-4)>5x +2?
[tex]\boldsymbol{\sf{3(x-4) > 5x +2 }}[/tex]
Use the distributive property to multiply 3 by x−4.
[tex]\boldsymbol{\sf{3x-12 > 5x+2 }}[/tex]
Subtract 5x on both sides.
[tex]\boldsymbol{\sf{3x-12-5x > 2 } }[/tex]
Combine 3x and −5x to get −2x.
[tex]\boldsymbol{\sf{-2x-12 > 2 }}[/tex]
Add 12 to both sides.
[tex]\boldsymbol{\sf{-2x > 2+12 \ \longmapsto \ \ [Add \ 2 +12]}}[/tex]
[tex]\boldsymbol{\sf{-2x > 14}}[/tex]
Divide both sides by −2. Since −2 is < 0, the inequality direction is changed.
[tex]\boldsymbol{\sf{x < \dfrac{14}{-2} \ \ \longmapsto \ \ \ [Split]}}[/tex]
[tex]\boxed{\boldsymbol{\sf{x < -7 }}}[/tex]
So in the inequality 3(x-4)>5x +2, the value of x is -7.
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https://brainly.com/question/17070130Solve the system of equations.
y equals x plus 8
y equals 3 x plus 2
Answer:
The answer is (3,11) or x = 3, y = 11
Step-by-step explanation:
:)
Answer:
(3, 11 )
Step-by-step explanation:
y = x + 8 → (1)
y = 3x + 2 → (2)
substitute y = 3x + 2 into (1)
3x + 2 = x + 8 ( subtract x from both sides )
2x + 2 = 8 ( subtract 2 from both sides )
2x = 6 ( divide both sides by 2 )
x = 3
substitute x = 3 into either of the 2 equations and solve for y
substituting into (1)
y = 3 + 8 = 11
solution is (3, 11 )
Build Your Math Skills 2C, Round decimals to the nearest hundredth (0.01): 2.364
Answer:2.36
Step-by-step explanation:
help me please 20 points
Based on the samples that the scientists picked, and the weight of these samples, the various sample means are:
3.4 pounds 3.4 pounds 3.6 pounds3.8 poundsThe range of the sample means is 0.4 pounds.
The true statements on the mean weights to be used by the scientists are:
A single sample mean will tend to be a worse estimate than the mean of the sample means. The closer the range of the sample mean is to 0, the more confident they can be in their estimate. What does the means show?First, find the sample means of each sample.
Sample 1:
= (3 + 2 + 6 + 4 + 2) / 5
= 3.4 pounds
Sample 2:
= (2 + 2 + 3 + 7 + 3) / 5
= 3.4 pounds
Sample 3:
= (6 + 4 + 2 + 2 + 4) / 5
= 3.6 pounds
Sample 4:
= (5 + 3 + 2 + 5 + 4) / 5
= 3.8 pounds
The range is;
= 3.8 - 3.4
= 0.4
The closer the range of the mean is to 0, the better the sample because it shows that in general, the sample means are the same. This is good for the research because it points to the uniformity of fish weights.
Using all the sample means as an average captures the data better than if a single sample mean is used.
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While playing baseball, sofia takes note of the extreme vectors for which she bats. what is the angle between her two extreme bats? extreme 1: <-8, 12> extreme: 2: <13, 15>
The angle between the two extreme vectors of Sofia bats is 74.60 degrees.
In this question,
The angle between two vectors will be deferred by a single point, which is called as the shortest angle at which we have to turn around one of the vectors to the position of co-directional with another vector.
The extreme vectors of Sofia bats are [tex]\vec u = < -8, 12 >[/tex] and [tex]\vec v = < -8, 12 >[/tex]
The angle between the vectors is
[tex]\theta = cos^{-1} \frac{\vec u.\vec v}{||\vec u|| ||\vec v||}[/tex]
The dot product is calculated as
[tex]\vec u. \vec v = (-8)(13)+(12)(15)[/tex]
⇒ [tex]-104+180[/tex]
⇒ 76
The magnitude can be calculated as
[tex]||\vec u|| = \sqrt{(-8 )^{2} +(12)^{2} }[/tex]
⇒ [tex]\sqrt{64+144}[/tex]
⇒ [tex]\sqrt{208}[/tex]
[tex]||\vec v|| = \sqrt{(13 )^{2} +(15)^{2} }[/tex]
⇒ [tex]\sqrt{169+225}[/tex]
⇒ [tex]\sqrt{394}[/tex]
Thus the angle between the vectors is
[tex]\theta = cos^{-1} \frac{76}{(\sqrt{208} )(\sqrt{394} )}[/tex]
⇒ [tex]\theta = cos^{-1} \frac{76}{\sqrt{81952} }[/tex]
⇒ [tex]\theta = cos^{-1} \frac{76}{286.27 }[/tex]
⇒ [tex]\theta = cos^{-1} (0.2654)[/tex]
⇒ [tex]\theta=74.60[/tex]
Hence we can conclude that the angle between the two extreme vectors of Sofia bats is 74.60 degrees.
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PLEASE HELP IM STUCK
Answer:
y = -3x + 1
Step-by-step explanation:
First, we can find the slope of the line.
The slope is (change in y)/(change in x).
We can use the points that are marked in orange: (0,1) and (1,-2)
The change in y is 1 to -2, which is -3.
The change in x is 0 to 2, which is 1.
The slope will be -3/1, which is also: -3.
We have y = -3x + b currently.
The b is the y-intercept, meaning (the point that touches the y axis, the vertical line).
The point (0,1) touches the y-intercept, so b will be 1.
We can finish our equation as: y = -3x + 1
The motion of an object was recorded by measuring the velocity of the object in meters per second at various times, as shown in the table.
The scatterplot below was graphed from the data in the table, where t represents the time, and v represents the velocity. Based on the scatterplot, which equation BEST represents the relationship between velocity and time?
The equation BEST represents the relationship between velocity and time is y = 2.2x + 6.
According to the statement
we have given some data in the form of graph according to the velocity per time and we have to find the relationship between the velocity and time.
So, for this purpose,
we know that the best method show the relationship is a slope intercept form.
So,
The slope intercept form is a the equation of a straight line in the form y = mx + b where m is the slope of the line and b is its y-intercept.
And
Using the coordinate points on the plane (0, 6) and (10, 28)
now we Determine the slope
Slope = 28-6/10-0
Slope = 22/10
Slope = 2.2
And then Determine the y-intercept
6 = 2.2(0) + b
b = 6
And now we have to put in the general form of the slope intercept form which is y = mx + b
Then the equation become
y = 2.2x + 6
So, The equation BEST represents the relationship between velocity and time is y = 2.2x + 6.
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