After solving the quadratic equation x² + 3x = 40 using the quadratic formula, (A) x = –8, x = 5
We can solve this quadratic formula by following a few steps.
The given equation is,
x² + 3x =40
Let's subtract 40 from both sides,
x² + 3x - 40 =40 - 40
Or, x² + 3x - 40 = 0
Now, we have to find a suitable pair of factors of -40 which is capable to generate +3 ( coefficient of x ).
The required pair is 8 and -5, and ( 8 - 5 ) = 3
[ -40 = 8 × -5 ]
Therefore, x² + 3x - 40 = 0
Or, x² + ( 8 - 5 )x - 40 = 0
Or, x² + 8x - 5x - 40 = 0
Or, x ( x + 8 ) - 5 ( x + 8 ) = 0 [ taking x and 5 as common ]
Or, ( x + 8 ) ( x - 5 ) = 0 [ taking ( x + 8 ) as common ]
If the multiplication or product of two or more terms is zero, then we can write each term as zero.
Hence we can write,( x + 8 ) = 0
Or, x = -8 ( by subtracting 8 from both sides )
Again we can write,( x - 5 ) = 0
Or, x = 5 ( by adding +5 with both sides )
Now, we can conclude that x = -8 and 5.
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What is the rate of change of the following equation? y=5/3x - 3
Answer:
5/3 is the slope. slope is the same thing as rate of change
Step-by-step explanation:
Guys i need help is this right?
The domain of the function in this situation as required in the task content is; Choice H; 0 ≤ x ≤ 5.
What is the domain of the function for this situation?It follows from the task content that the domain of the function described by the situation is to be determined.
Since the domain is the set of all possible input values, otherwise termed the independent variable, x.
It follows that since one runner runs for at most t hours; the domain is; Choice H ; 0 ≤ x ≤ 5.
Please Note: The set of all possible output values of a function, otherwise termed the dependent variable, y is called the Range.
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a couple plans to have three children. there are eight possible arrangements of girls and boys. for example, ggb means the first two children are girls and the third child is a boy. all eight arrangements are (approximately) equally likely.
The sample space of the three children that the couple will have will be:
S = (BBB, BBG, BGB, GBB, BGG, GBG, GGB, GGG)
How to illustrate the information?From the information given, the couple plans to have three children. there are eight possible arrangements of girls and boys.
Therefore, the sample space of the three children will be:
N(S) = 2³
= 2 × 2 × 2
= 8
The eight arrangements are illustrated above.
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1. Compare two spheres. The first has a diameter of 4 inches.
The second sphere has a diameter of 428 inches.
Determine the ratio of the volume of the large sphere to the volume
of the small sphere.
Ratio =
Answer:
1,225,043
Step-by-step explanation:
You want the ratio of volumes of spheres 428 inches and 4 inches in diameter.
VolumeThe volume of a sphere in terms of its diameter is ...
V = (π/6)d³
The ratio of the volumes of the larger to smaller sphere is ...
[tex]\dfrac{V_{large}}{V_{small}}=\dfrac{\pi/6\cdot428^3}{\pi/6\cdot4^3}=\left(\dfrac{428}{4}\right)^3=107^3=\boxed{1,\!225,\!043}[/tex]
The ratio of volumes is 1,225,043.
The ratio of the volume of the large sphere to the volume of the small sphere is 1225043:1
The following is the formula for finding the volume of a sphere:
V = [tex]\frac{4}{3} \pi r^3[/tex]
Now, the normal assumption is that we must use the formula to calculate the volume of both spheres in order to compare. However, observe that in comparing the volume of two different spheres, the only difference between them is the radius, thus we can compare the two spheres directly in this way:
[tex]\frac{(radius of sphere B)^3 }{(radius of sphere A)^3}[/tex]
So,
[tex](\frac{428}{4})^3[/tex]
[tex]107^3[/tex]:1
12,25,043:1.
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1.97 x 10 3 Standard Notation
The answer to the given notation is 1970
What is standard notation ?Any value between 1.0 and 10.0 that can be expressed as a decimal number and multiplied by a power of 10 is referred to as being in standard form. If you look closely, you will see that 1.23 is a decimal between 1.0 and 10.0, and as a result, we have the standard form of 123,000,000 as 1.23 108.
This is already an standard notation : 1.97 × 10³
10 raised to the power three means there are three zeroes.
thus if we were to solve this question it will be
1.97 × 1000
which is equal to 1970.00
= 1970 .
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A concession stand sells drinks and hotdogs. The number of drinks sold is 5 more than 4 times the number of hotdogs sold. The stand sold 500 items. How many hotdogs were sold?
Pleas help
Two or more expressions with an equal sign is called as Equation. We solve the problem by forming equations, After solving equations we came to know that 123 hotdogs were sold in the concession stand.
What is Equation?Two or more expressions with an equal sign is called as Equation.
Given that,
A concession stand sells drinks and hotdogs.
The number of drinks sold is 5 more than 4 times the number of hotdogs sold.
The stand sold 500 items.
Let the number of hotdogs=x
The number of drinks sold is 5 more than 4 times the number of hotdogs sold.
The number of drinks=5+4x
stand sold 500 items.
Let us formulate a equation by given data
5+4x=500
Let us separate the variable x on one side.
Subtract 5 on both sides
5+4x-5=500-5
4x=500-5
4x=495
Divide both sides by 4
x=123.25
Hence 123 hotdogs were sold in the concession stand.
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What must be the units of R, the gas constant, in this formula? A. Newton • meter per kelvin B. mole • kelvin per Newton • meter C. Newton • meter per mole • kelvin D. Newton • meter • kelvin per mole
Solve R:
Multiply both sides of the equation by V:
[tex]\begin{gathered} PV=V\cdot\frac{\text{nRT}}{V} \\ \\ PV=nRT \end{gathered}[/tex]Divide both sides of the equation by nT:
[tex]\begin{gathered} \frac{PV}{nT}=\frac{\text{nRT}}{nT} \\ \\ \frac{PV}{nT}=R \end{gathered}[/tex]Then, R is:
[tex]R=\frac{PV}{nT}[/tex]Use the given units in the equation above:
[tex]R=\frac{N\cdot m^3}{mol\cdot K}[/tex]Then, the units of R are: Newton*cubic meter per mol*Kelvinsimplify a5/a2. can someone help fast
Answer:
⇔[tex]a^{3}[/tex]
Step-by-step explanation:
Law of Indices
Division law: [tex]\frac{a^{5} }{a^{2} }[/tex] =[tex]a^{5-2} =a^{3}[/tex]
NEED HELP IMMEDIATELY!!!
Answer:
1. m∠P + m∠Q + m∠R = 180°
2. x = 10
Step-by-step explanation:
By the triangle sum theorem, the sum of the angles in a triangle is 180°. Therefore, using the given sum theorem, m∠P + m∠Q + m∠R = 180°. Using the substitution property, (5x)° + (5x)° + (8x)° = 180°. Simplifying the equation gets 18x = 180°. Finally, using the division property of equality, x = 10.
I hope this helps!
9 girls and 3 boys write left-handed what is the percent
Answer:
You need more context.
Step-by-step explanation:
What percentage are we solving for?
Alice was given 15.5 divided by 0.25 to divide. Alice says she knows the way that she can find the quotient without even dividing. Is Alice correct?
Answer:
i'm not sure i looked it up but from it says you you can find the quotient by using the opposite of division which is multiplying again I'm not sure i might be wrong but please let me know if its right
Step-by-step explanation:
Luis wants to buy a skateboard that usually sells for $79.01. All merchandise is discounted by 12%. What is the total cost of the skateboard if Luis has to pay a state sales tax of 6.75%. Round your intermediate calculations and answer to the nearest cent. The total cost of the skateboard is?
The total cost of the skateboard after being discounted by 12% and then sales tax of 6.75% is$74.22.
What is the percentage?The percentage is defined as a given amount in every hundred. It is a fraction with 100 as the denominator percentage is represented by the one symbol %.
As per the given,
Usually, the price of the skateboard = $79.01
The 12% of 79.01 ⇒ (12/100)79.01 = $9.4812
The price after a 12% discount
79.01 - 9.4812 = $69.5288
The 6.75% of 69.5288 ⇒(6.75/100)69.5288 = $4.693194
The total price after applying the 6.75% tax,
$69.5288 + $4.693194 = $74.22
Hence "The total cost of the skateboard after being discounted by 12% and then sales tax of 6.75% is$74.22".
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What are the next three terms
125, -25, 5, ...
Answer:
25, 125, 3125, 78125, 1953125
Answer:
-1 ; 1/5 ; -1/25
Step-by-step explanation:
125 : (-5) = -25
-25 : (-5) = 5
5 : (-5) = -1
-1 : (-5) = 1/5
1/5 : (-5) = -1/25
Point B' is the image of point B after a reflection in a line. Write the equation of the line.
B(2,-4), B'(6,-4)
Thanks! <3
The slope and intercept of the line are -2 and 0. The equation of the line is y = -2x
Equation of LineTo find the equation of line, we have to find the slope of the equation and its y-intercept.
The slope of a line can be calculated as
[tex]m = \frac{y_2 - y_1}{x_2 - x_1} \\m = \frac{-4 - (-4)}{6 - 2}\\m = \frac{-8}{4} \\m = -2[/tex]
The slope of the line is equal to -2.
Lets find the intercept of the line;
The line of an equation is given as
[tex]y = mx + c[/tex]
We can pick point A and substitute its values to find c
[tex]y = mx + c\\- 4 = -2(2) + c\\-4 = -4 + c\\c = -4 + 4\\c = 0[/tex]
The equation of the line is y = -2x
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i would really appreciate it, if I can get some help! Please look at both photos!
-
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An isosceles triangle has a perimeter of 46 inches. The base is 6 less than twice each of the congruent legs. What is the sum of the lengths of the two congruent legs?
Answer: 26 inches
Step-by-step explanation:
An isosceles triangle has two congruent legs.
1) Set up the equations
P = b + 2L
b = 2L-6
2) Substitute for variables
46 = (2L - 6) + 2L
3) Solve the equation
46 = 4L - 6
52 = 4L
13 = L
4) Solve the problem
It asks for what is the sum of the two congruent legs
13 + 13 = Ans
26 = Ans
Jake spent a total of $40 dollars on the items below 4 movie tickets for $6 each 2 bags of popcorn for $7 4 drinks for $2.25 each what percent of the $40 did jake spend on movie tickets?
Answer: Jake spent 62.5% of the money on movie tickets.
Step-by-step explanation: He spent 6 x 4 = $24 on movie tickets.
He spent 7 x 2.25 = 15.75 on drinks
However, it is asking for the amount of money he spent on MOVIE TICKETS. So then it would be 25/40 or 5/8.
customers send emails to a help desk of an online retailer every 2 minutes, on average, and the standard deviation of the inter-arrival time is also 2 minutes. the online retailer has three employees answering emails. it takes 4 minutes to write a response email, on average. the standard deviation of the service times is 2 minutes. this is a g/g/k queue. what is the arrival rate? what is the service rate?
The arrival rate is found to be 30 emails per hour and the service rate is calculated to be 45 emails per hour.
It has been mentioned in the question that in every 2 minutes, customers send emails to a help desk of an online retailer, on an average, and the standard deviation of the inter-arrival time is also given to be 2 minutes. The online retailer has three employees for answering those emails.
It takes almost 4 minutes to write a response email to the customer, on average. The standard deviation (SD) of the service times is 2 minutes. This is a g/g/k type queue.
Therefore the arrival rate per hour is given by the following relation:
Arrival rate in 1 hr = No. of minutes in an hr / inter arrival time of email taken in minutes
Given here,
No. of minutes in an hour = 60 minutes
Inter arrival time of the email taken in minutes = 2 minutes
∴ Arrival rate in 1 hr = 60 / 2
= 30 emails / hr
Hence the arrival rate is 30 emails per hour.
Now for finding out the service rate we have the following formula:
Service rate = No. of minutes in an hr x No. of employes answering/ average time that is required to write response email
Given here,
No. of minutes in an hr = 60 minutes
No. of employes answering = 3
Average time that for writing response email = 2 minutes
∴ Service rate = 60 * 3 / 4
= 45 emails / hr
Hence the service rate is 45 emails per hour.
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30 POINTS! What is the domain and range of g(x) = |x + 4|
Answer:
Domain: (−∞,∞),{x|x∈R}
Range: (−∞,∞),{y|y∈R}
An image of a book shown on a website is 1.5 inches wide and 3 inches tall on a computer monitor. The actual book is 9 inches wide.
Type the answers to the questions below in the boxes.
1. What scale is being used for the image?
inch to
inches
2. How tall is the actual book?
inches
The height will be 18 inches and the scale is 1 inch = 6 inches.
1.5 inches is the width of a book picture shown on a website.
And the book's length, as displayed on the website, is 3 inches
The book's real width is 9 inches.
The book image's size is
6 inches to one inch
The book is actually three and six pages long.
The size of the real book is 18 inches long and 9 inches broad.
Hence the scale is 1 inch is equal to 6 inches and height is 18 inches.
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Select all of the values that have exactly 3 significant digits.
0.0807
O 005.5
13.41
0367.0
☐ 1,990
All the values with exactly three significant digits are: 0.0807, 1990
Significant digits of a number tell us what the actual meaningful representation of a number is. There are certain rules to figure out which digits in a number are significant such as
All non-zero digits in any number are significant. Ex: 33.4 has 3 significant digits; 19875 has 5 significant digits.All zeros between two non-zero digits are significant. Ex: 103.0078 has 7 significant digits. 700519 has 6 significant digits.Leading zeros that is all zeros to the left of the first non-zero digit and all zeros to the right of a decimal point are insignificant. 0.00081 has 2 significant digits; 0.547 has 3 significant digits.Zeros to the right of a decimal point are significant if and only if they are not followed by a non-zero digit. Ex; 92.00 and 20.00 both have 4 significant digits.After a decimal point, all zeros after the last non-zero digit are significant. Ex: 0.0079800 has 5 significant digitsTrailing zeros are significant in a whole number with a decimal point shown and insignificant if there is no decimal point shown. Ex: 540. has 3 significant digits while 540 has 2 significant digits.Thus the numbers with 3 significant digits are: 0.0807, 1990
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is m parallel to n. If so state the theorem you can use
Find the equation of the line that is perpendicular to the line y =5x + 6 and passes through the point (-3,3). Write the equation in point slope form.
The point-slope form of equation of the line perpendicular to the line y = 5x + 6 nd passing through (-3,3) is x + 5y = 12.
If two lines are perpendicular to each other, then the product of slopes of these two lines is equal to -1.
The provided line is y = 5x + 6,
The slope M₁ of the line is equal to the coefficient of x,
M₁ = 5
Let the slope of the perpendicular line is M₂,
So, we can write,
M₁M₂ = -1
M₂ = -1/5.
Now, we can use the point slope form of the equation of line, according to which is if line passes through (a,b) and have slope m then the equation of the line will be,
(y-a) = m(x-a)
This form of line is called Point-slope form of line.
Then, the equation of the line with slope -1/5 and passing through (-3,3) will be,
(y-3) = -1/5(x+3)
-5y+15 = x+3
x + 5y = 12
The above equation is the required equation of line in point slope form.
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Evaluate. Write your answer as a whole number or as a simplified fraction.
Submit
Answer: 1/121
Step-by-step explanation:
Any number raised to the power of 0 is 1
11^2 = 121
whait is the formula of mean deviation
The formula of mean deviation = [Σ |X – µ|]/N
What is mean deviation?
Mean deviation defined as a statistical measure that is used to calculate the average deviation from the mean value of the given data set.
The formula of mean deviation is [Σ |X – µ|]/N
Here,
Σ represents the addition of values
X represents each value in the data set
µ represents the mean of the data set
N represents the number of data values.
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The graph of the equation y = 4x + 2, what is the y when x = 1?
Answer: 6
Step-by-step explanation:
[tex]y=4(1)+2=6[/tex]
solve the absolute value inequality and express the solution in interval and algebraic notation
Answer:
[-10, - 2]
Step-by-step explanation:
1
Solve the inequality: ly+ 61 - 4 <0
-10 ≤ and ≤-2
2 Express solution set in interval notation:
[-10, -2]
when a study uses – , each member of a population has an equal chance of being selected. – occurs when researchers randomly sample subsets of the population and then use all individuals within the subsets. – is often used to select participants to represent, in an unbiased way, subsets of the population that are not large enough to be accurately measured. all three of these techniques are – sampling techniques.
When a study uses random sampling, each member of a population has an equal chance of being selected.
Cluster sampling occurs when researchers randomly sample subsets of the population and then use all individuals within the subsets.
Oversampling is often used to select participants to represent, in an unbiased way, subsets of the population that are not large enough to be accurately measured.
All all three of these techniques are representative sampling techniques.
What is sampling?It should be noted that sampling simply means the selection of subjects from the entire population.
In a random sampling, everyone has equal opportunity of being picked.
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Simplify the expression.[(-5)1]3
The simplified expression is -125.
The expression given to us is [(-5)^1]³.In contrast to algebraic expressions, which include variables, numbers, and mathematical operators, arithmetic expressions simply contain numbers and mathematical operators.There are several laws of indices, often known as indices rules, including those governing division, multiplication, power of 0, brackets, negative powers, and fractional powers.We need to apply the laws of indices given below :(a^m)^n = a^(mn)Applying the above rule to our given expression.[(-5)^1]³ = (-5)^(1*3)The expression is simplified further.[(-5)^1]³ = (-5)³We know that a negative number raised to an odd power is always negative.[(-5)^1]³ = -125.Thus, the final simplified expression is -125.To learn more about indices, visit :
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Subtract -1 3/5 - (-2 7/8)
Answer:
Answer down below!
Step-by-step explanation:
Your answer would be 1 11/40
For the steps, refer to the image below!