The value of ab=6.
What is [tex](a-b)^2[/tex] formula ?
To find the square of a binomial, use the [tex](a-b)^2[/tex] formula. One of the most common algebraic identities is the a minus b Whole Square Formula. This formula is also known as the difference between two terms squared formula. To factorise some special types of trinomials, the [tex](a-b)^2[/tex] formula is used.
Here [tex](a-b)^2 = a^2+b^2-2ab[/tex] then,
=> [tex](a-b)^2 = a^2+b^2-2ab[/tex]
Here a-b=5 and [tex]a^2+b^2[/tex] = 37.
=> [tex]5^2[/tex] = 37-2ab
=> 25 = 37-2ab
=> 2ab=37-25
=> 2ab = 12
=> ab=6.
Hence the value of ab=6.
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Select the correct answer. Based on these segment lengths, which group of segments can form a triangle? A. 3, 10, 14 B. 8, 7, 13 C. 3, 2, 5 D. 20, 7, 13 Reset Next
Using the triangle rule, the option B can form a triangle.
In the given question,
We have to choose the correct segment from the given segment, which group of segments can form a triangle.
The given options are
A. 3, 10, 14
B. 8, 7, 13
C. 3, 2, 5
D. 20, 7, 13
To check which segment form a triangle we check that sum of two sides is always greater than the third side.
Now checking the first option.
The points is 3,10,14
When we add 3 and 10 we get 13 which is not greater than the 14. So the option A is not form a triangle.
Now checking the second option.
The points is 8,7,13
When we add 8 and 7 we get 15 which is greater than the 13. Similarly when we add 13 and 7 we get 20 which is also greater than the 8. Similarly when we add 8 and 13 we get 21 which is also greater than the 7. So the option B can form a triangle.
Since we get the right answer so we didn't check further option. The way of checking the remaining option is same.
Hence, the option B can form a triangle.
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simon had $.30 he spent $6.97 at the mall , $11.37 at the dinner , and $5.50 at the arcade . How much money does have left
Answer: 6.16
minus all the values from 30
Answer:
$6.16
Step-by-step explanation:
30-6.97-11.37-5.5
=6.16
Shondra used four ounces of chocola? Sips to make ivo dozen cookies. At that rate, how many ounces of chocolate chips would she need to make five dozen cookies?
20 ounces of chocolate chips would be required to make 5 dozen cookies.
According to the question,
We have the following information:
Shondra used four ounces of chocolate chips to make 1 dozen cookies.
We know that when we find the cost or required amount of any product which is more than 1 then we use multiplication to find the result.
So, we will multiply 5 dozen of cookies by the number of ounces of chocolate chips required for 1 dozen cookies.
Chocolate chips for 5 dozen cookies = 5*4
Chocolate chips for 5 dozen cookies = 20 ounces
Hence, 20 ounces of chocolate chips would be required to make 5 dozen cookies.
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In 6 minutes, a conveyor belt moves 300 pounds of recyclable aluminum from the delivery truck to a storage area. A smaller belt moves the same quantity of cans the same distance in 18 minutes. If both belts are used, find how long it takes to move the cans to the storage area.
If we use both belts, it takes 4.5 minutes to carry the can to the storage area.
Let's assume, t = time required to move 300 pounds using both belts.
For this first calculate the speed or mass flow rate of each conveyor belt.
The big one can do 300 pounds in 6 minutes, so its speed is 300 pounds/6 minutes = 50 pounds/minute.
The smaller one takes 18 minutes, so the speed is 300 pounds/18 min = 50/3 pounds/minute.
We can see that the combined speed of both machines when working together is 50 + 50/3 = 50 (1 + 1/3) = 50 x 4/3 = 200/3 pounds/minute.
Then we find that the two machines together can transfer 300 pounds in t = 300/200/3 = 300/200 x 3 = 4.5 minutes.
Alternate Method:
We can do that too
Let t = the time required to move 300 pounds on both belts.
Job completed = 1 (300 pounds moved)
t/6 + t/18 = 1
Taking L.C.M
=> (3t + t)/18 = 1
=> 4t/18 = 1
=> t = 4.5 minutes
Hence, it takes 4.5 minutes to carry the can to the storage area.
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Which is more, 70 inches or 6 feet?
A city bus has a wheelchair ramp. When the bus is raised so that the door is 2 feet above the ground, the end of the ramp is 3 feet away from the bus. If the bus is lowered so the door is 1.5 feet above the ground, approximately how far away will the end of the ramp be from the bus?
Answer:
.5 feet away
Step-by-step explanation:
3 divided in half is 1.5
so 2 in half is .5
hope this helps!
Answer:
3.3
Step-by-step explanation:
Plato(edmentum) users
Barry completed his first semester in college. His grades are in the table below. Using the information: A = 4 points, B = 3 points, C = 2 points, D = 1 point, F = 0 points, calculate Barry's semester grade point average (GPA). Round to the nearest hundredth.
Barry's semester grade point average (GPA). Round to the nearest hundredth is 2.67
How to calculate the GPAThe GPA is calculated by following the procedures
the multiplication
credit hour * grade
= 4 * 3 = 12
= 2 * 4 = 8
= 3 * 2 = 6
= 3 * 2 = 6
sum of the products = 12 + 8 + 6 + 6 = 32
sum of credit hour = 4 + 2 + 3 + 3 = 12
The GPA
= sum of the products / sum of credit hour
= 32 / 12 = 2.67
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Out of 53 people 24 are men what percentage is men
Answer: 24% out of 53 people
Step-by-step explanation:
Answer:
45.3% are men
Step-by-step explanation:
Find the measure of the requested angle.
d =
e =
Answer:
e is 63 degrees
d is 31 degrees
The number of newly reported crime cases in a county in New York State is shown in the accompanying table, where x represents the number of years since 2011, and y represents number of new cases. Write the linear regression equation that represents this set of data, rounding all coefficients to the nearest hundredth. Using this equation, estimate the calendar year in which the number of new cases would reach 1141.
The linear regression equation that represents this set of data is given by:
y = 30x + 854.6.
The predicted calendar year in which the number of new cases would reach 1141 is:
2020.
How to obtain the linear regression equation?The format of the linear regression equation is given as follows:
y = mx + b.
In which the coefficients are listed as follows:
m is the slope.b is the y-intercept.The equation is built inserting the points given on the table into a linear regression calculator.
The points from the table given by the image at the end of the answer are given as follows:
(0, 856), (1, 871), (2, 924), (3, 961), (4,961).
Inserting these points into a calculator, the equation is given as follows:
y = 30x + 854.6.
The predicted calendar year in which the number of new cases would reach 1141 is 2011 + integer part of x, when y = 1141, hence:
1141 = 30x + 854.6
x = (1141 - 854.6)/30
x = 9.54.
Hence during the year of 2020.
Missing InformationThe table is given by the image shown at the end of the answer.
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"A toy rocket is shot vertically into the air from a launching pad 7 feet above the ground with an initial velocity of 72 feet per second. The height in feet, of the rocket above the ground at t seconds after launch is given by the function h(t)=-16 t²+72 t+7. How long will it take the rocket to reach its maximum height? What is the maximum height?
The rocket reaches its maximum height at second(s) after launch.
(Simplify your answer.)
The maximum height reached by the object is feet.
(Simplify your answer.)"
The time taken for the rocket to reach its maximum height is; 2.25 seconds.
The maximum height reached by the toy rocket whose initial velocity is; 72 feet per second is; 88 feet.
What is the maximum height reached by the rocket?It follows from the task content that the maximum height reached by the rocket is to be determined.
The given function is; h (t) = -16 t² + 72t + 7.
Since it follows from evaluation that; at maximum height, the rate of change of height to time is equal to 0.
Therefore; at maximum height;
h'(t) = 0
h'(t) = -32t + 72 = 0
-32t = -72
t = -72/-32
t = 2.25 seconds.
Therefore, the time taken for the rocket to reach its maximum height is; 2.25 seconds.
Also, the maximum height reached by the rocket is at; h (2.25);
h(2.25) = -16(2.25)² + 72 (2.25) + 7
= -81 + 162 + 7
= 88.
The maximum height reached is; 88 feet.
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At the end of a snow storm, Audrey saw there was a lot of snow on her front lawn.
The temperature increased and the snow began to melt at a steady rate. There was a
depth of 10 inches of snow on the lawn when the storm ended and then it started
a melting at a rate of 2 inches per hour. Write an equation for S in terms of t,
snow
representing the depth of snow on Audrey's lawn, in inches, t hours after the snow
stopped falling.
An equation that represents the depth of snow on Audrey's lawn, in inches, t hours after the snow stopped falling is S = 10 - 2t
In this question, there was a depth of 10 inches of snow on the lawn when the storm ended and then it started a melting at a rate of 2 inches per hour.
We need to write an equation for S in terms of t, snow representing the depth of snow on Audrey's lawn, in inches, t hours after the snow stopped falling.
So, the equation would be,
S = 10 - 2t
Therefore, an equation that represents the depth of snow on Audrey's lawn, in inches, t hours after the snow stopped falling is S = 10 - 2t
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IXL help FAST PLEASE !
Answer:
x=9
Step-by-step explanation:
these 2 angles are equivalent so we set them equal to each other
124-x=8x+43
81-x=8x
81=9x
9=x
Hopes this helps please mark brainliest
Find the y-intercept of the linear functions with a slope -4 and the point ( 2, 20 )
need asap
Answer:
[tex]\huge\boxed{\sf b = 28}[/tex]
Step-by-step explanation:
Point (x,y) = (2,20)
So, x = 2 and y = 20
Also,
Slope = m = -4
Slope-intercept equation:y = mx + bWhere b is y-intercept.
Put the above given data in this equation.
20 = (-4)(2) + b
20 = -8 + b
Add 8 to both sides
20 + 8 = b
28 = b
b = 28[tex]\rule[225]{225}{2}[/tex]
y=mx+c. y=20
x=2
m=-4
20= -4(2)+c
20= -8+c
20+8=c
28=c
Given right triangle ABCABC with altitude \overline{BD} BD drawn to hypotenuse \overline{AC} AC . If AD=9AD=9 and DC=4,DC=4, what is the length of \overline{BD}? BD ?
The length of BD is 6.
Given, a right triangle ABC with an altitude BD.
On using concept of Similarity in triangle ADB and CDB,
AD/BD = BD/CD
9/BD = BD/4
36 = BD²
BD² = 36
BD = 6
So, the length of BD is 6.
Hence, the length of BD is 6.
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Peter got 40 for his birthday his mom told him that he needed to put one-fourth of it into his bank to save .How much must he put into his bank
If Peter were to put one fourth of what he got in his birthday to the bank then peter is putting 10 in the bank
How to find the one fourth of what peter gotInformation given in the problem
Peter got 40 for his birthday
one-fourth of it into his bank to save
The problem requires multiplication of fractions
one fourth means 1 / 4
one fourth of what Peter got is 1/4 * 40
this is calculated as follows
= 1/4 * 40
= 10
Therefore peter have to put 10 into the bank
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The difference between two whole numbers is 6. Twice the smaller number is 10 more than the larger number. What is the smaller number?
The smaller number from the given situation is 16.
Given that, the difference between two whole numbers is 6.
What is an equation?In mathematics, an equation is a formula that expresses the equality of two expressions, by connecting them with the equals sign =.
Let the larger number be x and the smaller number be y.
The difference between two whole numbers is 6.
So, x-y=6
x=6+y --------(I)
Twice the smaller number is 10 more than the larger number.
x+10=2y
x=2y-10 --------(II)
Substitute equation (I) in equation (II), we get
6+y=2y-10
⇒ y=16
Hence, the smaller number from the given situation is 16.
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FELLOW K12 STUDENTS I NEED YOUR HELP!!! I NEED THE CORRECT ANSWER....I'LL GIVE BRAINLIEST TO THE FIRST ONE WITH THE RIGHT ANSWER!!
The comparison of the equations are
Parallel to line a: y = 1/4x + 1Perpendicular to line a: 4x + y = -3Neither parallel not perpendicular to line a: -4x + y = -8How to compare the equations?From the question, we have the following equation that can be used in our computation:
-x + 4y = 32
Add x to both sides of the equation
So, we have the following representation
4y = x + 32
Divide through by 4
So, we have
y = 1/4x + 32/4
Evaluate
y = 1/4x + 8
A linear equation is represented as
y = mx + c
Where
Slope = m
As a general rule, linear equations that have the same slope are parallel
This means that the equation y = 1/4x + 1 is parallel to y = 1/4x + 8
Also;
The slopes of perpendicular lines are opposite reciprocals
This means that the equation 4x + y = -3 is perpendicular to y = 1/4x + 8
Lastly, the third equation would neither parallel not perpendicular to the line.
This is because the first equation is parallel and the second equation is perpendicular
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A website is selling toy rockets for $41, but mentions that they originally cost $50. What is the discount percentage?
Answer:
18%
Step-by-step explanation:
percentage discount is calculated as
[tex]\frac{discount}{original}[/tex] × 100%
here discount = $50 - $41 = $9 , then
% discount = [tex]\frac{9}{50}[/tex] × 100% = 9 × 2% = 18%
What is the equation of these lines with a gradient and point: gradient of -3 passing through the point (-2, -6)?
Equation of the line which is passing through the point (-2, -6) and has the gradient of -3 is equal to y = -3x -12.
As given in the question,
Gradient of the required equation of the line is given by :
Gradient is slope.
Let slope is represented by m = -3
Line passing through the point (-2, -6) is given by :
( x₁ , y₁) = ( -2 , -6)
Equation of the line which is passing through the point (-2, -6) and has the gradient of -3 is given by :
y - y₁ = m ( x - x₁)
⇒ y - (-6) = (-3)(x - (-2))
⇒ y + 6 = -3( x + 2)
⇒ y + 6 = -3x - 6
⇒ y = -3x -12
Therefore, equation of the line which is passing through the point (-2, -6) and has the gradient of -3 is equal to y = -3x -12.
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half a number less than 3 is at most 5. translate as a equation or inequality.
It will be written as inequality
3 - (x / 2) ≤ 5
Inequality is a mathematical relation which is use to make non-equal comparisons between equations or numbers.
Now let us look at the question.
Half a number less than 3. Let us suppose the number to be 'x' so
3 minus half of x which can be written as 3 - (x / 2)
Next it says that it is at most 5 which means it will be 5 or less than that.
Therefore we can easily write it as inequality 3 - (x / 2) ≤ 5
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Calculate the range, population variance, and population standard deviation for the following data set. If necessary, round to one more decimal place than the largest number of decimal places given in the data.
10,20,11,17,15,8,7,16,19,15
The range from the given table is 9, the population variance is 18.56, and the population standard deviation is 4.30.
Given the value:
xi 10 20 11 17 15 8 7 16 19 15 Total = 138
xi^2 100 400 121 289 225 64 49 256 361 225 Total = 2090
From the above, we get
n =10, ∑xi = 138, ∑xi^2 = 2090
(a) For the range:
Here, the smallest value = 10, and largest value = 19
Therefore, Range = Largest value - Smallest value
Range = 19 - 10 = 9
(b) For population variance:
For mean:
Mean of x = ∑xi/n = 138/10 = 13.8
V (X) = ∑(xi^2)/n - Mean of x^2
= 2090/10 - 13.8^2
= 209 - 190.44
V (X) = 18.56
(c) For population standard deviation:
[tex]SD (X) = \sqrt{VAR(X)}[/tex]
SD(X) = [tex]\sqrt{18.56}[/tex]
SD(X) = 4.30
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Step-by-step explanation:
The range from the given table is 9, the population variance is 18.56, and the population standard deviation is 4.30.
Given the value:
xi 10 20 11 17 15 8 7 16 19 15 Total = 138
xi^2 100 400 121 289 225 64 49 256 361 225 Total = 2090
From the above, we get
n =10, ∑xi = 138, ∑xi^2 = 2090
(a) For the range:
Here, the smallest value = 10, and largest value = 19
Therefore, Range = Largest value - Smallest value
Range = 19 - 10 = 9
(b) For population variance:
For mean:
Mean of x = ∑xi/n = 138/10 = 13.8
V (X) = ∑(xi^2)/n - Mean of x^2
= 2090/10 - 13.8^2
= 209 - 190.44
V (X) = 18.56
(c) For population standard deviation:
SD (X) = \sqrt{VAR(X)}SD(X)=
VAR(X)
SD(X) = \sqrt{18.56}
18.56
SD(X) = 4.30
Learn at brainlyWhich triangle congruence postulate or theorem proves that these triangles
are congruent?
These triangles can be proven congruent by using S-A-S rule.
What is congruent triangles?
Two triangles are same to be congruent if all 3 corresponding sides ar equal and every one the 3 corresponding angles ar equal in measure. These triangles will be slides, rotated, flipped and turned to be looked identical. If repositioned, they coincide with one another. The symbol of congruence is’ ≅’.
Main body:
In ΔABC and ΔXYZ
AC = XZ ---(1)
∠C = ∠ Z ---(2)
BC = YZ ---(3)
using 1, 2 ,3 we can prove that ΔABC and ΔXYZ are congruent.
Hence ΔABC and ΔXYZ are congruent.
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Plsssssssss helpppppppppppp
Answer: Troy
Step-by-step explanation:
Troy’s equation has a slope of 28, so next you need to calculate Lucy’s slope: Go up 25, over to the right 1, so the slope is 25.
Troy has a greater slope, so his is steeper.
10 points :) Brainiest first answer :))
the typical person gets to bring home 77% of their paycheck. Assuming that Joe is a typical person that makes $5.25 an hour, and works 32 1/2 hours a week, how much money would Joe get to bring home each week (net pay)?
Answer:
below
Step-by-step explanation:
$ 5.25 /hr * 32.5 hr * .77 = 131.38 dollars
A fast-growing strain of bacteria doubles in population every
20 minutes. A laboratory has a culture of 200 of these
bacteria cells. Which of the following is closest to the total
number of bacteria cells after 2 hours?
Answer:
Im pretty sure its 12,800 bacteria
Step-by-step explanation:
Which expressions are equal to 3 1/4 - (-5/8)
Answer:B 3 1/4 + (5/8)
D 3 1/4 + (+5/8)
Step-by-step explanation:
Calculation
an expression is the combination of numbers and operators like +, - * or /
If we have any equal sign then it is an equation .
Given expression is :
to find out equivalent expression we remove the parentheisis by multiplying negative inside the parenthesis
Negative times negative becomes positive
first fraction is positive . So it remains the same
Multiply negative inside the parenthesis . Negative times negative is positive
so, the equivalent expressions are
5+8(3+x) simplify the expression. Please show your work
Answer:
29+8x
Step-by-step explanation:
5+8(3+x)
5+24+8x - Open parentheses
29+8x - Add like terms
What is the equation of the line that passes through the point (-4, -8) and hads a slope of
5/2
Answer:
y = 5/2x - 8
Step-by-step explanation:
Question 12(Multiple Choice Worth 2 points)
(Writing Two-Step Equations MC)
A new gaming chair costs $455.95. You have already saved $136.45 and earn $35.50 each week babysitting. Write and solve an equation to determine how many weeks, w, you must babysit to earn enough money to buy the new gaming chair.
35.5 + 136.45w = 455.95; w = 9
35.5w + 136.45 = 455.95; w = 9
35.5w − 136.45 = 455.95; w = 17
35.5w − 455.95 = 136.45; w = 17
Answer:
(b) 35.5w + 136.45 = 455.95; w = 9
Step-by-step explanation:
You want an equation to determine how many weeks, w, you must babysit to earn $455.95 at the rate of $35.50 each week, having already saved $136.45.
RelationsIf you earn $35.50 each week for w weeks, your total earnings will be ...
35.50w
When that amount is added to the amount you already have, $136.45, the sum is ...
35.5w +136.45
You want that total to be $455.95, which gives you the equation ...
35.5w +136.45 = 455.95
SolutionTo solve this 2-step equation, subtract the left-side constant:
35.5w = 319.50
The second step is to divide by the coefficient of the variable:
w = 319.50/35.5
w = 9
