Answer:
a + 8
Step-by-step explanation:
Note that
(x + y)² = x² + 2xy + y²
= x² + y² + 2xy
= a + 2(4) = a + 8
Here, we are required to determine an expression equal to (x + y)²
The correct answer is therefore (a + 8)
First, x² + y² = a can be rewritten completing the square method as;
(x+y) (x+y) = a + 2xy
when we expand the expression above; we have;
x² + 2xy + y² = a + 2xy
since, 2xy is present on both sides of the equation;
we still get the expression; x² + y² = a
Therefore, (x+y)² = a + 2xy
we can then substitute the value 4 for xy in the equation above;
Thus, since xy = 4, therefore 2xy = 8
Consequently, (x+y)² = a + 8
The correct answer is therefore (a + 8)
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Jason worked to earn $298.45 and William worked to earn $190.00. If the
both earn $6.35 per hour, how many hours did Jason work?
Answer:
47
Step-by-step explanation:
298.45/6.35=47 its ez just some division
Answer:
47
Step-by-step explanation:
298.45/6.35= 47
Simplify the expression 3a + b, when a=1.4 -2x and b=-0.2x + 1.7*
Answer:5.9-6.2x
Step-by-step explanation:
a=1.4-2x
b=-0.2x+1.7
3a+b
=3(1.4-2x)+(-0.2x+1.7)
=4.2-6x-0.2x+1.7
=4.2+1.7-6x-0.2x
=5.9-6.2x
Answer:
Step-by-step explanation:
3a + b
a = 1.4 - 2x
b = -0.2x + 1.7
3 ( 1.4 - 2x ) + -0.2x + 1.7
= 4.2 - 6x - 0.2x + 1.7
= 4.2 + 1.7 - 6x - 0.2x ( by rearranging the like terms )
= 5.9 - 6.2 x
hope this helps
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4x - 2y +z = 6, -2x + y = -4, 3y - 2z = 4 x= y= z=
The required simplified value of x, y, and z is 2, 2, and 2.
Given that,
The system of the equation is given
4x - 2y +z = 6,
-2x + y = -4,
3y - 2z = 4
And also x= y= z
In mathematics, it deals with numbers of operations according to the statements. There are four major arithmetic operators, addition, subtraction, multiplication and division,
What is simplification?The process in mathematics to operate and interpret the function to make the function or expression simple or more understandable is called simplifying and the process is called simplification.
Here,
Since, x = y = x
taking any one equation
4x - 2y +z = 6
Now,
4x - 2x + x = 6
3x = 6
x = 2
Thus, the required simplified value of x, y, and z is 2, 2, and 2.
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In the polynomial below, what number should replace the question mark to produce a difference of squares? X^2 + ?x -49 A. 0 B. 14 C. 49 D.7
Answer:
A
Step-by-step explanation:
The difference of squares formula is a² - b² = (a + b)(a - b). We want this polynomial to be in the form a² - b². We notice that x² and 49 are perfect squares already which means that we don't need the x term. To get rid of it, its coefficient must be 0 because 0 times anything is 0, thus the x term will be removed and we'll be left with x² - 49 which is a difference of squares.
Determine what type of model best fits the given situation: The temperature of a cup of coffee decreases by 5 F every 20 minutes.
Answer:
A first-order polynomial best fits the given situation.
Step-by-step explanation:
The statement indicates a constant rate of change in a given time interval, so the model that best fits the given situation is a first-order polynomial model, which is a generalized form of a model with direct proportionality. That is:
[tex]T = T_{o} + r \cdot t[/tex]
Where:
[tex]T[/tex] - Current temperature, measured in Fahrenheit degrees.
[tex]T_{o}[/tex] - Initial temperature, measured in Fahrenheit degrees.
[tex]r[/tex] - Temperature rate of change, measured in Fahrenheit degrees per minute.
[tex]t[/tex] - Time, measured in minutes.
The statement describes the temperature rate of change, which is equal to:
[tex]r = \frac{5\,^{\circ}F}{20\,min}[/tex]
[tex]r = \frac{1}{4}\,\frac{^{\circ}F}{min}[/tex]
What is the area of a rectangle that is 3.1 cm wide and 4.4 cm long?
Answer: 13.64 cm squared
Step-by-step explanation: Area of a rectangle is l x w so 3.1 x 4.4 = 13.64
solve 10^2n-6=10,000
Answer:
[tex]\Large \boxed{{n=5}}[/tex]
Step-by-step explanation:
10^2n-6 = 10,000
Make 10,000 with base 10.
10^2n-6 = 10^4
Cancel same bases.
2n-6 = 4
Add 6 to both sides.
2n = 10
Divide both sides by 2.
n = 5
Answer:
[tex]\huge\boxed{n = 5}[/tex]
Step-by-step explanation:
[tex]10^{2n-6} = 10,000[/tex]
Write 10,000 as a base of 10
[tex]10^{2n-6} = 10^4[/tex]
Comparing both sides , we get:
[tex]2n - 6 = 4[/tex]
Adding 6 to both sides
2n = 4+6
2n = 10
Dividing both sides by 2
n = 10 / 2
n = 5
Point A (-2,-10) is reflected over the x-axis. Write the coordinates of A'. * (2.-10) O (2.10) O (-2,-10) (-2, 10) Send me a copy of my responses. Submit
Answer:
(2, -10)
Explanation:
Reflection over the x-axis puts a negative sign on the x value.
Answer:
-2,10
Step-by-step explanation: i took the test and when doing this you only change the y but keep the x.
2. How do you find P(A or B) if A and B are independent events for one action, such as spinning a four-color spinner once and finding P(red or blue)?
Answer:
P(red or blue) = [tex]\frac{7}{16}[/tex].
Step-by-step explanation:
We have to find P(A or B), if A and B are independent events for one action, such as spinning a four-color spinner once.
Firstly, as we know that the formula for finding P(A or B) is given by;
P(A or B) = P(A) + P(B) - P(A and B)
Since it is stated that event A and B are independent, this means that there is no dependence of any one event on another event, so;
P(A and B) = P(A) [tex]\times[/tex] P(B)
Now, we can find P(A or B) = P(A) + P(B) - P(A) [tex]\times[/tex] P(B); is we know that the probabilities of happening of both events.
Similarly, P(red or blue) = P(red) + P(blue) - P(red) [tex]\times[/tex] P(blue).
Since the event is spinning a four-color spinner once and assuming there are four different colors, so the probability of wheel stopping on each color is ([tex]\frac{1}{4}[/tex]).
So, P(red or blue) = [tex]\frac{1}{4} +\frac{1}{4} -(\frac{1}{4} \times \frac{1}{4} )[/tex]
= [tex]\frac{2}{4} -\frac{1}{16}[/tex] = [tex]\frac{7}{16}[/tex].
Arrange 0.1, 0.25, 0.15, 0.5 in ascending order
Answer:
0.1, 0.15, 0.25, 0.5
Step-by-step explanation:
0.1, 0.15, 0.25 ,0.5
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What is 5 ∙ P ∙ 2 Simplified?
If a is an arbitrary nonzero constant, what happens to a/b as b approaches 0
Answer:
a/b tends to an infinite value
Step-by-step explanation:
If If a is an arbitrary nonzero constant, and we are to look for a/b as b approaches zero, we can represent this statement using limits. The statement is expressed as:
[tex]\lim_{b \to 0} \dfrac{a}{b}[/tex]
Substituting b = 0 into the function
[tex]= \dfrac{a}{0} \\\\= \infty \\\\\lim_{b \to 0} \dfrac{a}{b} = \infty\\ \\\\[/tex]
Since the limits of a tends to infinity as b tends to zero hence we can conclude that If a is an arbitrary nonzero constant then a/b tends to infinity or is undefined as b approaches 0
a rectangle has a width w and it's length is 3w-2. if the area is 65ft^2, find the length and width of the rectangle.
Answer:
Width = 5
Length = 13
Step-by-step explanation:
Area of a rectangle:
=> L x W = Area
After knowing this, we could find the factors of 65
=> 65 = 5 x 13, 1 x 65
So, the only way is 5 x 13.
So, Width = 5
Length = 13
Let's check whether our answer is correct.
=> (3w - 2) * w = 65
=> (3 (5) - 2) * 5 = 65
=> (15 - 2) * 5 = 65
=> 13 * 5 = 65
=> 65 = 65
So, our answer is correct.
Aubrey prepared 15 kilograms of dough after working 5 hours. How many hours did Aubrey work if she prepared 18 kilograms of dough?
Answer:
6 hours
Step-by-step explanation:
Set up a proportion:
15kg/5 hrs = 18kg/x hrs
Cross multiply:
5(18)=15x
90 = 15x
Divide by 15:
90/15 = x
6 = x
Answer:
21
Step-by-step explanation:
x=1 y= 2
3(x+2y)-2x+10 =
Answer: 23
Step-by-step explanation:
brainlist if answer correct:
Two cars start out at the same point and at the same time one starts driving north while the other starts driving east at a speed that is 10 mph faster than the car driving north. 12 hours after the cars start driving they are 600 miles apart. What was the speed of each car?
Let x be the speed of the first car in miles per hour. After 12 hours it will have gone 12x miles. The other car, driving east, has speed x+ 4. After 12 hours it will have gone 12(x+ 4) miles. Again by the Pythagorean theorem,
(12x)^2+(12(x+4)^2=600^2. Solve that equation for x.
In your gym class, your teacher can create teams of 4 for a relay race and have no students left over.The next day, your teacher creates teams of 5 for dodge ball and has no students left over. What are some possible numbers of students in your class
Answer: 20,40,60,80,100
Step-by-step explanation:
The possible numbers has be the multiples of 5 and 4 in other words the LCM.
The LCM of 5 and 4 are,
20,40,60, 80,100 ....
15) Luke needs to fix the given marble slide. Explain what changes Luke needs to make to the given equation
to successfully capture all the stars.
VALO
TTTTTT
onde esta a altenaativas
In a class of students, the following data table summarizes the gender of the students
and whether they have an A in the class. What is the probability that a student who
has an A is a female?
Answer:
5/13
Step-by-step explanation:
number of female students who have an A: 5
total number of female students: 13
The probability that a student who has an A is a female is 3/8
How to calculate the probability of an event?Suppose that there are finite elementary events in the sample space of the considered experiment, and all are equally likely.
Then, suppose we want to find the probability of an event E.
Then, its probability is given as
[tex]P(E) = \dfrac{\text{Number of favorable cases}}{\text{Number of total cases}} = \dfrac{n(E)}{n(S)}[/tex]
where favorable cases are those elementary events who belong to E, and total cases are the size of the sample space.
What is chain rule in probability?For two events A and B, by chain rule, we have:
[tex]P(A \cap B) = P(B)P(A|B) = P(A)P(B|A)[/tex]
where P(A|B) is probability of occurrence of A given that B already occurred.
We're specified a frequency table as:
Female Male
Has an A 3 5
Does not have an A 8 13
We want to get P(Student is female if its given that student has an A).
Symbolically, we need P(Female | Has an A).
P(Student is female | Student has an A) = P(Student is female ∩ Student has an A) / P(Student has an A)
Now, P(Student is female ∩ Student has an A) = n(Student is female∩ Student has an A) / n(all type of students) = 3/(3+5+8+13) = 3/29
Also, P(Has an A) = n(has an A)/ n (All type of students) = n(has an A)/29
Since n(has an A) = number of students having A = females having A + males having A = 3+5 = 8
Thus, P(Has an A) = 8/29
Thus, we get:
P(Female | Has an A) = P(Female ∩ Has an A) / P(Has an A) = [tex]\dfrac{3/29}{8/29} = \dfrac{3}{8}[/tex]
Thus, the probability that a student who has an A is a female is 3/8
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The table shows the estimated number of lines of code written by computer programmers per hour when x people are working. A 2-column table with 6 rows. The first column is labeled people working with entries 2, 4, 6, 8, 10, 12. The second column is labeled lines of code written hourly with entries 50, 110, 160, 210, 270, 320. Which model best represents the data?
Answer:
We make the table of these values at different values of x.
x A B C D
2 66.66 49.3 52.5 50
4 94.57 71.44 106.3 104
6 134.14 103.57 160.1 158
8 190.27 150.14 213.9 212
10 269.91 217.64 267.7 266
12 382.85 315.5 321.5 320.
Hence, the function that best represents the data is:
Option C.
y=26.9x-1.3
Step-by-step explanation:
Considering the situation described, it is found that a linear model best represents the data, because there is a relatively consistent additive rate of change.
When to use a linear model and when to use an exponential model?If the rate of change is additive, that is, the difference between consecutive terms is the same, a linear model is used.If the rate of change is multiplicative, that is, the quotient between consecutive terms is the same, an exponential model is used.In this problem, when the input changes by 2, the output always increases between approximately 50 and 60, that is, the same values, hence a linear model best represents the data, because there is a relatively consistent additive rate of change.
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Quadrilateral A has side lengths 6, 9, 9, and 12. Quadrilateral B is a scaled copy of Quadrilateral A, with its shortest side of length 2. What is the perimeter of Quadrilateral B?
Answer:
Look below
Step-by-step explanation:
Ok, you got a Quadrilateral with the side lengths 6, 9, 9, 12
The shortest of B is 2
Find the scale factor of the A to B
6 -> 2
6/2 = 3
Scale factor is 3
Now divide all the sides by scale factor
6/3, 9/3, 9/3, 12/3 = 2, 3, 3, 4
Add them all together to get the perimeter
2+3+3+4 = 12
Perimeter of B is 12
The function y = 4/5x - 6 is shifted up 13 units. What is the equation of the new function?
Help needed ASAP will give brainliest! Pls help me
Answer:
1740 N
Step-by-step explanation:
To find the force, you need to multiply the mass by the acceleration.
(60.0 kg) × (29.0 m/s²) = 1740 N
The force will be 1740 N.
An amoeba divides to form two amoebas after one hour. One hour later, each of the two
amoebas divides to form two more. Every hour, each amoeba divides to form two more.
1. How many amoebas are there after 1 hour?
2. How many amoebas are there after 2 hours?
3. Write an expression for the number of amoebas after 6 hours.
Step-by-step explanation:
Given that the number of amoeba is 1
in 1 hour it divides to form 2
1 hour later (2 hours): 1 amoeba(forms 2), 1 amoeba(forms 2)= 4
1 hour again(3 hours): 1=2,1=2,1=2,1=2 hence a total of 8 after 3 hours
Question and answers
1. How many amoebas are there after 1 hour
=2 amoebas
2. How many amoebas are there after 2 hours
=4 amoebas
3. Write an expression for the number of amoebas after 6 hours.
let the number of amoeba be y, and the time be n
so in 6 hours n= 6
[tex]y=2^n[/tex]
[tex]y= 2^6\\\\y= 64 amoebas[/tex]
Marc mows lawns for $25 each lawn, plus $5 for every hour he spends mowing. The equation for his total earnings per lawn is y = 25 + 5h, where y represents his total earnings and h represents the number of hours he works. What does the flat pay of $25 represent in this situation? Dependent variable Independent variable Intercept Slope
Answer:
The flat pay $25 represents the interceptStep-by-step explanation:
To answer this question we need to first understand and compare it with the equation of straight line.
i.e [tex]y= mx+c[/tex] which is the equation of line
where m= slope
y= dependent variable
x= independent variable
c= intercept
Given
[tex]y= 25+5h[/tex]
comparing both expression we can see that
25 corresponds to c which is the intercept
The flat pays $25 represent the intercept.
Given that,
Marc mows lawns for $25 each lawn, plus $5 for every hour he spends mowing. The equation for his total earnings per lawn is y = 25 + 5h, where y represents his total earnings and h represents the number of hours he works.Based on the above information, the calculation is as follows:
y = mx + c
where m= slope
y= dependent variable
x= independent variable
c= intercept
And,
y = 25 + 5h
So it is an intercept
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what is 5/8 minus 3/10
Answer:
13/40
Step-by-step explanation:
5/8 - 3/10
get a common denominator of 40
5/8*5/5 - 3/10 *4/4
25/40 - 12/40
13/40
Answer:
13/40
Step-by-step explanation:
We can find the lowest common multiple of 8 and 10, so that the two fractions will have the same denominator.
The LCM of 8 and 10 is 40, so we can rewrite 5/8 as 25/40 by multiplying the numerator and denominator by 5, and rewrite 3/10 as 12/40 by multiplying the numerator and denominator by 4.
This makes the subtraction easier, as we find 25/40 - 12/40.
We get (25-12) / 40, or 13/40.
Solve for x:2/7(x − 2) = 4x
Answer:
[tex]x = - \frac{2}{13} [/tex]Step-by-step explanation:
[tex] \frac{2}{7} (x - 2) = 4x[/tex]Multiply through by 7 inorder to clear out the fraction
That's
[tex]2 \times \frac{2}{7} (x - 2) = 4x \times 7[/tex]We have
[tex]2(x - 2) = 28x[/tex]Multiply the terms in the bracket
That's
2x - 4 = 28x
Subtract 28x from both sides
We have
2x - 28x - 4 = 28 - 28x
Simplify
- 26x = 4
Divide both sides by - 26
That's
[tex] \frac{ - 26x}{ - 26} = - \frac{4}{26} [/tex]We have the final answer as
[tex]x = - \frac{2}{13} [/tex]Hope this helps you
LAST QUESTION -4/5 divided by (-7/6)
Answer:
24/35
Step-by-step explanation:
(I posted an explanation on your previous question explaining how to do these problems. You can go read that if you want because my explanation applies to any question in this concept.)
Does x=-3 fall on the interval [-1, ♾)? Yes or no and why:
Answer:
Yes
Step-by-step explanation:
All numbers between 1 and 6 are intervals
Can someone please help me with this question, I will mark branliest if it’s correct