The area of the rectangle is 105 square cm
How to determine the rectangle area?Represent the dimensions of the rectangle with x and y
So, the length of the square would be:
Length = x - 2
Width = y + 6
The areas are then calculated as:
Rectangle = xy
Square = (x -2)(y + 6)
The relationship between the areas is:
(x -2)(y + 6) = 64 + xy
Expand
xy + 6x - 2y - 12 = 64 + xy
This gives
6x - 2y - 12 = 64
Add 12 to both sides
6x - 2y= 76
Divide through by 2
3x - y = 38
By trial by error, we have:
x = 15 and y = 7
The rectangle area is then calculated as:
Rectangle = xy
This gives
Rectangle = 15 * 7
Evaluate
Rectangle = 105
Hence, the area of the rectangle is 105 square cm
Read more about areas at:
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find the 7th term of 4,5,6.25
Answer:
same i dont know just need points but good luck
List the domain and range of the relation. {(7,-8), (4,4), (0,-8), (4,1),(7,8)}
Answer:
Domain: {7, 4, 0} Range: {-8, 4, 1, 8}
Step-by-step explanation:
the domain is just the x values and the range is just the y values when just a list of cordinates are given.
What would be the answer if x= -8
Y = -3/4x +10
Answer:
y= 16
Step-by-step explanation:
y= -3/4(-8)+10
(-3/4 x -8= 6)
y= 6 + 10
y=16
The length of a rectangle is 4 meters less than twice its width. The are of a rectangle is 70m^2. Find the dimensions of the rectangle.
Answer:
The length is 7 m
The width is 10 m
Step-by-step explanation:
length = x
width = 2x - 4
length * width = area
It is given that the area is 70 [tex]m^{2}[/tex]
From there
x * (2x - 4) = 70
[tex]2x^{2}[/tex] - 4x = 70
[tex]2x^{2}[/tex] - 4x - 70 = 0
[tex]x^{2}[/tex] - 2x - 35 = 0
Now we have a quadratic equation, which is a[tex]x^{2}[/tex] + bx + c = 0, where a [tex]\neq[/tex] 0
In this equation a = 1, b = -2 and c = -35
Discriminant (D) formula is b² - 4ac
D = [tex]-2^{2}[/tex] - 4 * 1 * (-35) = 144 > 0
This discriminant is more than 0, so there are two possible x
Their formulas are [tex]\frac{- b - \sqrt{D} }{2a}[/tex] and [tex]\frac{- b + \sqrt{D} }{2a}[/tex]
[tex]x_{1}[/tex] = [tex]\frac{- (-2) - \sqrt{144} }{2}[/tex] = -5 < 0 (the length of the rectangle has to be more than 0, so we don't use this x)
[tex]x_{2}[/tex] = [tex]\frac{- (-2) + \sqrt{144} }{2}[/tex] = 7 > 0 (this one is right)
Calculating the dimensions
length = x = 7 (m)
width = 2x - 4 = 2 * 7 - 4 = 10 (m)
Circumscribe a circle about the given triangle.
Answer:
Step-by-step explanation:
To circumscribe a circle to a given triangle implies constructing a circle outside the triangle, so that it touches the three vertices of the given triangle externally.
The step requires bisecting two sides of the triangle so as to locate the center of the circle. Then with the center and one of the edges, draw a complete circle. The circles should be outside the triangle and passing through its three vertices.
The construction is as shown in the attachment to this answer.
Which statement is true about their work? Neither student solved for k correctly because K = 2 and StartFraction 1 over 8 EndFraction. Only Adler solved for k correctly because the inverse of addition is subtraction. Only Erika solved for k correctly because the opposite of One-half is Negative one-half. Both Adler and Erika solved for k correctly because either the addition property of equality or the subtraction property of equality can be used to solve for k.
Question:
Adler and Erika solved the same equation using the calculations below.
Adler’s Work
[tex]\frac{13}{8}= k + \frac{1}{2}[/tex]
[tex]\frac{13}{8} - \frac{1}{2} = k + \frac{1}{2} -\frac{1}{2}[/tex]
[tex]\frac{9}{8}= k[/tex]
Erika’s Work
[tex]\frac{13}{8}= k + \frac{1}{2}[/tex]
[tex]\frac{13}{8}+ (-\frac{1}{2}) = k + \frac{1}{2} + (-\frac{1}{2}).[/tex]
[tex]\frac{9}{8}= k[/tex]
Which statement is true about their work?
Answer:
Both Adler and Erika solved for k correctly because either the addition property of equality or the subtraction property of equality can be used to solve for k.
Step-by-step explanation:
Given
[tex]\frac{13}{8}= k + \frac{1}{2}[/tex]
Required
What is true about Adler and Erika's workings
Analyzing Adler's work;
[tex]\frac{13}{8}= k + \frac{1}{2}[/tex]
Adler subtracted 1/2 from both sides
[tex]\frac{13}{8} - \frac{1}{2} = k + \frac{1}{2} -\frac{1}{2}[/tex]
Solving the expression on the left-hand side
[tex]\frac{13}{8} - \frac{1}{2} = \frac{13 - 4}{8} = \frac{9}{8}[/tex]
Solving the expression on the right-hand side
[tex]k + \frac{1}{2} - \frac{1}{2} = k[/tex]
Hence:
[tex]\frac{9}{8}= k[/tex]
So, Adler's workings is correct
Analyzing Erika's work;
[tex]\frac{13}{8}= k + \frac{1}{2}[/tex]
Erika added -1/2 to both sides
[tex]\frac{13}{8}+ (-\frac{1}{2}) = k + \frac{1}{2} + (-\frac{1}{2}).[/tex]
Solving the expression on the left-hand side
[tex]\frac{13}{8} + (-\frac{1}{2}) = \frac{13}{8} - \frac{1}{2} = \frac{13 - 4}{8} = \frac{9}{8}[/tex]
Solving the expression on the right-hand side
[tex]k + \frac{1}{2} + (-\frac{1}{2}) =k + \frac{1}{2} - \frac{1}{2} = k[/tex]
Hence:
[tex]\frac{9}{8}= k[/tex]
So, Erika's workings is correct
Both workings are correct
Answer: Both Adler and Erika are correct
Step-by-step explanation:
On Edge 2021
Dado los puntos p1 (-7/2-9/2) y p2 (5/2, 3/2) calcular la representación gráfica, d p1 p2, pto medio de p1 p2, la pendiente (m) de la recta que pasa por medio de ellos. Porfavor ayúdenme la tarea es para el viernes y no entendió
Answer:
Ce clasă ești sa văd daca te pot ajuta
...what's
[tex] \sqrt{224} [/tex]
Answer:
it doesnt have any perfect root
Step-by-step explanation:
but in decimal it is 14.97......
Answer:
4√14
Step-by-step explanation:
√224 = √2^5 · 7
= 4√14
Which quotient is reasonable? Do not perform the division. 7315 ÷ 12 A. 6 R 9 B. 60 R 9 C. 609 D. 6,009
Answer:
C. 609
Step-by-step explanation:
In the question, 4-digits number were given to be divided by a 2-digits number. Without performing the division, it is only reasonable to say that the quotient will be a 3-digits number.
In the given options, the only 3-digits number is 609
Also, you can multiply 609 by 12 to check how reasonable your guess is.
⇒ 609 x 12 = 7308
The difference between 7315 and 7308 is 7.
The remaining number (7) is not up to 12 and when 7 is divided by 12 it will not give a whole number digit.
Therefore, the only reasonable quotient in the given options is 609.
use the table to solve the equation -6x>18
The answer is,
[tex]x < - 3[/tex]
Round The Following Number: 194,332.125
Jackson has scores of 80, 90, 83, and 81 on four Math quizzes. What is the score he needs on the next quiz to achieve an average above 85?
Can someone help me please?
Which is equivalent to b6/b2
Answer:
yuojsjsjskakavbhjsmsnnxjxj
Which choice is equivalent to the fraction below when x is an appropriate value? Hint: Rationalize the denominator and simplify. 7/7+√14x
A. 7-√14x/7-2x
B.7-√14x/49-14x
C.7-√14x/49-2x
D.7-√14x/7-14x
Answer:
A. (7 - √14x) /(7 - 2x)Step-by-step explanation:
Given the fraction:
7 / (7 + √14x)Rationalize the denominator by multiplying (7 - √14x):
7 / (7 + √14x) =7(7 - √14x) / (7 + √14x)(7 - √14x) =7(7 - √14x) /(49 - 14x) =7(7 - √14x) /7(7 - 2x) =(7 - √14x) /(7 - 2x)Matching choice us A
Mr. Berkholz wants to invest $5000 into an account to save for his daughter for college. He is 'guaranteed' a 5.2% annual return on his investment by his financial advisor. How much will the account be worth in 12 years when she goes to college?
The answer is: $9,186.69
geometry: help me please!
Answer:
DF = 28 units
AC = 64 units
CF = 32 units
Step-by-step explanation:
In the given triangle ABC points D, E and F are the midpoints of the sides AB, BC and AC.
By midsegment theorem,
"Segment joining the midpoints of each side is parallel and measure the half of the opposite side"
DF = [tex]\frac{1}{2}(BC)[/tex]
= [tex]\frac{56}{2}[/tex]
= 28 units
AC = 2(DE)
= 2 × 32
= 64 units
CF = [tex]\frac{1}{2}(AC)[/tex]
= [tex]\frac{64}{2}[/tex]
= 32 units
Emily is entering a bicycle race for charity. Her mother pledges $0.20 for every 0.75 miles she bikes. If Emily bikes 15 miles, how much will her mother donate? plz help :D
Answer:
24 dollars
Step-by-step explanation:
Having trouble solving this:
Answer:
option b.
61/1000.
................
Answer:
B: 61/1000
Step-by-step explanation:
B: 61/1000 = 0.061
as a percent is 6.1%
Therefore B or 61/1000 is correct hope this helped!
Please help! image below
Answer:
28 units
hope this helps have an amazing day
WILL MARK BRAINLIEST PLS DO MY MATH DUE: 1 HOUR
1. a=9 2. k=0 3. w=3 4. x= 5 5. v=14 6. f=8 7. u=5 8. c=1 9. s=8 10. q=1/7 11. k= 1/5 12. j=9 13. r=120 14. b=1.4 15. g= 3.1 and 16. m=25
I also post a picture on how I got each answer.
Hope this helped you out
Answer:
a=9 2. k=0 3. w=3 4. x= 5 5. v=14 6. f=8 7. u=5 8. c=1 9. s=8 10. q=1/7 11. k= 1/5 12. j=9 13. r=120 14. b=1.4 15. g= 3.1 and 16. m=25
Step-by-step explanation:
convert 4/6 into a decimal
Answer:
.66
Step-by-step explanation:
cmon bro how do u not know this
4 divide 6
.66666666666666666666666666666666666
What is the value of x
Answer:
x = 1.6
Step-by-step explanation:
If you count the lines, it is the sixth line. Each line seems to represent .1 since when you count from 1 to 2, it would work out with 2 being the tenth line.
1, 1.1, 1.2, 1.3, 1.4, 1.5, 1.6, 1.7, 1.8, 1.9, 2
Decide if the ansewer to 7/5x11 is less than greater than or equal to 11. A.greater than B.less than C.equal to
Answer:
The answer to 7/5x11 is 15.4, so A. Greater than.
Step-by-step explanation:
7/5= 1.4, 1.4x11=15.4.
Ok so I need help with multiplying fractions, this is the way my teacher did it but I have no idea how to do it the way he did it so if someone can, please explain to me on how to do it
example 1: this is basically reducing WHILE multiplying. since 5 and 10 have a greatest common factor and is able to be reduced by each other, we do so. hence the reason 5 went to 1 and 10 went to 2 because 5 goes into 5 once and 5 goes into 10 twice. it was a different case for 3 and 8. 3 obviously cant go into 8 and 3 is prime so nothing can be done with those. ONLY REDUCE WHILE MULTIPLYING DIAGONALLY you CANNOT do up and down or side to side. so our new fractions are [tex]\frac{3}{2}[/tex] and [tex]\frac{1}{8}[/tex] so multiply across and get [tex]\frac{3}{16}[/tex] which cant be reduced more.
example 2: this one in my opinion is pretty easy. you take the two fractions and multiply regularly across. you get [tex]\frac{27}{80}[/tex]. that fraction can be reduced. so we find the prime factorization of each number. 3 is a prime factor. 3x3x3=27 which is our top number. 2 and 5 are all prime numbers used to reach 80. 2x2x2x2x5=80. that's the prime factorization method its an easier way to check your work also.
example 3: this one is practically a combination of the two previous ones. [tex]\frac{16}{21}[/tex] and [tex]\frac{7}{8}[/tex] can be diagonally reduced on both diagonals. 7 goes into 7 once and 7 goes into 21 three times 8 goes into 8 once and 8 goes into 16 twice. now we have [tex]\frac{1}{1}[/tex] and [tex]\frac{2}{3}[/tex] multiply across and get just [tex]\frac{2}{3}[/tex]. prime factorization is the best way to do this but, more effective with larger numbers. [tex]\frac{2*2*2*2*7}{3*7*2*2*2}[/tex] now cross out the numbers that are the same on the top and bottom. three 2's cancel out, one 7 cancels out, and now we're left with [tex]\frac{2}{3}[/tex].
I really hope this helps you!!
Marcus believes he can score a goal at least 70% of the time.He runs a simulation where he tracks the number of successful goals out of ten attempts. He runs the simulation 100 times.
Goals 0 1 2 3 4 5 6 7 8 9 10
Frequency 0 1 2 2 1 0 1 18 40 30 5
He decides to use a significance level of 0.05. What can he conclude about his null hypothesis that he will score no more than 6 goals out of 10?
Answer:
The p-value is 0.07, which is more than 0.05. Fail to reject the null hypothesis.
Step-by-step explanation:
if Seth used 4 ounces of black beans, how many beans did he use altogether?
Answer: 4 Ounces.
Step-by-step Explanation: I don't know the full context of the problem, but if Seth used 4 ounces, that means that he used 4 ounces all together.
Simplify the expression below.
−9×(−11)×(−4)
Step-by-step explanation:
=-8×(-11)×(-4)
=22×(-4)
= -88
hope it helps.
Answer: −9×(−11)×(−4)=−396
Step-by-step explanation:
If the perimeter of the rectangle shown is 60 feet, we can use the equation 8x + 4 = 60 to find its dimensions. If the solution to this equation is x = 7, what are the dimensions of the rectangle?
Answer:
l= 28 feet
b = 2 feet
Step-by-step explanation:
The perimeter of a rectangle is given by;
P= 2(l + b)
Comparing this to the equation; 8x + 4 = 60, i can write;
2(4x + 2) = 60
This means that;
l = 4x
b = 2
but x =7
So;
l = 4* 7 = 28 feet
b = 2 feet
Find the HCF of 45 and 81.
Answer:
3² = 9
Step-by-step explanation:
45 = 3² × 5
81 = 3⁴
================
HCF = 3²