The width of the rectangles is 4.
Step-by-step explanation:
Given that two rectangles have same width. So, let be the two rectangles [tex]R_{1}[/tex] and [tex]R_{2}[/tex] and width of rectangle is ‘x’. So, according to question, we have
Length of one rectangle , [tex]R_{1}[/tex] = x + 1
Length of other rectangle, [tex]R_{2}[/tex] = x + 2
But we also know that,
[tex]\text { Area of rectangle } = \text { Length } \times \text { width }[/tex]
So, then the area for one rectangle,
[tex]\text { Area of rectangle } R_{1} = x \times(x+1)[/tex]
Similarly,
[tex]\text { Area of rectangle } R_{2} = x \times(x+2)[/tex]
So, according to question,
[tex]\text {Area of rectangle } R_{2} = 4 \times \text { Area of rectangle } R_{1}[/tex]
[tex]x \times(x+2) = 4+x \times(x+1)[/tex]
Now, by solving the above equation, we get
[tex]x^{2}+2 x = 4+x^{2}+x[/tex]
[tex]x = 4[/tex]
So, from the above equation, we found that width of the rectangle is 4.
How do you express 1/2% as a decimal?
Fill the blanks.
__ divided by 100 = __
To find 1/2% as a decimal we can divide this by 100. (This is shown in the question)
1/2 = 0.5
0.5 / 100 = 0.005 (0.5% divided by 100 = 0.005)
_______
Best Regards,
Wolfyy :)
Circle A has been dissected into 16 congruent sectors. The base of one sector is 1.56 units, and it's height is 3.92 units. what is the approximate area of circle A?
Answer:
48.92
Step-by-step explanation:
A= (1/2)(b)(h)
A=(1/2)(1.56)(3.92)=3.0576
A=(3.0567)(16)=48.9216
A=48.92
The approximate area of Circle A can be found by understanding that the base of a sector is part of the circumference, and using the radius (height) value of 3.92 units in the area formula A = πr². Accounting for significant figures, the area of Circle A is approximately 48 units².
Explanation:To find the approximate area of Circle A, we need to understand that the base of a sector, which is a part of the circumference of the circle, is close to the length of the arc for a small sector. By dissecting the circle into 16 congruent sectors, each sector represents 1/16 of the circle's full circumference. Since the base of one sector is given as 1.56 units, if we multiply this by 16, we would have the total circumference of the circle. However, the value provided for the 'height' is indeed the radius of the whole circle, which is 3.92 units. The area of a circle is calculated using the formula A = πr².
Using the radius (3.92 units), we can calculate the area:
A = π * (3.92 units)²
A = 3.1415927 * 15.3664 units²
A = 48.2544695988 units²
Considering the significant figures provided in the question, we should limit the calculated area of the circle to two significant figures, matching the least number of significant figures we were originally given, which were in the radius measurement. Therefore, the approximate area of Circle A is:
A = 48 units²
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ok, i need to determine if it can be written as a fraction. Then state the reason.
Answer:
a) YES. Repeating decimal
b) YES. Repeating decimal
c) NO. Decimal neither terminates nor repeats
d) YES. Terminating decimal
Step-by-step explanation:
Any rational number can be written as a fraction, that is, a division of integers.
a) The number [tex]\overline{0.54}[/tex] has a repetitive period of 54. It can be expressed as a fraction because its decimal are repeating forever
b) The number 0.16666... (expressed as a repeating 6) can also be converted to a fraction because it's a repeating decimal
c) The number 0.5473... cannot be expressed as a fraction because the ellipsis (...) means the decimals continue with no limit and no pattern can be found (no repetitive decimal)
d) The number 0.378 can be easily expressed as a fraction because it has a finite number of decimals (no ellipsis) or a terminating decimal
Can someone help me solve #4! Please and thank you! :)
Answer:
X=16
Step-by-step explanation:
Line QT is congruent with line RS, while line RQ is also congruent with line TS. All in all, each line is congruent to the other. Meaning all sides equal the same amount. We know that angle measure must equal 180, so you must take 3x+5+9x-17=180. Then you will get the variable X to equal 16.
How many degrees would a kite need to be rotated to carry it onto itself?
A student claims that a linear-quadratic system of equations has three solutions. Explain the error the student made.
Step-by-step explanation:
A line and a quadratic (parabola) can have either 0, 1, or 2 solutions.
0 solutions: the line and quadratic do not intersect.1 solution: the line and quadratic are tangent (intersect at one point), or the line is the axis of symmetry (intersects only at the vertex).2 solutions: the line and quadratic intersect at two points.It is impossible for a linear-quadratic system to have more than 2 solutions.
Evaluate the expression when m=6 and n=7
The value of the expression is : 61
Using the expression given :
n + 9mUsing the values of n and m given ;
n = 7m = 6Substituting our values into the expression ;
7 + 9(6)
7 + 54
= 61
Hence, the value of the expression is. 61
Complete Question :
Evaluate the expression n + 9m when m=6 and n=7
Prove LO bisects angle MLN and identify which given statement is unnecessary.
Given:
LM = LN, KM = KN, KO bisects angle MKN
What we want to prove:
LO bisects angle MLN
=====================================
Proof:
Statement 1: KM = KN
Reason 1: Given
---------------------
Statement 2: KO bisects angle MKN
Reason 2: Given
---------------------
Statement 3: Angle MKO = Angle NKO
Reason: Definition of angle bisection
---------------------
Statement 4: KO = KO
Reason 4: Reflexive property of congruence
---------------------
Statement 5: Triangle MKO = Triangle NKO
Reason 5: SAS postulate
note: this combines statements 1, 3, and 4 (for the "S", "A", and "S" in that order)
---------------------
Statement 6: MO = ON
Reason 6: CPCTC
note: CPCTC stands for "corresponding parts of congruent triangles are congruent"
---------------------
Statement 7: Angle KOM = Angle KON
Reason: CPCTC
---------------------
Statement 8: OL = OL
Reason 8: Reflexive property of congruence
---------------------
Statement 9: Triangle MOL = Triangle NOL
Reason 9: SAS postulate
note: used statements 6, 7, 8 for the "S", "A", "S" in that order
---------------------
Statement 10: Angle MLO = Angle NLO
Reason 10: CPCTC
---------------------
Statement 11: LO bisects angle MLN
Reason 11: Definition of angle bisection
---------------------
That concludes the proof. We did not use the statement "LM = LN", so it is unnecessary.
To prove that LO bisects angle MLN, we can use the Angle Bisector Theorem. According to this theorem, if a line bisects an angle, it divides the opposite side into two segments that are proportional to the adjacent sides of the angle. We can prove this by using the given information and applying the theorem.
Explanation:To prove that LO bisects angle MLN, we can use the Angle Bisector Theorem. According to this theorem, if a line bisects an angle, it divides the opposite side into two segments that are proportional to the adjacent sides of the angle. In this case, LO is the angle bisector of angle MLN if and only if (MN/NO) = (ML/LO). We can prove this by using the given information and applying the theorem.
Given:
LO bisects angle MLNTLX TLTo prove:
LO bisects angle MLNProof:
Since LO bisects angle MLN, TLX and TL are alternate interior angles and are therefore congruent.In triangle MLN, using the Law of Sines, we can express the ratio of sides as follows: MN/sin(TLX) = ML/sin(TL)Since sin(TLX) = sin(TL) (by the congruent angles), we can simplify the expression to: MN/ML = sin(TLX)/sin(TL)According to the Angle Bisector Theorem, we know that TO/OL = TN/NL, which can be written as: OL/TN = LO/NLUsing the Sine Law in triangle OTL, we have: LO/sin(OTL) = TL/sin(LOT)Since OTL is congruent to TLX (by the congruent angles), we can simplify the expression to: LO/TL = sin(TLX)/sin(TL)Comparing the expressions MN/ML = sin(TLX)/sin(TL) and LO/TL = sin(TLX)/sin(TL), we can conclude that MN/ML = LO/TLTherefore, LO bisects angle MLN (by the Angle Bisector Theorem)So, we have proven that LO bisects angle MLN.
The given statement that is unnecessary for this proof is 'TLX TL' because it does not provide any additional information or requirement for proving that LO bisects angle MLN.
Apolline is mowing lawns for a summer job.For every mowing job,she charges an initial fee plus constant fee for each hour of work.Her fee for a 5-hour job, for instance,is $42.Her fee for a 3-hour job is $28
Answer:
A. Therefore, the slope of the above equation is 7 and x-intercept is (-1,0)
B. The slope 7 and y-intercept (0,7)
C. The slope is 7 and (1,14) is the point.
D. Y-intercept = (0,7) and X-intercept = (-1,0).
E. (1,14) is the point and the y-intercept is (0,7).
F. Points (1,14) and (2,21) are the two points.
Step-by-step explanation:
Apolline charges a fixed initial fee and a constant fee for each hour for mowing work.
If we try to model the above conditions with a total cost for mowing as C for working for h hours then we will get
C = a + bh ....... (1)
Where a is the initial fee and b is the rate of charge per hour of work.
Now, her fee for a 5-hour job is $42 and her fee for a 3-hour job is $28.
Hence, from equation (1),
42 = a + 5b ........ (2) and
28 = a + 3b ......... (3)
Now, solving equations (2) and (3) we get 2b = 42 - 28 = 14
⇒ b = 7 dollars per hour of work.
And from equation (3) we get, a = 28 - 3b = 7 dollars.
So, the equation (1) becomes C = 7 + 7h ....... (4)
A. Therefore, the slope of the above equation is 7 and x-intercept is (-1,0)
B. The slope 7 and y-intercept (0,7)
C. The slope is 7 and (1,14) is the point.
D. Y-intercept = (0,7) and X-intercept = (-1,0).
E. (1,14) is the point and the y-intercept is (0,7).
F. Points (1,14) and (2,21) are the two points. (Answer)
Answer:
in short response the answer is F
Step-by-step explanation:
the two points dont intercept
please help solve
25 increased by twice a number. Use the variable n to represent the unknown number.
Answer:
25 + 2n
Step-by-step explanation:
25 increased by twice the number n.
25 increased by 2 x n
25 + 2n
Bonus: In Triangle STP, the measure of <T is twice the measure of <S and the
measure of <P is three times the measure of <S. What is the measure of all three angles?
ENTER ONLY NUMBERS IN THE BOXES:
m<S = degrees
m<T= degrees
m<P= degrees
Answer:
m∠S=30°
m∠T=60°
m∠P=90°
Step-by-step explanation:
we know that
The sum of the interior angles in a triangle must be equal to 180 degrees
so
In the triangle STP
m∠S+m∠T+m∠P=180° ----> equation A
m∠T=2(m∠S) ----> equation B
m∠P=3(m∠S) ----> equation C
Solve the system of equations by substitution
Substitute equation B and equation C in equation A
m∠S+2(m∠S)+3(m∠S)=180°
Solve for m∠S
6m∠S=180°
m∠S=30°
Find m∠T
m∠T=2(m∠S)
m∠T=2(30°)=60°
Find m∠P
m∠P=3(m∠S)
m∠P=3(30°)=90°
Use the properties of operations to determine if each pair of expressions is equivalent
1/2(4-2x); 2-2x
Using the properties of operations the given pair of expressions are not equivalent
Solution:
Given that, we have to use the properties of operations to determine if each pair of expressions is equivalent
And the two expressions are:
[tex]\frac{1}{2}(4-2 x) \text { and } 2-2 x[/tex]
Now, we know that, there are four (4) basic properties of operations:
Commutative, Associative, Distributive and Identity. These properties only apply to the operations of addition and multiplication.
So, if we observe we can apply distributive property on 1st expression
The distributive property of multiplication states that when a number is multiplied by the sum of two numbers, the first number can be distributed to both of those numbers and multiplied by each of them separately, then adding the two products together for the same result as multiplying the first number by the sum.
[tex]\begin{array}{l}{\frac{1}{2}(4-2 x) \rightarrow \frac{1}{2}(4)-\frac{1}{2}(2 x)} \\\\ {\rightarrow 2-x}\end{array}[/tex]
Here the resulting expression is 2 – x and it is not equivalent to 2 – 2x
Hence, the given two expressions are not equal.
Answer:
Using the properties of operations the given pair of expressions are not equivalent
Solution:
Given that, we have to use the properties of operations to determine if each pair of expressions is equivalent
And the two expressions are:
Now, we know that, there are four (4) basic properties of operations:
Commutative, Associative, Distributive and Identity. These properties only apply to the operations of addition and multiplication.
So, if we observe we can apply distributive property on 1st expression
The distributive property of multiplication states that when a number is multiplied by the sum of two numbers, the first number can be distributed to both of those numbers and multiplied by each of them separately, then adding the two products together for the same result as multiplying the first number by the sum.
Here the resulting expression is 2 – x and it is not equivalent to 2 – 2x
Hence, the given two expressions are not equal.
Step-by-step explanation:
Section #1: Solvi
1) Find the solution to each equation
A) 4(2x - 1) = -3x + 32
what is the answer
Answer:
x=36/11
Step-by-step explanation:
4(2x-1)=-3x+32
8x-4=-3x+32
8x-(-3x)-4=32
8x+3x-4=32
11x-4=32
11x=32+4
11x=36
x=36/11
Suppose a ball is thrown directly upward from a height of 7 feet with an initial velocity of 50 feet per second. Use the quadratic formula or a graphing calculator to find the number of seconds it takes the ball to hit the ground. Round the nearest tenth of a second.
Answer:
t = 3.3 seconds
Step-by-step explanation:
From the formula of vertical motion of an object under gravity we can write the equation
[tex]H = ut + \frac{1}{2} gt^{2}[/tex] ....... (1)
Where u is the initial velocity (in feet per second) of throw of the object and t is time of travel in seconds and the value of g i.e. gravitational acceleration is 32 feet/sec².
Now, while a ball is thrown vertically upward with velocity 50 ft/sec from a height of 7 ft then the time of travel of the ball before reaching the ground, the equation (1) will be written as
[tex]- 7 = 50t - \frac{1}{2} \times 32 \times t^{2}[/tex]
As we have selected the upward direction as positive so, gravitational acceleration,g will be negative and as the displacement is downward by 7 feet, so it will be negative.
⇒ 16t² - 50t - 7 = 0 ........ (2)
Now, applying Sridhar Acharya formula,
[tex]t = \frac{-(-50) + \sqrt{(-50)^{2} - 4(16)(-7)}}{2(16)}[/tex] {Neglecting the negative root as t can not be negative}
⇒ t = 3.3 seconds {Rounded to the nearest tenth}
(Answer)
A rectangle has a length of 28 meters less than 7 times its width. If the area of the rectangle is 9555 square meters, find the length of the rectangle.
Answer:
7 meters
Step-by-step explanation:
Assume that the length is l and the width is w. Therefore, l is equal to 7 times its width (7*w) minus 28, or l=7*w-28. As we know that w*l = area = 9555, we can plug our value for l in to limit our equation to 1 variable, resulting in w*(7*w-28) = 9555. Adding 28 to both sides to separate the 7w (because we want to solve for that), we get 9583=7w. Then, to solve for the width, we can divide both sides by 7 to get that 9583/7=1369=w. Plugging that back into the formula that w*l=area, we get that 1369*l=9583 -- dividing 1369 from both sides to separate l, we get that l=7.
To find the length of a rectangle where the area is 9555 square meters and the length is 28 meters less than 7 times its width, express the length in terms of the width, use the area to form a quadratic equation, solve for the width, and substitute it back to find the length.
Explanation:To find the length of the rectangle when the area is 9555 square meters and the length is 28 meters less than 7 times its width, let's denote the width of the rectangle as w and the length as l. According to the problem, the length l can be expressed as l = 7w - 28. The area of a rectangle is the product of its length and width, which gives us the equation w × (7w - 28) = 9555.
To find the value of w, we need to solve the quadratic equation 7w2 - 28w - 9555 = 0. Factoring or using the quadratic formula leads to the width, and substituting this back into l = 7w - 28 gives us the length of the rectangle. In solving, ensure to discard the negative value of w as a width cannot be negative.
Once we calculate the width w, the length is found by multiplying it by 7 and then subtracting 28. This process will provide the final length of the rectangle.
Can someone help me and explain to me what to do
Answer:
25.12^2
Step-by-step explanation:
So, you are being asked to find the area of the circle. It says that the area is equal to pi times the radius squared, which would be pie times the diameter, or d.
So the diameter is 8 cm.
It tells you to use 3.14 for pi.
8 x 3.14= 25.12^2
So the area of the circle would be 25.12^2, and you would keep it like that.
Hope this helps!
(BTW, pi is the symbol at the bottom, where is says A= pi R^2)
Answer:
50.24
Step-by-step explanation:
Area of a circle is:
A = πr²
where π is approximately 3.14, and r is the radius of the circle (half the diameter).
The diameter is 8 cm, so the radius is 4 cm. Therefore, the area is:
A = π (4 cm)²
A = 50.24 cm²
In a school with 400 students, 120 ride the bus to school. What percent of the students ride the bus to school?
Answer:
30%
Step-by-step explanation:
120/400= 0.3
0.3x100=30
9 inches of rain in 72 hours as a unit rate
Answer:
Step-by-step explanation:
the unit rate of rainfall is [tex]\( \frac{1}{8} \)[/tex] inches per hour.
To find the unit rate of rainfall, which is the amount of rain per unit of time, we divide the total amount of rain by the total time.
Given:
Total amount of rain: 9 inches
Total time: 72 hours
Step 1: Divide the total amount of rain by the total time:
[tex]\[ \text{Unit rate} = \frac{\text{Total amount of rain}}{\text{Total time}} \][/tex]
[tex]\[ \text{Unit rate} = \frac{9 \text{ inches}}{72 \text{ hours}} \][/tex]
Step 2: Simplify the expression:
To simplify the unit rate, we divide 9 by 72.
[tex]\[ \text{Unit rate} = \frac{9}{72} \text{ inches per hour} \][/tex]
Step 3: Simplify the fraction:
[tex]\[ \text{Unit rate} = \frac{1}{8} \text{ inches per hour} \][/tex]
So, the unit rate of rainfall is [tex]\( \frac{1}{8} \)[/tex] inches per hour.
It takes 3 1/3 kilometers of thread to make 3 1/2 boxes of shirts. How many kilometers of thread will it take to make 8 boxes?
[tex]7\frac{13}{21}[/tex] km thread will be needed for 8 boxes of shirts
Step-by-step explanation:
The proportion will be used to find the measurement of thread
Given
It takes 3 1/3 kilometers of thread to make 3 1/2 boxes of shirts.
Now,
As there are more boxes, more thread will be needed. So it is a direct proportion
So,
[tex]Km:box::Km:box\\3\frac{1}{3}: 3\frac{1}{2}::x:8\\\frac{10}{3}:\frac{7}{2}::x:8\\\frac{\frac{10}{3}}{\frac{7}{2}} = \frac{x}{8}\\\frac{10}{3} * \frac{2}{7} = \frac{x}{8}\\\frac{20}{21} = \frac{x}{8}\\x = \frac{20}{21} * 8\\x = \frac{160}{21}\\x = 7\frac{13}{21}[/tex]
Hence,
[tex]7\frac{13}{21}[/tex] km thread will be needed for 8 boxes of shirts
Keywords: Unit rate, conversion
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The table shows how the number of cars, c, depends on the number people, t. How would you write this as an equation?
C T
2 1
3 4
4 7
5 10
t=3c-5 t=3c+5
t=5c+3 t=5c-3
Answer:
t = 3c - 5
Step-by-step explanation:
The relation between c and t is linear as the increase of the value of t is uniform for each unit increase in the value of c.
Now, any two points on the graph of the t = f(c) equation are sufficient to determine the equation.
Let the points are (2,1) and (3,4).
So, using two points formula of straight line we get the equation is
[tex]\frac{t - 4}{4 - 1} = \frac{c - 3}{3 - 2}[/tex]
⇒ t - 4 = 3(c - 3)
⇒ t - 4 = 3c - 9
⇒ t = 3c - 5 (Answer)
A school is repainting some of its classrooms. Each classroom is repainted with 5.5 gallons of paint. Write and solve an equation to determine the gallons of paint the school must purchase if they repaint 18 classrooms.
Idk how to write the equation
Answer:
a
Step-by-step explanation:
because i dont know
Answer: 99 gallons
Equation: 5.5 x 18 = 99
Which of the following numbers can be expressed as repeating decimals? (5 points) 5 over 7 , 4 over 5 , 7 over 9 , 5 over 8
Answer:
5 over 7 and 7 over 9
Step-by-step explanation:
Answer:
5 over 7 and 7 over 9 is the answer 0w0
Solve the given system of equations by substitution
x - y = 2, 2x + y = 7
Answer:
x=10/3, y=4/3. (10/3, 4/3).
Step-by-step explanation:
x-y=2
2x+y=7
-----------
x=y+2
2(y+2)+y=7
2y+4+y=8
3y+4=8
3y=8-4
3y=4
y=4/3
x-4/3=2
x=2+4/3
x=6/3+4/3=10/3
x=10/3, y=4/3.
Please explain how you found the measure of angle one angle two and angle three and angle four
Answer:
IT IS ETHER A OR B BROBABLY
Step-by-step explanation:
Arlene has 1/3 as many goldfish as Isabelle. Isabelle has 5 times as many goldfish as Anaele. If Anaele has 18 goldfish, how many goldfish does Arlene have?
Answer:
30
Step-by-step explanation:
to find how many Isabelle has, we multiply Anaele's number by 5. 18(5)=90. Isabelle has 90. Arlene has one third (1/3) of the number of Isabelle. So, we divide 90 by 3. 90/3=30. Arlene has 30 goldfish
After 56 cans of soup were sold, a clerk moved the remaining cans to a display
case. The display case had shelves that could each hold 9 cans. How many
shelves were needed to fit all the remaining cans?
Answer:
(x - 56) / 9
Step-by-step
We represent the original number of cans of soup by the variable x. After 56 cans of soup were sold, the remaining number of cans of soup is x - 56. Since we have shelves that can hold 9 cans, the number of shelves needed to fit all the remaining cans is
Solve for b 2/3+5=20-b
Answer:
b=43/3
Step-by-step explanation:
2/3+5=20-b
2/3+15/3=20-b
17/3=20-b
b=20-17/3
b=60/3-17/3
b=43/3
4. Tickets for a matinee are $5 for children and $8 for adults. The theater sold a total of 142 tickets for one matince Ticket
sales were $890. How many of each type of ticket did the theater sell?
System of equations:
The theater sold 82 children tickets and 60 adult tickets.
Step-by-step explanation:
No. of tickets sold = 142
Total sales = $890
Cost of one child ticket = $5
Cost of one adult ticket = $8
Let,
x be the number of children tickets
y be the number of adult tickets
According to given statement;
x+y=142 Eqn 1
5x+8y=890 Eqn 2
Multiplying Eqn 1 by 5
[tex]5(x+y=142)\\5x+5y=710\ \ \ Eqn\ 3[/tex]
Subtracting Eqn 3 from Eqn 2
[tex](5x+8y)-(5x+5y)=890-710\\5x+8y-5x-5y=180\\3y=180[/tex]
Dividing both sides by 3
[tex]\frac{3y}{3}=\frac{180}{3}\\y=60[/tex]
Putting =60 in Eqn 1
[tex]x+60=142\\x=142-60\\x=82[/tex]
The theater sold 82 children tickets and 60 adult tickets.
Keywords: linear equations, subtraction
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Eve split 42 marbles between herself and 5 friends. Her mom then gave her 2 more packs of marbles with 4 in each. How many does she now have?
Answer:
$15
Step-by-step explanation:
The grocery store sells 3 packages of biscuits for $1.35. At this rate, how much will 8 packages of biscuits cost?
A
$3.60
B
$10.80
C
$12.35
D
$17.78
Answer:
the answer is A
Step-by-step explanation:
1.35 divided by 3 = 0.45
0.45 multiplyed by 8 = $3.60