The point of intersection of the diagonals of a rectangle is 4 cm further away from the smaller side than from the larger side of the rectangle. The perimeter of the rectangle is equal to 56cm. Find the lengths of each side of the rectangle
Answers
Answer:
smaller side: 10 cmlarger side: 18 cmStep-by-step explanation:
The given relationships can be translated to equations using L and W for the length and width of the rectangle. The distance from the center to the short side is L/2, and the distance from the center to the long side is W/2.
SetupP = 2(L +W) . . . . . formula for the perimeter
56 = 2(L +W) . . . . . the perimeter is 56 cm
L/2 = 4 + W/2 . . . . . distance to short side is 4 cm longer
__
SolutionDividing the first equation by 2 gives ...
28 = L +W
Multiplying the second equation by 2 gives ...
L = 8 + W
Substituting for L in the first equation, we have ...
28 = (8 +W) +W . . . . . . use L=8+W
20 = 2W . . . . . . . . .subtract 8
10 = W . . . . . . . . divide by 2
L = 8 +10 = 18 . . . . . find the length
__
The smaller side is 10 cm; the larger side is 18 cm.
Related Questions
So can someone explain how the heck does 4 x 4 x 4 = 64??
Cause I keep on getting 12 so like wth??
Answers
Answer:
it is more like, 4x4=16
16x4=64
Step-by-step explanation:
I know it can be confusing, but you will eventually get it :)
i think you were adding 4+4+4=12, but that is not what you are supposed to do here.
Hope i helped :)
Using scales of 1cm to 30° on the x axis and 2cm to 1 unit on the y axis,draw the graph of y=sin 0 for 0°less than or equal to 0 less than or equal to 360°.Using the graph to a)find the equation b) solve the equation i)sin0=0.6 ii)4sin0=-3
Help me and will mark brainlest
Answers
Answer:
Attachment 1: graph of [tex]y=\sin(\theta)[/tex]
(using given scale)
Question (a) (Attachment 2)
[tex]\sin(\theta)=0.6[/tex]
Draw the line [tex]y=0.6[/tex] (shown in blue).
Find the points of intersection of the sine curve and the line.
Measure to find the values of [tex]\theta[/tex]
[tex]\theta=37^{\circ},143^{\circ}\:\textsf{(nearest degree)}[/tex]
Question (b) (Attachment 3)
[tex]4\sin(\theta)=-3[/tex]
[tex]\implies \sin(\theta)=-\dfrac34[/tex]
Draw the line [tex]y=-\dfrac34[/tex] (shown in red).
Find the points of intersection of the sine curve and the line.
Measure to find the values of [tex]\theta[/tex]
[tex]\theta=229^{\circ},311^{\circ}\:\textsf{(nearest degree)}[/tex]
Which is the graph of the equation y-1=2/3(x-3)
Answers
Answer:
Step-by-step explanation:
Which figures below have perpendicular lines?
1
2
3
4
5
6
7
Answers
Answer:
Square, purple triangle, and red arrow
Step-by-step explanation:
What is the distance between points A and B?
0-6 units
-1 units
O 5 units
O6 units
Answers
Step-by-step explanation:
d 6 units .................
The distance between the points A and B is given by D = 6 units
What is the distance between two points?Let the two points be A ( x₁ , y₁ ) and B ( x₂ , y₂ )
The distance from A to B is the same as the distance from B to A
Distance between two points is the length of the line segment that connects the two points in a plane.
The formula to find the distance between the two points is usually given by D = √( ( x₂ – x₁ )² + ( y₂ – y₁ )²)
This formula is used to find the distance between any two points on a coordinate plane or x-y plane
Given data ,
Let the distance between 2 points be represented as D
Now , let the first point be P ( -5 , 0 )
Let the second point be Q ( 1 , 0 )
Now , distance D = √( ( x₂ – x₁ )² + ( y₂ – y₁ )²)
On simplifying , we get
D = √ ( -5 - 1 )² + ( 0 )²
D = √ ( 6 )²
D = 6 units
Hence , the distance is 6 units
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If p(x)=x3-1 then find p(1) and P(-1)
Answers
Step-by-step explanation:
p(x)=x³-1
p(-1)=(-1)³-1=(-1)-1=(-2)
p(-1)=(-2)
p(1)=(1)³-1=1-1=0
p(1)=0
square route of 482930 free brain liest
Answers
Answer:
694.9
Step-by-step explanation:
Answer:
This is your answer 694.931651315437
Have a good day!
A rectangular lot is 80 yards wide and 125 yards long.
Give the length and width of another rectangular lot that has the same perimeter but a smaller area.
Answers
Answer:
70 yards wide and 135 yards long
Step-by-step explanation:
The perimeter of a rectangle will be the same if the sum of length and width is the same. The area will be smaller if the difference between lenth and width is greater.
__
The sum of length and width will be the same if the length is increased by the same amount that the width is decreased. Changing each by 10 yards is one possibility.
A lot 70 yards wide and 135 yards long will have the same perimeter and a smaller area.
_____
Check
Given perimeter: 2(80 +125) = 410 yds.
Modified perimeter: 2(70 +135) = 410 yds. (same)
Given area = 80(125) = 10000 yd².
Modified area: 70(135) = 9450 yd². (smaller)
__
Additional comment
The area is greatest when the difference between the length and width is zero. That is, the rectangle will be a square.
A bag contains 10 white, 12 blue, 13 red, 7 yellow, and 8 green wooded balls. A ball is selected from the bag and kept. You then draw a second ball and keep it also. What is the probability of selecting two blue balls
Answers
Answer:
[tex]someone \: needs \: to \: g et \: laid \\ [/tex]
The value of y varies directly with x, and y = 18 when x = 12. Find y when x = 60.
Answers
[tex]\qquad \qquad \huge \pink {\sf{☁Answer☁}} \\ \\ [/tex]
→ Here,
y varies directly as x means that y = kxhere value of (k) is not knownby substituting the values of x and y, y = 18 when x = 12
[tex]\rm{y = kx} \\ \\ \rm{18 = 12k} \\ \\ \rm{k = \cancel \frac{18}{12} } \\ \\ \rm{ k = 1.5}[/tex]
Now, substituting value of k nd x in y = kx
x = 132k = 1.5 in y = kx[tex] \rm{y = (1.5 \times 60 )} \\ \\ \rm{y = 90}[/tex]
[tex]\sf{\:мѕнαcкεя\: ♪...}[/tex]
How do u substitute 5x-y=-5 3x-6y=24
Answers
5x-y=-5
Subtract 5x from both sides
-y = -5-5x
Multiply both sides by -1
Y = 5+5x
Now plug this in for y in the other equation
3x-6(5+5x) =24
Distribute
3x-30-30x=24
Simplify
-27x-30 = 24
Add 30
-27x = 54
Divide
X = -2
Now plug this in the first equation
Y = 5+5(-2)
Y = 5 -10
Y = -5
So X = -2, Y = -5
Find two consecutive positive integers such that the sum of their squares is 761
Answers
Answer:
[tex]19^{2} +20^{2}[/tex] is 761
Step-by-step explanation:
Answer:
19 and 20
Step-by-step explanation:
Let the integers be x and x + 1.
According to the question,
x² + (x + 1)² = 761x² + x² + 2x + 1 = 7612x² + 2x - 760 = 0x² + x - 380 = 0x² + 20x - 19x - 380 = 0x(x + 20) - 19(x + 20) = 0(x - 19)(x + 20) = 0x = 19, -20But x is a positive integer⇒ x = 19Therefore, the integers are :
x = 19x + 1 = 20Which of the following shows the Commutative Property of Multiplication?
(3 × 2) × 7 = 3 × (2 × 7)
4 × (5 + 8) = (4 × 5) + (4 × 8)
4 × 5 = 5 × 4
9 × 7 = 63
Answers
Answer:
The options that show the Commutative Property of Multiplication are:
A) 4x5=5x4
C) (3 x 2) × 7 = 3 ×(2 x 7)
------------------------------
The commutative property of multiplication states that the order in which the factors are multiplied does not change the product, that is:
Of the options, the ones which show it are:
A) 4x5=5x4
C) (3 x 2) × 7 = 3 ×(2 x 7)
In C), on the left side, the first 3 is multiplied by 2, then the result 6 is multiplied by 7, resulting in 42. On the right side, 2 is multiplied by 7, resulting in 14, which is multiplied by 3, resulting in 42.
Step-by-step explanation:
-lukelaws
Answer:
(3 × 2) × 7 = 3 × (2 × 7)4 x 5 = 5 x 4Step-by-step explanation:
These shows the commutative property.
Regardless of which number you group together, the answer remains the same as numbers on each side are identicalHope it helps~
Solve the inequality: 3 < -5X+2X
Answers
Answer:
Inequality Form:
X< −1
Interval Notation:
(−∞,−1)
Step-by-step explanation:
Answer:
[tex]x < -1[/tex]
Step-by-step explanation:
First you need to combine the like terms -5x and 2x to get [tex]3 < -3x[/tex]
Then, you need to devide both sides by -3 to get [tex]-1 < x[/tex] , but because the factor is negative, we flip the relation to get [tex]x < -1[/tex]
What type of association is seen in the scatter plot.
Answers
Answer:
Girl how do you not know this is the most easiest thing /hj
Step-by-step explanation:
its a linear and strong association bc the dots are very refined and stuck together very well
Select the quadratic that has roots x = 8 and x = -5.
A
x2 + 3x - 40
B
x² – 3x – 40
C
x? + 13x + 40
D
x? - 13x + 40
Answers
[tex]\text{ The roots are}~ \alpha = 8~ \text{and}~ \beta = -5\\\\\text{Equation for the given roots,}\\\\x^2 -(\alpha +\beta )x +\alpha \beta = 0\\\\\implies x^2 -(8-5)x + 8(-5)=0\\\\\implies x^2 -3x -40=0\\\\\text{Hence, the answer is option B}[/tex]
Find the product of (x - 5)2
-
O x2 + 10x + 25
O x2 - 10x + 25
O x2 - 25
-
O x2 + 25
Answers
Quentin works as a used car salesman, where he earns $8 per hour and an average commission
of $260 per car sold. He wants to earn at least $1040 per week. Write an inequality to represent this scenario, define your variables and explain why you chose them.
Answers
Answer:
Step-by-step explanation:
$8 per hour + average commision $260 per car sold ≥ $1040 per week.
This two numbers can make 1040 dollars a week or less. It depends on how many cars he can sell.
how to convert a improper fraction to a mixed number
Answers
Answer:
Step-by-step explanation:
Divide the numerator by the denominator.
Write down the whole number part of the quotient.
Take the remainder and write it over the original denominator.
PLEASE HELP!! WILL GIVE BRANLIEST
Answers
Explain
we use the vertex form
y=a(x-h)^2+k where the vertex is (h,k)
Select ( -4,-1)
Where h=-4
K=-1
y=a(x-h)^2+k
We get
y=a(x-(-4))^2+ -1
Y= a(x+4)^2+-1
Now replace to 0,7
7=a(0+4)^2-1
7=a(4)^2-1
7=16a-1
So now
7=16a-1
7+1=16a
8=16a
a=8/16
That should 1/2
So y=a(x+4)^2 -1
Should become
Y=1/2(x+4)^2 -1
Do you have any doubts now !
if Bill
deposits $3000 in an account that earns 6.5% compound interest annually for 3.5 years.
How much interest will he have earned?
Answers
Answer:
$3,623.84 Exact answer without rounding | $3,623.85 ~ (Approximent Answer with rounding.)
Step-by-step explanation:
Compound Interest Has a Specific Formula:
This case is Exponential Growth.
Formula: y= ab^x
You need to set up the equation.
First we need to define the rate of growth meaning what do you have to do for the 6.5%.
You need to do 100% + 6.5% = 106.5%
You need to convert the percent to a decimal which will be 1.065
Now we need to start plugging things into our formula to solve.
Your initial Starting amount was $3000
So you need to have y=3000(b)^x
We now know that the rate of growth is 1.065 so the b would be 1.065
y=3000(1.065)^x
Our power to x is our 3.5 years.
Our Equation now:
y=3000(1.065)^3
Now you need to use a calculator to do this due to the amount of decimals and digits.
Remember pemdas when doing this!!!
The answer should result to $3,623.84 but if rounded then: $3,623.85
i will give brainliest
Answers
Answer:
Below
Step-by-step explanation:
Population: 10,000
Sample: 250
$
6
4
No
2+
of
black
tan
gray white
Color
green
orange
O green
O orange
(a) Which color had the fewest T-shirts sold?
black
o tan
O gray O white
How many T-shirts of that color were sold?
T-shirt(s)
(b) How many more gray T-shirts were sold than tan T-shirts?
more T-shirt(s) sold
(C) For how many colors were there fewer than 10 T-shirts sold?
color(s)
Explanation
Check
© 2022 McGraw HIN
Answers
Answer:
a. tan
3 T-shirts
b. 7 - 3 = 4 T-shirts
A line passes through the point (–6, –2), and its y-intercept is (0, 1). What is the equation of the line that is perpendicular to this line and passes through the point (2, 3)?
Answers
Step-by-step explanation:
Gradient = y2-y2/x2-x1
= 1-(-2) / 0-(-6)
= 1/2
m1 × m2 = -1
1/2 × m2 = -1
m2 = -2
y= mx+c
(3)=(-2)(2) + c
c=7
°y= -2x +7
What is the value of z?
Answers
Answer:
z=58
Step-by-step explanation:
Sum of interior angles of a n-gon = (n-2) 180
for this 7-gon (heptagon) (7-2)(180) = 900
so all of the angles added togehter = 900
z+50 + 2z + 2z+23 + 3z-37 + 2z+31 + 113 + 140 = 900
z = 58
Mr. Torres has a class of 17 students. He can spend $24 on each student to buy math supplies for the year. He first buys all of his students calculators, which
costs a total of $77.35. After buying the calculators, how much does he have left to spend on each student?
Answers
Answer:
She has a class of 17 kids. At $24 each, she can spend 17*$24 = $408. Since she spent $125.36, she has $408 - $125.36 = $282.64 left to spend.
Step-by-step explanation:
408-77.35= 330.65
330.65/17=19.45
After buying the calculators, Mr. Torres has $19.45 timo spend on each student.
Erik is learning how to make hachapuris. He uses 5 eggs for each hachapuri.
Erik has 12 eggs, and he makes as many hachapuris as he can. How many
hachapuris does Erik make? How many eggs are left?
unters
Answers
Answer:
2
Step-by-step explanation:
he has 12 eggs and each hachapuri needs 5 so for one hachpuri we have 7 then for the second hachapuri we need 5 so we are left with 2 we cant make them anymore so there you go
Mrs Li's classroom is 34 feet wide and 42 feet long. Objects in classroom Mrs. Li's Desk, Fish Tank, Math Center, or Reading Center. Area of Objects (square feet) 8, 6, 100, or 120. what is the area of the classroom?
Answers
Answer:
multiply length with breadth which is 34 *42
Answer:1'428 sq ft because you multiply 34x42 witch= to 1,428
13tX 9
7. Dareen's family now wants to Install 1-foot-square terra-cotta tiles in the entryway and kitchen, and 4-inch-square blue tiles on each bathroom floor. The
terra-cotta tiles cost $ each, and the bathroom tiles cost 45€ cach. How many of each kind will they need? What will all the tiles cost?
Answers
The total number of terra-cotta tiles needed is 220 tiles.
The total number of blue tiles needed is 4428 tiles.
The cost of all the tiles would be $3,092.60.
What is the total number of tiles needed?The first step is to determine the area of the entryway and the kitchen.
Area of the entryway = length x width
(22 - 18) x 10 = 40 ft²
Area of the kitchen = 10 x 18 = 180ft²
Sum of the areas of the entryway and the kitchen = 180 + 40 = 220 ft² = 220 tiles
Total cost = 220 x $5 = $1100
Areas of the bathroom floors = (10 x 6) + (7 x 9) = 123ft²
Convert ft² to in²
1 ft² = 144in²
123 x 144 = 17,712 in²
Number of tiles needed = 17,712 / 4 = 4428 tiles
Total cost = 4428 x 0.45 = $1992.60
Total cost = $1992.60 + $1100 = $3,092.60
Here is the complete question: Dareen's family now wants to Install 1-foot-square terra-cotta tiles in the entryway and kitchen, and 4-inch-square blue tiles on each bathroom floor. The
terra-cotta tiles cost $5 each, and the bathroom tiles cost 45€ cach. How many of each kind will they need? What will all the tiles cost?
To learn more about how to calculate the area of a rectangle, please check: https://brainly.com/question/16595449
A distribution has a mean of 70.If 5 points are added to each individual score, the new mean would be
Answers
Answer:
well its free
Step-by-step explanation:
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