Answers
Answer:
Step-by-step explanation:
Rectangle:
length = l = 12 cm
Width = w = 0.8 cm
Use Pythagorean theorem to find the diagonal
Diagonal² = l² + w²
= 12² + 0.8²
= 144 + 0.64
= 144.64
Diagonal = √144.64 = 12.03 cm
Diagonal of square = diagonal of rectangle
= 12.03 cm
To find the side of square again use Pythagorean theorem,
side² + side² = 12.03²
2 sides² = 144.64
side² = 144.64/2
side² = 72.32
side = √72.32
Side = 8.50 cm
Related Questions
Maths!
1) Calculate the variance and standard division of the set of the data
2) If each value is added by 2, calculate the new standard deviation of the set
3) What is the effect on the measure of dispersion if each value is changed uniformly
Answers
Answer:
(1) Variance = 4.5 and Standard deviation = 2.121.
(2) Variance = 4.5 and Standard deviation = 2.121.
(3) The effect on the measure of dispersion if each value is changed uniformly is that it remains unchanged.
Step-by-step explanation:
We are given with the following set of data below;
X [tex]X-\bar X[/tex] [tex](X-\bar X)^{2}[/tex]
5 5 - 8 = -3 9
5 5 - 8 = -3 9
8 8 - 8 = 0 0
10 10 - 8 = 2 4
10 10 - 8 = 2 4
10 10 - 8 = 2 4
9 9 - 8 = 1 1
9 9 - 8 = 1 1
6 6 - 8 = -2 4
Total 72 36
Firstly, the mean of the above data is given by;
Mean, [tex]\bar X[/tex] = [tex]\frac{\sum X}{n}[/tex]
= [tex]\frac{72}{9}[/tex] = 8
(1)Now, the variance of the given data is;
Variance = [tex]\frac{\sum (X-\bar X)^{2} }{n-1}[/tex]
= [tex]\frac{36}{9-1}[/tex] = 4.5
So, the standard deviation, (S.D.) = [tex]\sqrt{\text{Variance}}[/tex]
= [tex]\sqrt{4.5}[/tex] = 2.12
(2) Now, each value is added by 2; so the new data set is given by;
X [tex]X-\bar X[/tex] [tex](X-\bar X)^{2}[/tex]
7 7 - 10 = -3 9
7 7 - 10 = -3 9
10 10 - 10 = 0 0
12 12 - 10 = 2 4
12 12 - 10 = 2 4
12 12 - 10 = 2 4
11 11 - 10 = 1 1
11 11 - 10 = 1 1
8 8 - 10 = -2 4
Total 90 36
Firstly, the mean of the above data is given by;
Mean, [tex]\bar X[/tex] = [tex]\frac{\sum X}{n}[/tex]
= [tex]\frac{90}{9}[/tex] = 10
(1)Now, the variance of the given data is;
Variance = [tex]\frac{\sum (X-\bar X)^{2} }{n-1}[/tex]
= [tex]\frac{36}{9-1}[/tex] = 4.5
So, the new standard deviation, (S.D.) = [tex]\sqrt{\text{Variance}}[/tex]
= [tex]\sqrt{4.5}[/tex] = 2.12
(3) The effect on the measure of dispersion if each value is changed uniformly is that it remains unchanged as we see in the case of variance or standard deviation.
Given: D is the midpoint of AB; E is the midpoint of AC.
Prove: DE BC
y
Complete the missing parts of the paragraph proof.
Proof:
To prove that DE and BC are parallel, we need to show
that they have the same slope.
slope of DE = 12-11=_C-C
X2 - x1 a + b - b
A(2b, 2c)
D(b, c)
Ela + bc)
slope of BC =
B(0,0)
C(2a, 0)
Therefore, because
DE 1 BC.
Answers
Answer:
The lines DE and BC have the same slope, therefore the two lines, DE and BC, are parallel
Step-by-step explanation:
To prove that DE is parallel to BC, we have;
The slope, m of the lines DE and BC are found from the following equation;
[tex]Slope, \, m =\dfrac{y_{2}-y_{1}}{x_{2}-x_{1}}[/tex]
Where;
(x₁, y₁) and (x₂, y₂) = (b, c) and (a + b + c) for DE, we have;
[tex]Slope, \, m =\dfrac{c - c}{a + b-b} = 0[/tex]
Where we have (x₁, y₁) and (x₂, y₂) = (0, 0) and (2a, 0) for BC, we have;
[tex]Slope, \, m =\dfrac{0 - 0}{2a-0} = 0[/tex]
Therefore, because the lines DE and BC have the same slope, the two lines DE and BC are parallel.
Answer:
slope of DE = 0
slope Bc = 0
slopes are =
Step-by-step explanation:
Which of the variable expressions below is a trinomial with a constant term? A. 3x5 – 2x3 B. x5 – 3x2 + 5x C. 7x6 + 2x4 – x3 + 7 D. 4x2 – 3 + x3
Answers
Answer:
Option (D)
Step-by-step explanation:
Option (A).
3x⁵ - 2x³
There are two terms with the variable 'x' in the given expression. therefore, it's a binomial with no constant term.
Option (B).
x⁵ - 3x² + 5x
This expression has three terms with variable 'x'.
Therefore, it's a trinomial without no constant term.
Option (C).
7x⁶ + 2x⁴ - x³ + 7
It's a quadrinomial having 4 terms. '7' is the constant term in the given expression.
Option (D).
4x² + x³ - 3 ≈ x³ + 4x² - 3
It's a trinomial with a constant term 3.
Therefore, Option (D) is the answer.
The city plans a roadway to have trees every mile. If the path is miles long, how many trees will the city need?
30 trees
31 trees
32 trees
33 trees
Answers
Answer:
32
Step-by-step explanation:
the country would need 30 to 33 trees
14 POINTER IF YOU HIT THE BULLSEYE!!!!! HELP!
Billy, Bob, and Joe found a question in their test that said this and they NEED HELP!!!!! with flying promises to give brainliest they now wait.......
Answers
Answer:
mean would decrease
Step-by-step explanation:
The shape on the left is translated to the shape on the right.
Which statement about the transformation is true?
A.The name of the shape on the right is MNOPQRS' because it is the image of the shape on the left.
B.The name of the shape on the right is MNOPORS' because it is the pre-image of the shape on the left.
C.The name of the shape on the right is M’N’O’P’Q’R’S because it is the pre-image of the shape on the left.
D. The name of the shape on the right M’N’O’P’Q’R’S
Because it is the pre-image if the shape in the left.
Answers
Answer:
sorry i am late but the answer is The name of the shape on the right is M prime N prime O prime P prime Q prime R prime S prime because it is the image of the shape on the left. and if you dont want to read that its D
hope it helped anyone :)
The name of the shape on the right is M’N’O’P’Q’R’S' because it is the pre-image of the shape on the left
TransformationTransformation is the movement of a point from its initial location to a new location. Types of transformation are rotation, reflection, translation and dilation.
Translation is the movement of a point up, down, left or right.
The name of the shape on the right is M’N’O’P’Q’R’S' because it is the pre-image of the shape on the left
find out more on Transformation at: https://brainly.com/question/1462871
Part
This table shows the prices of the three TVs in addition to their length and width. Is the price of a TV proportional to the length of its screen? How
do you know
Answers
Answer:
No! They are not proportional!
Step-by-step explanation:
Proportional prices to the length means that
(price 1/length 1)=(price 2/length 2)=(price 3/length 3)
Even by plugging in the numbers yourself to double check my numbers, and getting and answer for each ratio, it is clear that they are not proportional.
Answer:
The ratio of screen length to price in the first row is 16/160, which simplifies to 1/10.
The ratio of screen length to price in the second row is 20/180, which simplifies to 1/9.
The ratio of screen length to price in the third row is 24/200, which simplifies to 3/25.
Because 16/160 doesn't = 20/180 doesn't = 24/200, the ratios are not equivalent. This is not a proportional relationship.
Show by shading , the region in a Venn diagram represented by the set notations I)(AUB) NC ii) AU ( BNC)
Answers
See the diagram, and tell me if it's clear
The line plot below displays the fraction of incoming calls answered before the second ring by a group of employees. What fraction of employees answered less than of their incoming calls before the second ring?
Answers
Answer:
1/6
Step-by-step explanation:
People who answered less than 1/2 were: 2 + 1 + 3 = 6 people.
There are a total of 36 people.
People who answered their calls before the second ring were only 6/36.
When we simplify the fraction, we get 1/6.
So, the answer is 1/6
this is urgent...please help!
the brown family is ordering pizza. they are trying to decide whether to order a large pizza or a monster pizza. a monster pizza (m) has six fewer slices than twice the number of slices on a large pizza (l). the difference between the number of slices on a monster pizza and the number of slices on a large pizza is five slices. which system of equations below can be used to determine the number of slices on a large pizza and a monster pizza?
a) m - 2 l = 5
m - l = 6
b) 2m - l = 6
m - l = 5
c) 2m - l = -6
m - l = 5
d) m - 2 l = - 6
m - l = 5
Answers
Answer:
d) m - 2 l = - 6; m - l = 5
Step-by-step explanation:
Twice the number of slices on a large pizza is 2l. 6 fewer than that is 2l-6. This is the number on a monster pizza, so we have ...
m = 2l -6
Subtracting 2l from both sides gives the equation ...
m -2l = -6 . . . . . matches choice D
what is the value of 600.79-40.0032+5.01 to the nearest Hundredths
Answers
Answer:
565.80
Step-by-step explanation:
600.79-40.0032+5.01 = 565.7968
565.7968 to the nearest Hundredths =
565.80
Answer:
565.80
Step-by-step explanation:
600.79 - 40.0032 + 5.01
600.79 - 40.0032 = 560.7868
560.7868 + 5.01 = 565.7968
565.7968 to the nearest hundredth = 565.80
Help, Answer ASAP; will give brainliest
Answers
Answer:
PY = 14.5
Step-by-step explanation:
The diagonals of a rectangle are congruent and bisect each other, thus
XZ = WY , that is
4x - 1 = x + 7 + x + 7
4x - 1 = 2x + 14 ( subtract 2x from both sides )
2x - 1 = 14 ( add 1 to both sides )
2x = 15 ( divide both sides by 2 )
x = 7.5
Thus
PY = x + t = 7.5 + 7 = 14.5
Step-by-step explanation:
py is equal to wp because the figure is a rectangle.x+7+x+7= 4x-1
2x+14=4x-1
14= 2x-1
15= 2x (divide)
x = 7.5
wp= 7.5cm
not really sure
Simplify
2x + 5x^3 + 3x - 4x^3
Answers
Answer:
x³ + 5x
Step-by-step explanation:
2x+5x3+3x−4x3
=2x+5x3+3x+−4x3
Combine Like Terms:
=2x+5x3+3x+−4x3
=(5x3+−4x3)+(2x+3x)
=x3+5x
Answer:
[tex]\large \boxed{x^3+5x}[/tex]
Step-by-step explanation:
[tex]2x + 5x^3 + 3x - 4x^3[/tex]
[tex]\sf Group \ like \ terms.[/tex]
[tex]5x^3 - 4x^3+2x+3x[/tex]
[tex]\sf Combine \ like \ terms.[/tex]
[tex]x^3+5x[/tex]
I need help please so if you could help that would be nice. Also i will make brainliest
Answers
find y.
picture attached
Answers
y = 2.97167
-\dfrac{1}{6} \times \left(-\dfrac{9}{7}\right)− 6 1 ×(− 7 9 )minus, start fraction, 1, divided by, 6, end fraction, times, left parenthesis, minus, start fraction, 9, divided by, 7, end fraction, right parenthesis
Answers
Answer:
[tex]\dfrac{3}{14}[/tex]
Step-by-step explanation:
The even number of minus signs means the product will be positive. A factor of 3 can be removed to simplify the product. As usual, the numerator of the product is the product of numerators, and the denominator of the product is the product of denominators.
[tex]-\dfrac{1}{6} \times \left(-\dfrac{9}{7}\right)=\dfrac{1\cdot 9}{6\cdot 7}=\dfrac{3\cdot 3}{3\cdot 14}=\boxed{\dfrac{3}{14}}[/tex]
Answer:
→ 3/4 ←
-1/6 × (-9/7)= 1·9/6·7 3·3/3·14 = 3/4
Find the measure of f.
Answers
Answer:
44 degrees.
Step-by-step explanation:
The 3 small triangles are isosceles so m < a = m < b , therefore
m < a = (180 - 92) / 2 = 44 degrees.
m < f = m < a ( they are both subtended on the circle by the same chord (cd)),
So m < f = 44.
I need help with 6 and 7
Answers
Answer:
Step-by-step explanation:
6):
Take the small right triangle with the sides 25 and 7.
☆ The Pythagorian theorem ☆
Let x be the third side.
● 25^2 = x^2 + 7^2
Substract 7^2 from both sides
● 25^2 -7^2 = x^2 +7^2 -7^2
● x^2 = 25^2 -7^2
● x^2 = 576
● x = 24 inches
The third that we find is the half of the side of the square.
Multiply it by 2 and get the side of the square.
● 24 × 2 = 48 inches
The perimeter of the square is the side times 4.
● P = 48 × 4
● P = 192 inches
■■■■■■■■■■■■■■■■■■■■■■■■■■
7):
Both triangles are righr and they have a khown angle.
Start with the small one and calculte the third angle.
The sum of a triangle angles is 180°
Let B be the third angle.
● B = 180-(90+51) = 39°
That's equal to the second angle of the second's triangle.
So it's an AA similarity.
So:
● x/24 = 7/15
● x = (7/15)×24
● x = 11.2
Positive numbers are not closed under subtraction. Give an example of this 1
below.
Answers
Answer:
5 -3 = 2
3-5 = -2
Step-by-step explanation:
In this question, we want to examine the validity of the statement by the use of an example.
Firstly, we need to understand the meaning of the fact that they are ‘closed’
By saying these numbers are closed under this arithmetic operation i.e subtraction, we directly mean that they obey the closure property.
Now, to obey the closure property means that if we move either way i.e by switching the numbers and performing the same arithmetic operation of subtraction, we are supposed to get same answer.
What this means in terms of examples is as follows;
Consider two positive numbers, 5 and 3
Now we know that 5-3 = 2
To check if the closure property is obeyed, switch the place of the numbers.
This means we would have;
3-5 = -2
We can see that both results are not the same. We can then conclude that the arithmetic operation of subtraction is not closed or does not obey the closure property for positive numbers.
Make the biggest possible number using the digits below only once 0 , 3 , 4
Answers
Answer:
12,157,665,459,057,000,000
Step-by-step explanation:
It seems like it would have to involve exponents. 3 to the 40th power would be 12,157,665,459,057,000,000.
consider the polynomial 8x^3+2x^2-20x-5 factor
Answers
Answer:
(4x + 1)(2x² - 5)
Step-by-step explanation:
Given
8x³ + 2x² - 20x - 5 ( factor the first/second and third/fourth terms )
= 2x²(4x + 1) - 5(4x + 1) ← factor out (4x + 1) from each term
= (4x + 1)(2x² - 5)
Answer:
blank 1 is -20-5
blank 2 is 4x+1
blank 3 is -5
blank 4 is 2x^2-5
Step-by-step explanation:
if "f" varies directly with "m," and f = -19 when m = 14, what is "f" when m = 2
Answers
Answer:
f = - [tex]\frac{19}{7}[/tex]
Step-by-step explanation:
Given f varies directly with m then the equation relating them is
f = km ← k is the constant of variation
To find k use the condition f = - 19 when m = 14, thus
- 19 = 14k ( divide both sides by 14 )
- [tex]\frac{19}{14}[/tex] = k
f = - [tex]\frac{19}{14}[/tex] m ← equation of variation
When m = 2, then
f = - [tex]\frac{19}{14}[/tex] × 2 = - [tex]\frac{19}{7}[/tex]
A spray irrigation system waters a section of a farmer’s field. If the water shoots a distance of 85 feet, what is the area that is watered as the sprinkler rotates through an angle of 60 degrees? Use 3.14 for pi . Round your answer to the nearest square foot, and enter the number only.
Answers
Answer:
3,781
Step-by-step explanation:
To solve this problem, we will find the area of the whole circle and use that to find teh area of the 60º section.
First, recognize the formula for the area of a circle:
A = 3.14[tex]r^{2}[/tex]
In this scenario, the radius (r) is 85 feet:
A = 3.14(85[tex])^{2}[/tex]
A circle is 360º and we only require the area of 60º. 360º / 60º = 6 so we will divide by 6:
A = [tex]\frac{3.14(85)^{2} }{6}[/tex]
Finally, we will simplify and round:
A = 3,781
P(x) =2x3 -11x2 -4x +1 g(x) =2x +1
Answers
Answer:
see explanation
Step-by-step explanation:
If (2x + 1) is a factor then x = - [tex]\frac{1}{2}[/tex] is a root and P(- [tex]\frac{1}{2}[/tex] ) = 0 ← Factor theorem
P(- [tex]\frac{1}{2}[/tex] )
= 2(- [tex]\frac{1}{2}[/tex] )³ - 11(- [tex]\frac{1}{2}[/tex] )² - 4(- [tex]\frac{1}{2}[/tex] ) + 1
= - [tex]\frac{1}{4}[/tex] - [tex]\frac{11}{4}[/tex] + 2 + 1
= - [tex]\frac{12}{4}[/tex] + 3
= - 3 + 3
= 0
Since P(- [tex]\frac{1}{2}[/tex] ) = 0 then g(x) is a factor of P(x)
The length of a rectangle is 5/6 feet. The width is 3/8 feet. How much greater is the length of the rectangle than the width?
Answers
Answer:
0.46 feet
Step-by-step explanation:
Length = 5/6 feet (or 0.254 m)
Width = 3/8 feet (or 0.114 m)
(5/6 - 3/8) feet = 11/24 feet or 0.46 feet (0.140 m)
Determine if the event described is independent or dependent. You pick a marble at random from a group of marbles, don't replace the marble, and pick a second marble.
Answers
Answer:
dependent
Step-by-step explanation:
This is a dependent event. There is one less marble in the bag to choose from
Say there was 1 red marble and 4 blue marble. You drew the red marble on the first pick, now you cannot get a red marble on your second pick.
If you drew a blue marble on the first pick you could get a red marble on the second pick.
So what happens on the first pick affects the second pick
Please help i need this answered!!
Answers
Everything you answered so far looks good. Nice work.
For question 10, we need to find two numbers that multiply to 3(-1) = -3 and also add to 2. The 3 and -1 are the first coefficient and last term. The 2 is the middle coefficient.
Through trial and error, the two numbers we're after are 3 and -1
3 times -1 = -3
3 plus -1 = 2
We break up the 2x into 3x - 1x and factor like so...
3x^2 + 2x - 1
3x^2 + 3x - 1x - 1 ... replace 2x with 3x-1x
(3x^2+3x) + (-1x-1) ... pair up terms
3x(x+1) - 1(x+1) .... factor each parenthesis group
(3x-1)(x+1) ... pull out the gcf (x+1)
You can use FOIL, the box method, or distribution to go from (3x-1)(x+1) back to 3x^2+2x-1 again.
The answer to problem 10 is (3x-1)(x+1)Answer:
Step-by-step explanation:
A 51-foot wire running from the top of a tent pole to the ground makes an angle of 58° with the ground. If the length of the tent pole is 44 feet, how far is it from the bottom of the tent pole to the point where the wire is fastened to the ground? (The tent pole is not necessarily perpendicular to the ground.)
Answers
Answer:
35.11 ft
Step-by-step explanation:
This given situation can be thought of as triangle [tex]\triangle PQR[/tex] where PQ is the length of pole.
PR is the length of rope.
and QR is the distance of bottom of pole to the point of fastening of rope to the ground.
And [tex]\angle Q \neq 90^\circ[/tex]
Given that:
PQ = 44 ft
PR = 51 ft
[tex]\angle R = 58^\circ[/tex]
To find:
Side QR = ?
Solution:
We can apply Sine Rule here to find the unknown side.
Sine Rule:
[tex]\dfrac{a}{sinA} = \dfrac{b}{sinB} = \dfrac{c}{sinC}[/tex]
Where
a is the side opposite to [tex]\angle A[/tex]
b is the side opposite to [tex]\angle B[/tex]
c is the side opposite to [tex]\angle C[/tex]
[tex]\dfrac{PR}{sinQ}=\dfrac{PQ}{sinR}\\\Rightarrow sin Q =\dfrac{PR}{PQ}\times sinR\\\Rightarrow sin Q =\dfrac{51}{44}\times sin58^\circ\\\Rightarrow \angle Q =79.41^\circ[/tex]
Now,
[tex]\angle P +\angle Q +\angle R =180^\circ\\\Rightarrow \angle P +58^\circ+79.41^\circ=180^\circ\\\Rightarrow \angle P = 42.59^\circ[/tex]
Let us use the Sine rule again:
[tex]\dfrac{QR}{sinP}=\dfrac{PQ}{sinR}\\\Rightarrow QR =\dfrac{sinP}{sinR}\times PQ\\\Rightarrow QR =\dfrac{sin42.59}{sin58}\times 44\\\Rightarrow QR = 35.11\ ft[/tex]
So, the answer is 35.11 ft.
Josephine is going on a run around the lake. She knows the distance around the lake. but she would like to complete her run in a certain amount of time. Josephine knows she can used the formula d=rt Which equation correctly rearranges the formula to find the time it will take her to run around the lake? (Solve for t)
Answers
Answer:
D
Step-by-step explanation:
To solve for T in this, you need to to divide r from both sides of the equation.
d=rt
divide r
d/r=t
The correct equation is t= d/r.
The answer is option D.
How do you reorganize an equation?Rearrange the equation in order that the unknown variable is by itself on one aspect of the equals sign (=) and all the different variables are on the opposite side. Rule 1: you could add, subtract, multiply and divide by means of something, so long as you do the identical aspect to both aspects of the equals sign.
What does it mean to rearrange a formula?We can express an equation in phrases of the opposite variable. For example, to arrange the equation in order that it's far written as taking each time period and circulate to the opposite side of the equal sign the usage of the opposite operation till you most effective have.
Learn more about the equation here: https://brainly.com/question/1214333
#SPJ2
3/4a-1/6=2/3a+1/4? Please i need help!!!!
Answers
Answer: a=5
Step-by-step explanation:
1/12a=10/24
24a=120
a= 5
