Answers
Answer:
[tex]\huge\boxed{\bf\:2\sqrt{5} \:\: units }[/tex]
Step-by-step explanation:
We have a figure given in the shape of a square with a diagonal (x) passing from one edge to another. We need to find the measure of its diagonal if the side of the square is [tex]\sqrt{10}[/tex] units.
We know that, a square has all equal sides. Then, all the sides of the square will be equal to [tex]\sqrt{10}[/tex] units.
Now, let's find the diagonal.
To find the diagonal of a sqaure from one of its sides, we need to know the formula ⟶ Diagonal = side [tex]\bf\:\sqrt{2}[/tex].
By using this formula,
[tex]Diagonal (x)\\= side *\sqrt{2} \\= \sqrt{10} *\sqrt{2}\\ = \sqrt{5*2*2} \\= \boxed{\bf\:2\sqrt{5} \:units}[/tex]
→ The diagonal of the square = 2√5 units.
[tex]\rule{150pt}{2pt}[/tex]
Related Questions
Match each rational expression to its simplest form.
2m2-4m
2(m2)
m2-2m+1
m-1
m-
m
m-1
EE
m
m²-3m +2
m2.
m
m
m
Reset
m²-m-2
m²-1
Next
Answers
The first rational expression simplifies to (m - 1).
The second rational expression simplifies to (m - 2) / m.
The third rational expression simplifies to (m - 2) / (m - 1).
What is an expression?An expression contains one or more terms with addition, subtraction, multiplication, and division.
We always combine the like terms in an expression when we simplify.
We also keep all the like terms on one side of the expression if we are dealing with two sides of an expression.
Example:
1 + 3x + 4y = 7 is an expression.com
3 + 4 is an expression.
2 x 4 + 6 x 7 – 9 is an expression.
33 + 77 – 88 is an expression.
We have,
(m² - 2m + 1) / (m - 1)
(m² - 2m + 1) / (m - 1)
= (m - 1) / 1
= m - 1
The first rational expression simplifies to (m - 1).
(m² - 3m + 2) / (m² - m)
(m² - 3m + 2)
= (m - 1)(m - 2)
(m² - m)
= m(m - 1)
So,
(m² - 3m + 2) / (m² - m)
= (m - 2) / m
The second rational expression simplifies to (m - 2) / m.
(m² - m - 2) / (m² - 1)
(m² - m - 2)
= (m - 2)(m + 1)
(m² - 1)
= (m - 1)(m + 1)
So,
(m² - m - 2) / (m² - 1)
= (m - 2) / (m - 1)
The third rational expression simplifies to (m - 2) / (m - 1).
Thus,
The first rational expression simplifies to (m - 1).
The second rational expression simplifies to (m - 2) / m.
The third rational expression simplifies to (m - 2) / (m - 1).
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The complete question.
Match each rational expression to its simplest form.
(m² - 2m + 1) / (m - 1)
(m² - 3m + 2) / (m² - m)
(m² - m - 2) / (m² - 1)
Options:
(m - 2) / m
(m - 1)
(m - 2) / (m - 1)
x
Benchmark Assessment - 29/34
Choose two number sentences below that equal 39:
A) 71-32
B) 49 - 20
C) 85-46
D) 50 - 29
Answers
C, 85-46 is also equal to 39
The circle passes through the point (−2, 3) with a center of (-4,6). What is its radius?
Answers
Answer:
radius = √13
Step-by-step explanation:
Forming the equation :
(x - h)² + (y - k)² = r²
(x, y) = point on circle(h, k) = center of circler = radiusSolving :
(-2 + 4)² + (3 - 6)² = r²r² = 4 + 9radius = √13What is the quotient of 552/58
Answers
The quotient of 552/58 is 276/29.
What is the quotient of a number?The quotient of a number is the result or the outcome when you divide two numbers together.
From the given information, the quotient of [tex]\mathbf{\dfrac{552}{58}}[/tex] is can be determined by dividing both the numerator and the denominator by (2):
i.e.
[tex]\mathbf{=\dfrac{276}{29}}[/tex]
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What’s the value of x?
Answers
Convert the decimal or whole number to a percent. 0.32 1/2
Answers
Please help I need it asap
Answers
Answer:
The answer is origin
Answer: orgin
Step-by-step explanation: orgin
How to find x=?
How to solve step by step
Answers
Answer:
230 degrees
Step-by-step explanation:
draw a horizontal line from x and use congruent rule to have a full 360 degree circle. You can now subtract 60 and 70 from 360 degrees leaving you with 230 degrees as x
What is The converse of p→q
Answers
Answer:
q→p
Step-by-step explanation:
The converse of p→q is q→p.
which means If q ,then p.
If you draw a card out of a deck of cards at random, what is the probability
that you will draw a 6?
Answers
Answer:
[tex]\frac{1}{13}[/tex]
Step-by-step explanation:
Probability is the number of favorable outcomes divided by the number of total outcomes. The total outcomes are all the situations that could possibly happen. There are 52 cards in the deck, so there are 52 total outcomes. Next, the favorable outcomes are the outcomes we want. In this case it is drawing a 6. There are four 6's in a deck of cards: 6 of hearts, 6 of spades, 6 of diamonds, and 6 of clubs. This means there are 4 favorable outcomes.
We can write the probability as a fraction: [tex]\frac{favorable-outcomes}{total-outcomes}[/tex], so we can get [tex]\frac{4}{52}[/tex]. Since both 4 and 52 are divisible by 4, the fraction can be simplified to [tex]\frac{1}{13}[/tex].
Answer:
1/13
Step-by-step explanation:
that's the answer to the question
Find a. (f+ g)(x) b. (f+g)(7).
f(x) = 5x +2, g(x) = 5x – 1
a. (f+g)(x)=
Answers
A. 10x + 1
B. 71
(WORK SHOWN BELOW)
50 POINTS A point in the figure is selected at random. Find the probability that the point will be in the shaded region.
about 70%
about 80%
about 95%
about 67%
Answers
The first step that we need to take before attempting to solve the problem is to understand what the problem is asking us to do and what they are giving us to help solve the problem. Looking at the problem statement they are asking for us to determine the probability that a point will randomly be plotted in the shaded region. We are not given much of anything else which means that we will need to use our own numbers.
The picture that was provided has a square with four equal circles inside right next to each other. Therefore, we can say that each side of the square is going to be 2 units which causes the diameter of the circle to be half that or 1 unit. We can go even further and determine that the radius is going to be 0.5 units for each circle. Let's determine the area of all the shapes.
Area of the square
[tex]A_{square} = s^2[/tex][tex]A_{square} = (2\ units)^2[/tex][tex]A_{square} = (2)^2 * (units)^2[/tex][tex]A_{square} = 4\ units^2[/tex]Area of a circle
[tex]A_{circle} = \pi * r^2[/tex][tex]A_{circle} = \pi * (0.5\ units)^2[/tex][tex]A_{circle} = \pi * (0.5)^2 * (units)^2[/tex][tex]A_{circle} = \pi * (0.25\ units)^2[/tex][tex]A_{circle} = 0.7854\ units^2[/tex]The area that we got from the circle only gives us the area for one of the circles so we need to multiply the number by four to give us the total area of the circles.
Total area of the circles
[tex]A_{circles} = 0.7854\ units^2 * 4[/tex][tex]A_{circles} = 3.1416\ units^2[/tex]Now that we determined the area of both the square and the circles we can move onto the part of finding the probability of a point randomly landing on a circle.
Determine the probability
[tex]\textsf{probability = circles / square}[/tex][tex]\textsf{probability = } \frac{3.1416\ units^2}{4\ units^2}[/tex][tex]\textsf{probability = } \frac{3.1416}{4}[/tex][tex]\textsf{probability = } 0.785[/tex]However, now that we have determined what the probability, looking at the answer options we can see that all of the are in percentages. So let's convert our probability into a percentage.
Convert to percentage
[tex]\textsf{probability = } 0.785 * 100[/tex][tex]\textsf{probability = } 78.5\%[/tex]Therefore, looking at the options given, the option that would best fit this choice would be option B, about 80%.
Simplify the expression.
Show your work.
4 √81m^8n^16
Answers
Answer:
hope you can understand
Answer:
3m²n⁴
Step-by-step explanation:
Given :
⇒ [tex]\sqrt[4]{81m^{8}n^{16} }[/tex]
=============================================================
Solving :
⇒ [tex]\sqrt[4]{81}[/tex] × [tex]\sqrt[4]{m^{8} }[/tex] × [tex]\sqrt[4]{n^{16} }[/tex]
⇒ [tex]\sqrt[4]{3^{4} }[/tex] × [tex]\sqrt[4]{(m^{2})^{4} }[/tex] × [tex]\sqrt[4]{(n^{4})^{4} }[/tex]
⇒ 3 × m² × n⁴
⇒ 3m²n⁴
Discuss the refusal of some individuals to answer questions by authorized Stats SA officials ?
Answers
Answer:
I think the letter B is a good idea for me to do the same as oneroure and I have a module that I can use to make sure that I have the right to use the periodic table to find the element name and its symbol then calculate the total amount of the main crop between the rows of the main crop between the rows of the main crop between the rows of the main crop between the rows of the main crop between the rows of the main crop between the rows of the main crop between the rows of the main crop between the rows of the main crop between the rows of the main crop between the rows of the main crop between the rows of the main crop between the rows of the main crop between the rows of the main crop between the rows of the main crop between the rows of the main crop between the rows of the main crop between the rows of the main crop between the rows of the main crop between the rows of the main crop between the rows of the main crop between the rows of the main crop between the rows of the main crop between the rows of the main crop between the rows of the main crop between the rows of the main crop between the rows of the main crop between the rows of the main crop between the rows of the main crop between the rows of the main crop between the rows of the main crop between the rows of the main crop between the rows of the main crop between the rows of the main crop between the rows of the main crop between the rows of the main crop between the rows of the main crop between the rows of the main crop between thank you
What percent of your budget of $4000 would your rent be if you pay $800 in rent?
Answers
Answer:
20%
Step-by-step explanation:
Take the amount of rent and put it over the total amount of money to find the percent
800/4000 =.2
Change to percent form by multiplying by 100
.2 * 100 = 20%
Which graph shows the solution to the inequality?
Answers
Answer:
Option D graph
Step-by-step explanation:
x - 4 ≥ - 1
add 4 to both sides, x - 4 + 4 ≥ - 1 + 4
x ≥ 3
so x is greater than or equal to 3
- equal to means closed dot at 3
- greater than means arrow to the right of 3
What is the linear function equation represented by the graph? Enter your answer in the box. f(x) =
Answers
Answer:
f(x) = -1/2x + 1
Step-by-step explanation:
y intercept is +1
For slope, used points on the graph (2,0) and (0,1)
m= y2-y1/x2-x1
= (1-0)/(0-2)
= -1/2
Find the slope of the line containing the pair of points.
(2, -9) and (12,6)
Answers
Answer:
slope = [tex]\frac{3}{2}[/tex]
Step-by-step explanation:
calculate the slope m using the slope formula
m = [tex]\frac{y_{2}-y_{1} }{x_{2}-x_{1} }[/tex]
with (x₁, y₁ ) = (2, - 9 ) and (x₂, y₂ ) = (12, 6 )
m = [tex]\frac{6-(-9)}{12-2}[/tex] = [tex]\frac{6+9}{10}[/tex] = [tex]\frac{15}{10}[/tex] = [tex]\frac{3}{2}[/tex]
-7(6 - 3m) = 26 + 4m
Answers
Distribute -7 into the parenthesis to get -42 + 21m = 26+ 4m. Subtract 4m from both she's to get -42 + 17m = 26. Add 42 to both sides t get 17m = 68. Divide both sides by 17 to get 4= m.
Answer:
4
Step-by-step explanation:
do distributive property first. -7 * 6 and -7 * 3
now you should have -42+21m = 26 + 4m
subtract 4m to the other side 21m-4m=17m
then add 42 to the other side which would give you 68
17m=68
17 divided by 17 =1
68 divided by 17=4
if u=6i-2j and v=-3i+7j, find u-v
Answers
[tex]\begin{cases} u=6i-2j\\\\ v=-3i+7j \end{cases}\qquad \begin{cases} < 6~~,~~-2 > \\\\ < -3~~,~~7 > \end{cases} \\\\[-0.35em] ~\dotfill\\\\ u-v\implies < 6~~,~~-2 > ~~ - ~~ < -3~~,~~7 > \\\\\\ < 6-(-3)~~,~~-2-7 > \implies < 6+3,-9 > \implies < 9,-9 > \implies 9i-9j[/tex]
What is the measure of ø?
5 cm
20cm
Ø
Answers
Answer:
4 radians
Step-by-step explanation:
[tex]s = \theta r[/tex]
[tex]20 = 5 \theta[/tex]
[tex] \theta = 4[/tex]
How many quarts of pure antifreeze must be added to 2 quarts of a 20% antifreeze solution to obtain a 60% antifreeze solution?
Answers
The quantity of pure antifreeze that must be added to 2 quarts of a 20% antifreeze solution to obtain a 60% antifreeze solution 2 quarts
How to solve equation?
x = quarts of 100% antifreeze
You have 2 quarts of 20% antifreeze.
(100%)x + (20%)2 = 60%(x + 2)
100x + 40 = 60(x + 2)
100x + 40 = 60x + 120
100x - 60x = 120 - 40
40x = 80
x = 80/40
x = 2 quarts
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. A chef randomly pulls cupcakes from a box containing 6 cupcakes of the same shape and size. There is 1 cupcake with vanilla frosting, 3 cupcakes with chocolate frosting, and 2 cupcakes with pink frosting. He draws 1 cupcake and then draws out another cupcake without replacing the first one. Find the probability of picking 1 cupcake with chocolate frosting followed by another cupcake with chocolate frosting, and show the equation used, and solve it.
Answers
Answer:
Step-by-step explanation:
there is a 50/50 chance of getting a chocolate cupcake. :P
the cost of a table is 5 times the chair what is the price of chair if the total is 1050
Answers
Answer:
the cost of the chair is 175.
Step-by-step explanation:
if the chair is x, the table will be 5x
now,
the equation formed will be,
5x+x = 1050
on solving,
6x= 1050
x= 1050÷6
x= 175
therefore, the cost of the chair will be x= 175.
and the cost of the table will be 5x= 5×175 = 875.
hope it helps!!PLEASE MARK BRAINLIEST ♡What is the value of X in the equation 8X minus 2Y equals 48 when Y equals four
Answers
Answer:
It should be 7.
Step-by-step explanation:
If y = 4 multiply 2 by 4 equals eight, then you have 8x-8=48. Do the opposite of subtraction to both sides the 8 cancels on the left side add 8 to 48 you get 56 now all you have to is get x by it self to get that do the opposite of multiplication divide both sides by 8 and you should get 7.
A person bought three lots for $22,000 net each and divided them into four lots of equal frontage. The lots were
then sold for $18,000 each. What was the approximate percentage of gross profit?
Answers
Answer:
A person bought three lots for $22,000 net each and divided them into four lots of equal frontage. The lots were then sold for $18,000 each. What was the approximate percentage of gross profit? 9%The initial investment was $66,000 (3 lots at $22,000 each).
The cost of packing a box of chocolates is given by 1/4x^2, where x is the number of chocolates (a box can never have fewer than 3 chocolates). If the weight of a box of chocolates is given by x + 2, what is the cost of packaging per weight unit?
A.1/4x-1/2+1/x+2
B.1/4x^2-1/2x+1
C.1/4x^2-1/2+1
D.1/4x-1/2x-1/x+2
Answers
The cost of packaging the box of chocolates per weight unit is; ¹/₄x²/(x + 2)
How to Solve Algebra problems?We are given the cost of packing the box as;
C(x) = ¹/₄x²
where;
x is the number of chocolates
We are told that a box can never have fewer than 3 chocolates.
Now, the weight of a box of chocolates is given by; W(x) = x + 2
Thus, cost per unit weight is;
C(x)/W(x) = ¹/₄x²/(x + 2)
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please help please please
Answers
a.0+3
b.3
c.3-4
d.-1
....................
This is Raoul’s solution for the equation x^2-6x-27=0:
STEP 1: x^2-6x-27=0
STEP 2: x^2-6x-27+27=0+27
STEP 3: x^2-6x+?=27+?
STEP 4: x^2-6x+9=27+9
STEP 5: 〖(x-3)〗^2=36
STEP 6: √[(x-3)^2]=√36
STEP 7a: x-3=36
STEP 8a: x=39
STEP 7b: x-3=-36
STEP 8b: x=-33
Answers
The solution to the Raoul's equation x² - 6x - 27 = 0 is x = 9; or x = -3
What is an equation?An equation is an expression that shows the relationship between two or more numbers and variables.
Given the equation:
x² - 6x - 27 = 0
Adding 27 to both sides:
x² - 6x - 27 + 27 = 0 + 27
x² - 6x = 27
Adding to both sides the square of half the coefficient of x, that is 9:
x² - 6x + 9 = 27 + 9
(x - 3)² = 36
taking square root of both sides:
√(x - 3)² = √36
x - 3 = ±6
x = 3 ± 6
x = 3 + 6 or; x = 3 - 6
x = 9; or x = -3
The solution to the Raoul's equation x² - 6x - 27 = 0 is x = 9; or x = -3
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One manufacturer boxes screws so that each box weighs the same no matter what size the screws are. The graph shows the amount of allowed weight remaining in a given shipment depending on the number of boxes of screws already included.
What does the y-intercept represent in this situation?
the maximum weight allowed in a shipment
the minimum weight of a single box of screws
the minimum number of screws in a single box
the maximum number of single boxes for a shipment
Answers
Because x is the number of boxes in the shipment, we conclude that the correct option is "the maximum weight allowed in a shipment"
What does the y-intercept mean in this case?
Remember that for a function f(x), the y-intercept is given by f(0).
In this case, the graph represents the amount of allowed weight remaining in a shipment depending on the number of boxes of screws included.
Then the variable x represents "the number of boxes of screws in the shipment".
So when x = 0, there are no boxes.
Then the y-intercepts represents the remaining weight when there are no boxes of screws, which would be all the allowed weight on the shipment.
The correct option is:
"the maximum weight allowed in a shipment"
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Answer:
A
Step-by-step explanation:
the maximum weight allowed in a shipment