The figure below is a square. Find the length of side x in simplest radical form with a rational denominator.
Answers
Answer:
[tex]\frac{\sqrt{10}}{2}[/tex]
Step-by-step explanation:
The diagonal forms two 45-45-90 triangles, with the diagonal being the hypotenuse of both. The Pythagorean Theorem states that [tex]a^2+b^2=c^2[/tex], where [tex]c[/tex] is the hypotenuse of the triangle, and [tex]a[/tex] and [tex]b[/tex] are the two legs of the triangle.
From the Isosceles Base Theorem, the two legs of a 45-45-90 triangle are always equal. Since we're given a diagonal of [tex]\sqrt{5}[/tex], we have:
[tex]x^2+x^2=\sqrt{5}^2,\\2x^2=5,\\x^2=\frac{5}{2},\\x=\sqrt{\frac{5}{2}}=\frac{\sqrt{5}}{\sqrt{2}}=\frac{\sqrt{5}}{\sqrt{2}}\cdot \frac{\sqrt{2}}{\sqrt{2}}=\boxed{\frac{\sqrt{10}}{2}}[/tex]
Related Questions
Which line intersects the parabola y = x^2 + 6x – 2 at two points?
A.y = 6x – 4
B.y = 6x – 3
C.y = 6x – 2
D.y = 6x – 1
Answers
Answer:
C
Step-by-step explanation:
U fisrt find the y intercept where x=0 and deferentiate to find gradient
If f(x) = \XI + 9 and g(x) = -6, which describes the range of (f + g)(x)?
O (f + g)(x) > 3 for all values of x
O (f + g)(x) < 3 for all values of x
O (f + g)(x) < 6 for all values of x
O (f + g)(x) > 6 for all values of x
Answers
Answer:
the first option
Step-by-step explanation:
well, 9 +(-6) = 3
so the equations last part is changed, but the rest stays the same
The range of (f + g)(x) is (f + g)(x) > 3 for all values of x.
What is a function?A function is a relation from a set of inputs to a set of possible outputs where each input is related to exactly one output.
Gives are two function, f(x) = |XI + 9 and g(x) = -6, we need to find the range of (f + g)(x),
f(x)=|x|+9 and g(x)= -6
Taking the sum of the functions:
f(x) + g(x) = |x|+9 + (-6)
f(x) + g(x) = |x|+9 - 6
f(x) + g(x) = |x|+3
Due to the modulus of x which is positive,
Hence (f + g)(x) is greater to 3 for all values of x
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Find the area of PQRS. (Hint: Use the Pythagorean Theorem to find the height .)
Answers
Area = length x height
Area = 8 x 3 = 24m^2
Please help with this question
Answers
Answer:
ans is g=x^3+1
x=(-2-1,0,1,2,3)
again put the value of x
therefore g(x)=(-7,0,1,2,9,28)
anyone know the answer to this??
Answers
============================================================
Explanation:
Use the slope formula to find the slope of the given line through those two points (-3, 4) and (5, 1)
m = (y2-y1)/(x2-x1)
m = (1 - 4)/(5 - (-3) )
m = (1-4)/(5+3)
m = -3/8
The line shown has a slope of -3/8
----------
We do two things from here:
flip the fractionflip the signThat will have -3/8 turn into +8/3 or simply 8/3 which is the perpendicular slope. That's why the answer is choice A.
Multiplying the original slope -3/8 with the perpendicular slope 8/3 will lead to -1. This is true of any perpendicular pair of lines, as long as neither line is vertical.
CONTEST Each ple entered into the annual pie baking contest has been scored out of 10, as shown in the table.
Answers
Answer:
Of your choices, 87.5
Step-by-step explanation:
There may be a formula for figuring this out, but here's what I know how to do to solve this:
First we'll organize the data in ascending order:
3.9, 4.5, 5.7, 6.2, 7.4, 8.1, 8.4, 9.2
The median is (6.2 + 7.4)/2 = 6.8
The first quartile is (4.5 + 5.7)/2 = 5.1
The third quartile is (8.1 + 8.4)/2 = 8.25
So the 75th percentile is 8.25
Since 9.2 is higher than that, I'd choose 87.5
Mildred's pie scored at the 87.5 percentile.
What is a percentile?'A percentile is a measure used in statistics indicating the value below which a given percentage of observations in a group of observations fall.'
According to the given problem,
Organizing the data in ascending order:
3.9 < 4.5 < 5.7 < 6.2 < 7.4 < 8.1 < 8.4 < 9.2
Median of the given data = [tex]\frac{6.2+7.4}{2}[/tex]
= 6.8
First quartile = (4.5 + 5.7)/2
= 5.1
Third quartile = (8.1 + 8.4)/2
= 8.25
The third quartile is the 75th percentile,
⇒ 75th percentile = 8.25
Since, 9.2 > 8.25 , Mildred's pie scored at 87.5 percentile.
Hence, we can conclude, Mildred's pie scored at the 87.5 percentile.
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1] Angelo used 425 centimeters of ribbon to trim banners he made. How many meters of ribbon did he use? ***HINT: 1 meter = 100 centimeters*** *
Answers
Answer:
4.25 meters
Step-by-step explanation:
425/100 = 4.25
or move the decimal to the left 2 places. One place for each zero in 100.
3) How could Tyler have made a more specific request for 2 sides and an angle so that his triangle was guaranteed to match Jada's?
Answers
Answer:
His specific request will be any of the following:
A triangle of side lengths 4 and 5, with a measure of 143 degrees between themA triangle of side lengths 5 and 8.5, with a measure of 16 degrees between themA triangle of side lengths 8.5 and 4, with a measure of 21 degrees between themStep-by-step explanation:
Given
See attachment for complete question
Required
Specific information to match Jada's request
From the attachment, we have the following:
Triangle 1: Jada's request
Triangle 2: The triangle made by Tyler
The two triangles are not congruent because:
The side lengths do not correspondHow did we know this?
On Jada's triangle, the longest side is 8.5
On the triangle, Tyler made; the longest side is 5 and does have a corresponding ratio to Jada's triangle
Having said this; this is what Jada needs to do;
He needs to make his request based on any of the following postulate
[tex]SSS \to Side\ Side\ Side[/tex]
[tex]SAS \to Side\ Angle\ Side[/tex]
[tex]ASA \to Angle\ Side\ Angle[/tex]
However, the best postulate to use in this regard is:
[tex]SAS \to Side\ Angle\ Side[/tex]
So, his specific request will be any of the following:
A triangle of side lengths 4 and 5, with a measure of 143 degrees between themA triangle of side lengths 5 and 8.5, with a measure of 16 degrees between themA triangle of side lengths 8.5 and 4, with a measure of 21 degrees between themwhat is the volume of the rectangular prism??
Answers
Answer:
Step-by-step explanation:
volume of rectangular prism = length * breadth * height
=6m * 5.5m * 4.5m
=148.5 m^3
What is the difference of the polynomials?
(8r6s3 – 9r5s4 + 3r4s5) – (2r4s5 – 5r3s6 – 4r5s4)
6r6s3 – 4r5s4 + 7r4s5
6r6s3 – 13r5s4 – r4s5
8r6s3 – 5r5s4 + r4s5 + 5r3s6
8r6s3 – 13r5s4 + r4s5 – 5r3s6
Answers
Answer:
8r6s3 – 13r5s4 + r4s5 – 5r3s6 it is D
DStep-by-step explanation:
The value of the difference of the polynomials is,
⇒ 8r⁶s³ - 13r⁵s⁴ + r⁴s⁵ - 5r³s⁶
What is mean by Subtraction?Subtraction in mathematics means that is taking something away from a group or number of objects. When you subtract, what is left in the group becomes less.
Given that;
The expression is,
⇒ (8r⁶s³ – 9r⁵s⁴ + 3r⁴s⁵) – (2r⁴s⁵ – 5r³s⁶ – 4r⁵s⁴)
Now, We can find the difference as;
⇒ (8r⁶s³ – 9r⁵s⁴ + 3r⁴s⁵) – (2r⁴s⁵ – 5r³s⁶ – 4r⁵s⁴)
⇒ (8r⁶s³ – 9r⁵s⁴ – 4r⁵s⁴ + 3r⁴s⁵ – 2r⁴s⁵ – 5r³s⁶
⇒ 8r⁶s³ - 13r⁵s⁴ + r⁴s⁵ - 5r³s⁶
Thus, The value of the difference of the polynomials is,
⇒ 8r⁶s³ - 13r⁵s⁴ + r⁴s⁵ - 5r³s⁶
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2(1/3x)(2/5y)
i cant solve this one can anyone help me I am stuck over here
Answers
Answer:
4/15xy
step-by-step explanation:
2(1/3x) (2/5y)
= 2/3x × (2/5)y
= 2×2
xy
3×5
= 4/15xy
Hope this answer helps you :)
Have a great day
Mark brainliest
Answer:
4/15xy
Step-by-step explanation:
2(1/3x) (2/5y)
= 2/3x × (2/5)y
= 2×2
xy
3×5
= 4/15xy
Graph the line that passes through the points (7, 0) and (-2, 9) and determine the equation of the line.
Answers
Answer:
y = -1x + 7
Step-by-step explanation:
y2 - y1 / x2 - x1
9 - 0 / -2 - 7
9 / -9
= -1
y = -1x + b
0 = -1(7) + b
0 = -7 + b
7 = b
please help with question!
Answers
Answer:
Step-by-step explanation:
Find the length of AB pls and thank you
Answers
Answer:
x=4
AB=19
Step-by-step explanation:
in such a parallelogram the length of AD must be equal to the length of BC.
=>
18x = 17x + 4
x = 4
AB = 4x + 3 = 4×4 + 3 = 19
After studying the growing population of a certain species of fish, Dr. Goldthwait has determined that the population will grow
in such a way that the population each year will be 27 less than the square of the previous year's population. If he introduces
this species of fish to a new environment by placing a population of 15 fish, and the population grows according to his results
which of the following recursive formulas can be used to determine the number of fish that will be in the environment in the
future? Assume that the space for the population to grow is unlimited.
OA
NEXT = Now2 - 27 starting at 15
OB. NEXT = (NOW + 27) starting at 15
OC. NEXT = now? + 27 starting at 15
OD. NEXT =
(NOW - 27) starting at 15
Answers
Answer:
OB. NEXT
Step-by-step explanation:
Sum1 plz help with this
Answers
Answer:
ur answer is 8.06
Step-by-step explanation:
a² + b²= c²
4² + 7² = c²
16 + 49 = c²
65 sooo u do √65= 8.06
URGENT SOMEBODY PLZ HELP
Answers
First one is B (43) and the second one is C (35)!
Frank earned f dollars mowing lawns. Bryce's earnings, b, were $15.25 less than 3.5 times as
much as Frank's earnings. Which of the following equations best represents this situation?
A. b = 3.5f + 15.25
B. f= 3.5b - 15.25
C. b = 3.5f-15.25
D. f = 3.5b + 15.25
Answers
7th-grade students decided to start fundraising money by selling raffle tickets. The administration promised to contribute $2 extra for each raffle ticket sold. The 7th graders sold 223 tickets and raised a total of $1,115. Write an equation to represent this situation. Remember to define your variable.
Answers
Answer:
Let x be the price of a raffle ticket
(x+2)*223 = 1115
x=3
Step-by-step explanation:
Let x be the price of a raffle ticket
The amount they get is now x+2 since the admin is donating 2 dollars per ticket
The sold 223 tickets
(x+2) *223 = amount raised
(x+2)*223 = 1115
Divide each side by 223
x+2 = 1115/223
x+2 = 5
Subtract 2 from each side
x+2-2 =5-2
x=3
[tex] \quad \quad \quad \quad \tt{(x + 2) 223 = 1,115}[/tex]
[tex]\quad \quad \quad \quad \tt{ \huge x + 2 = \frac{1,115}{223} }[/tex]
[tex]\quad \quad \quad \quad \huge\tt{ x + 2 = 5 }[/tex]
Covert the 2 like this:[tex]\quad \quad \quad \quad \huge\tt{ x = 5 - 2}[/tex]
[tex]\quad \quad \quad \quad\huge \tt{ x = 3 }[/tex]
Hence, the answer is:[tex]\quad \quad \quad \quad \boxed{ \huge \tt{ \color{green} x = 3 }}[/tex]
_________
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Use the graph that shows the solution to
f(x) = g(x).
f(x) = 1+2x/x=
g(x) = 2+x
What is the solution to f(x) = g(x)?
Select each correct answer.
Answers
Answer:
The solution for f(x) = g(x) are;
x = 1 and x = -1
Step-by-step explanation:
The given equations for the functions, g(x) are;
[tex]f(x) = \dfrac{1 + 2\cdot x}{x}[/tex]
g(x) = 2 + x
The solution for f(x) = g(x), is given by equating the equations of the two functions as follows;
When f(x) = g(x), we have;
[tex]\dfrac{1 + 2\cdot x}{x} = 2 + x[/tex]
By cross multiplication, we have;
1 + 2·x = x × (2 + x) = 2·x + x²
∴ x² + 2·x - 2·x - 1 = 0
x² - 1 = 0
(x - 1)·(x + 1) = 0
x = 1, or x = -1
f(x) = g(x) = 2 + 1 = 3, or 2 - 1 = 1
Therefore, the solution for f(x) = g(x) are;
f(x) = g(x) = 3 or 1 where x = 1 and x = -1.
Answer: a , b
Step-by-step explanation:
Evaluate the function.
f(x) = -x^2 + 6
Find f(-3)
Answers
Answer:
-3
Step-by-step explanation:
You plug the value of -3 into where the x is {-(-3)^2} + 6, resulting in -3.
25 divided by 94,056
Answers
Answer:
0.00026579909 is what 25 divided by 94,056 equals
Consider the probability model that allows you to determine probability that there will be X number of successes out of n trials; when the outcomes from each trial (each defined as either a success or a failure), are independent, and subject to the same probability of success from one trial to the next. How will the coefficient of variation for this model change
Answers
Answer:
The probability of number of success = C (n,k)p^kq^(n-k)
Step-by-step explanation:
This is the case of Bernoulli's experiment in which there are n independent trials with X number of success
The probability of number of success = C (n,k)p^kq^(n-k)
Where k = 0,1,2,3...n
A gas station sold 300.5849 gallons of gas in a day. How many
gallons of gas did the gas station sell, rounded to the nearest
hundredth?
Answers
Answer:
30058.49
Step-by-step explanation:
b/c when u multiply it in hundredth u can get your answer
Factorise the following
c) x2 – 3x + 2
Answers
Answer:
(x−1)(x−2)
Step-by-step explanation:
Find the aspect ratio of a computer screen that measures 12 inches by 16 inches.
Answers
Answer:
3:4
Step-by-step explanation:
That ratio would be 12:16, or 3:4.
The aspect ratio of a computer screen will be 4: 3.
What are ratio and proportion?A ratio is a collection of ordered integers a and b represented as a/b, with b never equaling zero. A proportionate expression is one in which two items are equal.
The computer screen measures 12 inches by 16 inches.
Then the aspect ratio will be given by the number 16 inches divided by 12 inches.
We know that the aspect ratio will be greater than 1. Then the aspect ratio will be
Aspect ratio = 16 / 9
Aspect ratio = 4/3
Aspect ratio = 4: 3
The aspect ratio of a computer screen will be 4: 3.
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Jane and Sophia went to the corner store where packages of gum cost 54¢ each and candy bars cost 88¢ each. They spent $26.38 total and bought 35 items total. How many candy bars did they buy?
Answers
Answer:
22
Step-by-step explanation:
number of gum = x
number of candy bar = y
0.54x + 0.88y = 26.38
x + y = 35
0.54x + 0.88y = 26.38
(+) -0.54x - 0.54y = -18.9
-----------------------------------------
0.34y = 7.48
y = 7.48/0.34
y = 22
Answer: 22
The number of the gum is 13 and the number of the candy will be 22.
What is linear system?A linear system is one in which the parameter in the equation has a degree of one. It might have one, two, or even more variables.
Jane and Sophia went to the corner store where packages of gum cost 54¢ each and candy bars cost 88¢ each.
They spent $26.38 total and bought 35 items total.
Let x be the number of the gum and y be the number of the candy.
Then the equation will be
x + y = 35 ...1
0.54x + 0.88y = 26.38 ...2
By solving the equations 1 and 2, then we have
x = 13 and y = 22
Then the number of the gum is 13 and the number of the candy will be 22.
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Can y’all help me with this ASAP please?
Answers
Answer:
x + 3
5
Explanation:
x+3 is the equation for the first line to the left, and f(x)=5 is the second equation for the second line at the top.
HELP ME FOR 30 POINTS!!
Determine the equation of the circle graphed below.
Answers
Answer:
(x-7)²+y²=9
Step-by-step explanation:
There is a formula used for the equation of a circle:
(x-h)²+(y-k)² = r²
(h, k) is the center of the circle
r is the radius
In this case, (h, k) is (7, 0)
Plug in the values for h and k
∴ (x-7)²+(y-0)²=3² which can be simplified to (x-7)²+y²=9 (No need to expand the brackets)
What is the solution to this equation?
X+ 7 = -8
O A. x= 15
O B. x= 1
O c. x = -15
O D. x= -1
Answers
Explanation:
Replace x with -15 to check ur answer
-15 + 7 = -8
THIS EQUATION IS TRUE.
Mark me brainliest ty!