diagonal = 9√2 ≈ 12.73
the diagonal splits the square into 2 right triangles with the hypotenuse being the diagonal of the square
using Pythagoras' identity
d = √(9² + 9²) = √162 = 9√2 ≈ 12.73 ( to 2 dec. places )
To find the diagonal of a square with side lengths of 9 inches, use the Pythagorean theorem, yielding a diagonal length approximately equal to 9√2 inches.
To calculate the diagonal of a square, you can use the Pythagorean theorem for a right triangle formed by two adjacent sides of the square and the diagonal. The formula for the diagonal (d) of a square with side length (s) is given by d = s√2. Therefore, the diagonal of the square is:
d = 9√2
d = 9 × 1.414 (approx)
d = 12.726 inches (approx)
Rounded to the nearest whole number or given options, the length of the diagonal is closer to 9√2 inches.
The complete question is:
A square has a side lengths of 9, use the pythagorean theorem to find the length of the diagonal of the square.
The length of a rectangular garden is 7 feet longer than its width. The garden's perimeter is 186 feet. Find the width of the garden.
We have a rectangular garden. The length of the garden is 7 feet longer than its width.
Lets say the width of the garden is 'x' feet. So, the length of the garden must be [tex](x+7)[/tex] feet.
Length [tex]=(x+7)[/tex] feet
Width [tex]=x[/tex] feet
We have been given that the perimeter of the garden is 186 feet.
Now as we know that the perimeter of the rectangle is:
[tex]2(length+width)[/tex]
Plugging the values of length and width in the equation, we get:
Perimeter [tex]= 2((x+7)+x)=2(2x+7)=4x+14[/tex]
We know that perimeter of the garden is equal to 186 feet,
So,
[tex]186=4x+14[/tex]
Solving for 'x' we get:
[tex]4x+14=186[/tex]
[tex]4x=186-14=172[/tex]
[tex]x=\frac{172}{4} =43[/tex]
We had assumed that the width of the garden is 'x' feet and now that we have the value of 'x'. We can say that:
The width of the rectangular garden is 43 feet.
The width of the garden is found by using the perimeter formula for a rectangle and the given information that the length is 7 feet longer than the width. Solving the resulting equation gives a width of 43 feet.
To find the width of the garden, we use the fact that the perimeter (P) of a rectangle is given by the formula P = 2l + 2w, where l is the length and w is the width. We are told that the length is 7 feet longer than the width, so we can express the length as w + 7. Substituting the given perimeter of 186 feet, we set up the equation as follows: 186 = 2(w + 7) + 2w. Simplifying further, we get 186 = 4w + 14. Subtracting 14 from both sides gives us 172 = 4w and dividing both sides by 4, we find w = 43. Therefore, the width of the garden is 43 feet.
Raise to the power: (–am)^3
- a³m³
each term inside the parenthesis is raised to the power of 3
note that (- 1 )³ = - 1, thus
(-am)³ = - a³m³
help asap! will mark brainlyst
Answer:
The answer will be 3.55
Step-by-step explanation:
Answer:
3.55
Step-by-step explanation:
26.30 - 22.75 = 3.55
So, you got it right.
[tex]Echy[/tex]
At a basketball game, student tickets are sold for $4.50 each.
a) Write an equation that models the income y from the sale of x student tickets.
b) How many student tickets must be sold to have $1125 in student ticket sales?
Show all work
I need help with this problem, please help!!!
Answer:
Yes. (See below for explanation.)
Step-by-step explanation:
The number of servings is found by dividing the quantity available by the size of a serving. The quantity of punch is the sum of the quantities of the juices that go into the punch. The serving size of 3/4 cup is the same as 6 ounces, since a cup is 8 ounces. (3/4 × 8 oz = 6 oz)
The quantity available is (64 oz + 28 oz + 76 oz). The serving size is 6 oz. Since the units of numerator and denominator are the same, they cancel, leaving ...
... number of servings = (quantity available)/(serving size)
... = (64 +28 +76)/6 . . . . as shown in the problem statement
_____
It might not be obvious that the above ratio gives the number of servings. However, if you look at the real units, you see how it happens.
[tex]\dfrac{oz}{(\frac{oz}{serving})}= oz\dfrac{serving}{oz}=\dfrac{oz}{oz}serving=serving[/tex]
Given any linear equation, explain how to find the slope for a line that is perpendicular to the given equation. please help i suck in math :(
given a linear equation in slope- intercept form y = mx + c
where m is the slope and c the y -intercept
the slope of a line perpendicular to it is - [tex]\frac{1}{m}[/tex]
If equation is y = 2x + 3 ( with slope m = 2 )
then the perpendicular slope = - [tex]\frac{1}{2}[/tex]
Please help me on my math?
As written, the inequality has a negative coefficient for the variable n. It can be convenient to add the opposite of the right side of the inequality to both sides, so the comparison is to zero:
... 25 +3(4n -3) > 0
... 25 + 12n -9 > 0 . . . . . . eliminate parentheses using the distributive property
... 12n + 16 > 0 . . . . . . . . . collect terms
... n + 4/3 > 0 . . . . . . . . . . divide by 12*
... n > -4/3 . . . . . . . . . . . . add the opposite of the constant (first of answer choices)
_____
1.6w -8 ≥ 22 . . . . . . . given
6w ≥ 30 . . . . . . . . . add 8
w ≥ 5 . . . . . . . . . . . .divide by 6* (second of answer choices)
_____
* When solving inequalities, solution can proceed in the same way it does for solving equations, with one exception. When multiplying or dividing by a negative number, the direction of the comparison changes. Consider the inequality
... 1 < 2
Now, see what happens when we multiply by -1:
... -1 > -2
You may note that we were always dividing by a positive number in the solutions above. That is intentional. In other words, we specifically chose the solution method for problem 3 so that we would avoid dividing by a negative number.
Please help. Question in photo
Answer:
1/8
Step-by-step explanation:
The relations can be written as ...
... blue = (3/5)×shirt
... sale = (5/8)×blue
... medium = (1/3)×sale
Substituting, we get
... medium = (1/3)×((5/8)×((3/5)×shirt)) = (1·5·3)/(3·8·5) × shirt = (1/8)×shirt
_____
1/8 of the shirts in the shop are medium blue T-shirts on sale.
Maria is applying for a summer job. Six employees who do various jobs at the company earn $8.00, $8.50, $9.00, $9.50, $10.00, and $23.50 per hour. In the interview, the boss tells Maria that the median of the hourly wages is $9.25. Is the boss’s statement misleading? Why or why not?
I need help with this question
The only factorial expression that is shown properly evaluated is that of selection A.
_____
If you number the terms starting from 0 on the left, you find that 20 is term #3 on the row that has 6 as term #1. In combination notation, this would be
... 6C3 or C(6, 3)
It is computed as
... 6!/(3!·(6-3)!) = 6·5·4/(3·2·1) = 20
Jake and erica were solving a system of equations. They both noticed that the two lines had the same slope. Jake said that because each line in the system had the same slope, the two lines had to be the same, which meant there were infinitely as many solutions to the solutions to the system. Erica disagreed, and said they ahould also look at the y-intercepts before determining how many solutions there were. Who is correct?
Answer:
Erica
Step-by-step explanation:
Two lines with the same (defined) slope will only have infinite solutions if their y-intercepts are the same. Otherwise, the number of solutions (points on both lines) is zero.
Since the 2 lines have the same slope, then the lines are parallel and never intersect. Thus there is no solution to the system of equations
Neither Jake nor Erica are correct.
find the equation of the line parallel to y=5x+1 that contains the point (4,8)
The equation of a parallel line will have the same x-term, but a different constant (y-intercept). The required value can be found by putting the given point values in to the equation to see what it needs to be.
... y = 5x + ___
... 8 = 5·4 + ___
... 8 - 20 = -12 = ___
Your equation is ...
... y = 5x -12
Find the first fourth and tenth terms of the arithmetic sequence described by the givin rule a (n) = -3 + (n -1) (-2.2)
- 3, - 9.6 and - 22.8
to generate the first, fourth and tenth term substitute n = 1, 4, 10 into the rule
a(1) = - 3 + 0 = - 3
a(4) = - 3 - 6.6 = - 9.6
a(10) = - 3 - 19.8 = - 22.8
Which of the following is a solution to 2cos x + 1 = 0?
A.
60°
B.
120°
C.
210°
D.
300°
Answer:
B. 120
Step-by-step explanation:
2cos x + 1 = 0
2 cos x = -1
cos x = -1/2
x = cos^1(-1/2)
(cos inverse (-1/2))
x = 120°
Two perpendicular lines have opposite y-intercepts. The equation of one of these lines is y = mx + b. Express the x-coordinate of the intersection point of the lines in terms of m and b.
The x-coordinate of the intersection point of two perpendicular lines, one with equation y = mx + b and the other with equation y = -x/m - b, is given by x = 2b/(m + 1/m).
Explanation:Given two perpendicular lines, one has the equation y = mx + b. The y-intercept of this line is b, and the slope is m. The equation of the second line, which is perpendicular to the first, will have a negative reciprocal slope, -1/m, and for opposite y-intercepts, we'll assume its y-intercept to be -b. Thus the equation of the second line is y = -x/m - b.
For the intersection point, equal the y-values of the two equations: mx + b = -x/m - b. Simplify to obtain the x-coordinate of the intersection point:
mx + x/m = 2b or x(m + 1/m) = 2b. Therefore, the x-coordinate of the intersection point is x = 2b/(m + 1/m).
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To find the x-coordinate of the intersection point of two perpendicular lines with opposite y-intercepts, set the equations of the lines equal to each other and solve for x.
Explanation:To find the x-coordinate of the intersection point of two perpendicular lines with opposite y-intercepts, we need to find the equations of both lines. Let's assume the equation of one line is y = mx + b. Since the lines are perpendicular, the slope of the other line will be the negative reciprocal of m. Let's call the slope of the other line n. Therefore, the equation of the other line will be y = -nx + c, where c is the y-intercept of the second line. To find the x-coordinate of the intersection point, we can set the two equations equal to each other and solve for x:
mx + b = -nx + c
x(m + n) = c - b
x = (c - b)/(m + n)
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Find absolute value of the following numbers -37, 2.987, 53, -2/3, -45
Drop all the minus signs (change them to +) to get your answers:
37, 2.987, 54, 2/3, 45
Over 25.5 days, a pond's water level changed by an average of −0.32 centimeter each day. What was the total change in the water level? Drag and drop the correct answer into the box.
numbers
-10.55
-8.16
10.55
8.16
Answer:
So the water level of pond reduces by 8.16 centimeter over 25.5 days.
Explanation:
Average change in pond's water level = -0.32 centimeter.
Duration considered for taking the average of change in pond's water level = 25.5 days.
Total change in the pond's water level = -0.32*25.5 = -8.16 centimeter
So the water level of pond reduces by 8.16 centimeter over 25.5 days.
adam is three years younger than twice bobs age. in 5 years adams age will be 8 years more than bobs age. what are their 2 ages
Adam will be 14, and it is 8 more than 6.
We have given that,
Adam is three years younger than twice bobs age. in 5 years Adams's age will be 8 years more than bobs age.
We have to determine the what are their 2 ages.
What is the age?The age of majority is the age when children legally become adults.
Adam is 9 years old and Bob is 6.
Twice Bob’s age is 12, and three years younger than that is 9.
If Adam is 9 now then in five years, Adam will be 14, which is 8 more than 6.
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How do I get this form?
Short answer: you don't.
The linear term in the numerator of the integral means the form shown is not applicable. Rather, you perform the integration using partial fraction expansion.
[tex]\displaystyle\int{\frac{5x+1}{25x^2+60x-13}}\,dx=\int{\frac{5x+1}{(5x-1)(5x+13)}}\,dx\\\\=\frac{1}{35}\int{\frac{5}{5x-1}}\,dx+\frac{6}{35}\int{\frac{5}{5x+13}}\,dx[/tex]
The integral is ...
... (1/35)ln|5x-1| +(6/35)ln|5x+13| +C
_____
If the numerator of your integral were a constant, then the fractions multiplying the separate partial fraction integrals would have the same magnitude and opposite signs. You would end with the difference of logarithms, which could be expressed as the log of a ratio as shown in your problem statement.
Viete's Formulas - what are they used for?
If we have a quadratic equation 2X^2 + 4X -6 = 0, whose roots are x1=1 and x2=-3 and where a = 2 b=4 and c=-6 then according to Viete's formulas (x1 + x2) = (-b/a) and (x1 • x2) = (c/a).
I suppose these formulas could be used as a double check for calculating the roots but do they serve any other purpose? (I also know there are other Viete's formulas for cubic, quartic, etc. equations).
For quadratics, these formulas are used mainly for factoring.
Your equation can be written as ...
... 2(x² +2x -3) = 0
You factor this by looking for factors of -3 (c=x1·x2) that add to give +2 (b=-(x1+x2)). These are {-1, +3}, so the factorization is ...
... 2(x -1)(x +3) = 0
The roots are then 1 and -3, which sum to -b = -2.
(You will note that the numbers used in the binomial factors are the opposites of the roots x1 and x2 in the Viete's Formulas. That is how we can look for them to sum to "b", rather than "-b".)
What describes a rational number? please be specific and show examples of the number ASAP!! XD
In this figure, AB¯¯¯¯¯∥CD¯¯¯¯¯ and m∠6=75°.
What is m∠3?
m∠3 + m<6 = 180
Given: m∠6 = 75°
so
m<3 + 75°= 180°
m<3 = 105°
Answer:
Here is the answer! Hope I helped! Have a nice day! Really helpful for k12 users! And sorry I am late!!!!
Step-by-step explanation:
What is the median of this set of values? 6, 8, 10, 8, 4, 2, 12
The median is the middle number in order of the set of values:
2, 4, 8, 10, 12
8 is the median in the set of values!
Answer:
its 8
Step-by-step explanation:
No
Which value for the number makes this statement true? The quotient of a number and five is eight
Answer: The answer is 40
Step-by-step explanation:
The vertices A(–2, –1), B(–3, 2), C(–1, 3), and D(0, 0) form a parallelogram. The vertices A’(–1, –2), B’(2, –3), C’(3, –1), and D’(0, 0) are the image of the parallelogram after a sequence of transformations. Which sequence of transformations could produce the image from the pre-image?
a reflection over the x-axis and then a reflection over the y-axis
a reflection over the y-axis and then a 90 degree clockwise rotation about the origin
a 90 degree clockwise rotation about the origin and then a reflection over the y-axis
a 90 degree counterclockwise rotation about the origin and then a reflection over the x-axis
In the attachment, the original parallelogram is shown in red. Its image is shown in blue. The purple parallelogram is the original reflected across the y-axis. You can see that it becomes the blue parallelogram if rotated 90° clockwise around the origin.
The appropriate choice is ...
... a reflection over the y-axis and then a 90 degree clockwise rotation about the origin
Answer:
B. a reflection over the y-axis and then a 90degree clockwise rotation about the origin
Step-by-step explanation:
I just did it, and all was well! :) :) :)
Given the graph of a line y=−x. Write an equation of a line which is parallel and goes through the point (8,2).
The slope of y = -x is m = -1. Thus, starting with the slope-intercept form y = mx + b, we substitute -1 for m, 8 for x and 2 for y, to determine the vaue of b:
2 = -1(8) + b, or 10 = b. Then the equation of the line parallel to y = -x and passing thru (8,2) is:
y = -x + 10.
what is the equation of a line, in point-slope form, that passes through (5, -3) and has a slope of 2/3? please help me
y + 3 = [tex]\frac{2}{3}[/tex] (x - 5)
the equation of a line in point- slope form is
y - b = m ( x - a )
where m is the slope and (a, b) a point on the line
here m =[tex]\frac{2}{3}[/tex] and (a,b) = (5 , - 3 )
y + 3 = [tex]\frac{2}{3}[/tex] (x - 5 ) ← in point-slope form
The equation of the line that passes through the point (5, -3) and has a slope of 2/3 is y = 2/3x - 19/3, using the point-slope form for the equation of a line.
Explanation:
The line that you're looking for can be represented using the point-slope form of a linear equation. This form is written as y - y1 = m(x - x1), where (x1, y1) are the coordinates of a point on the line and 'm' is the slope of the line. For a line that passes through the point (5, -3) and has a slope of 2/3, you replace x1 with 5, y1 with -3, and m with 2/3. So, the equation of the line becomes y - (-3) = 2/3(x - 5), which simplifies to y + 3 = 2/3x - 10/3. Further simplifying, we get y = 2/3x - 10/3 - 3, or y = 2/3x - 19/3.
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5.1(3+2.2x)>-14.25-6(1.7x+4)
Answer:
(-2.5, ∞)
Step-by-step explanation:
You can add the opposite of the right side.
5.1(3 +2.2x) +14.25 +6(1.7x +4) > 0
15.3 +11.22x +14.25 + 10.2x +24 > 0 . . . eliminate parentheses
21.42x +53.55 > 0 . . . . . . . . . . . . . . . . . . collect terms
x + 2.5 > 0 . . . . . . . . . . . . . . . . . . . . . . . . .divide by the coefficient of x
x > -2.5 . . . . . . add the opposite of the constant
(- 2.5, ∞ )
distribute parenthesis on both sides of inequality and simplify
15.3 + 11.2x > - 14.25 - 10.2x - 24
15.3 + 11.2x > - 38.25 - 10.2x ( add 10.2x to both sides )
15.3 + 21.42x > - 38.25 ( subtract 15.3 from both sides )
21.42x > - 53.55 ( divide both sides by 21.42 )
x > - 2.5
solution x ∈ (- 2.5, ∞ )
Factor. 8a2−2ac+12ab−3bc
A. (2a+3b)(c-4a)
B. (2a+3b)(4a-c)
C. (2a-3b)(4a+c)
D. (2a-3b)(c-4a)
Answer:
B. (2a +3b)(4a -c)
Step-by-step explanation:
Group the terms pairwise, then factor each pair.
... (8a² -2ac) +(12ab -3bc)
2a is a common factor in the first pair of terms; 3b is a common factor in the second pair of terms. We can factor those out.
... = 2a(4a -c) +3b(4a -c)
Then we see that (4a-c) is a common factor in the result. We can factor that out.
... = (2a +3b)(4a -c) . . . . matches selection B
7/10=x/100 Show work please
First you had to switch sides of equation form.
[tex]\frac{x}{100}= \frac{7}{10}[/tex]
Then you multiply by one-hundred from both sides of equation form.
[tex]\frac{x}{100}*100= \frac{7}{10}*100[/tex]
And finally, simplify by equation.
[tex]\frac{x}{100}*100=x[/tex]
[tex]\frac{7}{10}*100=70[/tex]
[tex]70*1=70[/tex]
[tex]x=70[/tex]
Final answer: [tex]\boxed{x=70}[/tex]
[tex]70/10=7[/tex]
[tex]70/7=10[/tex]
[tex]10*7=70[/tex]
[tex]7*10=70[/tex]
Hope this helps!
And thank you for posting your question at here on brainly, and have a great day.
-Charlie
x = 70
given [tex]\frac{7}{10}[/tex] = [tex]\frac{x}{100}[/tex] ( cross-multiply )
10x = 7 × 100 = 700 ( divide both sides by 10 )
x = [tex]\frac{700}{10}[/tex] = 70