The size of a laptop monitor is usually measured along the diagonal. A rectangular monitor is 12 inches long and 7 inches tall. What is the length of the diagonal of this monitor, to the nearest tenth of an inch? Enter your answer, as a decimal, in the box.
The length of the diagonal of this monitor, to the nearest tenth of an inch, would be 14.
What is Pythagoras Theorem?If ABC is a triangle with AC as the hypotenuse and angle B with 90 degrees then we have:
[tex]|AC|^2 = |AB|^2 + |BC|^2[/tex]
where |AB| = length of line segment AB. (AB and BC are rest of the two sides of that triangle ABC, AC being the hypotenuse).
The size of a laptop monitor is usually measured along the diagonal. A rectangular monitor is 12 inches long and 7 inches tall.
[tex]a^2 + b^2 = c^2\\12^2 + 7^2 = c^2\\144 + 49 =c^2\\193 = c^2\\c= 13.89 14[/tex]
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Express the complex number in trigonometric form.
-5i
A) 5(cos 270° + i sin 270°)
B) 5(cos 180° + i sin 180°)
C) 5(cos 90° + i sin 90°)
D) 5(cos 0° + i sin 0°)
By connecting two non-intersecting vertices of a regular pentagon, the figure can be split into a triangle and a quadrilateral. Always Sometimes Never
122% in simplest form
Answer: The simplest form of 122% is [tex]\frac{61}{50}[/tex] in fraction and [tex]1.22[/tex] in decimal.
Step-by-step explanation:
We know that to simplify percentage into fractions or decimals, we need to divide it by 100.
The percent value = 122%
Therefore , to simplify it into the simplest form we divide it by 100, we get
[tex]122\%=\frac{122}{100}=\frac{61}{50}[/tex]
In decimal , [tex]122\%=\frac{122}{100}=1.22[/tex]
Hence, the simplest form of 122% is [tex]\frac{61}{50}[/tex] in fraction and [tex]1.22[/tex] in decimal.
37.5 x 10(-6) in scientific notation?
you are starting your own small business in Albuquerque. you borrow $10,000 from a bank at 9% rate for 5 years find the interest you will pay on this loan
I will have to pay $4500 interest for the loan I have taken to start a small business.
What is simple interest?We know simple interest (SI) is given by SI = (p×r×t)/100, where
p = principle, r = rate in percentage, and t = time in years.
Given, P = $10,000, r = 9% and t = 5.
∴ SI = (10000×9×5)/100.
SI = 100×45.
SI = 4500.
So, I need to pay $4500 for the loan.
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For each pair of numbers, tell: By what percent of the first number is the second number larger? By what percent of the second number is the first number smaller? 15 and 20
By using a rule of 3, we will see that:
The second number is 33.33% larger than the first one.The first number is 25% smaller than the second one.How to find the percentages?
In the first case, we want to know by what percent of the first number is the second larger.
Then the 100% will be taken as the first number, so we have the relation:
100% = 15
And the other number will represent a percentage X, so we write:
X = 20
By taking the quotient of these two equations, we get:
X/(100%) = 20/15
Solving this for X, we get:
X = (20/15)*100% = 133.33%
We can conclude that the second number is 33.33% larger than the first number.
For the second part, we take 20 as our 100%, and we do the same thing:
X = (15/20)*100% = 75%
Then 15 is (100% - 75% = 25%) 25% smaller than 20.
As you can see the percentages are different. Why does this happen? because in each case the 100% represents a different number.
Finally, we can conclude that:
The second number is 33.33% larger than the first one.The first number is 25% smaller than the second one.If you want to learn more about percentages, you can read:
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What is the general term for the sequence 1, 6, 11, 16
Which is a focus of the hyperbola shown? (0, −26) (0, −24) (0, 25) (0, 30) BRAINLIESTT
Answer:its (0 -26)
Step-by-step explanation:
THATS THE ANSWER NO NEED TO explain
Answer:
A (0,-26)
Step-by-step explanation:
Which of the following statements is true about lines 3y + 2x - 9 = 0 and 12y + 8x - 5 = 0? They are parallel They are perpendicular They are parallel to the x-axis They are parallel to the y-axis
Answer:
The statement "They are parallel" is true.
Step-by-step explanation:
The general form of the equation of a straight line is:
[tex]Ax+By+C=0[/tex]
where A, B, and C are three real numbers.
A line parallel to the x-axis has this form [tex]y=C[/tex] where C is a real number.
A line parallel to the y-axis has this form [tex]x=C[/tex] where C is a real number.
From the lines given none of these have the form of a line parallel to the x-axis or the y-axis. Therefore the statements "They are parallel to the x-axis" and "They are parallel to the y-axis" are false.
Two non-vertical lines in a plane are parallel if they have both:
the same slopedifferent y-interceptsTwo non-vertical lines are perpendicular if the slope of one is the negative reciprocal of the slope of the other.
To check if the lines are parallel of perpendicular you must transform these lines into the slope/intercept form
[tex]y=mx+b[/tex]
where m represents the slope and b represents the y-intercept.
The slope/intercept form for the first line is:
[tex]3y+2x-9=0\\\\3y+2x-9-2x=0-2x\\\\3y-9=-2x\\\\3y-9+9=-2x+9\\\\3y=-2x+9\\\\y=\frac{-2x+9}{3}\\\\y=\frac{-2}{3}x+3[/tex]
The slope/intercept form for the second line is:
[tex]12y+8x-5=0\\\\12y+8x-5-8x=0-8x\\\\12y-5=-8x\\\\12y-5+5=-8x+5\\\\12y=-8x+5\\\\y=\frac{-8x+5}{12}\\\\y=\frac{-2}{3}x+\frac{5}{12}[/tex]
We can see that the lines have the same slope and different y-intercepts. Therefore the statement "They are parallel" is true.
We can check our work with the graph of the lines.
what is the radius and center of this circle?
[tex] {x}^{2} + {y}^{2} + 2x - 4y - 2 = 0[/tex]
3(p+8) = -6 ( p + 6 )
Quadrilateral ABCD is inscribed in this circle.
What is the measure of ∠A ?
Enter your answer in the box.
____°
Answer:
Measure of ∠A is 106°
Step-by-step explanation:
We are given that, 'Quadrilateral ABCD is inscribed in the circle'.
So, we get that,
'ABCD is a cyclic quadrilateral' i.e. The sum of the opposite interior angles is 180°.
Thus, we have,
∠A +∠C = 180°
i.e. ∠A + 74° = 180°
i.e. ∠A = 180° - 74°
i.e. ∠A = 106°
Thus, the measure of ∠A is 106°.
Natasha had d dollars. She bought two ice creams which cost x dollars each. How much money does she have left?
How do I double the volume of a pyramid
Find a1 for the arithmetic series with s20 = 80 And d = 2
Among 81678167 cases of heart pacemaker malfunctions, 457457 were found to be caused by firmware, which is software programmed into the device. if the firmware is tested in 33 different pacemakers randomly selected from this batch of 81678167 and the entire batch is accepted if there are no failures, what is the probability that the firmware in the entire batch will be accepted? is this procedure likely to result in the entire batch being
If an object is dropped from a height of 55 feet, the function d=-16t^2+55 gives the height of the object after t seconds. Graph this function. Approximately how long does it take the object to reach the ground (d=0)
you deposit 2800 in a savings account that earns 1% annual intrest compounded semiannually.Write a function that represents the balance after t years
The function which represent the given situation for Amount by compound interest is [tex]A = 2800 X 1.005^{2t}[/tex]
What is Compound Interest?Compound interest is the addition of interest to the principal sum of a loan or deposit, or in other words, interest on principal plus interest.
Here, P = $2800
I = 1 % compounded semiannually = 0.5 % = 0.005
Time = t years
n = 2t semi-years
We know that,
[tex]A = P(1+i)^n[/tex]
[tex]A = 2800 ( 1 + 0.005 )^{2t}[/tex]
[tex]A = 2800 X 1.005^{2t}[/tex]
Thus, The function which represent the given situation for Amount by compound interest is [tex]A = 2800 X 1.005^{2t}[/tex].
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Which of the following is a perfect square?
A. 127
B. 100
C. 13
D. 102
The total land area of the United stated is about 3483511 square miles more than the total land area of Tennessee, which is about 53927 square miles. Write and solve an equation to find the total land area of the United stayed.
Let us denote the total land area of Tennessee by [tex] T [/tex].
Now, It has been given to us that the total land area of Tennessee is about 53927 square miles.
Therefore, [tex] T=53927 [/tex]
It has also been given to us that the total land area of the United States is about 3483511 square miles more than the total land area of Tennessee.
Let us denote the total land area of the United States by [tex] U [/tex].
Now, if the total land area of the United States (denoted by [tex] U [/tex]) is 3483511 square miles more than the total land area of Tennessee (which is 53927 square miles and is denoted by [tex] T [/tex]), then that means that we have to add 3483511 square miles to the total land area of Tennessee to get the total land area of the United States. This can be written in the equation form as:
[tex] U=3483511+T=3483511+53927=3537438 [/tex]
Thus the total area of the United States is 3537438 square miles.
Final answer:
The total land area of the United States is calculated by adding the land area of Tennessee to the difference given in the question. The equation is US Area = 53,927 + 3,483,511. Solving this equation, the total land area of the United States is approximately 3,537,438 square miles.
Explanation:
To find the total land area of the United States, we can use the given information and set up an equation. The total land area of Tennessee is about 53,927 square miles. The question states that the total land area of the United States is about 3,483,511 square miles more than Tennessee's land area. We can express this relationship with the following equation:
Total land area of the United States = Land area of Tennessee + 3,483,511 square miles
US Area = 53,927 + 3,483,511
Solving for the total land area of the United States:
US Area = 3,537,438 square miles
Therefore, the total land area of the United States is approximately 3,537,438 square miles.
what fractions are equivalent to 8 over 12
What are the solutions of the equation x4 + 95x2 – 500 = 0? Use factoring to solve.
Using factorization, the factors of the given equation are; ±√5 and ±10i.
What is Factorization?In mathematics, factorization or factoring consists of writing a number or any mathematical item as a product of several factors, typically small or easier objects of the same.
we have been given the equation:
x⁴ + 95x² – 500 = 0
Factorizing the above equation,
x⁴ + 100x² - 5x² - 500 = 0
x²(x² + 100) - 5(x² + 100) = 0
(x² - 5)(x² + 100) = 0
Solving further:
x² = 5
x² = -100
x = ±√5
x = √-100
Factors : ±√5 and ±10i
Therefore, we know that the factors of the given equation are; ±√5 and ±10i.
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A: 2x + 8y = 5 B: x + 9y = 10 To solve this system of equations by elimination, what could you multiply equation B by if you want to add the equations together and have a resulting equation with only the y-variable (the x-variable is eliminated)?
PLEASE HELP BABES!!
Heather is trying to decide what classes to take next year. She must take one of each and can choose from 3 math classes, 2 science classes, 4 history classes, and 3 English classes. How many different schedules can she have?
A) 4
B) 12
C) 48
D) 72
What is the length of YX¯¯¯¯¯¯? Enter your answer as a decimal in the box. Round your final answer to the nearest hundredth. m_https://static.k12.com/nextgen_media/assets/8107298-NG_GMT_SemB_10_UT_06.png'
Final answer:
To find the actual length represented by YX, we set up a proportion using the given scale length and solve for the unknown length x. Using one of the provided scale ratios, such as 0.5 inches representing 2000 miles, we perform cross-multiplication to solve for x and determine the accurate length after calculations.
Explanation:
The student is asked to find the actual length represented by the segment YX on a map or a diagram when given a scale length. To solve the problem, we set up a proportion based on the scale provided and solve for the unknown length x. There are different given scales in the prompts such as 0.5 inches representing 2000 miles, 8 inches representing an unknown number of miles, and 3 inches also representing an unknown number of miles.
Example with a Scale Ratio of 0.5 inches to 2000 miles
To solve for x when the scale is 0.5 inches on the map corresponds to 2000 miles in reality, we use a proportion: 1 inch/2000 miles = 0.5 inches/x miles. After cross-multiplication, we get x = 0.5 inches * 2000 miles, which after calculation will give us the value of x rounded to the nearest hundredth.
Example with a Scale Ratio of 0.25 inches to 2000 miles
Similar steps are taken if the scale is 0.25 inches. We set up the proportion 1 inch/2000 miles = 0.25 inches/x miles and solve for x after cross-multiplication.
The ice rink sold 95 tickets for the afternoon skating session, for a total of $828. answer General admission tickets cost $10 each and youth tickets cost $8 each. How many general admission tickets and how many youth tickets were sold?
I think it is 34 general and 61 youth
It took the race car 22 minutes to travel 114.4 kilometers. At what rate did the car travel?Use the formula r = d/t, where r is the rate, d is the distance, and t is the time. Round your answer to the nearest tenth.
GIVEN circle P with arc AE = 53 , arc BA =68 and arc CB =72
match the following angles with their corresponding measurements
All the answers are
m∠1= 63.5°
m∠2 = 124°
m∠3 = 29.5°
m∠4 = 90°
m∠5 = 54°
m∠6 = 116.5°
m∠7 = 121°
m∠8 = 90°
The theory that is mainly used to find out the angles of the above diagram is that;
the sum of the internal angles of a triangle is 180°.
when the angles of arcs have been given(e.g: BA) that means from the centre of the circle to point B has been rotated by 53° to point A.
Next from point A to point E, the angle rotated is 68°
the addition of these 2 angles give the angle rotated from point B to point E,
that is angle no.7
m∠7 = 53° + 68° = 121°
consider ΔPBE,
PB and PE are radii therefore isosceles triangles
In isosceles triangles the angles opposite equal sides are equal
if the angle is x°, then there are 2 angles with values x each
x° +x° + 121° = 180°
2x° = 59°
x = 29.5°
therefore m∠3 = 29.5°
next connect PC and consider ΔPCB,
according to given information, C∠PB = 72°
as PC and PB are radii ΔPCB is an isosceles triangle, then the angles (y°) opposite radii are equal
2y° + 72° = 180°
y° = 54°
then consider ΔPCD, again an isosceles triangle
as a straight line has an angle of 180°
B∠PC + C∠PD = 180°
72° + C∠PD = 180°
C∠PD = 108°
as ΔPCD is an isosceles triangle, P∠CD and P∠DC are equal (take this angle as z°)
2z° + 108° = 180°
z° = 36°
B∠CD is a sum of y and z angles
therefore m∠8 = y + z
m∠8 = 54° + 36° = 90°
there is also a tangent line that cuts point D of the circle. this tangent cuts D and is perpendicular to the PD radius
this indicates that lines PD and HD are perpendicular to each other
hence, forms a right angle where it cuts each other.
therefore H∠DP / m∠4 = 90°
C∠DH /m∠5 is the difference between P∠DH and P∠DC
m∠5 = 90° - 36° = 54°
m∠1 and m∠6 together make a straight line therefore the sum of these 2 angles is 180°
by looking at the options of answers given the 2 angle values given that add up to 180° are 116.5° and 63.5°.
m∠1 is the acute angle therefore m∠1 = 63.5°
m∠6 is the obtuse angle therefore m∠6 = 116.5°
consider ΔDFB
D∠FB is 180° - m∠1 = 180° - °63.5 = 116.5°
D∠FB + F∠DB(w°) + D∠BF (m∠3)= 180°
116.5 + w° + 29.5° = 180°
w° = 34°
m∠2 = m∠4 + w°
= 90° + 34°
= 124°
finally all the answers are
m∠1= 63.5°
m∠2 = 124°
m∠3 = 29.5°
m∠4 = 90°
m∠5 = 54°
m∠6 = 116.5°
m∠7 = 121°
m∠8 = 90°
The functions f and g are defined as follows f(x)=5x+3/6x+7 and g(x)= square root sign x^2-4x
find f(6/x) and g(x-4)