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)?
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°.
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 general term for the sequence 1, 6, 11, 16
3(p+8) = -6 ( p + 6 )
Which of the following is a perfect square?
A. 127
B. 100
C. 13
D. 102
The area of a rectangle is 30 sq meters. The perimeter is 26 feet. What are the dimensions of the rectangle?
Answer:
The given rectangle is not possible.
Step-by-step explanation:
The minimum perimeter of such a rectangle is 4√30 meters, about 21.9 meters. That is about 71.9 feet. The largest rectangle with a perimeter of 26 feet will have an area of about 3.93 square meters.
The rectangle described cannot exist.
what is the radius and center of this circle?
[tex] {x}^{2} + {y}^{2} + 2x - 4y - 2 = 0[/tex]
Complete the table of values for the linear equation -2x-5=30 brainly. Enter your answers in the boxes.
The value of x is x = -17.5.
The linear equation in question is -2x - 5 = 30. To complete a table of values for this equation, solve for x first:
Add 5 to both sides of the equation to isolate the term with x: -2x = 35.
Divide both sides by -2 to solve for x: x = -17.5.
Now that you have the value of x, you can fill in the table with x = -17.5, since a table of values typically includes various values for x and the corresponding values for the equation. However, in this case, the equation is simply solved for a single value of x without needing different values for it.
alvin's age is two times elga's the sum of their ages is 87 what is elga's age?
By forming an algebraic equation based on the given information, we find that Elga's age is 29 years.
Explanation:This question belongs to the category of Algebraic equations. We know that Alvin's age is two times Elga's, so we could represent Alvin's age as 2E, where E represents Elga's age.
The problem also tells us that the sum of their ages equals 87. That means we can form this equation: E + 2E = 87.
Combining like terms, we get 3E = 87. Finally, dividing each side by 3, we find the value of E (Elga's age).
So, Elga's age is 87 / 3, which equals 29 years.
Learn more about Algebraic equations here:https://brainly.com/question/32183344
#SPJ2
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.
How do I double the volume of a pyramid
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:
https://brainly.com/question/843074
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.
Know more about Factorization here:
brainly.com/question/25829061
#SPJ2
Maya added 10 grams of salt to 40 grams of water.
She made ___ grams of ___% solution.
Please help
*show work*
Answers:
She made __50__ grams of __20__% solution
-------------------------------------------------------------------
Work Shown:
There's 10+40 = 50 grams of stuff overall (that "stuff" being salt and water). Of this total, 10 grams are salt so 10/50 = 1/5 = 0.20 = 20% is salt. Therefore this is a 20% salt solution.
We can say "20% solution" or "20% salt solution" to be more specific of what kind of chemical mix it is.
which equation can be solved to find x, the measure of BD in the diagram below?
Answer:
A. [tex]\frac{1}{2} (233^{o}-x)=53^{o}[/tex]
Step-by-step explanation:
Let x be the measure of arc BD.
Since we know that an angle formed by two intersecting tangents equals one-half the difference of the measures of the intercepted arcs (the major arc-minus the minor arc).
[tex]\text{ Measure of tangent-tangent angle}=\frac{1}{2} (\text{measure of major arc-measure of minor arc})[/tex]
We can see from our given graph that the tangent-tangent angle's measure is 53 degree. The measure of its intercepting major arc equals 233 degrees and minor arc equals x.
Upon substituting our given values in above formula we will get,
[tex]53^{o}=\frac{1}{2} (233^{o}-x)[/tex]
[tex]\frac{1}{2} (233^{o}-x)=53^{o}[/tex]
Therefore, the equation that can be solved to find x (the measure of arc BD) will be [tex]\frac{1}{2} (233^{o}-x)=53^{o}[/tex] and option A is the correct choice.
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.
Can you please help me out ?
ordered: 0.5 mg
Available: 2 mg/ml
how many mls should be given?
Final answer:
The patient should be given 0.25 mls of the medication.
Explanation:
To calculate the volume of medication a patient should be given, we can use a basic formula that relates the ordered dose, the concentration of the medication available, and the volume required to deliver the ordered dose. In this case, the student has been asked to determine how many milliliters (mls) of medication to administer when 0.5 mg is ordered and the medication concentration available is 2 mg/ml.
The formula to use is:
Dose ordered (mg) / Concentration of medication (mg/ml) = Volume to administer (ml)
So for this problem:
0.5 mg / 2 mg/ml = 0.25 ml
Therefore, the patient should be given 0.25 mls of the medication.
3/10n = 4/5
what value of n will make this equation correct?
Answer:
the answer is 2 and 2/3 if that doesn't pop up then 8/3 also works.
Step-by-step explanation:
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)
David and Josh are both practicing for an upcoming swim tournament. Every week, David swims for 3x hours at an average speed of x laps per hour. Josh swims 5 more hours per week than David, but at an average speed that is 4 laps per hour less than David's average speed.
Which of the following functions will give the total distance, in laps, that Josh swims each week?
Write an expression using variables for the sum of two consecutive numbers
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.
learn more about simple interests here :
https://brainly.com/question/25845758
#SPJ2
a rectangle is 1/3 yards long and 2/3 yards wide.
what is the area of the rectangle?
enter your answer in the box as a fraction in simplest form
[tex] \frac{?}{?} \: {yd}^{2} [/tex]
Final answer:
The area of a rectangle with dimensions of 1/3 yards by 2/3 yards is calculated using the formula length × width, resulting in an area of 2/9 square yards. This value is already in simplest form.
Explanation:
The question asks us to find the area of a rectangle that is 1/3 yards long and 2/3 yards wide. The formula to calculate the area of a rectangle is length × width. Therefore, to find the area, we multiply 1/3 yards by 2/3 yards.
Area = (1/3) yd × (2/3) yd = 2/9 yd²
This calculation shows that the area of the rectangle is 2/9 square yards. It is important to express the answer in simplest form, as the question requests, and 2/9 is already in its simplest form.
I am an odd number. I am less than 100. The sum of my fights is 12. I am a multiple of 15. What number am I?
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]
Learn more about Pythagoras' theorem here:
https://brainly.com/question/12105522
#SPJ2
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
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.