In a triangle ABC, with angles A, B, and C and sides AB, BC, and AC, angle B is a right (90°) angle. If the sin of angle A is 0.5 and side BC is 8 inches long, what is the length of side AC?
Which of the points shown below are on the line given by the equation y = 5x? Check all that apply.
A. Point A: (5, -1)
B. Point B: (1, 5)
C. Point C: (0, 0)
D. Point D: (-3, 2)
The correct Options are B and C.
What is Function of graph ?The collection of all points in the plane with the form (x, f(x)) that make up a function f's graph. We may alternatively say that the graph of f is the graph of y = f. (x). As a result, the graph of an equation is a particular instance of the graph of a function. Allow f(x) to equal x2 - 3.The graph is a function if a vertical line drawn across it is moved and only ever touches it at one point.To solve y = 5x we check all options in equation by value putting.
let y = 5x .......................(1)
Put point A ( 5, -1) in equation (1)
So, x = 5 & y = -1
y = 5x ⇒ -1 = 5 ×5= 25
Put point B (1,5) in equation (1)
So, x = 1 & y = 5
y = 5x ⇒ 5 = 5 × 1 = 5
Put point C (0,0) in equation (1)
x = 0 & y = 0
y = 5x ⇒ 0 = 5 × 0 =0
Put point D ( -3 ,2) in equation (1)
x = -3 & y = 2
y = 5x ⇒ 2 = -3× 2 = -6
In all these points , B & C points are have same value on both side.
So, we can say that b&c are the points which are shown on the line.
Therefore, The correct Options are B and C.
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1/3 and 7/9 rewrite using the least common denominator
To rewrite 1/3 and 7/9 using the least common denominator, you need to find the smallest number that both 3 and 9 can divide evenly into. The least common denominator (LCD) of 3 and 9 is 9. Rewrite the fractions as 3/9 and 7/9, respectively.
Explanation:To rewrite the fractions 1/3 and 7/9 using the least common denominator, we need to find the smallest number that both 3 and 9 can divide evenly into. The least common denominator (LCD) of 3 and 9 is 9. We can now rewrite the fractions:
1/3 becomes 3/9 (multiply the numerator and denominator by 3)7/9 remains the sameSo, 1/3 and 7/9 can be rewritten as 3/9 and 7/9, respectively, using the least common denominator.
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Mark is solving the following system.
x+y+z=2 (1)
3x+2y+z=8 (2)
4x-y-7z=16 (3)
Step 1: He multiplies equation (1) by 7 and adds it to equation (3).
Step 2: He multiplies equation (3) by 2 and adds it to equation (2).
Which statement explains Mark’s mistake?
- He added equation (3) instead of equation (2) in step 1.
- He did not multiply equation (3) by the correct value.
- He did not eliminate the same variables in steps 1 and 2.
- He added equation (3) and equation (2) instead of subtracting.
Solving the system of linear equations Mark tries to apply elementary transformations in order to eliminate one variable.
He makes such steps:
1. He multiplies equation (1) x+y+z=2 by 7 and adds it to equation (3) 4x-y-7z=16. This gives him:
7x+7y+7x+4x-y-7z=14+16,
11x+6y=30.
2. He multiplies equation (3) 4x-y-7z=16 by 2 and adds it to equation (2) 3x+2y+z=8. This step gives him:
8x-2y-14z+3x+2y+z=32+8,
11x-13z=40.
Thus, he did not eliminate the same variables in steps 1 and 2.
Answer: correct choice is C
Traveling at 45 miles per hour, how many minutes, rounded to the nearest whole number, does it take to drive 240 miles from Orlando to Miami?
a. 5
b. 195
c. 285
d. 320
what is the equivalent ratio to 12:20
John has read the first 114 pages of a novel. He has read 3 pages less than one-third of the novel.
Write an equation to describe the total number of pages p in the novel, and find the value of p.
What is the product of written in simplest form? 7/10 divided by 5/6
What is the absolute value of 6?
Answer:
absolute value is 6
In the equation y = mx + b, b represents:
A. slope
B. rise
C. y - intercept
D. x - intercept
If a road has a 4% grade and rises 200 feet, what is the run?
Answer:
5000
Step-by-step explanation:
400 ÷ 4% = 5000
Two numbers are 10 units away in different directions from their midpoint, m, on a number line. The product of the numbers is –99.
Which equation can be used to find m, the midpoint of the two numbers?
(m – 5)(m + 5) = 99
(m – 10)(m + 10) = 99
m2 – 25 = –99
m2 – 100 = –99
The equation can be used to find m, is [tex]m^{2} -100 = -99[/tex].
What is equation?An equation is a mathematical statement that is made up of two expressions connected by an equal sign.
According to the given question.
We have two numbers.
Both are 10 m away from their midpoint, m.
Therefore,
If the first number is ( m + 10).
Then the second number will (m-10).
Also it is given that the product of these two numbers is 99.
⇒ [tex]( m + 10)( m - 10) = -99[/tex]
⇒ [tex]m^{2} -10m + 10m -100 = -99[/tex]
⇒ [tex]m^{2} - 100 = -99[/tex]
Hence, the equation can be used to find m, is [tex]m^{2} -100 = -99[/tex].
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How many days equals 7344 minutes??
Answer:
as a decimal: 5.1
12x=4(x-5) then x equals?
A survey by the state health department found that the average person ate 208 pounds of vegetables last year and 125 5/8 pounds of fruit.What fraction of the total pounds of fruit and vegetables do the pounds of fruits represent?
Answer: The fraction of pounds of fruits over total pounds of fruits and vegetables is given by
[tex]\frac{25125}{66724}[/tex]
Step-by-step explanation:
Since we have given that
Total amount of vegetables = 208 pounds
Total amount of fruits is given by
[tex]125\frac{5}{8}\text{ pounds}[/tex]
Total amount of fruits and vegetables is given by
[tex]208+125\frac{5}{8}\\\\=208+\frac{1005}{8}\\\\=\frac{1664+1005}{8}\\\\=\frac{2669}{8}\\\\=333.625\text{ pounds }[/tex]
So, we need to find the fraction of pounds of fruits over the total pounds of fruit and vegetables :
[tex]\frac{\text{Pounds of fruits }}{\text{ total pounds of fruits and vegetables}}\\\\=\frac{\frac{1005}{8}}{333.62}\\\\=\frac{1005}{8\times 333.62}\\\\=\frac{1005}{2668.96}=\frac{25125}{66724}[/tex]
The fraction of the total pounds of fruit and vegetables that fruits represent is approximately 0.377, or 37.7%.
Explanation:To find out what fraction the pounds of fruits represent out of the total pounds of fruits and vegetables, we first need to calculate the total pounds of fruits and vegetables consumed. This is found by adding the pounds of vegetables (208) to the pounds of fruits (125 5/8). So, 208 + 125 5/8 = 333 5/8 pounds.
Now, to determine the fraction, we take the pounds of fruits and divide by the total. Hence, the fraction is given by 125 5/8 ÷ 333 5/8. To divide fractions, we multiply by the reciprocal of the divisor, which gives us (125 5/8) * (8/333) = 0.377 (rounded to three decimal places).
Therefore, fruits represent approximately 0.377, or 37.7% of the total pounds of fruits and vegetables consumed.
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During the National Football League’s 1999 season, Troy Aikman, the quarterback for the Dallas Cowboys, earned $0.467 million more than Deion Sanders, the Cowboys cornerback. Together they cost the Cowboys $12.867 million. How much did each player make?
Troy Aikman make 6667000 and Deion Sanders makes 6200000 for the Cowboys cornerback.
What is Equation?Two or more expressions with an Equal sign is called as Equation.
Given,
Troy Aikman, the quarterback for the Dallas Cowboys, earned $0.467 million more than Deion Sanders
Let Deion Sanders earning is x.
Troy Aikman earning is x+467000
Together they cost the Cowboys $12.867 million
x+x+467000=12867000
2x+467000=12867000
Subtract 467000 on both sides
2x=12867000-467000
2x=12400000
Divide both sides by 2
x=6200000
So Troy Aikman make 6200000+467000=6667000 and
Deion Sanders makes 6200000
Hence Troy Aikman make 6667000 and Deion Sanders makes 6200000 for the Cowboys cornerback.
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Goran rented a truck for one day. there was a base fee of $15.99, and there was an additional charge of 96 cents for each mile driven. goran had to pay $288.63 when he returned the truck. for how many miles did he drive the truck?
at her job, mary works 4 hours on monday, 3 hours on wednesday, and 6 hours on saturday. her boss adds a $10 bonus to her paycheck, which then totals $120.50. what is mary's hourly pay?
a. $8.50
b. $9.27
c. $5.24
d. $8.05
Find the values of x and y drawing not to scale
Part 1)
In this problem we know that
[tex]4y\°+112\°=180\°[/tex] ------> by supplementary angles
solve for y
[tex]4y\°=180\°-112\°[/tex]
[tex]y=68\°/4[/tex]
[tex]y=17\°[/tex]
Part 2)
In this problem we know that
[tex]7x+7=112\°[/tex] ------> by vertical angles
solve for x
[tex]7x=112\°-7\°[/tex]
[tex]x=105\°/7[/tex]
[tex]x=15\°[/tex]
therefore
the answer is the option A
[tex]x=15\°, y=17\°[/tex]
In 1991, the federal minimum wage rate was $4.25 per hour. In 1997, it was increased to $5.15. Find the annual rate of change in the federal minimum wage rate from 1991 to 1997
The annual rate of change in the federal minimum wage rate from 1991 to 1997 is $0.15 per year.
Explanation:The annual rate of change in the federal minimum wage rate from 1991 to 1997 can be found by calculating the difference between the final and initial values, and then dividing it by the number of years.
Initial value in 1991: $4.25
Final value in 1997: $5.15
Difference: $5.15 - $4.25 = $0.90
Number of years: 1997 - 1991 = 6 years
Annual rate of change: $0.90 / 6 = $0.15
Therefore, the annual rate of change in the federal minimum wage rate from 1991 to 1997 is $0.15 per year.
Write the time 12 hours after 8 p.m. use an or pm
a scale model of a statue is 7 inches tall. The scale of the model is 1in./1.5ft. what is the actual height of the statue?
if you found 259 to the nearest hundreds,what is the answer
Let U = {21, 22, 23, ..., 40}, A = {21, 22, 23, 24, 25}, B = {26, 27, 28, 29}, C = {21, 23, 25, 27, ..., 39}, and D = {22, 24, 26, 28, ..., 40}.
Use the roster method to write the following set.
11) Aʹ
The complement of set A with respect to the universal set U (A') is {26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40}, which contains all elements in U that are not in set A.
Explanation:The student is asked to use the roster method to write the set A', which represents the complement of set A with respect to the universal set U. The set A' consists of all elements in the universal set U that are not in set A.
First, we list all the elements of the universal set U, which are {21, 22, 23, ..., 40}. Set A contains {21, 22, 23, 24, 25}. To find A', we remove the elements of A from U, resulting in A' = {26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40}.
Final answer:
The set A' includes all numbers from 26 to 40 in the universal set U, which are not included in set A.
Explanation:
To find the set A' or the complement of set A in the universal set U, we need to list all the elements in U that are not in A. Given that the universal set U consists of the numbers 21 through 40, and the set A includes the numbers 21, 22, 23, 24, and 25, we can determine A' by subtracting these from U.
The roster method simply lists out all of the elements. Doing so for A' yields the following:
A' = {26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40}
These are all the numbers in U that are not in A.
simplest form for 21/49
find (2 × 107) (3 × 104).
Jen is making a frame to stretch a canvas over for a painting. She nailed four pieces of wood together at what she believes will be the four vertices of a square. How can she be sure that the canvas will be a square?
a. All four of the pieces of wood are the same length & at least two interior angles are congruent.
b. At least two pieces of wood are the same length & at least two interior angles are congruent.
c. At least two pieces of wood are the same length & all four interior angles are congruent.
d. All four of the pieces of wood are the same length & all four interior angles are congruent.
break apart and distribute to solve 72÷8
72÷8=(40÷8)+(32÷8)
9=5+4
9=9
Answer:
72 ÷ 8 is equal to 9
Step-by-step explanation:
If we want to solve 72 ÷ 8 by breaking apart and distributing, the first step is to write the number ''72'' as the sum or subtraction of two numbers that are divisible by ''8''.
We can write :
[tex]72 = 40+32[/tex]
If we replace this last expression in the original one :
72 ÷ 8 = (40 + 32) ÷ 8 (II)
Now in (II) we can use the distributive property of the division :
(40 + 32) ÷ 8 = (40 ÷ 8) + (32 ÷ 8) (III)
Finally, we need to solve the expression (III) :
(40 ÷ 8) + (32 ÷ 8) = 5 + 4 = 9
We find that 72 ÷ 8 is 9 by breaking apart and then distributing.
Question. I have some math problems that I really need help with and this is all new to me. The direction are as follows:
Combine like terms 7x4 -5x4 the number four is square root. I don't understand at all what to do. Please help.
Answer:
-7 + x + 4 + 4x = x - 3 + 6 + 3x
Step-by-step explanation:
The area of a triangle is 25 sq cm and the base of the triangle is 5 cm. Which equation could be used to find the height of the triangle?
A.
B.
C.
D.