Given :
cos x = 1.7/2 .
Also, x is an acute angle.
To Find :
The value of angle x.
Solution :
cos x = 1.7/2
Applying cos inverse both the sides, we get :
[tex]cos ^{-1} (cos\ x ) = cos^{-1} \dfrac{1.7}{2}\\\\x = cos^{-1} \dfrac{1.7}{2}[/tex]
Calculating the value of [tex]cos ^{-1} \dfrac{1.7}{2}[/tex] from calculator, we get :
x = 31.79°
Therefore, the acute angle x is 31.79°.
Which best explains why you can use multiplication to solve equations involving division?
A. Multiplication is easier to do than division.
B. Multiplication involves the same facts as division.
C. Multiplication is the inverse operation of division so it can undo division.
D. Multiplication involves commutative Property so it can undo division.
Answer:
C
Step-by-step explanation:
The Ferry family rented 50 chairs for $150. Which expression can be used to find the cost per chair?There are 330 walnuts in 6 bags. If each bag has the same number of walnuts, how many walnuts are in 2 bags? Which is a unit rate? A 47¢ for 2 pens B 20 gallons for 2 hours C 15 hours for 3 months D 18 miles driven in a week
Step-by-step explanation:
Quesion 1
The cost of one chair can be found by dividing the cost of the total chairs by the number of chairs
hence, cost per chair= 150/50= $3 per chair
Question 2
let us find the number of walnuts per bag
= 330/6
=55 walnuts per bag
hence in two bags there will be 55*2= 110 walnuts
Question 3
Option D is an example of a unit rate.
The unit rate is defined as the cost of one unit of an item, or the value that represents a unit of a quantity... D 18 miles driven in a week
An art teacher had 57 grams of blue clay. She combined it with 31 grams of yellow clay to make green clay. She let students use the green clay during the week. At the end of the week, the remaining green clay weighed 18 grams.
Step-by-step explanation:
Amount of green clay at the start = 57g + 31g = 88g.
Amouny of green clay used = 88g - 18g = 70g.
Hence 70g of green clay was used during the week.
Sara wants to find the input value that produces the same output for the functions represented by the tables.
A table headed with f(x) equals negative 0.5 x plus 2, with 2 columns and 8 rows. The first column, x, has the entries, negative 3, negative 2, negative 1, 0, 1, 2, 3. The second row, f(x), has the entries 3.5, 3, 2.5, 2, 1.5, 1, 0.5. A table headed with g(x) equals 2 x minus 3, with 2 columns and 8 rows. The first column, x, has the entries, negative 3, negative 2, negative 1, 0, 1, 2, 3. The second row, g(x), has no entries.
What is the input value that produces the same output value in both charts?
–2
–1
1
2
Answer:
2 is the value that provides the same result with f(x) and g(x).
Step-by-step explanation:
You can solve this by saying:
f(x) = g(x)
and then solving for x.
So let's do it:
[tex]f(x) = g(x)\\-0.5x + 2 = 2x - 3\\2x + 0.5x = 2 + 3\\2.5x = 5\\x = 2[/tex]
This tells us that when x = 2, the two functions will have identical values. Let's try them out to confirm it!
f(x) = -0.5x + 2
f(2) = -0.5 * 2 + 2
f(2) = -1 + 2
f(2) = 1
g(x) = 2x - 3
g(2) = 2 * 2 - 3
g(2) = 4 - 3
g(2) = 1
So we can see that 2 is the value that produces the same result in both charts.
The input value that produces the same output value in both charts is 2. so the correct answer is option D.
What is a function?A function is defined as the expression that set up the relationship between the dependent variable and independent variable.
here, we have,
You are given two functions f (x) = -0.5X +2 and g(x) = 2x - 3
x f(x)
-3 3.5
-2 3
-1 2.5
0 2
1 1.5
2 1
3 0.5
The second table is given below:-
x g(x)
-3
-2
-1
0
1
2
3
We will put the points and will find the value of functions:-
g(-3) = 2(-3) - 3 = -6 -3 = -9
g(-2) = 2 -(-2) -3 = -7
g(-1) = 2( -1) -3 = -3
g(0) = 2 - 0 - 3 = -3
g(1) = 2.1 - 3 = -1
g(2) = 2.2 -3 = 1
g(3) = 2.3 -3 = 3
Hence the second table will be
x g(x)
-3 -9
-2 -7
-1 -5
0 -3
1 -1
2 1
3 3
The input value that produces the same output value in both charts is 2.
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I'm confused, can somebody help?
I only need the answer to the question. Thank you!
Answer:
10
Step-by-step explanation:
refer attachment for detailed answer
What is the y-intercept of a line that has a slope of -3 and passes through point (0, -7)?
-7
3
0
4
Answer:
-7
Step-by-step explanation:
The y intercept of a line is the y value of the line when the x value = 0
In this case we are given the coordinates (0, -7)
so when x =0 y= -7
Therefore, the y- intercept is -7
Answer:
-7
Step-by-step explanation:
The y intercept of a line is the y value of the line when the x value = 0
In this case we are given the coordinates (0, -7)
so when x =0 y= -7
Therefore, the y- intercept is -7
The two shapes are similar. Solve for x. Show all work.
Answer:
X= 24
Step-by-step explanation:
Answer:
x = 25Step-by-step explanation:
The two shapes are similar
As per similarity, the corresponding sides have same ratio. Knowing the ratio we can find the value of the side x:
10/4 = 15/6 = 30/12 = x/102.5 = x/10x = 2.5*10x = 25Please answer ASAP! A function graphed f(x) is graphed on the coordinate plane. What is the function rule in slope-intercept form? Enter your answer in the box.
Solve the equation.
-0.06 m = 7.2
m =
Answer: -120
Hope this helps!!
Answer:
-120
Step-by-step explanation:
Complete the statements.
Graph__ has one real root.
Graph__ has a negative discriminant.
Graph __ has an equation with coefficients.
A=1 B=4 C=-2
Answer:
1. B
2. A
3.C
Step-by-step explanation:
Tickets for 2 adults and 4 children at a theme park cost £152.
An adult ticket costs twice as much as a child ticket.
Write and solve an equation to work out the price of an adult ticket
hope it helps!!!!
please mark brainliest
Answer:
The price of adult ticket is £38.
Step-by-step explanation:
First, you have to form equations in terms of a (adult) and c (child) :
[tex]2a + 4c = 152 - - - (1)[/tex]
[tex]a = 2c - - - (2)[/tex]
Next, you have to solve these equations by substitution :
[tex](2)→(1)[/tex]
[tex]2(2c) + 4c = 152[/tex]
[tex]8c = 152[/tex]
[tex]c = 152 \div 8[/tex]
[tex]c = 19[/tex]
[tex]substitute \: c = 19 \: into \: (2)[/tex]
[tex]a = 2 \times 19[/tex]
[tex]a = 38[/tex]
Graph the equation on the coordinate plane.
y=1/2x
Answer:
hope this helps
Step-by-step explanation:
Quick question. Is the term “at least” < with equal sign or > with equal sign?
Answer:
if you mean that it look like this < or this > then its “less than or equal to“ or “greater than or equal to”
I hope this helped!!
OH and have a merry Christma!!!!!
In 1867, the United States purchased Alaska from Russia. Alaska is about 5.9 × 105 square miles. The United States paid about $12.20 per square mile. Approximately how much did the United States pay Russia for Alaska? Complete the steps to answer the question. 1. Write the expression: (5.9 × 105)(12.2) 2. Multiply the decimal values: × 105 3. Write in scientific notation: × The United States paid Russia approximately for Alaska.
Answer:
$7.198 * 10^6
Step-by-step explanation:
Given that :
Total Area of Alaska = 5.9 * 10^5 mi²
Cost of Alaska per square mile = $12.20
Total amount paid to purchase Alaska:
(Total area in square miles * Cost per square mile)
(5.9 × 10^5) * $12.20
(5.9*12.20) * 10^5
71.98 * 10^5 dollars
= $7.198 * 10^6
Hence, amount the United States paid Russia for the purchase of Alaska is approximately $7.198 * 10^6
Answer:
1. Write the expression: (5.9 × 105)(12.2)
2. Multiply the decimal values:
✔ 71.98
× 105
3. Write in scientific notation:
✔ 7.198
×
✔ 10 to the sixth power
The United States paid Russia approximately
✔ $7,200,000
for Alaska.
Step-by-step explanation:
Find the values of x in [0, 360°) which satisfy the
equation below.
2 cota x = -3 SC X
Given :
An equation 2cot x = -3sec x .
To Find :
the values of x in [0, 360°) which satisfy the given equation.
Solution :
Converting cot x and sec x in the form of sin x and cos x.
[tex]\dfrac{2cos \ x}{sin\ x}= \dfrac{-3}{cosx}\\\\2cos^2 x +3 sin\ x =0\\\\2( 1 - sin^2 x ) + 3sin \ x = 0 \\\\2sin^2 x -3sin\ x -2 = 0\\\\2sin^2\x -4sin\ x + sin\ x -2 = 0\\\\2sin\ x( sin\ x - 2 )+ 1( sin \ x - 2 ) = 0\\\\sin \ x = \dfrac{-1}{2} \ or\ sin \ x = 2[/tex]
Neglecting sin x = 2 because sin x cannot be greater than 1.
x = π - π/6, π + π/6
x = 5π/6 and x = 7π /6
Therefore, the values of x in [0,360°) is 5π/6 and x = 7π /6 .
PLEASE help me with this <3
Answer:500 miles
Step-by-step explanation:
Divide by using synthetic division .
(5x²-4x+12) : (x+3)
Answer:
5x-19+[tex]\frac{69}{x+3}[/tex]
Step-by-step explanation:
what is 3^-3 * 10^-2 evaluated?
Step-by-step explanation:
3^(-3) * 10^(-2)
= 1/27 * 1/100
= 1/2700.
Answer:
1/2700
Step-by-step explanation:
3^-3=1/3^3
10^-2=1/10^2
1/3^3 x 1/10^2 = 1/2700 or .00037
-2(x - 5) < 8 what is x
Answer:
The answer is X > 1 hope that helps!
Step-by-step explanation:
The length of a rectangle board is 10 centimeters longer than its width. The width of the board is 26 centimeters. The board is cut into 9 equal pieces. What is the area of each piece? What are the possible dimensions of each piece? (Take the dimensions to be whole numbers.)
Answer:
Area of each piece = 104 [tex]cm^{2}[/tex]
Possible dimensions are 26 cm by 4 cm, 13 cm by 8 cm.
Step-by-step explanation:
Given that:
Dimensions of the rectangular board as:
Length of the board is 10 cm longer than its width.
Width of the board = 26 cm
Length of the board = 26 + 10 = 36 cm
The rectangular board is divided into 9 equal pieces.
To find:
Area of each piece and
the possible dimensions of each piece = ?
Solution:
First of all, let us calculate the area of bigger rectangular board.
Area of a rectangle is given by the following formula:
[tex]Area = Length \times Width[/tex]
Area = 26 [tex]\times[/tex] 36 [tex]cm^2[/tex]
Area of each smaller rectangle = [tex]\frac{26\times 36}{9} = 104\ cm^2[/tex]
To find the possible dimensions, we need to find the factors of 104.
104 = 26 [tex]\times[/tex] 4
104 = 13 [tex]\times[/tex] 8
Therefore, the Possible dimensions are 26 cm by 4 cm
and
13 cm by 8 cm.
Robert started to save money to purchase a new game console. His savings at the end of the first week included a jar of 368 nickels and dimes. The total value of the coins was $24.40. Which system of equations below would be the best to use to find the number of nickels and dimes Anthony had at the end of the first week?
a. n+ d = 368
5n + 10d = 24.40
b. n+ d = 24.40
0.05n + 0.10d = 368
c. n + d = 368
0.05n + 0.10d = 24.40
d. n + 9 = 368
0.5n + 0.10d = 24.40
Answer:
0.05n + 0.10 d =24.40
Step-by-step explanation:
Nickel is worth 0.05 of a dollar(1)
The system of equations below would be the best to use to find the number of nickels and dimes Anthony had at the end of the first week is:
n + d = 368
0.05n + 0.10d = 24.40
The number of nickels and dimes Anthony saved at the end of the first week can be determined using two equations. This is known as simultaneous equations.
The total number of nickels and dimes in the jar is 368. This can be represented with the equation:
nickels + dimes = 368
n + d = 368. This would be the first equation.
A nickel is equal to 0.05 of a dollar and a dime is equal to 0.1 of a dollar. The total sum of money in the jar is $24.40. This means that the value of dimes and nickels in the jar is $24.40. This can be represented with the equation: 0.05n + 0.10d = 24.40. This is the second equation.
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The distance between Dallas and San Antonio is on a map is 13.7 inches. If 2 inches = 40 miles, what is the distance, in miles, from Dallas to San Antonio?
Answer:
Distance= 308 miles
Step-by-step explanation:
Giving the following information:
The distance between Dallas and San Antonio is on a map is 13.7 inches.
2 inches = 40 miles
To calculate the distance between Dallas and San Antonio, we will use the following formula:
Distance= (12/2)*40 + 1.7*40
Distance= 308 miles
12/2= first 12 inches
During a period of time a reservoir is drained for 2 hours per day 3 times per week. Each time 12 gallons per minute are drained. What integer represents the change in the number of gallons drained from the reservoir each week?
Answer:
The integer representing the change is -43,200 gallons
Step-by-step explanation:
Here, we want to get the integer that represents the change in the number of gallons drained from the reservoir each week
Total number of hours per week would be 2 * 3 = 6 hours ;
6 hours is same as 6 * 60 = 3600 minutes
in a minute 12 gallons are drained
In 3600 minutes, the number of gallons drained would be;
3600 * 12 = 43,200 gallons are drained
PLEASEEEEEE HELPPPPP!
Answer:
2
Step-by-step explanation:
What is the area of half of a circle with a diameter of 3.5cm, round to the nearest hundredth, if
necessary?
a. 38.47 cm2
b. 19.23 cm2
c. 9.62 cm2
d. 4.81 cm2
Answer:
I think it is A (38.47)
Step-by-step explanation:
I believe this because I had a math qouiston like this and when I found this A was the only comen answer and when I clicked on my 38.47 I was right
I wanna be in a gc someone add me to one
Sc-maddison_camp20
Ig- mads_070
A pair of jeans is on sale for 20% off. The sale price is $55.00. What is the original amount of the pair of jeans?
Answer: 275$
I'm not entirely sure I did this right! But at least try!!!
Step-by-step explanation:
20/100 = 55/x (cross multiply)
20x = 5,500 (divide)
X = 275
The original price of the pair of jeans is $ 68.75
What is Percentage?
A percentage is a number or ratio expressed as a fraction of 100. It is often denoted using the percent sign, %
Given data ,
The sale price of the jeans = $ 55.00
The discounted percentage of the pair of jeans = 20 %
Let the original price of the jeans be = A
To calculate the original price of the jeans ,
Original price of the jeans A will be discounted percentage less than and is equal to the sale price of the jeans
So ,
Original price of the jeans A - discounted percentage of the pair of jeans = Sale price of the jeans
And ,
A - ( 20/100 ) A = 55
( ( 100A - 20A ) / 100 )A = 55
(80/100 ) A = 55
( 4/5 ) A = 55
Multiply by 5/4 on both sides , we get
A = ( 55 x 5 ) / 4
A = 275/4
A = $ 68.75
Therefore , Original price of the jeans A = $ 68.75
Hence , the original price of the jeans is $ 68.75
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PLEASE I ONLY HAVE 5 MINS TO FINISH THIS!!!!!!!!!!!
50 !
hope this helps :)
1/b+x=3b/2x^2 - 1/x
btw ^2 means square
Answer:
[tex]x = \frac{ - 3b}{4} \: or \: b[/tex]
Step-by-step explanation:
[tex] \frac{1}{b + x} = \frac{3b}{2 {x}^{2} } - \frac{1}{x} [/tex]
[tex] = > \frac{1}{b + x} = \frac{3b - 2x}{2 {x}^{2} } [/tex]
[tex] = > 2 {x}^{2} = (b + x)(3b - 2x)[/tex]
[tex] = > 2 {x}^{2} = 3 {b}^{2} - 2bx + 3bx - 2 {x}^{2} [/tex]
[tex] = > 2 {b}^{2} = 3 {b}^{2} + bx - 2 {x}^{2} [/tex]
[tex] = > 3 {b}^{2} + bx - 4 {x}^{2} = 0[/tex]
[tex] = > 3 {b}^{2} + 4bx - 3bx - 4 {x}^{2} = 0[/tex]
[tex] = > b(3b + 4x) - x(3b + 4x) = 0[/tex]
[tex] = > (3b + 4x)(b - x) = 0[/tex]
Hence,
[tex]x = \frac{ - 3b}{4} \: or \: b[/tex]