Answer:
4, 7, 10
Step-by-step explanation:
There is a common difference d between consecutive terms, that is
d = - 2 - (- 5) = 1 - (- 2) = 3
To obtain a term in the sequence add d = 3 to the previous term, then
a₄ = a₃ + 3 = 1 + 3 = 4
a₅ = a₄ + 3 = 4 + 3 = 7
a₆ = a₅ + 3 = 7 + 3 = 10
Evaluate the following:
PLEASE HELP!!!!! Find the magnitude and direction of the vector <2,7>. Round angles to the nearest degree and other values to the nearest tenth.
7.3; 73°
7.3; 74°
7.4; 73°
7.4; 74
Answer:
It's 7.3; 74!
Step-by-step explanation:
This was a lucky guess for me on my homework and it was correct sooooo.... I don't really have an explanation...
Definition: For vector [tex]v=<a,b>[/tex], the magnitude is defined as [tex]|v|=\sqrt{a^{2} +b^{2} }[/tex], and the direction of the vector is defined as [tex]tan^{-1}(\frac{b}{a} )[/tex].
Here, [tex]v=<2,7>[/tex].
Then, magnitude is:
[tex]|v|=\sqrt{2^{2}+7^{2} } \\|v|=\sqrt{4+49 } \\|v|=\sqrt{53} \\|v|=7.3[/tex]
The direction is:
[tex]tan^{-1}(\frac{7}{2} )=74^{o}[/tex].
So, the correct option is 7.3,74°.
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Geometry help please and thank you
Answer:
125°
Step-by-step explanation:
By exterior angle theorem:
(3x - 70)° = 60° + x°
(3x - 70)° - x°= 60°
(3x - 70 - x)° = 60°
(2x - 70)° = 60°
2x - 70 = 60
2x = 60 + 70
2x = 130
x = 130/2
x = 65
(3x - 70)° = (3*65 - 70)° = (195 - 70)° = 125°
[tex] m\angle LKM = 125\degree [/tex]
PLS HELP ASAP rob is saving money for a new mp3 player. For every $15 he saves $8. On Sunday he earns $45 how much does he save
Answer:
the answer for this problem would be 24 dollars.
What is the slope of a line that passes through the origin and the point (6, 3)
Answer:
Slope = 1/2
Step-by-step explanation:
Formula for getting slope using 2 points...
(y2 - y1) / (x2 - x1)
= (3 - 0) / (6 - 0)
= 3 / 6
= 1/2
So...
Slope is 1/2
Hope this helps :)
Let me know if there are any mistakes!!
Answer: The slope is 1/2
Step-by-step explanation:
When a line passes through the origin the equation of the line will be represented in the form y= kx where k is the slope.
To to find k you will need to divide both sides by x.
y = kx
y/x = kx/x
k = y/x
This means that to find k, you will need to divide the y coordinate of the point by the x coordinate.
k = 3/6
K = 1/2
A farmer wants to fence a piece of his land. Two sides of the triangular field have lengths of 120 feet and 325 feet. The measure of the angle between those sides is 70 degrees. How much fencing will a farmer need?
Farmer need 750.5 feet fencing for his triangular field.
What is triangle?"Triangle is two dimensional geometrical shape with three sides and three vertices. Sum of all the angles of a triangle is equals to 180°.
Formula used
Cosine rule
As per the diagram,
cosθ = (b² +c² -a²) / 2bc
cos 70° = 0.3420
According to the question,
Let AB = c , AC = b are given sides of measure 120 feet and 325 feet respectively.
and BC = a
Angle between given sides be θ = 70°
Substitute the value in the formula we get,
cos70° = [ (325)² +(120)² - a²] / 2(120)(325)
⇒ 0.3420 = [ 120025 - a²] / 78000
⇒ 120025 -a² = 26676
⇒ a² = 93349
⇒ a = 305.5
Total fencing required for triangular field = AB + BC +CA
= 120 + 325 + 305.5
= 750.5 feet
Hence, farmer need 750.5 feet fencing for his triangular field.
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I need the answer key for mid chapter check point grade 5 chap 7!! ASAP
Answer:
3/8
Step-by-step explanation:
1/2 x 3/4 = 3/8
You multiply the top by the number beside it and do the same for the bottom.
solve for x 5x + 3 - 2x = 24 (also don't have the answer be a fraction)
Answer:
x=7
Step-by-step explanation:
Let's solve your equation step-by-step.
5x+3−2x=24
Step 1: Simplify both sides of the equation.
5x+3−2x=24
5x+3+−2x=24
(5x+−2x)+(3)=24(Combine Like Terms)
3x+3=24
3x+3=24
Step 2: Subtract 3 from both sides.
3x+3−3=24−3
3x=21
Step 3: Divide both sides by 3.
Answer: x=7
Step-by-step explanation:
Given
5x + 3 - 2x = 24
Subtract both sides by 3
5x + 3 - 3 - 2x = 24 - 3
5x - 2x = 21
Simplify
3x = 21
Divide both sides by 3
3x / 3 = 21 / 3
x=7
Hope this helps!!
Please let me know if you have any questions
How can you tell that the following number is a rational number?
0.251
A. It is a rational number because the decimal terminates
B. It is a rational number because there is a value of 0 in the ones place
C. It is a rational number because the sum of the digits is less than 10
D. It is a rational number because it is not a repeating decimal
Answer:
In order to be called a 'rational' number, a number must be the quotient that results when one non-zero integer is divided by another. An irrational number can be written as a decimal, but not as a fraction. Your number is (3 sqrt(2)) / sqrt(2) = 3, and is a rational number indeed.
I need help bad I'm hella confused!
Answer:
a. x=-7 b. -8 hope this helps with the rest of them.
Step-by-step explanation:
a you -28 divided by 4 to simplify x
b. this is a little harder because 6 is a double negative. when it has 2 minus signs that makes it a positive. we have to put 6 on the other side of the equal sign. so we have to minus 6 to put it on the other side. This is because on the left its positive so to put it on the right it has to be a negative. -6 plus -2 = -8. so x is = to -8
Pretty Please answer this!
Analyze the following image and state
Line of Symmetry
Coordinates of the Vertex, X - intercepts, Y - Intercepts.
Whether the graph is positive or negative.
Answer:
The x-intercept is where the graph crosses the x-axis, so in this case, the x-intercepts are (-4, 0) and (-2, 0).
The y-intercept is where the graph crosses the y-axis, so in this case, the y-intercept is (0,8).
The line of symmetry splits the graph in two equal halves, and it is x=-3.
Finally, because this graph opens up, the graph is positive.
Let me know if this helps!
James rolling A 1-6 Number cube. Which statement is true ? James is equally likely to roll a 4 as an even number. True or false? James is equally likely to roll a 3 as an odd number? True or false? James is more likely to roll a 5 than 2 . True or false? James is equally likely to roll an even number as an odd number.? True or false?
Answer: James is equally likely to roll an even number as an odd number. this is the answer give me brainliest
A jar contains sugar. The jar and the sugar have a total weight of 850 g. Anna uses 2/3 of the sugar. The jar and the sugar now have a total weight of 530 g. Work out the weight of the jar.
Answer:
[tex]J = 370g[/tex]
Step-by-step explanation:
Given
Represent the weight of the Jar with J and the sugar with S
Initially, we have:
[tex]J + S = 850g[/tex]
After 2/3 of sugar is removed we have:
[tex]J + S -\frac{2}{3}S= 530g[/tex]
Required
Determine the weight of the jar
[tex]J + S = 850g[/tex] --- (1)
[tex]J + S -\frac{2}{3}S= 530g[/tex] --- (2)
Simplify (2)
[tex]J + S -\frac{2S}{3}= 530g[/tex]
Take LCM
[tex]J + \frac{3S - 2S}{3}= 530g[/tex]
[tex]J + \frac{S}{3}= 530g[/tex]
Make S the subject in (1)
[tex]J + S = 850g[/tex]
[tex]S = 850g - J[/tex]
Substitute 850g - J for S in [tex]J + \frac{S}{3}= 530g[/tex]
[tex]J + \frac{850g - J}{3}= 530g[/tex]
Multiply through by 3
[tex]3 * J + 3*\frac{850g - J}{3}= 530g * 3[/tex]
[tex]3J + 850g - J= 1590g[/tex]
Collect Like Terms
[tex]3J - J= 1590g-850g[/tex]
[tex]2J= 740g[/tex]
Make J the subject
[tex]J = \frac{1}{2} * 740g[/tex]
[tex]J = 370g[/tex]
The jar weighs 370g
Answer:
370
Step-by-step explanation:
A coat was originally priced at $80. It went on sale for $70.40. What was the percent that the coat was discounted?
Answer:
12%
Step-by-step explanation:
(80 - 70.40)/80 * 100 = 12
A group of 15 people each bought both a book that cost x dollars and a bookmark that cost $1. A group of 3 people each bought both a book that cost x dollars and a backpack that cost $36. Both groups spent the same amount of money. What is the price of the book?
Answer:
$1.40
Step-by-step explanation:
Answer:
The price of the book is $7.75.
Step-by-step explanation:
Let's first establish an equation.
If I buy a book costing [tex]x[/tex] dollars and a bookmark costing 1 dollars, I will have spent [tex]x + 1[/tex] dollars. So a group of 15 people doing the same will have spent [tex]15(x+1) = 15x + 15[/tex] dollars.
Analogously, the group of 3 people has spent [tex]3(x+36) = 3x + 108[/tex] dollars.
Since we know that both groups spent the same amount of money, we can set the two expressions equal to each other:
[tex]15x+15=3x+108\\12x=93\\x=7.75[/tex]
Because [tex]x[/tex] was the price of the book, which was asked for in the question, we conclude that the answer is $7.75.
Last week, a pharmacy sold a bottle of shampoo for $5.00. This week, the shampoo sells for $6.50. By what percent did price increase?
Answer:
The percent increase is 30%
Step-by-step explanation:
First find the difference
6.50 - 5.00 = 1.50
Divide by the original cost
1.50 / 5.00
.3
Change to percent
.3 = 30%
The percent increase is 30%
Answer:
30%
Step-by-step explanation:
5.0*30%=1.50
5.0+1.50=6.50
In 1983, a cast-iron pan cost $28.35. Today, a cast-iron pan costs $52.95. If the CPI is 166, what is the percent relation
of the actual price of a cast-iron pan to the expected price?
a The actual price is 11.1% lower than the expected price.
b The actual price is 20.8% lower than the expected price.
The actual price is 31.5% higher than the expected price.
d. The actual price is 12.5% higher than the expected price.
с.
Answer:
d.
The actual price is 12.5% higher than the expected price
Step-by-step explanation:
The percent relation of the actual price and the expected price is 12.5%
What is the consumer price index?The consumer price index measures the changes in price of a basket of good. It is used to measure inflation.
Price of the cast iron today = $28.35 x (166/100) = $47.06
The percent relation of the actual price and the expected price = ($52.95/$47.06) - 1 = 12.5%
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You bought a car for $5,000. Each year it depreciates in value by 8.5% which equation can be use to find the value, v, of the car x years after it was purchased?
Answer:
I believe this is the answer
V=5000(1•0.085)^x
Step-by-step explanation:
sorry if its incorrect i just wanted to help
"v = 5000 * (1-0.085)x" is the formula that is used to determine the car's worth.
What is depreciation?An asset loses value over time as a result of use, damage, or obsolescence. Depreciation is the measurement of this decline. Depreciation, or a decline in asset value, can be brought on by a variety of other variables, such as bad market conditions, etc.
Given, You bought a car for $5,000. Each year it depreciates in value by 8.5%
In this case, we have the following formula:
v = C. (1 - r)ˣ
Where C is the original value of the car, r is the depreciation rate and x is the time in years
Equation to find the value = 5000 * (1- 0.085)ˣ
Therefore, the equation that helps in calculating the value of the car is
"v = 5000 * (1- 0.085)ˣ".
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Find the length of WV
Answer:
I believe the answer would be 20.
Step-by-step explanation:
28/7 = 4
5*4 = 20
Pls mark brainliest <3
0Answer: The answer is 20
Step-by-step explanation:
5. A mountain has a base and peak that are inaccessible. At point A, the angle of elevation of the peak is
30°. One kilometer closer to the mountain, at point C, the angle of elevation of 35º. Find the height
PB of the mountain.
Answer:
1.366km
Step-by-step explanation:
The height of the mountain is [tex]3.34Km[/tex]
Right angle triangle:A diagram of right angle triangle PBA is attached below which describe the situation as given in the question.
Let us consider that H represent the height of mountain.
Angle of elevation at point A and C shown in the diagram.
Apply tan function in triangle CBP.
[tex]tan(35)=\frac{H}{x} \\\\H=xtan(35)=0.7x.........(1)[/tex]
Apply tan function in triangle ABP.
[tex]tan(30)=\frac{H}{x+1}\\ \\(x+1)tan(30)=H\\\\(x+1)=\sqrt{3}H\\ \\x=\sqrt{3}H-1........(2)[/tex]
Substituting the value of equation 2 into equation 1.
[tex]H=0.7(\sqrt{3}H-1)\\\\H=1.21H-0.7\\\\0.21H=0.7\\\\H=0.7/0.21=3.34Km[/tex]
Hence, The height of the mountain is [tex]3.34Km[/tex]
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Find the perimeter of a
square that has a side
length of x +5.
x + 20
2x + 10
4 + 20
PLEASE HELP MEE FAST
solve for x? please help
Answer:
x = [tex]\sqrt{10}[/tex]
Step-by-step explanation:
The 2 right triangles and the outer right triangle are similar, then ratios of corresponding sides are equal, that is
[tex]\frac{x}{5}[/tex] = [tex]\frac{2}{x}[/tex] ( cross- multiply )
x² = 10 ( take the square root of both sides )
x = [tex]\sqrt{10}[/tex]
Answer:
√10
Step-by-step explanation:
taking the smallest triangle;
y as the hypotenuse, x as the adjacent side, 2 as the opposite side
then: y²=x²+2²
x²=y²-2²= y²-4
taking the other triangle;
z as the hypotenuse, x as the adjacent side, 5 as the opposite side
then: z²=x²+5²
x²=z²-5² = z²-25
take both equations,
x²= y²-4
x²= z²-25
y²-4= z²-25
y²= z²-25+4 = z²-21
taking the biggest triangle (whole triangle);
(5+2)= 7 as the hypotenuse, z as the adjacent side, y as the opposite side
then; 7²=z²+y²
z²+y²=7² =49
but y²= z²-21;
z²+y² =49
z²+ z²-21 =49
2z²-21=49
2z²=49+21= 70
z²= 70/2 = 35
take x²= z²-25
x²= 35-25 = 10
[tex]x = \sqrt{10} [/tex]
A fraction is written in simplest form when the GCF of the
numerator and the denominator is
Answer:
simplified
Step-by-step explanation:
Answer: 1 -- that is, if they share no common factors other than 1
Step-by-step explanation:
Ken placed a 6. feet ladder against a wall , creating the triangle shown in the figure below at what height on the wall does the top of the ladder reach
Answer: c
Step-by-step explanation:
please help!!!!!!!! it’s due in an hour!!!!!!!
A line passes through the points (-4,-1) and (4,3) a second line passes through the points (-2,-2) and (2,6) at what point do the two lines intersect
Answer:10
Step-by-step explanation:
Pls help me out ty..
Answer:
3.14159265359
Step-by-step explanation:
Hope this helps :)
Answer:
3.14
Step-by-step explanation:
Technically, pi is a an irrational number, meaning that its decimal form neither ends or repeats. But we always shorten it to 3.14.
In the right triangle ABC, CD is an altitude, and c=e+f,by combining three equations it can be shown that a^2+b^2=c^2.One of the equations is c=e+f.which of the following could be the other two equations
Answer:
Please provide a diagram as the question is confusing.
Will give Brainliest!!!
What is the y=mx+b for the equation x−y=−8?
Find the value for M.
Answer:
it is 10
Step-by-step explanation:
Answer:
g
Step-by-step explanation:
g