Answer:
a = - 10
Step-by-step explanation:
Given
[tex]\frac{a}{5}[/tex] = - 2
a is divided by 2. The inverse operation to division is multiplication, thus
Multiply both sides by 5 to clear the fraction
a = 5 × - 2 = - 10
Lashonda worked for 13 hours each day for 5 days. Then the next day she worked 6 hours. How many hours did Lashonda work in all?
Answer: 71 hours
Step-by-step explanation:
Find f'(x) for f(x)=cos^2(5x^3).
d/dx cos^2(5x^3)
= d/dx [cos(5x^3)]^2
= 2[cos(5x^3)]
= - 2[cos(5x^3)] * sin(5x^3)
= - 2[cos(5x^3)] * sin(5x^3) * 15x^2
= - 30[cos(5x^3)] * sin(5x^3) * x^2
Explanation:
d/dx x^n = nx^(n - 1)
d/dx cos x = - sin x
Chain rule:
d/dx f(g(...w(x))) = f’(g(...w(x))) * g’(...w(x)) * ... * w’(x)
Step-by-step explanation:
f(x) = cos²(5x³)
f(x) = (cos(5x³))²
Use chain rule to find the derivative:
f'(x) = 2 cos(5x³) × -sin(5x³) × 15x²
f'(x) = -30x² sin(5x³) cos(5x³)
If desired, use double angle formula to simplify:
f'(x) = -15x² sin(10x³)
Find the value for θ.
sinθ=cos(θ−18.5)
Question 6 options:
35.75°
71.5°
54.25°
161.5°
Answer:
[tex]\theta=54.25\°[/tex]
Step-by-step explanation:
we know that
When the sine of angle X is equal to the cosine of angle Y, then angle X and angle Y are complementary angles
so
[tex]X+Y=90\°[/tex]----> equation A
In this problem
[tex]X=\theta[/tex]
[tex]Y=(\theta-18.5)[/tex]
substitute in the equation A
[tex]\theta\°+(\theta-18.5)\°=90\°[/tex]
[tex]2\theta=90+18.5[/tex]
[tex]2\theta=108.5[/tex]
[tex]\theta=54.25\°[/tex]
Eric is swimming along the surface of the sea. He uses
positive numbers to represent elevations above the
surface of the sea and negative numbers to represents
depths under the surface of the sea.
Mark is sitting on the deck of a ship above Eric, and Ariel
is diving beneath Eric.
Who could be at an elevation of -3 m?
Choose 1 answer:
©
Ariel
©
Eric
©
Mark
Answer:
Ariel
Step-by-step explanation:
Ariel is diving which is below the surface of the water
Answer:
ariel
Step-by-step explanation:
I NEED FAST HELP!!!!!!!!!!!!!!!!!!!
Answer:
The student is expected to spend 15.4 hours doing homework
Step-by-step explanation:
The scattered plot shows there is a close correlation between the variables. A line of best fit will go through the 'center' of the points. Since we are not required to find an exact line, we'll draw it in red color as shown below
To know the equation of that line, we must take two clear points of it from the graph. We'll pick (28,4) and (4,25)
The equation of a line, given two points (a,b) and (c,d) is
[tex]\displaystyle y-b=\frac{d-b}{c-a}(x-a)[/tex]
Using the selected points
[tex]\displaystyle y-4=\frac{25-4}{4-28}(x-28)[/tex]
Simplifying and computing results, the equation is
[tex]\displaystyle y=-\frac{7}{8}x+\frac{57}{2}[/tex]
Using that equation, we can predict how many hours the students will spend doing homework if they spend 15 hours watching TV
[tex]\displaystyle y=-\frac{7}{8}(15)+\frac{57}{2}[/tex]=15.4 hours
So the student is expected to spend 15.4 hours doing homework
ASAP Can someone help with this problems just I only need which formula do I used I just need for 4,5 and 6 just tell me the formulas for Law of Cosines
Explanation:
The formula for law of cosines is:
[tex]a^{2} = b^{2} + c^{2} - 2bc(cosA)[/tex]
This is written at the top of your paper.
The angle is substituted where the capital A is. The side opposite to the angle is the angle name's lowercase. The two other sides are b and c.
Substitute all the information you know, then isolate the variable that you do not know.
When your formula is rearranged to look like this:
[tex]\frac{a^{2} - b^{2} - c^{2}}{- 2bc} = (cosA)[/tex]
Solve the left side and punch into your calculator:
cos⁻¹(left side) to find the angle A.
Prove that if sin (2 + y) = 3 sin (x - y), then tan x = 2 tany.
Answer:
The proof is given below.
Step-by-step explanation:
Given: ( the correct question and ans is as follow )
sin (x + y) = 3sin ( x - y)
To Prove
tan x = 2 tan y
Proof:
[tex]\sin (x+y) = 3\sin (x-y)[/tex]
Using the identities
[tex]\sin (A+B) = \sin A.\cos B + \cos A.\sin B\\and\\\sin (A-B) = \sin A.\cos B - \cos A.\sin B\\[/tex]
we get
[tex]\sin x.\cos y + \cos x.\sin y = 3(\sin x.\cos y - \cos x.\sin y)\\\sin x.\cos y + \cos x.\sin y = 3\sin x.\cos y - 3\cos x.\sin y[/tex]
Now we will take sin x . cos y to the left hand side and cos x . sin y to the right hand side,we get
[tex]3\sin x.\cos y - \sin x.\cos y = 3\cos x.\sin y +\cos x.\sin y\\2\sin x.\cos y =4\cos x.\sin y\\\sin x.\cos y =2\cos x.\sin y \ \textrm{4 divide by 2}\\ \frac{\sin x}{\cos x} =2\times \frac{\sin y}{\cos y} \\\textrm{we know identity }\\\frac{\sin x}{\cos x} = \tan x\\\frac{\sin y}{\cos y} = \tan y\\\therefore \tan x = 2\tan y\ ...............{PROVED}[/tex]
Which of the following is approximately equal to the product of the multiplication problem below?
18/4 × 20/17
A.
10
B.
7
C.
5
D.
4
Answer:
5
Step-by-step explanation:
We have: [tex]$ \frac{18}{4} \times \frac{20}{7} $[/tex]
Simplifying we get: [tex]$ 18 \times \frac{5}{7} $[/tex]
⇒ [tex]$ \frac{90}{17} $[/tex]
This is equal to 5.2 ≅ 5.
So, Option C - 5 is the answer.
What can you conclude about the relationship between the time spent watching tv and the grades received on the quiz?
Answer:
Step-by-step explanation:
It's perfectly logical that as the number of hours spent watching TV increases, the grades received on the quizzes drop. There's a negative correlation between the two variables.
Need help with this math problem
z = 37°
Step-by-step explanation:
The exterior angle theorem says that the sum of two internal angles is equal to the exterior angle
In this case the sum of z and z+4 will be equal to z+41
Writing mathematically
[tex]z + z+ 4 = z + 41\\2z+4 = z + 41\\2z -z = 41 -4\\z = 37[/tex]
Hence
z = 37°
Keywords: Angles, Triangles
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Darren has a piece of wood that is 7 in by 8 in. Explain how he can divide this large rectangle into two small rectangles
Answer:
Cut it in half so that the two pieces are each 7 in by 4 in.
Mika placed $4200 in a savings account which compounds interest continuously at a rate of 2.3%. How much will she have in the account after 3 years? Round to the nearest dollar.
Answer:
$4,500
Step-by-step explanation:
4,200e^3(.023)
What the sum of -1 2/3÷(2 1/5)
Answer:
-20/21
Step-by-step explanation:
I don’t know how to fine the square root
Answer:
Look the square root up on the internet.
Step-by-step explanation:
Original price of a hotel: $240.00 per night.
You are staying four nights because then you get a 25% discount.
State and local taxes and 'resort fee' add up to a 29% surcharge.
How much will you pay for four nights?
Answer:
$ 929
Step-by-step explanation:
Given: Original price of stay in hotel= $240 per night
Discount= 25%
Total taxes and fee = 29%
Now, finding the price of stay for four night.
Using unitary method to solve:
As we know original price of hotel stay per night is $240
∴ Price of four night stay at original price is [tex]240\times 4 = \$ 960[/tex]
Next, 25% discount given on the price of four night stay.
∴ [tex]960 - \frac{25}{100} \times 960 = 960 - 240[/tex]
= [tex]\$ 720[/tex]
∴Price of four night hotel stay after discount is [tex]\$ 720[/tex]
Now, 29% taxes and fees been added to the price.
Price of hotel stay after discount + Taxes paid.
[tex]720 + ( \frac{29}{100} \times 720) = 720 + 209[/tex]
= [tex]\$ 929[/tex]
∴ [tex]\$ 929[/tex] is the price to be paid for four night stay at hotel after discount and taxes.
Maine has one of the lowest sales tax rates in the country. If an item costs $40, you will pay $2 in sales tax. What percent of sales tax will you pay?
You will pay 5% sales tax.
Step-by-step explanation:
Given,
Cost of item = $40
Sales tax = $2
Percent of sales tax = [tex]\frac{Sales\ tax}{Cost\ of\ item}*100[/tex]
[tex]Percent\ of\ sales\ tax=\frac{2}{40}*100\\Percent\ of\ sales\ tax=\frac{200}{40}\\Percent\ of\ sales\ tax=5\%[/tex]
You will pay 5% sales tax.
Keywords: sales tax, division
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Which graph shows the strongest positive correlation?
A. Graph A
B. Graph B
C. Graph C
D. Graph D
Answer:
C
Step-by-step explanation:
the quotient of a number and -7, decreased by 2, is 10
Answer:
The number is -84.
Step-by-step explanation:
-x/7-2=10
-x/7=10+2
-x/7=12
-x=12*7
-x=84
x=-84
2. The sequence 5, 20, 35, 50….. shows the number of sit ups Margie did each week, starting with her first week of the new year.
(a) What is the recursive rule for the sequence?
(b) What is the explicit rule for the sequence?
(a) The recursive rule for the sequence is:
[tex]a_{1}[/tex] = 5 ; [tex]a_{n}=a_{n-1}+15[/tex]
(b) The explicit rule for the sequence is: [tex]a_{n}=15n-10[/tex]
Step-by-step explanation:
The form of the recursive rule of an arithmetic sequence sequence is
[tex]a_{1}[/tex] = first term ; [tex]a_{n}=a_{n-1}+d[/tex] , where
[tex]a_{1}[/tex] is the first term in the sequence[tex]a_{n}[/tex] the nth term in the sequence [tex]a_{n-1}[/tex] the term before the nth term n is the term numberd is the common difference between each two consecutive termsThe form of the explicit rule of nth term of an arithmetic sequence is
[tex]a_{n}=a+(n-1)d[/tex] , where
a is the first termd is the common difference between each two consecutive terms∵ The sequence is 5, 20, 35, 50, ….......
∵ 20 - 5 = 15 , 35 - 20 = 15 and 50 - 35 = 15
∴ The sequence is an arithmetic sequence with a common
difference 15
∵ The form of the recursive rule of the arithmetic sequence is
[tex]a_{1}[/tex] = first term ; [tex]a_{n}=a_{n-1}+d[/tex]
∵ First term = 5
∵ d = 15
∴ [tex]a_{1}[/tex] = 5 ; [tex]a_{n}=a_{n-1}+15[/tex]
(a) The recursive rule for the sequence is:
[tex]a_{1}[/tex] = 5 ; [tex]a_{n}=a_{n-1}+15[/tex]
∵ The form of the explicit rule of nth term of an arithmetic
sequence is [tex]a_{n}=a+(n-1)d[/tex]
∵ a = 5 and d = 15
- Substitute these values in the rule
∴ [tex]a_{n}=5+(n-1)15[/tex]
- Simplify the right hand side
∴ [tex]a_{n}=5+15n-15[/tex]
- Add like terms
∴ [tex]a_{n}=15n-10[/tex]
(b) The explicit rule for the sequence is [tex]a_{n}=15n-10[/tex]
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Jack's mother gave him 50 chocolates to give to his friends at his birthday party. He gave 3 chocolates to each of his friends and still had 2 chocolates left.
Write an equation to determine the number of friends (x) at Jack's party.
Find the number of friends at Jack's party.
friends
Answer:
Equation: 3x + 2 = 50
# of friends: 16
Step-by-step explanation:
3 chocolates each or 3x because what "each" means is not known yet-
3x
Note: Always use x for an unknown value
2 remaining chocolates-
3x + 2
50 total chocolates-
3x + 2 = 50
Remove two to keep the x alone-
3x = 48
Remove the 3 or the "Coefficient" by dividing-
48/3 = 16
x = 16
Equation: 3x + 2 = 50
# of friends: 16
The Bridal Shop bought a dress from a supplier for $105 wholesale and applied a 65% markup to the price. If a 7.5% sales tax were added after a 20% discount was used, what would be the total cost to purchase the dress? A $146.20 B $149.00 C $158.48 D $160.17
Answer:
The correct answer is 149.00.
Step-by-step explanation:
Part = Percent • Whole
Adding a 65% markup to the original price of 105 is simply multiplying the price by the decimal form of the markup, then adding that to the original price. Next, you would find 20% of your sum by multiplying the sum by 0.20. Then you would find 7.5% of that and add this to the price.
Solve:
105 • 0.65 = 68.25 Find 65% of 105
105 + 68.25 = 173.25 Add the markup to the price
173.25 • 0.20 = 34.65 Find the discount of the new price
173.25 - 34.65 = 138.60 Subtract discount from price
138.60 • 0.075 = 10.395 Find sales tax of new price (Or round to 10.40)
138.60 + 10.395 = 148.995 Add sales tax to new price (Or 149)
Because money only goes to the hundredths place, we can either start rounding to that place in the second to last step - rounding 10.395 to 10.40 - or we can round our answer - 148.995 rounds to 149. Either way, we will still get an answer of $149.00.
Hope this helps.
♥A.W.E.S.W.A.N.♥
Answer:
B $149.00
Step-by-step explanation:
105 * 1.65 = 173.25 (100%+ 65%) Price with the markup
173.25 *0.80 138.60 (Price after 20% discount .The price will be the 80%)
138.60 * 1.075 = 148.995 (price with 7.5 sales tax.)
What is an equation that represents the line that passes through the point (-2, 2) and is parallel to
Y=1/2X+ 8?
Answer:
[tex]y = \frac{1}{3}x + 3[/tex]
Step-by-step explanation:
The slope of two parallel straight lines are the same.
Now, the slope of the line [tex]y = \frac{1}{2} x + 8[/tex] is [tex]\frac{1}{2}[/tex] as the straight line equation is in slope-intercept form.
Now, the equation of the straight line in slope-intercept form which is parallel to the above line is [tex]y = \frac{1}{2} x + c[/tex] ............. (1) , where c is any constant.
Now, point (-2,2) is on the line (1) {Given}
So, this point will satisfy the equation.
Hence, [tex]2 = \frac{1}{2} (- 2) + c[/tex]
⇒ c = 3.
Therefore, the equation of the required straight line is [tex]y = \frac{1}{3}x + 3[/tex] (Answer)
What is the slope of the line of the best fit for this scatter plot?
What is the equation of the line of the best fit?
Answer:
see explanation
Step-by-step explanation:
The equation of a line in slope- intercept form is
y = mx + c ( m is the slope and c the y- intercept )
Calculate m using the slope formula
m = (y₂ - y₁ ) / (x₂ - x₁ )
with (x₁, y₁ ) = (2, 7) and (x₂, y₂ ) = (4, 6) ← 2 points on the line
m = [tex]\frac{6-7}{4-2}[/tex] = - [tex]\frac{1}{2}[/tex]
Note the line crosses the y- axis at (0, 8) ⇒ c = 8
y = - [tex]\frac{1}{2}[/tex] x + 8 ← equation of line
Answer : The slope of the line and equation of the line is, [tex]\frac{-1}{2}[/tex] and [tex]y=\frac{-1}{2}x+8[/tex] respectively.
Step-by-step explanation :
The general form for the formation of a linear equation is:
[tex](y-y_1)=m\times (x-x_1)[/tex] .............(1)
where,
x and y are the coordinates of x-axis and y-axis respectively.
m is slope of line.
First we have to calculate the slope of line.
Formula used :
[tex]m=\frac{(y_2-y_1)}{(x_2-x_1)}[/tex]
Here,
[tex](x_1,y_1)=(2,7)[/tex] and [tex](x_2,y_2)=(4,6)[/tex]
[tex]m=\frac{(6-7)}{4-2)}[/tex]
[tex]m=\frac{-1}{2}[/tex]
Now put the value of slope in equation 1, we get the linear equation.
[tex](y-y_1)=m\times (x-x_1)[/tex]
[tex](y-7)=\frac{-1}{2}\times (x-2)[/tex]
[tex]y-7=\frac{-1}{2}x+1[/tex]
[tex]y=\frac{-1}{2}x+1+7[/tex]
[tex]y=\frac{-1}{2}x+8[/tex]
Thus, the slope of the line and equation of the line is, [tex]\frac{-1}{2}[/tex] and [tex]y=\frac{-1}{2}x+8[/tex] respectively.
Write the three digit number for 500+30+8
The figure shown is a rectangle. The green shape in the figure is a square. The blue and white shapes are rectangles, and the area of the blue rectangle is 24 square inches.
A. Write an expression for the area of the entire figure that includes an exponent. Then find the area.
B. Find the dimensions of the entire figure.
Answer:
A. (2 × 6) + (3 × 8) + 6²
72 sq. inches.
B. 9 in. by 8 in.
Step-by-step explanation:
The white shape has dimensions of 2 in. by 6 in. and the green shape is a square.
So, the dimension of the green shape is 6 in. by 6 in.
Therefore, the length of the blue shape is (6 + 2) = 8 in.
Now, given that the area of the blue shape is 24 sq. in.
So, the width of the blue shape is [tex]\frac{24}{8} = 3[/tex] in.
Now, if we consider the total figure, then area of the entire figure = area of the white shape + area of the green shape + area of the blue shape.
= (2 × 6) + (3 × 8) + 6² (Answer)
= 12 + 24 + 36
= 72 sq, inches. (Answer)
Now, the length of the entire figure is (6 + 3) = 9 in. and width of the entire figure is (2 + 6) = 8 in.
Therefore, the dimensions of the entire figure will be 9 in. by 8 in. (Answer)
harry, regan and kelan share £450 in the ratio 2 : 5 : 3 . how much money does kelan get?
Answer:
Kelan gets 135 Euros.
Step-by-step explanation:
First of all you add up the ratio getting 10, with 10 you divide it from 450 getting 45. Then you multiply 3 (Kelan's Part) by 45 getting your answer. Tell me if this helped, i'd appreciate knowing.
This question is based on simple mathematics. Therefore, the answer is £135.
Given:
Harry, regan and kelan share £450 in the ratio 2 : 5 : 3.
We have to determined the money would kelan get.
According to questions,
First of all, adding up the ratios.
We get,
2+5+3 = 10
Regan and kelan share £450. So divided £450 by 10, and solve it further.
We get,
[tex]\dfrac{450}{10} = 45[/tex]
Now, multiplying 45 by 3 (Kelan's part).
We get,
[tex]45\times3= 135[/tex]
Therefore, the money that kelan get is £135.
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Please help quick will give brainliest
Answer:
a(1) = 8, a(n + 1) = a(n) + 5
Checking this:
a(2) = a(1) + 5 = 8 + 5 = 13
a(3) = a(2) + 5 = 13 + 5 = 18
a(4) = a(3) + 5 = 18 + 5 = 23
a(5) = a(4) + 5 = 23 + 5 = 28
Alvin’s age is three times Elga’s age. The sum of their ages is 20. What is Elga’s age?
Answer:
Elga's age is 5.
Step-by-step explanation:
3x=y
x+y=20
-------------
x+3x=20
4x=20
x=20/4
x=5
3(5)=15
y=15
x=5, y=15
y=-4x+2 y=6x-8 in substitution ordered pairs
Answer:
(1, -2).
Step-by-step explanation:
y=-4x+2
y=6x-8
Substitute y = 6x - 8 in the first equation
6x - 8 = -4x + 2
10x = 10
x = 1
So y = 6x - 8
= 6(1) - 8
= -2.
The pair should be (1, -2).
Given information:The equation is y=-4x+2 and y=6x-8
Calculation of pairs:here we Substitute y = 6x - 8 in the first equation
So,
6x - 8 = -4x + 2
10x = 10
x = 1
Now
y = 6x - 8
= 6(1) - 8
= -2.
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Concession stand made a profit of $135 on Saturday and lost $12 on Sunday how much profit did the concession stand make
Answer:
123
Step-by-step explanation:
135 - 12 = 123
The concession stand made $123
What is profit and loss?Profit and loss are the terms used to identify whether a deal is profitable or not. We use these terms very often in our daily lives. If the selling price is greater than the cost price, then the difference between the selling price and cost price is called profit. If the selling price is less than the cost price, then the difference between the cost price and the selling price is called loss.
When, in a transaction, the selling price is greater than the cost price, it means we earn a profit.
When, in a transaction, the cost price is greater than the selling price, it means we incur a loss.
Given:
profit on saturday = $135
loss on sunday = $12
So,
the total profit concession stand made= $135 + (-$12)
= $135 - $12
= $123
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