Answer:13
Step-by-step explanation:(2)²+3(3)=4+9=13
Answer:
2a^n+ 3b
Differentiate w.r.t a
2na^n - 1
= 13
2x - 3 = -5
What is X?
Answer: x=-1
Step-by-step explanation:
2x - 3 = -5
2x - 3 +3= -5+3
2x=-2
x=-1
Answer:
x = -1
Step-by-step explanation:
To find x, we have to get x by itself.
2x - 3 = -5
Add 3 to both sides
2x - 3 +3 = -5 +3
2x = -2
Divide by 2 to both sides
2x ÷2 = -2 ÷2
x = -1
Have a good rest of your day! :)
If the surface area is 275 square inches, then what is the radius r ? In other words, evaluate r(275) . Round your answer to 2 decimal places.
When the surface area is 275 square inches, the radius is approximately 6.17 inches.
The entire area that is occupied by the flat surfaces of the cylinder's bases and its curving surface is known as the surface area of a cylinder. A curved surface area and two flat surface areas make up the cylinder's total surface area.
Let's find out more about what a cylinder's surface area is and how to determine a cylinder's total surface area and lateral surface area.
Total surface area of cylinder=[tex]2\pi r^2 + 2\pi rh[/tex]
Let the total surface area of the given cylinder be written as A(x).
[tex]A(x)=2\pi r^2+2\pi rh\\[/tex]
Now given A(x)=275 and h=8 inches.
[tex]A(x)=2\pi r^2+2\pi rh\\or,275=2\pi(r^2+r8)\\or,r^2+r8=275\div 2\pi\\or,r^2+8r+16=87.535+16\\or,(r+4)^2=\sqrt{103.535}\\or,r+4=10.1752\\or,r=6.1752\\or,r\approx6.17[/tex]
The radius is 6.17 inches when the surface area is 275.
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The formula for the nth pentagonal number is
[tex]P_{n}[/tex] = n(3n-1)/2
Use the formula to find the 16th pentagonal number.
The 16th pentagonal number is 376
What is a function?A function can be defined as an expression that explains the relationship between a dependent and an independent variable.
Given the function for the nth pentagonal number as;
Pn = n( 3n -1 )/ 2
To determine the 16th pentagonal number, we need to substitute the value of n as 16
We have;
P16 = 16(3(16) - 1)/ 2
P16 = 16( 48 - 1)/ 2
P16 = 16(47)/ 2
expand the bracket
P16 = 376
Thus, the 16th pentagonal number is 376
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Urgent Please!
• What expression would represent the area of a square with side length 10?
—-
•Part C: What expression would represent the area of a square with side length 20?
—-
•Part D: What expression would represent the increase in area caused by changing the side length from 10 to 20?
Answer: B. 100
C. 400
D. 300
Step-by-step explanation:
A=area of square. s=side length of square.
B. A=s^2
A=10^2
A=100
C. A=20^2
A=400
D. I=Increase in Area
I=20^2 -10^2
I=400-100
I=300
Mia has 7 boxes of cherry tarts. Each box has 8 cherry tarts. Explain how to use an open number line to solve.
Use of open number line is
7 boxes of cherry tarts
Each box has 8 cherry tarts.
Total cheny tarts is
[tex]$$7 \times 8=7+7+7+7+7+7+7+7$$[/tex]
A straight line of numbers is shown visually as a number line. This line is used to compare integers on an endless line that extends on both sides, either horizontally or vertically, at equal intervals. On a horizontal number line, the numbers grow as we walk to the right and drop as we move to the left.
A number line is a visual depiction of numbers on a straight line drawn either horizontally or vertically. It is simple for humans to compare numbers and carry out simple arithmetic operations on them when they are written down on a number line. A number line is said to begin at zero (0). Left of zero, there are only negative numbers, and right of zero, there are only positive numbers. So, on a number line, we may say that the value of numbers grows as we travel to the right. This indicates that there are more numbers on the right than on the left.
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Jessica is putting money into a checking account. Let y represent the total amount of money in the account (in dollars). Let x represent the number of weeks Jessica has been adding money. Suppose that x and y are related by the equation =+55030xy.
After differentiating, the amount when x=0 yields starting amount,
300 dollars.
What is diffrentiation?
A technique for determining a function's derivative is differentiation.A technique for determining a function's derivative is differentiation. Mathematicians use a procedure called differentiation to determine a function's instantaneous rate of variation based on a particular variables. The most typical illustration is velocity, which is the rate at which a distance changes in relation to time.In mathematics, differentiation is used to determine change rates.Differentiating the given equation with respect to x,
Given equation,
y= 55x+ 300
[tex]\frac{dy}{dx} =\frac{d(55x+300)}{dx} = 55+0 =$55[/tex] dollars.
The amount when x=0 yields starting amount,
y=55(0)+300=300
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A rectangular picture has dimensions of length (2x-1) inches and width (x+7) inches. The area of the picture is 108 in^2. What are the length and width of the picture?
The numerical length and width of the rectangular picture are 9in and 12in respectively.
What are the length and width of the picture?Area of a rectangle is expressed as;
A = length × width
Given the data in the question;
Length = 2x -1Width = x + 7Area = 108in²To determine the numerical length and width of the rectangular picture, first plug the given values into the equation and solve for x.
A = length × width
108 = (2x -1)(x+7)
Expand
108 = 2x² + 14x - 1x -7
108 = 2x² + 13x -7
Reorder
2x² + 13x -7 = 108
2x² + 13x - 7 - 108 = 0
2x² + 13x - 115 = 0
Solve by grouping
(x-5)(2x+23) = 0
x-5 = 0, 2x+23 = 0
x = 5, 2x = -23
x = 5, x = -23/2
x = 5, x = -11.5
But the dimension cannot be negative, hence;
x = 5
Next, determine the numerical length and width.
Length = 2x - 1 = 2(5) - 1 = 10 - 1 = 9in
Width = x + 7 = 5 + 7 = 12in
Therefore, the numerical length and width of the rectangular picture are 9in and 12in respectively.
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For the equation, find three ordered pair solutions by completing the table. Then use any two of the ordered pairs to graph the equation.
x - y = 4
Answer:
Please see picture below.
Step-by-step explanation:
A teacher records your grade points as 197. Your notes say that you have 205 points. What is
your percent error?
The percent error is 8%
How to calculate the percent error ?The formular for percent error is approximate value -exact value/exact value multiplied by 100
The approximate value is 197 points
The exact value is205 points
Percent error = 197 - 205 /205 × 100
= -8/205 × 100
= 0.0390 × 100
= 3.9
Hence the percent error is 8%
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A rectangle has a length 3x + 1 of and a width of Write an expression for the 3-9
perimeter of the rectangle.
The expression for the perimeter is P = 12x - 16
How to write an expression for the perimeter?The given parameters are
Length = 3x + 1
Width = 3x - 9
The perimeter is calculated as
P = 2 * (Width + Length)
So, we have
P = 2 * (3x + 1 + 3x - 9)
Evaluate
P = 2* (6x - 8)
Expand
P = 12x - 16
Hence, the expression for the perimeter is P = 12x - 16
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Just like Earth, other planets have
seasons. In fact, Neptune's seasons last
for 40 years! How many days would
winter last? (Hint: A year is 365 days).
Winter would last for 14,600 days
How to calculate the number of days that winter would last ?Planet can be described as celestial bodies that move around the sun. The earth and Neptune are typical examples of planets. There are 8 planets in the solar system.
Other planets have different seasons same way as Earth
Neptune's season last for 40 years
Therefore the number of days that winter would last can be calculated by multiplying the number of years which is 40 by the number of days in a year which is 365
1 year is 365 days
Since it 40 years then we multiply by 365
= 365 × 40
= 14,600
Hence Winter would last for 14,600 days
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Find the -intercept and the slope of the line 4x8y=3. Write your answers in simplest form.
The slope of the straight line is -1/2 whereas the y-intercept is 3/8.
What is defined as the equation of line in slope intercept form?Recognize that the y-intercept is the point at which the graph intersects the y-axis; that's where we usually begin.
Determine the slope first, then the y-intercept. For the time being, just consider if the slope is either positive or negative.The following are the variables that we will begin to use in our function:slope = mb = the y-interceptThe formula is y = mx + b. The variables x and y remain alphabets, but m and b have been replaced by numbers (for example, y = 2x + 4, slope = 2, and y-intercept = 4).Because the two quantities in the equation are now the slope and the intercept, this equation is known as the slope-intercept form.
y = mx + b
Remember that the slope (m) is the number multiplied by x, while the intercept (b) is indeed the number added or subtracted.
The given equation is;
4x + 8y = 3
Re-arranging the equation;
8y = -4x + 3
Divide the whole equation by 8.
y = -4x/8 + 3/8
Further simplifying;
y = -x/2 + 3/8
Comparing the result with the general form of equation.
m = -1/2; which is the slope.
c = 3/8; which is the y-intercept.
Thus, the values for slope and y-intercept are estimated.
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The correct question is-
Find the -intercept and the slope of the line 4x + 8y=3. Write your answers in simplest form.
A 10-lb bag of flour costs $3.69. A
5-lb bag costs $1.55. How much can
you save if you buy the big bag
instead of 2 small bags?
$0.29 you save if you buy the big bag instead of 2 small bags .
The unitary method is a strategy that determines the value of many units based on the value of a single unit in addition to calculating the value of a single unit using the values of multiple units.
We must divide the value of one thing by the number of other items we wish to calculate the value of before multiplying that result by one.
From the question,
A huge bag of flour weighing 10 lbs costs $3.69 in total.
Currently, one 5-lb small bag costs $1.55.
Consequently, two 5-lb little bags cost $3.10 each.
Cost difference equals big bag cost minus two small bag expenses.
The price difference is equal to $3.69 minus $3.10.
$0.29 is the cost difference.
By purchasing two small bags of floor instead of one large bag, you will save $0.29.
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Translate the sentence into an equation.
Five times the sum of a number and 3 equals 7.
Use the variable x for the unknown number.
Answer:
(5x) + 3 = 7
Step-by-step explanation:
Times means 'The answer when you multiply' So we are working in multiplication. ( x )
5x is the multiplication.
It says 'and' which can also mean addition. So we add 3. So far our equation is: (5x) + 3 (Brackets are needed as we are multiplying 5 by x and not multiplying 5 by x+3)
Lastly it says the answer must be 7 so we add that at the end. So the answer is:
(5x) + 3 = 7
Please solve. NO EXPLAINATION NEEDED. I NEED ANSWER FAST
Answer: x=28/3
Step-by-step explanation:
6/8=7/x
3/4=7/x
3x/4=7
3x=28
x=28/3
Answer: the answer is 9 or 9.333333
Question Write an equation of the line that passes through point (−3, 8) and has the slope m=−2.
Answer:
y = - 2x + 2
Step-by-step explanation:
[tex]y-8=-2(x-(-3))\\y-8=-2(x+3)[/tex]
[tex]y-8=-2x-6[/tex]
[tex]y=-2x-6+8[/tex]
[tex]y=-2x+2[/tex]
Hope this helps
Which of the following is not a function for all values of x?
Answer:
f(X) = ( - X) ½
is the answer
pls brainliest
What transformation carries the parallelogram below onto itself?
M(-2,3),
H(-4,-3)
A(4,3)
T(2,-3)
The transformation that carries the parallelogram below onto itself is a rotation by 180 degrees
How to determine the transformation?The coordinates are given as:
M(-2,3),
H(-4,-3)
A(4,3)
T(2,-3)
The rule of rotation by 180 degrees is
(x, y) = (-x, -y)
When the above rule is applied, we have
M(-2,3), = T(2,-3)
H(-4,-3) = A(4,3)
A(4,3) = H(-4,-3)
T(2,-3) = M(-2,3)
Hence, the transformation that carries the parallelogram below onto itself is a rotation by 180 degrees
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i need help on this! its due today
Answer:
a) It's growing by 1 Hexagon in each term
b) (Self Explanatory, but if you still font know, just add 1 hexagon on the bottom tail)
c) 1-4
2-5
3-6
4-7
5-8
d) 1 hexagon is added each time
e) Common Difference = a1 - a
= 5 - 4
= 1
f) Consider the equation n + 3
where n is the number of terms.
In this case, n = 12
= 12 + 3
= 15 Hexagons
g) f(n) = 4 + 1(n-1)
f(1) = 4 + 1 ( 1 - 1)
f(1) = 4 + 1 (0)
f(1) = 4 + 0
f(1) = 4
h) (Forgive me, I actually don't know the answer for this one :'( )
Sam had 233 dollars to spend on 7 books. How much did each book cost ?
Answer:
0
3
3
7
2
3
3
-
0
2
3
-
2
1
2
3
-
2
1
2
Step-by-step explanation:
SOOOOOOOOOO THE ANSWER 33 with the reamder of 2
Use units to help you answer the question. If necessary, round your answer to two decimal places.
An acre is equal to 43,560 square feet, and there are 5280 feet in a mile. If a farm has the shape of a rectangle measuring 0.9 miles by 1.5 miles, what is the area of the farm in acres?
The area of the farm in acres is 864 acres.
How to find the area of a farm?An acre is equal to 43,560 square feet, and there are 5280 feet in a mile.
Therefore,
1 mile = 5280 feet's
The farm has the shape of a rectangle measuring 0.9 miles by 1.5 miles. Therefore, let's convert to feet's
1 mile = 5280 feet's
0.9 miles = ?
cross multiply
length = 0.9 × 5280 = 4752 feet
1 mile = 5280 feet's
1.5 miles = ?
width = 1.5 × 5280 = 7920 feet's
Hence,
area of the farm = 4752 × 7920
area of the farm = 37635840
Therefore, the area of the farm in acres can be calculated as follows:
43560 ft = 1 acre
37635840 ft = ?
cross multiply
area of farm = 37635840 / 43560
area of the farm = 864 acres.
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9x = 7x + 22 need help
Answer:
x=11
Step-by-step explanation:
9x=7x+22
9x-7x=22
2x=22
2x/2=22/2
x=11
Use the given point, P, on the unit circle to find the value of sine and cosine of t. Answer exactly.
sin(t)
P is at the point (0, - 1).
cos(t)
=
=
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Value of Sine and Cosine of T is -1 and 0 respectively.
According to the question statement, P is at the point (0,-1)
We are supposed to find the value of trigonometric ratios sine and cosine of T
Let Point P (0,-1)
[tex]x=0, y=-1[/tex] and radius r = 1
[tex]sin(t) = \frac{y}{r}\\sin(t)=\frac{-1}{1} \\sin(t)=-1[/tex]
Therefore, sine of t is -1
[tex]cos(t)=\frac{x}{r} \\cos(t)=\frac{0}{1} \\cos(t)=0[/tex]
Therefore, cosine of t is 0
Trigonometric ratios: Sine (sin), cosine (cos), tangent (tan), cotangent (cot), cosecant (cosec), and secant are the six trigonometric ratios (sec). A branch of mathematics called trigonometry in geometry deals with the sides and angles of a right-angled triangle. Trigonometric ratios are therefore assessed in relation to sides and angles.To learn more about trigonometric problems, click on the link given below:
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Rewrite 9/4 as a mixed number
Can someone help me with this part and explain me, please?
Susan Marciano invested part of her $12,000 bonus in a fund that paid 8% profit and invested the rest in stock that suffered a 3% loss. Find the amount of each investment if her overall net profit was $300 .
Answer:y=mx+b
Step-by-step explanation:
Answer:
Let x be the amount invested in funds that earned 8%.
Then the amount invested in stock that suffered 3% loss is 18,000 - x.
The profit from investment in funds is 8%x
The loss from investment in stock is 3%(18,000 - x).
The net profit is 8%x - 3%(18,000 - x).
As the net profit given in the problem is $780, we have:
8%x - 3%(18,000 - x) = 780
Step-by-step explanation:
-1/3y+4x=3 solve for y
Answer: y = 12x − 9
Step-by-step explanation:
Let's solve for y
-1/3y +4x = 3
Step 1: Add -4x to both sides.
4x + -1/3y + -4x = 3 + -4x
-1/3y = -4x+3
Step 2: Divide both sides by (-1)/3.
-1/3y / -1/3 = -4x+3 / -1/3
y = 12 - 9
What is the linear speed in miles per hour of the tip of a lawnmower blade spinning at 2800 revolutions per minute in a lawnmower that cuts a path that is 26 inches wide?
What is the angular speed in degrees per hour?
The linear speed in miles per hour of the tip of a lawnmower blade spinning is 0.0601509076 miles per hour and angular velocity is 293.276 rad/hr.
What is linear speed?The measurement of a moving object's actual distance traveled is called linear speed. Linear speed is the rate of motion of an item along a straight line. It is the distance traveled along a linear path in the allotted amount of time.
2800 rotations per minute on a lawnmower blade.
Specifically, the frequency of the blade is 2800 revolutions per hour,
f = 2800 / 60, or 46.66.
The angular velocity is
ω = 2πf
where f = frequency
ω = 2 × 3.14 × 46.7
ω = 293.276 rad/hr
The diameter of the circle centered at the blade's middle determines the path's breadth.
26 inches in diameter
radius = 26 / 2 = 13
13 inch = 0.0002051 miles
Velocity is given by -
V = ωR
V = 293.276 × 0.0002051
Velocity = 0.0601509076 miles per hour
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What is an equation of the line that passes through the point ( − 3 , − 1 ) (−3,−1) and is perpendicular to the line x − 2 y = 6 x−2y=6?
The equation of the line passing through given points (-3, -10) and perpendicular to other is y + 2x + 7 = 0.
When the equation of line in point-slope form?A line's equation in point slope form is (y - y₁) = m. (x – x₁). As a result, the equation of a line with slope m passing through the origin is: y - 0 = m(x = 0), i.e. y = mx.where m is the line's slope and (x₁, y₁) are the coordinates of a provided point on the line .The equation of the perpendicular line is given as;
x − 2y = 6
Write the equation in standard form;
y = x/2 - 3
Where, slope of the line m₁ is (1/2) and y -intercept is (-3).
The other line passing perpendicular on this line has a slope: m₂.
The relation between slopes of perpendicular lines are-
m₁ × m₂ = -1
m₂ = -1/m₁
m₂ = -1/(1/2)
m₂ = -2
Now, the coordinates of the line are: (-3, -1)
The equation of the line will be;
(y - y₁) = m₂ (x – x₁)
Put the values;
(y - (-1)) = -2(x - (-3))
y + 1 = -2x - 6
y + 2x + 7 = 0
Thus, the equation of line is y + 2x + 7 = 0.
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HELP PLEASE I NEED HELP! Please solve
4(0.5n-6)=n-0.25(12+8n)
Brainiest given
Answer: -21
Step-by-step explanation: