Answer:
-9
Step-by-step explanation:
-9, -2, 5, 12,.........
The first term is the first number in the sequence
-9
[tex]\sf{ }[/tex]
The first first term in the following arithmetic sequence
-9, -2, 5, 12, .. is -9
A number is raised to the 4 th power, then divided by half the of the original number, and finally increased by 141/2. If the result is 100, what was the orginal number
Answer:
the number is 2.45
Step-by-step explanation:
let the original number = n
[tex]\frac{n^4}{n/2} = \frac{2n^4}{n} = 2n^3\\\\2n^3 + \frac{141}{2} = 100\\\\4n^3 + 141= 200\\\\4n^3 = 200 - 141\\\\4n^3 = 59\\\\n^3 = \frac{59}{4} \\\\n^3 = 14.75\\\\n = \sqrt[3]{14.75} \\\\n = 2.45[/tex]
Therefore, the number is 2.45
At 11:00 a.m., John started driving along a highway at constant speed of 50 miles per hour. A quarter of an hour later, Jimmy started driving along the same highway in the same direction as John at the constant speed of 65 miles per hour. At what time will Jimmy catch up with John?
Answer:
12:05 pm
Step-by-step explanation:
Let z be the number of hours, from 11:00 am, when Jimmy would catch up with John. The time that Jimmy will have to drive to catch up with John is z - 1/4 as he started a quarter of an hour late. When Jimmy would catch up with John, they would have traveled the same distance. Hence
50 z = 65 (z - 1/4)
Solve for t
50z = 65z - 65/4
z = 65/60 = 1.083 hours = 1 hour and 5 minutes
Jim will catch up with John at
11:00 am + 1 hour 5 minutes = 12:05 pm
Answer From Gauth Math
Giải phương trình
2x+6=0
Answer: x = -3
[tex]2x+6=0\\\\2x=-6\\\\x=\frac{-6}{2} =-3[/tex]
Answer:
x= -3
Step-by-step explanation:
Solve the equation:
2x +6 = 0
We have isolate 'x'.
First subtract 6 from both sides
2x = 0-6
2x = -6
Divide each side by 2
x = -6/2
x = -3
Type the correct answer in the box. Use numerals instead of words.
Betty sets up a lemonade stand and charges $1 per glass. It cost her $50 to set up the stand. Which function gives the profit, p, she makes by selling g glasses of lemonade?
The number of glasses of lemonade, g, that Betty needs to sell to make a profit, p, if the setup cost her $50 is given by the function p(g) =
.
Answer:
1g - 50 = p(g)
Step-by-step explanation:
The profit function is,
⇒ p(g) = g - 50
What is an expression?Mathematical expression is defined as the collection of the numbers variables and functions by using operations like addition, subtraction, multiplication, and division.
Given that;
Betty sets up a lemonade stand and charges $1 per glass.
It cost her $50 to set up the stand.
And, We have to find the function gives the profit, p, she makes by selling g glasses of lemonade.
Now, The number of glasses of lemonade sold = g,
And, A profit, p by function p(g)
Setup cost = $50
Since, Charges for 1 glass = 1 $
Hence, Charges for g glasses = 1.g = $g
Here, The cost = $50
Hence, Profit = $g - 50
⇒ p(g) = g - 50
Therefore, The profit function is,
⇒ p(g) = g - 50
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Use the substitution method to find the solution for the system of equations. Write the answer as an ordered pair. 3x+2y=23 (1/2)-y=4
Answer:
x = 7.75 y = -0.125
Step-by-step explanation:
3x + 2y = 23 1/2x - y = 4
2(1/2x - y) = (4)2 1x - 2y = 8
3x + 2y = 23
+ 1x - 2y = 8
4x = 31
x = 7.75
3(7.75) + 2y = 23
23.25 + 2y = 23
2y = -0.25
y = -0.125
find the surface area
Answer:
160π in²
Step-by-step explanation:
The formula for the surface area of a cylinder is: A = 2πrh + 2πr²
From here we can plug in what we know (r = 4, h = 16):
A = 2π(4)(16) + 2π(4²)
A = 128π + 32π
A = 160π in²
The surface area of a cylinder is 160π in².
What is the surface area of a cylinder?The surface area of a cylinder is also called the total surface area of the cylinder.
Suppose that:
Radius of the considered cylinder = 'r' units
Height of the considered cylinder = 'h' units
The formula for the surface area of a cylinder is:
A = 2πrh + 2πr²
From here we can plug in what we know that,
(r = 4, h = 16):
A = 2π(4)(16) + 2π(4²)
A = 128π + 32π
A = 160π in²
Hence, the surface area of a cylinder is 160π in².
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The rate of change is constant in each table. Find the rate of change. Explain what the rate of change means for the situation. (Help ASAP)
Is it a, b, c or d?
Answer:
C.
Step-by-step explanation:
212/4 = 53, so 53/1, or 53 miles are driven every hour.
Solve for a.
a
2
8
a =
✓ [?]
Pythagorean Theorem: a2 + b2 = c2
Enter
Answer: [tex]a=\sqrt{60}[/tex]
Step-by-step explanation:
To solve for a, we want to use Pythagorean Theorem as provided int eh problem. a and 2 are the legs while 8 is the hypotenuse.
[tex]a^2+2^2=8^2[/tex] [exponent]
[tex]a^2+4=64[/tex] [subtract both sides by 4]
[tex]a^2=60[/tex] [square root both sides]
[tex]a=\sqrt{60}[/tex]
Now we know that [tex]a=\sqrt{60}[/tex].
please help me !! :)
Answer: c
Step-by-step explanation:
c is the same and it is the correct answer
15. The perimeter of the triangular field is 540m and its sides are in the ratio 25:12:5 find the area of the field.
Answer:
let the sides be 25x,12x and 5x ......then
25x+12x+5x=540
45x=540
x=25
sides are 25×12=300
12×12=144
5×12=60
we can find area by herons formula
At 5:00 a.m., the temperature outside was 6°F below zero. By noon, it rose by 15°F.
At 7:00 p.m., the temperature dropped by 5°F. What was the evening temperature?
Answer:
The evening temperature is 4° F
Step-by-step explanation:
6° F below 0 = -6.
15° F. -6 + 15 is 9.
9° F. 5° F. 9 - 5 = 4
Which equation is equivalent to -2(2 − 2x) = 4 − 8(1 − x)?
Answer:
x = 0
Step-by-step explanation:
-2(2 − 2x) = 4 − 8(1 − x)
Apply the distributive property:
−2(2 − 2x) = 4 − 8(1 − x)
(−2)(2) + (−2)(−2x) = 4 + (−8)(1) + (−8)(−x)
−4 + 4x = 4 + (−8) + 8x
Combine like terms:
4x − 4 = (8x) + (4+−8)
4x − 4 = 8x + (−4)
4x − 4 = 8x − 4
Subtract 8x from both sides:
4x − 4 − 8x = 8x − 4 − 8x
−4x − 4 = −4
Add 4 to both sides:
−4x − 4 + 4= −4 + 4
−4x = 0
Divide both sides by -4:
-4x/-4 = 0/-4
x = 0
Answer: 0
Step-by-step explanation:
Last year 160 new candidates submitted applications to work for an agency. This year, that number is on target to increase by 25%. There are 6 months left in the year. How many new applications has the agency received so far this year?
Answer:100
Step-by-step explanation:
Given
Last year 160 new candidates submitted to work for agency
It is expected to increase by 25% that is , increase in one year should be
[tex]\Rightarrow 160+160\times 25\%\\\Rightarrow 160(1+0.25)\\\Rightarrow 160\times 1.25\\\Rightarrow 200[/tex]
200 application in the upcoming year. So, in 6 months, agency must have accepted 100 applications.
[tex]x^2-x-6=0[/tex]
Answer:
x = 3 or x = -2
Step-by-step explanation:
x² - x - 6 = 0
(x - 3)(x + 2) = 0
x - 3 = 0 or x + 2 = 0
x = 3 or x = -2
On Monday a post office employee processed a batch of letters, on Tuesday she processed three times as many, and on Wednesday she processed 5,000 cards. In the 3 days she processed 15,000 letters. How many did she process on Tuesday
Let the number of letters processed on Monday = x
She processed 3 times letters on Tuesday.
Therefore, number of letters processed on Tuesday = 3x
Number of letters processed on Wednesday = 5000
Total number of cards processed in 3 days = 15000
Therefore, equation for the situation will be,
x + 3x + 5000 = 15000
4x = 15000 - 5000
4x = 10000
x = 2500
Since, number of letters processed on Tuesday = 3x
Therefore, number of letters processed on Tuesday = 3(2500)
= 7500
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what is the value of x
Answer: 24(option A) is the answer
exterior angle = 360/n
so, n = 15
then, 360/15 = 24
The cost,c(x), for a taxi ride is given by c(x)=3x+2.00, where x is the number of minutes. What does the slope mean for this situation
Answer:
for every minute it will cost 3 dollars
Step-by-step explanation:
c(x)=3x+2.00
The cost to get in the taxi is 2 dollars
The slope is 3
3x means that for every minute it will cost 3 dollars
The diagram below represents which percent?
An area model with 4 shaded sections and 1 unshaded section.
Answer:
25%
Step-by-step explanation:
1 ÷ 4 = 0.25
0.25 x 100 = 25 = 25%
lf y 1/4 · when x=5, find y when x=7. given that y varies directly with x.
y=
Answer:
y= 0.35
Step-by-step explanation:
y 1/4
when x=5,
find y=? when x=7.
given that y varies directly with x.
y = kx
Where k is the constant of proportionality
k= y/x
k= (1/4)÷ 5
k= 0.05
y= kx
y= (0.05)(7)
y= 0.35
I Hope this will helpful...
Help anyone can help me do the question,I will mark brainlest.
Step-by-step explanation:
h) p^2+b^2=h^2
5^2+x^2=8^2
25+x^2=64
x^2=64-25
x^2=39
x=√39
x=6.244998
We know that
p² + b² = h²
Part a
5² + x² = 8²
x² = 64 - 25
x = √39
Part B
4² + 6² = x²
16+36 = x²
√52 = x
√2×2×13 = x
x = 2√13
Must click thanks and mark brainliest
The perimeter of a rectangular plot of land whose length is (2x+5) and width is (x-10) is 80cm. Find the
i)value of x
ii) area
iii)cost of weeding the plot at GHc 0.24 per m²
Answer:
P.=2(2x+5)+2(x-10)=80cm
6x-10=80
x=90/6=15cm
Area= L*W= 35*5=175 squared cm= 0.0175 squared m
Cost= 0.24 * 0.0175 = GHc 0.0042
A parallelogram in which adjacent sides are perpendicular to each other is called a rectangle. The cost of weeding the rectangular plot is 0.0042 GHc.
What is a rectangle?That parallelogram in which adjacent sides are perpendicular to each other is called a rectangle. A rectangle is always a parallelogram and a quadrilateral but the reverse statement may or may not be true.
A.) The perimeter of a rectangular plot of land whose length is (2x+5) and width is (x-10) is 80cm. Therefore, we can write,
Perimeter of the rectangel = 2(L+W)
80 = 2[(2x+5)+(x-10)]
80/2 = 2x+5+x-10
40 = 3x -5
40+5 = 3x
x = 15
Hence, the value of x is 15.
B.) The length of the rectangle = (2x+5) = 2(15)+5 = 35 cm = 0.35 m
The width of the rectangle = (x-10) = 15-10 = 5 cm = 0.05 m
Now, the area of the rectangle = L×B = 0.35m × 0.05m = 0.0175m²
C.) Given the cost of weeding 1m² is 0.24, therefore, the cost of weeding the rectangular plot is
Cost = 0.0175 × 0.24 = 0.0042 GHc
Hence, the cost of weeding the rectangular plot is 0.0042 GHc.
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7+3√5/3+√5 - 7-3√5/3-√5
Answer:
0
Step-by-step explanation:
We can write the equation in a simpler form so it doesn't look like a mess of numbers:
[tex]7+\frac{3\sqrt{5}}{3}+\sqrt{5} -7 -\frac{3\sqrt{5}}{3}-\sqrt{5}[/tex]
Because we are just adding three terms together and then subtracting those exact terms, we have the answer as 0.
Brainliest 70 Points! Write an equation representing the translation of f(x) = 7x + 3 down 4 units.
The transformation of a function may involve any change. The function, g(x) that represents function f(x) moved 4 units downwards is g(x)=7x-1.
How does the transformation of a function happen?The transformation of a function may involve any change.
Usually, these can be shifted horizontally (by transforming inputs) or vertically (by transforming output), stretched (multiplying outputs or inputs) etc.
If the original function is y = f(x), assuming horizontal axis is input axis and vertical is for outputs, then:
Horizontal shift (also called phase shift):
Left shift by c units: y=f(x+c) (same output, but c units earlier)Right shift by c units: y=f(x-c)(same output, but c units late)Vertical shift:
Up by d units: y = f(x) + d Down by d units: y = f(x) - dStretching:
Vertical stretch by a factor k: y = k × f(x)Horizontal stretch by a factor k: y = f(x/k)Given the function f(x)=7x+3, now, if the function is moved down by d units, then the function can be transformed down wards by 4 units as shown below.
g(x) = f(x) moved down by 4 units
g(x) = f(x) - 4
g(x) = 7x + 3 - 4
g(x) = 7x - 1
Hence, the function, g(x) that represents function f(x) moved 4 units downwards is g(x)=7x-1.
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The formula for the lateral surface area of a cone—that’s the surface that isn’t the base—is π × r × sqrt(h² + r²); h is the height of the cone and r is the radius of its base. A circular #2 pencil is 6 mm in diameter, and a pencil sharpener creates a cone-shaped end that is 20 mm in height. Find the surface area of the sharpened part of the pencil.
Which expression is equal to "13 more than the quotient of n and 8"? *
A) 13n + 8
B) n - 8 + 13
C) n * 8 + 13
D) (n / 8) + 13
Answer:
D
Step-by-step explanation:
The quotient of n and 8 is [tex]\frac{n}{8}[/tex] and 13 more than this is
[tex]\frac{n}{8}[/tex] + 13 → D
2. What is the area of rhombusABCD? (Assume the diagonals of rhombus ABCD are equal).
Answer:
A=pq/2
=4.25·4.25/2
=9.03125
Step-by-step explanation:
If you like my answer than please mark me brainliest
Answer:
Step-by-step explanation:
Diagonal of rhombus bisect each other.
d₁ = AC = 4.25*2 = 8.5 cm
d₂ = 8.5 {Given diagonals are equal}
Area of rhombus = [tex]\frac{d_{1}*d_{2}}{2} \ where \ d_{1} \ and \ d_{2} \ are \ diagonals[/tex]
[tex]=\frac{8.5*8.5}{2}\\\\= \frac{72.25}{2}\\\\= 36.125 \ cm^{2}[/tex]
Find the measure of side C and round to the nearest whole number. Pls help ASAP
Answer:
Step-by-step explanation:
Side a is across from angle A, and side c is the hypotenuse. The trig ratio that utilizes the side opposite and the hypotenuse is the sin of an angle, namely:
[tex]sin(30)=\frac{28}{c}[/tex] and solving that for c:
[tex]c=\frac{28}{sin(30)}[/tex] so
c = 56
10 points please help im confused
What is the volume of the prism?
103.8 cubic inches
114.9 cubic inches
140.6 cubic inches
110.5 cubic inches
Answer:
110.5 cubic inches
Step-by-step explanation:
Base is parallelogram, so area is
A = 4.7×5 = 23.5
Height(h) is 4.7, so volume is,
V = A×h
= 23.5×4.7
= 110.45 ≈ 110.5
Answered by GAUTHMATH
Lusine saw birds and mice eating seeds on the ground. She calculated 12 heads and 39 legs in total. How many birds and mice are on the ground?
Answer:
4.5 birds, 7.5 mice
Step-by-step explanation:
We know that birds have 2 legs and mice have 4. Furthermore, birds have 1 head as well as mice.
If b represents the amount of birds and m represents the amount of mice, because there are only birds and mice here, the total amount of birds and mice (b + m) must equal 12.
b + m = 12
Next, to find the total amount of bird legs, we must add 2 legs for each bird. Another way of putting this is to multiply 2 by the amount of birds, or b * 2. Similarly, the amount of mice legs is equal to m * 4. The total amount of legs is equal to 39, so
2b + 4m = 39
Our two equations are thus
b + m = 12
2b + 4m = 39
One way to solve this is to solve for m in the first equation and plug that into the second. We have
b + m = 12
subtract b from both sides
m = 12-b
substitute that into the second equation
2b + 4(12-b) = 39
2b + 48 - 4b = 39
-2b + 48 = 39
subtract 48 from both sides to isolate the b and its coefficient
-2b = -9
divide both sides by -2 to isolate b
b = 4.5
Therefore, there are 4.5 birds on the ground (there is somehow a half of a bird!)
Plugging that into m = 12-b, we have m = 12-4.5 = 7.5
The freezing point of oxygen is –218.790C and hydrogen is –252.80C. A lab is lowering the temperature inside a fridge. Which freezes first? How much colder does it have to be for both to freeze?
Answer:
Oxygen; 34.01°C
Step-by-step explanation:
The oxygen freezes first as it has a higher (warmer) freezing point. For both to freeze, the temperature must drop a further 34.01°C as:
-218.79 - (-252.8)
= 252.8 - 218.79
= 34.01
