Simplify each exponential expression using the properties of exponents and match it to the correct answer.
Answers
The match of solutions with the exponential expressions is
1) [tex]\frac{(2(3^{-2}) )^{3} (5(3^{2}) )^{2} }{(3^{-2})((5)(2))^{2}}=2[/tex]
2) [tex](3^3) (4^0)^2 (3(2))^{-3} (2^2)=1/2[/tex]
3) [tex]\frac{(3^74^7) (2(5))^{-3} (5)^2}{(12^7) (5^{-1}) (2^{-4})} =2[/tex]
4) [tex]\frac{(2(3))^{-1} (2^0)}{(2(3))^{-1}}=1[/tex]
What are properties of exponents?The base will be multiplied by itself a certain number of times, as indicated by the exponent (also known as a power or degree).
What are the formulae/ properties for exponents?Formulae for solving exponents are referred to as exponents formulas. The exponent of a number is written as [tex]x^{n}[/tex], which means that x has been multiplied by itself n times.
[tex]x^{n}(x^{m})=x^{n+m} \\\frac{x^{n} }{x^{m} }=x^{n-m} \\(x^{n} )^{m} =x^{nm} \\((x)(y))^{n}=x^{n}(y^{n} \\x^{0}=1[/tex]
1) the solution of the first expression will be
[tex]\frac{(2(3^{-2}) )^{3} (5(3^{2}) )^{2} }{(3^{-2})((5)(2))^{2}}[/tex]
[tex](2^3) (3^{-6} ) (5^2) (3^4) / (3^{-2}) (10^2)= (2.2^2.5^2) (3^{-6}.3^4) / (3{^-2}) (10^2)= (2)(10^2) (3^{-2}) / (3^{-2}) (10^2)\\=2[/tex]
2)The solution of the second expression will be
[tex](3^3) (4^0)^2 (3(2))^{-3} (2^2)[/tex]
Any number with power zero is 1.
So,
[tex](3^3) (1^2) (3^{-3}) (2^{-3}) (2^2)= (2^{(-3+2)})=2^-1\\= 1/2[/tex]
3) The solution of third expression will be
[tex]\frac{(3^74^7) (2(5))^{-3} (5)^2}{(12^7) (5^{-1}) (2^{-4})} \\= \frac{(12^7) (2^{-3}) (5^{-3}) (5^2)}{(12^7) (5^{-1}) (2^{-4})} =\frac{(2^-3) (5^{(-3+2)})}{(5^{-1}) (2^{-4})} = \frac{(2^{-3}) (5^{-1})}{(5^{-1}) (2^{-}4)} = \frac{1}{(2^{-1})} = 2[/tex]
4) The solution to the forth expression will be
[tex]\frac{(2(3))^{-1} (2^0)}{(2(3))^{-1}}\\=2^{0}\\ =1[/tex]
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Answer:
The person above litteraly gave you the answer just reread the first equations and then you will figure it out
Step-by-step explanation:
Related Questions
Drag the factors to the correct locations on the image.
Each factor can be used more than once, but not all factors will be used. What is the factored form of this expression? x3 - 6x2 - 9x + 54
Tiles go here
( )( )( )
Tile options:
x - 6
x - 9
x + 9
x - 3
x + 3
x + 6
Answers
Answer: x-6, x+3, x-3
Step-by-step explanation;
Split the equation into two.
x2(x-6)-9(x-6)
(x-6) is seen as one of the tiles. Now work on x2-9
x2-9 is a difference of squares meaning the last two are (x+3) and (x-3).
How to Simplify using suitable property: (-3/7) * 6/5 + (3/2) - (6/5) * 1/14
I will mark the first answerer as brainliest
Answers
The value of the given expression is 9/10. The properties of real numbers, such as commutative and distributive are used for solving this expression.
What are the required properties for solving an expression?The properties are:
Associative property: (a + b) + c = a + (b + c) Commutative property: a + b = b + c or a × b = b × aDistributive property: a × (b + c) = a × b + b × cCalculation:The given expression is
(-3/7) × 6/5 + (3/2) - (6/5) × 1/14
applying commutative law (a + b = b + c)
⇒ (-3/7) × 6/5 - (6/5) × 1/14 + (3/2)
again applying commutative law (a × b = b × a)
⇒ (-3/7) × 6/5 - 1/14 × (6/5)+ (3/2)
applying distributive law (a × (b + c) = a × b + b × c) in reverse order
⇒ (-3/7 - 1/14) × (6/5)+ (3/2)
⇒ (-7/14) × (6/5)+ (3/2)
⇒ (-1/2) × (6/5)+ (3/2)
⇒ (-6/10) + (3/2)
⇒ (-6 + 15)/10
⇒ 9/10
Thus, the required value is 9/10 and the suitable properties are commutative and distributive.
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The smallest bone on the body, the stirrup-shaped stapes found in the middle ear, has a typical length of less than 0.33 cm. how long in inches is the typical maximum length of the stapes?
Answers
Answer:
0.13 inches.
Step-by-step explanation:
1 inch = 2.54 cm
So 1 cm = 1/ 2.54 in
0.33 cm = 0.33/2.54 in
= 0.13 inches.
Marissa is selling paintings for $15 each and bracelets for $7 each. Her goal is to sell at least $800 in products, and she must sell at least 60 bracelets. Which of the following combinations will satisfy these constraints?
Answers
The first inequality is represented by the purple area seen in the picture and the second inequality by the black area seen in the picture, the solutions set is the region where the two areas overlap each other.
How to find posible solutions from a system of inequalities
In this question we have two inequalities representing constraints that Marissa should satisfy, provided that she wants to make a profit in selling paintings and bracelets.
The first inequality represents the minimum profit required from the sales of paintings (x) and bracelets (y) and the second one represents the minimum number required of sold bracelets. The two inequalities are described below:
15 · x + 7 · y ≥ 800 (1)
y ≥ 60 (2)
Since there are more than one solution, we decided to define a solutions set with the help of graphing tool. The first inequality is represented by the purple area seen in the picture and the second inequality by the black area seen in the picture, the solutions set is the region where the two areas overlap each other.
Remark
The statement is incomplete and such issue cannot be resolved. We decided to modify the statement as follows:
Marissa is selling paintings for $ 15 each and bracelets for $ 7 each. Her goal is to sell at least $ 800 in products, and she must sell at least 60 bracelets. Please show the set of all possible solution that will satisfy these constraints?
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Answer:
26 paintings and 61 bracelets
Step-by-step explanation:
if you do 26x15=390 and 61x7=427
390+427=817
so the answer is 26 paintings and 61 bracelets
also, I took the test so I know its right
Thanks for the help in advance
Answers
Answer:
60
Step-by-step explanation:
Answer: 60
Step-by-step explanation:
7x-x
simplify please
Answers
Based on the given task content; the simplification of 7x - x to its simplest form is 6x.
SimplificationSimplify 7x - x
There are two terms in the expressionThe terms are;7x and -x
The terms both have the same variable xThe term -x have an imaginary coefficient of 1So,
7x - x
= 6x
Therefore, 6x is the result of the simplification of 7x - x to its simplest form.
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can someone pls solve this
Answers
The value of Z in given equation is -55.
According to the statement
We have given that a linear equation which is
2 = 1/5z +13
And from this equation we have to find the value of the z.
So, For this purpose
we know that the
A linear equation is an algebraic equation of the form y=mx+b. involving only a constant and a first-order (linear) term, where m is the slope and b is the y-intercept.
So, The equation is
2 = 1/5z +13
1/5z +13-2 = 0
1/5z +11 = 0
z = -11*5
z = -55
here z + 55 =0
So, The value of Z in given equation is -55.
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4m^2-5m when m= -4 solve
Answers
Answer:
84
Step-by-step explanation:
4 (-4)^2 - 5(-4)
4 × 16 - 5 × -4
64 + 20
84
Box a has a volume of 32 cubic meters. box b is similar to box a. to create box b, box a's dimensions were tripled. what is the volume of box b?
Answers
The volume of box B is (A) 864 cubic meters.
What is volume?The amount of three-dimensional space enclosed by a closed surface is expressed as a scalar quantity. For example, the space occupied or contained by a substance or 3D object.Volume is frequently mathematically quantified using the SI-derived unit, the cubic meter.To find the volume of box B:
We have been assigned a volume of 32 cubic meters. The cubic root of 32 yields the box's dimensions, which are 3.1748 x 3.1748 x 3.1748 meters. Meters when the dimensions are tripled: 9.5244 x 9.5244 x 9.5244= 864 cubic meters.
Therefore, the volume of box B is (A) 864 cubic meters.
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The complete question is given below:
Box A has a volume of 32 cubic meters. Box B is similar to box A. To create box B, box A's dimensions were tripled. What is the volume of box B?
a. 864 m3.
b. 288 m3.
c. 96 m3.
d. 32 m3
PLEASE HELP IM BEGGINGGGGGGG ANSWERRRRRR
Answers
Answer:
Step-by-step explanation:
i'd say with the given info it will be the same
i cant get this wrong or i fail
Answers
Answer: x < -2
Step-by-step explanation:
[tex]\frac{1}{2} x-7 < -8[/tex]
First add 7 to both sides
[tex]\frac{1}{2} x-7 +7 < -8+7[/tex]
[tex]\frac{1}{2} x < -1[/tex]
Now multiply by 2 to cancel out 1/2 and leave you with x
[tex]2*\frac{1}{2} x < -1(2)[/tex]
[tex]x < -2[/tex]
A 400 L tank is filled with pure water. A copper sulfate solution with a concentration of 20 g/L flows into the tank at a rate of 4 L/min. The thoroughly mixed solution is drained from the tank at a rate of 4 L/min. a. Write a differential equation (initial value problem) for the mass of the copper sulfate. b. Solve the differential equation
Answers
(a) Let [tex]C(t)[/tex] denote the amount (in grams) of copper (II) sulfate (CuSO₄) in the tank at time [tex]t[/tex] minutes. The tank contains only pure water at the start, so we have initial value [tex]\boxed{C(0)=0}[/tex].
CuSO₄ flows into the tank at a rate
[tex]\left(20\dfrac{\rm g}{\rm L}\right) \left(4\dfrac{\rm L}{\rm min}\right) = 80 \dfrac{\rm g}{\rm min}[/tex]
and flows out at a rate
[tex]\left(\dfrac{C(t)\,\rm g}{400\,\mathrm L + \left(4\frac{\rm L}{\rm min} - 4\frac{\rm L}{\rm min}\right) t}\right) \left(4\dfrac{\rm L}{\rm min}\right) = \dfrac{C(t)}{100} \dfrac{\rm g}{\rm min}[/tex]
and hence the net rate of change in the amount of CuSO₄ in the tank is governed by the differential equation
[tex]\boxed{\dfrac{dC}{dt} = 80 - \dfrac C{100}}[/tex]
(b) This ODE is linear with constant coefficients and separable, so we have a few choices in how we can solve it. I'll use the typical integrating factor method for solving linear ODEs.
[tex]\dfrac{dC}{dt} + \dfrac C{100} = 80[/tex]
The integrating factor is
[tex]\mu = \exp\left(\displaystyle \int \frac{dt}{100}\right) = e^{t/100}[/tex]
Distributing [tex]\mu[/tex] on both sides gives
[tex]e^{t/100} \dfrac{dC}{dt} + \dfrac1{100} e^{t/100} C = 80 e^{t/100}[/tex]
and the left side is now the derivative of a product,
[tex]\dfrac d{dt} \left[e^{t/100} C\right] = 80 e^{t/100}[/tex]
Integrate both sides. By the fundamental theorem of calculus,
[tex]e^{t/100} C = e^{t/100}C\bigg|_{t=0} + \displaystyle \int_0^t 80 e^{u/100}\, du[/tex]
The first term on the right vanishes since [tex]C(0)=0[/tex]. Then
[tex]e^{t/100} C = 8000 \left(e^{t/100} - 1\right)[/tex]
[tex]\implies \boxed{C(t) = 8000 - 8000 e^{-t/100}}[/tex]
An apartment building contains 12 units consisting of one- and two-bedroom apartments that rent for $360 and $450 per month, respectively. When all units are rented, the total monthly rental is $4,950. What is the number of two-bedroom apartments?
Answers
Answer:
There are 7 two bed bedroom apartments.
Step-by-step explanation:
Solution Given:
let the one bedroom apartment be x and two bedroom apartment be y.
By the question we can make an equation as
x+y=12
or y=12-x............................[1]
Again:
$360x+$450y=$4,950
Now substituting value of y, we get
$360x+$450(12-x)=$4,950
Opening Bracket
$360x+$5400-$450x=$,4,950
solving equation
-90x=-450
dividing both side by -90,we get
x=5
again,
substituting value of x in equation 1,we get
y=12-5=7 two bed bedroom apartments.
Let, x represents the number of one bedrooms and 12 - x represents the number of two bedrooms.
According to the question,
[tex]360x + 450(12 - x) = 4950[/tex]
[tex]360x + 5400 - 450x = 4950[/tex]
[tex]5400 - 4950 = 450x - 360x[/tex]
[tex]450 = 90x[/tex]
[tex] \frac{450}{90} = x[/tex]
[tex]5 = x[/tex]
Therefore, one bedrooms = x = 5
For number of two bedrooms which is equal to 12 - x
= 12 - 5
= 7
So your required answer is 7
If two 12-sided dice are rolled what is the probability that both numbers will be even?
Answers
Answer:
probability result of sample space would result in 12/144
Step-by-step explanation:
as result there is 12 numbers on each dice, blth have exact same numbers, resulting in 144 combinations ti be thrown as sample space event outcome wluld be;
1/1 1/2 1/3 1/4 1/5 1/6 1/7 1/8 1/9 1/10 1/11 1/12
2/1 2/2 2/3 2/4 2/5 2/6 2/7 2/8 2/9 2/10 2/11 2/12
3/1 3/2 3/3 3/4 3/5 3/6 3/7 3/8 3/9 3/10 3/11 3/12
4/1 4/2 4/3 4/4 4/5 4/6 4/7 4/8 3/9 4/10 4/11 4/12
5/1 5/2 5/3 5/4 5/5 5/6 5/7 5/8 5/9 5/10 5/11 5/12
6/1 6/2 6/3 6/4 6/5 6/6 6/7 6/8 6/9 6/10 6/11 6/12
7/1 7/2 7/3 7/4 7/5 7/6 7/7 7/8 7/9 7/10 7/11 7/12
8/1 8/2 8/3 8/4 8/5 8/6 8/7 8/8 8/9 8/10 8/11 8/12
9/1 9/2 9/3 9/4 9/5 9/6 9/7 9/8 9/9 9/10 9/11 9/12
10/1 10/2 10/3 10/4 10/5 10/6 10/7 10/8 10/9 10/10 10/11 10/12
11/1 11/2 11/3 11/4 11/5 11/6 11/7 11/8 11/9 11/10 11/11 11/12
12/1 12/2 12/3 12/4 12/5 12/6 12/7 12/8 12/9 12/10 12/11 12/12
giving 12 matching numbers in a 144 possible rolled outcome
mathematic formula would be P(A) = n(A)/n(S)
As P(A)= probabolity of event A
n(A)= number of favouravle outcome
n(S)= total number of outcome in sample space
giving
12=2/144=0,0138888889
A fourth-degree polynomial with a leading coefficient of 1 has gone through several transformations, including a vertical compression by a scale factor of 1/3 and a reflection across the x-axis. Two of the zero polynomials are -i and 3i.
Find a y-intercept of this polynomial, if it exists
Answers
The y-intercept of the resulting polynomial is equal to - 3.
How to derive a fourth-degree polynomial generated by rigid transformations
Herein we assume that the other two zeros of the polynomial are i and - i 3, otherwise the polynomial will have at least a complex number as coefficient of the expression. This is because we need to find values from a Cartesian plan, whose ordered pairs are real numbers.
Initially, we have the following expression by algebra properties:
f(x) = (x + i) · (x - i) · (x + i 3) · (x - i 3)
f(x) = (x² + 1) · (x² + 9)
f(x) = x⁴ + 10 · x² + 9
Then, we proceed to use the two rigid transformations described in the statement. Please notice that rigid transformations are transformations applied on polynomials such that Euclidean distance is conserved:
Vertical compression
f'(x) = (1 / 3) · f(x)
f'(x) = (1 / 3) · (x⁴ + 10 · x² + 9)
f'(x) = (1 / 3) · x⁴ + (10 / 3) · x² + 3
Reflection across the x-axis
g(x) = - f'(x)
g(x) = - (1 / 3) · x⁴ - (10 / 3) · x² - 3
The y-intercept is found for x = 0:
g(0) = - (1 / 3) · 0⁴ - (10 / 3) · 0² - 3
g(0) = - 3
The y-intercept of the resulting polynomial is equal to - 3.
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two buildings are built 10m apart. *the angle of depression from the top of the shorter building (y) to the foot of the taller building (p) is 53. *the angle of elevation from the top of the shorter building to the top of the taller building (x) is 28. *calculate the height (xp) of the taller building. page 262 trigonometry topic 11 of text book
Answers
The height of the taller building is 18.6 meters
How to find the side of a right triangle?A right triangle has one of its angles as 90 degrees. The side of a right angle triangle can be found using trigonometric ratios.
Therefore, the height of the taller building is the sum of the height of the smaller building and upper part of the taller building.
tan 53 = opposite / adjacent
tan 53 = x / 10
cross multiply
x = 10 tan 53
x = 10 × 1.32704482162
x = 13.2704482162
x = 13.3 m
tan 28 = y / 10
y = 10 tan 28
y = 5.31709431661
y = 5.3
Therefore, the height of the taller building is 13.3 + 5.3 = 18.6 meters.
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Near the equator, the earth rotates approximately 34 kilometers every 32 seconds. what is the speed of earth's rotation near the equator? show your reasoning and include the unit of measure.
Answers
Answer:
Step-by-step explanation: The earth rotates 34 km every 32 seconds. We can simplify this by dividing both sides by 32. Now, we have 34/32 km every 32 seconds. Now, to further simplify this, we need to convert 34/32 to a mixed number 34/32 = 1 2/32 which then can be simplified to 1 1/16. So, near the equator, the speed of Earth's rotation is 1 1/16 km per second.
work out the value of x
Answers
Answer:
x = 36
Step-by-step explanation:
The two lines are parallel and intersected by a transversal line.
The co-interior angles formed will sum up to 180°
Here angles 3x and 2x are the co-interior angles
So 3x + 2x = 180
5x = 180
x = 180/5 = 36
Answer:
x = 18°Step-by-step explanation:
2x + 2x + 3x + 3x = 180°
10x = 180°
x = 180° : 10 =
x = 18°
-----------------------
check
2 × 18 + 2 × 18 + 3 × 18 + 3 × 18 = 180°
the answer is good
does anyone know the answer to this?
Answers
Answer:
C
Step-by-step explanation:
for AB to be parallel to CD then the slopes of both segments must be equal
using the slope formula to find the slopes , then
A (x₁, y₁ ) and B (x₂, y₂ )
[tex]m_{AB}[/tex] = [tex]\frac{y_{2}-y_{1} }{x_{2}-x_{1} }[/tex]
C (x₃, y₃ ) and D (x₄, y₄ )
[tex]m_{CD}[/tex] = [tex]\frac{y_{4}-y_{3} }{x_{4}-x_{3} }[/tex]
then
[tex]m_{CD}[/tex] = [tex]m_{AB}[/tex]
[tex]\frac{y_{4}-y_{3} }{x_{4}-x_{3} }[/tex] = [tex]\frac{y_{2}-y_{1} }{x_{2}-x_{1} }[/tex] → C
In the power function f(x) = -2x, what is the end behavior of f(x) =3^-x 2 as x goes to [infinity]?
Answers
The end behavior of the power function is as x tends to infinity, f(x) tends to zero.
In this question,
The power function is [tex]f(x)=3^{-x}2[/tex]
The end behavior of a polynomial function is the behavior of the graph of f(x) as x approaches positive infinity or negative infinity.
The degree and the leading coefficient of a polynomial function determine the end behavior of the graph.
The graph below shows the behavior of the function f(x).
The above equation has the degree of 1, which is odd and the leading coefficient has the positive coefficient.
Then the end behavior is
As x -> ∞,
⇒ [tex]\lim_{x \to \infty} f(x)[/tex]
⇒ [tex]\lim_{x \to \infty} 3^{-x}2[/tex]
⇒ [tex]2\lim_{x \to \infty} 3^{-x}[/tex]
⇒ [tex]2\lim_{x \to \infty} 3^{-\infty}[/tex]
⇒ 2(0)
⇒ 0
Thus as x → ∞, f(x) → 0.
Hence we can conclude that the end behavior of the power function is as x tends to infinity, f(x) tends to zero.
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A right circular cylinder has a diameter of 12 in and a height of 12 in. if water is flowing in at the rate of 4π in3 per minute, find the rate of change of the height when the height is 4 in?
Answers
The rate of change of the height is [tex]\frac{1}{9}[/tex] in/min.
What is a right circular cylinder?A right circular cylinder is a cylinder that has a closed circular surface having two parallel bases on both the ends and whose elements are perpendicular to its base. It is also called a right cylinder.
Volume of the cylinder = [tex]\pi r^{2}h[/tex]
Rate of change of height is [tex]\frac{dh}{dt}[/tex] = ?
At any time t,
Volume, V = [tex]\pi r^{2}h[/tex]
Since r does not change with time, then r is a constant, so,
V = [tex]\pi (6)^{2}h[/tex]
V = [tex]36\pi h[/tex]
Differentiate both sides with respect to time t,
[tex]\frac{dV}{dt} = 36\pi \frac{dh}{dt}[/tex] -------------(i)
Since [tex]\frac{dV}{dt}[/tex]is given as 4[tex]\pi[/tex] cu.in. per min,
[tex]4\pi = 36\pi \frac{dh}{dt}[/tex]
[tex]\frac{dh}{dt} = \frac{4\pi }{36\pi }[/tex]
[tex]\frac{dh}{dt} = \frac{1 }{9 }[/tex] in/min.
Hence, The rate of change of the height is [tex]\frac{1}{9}[/tex] in/min.
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Find the surface area of the composite figure.
4 cm
13 cm
3 cm
4 cm
SA
=
12 cm
[?] cm²
5 cm
3 cm
Answers
The surface area of the composite figure is: 300 cm².
What is the Surface Area of a Triangular Prism?Surface area of a triangular prism = (P)L + bh, where we have the following:
P = perimeter of the base
L = length of the triangular prism
h = height of the triangular base
b = base of the triangular base
What is the Surface Area of a Rectangular Prism?Surface area = 2(wl + hl + hw), where:
h = height of prism
w = width of prism
l = length of prism.
The surface area of the composite figure = surface area of triangular prism + surface area of rectangular prism - 2(the area where both figures are joined at).
Surface area of the triangular prism = (5 + 12 + 13)4 + (5)(12)
Surface area of the triangular prism = 180 cm²
Surface area of rectangular prism = 2(wl + hl + hw) = 2·(4·12+3·12+3·4) = 192 cm²
The area where both figures are joined at = (l)(w) = (3)(12) = 36 cm².
The surface area of the composite figure = 180 + 192 - 2(36)
The surface area of the composite figure = 180 + 192 - 72
The surface area of the composite figure = 300 cm².
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Bond Valuation with Semiannual Payments
Renfro Rentals has issued bonds that have an 8% coupon rate, payable semiannually. The bonds mature in 12 years, have a face value of $1,000, and a yield to maturity of 7.5%. What is the price of the bonds? Round your answer to the nearest cent.
Answers
If Renfro Rentals has issued bonds that have an 8% coupon rate, payable semiannually. The price of the bonds is: $1,039.11.
Price of the bondsWe would be making use of financial calculator to find or determine the price of the bonds (Present value) by inputting the below data:
N represent Number of years = 12 x 2 = 24
I represent Interest rate= 7.5 % / 2 =3.75 %
PMT represent Periodic payment= (8% x 1000) / 2 = $40
FV represent Future value= $1,000
PV represent Present value=?
Hence;
PV (Present value) = $1,039.11
Therefore if Renfro Rentals has issued bonds that have an 8% coupon rate ,payable semiannually. The price of the bonds is: $1,039.11.
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PLS HELP ITS MATH PLS
Answers
Answer: x is -1/2,0 and y is 0,2
Step-by-step explanation:
Answer:
(4,0) , (0,2)
Step-by-step explanation:
Similar to the previous question.
x-intercept is where the line touches the x-axis , and y = 0.
when y = 0,
8x + 16(0) = 32
8x = 32
x = [tex]\frac{32}{8}[/tex]
x = 4
Therefore the coordinates of the x-intercept is (4,0)
y-intercept is where the line touches the y-axis, and x = 0.
when x = 0,
8(0) + 16y = 32
16y = 32
y = [tex]\frac{32}{16}[/tex]
y = 2
Therefore the coordinates of the y-intercept is (0,2)
A person bought a safe which can be unlocked by entering a 2-digit
secret code. After some time, he forgot the secret code of his safe.
However, he remembers some numbers that could be the secret code.
The secret code is one among the following numbers.
5 17 29 22 11 26 27 35 39 41
Let us give him some clues to find the secret code of his safe.
It is greater than 20
It is not a prime number
It is smaller than 40
It has 13 as one of its factors
It is an odd number.
It has only 4 factors
The secret code is ____________________
Answers
39 number is the secret code as the unlock code for the safe.
According to the statement
we have given that a some numbers as a code and we have to find the correct code after applying the given conditions.
So, For this purpose
The given number set is
5 17 29 22 11 26 27 35 39 41
So,
A. One condition : It is an odd number
so, the number set become
5 17 29 11 27 35 39 41
And
B. Second condition : It is greater than 20
so, the number set become
29 27 35 39 41
And
C. Third condition : It is smaller than 40
so, the number set become
29 27 35 39
And
D. Fourth condition : It is not a prime number
so, the number set become
27 35 39
And
E. Fifth condition : It has 13 as one of its factors
so, the number set become
39.
So, 39 number is the secret code as the unlock code for the safe.
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**The equation y = 15x + 100 can be used to model the amount of money, y, that has
been saved by Jared for his bike based on the number of months that have passed. What
does the coordinate (0, 100) mean in the context of the problem?
Answers
If the equation is y=15x+100 then the coordinate (0,100) of the equation shows that Jared had $100 when he started his saving.
Given an equation y=15x+100 that shows the amount of money saved by Jared for his bike based on the number of months that have passed.
We are required to find what the coordinate (0,100) mean in the context of the equation.
Equation is like relationship between two or more variables that are expressed in equal to form. Equations of two variables look like ax+by=c.It may be linear equation, quadratic equation, cubic equation or many more dependng on the power of variable present in that equation.
When we put x=0 in the equation we get the following:
y=15*0+100
y=100
It means that he had $100 in the beginning when he just started doing his savings.
Hence if the equation is y=15x+100 then the coordinate (0,100) of the equation shows that Jared had $100 when he started his saving.
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A serving of fish contains 50 g of protein and 4. 0 g of fat. How many kcal are in the serving report your answer to 2 significant figures
Answers
2 x 10² kcal are in the serving report your answer to 2 significant figures.
According to the question
A serving of fish contains 50 g of protein and 4. 0 g of fat.
i.e. content of protein = 50 g
Content of fat = 4 g
kcal are in the serving report your answer to 2 significant figures:
As the serving of fish contains 50g of protein that is 4.0kcal/g
Calories in 50 g protein = (Content of protein) × (caloric value in protein)
50g × (4.0kcal/g) = 200kcal
That means the kcal of the serving is 200kcal
In 2 significant figures: 2 x 10² kcal
Hence,
2 x 10² kcal are in the serving report your answer to 2 significant figures.
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a.) 6(x+2) = 5(x-y)
b.) 5(a-2x) = 9(x+1)
make x the subject
Answers
a) 6x + 12 = 5x - 5y
6x-5x = -5y-12
x = -5y-12
b) 5a-10x = 9x+9
-10x-9x = 9-5a
-19x = 9-5a
x = 9-5a/-19
0.7 as a fraction or mixed number
Answers
Which number best represents the slope of the graphed line?
A graph is a line that extends from second quadrant to fourth quadrant through left parenthesis 0, 2 right parenthesis, and left parenthesis 0.5, 0 right parenthesis.
Answers
The number that best represents the slope of the graphed line that is given is: -4.
What is the Slope of a Line?The slope of a line is the ratio of the vertical distance to the horizontal distance across the line. It is calculated using the formula:
Slope (m) = rise/run = change in y / change in x = (y2 - y1)/(x2 - x1)
Given the two points on a coordinate plane as shown in the mage below, let:
(x1, y1) represent (0, 2)
(x2, y2) represent (0.5, 0)
Plug in the values
Slope (m) = change in y / change in x = (0 - 2) / (0.5 - 0)
Slope (m) = -2/0.5
Slope (m) = -4
Therefore, we can state that, the number that best represents the slope of the graphed line that is given is: -4.
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The actual answer is C.1/2
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