Answers
All answer choices are equivalent
All the expressions given in option is equivalent to the expression
([tex]10^{t^{2}+2t-3 }[/tex])
What is an expression?An expression in maths, a sentence with a minimum of two numbers or variables and at least one maths operation. This maths operation can be addition, subtraction, multiplication, or division.
Given is an expression, ([tex]10^{t^{2}+2t-3 }[/tex])
We know, when equal base get multiplied with different powers, the power get added and in case of division they get subtracted,
([tex]10^{t^{2}+2t-3 }[/tex]) = [tex]10^{t^{2} }[/tex]x[tex]10^{2t}[/tex]x[tex]10^{-3}[/tex]
[tex]10^{t^{2} }[/tex]x[tex]10^{2t}[/tex]x[tex]10^{-3}[/tex] = [tex]\frac{10^{t^{2} +2t } }{1000}[/tex]
When we factorize, t²+2t-3, we get,
t²+2t-3 = (t+3)(t-1)
Therefore, ([tex]10^{t^{2}+2t-3 }[/tex]) = [tex]10^{t^{2} }[/tex]x[tex]10^{2t}[/tex]x[tex]10^{-3}[/tex] = [tex]\frac{10^{t^{2} +2t } }{1000}[/tex] = [tex]10^{(t+3)(t-1)}[/tex]
Hence, we can say that, All the expressions given in option is equivalent to the expression ([tex]10^{t^{2}+2t-3 }[/tex])
For more references on expression, click;
https://brainly.com/question/14083225
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Related Questions
in a hostel 50 students have food enough for 32 days. how many students should be leave the hostel so that the food is enough for 14 days.
Answers
Answer:
22 days
Step-by-step explanation:
Given data
Number of students= 50
Number of days= 32days
We want to find the number of students that can have food for 14days
If 50 students will have food for 32 days
x students will have food for 14 days
cross multiply
32*x= 14*50
32x= 700
x= 700/32
x=21.8
Hence 14 students will have for 22 days
At Sam’s Warehouse, a member pays $25 a year for a membership, and then buys all products at the regular store prices. A non-member does not pay the membership fee, but does pay an additional 5% above the store prices. Write and solve a system of equations to represent this situation where is the store price and is the total amount paid.xy
Answers
Answer:
[tex]y = 25 + x[/tex] --- Members
[tex]y = 1.05x[/tex] --- Non-members
Step-by-step explanation:
Given
[tex]x \to store\ price[/tex]
[tex]y\to total\ amount[/tex]
Members
[tex]Membership =\$25[/tex]
Non-members
[tex]Rate = 5\%[/tex] increase
For the members, the equation is:
[tex]y = Membership + Store\ price[/tex]
[tex]y = 25 + x[/tex]
For non-members, the equation is:
[tex]y = Store\ price * (1 + Rate)[/tex]
[tex]y = x * (1 + 5\%)[/tex]
[tex]y = x * (1.05)[/tex]
[tex]y = 1.05x[/tex]
Solve this quadratic equation using the quadratic formula
(3 - y)(y + 4) = 3y - 5
Answers
Please help with this, will give brainliest.
Answers
Explanation:
The negative exponent means we apply the reciprocal to get the exponent to be positive.
The rule is (a/b)^(-c) = (b/a)^c
That means (1/4)^(-3) = (4/1)^3 = 64 which is a whole number.
Something like 2^(-3) = 1/(2^3) = 1/8 = 0.125 isn't a whole number, so we can cross that off the list. The same goes for choices A and C as well.
Answer:
B
Step-by-step explanation:
1/1 ÷ (1/4)³ = 1 x 4³ = 64
Quick! Taking a test, this could decide whether I fail or pass the grade..
Answers
Answer:
the second option!
Step-by-step explanation:
According to Math.way the second option is the correct answer.
The price of an article is increased from Rs 75 to Rs 78. Find the percentage increase in the price of the article.
WITH FULL CALCULATION PLEASE!!!!!
Answers
======================================================
Work Shown:
A = old value = 75
B = new value = 78
C = percent change
C = [ (B-A)/A ] * 100%
C = [ (78-75)/75 ] * 100%
C = (3/75) * 100%
C = 0.04 * 100%
C = 4%
The positive C value means we have a percent increase.
The price has increased by 4%
hi! i’ll give brainliest please help
Answers
Answer:
deposition of eroded materials
Step-by-step explanation:
Answer:
now that i have the answer button the answer is B im not copying the other guys answer i have answered first in the ch-at so please don't come at me lol
Step-by-step explanation:
Find the distance between the points (4,5) and (10, – 3). Round decimals to the nearest tenth
Answers
Answer:
10 is the distance.
pls help! its due today i would mark u brainliest! but pls it's an emergency do both problems!
Answers
Answer:
Step-by-step explanation:
The coordinate is (x,-y)
please factor and find the zeros of each relation (18 marks)
C. y = 30x^2 + 44x +16
D. y = 10x^2 + 60x + 80
Answers
Answer:
[tex]C. \ \frac{-2}{3} , \ \frac{-4}{5}\\\\D. \ -2, \ -4[/tex]
Step-by-step explanation:
C.
[tex]30x^2 + 44x +16 = 0\\\\2(15x^2 + 22 + 8) = 0\\\\2(15x^2 + 12x + 10x + 8) = 0\\\\2(3x(5x + 4)+2(5x + 4))=0\\\\2((3x + 2)(5x + 4)) = 0\\\\Zeroes : 3x + 2 = 0 => x = \frac{-2}{3}\\[/tex]
[tex]5x+ 4 = 0 => x = \frac{-4}{5}[/tex]
D.
[tex]10x^2 + 60x +80 = 0\\\\10(x^2 + 6x + 8)= 0\\\\10(x^2 + 4x + 2x + 8)=0\\\\10(x(x+4)+2(x+4))=0\\\\10((x+2)(x+4))=0\\\\Zeroes : x + 2 = 0 =>x = -2[/tex]
[tex]x + 4 = 0 => x= -4[/tex]
two rational numbers between 2/3 and 5/3
Answers
Answer:
1.333333333333 or 4/3
Which type of line of symmetry does the figure have?
Answers
2.2 × 1019) + (1.5 × 1016)
Answers
Answer:
Use calculator it's easy ....
Answer :
3765.8
Answer:
[tex](2.2 \times 1019) + (1.5 \times 1016) \\ = 2241.8 + 1524 \\ = 3765.8[/tex]
if the simple interest eamed on $8000 for 9 years is $2,160. Then what is the interest rate?
Answers
Answer:
3%
Step-by-step explanation:
2160/9 years =240/year
240/8000=3%
PLEASE HELP ME ASAP In the equation Log2x = y, which of the following CANNOT be true?
O y is negative
O y is positive
x is negative
O x is positive
Answers
Answer:
option : x is positive
Step-by-step explanation:
[tex]log_2 x = y => x = 2^y[/tex]
Therefore, x is always positive
Which symbol correctly compares the two angle measures?
radians
60°
A. =
B. <
C. >
Answers
Answer:
Is B
Step-by-step explanation:
Help pleasee MARKED BRAILIEST!!!
Answers
Answer:
10 dance classes
Step-by-step explanation:
The last option is the correct answer.
( A student needs to take 10 dance classes to learn the routine. )
Find the arc length of the semicircle
Answers
Answer:
Arc length of the semicircle is 12.57 cm.
Step-by-step explanation:
From the given picture,
Measure of diameter = 8 units
Radius of the semicircle = [tex]\frac{\text{Diameter}}{2}[/tex]
= [tex]\frac{8}{2}[/tex]
= 4 units
Since, circumference of a semicircle is given by the expression,
C = πr
Here, r = radius of the semicircle
Circumference of the given semicircle = π(4)
= 4π
= 12.57 cm
Therefore, arc length of the semicircle is 12.57 cm.
Answer:
Its 16 pi
Step-by-step explanation:
Solve for x in the system of equations
2x+5y=20
-2x+10y=25
Answers
Hi there!
[tex]\large\boxed{x = 2.5}[/tex]
We can solve for x by using an elimination of variables.
2x + 5y = 20
-2x + 10y = 25
Add the two equations to eliminate x:
0x + 15y = 45
15y = 45
y = 3
Substitute this value of y into an equation to solve for x:
2x + 5(3) = 20
2x + 15 = 20
2x = 5
x = 2.5
Answer:
I believe it is (5/2,3)
Step-by-step explanation:
Hope this works for u :)
answer pls with a detailed explanation
Answers
Answer:
SA = 225 cm²
Step-by-step explanation:
The given pyramid dimensions are;
The length of the rectangular base of the pyramid, l = 12 cm
The width of the base, w = 6 cm
The area of the rectangular base, Aₐ = 12 cm × 6 cm = 72 cm²
The height of one of the triangles forming the side of the pyramid, h₁ = 8 cm
The base length of the above triangle, b₁ = 12 cm
The area of the above triangle, A₁ = (1/2)×12 cm × 8 cm = 48 cm²
The height of the other of the triangles forming the other side of the pyramid, h₂ = 9.5 cm
The base length of the above triangle, b₂ = 6 cm
The area of the above triangle, A = (1/2) × 9.5 cm × 6 cm = 28.5 cm²
The surface area of the pyramid, SA = Aₐ + 2 × A₁ + 2 × A₂
Therefore;
SA = 72 cm² + 2 × 48 cm² + 2 × 28.5 cm² = 225 cm²
SA = 225 cm²
The difference between two positive numbers is 5 and the square of their sum is 169. find the two numbers.
Answers
ArmyCee:)
Answer:
The two number are 9 and 13
Step-by-step explanation:
9-4=5
9+4=13 and 13*13is 169
Can you find the
triangle's perimeter
I’m marking branliest
Answers
Answer:
The perimeter would be 6x + 12
Step-by-step explanation:
The perimeter of a triangle is the sum of all its sides.
The measures of the sides of the given triangle are:-
3x + 2, x + 6 and 2x + 4
So, to find perimeter add these values together:-
3x + 2 + x + 6 + 2x + 4
Bring all the 'x' terms together first and then the other numbers so we can add them:-
3x + 2x + x + 2 + 6 + 4
6x + 12
The perimeter of the triangle would be 6x + 12AB = [tex]x[/tex] + 6
BC = 2 [tex]x[/tex] + 4
AC = 3 [tex]x[/tex] + 2
To find:-The perimeter of the triangle.
Solution:-[tex]{\boxed{\mathcal{\red{The\: perimeter \:of\:the\:triangle\:is\: 6x\:+\:12.\:✅}}}}[/tex]
Step-by-step explanation:-We know that,
[tex]\sf\pink{Perimeter\:of\:a\:triangle\:=\:Sum\: of\: all \:three\: sides}[/tex]
[tex] = AB + BC + AC \\ = x + 6 + 2x + 4 + 3x + 2 \\ = 6x + 12[/tex]
[tex]\sf\red{Therefore, \:the\: perimeter\:of \:the\:triangle\: is \:6x\:+\:12.}[/tex]
[tex]\bold{ \green{ \star{ \orange{Hope\:it\:helps.}}}}⋆[/tex]
what is the soultion 3-6x = 9-6x
Answers
Answer:
x=-6
Step-by-step explanation:
3-9= -6x+6x
x=-6
ans=-6
PLEAEE NEED HELP!!
Find the area of the shaded region in the regular polygon with AB = 5.5 ft.
Answers
Answer:
88 ft^2
Step-by-step explanation:
please find attached the diagram used in answering this question
Area of shaded region = area of regular polygon - area of triangle
area of regular polygon = 1/2 x height x perimeter of the polygon
perimeter of the polygon = number of sides x length of side
5 x 8 = 40
1/2 x 40 x 5.5 = 110 ft²
Area of a triangle = 1/2 x ( base x height)
1/2 x 5.5 x 8 = 22 ft²
Shaded portion = 110 - 22 = 88 ft²
The length of a cuboid is thrice the breadth and twice the length.if the volume of a box is 750 cm3 then find the measure of the box.
Answers
Step-by-step explanation:
Let b is breadth and l is length of the cuboid such that,
Length, l = 3b and l = 2h
or
h = l/2
We know that, the volume of a cuboid box is given by :
V = lbh
Put all the values,
[tex]V=l\times \dfrac{l}{3}\times \dfrac{l}{2}\\\\750=l\times \dfrac{l}{3}\times \dfrac{l}{2}\\\\750\times 6=l^3\\\\l=(750\times 6)^{1/3}\\\\l=16.5\ cm[/tex]
Breadth, b = 16.5/3 = 5.5 cm
Height, h = 16.5/2 = 8.25 cm
Hence, this is the required solution.
The total cost of a gym membership, C, in Australian dollars (AUD), in John's Gym can be modelled by the function C = 65t+30, where t is the time in months. Calculate the gym membership cost over 12 month duration
Answers
Answer:
810 AUD
Step-by-step explanation:
t is time in months: you have to substitute with the number of months given from the question.
C=65t + 30 ==> substitute t with 12 since the question provided you the number of months.
--> C = 65(12) + 30 = 780 + 30 = 810
Determine the value of x.
A) 12
B) 2√3
C) 12√3
D) 6√3
Answers
Answer:
D
Step-by-step explanation:
Using the tangent ratio in the right triangle and the exact value
tan60° = [tex]\sqrt{3}[/tex] , then
tan60° = [tex]\frac{opposite}{adjacent}[/tex] = [tex]\frac{x}{6}[/tex] = [tex]\sqrt{3}[/tex] ( multiply both sides by 6 )
x = 6[tex]\sqrt{3}[/tex] → D
pupils are required to spend 3/8 of the day at school and 2/3 of that time in class. How much time do they spend doing Mathematics? Give your answer in minutes.
Answers
Answer:
[tex]Time \ in\ school = \frac{3}{8} \ of \ the \ day[/tex]
= [tex]\frac{3}{8} \times 24 = 9 \ hours \ in \ school[/tex]
[tex]Time \ in \ class = \frac{2}{3} \ of \ the \ time \ in \ school = \frac{2}{3} \times 9 = 6 \ hours \ in \ class[/tex]
1 hour = 60 minutes
Therefore, 6 hours = 360 minutes
So , 360 minutes they spent doing mathematics.
123
30°
у
Find the values of x and y. Write your answers in simplest form.
x =
y=
Answers
Answer:
[tex]y=6\sqrt{3}[/tex]
[tex]x=18[/tex]
Step-by-step explanation:
[tex]Sin30=\frac{9}{12\sqrt{3} }[/tex]
[tex]1/2=y/12\sqrt{3}[/tex]
[tex]y=6\sqrt{3}[/tex]
[tex]tan30=y/x[/tex]
[tex]x=y/tan30=x=\frac{6\sqrt{3} }{1/\sqrt{3} }[/tex]
[tex]x=18[/tex]
------------------------
hope it helps...
have a great day!
A rectangle is 21 meters long and 11 meters wide.
What is the perimeter of this rectangle?
32 m
42 m
64 m
84 m
Answers
Answer:
P = 64 meters
Step-by-step explanation:
P = 2(l+w) for a rectangle
Substitute in the length and the width
P = 2( 21+11)
P = 2( 32)
P = 64 meters
Answer:
P = 2(l+w)
= 2 ( 21+11)
= 2(32)
= 64m