The given expressions written in standard form are;
A) 21 × 10⁷
B) 5 × 10²
This is about expression of given algebra in standard form making use of laws of indices.
A) We are given;
(7 × 10⁵) × (3 × 10²)
Now according to the law of indices, when we want to multiply 2 numbers with same bases and different exponents, we retain the bases and add the exponents.
Also, when we want to multiply 2 numbers with different bases and same exponent, we multiply the bases and retain the exponent.
Applying that to our question gives;
(7 × 3)¹ × (10)⁽⁵ ⁺ ²⁾
⇒ 21 × 10⁷
B) We are given;
(2 × 10⁵)/(4 × 10²)
According to the law of indices, when we want to divide 2 numbers with same bases and different exponents, we retain the bases and subtract the exponents.
Also, when we want to divide 2 numbers with different bases and same exponent, we divide the bases and retain the exponent.
Thus;
(2/4)¹ × (10)⁽⁵ ⁻ ²⁾ = 0.5 × 10³
0.5 can also be expressed as; 5 × 10⁻¹
Thus, 5 × 10⁻¹ × 10³ = 5 × 10²
Read more at; brainly.in/question/18681990
EASY question for y’all mathy people, multiple choice. Ez points, question in photo
Answer: c
Step-by-step explanation:
Answer:
Subtract both sides by 2x
Divide each side by 6
Step-by-step explanation:
2x+6 = 8x
Subtract both sides by 2x
2x+6 -2x = 8x-2x
6 = 6x
Divide each side by 6
6/6 = 6x/6
1 =x
3
7 2 4 7
5 7 1
1 8 8
What is the range?
Answer: 5
Step-by-step explanation:
Range means the difference between the largest and smallest values. Which would be 3 and 8.
PLEASE HELP ME SHOW ME HOW U GOT YOUR ANSWER PLZ AND THANK U
Answer:
2/3
Step-by-step explanation:
There are 6 marbles in the jar
4 are not purple
P(not purple) = marbles that are not purple/ total marbles
= 4/6 = 2/3
Answer:
2/3
Step-by-step explanation:
since there are 6 total marbles and 4 of them are colors other than purple, there is a 4/6 chance of drawing a marble that is not purple which can be simplified to 2/3.
4. The sales price of a car is $12,590, which is 20% off the original price. What is the original price?
1. $14,310.40
2. $14,990.90
3. $15,290.70
4. $15,737.50
5. $16,935.80
Answer:
12590/80*100 = $15,737.50 4. Is your Answer
Step-by-step explanation:
12590 is 80% so simply divide by 80 and multiply by 100 to get the answer.
Please help! Correct answer only!
There are 10 cards in a hat, numbered 1 to 10. The game is to draw one card out of the hat. If the number you draw is even, you win $30. If the number you draw is odd, you win nothing. If you play the game, what is the expected payoff?
$___
Answer:
$15
Step-by-step explanation:
Since there are 10 cards and a total possible prize of 30 dollars, the probability for each one is 30/10=3 dollars. And since 5 out of the 10 are even, you can multiply the individual amount by 5 to get a total estimated payout of $15. Hope this helps!
Help!!! Which of the following best describes abc?
Answer:
Inscribed Angle (A)
Step-by-step explanation:
in geometry, an inscribed angle is the angle formed in the interior of a circle when two secant lines (or, in a degenerate case, when one secant line and one tangent line of that circle) intersect on the circle. It can also be defined as the angle subtended at a point on the circle by two given points on the circle.
Can someone help meee!
Answer:
X intercept = 4
Y intercept = -4
Step-by-step explanation:
X-intercept is when the graph crosses the X-axis or where the y is 0 for a X value. Here the (4,0) is where Y is 0 for a given x value and you see the graph crosses it on X-axis thus X intercept is 4.
Y-intercept is when the graph crosses the Y-axis or where the x is 0 for a Y value. Here the (0,-4) is where X is 0 for a given Y value and you see the graph crosses it on Y-axis thus Y intercept is -4.
Can someone help me with math please?
Answer:
Multiply 60 by 2.5 centimetres
60×2.5=150
10+12+14+...+(2n)=90 n=?
Answer:
n=10
Step-by-step explanation:
The given equation is
[tex]10+12+14+...+2n=90[/tex] ...(1)
Let nth term is 2n.
We need to find the values of n.
It is clear that [tex]S_n=10+12+14+...+2n[/tex] is sum of A.P., whose first term is 10 and common difference is 2.
Sum of A.P. is
[tex]S_n=\dfrac{n}{2}[2a+(n-1)d][/tex]
where, a is first term and d is common difference.
Substitute a=10 and d=2 in the above formula.
[tex]S_n=\dfrac{n}{2}[2(10)+(n-1)2][/tex]
[tex]10+12+14+...+2n=n[10+n-1][/tex]
[tex]10+12+14+...+2n=n[9+n][/tex] ...(2)
From (1) and (2), we get
[tex]n(9+n)=90[/tex]
[tex]n^2+9n-90=0[/tex]
Splitting middle term, we get
[tex]n^2+15n-6n-90=0[/tex]
[tex]n(n+15)-6(n+15)=0[/tex]
[tex](n+15)(n-6)=0[/tex]
[tex]n=-15,6[/tex]
Since, n represents the number of terms so n cannot be a negative number, therefore number of term is 6.
Note: nth term and variable n both are different.
[tex]a_n=a+(n-1)d[/tex]
[tex]a_6=10+(6-1)2=10+10=20[/tex]
Sixth term is 20. So,
[tex]2n=20[/tex]
[tex]n=10[/tex]
Therefore, the value of n is 10.
Rewrite the expression 24x - 12 using the distributive property
Answer:
12(2x-1)
Step-by-step explanation:
24x - 12
Factor out a 12 from each term
12*2x -12*1
12(2x-1)
Answer:
[tex]12(2x - 1)[/tex]
Step-by-step explanation:
[tex]24x - 12[/tex]
Factor out a 12 from each
[tex]24x - 12 \\ 12(2x - 1)[/tex]
hope this helps
brainliest appreciated
good luck! have a nice day!
A rectangular garden has dimensions of 12 feet by 20 feet. The homeowner wants to increase each dimension by 20%.
A. Find the original perimeter and area of the garden
B. Find the perimeter and area of the garden with a 20% increase in each dimension.
C. By what percent will the perimeter increase? By what percent will the area increase?
D. Explain why the area and perimeter will not increase by the same percentage.
Answer:
w=12 ft
l= 20 ft
A.
P= 2(12+20)= 64 ft
A= 12*20= 240 ft²
B.
P=2(12*1.2+20*1.2)= 76.8 ft
A= 12*1.2*20*1.2= 345.6 ft²
C.
(76.8-64)/64*100%= 20%
(345.6- 240)/240*100%= 44%
D.
perimeter increase is linear function of one dimension increase
area increase is function of 2 dimensions increase
Kaleb looks at a tennis court and uses a geometric term to describe two lines that cross at a right angle. What term could use Kaleb use? A. Acute angle B. Parallel lines C. Perpendicular lines D. Straight angle
What is the surface area of a sphere with the given dimension? Express your answer to nearest hundredth. Use 3.14 for pi.
Radius = 5cm.
a. 982 sq. cm
C. 314 sq.cm
b. 1481.34 sq.cm
d. 628 sq. cm
Answer:
314cm²
Step-by-step explanation:
Surface area(sphere) =4πr²
4 * 3.14 * (5²)
4 * 3.14 * 25
Hence, Surface area is 314sq.cm
PLEASE HELP ME WITH THIS! VERY IMPORTANT!!! SMART PEOPLE PLEASEEE
(2x+3)²=125 find x
with full solution please
Answer:
x = ± ( 5√5 - 3 ) / 2
Step-by-step explanation:
We are given the equation ( 2x + 3 )² = 125;
[tex]( 2x + 3 )^{ 2 } = 125 - Take Square Root on Either Side,\\| 2x + 3 | = \sqrt{ 125 } - Simplify Square Root of 125,\\\\| 2x + 3 | = \sqrt{ 5 * 25 } - Simplify Further,\\| 2x + 3 | = 5\sqrt{ 5 } - Take | |,\\\\2x + 3 = 5\sqrt{ 5 } , and , 2x + 5 = - 5\sqrt{ 5 } - Algebra, \\2x = 5\sqrt{ 5 } - 3 , and , 2x = - 5\sqrt{ 5 } - 3 - Divide Either Side by 2\\\\x = ( 5\sqrt{ 5 } - 3 ) / 2, and , x = ( - 5\sqrt{ 5 } - 3 ) / 2\\Conclusion ; x = ( + / - 5\sqrt{ 5 } - 3 ) / 2[/tex]
Solution ; x = ± ( 5√5 - 3 ) / 2
are the ratios 1:3 and 4:12 equivalent
Answer:
Yes.
Step-by-step explanation:
When you simplify the ratio of 4:12, dividing it by 4, you will get 1:3.
Answer:
Yes it is equivalent
Step-by-step explanation:
Yes because 1*4= 4
And 3*4=12
That is 1/3 is equivalent to 4/12
You can say that 1:3 is in proportion with 4:12
or 1:3::4:12
que se necesita para que una magnitud vectorial esté completamente definida ?
Answer:
Dirección y magnitud
Espero que esto ayude.
Answer:
Dirección y magnitud
Step-by-step explanation:
How would you describe the curve?
the answer is C, the curve is a one to one function
A bottle of iron supplement has 45g of iron in 330ml of solution. How many grams of iron are in
100ml of solution?
Answer:
45 * 100 / 330 = amount in 100 ml of solution
13.6363636364 grams
Step-by-step explanation:
*
1. Find the measure of the indicated angle to the nearest degree.
?
O A. 31
O B. 51°
O C.37°
O D. 59°
Answer:
The answer is 37° (C)
Step-by-step explanation:
how do I solve: 8 – (m - 3) = 7 – 3m
Answer:
m=-2
Step-by-step explanation:
8-(m-3)=7-3m
8-1(m)-1(-3)=7-3m
8-m+3=7-3m
-m+3m+8+3=7-3m+3m
2m+8+3=7
2m+11=7
2m=-4
m=-2
Hope this helps!
Step-by-step explanation:
So, this is how you do it.
2. A triangle with angle measures 48 degrees, 65 degrees, and 67 degrees is a(n) ________ triangle. *
__________________________________
The right answer is Acute.
Explanation
Acute angle triangle are those which is more than 0 degree and less than 90 degree.
Hope it help
Good luck on your assignment
________________________________
Pls solve for x. (Pls show step by step explanation)
3(x-2)+7x=1/2(6x-2)
Answer:
x=5/7
Step-by-step explanation:
Distribute
3x-6+7x=3x-1
Combine Like Terms
10x-6=3x-1
7x-6=-1
7x=5
x=5/7
Answer:
[tex]x=5/7[/tex]
Step-by-step explanation:
[tex]3(x-2)+7x=1/2(6x-2)[/tex]
Use algebraic distribution.
[tex]3x-6+7x=3x-1[/tex]
Add like terms.
[tex]10x-6=3x-1[/tex]
Add [tex]-3x[/tex] and [tex]+6[/tex] on both sides of the equation.
[tex]10x-3x=-1+6[/tex]
Add and subtract.
[tex]7x=5[/tex]
Divide [tex]7[/tex] on both sides of the equation.
[tex]x=5/7[/tex]
The square of a number I see equal to two less than three times the number. What are two possible values of the number? A. 1,2 B. -1,2 C. 1,-2 D. -1,-2 E. 2,3
Answer:
Option A
Step-by-step explanation:
Let us take this number as x, translating this description of the equation into mathematical language;
[tex]x^2 = 3x - 2[/tex]
Now let us solve for x;
[tex]x^2 = 3x - 2,\\x^2+2=3x-2+2,\\x^2+2=3x,\\x^2+2-3x=3x-3x,\\x^2-3x+2=0,\\\\Factored = \left(x-1\right)\left(x-2\right)=0,\\Zero Factor Principle, \\x = 1, x = 2\\\\Solution - Option A[/tex]
* Note that for the the previous problem I solved, I set up a similar equation that had two values for the width, one negative and the other positive. Now the width could only be a positive number, so there was only one solution out of the two.
What is a rigid motion?
Answer:
Rigid motion is otherwise known as a rigid transformation and occurs when a point or object is moved, but the size and shape remain the same. This differs from non-rigid motion, like a dilation, where the size of the object can increase or decrease.
Step-by-step explanation:
Which statement best describes the function below
Answer:
Option D. will be the answer.
Step-by-step explanation:
Given function is f(x) = 2x³ + 2x² - x
Table of input and output:
Input (x) -2 -1 0 1 2
Output (y) -6 1 0 3 22
Option (A).
From the graph attached,
It passes the vertical line test.
Option (B).
Since every input value gives a unique output value, it's not a many-to-one function.
Option (C).
It's a function.
Option (D).
It's a one-to-one function.
Answer: It is a many-to-one function.
Step-by-step explanation:
just did the test
Is the following shape a rectangle
Answer:
c
Step-by-step explanation:
no because the adjacent sides are not perpendicular.
Simplify an Expression
Quick
Check
Simplify each expression involving signed numbers
-7-2=
12 + (-4)= |
-3(-6) = 1
18
Answer:
-10827is the answer for your question I think
Answer:
[tex]-9[/tex]
[tex]8[/tex]
[tex]18[/tex]
Step-by-step explanation:
[tex]-7-2=-9[/tex]
[tex]12+(-4)=8[/tex]
[tex]-3(-6)=18[/tex]
I need to know the answer for the picture
Answer:
a = 2
Step-by-step explanation:
We can use cross products to solve
8 a
----- = -------
28 7
8*7 = 28*a
Divide each side by 28
56/28 = 28a/28
2 =a
Answer:
2
Step-by-step explanation:
Given:
8 a
------- = ------ Find the value of a that makes this equation true.
28 7
Cross multiplying, we get 28a = 56, and so a works out to 2.
Check: Does 8/28 = 2/7? Yes.
Help please
What are the coordinates of the hole in the graph of the function?
f(x)=x2−3x−10/x−5
Enter your answer in the boxes.
Answer:
(5, 7)
Step-by-step explanation:
A hole is found in the graph of a rational function where numerator and denominator factors cancel each other.
The x-coordinate of the hole is the value of x that makes the factor zero. The y-coordinate of the hole is the value of the simplified function after the cancelled factors are removed. It is the limit of the function value as x approaches the hole location.
__
[tex]f(x)=\dfrac{x^2-3x-10}{x-5}=\dfrac{(x+2)(x-5)}{x-5}=x+2\qquad x\ne 5[/tex]
The hole is found at x = 5. The limit of the function value as x approaches 5 is 5+2 = 7. The coordinates of the hole are (5, 7).