[tex] \mathfrak{Solution : }[/tex]
The sum of two complementary angles is 90° , so
(5x + 7)° + (8x - 21)° = 90°5x + 8x + 7° - 21° = 90°13x - 14 = 90°13x = 90° + 14°13x = 104°x = 104° ÷ 13x = 8°1st angle :
(5x + 7)° ((5×8) + 7)° (40 + 7)° 47°2nd angle :
(8x - 21)°((8×8) - 21)°(64 - 21)°43°Collect 5 large numbers and 5 small numbers related in life and express them as exponents. Sample- Distance of the Earth from the moon
384400 km = 3.844 × 10⁵ km
Answer:
Exponential notation is a powerful way to express repeated
multiplication of the same number. Specifically, powers of 10
express very large and very small numbers in a manner which is
convenient to read, write and compare.
• For any non-zero integer a, a–m 1
m a
=
• Laws of exponents are
(a) am × an = am+n
(b) am ÷ an = am–n
(c) (am)
n = amn
(d) am × bm = (ab)
m
(e) a° = 1, where a ≠ 0
(f)
m m
m
a a
b b
=
• Numbers can be expressed in expanded form by using exponents.
• Very large and very small numbers can be expressed in standard
form.
• Standard form is also called scientific notation form.
Step-by-step explanation:
Example 1 : Multiplicative inverse of 27 is
(a) 2–7 (b) 72 (c) – 27 (d) – 27
Solution : The Correct answer is (a).
Example 2 : The human body has about 100 billion cells. This number
can be written in exponential form as
(a) 10–11 (b) 1011 (c) 109 (d) 10–9
Solution : The correct answer is (b).
In examples 3 to 5, fill in the blanks to make the statements true.
Example 3 :
4
4 5 (– 4) ______ 4
× =
Solution : 54
Example 4 : ( ) ( ) 2 3 –3 –2 2 3 _____ × =
Solution : 6–6
Example 5 : The distance between earth and sun is 150 million
kilometres which can be written in exponential form as
_______.
Solution : 1.5 × 108 km
In examples 6 and 7, state whether the statements are true (T) or false (F):
Example 6 : Very small numbers can be expressed in standard form
using positive exponents.
Solution : False.
Example 7 : (–10) × (–10) × (–10) × (–10) = 10–4
Solution : False.
Step-by-step explanation:
Does the quotient of 4554 divided by 9 have a remainder? How can you tell without dividing?
Answer:
No; Because 9 is a factor of 4554. By divisibility rules sum of digits of 4554 is 18, which is a number divisible by 9. Hence 4554 is divisible by 9.
Step-by-step explanation:
:)
is 53 an improper fraction or a proper fraction?
length and width of a field are in the ratio 5.3 If the wilth of 아 the field is 42m, then its length is
Answer:
The length of the feild is:
(42 / 3) x 5 = 70m
So the length of the feild is 70m
Hope it helps, Brainliest please <3
What is 6a +9 ≤ -15?
Answer:
a = -5
Step-by-step explanation:
IF A = -5
6 ( - 5 ) + 9
- 30 + 9
-21
-21 is less than -15 so it works
Find the value of x
Answer:
Step-by-step explanation:
The exterior angle (shown) is equal to the two remote interior angles ( the ones marked with values in x).
5x + 2 + 5x = 11x - 11 Combine the terms on the left.
10x + 2 = 11x - 11 Add 11 to both sides
10x + 2 + 11 = 11x
10x + 13 = 11x Subtract 10x from both sides.
13 = x
Teacher: Who can tell me how to simplify 3 + 5 x 2 – 4?
Student -girl: I think you should do 3 + 5 first and the answer is 12.
Student -boy: I think you do 5 x 2 first and the answer is 9
Teacher: Why did the boy and girl get different answers?
Answer:
3+5×2-4
3+10-4
13-4
9
Step-by-step explanation:
But I solve like this and the answer is 9 I am student girl.
Answer:
The girl didn't follow PEMDAS
Step-by-step explanation:
PEMDAS is the order in which you solve mathematical equations.
Parentheses, Exponents, Multiplication, Division, Addition and Subtraction.
If you add before multiplying you'll get a completely different answer.
The boy followed PEMDAS, while the girl didn't.
Find the radius of the two other circles
Answer:
We draw the circles on a coordinate system. We know that a circle is has points that are equidistant from its centerpoint. So the point where these circles are tangent is the midpoint between the centerpoints.
We can use the midpoint formula.
M = ((x1 + x2) / 2 , (y1 + y2) / 2)
M = ((-2 + 6) / 2 , (3 + 9) / 2)
M = (2, 6)
These circles will have the same radii.
If we take the distance between the midpoint and (-2,3), we will have the radius of the circle with this centerpoint.
If we take the distance between the midpoint and (6,9), we will have the radius of the circle with this centerpoint.
Step-by-step explanation:
If a block has a volume of 216 cm³ in length and width of sides respectively 12 cm and 6 cm. What is the height of the cuboid?
Step-by-step explanation:
I hope it helped U
The table represents the equation y = 2 - 4x
х
y
Use the drop-down menus to complete the statements
The x-values are the
The y-values are the
The missing value in the table for x = -1 is y = 1
V
-2
10
-1
0
2
1
-2
-6
N
It
Answer:
the x-values are the inputs
the y-values are the outputs
the missing value in the table for x = -1 is y = 6
Step-by-step explanation:
i need help pleaseee!!
Answer:
[tex]320 \sqrt{2} [/tex]
If the digits A, B and C are added, the sum is the two-digit number AB as shown. What is the value of C?
A
B
+ C
______
AB
Answer:
C=9
Step-by-step explanation:
If A, B, and C are all single digits the mimimum sum for AB would be 10 as it is a two-digit number (or 11 if you do not consider 0 a digit)
AB-(A+B)=C
10-(1+0)=9 or 11-(1+1)=9
therefore C=9
YALL I NEED HELP PLZ
Answer: 6.9
Step-by-step explanation: search sqrt 48
Una cisterna con forma de prisma rectangular mide 1.5 m de ancho, 2 m de largo y 1 m de alto. Si está vacía y se vierten en su interior 150 L de agua por minuto, ¿cuánto tiempo tardará en llenarse?
Step-by-step explanation:
V = 1.5 × 2 × 1 = 3 m³ = 3000 L
tiempo = 3000 ÷ 150 = 20 minutos
please help, this is geometry
Answer:
Step-by-step explanation:
The formula is the same almost as the previous question you posted.
You want to find the major arc. That's almost the whole circle. If it was the whole circle, the formula would be 2 * pi * r
But we only want a part of it. Just how big is the angle we use in the formula?
A circle has 360 degrees to go around it. We've cut out a slice of it that is 30 degrees.
The remaining part is 360 - 30 = 330
Arc length = angle / 360 * 2 * pi * r
r = 3 m
Arc length = 330 / 360 * 2 * pi * 3
Arc length = 0.9167 * 6 * 3.14
Arc length = 17.27
Which of the following transforms the graph of
y = x2 to the graph of y=x2-77
a translation 7 units to the right
a translation 7 units to the left
translation 7 units down
a translation 7 units up
Answer:
a translation 7 units down
Step-by-step explanation:
the value of -7 will be added to the value of y in the original one ( y = x2) and it will decrease it by 7 units
Answer:
c
Step-by-step explanation:
assignment said so
Evaluate each expression for t = 0, x = 1.5, y = 6, and z = 23
1. y + 5 = ??
2. z - 2x = ??
3. 2z - 2y = ??
4. 2.6y - 2x =??
5. 4(y - x) = ??
6. 4(2 + z) + 5 = ??
Answer:
1. 11
2. 20
3. 34
4. 12.6
5. 18
6. 105
Step-by-step explanation:
We are told that ---> t = 0, x = 1.5, y = 6, and z = 23
1. y + 5
= 6 + 5
= 11
2. z - 2x
= 23 - 2(1.5)
= 23 - 3
= 20
3. 2z - 2y
= 2(23) - 2(6)
= 46 - 12
= 34
4. 2.6y - 2x
= 2.6(6) - 2(1.5)
= 15.6 - 3
= 12.6
5. 4(y - x)
= 4(6 - 1.5)
= 24 - 6
= 18
6. 4(2 + z) + 5
= 4(2 + 23) + 5
= 8 + 92 + 5
= 105
Find the sum of the given arithmetic series. 14 + 28 + 42 + 56 + ... + 280
14 + 28 + 42 + 56 + … 280
= 14 (1 + 2 + 3 + 4 + … + 20)
= 14 × 20 × 21 / 2
= 2940
where we use the well-known identity,
[tex]\displaystyle \sum_{i=1}^ni = 1 + 2 + 3 + \cdots + n = \dfrac{n(n+1)}2[/tex]
If tom had 557 oranges and Billy had 676 more oranges than tom. How many oranges does Billy have.
Answer:
billy has 1233 oranges
Step-by-step explanation:
557+676=1233
you add 557 and 676 to figure out how much billy has
you can check your answer by subtracting 1233-557=676
Answer:
Billy has 1233 oranges.
Step-by-step explanation:
This is a simple, they have this many more than this person has, so an example is the B has 1 book, but Alex has a book collection of 10 books. They both have more than one book, but Alex has 10 books in total, with 9 more than B does.
So, for this question, Tom has 557, and Bill had 676 more than him, so that would mean you need to add 676 and 557 together to get 1233 oranges for just Billy. So that would be our answer.
Help! I don’t get this ine
[tex]3|2x+4|-1=11 \ \ /+1\\\\3|2x+4|=12 \ \ /:3\\\\|2x+4|=4\\\\2x+4=4 \ \ \text{or} \ \ 2x+4=-4\\\\2x=0 \ \ \text{or} \ \ 2x=-8\\\\\boxed{x=0} \ \ \text{or} \ \ \boxed{x=-4}[/tex]
(2sinx+3cosx)²+(3sinx-2cosx)²=13 prove plz
Answer:
LHS:-(4sin²x +9cos²x + 12sinxcosx) +(9sin²x+ 4 cos²x -12sinxcosx)
13 (sin²x + cos²x)
13*1 =
13RHSHP
Answer:
see explanation
Step-by-step explanation:
Using the identity
sin²x + cos²x = 1
Consider left side
(2sinx + 3cosx)² + (3sinx - 2cosx)² ← expand parenthesis using FOIL
= 4sin²x + 12sinxcosx + 9cos²x + 9sin²x - 12sinxcosx + 4cos²x
Collect like terms
= 13sin²x + 13cos²x ← factor out 13 from each term
= 13(sin²x + cos²x)
= 13 × 1
= 13
= right side , thus proven
Help me with 19 and 20
19 find x
20 find y
Answer:
19) x = 48
20) y = 21
Step-by-step explanation:
19)
7x - 248 + x + 44 = 180
(because they're supplementary angles)
8x - 204 = 180
8x = 180 + 204
8x = 384
x = 48
20)
2y + 50 + 5y - 17 = 180
7y + 33 = 180
7y = 180 - 33
7y = 147
y = 21
Write the following numbers in words.
11)
644.112
12)
11.560
13)
200,006 4
14)
1.067
Answer:
Step-by-step explanation:
11)six hundred forty four and one hundred and twelve thousandths
Monique has 12$ in her account
solve for x pls show your work
1/6x-1/8=11/12
Answer:
6 and 1/4
Step-by-step explanation:
1/6 x - 1/8 = 11/12
First, let's find the least common denominator (24) to make these fractions manageable to work with: 4/24 x - 3/24 = 22/24.
Next, add 3/24 to both sides: 4/24 x = 25/24.
We can cancel out the denominators at this point to get: 4x=25.
Divide both side by 4, and x = 25/4 = 6 and 1/4 or 6.25
How much simple interest is earned on $6,000 at an interest rate of 4.52% in 4 1/2 years?
Answer:
1220.4
Step-by-step explanation:
S.I.=P×R×T÷100
=6000×4.52×4 1/2÷100
=6000×4.52×9÷2×100
=60×4.52×9÷2
=30×4.52×9
=1220.4
Find the median of the data. 7, 5, 12, 8, 2, 9, 4
The median of the data is: 7
Simplify the expression
Answer:
[tex] {( - 4)}^{5} \times {( - 4)}^{7} \\ = {( - 4)}^{5 + 7} \\ = {( - 4)}^{12} \\ = 16777216 \\ thank \: you[/tex]
PLS HELP ME SLOPE INTERCEPT FORMMM
through: (1, -1), parallel to y=5/3x
Step-by-step explanation:
the slope = 5/3
through (1, -1)
the equation :
y -(-1) = 5/3 (x -1)
y+1 = 5/3 x -5/3
y = 5/3 x -5/3 -1
y = 5/3 x - 8/3 or y = 5/3 x - 2⅔
f(x) = x-4.
find f(b)
Answer:
x0.4
Step-by-step explanation: