To solve the equation [tex]2^{x-1} - 7 = 9[/tex], we add 7 to both sides make the bases the same, and equate the exponents.
What are some rules of exponents?Some common rules of exponents are
xᵃ×xᵇ = xᵃ⁺ᵇ.
xᵃ/xᵇ = xᵃ⁻ᵇ.
Addition and subtraction of exponents are only possible for the same base value and when the base is different and both have the same exponent we just multiply the bases and write the exponent.
Given, An exponential expression
[tex]2^{x-1} - 7 = 9[/tex].
[tex]2^{x -1} = 9 + 7.[/tex]
[tex]2^{x-1} = 16.[/tex]
[tex]2^{x-1} = 2^4[/tex].
x - 1 = 4.
x = 5.
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What is the measure of angle y in this figure?
Enter your answer in the box.
y=__
Answer:
163°
Step-by-step explanation:
Since those 2 arrows are straight lines that go through each other, angles that are opposite are the same. So the opposite of y is 163°.
-12x - 7 = show me the steps please
thank you
Answer:
is there a number after the =? there are no like terms to solve this if you don't have that so you would put -12×-7...
Calculate the difference between the 10th term and 50th term of the sequence 9,14,19,24, ... ...
Answer:
Step-by-step explanation:
Number series : 9, 14, 19, 24
First term = a1 = 9
common difference = a2 - a1 = 14 - 9=5
Find the nth term:
an = a1 + + (n - 1)d
an = 9+ (n - 1)(5)
an = 9+5n - 5
an = 4 + 5n
Find the 10th term:
an = 4 + 5n
a10 = 4 + 5(10)
a10 = 4 + 50
a10 = 54
Find the 50th term:
an = 4 + 5n
a50 = 4 + 5(50)
a50 = 254
Find the difference between the 10th and
50th term:
Difference = 254 - 54 = 200
Answer: The difference is 200
Given the data from the question, the difference between the 10th term and the 50th term is 200
What is an arithmetic sequence?This is a type of sequence which have common difference between each term. It is represent mathematically as:
Tₙ = a + (n – 1)d
Where
Tₙ is the nth terma is the first term n is the number of termsd is the common difference How to determine the 10th termSequence: 9,14,19, 24First term (a) = 9Common difference = 14 – 19 = 5Number of terms (n) = 1010th term (T₁₀) =?Tₙ = a + (n – 1)d
T₁₀ = 9 + (10 – 1)5
T₁₀ = 9 + (9)5
T₁₀ = 9 + 45
T₁₀ = 54
How to determine the 50th termSequence: 9,14,19, 24First term (a) = 9Common difference = 14 – 19 = 5Number of terms (n) = 5050th term (T₅₀) =?Tₙ = a + (n – 1)d
T₅₀ = 9 + (50 – 1)5
T₅₀ = 9 + (49)5
T₅₀ = 9 + 245
T₅₀ = 254
How to determine the difference 50th term (T₅₀) = 25410th term (T₁₀) = 54Difference =?Difference = T₅₀ – T₁₀
Difference = 254 – 54
Difference = 200
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does anyone know the answer to ts ?
Answer: C
Step-by-step explanation:
Answer:
c
Step-by-step explanation:
level of the sea 3 meter is true and fish lives in water.
Write an expression for the area of the shaded region in its simplest form. Show all of your steps. Show your work!
Answer:
[tex]A=x^2+23x+49[/tex]
Step-by-step explanation:
Hi there!
The area of the shaded region is equal to the area of the big rectangle minus the area of the square.
Area of the big rectangle:
[tex]A=lw\\A=(x+10)(2x+5)[/tex]
Area of the square:
[tex]A=a^2\\A=(x+1)^2[/tex]
Area of the shaded region:
[tex]A=(x+10)(2x+5)-(x+1)^2[/tex]
Expand:
[tex]A=(x+10)(2x+5)-(x+1)^2\\A=2x^2+5x+20x+50-(x+1)^2\\A=2x^2+5x+20x+50-(x^2+2x+1)\\A=2x^2+5x+20x+50-x^2-2x-1[/tex]
Combine like terms:
[tex]A=2x^2-x^2+5x+20x-2x+50-1\\A=x^2+23x+49[/tex]
I hope this helps!
Let f(x)=4x2 6. The function g(x) is f(x) translated 4 units down. What is the equation for g(x) in simplest from? Enter your answer by filling in the box. G(x) =.
The G(x) is the new function of the f(x) which is translated 4 units down is 4x²+2.
What is Function?A function assigns the value of each element of one set to the other specific element of another set.
The given function can be transformed from the initial position of the new position by subtracting the 4 from the initial function.
We know that in the initial function y=4x²+6, y is the output, while x is the input for the function f(x).
As the G(x) is the new function of the f(x) which is translated 4 units down. therefore,
[tex]G(x) = f(x)-4\\\\G(x) = 4x^2+6-4\\\\G(x) =4x^2+2[/tex]
hence, the G(x) is the new function of the f(x) which is translated 4 units down is 4x²+2.
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Which of the following represent the three sides of the right triangle shown below? Select all that
apply
20
18
16
14
12
10
8
6
4
2
0
1
2
3
4
5
6
7
8
9
10
you want a better price to pay the bill on leaderboard than a year old but the only other person would need points on a few days is a bit less expensive for you but you are going a good job in my career that will give my heart and legendary domortu for my son who loves the music he deserves as much for as a person can see it all of you can be very creative as I
can someone help, thanks!
Answer:
16, 10
Step-by-step explanation:
There are 4 quarts in a gallon, so 4 gallons has 16 qt.
There are 2 pints in a quart, so 5 quarts has 10 pt.
if x+b=6 then what is b
Answer: 3
Step-by-step explanation: 6 is 3 and 3 so b is 3 and x is 3
How many triangles can I make with 3cm, 5cm, 4cm?
Answer:
You will need “paper sticks” that are 3cm, 4cm and 5cm long. Each measurement should have its own colour (e.g., 3cm red, 4cm green, 5cm blue). You will need to make approximately 12 of each “stick”.
Step-by-step explanation:
Is (0,7) a solution to the equation 2x+y=6
Answer:
No
Step-by-step explanation:
2(0)+7
=0+7
=7
therefore,(0,7) is not a solution to the equation 2x+y=6
0=×
7=y
Answer: no it isn’t
Step-by-step explanation: this is super simple so do solve this you have know your x and y values on coordinate points in this case (0,7) our x here is 0 and our y is 7 (the x will always be the first number and the y will be the last)
Here we are given a equation all we have to do is plug 0 for x and 7 for y.
2(0)+7=6
2 x 0= 0
So: 0+7=7
7 does NOT equal to 6 therefor (0,7) is NOT a solution
Perform the indicated operation.
3.26 + (-4)
0.74
-0.64
3.22
-0.74
Answer:
-0.74
Step-by-step explanation:
[tex]3.26 + ( - 4) \\ + \times - = - \\ 3.26 - 4 \\ substract \: the \: terms \\ - 0.74[/tex]
I need help ls thank you!!!!!
Answer:
mean = 24
Step-by-step explanation:
From inspection, there are 7 values.
The values are 12, 13, 15, 28, 28, 30, 42
To find the mean, sum the numbers: 12 + 13 + 15 + 28 + 28 + 30 + 42 = 168
Divide by the number of values: 168 ÷ 7 = 24
Therefore, mean = 24
With the baby in his arms, Mr. Greer weighed 180 pounds. Without the baby, he weighed 165 1/2 pounds. How much did the baby weigh?
ANSWERS ASAP!
Answer:
14.5 Pounds
Step-by-step explanation:
Subtracting 165.5 lb from 180 lb gives you 14.5 lb
Please help with solution needed!!
Step-by-step explanation:
you know how to multiply two expressions ?
every term of every expression is multiplied with every term of the other expression and the results are added (while considering any specific signs, if course).
(2x² + 3)(2x² - 3) = 2x²×2x² + -3×2x² + 3×2x² + 3×-3 =
4x² - 6x² + 6x² - 9 = 4x² - 9
and that is exactly the right side of the original equation.
so, it is correct.
Can someone please help me with this square root problem?
Answer:
c = 14.9
Step-by-step explanation:
use the pythagorean thereom:
a² + b² = c²
a² = 11 × 11 = 121
b² = 10 × 10 = 100
c² = 121 + 100 = 221
now find the square root of 221:
√221 = 14.866...
round to the nearest tenth:
the 6 next to the 8 means round up.
so the hypotenuse is 14.9
can someone please teach me how to do percentage
Answer:
value/total value • 100 = percentage
Step-by-step explanation:
if 5 out 100 kids have red backpacks then 5% of kids have red backpacks
5/100 • 100 = percentage
0.05 • 100 = percentage
5% = percentage
if 13 cars out of 41 have flat tires, then 32% of the cars have flat tires
13/41 • 100 = percentage
0.31707317073... • 100 = 31.707317073... %
depending on your precision, you may include as many decimal places as you like, unless the question specifies it. For our example, we will round to 2 decimal places.
31.707317073... % = 31.71%
if you're looking to find percentages for probability, you will use the same equation.
the odds of flipping a coin and it landing on heads are 50%
possibilities:
Heads, Tails
there is one outcome where our result occurs out of the two possible outcomes
1/2 • 100 = percentage
0.5 • 100 = percentage
50% = percentage
Hope this helps and wasn't confusing
Question 7 of 10
What is the midpoint of the segment shown below?
10+
O A. (-1,-3)
O B. (-2, -3)
(-11.0)
- 10
(9,-1)
O C. (-2, -1)
- 10
O D. (-1,-1)
Answer:
A. (-1, -1/2) is the correct answer.
a) Write down all the factors of 120.
Answer:
Factors of 120:
1, 2, 3, 4, 5, 6, 8, 10, 12, 15, 20, 24, 30, 40, 60 and 120
Prime Factors:
2, 3,and 5
Step-by-step explanation:
Factors are: numbers that can be multiplied together to get a certain number
Hope this helps! Plz give brainliest! Also, plz sub to Kgirl633 on yt.
2x^2-19x+9=0 does anyone know the answer
Answer:
x=1/2,x=9
Step-by-step explanation:
[tex]2x^{2} -19+9=0\\\\2x^{2} -18x-x+9=0\\\\2x(x-9)-1(x-9)=0\\\\(2x-1)(x-9)=0[/tex]
2x-1=0......I
x-9=0.......II
Solving I
2x-1=0
2x=1
x=1/2
Solving II
x-9=0
x=9
1234567890987654321123456789
Answer:
1234567890987654321123456789 is the answer
Step-by-step explanation:
and also hey
I NEED HELPPPPP ON THISSS ASAPPPPPPPP!!!!!!!!
- THIS IS A 50 POINT QUESTION
Answer:
40
Step-by-step explanation:
Sum of all angles of triangle = 180°
∠W + ∠X + ∠Y = 180
10x + 17 + 2x - 9 + 3x + 7 = 180
10x + 2x +3x + 17 - 9 + 7 = 180
Combine like terms
15x + 15 = 180
15x = 180- 15
15x = 165
x = 165/15
x = 11
∠Y = 3x +7 = 3*11 + 7 = 33 + 7 = 40
Answer:
X is 11 and after substitution y is 40
Need some help if anyone can
Answer:
Step-by-step explanation:
What is the process where cells divides and replace old or damaged cells?
chromosomes
mitosis
photosynthesis
cell theory
Answer:
The answer is chromosomes.
please show work and explain every step!
Answer:
x = 6
FE = 28
Step-by-step explanation:
The triangles are similar so their side lengths are proportional
we can use that proportional value to find x and FE
(5x-2)/42 = (4x+2)/39 cross multiply expressions
195x - 78 = 168x + 84 get like expressions to the same side of the equation
195x - 168x = 84 + 78
27x = 162 divide both sides by 27
x = 6 now to find FE replace x with 6 in the expression
5x - 2 = 5×6 - 2
FE = 28
PERFOMANCE TASK: Solve the word problem below. You may draw the figure to solve the problem The legs of a right triangle are congruent, and the hypotenuse is 5v2 units long. Find the length of each leg. (Use the Pythagorean Theorem, c2 al + b2D
Answer:
x =5
Step-by-step explanation:
c = 5√2
a = x
b = x
Formula
x^2 + x^2 = c^2 Combine the x^2
Solution
2x^2 = (5√2)^2 Expand the right side
2x^2 = 2*25 Divide both sides by 2
x^2 = 25 Take the square root of both sides.
x = 5
Kathleen and christine compared thier results on their results. Kathleen had 50 correct and christine had 60 correct answers. There were 42 words they both had correct and 6 they both had wrong. How many words were there on the spelling test.
Answer:
48
Step-by-step explanation:
42 + 6 = 48 total words
Answer:
74
Step-by-step explanation:
42+6+(50-42)+(60-42)
Dave bought a golf club priced at $261.Shipping and handling cost an additional 15% of the price.What was the total cost of the golf club,including shipping and handling?
Answer:
$300.15
Step-by-step explanation:
The price of the golf club is 100% of its price.
The shipping and handling add 15% of the price.
That means he will pay a total of 115% of the price of the golf club.
115 of $261 = 1.15 × $261 = $300.15
Answer: $300.15
30 is 10 times as much as
Answer:
3
Step-by-step explanation: 10*3 is equal to 30.
Answer:3
Step-by-step explanation:3 is 10 times as much as 30 which is 3x10=30
50 Points
Show your steps of the conversion of the decimal numbers write in your own steps.
1. 3
2. 8
3. 15
4. 18
5. 33
6. 49
7. 64
8. 108
9. 251
[tex]\\ \tt\longrightarrow 3=\dfrac{3}{10}=0.3[/tex]
[tex]\\ \tt\longrightarrow 8=\dfrac{8}{10}=0.8[/tex]
[tex]\\ \tt\longrightarrow 15=\dfrac{15}{100}=0.15[/tex]
[tex]\\ \tt\longrightarrow \dfrac{18}{10}=1.8[/tex]
[tex]\\ \tt\longrightarrow 33=\dfrac{33}{100}=0.33[/tex]
[tex]\\ \tt\longrightarrow 49=\dfrac{49}{100}=0.49[/tex]
[tex]\\ \tt\longrightarrow 64=\dfrac{64}{100}=0.64[/tex]
[tex]\\ \tt\longrightarrow 108=\dfrac{108}{100}=1.08=1.1[/tex]
[tex]\\ \tt\longrightarrow 251=\dfrac{251}{1000}=0.251[/tex]