Hence, the complete the point-slope equation of the line through ( − 2 , 6 ) (−2,6) is y = 6 .
Point slope kind is employed to represent a line victimisation its slope and a degree on the road. That means, the equation of a line whose slope is 'm' and that passes through a degree is found victimisation the purpose slope kind. totally different forms are often wont to categorical the equation of a line. one amongst them is purpose slope kind. The equation of the purpose slope kind which is given by y - y₁ = m(x - x₁) .We have given two points ( − 2 , 6 )and (−2,6) .
Using slope formula , we get
m = 6 - 6 / -2 -(-2)
m = 0
Putting m = 0 , x₁ = -2 and y₁ = 6 in equation (1) , we get
y - 6 = 0
y = 6
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Compute $2^{10}\cdot 2^8\cdot 2^6\cdot 2^4\cdot 2^2\cdot 2^{-1}\cdot 2^{-3}\cdot 2^{-5}\cdot 2^{-7}\cdot 2^{-9}$.
[tex]2^{10}.2^8.2^6.2^4.2^2.2^{-1}.2^{-3}.2^{-5}.2^{-7}.2^{-9}[/tex] = 32
We need to compute [tex]\bold{2^{10}.2^8.2^6.2^4.2^2.2^{-1}.2^{-3}.2^{-5}.2^{-7}.2^{-9}}[/tex] .
This is the product of exponential numbers with same bases.
We use rules of exponents:
[tex]a^b.a^c=a^{b+c}[/tex][tex]a^{-b}=\frac{1}{a^b}[/tex]Using the first rule we can rewrite
[tex]2^{10}.2^8.2^6.2^4.2^2.2^{-1}.2^{-3}.2^{-5}.2^{-7}.2^{-9}[/tex]
as,
[tex]2^{10+8+6+4+2}.2^{-1-3-5-7-9} = 2^{10+8+6+4+2}.2^{-(1+3+5+7+9)}[/tex]
Using the second rule,
[tex]2^{10+8+6+4+2}.2^{-(1+3+5+7+9)} = \frac{2^{10+8+6+4+2}}{2^{1+3+5+7+9} }[/tex]
[tex]=\frac{2^{30}}{2^{25}}[/tex]
[tex]\bold{= 2^5 = 32}[/tex]
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There are many different kinds of growth patterns. Patterns that increase by a constant rate are linear. Patterns that grow exponentially increase by an ever-increasing rate. If your allowance doubles each week, does that represent linear growth or exponential growth?
If the allocation doubles every week, that represents exponential growth.
Given there are many types of growth models, and models that grow at a constant rate are linear and models that grow exponentially at an increasing rate.
Linear growth is characterized by growth by the same amount per unit time.
Exponential growth is a process of increasing numbers over time. This happens when the instantaneous rate of change of a quantity over time is proportional to the quantity itself.
Exponential growth because the first week you may only get a dollar, but the next week you get 2, then 4, and so on. Your allowance doesn't grow by the same amount every week, so the number it doubles is exponential.
Therefore, if the allowance doubles every week, it represents a exponential growth multiplier because samples growing at a constant rate are linear.
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The number below is not correctly written in scientific notation.
145 × 105
What is the new exponent for the power of 10 after rewriting the number correctly in scientific notation?
1.45 × 10?
Write the new exponent in the blank below. PLEAZ HELP will give brainliest
The new exponent for the power of 10 after rewriting the number correctly in scientific notation would be 1.45 × 10^7
How does scientific notations work?The number is written in the form [tex]a \times 10^b[/tex]where we have [tex]1 \leq a < 10[/tex]
The number b shows the order, which is the most important figure for which scientific notation is used. It tells us how much order large or small a value is in powers of 10. We can for a time, ignore the value of 'a' for two comparable quantities and only compare their orders(this type of comparison is useful when difference is too big, like size of human to size of a star etc sort of comparisons).
The scientific notation is value in terms of power of 10 is known, which helps in easy comparison of quantities differing by a large value.
We have been given that number below is not correctly written in scientific notation.
145 × 10⁵
Therefore, new exponent would be 1.45 × 10^7
Hence, The new exponent for the power of 10 after rewriting the number correctly in scientific notation would be 1.45 × 10^7
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if a1=5 and an=-3an-1 then find the value of a5
Recursive expressions are ways of expressing sequence using functions. The fifth term of the recursive sequence is 405.
Recursive functionsRecursive functions are ways of expressing sequence using functions.
Given the following recursive functions
a₁=5 and;
aₙ = -3aₙ₋₁
For the second term;
a₂ = -3a₁
a₂ = -3(5)
a₂ = -15
For the third term a₃
a₃ = -3a₂
a₃ = -3(-15)
a₃ = 45
For the fourth term
a₄ = 3a₃
a₄ = 3(45)
a₄ = 135
For the fifth term
a₅ = 3a₄
a₅ = 3(135)
a₅ = 405
Hence the fifth term of the recursive sequence is 405.
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Julian describes an angle in the triangle using these statements.
GH is the adjacent side.
HK is the opposite side.
GK is the hypotenuse.
Triangle G H K is shown. Angle G H K is a right angle.
Which angle(s) is Julian describing?
∠G
∠H
∠K
∠H and ∠K
Step-by-step explanation:
The hypotenuse is the longest side of the right-angled triangle. The angle about which Julian is describing is ∠G.
Answer:
A. <G
Step-by-step explanation:
Took the test on edge, hope this helps
Select all parts from the expression above that represents a coefficient. (Just the coefficient... not the coefficient AND the variable.) Group of answer choices -4.9t2 -4.9 22 1.8 22t
The part from the expression above that represents a coefficient is -4.9
How to determine the parts from the expression above that represents a coefficient?The expression is given as
-4.9t^2
To solve this question, we make use of the following illustration.
Let an expression be represented as
ax^n
Where the variable is n
In the expression
Coefficient = a
Variable = x
Power = n
Using the above as a guide, the part from the expression above that represents a coefficient is -4.9
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A rocket is launched from the top of a platform 50 feet above the ground. The rocket will fall after exploding at its maximum height. The rocket's height above the ground is given by the function h(r) = −16r2 + 64r + 50.
The function g(r) is shown in the graph.
graph with r on the x axis and g of r on the y axis that is increasing from the left going through about negative 8 and one half comma 0 to negative 4 comma 100 and then decreasing through negative 1 comma 55 and continuing down and to the right
Which function has the greater maximum?
a
h(r)
b
g(r)
c
h(r) and g(r) have the same maximum.
d
h(r) and g(r) do not have a maximum.
Answer:
The maximum height that the rocket will reach is 271 feet.
Step-by-step explanation:
We first calculate the time, t it takes the rocket to reach maximum height from v = u - gt. Since u = initial velocity = 128 ft/s, v = velocity at maximum height = 0 ft/s and g = acceleration due to gravity = 32 ft/s².
So, v = u - gt.
t = (u - v)/g
= (128 ft/s - 0 ft/s)/32 ft/s²
= 128 ft/s ÷ 32 ft/s²
= 4 s.
We calculate the maximum height from
y - y₀ = ut - 1/2gt² where y₀ = 15 ft and all other variables are as above.
Substituting these values into the equation, we have
y - y₀ = (u - 1/2gt)t
y - 15 ft = (128 ft/s - 1/2 × 32 ft/s² × 4 s) × 4 s
y - 15 ft = (128 ft/s - 64 ft/s)4 s
y - 15 ft = 64 ft/s × 4 s
y - 15 ft = 256 ft
y = 256 ft + 15 ft
y = 271 ft
So, the maximum height that the rocket will reach is 271 feet.
Step-by-step explanation:
How do I factorise this Quadratic Equation to find x?[tex]2x^2-x-120=0[/tex]
The factors of the given Quadratic Equation 2x² - x - 120 = 0 is 8 and -15/2.
What are zeros ?
zeros denotes the factors of the given equation in other words the zeros of the function are the values that make the factors zero. The factors need to multiply out to give the original standard-form equation.
Polynomial roots are the same as polynomial zeros, so they can be found by factoring the quadratic equation into two linear factors, after which they can be equating to zero.
Now, considering the given Quadratic Equation to find x :
2x² - x - 120 = 0
writing the above equation into two linear factors as :
2x² - 16x + 15x - 120 = 0
2x(x-8) + 15(x-8) = 0
(x-8)(2x+15) = 0
Now, equating each linear equation to zero to find the factors:
(x-8) = 0 and (2x+15) = 0
x = 8 and x = -15/2.
Therefore, the factors of the given Quadratic Equation is 8 and -15/2.
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Let f(x)=3 x-2 and g(x)=x^{2}+1 . Perform each function operation.
f(x)-g(x)
Function operations are the rules we use to solve functions. There is a specific way to deal with function addition, subtraction, multiplication, and division.
-x² + 3x +3 is the domain of all real numbers.
What is meant by function operation?Function operations are the rules we use to solve functions. There is a specific way to deal with function addition, subtraction, multiplication, and division.
Let the two functions be f and g then f(x) = 3x - 2 and g(x) = x² + 1.
we have to calculate (f - g)(x)
Which is equivalent to:
(f - g)(x) = f(x) - g(x)
Taking the two functions and substituting them into this expression, we get,
f(x) - g(x) = (3x - 2) - (x² + 1)
simplifying the above function, we get
f(x) - g(x) = 3x - 2 - x² - 1
(f - g)(x) = -x² + 3x - 2 - 1
Therefore, (f - g)(x) = -x² + 3x +3
We must also determine the domain of the new function. However, because this is a second-order function with no denominators, logarithms, or roots, there are no restrictions on the value of x; thus, the domain is all real numbers.
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Write each equation in logarithmic form.
4= (1/2)⁻²
The equation in logarithmic form is log base (1/2) of (4) = -2
Given the equation is:
4= (1/2)⁻²
The fundamental logarithmic function has the notation f(x) = log(r) y = log(x), where a > 0. The exponential function ay = x's inverse is represented by this. The common logarithm (log) or natural logarithm (ln) are examples of log functions (log).
Convert the exponential equation to a logarithmic equation using the logarithm base (10)of the right side (0.01) equals the exponent (−2).
A popular method for changing a mathematical equation from one form to another is to transform it from exponential to log form. The exponential form an x = N is translated into the logarithmic form.
Log aⁿ= x.The exponent of x, which is equal to N, has the exponential form a to it is converted to the logarithm of a number N to the base of a, which is equal to x.
log base (1/2) of (4) = -2
log₁/₂ (4) = ₋2
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Find each product or quotient. √5(√5)
The product of √5(√5) is 5.
To find : the product of √5(√5).
This question can be easily solved using the concept of square root. It can be solved in a few simple steps
Step 1 : Check the power of roots for each term
Both the terms are √5
Since both the numbers have the same root power they can be combined under the same sqaure root for further operation
=> √ ( 5 x 5 )
=> √ 25
It can also be written as √ 5²
square root can also be mentioned as number raised to 1/2
If we solve the powers of 5 => 1/2 x 2 = 1
=> √ 25 = √ 5² = 5
Therefore, we get the product of √5(√5) as 5.
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Gerald ordered a small pizza, asked for it to be divided into 8 equal slices and ate 3 of them. Sarah also ordered a small pizza asked it to be divided into 24 slices, and ate 6 of them. Who ate more pizza? ( My sister's 6th grade question, please help her)
The Gerald ordered and ate more pizza than Sarah .
What is fraction?
A fraction having whole numbers for the numerator and denominator. A fraction is a number of the form: ab where a and b are integers and b≠0. It represents the division of two numbers.
Given:
Gerald ordered a small pizza, divided into 8 equal slices and ate 3 of them.
Sarah also ordered a small pizza ,divided into 24 slices, and ate 6 of them.
According to given question we have
Gerald divided into 8 equal slices and ate 3 of them.
=3/8
Sarah divided into 24 slices, and ate 6 of them.
=6/24
=1/4
Multiply with 2 in both numerator and denominator we get,
=1*2/4*2
=2/8
∴3/8>2/8
So, Gerald ate more pizza.
Therefore, the Gerald ordered and ate more pizza than Sarah .
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Simplify each expression. x²/₇ . x³/₁₄
The result of simplifying each number x²/₇ . x³/₁₄ using the exponent rules is [tex]\sqrt{}[/tex]x
To solve this exercise we have to resolve algebraic operations following the exponent rules.
(x²/₇) * (x³/₁₄)
Base= x
Using the product rule that indicates that: the exponent result will be the addition of these exponents, we have:
(x) ⁽²/₇ ⁺ ³/₁₄⁾
(x) ⁽⁴⁺³⁾/₁₄
(x) ⁽⁷/¹⁴⁾
(x) ⁽¹/²⁾
As we have a fractional exponent, you must convert the exponent to root:
[tex]\sqrt{}[/tex]x
What is an exponent?In mathematics an exponent is the number of time that a number, called (base) is multiplied by itself. It is also called, power or index.
Example: 3² = 3*3 = 9
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The number below is not correctly written in scientific notation. Write it using correct scientific notation.
6.57*1000
Answer: 6.57x10^3
Step-by-step explanation:
Move the decimal so there is one non-zero digit to the left of the decimal point. The number of decimal places you move will be the exponent on the 10. If the decimal is being moved to the right, the exponent will be negative. If the decimal is being moved to the left, the exponent will be positive.
Hope this helped :)
Mckenzie and Cara both tried to find the missing side of the right triangle. HURRY PLEASE DUE TODAY. I WILL MARK BRANLIEST IF MULTIPLE PEOPLE ANSWER.
Mckenzie's Work: Cara's Work:
a2 + b2 = c2 a2 + b2 = c2
52 + 132 = c2 52 + b2 = 132
25 + 169 = c2 25 + b2 = 169
194 = c2 b2 = 144
Square root 194 equals square root c squared. Square root b squared equals square root 144.
13.93 ≈ c b ≈ 12
McKenzie is right and Cara is wrong.
Step-by-step explanation:a² + b² = c²
[The Pythagoras theorem a , b are the square edge)
5² + 13² = c²25 + 169 = c²194 = c²[tex]\sqrt{194}[/tex] = c13.93 = cSo, McKenzie is right and Cara is wrong.Answer:
the correct answer is McKenzie's
Step-by-step explanation:
the problem looks for the measure of the hypotenuse, which is the longest side of a right triangle, so it cannot be 12 in because we have a cathetus of 13 in, therefore, without making calculations but following a simple reasoning, the correct answer is McKenzie's , about 13.93, the only possible option
Ms.Shultis is driving along the road moves at a rate of 56 miles per hour driven. How long does it take for her to travel 84 miles?
Answer:
: A person driving along the road moves at a rate of 56 miles per hour driven.
Step-by-step explanation:
Which line from section 1 reveals Hawthorne's informal, fatherly tone for this story?
A. A boy used to be seen in the streets of Boston.
B. Ben was born in 1706; so that he was now about 10 years old.
C. His father, who had come over from england.
Answer if you're 100 percent sure, this is for a test.
If a gas has a volume of 1 l at a pressure of 200 kpa, what volume would it have when the pressure is increased to 400 kpa? assume the temperature and number of particles are constant.
With an inverse relationship, when the pressure is increased to 400 kPa, the volume will be 0.5L, assuming that the temperature and number of particles are constant.
Boyle's Law states the inverse relationship between volume and pressure. It states that a constant amount of gas at a constant temperature, decreasing the volume will increase its pressure, and increasing its volume will decrease its pressure.
V = k/P or P1V1 = P2V2
where V = volume
P = pressure
If a gas has a volume of 1 L at a pressure of 200 kPa, and assuming that the temperature and number of particles are constant, using the inverse relationship, solve for the volume of the gas at a pressure of 400 kPa.
P1V1 = P2V2
200 kPa(1L) = 400 kPa(V2)
V2 = 200/400
V2 = 0.5 L
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A bubble gum machine in a grocery store is filled with 500 candies. Each time a person puts in money, 10 candies come out. This function is a model for the number of candies left in the machine after a person buys some candy.
The required function will be
y= 500-10x
function, in mathematics, an expression, rule, or law that defines a relationship between one variable (the independent variable) and another variable (the dependent variable).
let amount of money = x and
number of remaining candy =y
total 500 remaining candies= total 10x amount of money
y= 500-10x
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A desktop world globe has a volume of about 1386 cubic inches. The radius of Earth is approximately equal to the radius of the globe raised to the 10 th power. Find the radius of Earth. (Hint: Use the formula V=⁴/₃πr³ for the volume of a sphere.)
The radius of the Earth, approximately equal to the radius of the globe raised to the 10th power, is 250,562,113.2 inches.
First, solve for the radius of the desktop world globe using the formula for the volume of a sphere given by:
V = 4/3 π r^3
If the desktop world globe has a volume of about 1386 cubic inches, then
1386 cubic inches = 4/3 π r^3
r = 6.916582163 inches
Next, solving for the radius of the Earth if it is approximately equal to the radius of the globe raised to the 10th power.
Exponent, or power, is the small number written at the upper right of a constant or variable that tells how many times that constant or variable should be multiplied to itself.
If the radius of the Earth if it is approximately equal to the radius of the globe raised to the 10th power, then
r of Earth = r of globe ^10
r = 6.916582163^10
r = 250,562,113.2 inches
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I feel du mb today and i have another test
iliana signed up for a store credit card with no annual fee to get a discount of 12.5 percent off her entire first purchase.
percents
total
100%
if she saved $7.29 on her first purchase by using this credit card, what was the total price of the items before the discount?
$0.91
$1.71
$58.32
$91.13
Answer:
58.32
Step-by-step explanation:
100÷12.5=8, 7.29×8=58.32.
can someone check if I did this question right, ?.
Answer:
Yes, you did it correctly. Note that shape B is 3 bigger than shape A, so it has much larger dimensions and properties.
If x= -1 in the equation y = 2x + 2, then what is the value of y?
A/
If f(x) = −3x + 4 and g(x) = 2, solve for the value of x for which f(x) = g(x) is true.
Answer: -3x+4=2 is the new equation x= 2/3
Step-by-step explanation: brainliest?
the coefficients of variation for each data set are within 5 percentage points of each other. therefore, the systolic measurements vary ▼ the diastolic measurements.
The answer is 16.7 %.
What is meant by mean?The average of a group of variables is referred to as the mean in mathematics and statistics. There are several methods for calculating the mean, including the geometric mean, the harmonic mean, and the simple arithmetic mean.Why are you being so cruel, it demands to know. So, someone would ask you that if they thought you were being harsh or disrespectful.In just two easy steps, you can determine the mean, or average, of a set of data: Add up all of the values to determine the sum. By how many values there are in the data collection, divide the total.adjective Being cruel to another person, such as by denying them the opportunity to do something, is what it means to be mean.The necessary calculation is below:
observations Systolic(x) Diastolic(y) x^2 y^2
1 120 79 14400 6241
2 130 74 16900 5476
3 157 75 24649 5625
4 96 50 9216 2500
5 156 89 24336 7921
6 124 87 15376 7569
7 116 59 13456 3481
8 137 66 18769 4356
9 124 71 15376 5041
10 118 81 13924 6561
sum 1278 731 166402 54771
For Systolic (x)
mean= sum(x)/10 = 1278/10 = 127.8
stdev= s =sqrt( (sum(x^2 - 10*127.8^2)/9) = sqrt ( (166402 - 10*127.8^2)/9) =18.48
So coefficient of variation ( systolic) is = (stdev/mean )*100 = (18.48/127.8)*100 = 14.5 %
For Diastolic (x)
mean= sum(y)/10 = 731/10 = 73.1
stdev= s =sqrt( [tex](sum(x^2 - 10*73.1^2)/9) = sqrt ( (54771 - 10*73.1^2)/9)[/tex]= 12.18
so coefficient of variation ( systolic) is = (stdev/mean )*100 = (12.18/73.1)*100 = 16.7 %
Here, systolic is less varied than the diastolic.
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A and B are complementary angles. If mA = (6x + 2)° and m
B = (4x + 18)°, then find the measure of ZA.
The measurement of angle A and B is 44° and 46° respectively.
What are complementary angles ?
When the sum of two angle is 90 degree it is known as complementary angles and when a line divides the line than the sum of angles formed with the given straight line is always equals to 90 degree.
It is given that the angle A and B are complementary angles whose measurements are :
∠A = (6x + 2)°
and , ∠B = (4x + 18)°
The sum of angle A and B will be 90 degree as they are complementary angles that is :
∠A + ∠B = 90°
Now, solving by adding like terms and finding the value of x :
6x +2 + 4x + 18 = 90°
10x + 20 = 90°
10x = 90-20
10x = 70°
x = 7°
now, the measurement of angle A will be :
∠A = (6x + 2)°
∠A = (6 · 7 + 2)°
∠A = (42 + 2)°
∠A = 44° and ∠B = 46°
Therefore, the measurement of angle A and B is 44° and 46° respectively.
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Solve. Check for extraneous solutions. √4 x-23 -3=2
The solution for given equation is 196 and there are no extraneous solutions.
Extraneous solutions refer to the solution, which on being placed in the equation, does not make Left Hand Side and Right Hand Side equal.
Rewriting the equation and solving it by addition or subtraction of values on both sides as per the requirement -
✓4x - 23 - 3 = 2
Adding 3 on both sides of the equation
✓4x - 23 - 3 + 3 = 2 + 3
✓4x - 23 = 5
Adding 23 on both sides of the Equation
✓4x - 23 + 23 = 5 + 23
✓4x = 28
Taking square on both sides
(√4x)² = 28²
4x = 784
Shifting 4 to Right Hand Side
x = 784 ÷ 4
Performing division
x = 196
Keep the value of x in equation to find it it is extraneous or not -
✓(4 × 196) - 23 - 3 = 2
✓784 - 23 - 3 = 2
28 - 23 - 3 = 2
25 - 3 = 2
2 = 2
Since RHS and LHS are equal, there is no extraneous solution for the given equation.
Hence, the solution for given equation is 196 and there are no extraneous solutions.
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Decrease the number 724,062.58 by 100,000
Answer:
624,062.58 is your answer :)
Step-by-step explanation:
Which angle is vertical to 2?
Answer:
angle 5 is vertical to 2
Step-by-step explanation:
Vertical angles are pair angles formed when two lines intersect.
Answer: <5
Step-by-step explanation:
Find the real and imaginary solutions of each equation.
81 x⁴-1=0
A solution that is real in its nature is called the real solution of that equation.
X + 5 = 0
We can solve the above equation as,
X + 5 = 0
X = -5
Now, if we plug the value of X into the equation,
X + 5 = 0
-5 + 5 = 0
0 = 0
The solution is real and is true for this equation.
While the solution of an algebraic expression solution is imaginary if it is the square root of a negative number. It involves the imaginary unit iota.
The complete solution of the expression is given below in the picture.
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