Remark
10^-5 means there are 4 zeros to the right of the decimal point before you encounter a digit other than zero.
That means that the answer is B
What are the domain and range of the function f(x)=5^x-3 +1
Final answer:
The domain of the function f(x)=5ˣ-3+1 is all real numbers (-∞, +∞), and the range is all real numbers greater than -2 (-2, +∞).
Explanation:
For the given function f(x) = 5ˣ - 3 + 1, the domain and range can be determined by understanding the behavior of the function's formula. The domain refers to all possible x-values that can be input into the function, and the range refers to all possible y-values that the function can output.
The domain of any exponential function like 5ˣ is all real numbers because you can raise 5 to any power, whether it's positive, negative, or zero. Therefore, the domain of f(x) is (-∞, +∞).
To find the range of the function, we look at the output values. Since exponential functions grow without bound as x increases and approach zero as x decreases (but never actually reaches zero), 5^x will do the same. When we subtract 3 and then add 1, we're simply moving the graph down by 2 units. Thus, where the original function 5ˣ would never be less than 0, after the transformation, the function will never be less than -2. So, the range of f(x) is (-2, +∞).
Stacie is a resident at the medical facility where you work. You are asked to chart the amount of solid food that she consumes. For the noon meal, today she ate 1/2 of a 3-ounce serving of meatloaf, 3/4 of her 3-ounce serving of mashed potatoes, and 1/3 of a 2-ounce serving of green beans. How many ounces of solid food did Stacie consume? Round final answer to two decimal places.
Remark
The general formula is fraction * solid food = amount
Total amount = 1/2 * 3 oz + 3/4 * 3 oz + 1/3 * 2 oz
Total amount = 3/2 oz + (9/4) oz + 2/3 oz
The lowest common denominator of 2 4 and 3 = 12
Total amount = 3*6/2*6 + 9*3/4*3 + 2*4/3*4
Total amount = 18/12 + 27/12 + 8/12
Total amount = 53/12 = 4 5/12 <<< Answer oz of food.
4.42 oz of food <<<< Answer
A^3+4a^2+4a factor completely
So firstly, factor out the GCF, or greatest common factor. To find the GCF, list the factors of every term and the greatest one they all share is their GCF. In this case, the GCF is "a":
[tex]a(a^2+4a+4)[/tex]
Next, we are going to apply the square of binomials rule in this situation, which is [tex](x+y)(x+y)=x^2+2xy+y^2[/tex] In this case:
[tex]a^2+4a+4=(a+2)(a+2)\\\\a(a+2)(a+2)[/tex]
Your final answer is [tex]a(a+2)(a+2)[/tex]
you have 5 cups of rice to make bibimbap, a popular Korean meal. The recipe calls for 4/5 cup of rice per serving. How many full servings of bibimbap can you make? How much rice is left over?
The number of full servings of bibimbap can you make is dividing the total cups of rice by cups of rice per serving.
You can make 6 whole servings remainder 1 cup of rice
Given:
Total cups of rice = 5 cups
Cups of rice per servings = 4/5 cup
Number of servings of bibimbap can you make = Total cups of rice ÷ Cups of rice per servings
= 5 cups ÷ 4/5 cup
= 5 × 5/4
= (5 × 5) / 4
= 25 /4
= 6 whole servings remainder 1 cup of rice
Therefore, you can make 6 whole servings remainder 1 cup of rice
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Flowchart Proof-
Given: line a is parallel to line b, and angle 7 is congruent to angle 10
Prove: line c is parallel to line d
Please help and use the correct postulates and theorems for reasons.
In this flowchart proof, we utilised the Corresponding Angles Postulate to conclude that line c is parallel to line d. Given that line a is parallel to line b, and angle 7 is congruent to angle 10, we can say that corresponding angles on line c and line d are also congruent, hence proving line c is parallel to line d.
Explanation:For this flowchart proof, we will use the idea of corresponding angles and the postulate that if a transversal intersects two lines and the corresponding angles are congruent, then the lines are parallel.
Given that line a is parallel to line b.Next, it's given that angle 7 is congruent to angle 10. Assume angle 7 is the angle made by line a and a transversal line, and angle 10 is the angle made by line b and the same transversal.Since line a is parallel to line b and they are cut by a transversal, corresponding angles will be congruent (Corresponding Angles Postulate).We know that angle 7 is congruent to angle 10 (Given).Assume line c and line d are cut by the same transversal as line a and line b, and angle 7 is the corresponding angle to a certain angle on line c, and angle 10 is the corresponding angle to a certain angle on line d. Since angle 7 is congruent to angle 10, the corresponding angles on line c and line d will also be congruent.Hence, line c is parallel to line d (Corresponding Angles Postulate).Learn more about Flowchart Proof here:https://brainly.com/question/12611050
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How much wood $400 be worth after 11 years if it were invested at 4% interest compounded monthly? (Use the formula below and round your answer to the nearest cent.) A(t)=P(1+r/n)^nt
Here we are given the formula for compound interest as :
[tex]A=P(1+\frac{r}{n})^{nt}[/tex]
Here
A= Amount
P=Principal
r=rate of interest
n=number of times interest is compounded per year
t=time(years)
So we are given
P= $400
r=4% or 0.04
t= 11 years
n= 12
Plugging these values in the formula for compound interest we have,
[tex]A=400(1+\frac{0.04}{12})^{12*11}[/tex]
A= $620.6286
Amount = $620.6
Answer: The final amount after 11 years will be $620.6 .
To find the value of $400 invested at 4% interest compounded monthly for 11 years, use the compound interest formula A(t) = P(1 + r/n)^(nt) and solve for A(t). After calculations, the amount comes to approximately $660.44 when rounded to the nearest cent.
To calculate the future value of $400 invested at 4% interest compounded monthly over 11 years, we can use the compound interest formula provided: A(t) = P(1 + r/n)^(nt). In this formula, P represents the principal amount ($400), r is the annual interest rate (0.04), n is the number of times interest is compounded per year (12 for monthly compounding), t is the number of years the money is invested (11 years), and A(t) is the amount of money accumulated after t years, including interest.
Using the formula:
Calculate the monthly interest rate: r/n = 0.04/12 = 0.003333...Determine the total number of compounding periods: nt = 12 * 11 = 132.Substitute the values into the formula: A(t) = $400(1 + 0.003333...)¹³².Calculate A(t) to find the future value of the investment.The calculation is as follows:
A(t) = $400(1 + 0.003333...)¹³²
A(t) = $400(1.003333...)¹³²
A(t) = $400(1.6511)
A(t) = $660.44
After rounding to the nearest cent, $400 invested at 4% interest compounded monthly for 11 years would be worth approximately $660.44.
Determine the multiplicity of the roots of the function k(x) = x(x + 2)3(x + 4)2(x − 5)4. 0, -2, -4, 5
Answer:
The polynomial function [tex]k(x)=x(x+2)^3(x+4)^2(x-5)^4[/tex]
To determine the multiplicity of 0, -2, -4, 5.
The multiplicity of a root is the number of times the root appears.
First find the root of the equation, set the function equals to zero.
[tex]x(x+2)^3(x+4)^2(x-5)^4=0[/tex]
therefore, the root of this function are, x=0,-2, -4, 5
To find the multiplicity of the roots:
A factor of x would have a root at x=0 with multiplicity of 1
similarly, x=-2 with multiplicity of 3
x=-4 with multiplicity of 2
x=5 with multiplicity of 4.
Answer:
0 has multiplicity 1
−2 has multiplicity 3
−4 has multiplicity 2
5 has multiplicity 4
The domain for f(x) and g(x) is the set of all real numbers.
Let f(x) = 2x^2 + x − 3 and g(x) = x + 2. Find (f • g)(x).
The product of the functions f(x) and g(x), (f • g)(x), is found by multiplying the two functions together. The resulting function is 2x^3 + 5x^2 - x - 6.
Explanation:The question is asking for the product of functions f(x) and g(x), denoted as (f • g)(x). To find (f • g)(x), we simply have to multiply function f(x), which is 2x^2 + x - 3, and function g(x), which is x + 2, together.
Let's do it: (2x^2 + x - 3) * (x + 2). Multiplying these two functions out, we get: 2x^3 + 4x^2 + x^2 + 2x - 3x - 6. Simplifying these, we arrive at 2x^3 + 5x^2 - x - 6.
So, (f • g)(x) = 2x^3 + 5x^2 - x - 6.
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Which inverse operation would be used to verify the following equation?
102 ÷ 3 = 34
For this case we have:
The division given by:
102 ÷ 3 = 34
The dividend is 102 The divisor is 3 The quotient is 34To verify its result we use multiplication as a reverse operation, that is:
We multiply the quotient by the divisor and its result must be the dividend.
So:
[tex](34) (3) = 102\\[/tex]
Answer:
Multiplication, [tex](34) (3) = 102[/tex]
4 times the sum of 12 and 26
It would be 4(12 + 6). The answer to this is 7.
Hope that helps :)
the temperature changed from -7 degrees f at 6:00 am to 7 degrees f at noon write an expression
Please help!!
Choose which best explains the distributive property.
a property of the real numbers that states that the order in which numbers are added or multiplied does not change the value
a property of the real numbers that states that how numbers are grouped in a sum or product does not change the value
a(b + c) = ab + ac, or a(b - c) = ab - ac
I would say that the answer that best describes the distributive property is "a property of the real numbers that states that the order in which numbers are added or multiplied does not change the value". Distributive property says that when you have a(b+c), you can add b and c together and then multiply by a or multiply b and c by a separately and then add them together after. It does not matter what order you choose to add and multiply in.
I hope this helps :)
how much is 36 nickels 24 dimes 19 quarters and 15 fifty cent?
Fifty Cent = 50 cents
Quarter = 25 cents
Dime = 10 cents
Nickel = 5 cents
__________________________________________________________________
15 Fifty Cent coins = 7.50 dollars
19 Quarters = 4.75 dollars
24 Dimes = 2.40 dollars
36 Nickels = 1.80 dollars
__________________________________________________________________
Total: $16.45
Hope that helps!
which one is this answer if you are good a math
[tex]a=\dfrac{2d}{t^2}\ \ \ \ \ |\text{solve for t} \\ \\\\\dfrac{2d}{t^2}=\dfrac{a}{1}\ \ \ \ \ |\text{cross multiply}\\\\at^2=2d\ \ \ \ \ |:a\\\\t^2=\dfrac{2d}{a}\to t=\sqrt{\dfrac{2d}{a}}\\\\\text{We have}\\ \\a=2\dfrac{m}{s^2},\ d=10m\\\\\text{substitute}\\\\t=\sqrt{\dfrac{2\cdot10m}{2\frac{m}{s^2}}}=\sqrt{10m\cdot\dfrac{s^2}{m}}=\sqrt{10s^2}=\sqrt{10}\ s\\\\Answer:\ C.\ \sqrt{10}\ seconds[/tex]
A hybrid car gets 45 miles per gallon. At that rate, how much gas would it take to travel across country, a distance of about 2600 miles
To travel 2600 miles in a hybrid car with a fuel efficiency of 45 mpg, it would require approximately 57.78 gallons of gas.
To calculate the amount of gas needed for a hybrid car to travel 2600 miles with a fuel efficiency of 45 miles per gallon (mpg), you can use the formula:
Divide the total distance by the fuel efficiency: 2600 miles \/ 45 mpg.This gives the total gallons of gas needed: ~57.78 gallons.So, it would take approximately 57.78 gallons of gas to travel across the country in a hybrid car with a fuel efficiency of 45 mpg.
Willis bought a gallon of paint. He painted a wall that is 9 feet high and 10 feet wide. Then
he used the rest of the paint to paint 46 square feet in the hall. How many square feet did the gallon of paint cover?
Answer:
Step-by-step explanation:
9 *10= 90 feet
90+ 46= 136 square feet
10 times 5+4 to the 2nd power /4
Equals to 54...
Hope this helps....
If f(x)=4x-11 what is the value of f(5)
f(5) = 4(5) - 11
f(5) = 20 - 11
f(5) = 9
The answer is 9 :)
Please give BRAINIEST :)
Thanks
By assigning the value of X to the function, we have:
f( x ) = 4 x - 11
f ( 5 ) = 4 * 5 - 11
f ( 5 ) = 20 - 11
f(5 ) = 9
therefore f ( 5 ) = 9
I need your help please !
Determine the slope - down 1, right 3. This is -1/3.
Determine the y-intercept. Up 3 from the origin.
Use this information to form an equation:
[tex]y = -1/3x + 3[/tex]
You need at least $635 to go on a trip to Washington, DC. You already have $75 saved for the trip. You decide to save an additional $65 per week. Which inequality shows the number of weeks, w, you need to save to be able to go on the trip?
75+65w≥635
This is the inequality because you already saved 75 so you just add it to the amount you save after a certain amount of weeks. It needs to be more than 635 for the the trip.
Is 2pi greater than or less than .38
[tex]2\pi\approx6.28\\.38=0.38\\\\2\pi >.38[/tex]
−3 1/3 ÷ 9 pllllllllllllllllllllllllllllllllllllllllllllllllll
[tex]-\frac{10}{27}[/tex] hope this helps :)
Ricardo is considering the following jobs as summer employment.
If he wants to earn $1,000 this summer working the least amount of hours, which job should he choose?
A. babysitting
B. yard work
C. lifeguarding
D. camp counselor
Answer:
I would say you lifeGuarding
Step-by-step explanation:
Answer:
Its lifegaurding doing the quiz rn
Step-by-step explanation:
a recipe for one batch of cookies calls 1 1/2 cups of flour how many cups of flour are needed for 3 batches
What is the justification for each step in the solution of the equation?
1.) 5x-4/2 = 2x-1
2.) 5x-4 = 2(2x-1)
3.) 5x-4 = 4x - 2
4.) 5x = 4x+2
5.) x = 2
Step 1 : (5x-4)/2 = 2x-1 [Given]
Step 2 : ((5x-4)/2) × 2 = 2 × (2x-1) [Multiplicative Property of Equality i.e. by multiplying both sides of the equation by same number]
Step 3 : (5x-4) = 4x-2 [By Distributive Property]
Step 4 : 5x - 4 + 4 = 4x - 2 + 4 [By addition property of equality i.e. by adding both sides of the equation by same number]
⇒ 5x = 4x + 2
Step 5 : 5x - 4x = 4x + 2 - 4x [By subtraction property of equality i.e. by subtracting both sides of the equation by same number]
⇒ x = 2
Answer:
Step 1 : (5x-4)/2 = 2x-1 {Given}
__________________________________________________________
Step 2 : ((5x-4)/2) × 2 = 2 × (2x-1) {Multiplicative Property}
__________________________________________________________
Step 3 : (5x-4) = 4x-2 {Distributive Property}
__________________________________________________________
Step 4 : 5x - 4 + 4 = 4x - 2 + 4 {Addition property}
5x = 4x + 2
__________________________________________________________
Step 5 : 5x - 4x = 4x + 2 - 4x {Subtraction property}
x = 2
x power 3 minus 8
can you tell me how to do it and thanks in advance
is the following statement true or false? if the sum of three numbers is negative then all three numbers are negative, explain.
it is true!!!! hope this helps
Solve the equation 425x=850
Answer:
x=2
Step-by-step explanation:
To solve this, you must isolate x. To do this, divide both sides by 425 because that is what x is being multiplied by (and dividing is its opposite). Then, you get the answer, x=2.
solve the quadratic equation by completing the square: x^2+2x-2=0
ANSWER
[tex]x=\sqrt{3}-1[/tex] or [tex]x=-\sqrt{3}-1[/tex]
EXPLANATION
To complete the square for [tex]x^2+2x-2=0[/tex].
We rewrite the equation to get
[tex]x^2+2x=2[/tex].
We now add [tex](1)^2[/tex] to both sides to get
[tex]x^2+2x+1^2=2+1^2[/tex].
The expression on the Left Hand Side of the equation is a perfect square.
So our equation becomes
[tex](x+1)^2=2+1[/tex]
This gives us,
[tex](x+1)^2=3[/tex]
We take square root of both sides to obtain,
[tex]x+1=\pm \sqrt{3}[/tex]
[tex]x=-1\pm \sqrt{3}[/tex]
We split the [tex]\pm[/tex] to obtain,
[tex]x=\sqrt{3}-1[/tex]
or
[tex]x=-\sqrt{3}-1[/tex]
Answer:
x = √3 - 1 and x = -√3 - 1
Step-by-step explanation:
x^2 +2x - 2 = 0
To solve this equation, keep the variables on one side and constants on the other
x^2 + 2x = 2
Now to complete the square, divide the coefficient of x by 2:
2x ---> coefficient of x is 2
so 2/2 = 1
Now add the square of 1 to both the sides of the equation:
x^2 + 2x + (1)^2 = 2 + (1)^2
which makes it
(x + 1)^2 = 3
To solve it, take square root of both sides which gives
x = √3 - 1 and x = -√3 - 1
Solve for m.
3m+7/2=−2m+5/2
A.-1
B.-1/5
C.6
D.6/5
To solve this we must isolate x which involves having the variables on one side and the numbers on the other.
First add 2m to both sides
3m+7/2=-2m+5/2
5m+7/2=5/2
Then we subtract 7/2 from both sides
5m+7/2=5/2
5m=-1
Finally we divide both sides by 5
5m/5=-1/5
Our final answer is -1/5
So the answer is B
Hope this helps!