Answer: 3, 6, 15, 17, 21
Step-by-step explanation:
State the property of logarithms used to rewrite the expression:
logs 6 - logs 2 = log: 3
Answer:
[tex] log_{s}6 - log_{s}2 \\ = log_{s}( \frac{6}{2} ) \\ = log_{s}3[/tex]
Suppose you leave your house and travel 13 mi due west. Then you travel 3 mi due south. How far, in miles, are you from your house as the crow flies (a straight line)? Round your answer to the nearest tenth if necessary.
Answer: [tex]13.34\ \text{miles}[/tex]
Step-by-step explanation:
Given
First the person travels 13 mi west and then 3 mi due to south
The distance traveled by crow is represented by line BO
using Pythagoras theorem, we can write
[tex]\Rightarrow AO^2+AB^2=BO^2\\\Rightarrow BO^2=13^2+3^2\\\Rightarrow BO^2=178\\\Rightarrow BO=\sqrt{178}\\\Rightarrow BO=13.34\ \text{miles}[/tex]
NEED HELP ASAP - Algebra 2
Every complex number has the form a+bi with a and b as real numbers. Is it possible to create a complex number in which b=0? If so, create two examples to show your hypothesis is true. If not, explain why it is not possible.
Your response must be at least 50 words.
No, It is not possible to have a complex number in the form of a + bi when b = 0.
What is an expression?An expression is a way of writing a statement with more than two variables or numbers with operations such as addition, subtraction, multiplication, and division.
Example: 2 + 3x + 4y = 7 is an expression.
We have,
Complex number.
It is in the form of a + ib.
Where a and b are real numbers.
Now,
If b = 0 then we can not have a complex number.
Example:
a + bi
a = 1 and b = 0
1 + 0i = 1 which is not a complex number.
In order to have a complex number a can be any real number and 0 but b can not be a zero.
Thus,
It is not possible to have a complex number in the form of a + bi when
b = 0.
Learn more about expressions here:
https://brainly.com/question/3118662
#SPJ1
Amelie is making a recipe that uses 134 cups flour. She is making 212 times the original recipe. Amelie draws this model to represent the number of cups of flour she needs. How many cups of flour does Amelie need
Amelie needed 335 cups of flour for the recipe.
How is quantity calculated?The whole centre line length, as well as the construction's breadth and depth, must be multiplied in order to determine the required amount of quantity. Every time the main wall is attached to a cross wall, a partition, or a verandah, the centre line length will be halved at that intersection.Any number, variable, or algebraic combination of other numbers can be a quantity in a mathematical equation. Seven, ten, x, and the product of x and seven, or x + seven, are the four numbers in the equation x + 7 = 10.The unit price is the cost per unit of the product you are purchasing. The amount might be given per thing or per measurement type, such ounces, grammes, gallons, or litres.Given data :
She is making 2 1/2 or 2.5 times the original recipe.
Cups in original recipe= 134 cups
cups Amelie will need= 2.5 × 134
= 335 cups
Learn more about find the quantity refer to :
https://brainly.com/question/24264484
#SPJ4
What is a 3 variable system?
The three variable system is written as (x, y, z).
Here we have to find the definition of three variable system.
basically a solution of a system in three variables is an ordered triple (x, y, z) that makes all three equations true.
On the other hand it is what they all three have in common.
Where as the solution to a system of three equations in three variables (x, y, z) is called an ordered triple.
In order to solve these one we have to do the following:
First we have to pick any two pairs of equations from the system.
And then we have to eliminate the same variable from each pair using the Addition/Subtraction method.
Final step is to solve the system of the two new equations using the Addition/Subtraction method.
To know more about equation here.
https://brainly.com/question/10413253
#SPJ4
Park rangers plan to expand the area of a park to 506 square miles. Currently, the length of the park is 18 miles and the width is 17 miles. They want to extend the length and the width by the same number of miles. If they are successful, what will the new dimensions of the park be? Explain and I need this before tomorrow
As 200 is not a perfect square it is not possible to increase the dimensions of the park by the same number of miles.
What are the area and perimeter of a rectangle?The area of a rectangle is the product of its length and width.
The perimeter of a rectangle is the sum of the lengths of all the sides.
We know the area of a rectangle is (length×width).
Given, Park rangers plan to expand the area of the park to 506 square miles.
Currently, the park has an area of (18×17) = 306 square miles.
Therefore, The amount of square miles they need to increase is (506 - 306)
= 200 miles.
Now, They also want to increase the length and the width by the same amount but 200 is not a perfect square so it is not possible to increase the dimensions by the same amount.
learn more about rectangles here :
https://brainly.com/question/29123947
#SPJ1
-21:(-7)+4.(-7-12 =
CUANTOS ES??
A student has two different samples of soils. She drops a small amount of water on each sample and squeezes the soil in her hand. Her results are shown below. one hand shown holding crumbly soil, the other hand with soil held together and smooth Which statement best describes this test? A. The student is testing each soil's permeability, and soil X is more permeable than soil Y. B. The student is testing each soil's porosity, and soil Y is more porous than soil X. C. The student is testing each soil's texture, and soil Y has more clay than soil X. D. The student is testing each soil's minerals, and soil X has more minerals than soil Y.
The student is testing each soil's permeability, and soil X is more permeable than soil Y. The correct option is A.
What is an experimental approach?An experiment is a technique used to confirm or deny a hypothesis, as well as assess the likelihood or effectiveness of something that has never been tried before. Experiments show what happens when a specific factor is modified, which sheds light on cause-and-effect relationships.
Porosity can be defined as the quality of the material having pores or holes. The permeability can be defined as the state or quality of a material that allows liquids or gases to pass through it.
The soil which does not hold much water can be considered of high porosity and high permeability. As it is only possible if the soil has a large number of pores and it is not in compact form.
To know more about an experimental approach follow
https://brainly.com/question/6665872
#SPJ1
There are 630 calories in seven ounces of a certain ice cream. How many calories are there in two pounds?
\text{1 pound}=
1 pound= 16 ounces
How many calories are there in 32 ounces?
Answer:
630c=7ou
1ou=90c,
1po=16(90c)
2po=x
x=288calories
Mason has 2 cups of peanut
butter. He is making peanut butter
sandwiches. If he uses a cup of
peanut butter in each sandwich,
how many sandwiches can he
make?
[?] sandwiches
Simplify your answer.
Enter
Use the number line to plot –3, 1, and 3. Which statements are true? Select all that apply. –3 > 1 –3 = 3 1 < 3 –3 < 1
By the Number line, the true statements are,
⇒ 1 < 3
⇒ - 3 < 1
What is Number line?Number line is a horizontal line where numbers are marked at equal intervals one after another form smaller to greater.
We have to given that;
In Number line, Plot the numbers - 3, 1 and 3.
Now, After plotting the numbers in Number line, we get;
⇒ - 3 < 1 < 3
Thus, The correct statements are,
⇒ 1 < 3 and - 3 < 1
Learn more about the number line visit:
https://brainly.com/question/28223520
#SPJ1
An investment of $1,500 is earning 7% simple interest each year. How much will the investment be worth after one year?
A.$105
B.$1,605
C.$2,550
D.$10,500
Answer:
B
Step-by-step explanation:
1500 * 0.07 = 105
105 + 1500 = 1605
Brianna has a gift card for $15 that she will use to help buy a new pair of jeans. The jeans that she wants were originally priced at $62.80, but this weekend they are marked down 25% as part of a back-to-school sale. Also, because of a sales tax holiday, Brianna will not have to pay any sales tax on the jeans. How much will Brianna have to pay for the jeans, after the value of the gift card has been deducted?
$0.70
$32.10
$35.85
$47.10
Answer:
32.10
Step-by-step explanation:
25% of 62.80 is 15.70
62.80- 15.70 = 47.10
47.10- the 15 dollar giftard = 32.10
(Hope this helps! Please ask questions in the comments) :D
The two congruent angles of an isosceles triangle are called _____ angles.
Answer:
isosceles triangles have two congruent acute angles
Five hundred fifty students attended the assembly. If the ratio of boys to girls in the assembly was 6 to 5, how many girls attended the assembly?
Step-by-step explanation:
let, the ratio of boys and girls be 6x:5x
total student=550
now,
6x+5x=55011x=550x=550/11x=50number of girls who attended the assembly are 5x=5×50=2hope it helps.Answer:
hope it helps you have a good day
Factorise fully the following:
a) x² + x
b) 3x-9x²
c) 7x³ - 35x
d) 4x³ + 24x²
The correct factorization are as follows:
(a) x² + x = x(x + 1)
(b) 3x-9x² = 3x(1 - 3x)
(c) 7x³ - 35x = 7x(x^2 - 5)
(d) 4x³ + 24x² = 4x^2(x + 6)
What do you mean by "factorization"?
The most crucial step in factorization is to identify the terms points of commonality. Divide each term by the common factor between them, then multiply the result by the entire expression to maintain the value.
One of the key techniques for reducing an algebraic or quadratic equation to a simple form is factorization. Thus, one should be familiar with factorisation formulas in order to simplify the complex problem.
Additionally, you can always multiply your response to see if you end up with the same result as your starting point.
Step by step solution:
(a): x² + x, [Here both terms have 'x' in common]
=x( (x²/x) + (x/x) )
= x(x+1)
(b): 3x - 9x², [Here both terms have '3x' in common]
=3x( (3x/3x) - (9x²/3x) )
= 3x(1-3x)
(c): 7x³ - 35x, [here both terms have '7x' in common]
=7x( (7x³/7x) - (35x/7x) )
= 7x(x²-5)
(d): 4x³+ 24x² [here both terms have 4x² in common]
=4x²( (4x³/4x²) + (24x²/4x²) )
= 4x²(x+6)
To know more about "factorization" here:
brainly.com/question/25829061
Please please please pleasepfoodifieiff
Answer:
8 quadrilaterals
Step-by-step explanation:
a quadrilateral is a shape with 4 sides and vertices
Find the measure of the indicated angle. Need help please.
I also need explanation...
Thank you!!!
Answer:
The measures of interior angles of a triangle sum to 180°.
63+60=123
180-123=57
Angle AB is 57°
Please help!!! NO LINKS PLEASE! Links will be reported. I'll pick Brainliest to the person that explains!
There were two parts I got 36pie for the first.
Part two: A circular frame that is 3-inches wide surrounds the mirror. What Is the combined area in square inches of the circular mirror(36pie) and the frame?
Answer:
81π sq. in.
Step-by-step explanation:
A = 36π = [tex]\pi r^{2}[/tex]
[tex]r^{2}[/tex] = 36
r = 6 = radius of the mirror
Add 3 to the 6 to get the radius(R) including the frame
R = 9
A = [tex]\pi 9^{2}[/tex] = 81π sq. in.
ACTIVITY 6: Modeling Real Life
A company is loading recliners and sofas onto a trailer that has a volume of about 3800 cubic feet. Each recliner takes up about 40 cubic feet and each sofa takes up about 80 cubic feet. The company wants the shipment to have at least 30 recliners and more than 25 sofas. Write and graph a system that represents the situation. Give one example of the numbers of recliners and sofas the company can have in the shipment.
The equation is 80x + 1200 = 3800. And the numbers of at least 30 recliners and 32 sofas the company can have in the shipment.
What is linear equation?Equations whose variables have a power of one are called linear equations. One example with one variable is where ax+b = 0, where a and b are real values and x is the variable.
Given:
A company is loading recliners and sofas onto a trailer that has a volume of about, 3800 cubic feet.
Each recliner takes up about 40 cubic feet and each sofa takes up about 80 cubic feet.
The company wants the shipment to have at least 30 recliners and more than 25 sofas.
The equation that represents the situation is,
80x + 40y = 3800,
where x is the volume of a sofa and y is the volume of a recliner.
If y = 30 then,
80x + 1200 = 3800
80x = 2600
x = 2600/80
x = 32.5
x ≈ 32
Therefore, 30 recliners and 32 sofas.
To learn more about the linear equation;
https://brainly.com/question/29739212
#SPJ1
How do you simplify F G?
F G cannot be simplified because it is not an equation, it is a phrase.
1. First, determine what F G is. In this case, F G is a phrase and not and equation.
2. Since F G is a phrase, it cannot be simplified.
Determining what F G is the first step to simplifying it. F G is a phrase and not an equation, so it cannot be simplified. Simplifying an equation or expression requires breaking it down into its individual parts and then combining like terms or rearranging the equation to make it simpler. However, F G is not an equation and therefore cannot be simplified.
F G cannot be simplified because it is not an equation, it is a phrase.
Learn more about equation here
https://brainly.com/question/29657992
#SPJ4
1. For the three-part question that follows, provide your answer to each question in the given workspace.
Be sure to clearly label each part of your response as Part A, Part B, and Part C.
Part A:
Evaluate the expression 4x² when
S
5
6
Part B:
1
Evaluate the expression 4x² when x =
2
Write the answer as a mixed number if necessary.
Write the answer as a mixed number if necessary.
Part C:
Show all of your work for Parts A and B to justify your answers.
Therefore , the solution of the given problem of function comes out to be x(3x²- 15 ) + 8 / 12x² , Domain : x ∈ R : x≠ 0 and
Domain :[ -∞,0 ] U [ 0,∞].
Function is what?
According to a function's rule, every x value in the domain has one and only one range of y values. Definition. A one-to-one function exists when there is just one and only one value of x such that f(x) = y.
Here,
Part A:
=> 4/6x² - 5x²/4x
=> 8 - 15x + 3x³/12x²
=> 3x³- 15x +8 / 12x²
=> x(3x²- 15 ) + 8 / 12x²
Part B:
Domain : x ∈ R : x≠ 0
Part c:
The function domain at x= 0 Domain :[ -∞,0 ] U [ 0,∞]
Therefore , the solution of the given problem of equation comes out to be x(3x²- 15 ) + 8 / 12x² , Domain : x ∈ R : x≠ 0 and Domain :[ -∞,0 ] U [ 0,∞].
To know more about function , visit
brainly.com/question/12431044
#SPJ1
The two spinners below are spun. Find the probability of spinning a 4 and a C.
Step-by-step explanation:
S = { 1, 2, 3, 4, 5, 6 7, 8 }
n ( S ) = 8
Let A be the event of getting 4,
A = { 4 }
n ( A ) = 1
P ( A )
= n ( A ) / n ( S )
= 1 / 8
Therefore, the probability of spinning a 4 is 1 / 8.
S = { A, B, A, C, A, B }
n ( S ) = 6
Let Y be the event of getting C,
Y = { C }
n ( Y ) = 1
P ( Y )
= n ( Y ) / n ( S )
= 1 / 6
Therefore, the probability of spinning a C is 1 / 6.
the diagram shows a partly-filled oil tank.
3 m
2 m
5 m
the depth of oil present in the tank is 1.2m
1 cubic metre is equivalent to 1000 litres.
work out the quantity of oil in the tank.
give your answer in litres.
if you can please help !! i would really appreciate it. :)
Answer:
12,000 Litres
Step-by-step explanation:
From the measurements given in the figure, we can understand that the tank is cuboidal in shape.
Thus,
Volume of a cuboid = Width*Length*Height
Volume of Oil in the tank = 5 * 2 * 1.2
= 12 cubic metres
1 cubic metre = 1000 litres
12 cubic metres = 12,000 litres
Hope it helps (:
x - y if X is -11 and y is 26
Answer: -37
Step-by-step explanation: -11-26
The lifespans of lions in a particular zoo are normally distributed. The average lion lives 12.512.512, point, 5 years; the standard deviation is 2.42.42, point, 4 years.
Use the empirical rule (68 - 95 - 99.7\%)(68−95−99.7%)left parenthesis, 68, minus, 95, minus, 99, point, 7, percent, right parenthesis to estimate the probability of a lion living longer than 10.110.110, point, 1 years.
The probability of a lion living longer than 10.1 will be 0.1585.
What is a normal distribution?The Gaussian Distribution is another name for it. The most significant continuous probability distribution is this one. Because the curve resembles a bell, it is also known as a bell curve.
The lifespans of lions in a particular zoo are normally distributed. The average lion lives 12.5 years; the standard deviation is 2.4 years.
The lifespan of a lion in a particular zoo is normally distributed with average lion lives:
Mean u = 12.5 years
Standard deviation s = 2.4 years
We are to use the empirical rule ( 68-95-99.7% ) to estimate the probability of a lion living between 5.3 and 10.1.
The empirical rule ( 68-95-99.7% ) states:
P ( u - s < X < u + s ) = 68%
P ( u - 2s < X < u + 2s ) = 95%
P ( u - 3s < X < u + 3s ) = 99.7%
The test has the following number of standard deviations (s):
u - s < X < u + s = 12.5 - 2.4 < X < 12.5 + 2.4 = 10.1 < X < 14.9
u - 2s < X < u + 2s = 12.5 - 4.8 < X < 12.5 + 4.8 = 7.7 < X < 17.3
u - 3s < X < u + 3s = 12.5 - 7.2 < X < 12.5 + 7.2 = 5.3 < X < 19.7
Then the probability is calculated as,
P ( 10.1 < X < 14.9 ) = 0.68
P ( 7.7 < X < 17.3 ) = 0.95
P ( 5.3 < X < 19.7 ) = 0.997
We need P ( X < 10.1 ) and P ( X < 5.3 ):
P ( X < 10.1 ) = [ 1 - P ( 10.1 < X < 14.9 ) ] / 2
P ( X < 10.1 ) = [ 1 - 0.68 ] / 2
P ( X < 10.1 ) = 0.16
P ( X < 5.3 ) = [ 1 - P ( 5.3 < X < 19.7 ) ] / 2
P ( X < 5.3 ) = [ 1 - 0.997 ] / 2
P ( X < 5.3 ) = 0.0015
P ( 5.3 < X < 10.1 ) = P ( X < 10.1 ) - P ( X < 5.3 )
P ( 5.3 < X < 10.1 ) = 0.16 - 0.0015
P ( 5.3 < X < 10.1 ) = 0.1585
More about the normal distribution link is given below.
https://brainly.com/question/12421652
#SPJ1
Find each product. (Please help me on this-i will give you brainlist!)
l think it's answer is this .
You can use your calculator.
PLS HELP I;LL GIVE BRASINLIEST
Answer:
C
Step-by-step explanation:
q3 - q1
7 -1 = 6
Answer:
6 is the IQR
Step-by-step explanation:
To determine the IQR, you need to evaluate the box. The first quartile starts at 1, and the third quartile ends at 7. To calculate IQR, subtract Q1 (1) from Q3 (7). So it would be 7 - 1 = 6
So your answer is 6.
Graph the opposite of the ppposite of 2 on the number line. Click on the number line to
Identify the nynber localjon.
-3
-2
-1
0
1
2
3
4
PLEASE HELP
What is the solution of 7x =- 63?
The answer to 7^2 is 49. This means that 7 is multiplied by itself two times. To solve the given problem following steps should be followed :
Step 1: To calculate the value of 7 power 2, we need to use the exponentiation operator (^).
Step 2: The operator is written as 7^2, which is read as "seven to the power of two".
Step 3: We can calculate the value of 7 power 2 by multiplying 7 by itself 2 times.
Step 4: 7 × 7 = 49
Therefore, 7 power 2 = 49.
An expression known as "power" is defined as the process of repeatedly multiplying a value or integer. An is often a power where n is the exponent and an is the base.
To know more about power here
https://brainly.com/question/23519885
#SPJ4