Rectangle ABCD has side lengths of 6 centimeters and 8 centimeters. Rectangle EFGH has side lengths of 9 centimeters and 12 centimeters. Determine the ratio of corresponding side lengths if ABCD is similar to EFGH.
1:3
2:3
3:1
3:2
Answer:
2/3
Step-by-step explanation:
6/9=8/12=2/3
........
There are 3 islands A,B,C. Island B is east of island A, 8 miles away. Island C is northeast of A, 5 miles away and northwest of B, 7 miles away. What is the bearing needed to navigate from island B to C? Round to the nearest degree
Answer:
[tex]B = 38[/tex]
Step-by-step explanation:
This question can be illustrated using the attachment and the required bearing will be calculated using cosine theorem;
[tex]b^2 = a^2 + c^2 - 2ac\ CosB[/tex]
In this case:
[tex]b = 5[/tex]
[tex]a = 7[/tex]
[tex]c = 8[/tex]
[tex]<B = ??[/tex]
Substitute these values in [tex]b^2 = a^2 + c^2 - 2ac\ CosB[/tex]
[tex]5^2 = 7^2 + 8^2 - 2 * 7 * 8\ CosB[/tex]
[tex]25 = 49 + 64 - 112\ CosB[/tex]
[tex]25 = 113- 112\ CosB[/tex]
Collect Like Terms
[tex]25 -113=- 112\ CosB[/tex]
[tex]-88=- 112\ CosB[/tex]
Divide through by -112
[tex]\frac{-88}{-112}= \frac{- 112\ CosB}{-112}[/tex]
[tex]\frac{-88}{-112}= CosB[/tex]
Reorder
[tex]Cos\ B = \frac{-88}{-112}[/tex]
[tex]Cos\ B = 0.7857[/tex]
Take arccos of both sides
[tex]B = cos^{-1}(0.7857)[/tex]
[tex]B = cos^{-1}(0.7857)[/tex]
[tex]B = 38[/tex] --- (approximated)
Hence, the bearing is approximately 38 degrees
PLS HELP MEEEEE!!!!!!!!!!!!
Answer:
(1,2)
Step-by-step explanation:
The solution is the point where the two lines intersect at.
In other words the point where the two lines make an x.
Hope this helps ya!!
Answer: (2,1)
Step-by-step explanation:
solve the value of x: x + 13.8 ≥ 20.23
Answer:
x≥6.43
Step-by-step explanation:
Let's solve your inequality step-by-step.
x+13.8≥20.23
Step 1: Subtract 13.8 from both sides.
x+13.8−13.8≥20.23−13.8
x≥6.43
For what values of x would the following be true?
-2(x-3)<4
Answer:
x > 1
General Formulas and Concepts:
Pre-Algebra
Order of Operations: BPEMDAS
Brackets Parenthesis Exponents Multiplication Division Addition Subtraction Left to RightEquality Properties
Step-by-step explanation:
Step 1: Define
-2(x - 3) < 4
Step 2: Solve for x
Divide -2 on both sides: x - 3 > -2Add 3 to both sides: x > 1Here we see that any value x greater than 1 would work as a solution to the equation.
please help before it’s too late lol
Answer:
15625
Step-by-step explanation:
To multiply powers of the same base, add their exponents. Add 2 and 4 to get 6.
Calculate 5 to the power of 6 and get 15625.
3. Stamps are sold in a 10 by 10 sheet. The total value of a sheet of stamps is $60.00.
a) Express the number of stamps as a power and in standard from
Answer:
There is a total of 100 stamps, or 10² stamps.
Explanation:
10•10=100 (standard form)
100 can be written as 10² in scientific notation (power)
Help!!!!!! Triangle ABC and DEF are similar.
What is the scale factor?
Answer:
1.66666666667
Step-by-step explanation:
4/2.4 = 1.66666666667
All you do is choose two lenghts and divide to see what factor was used for the dilation.
Mohamed purchased a car for $30,000. It deprecates by 25% of its current value every year. How much will the car be worth 3 years after it is purchased?
Answer:
$12,656.25
Step-by-step explanation:
year 1: 30,000-25%=22,500
year 2: 25,000-25%=16,875
year 3: 16,875-25%=12,656.25
Write 2.454545... as a fraction in lowest terms
490909/200000 is the answer
Have a great day!
Stay safe and healthy!
Happy holiday seasons!
May I please have brainliest?
Will give you brainliest
Answer:
x = 36°
Step-by-step explanation:
m<RST + m<TSV = m<RSV
m<RST = 5x + 5
m<TSV = 46
RSV = 232
Plug in these values
5x + 5 + 46 = 232
5x + 51 = 232
5x = 181
x = 36.2, if rounding down;
x = 36°
The sum of two numbers is 22. One of the numbers is two times the other. What are the numbers
The numbers is 44/3 and 22/3 are that numbers.
Given that
The sum of two numbers is 22.
One of the numbers is two times the other.
To find
What are the numbers ?
So, according to the question
Let's assume that numbers are x and y, where x is greater then y.
So, we can say that
The sum of that numbers,
x+y = 22, -------------(1)
And
One of the numbers is two times the other.
x = 2y ---------------(2)
Now, put the value of eq(1) in eq(2)
So, we will get
x+y = 22, -------------(1)
2y+y = 22
3y = 22
y = 22/3
Now, put the value of y in eq(2)
So, we will get
x = 2y ---------------(2)
x = 2 (22/3)
x = 2 ×[tex]\frac{22}{3}[/tex]
x = 44/3
That numbers are 44/3 and 22/3.
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Question 5
Which graph shows a linear function?
PLEASE HELP!!
Answer:
Top Left
Their the straight line
my teacher tried to explain this to me but im still confused
600 mL corresponds to 15 teaspoons of sugar
That gives the ratio 600:15
Divide both parts of that ratio by 3 so we get to 200:5
Then multiply both parts by 10 to get 2000:50
This says 2000 mL, aka 2 liters, of soda has an estimated 50 teaspoons of sugar.
To convert from teaspoons to grams, we multiply by 4. This is directly from the equation of 1 teaspoon = 4 grams of sugar
So 50 teaspoons = 50*4 = 200 grams of sugar.
To go from grams to teaspoons, we divide by 4.
-----------------
To find the actual amount of sugar, you'll need to find a 2 liter bottle of soft drink and look at the nutrition facts label. You can search for the nutrition facts label online if you don't have a bottle near you. Keep in mind you're looking for the 2 liter plastic bottle version and NOT the 12 fluid-ounce can version.
Also, keep in mind that the nutrition facts label will list the amount of sugar per serving. This isn't the total sugar since it's just a small portion. Multiply the number of servings by the amount of sugar per serving.
Example: If there are 7 servings and 20 grams of sugar per serving, then that's a total of 7*20 = 140 grams of sugar total.
Side note: the amount of sugar will vary from brand to brand. However, they should all be in the same basic ballpark.
What is the equation, in slope-intercept form, of a line that passes through the points (-2, 4) and (3, -1)?
Answer:
Step-by-step explanation: The equation of the line passing through the points (2, –1) and (5, –10) is y = -3x + 5 .Jun 9, 2017
Unit rate of $99 for 15 movies
Answer:
6.60$ dollars per movie
Step-by-step explanation:
99/15=6.6
Answer:
$6.60
Step-by-step explanation:
[tex]\frac{99}{15}[/tex] = 6.60
please answer this. ty
Answer:
its 1
Step-by-step explanation:
Please help me! For algebra 2 class. 45 points!
Using the Fundamental Theorem of Algebra, complete the following exercises. Show your work.
Determine how many, what type, and find the roots for f(x) = x4 + 21x2 − 100.
Determine how many, what type, and find the roots for f(x) = x3 − 5x2 − 25x + 125.
The following graph shows a seventh-degree polynomial:
(see attachment)
Part 1: List the polynomial’s zeroes with possible multiplicities.
Part 2: Write a possible factored form of the seventh degree function.
Without plotting any points other than intercepts, draw a possible graph of the following polynomial:
f(x) = (x + 8)3 (x + 6)2 (x + 2)(x − 1)3 (x − 3)4 (x − 6).
Answer:
1) There are four roots, with two real and two imaginary roots
The roots are x ±2, ±5·i
2) Therefore, there are 2 roots
The roots are real
The roots are x = -5 and x = 5
3) The possible factored form is therefore; (x + 5)²×(x + 1)×(x - 4)³×(x + 7)
4) Please see the attached graph of the function drawn with Microsoft Excel
Step-by-step explanation:
1) The given equations is as follows;
f(x) = x⁴ + 21·x² - 100
Let a = x², we have;
f(x) = a² + 21·a - 100
a = (-21 ± √(21² - 4 × 1 ×(-100))/(2 × 1)
a = -25 or 4
Therefore, x = √4 = ±2 or x = √(-25) = ±5·i
There are four roots, with two real and two imaginary roots
2) For f(x) = x³ - 5·x² - 25·x + 125
We have;
f(x) = x³ - 5·x² - 25·x + 125
From the equation, we see that x = 5 is a solution of the equation, therefore;
f(5) = 5³ - 5·5² - 25·5 + 125 = 0
Which gives, (x - 5) is a factor of the equation,
Dividing x³ - 5·x² - 25·x + 125 by (x - 5) gives;
x² - 25
(x³ - 5·x² - 25·x + 125)/(x - 5)
x³ - 5·x²
[tex]{}[/tex]- 25·x
[tex]{}[/tex] -25·x + 125
[tex]{}[/tex] 0 + 0
Therefore, by long division, (x³ - 5·x² - 25·x + 125)/(x - 5) = x² - 25
(x - 5)×(x² - 25) = (x - 5) × (x - 5) × (x + 5)
Therefore, there are 2 roots
The roots are real
The roots are x = -5 and x = 5
3) From the polynomial zeros, we have x = -5, x = -1, x = 4, and x = 7
At x = -5 the polynomial touches the x-axis given two real roots with (x + 5)² being a factor
With the root at x = -1, a factor is (x - 1)
With the root at x = 4 which has the shape of a cubic function, we have a factor of (x - 4)³
For the root at x = 1, the factor is taken as (x + 7)
The possible factored form is therefore; (x + 5)²×(x + 1)×(x - 4)³×(x + 7)
4) The given function is therefore;
f(x) = (x + 8)³(x + 6)²(x + 2)(x - 1)³(x - 3)⁴(x - 6)
(x + 8)³(x + 6)²(x + 2)(x - 1)³(x - 3)⁴(x - 6)
Please see the attached graph of the function drawn with Microsoft Excel
The function p(t)=3(2)t represents the population of a certain type of bacteria after t days what is the population of the bacteria after 5 days
Answer:
p(5) = 30
Step-by-step explanation:
p(t) and if t=5 then p(5)
p(5) = 3(2)(5)
p(5) = 6(5)
p(5) = 30
Hope this helps and I hope u have an Amazing day!!
2x – 3y = 15
-2x + y = -1
Answer: -y=7
Explanation:
Think of your problem as subtraction:
2x-3y+15
-2x+3y=-1
A snack mix recipe calls for 1 1/2 cups of dip and 1/3 cup of vegetables. Cole wants to make the same recipe using 1 cup of vegetables. How many cups of dip will cole need.
Answer:
4 1/2 cups of dipStep-by-step explanation:
Let required amount be x
Using the ratio to find x:
1 1/2 ÷ x = 1/3 ÷ 1x = 1 1/2 × 3x = 3/2×3 x = 9/2 x = 4 1/2 cupsQuestion 6
1 pts
Verizon charges a $100 initial contract fee, then $70 a month for a basic cell
phone plan. What is the slope (rate of change)?
Answer:
Slope is rate of change, so define your values.
-$100 is the initial fee
-$70 is charged per month
per month is the constant rate of change
70 is the slope
The slope (rate of change) of the function is 70.
What is a slope?In mathematics, a line's slope, also known as its gradient, is a numerical representation of the line's steepness and direction
If a line passes through two points (x₁ ,y₁) and (x₂, y₂) ,
then the equation of line is
y - y₁ = (y₂- y₁) / (x₂ - x₁) x (x - x₁)
To find the slope;
m = (y₂- y₁) / (x₂ - x₁)
Given:
Verizon charges a $100 initial contract fee,
then $70 a month for a basic cell phone plan.
Let the x be the number of months.
So, the equation,
y = 70x + 100
By comparing with the slope-intercept form,
y = mx + b, where m is the slope.
So, m = 70.
Therefore, 70 is the slope.
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Linear Review: Billy Bob recently purchased solar panels for his home. After 5 months he still owed 2850. He makes a $30 payment each month towards his loan. Build a model. Write an explanation for slope and y-intercept. How many months will it take Billy Bob to finish making payments.
Answer:
Step-by-step explanation:
B) The first step is to calculate the monthly payment using a present value (PV) of $59,000 , monthly interest rate of 7.60 /12 = 0.633333 %, and 60 periods, which = $1185.04 ; the second step is to add $50 to this monthly payment giving the new monthly payment of $1235.04 ; the last step is to calculate the time required to pay off the loan = 57.0740 months.
I need help on what a slope and y-intercept and how to find the equation
Answer:
y=mx+b is the slope intercept form.
Step-by-step explanation:
m is the slope (how the line is moving across the graph)
b is y-intercept (where the line crosses the y axis)
Hope this helps!
There are 10 crustaceans and 25 fish the deep blue tank has the same ratio of crustaceans to fish. There are 50 crustaceans in the deep blue tank.
Answer:
125
Step-by-step explanation:
C : F
10: 25
×5: ×5
50: ?
No. of fish in the tank = 25 × 5
= 125
(7.36×10 9 )−(6.2×10 9 )
Answer:
[tex] \sf \: 104.4[/tex]
Step-by-step explanation:
(7.36)(10)(9)−(6.2)(10)(9)
=(73.6)(9)−(6.2)(10)(9)
=662.4−(6.2)(10)(9)
=662.4−(62)(9)
=662.4−558
=104.4
4 cups of peanut butter is needed to make 80 cookies how many cups of peanut butter would be needed to make 400 cookies
Answer:
20 Cups of peanut butter
Step-by-step explanation:
You take 400 divided by 80, which would give you 5, multiply that by the number of cups (4x5) and you final answer will be 20.Answer:
20 cups
Step-by-step explanation:
80 cookies are made by 4 cups
which means 1 cookie is made by
[tex] \frac{4}{80} cups[/tex]
Therefore 400 cookies would require
[tex]400 \times \frac{4}{80} cups = 20cups[/tex]
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Aimee tossed a coin and spun a spinner that is divided into 3 equal sections. She did this 50 times.What is the experimental probability that the next time Aimee tosses the coin and spins the spinner she will get a Tails and a 2?
Answer:12.5 times out of 50
Step-by-step explanation:think about it add tails and 2
The temperature in Quebec City was 5 degrees Celsius at 4 pm. By midnight, the temperature dropped 15 degrees. A number line has points negative 20, blank, A, B, 0, 5, C, blank, D. Which point is a representation of the colder midnight temperature in degrees Celsius?
Answer: Point A
Step-by-step explanation:
The temperature at midnight is;
= 5 - 15
= -10°C
Looking at the number line, one can surmise that the scale is in multiples of 5. This means that C is 10, B is -5 and A is -10.
With point A being -10°C, it represents the colder midnight temperature.
Answer:
Point A
Step-by-step explanation:
We know that the temperature dropped 15 degrees, and that it was initially of 5°C. So, by midnight, the temperature will be of -10°C (5-15=-10).
We also know that the distance between points is of 5°C. So, the point that we have to mark is point A, which represents -10°C.
100 students are interviewed to see which of biology, chemistry or physics they prefer.
36 of the students are girls. 15 of the girls like biology best.
14 of the boys prefer physics.
7 out of the 31 who prefer chemistry are girls.
What percentage of the students prefer biology?
Answer: 41%
Step-by-step explanation:
15 girls prefer biology.
Find the boys who prefer biology;
There are 36 girls in total so;
= 100 - 36
= 64 boys interviewed
14 boys prefer Physics
= 64 - 14
= 50 boys prefer Biology and Chemistry
7 out of the 31 who prefer chemistry are girls so the boys who prefer chemistry are;
= 31 - 7
= 24 boys
Boys who prefer Biology;
= 50 - 24
= 26 boys
Total who prefer biology;
= 15 girls + 26 boys
= 41 students
Percentage = 41/100 = 41%