To do a two-column proof, you must know the definitions of the terms that are being used. Also, you must know the postulates and theorems you have learned so far. You look at the given information, and using the definitions, postulates, and theorems, you reason in your mind how to go from the given to the conclusion, step by step. You write each step and the accompanying reason that allows you to conclude each step.
Which of the following is the correct expansion of (x - 2)(x - 5)?
x2 + 7x + 10
x2 + 7x - 10
x2 - 7x - 10
x2 - 7x + 10
Use distributive property:
(a + b)(c + d) = ac + ad + bc + bd
(x - 2)(x - 5) = (x)(x) + (x)(-5) + (-2)(x) + (-2)(-5) = x² - 5x - 2x + 10
Answer: (x - 2)(x - 5) = x² - 7x + 10Can someone please help me?
The graph shows a journey in a car. Which of the statements most likely describes the start of the journey at the portion of the graph labeled I?
What is the general form of the equation of a circle with its center at (-2, 1) and passing through (-4, 1)?
A.
x2 + y2 − 4x + 2y + 1 = 0
B.
x2 + y2 + 4x − 2y + 1 = 0
C.
x2 + y2 + 4x − 2y + 9 = 0
D.
x2 − y2 + 2x + y + 1 = 0
Answer:
B. x² + y² + 4x − 2y + 1 = 0Step-by-step explanation:
The standard form of an equation of a circle:
[tex](x-h)^2+(y-k)^2=r^2[/tex]
(h, k) - center
r - radius
The formula of a distance between two points:
[tex]d=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}[/tex]
We have the center (-2, 1) → h = -2 and k = 1.
The radius is the distance between the center and the given point.
Therefore put the coordinates of the points (-2, 1) and (-4, 1) to the formula of a distance between two points:
[tex]r=\sqrt{(-4-(-2))^2+(1-1)^2}=\sqrt{(-2)^2+0^2}=\sqrt{4}=2[/tex]
We have the equation in standard form:
[tex](x-(-2))^2+(y-1)^2=2^2\\\\(x+2)^2+(y-1)^2=4[/tex]
Convert to the genereal form using:
[tex](a\pm b)^2=a^2\pm2ab+b^2[/tex]
[tex](x+2)^2+(y-1)^2=4\\\\x^2+2(x)(2)+2^2+y^2-2(y)(1)+1^2=4\\\\x^2+4x+4+y^2-2y+1=4\\\\x^2+y^2+4x-2y+5=4\qquad\text{subtract 4 from both sides}\\\\\boxed{x^2+y^2+4x-2y+1=0}\to\boxed{B.}[/tex]
Sam took out an 80/20 mortgage on a $205,000 home. What is the amount financed under the first mortgage
a.$164,000
b.$41,000
c.$205,000
d$120,000
Given condition is: Sam took out an 80/20 mortgage on a $205,000 home.
Here, 80/20 refers to 80% mortgage amount means it will be paid as mortgage and 20% loan amount.
So, to find the amount financed under the first mortgage, we will find 80% of 205000.
[tex]\frac{80}{100}\times205000[/tex]
= $164000
Hence, option A is the correct answer.
Denzel can mow 1/8 of his yard every 7 minutes. If he had 40 minutes to mow 3/4 of the yard, will he have enough time
Answer:
No. He is short by 2 minutes
Step-by-step explanation:
Given that Denzel can mow 1/8 of his yard every 7 minutes.
Hence he can mow the full yard in 7(8) = 56 minutes.
Now he has to do 3/4 of his yard and time is 40 minutes
For 3/4 of yard time taken would be = 3/4 (56) = 42 minutes.
If he had 40 minutes to mow 3/4 of the yard, he will not have enough time since he is short of time by 2 minutes.
1.Suppose f(x)=6x^2+2x-7 and g(x)=4x-3.Find Each Of The Following Function.
a. (f+g)(x)
b.(f-g)(x)
2.Suppose f(x)=2x-3x and g(x)=1-2x. Find Each Of The Following Functions.
a. (f+g)(x)
b.(f-g)(x)
(1)
(f+g)(x) = 6x^2+2x-7+4x-3=6x^2+6x-10
(f-g)(x)=6x^2+2x-7-4x+3 = 6x^2-2x-4
(2)
(f+g)(x)=2x-3x+1-2x=-3x+1
(f-g)(x)=2x-3x-1+2x=x-1
WILL GIVE BRAINLIEST
Marty ran 4 miles more than Shana ran. Write an expression for how far Shana ran using Marty’s variable “m”
Explain what the 4 inequality signs represent in your own words
The expression would be m - 4 because if Marty ran 4 more miles than Shana, that means that Shana ran 4 less miles than Marty.
The four inequalities are less than, less than or equal to, greater than, and greater than or equal to. Less than means that a number is less than the other number. For example, if you say 4 is less than 7 it is because 4 is less than 7 by 3 which makes 7 value more than 4. For less than or equal to, it means that the number or variable is less than or the same number as the other number. For example, if you say x is less than or equal to 9, that means that x is less than 9 or equal to 9. For greater than, it means that the variable is greater than the other number. For example, if x if greater than 10 than the variable has to be greater than 10 or 11 and so on. For greater than or equal to, it means that the variable is greater than the other number or equal to that number. For example, if x is greater than or equal to 12, then x is greater than 12 or 13 and up or x is equal to 12 or x is 12.
***PLEASE HELP WILL GIVE BRAINLIEST!!!***
If DG equals 88, DO = 5x+12 and OG =2x, find DO
.______________.________.
D O G
in the number line, the end points are DG, and the point in between is O
DG = 88
DO = 5x + 12
OG = 2x
Set the equation. The two parts (DO & OG) are equal to the whole (DG)
2x + 5x + 12 = 88
Simplify. Combine like terms
(2x + 5x) + 12 = 88
7x + 12 = 88
Isolate the x. Remember to do the opposite of PEMDAS. Subtract 12 from both sides
7x + 12 (-12) = 88 (-12)
7x = 76
Isolate the x. Divide 7 from both sides:
7x/7 = 76/7
x = 76/7
----------------------------------------------------------------------------------------------------------------------------
Find DO. Plug in "76/7" for x:
DO = 5x + 12
DO = 5(76/7) + 12
Simplify. Remember to follow PEMDAS. Multiply 76 with 5
DO = 380/7 + 12
Next, divide 380 with 7
DO = 54.29 (rounded)
Finally, add
DO = 54.29 + 12
DO = 66.29
66.29 is your answer
hope this helps
Martina works mowing lawns and babysitting. She earns 7.90 for mowing lawns and 6.90 for babysitting. How much will she earn for 7 hours of mowing and 1 hour of babystting
mowing lawns: 7 * $7.90 = $55.30
+ babysitting: 1 * $6.90 = $ 6.90
$62.20
Answer: $62.20
Please help with geometry homework!!!!
Area of Parallelogram ABCD is equivalent to the area of rectangle AXBY.
Area of rectangle AXBY= Length AX * Length AB= 3 ft * 4√2 ft = 12√2 sq.ft.
Thus Area of Parallelogram is 12√2 sq.ft.
Picture of an inequality word problem. It says the answer is between 2 and 5 hours but I have no idea how to get that answer. Please help me with how to get that answer :(
it should be about 4-5 hours because her mom sleeps half the time that Mei sleeps!! you are welcome!
please help on this one?
I think it is B. If you drew a graph of this and the x axis was time and the y axis is the enrollment then you would get 3 different x values and 1 y value. That's still a function. I've drawn it below.
An urn contains 10 marbles: 4 red, 3 white, 2 blue, and 1 orange. (4 points) (a) What is the probability of drawing a marble that is red or white? (b) What is the probability of drawing a marble that is neither red nor white? (c) What is the probability of drawing a pair of marbles, one red and one white at the same time? (d) What is the probability of drawing a pair of marbles, one blue and one orange at the same time?
Answer:
a) 0.70
b) 0.30
c) 12/45 =4/15
d) 2/45
Step-by-step explanation:
a) Prob of drawing a marble red or white = No of red and white marbles/total marbles
= 7/10 = 0.70
b) Prob of drawing a marble neither red nor white = 1-7/10 = 0.30
c) Prob of drawing two marble one red and one white at the same time
= [tex]\frac{4C1 (3C1}{10C2 } =\frac{12}{45}[/tex]
d) Prob of drawing two marble one blue and orange white at the same time
= [tex]\frac{2C1 (1C1}{10C2 } =\frac{2}{45}[/tex]
At a restaurant, the bill comes to $60. If you decide to leave a 14% tip, how much is the tip?
60 times 0.14 = 8.4
You would give $8.40 as a tip of 14% from a bill of $60
Final answer:
To calculate a 14% tip on a $60 bill, you multiply 0.14 by $60, resulting in a tip of $8.40.
Explanation:
To find out how much a 14% tip is on a $60 bill, we need to convert the percentage into a decimal by dividing by 100.
This gives us 0.14 as the decimal form of 14%.
We then multiply this decimal by the total bill amount to calculate the tip: 0.14 × $60 = $8.40
Therefore, the tip would be $8.40.
When evaluating a complex expression which of the following rules should be followed
A - Evaluate from left to right
B - Evaluate from right to left
C- Evaluate using order of operations
D- Evaluate in any order
c : evaluate using order of operations ( pemdas )
Option: C is the correct answer.
C- Evaluate using order of operations
Step-by-step explanation:We know that while solving a algebraic expression we must follow the rule:
PEMDAS
whose full form is:
Parenthesis , Exponents,Multiplication division addition and subtraction.
This means that parenthesis is to be solved first then the preference is given to the exponent, then division and multiplication are treated at the same level and the last preferred operation is addition and subtraction.
Hence, the correct answer is:
Option: C
Jim has answered 7 e-mails this is 35% of the e-mails he must answer how many emails does he need to answer?
Answer: He needs to answer 20 emails.
Step-by-step explanation:
Given : Jim has answered 7 e-mails . (1)
This is 35% of the e-mails he must answer .
We can write 35% as 0.35.
Let x be the number of emails he need to answer.
Then, Number of mails he has answered = 0.35x (2)
From (1) and (2), we have
[tex]0.35=7\\\\\Rightarrow\ x=\dfrac{7}{0.35}=\dfrac{700}{35}=20[/tex]
Hence, he needs to answer 20 emails.
Multiply. (7x-4)(4x-3)
Your answer is 28x^2-37x+12
1) Use the FOIL method: (a+b)(c+d)=ac+ad+bc+bd
28x^2-21x-16x+12
2) Collect like terms
28x^2+(-21-16x)+12
3) Simplify
28x^2-37x+12
Use FOIL
28x-21x-16x+12
-9x+12
The metric system is based on the number ___. 1 2 10 12
Answer:
The metric system is based on the number 10.
Step-by-step explanation:
We have been given an incomplete statement. We are asked to fill in the blank for given statement.
The metric system is based on the number ___.
We know that metric system is an alternative system of measurement used in most countries including the United States. This system includes prefixes like kilo-, hecto-, deka-, deci-, centi-, and milli.
The metric system is based on number 10 as all these units are based on power of 10.
Therefore, option C is the correct choice.
The metric system is based on the number 10.
Here, we have,
The metric system is a decimal-based system of measurement that is widely used around the world. It is designed to be a coherent and consistent system, with units of measurement that are related to each other by powers of 10.
In the metric system, there is a base unit for each quantity being measured, such as meters for length, grams for mass, and liters for volume. The prefixes are then used to indicate multiples or fractions of the base unit. These prefixes are based on powers of 10, which allows for easy conversions between different units within the system.
For example, when we go from a larger unit to a smaller unit within the same measurement category, we move the decimal point to the right by powers of 10. Likewise, when we go from a smaller unit to a larger unit, we move the decimal point to the left by powers of 10.
This decimal-based nature of the metric system makes it highly convenient for scientific and everyday use, as it simplifies calculations and conversions.
The metric system is based on number 10 as all these units are based on power of 10.
Therefore, option C is the correct choice.
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write an equation of a parabola with vertex at origin (0,0) with the given focus, and find the directrix. given the focus at (0,-4)
Directrix:
If the vertex of the parabola is at (0, 0) and the focus is (0, -4) which is 4 units down then the directrix will be the line 4 units UP.
Answer: y = 4
Equation of parabola:
[tex]y = \frac{1}{4p}x^{2}[/tex] ; where p is the distance from the vertex to the focus.
As stated above, the focus is 4 units down, so p = -4
[tex]y = \frac{1}{4(-4)}x^{2}[/tex]
[tex]y = \frac{1}{-16}x^{2}[/tex]
Answer: [tex]y = -\frac{1}{16}x^{2}[/tex]
Her goal was to rased 5000 dollers to help protect the manites she rased 3500 what persent of the goal did she rase
The product of two numbers is 40. If one of the numbers is 8/15, what is the other number?
When the product of two numbers is 40 and one of the numbers is 8/15, the other number can be found by dividing 40 by 8/15, which is 937.5.
Explanation:The question is asking for the other number when the product of two numbers is 40 and one of the numbers is given as 8/15. To answer this, we need to use the concept that the product of two numbers is equal to one number multiplied by the other. Therefore, to find the missing number, we need to divide 40 (the product) by the given number (8/15).
So, the calculation will look like this: 40 ÷ (8/15) = 7500/8 = 937.5.
Thus, the other number is 937.5 .
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A box of 20 dictionaries costs $84. An individual dictionary costs $5. You need at least 55 dictionaries. Find the price of each combination of items.
55/20=2 as qutiont and 15 as remainder
2X84=168
15X5=75
answer=243
find the quotient and remainder. Please select the vest abswer from the answer choices
Answer:
Quotient = x^4 + x^3 + x^2 + x + 1
Remainder = 0
Step-by-step explanation:
(x^5 +1) is divided by (x - 1) as shown below:
(x^5 +1) / (x - 1)
where x^5 is divided by (x - 1) when multiplied by x^4 (quotient) to give x^4 - 1.
Now x^4 - 1 is divided by is divided by (x - 1) when multiplied by x^3 (quotient) to give x^3 - 1.
Then again x^3 - 1 is divided by (x - 1) when multiplied with x^2 (quotient) to give x^2 -1.
x^2 - 1 is divided by (x - 1) when multiplied by x to give (x - 1).
Lastly, (x - 1) is divided by (x - 1) when multiplied by 1 to cancel the terms with remainder 0.
Georgia bought a pair of flip-flops that cost $3.46 and a pair of slip-on shoes that cost $9.87. She paid a total of what dollars for the two pairs of shoes.
Answer:
13.33
Step-by-step explanation:
Complete the two column proof
a. is Substitution Property
b. might be definition of supplementary angles
Answer:
B is the sum of adjacent angles is 180 degrees
Step-by-step explanation:
It is showing you that m∠3 and m∠4 "=" 180
10 rubber stamps cost $10.30. What is the cost for 2 rubber stamps?
Answer:
2.06
Step-by-step explanation:
you should divide the 10.30 dollars by 10 which wlll give you the answer of one of them then you just multiply what you got by 2 ((:
To find the cost for 2 rubber stamps from the given information about 10 rubber stamps costing $10.30, the cost for 2 stamps is $2.06.
The cost for 10 rubber stamps is $10.30. To find the cost for 2 rubber stamps, we need to calculate the cost per rubber stamp and then multiply it by 2.
Cost per rubber stamp = Total cost / Number of rubber stamps = [tex]\frac{10.30}{10} = 1.03[/tex]
Cost for 2 rubber stamps = $1.03 per rubber stamp [tex]\times[/tex] 2 rubber stamps = $2.06
PLEASE HELP ASAP!!! CORRECT ANSWER ONLY PLEASE!!
Solve.
x^2 − 9x + 3 = 0
PLEASE HELP ASAP
The length of a rectangle is 6m longer than its width. What are the possible widths if the area of the rectangle is at least 775cm^2?
Hey there!!
What is the area of a rectangle?
The area of a rectangle = Length × Breadth
Given :
Length is 6m longer than the width.
Hence, length = 6 + breadth
Area = ( 6 + breadth ) ( breadth )
Area = 6 breadth + breadth²
Area = 775
Hence, 775 = 6 breadth + breadth²
( Let's take the breadth as ' b ' )
775 = 6b + b²
... b² + 6b - 775 = 0
... b² - 25b + 31b - 775 = 0
... b ( b - 25 ) + 31 ( b - 25 ) = 0
... ( b + 31 ) ( b -25 ) = 0
There are two solutions found :
b + 31 = 0 and b - 25 = 0
Hence,
b = -31 and b = 25
As the values can not be in negatives, we take 25
Hence, the value of the breadth is 25.
Length = 6 + b
Length = 31
Hence, the value of the length = 31
Hope my answer helps!!
Find the product of (3x+7y)^2
A) 9x^2 - 42xy + 49y^2
B) 9x^2 - 49y^2
C) 9x^2 + 49y^2
D) 9x^2+42xy+49y^2
Answer:
9x^2 − 42xy + 49y^2
Step-by-step explanation:
The product of [tex](3x + 7y)^2[/tex] is: D)[tex]9x^2 + 42xy + 49y^2[/tex]
How to find the productsThe product of (3x + 7y)^2 can be found using the formula for squaring a binomial:
(3x + 7y)^2 = (3x + 7y)(3x + 7y)
To calculate this product, you can use the distributive property (FOIL method):
(3x + 7y)(3x + 7y) = (3x * 3x) + (3x * 7y) + (7y * 3x) + (7y * 7y)
Now, simplify each term:
(9x^2) + (21xy) + (21xy) + (49y^2)
Combine like terms:
9x^2 + 42xy + 49y^2
So, the product of [tex](3x + 7y)^2[/tex] is:
D)[tex]9x^2 + 42xy + 49y^2[/tex]
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Solve the system equation.
Answer:
A) (0, 2)
Step-by-step explanation:
Rewriting the second equation to the same form as the first, it becomes
... 1/2y = x + 1
... y = 2x + 2
Now, it is clear that both equations have the same y-intercept at y=2, so that is the solution.
... (x, y) = (0, 2)