Answers
Final answer:
To factor a quadratic expression in the form of x² + bx + c, find two numbers whose sum is equal to b and whose product is equal to c.
Explanation:
To factor a quadratic expression in the form of x² + bx + c, we look for two numbers whose sum is equal to b and whose product is equal to c. Let's illustrate with an example:
For the expression x² + 5x + 6, we need to find two numbers whose sum is 5 and whose product is 6. In this case, the numbers are 2 and 3.
Therefore, we can factor the expression as (x + 2)(x + 3).
Related Questions
TRUE OR FALSE: The number 532 has 2 significant digits.
Select one:
True
False
Answers
G(a)=2a-1 h(a)=3a-3
Find (g-h)(-4)
Answers
Final answer:
To find (g-h)(-4), we calculate g(-4) as -9 and h(-4) as -15. Subtracting the latter from the former results in -9 + 15, which equals 6.
Explanation:
To find (g-h)(-4), we need to calculate the value of g at -4 and the value of h at -4, and then subtract the value of h from g.
The functions are defined as G(a)=2a-1 and h(a)=3a-3. Let's compute these step-by-step:
Calculate g(-4):
G(-4) = 2(-4) - 1
= -8 - 1
= -9
Calculate h(-4):
h(-4) = 3(-4) - 3
= -12 - 3
= -15
Calculate (g-h)(-4):
= g(-4) - h(-4)
= -9 - (-15)
= -9 + 15
= 6
Therefore, (g-h)(-4) equals 6.
A rectangle has a perimeter of 112 centimeters. if the length of the rectangle is 3 times its width, find the dimensions of the rectangle.
Answers
4x=56
x=14
length=42
width=14
Verify the identity. quantity one minus sine of x divided by cosine of x equals cosine of x divided by quantity one plus sine of x
Answers
so hmmm let's multiply the left-side by the conjugate of the numerator then.
[tex]\bf sin^2(\theta)+cos^2(\theta)=1\implies cos^2(\theta)=1-sin^2(\theta) \\\\\\ \textit{difference of squares} \\ \quad \\ (a-b)(a+b) = a^2-b^2\qquad \qquad a^2-b^2 = (a-b)(a+b)\\\\ -------------------------------\\\\[/tex]
[tex]\bf \cfrac{1-sin(x)}{cos(x)}=\cfrac{cos(x)}{1+sin(x)} \\\\\\ \cfrac{1-sin(x)}{cos(x)}\cdot \cfrac{1+sin(x)}{1+sin(x)}\implies \cfrac{[1-sin(x)][1+sin(x)]}{cos(x)[1+sin(x)]} \\\\\\ \cfrac{1^2-sin^2(x)}{cos(x)[1+sin(x)]}\implies \cfrac{\underline{cos^2(x)}}{\underline{cos(x)}[1+sin(x)]}\implies \cfrac{cos(x)}{1+sin(x)}[/tex]
If, while training for a marathon, you ran 54 miles in 2 2/3 months, how many miles did you run each month?
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54 / 2 2/3 =
54/1 / 8/3 =
54/1 x 3/8 = 162/8 = 20 1/4 miles per month
One angle in a triangle measures twice the smallest angle, whereas the largest angle is nine times the smallest angle. find the measures of all three angles.
Answers
The measures of all three angles are 15, 30, and 135 degrees respectively.
What is the angle sum property?The angle sum property of a triangle states that the sum of the interior angles of a triangle is 180 degrees.
Let the smallest angle be represented as x,
one angle = 2x
largest angle = 9x
Therefore, x + 2x + 9x = 180° (by angles sum in a triangle)
12x = 180°
x = 15°
Then 2x = 15° x 2
= 30°
Also, 9x = 15° x 9
= 135°
Hence, The smallest angle is 15° and the one angle is 30°.
The largest angle is 135°.
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round 689002 to the nearest1,000,000
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if you round by hundred thousands, it will be 1,000,000
hope this helps
If 8 is subtracted from 7 times a number the result is 34
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Solving:
7x = 34 + 8
7x = 42
x = 6
Hope this helps!
What is 380,303 rounded to the nearest ten thousands
Answers
The required number is 380,303.
It is required to find nearest ten thousands of the number.
What is "Rounding" ?
Rounding means making a number simpler but keeping its value close to what it was.
Given that:
We have to find the nearest ten thousands of the number 380.303.
We know that to round a number to the nearest 10,000, check the thousands digit to decide whether to round up or round down. If the thousands are 5000 or more, round up. If they are 4999 or less, round down. 45,000 to the nearest 10,000 is 50,000.
So, the number is less than 5000 so, round down or unchanged.
Therefore, the required number is 380,303.
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What is the answer to 7x+5-8x
Answers
7x-8x=-1x
Final answer: -x+5
marcella divide 40.8 gallons of paint among 8 containers. how much paint is in each container
Answers
Use division to solve.
40.8/8 = 5.1
5.1 gallons of paint are in each container.
hope this helps! :D
if you have any other questions
on THIS specific problem, let me know!
Which number produces an irrational number when multiplied by 0.4? A. B. 0.444... C. 3 D.
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The number produces an irrational number when multiplied by 0.4 would be C) 3π.
What are irrational numbers?Irrational numbers are those real numbers that are not rational numbers.
Know that all natural numbers are integers, and all integers are rational numbers. That means natural numbers are not irrational.
π is irrational, and so is 3π
The expression 3π +0.4 is an irrational term as well.
If x is irrational and y is rational, then x + y is the irrational term.
Thus, choice C is the answer.
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Simplify the trigonometric expression. Show your work.
1/1+sin theta + 1/1-sin theta
Answers
[tex] \dfrac{1}{1+sin(\theta)} + \dfrac{1}{1-sin(\theta)} \\\\ \dfrac{1-sin(\theta) + 1+sin(\theta)} {1-sin^2(\theta) }}\\\\ = \dfrac{2} {cos^2(\theta)} [/tex]
trigonometric identites
1. D
2. B
3. tangent identity
4. A
5. B. 2sec2 therma.
(also, the answer above me is NOT correct. the asnwer was 2sec2 therma.
In angle abc , m angle A =x , m angle B =2x+2, m angle C = 3x+4.what is value x
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x + 2x + 2 + 3x + 4 = 180
6x + 6 = 180
6x = 174
x = 29
How do I round 123834392 to the nearest thousand
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To round to the nearest thousand, take apart the number so that you only have x thousand.
4,392
Now, take the second highest number (hundred) and if it is 1-4 then it stays the same. If it's 5+, then it would go up one. In this case, since the hundreds place is 3, the number would stay the same.
Which of the following shows the correct order of the numbers below? (1/2) 2 , , 0.45
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Hope I helped :)
nine less than the product of ten and a number d is eleven
Answers
Add 9 to both sides.
10d = 20
Divide both sides by 10.
d = 2
The answer is d = 2.
A total of 252 tickets were sold for the school play. They were either adult tickets or student tickets. The number of student tickets sold was two times the number of adult tickets sold. How many adult tickets were sold?
Answers
Students= 2x
Adults= x
Total=3x
3x=252
x= 252/3
=84
Thus, number of adult tickets sold is 84
The number of adult ticket sold are 28.
What is a ticket ?"a piece of paper or card that shows you have paid for a journey, or that allows you to enter a theatre, cinema, etc."
Let, the number of student ticket be x
Let, the number of adult ticket be y
So, [tex]x = 2y[/tex]
And Given,
Total number of tickets are 252
So, [tex]x+y = 252[/tex]
[tex]2y + y = 252\\3y = 252 \\y = 28[/tex]
Hence, the adult tickets sold are 28.
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Value rent-a-car rental a luxury car at a daily rate of $43.09 plus 4 cents per mile. a business person is allotted $100 for car rental each day. how many miles can the business person travel on the $100
Answers
Find the value of x that makes lines u and v parallel
Answers
34x - 2 + 11x +2 = 180
If consecutive interior angles are supplementary then the 2 lines are parallel
Which expression is the correct translation of the following word phrase?
"3 multiplied by the sum of a number and 5"
Answer choices:
A) 5X+3
B)3X+5
C)X+(3)(5)
D)3(X+5)
I think the answe is B ,but I think it could be A as well ,but I just need toconfirm if I'm correct or not.Thanks in advance:).
Answers
The parentheses would make it multiplication
The word sum means add
A number was unknown, so we will label it as "x"
So, let's see what we're working with here!
If you chose "Option A" the question would be "five multiplied by a number and the sum of 3" (that doesn't give you the right answer"
For B. same thing with option A
For "Option C" its not asking you "a number with sum of three times five"
So, this leaves "Option D." as your answer because 3 is getting multiplied by the sum of some number and five
Good luck on your assignment and enjoy your day!
~MeIsKaitlyn:)
The correct translation of the word phrase '3 multiplied by the sum of a number and 5' is option D) 3(X+5).
Explanation:The correct translation of the word phrase '3 multiplied by the sum of a number and 5' is option D) 3(X+5).
In this expression, the number is represented by X. The sum of the number and 5 is represented by (X+5). Multiplying 3 by the sum gives us 3(X+5).
You roll a six sided dice four times, what is the probability of rolling four sixes?
Answers
6×6×6×6
6×6=36
36×6=216
216×6=1296
1/1296
A six-sided number cube is labeled with the numbers 1–6, one number on each face. Each number is used exactly once. How many possible outcomes exist when the cube is rolled two times?
Answers
Answer:
36
Step-by-step explanation:
When the cube is rolled two times
Let (a,b) denote a possible outcome of rolling the cube twice , with a the number on the top of the first roll and b the number on the top of the second roll
(1,1) (1,2) (1,3) (1,4) (1,5) (1,6)
(2,1) (2,2) (2,3) (2,4) (2,5) (2,6)
(3,1) (3,2) (3,3) (3,4) (3,5) (3,6)
(4,1) (4,2) (4,3) (4,4) (4,5) (4,6)
(5,1) (5,2) (5,3) (5,4) (5,5) (5,6)
(6,1) (6,2) (6,3) (6,4) (6,5) (6,6)
There are 36 possibilities for (a,b).
It can be obtained from the multiplication principle: there are 6 possibilities for a, and for each outcome for a, there are 6 possibilities for b.
So, the total number of outcomes (a,b) is [tex]6 \times 6 =36[/tex]
Hence the total number of possible outcomes is 36
When the cube is rolled two times, there are a total of 36 possible outcomes.
Use the concept of probability defined as:
Probability is the ratio of:
The number of favorable outcomes to the total number of outcomes for an event's taking place.
Given that,
A six-sided number cube is used, with numbers 1-6 labeled on each face.
Each number is used exactly once on the cube.
The cube is rolled two times.
The objective is to determine the number of possible outcomes when rolling the cube two times.
To find the number of possible outcomes when a six-sided number cube is rolled two times:
Use a simple principle called the multiplication principle.
Since there are six possible outcomes for each roll,
The total number of outcomes for rolling the number cube two times is found by multiplying the number of outcomes for each roll together.
So, if you roll the number cube two times,
There would be 6 outcomes for the first roll and 6 outcomes for the second roll.
Multiplying them together gives us a total of 36 possible outcomes.
Hence,
The answer is 36 possible outcomes when the cube is rolled two times
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Find the complex conjugate of the given number -1+4i
Answers
Please help:
[tex]5^{x-1} + 5 [/tex] x [tex]0.2^{x-2} = 26[/tex]
When I tried it, I got up until canceling the 5s and getting x - 1 - x - 2 = 21
What did I do wrong?
Answers
How to calculate percentage increase
Answers
A percentage increase can be calculated by first finding the difference between the new and original values, then dividing that difference by the original value. The result is then multiplied by 100 to get the percentage increase. This method can also help calculate inflation rates and various other mathematical problems.
Explanation:To calculate a percentage increase, you need to understand the basic principles of mathematics. Using the context provided, we can define calculating a percentage increase in the following way:
Steps to Calculate Percentage Increase:
For example, suppose the original price for a basket of goods was $20 and the new price is $25. First, find the difference: $25-$20 = $5. This is the increase. Then, divide the increase ($5) by the original price ($20) to get 0.25. Multiply by 100 and you get a 25% increase.
This method can be applied to many scenarios including calculating the rate of inflation. There are also online calculators and computers that can assist in finding these percentages quickly.
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What is the slope of the line that passes through points (5,0) and (10, 0)? How do you know?
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please Sara recorded the height of the ocean at low tide, with respect to sea level, for four days. Time Low Tide (inches) Monday a.m. −4 Monday p.m. −6 Tuesday a.m. −3 Tuesday p.m. −1 Wednesday a.m. 0 Wednesday p.m. 2 Thursday a.m. −1 Thursday p.m. −3 What is the average height of the ocean at low tide with respect to sea level? Enter your answer in the box.
Answers
Answer:
-2
Step-by-step explanation:
The averge of low tide is of -2 inches
What is the area, in square millimeters, of a right triangle with a hypotenuse of 68 millimeters and a leg of 60 millimeters?
Answers
x² + 60² = 68²
x² + 3600 = 4624
x² = 1024
x = √1024
x = 32 = length of the other side
A = (1/2)(32) (60) = 960 mm²
A three sided regular polygon is called equilateral.
a. True
b. False