In this figure, ∠a and ∠b are 15 points here
Rewrite the standard equation in slope-intercept form: 3x-8y=24
The equation 3x - 8y = 24 can be written in slope intercept form as y = [tex]\frac{3}{8}[/tex] x - 3.
What is Slope?Slope of a line is defined as the value of the change in the values of the y coordinates with respect to the change in the values of the x coordinate.
It can also be defined as the tangent of the angle that the line makes with the X axis.
The standard equation of a line in slope intercept form is, y = mx + c, where m is the slope and c is the y intercept.
y intercept is the y coordinate when the line touches with the Y axis. The x coordinate of that point will be zero.
The given equation is,
3x - 8y = 24
Subtracting both sides of the equation with -3x,
3x - 8y - 3x = 24 - 3x
-8y = 24 - 3x
Dividing both sides by -8, we get,
y = -3 + [tex]\frac{3}{8}[/tex] x
y = [tex]\frac{3}{8}[/tex] x - 3
Hence the standard equation in slope intercept form for 3x - 8y = 24 is y = [tex]\frac{3}{8}[/tex] x - 3.
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which equation is equivalent to log3(x+5)=2
Explain what a polynomials is and identify the different parts of a polynomial.
Explain the different labels used to categorize polynomials
Explain how addition and subtraction of polynomials is accomplished
When multiplying polynomials, we are taking every term of one polynomial and multiplying them by every term of the second polynomial, then collecting like terms explain how foil helps us to accomplish this and what category of polynomials foil applies to.
There are tow special case products where the product takes on special patterns explain these two cases and when they occur.
For each of the two special cases, illustrate your explanation with an appropriate exercise from the ( a+b)2=a2+2ab+b2 )(a-b)2=a2-2ab+b2 ) showing how the multiplication is performed using the special pattern formula then also showing the same result using foil.
A polynomial is an expression of more than one term. An expression is considered a polynomial when is has more than one term, otherwise, it would be called a monomial. These can be combined together through multiplication, addition and subtraction only. (Meaning no division or fractions)
Ex.
[tex]3 x^{2} + 3x - 3[/tex]
x is a variable (There can be more than 1 variable in a term. Ex. 3xy, 4xyz, 4ab)
*A variable may be represented by letters.
2 is an exponent
3 is a constant
Those are the parts of a polynomial.
Polynomials can be categorized depending on the number of terms and their degree.
A polynomial with two terms is called a binomial. If it has three terms it is called a trinomial. If the expression has more than 3 terms, they are generally called polynomials.
A polynomial can be categorized by degree as well. You can determine the degree of a polynomial by looking at the term that has the highest exponent.
Using the example above, you can categorize the polynomial as a 2nd degree trinomial because 2 is the highest exponent and it has three terms.
When you add and subtract polynomials you need to take note of the variables. You can only subtract and add like terms, which means that the variables and the exponents are the same.
Ex.
[tex]( 2x^{3} + 2 y^{2} + x + 1) + (4 x^{2} - y^{2} + y + 2)[/tex]
When you add these two polynomials, you can disregard the parentheses because according to the associative property of addition, no matter how you group the terms, the answer will be the same.
Like mentioned before you can only add and subtract like terms. It would be easier if you just group like terms together by rearranging the expression. Do not forget that the sign or operation comes along with them.
[tex]2 x^{3} + 2 y^{2} - y^{2} + 4 x^{2} + x + y + 2 + 1[/tex]
Now combine the like terms.
[tex]2 x^{3} + y^{2} + 4 x^{2} + x + y + 3[/tex]
Notice that we retained the terms [tex]2 x^{3} [/tex] , [tex]4 x^{2} [/tex], x and y, this is because they have no similar terms.
FOIL method is used when multiplying 2 BINOMIALS. Remember that a binomial is an expression with 2 terms.
FOIL means:
FIRST term: first terms of each binomial.
OUTSIDE term: The two outer terms when taking the equation as a whole.
INSIDE term: The two inner terms when taking the equation as a whole.
LAST term: Last term of each binomial (2nd term of each binomial)
To get the answer, you need to multiply them with their corresponding term.
Ex. (2x+3)(x-4)
F: 2x and x (2x)(x) = [tex] 2x^{2} [/tex]
O: 2x and -4 (2x)(-4) = -8x
I: 3 and x (3)(x) = 3x
L: 3 and -4 (3)(-4) = -12
Resulting expression:
[tex]2 x^{2} - 8x + 3x -12[/tex] -8x and 3x are similar or like terms, so you can combine them
[tex]2 x^{2} - 5x -12[/tex]
When doing multiplication with binomials, there are two special cases you can consider doing, which follow a pattern. The first is multiplying sum and difference.
The condition where you can apply the first special case is the first term needs to be the same and the second term are additive inverses.
(a+b)(a-b)
The resulting expression follows this pattern [tex] a^{2} - b^{2} [/tex]
Ex. (x+3)(x-3) = [tex] x^{2} - 3^{2} [/tex] or [tex] x^{2} -9[/tex]
You can use FOIL to check your answer:
F: (x)(x) = [tex] x^{2} [/tex]
O: (x)(-3) = [tex]-3x[/tex]
I: (3)(x) = [tex]3x[/tex]
L: (3)(-3) = [tex]-9[/tex]
Arrange the expression:
[tex] x^{2} - 3x + 3x - 9[/tex] Combining -3x+3x = 0
[tex] x^{2} -9[/tex]
The next special case is squaring a binomial and there are two scenarios that you can consider.
[tex] (a+b)^{2} [/tex] and [tex] (a-b)^{2} [/tex]
The resulting expression follows a certain pattern for each:
[tex] (a+b)^{2} [/tex] = [tex] a^{2} + 2ab + b^{2} [/tex]
[tex] (a-b)^{2} [/tex] = [tex] a^{2} - 2ab + b^{2} [/tex]
Let's use an example of each to demonstrate this and check with FOIL:
[tex] (a+b)^{2} [/tex]
[tex] (2x+4)^{2} [/tex]
a = 2x b = +4
Let's insert that into our pattern:
[tex] a^{2} + 2ab + b^{2} [/tex]
[tex] 2x^{2} + 2(2x)(4) + 4^{2} [/tex]
Simplify the expression:
[tex] 2x^{2} + 16x + 4^{2} [/tex]
[tex] 4x^{2} + 16x + 16 [/tex]
Let's check with FOIL
[tex] (2x+4)^{2} [/tex] = [tex] (2x+4)(2x+4) [/tex]
F: (2x)(2x) = [tex] 4x^{2} [/tex]
O: (2x)(4) = [tex]8x[/tex]
I: (4)(x) = [tex]8x[/tex]
L: (4)(4) = [tex]16[/tex]
Let's arrange the terms:a = 2x b = -4
Let's insert that into our pattern:
[tex] a^{2} - 2ab + b^{2} [/tex]
[tex] 2x^{2} - 2(2x)(-4) + (-4)^{2} [/tex]
Simplify the expression:
[tex] 2x^{2} - 16x + (-4)^{2} [/tex]
Let's check with FOIL
[tex] (2x+4)^{2} [/tex] = [tex] (2x-4)(2x-4) [/tex]
F: (2x)(2x) = [tex] 4x^{2} [/tex]
O: (2x)(-4) = [tex]-8x[/tex]
I: (-4)(x) = [tex]-8x[/tex]
L: (-4)(-4) = [tex]16[/tex]
Let's arrange the terms:John has 51 cards. Paul has 32 cards. George has a number of cards greater than either Paul or John. How many cards might George have?
John has 51 cards.
Paul has 32 cards.
George has a number of cards greater than either Paul or John.
This means, George does have number of cards greater than both Paul and John.
Number of Cards with John is 51 and number of cards with Paul is 32 cards.
Therefore the number of cards that George may have is in between 33 and 51
If George has any number of cards greater than 32 and less than 52, then this number of cards is greater than cards with Paul but less than the cards with John.
Number of cards George has is > 32 but < 52
Hope this helps..!!
Thank you:)
Cora is taking three AP classes and two regular classes. Her AP classes count twice as much as her regular classes in her GPA. Each A is worth 4 points, Bs are worth 3 points, Cs are worth 2 points, and Ds are worth 1 point. What is Cora's GPA? Class Cora's grade AP English A AP Government A AP Algebra II A Spanish B Physics A
Cora's GPA, considering the weighted AP classes and grades achieved, calculates to be 3.875.
To calculate Cora's GPA with her AP and regular classes, we need to account for the weight of her AP classes.
Cora has five classes with three being AP and two regular.AP classes count twice as much as regular classes. Thus, AP classes will be counted as double credits.Calculate the points for each grade:AP English (A): 4 points, counted double = 4 × 2 = 8 pointsAP Government (A): 4 points, counted double = 4 × 2 = 8 pointsAP Algebra II (A): 4 points, counted double = 4 × 2 = 8 pointsSpanish (B): 3 pointsPhysics (A): 4 pointsTotal points = 8 + 8 + 8 + 3 + 4 = 31 pointsTotal credit count = 6 (for AP) + 2 (for regular) = 8 creditsCalculate GPA = Total points / Total credits = 31 / 8 = 3.875Therefore, Cora's GPA is 3.875.
54 equals 9 more than a number t
find the value of x
Answer with Step-by-step explanation:
since, DAC is a straight line
Hence, ∠BAD+∠BAC=180°
98°+∠BAC=180°
⇒ ∠BAC=180°-98°
= 82°
Now, we know that sum of angles of a triangle=180°
Hence, ∠BAC+∠ABC+∠BCA=180°
82°+32°+x=180°
x=180°-82°-32°
x= 66°
Hence, correct option is:
C. 66°
A dice is rolled, then a coin is tossed. What is the probability of getting a 5 then tails?
The chance of rolling a 5 on a six-sided dice is 1/6, and the probability of getting a tails in a coin toss is 1/2. The total probability of both these independent events occurring is (1/6) * (1/2) = 1/12 or approximately 0.0833 on a decimal scale.
Explanation:The question is asking for the probability of rolling a 5 on a dice and then getting a tails on a coin toss. To get the total probability, we multiply the individual probabilities together.
First, let's consider a fair six-sided die. The chance of rolling a 5 (or any specific number between 1 and 6) is 1/6.
Next, we consider a fair coin, which has two outcomes: heads or tails. So, the probability of getting tails is 1/2.
The total probability of both these events occurring is (1/6) * (1/2) = 1/12. So, the probability of rolling a 5 and then tossing a tail is 1 in 12 or approximately 0.0833 on a decimal scale.
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If rectangle ABCD was reflected over the y-axis, reflected over the x-axis, and rotated 180°, where would point A' lie?
Answer:
A' would be return to its original position .
Step-by-step explanation:
Given : If rectangle ABCD was reflected over the y-axis, reflected over the x-axis, and rotated 180°.
To find : where would point A' lie.
Solution : We have given that ABCD was reflected over the y-axis, reflected over the x-axis, and rotated 180°
By the reflection rule over y axis .( x ,y) →→ ( -x ,y)
Suppose A ( x ,y) if we reflect it over y axis then
A( x ,y) →→ A'( -x ,y)
Now reflect it over x axis (-x ,y) →→( -x ,-y)
Now rotate by 180° it become ( -x, -y) →→( x ,y)
Hence , it return to its original position .
Therefore, A' would be return to its original position .
Please help me with questions 20
What is the sum of the polynomials? (8x2-9y2-4x)+(x2-3y2-7x)
Answer:
D
Step-by-step explanation:
Find the measure of the third angle of a triangle given that the first two angles are 44o and 72 o. Show your work.
Answer: The measure of the third angle of a triangle is 64°.
Step-by-step explanation:
Since we have given that
First angle = 44°
Second angle = 72°
Let the third angle be x.
As we know that the sum of all three angles of a triangle is supplementary.
[tex]44^\circ+72^\circ+x=180^\circ\\\\116^\circ+x=180^\circ\\\\x=180^\circ-116^\circ\\\\x=64^\circ[/tex]
Hence, the measure of the third angle of a triangle is 64°.
Mario has 3.875 liters of juice at the beginning of the day he drinks 2.79 liters during the day how much juice is left over st the end of the day
Answer:
The juice left at the end of the day is 1.085 liters.
Step-by-step explanation:
Juice at the beginning of the day: 3.875 liters
Juice drink by Mario during the day: 2.79 liters
Juice left at the end of the day = Juice at the beginning of the day - Juice drink by Mario during the day
= 3.875 - 2.79
= 1.085 liters
What is the following product? Assume
The answer is B 10x56 Sq 6xy
Answer:
B
Step-by-step explanation:
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Texas has 254 counties, California has 58 counties, Florida has 67 counties,how many more counties does texas have than the number of counties in California and Florida combined
An error occurred in your bookkeeping department this month. The price of one of the smart phones that you sell is $489. Several customers were charged $565 for the phone instead. You know that the total sales for this month were $213,873 and that 401 phones were sold. How many phones were sold at the wrong price?
What is the axis of symmetry of h(x)=5x^2+40x+64
Answer:
2
Step-by-step explanation:
give me brainliest
How can you convert 5 feet 6 inches to inches
ASAP! hurry please! :)
Evelyn is waiting in line for concert tickets. She is 2.5 blocks from the ticket booth. 16 blocks equals 1 mile. Each person takes up about 2 feet in the line. Which calculation can be used to find about how many people are ahead of Evelyn in line?
Answer:
1/2 person over feet
Step-by-step explanation:
yw!
Compounding with different interest rates a deposit of $750 earns interest rates of 10.5 percent in the first year and 7.5 percent in the second year. what would be the second year future value? $890.91 $885.00 $829.43 $1,635.00
a sticker price on a new vehicle is $33985 , but the dealer cost is $27700 and you want to offer 4% over the dealer cost. what would be the offered amount?
A student needs to earn 80 points on the test in order to keep an A grade for the semester. Write an equation that represents the situation in terms of the number of correct answers
The equation that represents the situation is x = 80.
Explanation:To write an equation representing the situation, let's use the variable x to represent the number of correct answers on the test. Since each correct answer is worth 1 point, the total number of points earned is the same as the number of correct answers. Given that the student needs to earn 80 points to keep an A grade for the semester, the equation is:
x = 80
Therefore, if the student answers 80 questions correctly, they will maintain an A grade for the semester.
Write at least three different expressions that mean “slope”
Answer:
Step-by-step explanation:
Considering 'm' as the slope of a function y=f(x) we can have:
1. m=(y2-y1)/(x2-x1) which is the slope of a line based on two points from the line.
2. m=dy/dx which is the slope of the function y=f(x) in (x,y) by the derivative.
3. m=tan(Ф) which is the slope of a line when the angle (Ф) with respect x-axis is known.
Consider a population of bacteria that grows according to the initial value problem dP/dt=P/10, P(0)=300. Find the population size after 40 hours
A principal of $2000 is invested at 8% interest, compounded annually. How much will the investment be worth afte 5 years?
10 points thanks in advanced
Simplify the expression. 12P5 : 11,880 95,040 7,920 1,235,520
So the correct answer is B. 95,040
A train traveled 300 km in 5 hours and then increased in speed, traveling the final 100 km in 1.5 hours. What was the train's average speed in km/h?
66.7 km/h
60 km/h
61.5 km/h
54 km/h
Answer:
vm=( 57.1+66,6)/2≈ 61,5 km/h
Step-by-step explanation: