Answers
x = sqrt(17^2 + 15^2)
x = 8
missing side = 8
Related Questions
54 equals 9 more than a number t
Answers
"more than" indicates addition. 9 more than a number t is t + 9:
54 = t + 9
If you need the solution, it follows:
54 = t + 9
45 = t
t = 45
Hope this helps!
Find the measure of the third angle of a triangle given that the first two angles are 44o and 72 o. Show your work.
Answers
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°.
find the volume of a sq pyramid with height of x+8 and length of 3x and width of 3x
Answers
[tex]\bf V=\cfrac{1}{3}(3x)(3x)(x+8)\implies V=\cfrac{1}{3}(9x^2)(x+8) \\\\\\ V=(3x^2)(x+8) \implies V=3x^3+24x^2[/tex]
A principal of $2000 is invested at 8% interest, compounded annually. How much will the investment be worth afte 5 years?
Answers
8% of $2000 = 2000 · 0.08 which equals $160. So $160 is added the first year.
2. 2160 · 0.08 = $172.8 = $2332.80
3. 2332.80 · 0.08 = $186.624 = $2519.424
4. 2519.424 · 0.08 = $201.55392 = $2720.97792
5. 2720.97792 · 0.08 = $217.6782336 = $2938.6561536
Rounded to the nearest hundredth, after 5 years there will be $2938.66.
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?
Answers
We have then:
x: number of phones that were sold at the wrong price.
y: number of phones that were sold with the correct price.
We now write the system of equations that represents the problem.
We have then:
[tex]565x + 489y = 213873 x + y = 401 [/tex]
Resolving the system graphically we have:
[tex]x = 234 y = 167[/tex]
Note: see attached image for the graphic solution.
Answer:
234 phones were sold at the wrong price
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.
Answers
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:[tex] 4x^{2} + 8x + 8x + 16[/tex] Combine the like terms
[tex] 4x^{2} + 16x + 16[/tex] It's the same.
Now let's use the second scenario:
[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]
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:[tex] 4x^{2} - 8x - 8x + 16[/tex] Combine the like terms
[tex] 4x^{2} - 16x + 16[/tex] It's the same.
Please help me with questions 20
Answers
--------------------------------------------------------------
tan(angle) = opposite/adjacent
tan(x) = 100/150
tan(x) = 2/3
x = arctan(2/3)
x = 33.6900675
which rounds to 34 degrees
the functions f(x) and g(x) are graphed
Answers
_____
The curves intersect where f(x) = g(x). That is, the argument "x" must be the same in both cases.
Answer:
AAAA
Step-by-step explanation:
I just took the test
What are the zeros of the polynomial y = (3x − 1)(x + 2)(2x + 1)?
Answers
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
Answers
dP / dt = P / 10
We apply separable variables:
dP / P = dt / 10
We integrate both sides:
Ln (P) = t / 10 + C
We rewrite the equation:
Exp (Ln (P)) = Exp (t / 10 + C)
P = Exp (C) * Exp (t / 10)
P = C * Exp (t / 10)
We look for the constant using:
P (0) = 300
300 = C * Exp (0/10)
300 = C * 1
C = 300
We rewrite the equation:
P = 300 * Exp (t / 10)
After 40 hours we have:
P = 300 * Exp (40/10)
P = 16379.44501
Answer:
the population size after 40 hours is:
P = 16379
A dice is rolled, then a coin is tossed. What is the probability of getting a 5 then tails?
Answers
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.
Learn more about Probability here:https://brainly.com/question/32117953
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A sales representative for a baby food company wants to survey 300 random couples who are new parents to find out if their newborn child is a boy or a girl. The rep uses a 1 for a girl and a 2 for a boy when running a simulation. Would the simulation be a fair representation of possible survey results? Why or why not?
A. Yes, because each of the two outcomes are equally likely.
B. No, because each of the two outcomes are not equally likely.
C. No, because the survey includes 300 results.
D. Yes, because the survey includes 300 results.
Answers
Answer:
A. Yes, because each of the two outcomes are equally likely.
Step-by-step explanation:
A sales representative for a baby food company wants to survey 300 random couples who are new parents to find out if their newborn child is a boy or a girl.
The representative uses a 1 for a girl and a 2 for a boy when running a simulation.
Yes, the simulation will be a fair representation of possible survey results.
A. Yes, because each of the two outcomes are equally likely.
In this figure, ∠a and ∠b are 15 points here
Answers
So, the correct answer is Supplementary angels because angles A and B equal a sum of 180*.
Hope this helps!
is 1,200mm greater or less than 12m
Answers
Final answer:
1,200 millimeters (mm) is less than 12 meters (m). To compare, we convert 1,200 mm to 1.2 m and directly compare it with 12 m, clearly seeing that 1.2 m is less than 12 m.
Explanation:
To determine whether 1,200 millimeters (mm) is greater or less than 12 meters (m), we need to convert mm to meters. We know that 1 meter is equal to 1,000 millimeters. Therefore, we can convert 1,200 mm to meters:
1,200 mm ÷ 1,000 = 1.2 m
Now we can compare 1.2 m with 12 m directly. Since 1.2 is less than 12, we can conclude that 1,200 mm is less than 12 m.
To use an example for further clarification, imagine you are measuring the length of a room with a tape measure:
If the room is 1,200 mm (or 1.2 m) long, it is shorter than a room that is 12 m long.
What is the axis of symmetry of h(x)=5x^2+40x+64
Answers
.. x = -b/(2a)
You have
.. a = 5
.. b = 40
so the axis of symmetry is
.. x = -40/(2*5)
.. x = -4
Answer:
2
Step-by-step explanation:
give me brainliest
find the value of x
Answers
x = 180 - (82+32)
x = 180 - 114
x = 66
answer
C, 66
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 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
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.
How can you convert 5 feet 6 inches to inches
Answers
1 foot = 12 inches
We need to convert 5 feet 6 inches to just inches. To do this, let's multiply how many inches there are in one foot by 5 feet.
12 × 5 = 60
That means that 5 feet are equal to 60 inches. We still have 6 inches left. Add them:
60 + 6 = 66
ANSWER:
5 fest 6 inches = 66 inches.
5 × 12 = 60
Now, we add the 6 extra inches:
60 + 6 = 66
Therefore, 5 feet 6 inches equals 66 inches.
Hope this helps!
Divide (5.6 x 10^15) by (6.4 x 10^2). Express your answer in scientific notation.
Answers
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
Answers
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.
Melanie is reading a book that is 300 pages long. If she has read 210 pages of the book, what percent of the book has she read?
Answers
Answer:
She has read 70 % of the book.
Step-by-step explanation:
Given : Melanie is reading a book that is 300 pages long. If she has read 210 pages of the book,
To find : what percent of the book has she read.
Solution : We have given
Total pages in book = 300 pages .
She read = 210 .
Percentage she read (%) = [tex]\frac{She\ read\ pages}{total\ pages}*100[/tex].
Percentage she read (%) = [tex]\frac{210}{300}*100[/tex].
Percentage she read (%) = [tex]\frac{210}{3}[/tex].
Percentage she read (%) = 70 % .
Therefore, She has read 70 % of the book.
Example: y = -2x and y = x + 3 2)
Does the point (2, 5) make either equation true? Explain.
Answers
5= -2(2)
5 = -4
So no, the first one y=-2x would not work since -4 is not equal to 5.
5=2+3
5=5
Yes, that second one y=x+3 does work since 5 is equal to 5.
What is the following product? Assume
Answers
The answer is B 10x56 Sq 6xy
Answer:
B
Step-by-step explanation:
edgen 2020
10 points thanks in advanced
Answers
The area (A) of the rectangle is:
A = w * l
w - width
l - length
We have:
w = 7/8 ft
l = 1 3/5 ft = 1 + 3/5 = 5/5 + 3/5 = (5 + 3)/5 = 8/5 ft
A = w * l
A = 7/8 * 8/5
A = 7/5 = (5+2)/5 = 5/5 + 2/5 = 1 + 2/5 = 1 2/5 ft²
ASAP! hurry please! :)
Answers
Cool you're in K12 so am I.
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
Answers
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
The volume of a shampoo filled into a container is uniformly distributed between 374 and 380 milliliters. (a) what are the mean and standard deviation of the volume
Answers
The mean volume of the shampoo is 377 milliliters, and the standard deviation is approximately 1.732 milliliters.
The standard deviation is calculated using the following formula:
[tex]\[ \sigma = \frac{{\text{max} - \text{min}}}{{\sqrt{12}}} \][/tex]
Given the range (374 to 380 milliliters):
(a) Mean[tex](\(\mu\))[/tex]:
[tex]\[ \mu = \frac{{\text{min} + \text{max}}}{2} \][/tex]
[tex]\[ \mu = \frac{{374 + 380}}{2} \][/tex]
[tex]\[ \mu = 377 \text{ milliliters} \][/tex]
(b) Standard Deviation:
[tex]\[ \sigma = \frac{{\text{max} - \text{min}}}{{\sqrt{12}}} \][/tex]
[tex]\[ \sigma = \frac{{380 - 374}}{{\sqrt{12}}} \][/tex]
[tex]\[ \sigma \approx \frac{{6}}{{\sqrt{12}}} \][/tex]
[tex]\[ \sigma \approx \frac{{6}}{{3.464}} \][/tex]
[tex]\[ \sigma \approx 1.732 \text{ milliliters} \][/tex]
So, the mean volume of the shampoo is 377 milliliters, and the standard deviation is approximately 1.732 milliliters.
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?
Answers
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:)
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
Answers
100 km........1,5 h
v1= 200/3,5=57,1
v2= 100/1,5= 66,6
vm=( 57.1+66,6)/2≈ 61,5 km/h
Answer:
vm=( 57.1+66,6)/2≈ 61,5 km/h
Step-by-step explanation:
Write at least three different expressions that mean “slope”
Answers
2. y=mx+b
3. rise over run
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.