m∠1=29
In this question,
1) Since we have, vertical angles, whose measure are written as polynomials then we can write according to the Vertical angles theorem:
3y² + 2y – 10 =2y² + 7y + 4
3y²-2y² -7y+2y-10-4=0
y²-5y-14=0
1.1) Finding the roots by Sum and Product
S(x) = ___ +___ = -5
P(x) =____ x ___ = -14
x1=-2 or 7
Since our Domain, cannot allow negative numbers, let's keep the positive one 7
2) Moreover to that, m∠1 + 2y² + 7y + 4 = 180º
m∠1 +2(7)²+7(7)+4=180
m∠1 +151 =180
m∠1=180-151
m∠1=29
[tex]y {}^{2} + 5y - 24[/tex]Help to do this problem by Factoring triinomials by Box Method. please
Factor the trinomial
[tex]y^2+5y-24[/tex]by the box method.
The multiplication gives -24y^2. Now we need to find two factor that gives 5x. It should be creal that this factor are 8y and -3y. Then:
Now we find the common factor for each column and row:
Therefore:
[tex]y^2+5y-24=(y-3)(y+8)[/tex]you deposit $4000 each year into an account earning 3% interest compounded annually. How much will you have in the account and 35 years?
ANSWER:
$ 241848.33
STEP-BY-STEP EXPLANATION:
Given:
P = $4000
r = 3% = 3/100 = 0.03
n = 35 years
The formula for the future value is:
[tex]\begin{gathered} FV=P\mleft(\frac{\left(1+r\right)^n-1}{r}\mright) \\ \text{ replacing} \\ FV=4000\cdot\mleft(\frac{\mleft(1+0.03\mright)^{35}-1}{0.03}\mright) \\ FV=241848.33 \end{gathered}[/tex]Therefore, after 35 years, he would have $ 241848.33 in the account.
A delivery servive charges $8 as base price for an overnight delivery of a package plus extra charge of $2.50 "PER" pound the package weighs.a. write and equation for the given information- y=_____x+_____b. Find the cost of shipping a 15-pound package.
We know that
- $8 is the base price
- $2.50 "PER" pound
The more weight there is the more it will cost. In order to find the cost due to the weight we just have to multiply $2.50 by the number of pounds:
$2.50x
Since it will cost $8 more, then the total cost is $8 added to the cost due to the number of pounds:
y = $2.50x + $8In order to find the cost of shipping a 15-pound package,
we just replace x = 15 in the equation:
y = $2.50x + $8
y = $2.50 · 15 + $8
y = $37.5 + $8
y = $45.5
Answer: the cost of shipping a 15-pound package is $45.5Find the slope of the tangent to thefunction f(x) = 2x4 + 6x² +4 at x = -1
-20
Explanations:Given the function f(x) = 2x^4 + 6x^2 + 4 at x = 1, the slope of the tangent of the function is expressed as:
[tex]f^{\prime}(x)=8x^3+12x[/tex]Substitute the value of x = -1 into the fucntion
[tex]\begin{gathered} f^{\prime}(-1)=8(-1)^3+12(-1) \\ f^{\prime}(-1)=8(-1)-12 \\ f^{\prime}(-1)=-8-12 \\ f^{\prime}(-1)=-20 \end{gathered}[/tex]Hence the slope of the tangent to the function at x = -1 is -20
what is the positve solution for this equation? 4x2 + 12 x= 135
We need to solve the following equation for x, and choose the positive solution
[tex]4x^2+12x=135[/tex]we substract 135 from both sides of the equation obtaining the canonical form of a quadratic equation, the we apply the quadratic formula with a=4, b=12 and c=-135 then x will be equal to:
[tex]x=\frac{-12+\sqrt[]{144-4(4)(-135)}}{8}=\frac{48-12}{8}=\frac{9}{2}=4.5[/tex]then the positive solution to the equation will be x=4.5I need help please it’s due tomorrow For lines a and b identify which inverse operation should come first
Answer:
[tex]\begin{gathered} a\text{. }\frac{k}{7}=11+11\text{ Addition} \\ b\text{. }k=22\cdot7\text{ Multiplication} \\ c\text{. }k=154 \end{gathered}[/tex]Step-by-step explanation:
Solve the following equation:
[tex]\frac{k}{7}-11=11[/tex]To solve the following equation use inverse operations. Addition and subtraction are inverse operations, multiplication, and division too.
[tex]\begin{gathered} \frac{k}{7}-11=11 \\ \frac{k}{7}=11+11\text{ Addition} \\ k=22\cdot7\text{ Multiplication} \\ k=154 \end{gathered}[/tex]there are 117 staff members in your school. One third of them are going away for the Thanksgiving holiday. How many staff members are not traveling
78 members are not traveling
Explanation
Step1
we need to use fractions to find the number of memebers are going away, so the whole number (117) is represented by 1
then,Let
whole number=full staff= 117
One third of them are going away for the Thanksgiving holiday, to find the number of members just do:(fraction by number)
[tex]\begin{gathered} \text{Members are going away=}\frac{1}{3}\cdot117 \\ \text{Members are going away=}39 \end{gathered}[/tex]Step 2
now, let's use subtraction to find the number of members that are not traveling
[tex]\begin{gathered} \text{Members are not traveling=full staff -member are going away} \\ \text{Members are not traveling=117-39} \\ \text{Members are not traveling=}78 \end{gathered}[/tex]I hope this helps you
Answer:
78
Step-by-step explanation:
So, to solve this problem, we have to divide 117 by 3, because one third of the staff is going away. 117 divided by 3 equals 39, which is number of staff this is going away. Next we have to subtract 39 from 117, which will give us our answer. 117 - 39 = 78
Happy Holidays!
6. A local deli kept track of the sandwiches itsold for three months. The polynomialsbelow model the number of sandwiches sold, where s represents days.Ham and Cheese: 453-285 +33s + 250 Pastrami:-7.452 + 32s +180Write a polynomial that models the total number of these sandwiches that were sold.
ok
Total sandwiches = Hand and Cheese + Pastrami
= 4s^3 - 28s^2 + 33s + 250 - 7.4s^2 + 32s + 180
= 4s^3 - 35.4s^2 + 55s + 430
[tex]\text{ 4s}^3-35.4s^2\text{ + 55s + 430}[/tex]
If the function fis defined by f(x) = x ^ 5 - 1 then the inverse, f ^ - 1 is defined by f ^ - 1 * (x) =
Given the function:
[tex]f(x)=x^5-1[/tex]We have that f(x) = y, so:
[tex]y=x^5-1[/tex]Substitute x with y:
[tex]x=y^5-1[/tex]And solve for y:
[tex]\begin{gathered} x+1=y^5-1+1 \\ x+1=y^5 \\ y=\sqrt[5]{x+1} \end{gathered}[/tex]Answer:
[tex]\sqrt[5]{x+1}[/tex]I need help please!!
Ok, well, I think I need to the see previous problem. But from the information given, I think the right choices are:
a) tenth
b) 31.8
c) 32
Use the sample data and confidence level given below to complete parts (a) through (d). A research institute poll asked respondents if they felt vulnerable to identity theft. In the poll, n=1024 and x=584 who said "yes"
If a research institute poll asked respondents if they felt vulnerable to identity theft:
The best point estimate of the population proportion p is 0.57.The value of the margin of error E is 0.030The confidence interval 0.54; 0.6The statement that correctly interprets the confidence interval is: Option A.How to find the population proportion p?a) Population proportion p
Using this formula to find the population proportion p.
p = (x/n)
Let plug in the formula
p = 584/1024
p= 0.57
b) Margin of error
Value of z-score for a confidence level of 95%= 1.96
Using this formula to margin of error
MOE =( z alpha x √(p) (1-p) / n )
Let plug in the formula
MOE =( 1.96 x √(.57)(1-.57) / 1024)
MOE =( 1.96 x √(.57)(.43) / 1024)
MOE =( 1.96 x √0.000239
MOE =( 1.96 x 0.015459)
MOE = 0.030
c) Confidence interval
Confidence interval =0.57 ± 0.030
Confidence interval = (0.57 -0.030) , (0.57 +0.030)
Confidence interval = 0.54; 0.6
Confidence interval = 0.54 <p< 0.6
d) The statement that correctly interprets the confidence interval is:
a) One has 95% confidence that the interval from the lower bound to the upper bound actually does contain the true value of the population proportion.
Therefore the Population proportion p is 0.57, MOE is 0.030 and CI is 0.54; 0.6.
Learn more about population proportion p here:https://brainly.com/question/18514274
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The complete question is:
Use the sample data and confidence level given below to complete parts (a) through (d). A research institute poll asked respondents if they felt vulnerable to identity theft. In the poll, n=1024 and x=584 who said "yes" Use a 95% confidence level.
a) Find the best point estimate of the population proportion p.
b) Identify the value of the margin of error E.
c) Construct the confidence interval.
d) Write a statement that correctly interprets the confidence interval. Choose the correct answer bellow
a) One has 95% confidence that the interval from the lower bound to the upper bound actually does contain the true value of the population proportion.
b) 95% of sample proportions will fall between the lower bound and the upper bound.
c) there is a 95% chance that the true value of the population proportion will fall between the lower bound and the upper bound.
d) One has 95% confidence that the sample proportion is equal to the population proportion
6) What is the slope of the line represented in the table?02d)-112Choose
The equation of slope of the graph is,
[tex]Slope=\frac{y_2-y_1}{x_2-x_1}[/tex]Consider,
[tex]x_1=2,x_2=4,y_1=9,y_2=13[/tex]Then,
[tex]\text{Slope =}\frac{13-9}{4-2}=2[/tex]Therefore, the correct option is A
lonny and mia each take out a 250,000 loan for a new house. each has to repay the loan in 25 years. lonny will pay an interest rate of 3.4% per year. his monthly payments will be $1250. because mia has a lower credit score she will have to pay an interest rate of 4.1% per year. her monthly payments will be $1360. how much more will a 250,000 loan cost mia than lonny?
Lonny takes a loan of 250000 and repays $1250 /month
in a year he pays 1250 x 12 =$15000
in 25 years he pays 15000 x 25 =$375000
mia pays 1360/ month. In a year she pays 1360 x 12 =$16320
in 25 years she pays 16320 x 25= $408000
difference in cost = 408000 -37500 = $33000
it will cost mia $33000 more for the loan.
Please help me with this quickly, the questions says to show work or explain but I want explanation, thank you!
Solution
- Experimental probability is the probability gotten from conducting experiments and it is different from theoretical probability which is derived from hypothetical situations.
- In this question, the hypothetical situation that leads to the theoretical probabilities of getting a red, an orange, and so on, is the fact that the question already said the smallest section of the circle is 1/16 and every other portion is a multiple of this.
- The experimental probabilities are gotten from the table and the formula for calculating this probability is given below:
[tex]\begin{gathered} Given\text{ Event \lparen E\rparen,} \\ P(E)=\frac{Number\text{ of times an event occurs}}{Total\text{ number of trials}} \end{gathered}[/tex]- Thus, we can proceed to find the experimental probabilities of finding any of these colors as follows:
Orange:
[tex]\begin{gathered} E=\text{ Event of spinning an Orange} \\ P(orange)=\frac{3}{30}=\frac{1}{10} \end{gathered}[/tex]Green:
[tex]P(green)=\frac{6}{30}=\frac{1}{5}[/tex]Blue:
[tex]P(blue)=\frac{5}{30}=\frac{1}{6}[/tex]14 Select all that apple Which of these fractions are equivalent to ?
the initial fraction es 1/4, so if we multiply the fraction by 2/2 it become:
[tex]\frac{2}{2}\cdot\frac{1}{4}=\frac{2}{8}[/tex]and if we multiply by 6/6
[tex]\frac{6}{6}\cdot\frac{1}{4}=\frac{6}{24}[/tex]So the solution is fraction 2/8 and fraction 6/24
I have the answers to the question but I’m not sure how they got them?
Hello there. To solve this question, we'll have to use the data from the graph (dot plot) and determine the answers for each letter.
a) How many babies begin walking before 13 months of age?
For this, we have to add all the number of babies walking from the dot plot that are less than 13.
In this case, we add the values of babies walking with 9, 10, 11 and 12 months:
1 + 1 + 3 + 5 = 10
Therefore 10 babies have begun walking before 13 months of age.
b) What percent of babies begin walking at 12 months?
For this, we add the entire number of babies walking by age and calculate the ratio between the number of babies walking at 12 months and this result.
We have 25 babies at total and 5 of them began walking at 12 months of age, so now we take the ratio:
[tex]\frac{5}{25}=\frac{1}{5}=20\%[/tex]c) Which three ages combined account for less than 16% of the babies?
For this, we find how many is 16% of 25, that is, the total of babies:
[tex]0.16\cdot25=4[/tex]So we have to find which three ages combined gives us less than 4 babies.
Notice we cannot choose the ages 12, 13, 14 because their number of babies, alone, are already bigger than 4.
We cannot also choose 11, because it is equal to 3 and all the other options are bigger than or equal to 1, so adding it with something else already would be equal to 4.
The same happens to 15 and 16, because their assigned value is 2, so adding both together gives us 4 and since all the others are greater than or equal to 1, we could not add other two together with them.
That's why the final answer is 9, 10 and 17, because they are the only numbers left that add up to 3 and this is a number less than 4, that is, less than 16% of the babies.
Which of the following sets of numbers could be the lengths of thesides of a triangle?11, 1,41, 14, 2016, 9, 1511, 8, 19
as you may know the hypotenuse is the longest side in a triangle. So using pythagoras theorem:
c = √(a² + b²)
Where:
c = Hypotenuse
a = adjacent side
b = opposite side
11, 1,4 Since 11 is the greater number
c = 11
the others will be a and b, the order does not matter
a=1
b=4
11 = √(1² + 4²
Solve the system of two equations in two variables. Y=1/4x+42x - 8y =9
The given system is
[tex]\mleft\{\begin{aligned}y=\frac{1}{4}x+4 \\ 2x-8y=9\end{aligned}\mright.[/tex]To solve this system, we substitute the first equation in the second one.
[tex]2x-8(\frac{1}{4}x+4)=9[/tex]Now, we solve for x.
[tex]\begin{gathered} 2x-\frac{8}{4}x-32=9 \\ 2x-2x=9+32 \\ 0=41 \end{gathered}[/tex]This means the system has no solutions.In other words, the system represents parallel lines.
Hello, can you help me find the solutions to this problem?
Given,
The expression is,
[tex]\begin{gathered} x^3=216 \\ x^3-216=0 \end{gathered}[/tex]The rational theorem tells that if the polynomial has the rational 0 then it must be a fraction p/q, where p is a factor of constant term and q is the factor of leading coefficient.
The constant term 216 with factors:
[tex]1,2,3,4,6,8,9,12,18,24,27,36,54,72,108\text{ }and\text{ }216.[/tex]The leading coefficient is 1, with a single factor of 1.
[tex]\begin{gathered} \frac{p}{q}=\frac{factor\text{ of 216}}{factor\text{ of 1}}=\pm\frac{1}{1},\operatorname{\pm}\frac{2}{1},\operatorname{\pm}\frac{3}{1},\operatorname{\pm}\frac{4}{1},\operatorname{\pm}\frac{6}{1},\operatorname{\pm}\frac{8}{1},\operatorname{\pm}\frac{9}{1},\operatorname{\pm}\frac{12}{1}, \\ \operatorname{\pm}\frac{18}{1},\operatorname{\pm}\frac{24}{1},\operatorname{\pm}\frac{27}{1},\operatorname{\pm}\frac{36}{1},\operatorname{\pm}\frac{54}{1},\operatorname{\pm}\frac{72}{1},\operatorname{\pm}\frac{108}{1},\operatorname{\pm}\frac{216}{1} \end{gathered}[/tex]Substitute the possible roots one by one into the polynomial to find the actual roots. Start first with the whole numbers.
p(6)=0 so x=6 is a root of a polynomial p(x).
Using factor theorem to find the remaining roots,
[tex]\begin{gathered} \frac{x^3-216}{x-6}=x^2+6x+36 \\ By\text{ formula method,} \\ x=\frac{-6\pm\sqrt{36-144}}{2} \\ x=\frac{-6\pm\sqrt{108}}{2} \\ x=\frac{-6\pm6\sqrt{-3}}{2} \\ x=-3\pm3\sqrt{3i} \end{gathered}[/tex]Hence, the roots are 6, -3-3sqrt(3)i, and -3+3sqrt(3)i. So, option A is correct.
grading system 1. grading system 2test average-35% 45%final exam grade- 25% 15%projects-15% 15%homework-15% 10%class participation-10% 15%If your values are the following in your math class, which grading system would you prefer and why?test average=84final exam grade=72projects=68homework=88class participation=95
We have two grading systems, with different weights for different items.
We have to calculate, for a certain points of the different items, which grading systems gives a higher weighted average score.
To do so we multiply each percentage to each of the items points and add them all.
We start with grading system 1:
[tex]\begin{gathered} P1=0.35\cdot84+0.25\cdot72+0.15\cdot68+0.15\cdot88+0.1\cdot95 \\ P1=29.4+18+10.2+13.2+9.5 \\ P1=80.3 \end{gathered}[/tex]The grading system 1 gives an average score of 80.3.
We apply the grading system 2 coefficients and we get:
[tex]\begin{gathered} P2=0.45\cdot84+0.15\cdot72+0.15\cdot68+0.10\cdot88+0.15\cdot95 \\ P2=37.8+10.8+10.2+8.8+14.25 \\ P2=81.85 \end{gathered}[/tex]The grading system 2 gives an average score of 81.85.
With the grading system 2, the final score is a little higher than with grading system 1. So we would prefer the system 2.
The graph represents a quadratic function. Write an equation of the function in standard form. PLEASE HELP ME
Explanation:
Standard form is Ax + By = C
Known points are (-3, 6) and (-1.5, 6.75)
Find the slope:
6.75-6/-1.5+3 = 0.75/1.5 = 0.5
Put in point slope form first: y - y1 = m (x-x1)
y - 6 = 0.5 (x + 3)
Then rewrite to standard form:
y - 6 = 0.5x + 1.5
-0.5x + y = 1.5 +6
-0.5x +y = 7.5
the Santa Ana College theartre department sold 177 tickets to the spring play student tickets were sold for $7 each and general admission ticket were $9 if the total tickets sales were 1365 how many of each type of tickets were sold?
Let
x -----> number of play student tickets sold
y ----> number of general admission tickets sold
we have that
x+y=177 ------> x=177-y -----> equation A
7x+9y=1365 -----> equation B
solve the system
substitute equation A in equation B
7(177-y)+9y=1365
solve for y
1239-7y+9y=1365
2y=1365-1239
2y=126
y=63
Find the value of x
x=177-63
x=114
therefore
student tickets sold was 114general admission ticket sold was 63Lacie pays a babysitter an initial fee of $30 in addition to $7 per hour. When trying to solve this problem,Juan created the function y = 30x + 7. Explain his error.Juan assigned the wrong coefficient to x. He should have written the equation
he should have written the equation y=7x+30 because 30 is the fixed initial value and 7 is the value that increase with the number of hours
A line has a slope of 8 and passes through the point (1,4). What is its equation in slope-intercept form? Show work
The equation of the line in slope intercept form is:
y = 8x - 4
Given, we have slope = 8
Point = (1,4)
Equation in slope intercept form is:
y = mx+c
let the point (1,4) ne (x₁,y₁)
and slope (m) = 8
y - y₁ = m(x-x₁)
y - 4 = 8(x - 1)
y - 4 = 8x - 8
y = 8x - 8 + 4
y = 8x - 4
Hence the equation in slope intercept form is y = 8x-4
Learn more about Coordinate geometry here:
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estimate the quotient 612 and 60
612 is very close to 600 and 600 into 60 is 100
[tex]\frac{600}{60}=100[/tex]Also, we have 12 in front of 600 that makes it 612 and we know that 12 is not divisible by 60, and therefore, it will be the remainder.
Hence, the estimate of the quotient of 612 and 60 is 100
Find the length of x. Round answers to the nearest tenth if necessa 60° 30 у your answer
From our trig ratios, we can see that,
[tex]\begin{gathered} \frac{1}{x}\text{ =}\sin 30,\text{ x = }\frac{1}{\sin 30}\text{ = 2} \\ x=2 \end{gathered}[/tex]Find the roots of each quadratic equation by factoring. X² - 8x + 15
Given,
[tex]x^2-8x+15=0[/tex]To find the roots
[tex]\begin{gathered} x^2-8x+15=x^2-3x-5x+15 \\ =x(x-3)-5(x-3) \\ =(x-3)(x-5) \end{gathered}[/tex]The required roots are,
[tex](x-3)(x-5)[/tex]David drank 10 fluid ounces of juice. how much is this in cups? write your answer as a whole number or a mixed number in simplest form. Include the correct unit in your answer.
Given
David drank 10 fluid ounces of juice.
Find
how much is this in cups?
Explanation
As we know
1 cup = 8 ounces
so , 8 ounces = 1 cup
then
12 ounces =
[tex]\frac{1}{8}\times12=\frac{3}{2}=1\frac{1}{2}cups[/tex]Final Answer
hence , the required answer is
[tex]1\frac{1}{2}cups[/tex]As a janitor you make a cleaning solution by mixing 30 g of concentrated powdered cleanser into 2 L of water how much powder will you need for 5L of water?
30g - 2L
For 5L of water
[tex]\frac{5L\cdot30g}{2L}=75g[/tex]ANSWER
For 5L of water, we will need 75 g of concentrated powdered cleanser
Suppose that $2700 borrowed for two years at an interest rate of 4.5% per year, compounded continuouslyFind the amount owed, assuming no payments are made until the end. not round any intermediate computations , and round your answer to the nearest cent
To find:
The amount owed.
Solution:
It is known that the amount owed when the money is compounding continuously at a rate of r per year for the time t years is given by:
[tex]A=Pe^{rt}[/tex]Here, P = 2700, r = 0.045, t = 2, so the amount is:
[tex]\begin{gathered} A=2700e^{(0.045\times2)} \\ =2700e^{0.09} \\ =2700(1.094) \\ =2954.27 \end{gathered}[/tex]Thus, the amount he owed after 2 years is $2954.27.