Explanation
[tex]2x^2-3x-1=0[/tex]Step 1
remember the quadratic formula.
if you have the equation
[tex]ax^2+bx+c=0[/tex]the value for x is
[tex]x=\frac{-b^2+\sqrt{b^2}-4ac}{2a}[/tex]Step 2
let
[tex]ax^2+bx+c=2x^2-3x-1[/tex]a=2
b=-3
c=-1
Step 3
replace
[tex]undefined[/tex]Find the number that belongsin the green box.[?]109°13°6Round your answer to the nearest tenth.
step 1
Find the measure of the third interior angle of triangle
Remember that the sum of the interior angles in any triangle must be equal to 180 degrees
so
x+109+13=180
solve for x
x=180-122
x=58 degrees
step 2
Applying the law of sines
?/sin(13)=6/sin(58)
solve for ?
?=(6/sin(58))*sin(13)
?=1.6 unitsCan you help me answer part A and part B?
Part A.
Given:
P = (5, 4), Q = (7, 3), R = (8, 6), S = (4, 1)
Let's find the component of the vector PQ + 5RS.
To find the component of the vector, we have:
[tex]=\lparen Q_1-P_1,Q_2-P_2)=<7-5,3-4>[/tex]For vector RS, we have:
[tex]=\lparen S_1-R_1,S_2-R_2)=<4-8,1-6>[/tex]Hence, to find the vector PQ+5RS, we have:
[tex]\begin{gathered} =<7-5,3-4>+5<4-8,1-6> \\ \\ =\left(2,-1\right)+5\left(-4,-5\right) \\ \\ =\left(2,-1\right)+\left(5\ast-4,5\ast-5\right) \\ \\ =\left(2,-1\right)+\left(-20,-25\right) \end{gathered}[/tex]Solving further:
[tex]\begin{gathered} =<2-20,-1-25> \\ \\ =<-18,-26> \end{gathered}[/tex]Therefoee, the component of the vector PQ+5RS is:
<-18, -26>
• Part B.
Let's find the magnitude of the vector PQ+5RS.
To find the magnitude, apply the formula:
[tex]m=\sqrt{\left(x^2+y^2\right?}[/tex]Thus, we have:
[tex]\begin{gathered} m=\sqrt{\left(-18^2+-26^2\right?} \\ \\ m=\sqrt{324+676} \\ \\ m=\sqrt{1000} \\ \\ m=\sqrt{10\ast10^2} \\ \\ m=10\sqrt{10} \end{gathered}[/tex]Therefore, the magnitude of the vector is:
[tex]10\sqrt{10}[/tex]ANSWER:
Part A. <-18, -26>
Part B. 10√10
In TUV, the measure of V=90°, the measure of U=58°, and TU = 38 feet. Find the length of VT to the nearest tenth of a foot.
Answer:
32.2 feet
Explanation:
The diagram given is a right angled triangle
Using the SOH CAH TOA identity
Given the following
Hypotenuse = 38
Opposite = x
Sin theta = opposite/hypotenuse
Sin 58 = x/38
x = 38sin58
x = 38(0.8480)
x = 32.23
Hence the length of VT to the nearest tenth of a foot. is 32.2feet
Find any domain restrictions on the given rational equation:
X+2
-25
+1=
8x
2x-10
Select all that apply.
A. x = 5
127
B. x = -2
C. X = -5
D. x = 0
The domain restrictions on the rational equation
[tex]\frac{x +2}{x^{2} -25 }+1 =\frac{8x}{2x-10}[/tex] are Options A and C. x = 5 and x = - 5 .
What are domain restrictions?A domain restriction is a prescription or criterion that limits the range of possible values for a function. A domain in mathematics is the collection of all values for which a function produces a result. Domain constraints allow us to create functions defined over numbers that meet our needs.Functions defined in pieces are made up of various functions with distinct domain restrictions. Some functions are not allowed to accept values that would make them undefined.How to find the domain restrictions?
The numbers that makes the denominators zero and the entire expression infinite or undefined are the domain restrictions.
Consider the denominators,
[tex]x^{2}[/tex] - 25 ≠ 0 --(1)
[tex]x^{2}[/tex] ≠ 25
x ≠ 5 and x ≠ -5
2x - 10 ≠ 0 ---(2)
2x ≠ 10
x ≠ 10/2
x ≠ 5
The domain restrictions on the rational equation [tex]\frac{x +2}{x^{2} -25 }+1 =\frac{8x}{2x-10}[/tex] are
x ≠ 5 and x ≠ -5 .
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If the calculator gives us the following values number 7
we know that
The equation is of the form
y=ax+b
The given values are
a=0.872
b=25.263
substitute
therefore
The equation is
y=0.872x+25.263Find the surface area of a right cone that has a radius of 9 inches and a height of 12 inches. Round your answer to the nearest hundredth. The surface area is about ⬜ square inches.
The surface area of the right cone is:
[tex]678.58in^2[/tex]Explanation:The surface area of a right cone is:
[tex]A=\pi r(r+\sqrt[]{r^2+h^2})[/tex]Here, r = 9 in, and h = 12 in
so
[tex]\begin{gathered} A=9\pi(9+\sqrt[]{9^2+12^2}) \\ \\ =9\pi(9+15) \\ =216\pi \\ =678.58in^2 \end{gathered}[/tex]An item is regularly priced at $65. Lena bought it on sale for 60% off the regular price. How much did Lena pay?
The regular price of an item is $65
Lena bought it on sale for 60% off the regular price.
Then it means that she paid only (100% - 60% = 40%) of the price.
Let us find the 40% of $65
[tex]\frac{40}{100}\times\$65=\$26[/tex]Therefore, Lena paid only $26 for the item.
Given the matrices A and B shown below, find 4B – į A.3A=( 1215B5
Step 1 : To determine the matrices as shown below
What is 16m + 24n? (P.S, this is about factoring expressions.)
aWe can factorize by a common factor
[tex]16m+24n[/tex][tex](8\times2)m+(8\times3)n[/tex][tex]8(2m+3n)[/tex]ANSWER
8(2m+3n)
Study the diagram, where AB and C'D are chords that intersect inside of the circle at point P, which is not the center.
Answer:
answer of the given question
Given parallelogram JKLM, what could the expression 180 - (3x + 8) represents? Explain.
Based on the given figure, you can conclude:
The expression 180 - (3x + 8) represents a supplementary angle to the angle (3x + 8). This angle would be an angles subtended from side KL to a line that is a prolongation of line JK.
At an all-you-can-eat barbeque fundraiser, adults pay $6 for a dinner and children pay $4 for a dinner. 212 people attend and you raise $1,128. What is the total number of adults and the total number of children attending? A)140 adults and 72 children B)72 adults and 140 children C)142 adults and 70 children D)70 adults and 142 children
A)140 adults and 72 children
Explanation
Step 1
Let x represents the number of childrend attending
Let y represents the number of adults attending
then
total cost for the children=4x
total cost for the adults=6y
if you raise 1128,
[tex]4x+6y=1128\text{ Equation(1)}[/tex]Now, 212 people attend,Hence
[tex]x+y=\text{212 Equation(2)}[/tex]Step 2
solve for x and y
a)isolate x in equation (2), then replace in equation (1)
[tex]\begin{gathered} x+y=212 \\ x=212-y \\ \text{now, replace} \\ 4x+6y=1128 \\ 4(212-y)+6y=1128 \\ 848-4y+6y=1128 \\ 2y+848=1128 \\ \text{subtract 848 in both sides} \\ 2y+848-848=1128-848 \\ 2y=280 \\ d\text{ivide boths ides by 2} \\ \frac{2y}{2}=\frac{280}{2} \\ y=140 \end{gathered}[/tex]it means 140 adults are attending
b)replace y=140 in equatin (2) to find x
[tex]\begin{gathered} x+y=212 \\ x+140=212 \\ \text{subtract 140 in both sides} \\ x+140-140=212-140 \\ x=72 \end{gathered}[/tex]so, the number of children is 72 and 72 children
Systems of 2 Equations Word Problems
Let x and y be the two numbers
x + y = 72 ------------------------------(1)
x - y = 4 ----------------------------------(2)
Add equation (1) and equation (2)
2x = 76
Divide both-side of the equation by 2
x = 38
substitute x = 38 into equation (1) and then solve for y
38 + y = 72
subtract 38 from both-side of the equation
y = 72 - 38
y = 34
The two numbers are 34 and 38
If 340 grams of a substance are present initially and 50 years later only 170 grams remain, how much of the substance will be present after 120 years?Round to the nearest tenth of a graim.grams
Given -
Substance present initially = 340 grams
Substance present 50 years later = 170 grams
To Find -
How much of the substance will be present after 120 years =?
Step-by-Step Explanation -
Since the substance was reduced to half of what it is initially in 50 years.
So,
The half-life time of the substance = 50 Years.
It means that every 50 years, the substance will reduce to half of its quantity.
And, we know the formula:
[tex]\text{ A = S\lparen}\frac{1}{2}\text{\rparen}^{\frac{t}{h}}[/tex]Where,
A = the remaining amount of Substance =?
S = the amount of Substance you start with = 340grams
t = the amount of time in years = 120 years
h = the half-life time = 50 years
Simply putting the values, we get:
[tex]\begin{gathered} A\text{ = 340}\times(\frac{1}{2})^{\frac{120}{50}} \\ \\ A\text{ = 17\lparen}\frac{1}{2}\text{\rparen}^{2.4} \\ \\ A\text{ = 17}\times(0.5)^{2.4} \\ \\ A\text{ = 17}\times0.1894 \\ \\ A\text{ = 3.22 gram} \end{gathered}[/tex]Final Answer -
The substance that will remain after 120 years = 3.22 gram
Use the following results from a test for marijuana use, which is provided by a certain drug testing company. Among 143 subjects with positive test results, there are 24
false positive results; among 150 negative results, there are 5 false negative results. If one of the test subjects is randomly selected, find the probability that the subject
tested negative or did not use marijuana. (Hint: Construct a table.)
The probability that a randomly selected subject tested negative or did not use marijuana is.
(Do not round until the final answer. Then round to three decimal places as needed.)
The probability that the subject tested negative or did not use marijuana is 145/293.
What is probability?
Potential is described by probability. This branch of mathematics deals with the occurrence of a random event. The value's range is 0 to 1. Probability has been applied into mathematics to predict the likelihood of different events. Probability generally refers to the degree to which something is likely to occur. This fundamental theory of probability, which also applies to the probability distribution, can help you comprehend the possible outcomes for a random experiment. Before we can determine the probability that a certain event will occur, we must first know the total number of outcomes.
As given in the question,
Total positive results are 143 out of which 24 are false, and
total negative results are 150 out of which 5 are false.
We know that,
probability = favorable outcome/ Total outcome
so,
Total outcome = total tests
total tests = 143 + 150
total outcome = 293
and favorable outcome = true negative outcome
true negative outcome = total negative outcome - false negative outcome
true negative outcome = 150 - 5
favorable outcome = 145
Therefore, the probability is equal to 143/293
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AnimalPossible Locations Relativeto Ocean's Surface25. Reasoning Suppose you plot the locations ofthe animals on a number line. Which animalwould be represented by the point farthest fromO on the number line? Explain. MP2Bloodbelly comb jellyDeep sea anglerfish-0.8 km- km- 2 kmFanfin anglerfishGulper eel-1.1 km26. Which animal is closest to a depth of -0.7 km?Pacific blackdragon- šo kmSlender snipe eel-0.6 km
Number line
[tex]\ldots-5<-4<-3<-2<\text{ -1< 0<1<2<3<4<5}\ldots[/tex]Let's
[tex]undefined[/tex]I need help with this statistics question please!
The margin of error of a z-confidence interval is given by: [tex]$M=z \frac{\sigma}{\sqrt{n}}$$[/tex]
The margin of error of a z-confidence interval is 142.945936.
How to estimate the margin of error?The margin of error of a z-confidence interval exists given by:
[tex]$M=z \frac{\sigma}{\sqrt{n}}$$[/tex]
Where, z is the critical value.
[tex]$\sigma$[/tex] be the population standard deviation.
n is the sample size.
The first step is finding the critical value, which exists z with a p-value of [tex]$\frac{1+\alpha}{2}$[/tex] in which [tex]$\alpha$[/tex] is the confidence level.
In this problem, [tex]$\alpha[/tex] = 0.95, therefore, z with a p-value of 1 + 0.95 / 2 = 0.975, which means that it is z = 1.96.
The population standard deviation exists of 12.2 meters, thus [tex]$\sigma[/tex] = 12.2.
We want a width of 5 , thus a margin of error of M = 2. Therefore, we have to simplify the equation for the margin of error for n.
Let the equation be [tex]$M=z \frac{\sigma}{\sqrt{n}}$$[/tex]
substitute the values in the above equation, we get
[tex]$2=1.96 \frac{12.2}{\sqrt{n}}$[/tex]
[tex]$2 \sqrt{n}=1.96(12.2)$[/tex]
simplifying the above equation, we get
[tex]$\sqrt{n}=\frac{1.96(12.2)}{2}$[/tex]
[tex]$(\sqrt{n})^2=\left(\frac{1.96(12.2)}{2}\right)^2$[/tex]
n = 142.945936
Therefore, the value of n = 142.945936.
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2. Two of your classmates are arguing over the solution to a problem. Rhonda believes that the only method to solving the following theequation below is by using the quadratic equation. Max believes that you can use the quadratic formula but you can also factor theequation. Explain if Rhonda or Max is correct.2x^2-5x=88Some words/phrases to consider using in your response would be:factorFOIL MethodZero-Product PropertyStandard Formquadratic expressionquadratic equationscoefficientperfect square
Given data:
The given expression is x^2 -6x-7=0.
The given expression can be written as,
[tex]\begin{gathered} x^2-6x=7 \\ x^2-6x+(\frac{6}{2})^2=7+(\frac{6}{2})^2 \\ x^2-2(x)(3)+3^2=7+3^2 \\ (x-3)^2=16 \end{gathered}[/tex]Thus, the number 9 is added on both sides to complete square.
What is the y-intercept of f(x) =(3/5)^x?
Answer:
the y intercept is -1.
Step-by-step explanation:
the y intercept is -1 because it goes through the point (0,-1)
determine values of the variables that will make the following equation true, if possible. if not, state “not possible”
Given:
[tex]4\begin{bmatrix}{-r} & & {} \\ {-s} & {} & {} \\ & {} & {}\end{bmatrix}-\begin{bmatrix}{-2r} & & \\ {-2s} & {} & \\ {-2t} & {} & {}\end{bmatrix}=\begin{bmatrix}{-3} & & \\ {-1} & {} & {} \\ {5} & & {}\end{bmatrix}[/tex]As the first matrix has 2 rows and 1 column. And the second matrix has 3 rows and 1 column.
The dimension of both the matrix is not the same.
For the subtraction of two matrices must have the same size.
So, we can not determine the values of variables.
Answer: not possible.
i will drop a picture
B) y= -1/2x -4
1) Let's start by picking two points from that line: (0,3) and (-2,-1). Now we can plug them into the slope formula and find out the slope of that line:
[tex]m=\frac{y_2-y_1}{x_2-x_1}\Rightarrow m=\frac{-1-3}{-2-0}=\frac{-4}{-2}=2[/tex]2) Examining that graph we can see that when x=0 y=3, so the linear coefficient b is 3. Therefore we can write the equation as y= 2x-3.
2.2) Since the question wants a perpendicular line, then the slope of this perpendicular line must be reciprocal and opposite to m=2, so:
[tex]m\perp=-\frac{1}{2}[/tex]So, plugging the given point (6,-7) we can find out the linear coefficient of that perpendicular line:
y=mx +b
-7 = 6(-1/2) +b
-7 =-3 +b
-7+3 = b
b=-4
3) Hence, the answer is y= -1/2x -4
Math for Liberal Arts Lecture Class, Fall 2021 = Homework: Ch... Question 2, 1.1.3 Part 2 of 3 HW Score: Points: An election is held to choose the chair of a department at a university. The candidates are Professors Arg for short). The following table gives the preference schedule for the election. Use the table to complete pa Number of Voters 7 9 2 5 3 6 1st choice А A B D A 2nd choice B D D А E E 3rd choice D B E C B B 4th choice E C A B C D 5th choice C E C D A C (a) How many people voted in this election? ... 32 voters (Type a whole number.) (b) How many first-place votes are needed for a majority?
a) In this election voted: 7+9+2+5+3+6=32
b) For a majority you can follow the next rule:
The 50% of 32 is: 32*0.5=16, then, are needed at least 17 votes
c) Candidate A had 3 last-place votes, candidate B had 0 last-place votes, candidate C had 15 last-place votes, candidate D had 5 last-place votes and candidate E had 9 last-place votes.
Thus, the candidate with the fewest last-place votes is candidate B
Rachel is driving to Denver. Let y represent her distance from Denver (in miles). Let x represent the time she has been driving (in hours). Suppose that x and yare related by the equation y = 475 - 60x.Answer the questions below.Note that a change can be an increase or a decrease.For an increase, use a positive number. For a decrease, use a negative number.-Picture includes the questions-
Given the equation:
[tex]y=475-60x[/tex]Let y = distance
Let x = time
- The distance from Denver when she began is given by x = 0, therefore:
[tex]y=475-60(0)=475-0=475[/tex]Answer 1. 475 miles
- The change for each four hours, this is x = 4, so:
[tex]y=475-60(4)=475-240=235[/tex]Answer 2. 235 miles
for the polyhedron, find the missing numberneed a whole number of faces
The Euler's polyhedron formula states that, for a polyhedron with F faces, E edges and V vertices, we have:
F + V - E = 2
For E = 12 and V = 6, then we have:
F + 6 - 12 = 2
F = 2 + 12 - 6
F = 8
Mrs. Laurence just bought a new car for 26,304. She plans to pay her car off in 24 months. Mr. Gannon just bought a new car for 20,480 and plans to pay his car off in 20 months. How much more money a month does Mrs. Laurence pay in her car payment?
The amount of extra money a month that Mrs. Laurence pays in her car payment is $72.
How much more money does Mrs. Laurence pay each month?We can get the amount of extra amount that Mrs. Laurence pays each month when compared to Mr. Gannon by dividing the amount that they pay by the number of months they need to make these payments.
This can be done as follows:
26304 ÷ 24 = 1096
20480 ÷ 20 = 1024
1096 - 1024 - 72
So, the amount of extra money that Mrs. Laurence has to pay each month when compared to that of Mr. Gannon is $72.
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Angela bought a calculator on sale for 15% off. Sales tax is 7.5%. If the calculator cost x dollars, which expression represents the total cost of the calculator?A). (x-0.15) (0.075)B). (x-0.15) (1.075)C). (x-0.15x) (0.075)D). (x- .015x) (1.075)
Original price = x
Price with 15% off = x - 0.15x
Price with 15% off and 7.5% tax = (x - 0.15x)(1.075)
Answer:
Option B: (x - 0.15x)(1.075)
what is the geometric sequence of 2 4
an = ar^ (n- 1)
for n = 3 (3rd term)
r = common ratio = 4/ 2 = 2
a3 = 2 (2) ^ (3-1)
a3 = 2 (2)^2
a3 = 2 (4)
a3 = 8
n= 4 (4th term)
a4 = 2 (2)^(4-1)
a4 = 2 (2)^3
a4 = 2 (8)
a4 = 16
2, 4 , 8 , 16
help meeeeeeeeee pleaseee !!!!!
The function 2x + 3x^2 represents the result of adding the two provided functions, f(x) and g(x).
Composite performance.An operation known as "function composition" takes two functions, f and g, and produces a new function, h, that is equal to both g and f and has the property that h(x) = g.
Given the f(x) = 2x and g(x) = 3x^2 functions
The sum of the two functions must be calculated as illustrated;
f(x) + g = (f+g)(x)
Put the provided functions in place of (f+g)(x) to have:
(f+g)(x) = 2x + 3x^2
Standard version of the expression is (f+g)(x) = 2x + 3x^2
Consequently, the sum of the functions f(x) and g(x) is2x + 3x^2
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Solve. 0.25(60) + 0.10x = 0.15(60+x)
[tex]15 + 0.10x = 0.15(60) + 0.15(x) \\ 15 + 0.10x = 9 + 0.15x \\ \\ 0.10x - 0.15x = 9 - 15 \\ - 0.05x = - 6 \\ \frac{ - 0.05x}{ - 0.05} = \frac{ - 6}{ - 0.05} \\ x = 120[/tex]
ATTACHED IS THE SOLUTION
Find the coordinates P (-9, 10.5) after translating it 3 units left and 11 units up.
ANSWER
P'(-12, 21.5)
EXPLANATION
We are given the cordinates of P as:
P(-9, 10.5)
Cordinate points are given as A(x, y)
We want to translate it 3 units left and 11 units up.
That means that we are moving it 3 units towards the negative side of the x axis and 11 units towards the positive side of the y axis.
Therefore, we will subtract 3 from the x cordinate and add 11 to the y cordinate.
Therefore, the translation is:
P(-9, 10.5) => P'(-9 - 3, 10.5 + 11)
=> P'(-12, 21.5)
The cordinates of P have been translated.