Let's begin by identifying key information given to us:
[tex]undefined[/tex]Solve each equation by completing the square. X^2+10x=17
Completing squares
Before attempting to complete squares, let's recall the following identity
[tex](a+b)^2=a^2+2ab+b^2[/tex]the expression at the right side can be converted to the square of a binomial, provided we have the terms completed as shown
We have the equation:
[tex]x^2+10x=17[/tex]note the left side has TWO of the terms required for the square of a binomial. we only need the final number. but what number should we add?
the first term is the square of a, in this case, it's x
the second term has 10x and it should be 2ab, if we already know a=x, then
2ab=10x, then
b=10x/(2x)=5
now we know a=x and b=5, we only need to have b^2=25
that is exactly the number to add on both sides of the equation
[tex]x^2+10x+25=17+25=42[/tex]now we factor the left side:
[tex](x+5)^2=42[/tex]taking the square root, recall the square root can
The value of tan(alpha+beta) given sin(alpha)=40/41 and sin(beta)=15/17 and cos(∝ + β)= -528/697 and sin(∝ + β)= 455/679
Answer
Tan (∝ + β) = -455/528
Explanation
Tan (∝ + β) = ?
Given:
Sin ∝ = 40/41
Sin β = 15/17
Cos (∝ + β) = -528/697
Sin (∝ + β) = 455/697
Note: Tan ∝ = Sin ∝/Cos ∝
⇒ Tan (∝ + β) = (Sin ∝ + β)/(Cos ∝ + β)
Recall Sin (∝ + β) = 455/697 and Cos (∝ + β) = -528/697
∴ Tan (∝ + β) = (455/697)/(-528/697)
Tan (∝ + β) = 455 /697 x (-697/528)
Tan (∝ + β) = -455/528
An archaeologist found a fossil that has a length of 459.89 in.Use the table of facts to find the length of the fossil in feet.Round your answer to the nearest tenth.Conversion facts for length12 inches (in) = 1 foot (ft)3 feet (ft) = 1 yard (yd)36 inches (in) = 1 yard (yd)5280 feet (ft) = 1 mile (mi)1760 yards (yd) = 1 mile (mi)-0 1ftХ??
Answer: 38.3ft
We need to convert 459.89 inches into feet. Given that 12 inches is equal to 1 foot, we can solve this by dividing the length by 12
[tex]459.89in\times\frac{1ft}{12in}[/tex]*Cancel the inches sign leaving us with ft
[tex]459.89\times\frac{1ft}{12}=\frac{459.89}{12}ft=38.32\approx38.3[/tex]Therefore 459.89 inches is equal to 38.3 feet.
According to the data in the table which country has a more population density ?
The first step to solve the question presented is to calculate the population density for each country, which is defined as the ratio from the population and the area of the country, as follows:
[tex]D=\frac{P}{A}[/tex]Let us to perform the calculation for both countries with data in the table.
[tex]\begin{gathered} D_{\text{America}}=\frac{310,000,000}{3,539,225}\cong87.59\frac{people}{mi^2} \\ D_{\text{Mexico}}=\frac{122,000,000}{742,485}\cong164.31\frac{people}{mi^2}_{} \end{gathered}[/tex]From the solution presented we are able to conclude that the country with the highest population density from those in the table is Mexico
How much will a customer spend on a sweater that is $65.00 but discounted 20% and purchased in a state that has an 8% sales tax?
1) Gathering the data
Sweater $65
Discounted 20%
Tax: 8%
2) We can find this final price using this formula/calculation
Since the price has been discounted by 20% we can multiply $65 x 0.8 to find the discounted price, but the sweater will be sold with a tax of 8% so we can multiply by (1 + 0. 08) to get the final price, i.e. $56.16
A
in DEF, DE =29 feet, EF = 26 feet, and DF = 32 feet. Which correctly gives the order of the angle measure from largest to smallest?
Answer:
Choice A.
Explanation:
The sketch of the triangle is given below
The angle opposite the longest side is the widest.
The longest side is DF; therefore, the angle opposite to it (angle E) is the widest.
The second-longest side is DE; therefore, the angle opposite to it (angle F) is the second widest.
Lastly, the third-longest side is EF; therefore, the angle opposite to it (angle D) is the third widest (or the smallest angle).
Hence, the angle measures when ordered from greatest to smallest are
∠E, ∠F, ∠D
which is given by choice A.
A board game uses a spinner like one below, where 0, 1, 2, and 3 are all equally likely.Each turn, a player spins twice and subtracts the results of the spins. The game only looks at non-negativedifferences. For example, if a player spins a 1 and a 3, the difference is 2.Let X represent the difference in given turn.Which tables represents the theoretical probability distribution of X?Choose 1 answer:
The possible outcomes are:
0: 1-1, 2-2, 3-3, 4-4 => 4
1: |2-1|, |3-2|, |4-3|, |1-2|, |2-3|, |3-4| => 6
2: |3-1|, |4-2|, |1-3|, |2-4| => 4
3: |4-1|, |1-4| => 2
The total number of outcomes is 4+6+4+2 = 16. Then, the table that represents the theoretical distribution is:
Answer:
It should be B, the one that has 0,1,2,3 on the top.
Step-by-step explanation:
right on khan
Question 5 (1 point)A student takes a multiple-choice test with 8 questions on it, each of which have 4 choices. The student randomlyguesses an answer to each question.What is the probability that the student gets exactly 4 questions correct?Round to 3 decimal places.a0.886b0.9730.0870.208d
We can use Binomial distribution to calculate the probability of exactly 4 success
There are 8 questions which is our trial
Probability of succes (p)
Since in every question, there is 4 options with one right answer, then probability of success (p) = 1/4 = 0.25
probabiliti of failure (q) = 1- p = 1- 0.25 = 0.75
We will now use the formula below
[tex]p(x)^{}=^nC_xP^xq^{n-x}[/tex]substitute the values into the formula
[tex]p(x=4)=^{8\text{ }}C_4(0.25)^4(0.75)^{8-4}[/tex][tex]=\frac{8!}{(8-4)!4!}.(0.25)^4.(0.75)^4[/tex][tex]=\frac{8!}{4!4!}\text{.}(0.25)^4(0.75)^4[/tex][tex]=\frac{8\times7\times6\times5\times4!}{4\times3\times2\times1\times4!}\times(0.25)^4\times(0.75)^4[/tex][tex]=\frac{1680}{24}\times(0.00390625)\times(0.31640625)[/tex][tex]\approx0.087[/tex](6,3) and (2, -9)equation in slope intercept form
Let:
(x1,y1)=(6,3)
(x2,y2)=(2,-9)
[tex]\text{slope}=m=\frac{y2-y1}{x2-x1}=\frac{-9-3}{2-6}=\frac{-12}{-4}=3[/tex]Using the point-slope equation:
[tex]\begin{gathered} y-y1=m(x-x1) \\ y-3=3(x-6) \\ \text{Solve for y:} \\ y=3x-15 \end{gathered}[/tex]What is the image of (8,−4) after a dilation by a scale factor of 1/4 centered at the origin?
Answer:
[tex](2, -1)[/tex]
Step-by-step explanation:
When dilating with a scale factor of [tex]k[/tex] about the origin, [tex](x,y) \longrightarrow (kx, ky)[/tex].
We want to factor the following expression: x^3 - 25 which pattern can we use to factor the expression? U and V are either constant integers or single variable expression.
The pattern that is used to factor the expression x³ - 25 is given as follows:
B. (U - V)(U + V).
What is the subtraction of perfect squares?The subtraction of perfect squares is a notable product that gives the simplification of an expression containing the subtraction of perfect squares, as the multiplication of the square roots of the two terms subtracted by the square of the two terms subtracted, as follows.
a² - b² = (a - b)(a + b).
In the context of this problem, the expression is presented as follows:
x³ - 25.
The square root of x³ is obtained as follows:
sqrt(x³) = (x³)^(0.5) = x^(3 x 0.5) = x^1.5 = [tex]\sqrt{x^3}[/tex]
The square root of 25 is obtained as follows:
5.
Because 5² = 25.
Then, applying the subtraction of perfect squares notable product, the factored expression is given as follows:
[tex]x^3 - 25 = (\sqrt{x^3} - 5)(\sqrt{x^3} + 5)[/tex]
Which is the pattern given by option B.
Missing InformationThe complete problem is given by the image shown at the end of the answer.
A similar problem, also featuring subtraction of perfect squares, is presented at https://brainly.com/question/28792378
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Write 2.78 x 10-4in standard form.
Given ,
The scientific notation of the equation is,
[tex]2.78\times10^{-4}[/tex]The standard notation of the scientific notation is,
[tex]\begin{gathered} 2.78\times\frac{1}{10^4} \\ =\frac{2.78}{10000} \\ =0.000278 \end{gathered}[/tex]Hence, the standard form is 0.000278.
13/50 make as a decimal
To convert the fraction 13/50 to decimal, we have to divide 13 by 50.
We can also calculate it as:
[tex]\frac{13}{50}=\frac{13}{50}\cdot\frac{2}{2}=\frac{26}{100}=0.26[/tex]In this case, we multiply both the numerator and the denominator by 2. Then, we obtain a denominator of 100, which means that the numerator is in hundredths. Then, we can write is as 0.26.
Answer: the decimal expression of 13/50 is 0.26.
The probability distribution of a random variable x is given in the table below.X10-505101520Probability.2015.05.1.25.1.15Find the probability that x ⩾ 5
Answer:
0.6
Explanation:
From the given data:
[tex]\begin{gathered} P\left(x=-10\right)=0.20 \\ P\left(x=-5\right)=0.15 \\ P\left(x=0\right)=0.05 \\ P\left(x=5\right)=0.1 \\ P\left(x=10\right)=0.25 \\ P\left(x=15\right)=0.1 \\ P\left(x=20\right)=0.15 \end{gathered}[/tex]The probability that x is greater than or equal to 5 is:
[tex]\begin{gathered} P(x\geq5)=P\left(x=5\right)+P\left(x=10\right)+P\left(x=15\right)+P\left(x=20\right) \\ =0.1+0.25+0.1+0.15 \\ =0.6 \end{gathered}[/tex]i need the x and y intercept
so, the x intercept is when the line touches the x-axis, we can see from the graph, the line touches x-axis on 3, so the point is
[tex](3,0)[/tex]the y intercept is when the lone touches the y-axis, we can see from the graph, the line touches y-axis on -9, so the point is
[tex](0,-9)[/tex]Find two numbers whose sum is 256, but whose product is a maximum?
ANSWER
The two numbers are 128 and 128
EXPLANATION
Let the two numbers be x and y.
We have that:
[tex]\begin{gathered} x+y=256 \\ x\cdot y=A \end{gathered}[/tex]where A is a maximum.
From the first equation:
[tex]x=256-y[/tex]Substitute that into the second equation:
[tex]\begin{gathered} (256-y)\cdot y=A \\ \Rightarrow256y-y^2=A \\ \Rightarrow y^2-256y+A=0 \end{gathered}[/tex]The equation above is a quadratic equation in the general form:
[tex]ax^2+bx+c=0[/tex]The parabola is downward facing and so, its vertex will be the maximum.
We can find the vertex (x, y) of the parabola by using:
[tex]x=\frac{-b}{2a}[/tex]In the case given, the vertex can be found by using:
[tex]\begin{gathered} y=\frac{-(-256)}{2(1)}=\frac{256}{2} \\ y=128 \end{gathered}[/tex]Recall that:
[tex]x=256-y[/tex]Therefore, we have that:
[tex]\begin{gathered} x=256-128 \\ x=128 \end{gathered}[/tex]Hence, the two numbers are 128 and 128.
Find the explicit formula for the geometric sequence. Then find a8. 4, 8, 16, 64, ...
The given sequence is : 4,8, 16,64
The geometric series is exoress as :
[tex]\text{ Geometric series=a, ar, ar}^2\ldots.ar^n[/tex]where r i the common ratio
In the given sequence the ratio is
[tex]\begin{gathered} r=\frac{\sec ond\text{ term}}{first\text{ term}} \\ r=\frac{8}{4} \\ r=2 \end{gathered}[/tex]So, the series will express as :
[tex]\begin{gathered} \text{Explict formula = 4(2)}^{n-1} \\ \text{Explict form = }4(2)^{n-1} \end{gathered}[/tex]Now for the 8 term
n=8
[tex]\begin{gathered} a_n=4\cdot2^{n-1} \\ a_8=4\cdot2^{8-1} \\ a_8=4\cdot2^7 \\ a_8=512 \end{gathered}[/tex]Answer : C) an=4.2^n-1, 512
"A pump can fill a tank in 3 hours. A more powerful pump can fill the same tank in 2 hours. How long would it take to fill the tank with both pumps working?" Is my answer correct or incorrect? 1/3+1/2=3+2/3*2 5/15=15/515/5=3hrs
A pump can fill a tank in 3 hours. A more powerful pump can fill the same tank in 2 hours. How long would it take to fill the tank with both pumps working?" Is my answer correct or incorrect?
we have that
fisrt pump ------> fill a tank in 3 hours
that means
100% -----> 3 hours
1 hour ------> 33.33%
second pump
fill the same tank in 2 hours
100% -----> 2 hours
1 hour -----> 50 %
therefore
with both pumps working
1 hour ------> (33.33%+50%)=83.33%
applying proportion
1/83.33=x/100
x=100/83.33
x=1.2 hoursyour answer is not correctbecause the total time must be less than 2 hours (time of the second pump)that the triangles below are congruent select all options that would provide enough information to prove the triangles are congruent
The correct options are options C and D;
1) Angle C is congruent to E
2) BA and FD are congruent
Here, we want to select the options that would prove that the triangles are congruent
We can get that from the markings on the diagram
As we can see from the question, we already have two sides being equal as we can see from the markings
Hence, we need an extra information to see through that the two triangles are indeed congruent
If the sides BA and FD are equal, it will simply mean that the three sides of the triangle are equal. In that case, the two triangles are congruent by SSS (side-side-side)
Also, if the angles C and E are congruent, we will have that the two triangles are similar by the SAS (side-angle-side)
So, the correct options are C and D
An expression is shown. 14.1-(2.24*5); what is the value of the expression?
Given the expression:
[tex]14.1-(2.24\ast5)[/tex]Let's find the value of the expression.
To find the value of the expression, first evaluate the values in the parentheses:
[tex]\begin{gathered} 14.1-(2.24\ast5) \\ \\ =14.1-(11.2) \\ \\ \end{gathered}[/tex]Solving further:
[tex]\begin{gathered} 14.1-11.2 \\ \\ =2.9 \end{gathered}[/tex][tex]\begin{gathered} 14.1-(2.24\ast5) \\ \\ =14.1-(11.2) \\ \\ \end{gathered}[/tex]Solving further:
[tex]\begin{gathered} 14.1-11.2 \\ \\ =2.9 \end{gathered}[/tex][tex]undefined[/tex]Two ships were 700 miles apart at midnight and were headed directly towards each other if they collided at 10 a:m find the speeds of both ships if one was traveling 30 miles faster than the other
Given:
Two ships were 700 miles apart at midnight .
Let x be the speed of first ship and (x+30) be speed of second ship (faster ship).
The equation is,
[tex]\begin{gathered} Dis\tan ce=rate\times time \\ 10x+10(x+30)=700 \\ 10x+10x+300=700 \\ 20x=700-300 \\ 20x=400 \\ x=\frac{400}{20} \\ x=20 \end{gathered}[/tex]Answer: the speed of first ship ( slower) is 20 miles and the speed of second ship ( faster) is 20+30=50 miles.
In the diagram from question 15, which statement would prove that line a and b are parallel?
the answer is D
[tex]m\measuredangle1+m\measuredangle7=180[/tex]The amount of metal needed to be installed spring the workbench is
To answer this question we will use the following formula to compute the perimeter of a rectangle:
[tex]Perimeter=2(length+width)[/tex]Therefore the perimeter of the workbench is:
[tex]Perimeter=2(5ft+3ft).[/tex]Simplfying the above result we get:
[tex]Perimeter=2(8ft)=16ft.[/tex]Therefore we will need 16ft of metal stripping.
Answer: 16ft.
PLEASE HELP ME!!!!!
Subtract the linear expressions.
(-3 + 4x - 9x) - (9 - 11x + 7)
6x + 19 is the difference between both the linear expression.
What is linear equation ?In a linear equation, the variable's greatest power always equals 1. It is also referred to as a one-degree equation. The usual form of a linear equation with one variable is written as Ax + B = 0. In this case, x is a variable, A is a coefficient, and B is a constant.
Calculation-3 + 4x -9x - 9 + 11x - 7
= -19+6x
= 6x + 19
learn more about linear equation here :
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Answer:
Between the two linear expressions, there is a difference of 6x + 19.
How do linear equations work?
In a linear model, the largest power of the variable is always equal to 1. Another name for it is a one-degree equation. Ax + B = 0 is how a statistical model with one term is typically written. In this scenario, the variables x and A are coefficients, while B is a standard.
Calculation -3+4x-9x-09+11x-7-9
= -19+6x
= 6x + 19
Step-by-step explanation:
I'm also in k12 hope this helps! :3
Jonathan finds some nickels and quarters in his change purse. How many coins does he have if he has 12 nickels and 4 quarters? How many coins does he have if he has xx nickels and yy quarters?Total coins, 12 nickels and 4 quarters: Total coins, xx nickels and yy quarters:
Each nickel is worth 5 cents, and each quarter is worth 25 cents.
So, if we have 12 nickels, we can multiply this value by 5 to get its value in cents:
[tex]12\cdot5=60[/tex]Similarly, if we have 4 quarters, we can multiply this value by 25 to get its value in cents:
[tex]4\cdot25=100[/tex]So, in total, we have:
[tex]60+100=160[/tex]So, for 12 nickels and 4 quarter, we have the value of 160 cents.
We can do this generally by setting the values of nickel and quarter to x and y.
If we have x nickels and each one is worth 5 cents, we have the value:
[tex]5x[/tex]And if we have y quarters and each is worth 25 cents, we have the value:
[tex]25y[/tex]So, in total, we have:
[tex]5x+25y[/tex]So, for x nickels and y quarter, we have the value of 5x + 25y cents.
A _____ is a line that best approximates the linearrelationship between two variables in a data set. *
We have the following:
A line of best fit is a straight line that is the best approximation of the given data set. It is used to study the nature of the relationship between two variables.
Therefore, the answer is line of best fit.
A line of best fit is a line that best approximates the linear
relationship between two variables in a data set.
Question 15 ptsIf Martha puts $181 in the bank today at 2%, how much will she have have in 8 years? (Round to the 2decimal places)Question 25 ptsHow much will Bill and Mary need to put in the bank today at 5% to have $103,897 in 9 years? (Roundto 2 decimal places)
Question 1
Interest in 1 year at 2% per annum = 2/100 x $181 = $3.62
Total Interst after 8 years = 8 x $3.62 = $28.96
Total amount she has after 8 years = initial amount + Total Interst after 8 years
=$181 + $28.96 = $209.96 (2 decimal places)
Question 2
rate per annum, r = 5%
Time = 9years
Total amount = $103,897
Let the initial amount invested be p
interst after 1 year = 5% of p =$5p/100
Total interest after 9 years = 9 x 5p/100 = $45p/100
Total amount = p + 45p/100
That is,
103,897= p + 45p/100
[tex]undefined[/tex]The stock market opens on Monday morning, a stock was valued at 42.50. The value of that stock increase by the same amount each day for the next three days. After three days, the value of stock was 50.00. Which equation is used to find x, the amount the stock rose in value each day.
The stock market opens on Monday morning, a stock was valued at 42.50.
The intial value of stock = 42.50
The value of that stock increase by the same amount each day for the next three days.
Let the increase amount in each day is x
then, increase amount in three day = 3x
After three days, the value of stock was 50.00.
Net amount after three day = 50.00
Net amount after three day = Initial value of stock + Incease amount in three day
50 = 42.50 + 3x
3x + 42.50 = 50
Answer: 3x + 42.50 = 50
2. Zero can be a negative number.OTrueFalse
In the real numbers system, any negative number x meets the following property:
[tex]x<0[/tex]The symbol "<" means that x is smaller than 0 but never equal to 0 so the definition of negative numbers excludes the zero. Then this statement is False.
1) Write an equation of the line perpendicular to: y = 3x - 9 with a y-intercept of 4.
The given equation is
[tex]y=3x-9[/tex]The new line is perpendicular to the given equation, which means we have to use the following formula.
[tex]m\cdot m_1=-1[/tex]Where the slope of the given line is 3 (the coefficient of x).
[tex]m\cdot3=-1[/tex]We solve for m.
[tex]m=-\frac{1}{3}[/tex]So, the slope of the new perpendicular line is -1/3.
According to the problem, the y-intercept of the new perpendicular line is 4. Now, we use the slope-intercept form to write the equation.
[tex]\begin{gathered} y=mx+b \\ y=-\frac{1}{3}x+4 \end{gathered}[/tex]Therefore, the equation of the new line is[tex]y=-\frac{1}{3}x+4[/tex]