Answer:
[tex]\begin{gathered} x_1=4+\sqrt[]{11} \\ x_2=4-\sqrt[]{11} \end{gathered}[/tex]Step-by-step explanation:
Solve the following quadratic completing the square:
[tex]x^2-8x+5=0[/tex]Keep x terms on the left and move the constant to the right side:
[tex]x^2-8x=-5[/tex]Then, take half of the x-term and square it.
[tex](-8\cdot\frac{1}{2})^2=16[/tex]Now, add this result to both sides of the equation:
[tex]x^2-8x+16=-5+16[/tex]Rewrite the perfect square on the left.
[tex]\begin{gathered} (x-4)^2=-5+16 \\ (x-4)^2=11 \end{gathered}[/tex]Take the square root of both sides:
[tex]\begin{gathered} \sqrt[]{(x-4)^2}=\pm\sqrt[]{11} \\ x-4=\pm\sqrt[]{11} \\ x=\pm\sqrt[]{11}+4 \end{gathered}[/tex]Hence, the two solutions of the equation are:
[tex]\begin{gathered} x_1=4+\sqrt[]{11} \\ x_2=4-\sqrt[]{11} \end{gathered}[/tex]help me please i want to see if i did it correctly
-1/16
1) Considering that we have the following identity:
[tex]\begin{gathered} \cos (2x)=2\cos (2x)-1 \\ \end{gathered}[/tex]2) We can plug into that the cos (x).:
[tex]\begin{gathered} \cos (2x)=(\frac{\sqrt[]{15}}{4})^2-1 \\ \cos (2x)=\frac{15}{16}-\frac{16}{15} \\ \cos (2x)=-\frac{1}{16} \end{gathered}[/tex]Since for the Quadrant II cosine yields a negative value.
Pauline found the inverse of [9/7 4/3] to be [-3/7 4/-9]. Which calculations will confirm that his (or her) answer is correct? Select all that apply.
In this case, we'll have to carry out several steps to find the solution.
Step 01:
data:
matrix
Step 02:
inverse of a matrix:
[tex]AA^{-1}=\begin{bmatrix}{9} & {4} \\ {7} & {3}\end{bmatrix}\begin{bmatrix}{-3} & {4} \\ {7} & -{9}\end{bmatrix}=\begin{bmatrix}{1} & {0} \\ {0} & {1}\end{bmatrix}[/tex][tex]A^{-1}A=\begin{bmatrix}{-3} & {4} \\ {7} & {-9}\end{bmatrix}\begin{bmatrix}{9} & {4} \\ {7} & {3}\end{bmatrix}=\begin{bmatrix}{1} & {0} \\ {0} & {1}\end{bmatrix}[/tex]That is the full solution.
how many hours, x, do they run?
We know that
• Sean runs 6 miles per hour (rate).
,• Sean's initial condition is 0.25 miles.
,• Darryl runs 0.7 miles per hour faster than Sean (we have to sum).
Sean's expression would be 6x + 0.25.
Darryl's expression would be 6x + 0.7x = 6.7x.
Now, we make them equal
[tex]6x+0.25=6.7x[/tex]Hence, the right answer is C.What is the surface area of the following solid? *13 ft 12ft 5ft 5ft
In order to calculate the total surface area we just need to sum the area of the different faces.
From the picture we see that we have the following faces.
- 2 x A (two triangles)
- S (a rectangle)
- T (a rectangle)
- B (the base rectangle)
Now me calculate the area of each one:
[tex]A\text{ = }\frac{1}{2}\cdot12\cdot5\text{ = }30[/tex][tex]S\text{ = 5}\cdot5=\text{ 25}[/tex][tex]B=12\cdot5=60[/tex][tex]T=13\cdot5=65[/tex]Now that we have the area of each face, we sum all the areas, taking in account the ones that appears twice:
[tex]\text{Total area = 2}\cdot A+S+T+B=2\cdot30+25+60+65=210[/tex]And, because the lenghts are measured in ft, the final answer is:
[tex]\text{Total area = 210 ft}^2[/tex]Note:
[tex]\text{Area of a triangle = }\frac{1}{2}\cdot\text{base}\cdot\text{height}[/tex][tex]\text{Area of a rectangle = base }\cdot\text{ height}[/tex]p varies directly as q. When q = 31.2, p = 20.8. Find p when q = 15.3.a.10.2b.22.95c.42.4i got B ...?
A direct relationship is an association between two variables such that they rise and fall in value together. In another terms, one of the variables is equal to the other times a constant. In our case, we have
[tex]p=kq[/tex]Where k is a constant. To find k, we can use the relation we already know the values.
[tex]\begin{gathered} p(31.2)=20.8 \\ \implies20.8=31.2k \\ k=\frac{20.8}{31.2} \\ k=\frac{2}{3} \end{gathered}[/tex]Then, the relation between our variables is
[tex]p=\frac{2}{3}q[/tex]Evaluating q = 15.3 on this expression, we have
[tex]p=\frac{2}{3}\times(15.3)=10.2[/tex]The answer is 10.2.
What is the slope of the line that goes through the points (-4, 6) and (2, 8)
Hence the slope is 1/3
Find the value of b please I’m having some trouble
Given:
The expression given is,
[tex]3-\frac{2}{9}b=\frac{1}{3}b-7[/tex]Required:
To find the value of b.
Explanation:
We have the given expression as:
[tex]3-\frac{2}{9}b=\frac{1}{3}b-7[/tex]Let us find the value of b.
[tex]\begin{gathered} 3-\frac{2}{9}b=\frac{1}{3}b-7 \\ \Rightarrow\frac{b}{3}+\frac{2b}{9}=3+7 \\ \Rightarrow\frac{3b+2b}{9}=10 \\ \Rightarrow\frac{5b}{9}=10 \\ \Rightarrow5b=9\times10 \\ \Rightarrow5b=90 \\ \Rightarrow b=\frac{90}{5} \\ \Rightarrow b=18 \end{gathered}[/tex]Final Answer:
The value of b is,
[tex]b=18[/tex]URGENT!! ILL GIVE
BRAINLIEST!!!! AND 100 POINTS!!!!!
Answer:
c
Step-by-step explanation:
write the ratio of the first measurement. make sure to simply if possible
1. Ratio of 10 feet to 5 yards
A yard is equvalent to 3 feet
So we can say that ratio of 10 feet to 5 yards is the same as ratio of 10 feet to 5x3 feet, which is:
ratio of 10 feet to 15 feet = 10/15
10/15 simplified by dividing both numerator and denominator by 5:
2/3
Answer:
2/3
[tex]\frac{2}{3}[/tex]In the trapezoid below, if < BAC = 124 °, what is the measure of < DCA.
ANSWER
[tex]56[/tex]Option B
EXPLANATION
Given;
[tex]\angle BAC=124[/tex]Recall;
[tex]\begin{gathered} \angle DCA+\angle BAC=180 \\ \angle DCA+124=180 \\ \angle DCA=180-124 \\ =56 \end{gathered}[/tex]the length of cuboid is twice the breadth and thrice the height. if the volume of the cuboid is 972cm3 find the breadth of the cuboid
The breadth of the cuboid is 9 cm with the volume as 972 cm³.
Given:
length of the cuboid is twice the breadth and thrice of the height.
If the volume of the cuboid is 972 cm³ then find the breadth of the cuboid= ?
Let breadth of cuboid =x cm
(since length=2*breadth)
hence length=2x
(since given length=3*height
hence height=length/3)
hence height=(2x)/3
volume of cuboid
=length*breadth*height
=972 cm³ (given)
or x*2x*2x/3=972
or 4x³=972*3
or x³=243*3
hence x=(729)⅓
x=(9³)⅓ cm.
(breadth) x=9 cm
Hence the breadth of the cuboid is 9 cm.
Learn more about Cuboid here:
brainly.com/question/46030
#SPJ9
In the diagram, find the segment length of FD.(Assume FG is tangent.) G X +9 D 18 E 12
ANSWER
FD = 27
EXPLANATION
By the tangent-secant theorem:
[tex]FG^2=EF\cdot FD[/tex]So we have:
[tex]\begin{gathered} 18^2=12\cdot FD \\ FD=\frac{18^2}{12} \\ FD=27 \end{gathered}[/tex]what's the difference between a coefficient and a variable
we have that
variables" because the numbers they represent can vary—that is, we can substitute one or more numbers for the letters in the expression. Coefficients are the number part of the terms with variables
example
5x
In the term 5x
x is the variable
5 is a coefficient
Solve for w.182- w = 252
Given the equation :
[tex]182-w=252[/tex]solve for w, so:
subtract 182 from both sides:
[tex]\begin{gathered} 182-w-182=252-182 \\ \\ -w=70 \\ \end{gathered}[/tex]multiply both sides by -1
[tex]w=-70[/tex]So, the value of w = -70
pls today I have it for tomorrow
Answer:
6/5 x 5/3 is 2
if that's what you need help with
step-by-step explanation
What is the initial value of the function represented by this table?ху04192140004.0509
The initial value, or y-intercept, is the output value when the input of a linear function is zero.
From the table provided, the y-intercept is obtained when x=0
The answer
Linear Models: Glaciersm= 745-1000= -255, 15-0= 15, -255/15= -17The average annual rate of retreat of the glacier is 17 meters per year.2. Fill in the table below using the information about the average annual rate of retreatand the length of each glacier in 2010.YearLength in meters201020202030204020503. Create an equation that represents the length of the Easton Glacier as a function ofthe number of years since 2010.
I guess the annual retreat of the glacier is linear, and two points in the line are
[tex](0,1000),(15,745)[/tex]Where x is in years and y in meters.
We can find the equation of a line given two points by using the formula below
[tex]y-y_1=\frac{y_2-y_1}{x_2-x_1}(x-x_1)[/tex]In our case,
[tex]\begin{gathered} y-1000=\frac{745-1000}{15-0}(x-0) \\ \Rightarrow y-1000=-17x \\ \Rightarrow y=-17x+1000 \end{gathered}[/tex]2) Suppose that x=0 corresponds to the year 2010. Then, the information in the table is:
[tex]\begin{gathered} 2010\to-17(0)+1000=1000 \\ 2020\to-17(10)+1000=830 \\ 2030\to-17(20)+1000=660 \\ 2040\to-17(30)+1000=490 \\ 2050\to-17(40)+1000=320 \end{gathered}[/tex]The answers are 1000,830,660,490,320 to to bottom
c)
We already obtained the equation we are asked for in this part of the problem. Remember that we used the points (0,1000) and (15,745)
The equation is:
[tex]y=-17x+1000[/tex]y=-17x+1000
find the measure of the angles in the following triangles.x=______missing angle measures:_______ ______
First, we have to use the interior angles theorem
[tex]x-2+72+x=180[/tex]Then, we solve for x
[tex]\begin{gathered} 2x+70=180 \\ 2x=180-70 \\ 2x=110 \\ x=\frac{110}{2} \\ x=55 \end{gathered}[/tex]Then, we use this value to find each angle
[tex]\begin{gathered} (x-2)=55-2=53 \\ x=53 \end{gathered}[/tex]Hence, the interior angles are 72°, 55°, and 53°you're planning to supply cookies for a staff party. You're thinking of purchasing platters and cookies containing 80 sugar cookies and 15 chocolate chip cookies. what is the ratio of sugar cookies to chocolate chip cookies?
We have the following:
To calculate the proportion, we must calculate the quotient between sugar cookies and chocolate chip cookies, as follows
[tex]\frac{80}{15}=\frac{16\cdot5}{3\cdot5}=\frac{16}{3}[/tex]Which means that for every 3 chocolate chip cookies there are 16 sugar cookies.
can someone please help me with the following?
Answer:
y^2 = -12x
Explanation:
For a parabola whose vertex is at (0,0), its standard equation is
[tex]y^2=-4ax[/tex]where the directrix is given by x = a.
Now in our case, the vertex of our parabola is at (0,0) and the directrix is x = 3. This tells us that a = 3 and so the above equation gives
[tex]y^2=-4\cdot3x[/tex][tex]\boxed{y^2=-12x\text{.}}[/tex]which is our answer!
slo also has cell phone service from Varisoon Wireless. She pays a flat fee of $39.95for 350 minutes per month. Any minutes over 350 are at an additional cost. In November,Noslo's bill for wireless service was $108.70 for 475 minutes. What is the charge perminute for the minutes over 350 per month?
hello
Noslo spent 475minutes on call for that month, but we already know the price on the first 350 minutes
if Noslo is charged $39.95 for 350 minutes, we can subtract $39.95 from $108.70 and also 475 from 350 to know the cost and number of minutes respectively.
the number of minutes is
[tex]475-350=125\text{ minutes}[/tex]the cost of the minutes is
[tex]108.70-39.95=68.75[/tex]so, what this information implies is thar Noslo was charged $68.75 for 125 minutes.
we can easily find how much he's charged per minute from here.
let's make x represent that
[tex]\begin{gathered} 125=68.75 \\ 1=x \\ \text{cross multiply both sides} \\ x\times125=68.75 \\ 125x=68.75 \\ \text{divide both sides by the coefficient of x} \\ \frac{125x}{125}=\frac{68.75}{125} \\ x=0.55 \end{gathered}[/tex]from the calculations above, Nsolo was charged $0.55 per minute
Which polynomial matches the description below?A binomial with two different variables and a degree of five.
A binomial has two monomials, that discard b and d options.
Two different variables discard a.
Therefore, the correct option is c.
Meg plans to build a fence around her yard. She draws this diagram of the yard.How many meters of fencing material does Meg need?
The required figure is,
The length of fencing material required = Perimeter of the figure.
Perimeter is calculated as,
[tex]\begin{gathered} Perimeter\text{ = sum of the length of all the sides} \\ Perimeter\text{ = 11.8 m + 18.5 m + 12.1 m +5.4 m + 6.4 m + 6.4 m } \\ Perimeter\text{ = 60.6 m} \\ \end{gathered}[/tex]Thus 60.6 m of fencing material is needed.
Hi thank you so for all your time and help in advance
Question:
Solution:
Remember the following definition :
[tex]\cos (x)=\frac{adjacent\text{ side to the angle x }}{hypotenuse}[/tex]thus, if:
[tex]\cos (x)=\frac{adjacent\text{ side to the angle x }}{hypotenuse}=\frac{\sqrt[]{3}}{2}[/tex]then, according to the given triangles in the problem, the only angle that fulfills this, is:
[tex]x=30[/tex]so that, the correct answer is:
[tex]x=30[/tex]
Select the Coordinate point that is not a solution to the given system of linear inequalities. 3x + 5y 2-15 3x + y > 3
3x + 5y ≥ -15 (1)
3x - y > 3 (2)
From (1) let's solve for x:
3x + 5y ≥ -15
Subtract 5y from both sides:
3x ≥ -15 - 5y
Divide both sides by 3:
x ≥ -5 - 5y/3 (3)
Replace (3) into (2)
3(-5 - 5y/3) - y > 3
Using distributive property:
-15 - 5y - y > 3
-15 - 6y > 3
Solving for x:
Add 15 to both sides:
-6y > 18
Divide both sides by -6:
y < -3
Replacing y into (3)
x ≥ 0
3x - y > 3
if x = 4 and y =9
3*4 - 9 >3
12 - 9 > 3
3 > 3
this is false because 3 = 3
55°Angle FGH is a right angle.The measure of angle FGJ is 559.The measure of angle JGH is xº.What is the value of x?toХS
Given angle FGH is a right angle. This means angle FGH is 90 degrees
But
Which measurements could not represent the side lengths of a right triangle?A) 3cm, 4cm, 5cmB)3cm, 5cm, 9cmC)12cm, 16cm, 20cmD)16cm, 63cm, 65cm
The Pythagorean theorem states that for a rigth triangle, the square of the hypothenuse is equal to the sum of squares of the other two sides, symbolically:
[tex]a^2+b^2=c^2[/tex]To check if these sides lengths are of a rigth triangle you have to square them.
Remember that the hypothenuse is always the longest side.
So for the first set:
A)
3cm, 4cm and 5 cm
Lets take the side length 5cm as the hypothenuse
So a=3, b=4 and c=5
If the theorem checks then
[tex]3^2+4^2=5^2[/tex]Square all sides:
[tex]\begin{gathered} 3^2=9 \\ 4^2=16 \\ 5^2=25 \end{gathered}[/tex]Add both squared sides:
[tex]9+16=25[/tex]The result is equal to the square of the hypotenuse, this means that this side lengths corresponds to a rigth triangle.
*-*-*
B)
a=3 cm
b=5 cm
c=9 cm (hypothenuse)
Square the three sides:
[tex]\begin{gathered} a^2=3^2=9 \\ b^2=5^2=25 \\ c^2=9^2=81 \end{gathered}[/tex]If the theorem checks then 9 + 25 must be equal to 81
[tex]9+25=34[/tex]The square sum of both sides is different from the quare of the hypotenuse, these side lengths do not correspond to a rigth triangle.
C)
a=12cm
b= 16 cm
c= 20 cm (hypothenuse)
Square the sides:
[tex]\begin{gathered} a^2=12^2=144 \\ b^2=16^2=256 \\ c^2=20^2=400 \end{gathered}[/tex]If the theorem checks then 144 plus 256 must be 400
[tex]144+256=400[/tex]The sum of squares of the sides is equal to the square of the hypothenuse, this set of side lengths belong to a right triangle.
D)
a=16cm
b=63cm
c=65cm (hypothenuse)
Square the sides:
[tex]\begin{gathered} a^2=16^2=256 \\ b^2=63^2=3969 \\ c^2=65^2=4225 \end{gathered}[/tex]If the theorem checks out, then 256 + 3969 must be equal to 4225:
[tex]256+3969=4225[/tex]The sum of squares of the sides is equal to the square of the hypothenuse, this set of side lengths belong to a right triangle.
Help me with math and explain it with a Quick solution By explaining the you answer
EXPLANATION
Given the points (x_1,y_1) = (-9,2) and (x_2,y_2) = (-4,2)
We can apply the distance formula in order to get the distance between them as shown as follows:
[tex]\text{distance}=\sqrt[]{(x_2-x_1)^2+(y_2-y_1)^2}[/tex]Replacing terms:
[tex]\text{distance}=\sqrt[]{(-4-(-9))^2+(2-2)^2}[/tex]Adding numbers:
[tex]\text{distance}=\sqrt[]{(5)^2+(0)^2}[/tex]Computing the powers:
[tex]\text{distance}=\sqrt[]{25}=5[/tex]Hence, the distance is equal to 5 units.
This is a intro to statistics question, I was wondering if i can have the work shown soni can see the process, thanks :)Charges for advertising on a TV show are based on the number of viewers, which is measured by the rating. The rating is a percentage of the population of 110 million TV households. The CBS television show 60 Minutes recently had a rating of 7.8, indicating that 7.8% of the households were tuned to that show. An advertiser conducts an independent survey of 100 households and finds that only 10 were tuned to 60 Minutes. Assuming that the 7.8 rating is correct, find the probability of surveying 100 randomly selected households and getting 10 or fewer tuned to 60 Minutes. What does this suggest? Does the advertiser have grounds for claiming a refund on the basis that the size of the audience was exaggerated?
Step-by-step explanation:
7.8% were viewing the show.
so, when picking a single household the probability that is is watching the show is 0.078.
that also means that the probability that this household is not watching the show is 1 - 0.078 = 0.922.
"only" 10 of 100 were watching the show ? that is 10% and therefore a higher rate than measured by the rating agency.
there is no indication that the audience was exaggerated.
anyway, the probability to get 10 or fewer out of randomly picked 100 households to watch the show is
the probability of exactly 10 households watching +
the probability of exactly 9 households watching +
the probability of exactly 8 households watching +
...
the probability of exactly 1 household watching +
the probability of no (0) household watching.
to get the probabilty of any of these events :
x = number of households watching out of the overall 100.
w = probability of a household to watch = 0.078
a = probability of a household to be absent (= not watching) = 0.922
probability(x) = p(x) = w^x × a^(100-x) × c(100, x)
in other words :
the combined probability of "x" households watching and "a" households not watching (which must be 100-x) multiplied by the number of combinations of picking x households out of 100.
so, for the first one, x = 10, we get
p(10) = 0.078¹⁰ × 0.922⁹⁰ × 100! / (10! × (100 - 10)!) =
= 0.078¹⁰×0.922⁹⁰×100×99×...×91 / 10×9×8×...×2 =
= 8.335775831e-012 ×
0.00066955... ×
1.731030945644e+13 =
= 0.096612596...
the rest is then best via Excel or other spreadsheet applications.
p(9) = 0.125496...
p(8) = 0.145117...
p(7) = 0.147558...
p(6) = 0.129888...
p(5) = 0.096969...
p(4) = 0.059699...
p(3) = 0.0291
p(2) = 0.01053
p(1) = 0.002515...
p(0) = 0.000297...
and the sum of all that is the probability to have 10 or fewer households in randomly picked 100 watching the show :
0.843782...
the vast majority of samples of 100 households is expected to have 10 or fewer households watching the show.
this covers the general rating (that would suggest that 7.8 households of 100 are watching the show), some even better ranges (more than 7.8 households), but also everything that is worse than the original rating (below 7.8 households).
when we look at the individual probabilities, we see that the largest probabilities by far are in the categories of 9, 8, 7 and 6 households out of 100 are watching.
so, these are the main expected results when picking samples of 100 households.
therefore, I don't see any indication that the advertiser was "cheated".
Suppose a city's population grows by 5% each year. How long will it take for the population of the city to triple? Answer to the nearest hundredth of a year.
Since it is given that the population grows by 5% each year, it follows that the Exponential Growth Function is the appropriate function that can be used to model the problem.
The Exponential Growth Function is given by:
[tex]y=a(1+r)^t[/tex]Where
• a is the initial amount.
,• r is the percent of increase in decimal.
,• t is the time.
,• y is the amount after time t.
Since we want when the initial population will triple, substitute y=3a into the equation:
[tex]3a=a(1+r)^t[/tex]Substitute r=5%=0.05 into the equation:
[tex]3a=a(1+0.05)^t[/tex]Solve the resulting equation for t:
[tex]\begin{gathered} 3a=a(1+0.05)^t \\ \Rightarrow a(1+0.05)^t=3a \\ \Rightarrow a(1.05)^t=3a \\ Divide\text{ both sides by a:} \\ \Rightarrow(1.05)^t=3 \\ \text{Take logarithm of both sides:} \\ \Rightarrow\ln (1.05)^t=\ln 3 \\ \Rightarrow t\ln (1.05)=\ln 3 \\ \Rightarrow t=\frac{\ln 3}{\ln (1.05)}\approx22.52\text{ years} \end{gathered}[/tex]The population will triple after about 22.52 years.