Answer:
[tex](x -y)^2 = -1[/tex]
Step-by-step explanation:
[tex](x - y)^2 = x^2 + y^2 - 2xy[/tex]
[tex]= (x^2 + y^2 ) - 2(xy)\\\\=(9) - 2( 5)\\\\= 9 - 10 \\\\ = -1[/tex]
The binomial expansion of (x - y)² is
(x - y)² = x² - 2xy + y²
Substitute the given values to the equation
(x - y)² = x² - 2xy + y²
(x - y)² = x² + y² - 2xy
(x - y)² = 9 - 2(5)
(x - y)² = 9 - 10
(x - y)² = -1
Therefore the value of (x - y)² is -1.
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Please help thanks! Please put answer is square millimeters
Answer: 239
Step-by-step explanation:
3x7=21
(16+5)x16=336, 336/2=168
5x10=50
add them all together to get 239
hope this helps!
The density of a certain material is such that it weighs 4 kilograms per cubic foot of
volume. Express this density in ounces per cubic meter. Round your answer to the
nearest whole number.
Answer:
Step-by-step explanation:
4986 ounces/m³
Step-by-step explanation:
1 kilogram = 35.274 ounces
1 cubic foot = 0.0283 cubic metre
We are converting kg/ft³ to ounces/m³
Hence:
4kg/ft³ × 35.274 ounces/ 1 kg × 1 ft³/0.0283m³
= 4985.7243816 ounces/m³
Approximately to the nearest whole number = 4986 ounces/m³
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The density of the material is approximately 123 ounces per cubic meter.
Density [tex](\(D\))[/tex] is defined as mass [tex](\(m\))[/tex] per unit volume [tex](\(V\))[/tex], and it is calculated using the formula:
[tex]\[ D = \frac{m}{V} \][/tex]
In this case, the density is given in kilograms per cubic foot. To convert this to ounces per cubic meter, we need to perform the following steps:
Step 1: Convert kilograms to ounces:
1 kilogram = 35.27396 ounces
Step 2: Convert cubic feet to cubic meters:
1 cubic foot = 0.0283168 cubic meters
Now, let's substitute the given values and perform the conversion:[tex]\[ \text{Density in ounces per cubic meter} = \frac{4 \, \text{kg} \times 35.27396 \, \text{ounces/kg}}{1 \, \text{cubic foot} \times 0.0283168 \, \text{cubic meters/cubic foot}} \][/tex]
Solving this equation gives us the density in ounces per cubic meter:
[tex]\[ \text{Density} \approx 123 \, \text{ounces/m}^3 \][/tex]
Rounded to the nearest whole number, the density of the material is approximately 123 ounces per cubic meter.
In summary, we converted the given density from kilograms per cubic foot to ounces per cubic meter using unit conversions.
This involved converting the mass units and volume units before performing the calculation to obtain the final density value in the desired units.
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Solve the simultaneous equation:
8d - 4e = 28
6d + 3e = 3
Answer: d=2 and e= -3
Step-by-step explanation:
(8d-4e=28)*3 => 24d-12e=84
(6d+3e=3)*4 => 24d+12e=12
24d+24d-12e+12e=84+12
=> 48d=96
=> d=2
d=2 => 8*2-4e=28
=> e= -3
Jason Witten's Salary Negotiation Let's say that tight end Jason Witten (a football player) was given two options when negotiating his contract for the 2017 football season (which was his final season, ). Option 1 was that he would be paid an additional $0.01 (yes one red cent) if he makes only one catch for the season, $0.02 if he makes a total of two catches, $0.04 for a total of three catches and so on, doubling the amount with each catch. Option 2 was that he would be paid a flat $2,000,000 increase from the previous year. Basing this decision on the 2012 season (where he had a career high of 110 total receptions/catches), which option would increase his salary more? (In other words, is it better for him to be paid per catch, starting with 1 cent and doubling with each catch up to 110 or is it better to have a flat $2 million increase?)
Answer:
Option 1: It is better for him to be paid per catch, starting with 1 cent and doubling with each catch up to 110
Explanation:
If Jason were to be paid per catch given that he makes a total of 110 catches for the 2017 season in his new contract, he would make a total of :
0.01 × 2^109 = $6.4903711e+30(calculator result, means 6 then 30 digits after)
Therefore it is better for Jason to be paid per catch and not a flat fee of $2000000
Simplify fully
(x²+3)² - (x²-1)²
Answer:
8x² + 8
Step-by-step explanation:
Given
(x² + 3)² - (x² - 1)² ← expand factors using FOIL
= [tex]x^{4}[/tex] + 6x² + 9 - ([tex]x^{4}[/tex] - 2x² + 1) ← distribute by - 1
= [tex]x^{4}[/tex] + 6x² + 9 - [tex]x^{4}[/tex] + 2x² - 1 ← collect like terms
= 8x² + 8
Write an equation for the line that passes through E(4, -3) and is parallel to the line
0 = 5x - 7y - 27 Write the equation in general form.
Answer:
make y the subject first
Step-by-step explanation:
y=5/7(x) -27/7
parallel lines have equal gradient m1=m2
y-y1=m(x-x1)
y-(-3)=5/7(x-4))
y=5/7(x) -20/7 -3
final answer
y=5/7(x) -41/7
A triangle is shown. What is X?
Answer: 44º
Step-by-step explanation:
Hi there! To start out, disregard Y and Z, as they are just there to trip you up.
Use the Triangle Sum Theorem to find out the question! This theory states that all angles in a triangle add up to 180 degrees. So, just set up an equation, like the one down below!
82+54+X=180
Then, add the whole numbers!
136+X=180
Then isolate X by using inverse operations!
136+X-136=180-136
Then your answer is there!
X=44
If you have any follow up questions, please let me know! Have a nice day
if the probability that it will rain tomorrow is 1/5
what is the probability that it will not rain tomorrow?
Answer:
If the probability is that it WILL rain 1/5. Then the remaining chances are the number it will not rain. The denominator tells us that there are at total of 5 chances. That leaves a 4/5 chance it will not rain.
Step-by-step explanation:
If a salon charges rupees 99 for a haircut, how much money did the salon earn over the week?
Answer:
5940 rupees
Step-by-step explanation:
99 multiplied by 29×5 is 5940
Answer:
[tex]\text{(b) }[/tex] ₹[tex]5,940[/tex]
Step-by-step explanation:
Each pair of scissors on the chart represents 5 haircuts, as indicated by the key. There are 2 scissors on Saturday and 10 scissors on Sunday, hence a total of 12 scissors over the weekend. Therefore, there were [tex]12\cdot 5=60[/tex] haircuts over the weekend.
Since the salon charges 99 rupees per cut, they made a total of [tex]99\cdot 60=\boxed{5,940}[/tex] rupees over the weekend.
Find the missing segment
Answer:
The unknown side is 140
Step-by-step explanation:
Let the unknown side be x
Using ratios
90 90+36
------ = -----------
x x+56
90 126
------ = -----------
x x+56
Using cross products
90(x+56) = 126x
Distribute
90x+5040 = 126x
Subtract 90x
5040 = 36x
Divide by 36
140 =x
By visual inspection determine the best-fitting regression model for the data plot below
Answer:
Exponential
Step-by-step explanation:
By visual inspection the graph generated by the points plotted is an exponential graph as the graph curves upward. The graph is also continous and differs from either a decreasing or increasing Linear graph, which shows a straight best of fit pattern. Hence, the graph most closely represents an exponential graph from visual examination.
The best-fitting regression model for the considered data plot is given by:
Option A: Exponential.
What is fitting of curve for a data plot?When the data shows some trend, either linear (making a line), or non-linear (a predictable curve), we fit a mathematical curve on that data set, as a representative of the pattern in that data set, to predict the output based on the inputs.
The considered plot is not forming a straight line(so no linear fitting), but we can see that a smooth curve can be fitted in the considered data. Since the exponential functions' graph approximately goes the same way (for positive exponent, and increasing value of output).
Thus, the best-fitting regression model for the considered data plot is given by: Option A: Exponential.
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BD is the angle bisector of
Note: Let us consider, we need to find the [tex]m\angle ABC[/tex] and [tex]m\angle DBC[/tex].
Given:
In the given figure, BD is the angle bisector of ABC.
To find:
The [tex]m\angle ABC[/tex] and [tex]m\angle DBC[/tex].
Solution:
BD is the angle bisector of ABC. So,
[tex]m\angle ABD=m\angle DBC[/tex]
[tex]3x=x+20[/tex]
[tex]3x-x=20[/tex]
[tex]2x=20[/tex]
Divide both sides by 2.
[tex]x=\dfrac{20}{2}[/tex]
[tex]x=10[/tex]
Now,
[tex]m\angle DBC=(x+20)^\circ[/tex]
[tex]m\angle DBC=(10+20)^\circ[/tex]
[tex]m\angle DBC=30^\circ[/tex]
And,
[tex]m\angle ABC=(3x)^\circ+(x+20)^\circ[/tex]
[tex]m\angle ABC=(4x+20)^\circ[/tex]
[tex]m\angle ABC=(4(10)+20)^\circ[/tex]
[tex]m\angle ABC=(40+20)^\circ[/tex]
[tex]m\angle ABC=60^\circ[/tex]
Therefore, [tex]m\angle DBC=30^\circ,m\angle ABD=30^\circ[/tex] and [tex]m\angle ABC=60^\circ[/tex].
if r=1 and 0=5pi/6 what is the approximate arc length?
Answer:
B. 2.618 units
Step-by-step explanation:
the arc length = (5π/6) / 2π × 2×3.14×1
= 5/12 × 6.28
= 31.4/ 12
= 2.618 units
The arc length is = 2.618 units
what is arc length of a circle?Arc measure is a degree measurement, equal to the central angle that forms the intercepted arc. Arc length is a fraction of the circumference of the circle.
Given : r=1, [tex]\theta[/tex]= 5π/6
Now, arc length
= [tex]\theta[/tex]/ 2π * 2πr
= (5π/6) / 2π × 2×3.14×1
= 5/12 × 6.28
= 31.4/ 12
= 2.618 units
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Given that 3(x-1)-2(x-1)=7, then the value of x is MI 6 7 (A) (B) (C) (D) 8 9
Answer:
x = 8
Step-by-step explanation:
Given
3(x - 1) - 2(x - 1) = 7 ← distribute both parenthesis on left side
3x - 3 - 2x + 2 = 7 , simplifying
x - 1 = 7 ( add 1 to both sides )
x = 8
Pls help me and thank you!
Answer:
Substitute your answer for Step 1 into the second equation to solve for Z.
60 PTS PLS ANSWER WILL AWARD BRAINLIEST ASAP
Answer:
9. a) 180 - (55+90) = a
b) a=35 degrees
10. a) 2w + 3w + 40 = 180
b) w=28
c) 2w=56 3w=84
Step-by-step explanation:
Answer:
the person above is 100% right trust me :)
Step-by-step explanation:
The variable 100 POINTS!!!!
What is the value of 2 + (-2/3) ^2 ÷1/3 ?
16
3 1/3
-2
0
Answer:
second option is correct
..
What is the answer to this question?
I need help can someone please answer this for me
Solve this problem.
A pair of inline skates that usually sells for $40 is on sale at a 30% discount.
What is the sale price?
Answer:
$28
Step-by-step explanation:
original price = $40
discount = 30%
discount amount = 30% of original price
=30/100 * 40
=$1200/100
=$12
sale price = original price - discount amount
=$40 - $12
=$28
Which is the graph of f(x) = (2) -x
Answer:
In other words y = 2-x
Put in some values of x and see which graph matches the given ys.
The last graph
Answer:
b
Step-by-step explanation:
Someone help me on this Problem !!
Answer:
[tex] \frac{1}{2} [/tex]Negative1 divided by 1 = 12 divided by 4 = 2#Correct me if I'm wrong#Hope it's HelpI will give BRAINLIEST to the correct answer
Find the measure of angle 6.
Answer:
m∠6 = 116°
Step-by-step explanation:
first find x:
7x - 17 = 2x + 78
subtract 2x from both sides: 5x - 17 = 78
add 17 to both sides: 5x = 95
divide by 5: x = 19
plug x into 7x - 17
7(19) - 17 = 116
∠6 and 7x - 17 are vertical angles and therefore congruent, so m∠6 also = 116°
Round to 3 SF
0.0692494
rounding 0.0692494 to 3SF is 0.069
Maya buys candy that costs $8 per pound. She will buy less than 7 pounds of candy. What are the possible amounts she will spend on candy? Use c for the amount (in dollars) Maya will spend on candy. Write your answer as an inequality solved for c.
Answer:
c < 56
Step-by-step explanation:
Maya buys candy that costs $8 per pound. She will buy less than 7 pounds of candy. What are the possible amounts she will spend on candy? Use c for the amount (in dollars) Maya will spend on candy. Write your answer as an inequality solved for c.
c < 7 × $8
c < $56
At what rate percent per annum, will $4000 yield an interest of $780 in 18 months (simple interest)?
Answer:
13%
Step-by-step explanation:
780 interest/18 months=43.33 interest/month
43.33x12=520 interest/year
principal x interest rate = interest per year
4000 x interest rate =520
interest rate =520/4000
interest rate =.13 or 13%
How much is -1/4 is 1 1/3?
Answer:
4 option
Step-by-step explanation:
Lydia's school is holding a candy fundraiser. They are selling lollipops for $0.50 and candy bars for $1.50 Lydia buys 6 lollipops and some candy bars. If she spends $15.00 in total, how many candy bars, b, did Lydia buy?
Answer:
8
Step-by-step explanation:
Let's say that the amount of lollipops Lydia buys is represented by x and the number of candy bars is represented by y. For each x, Lydia spends 0.50, and for each y, Lydia spends 1.50. This means that the total amount she spends can be represented by the equation 0.50*x+1.50*y. Our equation is then 0.50*x+1.50*y=15
Using our equation, we can plug 6 in for x, resulting in 0.50*6+1.50*y=15, so [tex]0.50x+1.50y=15\\0.5(6)+1.50y=15\\3+1.50y=15\\1.50y=12\\y=8[/tex]
In this set of equations, we plugged 6 in, multiplied it out, then subtracted 3 from both sides, and finally divided both sides by 1.50 to get 8 as our answer.
Find the mean, median and mode(s) of the data.
4, 6, 5, 4, 4, 5, 4,8
Mean
Median
Mode
Answer:
mean = 5
median = 4.5
mode = 4
Step-by-step explanation:
Mean :
n = 8
sum of all items = 4+6+5+4+4+5+4+8
= 10+9+9+12
= 19+ 21
= 40
so,
mean = sum of all items/ n
= 40/8
= 5
mean = 5
Median:
ascending order: 4,4,4,4,5,5,6,8
n = 8
md = (n+1)/2 the term
= (8+1)/2 th term
= 9/2 th term
= 4.5 th term
= (4th + 5th) / 2
= (4+5)/2
= 9/2
= 4.5
median = 4.5
x. f.
4. 4
5. 2
6. 1
8. 1
here the highest frequency is 4 and 4 is corresponding to 4
so, mode = 4
Can someone work please so I can understand how
Answer:
[tex]\text{A. }\frac{4\sqrt{14}}{{7}}[/tex]
Step-by-step explanation:
In any right triangle, the tangent of an angle is equal to its opposite side divided by its adjacent side. Therefore, we can form a right triangle with non-right angle [tex]\theta[/tex] and its opposite side [tex]\sqrt{7}[/tex] and its adjacent side [tex]5[/tex].
By definition, [tex]\csc \theta=\frac{1}{\sin\theta}[/tex].
In any right triangle, the sine of an angle is equal to its opposite side divided by the hypotenuse, or longest side, of the triangle. To find the hypotenuse, use the Pythagorean Theorem: [tex]a^2+b^2=c^2[/tex], where [tex]c[/tex] is the hypotenuse, or longest side, of the right triangle and [tex]a[/tex] and [tex]b[/tex] are the two legs of the triangle.
Solving, we get:
[tex]5^2+\sqrt{7}^2=c^2,\\25+7=c^2,\\c^2=32,\\c=\sqrt{32}=4\sqrt{2}[/tex]
Therefore, we have:
[tex]\csc \theta = \frac{1}{\sin \theta}=\frac{1}{\frac{\sqrt{7}}{4\sqrt{2}}},\\\\\csc \theta=1\cdot \frac{4\sqrt{2}}{\sqrt{7}},\\\\\csc \theta =\frac{4\sqrt{2}}{\sqrt{7}}\cdot \frac{\sqrt{7}}{\sqrt{7}}=\boxed{\text{A. }\frac{4\sqrt{14}}{{7}}}[/tex]
Answer: Choice A) [tex]\frac{4\sqrt{14}}{7}[/tex]
======================================================
Explanation:
Refer to the figure below. We start off drawing a right triangle that has opposite side sqrt(7) and adjacent side 5.
This is because tan = opposite/adjacent.
Use the pythagorean theorem to find the hypotenuse is sqrt(32) which simplifies like so
sqrt(32) = sqrt(16*2) = sqrt(16)*sqrt(2) = 4*sqrt(2)
The last thing to do is to take the ratio of the hypotenuse over the opposite side. Recall that csc, aka cosecant, is the reciprocal of sine.
sin = opposite/hypotenuse
csc = hypotenuse/opposite
---------
So we get the following
[tex]\csc{\theta} = \frac{\text{hypotenuse}}{\text{opposite}}\\\\\csc{\theta} = \frac{4\sqrt{2}}{\sqrt{7}}\\\\\csc{\theta} = \frac{4\sqrt{2}*\sqrt{7}}{\sqrt{7}*\sqrt{7}}\\\\\csc{\theta} = \frac{4\sqrt{2*7}}{\sqrt{7*7}}\\\\\csc{\theta} = \frac{4\sqrt{14}}{\sqrt{49}}\\\\\csc{\theta} = \frac{4\sqrt{14}}{7}\\\\[/tex]
So that's why the answer is choice A.
