You get everything you need from factoring the last expression:
[tex]x^4-y^4=-176\sqrt7[/tex]
The left side is a difference of squares, and we get another difference of squares upon factoring. We end up with
[tex]x^4-y^4=(x^2-y^2)(x^2+y^2)=(x-y)(x+y)(x^2+y^2)[/tex]
Plug in everything you know and solve for [tex]x-y[/tex]:
[tex]-176\sqrt7=(x-y)\cdot4\cdot22\implies x-y=\boxed{-2\sqrt7}[/tex]
Answer:
-2sqrt(7)
Step-by-step explanation:
Solution:
From the third equation, $x^4 - y^4 = -176 \sqrt{7}.$
By difference of squares, we can write
\[x^4 - y^4 = (x^2 + y^2)(x^2 - y^2) = (x^2 + y^2)(x + y)(x - y).\]Then $-176 \sqrt{7} = (22)(4)(x - y),$ so $x - y = \boxed{-2 \sqrt{7}}.$
abby owns a square plot of land. she knows that the area of the plot is between 2200 and 2400 square meters. which of the following answers is a possible value for the side length of the plot of land?
Answer:
48
Step-by-step explanation:
The formula for the area of a square is A = s². Plug in each value and see if is in between 2200 and 2400.
A = s²
A = (46)²
A = 2116
A = s²
A = (48)²
A = 2304
A = s²
A = (50)²
A = 2500
A = s²
A = (44)²
A = 1936
The only value that fits in between 220 and 2400 is 48.
An umbrella has 8 ribs which are equally spaced (see fig.). Assuming umbrellato
be a flat circle of radius 45 cm, find the area between the two consecutive ribs of
the umbrella.
Answer:
Yes.
Step-by-step explanation:
You are correct except to the nearest hundredth it is 795.54 cm^2.
In the figure, m∠CED = m∠A. Complete the following proportions: ED/ A F= CE/? = CD/?
Answer:
The completed proportions are;
ED/A_F = CE/CA = CF/CD
Step-by-step explanation:
The given m∠CED = m∠A
∴ Angle ∠CDE = Angle ∠A_FC, (corresponding angles)
Angle ∠ECD = Angle ∠ACF (reflexive property)
Triangle ΔDCE is similar to triangle ΔACF (Angle Angle Angle (AAA) similarity)
In triangle ΔDCE and triangle ΔACF
m∠A is bounded by CA and A_F
m∠CED is bounded by CE and ED
∠DCE is bounded by CE and DE
∠C is bounded by CA and CF
Based on the orientation of the two triangles, we have
ED is the corresponding side to A_F, CD is the corresponding side to CF, CE is the corresponding side to CA
Therefore, we have;
ED/A_F = CE/CA = CF/CD.
Find the value of x.
Answer:
8.8Option A is the correct option.
Step-by-step explanation:
As PW is the median.
PW = [tex] \frac{1}{2} [/tex] ( YZ + TM )
Plug the values
x = [tex] = \frac{1}{2} (5.5 + 12.1)[/tex]
Calculate the sum
x = [tex] = \frac{1}{2} \times 17.6[/tex]
Calculate the product
x = [tex] = 8.8[/tex]
Hope this helps...
Best regards!
The side length of each square is 6 units. Find the areas of the inscribed shapes.
Answer:
a) 18
b) 20
c) 12
d) 12
Step-by-step explanation:
a) The triangle is half of the square, so you can find the area of the square(36) and divide by 2: so 18
b) There are 4 same sized blank triangles with area of 4 ( (2*4)/2 ) so 4 * 4 is 16. 16 is the blank area so the area of the shaded is 36 - 16: 20
c) There are 2 blank triangles which areas are 6, and 18, so you subtract those numbers from 36: 36 - (6+18) = 12
d) Another 2 same blank triangles with areas of 12 ( (6 *4)/2 )so you subtract them from 36 too: 36 - (12*2) = 36 - 24 = 12
Let f(x) = 3x + 5 and g(x) = x2. Find g(x) − f(x).
Answer:
2x-(3x+5) = -x-5
Step-by-step explanation:
2x + 0
-
3x + 5
-———————-
-x - 5
Based on your work in Question 1 through 3, what is the relationship between the radius, AB , and the tangent line, BC ? What can you conclude about any tangent line to a circle and the radius of the circle? Explain.
Without further context I can't say much other than the radius is perpendicular to the tangent. In other words, the radius and tangent line form a 90 degree angle. This is one particular radius and its not just any radius. The radius in question must have the point of tangency as its endpoint.
The radius, AB is perpendicular to the tangent line, BC so their slopes are negative reciprocals of one another. Because I generated a circle at random for this activity, this conclusion likely applies to any tangent line to a circle. In other words, the tangent line to any circle is perpendicular to the radius at their point of intersection.
Please give me the correct answer her please
Answer:
9.3 inStep-by-step explanation:
m∠UTV = 112° ⇒ m∠WTV = 180° - 112° = 68°
sin(68°) ≈ 0.9272
sin(∠WTV) = WV/TV
WV/10 ≈ 0.9272
WV ≈ 9.272
WV ≈ 9.3
If the m1 = 40, what is the m 3
Answer:
Your Answer is 120Step-by-step explanation:
m1=40
Taking m3
m3=40 ×3
m3= 120
Hope It helps UHelp please!!!!!thxxxx
Answer:
144
Step-by-step explanation:
An angle of a regular pentagon is of 180(5-2)/5=108°
and that all the sides are equal so angle MNL=108/3=36
then MNK=180-MNL=180-36=144
I don't know if you understand this but it's hard to work without more points :)
48 - 8x equivalent expression
Answer:
8(6-x)
Step-by-step explanation:
Both 48 and 8 can be divisible by 8.
48 ÷ 8 = 6
8 ÷ 8 = 1
Therefore you get the answer 8(6-x)
as the simplest form.
Hope this helps.
plzzz helpp ASAP 1. Why is it important to know what the limitations of a particular model are? A. so you can create a prototype based on your model B. so you don't make the mistake of confusing an object and a system C. so you can revise your model to represent every property of the real thing D. so you don't confuse properties of the model with properties of the real thing
2. Mathematical and computer models are similar because both involve _____. A. using calculations to represent an object or system B. comparisons between an object or system and something familiar C. building a complex object or system isolated from the natural world D. creating real-life objects that show features of the modeled object or system
3. Some models can illustrate a system. What does the term system refer to? A. a collection of interacting things B. a set of rules or laws about things C. something with advantages and limitations D. something illustrating parts of a real-life thing
4. J.J. Thomson's Plum Pudding Model is an example of _____. A. a picture B. an analogy C. a prototype D. a mathematical model
5. An advantage of describing a cell as being like a factory is that it _____. A. makes cells easier to understand B. shows the limitations of cells clearly C. prevents having to study the complexities of cells D. is cheaper to do experiments in a factory than on a cell
6. Scientists like using models because they are often _____ than the real thing. A. more accurate B. more enjoyable to study C. cheaper and more complex D. cheaper and easier to work with
7. An advantage of J.J. Thomson's Plum Pudding Model was that it _____. A. was a much less expensive way to study atoms B. simplified the calculations necessary to describe an atom C. clearly explained where electrons were located in an atom D. is much less expensive to bake a plum pudding than to look at an atom
8. A small clay model of a volcano is an example of _____. A. an analogy B. a prototype C. a physical model D. a computer model
9. An advantage of using a model instead of the real thing is that models _____. A. include better detail B. can be easier to change C. are much more interesting to study D. don't include any features of the real thing
Answer:
D. so you don't confuse properties of the model with properties of the real thing.
2-Mathematical and computer models are similar because both involve using calculation to represent an object or system
3- Some models can illustrate a system. What does the term system refer to
A. a collection of interacting things
4-J.J. Thomson's Plum Pudding Model is an example of _____B. an analogy
5. An advantage of describing a cell as being like a factory is that it _____
A. makes cells easier to understand
6- C. cheaper and more complex
7-C. clearly explained where electrons were located in an atom
8-C. a physical model
9-B. can be easier to change
GOOD LUCK
Please help I don't understand this at all
Answer:
Since ΔABC is equilateral, ∠ACB = 60°. Since ΔCED is isosceles (we know this because CE = ED from the graph), ∠ECD = ∠EDC from Base Angles Theorem, and since the sum of angles in a triangle is 180°, they measure (180 - 32) / 2 = 74° each. Since BCD is a straight line, it measures 180° so we can write:
60 + x + 74 = 180
134 + x = 180
x = 46°
Answer:
46 degrees
Step-by-step explanation:
Since triangle ABC is equilateral that means each angle in that triangle is 60 degrees.
We also know that for triangle ECD angle C and angle D have to be 74 degrees, because a triangle has 180 degrees in total and the only unique angle is at the top which is 32. So it is 180-32=148, than 148/2=74.
We than know that a half circle is 180 degrees aswell, so we do 180-60=120
120-74=46
Simplify (2^3)^–2. PLEASE I NEED HELP U WILL GET 10 POINTS
Answer:
I won't give you the answer straight away so you take the time to read my answer and understand
Step-by-step explanation:
We knoe that 2 to the third is 8. when you square to a negative power, you do squaring normally, and then take the reciprocal of that number. so 8 to the second power is 64, and we flip it over, sp the answer is 1/64
Determine the value of x.
Answer:
B. 6sqrt(2).
Step-by-step explanation:
Since the two legs of the right triangle are congruent, this is a 45-45-90 triangle. That means that the hypotenuse will measure xsqrt(2) units, and each leg will measure x units.
In this case, x = 6.
So, the hypotenuse is B. 6sqrt(2).
Hope this helps!
Solve for x. 60 10 20 120
Answer:
Hey there!
We have the angle is equal to half the measure of the arc of 120 degrees. (Just another rule for circles)
7x-10=0.5(120)
7x-10=60
7x=70
x=10
Hope this helps :)
Answer:
x = 10
Step-by-step explanation:
Tangent Chord Angle = 1/2 Intercepted Arc
7x-10 = 1/2 ( 120)
7x -10 = 60
Add 10 to each side
7x -10+10 = 60+10
7x = 70
Divide by 7
7x/7 = 70/7
x = 10
Starting at sea level, a submarine descended at a constant rate to a depth of −5/6 mile relative to sea level in 4 minutes. What was the submarine's depth relative to sea level after the first minute? Answer with a fraction :3
Answer:
-5/24 miles
Step-by-step explanation:
The submarine descends at a rate of -5/6 miles every 4 minutes.
To find the depth of the submarine relative to sea level after the first minute, we have to multiply the rate of descent by he time spent (1 minute). That is:
[tex]\frac{\frac{-5}{6} }{4} * 1[/tex]
=> D = -5 / (6 * 4) = -5/24 miles
Therefore, the submarine's depth is -5/24 miles.
Answer:
-1 1/5
Step-by-step explanation:
I took the test and this was the correct answer :D
(ii) Atrader gets a profit of 20% by selling an item for £ 150. Find the buying in price.
(iii) A bank charges 12% per annum on loans. If a person borrowed a loan of
£ 20000 find the total amount that he has to repay after one year.
(a) Six workers can build a wall in 10 days. At the same rate how many
workers are needed to complet in 4 days.
(c) How many extra workers to be employed ?
Answer:
ii) £120
iii) £2,400
a) 10 workers
c) 4 workers more to be employed.
Step-by-step explanation:
ii) To find the buying price we deduct 20% (percent) from the selling price of £150.
= 20/100 x 150
= £30 (Next we substract this value from the selling price of £150) = €150 - £30 = £120
iii) A 12% interest per annum Implies a 12 percent of the borrowed amount of 20,000, which is calculated as
12% or 12/100 x 20,000 = £2,400
a) Put simply, we create an equation for the problem.
4 men * 10 days = 40 man days.
X men * 4 days = 40 man days.
Let's substitute the equation:
(X/ 4) * (4/ 10) = 40 / 40
(X/4) * 0.4= 1 (collect like terms)
0.4 * x = 4
0.4x/0.4= 4/0.4
x = 10 workers.
(c) 4 extra workers to would need to be employed since we have six already available (10-6=4).
Please help i will mark brainliest
Answer:
See below.
Step-by-step explanation:
To find the equation, we need to find the slope and the y-intercept. Afterwards, we can put the numbers into the slope-intercept form:
[tex]y=mx+b[/tex]
From the graph, we can see that the line crosses the y-intercept at y=-6. Thus, the y-intercept (b) is -6.
Now we need to find the slope. Pick any two points where the line crosses. I'm going to pick (0,-6) and (4,-7).
[tex]m=\frac{y_2-y_1}{x_2-x_1}=\frac{-7-(-6)}{4-0}= -1/4[/tex]
Therefore, the equation of the line would be:
[tex]y=mx+b\\y=-1/4x-6[/tex]
Help please thanks don’t know how to do this
Answer:
a = 11.71 ; b = 15.56
Step-by-step explanation:
For this problem, we need two things. The law of sines, and the sum of the interior angles of a triangle.
The law of sines is simply:
sin(A)/a = sin(B)/b = sin(C)/c
And the sum of interior angles of a triangle is 180.
45 + 110 + <C = 180
<C = 25
We can find the sides by simply applying the law of sines.
length b
7/sin(25) = b/sin(110)
b = 7sin(110)/sin(25)
b = 15.56
length a
7/sin(25) = a/sin(45)
a = 7sin(45)/sin(25)
a = 11.71
Hope is the coach of the Wilson High School girls' soccer team. There are 3 minutes left in the game they are currently playing, and they are losing by 1 goal. In the past, when losing by 1 goal, Hope has pulled a defender out of the game and replaced her with a forward a total of 9 times. When in the same position, she has left the defender in the game 10 times. In the situations when Hope has pulled her defender, the team has lost 4 times, tied 2 times, and won 3 times. In situations when she has left her defender in the game, the team has lost 1 time, tied 3 times, and won 6 times. Based on the information above, if the goal is to either tie or win the game, should Hope pull the defender or leave her in the game?
Answer:
Hope should not pull her defender.
Step-by-step explanation:
When Hope has pulled her defender:
The team had lost 4 times, tied 2 times, and won 3 times.
Hence, the total number of times she meets her goal is:
6 times (Since the goal is to either tie or win the game )
Hence, the probability that she meets her goal is = 6/9=2/3=0.66
When she left her defender in the game:
The team has lost 1 time, tied 3 times, and won 6 times.
Hence, the total number of times she meets her goal is: 9
Hence, the probability that she meets her goal is: 9/10=0.9
As the probability of meeting her goal is more when she left her defender in the game is more.
Hence, Hope should not pull her defender.
In a particular year, a total 44,064 of students studied in two of the most popular host countries when traveling abroad. If 8382 more students studied in the most popular host country than in the second most popular host country, find how many students studied abroad in each country. There were ____ students who studied abroad in the most popular host country.
Step-by-step explanation:
Total=44,064
Host countries= 2
2nd most popular country= x
Popular country=x+8382
x+x+8,382=44,064
2x=44,064-8,382=35,682
2x=35,682
x=17,842
2nd most popular=17,842
Popular=17,842+8,382=26,224
Answer=26,224
There were students who studied abroad in the most popular host country by forming the equation is 26,224
How equations are formed?
Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side. It demonstrates the equality of the relationship between the expressions printed on the left and right sides. We have LHS = RHS (left-hand side = right-hand side) in every mathematical equation. To determine the value of an unknown variable that represents an unknown quantity, equations can be solved. A statement is not an equation if it has no "equal to" sign. It will be regarded as a phrase.
Here, It is given:
Total number of students = 44,064
Number of Host countries= 2
Let the 2nd most popular country= x
So, the Popular country becomes x+8382
Now, According to the question:
⇒x+x+8,382=44,064
⇒2x=44,064-8,382=35,682
⇒2x=35,682
⇒x=17,842
Hence, The number of students in 2nd most popular country=17,842
And, The number of students in a popular country
= 17,842+8,382=26,224
To learn more about forming equations, visit:
https://brainly.in/question/29041303
#SPJ2
James determined that these two expressions were equivalent expressions using the values of y=4 and yu 6. Which
statements are true? Check all that apply
7x+4 and 3x+5+4x-1
When - 2. both expressions have a value of 18.
The expressions are only equivalent for X-4 and X- 6.
The expressions are only equivalent when evaluated with even values.
The expressions have equivalent values for any value of x.
The expressions should have been evaluated with one odd value and one even value.
When - 0, the first expression has a value of 4 and the second expression has a value of 5.
The expressions have equivalent values if X-
Answer with explanation:
Two or more Algebraic expressions are said to be equivalent, if both the expression produces same numerical value , when variable in the expressions are replaced by any Real number.
The two expressions are
1. 7 x +4
2. 3 x +5 +4 x =1
Adding and subtracting Variables and constants
→7 x +5=1
→7 x +5-1
→7 x +4
→ When x=2,
7 x + 4 =7×2+4
=14 +4
=18
So, Both the expression has same value =18.
→So, by the definition of equivalent expression, when ,you substitute , x by any real number the two expression are equivalent.
Correct options among the given statement about the expressions are:
1.When x = 2, both expressions have a value of 18.
2.The expressions have equivalent values for any value of x.
3.The expressions have equivalent values if x = 8.
given that sin x equals to a over b then what is tan x
Answer:
Hey there!
Sine is equal to opposite/hypotenuse
Tangent is equal to opposite/adjacent
opposite=a
hypotenuse=b
adjacent=c
Thus, tangent x= a/c.
Hope this helps :)
Answer:
tan x = a/sqrt(b^2 - a^2)
Step-by-step explanation:
sin x = a/b = opp/hyp
tan x = opp/adj
adj^2 + opp^2 = hyp^2
adj^2 + a^2 = b^2
adj = sqrt(b^2 - a^2)
tan x = a/sqrt(b^2 - a^2)
the diagrams shows a right-angled triangle. find the size of angle x. give your answer correct to 1 decimal place.
Answer:
1. 40.8 degrees
2. 65.6 degrees
Step-by-step explanation:
1.
sin(x) = opposite / hypotenuse = 17/26
x = arcsin(17/26) = 40.83 degrees
2. tan(x) = opposite / adjacent = 11/5 = 2.2
x = arctan(11/5) = 65.56 degrees
Miriam is setting up a fishing game in a kiddie pool for her niece's birthday party. The pool has a circular base with a diameter of 4 feet and a height of 0.75 feet. She wants to fill the pool halfway so there is plenty of space left for the plastic fish. Approximately how many cubic feet of water does she need? 9.4 1.5 2.4 4.7
Answer:
4.7 feet³ of water
Step-by-step explanation:
Diameter of 4 feet
Radius = 2 feet
Height = 0.75 feet
Formula for Volume = 2·[tex]\pi[/tex]·radius·height
But she only wants to fill half, so divide by 2, cancels the 2 in the formula for volume, giving us: [tex]\pi[/tex]·radius·height
[tex]\pi[/tex]·2·0.75 = 4.71 feet³
HELP MEEEEEEE please
Answer:
scale factor = [tex]\frac{1}{3}[/tex]
Step-by-step explanation:
Consider the ratio of corresponding sides, image to original, that is
scale factor = [tex]\frac{T'V'}{TV}[/tex] = [tex]\frac{2}{6}[/tex] = [tex]\frac{1}{3}[/tex]
no clue how to do this, someone pls help
Answer:
6π
Step-by-step explanation:
First we need to find the circumference of the circle. We know that the radius is 4 and the formula is πd or 2πr
Leaving it in terms of pi, the circumference is 8π
Now we need to find the length of the arc.
Since the missing part of the circle is labeled with a right angle, we know that it's exactly 1/4 of the whole circle. That means the arc we need to find is 3/4 of the circumference.
3/4 of 8π is 6π
find the distance of the line segment joining the two points (-4 /2 - /12) and (/32, 2/3)
Answer: [tex]4\sqrt{3}[/tex] .
Step-by-step explanation:
Distance formula : Distance between points (a,b) and (c,d) is given by :-
[tex]D=\sqrt{(d-b)^2+(b-a)^2}[/tex]
Distance between points [tex](-4\sqrt{2},\sqrt{12}) \text{ and }(-\sqrt{32}, 2\sqrt{3})[/tex].
[tex]D=\sqrt{(2\sqrt{3}-(-\sqrt{12}))^2+(-\sqrt{32}-(-4\sqrt{2}))}\\\\=\sqrt{(2\sqrt{3}+\sqrt{2\times2\times3})^2+(-\sqrt{4\times4\times2}+4\sqrt{2})^2}\\\\=\sqrt{(2\sqrt{3}-\sqrt{2^2\times3})^2+(-\sqrt{4^2\times2}+4\sqrt{2})^2}\\\\=\sqrt{(2\sqrt{3}+2\sqrt{3})^2+(-4\sqrt{2}+4\sqrt{2})^2}\\\\=\sqrt{(4\sqrt{3})^2+0}\\\\=4\sqrt{3}\text{ units}[/tex]
Hence, the correct option is [tex]4\sqrt{3}[/tex] .
Rectangle ABCDABCDA, B, C, D is graphed in the coordinate plane. The following are the vertices of the rectangle: A(2, 0), B(6, 0), C(6, 7), D(2, 7). What is the area of rectangle A, B, C, D? square units NEED ASAP 40 POINTS LIGIT
Answer:
[tex]\boxed{\sf \ \ 28 \ \ }[/tex]
Step-by-step explanation:
Hello,
Please find attached the graph
AB = 6-2 = 4
DA = 7-0 = 7
So the area of the rectangle is AB * DA = 4 * 7 = 28
Hope this helps