The length of one of the legs of an isosceles right triangle and has a hypotenuse length of seven times the square root of two is 7 units.
What is an Isosceles triangle?Isosceles triangles are triangles that has two of it sides equal to each other. The base angles of an isosceles triangle are equal.
The isosceles triangle is also a right angle triangle. The hypotenuse is the longest side of a right angle triangle.
Therefore,
hypotenuse = 7(√2)
let the length of the other legs = x
Therefore, using Pythagoras theorem
c² = a² + b²
(7(√2))² = x² + x²
49 × 2 = 2x²
98 = 2x²
x² = 98 / 2
x = √49
x = 7 units
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Given the polar coordinates (4,-pi/3) which of the following rectangular coordinate pairs represents the same point?
a) (-2,2sqrt3)
b) (2,-2sqrt3)
c) (2sqrt3,-2)
d) (2sqrt3, 2)
The rectangular point that represents (4, - pi/3) is the one in option b: (2, -2√3).
How to change the coordinates?
For a point (x, y), the polar coordinates are:
R = √(x^2 + y^2)θ = atan(y/x).Then we must have:
R = 4 = √(x^2 + y^2)
Notice that for all the given points we have the radius equal to 4, so the only part that we care is the angle one:
-pi/3 = Atan(y/x)
tan(-pi/3) = y/x = -1.73
So, y and x must have different signs, and because the angle is negative, we will say that the y-component must be negative.
So the correct option will be b: (2, -2√3)
y/x = -2*√3/2 = √3 = -1.73
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Answer: Quiz answer Unit 4 lesson 6
all answers are right
Step-by-step explanation:
1.) Given the polar coordinates (4,-pi3)which of the following rectangular coordinate pairs represents the same point?
Answer is B: (2,-2sqrt3)
2.) Given the rectangular coordinates (-5 5) which of the following polar coordinate pairs in, radians, represent the same points?
the correct option is D. (5√2,3π4)
3.)Rewrite in rectangular form: r=8 sin theta -2 cos theta.
Answer:
The equation in rectangular form is:
4.)Rewrite in polar form: x^2+y^2-6y-8=0
the Answer is B. r^2=6r sin 0+8
5.)The graph of r=-9 cos theta has which of the following characteristics?
Answer:
"circle; diameter of 9; center at (-4.5,0)"
6.)Which conic section is represented by the polar equation r=1/4-6 cos theta?
Answer:
Option 2 - Hyperbola
7.)Identify the horizontal and vertical intercepts of the limaçon represented by the equation r=7+3 cos theta ?
Answer:
vertical intercepts: (7, pi/2) and (-7, pi/2)
horizontal intercepts: (10,0) and (-4,0)
8.) Classify the limaçon represented by the equation r=1/2-1/2 sin theta.
A. Cardioid
9.)Write the equation for the graph of the rose curve.
answer C: r=9 sin 4 theta
10.) Write the equation for the graph of the lemniscate.
answer D: r^2=-49 sin 2theta
(pls don't report for me not explain it took a lot of time typing this and im just trying to help people have less stress on their shoulders :p )
Find the 10th term of the following geometric sequence 6,24,96,384,…
Answer:
1572864
Step-by-step explanation:
the nth term of a geoemtric series can be calculated using the following rule : [tex]a_n=a_1(r)^n^-^1[/tex]
where an = nth term, a1 = first term , r = common ratio and n = term position.
here, the first term is 6, the common ratio is 4 and the term position is 10 ( because we want to find the 10th term )
so a1 = 6 , r = 4 and n = 10
using these values we plug them into the rule
recall rule : [tex]a_n=a_1(r)^n^-^1[/tex]
==> plug in a1 = 6 , r = 4 and n - 10
[tex]a_1_0=6(4)^1^0^-^1[/tex]
==> subtract 10 and 1
[tex]a_1_0=6(4)^9[/tex]
==> simplify exponent
[tex]a_1_0=6(262144)[/tex]
==> simplify multiplication
[tex]a_1_0=1572864[/tex]
and we are done!
Note:
the common ration was found by dividing the first term by the next term
If 12 workers can dig a tunnel in 100 days, how long will it take 20 workers to dig the tunnel
Answer:
60 days.
Step-by-step explanation:
This is a proportion question. You compare two ratios. Unfortunately it is an inverse ratio.
12 = k/100 Multiply both sides by 100
1200 = k
20 = k/x Multiply both sides by x
20x = k
20x = 1200 Divide by 20
20x/20 = 1200/20
x = 60 days.
An inverse proportion works by making a constant k. The constant k makes the days shorter when the number of people increases. You should expect that. More people , less time.
Write an equation (a) in slope-intercept form and (b) in standard form for the line passing through (1,8) and perpendicular to 3x + 5y = 1
Step-by-step explanation:
a) 2y = 3x + 4
b) given the perpendicular
3x + 5y = 1
5y = 1 - 3x
y = 1/5 - 3x/5
m¹ = -3/5
perpendicular
m¹m² = -1
-3m²/5 = -1
m² = 5/3
so (1,8)
x¹ = 1 y¹ = 8
m² = (y - y¹)/(x - x¹)
5/3 = (y - 8)/(x - 1)
5x - 5 = 3y - 24
3y - 5x + 5 - 24 = 0
3y = 19 + 5x
HAPPY BIRTHDAY!
You have decided to give your best friend a bag of red
and green marbles for his birthday. Your friend likes
green marbles better than red ones, so the bag has
twice as many green marbles as red. The label on the
bag says it contains a total of 84 marbles.
How many green marbles are in the bag? Write a
system of equations for this problem. Then solve the
problem using any method you like. Be sure to check
your solution
Answer:
56
Step-by-step explanation:
(84÷3) · 2 = x
28 · 2 = 56
Hope that helps!
parts of an algebraic expression separated by plus or minus signs are
Answer: called tthe term of an algebraic expression.
Step-by-step explanation: We know an algebraic expression is a collection or combination of constant and variables of one or more terms, which are separated by the fundamental operations (+, –, × and ÷).Some of the examples of algebraic expression are 7b + 5m, 5x + 3y + 10, 5x/y + 3, x + y + z, etc.Terms of an algebraic expression:Each part of an algebraic expression which are separated by plus sign (+) or minus sign (-) is called the term of an algebraic expression. It’s important to remember that the division sign (÷) or multiplication sign (×) does not separate the terms of an algebraic expression.Examples of algebraic expressions and their terms:
(i) x + 10
We observe that the number of terms used in the expression x + 10 is 2. The terms are x and 10.
(ii) 5m + 2n - 7
We observe that the number of terms used in the expression 5m + 2n – 7 is 3. The terms are 5m, 2n and 7.
(iii) 3a/b
We observe that the number of term used in the expression 3a/b is 1. The term is 3a/b.
(iv) 3xy + 7xz + 2yz - 6
We observe that the number of terms used in the expression 3xy + 7xz + 2yz - 6 is 4. The terms are 3xy, 7xz, 2yz and 6.
) 2abc + 1
We observe that the number of terms used in the expression 2abc + 1 is 2. The terms are 2abc and 1.
Therefore, the algebraic expressions are either simple or compound.
(i) Simple algebraic expressions consist of one term.
(ii) Compound algebraic expressions consist of two or more terms.
Evaluate the expression for m = -3.
-4|5 + m|
Type the correct answer in the box. Use numerals instead of words.
Answer:
The answer is -8
-4 l5 +(-3)l
-4 (2) = -8
Answer: Correct answer is -8
Step-by-step explanation:
Substitute the given value of m into the expression:
-4|5 + (-3)|.
Then evaluate using the order of operations:
-4|5 + (-3)|
= -4|2|
= -4(2)
= -8
Edmentum Answer
Jonah's lunch cost $27.50, he paid $1.65 sales tax. What is the percent of sales tax?
Answer:
6%
Step-by-step explanation:
To get sales tax, you multiply the percentage of sell tax to the total price. In this case, we were looking for the percent of sell tax so we needed to divide the total amount into the amount he payed in sells tax. You will get the decimal value so you will have to multiply it by 100 to get the percent.
=
O FRACTIONS
Fraction multiplication
Multiply. Write your answer as a fraction in simplest form.
3 6
Х
4 5
OL
Х
?
Answer:
Perhaps 2/5, if I understand your question.
Step-by-step explanation:
i don't understand the format of your question:
"3 6
Х
4 5
OL
Х
?"
Is this meant to be (3/6)*(4/5) ??
If so:
(3/6)*(4/5) = (12/30)
(12/30) = 6/15
6/1`5 = 2/5
Select the expression that represents the following problem: A glass hols 1/4 liter of liquid. How many glasses of liquid are in 5 liters
1 glass..........1/4 liter
n glass.......... 5 liters
n = 1 x 5 : 1/4
n = 5 x 4
so there are 20 glasses
what is the area of this triangle?
NEED ANSWERS QUICKLY! CORRECT ONE GETS BRAINLIEST
Write a mixed number between 5 and 6, and then write its reciprocal.
Answer: 11/2
Reciprocal: 2/11
Step-by-step explanation: 11/2 is 5.5 (between 5 and 6) the reciprocal or 11/2 is 2/11
A kite is inscribed in a square with a side length of 9 units. What is the area of the kite? 27. 5 square units 36. 0 square units 40. 5 square units 45. 0 square units.
45. 0 square units.
The area of the kite is 40.5 unit square.
The side of the kite inscribed in square is 9
We have to find the area of the kite
What is the formula for the area of the kite?The area of a kite is,
[tex]A = (d_1d_2) / 2[/tex]
Where [tex]d_1[/tex] and [tex]d_2[/tex] are the diagonals of the kite.
The kite is inscribed in the square, and the sides of the square are 9 units, the diagonals of the kite are both 9 units.
Therefore we get,
[tex]d_1 = 9 units[/tex]
[tex]d_2 = 9 units[/tex]
[tex]A = (9units \times 9units) / 2[/tex]
[tex]A = 81units^2 / 2[/tex]
[tex]A = 40.5 units^2[/tex]
So the third option is correct .
Therefore ,The area of the kite is 40.5 unit square.
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2/5n+ 3/6+ 1/8n
what does it equal
Answer:
[tex]\frac{21}{40}n[/tex] + [tex]\frac{1}{2}[/tex]
Step-by-step explanation:
The important part to understand about this problem is that you need to find a common denominator. You can ONLY add two fractions if they have the same denominator. A way to change the denominator of a fraction is to multiply the numerator and denominator of the fraction by the same number.
So, You want to make the 2/5n and 1/8n to have the same denominator so you can add them. An easy rule of thumb is multiply the one of the fraction by the other fraction's denominator, so in this problem:
[tex]\frac{2 * 8}{5*8} n[/tex] and [tex]\frac{1*5}{8*5}n[/tex]
this comes out as
16/40n and 5/40n
NOW, they have the same denominator and you can add the numerators together to make it one happy fraction
[tex]\frac{16}{40} + \frac{5}{40} = \frac{16+5}{40} = \frac{21}{40}[/tex]
Then, for the 3/6, you can simplify this fraction into:
1/2
This is because if you divide the top and bottom of the fraction by 3 like so:
[tex]\frac{3/3}{6/3}[/tex] (Always make sure you do the same for the top as you do to the bottom)
This comes out as
[tex]\frac{1}{2}[/tex]
Then for the full equation:
[tex]\frac{21}{40} n + \frac{1}{2}[/tex]
What is m ZLMN?
OA) 40°
OB)
B) 60°
OC) 75°
OD) 80°
Answer:
A
Step-by-step explanation:
the exterior angle of a triangle is equal to the sum of the 2 opposite interior angles.
100° is an exterior angle of Δ MLN , then
∠ LMN + 60° = 100° ( subtract 60° from both sides )
∠ LMN = 40°
PLEASE HELP QUICK !!!!
For each of the following functions, list the excluded values from the
domain:
f (x) =
g(x) =
2-3
22 9
h(x) = V16 – 22
Answer:
fx is 4, gx is 3, hx is anything greater than, not equal to, 4.
Hope this helps!
What is 2+2 I think it’s still 2 but I am not sure yet
Answer:
it actually equals 5
Step-by-step explanation:
the reason it equals 5, is because there are 5 variables in there, so because of the addition sign, it becomes 1+1+1+1+1=5. you cannot prove me wrong.
Answer:
the correct answer is 4
Step-by-step explanation:
2 + 2 = 4
hope this helps
have an awesome day -TJ :)
What is the area Of the desk
Answer:
28 ft²
Step-by-step explanation:
area of the desk = (5×4) + (4×2) = 20 + 8 = 28 ft²
Answer:
28
Step-by-step explanation:
5 times 4 = 20
4 times 2= 8
20 plus 8=28
Please Help this is due soon
The table below represents an exponential function.
table represents an exponential function.
What is the interval between neighboring
x-values shown in the table?
1
What is the ratio between neighboring y-values?
4
What is the equation for this pattern?
y = _^x
I only need the last one answered
Answer:
[tex]y = {4}^{x} [/tex]
is the answer
please help if you are good at maths
on the image.
Answer:
x=74
Step-by-step explanation:
if angle ABE = 148. then, angle EBC = 32
and for angle ECB an BEC,
180-32 = 148
148/2 = 74
so, angle ECB and angle BEC = 74
we know, angle BCE and angle CEF are equal because they are alternate angles
so, x = 74
A flat-bottomed ice cream waffle cup is shaped like a 72 mm tall cone with a 42 mm diameter opening at the top, but with the bottom 24 mm of the cone replaced by a flat waffle bottom with a 14 mm diameter. to the nearest square millimeter, what area of waffle does the cone have?
a.) 4002
b.)4398
c.)4552
d.)4157
The area of waffle in the cone is the amount of space covered by the waffle
The cone has 5630 square millimeter of waffle
How to determine the surface area?
The surface area of a cone is calculated using:
A = πr * (r+[tex]\sqrt{[/tex](h^2 + r^2))
For the complete 72 mm tall cone, we have:
Height (h) = 72 mm
Radius (r) = 42 mm/2 = 21 mm
So, the surface area is:
A = πr * (r+[tex]\sqrt{[/tex](h^2 + r^2))
A = 3.142 * 21 * (21+[tex]\sqrt{[/tex](72^2 + 21^2))
Evaluate
A = 3.142 * 21 * (21+75)
A = 6334.272
When the cone is cut at the top, we have:
Height (h) = 24 mm
Radius (r) = 14 mm/2 = 7 mm
So, the surface area is:
A = πr * (r+[tex]\sqrt{[/tex](h^2 + r^2))
A = 3.142 * 7 * (7+[tex]\sqrt{[/tex](24^2 + 7^2))
Evaluate
A = 3.142 * 7 * (7 + 25)
A = 703.808
Calculate the difference (d) between the areas
d = 6334.272 - 2.5*703.808
Evaluate
d = 5630.464
Approximate
d = 5630
Hence, the cone has 5630 square millimeter of waffle
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Can anyone help?! Its for geometry. Please show your work and the answer for x
Bananas cost $0.48 per pound. If you spent $1.84, how many pounds of bananas did you
purchase?
Answer:
3 pounds of bananas
Step-by-step explanation:
1.84 ÷ 0.48 = 3.8333etc
since you can't buy 4 pounds with the money you have its 3 pounds of bananas
In ΔVWX, x = 110 inches, v = 700 inches and ∠W=9°. Find ∠X, to the nearest degree.
The value of ∠X in triangle VWX ( ΔVWX) to the nearest degree is 2 degrees.
The angle X can be found using the cosine rule.
Cosine rulew² = x² + v² - 2xv cos W
w² = 110² + 700² - 2 × 110 × 700 cos 9°
w² = 12100 + 490000 - 154000 cos 9°
w² = 502100 - 154000 × 0.98768834059
w² = 502100 - 152104.004452
w = √349995.995548
w = 591.604593921
w = 591.60 inches
Using sine rule, let's find ∠X
Sine rule
110 / sin X = 591.60 / sin 9°
Therefore,
110 sin 9 = 591.60 sin X
sin X = 110 sin 9 / 591.60
sin X = 110 × 0.15643446504 / 591.60
sin X = 17.2077911544 / 591.60
X= sin⁻¹ 0.02908686807
∠X = 1.66678986656
∠X = 2 degrees
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wich one' is the right answer need help
Answer:
C
Step-by-step explanation:
because density equal all the rest
Math tangent of a circle Also sorry my sister got a hold of it
ASAP!!!
Imagine we drew a line from the centre (2,0) to the point (0,4).
Essentially the line we drew from the centre to that point on the circle is perpendicular to the tangent line slope-wise.
The slope of that line from the centre to the point is -2 based on the slope's equation or formula.
slope = [tex]\frac{y2-y1}{x2-x1}=\frac{4-0}{0-2} =-2[/tex]
Therefore the tangent equation's slope is 1/2 since any perpendicular line's slope is the negative reciprocal of the original line's slope.
By using the point-slope form, we must have the point on the tangent plane (0,4) and the slope we found which is 1/2.
[tex]y - 4 = \frac{1}{2}(x-0)\\ y= \frac{1}{2}x + 4[/tex]
Hope that helps!
531x22 long mutipulcation
Answer:
11,682 the answer is that hope you get a A!
531
×22
+1062
+1062
=11682
Therefore:
531 × 22 = 11,682
100 BRAINLY POINTS!!!
Each point on the scatter plot below represents the number of hours a student studied for a test and the
student's test scores.
Which equation is the closest approximation to the line of best fit?
A. y = -10x + 92
B. y = 6x + 59
C. y = 10x + 45
D. y = 15x + 30
PLEASE HURRY CUH
EXPLAIN YOUR ANSWER
SHOW YOUR WORK
Let's take 1 of x axis from plot (It has three values in y so much useful)
#A
y=-10x+92=-10+92=82#B
y=6x+59=6+59=65#C
y=10x+45=10+45=55#D
y=15x+30=15+30=45A and D are out of radar .Now we need to find most approx between B and C
Go to 2 now.(Same 3 values)
#B
y=12+59=71#C
y=20+45=6565 lies between 60 and 70 ,most approximately equal .
Option C is correct
Answer:
C [tex]y=10x+45[/tex]
Step-by-step explanation:
Line of best fit (trendline) : a line through a scatter plot of data points that best expresses the relationship between those points.
All the given options for the line of best fit are linear equations.
Therefore, we can add the line of best fit to the graph (see attached), remembering to have roughly the same number of points above and below the line.
Linear equation: [tex]y=mx+b[/tex]
(where [tex]m[/tex] is the slope and [tex]b[/tex] is the y-intercept)
From inspection of the line of best fit, we can see that the y-intercept (where x = 0) is approximately 45. So this suggests that option C is the solution.
We can also see that the line of best fit appears to be the same distance from points (3, 75) and (4, 85). So we can use the slope formula with these points to give a rough estimate of the slope of the line of best fit:
[tex]\sf{slope=\dfrac{y_2-y_1}{x_2-x_1}}=\dfrac{85-75}{4-3}=10[/tex]
Therefore, this concurs that C is the solution and that the closet approximation to the line of best fit is [tex]y=10x+45[/tex]
What is the area of rectangle PQRS?
The area of a rectangle is l*w. We have the length as 4.5 in and we can find the width by doing 3+2+4.5 = 9.5 in.
Then, we multiply them. 4.5*9.5 = 42.75 inches²
is it adjacent or vertical
find the value of X
Answer:
Adjacent, x = 60°
Step-by-step explanation:
Adjacent angles are pairs of angles next to each other. Vertical angles make an x shape, are across from each other, and have the same measure. These are adjacent angles.
This is a 90° angles, which is signified by the little red box. To solve for x, make an equation by adding the two angles together and set them equal to 90.
x - 30 + x = 90
2x - 30 = 90
2x - 30 + 30 = 90 + 30
2x = 120
2x/2 = 120/2
x = 60°
Here, the angles x° and (x - 30)° both are complementary angles, so they will add upto 90°, thus we can obtain a equation as ;
[tex]{:\implies \quad \sf x^{\circ}+(x-30)^{\circ}=90^{\circ}}[/tex]
[tex]{:\implies \quad \sf 2x^{\circ}-30^{\circ}=90^{\circ}}[/tex]
[tex]{:\implies \quad \sf 2x^{\circ}=120^{\circ}}[/tex]
[tex]{:\implies \quad \sf x^{\circ}=\dfrac{120^{\circ}}{2}=\bf \boxed{60^{\circ}}}[/tex]
Hence, the required value of x is 60