Answer:
1.5
Step-by-step explanation:
Answer:
in triangle
tan60°=3/x
√3=3/x
x=(√3×√3)/√3=√3
4. Solve each system of equations.
4x^2 - x - 67y + 146 = 0
x - y = 2
Answer:
(7,5) and (10,8)
Step-by-step explanation:
x = y+2
4(y+2)^2 -(y+2) - 67y + 146 = 0
4(y^2+4+4y) -y - 2 - 67y + 146 = 0
4y^2+16y+16 - 68y + 144 = 0
4y^2 -52y + 160= 0
y^2 - 13y+40 = 0
(y-8)(y-5) = 0
y = 8
y = 5
x = 5+2 = 7
x = 8 + 2 = 10
Find the general indefinite integral. (Use C for the constant of integration.) ∫6√x7dx Evaluate the integral by making the given substitution. (Use C for the constant of integration.) ∫x2√x3+39dx,u=x3+39.
The general indefinite integral of 6 \(\sqrt{(x^7)}\ is\ 4/15(x^15/2) + C\). By making the substitution u = x^3 + 39, the integral of \(x^2\sqrt{(x^3 + 39)}\) dx becomes 1/9\((u^{2/3})\) + C.
To find the general indefinite integral of 6\(\sqrt{(x^7)}\), we can use the power rule for integration, which states that ∫\(x^n\) dx = \((1/(n+1))x^{n+1} + C\), where C is the constant of integration. Applying this rule, we have ∫6\(\sqrt{(x^7)}\) dx = 6∫\((x^7)^{1/2}\) dx = 6 * (2/9)\((x^{7/2})\) + C = 4/15\((x^{15/2})\) + C.
Now, let's evaluate the integral ∫x^2√(x^3 + 39) dx by making the substitution u = \(x^3\) + 39. Taking the derivative of u with respect to x gives du/dx = \(3x^2\). Rearranging this equation, we have dx = (1/3x^2) du. Substituting this back into the integral, we get ∫\(x^2\sqrt{(x^3 + 39)}\) dx = ∫\((x^2)(u^{1/2}) * (1/3x^2)\) du = (1/3)∫\(u^{1/2}\) du.
Integrating u^(1/2) with respect to u using the power rule, we have (1/3) * \((2/3)(u^{3/2}) + C = 2/9(u^{2/3}) + C\). Substituting back u = x^3 + 39, the final result is \(2/9(x^3 + 39)^{2/3} + C\).
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Does tripling the length of time for the investment double the interest earned with
compound?
No, tripling the length of time for the investment does not double the interest earned with compound interest.
Explaining if tripling the length double the interestWhen interest is compounded, the interest earned depends not only on the length of time, but also on the interest rate and the number of compounding periods.
For example, if an investment of $100 earns 5% annual interest compounded annually for 1 year, the interest earned would be:
Interest = $100 x 0.05 = $5
If the same investment is compounded for 2 years instead of 1, the interest earned would be:
Interest = $100 x (1 + 0.05)^2 - $100 = $10.25
As we can see, doubling the length of time for the investment does not double the interest earned with compound interest.
The interest earned depends on the interest rate and the number of compounding periods as well.
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Which side of triangle XYZ is the longest. x=62, y=55, and z=63
Answer: XY should be the answer
Step-by-step explanation: A guess I took and got right
12 people fit comfortably in a 5 x 5 foot square.use this value to estimate of a crowd that is 10 feet deep on both sides of the street along a 1 mil section of a parade route
Answer:
48 people
Step-by-step explanation:
It states that 12 people fit into a 5 x 5 ft² area.
Here, we are given the length and breath of the side, both 5 ft. And from that, we can estimate the area of the place.
Area of a square is gotten by multiplying both sides together, and thus
5 * 5 = 25 ft²
We are told 12 people fit into 25 ft². In order to get the number of people that fit a 10 x 10, we first need to calculate the area.
We already have the length and breadth to be 10 ft each, so
Area = 10 * 10 = 100 ft²
Now, we calculate.
If
12 people fit into 25 ft²
x people will fit into 100 ft²
If we cross multiply, we have
1200 = 25x
We then divide both sides by 25
x = 1200 / 25
x = 48
Therefore, 48 people will fit into a 10 x 10 ft area
Cesar debe confeccionar tres tipos de volantes rectangulares, pero solo recuerda algunas medidas. calcula la medida del lado restante a partir de los datos.
a. Volante 1: Diagonal de 34 cm y lado de 30 cm
b. Volante 2: diagonal de 4 cm y lado de 3 cm
c. Volante 3: Diagonal de 18 cm y lado de 12 cm
Answer:
a. El lado restante = 16 cm.
b. El lado restante = √7 cm
c. El lado restante = 6·√13 cm
Step-by-step explanation:
Debemos calcular la dimensión del otro lado del volante de la siguiente manera;
a. La diagonal = 34 cm
Longitud de un lado = 30 cm
Por lo tanto, según el teorema de Pitágoras, la longitud del lado restante viene dada por la siguiente relación
La longitud del lado restante = √ ((Diagonal) ² - (Longitud del lado dada) ²)
La longitud del lado restante = √ ((34) ² - (30) ²) = 16 cm
El lado restante = 16 cm.
b. La longitud del lado restante = √ ((Diagonal) ² - (Longitud del lado dada) ²)
La longitud del lado restante = √ ((4) ² - (3) ²) = √7 cm
El lado restante = √7 cm
C. La longitud del lado restante = √ ((Diagonal) ² - (Longitud del lado dada) ²)
La longitud del lado restante = √ ((18) ² - (12) ²) = 6·√13 cm
El lado restante = 6·√13 cm.
can someone help me AND explain how they got the answer?
Answer:
g=4
Step-by-step explanation:
this is a 30 60 90 triangle. the hypotenuse is 2x while the shortest side is x. if 8=2x then x must be 4.
PLEASEE HELP.!! ILL GIVE BRAINLIEST.!! *EXTRA POINTS* DONT SKIP:((
Answer:
Step-by-step explanation:
Take the two equations and equal them together (2.35 + 0.25x = 1.75 + 0.40x) 2. isolate x onto one side by canceling out (2.35 (- 1.75) + 0.25x (.25x) = 1.75 (-1.75) + 0.40x (.25x) ) 3. get what X equal (x=4) 4. plug the new value of x (4) into ONE of the equations (2.35 + 0.25(4) ) 5. get your answer (3.35)
23x+5=3-13x how to solve step by step
Step 1: Simplify both sides of the equation.
23x+5=3−13x
23x+5=3+−13x
23x+5=−13x+3
Step 2: Add 13x to both sides.
23x+5+13x=−13x+3+13x
36x+5=3
Step 3: Subtract 5 from both sides.
36x+5−5=3−5
36x=−2
Step 4: Divide both sides by 36.
Answer: −1/18
If x/y + y/x = -1 , find the value of x^3 - y^3
Answer:
0
Step-by-step explanation:
Multiplying the first equation by xy, we have ...
x^2 +y^2 = -xy
Factoring the expression of interest, we have ...
x^3 -y^3 = (x -y)(x^2 +xy +y^2)
Substituting for xy using the first expression we found, this is ...
x^3 -y^3 = (x -y)(x^2 -(x^2 +y^2) +y^2) = (x -y)(0) = 0
The value of x^3 -y^3 is 0.
7700 dollars is placed in an account with an annual interest rate of 5.5%. To the nearest year, how long will it take for the account value to reach 26500 dollars?
116 years it take for the account value to reach 26500 dollars
What is Percentage?percentage, a relative value indicating hundredth parts of any quantity.
Given that 7700 dollars is placed in an account with an annual interest rate of 5.5%.
We need to find the time it take for the account value to reach 26500 dollars
\(A=P(1+r)^{t}\)
A = final amount=26500
P = initial amount (7700)
r = annual interest rate (5.5%)
n = number of times interest is compounded per year
t = time in years
Solving for t, we get:
\(25600=7700(1+5.5/100)^{t}\)
\(25600=7700(1.055)^{t}\)
Divide both sides by 7700
\(25600/7700=1.055^{t}\)
3.32=tlog1.055
3.32=0.02t
t=116 years
Hence, 116 years it take for the account value to reach 26500 dollars
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Need help please with the step by step explanation
Answer:
exponential decay (0,8)
Step-by-step explanation:
A scuba diver descends 80 feet, rises 25 feet, descends 12 feet, and then
rises 52 feet where he will do a safety stop for five minutes before surfac-
ing. At what depth did he do his safety stop?
Answer: That would be 15ft
Special Cases
(Y+3)(y-3)
Answer:
Y^2-9
Step-by-step explanation:
Analyze the diagram below and answer the question that follows.If <1 congruent to <2, what conclusions can you draw about m<3 and m<4?
In geometry, a transversal is a line that intersects two or more other lines. When two or more lines are cut by a transversal, the angles which occupy the same relative position are called corresponding angles .
It is given that <1 = <2
Then m<3 = m<4, since
\(\begin{gathered} <1+m<3=90 \\ <2+m<4=90 \\ <1=<2=x \\ m<3=90-x=m<4 \end{gathered}\)Therefore, m<3 = m<4.
Which quadratic function is best represented by this graph?
A.) f(x)=x^2−6x−8
B.) f(x)=x^2−6x+8
C.) f(x)=x^2+8
D.) f(x)=x^2+6x+8
? Pick one graph
Step-by-step explanation:
There's no graph visible
f(x) is the same as y
Hope this helps!
Jada used `60` pepper slices to make `3` pizzas.
How many does it take to make `6` of Jada's pizzas?
Answer: 120 pepper slices
Step-by-step explanation: Since 6 pizzas is twice as many pizzas as 3 pizzas, you would also double the amount of pepper slices, giving you 120 pepper slices.
120
Step-by-step explanation:Step 1:First, divide 60 and 3
60 ÷ 3 = 20
Step 2:Then, multiply 20 and 6
20 × 6 = 120
How do you know if HL is congruent?
To determine if two triangles are congruent, the following conditions must be met:
All corresponding pairs of vertical angles are equal.All corresponding pairs of alternate interior angles are equal.All corresponding pairs of alternate exterior angles are equal.All corresponding pairs of consecutive interior angles are supplementary.Determining Congruence of Triangle HLTo determine if triangle HL is congruent, you must first compare the lengths of each side. If the lengths of each side are equal, then the triangles are similar. Next, you must compare the angles of each triangle. If the angles of each triangle are equal, then the triangles are congruent. Finally, you must compare the pairs of vertical angles, alternate interior angles, alternate exterior angles, and consecutive interior angles. If all of these pairs are equal or supplementary, then the triangles are congruent. If all three conditions are met, then it can be concluded that triangle HL is congruent.
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Given the circle below with secant EFG and IHJ find the length of EF round to the nearest 10th if necessary
Answer:
EF ≈ 23.3
Step-by-step explanation:
given 2 secants drawn from an external point to the circle.
then the product of the measures of one secant's external part and that entire secant is equal to the product of the measures of the other secant's external part and that entire secant , that is
GF × GE = GH × GI
8 × GE = 10 × (10 + 15) = 10 × 25 = 250 ( divide both sides by 8 )
GE = 31.25
then
EF = GE - GF = 31.25 - 8 = 23.25 ≈ 23.3 ( to the nearest tenth )
How do I give brainliest I forgot whoever lets me know how I will give them it
12. D(-5,-6), E(5,2), F(4,-4), G(-6,-12). Determine wether it as a parallelogram or not
Answer:
d(−5−6)(2.718282)(52)f(4−4)g(−6−12) =0
Step-by-step explanation:
d(−5−6)(2.718282)(52)f(4−4)g(−6−12) =0
PLEASE HELP WITH THIS, ITS FOR A TESTTT
Answer:
The answer is C
Step-by-step explanation:
Distribute first then combine like terms
Jolly Roger Peanut Butter cost $3. 59 for a small jar last year. This year the jar costs $4. 19. What is the inflation rate, to the nearest tenth percent?
The inflation rate is 16.71 %
As we know the inflation rate is given by the percentage error.
We know that the formula for the percentage error:
Percentage Error = [ ( | Measured Value - True Value | ) / True Value ] x 100
Let us assume that A represents the inflation rate of percentage error.
Here, the cost of the Jolly Peanut butter is = $ 3.59
So , the original cost = $ 3.59
The increased cost of Jolly Peanut butter is = $ 4.19
So , the new rate = $ 4.19
Now , the inflation rate is given by the formula of percentage error,
Percentage Error = [ ( | Measured Value - True Value | ) / True Value ] x 100
A = [ ( 4.19 - 3.59 ) / 3.59 ] x 100
A = ( 0.6 / 3.59 ) x 100
A = 0.16713 x 100
A = 16.71 %
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Triangle N L M is reflected over a line to form triangle A B C. Triangle NLM is reflected over the line segment as shown, forming triangle ABC. Which congruency statement is correct? ΔNLM ≅ ΔCAB ΔNLM ≅ ΔCBA ΔNLM ≅ ΔBCA ΔNLM ≅ ΔBAC
Answer:
A
Step-by-step explanation: edge 2021
Hope this helps :)
Answer:
A
Step-by-step explanation:
the line that passes through the given point and has the given slope for (-1,-4), m = -2
Answer:
y = -2x - 6
Step-by-step explanation:
y = -2x + b
-4 = -2(-1) + b
-4 = 2 + b
-6 = b
y = -2x - 6
Gavin and Brianna want to know how far a mountain peak is from their houses. They measure the angles between the line of sight to the peak and to each other’s houses and carefully make the drawing shown. The actual distance between Gavin and Brianna’s houses is 1.5 miles.
a. What is the actual distance of the mountain peak from Gavin’s house? Round your answer to the nearest tenth of a mile.
b. What is the actual distance of the mountain peak from Brianna’s house? Round your answer to the nearest tenth of a mile.
a. The actual distance of the mountain peak from Gavin’s house is 12.2 miles.
b. The actual distance of the mountain peak from Brianna’s house is 12.3 miles.
How to determine the actual distances?In Mathematics and Geometry, the scale factor of a geometric figure can be calculated by dividing the side lengths of the image by the side lengths of the pre-image:
Scale factor = side length of image (new figure)/side length of pre-image (actual figure).
Scale:
0.245 inch = 1.5 miles
Part a.
0.245/1.5 = New distance/Actual distance
0.25/1.5 = 2/Actual distance
Actual distance = (2 × 1.5)/0.245
Actual distance = 12.2 miles.
Part b.
For the actual distance of the mountain peak from Brianna’s house, we have:
Actual distance = (2.015 × 1.5)/0.245
Actual distance = 12.3 miles.
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Missing information:
The question is incomplete and the complete question is shown in the attached picture.
A ship leaves a port located at point a on a bearing of 030°. It sales a distance of 20 km to point B where it changes direction to a bearing of 75°. Then it sells 25 km to reach a port located at point C.
a) Find the distance between a and C.
B)Find the bearing between point C with respect to a
a. The distance between points A and C is 37.42 km.
b. The bearing between point C and point A is found to be 71.48°.
How do we calculate?a)
Segment 1: From point A to point B:
The ship sails a distance of 20 km on a bearing of 030°,
East displacement = 20 km * cos(30°)
= 20 km * (√3/2)
= 10√3 km
Segment 2: From point B to point C:
The ship sails a distance of 25 km on a bearing of 75°.
East displacement = 25 km * cos(75°)
= 25 km * (√3 + 1)/2
= 21.65 km
The total east displacement from point A to C :
Total east displacement = 10√3 km + 21.65 km
= 31.65 km
Distance between A and C = √(20 km)² + (Total east displacement)²
= √20² + (1.65²
≈ √400² + 1000.4225²
≈ √1400.4225 km²
= 37.42 km
b)
North displacement = (20 km * sin(30°)) + (25 km * sin(75°))
= 20 km * (1/2) + 25 km * (√3/2)
= 10 km + (25√3/2)
= 10 km + 21.65 km
= 31.65 km
Bearing of C with respect to A = arctan(31.65 km / Total east displacement)
= arctan(31.65 km / 10√3 km)
= 71.48°
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HELP ASAP!
Find the sum.
2+5+8+...+41
Answer:
56 is pretty sure.
Step-by-step explanation:
answer is up ahead.
Select all of the roots of x3 + 2x2 – 16x– 32.
Answer:
-2,-4,4
Step-by-step explanation:
just did edjunity
The root of the given equation x3 + 2x² - 16x - 32 is -2, -4 and 4.
What is root?Root is defined as a formula or number that, in most cases, represents the answer to an equation. There are some steps which are used to find the root. Divide the supplied number into its prime factors as the first step. Form similar factor pairings in which both factors are equal. This is step two. Take one element from the pair in step three. Calculate the product of the factors you got by taking one from each pair of factors if fourth step.
The equation is as follows: x3 + 2x2 - 16x - 32.
The equation's roots must all be located.
x3 + 2x2 - 16x - 32 = x2(x + 2) after common terms are removed.
- 16 (x + 2) = (x2 - 16)(x + 2)
We are aware that (a2-b2) = (a-b)(a+b)
So, (x2 - 16) = (x - 4)(x + 4)
x3 + 2x2 - 16x - 32 = (x + 2)(x - 4)(x + 4) is the result now.
To get the roots, use the formulas:
= (x + 2) = 0
x = -2 = (x - 4) = 0
x = 4 = (x + 4) = 0
x = -4
Thus, the root of the given equation x3 + 2x² - 16x - 32 is -2, -4 and 4.
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use the root test to determine whether the series is convergent or divergent. [infinity] n = 1 4 1 1 n n2 identify an. evaluate the following limit. lim n → [infinity] n |an| since lim n → [infinity] n |an| ? 1,
In this case, the limit is 0, so the series is indeed convergent.
The Root Test is used to determine the convergence or divergence of a series. and it is used the Root Test, we start by finding the nth root of each term in the series.
In this case, the series is
=> [∞] n = 1 4 1 1 n n²,
so we calculate the nth root of each term:
\(= > (1/n^{2} )^{1/n}\)
Then, we take the limit of this expression as n approaches infinity, to find the value of the root.
If this limit is less than 1, the series is convergent. If the limit is greater than or equal to 1, the series is divergent.
In this case, the limit of \((1/n^{2} )^{1/n}\) as n approaches infinity is 0, which is less than 1. This means that the series is convergent.
To confirm this, we can evaluate the limit of the absolute value of each term as n approaches infinity, using the formula
=> lim n → [∞] n |aⁿ|.
If this limit is finite, then the series is convergent.
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