Answer:
Base = 24 cm or 10cm
Step-by-step explanation:
REMEMBER:
An isosceles triangle ABC with base BC = ‘b' & height AD = ‘h' & its equal sides =13 cm & area = 60 cm²
Using the formulas
[tex]A=\frac{bh_b}{2}[/tex]
[tex]h_b=\sqrt{a^2-\frac{b^2}{4} }[/tex]
There are 2 solutions for [tex]b[/tex]
[tex]b=2\sqrt{2} \frac{A}{\sqrt{a^2+\sqrt{a^4-4A^2} } } =2*\sqrt{2} *\frac{60}{\sqrt{13^2+\sqrt{13^4-4*60^2} } }[/tex] ≈ [tex]10cm[/tex][tex]b=2\sqrt{2} \frac{A}{\sqrt{a^2+\sqrt{a^4-4A^2} } } =2*\sqrt{2} *\frac{60}{\sqrt{13^2-\sqrt{13^4-4*60^2} } }=24cm[/tex]
Less complex:
Area of a triangle = 1/2 * b * h = 60
=> h = 120/b
In right triangle ABD
13² = h² + b² /4 ( by Pythagoras law)
=>169 = 120²/b² + b²/4
=>676 b² = 57600 + b^4
=> b^4 - 676 b² + 57600 = 0
=> b² = 676 +- √(676² - 4*57600) / 2
=> b²= 676 +- √(226576) /2
=> b² = (676 +- 476 )/2
=> b² = 1152/2 , 200 /2
=> b² = 576 , 100
=> b = 24, 10
So, Base = 24 cm or 10cm
PLS HELP FAST!! WILL GIVE BRAINLEIST!
Examine the intersection of these two lines: In photo
Which of the following pairs of angles are
supplementary? Select all that apply.
1 and 2
1 and 3
1 and 4
2 and 3
2 and 4
3 and 4
Answer:
1 & 3
1 & 4
2 & 3
2 & 4
Step-by-step explanation:
Any angles that are next to each other on a straight line will add to 180. If they are across from each other (like 1 & 2 or 3 & 4) those are vertical angles. They are equal.
PLSS HELP ITS ANGLESSS
Answer: D. 66°
Step-by-step explanation:
A triangle has 180° and we already have the numbers for two sides. We must find the answer that adds up to 180°.
A. 43° + 71° + 19°= 133°
B. 43° + 71° + 77°= 191°
C. 43° + 71°+ 114= 228°
D. 43° + 71° + 66°= 180°
With this information, we know that the answer is D. 66°.
I hope this helps! Pls give brainliest :)
Which statements about the arcs and angles are true? select three options. ∠efd ≅ ∠egd ∠egd ≅ ∠ecd arc e d is-congruent-to arc f d marc e f = 60° marc f d = 120°
The true statements about the arcs and angles in circle C are:
∠EFD ≅ ∠EGD.Arc ED ≅ arc FD.m arc FD = 120°.How to analyze the arcs and angles?In Geometry, the sum of the measures of the interior angles in a quadrilateral is equal to 360°. Thus, we have:
m∠G + m∠GDC + m∠DCE + m∠GEC = 360°
60 + 90 + m∠DCE + 90 = 360
240 + m∠DCE = 360
m∠DCE = 360 - 240
m∠DCE = 120°.
Since ∠DFE is an inscribed angle that is subtended by arc DE, we have:
m∠DFE = m∠DCE
m∠DFE = 120
m∠DFE = 1/2 × 120
m∠DFE = 60°.
Therefore, ∠EFD ≅ ∠EGD.
From circle C, we can deduce that side ED is subtended by arc ED and side FD is subtended by arc FD (side ED ≅ side FD). Thus, arc ED ≅ arc FD and m arc FD is equal to 120°.
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Answer:
A C E
took quiz
if y= 2f(g(x)), then d^2y/dx^2=
Use the chain rule to differentiate both sides of the given equation with respect to [tex]x[/tex] :
[tex]y = 2 f(g(x))[/tex]
[tex]\dfrac{dy}{dx} = y' = 2 f'(g(x)) g'(x)[/tex]
Differentiate again with the product and chain rules to get the second derivative :
[tex]\dfrac{d^2y}{dx^2} = y'' = \boxed{2 f'(g(x)) g''(x) + 2 f''(g(x)) g'(x)^2}[/tex]
(D)
Which property allows you to write the expression (3 7i) (8 − 6i) as (8 − 6i) (3 7i)?
Answer:
Commutative property
Mr. Ramirez purchased 20 concert tickets for a total of $225. The concert tickets cost $15 for adults and $10 for children under the age of 12.
(AKS 16) What does the solution to the system of equations represent in the context of the problem? Explain.
Answer:
See below
Step-by-step explanation:
The solution will show the NUMBER Of adult and the NUMBER of child tickets purchased .
a = adult tickets cost = 15 a
c = children's tickets <=== this is equal to 20 - a
cost for children's tickets equals 10(20 - a)
15 a + 10c = 225 rememeber c = 20 -a <===put that in
15 a + 10 ( 20 -a) = 225 solve for a
15a + 200 - 10 a = 225
5 a = 25
a = 5 tix then c = 20 - a = 15 tix
If R = {(x, y): y = x = 2, 4, 6}, find the range of R. , 4 , 6 } , find the range of R.
10 point to Help with this ?
All the transformations for which A and B would be congruent are; Translation, Reflection, and Rotation.
What is congruence transformation?
A congruence transformation is defined as a movement of shape such that it can produce a shape that is congruent to the original.
There are three types of congruence transformation;
1. Translation
2. Reflection
3. Rotation
Given;
Shape B is made by applying a single transformation to shape A.
Hence, All the transformations for which A and B would be congruent are; Translation, Reflection, and Rotation.
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A plant was 8 in. tall last week, and grew x in. this week. 1. Which expression represents how tall, in inches, the plant is now? A. x + 8 B. 8x Explain your thinking. 2. For the expression not chosen, describe a scenario the expression might represent.
Answer:
Step-by-step explanation:
Solution
Total growth (2 weeks) = x + 8
Explanation
During the second week, the plant is already 8 inches tall. It adds x to its total growth. 8x is not the same thing.
Meaning of 8x
For plants, 8x could mean the amount of growth that took place in 8 weeks. x is the amount of growth that takes place in 1 week. You have to think that the growth (x) for each week is the same
which of these tables represents a function
Answer:
A: Table W.
Step-by-step explanation:
A function for tables are where the X-input NEVER repeat.
Graph W. Doesn't have any repeating inputs on the x side
Y can repeat as much as the problem make wants but the x CAN NOT.
each day you read 15 pages in your textbook. use the drop-down menu to choose the correct equation that represents the total number of pages you have read after any number of days.
Answer:
15x
Step-by-step explanation:
assum 1 day you read 15 pages then after X day you reads 15*X=15X
The first two terms of an arithmetic sequence are shown below. 1 2 x+2' x+3' ck to task your mistake. Find the third term of this sequence. Give your answer fully factorised. Watch video Answer > The first two terms of an arithmetic sequence are shown below . 1 2 x + 2 ' x + 3 ' ck to task your mistake . Find the third term of this sequence . Give your answer fully factorised . Watch video Answer >
Answer:
in picture
Step-by-step explanation:
added in the picture
Please Help! What is tan A?
Answer:
[tex]\fbox {tan A = 0.5333}[/tex]
Step-by-step explanation:
tan A = opposite side of ∠A / hypotenuse
tan A = 8 / 15
tan A = 0.5333
Answer:
tan A = perpendicular/ base
tan A = 8/15
tan A=0.5333
Step-by-step explanation:
please mark me as brainlest
Which expressions are equivalent to 8(-10x+3.5y-7)? Select two options.
A. -80x + 24.5y - 56
B. -80x + 28y - 56
C. 80x + 28y + 56
D. 4 (-20x + 7y - 14)
E. -4 (-20x + 7y - 14)
Answer:
B, D
Explanation:
8(-10x+3.5y-7)
= -80x + 28y - 56
4 (-20x + 7y - 14)
= 8(-10x+3.5y-7)
= -80x + 28y - 56
Answer:
B) -80x + 28y - 56
D) 4 (-20x + 7y - 14)
Original Expression:
⇒ 8(-10x+3.5y-7)
⇒ -80x + 28y - 56
Now confirmed that option B is correct when the expression is simplified which makes option A and C not applicable.
For option D:
⇒ 4 (-20x + 7y - 14)
⇒ -80x + 28y - 56
Option E is not correct as:
⇒ -4 (-20x + 7y - 14)
⇒ 80x - 28y + 56
can someone please help meee
Step-by-step explanation:
Well the first 3 you just plug in the value of x which results in.
a. f(0) = 7(0)^2 + 3(0) - 2
f(0) = -2
b. f(2) = 7(2)^2 + 3(2) - 2
f(2) = 7(4) + 6 - 2
f(2) = 28 + 4
f(2) = 32
c. f(-2) = 7(-2)^2 + 3(-2) - 2
f(-2) = 7(4) - 6 - 2
f(-2) = 28 - 8
f(-2) = 20
for the last ones it's essentially the same thing except the value a is not known
d. f(a+1) = 7(a+1)^2 + 3(a+1) - 2
f(a+1) = 7(a^2 + 2a + 1) + 3a + 3 - 2
f(a+1) = 7a^2 +14a + 7 + 3a + 1
f(a+1) = 7a^2 + 17a + 8
c. f(-a) = 7(-a)^2 + 3(a) - 2
f(-a) = 7a^2 + 3a - 2
A six-sided die is thrown three times. What is the probability of getting a prime number on all three rolls?
Answer:
3/216
Step-by-step explanation:
The sample space for this experiment is 6^3 which is 216
there are three prime numbers on die
namely 2 , 3 and 5
so the probability of getting a prime number on all three roles would be
(3/6)^3
Show work, can someone help me out having trouble with this problem
Answer:
Step-by-step explanation:
Formula
a = 9 / (f - 7)
Note
If you are going to try and isolate f, you must take the 7 with it, assuming that getting f to the left hand side will the your first step. It will be mine.
Solution
a = 9 / (f - 7) Multiply both sides by (f - 7) leave the brackets around (f - 7)
a(f - 7) = 9(f - 7)/(f - 7) Combine
a(f - 7) = 9 Remove the brackets
fa - 7a = 9 Add 63 to both sides
fa - 7a + 7a = 9 + 7a Combine
fa = 9 + 7a Divide by a
fa/a = (9 + 7a)/a Simplify
f = (9 + 7a)/a
Answer
f = (9 + 7a)/a
a parallelogram has an area of 160 square meters and a height of 4 meter. what is the length of the base of the parallellogram
Answer:
40
Step-by-step explanation:
the formula for area of a parallelogram is a = bh
you know area (a) = 160 and height (h) = 4, so:
160 = 4 * b
divide both sides of this equation by 4,
b = 40
the base is 40 meters long
If pound of cheese costs $3.43, what is the cost per pound?
PLS HELP
Answer:
$3.43
Step-by-step explanation:
Cost per pound means how much you are paying for one pound of the item. In this question it says a pound of cheese costs 3.43, therefore each pound of cheese costs 3.43. We can also use the equation 3.43x where x represents the amount of pounds you are purchasing. Just multiply the two and you will get a cost for any amount (pounds) of cheese.
What is the length of the hypotenuse? If necessary, round to the nearest tenth.
what is the length of EF if DE=17 and DF=13 in DEF
By the fact that the sum of internal angles in a triangle and the law of the cosines, the possible lengths of the side EF are represented by 16 ≤ EF ≤ 900.
How to determine the possible lengths of a missing side in a triangle
In this question we have a triangle with two known lengths and there many possible solutions for the length of the segment EF. By geometry we know that the sum of the internal angles in a triangle equals 180° and by the law of cosines we have the following expression for the missing length:
EF² = 17² + 13² - 2 · (13) · (17) · cos D
EF² = 458 - 442 · cos D, 0 ≤ θ ≤ 180°
As the cosine is a function bounded between - 1 and 1, then the possible lengths of the side EF are:
16 ≤ EF ≤ 900
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can someone pleasee
find the surface area of the pyramid
Answer:
145
Step-by-step explanation:
mutiply each 6 and 7 twice and add 7x7 from the bottom
Suppose y varies inversely as x², and y = 64 when x = 1/4. Find y when x = 7.
Finding the proportionality constant :
y = k/x²64 = k/(1/4)²k = 4Finding y when x = 7 :
y = 4/(7)²y = 4/49The value of y is 4/49 when x = 7.
[tex]y = \frac{k}{ {x}^{2} } \\ \\ 64 = \frac{k}{ { (\frac{1}{4}) }^{2} } \\ \\ 64 = \frac{k}{ \frac{1}{16} } \\ \\ 64 = 16k \\ \\ k = \frac{64}{16} \\ \\ k = 4.[/tex]
Finding 'y'
[tex]y = \frac{4}{ {7}^{2} } \\ \\ y = \frac{4}{49} .[/tex]
2. analyze the data you gathered about the number of births in the united states in 2011.
a. what do you observe about michigan and florida? justify your conclusion by using the cartogram. (5points)
b. there were 4,008,000 births in the united states during 2011. what proportion of all national births are accounted for by michigan? what proportion of all national births are accounted for by florida? (5 points)
c. suppose a person born during 2011 in the united states is chosen randomly. is the person more likely to have been born in florida or michigan? explain. (5 points)
d. the population of the united states was 308,745,538 in 2011. there were 18,801,310 people in florida and 9,883,640 people in michigan. compute the probability that a randomly selected us resident in 2011 was living in florida. do the same for michigan. which is greater? (5 points)
e. the number of births in a region depends mostly on population size. there are also random fluctuations and regional differences. consider your answers about populations and birth rates. are your answers consistent with this fact? (5 points)
The figures show that the number of births for Florida and Michigan reduced
How to compute the probability?From the data sourced, the number of births in Florida in 2010 was 214519 while in 2011, it was 213237. For Michigan, there was decrease from 114717 to 114159.
When a person born during 2011 in the United States is chosen randomly, the person is more likely to have been born in Florida.
The probability that a randomly selected us resident in 2011 was living in Florida will be:
= 18,801,310/308,745,538
= 0.061
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identify if each function is a polynomial function. justify your answer.
Functions which are polynomials are y=[tex]5x^{4} +x^{2} -8[/tex] ,y=[tex]7x^{3}[/tex] and y=[tex]6^{x}[/tex]
Given Functions : 1) y=[tex]-x^{2} +1/1-2x[/tex] 2)y=[tex]5x^{4} +x^{2} -8[/tex]. 3) y=[tex]7x^{3}[/tex]and g(x)=[tex]6^{x}[/tex].
We need to find which functions are polynomials. We know that polynomials is an expression consisting of indeterminates and coefficients that involves only the operations of addition, subtraction, multiplication and non negative integers .
First function is y=[tex]-x^{2} +1/1-2x[/tex]
The above function is not a polynomial because it has not a variable containing power in whole number and it is in fraction form. Two different polynomials can form numerator and denominator in a fraction.
Second function is y=[tex]5x^{4} +x^{2} -8[/tex]
The above function is a polynomial as it has a variable having power and it is not in fraction also.
Third function is y=[tex]7x^{3}[/tex]
The above function is also a polynomial for the same reason.
Fourth function is g(x)=[tex]6^{x}[/tex].
The above function is also a polynomial.
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What ordered pair is a solution of the equation?
y=-2x-5
[tex] \sf \underline{Answer:}
[/tex]
Pick any value for x, like x = 0, plug it into the equation, and get the value for y. For x = 0,
2(0) + y = 5
y = 5
The ordered pair is (0,5). Find other ordered pairs using the same reasoning.
[tex]2(0) + y = 5[/tex]
[tex]y = 5[/tex]
The ordered pair is (0,5).Solve for B:
1/5b=d+f
Answer:
b=5d+5f
solve for b by simplifying both sides and then isolating the variable.
376
Step-by-step explanation:
Simplify. Rewrite the expression in the form 9^n9
n
9, start superscript, n, end superscript.
(9^{-3})(9^{12})=(9
−3
)(9
12
)
[tex] {3}^{18n} [/tex]
Answer:
9^10
Step-by-step explanation:
khan
The work of a student to solve the equation 4(2x − 4) = 8 + 2x + 8 is shown below: Step 1: 4(2x − 4) = 8 + 2x + 8 Step 2: 6x − 8 = 16 + 2x Step 3: 6x − 2x = 16 + 8 Step 4: 4x = 24 Step 5: x = 6 In which step did the student first make an error and what is the correct step? (5 points) Step 2; 8x − 4 = 2(6 + x + 6) Step 2; 8x − 16 = 16 + 2x Step 3; 6x − 2x = 16 − 8 Step 3; 6x + 2x = 16 + 8
