Jill and Cheryl took 12 years and 18 years, respectively, to double their money.
What is Algebra?Algebra is the study of mathematical symbols and the rule involves manipulating these mathematical symbols.
Jill invested $500 in an account with a compound interest rate of 6%.
Cheryl invests $600 in an account with a compound interest rate of 4%.
The number of years each doubles their money. Using the relation of 72.
[tex]\rm t = \dfrac{72}{r}[/tex]
where r is the interest rate and t be the time
The time for the Jill will be
[tex]\rm t = \dfrac{72}{6}\\\\t = 12\\[/tex]
The time for the Cheryl will be
[tex]\rm t = \dfrac{72}{4}\\\\t = 18\\[/tex]
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On average, Shawnte drinks of a -ounce glass of water in hour. How much water
does she drink in an hour?
Answer:
a- ounce glass of water.
Three times the sum of a number and 7 is 4.
NO LINKS PLEASE OR ILL REPORT!! 20 POINTS!!!
Write an equation to represent the verbal description.
The difference of six times a number and four times another number is 20.
Answer:
x=6*4y=20
Step-by-step explanation:
the difference = x, six times = 6*, 4 times = 4y, number is 20 = 20
sin^2θtanθ+cos^2θcotθ+2sinθcosθ=tanθ+cotθ
[tex]\text{L.H.S}\\\\=\sin^2 \theta \tan \theta + \cos^2 \theta \cot \theta+2\sin \theta \cos \theta \\\\\\=\sin^2 \theta \cdot \dfrac{\sin \theta}{\cos \theta} + \cos^2 \theta \cdot \dfrac{\cos \theta}{\sin \theta} + 2\sin \theta \cos \theta\\\\\\=\dfrac{\sin^3 \theta}{\cos \theta}+ \dfrac{\cos^3 \theta}{\sin \theta}+ 2\sin \theta \cos \theta\\\\\\=\dfrac{\sin^4 \theta + \cos^4 \theta}{\cos \theta \cdot \sin \theta}+ 2\sin \theta \cos \theta\\\\[/tex]
[tex]=\dfrac{(\sin^2 \theta)^2 + (\cos^2 \theta)^2 }{\cos \theta \sin \theta}+ 2\sin \theta \cos \theta\\\\\\=\dfrac{(\sin^2 \theta + \cos^2 \theta)^2-2\sin^2 \theta \cos^2 \theta}{\cos \theta \sin \theta}+ 2\sin \theta \cos \theta\\\\\\=\dfrac{1-2 \sin^2 \theta \cos^2 \theta}{\cos \theta \sin \theta}+ 2\ sin \theta \cos \theta\\\\\\=\dfrac{1-2\sin^2 \theta \cos^2 \theta+2\sin^2 \theta \cos^2 \theta}{\cos \theta \sin \theta}\\\\=\dfrac 1{\cos \theta \sin \theta}\\\\[/tex]
[tex]=\dfrac{\sin^2 \theta + \cos^2 \theta}{\sin \theta \cos \theta}\\\\\\=\dfrac{\sin^2 \theta}{\cos \theta \sin \theta}+\dfrac{\cos^2 \theta}{\cos \theta \sin \theta}\\\\\\=\dfrac{\sin \theta}{\cos \theta}+\dfrac{\cos \theta}{\sin \theta}\\\\\\=\tan \theta + \cot \theta\\\\=\text{R.H.S}\\\\\text{Proved.}[/tex]
Sam would like to use his extensive stamp collection as collateral for a secured loan. sam has documentation that says his stamp collection is worth $10,525.00. sam's bank has a policy that permits loan officers to lend no more than 82.5% of the value of the collateral. what is the maximum loan amount sam can get from his bank using his stamp collection as collateral? a. $8,683.13 b. $9,700.00 c. $10,525.00 d. $12,382.35 please select the best answer from the choices provided a b c d
Answer:
A on edge 2021
Step-by-step explanation:
I got it correct.
Write the expression in radical form. (1pt)
x 2/7
Write the expression in exponential form.
∛2y
Please show steps I'm so lost
[tex]\\ \rm\dashrightarrow x^{\frac{2}{7}}[/tex]
[tex]\\ \rm\dashrightarrow x^{2(1/7)}[/tex]
[tex]\\ \rm\dashrightarrow \sqrt[7]{x^2}[/tex]
And
[tex]\\ \rm\dashrightarrow \sqrt[3]{2y}[/tex]
[tex]\\ \rm\dashrightarrow 2y^{\frac{1}{3}}[/tex]
Answer:
see below
Step-by-step explanation:
Problem-1:
[tex] {x}^{ \frac{2}{7} } [/tex]
remember that,
[tex]\displaystyle {x}^{ \frac{a}{b} } = \sqrt[b]{ {x}^{a} } [/tex]
here,
a=2b=7hence,
[tex] {x}^{ \frac{2}{7} } = \boxed{\sqrt[7]{ {x}^{2} } }[/tex]
Problem-2:
recall that,
[tex] \sqrt[n]{x} = {x}^{ \frac{1}{n} } [/tex]
therefore,
[tex] \sqrt[3]{2y} = (2y {)}^{ \frac{1}{3} } \implies \boxed{{2 }^{ \frac{1}{3} } {y}^{ \frac{1}{3} } }[/tex]
A cube is a regular prism with square faces. How can you write a simpler version of the surface area formula for a cube?
Answer:
A cube is a rectangular prism where all its sides are the same. The formula to find the surface area of a rectangular prism is A = 2wl + 2lh + 2hw, where w is the width, the l is the length, and the h is the height.
The surface area formula for a cube is 6l²
How to determine the surface area?A cube has the following features:
6 faces of equal areasEach face has equal side lengthThe area of a face of a cube is:
Area = l²
Where l represents the side length
The surface area formula for a cube is then calculated using:
Surface area = 6 * Area of a face
So, we have:
Surface area = 6 * l²
Surface area = 6l²
Hence, the surface area formula for a cube is 6l²
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please help me please
Answer:
Step-by-step explanation: y axis is 6units up (y=+6)
X axis is 2units to the right. (×=+2)
Rachel currently has $836 in a savings account that has earned 4. 5% annual compound interest for the past year. What was Rachel’s beginning balance one year ago if she has made no other deposits during the year?
Rachel's beginning balance one year ago was $800.
What is compound interest?Compound interest is applicable when there will be a change in the principle amount after the given time period.
For example, if you give anyone $500 at the rate of 10% annually then $500 is your principle amount. After 1 year the interest will be $50 and hence principle amount will become $550 now for the next year the interest will be $550, not $500.
Given that,
The current balance is $836 which is the result of compound interest of 4.5 % annually.
The original amount was a priciple amount P on which interest was applied and the final amount $836 made.
Compound interest formula;
A = P[ 1 + RT/100]^T
Where A is the final amount and T is the time period.
Here,
A = 836 , R = 4.5% and T = 1 year.
So,
836 = P[1 + 4.5/100]^1
P = 836/1.045 = $800
Hence "Rachel's beginning balance one year ago was $800".
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Fill in the table using this function rule.
y=15-3x
x y
1:
3:
4:
5:
Answer:
(1,12) ; (2,9) ; (3,6) ; (4,3) ; (5,0)
Step-by-step explanation:
You need to plug the x values into the equation.
Your equation: y=15-3x
Example:
Plug in 1
y=15-3
y=12
Plug in 2:
y=15-3(2)
y=15-6
y=9
Plug in 3:
y=15-3(3)
y=15-9
y=6
Plug in 4:
y=15-3(4)
y=15-12
y=3
Plug in 5:
y= 15-3(5)
y=15-15
y=0
The measure of an angle is 32 degrees . What is the measure of its complementary angle?
Answer:
an angle measuring 32 degrees has a complement that measures (2x-16) degrees. What is the value of x?
Step-by-step explanation:
let me know if its right
what is an equation of the line that passes through the point (-2,-8) and has a slope of 3?
a) y=3x-2
b) y=3x-22
c) y=3x+2
d) y=3x+22
Answer:
y = 3x -2
Step-by-step explanation:
General equation of a line in the slope intercept form is
y = mx + b ,
where m is the slope and b is the y-intercept ( where intercepts the y-axis)
y = 3x + b ,
because is given slope is m = 3
For point (x = -2, y = -8) we have
-8 = 3 (-2) + b
-8 = -6 + b
-8 + 6 = b
-2 = b
The equation of the line that passes through the point (-2,-8) and has a slope of 3 is
y = 3x -2
I need this done quick.
Which is a larger volume, a candle with a height of 6. 3 inches and a radius of 3. 1 inches, or a candle with both a height and a radius of 3. 9 inches?
Select "Growth" or "Decay" to classify each function.
y=(3.5)^t/2
f(x)=1/4(2)^t
y=10(0.99)^t
Answer:
1. Growth
2. Growth
3. Decay
Determine the equation of the circle with radius 99 and center (-1,-8)(−1,−8).
Generally, you'd see the equation of a circle organized in the following format:
[tex](x-h)^2+(y-k)^2=r^2[/tex]
[tex](h,k)[/tex] is the center[tex]r[/tex] is the radiusTo determine the equation given the center and the radius:
Plug both pieces of information into the general equationSimplifySolving the QuestionWe're given:
Radius: 99Center: (-1,-8)Plug the radius and center into the equation as r and (h,k):
[tex](x-(-1))^2+(y-(-8))^2=99^2\\(x+1)^2+(y+8)^2=9801[/tex]
Answer[tex](x+1)^2+(y+8)^2=9801[/tex]
please help asap tysm <33
One angle of an isosceles triangle measures 92°. What measures are possible for the other two angles? Choose all that apply.44 24 76 47
Answer:
44
Step-by-step explanation:
First remmember that all triangles will add up to equal 180 degrees
so we will have to subtract 180 by 92
whitch is 88
Now sence an isoclies are to equal sides we will have to divide 88 by 2
whitch is 44
Making 44 your answer.
The diagram below is used to sort out numbers.
Type each number in the correct location on the diagram.
7 8 9 10
7, 7, 9, 27, 27, are the numbers that we can fill these boxes starting from left.
What is a prime number?A prime number is not a composite number, prime numbers are only divisible by the number itself and one.
An example of a prime number is 2 which is only divisible by 2 and 1 it is also the only even prime number.
The only prime number is 7.
The intersection of prime and odd numbers is 7.
The only odd number is 9.
The intersection of odd and cube numbers is 27.
The only cube number is 27.
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What is the lower quartile of the following data set
53,49,43,59,63,76,40,71,47,66,57,30,48,58,35
The lower quartile is 43.
Determine the number of real solutions each quadratic equation has. y = 12x2 - 9x 4 real solution(s) 10x y = -x2 2 real solution(s) 4y - 7 = 5x2 - x 2 3y real solution(s) y = (-x 4)2 real solution(s)
All the given equations have 2 real solutions except for equation 4 which has only one real root.
What is a quadratic equation?A quadratic equation is the second-order degree algebraic expression in a variable. the standard form of this expression is ax² + bx + c = 0 where a. b are coefficients and x is the variable and c is a constant.
The given quadratic equation
[tex]y = 12x^2 - 9x+ 4[/tex]
where, a = 12, b = -9 and c = 4
x = [tex]-b + \sqrt{b^2 - 4ac} /2a[/tex]
x = [tex]-(-9)+ \sqrt{(-9)^2 - 4(12)(4)} /2(12)[/tex]
x = 1.063 or -0.313
Second Equation
[tex]10x +y = -x^2 +2 \\y = x^{2} +10x - 2[/tex]
where, a = 1, b = 10, c = -2
substitute the values into the equation
x = [tex]-b + \sqrt{b^2 - 4ac} /2a[/tex]
[tex]-10 + \sqrt{10^2 - 4(1)(-2)} /2(1)[/tex]
x = 0.195 or -10.195
Third Equation
[tex]4y - 7 = 5x^2 - x +2 +3y[/tex]
[tex]y = 5x^{2} -x -5[/tex]
where, a = 5, b = -1, c = - 5
x = [tex]-b + \sqrt{b^2 - 4ac} /2a[/tex]
[tex]-(-1) + \sqrt{(-1)^2 - 4(5)(-5)} /2(5)[/tex]
x = 0.905 or -0.55
Fourth Equation
[tex]y = (-x +4)^2 \\y = x^{2} -8x +16[/tex]
where, a = 1, b = -8, c = 16
x = [tex]-b + \sqrt{b^2 - 4ac} /2a[/tex]
x = [tex]-(-8) + \sqrt{(-8)^2 - 4(1)(16)} /2(1)[/tex]
x = 4
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Answer:
y = 12x2 - 9x + 4
✔ no
real solution(s)
4y - 7 = 5x2 - x + 2 + 3y
✔ no
real solution(s)
10x + y = -x2 + 2
✔ two
real solution(s)
y = (-x + 4)2
✔ one
real solution(s)
Step-by-step explanation:
hope this helps:)
A copper wire is submerged in a clear liquid in container A. After a while, the contents of the container changed to look like what is in container B, with a white crystal coating on the copper wire and the liquid turning light blue. Which are indicators that a chemical reaction has occurred? Check all that apply.
formation of a flame
formation of a precipitate
formation of a gas
change in odor
change in color
Answer:
B) formation of a precipitate
E) change in color
Step-by-step explanation:
just did the assignment on e.d.g.e
Answer:
B and E is correct
Step-by-step explanation:
what percent of numbers of the muffins sold were carrot
Melinda kept a record of her spending for the week. she spent $25 to put gas in the car, bought a new shirt for a total of $22.38, played putt-putt golf with some friends that cost $6.95 and paid $38.71 for a few groceries. what was the total of melinda’s expenses for the week? a. $68.24 b. $86.09 c. $91.94 d. $93.04 please select the best answer from the choices provided a b c d
The total of Melinda's expenses for the week is $93.04 option (c) $91.94 is correct.
What is expenses?It is defined as the money spends on the utility, the amount of money is required to buy something in other words it is the outflow of money from the solely earners income or the money incurred by any organization.
Melinda kept a record of her spending for the week as follows:
The amount she spent money to put gas in the car = $25
The amount to buy a new shirt = $22.38
The amount to play putt-putt golf with some friends = $6.95
The amount to buy groceries = $38.71
To calculate the total expenses for the week, we must add all the expenses:
= $25+$22.38+$6.95+38.71
= $93.04
Thus, the total of Melinda's expenses for the week is $93.04 option (c) $91.94 is correct.
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What is the missing value in the table below?
Number of Books
3. $10.00
9. $30.00
18. $60.00
$80.00
Answer:
24 books
Step-by-step explanation:
Books are valued at $10/3 books. 18 books would have a value of (18books)*($10/3books) = $60, and so on.
X books would have a value of X($10/3)=$80
X = ($80)*(3/$10)
X = 24 books
The depth of two lakes is measured at multiple spots. For the first lake, the mean depth is about 45 feet with a mean absolute deviation of 8 feet. For the second lake, the mean depth is about 60 feet with a mean absolute deviation of 27 feet.
Noah says the second lake is generally deeper than the first lake. Do you agree with Noah?
No, I do not agree with Noah because the second lake has greater variability with a higher MAD so even though the mean depth is deeper the data is very spread out away from that mean.
No, I do not agree with Noah. The MAD tells us how deep it is and the 1st MAD is more.
Yes, I agree with Noah. The MAD tells us how deep it is and the second MAD is more.
Yes, I agree with Noah because the first lake has a smaller mean and MAD than the second.
Answer:
Yes, I agree with Noah because the first lake has a smaller mean and MAD than the second
Step-by-step explanation:
Lorne subtracted 6x3 – 2x 3 from –3x3 5x2 4x – 7. use the drop-down menus to identify the steps lorne used to find the difference. 1. (–3x3 5x2 4x – 7) (–6x3 2x – 3) 2. (–3x3) 5x2 4x (–7) (–6x3) 2x (–3) 3. [(–3x3) (–6x3)] [4x 2x] [(–7) (–3)] [5x2] 4. –9x3 6x (–10) 5x2 5. –9x3 5x2 6x – 10
The difference between the polynomial is [tex]\rm 9x^3-5x^2-6x+10[/tex].
What is subtraction?The subtract means to take away from a group or a number of things.
Lorne subtracted 6x3 – 2x + 3 from –3x3 + 5x2 + 4x – 7.
The difference between the expression is;
[tex]\rm ( 6x^3 - 2x + 3 )- (-3x^3 + 5x^2 + 4x - 7)[/tex]
[tex]\rm 6x^3 - 2x + 3 +3x^3 -5x^2 -4x +7\\\\9x^3-5x^2-6x+10[/tex]
Hence, the difference between the polynomial is [tex]\rm 9x^3-5x^2-6x+10[/tex].
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Triangle LMN is similar to triangle OPQ. Find the measure of side PQ. Round your answer to the nearest tenth if necessary.
The measure of PQ if the triangle LMN is similar to triangle OPQ is 69.4
What are similar triangles?Similar triangles are triangles that have equal sides and angles. The ratio of the similar sides is a constant.
According to the triangle given:
PQ/17 = OQ/LM
PQ/17 = 49/12
12PQ = 833
PQ = 69.4
Hence the measure of PQ if the triangle LMN is similar to triangle OPQ is 69.4
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Part A
Construct a circle of any radius, and draw a chord on it. Then construct the radius of the circle that bisects the chord. Measure the angle between the chord and the radius. What can you conclude about the intersection of a chord and the radius that bisects it? Take a screenshot of your construction, save it, and insert the image below your answer.
Part B
Write a paragraph proof of your conclusion in part A. To begin your proof, draw radii OA and OC.
Part C
In this part of the activity, you will investigate the converse of the theorem stated in part A. To get started, reopen GeoGebra.
Draw a circle of any radius, and draw a chord on it. Construct the radius of the circle that is perpendicular to the chord. Measure the line segments into which the radius divides the chords. How are the line segments related? What can you conclude about the intersection of a chord and a radius that is perpendicular to it? Take a screenshot of your construction, save it, and insert the image below your answer.
Part D
Write a paragraph proof of your conclusion in part C. To begin your proof, draw radii OA and OC.
Answer:
All answers are bold and links are real photos
BTW THE PHOTOS ARE IN ORDER OF THE ANSWERS
Brainlyist??
Step-by-step explanation:
Task 1
Part A
Tangent Line
Part B
PHOTO WITH LARGE CIRCLE AND LINE OUT SIDE BUT CONNECTED
Part C
2034.7
PHOTO WITH EQUATION
We calculate the point from the center of the earth to the satellite and because we have the radius we can subtract it getting the distance from the satellite to the earth.
Task 2
Gears
Part A
Approximately 10.47 inches
Part B
300°
Part C
Approximately 125.66 inches
Part D
The distance traveled increases by approximately 62.83 inches
Task 3
Circle Theorems
Part A
PHOTO WITH LINE THROUGH CIRCLE AND ONE 90 DEGREE ANGLE
Part B
Prove OC is perpendicular to AB
We know that ΔAEC≅AED by SSS criteria (SSS criteria is when all three sides of a triangle is equal making them congruent)
To prove this that they apply to the SSS criteria: m∠ADO=m∠BDO m∠ADO=90°=m∠BDO
Part C
A radius is perpendicular to a chord when the chord is equally divided in half by the radius.
PHOTO OF LINE THROUGH CIRCLE AND LINE DISTANCES
Part D
Prove OC is perpendicular to AB
AO=BO because AO and BO are both radii
OD≅OD by reflexive theorem
ΔADO≅ΔBDO because they are both right triangle with the hypotenuse and a side
AB≅BC means that OC is perpendicular to AB
Disclaimer: The images to part A and part C is the same.
Two theorems we are proving are:
Line drawn from the center of the circle to bisect a chord is perpendicular to it.Perpendicular drawn from the center of the circle to a chord, bisects it.How do we solve the given question?Part A: The image is attached
Part B:
Let there be a circle with the center at O. Let AC be a chord. Let OE be a radius of the chord such that OE bisects AC at B, that is, AB = BC.
To prove: A line drawn from the center of the circle to bisect a chord is perpendicular to it.
Construction: We join OA and OB.
Proof:
In ΔOAB and ΔOCB,
OA = OC (Radius of the same circle)
AB = BC (Given, at B, the chord is bisected)
OB = OB (common side)
∴ ΔOAB ≅ ΔOCB [SSS axiom]
∴ ∠OBA = ∠OBC [Common parts of Congruent triangles]
Let ∠OBA = ∠OBC = x.
Since AC is a straight line,
∠OBA + ∠OBC = 180° [Linear pair]
or, x + x = 180°
or, 2x = 180°
or, x = 90°.
∴ ∠OBA = ∠OBC = 90°.
So, we can say that OB ⊥ AC, hence the theorem is proved.
Part C: The image is attached
Part D:
Let there be a circle with the center at O. Let AC be a chord. Let OE be a radius of the chord such that OE is perpendicular to AC at B, that is, AB ⊥ BC.
To prove: A line drawn from the center of the circle perpendicular to the chord bisects it.
Construction: We join OA and OB.
Proof:
In ΔOAB and ΔOCB,
OA = OC (Radius of the same circle)
∠OBA = ∠OBC = 90° (∵ OB ⊥ AC)
OB = OB (common side)
∴ ΔOAB ≅ ΔOCB [RHS axiom]
∴ AB = AC [Common parts of Congruent triangles]
So, we can say that OE perpendicular to the chord AC bisects it, hence the theorem is proved.
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The ratio of rides to games at the fair is 3 to 4. If there are 27 rides at the fair, how many games are there?
Answer: 36
Step-by-step explanation: Ratio 27:36 is also 3:4
Answer:
36 games
Step-by-step explanation:
since the ratio is 3:4 we must get what the original is.
27/3=9
27+9=36
27:36