Hey there!
Simple interest is based on only the original deposit of money, which in this case is $500.
To find 5.6% of 500, we can multiply it by the decimal that represents that part of a whole: 0.056.
[tex]500 \times 0.056 = 28[/tex]
The question asks for how much money is in the account after 8 1/2 years. This means we multiply the interest for 1 year (28) by 8 1/2.
[tex]28 \times 8.5 = 238[/tex]
Lastly, we add the interest to the original deposit.
[tex]500 + 238 = 738[/tex]
The answer is $738.
Hope this helps!
in a parking lot, 43% of the cars have GPS. express this percent as a decimal.
Answer: 0.43
Think of 43% as 43.0%
Move the decimal 2 spots to the left to go from 43.0 to 0.43
Alternatively, use a calculator to find that 43% = 43/100 = 0.43
"percent" means "per 100", so that's why we're dividing over 100.
What is 10 - (a + b)
If A=4.1 And B=5.7
Answer:
The answer is 0.2.
Step-by-step explanation:
10-(a+b)
A=4.1 B=5.7
10-(4.1+5.7)
10-4.1-5.7
10-9.8=
0.2
How do you write 9.7x10^4 (exponent 4) in standard form?
A.0.00097
B.0.000097
C. 97,000
D.970,000
Answer:
C. 97,000
Step-by-step explanation:
9.7x10^4 = 9.7 x 10000 = 97,000
Final answer:
To write 9.7x10^4 in standard form, you multiply 9.7 by 10,000, resulting in 97,000. Therefore, the correct answer is C. 97,000.
Explanation:
To write 9.7x10^4 in standard form, you multiply the coefficient (9.7) by 10 to the power of 4.
Since 10^4 means 10,000, you would perform the calculation 9.7 multiplied by 10,000. Doing this gives you 97,000. Therefore, the correct answer is:
C. 97,000
Here are steps to write numbers in scientific notation or standard form from the examples provided:
To convert the number 4,500 to scientific notation, you move the decimal three places to the left to get 4.5 x 10^3.
The number 2,220,000 would be 2.22 x 10^6 in scientific notation.
A smaller number like 0.0035 would be written as 3.5 x 10^-3.
For 0.7, the scientific notation is 7 x 10^-1.
The number 858.67 would be 8.5867 x 10^2 since the decimal is moved two places to the left.
Which ordered pair is the solution to the system of equations? PLS HELP
−3x+4y=−20y=x−4
(4, 8)
(0, −5)
(−2, −6)
(−4, −8)
Answer:
The correct answer is (−4, −8)
Step-by-step explanation:
You have to substitute!!! :)
−3x + 4y = −20 y = x − 4
-3(4) + 4(8) = -20 8 = 4 - 4
-12 + 32 = -20 8 = 0
20 = 20
−3x + 4y = −20 y = x − 4
-3(0) + 4(-5) = -20 -5 = 0 - 4
0 + 20 = -20 -5 = -4
20 = -20
−3x + 4y = −20 y = x − 4
-3(-2) + 4(-6) = -20 -6 = -2 - 4
6 - 24 = -20 -6 = -6
-18 = -20
−3x + 4y = −20 y = x − 4
-3(-4) + 4(-8) = -20 -8 = -4 - 4
12 - 32 = -20 -8 = -8
-20 = -20
Answer:
(-4,-8)
Step-by-step explanation:
This a system of equation that have two variables x and y and we have two equations that we have to solve simultaneously
−3x+4y=−20 ....(1)
y=x−4 ....(2)
We can substitute equation (2) and (1)
-3x+4y = −20
-3x+4(x−4) = −20
-3x + 4x -16 = -20
x = -4
Now we need to find the value of y
y=x−4 = -4 - 4 = -8
(-4,-8)
[tex]1 - \frac{1}{3} \div \frac{2}{3} [/tex]
Answer:
1/2
Step-by-step explanation:
[tex]\frac{1}{3}[/tex] ÷[tex]\frac{2}{3}[/tex] equals 1/2 so 1 mius that will be 1/2
state if each triangle is a right triangle
Answer:
16. No
18. Yes
20. Yes
Step-by-step explanation:
Because there is a right angle at at least one corner of the triangle.
What degree of rotation is represented on this matrix
Answer:
Option B is correct
the degree of rotation is, [tex]-90^{\circ}[/tex]
Step-by-step explanation:
A rotation matrix is a matrix that is used to perform a rotation in Euclidean space.
To find the degree of rotation using a standard rotation matrix i.e,
[tex]R = \begin{bmatrix}\cos \theta & -\sin \theta \\ \sin \theta & \cos \theta \end{bmatrix}[/tex]
Given the matrix: [tex]\begin{bmatrix}0 & 1 \\ -1 & 0\end{bmatrix}[/tex]
Now, equate the given matrix with standard matrix we have;
[tex]\begin{bmatrix}\cos \theta & -\sin \theta \\ \sin \theta & \cos \theta \end{bmatrix}[/tex] = [tex]\begin{bmatrix}0 & 1 \\ -1 & 0\end{bmatrix}[/tex]
On comparing we get;
[tex]\cos \theta = 0[/tex] and [tex]-\sin \theta =1[/tex]
As,we know:
[tex]\cos \theta = \cos(-\theta)[/tex][tex]\sin(-\theta) = -\sin \theta[/tex][tex]\cos \theta = \cos(90^{\circ}) = \cos( -90^{\circ})[/tex]
we get;
[tex]\theta = -90^{\circ}[/tex]
and
[tex]\sin \theta =- \sin (90^{\circ}) = \sin ( -90^{\circ})[/tex]
we get;
[tex]\theta = -90^{\circ}[/tex]
Therefore, the degree of rotation is, [tex]-90^{\circ}[/tex]
The degree of rotation represented on a matrix is measured in angles, such as degrees or radians.
Explanation:The degree of rotation represented on a matrix is typically measured in terms of angles, such as degrees or radians. In order to determine the degree of rotation on a matrix, you need to identify the angle of rotation.
If the matrix is rotated clockwise, the angle is considered negative (-). If the matrix is rotated counterclockwise, the angle is considered positive (+).
For example, if a matrix is rotated 90 degrees counterclockwise, the degree of rotation would be +90°.
A friend rewrote the expression 5(x+2)as 5x+2. Wrote a few sentences to your friend explaining the error. Then, rewrite the expression 5(x+2)
Answer:
5x+2
Step-by-step explanation:
Ok so the expression 5(x+2) is not 5x+2 because you have to use the distributive property. So with that being said:
5(x+2)=5 times x and 5 times 2
so the realest answer is 5x+10 instead of 5x+2
EXPLANATION: The error in the rewritten expression done by your 'friend' is that he/she did not multiply the five in the parenthesis by ALL terms (meaning numbers and/or variables) as he/she should have done according to the distributive property. In the distributive property, you distribute equally to all numbers and parts in the equation or expression.
Take, For example, 7(x+4). Instead of just multiplying 7 times x in the parenthesis, you would also multiply seven times to four and add that to the end of the expression, making the rewritten expression 7x+28.
So, the correct rewritten expression for this problem is 5x+10.
Nancy also has a mirror that measures 20.32 centimeters long. What is the length of Nancy’s mirror in inches?
A. 1.45
B. 2.03
C. 8
D. 14
Answer:
C: 8.00
Step-by-step explanation:
1 in = 2.54 cm
l = 20.32 × 1/2.54
l = 8.00 in
The length of Nancy’s mirror is 8.00 in.
Consider the function ƒ(x) = 3x2 + 6x + 5.
Write the function in the form of ƒ(x) = a(x – h)2 + k, where a, h and k are constants.
Answer:
f(x) = 3(x + 1)² + 2
Step-by-step explanation:
Use the method of completing the square
3x² + 6x + 5
= 3(x² + 2x) + 5
add/ subtract (half the coefficient of the x-term)² to x² + 2x
= 3(x² + 2(1)x + 1 - 1) + 5
= 3(x + 1)² - 3 + 5
f(x) = 3(x + 1)² + 2 ← in vertex form
A certain drug is made from only two ingredients: compound A and compound B. There are
milliliters of compound A used for every
milliliters of compound B. If a chemist wants to make
milliliters of the drug, how many milliliters of compound A are needed?
Answer:
425 milliliters of compound A are needed
Step-by-step explanation:
We were told that [tex]5[/tex] milliliters of compound A and [tex]6[/tex] milliliters of compound B is needed to make the drug.
This means that each drug contains 11 milliliters of both compounds.
[tex]\frac{935}{11}=85[/tex] milliliters is the volume of each drug.
Therefore the chemist needed [tex]5\times 85=425[/tex] millilirteres of compound A.
In order to find out how much of compound A is needed, we would set up a ratio using the amounts provided of compound A and B. Then, we cross multiply and solve for the unknown amount of compound A needed for the specific quantity of the drug.
Explanation:This problem is about ratios. We know that specific quantities of compound A and compound B are combined to make a certain amount of the drug. However, the quantities of compound A and B are not mentioned in the question. If they were provided, we would set up a ratio equal to the total amount of the drug and cross multiply to solve for the amount of compound A needed.
An example might look something like this: if the drug is made of 2 milliliters of compound A for every 3 milliliters of compound B and we wanted to make 5 milliliters of the drug. You would set it up like this:
2 (Compound A) / 3 (Compound B) = x (Amount of compound A needed) / 5 (Total Amount of drug needed)
Cross multiplying gives us: 2 * 5 = 3 * x
This simplifies to: 10 = 3x
Dividing each side by 3 then gives the amount needed of compound A: x = 3.33 milliliters.
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Find the total cost to the nearest cent. $58 bill; 20% tip
Answer:
$69.60
Step-by-step explanation:
20% of $58 is $11.60. So you add $11.60 + 58 which equals $69.60, so that is the total cost.
Answer:
$69.60
Step-by-step explanation:
The desired amount (total cost) is equivalent to the sum of the bill and 20% of the bill, or, equivalently, 120% of the bill.
1.20($58) = $69.60
The total cost is $69.60, including a 20% tip.
PLEASE ANSWER ASAP
Which table shows a proportional relationship?
b 1 4 5 7 11
c 3 12 15 21 33
p 1 3 5 7 9
q 0 2 4 6 8
r 3 6 10 12 15
s 2 4 6 8 10
x 1 2 3 4 5
y 9 10 11 12 13
Answer:
b
Step-by-step explanation:
olve for x. 3(3x - 1) + 2(3 - x) = 0 x = 3/7 x = -3/7 x = 1/3 x = -1/3
Answer:
x = -3/7
Step-by-step explanation:
We are given the following equation for which we have to solve for x:
[tex]3(3x - 1) + 2(3 - x) = 0[/tex]
So we will start by expanding the equation by multiplying the common factor with the brackets to get:
[tex]9x-3+6-2x=0[/tex]
Arranging the like terms together (variables on one side of the equation and constants on the other side) to get:
[tex]9x-2x=3-6\\\\7x=-3\\\\x=-\frac{3}{7}[/tex]
Therefore, x = -3/7.
order 34 x 10^2,1.2x10^7,8.11×10-^3 and 435 from least to greatest
Answer:
The ascending order is [tex]8.11\times 10^{-3},435, 34\times 10^2, 1.2\times 10^7[/tex]
Step-by-step explanation:
First of all find the exact value of each number.
[tex]34\times 10^2=34\times 100=3400[/tex]
[tex]1.2\times 10^7=1.2\times 10000000=12000000[/tex]
[tex]8.11\times 10^{-3}=\frac{8.11}{1000}=0.00811[/tex]
The fourth number is 435.
Using the above calculation we can easily arrange these numbers form least to greatest.
The ascending order is
[tex]0.00811, 435, 3400, 12000000[/tex]
It can be written as
[tex]8.11\times 10^{-3},435, 34\times 10^2, 1.2\times 10^7[/tex].
Which system of equations has a solution of approximately (1.8,-0.9)
A. 6x-5y=15 and x+2y =0
B. 4x+5y=8 and 6x-5y=15
C.x-2y=4 and 4x+5y=8
D.6x-5y=15 and x-2y=4
A.
6x - 5y = 15
L = 6(1.8) - 5(-0.9) = 10.8 + 4.5 = 15.3
R = 15
L ≈ R
x + 2y = 0
L = 1.8 + 2(-0.9) = 1.8 - 1.8 = 0
L = R
B.
4x + 5y = 8
L = 4(1.8) + 5(-0.9) = 7.2 - 4.5 = 2.7
R = 8
L ≠ R
C.
x - 2y = 4
L = 1.8 - 2(-0.9) = 1.8 + 1.8 = 3.6
R = 4
L ≈ R
4x + 5y = 8
L = 4(1.8) + 5(-0.9) = 7.2 - 4.5 = 2.7
R = 8
L ≠ R
D.
6x - 5y = 15
L = 6(1.8) - 5(-0.9) = 10.8 + 4.5 = 15.3
R = 15
L ≈ R
x - 2y = 4
L = 1.8 - 2(-0.9) = 1.8 + 1.8 = 3.6
R = 4
L ≈ R
Yeah so your answer is gonna be
A.
After testing the approximate values (1.8, -0.9) in the systems of equations, only option A satisfies both equations with the solution approximately equal to (1.8, -0.9).
Explanation:To find which system of equations has a solution of approximately (1.8,-0.9), we need to substitute the x-value into each equation to see if the corresponding y-value is approximately -0.9. Whichever system satisfies both equations with these approximate values will be our answer.
For option A, substituting x ≈ 1.8 into the first equation 6x - 5y = 15 gives us 6(1.8) - 5y ≈ 15. This simplifies to 10.8 - 5y ≈ 15, leading to -5y ≈ 4.2, and y ≈ -0.84, which is close to -0.9. Checking the second equation, x + 2y = 0 with x ≈ 1.8, we get 1.8 + 2(-0.9) = 0, which is true. So, option A is a candidate.For option B, using the same method, we test the first equation 4x + 5y = 8 with the given x-value. Substituting x ≈ 1.8 gives 4(1.8) + 5y ≈ 8, which simplifies to 7.2 + 5y ≈ 8. Solving for y does not give us a value close to -0.9.Option C and D will also not yield the approximate y-value of -0.9 when substituting x ≈ 1.8 into their respective equations.Therefore, the correct answer is option A, as it satisfies both equations with the solution approximately equal to (1.8, -0.9).
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Find the sale price of each item. Round to two decimal places when necessary. 8. Original price: $45.00; Markdown: 22% 9. Original price: $89.00; Markdown: 33% ___________________________________ ___________________ 10. Original price: $23.99; Markdown: 44% _______________________________ 11. Original price: $279.99, Markdown: 75% eh, might aswell do the last question too. sorry! :) 12. How can you determine the sale price if you are given the regular price and the percent of markdown?
Answer:
8) Sale price : 45* (100%-22%)= 45* 78/100= 35,1 $
9) 89* ( 100%-33%)= 89*67/100=59,63 $
10) 23,99* (100%-44%)= 13,43 $
11) 279,99*25/100= 69,99 $
12) Sell price= regular price* ( 100%- Markdown)
Step-by-step explanation:
What is the probability of an individual being born on Feb.28?
Answer:
1/365 (or 1/366 in the case of a leap year.)
find the exact value of y
ΔABC and ΔACD are similar. Therefore the sides are in proportion:
[tex]\dfrac{y}{7}=\dfrac{7}{6}[/tex] multiply both sides by 7
[tex]y=\dfrac{49}{6}\\\\\boxed{y=\dfrac{1}{6}}[/tex]
what is the value of y?
Answer: x=12, y=30
Step-by-step explanation: 180=40+5x+2y+20, 140=5x+2y+20, 120=5x+2y, 60+60=120, so 5*12=60, and 2*30=60
The value of y is determined by solving the algebraic equation presented, which after simplifying and isolating y, gives us a value of y equal to 3200.
Explanation:To find the value of y, we can use the given equations and perform the necessary algebraic manipulations. The question appears to contain a regression analysis problem where ŷ, read as 'y hat', represents the estimated value of y. This value is obtained from the regression line, which helps in making predictions about y based on corresponding values of x.
Here are the steps to solve the provided equations:
Begin by simplifying the equation with constants and coefficients next to y:
[tex]16x - (8x + 6) =90[/tex]
Answer:
x=12
Step-by-step explanation:
16x - (8x + 6) =90
The first step is to distribute the - sign
16x -8x -6 =90
Now we combine the like terms
8x-6 = 90
Add 6 to each side
8x-6+6 = 90+6
8x = 96
Divide each side by 8
8x/8 = 96/8
x =12
HELP you purchase a car using a $22,000 loan with a 6% simple interest rate for 5 years
(a) how much interest do you pay your loan? show your work
(b) what is the total amount that you will pay back? show your work
Answer: (a) $6,600
(b) $28,600
Step-by-step explanation:
Interest (I) = Principal (P) x rate (r) x time (t)
I = 22,000(0.06)(5)
= 6,600
Accrued (A) = Principal (P) + Interest (I)
A = 22,000 + 6,600
= 28,600
Anna picked 37 apples . She divided the apples equally among 7 baskets. How many apples are in each basket? How many are leftover?
Question
Anna picked 37 apples . She divided the apples equally among 7 baskets. How many apples are in each basket? How many are leftover?
Answer:
2Step-by-step explanation:
37 : 7 = 5 (2 left over)
check
(7 * 5) + 2 = 37
better solution in the picture
Answer:
5 apples in each basket with 2 left over
Step-by-step explanation:
37/7 =5 R 2
brainliest pls
Alba travels between the two mile markers shown and then finds her average speed in miles per hour. Select the three equations that represent this situation.
Alba travels between the two mile markers shown and then finds her average speed in miles per hour.
Select the three equations that represent this situation.
210 miles=3.5 hours×speed
speed/210 miles=3.5 hours
3.5 hours=210 miles/speed
speed=210 miles/3.5 hours
Answer:
210 miles=3.5 hours×speed
3.5 hours=210 miles/speed
speed=210 miles/3.5 hours
I Honestly Juat Guessed
Answer:
210 miles=3.5 hours×speed
3.5 hours=210 miles/speed
speed=210 miles/3.5 hours
Hope this helps =]
PLEASE HELPP!
The students at Midtown Middle school sold flowers as a fundraiser in September and October.
In October, they charged $1.50 for each flower. The October price was a 20% increase of the September price.
Part A:
What was the price of the flowers in September?
Part B:
The seventh-grade class earned 40% of the selling price of each flower.
In September, they sold 900 flowers.
In October, they sold 700 flowers.
Did they earn more money in September or October?
How much more?
Answer:
$1.25
September
$30
Step-by-step explanation:
Let's take this a step a time.
First we need to find how much the price of the flowers were in September.
We know that each flower cost $1.50 on October.
The October price was a 20% increase of the September price.
To calculate for the price of the flowers on September, we can solve it like this:
Let x = Price during September
1.2x = 1.50
We used 1.2 because the price of $1.50 is 120% of the original price.
Now we divide both sides by 1.2 to find x.
[tex]\dfrac{1.2x}{1.2}=\dfrac{1.5}{1.2}[/tex]
x = 1.25
The price of the flowers during September was $1.25 each.
Now the 7th grade class earned 40% of the selling price of each flower.
40% = 0.40
To find how much they made on each month, we simply multiply the percentage to the price and the number of flowers sold.
September = 0.40 x 1.25 x 900
September = 0.5 x 900
September = $450
Now for October.
October = 0.40 x 1.50 x 700
October = 0.6 x 700
October = $420
The 7th Graders earned more on September.
They earned $30 more on September than October.
write the equation (-3,6) m=1/2 in standard form
Answer:
x - 2y = -15
Step-by-step explanation:
Given: m = 1/2 and (-3, 6)
We are given slope and a point.
The equation of the line y - y1 = m (x - x1)
y - 6 = 1/2 (x - (-3))
y - 6 = 1/2 (x + 3)
y - 6 = 1/2x + 3/2
1/2x - y = -6 - 3/2
1/2x - y = -15/2
Taking LCD as 2, we get
x - 2y = -15
Thank you.
Express the number 220 as the sum of four numbers that form a geometric progression such that the third term is greater than the first by 44.
Answer:
Step-by-step explanation:
The first four terms of geometric series is:
[tex]a,ar,ar^2,ar^3[/tex]
Since, we have given information that the third number is greater than 44 that means:
[tex]ar^2=a+44[/tex]
Above equation can be rewritten as:
[tex]a(r^2-1)=44[/tex]
Now, using:
[tex]a^2-b^2=(a+b)(a-b)[/tex]
Here, a=r,b=1
[tex]a(r+1)(r-1)=44[/tex] (1)
The sum of first four terms is:
[tex]a+ar+ar^2+ar^3=220[/tex]
[tex]a(1+r+r^2+r^3)=220[/tex]
[tex]a(1(1+r)+r^2(1+r))=220[/tex]
[tex]a((1+r)(1+r^2))=220[/tex] (2)
Divide equation (2) by (1) we get:
[tex]\frac{r^2+1}{r-1}=\frac{220}{44}[/tex]
[tex]r^2+1=5r-5[/tex]
[tex]\Rightarrow r^2-5r+6=0[/tex]
[tex]\Rightarrow r^2-3r-2r+6=0[/tex]
[tex]\Rightarrow r(r-3)-2(r-3)=0[/tex]
[tex]\Rightarrow (r-2)(r-3)=0[/tex]
[tex]\Rightarrow r=2,3[/tex]
CASE1: When r=2 in [tex]ar^2=a+44[/tex]
[tex]a(4)=a+44[/tex]
[tex]3a=44[/tex]
[tex]a=\frac{44}{3}[/tex]
CASE2:When r=3 in [tex]ar^2=a+44[/tex]
[tex]a(3)^2=a+44[/tex]
[tex]\Rightarrow 9a=a+44[/tex]
[tex]\Rightarrow 8a=44[/tex]
[tex]\Rightarrow a=\frac{44}{8}=\frac{11}{2}[/tex]
The series becomes:
From CASE1: [tex]\frac{44}{3},\frac{44\cdot 2}{3},\frac{44\cdot 2^2}{3},\frac{44\cdot 2^3}{3}[/tex]
[tex]\Rightarrow \frac{44}{3},\frac{88}{3},\frac{176}{3},\frac{352}{3}[/tex]
From CASE2: [tex]\frac{11}{2},\frac{11\cdot 3}{2},\frac{11\cdot 3^2}{2},\frac{11\cdot 3^3}{2}[/tex]
[tex]\Rightarrow \frac{11}{2},\frac{33}{2},\frac{99}{2},\frac{297}{2}[/tex]
A geometric progression is characterized by a common ratio.
The terms of the progression are: [tex]\mathbf{T_n =5.5, 16.5, 49.5,148.5}[/tex] or [tex]\mathbf{T_n =\frac{44}{3}, \frac{88}{3}, \frac{176}{3},\frac{352}{3}}[/tex]
The given parameters are:
[tex]\mathbf{S_4 = 220}[/tex]
[tex]\mathbf{T_3 = T_1 + 44}[/tex]
The third term is represented as:
[tex]\mathbf{T_3 = ar^2}[/tex]
The first term is:
[tex]\mathbf{T_1 = a}[/tex]
So, we have:
[tex]\mathbf{ar^2 = a + 44}[/tex]
Subtract a from both sides
[tex]\mathbf{ar^2 - a = 44}[/tex]
Factor out a
[tex]\mathbf{a(r^2 - 1) = 44}[/tex]
Express as difference of two squares
[tex]\mathbf{a(r + 1)(r - 1) = 44}[/tex]
Make r + 1 the subject
[tex]\mathbf{r +1 = \frac{44}{a(r -1)}}[/tex]
Recall that:
[tex]\mathbf{S_4 = 220}[/tex]
This gives:
[tex]\mathbf{a + ar + ar^2 + ar^3 = 220}[/tex]
Factor out a
[tex]\mathbf{a(1 + r + r^2 + r^3) = 220}[/tex]
Factor out r^2
[tex]\mathbf{a(1 + r + r^2(1 + r)) = 220}[/tex]
Rewrite as:
[tex]\mathbf{a(1(1 + r) + r^2(1 + r)) = 220}[/tex]
Factor out 1 + r
[tex]\mathbf{a((1 + r^2)(1 + r)) = 220}[/tex]
Substitute [tex]\mathbf{r +1 = \frac{44}{a(r -1)}}[/tex] in [tex]\mathbf{a((1 + r^2)(1 + r)) = 220}[/tex]
[tex]\mathbf{a((1 + r^2)\times \frac{44}{a(r -1)} = 220}[/tex]
[tex]\mathbf{((1 + r^2)\times \frac{44}{(r -1)} = 220}[/tex]
Divide both sides by 44
[tex]\mathbf{(1 + r^2)\times \frac{1}{(r -1)} = 5}[/tex]
Multiply through by r - 1
[tex]\mathbf{1 + r^2 = 5r - 5}[/tex]
Collect like terms
[tex]\mathbf{r^2 - 5r + 5 +1 = 0}[/tex]
[tex]\mathbf{r^2 - 5r + 6 = 0}[/tex]
Expand
[tex]\mathbf{r^2 - 2r - 3r + 6 = 0}[/tex]
Factorize
[tex]\mathbf{r(r - 2) - 3(r - 2) = 0}[/tex]
Factor out r -2
[tex]\mathbf{(r - 3)(r - 2) = 0}[/tex]
So, we have:
[tex]\mathbf{r = 3\ or\ r = 2}[/tex]
Calculate a using: [tex]\mathbf{a(r^2 - 1) = 44}[/tex]
When r = 3
[tex]\mathbf{a(3^2 -1) = 44}[/tex]
[tex]\mathbf{a(9 -1) = 44}[/tex]
[tex]\mathbf{8a = 44}[/tex]
[tex]\mathbf{a = 5.5}[/tex]
When r = 2
[tex]\mathbf{a(2^2 -1) = 44}[/tex]
[tex]\mathbf{a(4 -1) = 44}[/tex]
[tex]\mathbf{3a = 44}[/tex]
[tex]\mathbf{a = \frac{44}{3}}[/tex]
The nth term of a GP is:
[tex]\mathbf{T_ = ar^{n-1}}[/tex]
So, the terms of the progression are:
[tex]\mathbf{T_n =5.5, 16.5, 49.5,148.5}[/tex]
or
[tex]\mathbf{T_n =\frac{44}{3}, \frac{88}{3}, \frac{176}{3},\frac{352}{3}}[/tex]
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What is the slope of the line?
4x−1=3y+5
Answer:
4/3 or D
Step-by-step explanation:
Let's get this equation into y=mx+b form.
m=slope b=y-int
Subtract 5 from both sides to isolate y on a side.
4x-6=3y
Divide both sides by 3 to isolate y on one side.
(4/3)x-2=y
y=(4/3)x-2
m=4/3
b=-2
So our slope is 4/3
Which of the following is the best definition of a circle?
Answer:
The set of all points on a plane equidistant to a given point
Step-by-step explanation:
"following"?
Answer:
The collection of all points in a plane that are the same distance from a given point.
Step-by-step explanation:
What is the length of Line BC?
The length of Line BC is 10
What is a triangle?A figure bounded by 3 sides and all the internal angles add up to 180 ° is called a triangle.
What are similar triangles?Triangles having the same corresponding angles measures and proportional side lengths are called similar triangles.
How to find the length of the line BC?Considering Δ AXY and ΔABC
∠AXY = ∠ACB (corresponding angles are equal)
∠AYX = ∠ABC (corresponding angles are equal)
∠A is common in both the triangles
∴ We can say the triangles are similar .
Now, let H be the height of ΔABC and h be the height of ΔAYX
So, we can say, [tex]\frac{XY}{BC} = \frac{h}{H}[/tex]
Now, we know that area of the triangle can be found with the help of the formula (1/2)x(base)x(height)So, [tex]\frac{AYX}{ABC} = \frac{7.5}{30}[/tex]
⇒ [tex]{\frac{\frac{1}{2} (XY) h }{\frac{1}{2}(BC) H } = \frac{1}{4}[/tex]
Now, substituting XY = 5 and [tex]\frac{XY}{BC} = \frac{h}{H}[/tex] in the above equation, we get
[tex]\frac{25}{BC^{2} } = \frac{1}{4}[/tex]
⇒ BC² = 100
⇒ BC = ± 10
Since BC is the length , so it cannot be negative.
So, the negative value is rejected.
∴ BC = 10
Option B is correct.
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