Calculate the partial sum S for the sequence 243,81,27,....
Answer:363
Step-by-step explanation:
We have to find partial sum for the sequence 243 , 81 , 27 ..... up to 5 terms(S5 given)
The sequence actually is 3^5,3^4.,3^3.....
Therefore first 5 terms are 1) 3^5 I.e. 243
2) 3^4 I.e. 81
3) 3^3 I.e. 27
4)) 3^2 I.e. 9
5) 3^1 I.e. 3
Adding all those no. we get partial sum of first 5 no. of the sequence
So, 243 + 81 + 27 + 9 + 3
= 363
Hope it helps!!!
Answer:
D. 363 is the one
The quantity (t + 4) exceeds 31
Answer:
t > - 27
Step-by-step explanation:
t + 4 > 31. Next, solve for t: t > -27
Answer:
t+4 > 31
t > 27
Step-by-step explanation:
(t + 4) exceeds 31
t+4 > 31
Subtract 4 from each side
t+4-4 > 31-4
t > 27
What is the nth term of the geometric sequence 4, 8, 16, 32, ... ?
Answer:
tn = a*2^(n - 1)
Step-by-step explanation:
a = 4
r = 2
tn= a*2^(n-1)
Try it
t3 = 4*2^(3 -1) Combine the power
t3 = 4 * 2^2 Find 2^2
t3 = 4 * 4 Multiply
t3 = 16 Answer for t3
Answer:
2^(n+1)
Step-by-step explanation:
You don't even need to use algebraic methods or the formula for this; it's just common sense. 4=2^2, 8=2^3, 16=2^4.
4 is the term 1
8 is term 2
2=term # (1) + 1 for 4
3 = term # (2) + 1 for 8
And so on
So it is 2 to the power of (term # + 1)
Help me with this porportional relationship please:
The table shows a proportional relationship.
x y
0 0
2 9
4 18
6 27
Complete the equation that represents the table.
Enter your answer as a decimal in the box.
y = [] x
Answer:
y = 4.5 x
Step-by-step explanation:
If this is a proportional relationship, we can find the slope
m = (y2-y1)/(x2-x1)
m = (27-0)/(6-0)
m = 27/6
m=9/2
The slope is 9/2
The y intercept, where it crosses the y axis is 0
Using the slope intercept form of the equation y=mx+b
y = 9/2 x+0
y =9/2x
It wants the decimal form
y = 4.5 x
Calvin goes shopping over the weekend and buys a new pair of shoes,a T-Shirt, a pair of sunglasses, and a hat that costs $9. The shoes are twice as much as the shirt, and the sunglasses are half as much as the shirt. The total cost of his purchase is $65. How much does each cost?
Let the costs of shoes, t-shirt, and glasses be represented by s, t, g, respectively. The problem statement tells us these relationships:
... s = 2t
... g = t/2
... s +t +g +9 = 65 . . . . . the $9 cost of the hat is added into the total
_____
Solution
Substituting for s and g, we have ...
... 2t +t +t/2 +9 = 65
... (3 1/2)t = 56 . . . . . collect terms
... t = 56/3.5 = 16 . . . . divide by the coefficient of t
The shoes are 2t, so $32.
The t-shirt is t, so $16.
The sunglasses are t/2, so $8.
The hat is $9.
which of the following is true for the graph of the quadratic function f(x)=3(x+2)(×-2)
Answer:
A
Step-by-step explanation:
given y = 3(x + 2)(x - 2) = 3(x² - 4) = 3x² - 12
for the y- intercept let x = 0
f(0) = - 12 → y-intercept is the point (0, - 12) → True
for x-intercepts let y = 0
3(x + 2)(x - 2) = 0
x + 2 = 0 ⇒ x = - 2
x - 2 = 0 ⇒ x = 2
x- intercepts are (- 2, 0) and (2, 0) → not (0, - 12)
since f(x) = 3x² - 12 is symmetric about the y-axis
the vertex is at (0, - 12 ) → not (- 2, 2)
in a sale, normal prices reduced by 10% nathalie bought a pair of shoes in the sale for 54£ what was the original price of shoe
Answer:
60 pounds
-hope this helps
Answer:
£60
Step-by-step explanation:
100% represents the original price of the shoes
then (100 - 10) = 90% of the original price
Divide the cost by 90% to find 1% then multiply by 100 for the original price
original price = [tex]\frac{54}{90}[/tex] × 100 = £60
Use the diagram to find the measurement of each of the angles
Answer:
1. ∠LOQ = 80°
2. ∠LRQ = 40°
3. ∠LBQ = 40°
Step-by-step explanation:
The measure of a central angle (angle that goes to the center of the circle) is EQUAL to the ARC from which it is intercepted. The measure of the angle that is on opposite side, on the circumference, of the circle is HALF of the ARC from which it is intercepted.It is given that ARC QL has a measure of 80.
Central angle from ARC QL (with same measure) are angle LOQ only.Opposite angles (half of measure of ARC QL) from ARC QL (on opposite side on circumference) are angles LRQ and LBQ.1.
m∠LOQ: ∠LOQ is the central angle from ARC QL so it has SAME MEASURE.
∠LOQ = 80°
2.
m∠LRQ: ∠LRQ is the opposite angle from ARC QL so it is HALF of ARC QL.
∠LRQ = [tex]\frac{1}{2}(80)=40[/tex]
∠LRQ = 40°
3.
m∠LBQ: ∠LBQ is also another opposite angle from ARC QL so it is HALF of ARC QL as well.
∠LBQ = [tex]\frac{1}{2}(80)=40[/tex]
∠LBQ = 40°
solve for h
A=1/2 bh
Answer:
2A /b = h
Step-by-step explanation:
A=1/2 bh
We want to isolate h
First we multiply by 2
2A = 2 * 1/2 bh
2A = bh
Then we divide by b to isolate h
2A /b = bh/b
2A /b = h
A ball rolling down an inclined plane travels, in successive seconds, k feet, 2.5k feet, 4k feet, etc… . Find the distance traveled by the ball
Final answer:
To calculate the total distance traveled by the ball in the first four seconds, we sum the distances for each second, yielding 13k feet.
Explanation:
The student has provided a sequence of distances that a ball rolls down an inclined plane, with distances increasing each second. The distances in successive seconds are given by k feet, 2.5k feet, 4k feet, and so on. To calculate the total distance traveled by the ball in the first four seconds, we use the arithmetic sequence formula.
Let's calculate the distance for each second:
1st second: k feet
2nd second: 2.5k feet
3rd second: 4k feet
4th second: By the same pattern it follows that the 4th second should cover 5.5k feet.
To find the total distance, we sum these values:
Total distance = k + 2.5k + 4k + 5.5k = 13k feet.
This is the total distance traveled by the ball in the first four seconds.
If a muffin calls for 1 and 3/4 cups of sugar, how many cups of sugar will be needed if only 1/4 of the recipe is being made?
Answer: 7/16 or .4375
Step-by-step explanation: 1/4 of 1 is 1/4. 1/4 of 3/4 is .1875 which also equals 3/16. Add 1/4 and 3/16 to get 7/16 cups of sugar or 0.4375. Hope this helps!
how much will the interest be for a $500 loan at 6% interest for one year
Answer:
300 dollars of interest
Step-by-step explanation:
5000 (0.06)
300
Answer:
$30
Step-by-step explanation:
You are being asked to figure out simple interest, I think.
Givens
i = ?P = 500r = 6%t = 1 yearFormula
i = P*r*t
Solution
i = 500*6%*16% = 6/100 = 0.06i = 500 * 0.06 * 1i = 30Edit
You want this to be done using a % proportion. Is that correct from what I read in the comments after the question (which I didn't see -- sorry).
6/100 = x/500 That's the proportion. Cross multiply6 * 500 = 100*x Multiply the numbers on the left3000 = 100 x Divide both sides by 1003000/100 = 100x/100 Do the division30 = xSo it comes to the same thing.
Lina invested $7,800 in a mutual fund at a simple interest rate of 4.35%. She earned $1,696.50 in interest. How long (in years) was the money invested?
Answer:
5 years.
Step-by-step explanation:
She earns $339.3 per year on interest rate. So I divided 1,696.50 by 339.3 to get the amount of ears.
Lina invested for 5 years.
What is simple interest?Simple interest is based on the principal amount of a loan or the first deposit in a savings account.The formula to calculate simple interest is Prt, where P is the principle amount, r is the rate and t is the time in years.How to know how long (in years) was the money invested?According to the problem,
Lina invested $7,800 in a mutual fund at a simple interest rate of 4.35%.She earned $1,696.50 in interest.So, we can say $ 1,696.50 is the interest
∴ Prt = 1696.50
⇒ (7800)(4.35/100)t = 1696.50
⇒ t = 5
∴ Line invested for 5 years.
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What is the x-intercept of the line with the equation 1/3x+y=-15
The x-intercept is for y = 0.
substitute y = 0 to the equation of the function:
[tex]\dfrac{1}{3}x+y=-15\\\\\dfrac{1}{3}x+0=-15\\\\\dfrac{1}{3}x=-15\qquad\text{multiply both sides by 3}\\\\\boxed{x=-45}[/tex]
Answer: x-intercept = -45 → (-45, 0).Answer:
(-45,0)
Step-by-step explanation:
I took the test
Find the area of 9.5 and 4.1
Answer:
38.94
Step-by-step explanation:
To find the area, multiply the length times the width. In this case 9.5 times 4.1.
A parabola with vertex (h, k) and a vertical axis of symmetry is modeled by the equation y - k = a(x - h)2. Determine the vertex for a parabola modeled by y = (x − 5)2 + 8
The vertex of the parabola y = (x – 5)² + 8 with a vertical axis of symmetry is the point (5, 8).
Explanation:The question is asking for the vertex of the parabola y = (x − 5)² + 8 which has a vertical axis of symmetry. In the general equation for a parabola, y - k = a(x - h)², the vertex is denoted by the (h, k). So, comparing this with the given parabola equation, we can determine that the h value corresponds to the value inside the brackets in the (x – h)² part of the equation, and the k value corresponds to the term added or subtracted outside the squared term.
For the given equation, y = (x – 5)² + 8, we can see that h = 5 and k = 8. Therefore, the vertex of the parabola is at the point (5, 8).
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Which subtraction expression has the difference 1 + 4i? (–2 + 6i) – (1 – 2i) (–2 + 6i) – (–1 – 2i) (3 + 5i) – (2 – i) (3 + 5i) – (2 + i)
Answer:
(3 + 5i) – (2 + i)
Step-by-step explanation:
(–2 + 6i) – (1 – 2i)
The real parts -2-1 = -3
The imaginary parts 6i--2i = 6i+2i = 8i
(–2 + 6i) – (–1 – 2i)
The real parts -2 +1 = -1
The imaginary parts 6i --2i = 6i+2i =8i
(3 + 5i) – (2 – i)
The real parts 3-2 =1
The imaginary parts = 5i --i = 5i+i = 6i
(3 + 5i) – (2 + i)
The real parts 3-2 =1
The imaginary parts 5i -i = 4i
Answer:
d.(3 + 5i) – (2 + i)
Step-by-step explanation:
In geometry the four sides of a square are all the same length. One side measures (3x+4) and the perimeter of the square is 76. Find the value of X. Hint: First set up an equation to help you solve for X
Answer:
Step-by-step explanation:
We can set up an equation:
4(3x+4)=76
We can distribute the left side and get:
12x+16=76
Subtract 16 from both sides:
12x=60
Divide 12 from both sides:
x=5
Check:
4(3*5+4)
4(15+4)
4(18)
76
So x=5
Miss teng, a school teacher, usually walks at a speed of 0.5 m/s for y km to reach her school on time. On one cloudy day, she decided to walk the y km at a faster speed of w m/s in case it rained. If she reached her school 5 minutes earlier than usual, calculate y.
Answer:
[tex]y=\frac{3w}{10\left(2w-1\right)}[/tex]
Step-by-step explanation:
We are given
Miss Teng normal walk:
speed =0.5 m/s
distance traveled =y km =y*1000
now, we can find time
we know
time = distance / speed
[tex]t_1=\frac{1000y}{0.5}[/tex]
[tex]t_1=2000y[/tex]
Miss Teng walk on cloudy day:
speed =w m/s
distance traveled =y km =y*1000
now, we can find time
we know
time = distance / speed
[tex]t_2=\frac{1000y}{w}[/tex]
If she reached her school 5 minutes earlier than usual
so,
[tex]t_1-t_2=5\times 60 sec[/tex]
[tex]t_1-t_2=300[/tex]
now, we can plug values
[tex]2000y-\frac{1000y}{w}=300[/tex]
now, we can solve for y
we can multiply both sides by w
[tex]2000yw-\frac{1000y}{w}w=300w[/tex]
[tex]2000wy-1000y=300w[/tex]
[tex]1000y\left(2w-1\right)=300w[/tex]
[tex]y=\frac{3w}{10\left(2w-1\right)}[/tex]
Your friend factors the expression 48x-16. Is your friend correct? Explain your reasoning.
Answer:
16(3x - 1)
Step-by-step explanation:
the greatest common factor of 48 and 16 is 16, hence
48x - 16 = 16(3x - 1)
Final answer:
After factoring out the greatest common factor of 16 from the expression 48x-16, the correct factored form is 16(3x - 1). The friend's factorization is correct if this result was obtained, demonstrating the universal application of mathematical rules.
Explanation:
To evaluate if your friend factored the expression 48x-16 correctly, we look for the greatest common factor that both terms in the expression share. Both 48x and 16 are divisible by 16. Factoring out the greatest common factor of 16, we get:
16(3x - 1)
This is the factored form of the expression 48x-16, which shows that your friend is correct if they arrived at this result. This method is an application of the distributive property, which states that a(b + c) = ab + ac. In this case, we take out a '16' from both terms, which is the inverse process - factoring.
Moreover, the principles that apply to factoring expressions are the same regardless of location or time, demonstrating the universality of mathematical rules. Whether we are factoring polynomials or checking arithmetic, using the correct rule and applying it properly is essential.
Help me!! <ABC = ____?
Triangles NPM and ABC are similar by SAS, establishing that angle ABC corresponds to angle NPM. Thus, <ABC = <MNP.
In triangles NPM and ABC, the given information suggests that these triangles are similar by the Side-Angle-Side (SAS) criterion. Specifically, MP = AC, AB = NM, and BC = PN, along with the corresponding equal angles A = M, B = N, and C = P.
The Angle-Angle Similarity Postulate asserts that if two angles of one triangle are congruent to two angles of another triangle, then the triangles are similar. Therefore, triangles NPM and ABC are similar.
The corresponding angles in similar triangles are equal. Hence, angle ABC is equal to angle NPM. Therefore, the correct answer is:
<MNP
This is because angle ABC in triangle ABC corresponds to angle NPM in triangle NPM.
What is the LCD? 7/x^2 +4x +4, 5/4 -x^2
Answer:
x^3 +2x^2 -4x -8
Step-by-step explanation:
The factors of x^2 +4x +4 are (x +2)^2.
The factors of 4 -x^2 are -1(x -2)(x +2).
The least common denominator is the least common multiple of these, excluding the -1 multiplier. That multiple is ...
... (x +2)^2 × (x -2) = x^3 +2x^2 -4x -8
_____
Comment on the minus sign
When the given fractions are expressed using the denominator above, the second one will need to have its numerator sign adjusted. The two fractions are ...
7(x -2)/(x^3 +2x^2 -4x -8)-5(x +2)/(x^3 +2x^2 -4x -8)The LCD or Least Common Denominator for the fractions 7/(x^2 + 4x + 4) and 5/(4 - x^2) is the product of the distinct denominators after factoring, which is (x+2)^2(4 - x^2), given they have no common factors.
The acronym LCD refers to the Least Common Denominator, which in mathematics, is the least common multiple of the denominators of a set of fractions. It is used to find a common denominator so that the fractions can be combined or compared. For the fractions 7/x^2 + 4x + 4 and 5/4 - x^2, the LCD would be the product of the distinct denominators assuming they cannot be factored into common factors. In this case, assuming x^2 + 4x + 4 cannot be further factored (it is a perfect square: (x+2)^2), the denominators are x^2 + 4x + 4 and 4 - x^2 (since we consider x^2 to have a negative coefficient here). Consequently, if there are no common factors, the LCD is (x^2 + 4x + 4)(4 - x^2) or (x+2)^2(4 - x^2).
how do I figure out 221 ÷0.0001
Answer:
221.0001
Step-by-step explanation:
Attempt to look at the number of 0s behind the decimal point, which you add those 0s and the digit number (1) into place
221
0.0001
221.0001
Sally scores 381 points in a game ty scores 262 points how many more points dose sally score than ty
Answer:
119
Step-by-step explanation:
381-262
PQR has medians QM and PM that intersect at Z. If ZM = 4, find QZ and QM.
Answer:
value of QZ = 8 units and QM = 12 units.
Step-by-step explanation:
Given: In triangle PQR has medians QM and PN that intersect at Z.
If ZM = 4 units.
In the figure given below; second median divided the two triangles formed by the first median in the ratio 2:1.
We have to find the value of QZ and QM;
QZ:ZM = 2: 1
⇒ [tex]\frac{QZ}{ZM} = \frac{2}{1}[/tex]
Substitute the value of ZM =4 units and solve for QZ;
[tex]\frac{QZ}{4} = \frac{2}{1}[/tex]
Multiply both sides by 4 we get;
[tex]QZ = 2 \times 4 = 8 units[/tex]
Now, calculate QM;
QM = QZ+ZM = 8 + 4 = 12 units.
Therefore, the value of QZ and QM are; 8 units and 12 units
find the exact value of y
Look at the picture.
Use the Pythagorean theorem to solve h:
[tex]h^2+5^2=7^2[/tex]
[tex]h^2+25=49[/tex] subtract 25 from both sides
[tex]h^2=24\to h=\sqrt{24}[/tex]
ΔADC and ΔCDB are similar. Therefore the sides are in proportion:
[tex]\dfrac{h}{5}=\dfrac{x}{h}[/tex] cross multiply
[tex]5x=h^2[/tex] put the value of h
[tex]5x=(\sqrt{24})^2[/tex]
[tex]5x=24[/tex] divide both sides by 5
[tex]x=4.8[/tex]
y = 5 + x → y = 5 + 4.8 = 9.8
Answer: y = 9.8Or other method. ΔADC and ΔACB are similar. Therefore the sides are in proportion:
[tex]\dfrac{y}{7}=\dfrac{7}{5}[/tex] multiply both sides by 7
[tex]y=\dfrac{49}{5}\\\\\boxed{y=9.8}[/tex]
What is the equation of the line that passes through (-2, 2) and (1, -4)? y = 2x - 2,
y = -2x - 4,
y = -2x - 2,
y = 2x + 4,
The point-slope form of line:
[tex]y-y_1=m(x-x_1)[/tex]
The fomula of a slope:
[tex]m=\dfrac{y_2-y_1}{x_2-x_1}[/tex]
Substitute the coordinates of the points:
[tex]m=\dfrac{-4-2}{1-(-2)}=\dfrac{-6}{1+2}=\dfrac{-6}{3}=-2[/tex]
[tex]y-(-4)=-2(x-1)[/tex] use distributive property
[tex]y+4=-2x+2[/tex] subtract 4 from both sides
[tex]\boxed{y=-2x-2}[/tex]
Answer:
y = -2x-2
Step-by-step explanation:
The line passes through the points (-2, 2) and (1, -4).
The slope of the line is given by
[tex]m=\frac{y_2-y_1}{x_2-x_1}\\\\m=\frac{-4-2}{1+2}\\\\m=\frac{-6}{3}\\\\m=-2[/tex]
The slope intercept form of a line is given by
y = mx +b, where m is the slope and b is the y-intercept.
We have, m = -2. Hence, the equation is
y = -2x + b
Now, use the point (-2,2) to find b
2 = -2(-2) + b
2 = 4 +b
b = -2
Hence, the equation of the line is y = -2x-2
Third option is correct.
A colony of bacterial doubled every week. If the colony began with 40 bacteria, how many bacteria are present after 4 weeks?
Answer:
640 bacteria.
Step-by-step explanation:
Make a chart.
Bacteria Weeks
40 0
80 1
160 2
320 3
640 4
It starts off with 40 bacteria, which means no weeks have passed so far. That is why 40 pairs with 0 rather than 1.
the temperature outside is -5f name the temperature that would make the sum of the two temperatures 0f
Answer:
5f
Step-by-step explanation:
-5+x=0
Add 5 to both sides of the equation.
x=5
Answer:
We need to add 5F to make the sum 0
Step-by-step explanation:
-5 + temperature = 0
Add 5 to each side
-5 + 5 + temperature=0 + 5
temperature = 5
We need to add 5F to make the sum 0
Please explain how I solve this thanks
Answer:
C
Step-by-step explanation:
$4.50 x 4 = $18.00 $6.00 x 2 = $12.00 $18 + $12 = $30
$4.50 + $6.00 = $10.50