$695.00 would be your answer :)
Numeric Response 4. In an arithmetic series, the first term is -12 and the 15th term is 40. The sum of the first 15 terms is (Record your answer in the numerical-response section below.)
Your answer should be in.0000
In any artihmetic sequence, consecutive terms differ by a fixed constant c. So given the first term a, the second term is a + c, the third terms is a + 2c, and so on, up to the n-th term a + (n - 1)c.
If the 15th term is 40, then
40 = -12 + (15 - 1) c ==> c = 52/14 = 26/7
We can then write the n-th term as
-12 + (n - 1) 26/7 = (26n - 110)/7
The sum of the first 15 terms is then
[tex]\displaystyle \sum_{n=1}^{15}\frac{26n-110}7 = \frac{26}7\sum_{n=1}^{15}n - \frac{110}7\sum_{n=1}^{15}n = \boxed{210}[/tex]
Another way to compute the sum: let S denote the sum,
S = -12 - 58/7 - 32/7 + … + 228/7 + 254/7 + 40
Reverse the order of terms:
S* = 40 + 254/7 + 228/7 + … - 32/7 - 58/7 - 12
Notice that adding up terms in the same position gives the same result,
-12 + 40 = 28
-58/7 + 254/7 = 28
-32/7 + 228/7 = 28
so that
S + S* = 2S = 28 + 28 + 28 + … + 28 + 28 + 28
There are 15 terms in the sum, so
2S = 15×28 ==> S = 15×28/2 = 210
The entrance fee to a local waterpark is $34 per person. At the waterpark, you can rent a raft for $1.50 per hour. Which expression is equivalent to the amount it would cost Leah for h hours in the park if she rented a raft?
Answer: 34+1.50h
Step-by-step explanation:
Algebraic Equation:
The entrance fee to the waterpark is the intial cost for Leah to get in the park. The amount of hours that Leah will spend at the park is a variable.
You need to add the intial cost and the variable amounts together.
34+h
You put the h in the equation because you don't know how long Leah will spend on the raft. You will be multiply by the rate per hour for a raft.
34+1.50h
Therefore the cost for Leah is 34+1.50.
34 + 1.50h
Therefore, Leah’s cost is 34 + 1.50h.
The points A,B,C and D divide the line segment AD in the ratio 4:3:1 , respectively , and AD = 72cm . What is the length of BD?
Segment addition postulate states that given points X, and Z, on a line, a point Y, can be located between X, and Z, ony if we have;
XZ = XY + YZ
The length of the segment BD is 36 cm
The reason the above value is correct is as follows:
Known:
The ratio in which the points A, B, C, and D divide the line segment = 4:3:1
The length of segment AD = 72 cm
Required:
The length of BD
Method:
Calculate the length of BC and CD and add their values to get BD
Solution:
Let the ratios be given unit proportions of the segment AD such that we have;
AB = 4 units
BC = 3 units
CD = 1 unit
By segment addition postulate, we have;
AD = AB + BC + CD
∴ AD = 4 units + 3 units + 1 unit = 8 units = 72 cm
∴ 1 unit = 72 cm/8 = 9 cm
1 unit = 9 cm
BD = BC + CD by segment addition postulate
BC = 3 units = 3 × 1 unit
∴ BC = 3 × 9 cm = 27 cm
BC = 27 cm
CD = 1 unit
∴ CD = 9 cm
∴ BD = 27 cm + 9 cm = 36 cm
The length of segment BD = 36 cm
Learn more about segment addition postulate here:
https://brainly.com/question/17015321
Apply the distributive property to factor out the greatest common factor of all three terms. {24c + 36d + 18} =24c+36d+18=24, c, plus, 36, d, plus, 18, equals
Answer:
[tex]6(4c + 6d + 3})[/tex]
Step-by-step explanation:
Given
[tex]{24c + 36d + 18}[/tex]
Required
Apply distributive property
We have:
[tex]{24c + 36d + 18}[/tex]
Factor out 6 (to apply distributive property)
[tex]{24c + 36d + 18} = 6(4c + 6d + 3})[/tex]
Hence, the equivalent is:
[tex]6(4c + 6d + 3})[/tex]
If (5^(k-1))+(5^(k+1)) = m, what is 2*5^k in terms of m?
If [tex]5^k^-^1+5^k^-^1=m[/tex], what is [tex]2*5^k[/tex] in terms of m?
A) 5m
B) 5m÷2
C) 5m÷13
D) 5m÷26
Answer:
5m
Step-by-step explanation:
5^(k-1)+5^(k-1)=m
Going to combine like terms on left:
2×5^(k-1)=m
Law of exponents applied:
2×5^k×5^(-1)=m
Reciprocal:
2×5^k×1/5=m
Multiply 5 on both sides to obtain the requested:
2×5^k=5m
Write (25x^2 + 30x + 12) in the form (ax + b)^2 + c.
Answer:
25 x^2 + 30 x + 12
Parcelas
Plots
Parcelas
Figura geométrica
parabola
Formas alternativas
x (25 x + 30) + 12
(5 x + 3)^2 + 3
5 x (5 x + 6) + 12
Raíces complejas
x = -1/5 i (sqrt(3) + -3 i)
x = 1/5 i (sqrt(3) + 3 i)
Step-by-step explanation:
How many hundred thousands 90 ten thousands
pls hurry
Answer:
0.9
Step-by-step explanation:
100,000 in 90,000
Write the following statement in equation form using variables x and y. "Sum of two numbers is 15 and difference is 11.
Answer:
see explanation
Step-by-step explanation:
Using x and y to represent the 2 numbers with x > y , then
x + y = 15 → (1)
x - y = 11 → (2)
Adding the 2 equations term by term to eliminate y
2x = 26 ( divide both sides by 2 )
x = 13
Substitute x = 13 into (1)
13 + y = 15 ( subtract 13 from both sides )
y = 2
The 2 numbers are 13 and 2
One of the angles of a triangle is 110° and the other two angles are equal.What is the measure of each of these equal angles?
Answer:
x = 35
Step-by-step explanation:
Let x be the one of the other angles
X is also the third angle since we know they are equal
The sum of the angles of a triangle is 180
110+x+x = 180
110 +2x= 180
2x = 180-110
2x= 70
Divide by 2
2x/2 = 70/2
x = 35
Answer:
[tex]x = 35 \degree[/tex]
Step-by-step explanation:
Let the unknown angle be x
Unknown Angles are equal to each other so,
[tex]x + x + 110 = 180[/tex]
sum of the interior angles in a triangle is 180°
[tex]2x + 110 = 180 \\ 2x = 180 - 110 \\ 2x = 70 \\ \frac{2x}{2} = \frac{70}{2} \\ x = 35 \degree[/tex]
Solve for the following. Type your answer using digits. A rectangle with a length ofx−4 and a width of 8 has a perimeter of 34. The value of x is .
Answer:
length = 13
Step-by-step explanation:
length =x-4
width = 8
perimeter =2( x-4) + 2× 8 = 34
= 2x - 8 + 8 =34
= 2x =34
= x = 17
Answer:
x = 13
Step-by-step explanation:
The opposite sides of a rectangle are equal, then
2(x - 4) + 2(8) = 34 ← distribute parenthesis and simplify left side
2x - 8 + 16 = 34
2x + 8 = 34 ( subtract 8 from both sides )
2x = 26 ( divide both sides by 2 )
x = 13
10.5125 rounded to the nearest cent plz help me ty <3
Answer: your answer should be 10.5130
Step-by-step explanation:
Combine like terms in the given polynomial. Then, evaluate for x = 4, y = – 2.
xy – 2xy + 3x2 y — 4x y2 + 2xy2
3x2 y + 2xy2 – xy; – 56
C - xy – 2xy2 + 3x2y; – 56
Cx? y2 – 2; 62
C
– 2x y2 + 3x2y – xy; – 120
Need explanation please
Answer:
- 2 x y^2+3 x^2 y -xy
-120
Step-by-step explanation:
xy – 2xy + 3x^2 y — 4x y^2 + 2xy^2
Combine like terms
xy – 2xy + 3x^2 y — 4x y^2 + 2xy^2
- x y+3 x^2 y - 2 x y^2
Let x = 4 y = -2
-(4)(-2) +3(4)^2 (-2) -2(4)(-2)^2
Exponents first
-(4)(-2) +3(16) (-2) -2(4)(4)
Multiply
+8 -96-32
Add and subtract
-120
$108.75 for working 15 hours as a holiday helper wrapping gifts. At this rate, how much money will she earn if she works 18 hours the next week. Explain.
Algebra 1 need help ASAP
Answer:
see explanation
Step-by-step explanation:
Given
10 - 3x < x + 30 ( subtract x from both sides )
10 - 4x < 30 ( subtract 10 from both sides )
- 4x < 20 ( divide both sides by - 4 and flip the sign )
x > - 5
1. 6/5 x 3/4
2. 2/3 x 8/5
3. 5/2 x 4/3
Answer:
hope this might help you
Help anyone can help me do this question,I will mark brainlest.
Answer:
8 cm
Step-by-step explanation:
AM = MC = BM = (1/2) BC => AM , MC , BM = 5, => BC = 10apply pytago => (AC ^ 2) + (AB ^ 2) = (BC ^2)AB = [tex]\sqrt{BC ^2 - AC ^2}[/tex] = [tex]\sqrt{10 ^2 - 6 ^ 2}[/tex] = 8 (cm)Answer:
4
Step-by-step explanation:
So first let's write the information we got
Angle BAC = 90 degrees
Midpoint of BC = M
AC = 6cm
Am= 5cm
Also I found MC = BM, since it has a line that represents both lines are same
so to find it we have to Pythagoras theorem (A^2 + B^2 = C^2), well it is question we have the 'A value and C Value', also we need to find the value of B to find the length of MC and BM
A = 5
C = 6
so therefore to find B^2, we have to do the reverse, we don't add but subtract
C^2 - A^2 = B^2
___________________________________________________________
Moving on to Calculation
6^2 - 5^2 = B^2
36 - 25 = B^2
B^2 = 9
B = √9
B = 3
MC and BM Length = 3 cm
____________________________
Now, we know the length we again need to use Pythagoras theorem to solve this.
Since we know
A = 5
B = 3
So..
A^2 + B^2 = C^2
5^2 + 3^2 = C^2
25 - 9 = C^2
C^2 = 16
C = √16
C = 4
Find an equation of the line having the given slope and containing the given point m= - 8, (2,5) The equation of the line is y= (Simplify your answer. Type your answer in slope-intercept form. Use integers or fractions for any numbers in the expression)
Answer:
Equation of line is y = -8x + 21
Step-by-step explanation:
Slope, m = -8
General equation of line:
[tex]{ \boxed{ \bf{y = mx + c}}}[/tex]
At point (2, 5), y = 5 and x = 2:
[tex]{ \tt{5 = ( - 8 \times 2) + c}} \\ { \tt{c = 21}}[/tex]
Therefore:
[tex]{ \sf{y = - 8x + 21}}[/tex]
[tex]{ \underline{ \blue{ \sf{christ \:† \: alone }}}}[/tex]
antara berikut yang manakah faktor perdana bagi 28 A.1 B.4 C.2 D.28
Answer:
C.2
Step-by-step explanation:
Faktor perdana adalah faktor numbor² bagi sesuatu nombor yang juga merupakan nombor perdana.
Faktor nombor 28 adalah 1 ,2, 4 , 7 ,14 dan 28.
Dalam list nombor perdana ini hanya 2 dan 7 merupakan nombor perdana. Maka , jawapan soalan ini adalah 2.
find the missing length for the following trapezoid
Answer:
15 is the answer I think.
help me find x please
Answer:
[tex]3\sqrt{3}[/tex]
[tex]\left(\frac{\left(6\cdot \:\:\:sin\left(30\right)\right)}{sin\left(90\right)}\right)^2+x^2=36[/tex]
Step-by-step explanation:
I need help with VOCAB!!!Please help ASAP
Answer:
SSS postulate
Step-by-step explanation:
its probab;py wrong im sorry
Answer:
SSS Postulate
Step-by-step explanation:
Since both triangles have 3 congruent sides, then
The triangles are congruent by the SSS postulate
Choose which is a statistical question: What are
the ages of the students in this class? or How
many pennies equal 1 dollar? Explain.
The statistical question is; "What are the ages of the students in this class?
What is a statistical question?A statistical question is always aimed at data collection which can subsequently used for analysis and decision making. Statistical questions are asked in the course of research.
Among the two questions, the statistical question is; "What are the ages of the students in this class?
Learn more about statistics:https://brainly.com/question/8058700
#SPJ1
Klog earns $6.30 per hour. He worked 3.5 hours each day Monday through Friday plus 4 on Saturday. How much did he earn altogether?
Answer:
Klog earned $135.45 altogether.
Step-by-step explanation:
Hours
Monday - Friday : 5 days / 3.5 hours
Saturday : 1 day / 4 hours
3.5 · 5 + 4
= 17.5 + 4
= 21.5
Money
$6.30 per hours / 21.5 hours
6.30 · 21.5
= $135.45
a teacher had 23 pupils to her class. all but 7 of them went on an excursion trip and thus were away for the day. how many students remains in the class that day.
Answer:
16
Step-by-step explanation:
If the teacher had 23 but then 7 had to go away for a trip, then all you do is subtract 23 and 7:
23-7= 16
Thus, the teacher had 16 students that day after the 7 went away.
calculate the area of shaded region
Answer:
528 cm squared
Step-by-step explanation:
A parallelogram (slanted shape at the bottom) is essentially the same area as a rectangle.
Therefore, both shapes have the same measurements.
Multiply the length and height of the rectangle to get its area: 22cm×12cm =264cm squared
Since the area of the rectangle corresponds geometrically to the area of the parallelogram, just multiply the area of the rectangle (264cm squared), by 2.
So 264×2, = 528cm squared
Ta da...
Which expression represents the prime factorization of 243?
A ) 3×3×3×3×2
B ) 3×3×3×3×3
C ) 3×3×3×3×2×2
D ) 3×3×3×3×3×3
Answer: B) 3 × 3 × 3 × 3 × 3
Concept:
In factorization, the easiest way is to divide the term multiple times by the least factor each time until the answer is not divisible. Then, multiply all the factors and the remainder together to get the factorization of a term.
Solve:
243 ÷ 3 = 81
81 ÷ 3 = 27
27 ÷ 3 = 9
9 ÷ 3 = 3
3 ÷ 3 = 1
Therefore, the prime factorization of 243 = 3 × 3 × 3 × 3 × 3
Hope this helps!! :)
Please let me know if you have any questions
Answer:
B
Step-by-step explanation:
how could it not be??
a school has 2500 pupils. when 52 boys and 1/9 of the girls are absent, the number of the boys present is equal to the number of girls. how many does doe he school have
a school has 2500 pupils. when 52 boys and 1/9 of the girls are absent, the number of the boys present is equal to the number of girls. how many pupils does the school have ?
Solution :Let the number of boys be x
Data :
Total pupils = 2500
Absent no. of boys and girls = 52 and 1/9
Now,
First of all we need to get the number of girls then add it with the no. of boys absent and then subtract the whole from 2500 to get the required answer.Remaining no of pupils = 2500 - 52 ➝ 2448
Hence, the no. of girls absent = 1/9 of 2448 ➝ 272
Therefore,
Total no. of pupils absent = 52 + 272 ➝ 324
No. of pupils present = 2500 - 324 ➝ 2176
Henceforth, 2176 pupils are present
HELP PLEASE!! ASAP
If triangles ABC and DEF are similar, what is y? Show your work.
If both triangles are similar then ratio of sides will be same.
[tex]\\ \sf\longmapsto \dfrac{12}{14}=\dfrac{y}{21}[/tex]
[tex]\\ \sf\longmapsto 12(21)=14y[/tex]
[tex]\\ \sf\longmapsto 14y=252[/tex]
[tex]\\ \sf\longmapsto y=\dfrac{252}{14}[/tex]
[tex]\\ \sf\longmapsto y=18[/tex]
Answer:
y = 18
Step-by-step explanation:
Since the triangles are similar, the corresponding sides are in proportion, that is
[tex]\frac{BC}{EF}[/tex] = [tex]\frac{AC}{DF}[/tex] , substitute values
[tex]\frac{y}{12}[/tex] = [tex]\frac{21}{14}[/tex] ( cross- multiply )
14y = 252 ( divide both sides by 14 )
y = 18
For a party Justin buys a pizza and cuts it into 24pieces.Marc eats 1/6 of portion of the pizza and claudine eats 1/4 of what remains after both of them have eaten, Sylvia eats 1/3 of the result.Justin gets to eat what is left over what fraction of the pizza did Justin not eat
Answer:
Justin did not eat 7/12 of the pizza
Step-by-step explanation:
Marc eats 1/6 × 24 = 4, 24 - 4 = 20 left over
Claudine eats 1/4 × 20= 5, 20 - 5 = 15 left over
Sylvia eats 1/3 × 15 = 5, 15 - 5 = 10 left over
Justin eats 10.
24 - 10 = 14
Justin did not eat 14/24 = 7/12
Ratio And Rates. Each ratio or rate needs to be a fraction in simples terms 1. 30 ft. To 60.Ft 2. 51 males to 21 females 3. 1,500 meters in 6 seconds 4. $36 for 4 rounds of shrimp
Given:
The ratio and rates:
1. 30 ft. To 60.Ft
2. 51 males to 21 females
3. 1,500 meters in 6 seconds
4. $36 for 4 rounds of shrimp
To find:
The fraction in simple terms for the given ratio and rates.
Solution:
1. 30 ft. To 60.Ft
[tex]\dfrac{30\text{ ft}}{60\text{ ft}}=\dfrac{1}{2}[/tex]
2. 51 males to 21 females
[tex]\dfrac{51}{21}=\dfrac{17}{7}[/tex]
3. 1,500 meters in 6 seconds
[tex]\dfrac{1500\text{ meters}}{6\text{ seconds}}=250\text{ meter/second}[/tex]
4. $36 for 4 rounds of shrimp
[tex]\dfrac{\$ 36}{4}=\$ 9\text{ per round of shrimp}[/tex]
