Based on the calculations, the value of the given mathematical equation is -7.
Given the following data:
[tex]10 + (-n + 6)[/tex]n = 11.To evaluate the given mathematical equation:
How to evaluate an equation.In this exercise, you're required to evaluate the given mathematical equation. Thus, we would substitute the given parameter into the mathematical equation and then simplify as follows:
[tex]10 + (-11 + 6)\\\\10 -11-6\\\\10-17=-7[/tex]
Read more on equations here: brainly.com/question/13170908
The 10th, 4th and 1st term of an A.P are three consecutive find the common ratio of the G.P and the sum of the 6th term, taking the 1st term to be 4
Answer:
Common ratio=1/2
Sum of first 6 terms of an A.P=31.5
Step-by-step explanation:
Let a be the first term and d be the common difference of an A.P
a=4
nth term of an A.P
[tex]a_n=a+(n-1)d[/tex]
Using the formula
[tex]a_4=a+3d=4+3d[/tex]
[tex]a_{10}=a+9d=4+9d[/tex]
According to question
We know that
For G.P
[tex]\frac{a_n}{a_{n-1}}=r[/tex]=Common ratio
[tex]r=\frac{4+3d}{4+9d}=\frac{4}{4+3d}[/tex]
[tex]\frac{4+3d}{4+9d}=\frac{4}{4+3d}[/tex]
[tex](4+3d)^2=\frac{4}{4+3d}[/tex]
[tex]16+9d^2+24d=16+36d[/tex]
[tex]9d^2+24d-36d-16+16=0[/tex]
[tex]9d^2-12d=0[/tex]
[tex]3d(3d-4)=0[/tex]
[tex]d=0, d=4/3[/tex]
Substitute the value of d
When d=0
[tex]r=\frac{4}{4+3d}=\frac{4}{4+0}=1[/tex]
When d=4/3
[tex]r=\frac{4}{4+3\times \frac{4}{3}}=\frac{1}{2}[/tex]
But we reject d=0 because if we take d=0 then the terms are not consecutive terms of G.P
Sum of n terms of an A.P
[tex]S_n=\frac{n}{2}(2a+(n-1)d)[/tex]
Using the formula
Substitute n=6 and d=1/2
[tex]S_6=\frac{6}{2}(2(4)+5\times \frac{1}{2})[/tex]
[tex]S_6=31.5[/tex]
(x + 1)^7
Use Pascal's Triangle and Binomial.Theorem
Answer:
x⁷+7x⁶+21x⁵+35x⁴+35x³+21x²+7x+1
Step-by-step explanation:
(x + 1)⁷: Pascal's Triangle for (a+b)⁷
a₇+7a⁶b+21a⁵b²+35a⁴b³+... + 7a¹b⁶ + b⁷
x⁷+7x⁶+21x⁵+35x⁴+35x³+21x²+7x+1
help help me please I'm not getting brain early plus just to get the answer please help
Answer:
Pearl pale hand
Step-by-step explanation:
Pleaseee helpp answer correctly !!!!!!!!!!!!!!! Will mark Brianliest !!!!!!!!!!!!!!!!!!!
Answer:
x = 146º
Step-by-step explanation:
opposite angles in a parallelogram are equal to each other, so x = 146º
median of 410, 400, and 375
Answer:
400
Step-by-step explanation:
375 , 400, 410 (arrange in asc or des)
median = (middle num) = 400
Hope its right!
Answer:
400
Step-by-step explanation:
Give the angle measure represented by 2 rotations clockwise.
a. -720°
c. -360°
d. 360°
b. 720°
Answer: B: 720
Step-by-step explanation: One turn is 360
2x - 4 < 12
???????????
Answer: x < 8
Reason: I did some math
Answer:
x<8
Step-by-step explanation:
$5 is what percent of $10?
Answer:
It was 50%
Step-by-step explanation:
Find g(x), where g(x) is the translation 7 units right of f(x)=x2. Write your answer in the form a(x–h)2+k, where a, h, and k are integers.
Answer:
[tex]g(x) =1(x + 7)^2 + 0[/tex]
Step-by-step explanation:
Given
[tex]f(x) = x^2[/tex]
Required
Determine g(x) where g(x) is a translation of f(x), 7 units to the right
When a point is translated to the right, the resulting point is:
[tex]x -> x + b[/tex]
Where b is the number of units to the right.
In this case:
[tex]b = 7[/tex]
So, we have:
[tex]g(x) = f(x +7)[/tex]
Solving f(x+7)
Substitute x + 7 for x in [tex]f(x) = x^2[/tex]
[tex]f(x + 7) = (x+7)^2[/tex]
So, we have:
[tex]g(x) = (x+7)^2[/tex]
To write in the form of [tex]a(x - h)^2 + k[/tex], we have:
[tex]g(x) =1(x + 7)^2 + 0[/tex]
Jennifer and Chelsea each improved their yards by planting rose bushes and geraniums. They bought their supplies from the same store. Jennifer spent $146 on 6 rose bushes and 14 geraniums. Chelsea spent $57 on 1 rose bush and 7 geraniums. What is the cost of one rose bush and the cost of one geranium?
Answer:
$15.00
Step-by-step explanation:
Suppose 1 rose bush costs r dollars,
Suppose 1 geranium costs g dollars.
Here are 2 equations:
1)6r+14g=146
3r+7g=73
2)r+7g=57
r=57-7g
Put 2) in 1)
3(57-7g)+7g=73
171-21g+7g=73
98=14g
g=7
r=8
7+8=$15.00
Hope I helped!
In the right triangle shown m angle A =45° and AB=12 how long is BC?
Answer: there u go this the correct answer if your on khan academy.
From the given right angle triangle, the length of side BC will be equal to 6√2.
What is a right angle triangle?Any triangle that has one 90º angle has a right angle. Right triangles are those with an angle of 90 degrees, or "right angles," and are therefore those with this angle. The Pythagorean rule can be used to clarify the relationship between both the triangle's different sides.
As per the data provided in the question,
If one of the angles in a right triangle is 45 degrees, therefore the complimentary angle must also be 45 degrees.
Then,
m∠B = 45°
From the triangle ABC.
Cos B = BC/AB
As we know, the value of cos at 45° = √2/2
AB = 12
BC = cos (B) (AB)
BC = (√2/2) × 12 = 6√2 units.
To know more about right angle triangle:
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Laura bought a notebook and a pencil for $4.50. The notebook cost twice the amount of the pencil. On your worksheet, solve the question and write your answer below. . How much was the pencil and how much was the notebook
Answer:
n+p=4.50
n=2p
2p+p=4.5
2p=4.5
p=$1.5
n=$3
Step-by-step explanation:
Answer:
Pencil: $1.50
Notebook: $3
Step-by-step explanation:
n = cost of notebook
p = cost of pencil
n + p = 4.5
n = 2p
substitute n into the first equation
2p + p = 4.5
3p = 4.5
p = 1.5
n = 2p
n = 2(1.5)
n = 3
please help me if you can pleasee
Answer:
Slope for #17 is 3/2
Slope for #18 is -18
Step-by-step explanation:
Anybody know the answer?
Answer:
no, no I don't know the answer. Sorry and hope you have a nice rest of the day
what is the common difference of the arithmetic sequence 5,8,11,14?
Answer:
3
Step-by-step explanation:
8-5= 3
11-8= 3
14-11= 3
Answer:
common difference = difference between two consecutive number in a given series
hence,
8-5=3
common difference =3
Fill in the missing term on each line. Simplify any fractions.
2d + 10 = 10
2d =
Subtract 10 from both sides
d =
Divide both sides by 2
the answer is,......
d = 0
Find the value of the expression.
•(- 12
1
4
Answer:
try mat.h way it will help
Step-by-step explanation:
what is the mean of this? 48, 12, 35, 57, 42, 15, 74, 29.
ILL GIVE U BRAINLYEST
answer:
48 + 12 + 35 + 57 + 42 + 15 + 74 + 29 = 312
divide by number of numbers,
312 / 8 = 39
the mean is 39.
if correct, please mark the brainliest :)
Answer:
the mean is 39.
Step-by-step explanation:
The dinner bill came to $24.29 before tax and tip. If the taxes were 6% and they decided to leave an 18% tip, what was the total cost of the dinner?
Answer:
$30.64 +6% tax and 18% tip
Step-by-step explanation:
Hope it helps
There are 12 trees on the Smith’s property. The Smith’s plant some trees, and now there are 21 trees. How many trees t do the Smith’s plant?
Answer:
The Smith's planted 9 trees
Step-by-step explanation:
21-12=9
Because the Smith's ending amount is 21, and their beginning amount is 12 you subtract 21-12=9
Answer:
Well, there can be two answers. One of them can be 9, since they planted 9 MORE trees on top of the 12 already there. (21-12=9) The other answer can be 33 if you count all the trees they planted. (12+21=33)
Step-by-step explanation:
please help I attached a picture
Answer:
option (3)
Step-by-step explanation:
The equation of a parabola in vertex form is
y = a(x - h)² + k
(h, k) are the coordinates of the vertex and a is a multiplier
Given
f(x) = x² - 12x + 7
Using the method of completing the square
add/subtract ( half the coefficient of the x- term )² to x² - 12x
f(x) = x² + 2(- 6)x + 36 - 36 + 7
= (x - 6)² - 29
with vertex (h, k ) = (6, - 29 )
The height of Moyo and that of
Adamu differs by 9. The difference of the squares of their height is 120.
Find their heights.
Answer:
The height of Moyo is
[tex]\frac{67}{6}[/tex]
The height of Adamu is
[tex]\frac{13}{6}[/tex]
Step-by-step explanation:
Equations
To solve the problem, we assign the variable:
x = height of Moyo
Since Moyo is 9 units taller than Adamu:
x - 9 = height of Adamu
The difference of the squares of their heights is 120, thus:
[tex]x^2-(x - 9)^2=120[/tex]
Operating:
[tex]x^2-(x^2-18x+81)=120[/tex]
[tex]x^2-x^2+18x-81=120[/tex]
Simplifying:
[tex]18x-81=120[/tex]
Adding 81:
[tex]18x=120+81=201[/tex]
Dividing by 18:
[tex]x=\frac{201}{18}=\frac{67}{6}[/tex]
The height of Moyo is
[tex]\frac{67}{6}[/tex]
The height of Adamu is
[tex]\frac{67}{6}-9=\frac{13}{6}[/tex]
Choose the numerical expression that matches the phrase.
Multiply 4 and 7, then add 3.
3 x 4 +7
Α.
B. 3 x 7 +4
C.4 x 7 + 3
D. 7 x 3 + 4
Answer:
Multiple 4 and 7, then add 3 is equivalent to
C. 4 x 7 + 3
Answer:
C. 4 x 7 + 3
Step-by-step explanation:
→ Multiply 4 and 7
4 × 7
→ Then add 3
4 × 7 + 3
Last week a pound of strawberries cost $4. This week they are 24% more expensive. What is the current price of a pound of strawberries? Enter your answer in the box. pls help me
Answer:
$5.96
Step-by-step explanation:
I divided 4 by 100 then multipley by 24
Help PLEASE!!!! Slope
Answer:
(We don’t have a picture so i’ll remind you about how to solve it.)
Step-by-step explanation:
Slope is rise over run. You find a point of the graph where the line goes through. Look for a 2nd point on the graph where the line goes through a point. Count up, and to the side and you have your answer :)
Can someone explain this?
#6 Find x to show that Quadrilateral ABCD is a parallelogram.
Answer:
x = 5
Step-by-step explanation:
Diagonals of a parallelogram bisect each other. Based on this knowledge, to show that the quadrilateral is a parallelogram, therefore:
3x - 4 = x + 6
Solve for x
Collect like terms
3x - x = 4 + 6
2x = 10
Divide both sides by 2
x = 5
What is the measure of N? A)23 B)25 C)27 D)45
look (this is what 2 + 2 equals)
5 (2 cups of vinegar+ 2 cups of baking soda = 5 cups of fizzy mess)
or 4
Angle 3 is equal to angle