We are given with an AP (Arithmetic Progression) with first term being -7, and the common difference being the difference between any succeding term from any term and the term itself, so common difference = -11 - (-7) = -11 + 7 = -4, so now before finding the sum of 21 terms, let's recall that ;
[tex]{\boxed{\bf{S_{n}=\dfrac{n}{2}\{2a+(n-1)d\}}}}[/tex]Where, d is the common difference, a is the first term, and n is the number of terms and [tex]{\bf S_n}[/tex], being the sum of n terms, so putting all the values in the formula, we will have ;
[tex]{:\implies \quad \sf S_{21}=\dfrac{21}{2}\{2\times -7+(21-1)-4\}}[/tex]
[tex]{:\implies \quad \sf S_{21}=\dfrac{21}{2}(-8+20\times -4)}[/tex]
[tex]{:\implies \quad \sf S_{21}=\dfrac{21(-8-80)}{2}}[/tex]
[tex]{:\implies \quad \sf S_{21}=\dfrac{21(-88)}{2}}[/tex]
[tex]{:\implies \quad \sf S_{21}=-21\times 44}[/tex]
[tex]{:\implies \quad \boxed{\bf{S_{21}=-924}}}[/tex]
Mr. Oppong makes monthly payments into his savings account. He saved Gh¢800.00 in the second month, Gh¢3,200.00 in the third month and he continued in tha same proportion in subsequent months. In what month would his savings first exceed Gh¢20,000.00?
Answer:
5th month
Step-by-step explanation:
the relationship between the second and third month is that the 2nd month's salary was multiplied 4 to get the third month's salary
therefore the salaries for the next months will be
4th month=Gh¢12800.00
5th month=Gh¢51,200.00 which exceeds 20,000
Directions: Type the correct answer in each box. Spell all words correctly, and use numerals instead of words for numb
For this problem any non-integer answers should be entered as fractions in simplest form using / as the fraction bar(s).
A spinner has five colored sections of different sizes. Felicia spins the arrow on the spinner and records the color of the section it
lands on in the table below.
Complete the statements based on the given table.
The experimental probability of landing on orange is__
The experimental probability of landing on___is 1/5
The experimental probability of landing on a color that is not blue is___
Answer:
1/3, Yellow, 3/4
Step-by-step explanation:
All the numbers add up to 60, so using fractions
Red is 11/60
Green is 2/60
Yellow is 12/60
Blue is 15/60
Orange is 20/60
Finding The probability of w/o blue is subtracting 15 from 60 which ends as 45/60, and simplifying that would be 3/4
Please help me find the area for this hexagon (please show work to) ,:)
Check the picture below.
so the area of the hexagon is really just the area of two isosceles trapezoids.
[tex]\textit{area of a trapezoid}\\\\ A=\cfrac{h(a+b)}{2}~~ \begin{cases} h=height\\ a,b=\stackrel{parallel~sides}{bases}\\[-0.5em] \hrulefill\\ a=2\\ b=4\\ h=2 \end{cases}\implies \begin{array}{llll} A=\cfrac{2(2+4)}{2}\implies A=6 \\\\\\ \stackrel{\textit{twice that much}}{2A = 12} \end{array}[/tex]
Which of the following numerical expressions results in a positive number?
A (-12) - (-21) - 10
B (-12) - (-21)
C 12 - 21
D (-21) – (-12)
1.Find the perimeter of the polygon with the given vertices
D(-3, 2), E(4,2), F(4, -3)
Answer:
perimeter = 12 + √74
area = 17.5
Step-by-step explanation:
See the drawing below.
This is a right triangle.
The legs have lengths 5 and 7.
We can find the length of the hypotenuse using the Pythagorean Theorem.
5² + 7² = e²
e² = 74
e = √74
perimeter = 5 + 7 + √74
perimeter = 12 + √74
area = bh/2
area = 5 × 7/2
area = 17.5
Find two consecutive positive integers such that the sum of their squares is 761
Answer:
[tex]19^{2} +20^{2}[/tex] is 761
Step-by-step explanation:
Answer:
19 and 20
Step-by-step explanation:
Let the integers be x and x + 1.
According to the question,
x² + (x + 1)² = 761x² + x² + 2x + 1 = 7612x² + 2x - 760 = 0x² + x - 380 = 0x² + 20x - 19x - 380 = 0x(x + 20) - 19(x + 20) = 0(x - 19)(x + 20) = 0x = 19, -20But x is a positive integer⇒ x = 19Therefore, the integers are :
x = 19x + 1 = 20How do I use Brainly math for solving stuff like this and how do I show my evidence on paper?
Answer:
a) 3
b) 1/3
Step-by-step explanation:
I've never used Brainly math before, but I can help you out with the work for these problems.
Part A
3(x + 1) - x = 15
3x + 3 - x = 15
4x + 3 = 15
4x = 12
x = 3
Part B
5(x + 2) - 2x = 11
5x + 10 - 2x = 11
3x + 10 = 11
3x = 1
x = 1/3
Hope this helps!
PLSSSS ANSWER THIS QUESTION FAST
WILL MARK BRAINLIEST
68 square inches
=============================================
Explanation:
Refer to the diagram below.
I'll make the yellow sheet of paper to be 8 by 10, where the horizontal part is 8 and the vertical is 10. The overlapped region has its horizontal part as 8 as well.
The other piece of paper is 8.5 inches by 11 inches. The vertical part of the overlapped region is 8.5 inches.
The overlapped region is a 8.5 inch by 8 inch rectangle with area 8.5*8 = 68 square inches. This makes choice D the final answer.
an effort to make room for new inventory, a college bookstore runs a sale on least popular mathematics books. The sales rate (books sold per day) on day of the sale is predicted to be 60 / t (for t >= 1), where t = 1 corresponds to the beginning of the sale, at which time none of the inventory of 595 books had been sold.
A) Find a formula for the number of books sold up to day t. S(t)=
B) Will the store have sold its inventory of 595 books by day t = 30? “Yes” or “No”
Answer:
The sun, eight plants and some other celestial
Answer:1
Step-by-step explanation:
The sun, eight plants and some other celestial
B
ca
(3y +9)°
1149
4yº
D C
А
1.
o
5 Write an equation for each of the following and solve it. (a) The sum of one-sixth ofx and -9 is -25.
Answer:
x= -96
Step-by-step explanation:
1
[tex] \frac{x}{6} + ( - 9) = - 25 \\ \frac{x}{6 } = - 25 - ( - 9) \\ \\ \frac{x}{6} = - 25 + 9 \\ \frac{x}{6} = - 16 \\ x = - 16 \times 6 \\ x = - 96[/tex]
Answer:
[tex]\huge\boxed{\bf\: Equation \rightarrow \frac{1}{6}*x - 9 = - 25}[/tex]
[tex]\huge\boxed{\bf\: Solution \rightarrow - 96}[/tex]
Step-by-step explanation:
Take the variable as 'x'.
Let's breakdown the given statement.
⅙th of x =⅙*xThe sum of ⅙*x & - 9 = ⅙*x + (-9)Is equal to = ⅙*x + (-9) = - 25Given equation,
⅙*x - 9 = - 25
By solving,
⅙*x - 9 = - 25
⅙*x = - 25 + 9
⅙*x = - 16
x = - 16 * 6
x = [tex]\boxed{\bf\: - 96}[/tex]
[tex]\rule{150pt}{2pt}[/tex]
Simplify the expression. 5^–3 • 7^0
a)–15
b)0
c)125
d)1/125
= 5^-3 × 7⁰
= 1/5³ × 1. ( a^-m = 1/a^m ), ( a⁰ = 1 )
= 1/125 × 1
= 1/125 ANSWER
Which of the following options have the same value as 10% of 33?
Choose 3 answers:
A. 0.1 • 0.33
B. 10 • 33
C. 1/10 • 33
D. 0.1 • 33
E. 10/100 • 33
(Please help I need this answer fast)
Answer:
C. 1/10 • 33
D. 0.1 • 33
E. 10/100 • 33
Step-by-step explanation:
Knowing that
10% = 0.1 in decimal form
10% = 1/10 or 10/100 in fraction form
of = multiply
Thus, the following is correct:
C. 1/10 • 33
D. 0.1 • 33
E. 10/100 • 33
We can also solve to find the answer:
10% of 33 = 3.3
0.1 x 0.33 = 0.033
10 x 33 = 330
1/10 x 33 = 3.3
0.1 x 33 = 3.3
10/100 x 33 = 3.3
Hence answer =
C. 1/10 • 33
D. 0.1 • 33
E. 10/100 • 33
[RevyBreeze]
Answer:
C. 1/10 • 33
D. 0.1 • 33
E. 10/100 • 33
Step-by-step explanation:
Before finding the solutions let's first note the following:
Notes :
Of = Multiply
10% ⇒ 0.1 ⇒ 1/10 ⇒ 10/100
Thus, substitute;
C. 1/10 • 33
D. 0.1 • 33
E. 10/100 • 33
Therefore,
C. 1/10 • 33
D. 0.1 • 33
E. 10/100 • 33
are the correct answer.
As well as if you multiply/divide all you will all get 3.3
~lenvy~
could i have some super quick quick help? graph part isn't necessary
y=4x²-1
#1
y=(2x)²-1²y=(2x+1)(2x-1)#2
Zeros are 1/2,-1/2
#3
Convert to vertex form y=a(x-h)²+k
y=(4x+0)²-1Vertex(h,k)=(0,-1)
#4
Graph attached
Answer:
i) [tex]y=(2x+1)(2x-1)[/tex]
ii) [tex]x=-\dfrac12, x=\dfrac12[/tex]
iii) (0, -1)
iv) see attached
Step-by-step explanation:
Given quadratic: [tex]y=4x^2-1[/tex]
Factored form
We can use the Difference of Two Squares to factor the given quadratic.
[tex]a^2-b^2=(a+b)(a-b)[/tex]
Therefore,
[tex]a^2=4x^2=(2x)^2\implies a=2x[/tex]
[tex]b^2=1=1^2 \implies b=1[/tex]
So the relation in factored form is:
[tex]y=(2x+1)(2x-1)[/tex]
Zeros
The zeros of the quadratic polynomial are the x-coordinates of the points where the graph intersects the x-axis, i.e. when y = 0
[tex]\implies y=0[/tex]
[tex]\implies (2x+1)(2x-1)=0[/tex]
[tex]\implies (2x+1)=0\implies x=-\dfrac12[/tex]
[tex]\implies (2x-1)=0\implies x=\dfrac12[/tex]
Therefore, the zeros are -1/2 and 1/2
Vertex
The x-coordinate of the vertex is the midpoint of the zeros.
[tex]\textsf{midpoint}=\dfrac{-\frac12+\frac12}{2}=0[/tex]
To find the y-coordinate of the vertex, substitute the found value of x into the given equation:
[tex]\implies y=4(0)^2-1=-1[/tex]
Therefore, the vertex is (0, -1)
I can't manage. Can you help? Ty :)
first question is true and second question is 6cm
If John had four pizzas and shared them equally to his three friends, how many slices will he have?
Answer:
Is this really college math?
He would have 8 slices of pizza
Step-by-step explanation:
8 * 4 = 32
32 / 4 = 8...
the number of slices John would have after distributing it among his friends.
solution8×4=32
32/4
= 8
John would have 8 slices of pizza.
the circumference of the hub cap of a tire is 79.38 cm. Find the area of this hub cap. use 3.14 for pi
Answer:
ans 19785.719
Step-by-step explanation:
formula πr^2
The perimeter of a triangle is 7 m. The longest side is twice the length of the shortest side. The sum of the
lengths of the shortest side and the middle side is 1 m more than the length of the longest side. Find the
lengths of the sides.
Answer:
See below in bold.
Step-by-step explanation:
Let the length of the shortest side be x, then the longest side = 2x.
Also x + y = 2x + 1 where y = length of the middle side,
Simplifying:
2x - x - y = -1
x - y = -1 (A)
Also as the perimeter = 7:
x + 2x + y = 7
3x + y = 7 (B)
Adding (A) and (B):
4x + 0 = 6
x = 6/4 = 1.5
Plug x = 1.5 into equation B:
3(1.5) + y = 7
y = 7 - 4.5 = 2.5.
Answer:
So the shortest side = 1.5, middle = 2.5 and longest = 2*1.5 = 3.
Nathaniel had $40 to spend on 9 beakers for his science class. After buying them, Nathaniel had $4 left. How much did each of the beakers cost?
Answer:
each baker cost $4
Step-by-step explanation:
4 times 9 is 36, and that leaves 4
PLEASE HELP PLEASE HELP PLEASE
Answer:
False
Please make this brianliest so others can learn from this answer
Happy to help :)
Step-by-step explanation:
Solve the equation below for y
3 ( y + 3 ) = 14
Answer:
y = 3/5
Step-by-step explanation:
3(y+3) = 14
3*y+3*3 = 14
3y+9 = 14
3y = 14-9
3y = 5
y = 3/5
can somebody help me on this pleaseee
Answer:
B I think or C or D or it could be A
3 Which list of integers is in order from
greatest to least?
A 24, 9, -33, -24, -11
B-11, -18, -33, 9, 24
C24, 9, -11, -24, -33
D-33, 24, -18, -11, 9. Which one is the answer
Larry, a chemistry student, needs 10% acetic acid solution for a chemistry experiment. He realizes he only has 5% and 20% acetic acid solutions available. He decides to make the 10% solution by combining the 5% and 20% solutions. How many liters of the 5% solution must he add to 8 liters of the 20% solution to get a solution that is 10% acetic acid?
a) 16.5
b) 32
c) 16
d) 8.5
e) 24
can someone tell me the answer
Answer:
A. 9/25
Step-by-step explanation:
There are a total of 25 T-shirts, which means that the denominator of the fraction is going to be 25 (which already rules out B and C). In the information they give us, they said that there are 9 red shirts. Therefore, the numerator will be 9. Our complete fraction is 9/25, or A.
I hope this helps! Have a lovely day!! :)
pls help. Consider the following expression 9u+7v+5+4v.
Select all of the true statements below.
Answer:
7v and 4v are like terms, 9u is a term, and 5 is a constant.
Step-by-step explanation:
Like terms are terms that can be added together, such as numbers being multiplied by the same variable. A term is a number, a variable, or a number and a variable combined. A constant is a number that is not being multiplied or divided by a variable, but just a number on its own.
Which of these graphs has its maximum point on the line x=3
Answer:
The last graph
Step-by-step explanation:
We are given two tips for finding our graph, it has a max point and the point of the line is x = 3. Meaning that this graph must open down and should not go anything further than 3 on the y graph.
The only one that fits this proposition is the last graph. Making it correct.
Answer:
see below
Step-by-step explanation:
To have a maximum, the parabola must be pointing down.
For the maximum to be at x=3, the vertex must have an x value at 3 and the line of symmetry must be 3
In a computer game , Reese scored 13,925 points. Manny scored 2,742 points more than Reese. How many points did manny score?
Answer:
16,667
Step-by-step explanation:
13,925 + 2,742 = 16,667
Answer:
Bonjour
Step-by-step explanation:
Reese : 13 925
Manny : 2 742 de plus que Reese donc 13 925 + 2 742
13 925 + 2 742 = 16 667
Manny a marqué 16 667 points.
Use the graph of f(x) to evaluate the following: 2 1 x 1 IN 2 3 4 5 -1 - 1 6 The average rate of change of f from x = O to L = 2 is 2 Give your answer as an integer or reduced fraction.
no se cómo se hace está operación de verdad lo siento
the area of a square 16/36sq foot how do u get side length of the sq?
We know that, the area of a square with side being s, is given by s², so if we here assume our side of square whose area is (16/36) sq. foot being s, so we will be having :
[tex]{:\implies \quad \sf s^{2}=\dfrac{16}{36}}[/tex]
[tex]{:\implies \quad \sf s=\pm \sqrt{\dfrac{16}{36}}}[/tex]
But, as length can never be -ve, so we will be taking only +ve length, and if we solve further for s, it will yield ;
[tex]{:\implies \quad \sf s=\sqrt{\dfrac{16}{36}}}[/tex]
[tex]{:\implies \quad \sf s=\dfrac{\sqrt{16}}{\sqrt{36}}}[/tex]
[tex]{:\implies \quad \sf s=\dfrac46}[/tex]
[tex]{:\implies \quad \boxed{\bf{s=\dfrac{4}{6}=\dfrac{2}{3}}}}[/tex]
Well, you might be thinking that (2/3)² willn't give (16/36) rather it will give (4/9), so for this, I'm telling that (2/3) ≈ 0.66666...7 and (4/6) ≈ 0.66666...7, so it's just the same thing and also, (16/36) and (4/9) are just too the same thing, dividing the numerator and denominator of (16/36) will just lead to (4/9) as same as (2/3)²
