Answer:
The sum of the arithmetic progression is 2520
Step-by-step explanation:
The sum, Sₙ, of an arithmetic progression, AP, is given as follows;
[tex]S_{n}=\dfrac{n}{2}\cdot \left (2\cdot a+\left (n-1 \right )\cdot d \right )[/tex]
Where;
n = The nth term of the progression
a = The first term = 100
d = The common difference = -2
Given that the last term = -10, we have;
-10 = 100 + (n - 1) ×(-2)
n = (-10 - 100)/(-2) + 1 = 56
Therefore, the sum of the 56 terms of the arithmetic progression is [tex]S_{56}=\dfrac{56}{2}\cdot \left (2\cdot 100+\left (56-1 \right )\cdot (-2) \right )[/tex]
Which gives;
[tex]S_{56}={28}\cdot \left (200-\left 110 \right ) = 2520[/tex]
Find the area of the green sector if m2 A-T
and the circle has a radius of 10 inches.
The area is:
A = πR² ------- 2π
A = x --------- π/6
x = πR²/12
x = π.(10)²/12
x = 26.18 in²
Hope it helps x
Point M is on line segment LN. Given MN=2 and LM=4, determine the length LN.
Answer:
LN = 6
Step-by-step explanation:
Since M is on LN, then
LN = LM + MN = 4 + 2 = 6
Answer:
[tex]\huge \boxed{6}[/tex]
Step-by-step explanation:
Point M is on the line segment LN.
LM = 4
MN = 2
LN = LM + MN
LN = 4 + 2 = 6
Create a figure with half the perimeter of a given figure.
you don't have to actually make a shape, can someone explain how to do this pls
Step-by-step explanation:
First you have to add up all of the numbers that make up the perimeter of this arrow.
3+3+1+.5+.5+1.8+1.8=11.6
You than want to divide this number by 2 to find the half perimeter you have to work with, which is 5.8.
A simple shape you can make is a square, with each side being 1.45 m.
Gary is using an indirect method to prove that segment DE is not parallel to segment BC in the triangle ABC shown below:
A triangle ABC is shown. D is a point on side AB and E is a point on side AC. Points D and E are joined using a straight line.
He starts with the assumption that segment DE is parallel to segment BC.
Which inequality will he use to contradict the assumption?
Answer:
That Ratios aren't equal.
Step-by-step explanation:
Given: DE is || to BC.
So in order to make this false then we have to say that the sides aren't proprtional, making it not possible to get the ratios equal.
(See the Triangle proprtionality theorem or the triangle midsegment theorem)
Answer:
4:10 ≠ 6:14
Step-by-step explanation:
bc i said so
The National Weather Service collects data on the number of hours of consecutive rainfall and the number of minor traffic accidents in a particular city. The scatter plot shows the data it gathered and the line of best fit. For a school project, Peyton uses technology to calculate the equation for line of best fit. If Peyton's calculation is correct, which equation could represent the line of best fit for this data?
The equation that could best represent the line of best fit for the given data is; y = 0.625x
How to find a linear equation from a scatter plot?The formula for the equation of a line in slope intercept form is;
y = mx + c
where;
m is slope
c is y-intercept which is the point where the line intersects the y-axis
Now, in this question, we see that the line intersects the y-axis at 0. Thus;
y-intercept; c = 0
Now, let us find the slope from the formula;
m = (y₂ - y₁)/(x₂ - x₁)
Using the first and penultimate coordinate which are;
(0, 0) and (8, 5), we have;
m = (5 - 0)/(8 - 0)
m = 0.625
Thus, the equation is;
y = 0.625x
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Answer:
y=0.625x
Step-by-step explanation:
plato
Please answer this question now
Answer:
m∠C = 102°
Step-by-step explanation:
This is a quadrilateral inscribed in a circle
The sum of opposite angles in a cyclic quadrilateral is equal to 180°
m∠D + m∠B = 180°
m∠B = 180° - m∠D
m∠B = 180° - 80°
m∠B = 100°
We know what m∠B
We have external angles outside the circle.
m∠CDA is opposite m∠B
m∠CDA = 2 × m∠B
m∠CDA = 2 × 100°
m∠CDA = 200°
m∠CDA is the sum of m∠CD and m∠DA
m∠CDA = m∠CD + m∠DA
m∠DA = m∠CDA - m∠CD
m∠DA = 200° - 116°
m∠DA = 84°
m∠DAB is an exterior angle also, hence,
m∠DAB is the sum of m∠DA and m∠AB
m∠DAB = m∠DA + m∠AB
m∠DAB = 84° + 120°
m∠DAB = 204°
Finally we can solve for m∠C
m∠DAB is Opposite m∠C
So, m∠C = 1/2 × m∠DAB
m∠C = 1/2 × 204
m∠C = 102°
Given [tex]f(x)=-x^{2} +6x-11[/tex], find [tex]f(x-3)[/tex]
Answer:
See below.
Step-by-step explanation:
[tex]f(x)=-x^2+6x-11\\f(x-3)=-(x-3)^2+6(x-3)-11\\f(x-3)=-(x^2-6x+9)+6x-18-11\\f(x-3)=-x^2+6x-9+6x-29\\f(x-3)=-x^2+12x-38[/tex]
How to solve -13 - ¼h = 7
Answer:
The solution is h = -80.
Step-by-step explanation:
Let's eliminate fractions here by multiplying all three terms by 4:
-52 - h = 28
Subtracting 28 from both sides results in -80 = h
The solution is h = -80.
Ms. Brown needs 8 eggs in order to make 2 cakes. What is the total number of cakes she could make with 24 eggs?
Answer:
Ms. Brown would need 4 eggs in order to make 1 cake, so if she has 24 eggs you would divide 24 by 4, which is 6. So, Ms. Brown could make 6 cakes with 24 eggs.
Hope this helps!
___H2 + ___Br2 → ___HBr
Answer:
H2+Br2 HBrH2+Br2. 2HBrWrite an equation for a line on the graph that passes through the points (0.4) and (12,16)
Answer:
[tex] y = x + 4 [/tex]
Step-by-step explanation:
Use the two-point form of the equation of a line.
[tex] y - y_1 = \dfrac{y_2 - y_1}{x_2 - x_1}(x - x_1) [/tex]
[tex] y - 4 = \dfrac{16 - 4}{12 - 0}(x - 0) [/tex]
[tex] y - 4 = \dfrac{12}{12}x [/tex]
[tex] y - 4 = x [/tex]
[tex] y = x + 4 [/tex]
Answer:
y = x + 4
Step-by-step explanation:
An equation for a line looks like:
=> y = mx +b
=> In this equation "m" is the slope.
=> "b" is the y-intercept.
To find the slope:
=> y/x - y1/x1
=> 16/12 - 4/0
=> 16 -4 / 12 - 0
=> 12 / 12
=> 1
So, the slope is 1.
Now our equation looks like:
y = 1x + b
=> y = x + b
Let's take some the values of "x" and "y" of (0,4)
So, our now look like:
=> 4 = 1 (0) + b
=> 4 = b
So, b (y-intercept) = 4
Now, our final equation is:
=> y = x + 4
The width of a rectangle measures (8.3c-8.4d)(8.3c−8.4d) centimeters, and its length measures (5.3c+4.8d)(5.3c+4.8d) centimeters. Which expression represents the perimeter, in centimeters, of the rectangle?
Answer:
P = 27.2c-7.2d
Step-by-step explanation:
It is given that,
The width of a rectangle is (8.3c-8.4d)
The length of a rectangle is (5.3c+4.8d)
The perimeter of a rectangle is equal to the sum of its all sides i.e.
P = 2(l+b)
P = 2(8.3c-8.4d+5.3c+4.8d)
P = 2[(8.3c+5.3c)+(4.8d-8.4d)]
P = 2(13.6c-3.6d)
⇒P = 27.2c-7.2d
Hence, the expression that represents the perimeter of the rectangle is 27.2c-7.2d.
this graph shows the solution to which inequality (3 3) (-3 -1)
Answer:
B
Step-by-step explanation:
since the graph shows dotted line the sign has to be < or > so C and D eliminated from your answer
y>2/3 x +1 is your answer (B)
Answer:
[tex] \boxed{y > \frac{2}{3} x + 1}[/tex]Option B is the correct option.
Step-by-step explanation:
point ₁ ( - 3 , - 1 ) x₁ = - 3 , y₂ = - 1
point ₂ ( 3 , 3 ). x₂ = 3 , y₂= 3
Now, let's find the slope:
Slope ( m ) = [tex] = \frac{y2 - y1}{x2 - x1} [/tex]
[tex] = \frac{3 - ( - 1)}{3 - ( - 3)} [/tex]
[tex] = \frac{3 + 1}{3 + 3} [/tex]
[tex] = \frac{4}{6} [/tex]
[tex] = \frac{2}{3} [/tex]
At ( 3 , - 1 )
y = mx + c , where m is the gradient / slope amd c is called the intercept on y-axis
[tex] - 1 = \frac{2}{3} \times ( - 3) + c[/tex]
Solve for c
[tex] - 1 + 2 = c[/tex]
[tex]c = 1[/tex]
Since, The red line is dotted line. Therefore it does not include the equal to part. And the shaded region is upper part. Hence, ' > ' should be used.
The answer would be:
[tex]y > \frac{2}{3} x + 1[/tex]
Hope I helped!
Best regards!
LESSON 2-1 PRACTICE
V 13. Attend to precision. Justify each step in the solution of 5x + 15 -
below by stating a property or providing an explanation for each
5x + 15 = 0
5x + 15 – 15 = 0 – 15
5x = -15
x = -3
Answer:
Value of x is -3
Step-by-step explanation:
Given:
5x + 15 = 0
Find:
Value of x
Computation:
5x + 15 = 0
From subtracting 15 from both side (LHS and RHS)
5x + 15 – 15 = 0 – 15
5x = -15
From dividing 5 from both side (LHS and RHS)
5x / 5 = -15 / 5
x = -3
So,
Value of x is -3
A circle is centered at C(-1,-3) and has a radius of 6. Where’d does the point P(-6,-6) lie?
4. A car is priced at $7200. The car dealer allows a customer to
pay a one-third deposit and 12 payments of $420 per month.
How much extra does it cost the customer?
Answer:
$240 extra
Step-by-step explanation:
1/3(7200) + 12(420) = 2400 + 5040 = 7440
7440 - 7200 = 240
The customer had to pay 1720 extra.
What is Unitary Method?The unitary technique involves first determining the value of a single unit, followed by the value of the necessary number of units.
For example, Let's say Ram spends 36 Rs. for a dozen (12) bananas.
12 bananas will set you back 36 Rs. 1 banana costs 36 x 12 = 3 Rupees.
As a result, one banana costs three rupees. Let's say we need to calculate the price of 15 bananas.
This may be done as follows: 15 bananas cost 3 rupees each; 15 units cost 45 rupees.
Given:
A car is priced at $7200.
If the deposit is one third = 7200/3
= 240
The amount after 12 payments will be
= 240 x 12
= 2880
total cost will be
= 2880 + 2400
= 5280
and, The customer had to pay extra amount
= 7200 - 5280
= 1720
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WikiTongues has
videos of 500 different
languages from around the
world. What percent of the
7,111 total languages
spoken globally
is represented on
WikiTongues?
Hey there! I'm happy to help!
We see that 500 languages is a certain percent of the 7,111 total languages. When working with percent equations, the word "is" means "equals", and "of" usually means "multiplied by" This means that 500 is equal to a certain percent multiplied by 7,111. We can use p to represent this certain percent and create an equation below.
500=7,111p
Let's flip the equation around so the p is on the left side. Variables are usually supposed to be on the left.
7,111p=500
We divide both sides by 7,111.
p=0.0703
As a percent, this is about 7.03%. Therefore, about 7.03% of the total languages spoken globally are represented on WikiTongues.
I hope that this helps! Have a wonderful day! :D
Answer:
7.03 %
Step-by-step explanation:
500 / 7,111 = 0.07031359865
0.07031359865 x 100 = 7.03 %
50 POINTSS!! While preparing a roof, patty drops a screwdriver from a height of 80 feet. The function (h)t = -16t^2 + 80 gives the height of the screwdriver in the feet as feet after t seconds during its fall. Which of these is the graph of the function
Answer:
Graph D
Step-by-step explanation:
(h)t = -16t^2 + 80
At time t = 0 the screwdriver is at 0+80 =80 ft
As time increases the height will decrease so we can eliminate graph B
We know this is a downward parabola by the - in front of the t^2 so we can eliminate graph A
We need to find where it meets the x axis
0 = -16t^2 + 80
-80 = -16t^2
5 = t^2
t = sqrt(5)
t =2.23
This is Graph D
Choose all true statements.
All real numbers are rational numbers.
Some rational numbers are natural numbers.
No real numbers are irrational numbers.
All whole numbers are integers.
Some integers are natural numbers.
No rational numbers are integers.
Answer:
- All real numbers are rational numbers. FALSE
- Some rational numbers are natural numbers. TRUE
- No real numbers are irrational numbers. FALSE
- All whole numbers are integers. TRUE
- Some integers are natural numbers. TRUE
- No rational numbers are integers. FALSE
Answer: B,D, and E
Step-by-step explanation:
A. All real numbers are rational numbers.
B. Some rational numbers are natural numbers
C.No real numbers are irrational numbers.
D.All whole numbers are integers.
E. Some integers are natural numbers.
F. No rational numbers are integers.
A number “x” increased by 5 is 19?
Answer:
x+5=19
Step-by-step explanation:
i think that right let me know...:/
Answer:
x= 14
Step-by-step explanation:
a number x increased by 5, so it will be x + 5 and is in math means equals to so it becomes
x+5=19
19-5=x
14=x
Helppp thank you!!!!!
Answer:
D
Step-by-step explanation:
x is greater than 12:
[tex]x>12 \text{ or } 12<x[/tex]
and x is less than or equal to 3 times the value of y:
[tex]12<x\leq 3y[/tex]
We can divide everything by 3:
[tex]4<\frac{x}{3} \leq y[/tex]
Coherence
5. Simon's teacher asked him to e-mail her a copy of the outline for his essay on American
History: When drafting the e-mail, what level of diction should Simon use?
informal
formal
standard
foundational
Answer:
The correct option is;
Formal
Step-by-step explanation:
The common levels of diction are formal, informal, and popular, with formal diction being the most selective of the word choices
Formal diction is used when when communicating in a situation that is formal
Formal diction uses languages that is devoid of slang and grammatically correct
Formal language is precise, grammatically correct language that does not use slang used in communication for legal, professional, business and academic purposes.
What is the value of x, when -25(x - 4) = -55(x - 10)? A) x = 5 B) x = -5 C) x = 8 1/ 8 D) x = 15
[tex]-25(x - 4) = -55(x - 10)\\-25x+100=-55x+550\\30x=450\\x=\dfrac{450}{30}=15[/tex]
Answer:
x=15
Step-by-step explanation:
whats the factored form of 6x 2 - 8x - 8 = 0
Answer:
x = -2/3 , 2
Step-by-step explanation:
Factor 2 out of 6 x^ 2 − 8 x − 8
2 ( 3 x^ 2 − 4 x − 4 ) = 0
Factor
2 ( 3 x + 2 ) ( x − 2 ) = 0
Set 3 x + 2 equal to 0 and solve for x
x = -2/3
Set x − 2 equal to 0 and solve for x
x = 2
The final solution is all the values that make 2 ( 3 x + 2 ) ( x − 2 ) = 0
x = -2/3 , 2
Hope this can help you
Consider the circle of radius 10 centered at the origin. Find an equation of the line tangent to the circle at the point (6, 8)
Answer:
y = -3/4 x + 25/2
Step-by-step explanation:
x² + y² = 100
Take derivative with respect to x.
2x + 2y dy/dx = 0
2y dy/dx = -2x
dy/dx = -x/y
Evaluate at (6, 8).
dy/dx = -6/8
dy/dx = -3/4
Use point-slope form to write equation:
y − 8 = -3/4 (x − 6)
Simplify.
y − 8 = -3/4 x + 9/2
y = -3/4 x + 25/2
24 is 75% percent of what number?
Answer:
32
Step-by-step explanation:
We can call the number x. 75% can be expressed as 0.75 so we can write the following equation: 0.75x = 24. Dividing both sides by 0.75 to get rid of the coefficient of x, we get that x = 32.
Answer:
32.
Step-by-step explanation:
Let's say the number we are trying to find is x.
24 = 0.75x
0.75x = 24
x = 24 / 0.75
x = 32
Hope this helps!
Convert from an improper fraction to a mixed number 17\6
━━━━━━━☆☆━━━━━━━
▹ Answer
2 5/6
▹ Step-by-Step Explanation
[tex]\frac{17}{6} \\\\6 * 2 = 12\\12 + 5 = 17\\\\2\frac{5}{6}[/tex]
Hope this helps!
CloutAnswers ❁
━━━━━━━☆☆━━━━━━━
Answer:
2 5/6
Step-by-step explanation:
17/6
6 goes into 17 2 times
2*6 = 12
17-12 = 5
There is a remainder of 5 this goes over the denominator
2 5/6
is 1+isqrt3 a complex number
Answer:
Step-by-step explanation:
Yes, due to the presence of that operator " i "
The lengths of the three sides of a triangle are 7, x+4 and 2x+1. The perimeter of the triangle is 36. What is the length of the longest side of the triangle?
Answer:
Length of the longest side = 17 units
Step-by-step explanation:
Given:
Three sides of triangle
A = 7
B = x+4
C = 2x + 1
Perimeter of the triangle = 36
Find:
Length of the longest side
Computation:
We know that
Perimeter of the triangle = A + B + C
Perimeter of the triangle = 7 + x + 4 + 2x + 1
36 = 12 + 3x
24 = 3x
x = 8
So
Side B = 8 + 4 = 12 unit
Side C = 2(8) + 1 = 17 units
Length of the longest side = 17 units
Answer:
17.
Explaination:
Dunno. I just put it on paper, and did the calculations there.
ASAP!!!!!!!!! PLEASE help me with this question! This is really urgent! No nonsense answers please.
=================================================
Explanation:
Arcs CBH and FGH are given, while arc CDF is unknown. Let's call this y
y = measure of arc CDF
Adding the three arcs forms a full circle of 360 degrees
(arc CBH)+(arc FGH)+(arc CDF) = 360
170+64+y = 360
y+234 = 360
y = 360-234
y = 126
arc CDF = 126 degrees
Then notice how inscribed angle x cuts off arc CDF. By the inscribed angle theorem, we take half of the arc measure to get the inscribed angle measure.
inscribed angle = (arc measure)/2
x = (arc CDF)/2
x = 126/2
x = 63
Answer:
rewrite the fromula 126
Step-by-step explanation:
