1) Se o 5o e o 9-o termos de uma PA são, respectivamente, 40 e 68, então a razão r da progressão é: a) r = 6 b) r = 7 c) r = 9 d) r = 11 e) r = 12 2) Inserindo-se 6 números entre 72 e 107, de modo que a sequência (72, a2, a3, a4, a5, a6, a7 ,107) seja uma progressão aritmética, tem-se a3 igual a: a) 78 b) 79 c) 80 d) 81 e) 82
Answer:
1) b) r = 7
2) e) 82
Step-by-step explanation:
Progressão aritmética:
Em uma progressão aritmética, a diferença entre termos consecutivos é sempre a mesma, chamada de razão.
O n-ésimo termo de uma PA é dado por, tomando o primeiro termo como referência:
[tex]a_n = a_1 + (n-1)r[/tex]
Tomando o m-ésimo termo como referência, tem-se que:
[tex]a_n = a_m + (n-m)r[/tex]
1) Se o 5o e o 9-o termos de uma PA são, respectivamente, 40 e 68, então a razão r da progressão é:
[tex]a_5 = 40, a_9 = 68[/tex]. Então:
[tex]a_n = a_m + (n-m)r[/tex]
[tex]68 = 40 + 4r[/tex]
[tex]4r = 28[/tex]
[tex]r = \frac{28}{4} = 7[/tex]
Então a resposta correta é dada pela alternativa b.
2) Inserindo-se 6 números entre 72 e 107, de modo que a sequência (72, a2, a3, a4, a5, a6, a7 ,107) seja uma progressão aritmética, tem-se a3 igual a:
O primeiro termo é [tex]a_1 = 72[/tex] e o oitavo termo é [tex]a_8 = 107[/tex]. Com isso, é possível encontrar a razão.
[tex]a_n = a_1 + (n-1)r[/tex]
[tex]107 = 72 + 7r[/tex]
[tex]7r = 35[/tex]
[tex]r = \frac{35}{7} = 5[/tex]
Então, o terceiro termo é:
[tex]a_3 = a_1 + 2r = 72 + 2(5) = 82[/tex]
Logo, a resposta correta é dada pela alternativa e.
Please help
I am giving all my points for this (15 points)
Select all input values for which g(x)=8.
Choose all answers that apply:
(Choice A)
x=−4
(Choice B)
x=6
(Choice C)
x=9
(Choice D)
None of the above
Answer:
D. none of the above
Step-by-step explanation:
If g(x)=8 is the only equation, then none of the answers are correct. The correct answer would have been 8 because 8=8.
The coordinates of the image of P(3,-4) under a reflection in the x-axis are:
A. (3,4)
B. (4, -3)
C. (-4, 3)
D. (-3,-4)
Answer:
D. (-3,-4)
Step-by-step explanation:
PLACE YOUR GRAPH TOWARDS A MIRROR.....
The new coordinate of the image after the reflection in the x-axis is [tex]P'(3, 4)[/tex].
What is reflection?Reflection is a type of rigid geometrical transformation that maintains the object's size and shape, unlike other transformations such as dilation, which changes the size of the shape, reflection results in congruent images.
What is the rule for the reflection in the x-axis?The rule for the reflection over the x axis is "if the point (x, y) reflected in axis the it becomes (x, -y).
According to the given question.
We have a coordinates of the image of P(3, -4).
So, when the coordinates of the image is reflected in the x-axis then the x coordinate remains same but the y coordinate changes its sign from negative to positive and we get the new coordinate of the image that is [tex]P'(3, 4).[/tex]
Hence, the new coordinate of the image after the reflection in the x-axis is [tex]P'(3, 4)[/tex].
Find out more information about reflection here:
https://brainly.com/question/15175017
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p% of m translate into an algebraic expression
Answer:
p/100*m
Step-by-step explanation:
Ok so first off, we know that,
percent means out of 100
therefore,
p/100 *of* (means multiplication in math) m
So if we would replace *of* with multiplication, the problem would look like this
p/100 * m and that would be your answer.
the reason we do not simplify it further is because it only asks for the algebraic expression, not the final result!
Cheers! I hope this helps and you can understand now.
An expression is defined as a set of numbers, variables, and mathematical operations. The given statement p% of m can be written in the form of an expression as pm/100.
What is an Expression?In mathematics, an expression is defined as a set of numbers, variables, and mathematical operations formed according to rules dependent on the context.
The given statement p% of m can be written in the form of an expression as shown below,
p% of m
p% × m
= (p/100) × m
= (p × m)/100
= pm/100
Hence, The given statement p% of m can be written in the form of an expression as pm/100.
Learn more about Expression here:
https://brainly.com/question/13947055
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A stationer buys a gel pen Rs 20 and sells it at 20% profit.For what price should he buy it so that he can make 25% profit by selling for the same selling price.
Answer:
Current selling price = Rs 20 × 120 %
= Rs 24
Cost price should be [100 ÷ 125 ] × 24
= Rs 19.20
If a zero is
, then the graph of its function only touches the x–axis at that zero.
Answer:
Step-by-step explanation:
Yes. The zeroes of a graph are the values of x where the graph touches (or crosses) the x-axis.
HELP ASAP!!
duskkdkdkdjdjdkddkkffkkkfkgkfkfkkf
A student buys 5-cent, 10-cent, and 15-cent stamps, with a total value of $6.70. If the
number of 5-cent stamps is 2 more than the number of 10-cent stamps, while the
number of 15-cent stamps is 5 more than one half the number of 10-cent stamps, how
many 15-cent stamps did the student obtain?
Identify the values of the variables. Give your answers in the simplest radical form
Answer:
Step-by-step explanation:
johnny wants to construct a circular area for his patio. he bought enough stones to cover 200.96m^2. If he wants to put an umbrella in the middle of the patio, how far away is the table going to be from the edge of the circular patio
Answer:
Step-by-step explanation:
area = πr² = 200.96
r = √(200.96/π) ≅ 8
The table is 8 meters from the edge.
can someone please help me with this question!
Answer:
A
Step-by-step explanation:
The x value of the center = 0
The y value of the center = 220/2 + 11 = 110 + 11 = 121
so the center is at (0,121)
The radius is 220/2 = 110
The equation of the Ferris Wheel is
x^2 + (y - 121)^2 = 110^2
x^2 + (y - 121)^2 = 12100
Can someone explain this to me thank you
Answer: x = 16.9
Concept:
Here, we need to know the idea of basic trigonometry.
Sine = Opposite / Hypotenues = O / H
Cosine = Adjacent / Hypotenues = A / H
Tangent = Opposite / Adjacent = O / A
Solve:
Angle θ = 50°
Opposite = x
Hypotenues = 22
Given formula
Sine = Opposite / Hypotenues
Substitute the value into the formula
sin (50) = x / 22
Multiply 22 on both sides
sin (50) × 22 = x/22 × 22
x = 22 sin (50)
x = 16.9
Hope this helps!! :)
Please let me know if you have any questions
Answer:
16.85
Step-by-step explanation:
SOH CAH TOA
sin 50 = about 0.766
times by 22 then u get
16.85
Hope this helps
What is the rate of change of the function shown on the graph? Round to the nearest tenth.
A 1-pound bag of sunflower seeds provides 96 grams of protein, There
are 58.5 grams of protein in a 6.5-ounce bag of pumpkin seeds. Which
type of seed has more grams of protein per ounce? How many more
grams of protein are there in 24 ounces of the higher-protein seeds?
Answer:
Pumpkin seed has more grams of protein per ounce
216 grams of protein
Step-by-step explanation:
1 pound = 16 ounce
16 ounce of sunflower seeds = 96 grams of protein
6.5 ounce of pumpkin seeds = 58.5 grams of protein
Which type of seed has more grams of protein per ounce?
Sunflower seeds:
Protein per ounce = 96 grams / 16 ounce
= 6 grams of protein per ounce
Pumpkin seeds:
Protein per ounce = 58.5 grams / 6.5 ounce
= 9 grams of protein per ounce
Therefore,
Pumpkin seed has more grams of protein per ounce
How many more grams of protein are there in 24 ounces of the higher-protein seeds?
Quantity of protein = 24 ounces ×
9 grams of protein per ounce
= 216 grams of protein
¿Qué se requiere para sumar o restar dos matrices?
3(5-4)+2(5)-5 squared
the answer should be -12 if I did the math right.
Step-by-step explanation:
3*1+10-5^2(we subtract 5 from 4 first because it was inside bracket)
3+10-25(Square of 5 is 25)
-12(subtracting the above equation 12 comes)
Can someone help me with this math homework please!
Answer:
negative
Step-by-step explanation:
Let,
x1 = 0
x2 = 1
y1 = 50
y2 = 44
Formula : -
Slope = ( y2 - y1 ) / ( x2 - x1 )
Slope
= ( 44 - 50 ) / ( 1 - 0 )
= - 6 / 1
= - 6
- 6 is a negative number.
So, the slope is negative.
Please asap find the area of this figure... picture attached
Answer:
1 911.484916 square units
Step-by-step explanation:
Area of the rectangle = 50 * 14 = 700 square units
thanks to the given informations we can find the height of the triangle by using sine.
sin = opposite/hypotenuse
opposite = hypotenuse * sin = 50 * 0,969188 = 48,459397
Area of the triangle = (50 * 48,459397)/2 = 1.211,484916 square units
Total area = 1.211,484916 + 700 = 1.911,484916 square units
What is the prime factorization of 750
Help pls appreciate it pls
Answer: D.
Step-by-step explanation:
If we know that 1 side equal along with 1 angle is equal to the other triangles angle and side. Than only one answer really stands out (at least to me) if that makes any sense
Hope this helps
:)
ASAP please help meeeeeeeeeeeeeee
Answer:
7/10
(-4×-7)/(5×8)
=28/40
=7/10
Find the measure of one exterior angle for the following regular polygon
Can you answer this math homework? Please!
Answer:
1
Step-by-step explanation:
Answer:
They are both correct
Step-by-step explanation:
They started isolating different variables but essentially they have found the same answers just with different isolated variables, thus their answers look different, but in reality, are the exact same.We can test by plugging 5 in for x, and 15 in for y.
Jared:
[tex]y=x+10\\[/tex][tex]15=5+10[/tex][tex]15=15[/tex]Nicole:
[tex]x=y-10[/tex][tex]5=15-10[/tex][tex]5=5[/tex]Equations are equal.
draw the Venn diagram of b union b
A=(2 4 6 8 10 12)
B=(1 3 5 7 9 11)
Step-by-step explanation:
Explanation is in the attachment
hope it is helpful to you ☺️
What are the steps to this problem (and the answer?)
Answer:
[tex](25 {x}^{2} + 20xy + 16 {x}^{2} )(5x - 4y) = \\ 125 {x}^{3} + 100 {x}^{2} y + 80x {y}^{2} - 100 {x}^{2} y \\ - 80x {y}^{2} - 64 {y}^{3} = \\ 125 {x}^{3} - 64 {y}^{3} \\ please \: give \: brainliest[/tex]
Been on this math problem for almost an hour will mark most brainly(just the bottom part)
Answer:
5. (8,33) (-1, -21) (5, 15)
6. (-5, 29) (2, 1) (4, -7)
7. (-4, -9) (0, -1) (7, 13)
8. (-9, 0) (1, 8) (5, 4)
Step-by-step explanation:
Since X is given, you plug it into the equations.
Then put the answers into the Y. hope it helps!!
Factor the following polynomial 9x2 + 21x – 18
Answer:
factors are
21 and x
Step-by-step explanation:
equation 9 × 2 + 21x - 18
terms 9 , 2, 21x, -18
factors 21x = 21 and x
Answer:
3(x + 3)(3x - 2)
Step-by-step explanation:
Given
9x² + 21x - 18 ← factor out 3 from each term
= 3(3x² + 7x - 6) ← factor the quadratic
Consider the factors of the product of the x² term and the constant term which sum to give the coefficient of the x- term
product = 3 × - 6 = - 18 and sum = + 7
The factors are + 9 and - 2
Use these factors to split the x- term
3x² + 9x - 2x - 6 ( factor first/second and third/fourth terms )
3x(x + 3) - 2(x + 3) ← factor out (x + 3) from each term
(x + 3)(3x - 2)
Then
9x² + 21x - 18 = 3(x + 3)(3x - 2) ← in factored form
x-(x-(x-y³)) use x=9, and y=1
Answer:
The answer: 8
Step-by-step explanation:
x-(x-(x-y³))
x=9 , y=1 —> 9 - (9-(9-1³)) —> 9 - (9-(8))—> 9 - ( 1) —> =8
The midpoint of AB is M(1,1). If the coordinates of A are (3, 3), what are the coordinates of B?
Answer:
The answer in (-1,-1) because it goes down by x-2 and y-2
I solved this, but apparently, my answer was incorrect. Could someone explain?
Answer:
24 cm^2
Step-by-step explanation:
Find Side Length:
20cm/4 = 5cm
Use x:
First Diagonal - 4x; Second Diagonal = 3x
Pythagorean Theorem:
a^2 + b^2 = c^2
Use Pythagorean Theorem:
a = 1/2 of First Diagonal
b = 1/2 of Second Diagonal
c = Side Length
2x^2 + 1.5x^2 = 5^2
4x^2 + 2.25x^2 = 25
6.25x^2 = 25
x^2 = 4
x = 2
Formula for Area of Rhombus:
1/2 * First Diagonal * Second Diagonal
Use Formula for Area of Rhombus:
1/2 * 4(2) * 3(2)
= 1/2 * 8 * 6
= 4 * 6
= 24 cm^2
