Part A
Answer: x = 20--------------------------------
Explanation:
AP = arithmetic progression, which is another way of saying arithmetic sequence.
Let d = common difference
first term = 10second term = first+d = 10+d = xthird term = second+d = x+d = 30Apply substitution like so
x+d = 30
10+d+d = 30 ... replaced x with 10+d
10+2d = 30
2d = 30-10
2d = 20
d = 20/2
d = 10 is the common difference
Therefore,
x = 10+d = 10+10 = 20
The AP {10,x,30} updates to {10,20,30}. We see the gap between terms is 10 units. All AP's have the same gap width between adjacent terms.
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Part B
Answers: x = 10 and y = 14--------------------------------
Explanation:
We use the same ideas mentioned back in part A.
d = common difference = unknown for now
first term = 6second term = first+d = 6+d = xthird term = second+d = x+d = (6+d)+d = 6+2d = yfourth term = third+d = y+d = (6+2d)+d = 6+3d = 18Hopefully you can see how each term builds up to form the next one. We'll solve that last equation like so
6+3d = 18
3d = 18-6
3d = 12
d = 12/3
d = 4
So we then can say:
x = 6+d = 6+4 = 10y = 6+2d = 6+2(4) = 6+8 = 14The arithmetic sequence {6,x,y,18} updates to {6,10,14,18}. There's a gap of 4 between each adjacent term.
IT
17) Between which two consecutive whole numbers does the length of the diagonal
fall? The length of the diagonal is between
a) 3 and 4 b) 4 and 5
c) 5 and 6 d) 6 and 7
V 18
기
D
Ос
Od
Answer:
4 and 5, closer to 4
Step-by-step explanation:
hope that helps>3
b) 20 labourers complete the construction of a building in 24 days. In how many days would 16 labourers complete the construction?
Answer:
16 labourers complete the construction
in 30 days
Step-by-step explanation:
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A square vegetable garden has side lengths of 9 feet. You plant flowers i
the center portion of the garden, a square that has side lengths of 5
feet.You divide the remaining space into 4 equal sections and plant
tomatoes,onions, zucchini, and peppers. What is the area of the pepper
section?
Answer:
14 Sq ft
Step-by-step explanation:
9×9=81
5×5=25
81-25=56
56÷4=14
The value of the 7 in 37,560 is blank the value of the 7 and 4,720
Answer:
The value of the 7 in 37, 560 is greater than the value of the 7 in 4, 720.Step-by-step explanation:
In 37, 560, the value of 7 is 7, 000; in 4, 720, the value of 7 is 700.7, 000 > 700[tex]\tt{ \green{P} \orange{s} \red{y} \blue{x} \pink{c} \purple{h} \green{i} e}[/tex]
Please help me with this! Write the equation of the line in fully simplified slope intercept form. Explanation and answer please ^^
Answer:
y = -1/2x - 8
Step-by-step explanation:
y = -1/2x - 8
If (x - 4) varies inversely as (y + 3) and x = 8 when y = 2, what is x when y = - 1?
Answer:
[tex]x=14[/tex]
Step-by-step explanation:
If two values are inversely proportional, their product must be maintained. That way, if one value goes up, the other goes down by the same extent.
Therefore, if [tex](x-4)[/tex] and [tex](y+3)[/tex] vary inversely, their product will be the same for all values of [tex]x-4[/tex] and [tex]y+3[/tex].
Let [tex]x=8[/tex] and [tex]y=2[/tex] as given in the problem. Substitute values:
[tex](8-4)(2+3)=(4)(5)=20[/tex]
Hence, the maintained product is [tex]20[/tex].
Thus, we have the following equation:
[tex](x-4)(y+3)=20[/tex]
Substitute [tex]y=-1[/tex] to find the value of [tex]x[/tex] when [tex]y=-1[/tex]:
[tex](x-4)(-1+3)=20,\\(x-4)(2)=20,\\x-4=10,\\x=10+4=\boxed{14}[/tex]
EMERGENCY A speeding ticket costs $80 plus $10 for each mile per hour over the speed limit the violator was traveling. How much would someone going 12 miles per hour faster than the speed limit have to pay for their ticket?
Answer:
$200
Step-by-step explanation:
Fine calculated per mile = $10
Fine calculated for 'm' mile = 10 * m = 10m
Cost paid by violator = 80 + 10m
m = 12 miles
Cost paid by the violator = 80 + 10*12
= 80 + 120
= $ 200
Sin A 4/5.
Find
COSA + tan A
Answer:
Step-by-step explanation:
The opposite side (the one not connected to A) = 4
The hypotenuse is 5
The adjacent side needs to be found for the cosine and the tangent.
a^2 + b^2 = c^2
a = opposite side = 4
b = adjacent side = ?
c = hypotenuse = 5
4^2 + x^2 = 5^2
16 + x^2 = 25
x^2 = 25 - 16
x^2 = 9
x = sqrt(9)
x = 3
cos(A) = adjacent / hypotenuse = 3/5
Tan(A) = opposite / adjacent = 4/3
cos(A) + tan(A) = 3/5 + 4/3
cos(A) + tan(A) = 9/15 + 20/15 = 29/15
if b = 5, what is b³
Answer:
125
Step-by-step explanation:
5³= 5 × 5 × 5 = 125
Answer:
125 is your answer.
Step-by-step explanation:
b = 5
=5 X 5 X 5
=125
When a new cellphone is put on the market, the demand each month can be described by the function C of t is equal to negative square root of the quantity t squared plus 4 times t minus 12 end quantity plus 3 where C (t) represents the demand of the cellphone (measured in millions of people) and the time, t, is measured in months. Which of the following solution(s) are valid for a positive demand?
A function is positive where it is above the x-axis
The valid solution for positive demand are; t = 3, and t = 2
The reason the above values are correct is as follows:
Known parameters:
The given function of the demand is; [tex]C(t) = \mathbf{ -\sqrt{t^2 + 4 \times t - 12} +3}[/tex]
Where;
C(t) = The demand of the cellphone (in millions of people)
t = The number of months
The condition positive demand is C(t) ≥ 0
Therefore;
[tex]-\sqrt{t^2 + 4 \times t - 12} +3 \geq 0[/tex]
[tex]-\sqrt{t^2 + 4 \times t - 12} \geq -3[/tex]
[tex]\sqrt{t^2 + 4 \times t - 12} \leq 3[/tex]
t² + 4·t - 12 ≤ 9
t² + 4·t - 12 - 9 ≤ 0
t² + 4·t - 21 ≤ 0
(t - 3) × (t + 7) ≤ 0
∴ t ≤ 3, or t ≥ -7
At t = 2 < 3, we have;
C(2) = -√(2² + 4×2 - 12) + 3 = 3
At t = 1 < 3, the function is; C(1) = -√(1² + 4×1 - 12) + 3 (Is undefined)
Therefore, the valid solution for positive demand are;
t = 3, and t = 2
Learn more about the functions here:
https://brainly.com/question/24249596
Answer:
3,3
Step-by-step explanation:
In a bakery, 70% of the doughnuts are glazed. If glazed doughnuts account for 21% of all pastries in the bakery, what percent of all pastries in the bakery are doughnuts
Answer:
30%
Step-by-step explanation:
You are adding two rational numbers with different signs.How can you tell if the sum will be positive, Negative,or Zero
slove for w -22=4(w=2)-7w
Find the least common multiple (LCM) of 6 and 10,
O A. 60
O B. 20
O C. 40
O D. 30
is 9.40 equal to 9.4
Answer:
no
Step-by-step explanation:
if it was 9.04 it would
its not equal because 9.40 is 10^2 but 9.4 is 10^1
please help me with this ixl please
Answer:
plot these points on the graph and connect them
Step-by-step explanation:
T(5,-10)
U(9,-10)
V(2,0)
Jen has 2 quarters, 5 dimes, 3 nickels, and 2 pennies in her pocket.
Solve the formula for the indicated variable.
B = qn + q, for n
Answer:
n=B-q/q
Step-by-step explanation:
PLEASE HELP ME! I am suck on this math assignment
Hey there! I'm happy to help!
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QUESTION 18
Here is how you multiply a 2×2 matrix by a column vector (just one column matrix).
[tex]\left[\begin{array}{ccc}a&b\\c&d\\\end{array}\right] *\left[\begin{array}{ccc}x\\y\\\end{array}\right] = \left[\begin{array}{ccc}ax&by\\cx&dy\\\end{array}\right][/tex]
Once you get that final matrix, you add the rows which will give you a final column vector. Let's do it with this question, as we are multiplying together the matrices A and v.
[tex]\left[\begin{array}{ccc}-1&4\\2&0\\\end{array}\right] *\left[\begin{array}{ccc}8\\6\\\end{array}\right] =\left[\begin{array}{ccc}-8&24\\16&0\\\end{array}\right] =\left[\begin{array}{ccc}16\\16\\\end{array}\right][/tex]
So, your answer is [tex]\left[\begin{array}{ccc}16\\16\\\end{array}\right][/tex].
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QUESTION 14
We have this equation of an ellipse and we need to solve for y. When we have a more complex equation to solve you get rid of the things furthest from the variable you are solving for first and then you get closer and closer to it.
[tex]\frac{x^2}{25} + \frac{y^2}{16}=1[/tex]
We subtract [tex]\frac{x^2}{25}[/tex] from both sides.
[tex]\frac{y^2}{16}=1-\frac{x^2}{25}[/tex]
We multiply both sides by 16.
[tex]y^2=1-\frac{x^2}{25}*16[/tex]
We square root both sides.
[tex]y=[/tex] [tex]\sqrt{1-\frac{x^2}{25}*16[/tex]
We can take a four out of our root (because 16 is a perfect square so it can be simplified more).
y= [tex]4\sqrt{1-\frac{x^2}{25}[/tex]
And we take out 1/5 (which is the square root of 1/25).
y=± [tex]\frac{4}{5}\sqrt{1-x^2[/tex]
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QUESTION 17
We see that Sea Slugs have 3/10 matches won, so they have won 30% of their matches.
From now on, they will be winning 2/3 of their games. Let's look at the answer options.
A. If they play 15 more games, they will win 10 of them. Our total matches will be 25 (our original 10+15). So, we will have 13/25, which is equal to 52%, so this is incorrect.
B. If they play 10 more games they win 6 2/3 games (like that makes any sense) for a total of 9 2/3 games out of 20. This is about 48%, so this is incorrect.
C. If they play 40 games, they are winning fractional games again. They win 29 2/3 games out of 50 total, which is about 59%, but not quite 60. This is also incorrect.
D. If they play 45 matches, they will win 30 games. Add the original 10 and you have 40 games. Our total is 55. 40/55 is about 73%, so they have passed that 60% threshold, so this is the correct answer.
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QUESTION 16
Our question tells us that if we have two numbers x and y, and we add them, it has to be 24 or greater. By saying it can be equal to 24 or greater, we are going to be using a ≤ or ≥ sign. The opening of the arrow always faces the equal or greater quantity, and in this case it is x+y, so it will look like x+y≥24.
This eliminates answer choices B and D as they do not have the equal part on the inequality.
Product means to multiply, so it will be written as xy. It has to be less than 60, so in this case the greater quantity is 60, so the arrow will opening towards 60, so it will look like xy<60.
So, our final answer is A.
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QUESTION 12
You can only multiply matrices if the number of columns in the first matrix is equal to the number of rows in the second. So basically the two interior numbers have to be the same (a,b) and (b,c). So, if we follow this, we get these answers:
2×2 times 2×1 YES
2×1 times 2×2= NO
3×3 times 3×1= YES
3×1 times 3×3= NO
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Have a wonderful day and keep on learning! :D
There is a plant whose growth can be represented by a linear function. At 1 week it is
2 inches tall and at 2 weeks it is 4 inches tall. Write a linear equation to represent the
growth of the plant.
O y = 2x + 2
O y = 2x
O y = 4x + 2
Answer:
y=2x
Step-by-step explanation:
we can set x=number of week, and y=inches
as you can see, 1 week-> x=1 :y=2(1) = 2 inches
2 week-> x=2 :y=2(2)=4 inches
**if we substitute x to y = 2x + 2 and y = 4x + 2, it will not works.
Zachy plays a game. He earns and loses the following amounts of points throughout the entire game
-5
5
-5
-5
5
5
The smallest number when subtracted from the difference of the square of 29 and 22 gives a perfect square is
Answer:
Your answer is 33.
step- by step :
29×29-22×22=841-484
= 357
Closest square of 18 which is 324.
So, 357-324= 33. ans.
The population of a city is increasing 4% per year and is now 7,200. If it continues to increase at the same rate, what will the population be after 3 years?
Answer:
A = 7200(1.04)^3
A = 8099
Step-by-step explanation:
If f(x) = x^2 + 8x – 2 and f(0), then the result is:
-2.
0.
8.
Answer:
-2.
Step-by-step explanation:
f(0) = 0^2 + 8(0) - 2
= -2.
Find the distance between the two points rounding to the nearest tenth (if necessary).
(5,-5) and (8,-8)
Answer:
4.2
Step-by-step explanation:
d=sqrt[(x1-x2)^2+(y1-y2)^2]
d=sqrt[(5-8)^2+(-5+8)^2]
d=sqrt[(-3)^2+(3)^2]
d=sqrt[9+9]
sqrt18=4.24
Delores works weekends at the local coffee shop. Last weekend, she worked for 7.5 hours on Saturday and 8 hours on Sunday. If she earns $9 per hour, how much did she earn last weekend?
Answer:
So she earned 148 dollars and 50 cents or 148.5
Step-by-step explanation:
Please help me with A B and C
Answer:
b)A box from all 4 sides increases as the number increase
c)
Step-by-step explanation:
a+(n-1)d
a-first terms
d- difference
5+(n-1)4
5+4n-4
4n+1(the nth term)
so for 50th
its 4*50+1
Answer is 201 tiles
Hope this helps you :))
HELP!! Use the properties of addition to simplify this expression. 6-8 +6f-2f
Answer:
-2 + 4f
Step-by-step explanation:
6 - 8 + 6f - 2f
2(3 - 4 + 3f -f) [Distributive Property]
=> 2(-1 + 3f - f)
=> 2(-1 + 2f)
=> -2 + 4f
Answer:
4f-2
Step-by-step explan:
6-8+6f-2f
6-8+4f
4f-2
When is ignorance delightful
Answer:
Ignorance, or a lack of knowledge, isn't usually viewed as a good thing. However, there may be situations when you're happier not knowing the truth. A common expression used to describe these situations is “Ignorance is bliss.” This phrase is an idiom, which is means that it isn't meant to be taken literally.
I am super late
PLZ HELPP
Q: Nitrates are organic compounds that are a main ingredient in fertilizers. When those fertilizers run off
into streams, the nitrates can have a toxic effect on
fish. An ecologist studying nitrate pollution in two
streams measures nitrate concentrations at 42 places on Stony Brook and 42 places on Mill Brook. The parallel dotplots display the data.
1. Explain what the dot above 12 in the Stony Brook graph represents.
By looking at the dot graph, we can see that the single dot above 12 in the Stony Brook graph, means that the ecologist find that in one of the 42 places measured in the Stony Brooks lake, the nitrate concentration was 12 mg/L
To understand this, first I want to give a brief explanation of how these graphs work.
You know that the ecologist did study the Nitrate pollution at 42 places in two lakes.
Each of these 42 places is represented with a dot in the corresponding graph. Now looking at the graph, the position of the dots represents the nitrate concentration (you can see it in the horizontal axis) on one of these 42 places (42 dots for 42 places).
So, having a single dot above 12 in the Stony Brook graph, means that the ecologist find that in one of the 42 places measured in the Stony Brooks lake, the nitrate concentration was of 12 mg/L
If you want to learn more, you can read:
https://brainly.com/question/16354226
