[tex]n^{th}\textit{ term of an arithmetic sequence} \\\\ a_n=a_1+(n-1)d\qquad \begin{cases} a_n=n^{th}\ term\\ n=\textit{term position}\\ a_1=\textit{first term}\\ d=\textit{common difference}\\[-0.5em] \hrulefill\\ a_1=9\\ d=-2 \end{cases} \\\\\\ a_n=9+(n-1)(-2)\implies a_n=9-2n+2\implies a_n=11-2n[/tex]
How many pounds of walnuts that cost $0.80 per pound must be mixed
with 8 pounds of cashews that costs $1.25 per pound to make a mixture of
nuts that costs $1.00 per pound?
Answer:
The number of walnut pounds we need to add is 10
Step-by-step explanation:
We need to make a mixture that costs $1 per pound.
That means that the total cost of our mixture, divided by the number of pounds must be equal to 1.
[tex]\frac{MixtureCost}{NumberOfPounds} = 1[/tex]
Well, we know that the total cost of our mixture is equal to the cost of the cashews + cost of walnuts.
[tex]MixtureCost = CashewsCost + WalnutsCost[/tex]
We also know that we'll buy 8 pounds of cashews that cost $1.25 each and some amount of pounds (which we'll call x) of walnuts that cost $0.80.
Knowing all of that, we can write this:
[tex]MixtureCost=8*1.25 + x*0.8[/tex]
If we make that multiplication, we have that
[tex]MixtureCost=10+x*0.8[/tex]
Now that we know the cost of our mixture, we just need to know the total number of pounds... But we already know that, don't we?
We know that there are 8 pounds of cashews and x pounds of walnuts, so here's what we can write:
[tex]NumberOfPounds=8+x[/tex]
Now, if we plug in the values we found in the first equation, here's what we have:
[tex]\frac{10+x*0.8}{8+x}=1[/tex]
The 8+x is dividing, so i'll pass it to the other side multiplying:
[tex]10+0.8*x=x+8[/tex]
The 10 in the left side will go to the right side with a negative sign:
[tex]0.8x=x-2[/tex]
Now, if I pass the x from the right side to the left one changing signs:
[tex]0.8x-x=-2\\\\-0.2x=-2[/tex]
By changing signs from both sides, we have that:
[tex]0.2x = 2\\\\x = 10[/tex]
Therefore, the number of walnut pounds we need to add is 10
HELP PLS
The function of F is defined by f(x)=x+2
find F(n-4)
Answer:
Step-by-step explanation:
f(n - 4)= n - 4 + 2 = n - 2
Please answer, thank you. Image below.
I need to find the missing angle. The letter represents the missing angle
Answer:
Top Image: 56°
Bottom Image: 134°
Step-by-step explanation:
I'm not sure which image you have a question on, so I'll just solve both.
Top Image:
We know that the sum of the angles will add up to 180 and that the angles of the triangle are f, f, and 68°. Therefore, we can set up the following equation:
f + f + 68° = 180°
Solving this gets f = 56°
Bottom Image:
We know that the sum of the angles will add up to 180 and that the angles of the triangle are 23°, 23°, and g. Therefore, we can set up the following equation:
23° + 23° + g = 180°
Solving this gets g = 134°
On a recent survey, 35% of those surveyed indicated that they preferred running. If 540 people were surveyed, how many people preferred running?
Answer: 189 people preferred running.
Step-by-step explanation: 35% is equal to 35/100. Since 540 people were surveyed, we can multiply 35/100 by 540 to find that 189 people out of 540 preferred running. Hope this helps!
Solve for D: 70D + 6 - 9D= 35 + 4D - 2.
70d+6-9d=35+4d-2
70d-9d-4d= 35-2-6
57d= 27
d= 27÷57
Joe thinks the area to be pantries on wall 2is 84 square feet.
Please put a picture next time :)
help me help me help me help me help me help me help me help me
Answer:
Hope it help
Step-by-step explanation:
1. B
2. A
3. C
4. C
5. D
Solve (x+7)^2=49 algebra
Answer: x = 0
Step-by-step explanation:
Given:
(x + 7)² = 49
Distribute:
x² + 7² = 49
Square:
x² + 49 = 49
Subtract 49 from both sides of the equation:
x² = 0
x = 0
The only solution to this equation is 0.
-> We can also see this with graphing. See attached.
answer:
x=0
Step-by-step explanation:
(x+7)^2=49
take the square root of both sides
√(x+7)^2=√49
x+7=7
x=0
Martin has a bag of marbles. He removed 1 marble at random, recorded the color and then placed it back in the bag. He repeated this process several times and recorded his results in a table. Find the experimental probability of drawing green color.
Using it's concept, it is found that there is a 0.3 = 30% experimental probability of drawing green color.
What is a probability?A probability is given by the number of desired outcomes divided by the number of total outcomes.
For an experimental probability, these numbers of outcomes are taken from previous trials.
Researching the problem on the internet, it is found that 15 out of 12 + 10 + 15 + 13 = 50 trials resulted in a green marble, hence the probability is given by:
p = 15/50 = 0.3.
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Which function has zeros of -8, 1, and 3?
Answer:
A?
Step-by-step explanation:
(x-3) (x+8)(x-1) would be the solution
Find the approximate values of the five-number summary for the data set represented by this box plot.
0 5 10 15 20 25 30 35 40 45 50 55 60 65 70 75 80 85 90 95 100
Answer:
Minimum: 0
Quartile Q1: 22.5
Median: 50
Quartile Q3: 77.5
Maximum: 100
Step-by-step explanation:
4.5,4.316,4.32,4.312 from least to greatest
4.5, 4.316, 4.32, 4.312
= 4.500, 4.316, 4.320, 4.312
Look at the thousandths and hundreths place in the decimal section.
Least to greatest = 4.312 < 4.316 < 4.32 < 4.5
I NEED HELP ON THE ONES THAT AREN'T CROSSED OFF!!!!!!!!!!!!!!!!!!!!! PLEASEEEEEEEEEEEEEEEEEEEEE ( i already did 8)
The computation of the word problem shows that the oranges will John have in 12 weeks will be 70 oranges.
How to solve the word problem?The word problem will be that John has 10 oranges and buys 5 more oranges every week. How many oranges will John have in 12 weeks.
The computation will be:
= 10 + 5x
where x= number of weeks.
= 10 + 5x
= 10 + 5(12)
= 10 + 60
= 70 oranges
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Which is true about the line whose equation is y + 3 = 0?
The slope is 3.
The y-intercept is 3.
The slope is zero.
The value of x always equals the value of y.
Answer:
The slope is 0
Step-by-step explanation:
Solve the equation for y
y+3=0
y = -3
The slope intercept form is
y = mx+b
where m is the slope and b is the y intercept
y = 0x-3
The slope is 0 and the y intercept is -3
Answer: The Slope Is 3
Step-by-step explanation:
You are missing the x after the 3.
considering the linear equation y=mx+b, the coefficient of x is ALWAYS the slope (rate of change)
what is the answer to this?
The domain of the function is from the point -5 up to infinity that is [-5, infinity)
Domain of a functionThe domain are the independent value of a function for which it exists.
From the given graph, the domain will be the inteval of the function along the x-axis.
From the graph, you can see that the domain of the function is from the point -5 up to infinity that is [-5, infinity)
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Having trouble with this, pretty sure the answers i have in there are wrong, please help. especially need help with the last question , thank you
The year in which the two quantities will be equal is 2133.
What is a linear equation?It is defined as the relation between two variables, if we plot the graph of the linear equation we will get a straight line.
Here we have the following data.
y=0.221x-368.264 For men
y=0.168x-255.196 for women
So when we will equate these two equation we will get the year in which two quantities will be same.
0.221x-368.264=0.168x-255.196
0.221x-0.168x=368.264-255.196
0.053x = 1123.068
x= 2133 year
Hence the year in which the two quantities will be equal is 2133.
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You purchase a hat for $50. There is a sales tax of 8.5%. What is the final cost with sales tax?
Answer:
Price before tax: $ 50.00
+ Sales tax (8.5%): $ 4.25
Total price including tax: $ 54.25
Step-by-step explanation:
A sales tax is a tax that is levied on the purchase of goods and services. Except for Alaska, Delaware, Montana, New Hampshire, and Oregon, all states in the United States and the District of Columbia charge a state sales tax when you buy goods or pay for services. Alaska, like many other states, allows local governments to levy local sales taxes. Certain kinds of goods are exempt from sales tax in some states. In Massachusetts, for example, there is no sales tax on ordinary supermarket goods. There are also extra tax surcharges in several states. Restaurants and motels in the hospitality business sometimes levy a tax rate greater than the state sales tax rate. Expected sales tax rates and potential tax surcharge rates should be checked with your state and area.
Sales Tax Calculation Formulas
Sales tax rate = sales tax percent / 100Sales tax = list price * sales tax rateTotal price including tax = list price + sales tax, orTotal price including tax = list price + (list price * sales tax rate), orTotal price including tax = list price * ( 1 + sales tax rate)1/3x + 5 x= -6 need expression 1/3x = 5 is equal to __ when x = -6
Answer:
3
Step-by-step explanation:
To evaluate an expression with a particular value of the variable, put that value where the variable is and do the arithmetic.
__
1/3(-6) +5 = -2 +5 = 3
For x = -6, the value of the expression is 3.
21 ounce of cat food equally among 4 cats
Answer:
5.25
Step-by-step explanation:
Using multiplication, if you do 4x5 you get 20, so adding .25 to the equation will add 1, therefore 20+1=21
So long story short 4 x 5.25 = 21
At 1:00 pm, Ryan realizes his computer has been unplugged. He needs to work on the computer in his car and wants it to be fully charged. The image on the right represents the time it took for the laptop to charge.
Resources:
Desmos Guide
Regression tool
Line of Best Fit Video
When can Ryan expect his laptop to be fully charged? Do a quick estimate and explain your reasoning.
He does a quick calculation at 1:17 and estimates the computer charges 1% a minute. He estimates it will be fully charged by 2:30. Was he right?
Was his prediction over or under?
Graph all the data points. Draw an original graph or use a digital graphing calculator. Hint: First, convert the minutes to decimals then create a table of values.
Use the regression tool on Desmos (see the Desmos guide) to graph the points on a line, or draw your own. Write a line of best fit in the form y = mx + b.
Based on the line of best fit, when will the computer be fully charged?
Was your first estimate correct? Why do you think Ryan's first estimate was not accurate?
The amount of time it will take for Ryan expect his laptop to be fully charged by following the example on the image attached.
What is the battery percentage about?16 %= 4m
28%= 15m
37%= 10m
51% = 24m
69% = 34m
81%= 17m
Based on his quick calculation at 1:17 and estimates that it will be fully charged by 2:30 is wrong because when you look at the i]steps above, you will see that it the minute used too charge varies.
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What is the perimeter of rhombus ABCD?
10 units
20 units
2√7 units
4√7 units
Answer:
The perimeter of the rhombus is 20 units
Step-by-step explanation:
One important fact about a rhombus is that all four of its sides are equal, so we only need to solve for one side in order to find the perimeter. We can use the Pythagorean Theorem to solve the side length of the rhombus. Using line AD as a reference, we know that the length of AD is the square root of the change in x squared plus the change in y squared, or [tex]\sqrt{3^{2}+4^{2} } =\sqrt{9+16} =\sqrt{25}=5[/tex] units. Multiply the length of AD by 4 and you'll get that the perimeter of rhombus ABCD is 5 × 4 = 20 un.
The perimeter of the rhombus ABCD is 20 units.
Option B is the correct answer.
What is a rhombus?A rhombus is a quadrilateral that has four equal sides.
Some of the properties we need to know are:
- The opposite sides are parallel to each other.
- The opposite angles are equal.
- The adjacent angles add upto 180 degrees.
We have,
We can use the distance formula to find the length of each side of the rhombus, and then add them up to find the perimeter.
The distance between points A and B is:
[tex]AB = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2}\\= \sqrt{(-2 - 1)^2 + (-3 - 1)^2}\\ = \sqrt{9 + 16}\\= \sqrt(25) \\= 5[/tex]
The distance between points B and C is:
[tex]BC = \sqrt{(x2 - x1)^2 + (y2 - y1)^2}\\= \sqrt{(-5 - (-2))^2 + (1 - (-3))^2}\\ = \sqrt{9 + 16}\\= \sqrt{25}\\= 5[/tex]
The distance between points C and D is:
[tex]CD = \sqrt{(x2 - x1)^2 + (y2 - y1)^2}\\ = \sqrt{(-2 - (-5))^2 + (5 - 1)^2}\\ = \sqrt{9 + 16}\\ = \sqrt{25}\\ = 5[/tex]
The distance between points D and A is:
[tex]DA = \sqrt{(x2 - x1)^2 + (y2 - y1)^2}\\ = \sqrt{(1 - (-2))^2 + (1 - 5)^2}\\ = \sqrt{9 + 16}\\= \sqrt{25}\\ = 5[/tex]
Since a rhombus has all sides of equal length, we can add up the lengths of the sides to find the perimeter:
P = AB + BC + CD + DA = 5 + 5 + 5 + 5 = 20
Therefore,
The perimeter of the rhombus ABCD is 20 units.
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Points A, B, and Care located on a circle, and chords exist between all three points. If the measure of ZBAC is 88°, what is the measure of BC?
OA. 88°
OB. 92°
O C. 176°
OD. 184°
Answer:
92
Step-by-step explanation:its right
The class was divided into 4 teams. Each team had 5 players. The
remaining class members- Ty, Keesha, and Sam- served as score keepers.
How many students were in the class?
EASY QUESTIONS EASY POINTS!!
Answer:
23 players.
Step-by-step explanation:
5 x 4 + 3 = 23
Find the area of the figure. Round to the nearest hundredth where necessary.
24 m
28 m
What are the values of x and y?
Step-by-step explanation:
In figure:
∠PRT+∠RTP+∠TPR=180
O
(angle sum property of triangle)
⇒x+(180
O
−∠RTQ)+60
O
=180
O
(linear pair)
⇒x+(180
O
−97
0
)+60
o
=180
O
⇒x=31
o
Now, ∠PRT+∠TRQ+∠QRS=180
O
(angle of straight line)
⇒x+48
o
+y=180
O
⇒31
o
+48
o
+y=180
O
⇒y=101
0
please help me with math i’d really appreciate it thank you
Answer:
Step-by-step explanation:
[tex]f(x) = \dfrac{2}{3}x-4\\[/tex]
When x = 0 ; f(x) = 0-4 = -4
When x = 3 ;
[tex]\sf f(3) =\dfrac{2}{3}*3-4\\\\ = 2-4\\\\ f(3) = -2[/tex]
When x = 6,
[tex]\sf f(6) = \dfrac{2}{3}*6-4\\\\ f(6) =2*2-4 = 4-4\\\\ f(6)= 0[/tex]
When x = -6;
[tex]\sf f(-6) =\dfrac{2}{3}*(-6)-4\\\\[/tex]
= 2*(-2)-4
= -4 - 4
f(-6) = -8
how do you write 10^3 / 10^7 in standard form for properties of exponents
Answer:
1 / 10000
Step-by-step explanation:
10^3 / 10^7
apply exponent rule: x^a / x^b = x^(a-b)
10^3 / 10^7 where a = 3 and b = 7
10^(3 - 7) = 10^(-4)
apply exponent rule: a^-b = 1 / a^b
1 / 10^(4)
10^4 = 10000
1 / 10000
Let me know if you have any questions !
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Answer:
10^-4
Step-by-step explanation:
In division of powers (when the numbers are the same), you subtract both the powers. In this case, it would be 3 - 7 = -4, resulting in a power of -4
Work out 2/15 of 5 Give your answer as a fraction in its simplest form.
Answer:
2/3
Step-by-step explanation:
2/15 of 5
Of means multiply
2/15 * 5
Multiply the numerators
2*5 = 10
Put over the denominator
10/15
We can divide the top and bottom by 5
10/5 =2
15/5 =3
2/3
Answer:
Step-by-step explanation:
help me slove this please i really need thee answer
Can someone help. I literally forgot this how
Answer:
Below.
Step-by-step explanation:
The 2 triangles are congruent ( By 2 angles and corresponding side).
The 2 marked angle are congruent so
5y - 30 = 2y + 6
3y = 36
y - 12.
So m < O = 5(12) - 30 = 30 degrees.
and m <N = 180 - 30 - 90 = 60 degrees, (as there are 180degrees in triangle)
EN = IV = 14.
It is possible to find the measure of OE and ON by using trigonometry of a right triangle.
tan 30 = EN / OE
OE = EN / tan30
= 14/tan30
= 24.3.
sin 30 = 14/ON
ON = 14 / sin 30
= 28.