The formula for the nth term of the arithmetic sequence whose first term is 7 and the common difference is -3 is - a[n] = 10 - 3n
What is an Arithmetic progression?An arithmetic progression is a sequence of numbers such that the difference between the consecutive terms is constant. A sequence -
a₁ , a₂, a₃ , a₄ ...... aₙ
will be an arithmetic progression if -
a₂ - a₁ = a₃ - a₂ = a₄ - a₃ = d (constant) is called common difference of A.P. and a₁ = 'a' as the first term.
Given is the the first term equal to 7 and the common difference equal to
- 3.
We can calculate the nth term of an A.P. using the formula -
a[n] = a + (n - 1)d
a[n] = 7 + (n - 1)(- 3)
a[n] = 7 - 3n + 3
a[n] = 10 - 3n
Therefore, the formula for the nth term of the arithmetic sequence whose first term is 7 and the common difference is -3 is -
a[n] = 10 - 3n
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14% of what number is 21
Answer:
150 is the number
Step-by-step explanation:
The equation we should set up is from the sentence "14% of what number is 21"
To rearrange it into a proper equation, replace "of what number" with " * x "
and "is" with "="
The sentence becomes:
14% * x = 21
since 14% = 0.14, replace 14% with 0.14 in the equation
0.14 * x = 21
divide both sides by 0.14
x = 21 / 0.14
x = 150
[tex]f(x)=x^{3}-3x^{2} -4x+12[/tex]
Answer:
the answer is f'(x)=3x^2-6x-4
Step-by-step explanation:
Our rental car company turns $42 50% per day to run a car in 10 cents for every mile driven video want to run a car knowing next plans drive 225 miles and she has at the most $150 to spend
a rental car company charges $42.50 per day to rent a car intense sense for every mile driven Lydia wants to run a car knowing that she plans to drive 225 miles in she has at most $150 to spend
Let
x -------> the number of miles
y -----> the total charge
we have that
the linear equation that represent this problem is
y=0.10x+42.50
For x=225 miles
substitute teh value of x
y=0.10(225)+42.50
y=$65
Can somebody please help me right now??? i’m stuck and i need help with this bad
Answer:
B
Step-by-step explanation:
Using a minor key within a song is usually to make it more sad or negative in emotion, though with this question the fast tempo should already rule out A because it is quite the opposite to laziness.
1. Mark bought a pen for $0.49, a box of pencils for $1.29, and a pad of paper for $0.98. How much did he spend in all? 2 The coach honght 10 ice cream cones for $0 35 each How much did he spend?
If Mark bought a pen for $0.49, a box of pencils for $1.29, and a pad of paper for $0.98, then he had spend a total of $ 2.76, and if 10 ice cream cones were brought for $0.35 each, then the total amount paid is $3.5
As per the question statement, Mark bought a pen for $0.49, a box of pencils for $1.29, and a pad of paper for $0.98,
And the coach bought 10 ice cream cones for $0.35 each.
We are required to calculate the following:
(a) The total amount Mark had to pay
(b) The total amount the coach had to pay
Starting with part (a),
If Mark bought a pen for $0.49, a box of pencils for $1.29, and a pad of paper for $0.98, then the total amount he will have to pay will simply be the summation of the individual costs, that is, $[0.49 + 1.29 + 0.98] = $ 2.76.
Now solving part (b),
If the coach bought 10 ice cream cones for $0.35 each, then the total amount he/she will have to pay, will be a simple multiplication of the price of one ice cream, with the number of ice creams bought, that is,
$[0.35 * 10] =$3.5
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Find an anti derivative for each function when C = 0
Given:
[tex]\frac{9}{8}\sqrt[8]{x}[/tex]You can find the antiderivative by integrating it:
1. Set up:
[tex]\int\frac{9}{8}\sqrt[8]{x}\text{ }dx[/tex]2. You can rewrite it in this form:
[tex]=\frac{9}{8}\int x^{\frac{1}{8}}dx[/tex]3. Apply this Integration Rule:
[tex]\int x^ndx=\frac{x^{n+1}}{n+1}[/tex]Then, you get:
[tex]=\frac{9}{8}(\frac{x^{\frac{1}{8}+1}}{\frac{1}{8}+1})+C[/tex][tex]=\frac{9}{8}(\frac{x^{\frac{9}{8}}}{\frac{9}{8}})+C[/tex]4. Simplify:
[tex]=\frac{9}{8}(\frac{x^{\frac{1}{8}+1}}{\frac{1}{8}+1})+C[/tex][tex]=\frac{9}{8}(\frac{8\sqrt[8]{x^9}}{9})+C[/tex][tex]=\sqrt[8]{x^9}+C[/tex]Remember this Property for Radicals:
[tex]\sqrt[m]{b^n}=b^{\frac{n}{m}}[/tex]You can rewrite the expression in this form:
[tex]=\sqrt[8]{x\cdot x^8}+C[/tex]Applying this Property for Radicals:
[tex]\sqrt[n]{b^n}=b[/tex]You get:
[tex]=x\sqrt[8]{x}+C[/tex]5. Knowing that:
[tex]C=0[/tex]You obtain:
[tex]=x\sqrt[8]{x}[/tex]Hence, the answer is:
[tex]=x\sqrt[8]{x}[/tex](3y+11) ° = _____ °
10y ° = ______ °
(4x-22) ° = _____ °
(7x+4) ° = _____ °
Answer:
(3y + 11)° = 50°
10y° = 130°
(4x - 22)° = 50°
(7x + 4)° = 130°
Explanation:
First, find the value of the variable. Let's find y.
(3y + 11) + 10y = 180 (sum of adjacent angles on a straight line)
Simplify and solve the equation.
13y + 11 = 180
13y = 169
y = 13
Substitute y into the angle measures to find values.
3(13) + 11 = 50
10(13) = 130
Hence, (3y + 11)° = 50° and 10y° = 130°.
Next, find x.
(7x + 4) + (4x - 22) = 180 (sum of adjacent angles on a straight line)
Simplify and solve the equation.
11x - 18 = 180
11x = 198
x = 18
Substitute x into the angle measures to find values.
4(18) - 22 = 50
7(18) + 4 = 130
Hence, (4x - 22)° = 50° and (7x + 4)° = 130°.
Alternatively, you do not have to find x to find (4x - 22)° and (7x + 4)°.
4x - 22 = 3y + 11 = 50° (vertically opposite angles)
7x + 4 = 10y = 130° (vertically opposite angles)
a=1/2h(b1+b2) is the formula for the area of a trapezoid. Rewrite the formula for b1. Then find the unknown base of the trapezoid that has an area of 78 in2, a height of 12 inches, and one base length of 8 inches.
The formula rewritten for b1 is b1 = 2a/h - b2
The unknown base of the trapezoid is 5 inches
What is subject of formula?A subject of formula is simply described as the variable that is made to stand alone on one side of the equality sign.
It is the variable expressed in terms of other variables in an expression.
Given the formula for the area of a trapezoid as;
a = 1/2h(b1+b2)
Where;
a is the area of the trapezoidh is the heightb1 and b2 are the basesLet's make b1 the subject of formula
cross multiply
(b1+b2)h = 2a
Now, divide both sides by h, we have!
b1 + b2 = 2a/h
Take b2 over the equality sign
b1 = 2a/h - b2
Now, substitute the values into the formula
b1 = 2(78)/12 - 8
Expand the bracket
b1 = 156/12 - 8
Find the quotient
b1 = 13 - 8
find the difference
b1 = 5 inches
Hence, the value is 5 inches
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the table below shows the rebeltonshir betweenth number of miles travledet, and the number of salle
The question is really asking for the unit rate but on a supposedly linear graph that is not to scale, so it is difficult to evaluate real rates.
values equivalent to -12/5
-12/5
This is a improper fraction, so lect's corvert it into a mixed fraction
2
5 12
2
Written as a mixed fraction -2 2/5
It's negative
The possible answers are -2 2/5
12/-5
-12/5
Graph the linear equation
y=4x-1
A line is uniquely defined by two points. So, we only need to find two points that lie on the line.
[tex]x=1 \implies y=4(1)-1=3\\\\x=2 \implies y=4(2)-1=7[/tex]
So, you can draw the line through (1, 3) and (2, 7).
group the labels according to the type of interest they describe
There aren't any SARS-CoV-2 variations listed as Variant Of Interest right now.
A genetic variant with certain genetic markers linked to altered receptor binding, decreased ability of antibodies to neutralise an infection or immunisation, decreased therapy effectiveness, potential impact on diagnosis, or anticipated rise in disease severity.
Potential characteristics of an interesting variant:
Certain genetic markers that are believed to influence immune evasion, diagnosis, or treatment.Evidence indicates it is the source of unusual outbreak clusters or a higher percentage of cases.Limited occurrence or spread in the US or other nations.To know more about SARS-CoV-2 refer to the given link :
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The complete question is-
Labels for SARS-CoV-2 Variants of Interest and Concern.
Richie Rich deposited $5,250 into an account. He made no additional deposits or withdrawals. Richie Rich earned 3.5% annual simple interest on the money in the account. What was the balance in dollars and cents in Richie Rich's account at the end of 5 years?
To calculate the balance on the account after 5 years you have to calculate the simple interest using the formula:
[tex]A=P(1-rt)[/tex]A= total accured amount
P= principal amount
r= interest rate expressed in decimals
t=time
For
P=$5250
r=0.035
t=5years
The balance on the account will be:
[tex]\begin{gathered} A=5250(1+0.035\cdot5) \\ A=6168.75 \end{gathered}[/tex]At the end of the 5 years there will be $6168.75
Which equations can be used to find the lengths of thelegs of the triangle? Select three options.0.5(x)(x + 2) = 24x(x + 2) = 24x2 + 2x - 24 = 0x2 + 2x - 48 = 0x2 + (x + 2)2 = 100
Triangle area is equal to
1/2 base x height x 0.5 base = x feet.Height = (x + 2) feet
= 24 square feet
24 = 0.5(x)(x+2) \s0.5(x)(x + 2) = 24
The formulas that can be used to determine the triangle's leg lengths must be equivalent to 0.5(x)(x + 2).
To elaborate on this: 0.5(x)(x + 2) = 24
0.5(x2+2x) = 24 b) x(x + 2) = 24 c) x2 + 2x - 24 = 0 0.5(x2+2x) = 24 x(x + 2) is not equal to 0.5(x2+2x)0.5(x)(x + 2) = 24 12(x)(x + 2) = 24 x2 + 2x = 2(24) x2 + 2x - 48 = 0 x2 + (x + 2) is not comparable to x2+2x- 24 = 0 or x2+2x- 48 = 0.² = 100 \sx² + x² + 4x + 4 = 1002x² + 4x = 962(x2 + 2x + 48)= 0 is equivalent to 0.5(x2 + 2x) = 24.
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P is a polynomial defined by P(x) = 4x³ - 11x² - 6x + 9. Two factors are (x - 3) and
(x + 1). Rewrite the expression for P as the product of linear factors. Here is a blank
diagram to use to organize your thinking, if needed.
4Use algebra to solve the following equation. Round decimal to two places.400 (1.065)t = 850
We need to solve the equation
[tex]400(1.065)t=850[/tex]In order to do so, we can first divide both sides of the equation by 400:
[tex]\begin{gathered} \frac{400}{400}(1.065)t=\frac{850}{400} \\ \\ (1.065)t=2.125 \end{gathered}[/tex]Now, to isolate the variable t on the left side and find its value, we can divide both sides by 1.065:
[tex]\begin{gathered} \frac{\mleft(1.065\mright)}{1.065}t=\frac{2.125}{1.065} \\ \\ t=1.9953\ldots \\ \\ t\cong2.00 \end{gathered}[/tex]Therefore, rounding to two decimal places, the answer is 2.00.
Which multiplication expression can you use to find
3/4 divided by 3/8
The given multiplication expression is 3/4÷3/8 or 3/4×8/3
What is multiplication expression?
Mathematical expressions that include multiplication are called multiplication expressions. We combine the integers and then the like variables to simplify the equation. We will therefore obtain x to the second power if we multiply two xs together.
An answer to a multiplication sentence is obtained by multiplying the various components. The multiplier (first number), multiplicand (second number), and product are the components of a multiplication phrase (third number).
The simplest form of an expression is one in which terms cannot be concatenated. In order to write 3 + (2 5) simply: Start by carrying out the procedure between parenthesis. The addition should then be done.
Given, 3/4÷3/8
3/4×8/3
=2
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The picture is attached. I have to solve each one and then choose the graph. Well I have to graph it.
Graphing the function:
[tex]\begin{gathered} x=-8 \\ f(-8)=\frac{1}{4}(-8)=-2 \end{gathered}[/tex][tex]\begin{gathered} x=1 \\ f(1)_{\text{ }}does_{\text{ }}not_{\text{ }}exist \end{gathered}[/tex][tex]undefined[/tex]Please help!!If the simple interest on $7,000 for 4 years is $1,960, then what is the interest rate?
Use the formula for the simple interest
[tex]I=p\cdot r\cdot t[/tex]I= interest
p= initial deposit
r=rate
t= time
clear the equation for r
[tex]\frac{I}{p\cdot t}=r[/tex]replace data in the formula
[tex]\begin{gathered} \frac{1960}{7000\cdot4}=r \\ \frac{1960}{28000}=r \\ 0.07=r \end{gathered}[/tex]pass the decimal to percentage
7%
the interest rate is 7%
Which of the following graphs shows a system of equations with the same end behavior for both functions? Thanks!
Solution
The answer is given in the graph below
Steps for graphing a quadratic equation from vortex form
Graphing a Quadratic Equation
Let's take as an example the function:
[tex]y=-2\mleft(x-3\mright)^2+5[/tex]The vertex form of a quadratic function is:
[tex]y=a\mleft(x-h\mright)^2+k[/tex]Where a is the leading coefficient and (h,k) is the vertex.
If a is positive, the function is concave up, if negative the function is concave down.
The first step is to obtain the parameters by comparing the given equation with the general equation.
Thus, we have: a = -2. Vertex = (3,5)
Now we locate the vertex in the coordinate plane and draw the parabola opening down.
For more precision, we can substitute some points around the vertex, like for example:
x={1,2,4,5}
We get the y-coordinates:
y={-3,3,3,-3}
Then we plot the graph as follows:
Find a degree 3 polynomial with real coefficients having zeros 3 and 4 − 3 i and a lead coefficient of 1. Write P in expanded form.
[tex]x^{3}[/tex]-2[tex]x^{2}[/tex]+9x-18 This is a degree 3 polynomial with real coefficients having zeros 3 and 4 − 3 i and a lead coefficient of 1
What is polynomial ?Algebraic expressions called polynomials include constants and indeterminates. Polynomials can be thought of as a type of mathematics. Nearly all branches of mathematics employ them to express numbers, and calculus is one of those branches where they play a crucial role.
complex zeros always occur in pairs.
zeros are 2,3i,-3i
f(x)=(x-2)(x-3i)(x+3i)=(x-2)([tex]x^{2}[/tex]-[tex]3i^{2}[/tex])
=(x-2)([tex]x^{2}[/tex]-[tex]9i^{2}[/tex])
=(x-2)([tex]x^{2}[/tex]+9)
=[tex]x^{3}[/tex]-2[tex]x^{2}[/tex]+9x-18
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PLEASE HELP HELP HELP HELP HELP
Answer:
WHAT IS THATT??
Step-by-step explanation:
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two mechanics worked on a car the first mechanic worked for 10 hours in the second mechanic worked for 15 hours together they charged a total of $2,450 what was the rate charge per hour by each mechanic if the sum of the two rates was $185 per hour
wo mechanics worked on a car the first mechanic worked for 10 hours and the second mechanic worked for 15 hours together they charged a total of $2,450 what was the rate charge per hour by each mechanic if the sum of the two rates was $185 per hour
Let
x -----> the rate of the first mechanic
y -----> the rate of the second mechanic
we have that
x+y=185 -------> equation A
10x+15y=2,450 ------> equation B
Solve the system of equations by graphing
see the attached figure
therefore
the rate of the first mechanic is $65 per hour the rate of the second mechanic is $120 per hourFor every 20 minutes spent riding his bike, Tim stops 3 times to drink water. if he rides for 80 minutes how many times, he will stop to for a drink.
Answer:
Tim will stop for a drink 12 times
Step-by-step explanation:
Tim drinks water 3 times every twenty minutes. 80 divided by 20 equals 4. Take the 4 times and multiply it by 3 to get the amount of times he stopped to drink water.
I hope this helps
3. What is the simple interest and the amount in the account if you invested$175.00 for 90 days at 8%?
The formula for the simple interest I after an amount P is invested for period t at a simple interest rate r is:
[tex]I=P\cdot r\cdot t[/tex]In this problem, the simple interest annual rate is 8% = 0.08. But the period t of the investment is
t = 90 days = 3 months = (12/4) months = (1/4) year
And the rate is:
[tex]r=\frac{0.08}{\text{year}}=\frac{\frac{0.08}{4}}{\frac{\text{year}}{4}}=\frac{0.02}{t}[/tex]Then, using P = 175, the interest, in dollars, is:
[tex]I=175\cdot\frac{0.02}{t}\cdot t=175\cdot0.02=3.5[/tex]And the amount A, in dollars, in the account after that period is:
[tex]A=P+I=175+3.5=178.5[/tex]Answers:
Simple interest: $3.50
Ammount: $178.50
What is the domain of the inverse function of f(x) =x³?
An art store sells packages of two different-sized square picture frames. The side length of the larger frame, S(x), is modeled by the function S(a) = 3v2- - 1, where x is the area of the smaller frame in square inches. Which graph shows S(x)?
The graph A is the one that accurately represents the side length of the bigger frame S(x).
Modeling the function S(x) by
S(x) has experienced the following changes:
a 1 shift to the right, as shown by the square root's value of -1;
S(x) travels to the right by 1 = 0 + 1 = 1 whereas f(x) stays at 0.
The graph is stretched by a factor of 3 (a number that multiplied the square root).
Consequently, the graph A shows the two changes on S. (x). As a result, it is the best choice.
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Ann Marie has a gross annual income of $98,000. According to Housing Recommendation #1, how much can she devote to monthly housing expenses?
Ben needs to buy so he can buy a package of three bars of soap for $3.75 or a package of eight bars of soap for $12. If he buys the cheapest soap how much will he save per bar
When he buys the cheapest soap, the amount he save per bar is $0.25.
What is money?Money is anything that's used as a medium of exchange.
In this case, three bars of soap cost $3.75. Each bar will bre:
= $3.75 / 3
= $1.25
Also, a package of eight bars of soap for $12. Each bar will be:
= $12 / 8
= $1.5
The amount that will be saved will be the difference between the values above. This'll be:
= $1.5 - $1.25
= $0.25
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