S5 = 20
A6 = 25
A1=
d=
The general formula for arithmetic sequence is:
An = A1 + (n - 1)d
25 = A1 + 6d - d (1)
And the formula for arithmetic sum:
Sn = n(A1 + An)/2
20 = 5(A1 + 25 - d)/2
8 = A1 + 25 - d (2)
We have a system of two equations with two variables.
25 = A1 + 5d
8 = A1 + 25 - d
For both equations, we can solve for d and then equal both equations as follows:
5 - A1/5 = d (1)
A1 + 17 = d (2)
A1 + 17 = 5 - A1/5
A1 = -10.
Now we just replace the value of A1 in equation 1:
d = 7
The ages of rocks in an isolated area are known to be approximately normally distributed with a mean of 7 years and a standard deviation of 1.8 years. Using the normalcdf function on your graphing calculator, what percent of rocks are between 5.8 and 7.3 years old?
The answer is B: 31.4%
Using a graphic calculator you have:
Mean: 7
SD: 18
Lower bound: 5.8
Upper bound: 7.3
Find the x-and y-intercepts.27x + 3y =-54
The x intercept of a line is where i
Write the equation of the line that passes through the given point and is parallel to the given line.
1 1 A company has budgeted 5 1/3hours to complete a project, with 1/4 of the time spent on research. How much time does the company plan to spend on research? Express your answer as a mixed number.
In order to determine the time for research, calculate one quarter of the time spend in the project of the company.
Express the time for the project as a normal fraction, as follow:
5 1/3 = 5/1 + 1/3 = (15 + 1)/3 = 16/3
Next, multiply 1/4 (one quarter) by the previous fraction 16/3:
(1/4)·(16/3) = 16/12
simplify the previous fraction:
16/12 = 4/3
as a mixed number the previous result is:
4/3 = 1 1/3
Refer to the figure below for 12-14. 15 in. bumper sticker 3.5 in. 12. Find the perimeter of the sticker.
The perimeter of a rectangle is the sum of its 4 sides:
[tex]P=15in+15in+3.5in+3.5in=37in[/tex]Then, the perimeter of the bumper sticker is 37 inchesThe geometric mean is 10 between 25 and what number ?
EXPLANATION
A special form of average is the Geometric Mean, where we sum the numbers together and then take a square root (for two numbers), cube root (for three numbers), etc.
The geometric mean between 10 and 25 is equal to:
sqrt(10*25)= 15.81
Answer is 5*sqrt(10) or 15.81
A line passes through point (2, 5) and has a slope of 3. Write an equation in Ax +By=C form for this line. Use integers for A, B, and C.
Answer:
[tex]3\, x + (-1)\, y = 1[/tex].
Step-by-step explanation:
Both the slope of this line and the coordinates of a point on this line are given. Therefore, start by finding the point-slope equation of this line: if the slope of a line in a plane is [tex]m[/tex], and this line goes through a point at [tex](x_{0},\, y_{0})[/tex], the point-slope equation of this line will be [tex](y - y_{0}) = m\, (x - x_{0})[/tex].
The slope of the line in this question is [tex]m = 3[/tex]. It is given that this line goes through the point [tex](2,\, 5)[/tex], where [tex]x_{0} = 2[/tex] and [tex]y_{0} = 5[/tex]. Substitute in these values to find the point-slope equation of this line:
[tex](y - y_{0}) = m\, (x - x_{0})[/tex].
[tex](y - 5) = 3\, (x - 2)[/tex].
Rewrite this point-slope equation in the requested format:
[tex]y - 5 = 3\, x - 6[/tex].
[tex]3\, x - 6 = y - 5[/tex].
[tex]3\, x = y + 1[/tex].
[tex]3\, x - y = 1[/tex].
[tex]3\, x + (-1)\, y = 1[/tex].
Find the exact value and the approximate value of the area of the triangle
From the big triangle we know that:
[tex]\begin{gathered} x^2+y^2=12^2 \\ x^2+y^2=144 \end{gathered}[/tex]From the triangle on the right we also know that:
[tex]h^2+9^2=y^2[/tex]From the triangle on the left we know:
[tex]3^2+h^2=x^2[/tex]Adding the last two equations we have that:
[tex]\begin{gathered} x^2+y^2=h^2+9^2+h^2+3^2 \\ x^2+y^2=2h^2+90 \end{gathered}[/tex]Equating the last equation with the first one we have that:
[tex]\begin{gathered} 2h^2+90=144 \\ 2h^2=144-90 \\ 2h^2=54 \\ h^2=\frac{54}{2} \\ h^2=27 \\ h=\sqrt[]{27} \end{gathered}[/tex]Then, the height of the triangle is the squared root of 27.
Once we know the height we can calculate the area.
[tex]\begin{gathered} A=\frac{1}{2}bh \\ =\frac{1}{2}12\sqrt[]{27} \\ =6\sqrt[]{27} \end{gathered}[/tex]Therefore the exact value of the area is:
[tex]6\sqrt[]{27}[/tex]This can be approximated to (rounding on the hundreths):
[tex]31.18[/tex]Using the unit circle, what is the exact value of tang?O AA.2OB. 13C. VSO D.3
Given the function:
x^2 + 2x - 8
x^2 - 2x - 8
we are to find the zeros of the function.
To find the zero of a function, we find the root of the numerator.
That is, equsting the numerator to zero
x^2 + 2x - 8 = 0
lets get factor of the above eqaution
= x^2 - 2x + 4x + 8
x(x-2) + 4(x-2) = 0
so,
x + 4 = 0 OR x - 2 = 0
x + 4 = 0
x = -4
OR
x - 2 = 0
x = 2
so, x = -4, 2
Therefore the zeros of the function x^2 + 2x - 8 are -4, 2
x^2 - 2x - 8
So, the correct option is D which is -4, 2
write an equation that demonstrates the relationship between x and y for the points plotted on the coordinate grid
The relationship between x and y points is a linear relationship of the form:
y = mx + b
where m is the slope of the line, and b is the coordinate y for the y-intercept.
Now, by definition, we have that the slope of the line is given by:
[tex]m\text{ = }\frac{Y2-Y1}{X2-X1}[/tex]where (X1,Y1) and (X2,Y2) are given points on the graph.
In our case, we can take
(X1, Y1) =(2,-1)
(X2,Y2) = (3,2)
then, te slope of the line would be:
[tex]m\text{ = }\frac{Y2-Y1}{X2-X1}\text{ = }\frac{2-(-1)}{3-2}\text{ = }\frac{2+1}{1}=\text{ 3}[/tex]then m = 3 and the new equation for our graph would be:
y = 3x+b
Now, to find b, take any point (x,y) on the graph. In this case, for example
(x,y) = (3,2) and replace this point in the above equation:
2= 3(3) + b
solve for b:
2-9 = b
then b = -7 and we can conclude that the equation for our graph is:
y = 3x-7
help meeeeeeeeeeeeeeeeeeeeeee
thank you
The height of the object based on the information is 1963 feet.
How to calculate the height?It should be noted that a function is important to show the relationship between the variables given in the data.
In this case, the function given for the height of the object is given as:
h = 16t² + 1899
where t = time
When the time is 2 seconds, the height will be:
h = 16t² + 1899
h = 16(2)² + 1899
h = 64 + 1899
h = 1963
The height is 1963 feet.
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Graph the line with slope of -4/5 and on the x intercept of 3
Solution
Note: Equation of a Line os given as
[tex]y=mx+c[/tex]We are given that the slope is -4/5
That is m = -4/5
[tex]y=-\frac{4}{5}x+c[/tex]It has x intercept of 3, that is the point (3, 0)
Substituting we have
[tex]\begin{gathered} y=-\frac{4}{5}x+c \\ 0=-\frac{4}{5}(3)+c \\ c=\frac{12}{5} \\ Thus,\text{ we have} \\ y=-\frac{4}{5}x+\frac{12}{5} \end{gathered}[/tex]The graph of the line is
triple c, then raise to the 10th power
Given the word expression:
Triple c, then raise to the 10th power.
Here the exponent of triple c is 10.
To express the above, we have:
[tex]\begin{gathered} \text{Triple C = (3c)} \\ \\ \text{Raised to the power of 10 = (3c)}^{10} \end{gathered}[/tex]Thus, we the expression below:
[tex](3c)^{10}^{}[/tex]ANSWER:
[tex](3c)^{10}[/tex]You, Newton, and Descartes walk dogs to earn spending money this summer. You spend 2 times as many minutes walking dogs as Newton. Descartes spends 3 times as many minutes walking dogs as Newton. You, Newton, and Descartes spend 3,030 minutes walking.dogs altogether. How many minutes does Newton walk dogs?
You, Newton, and Descartes walk dogs to earn spending money this summer. You spend 2 times as many minutes walking dogs as Newton. Descartes spends 3 times as many minutes walking dogs as Newton. You, Newton, and Descartes spend 3,030 minutes walking.dogs altogether. How many minutes does Newton walk dogs?
Let
x -----> minutes does Newton walk dogs
y ----> minutes does Descartes walk dogs
z ----> minutes does you walk dogs
so
z=2x ------> equation A
y=3x ------> equation B
x+y+z=3,030 ------> equation C
substitute equation A and equation B in equation C
x+(3x)+(2x)=3,030
solve for x
6x=3,030
x=505 minutes
therefore
the answer is
Newton walk dogs 505 minutesA cube is partially filled with 4 mmof water. If the water is 1 mm high, what is the length of one side of the cube?O 1 mmVx02 mmO 3 mm04 mmSave and ExitNextSubmitMark this and returnA cube is partially filled with 4 mm cubed of water. If the water is 1mm high, what is the length of one side of the cube?
Given:
a.) A cube is partially filled with 4 mm of water.
b.) The water is 1 mm high
Let's draw the scenario to better understand the problem,
half of the sum of six and three then divided by seven.
Answer:
0.64285714285
Step-by-step explanation:
6+3=9
9 divided by 2= 4.5
4.5 / 7= 0.64285714285
I don't think this is what you're looking for?
Find the missing side of this righttriangle.Х.911x= [?]✓Enter the number that belongs in the green box.
Using pythagorean theorem:
[tex]\begin{gathered} c^2=a^2+b^2 \\ _{\text{ }}where\colon \\ a=11 \\ b=9 \\ c=x \\ x=\sqrt[]{9^2+11^2}^{} \\ x=\sqrt[]{202} \end{gathered}[/tex]Answer:
[tex]x=\sqrt[]{202}[/tex]-2+{-3-[7+4(-2+5)]}-4
Answer:
- 28
Step-by-step explanation:
-2 + { -3 - [ 7 + 4·( -2 + 5 ) ] } - 4
1)
( -2 + 5 ) = 3
2)
[ 7 + 4·3 ] = [ 7 + 12 ] = 19
3)
{ -3 - 19 } = - 22
4)
- 2 + ( -22) - 4 = -2 - 22 - 4 = - 28
Help answer please. The graph of g and the graph of fare shown. Which of the following describes a single transformation that compares the graph of g with the graph of f?
Select all that apply.
The options that describes a single transformation that compares the graph of g with the graph of f are;
B) The graph of g is shifted 3 units right.
C) The graph of g is shifted 3 units up.
What is the Graph Transformation?Transformation is a method required to resize or change the orientation of a given shape or figure. The types of transformation are translation, reflection, rotation, and dilation.
Translation is a method of transformation that involves moving an object or shape from one point to another without changing any dimension.
Reflection is a method of transformation that involves flipping a given figure about a given reference point or line. In order words, a mirror image of the original object.
Rotation is a method of transformation that involves turning a given figure at an angle about a reference point.
Dilation is a method of transformation whereby the length of the sides of the figure is either increased or decreased.
Now, looking at the given graph, we see that the line showing the graph g is clearly shifted by either 3 units to the right or 3 units upwards to get the function line f.
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Which is more, 10 meters or 100 decimeters? 10 meters 100 decimeters neither; they are equal
Answer: They are both equal
1 meter = 10 decimeter
We need to convert 100 decimeters to meters
1 meter = 10 decimeter
x meter = 100 decimeter
Cross multiply
x * 10 = 1 x 100
10x = 100
Divide both sides by 10
10x/10 = 100/10
x = 10 meters
Hence, 10 meters is equal to 100 decimeter
Answer: They are both equal
consider the equation showing the distributive property 84+93=3(28+□)
We have that the distributive property states that the multiplication is done for all the terms inside the parenthesis. Then we have:
Since
3 · 28 = 84
and
3 · □ = 93
Since 3 · 31 = 93, then
□ = 31
Answer: 31What is the volume of the prism that is 5 meters wide, 4 meters high, and 8 meters long?A. 160 m³B. 180 m³C. 120 m³D. 200 m³
True or False? The denominator is the top number, or the part ofthe whole that is being talked about.
In a fraction, we have that the top number is the numerator and the bottom number is the denominator.
Also, in a mixed number, we have a whole number together with a fraction, but the denominator still is the bottom number of the fraction
So the statement of the question is FALSE.
12. A basketball teams wins 4/7 of their games. What is the probability that in a season of 15games they will win exactly 8 games. (circle one answer)A.,C,(4/7)*(3/7) B. S, (3/7)477' c. S.(4/7 (377)C*())* D. C, (4/7) (3/7)
A basketball game does not end in a tie. This means that it is either the team wins the game or they draw the game. These outcomes are independent becuase winning one game has no effect on the outcome of the next game. This means that we have a binomial distribution here. the formula for binomial distribution is expressed as
P(x) = nCx * p^x * q^(n - x)
where
n is the number of trials
x is the number of successess
p is the probability of success
q is the probability of failure
We are concerned with the outcome of winning. This means that success is when the team wins. Thus,
p = 4/7
q = 1 - p = 1 - 4/7 = 3/7
n = 15
x = 8
We want to find P(x = 8)
By applying the binomial distribution formula,
P(x = 8) = 15C8 * (4/7)^8 * (3/7)^(15 - 8)
P(x = 8) = 6435 * (4/7)^8 * (3/7)^7
P(x = 8) = 0.194
The probability that in a season of 15 games they will win exactly 8 games is
0.194
The table below shows the total number of drink sales at the football game last Saturday in the first hour: Drinks and number (45 Lemonade) (31 Fruit Punch) (47 Bottled Water) (27 Ice Tea) What percent of the drink sales came from lemonade and ice tea combined? A 42% 54% D 46%
Total number of drinks sold = 45 + 31 + 47 +27 = 150
Lemonade and ice tea = 45 +27 = 72
Divide the number of lemonades and ice tea drinks sold, by the total number of drinks sold.
72 / 150 = 0.48
Multiply by 100
0.48 x 100 = 48% (option A)
The function P(x)=x3−2x2 is dilated by the function I(x)=P(4x).Which function rule represents I(x)?
Given
[tex]P(x)=x^3-2x^2[/tex]And
[tex]I(x)=P(4x)[/tex]To find the value of I(x).
Explanation:
It is given that,
[tex]P(x)=x^3-2x^2[/tex]Then,
[tex]\begin{gathered} I(x)=P(4x) \\ \Rightarrow I(x)=(4x)^3-2(4x)^2 \\ \Rightarrow I(x)=64x^3-2(16x^2) \\ \Rightarrow I(x)=64x^3-32x^2 \end{gathered}[/tex]Hence, the answer is I(x)=64x³-32x².
Please help me with this math question
Answer:
145
Step-by-step explanation:
168-23 = 145
i hope this helps :)
What is (5x)(-2x) in words but I don’t need the answer (can give if u want to)?
(5x)(-2x) in words is Five times x multiplied by negative two times x
Define algebraic expression.Using variables, constants, and algebraic operations, an expression can be described as an algebraic expression in mathematics (addition, subtraction, etc.). Terms are used to construct expressions. Any combination of a number, a variable, and operation symbols is considered an expression. Two expressions are combined to form an equation, which is joined by the equal sign. Example of a word: The product of 8 and 3. Word illustration: 11 is the result of adding 8 and 3.
Given Data
Expression
(5x)(2x)
Translating algebraic expression into verbal expression:
Five times x multiplied by negative two times x
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Original price $30; Markup 7.5$The retail price is $ ?
Retail price = $37.5
Explanation:Original price = $30
Markup = $7.5
Retail price = cost price + markup
cost price = Original price = $30
Retail price = $30 + $7.5
Retail price = $37.5
PLS HELP!! and can you also break it down for me. thx ;)
solve for x. 4x^2+3=-7x
Answer: -1 -3/4
Step-by-step explanation:
1.Move terms to the left side
4x^{2}+3=-7x
4x^{2}+3-\left( -7x\right) =0
2.Rearrange terms
4x^{2}+3+7x=0
4x^{2}+7x+3=0
3.Use the quadratic formula
Once in standard form, identify a, b, and c from the original equation and plug them into the quadratic formula.
4x^{2}+7x+3=0
4.Simplify
Evaluate the exponent
Multiply the numbers
Subtract the numbers
Evaluate the square root
Multiply the numbers
-7+1/8
5.Separate the equations
To solve for the unknown variable, separate into two equations: one with a plus and the other with a minus.
x=\frac{-7+1}{8}
x=\frac{-7-1}{8}
6.Solve
Rearrange and isolate the variable to find each solution
x=-\frac{3}{4}
x=-1
