ANSWER
[tex]a_n=7n - 22[/tex]
EXPLANATION
The recursive rule for the sequence is
[tex]a_n=a_{n-1}+7[/tex]
In general the recursive rule is written as:
[tex]a_n=a_{n-1}+d[/tex]
This implies that, d=7
The first term of the sequence is
[tex]a_1= - 15[/tex]
The explicit rule is given by:
[tex]a_n=a_1 + d(n - 1)[/tex]
We substitute to get;
[tex]a_n= - 15 + 7(n - 1)[/tex]
[tex]a_n= - 15 + 7n - 7[/tex]
[tex]a_n=7n - 22[/tex]
Which composition of similarity transformations maps A
LMN to AL'M'N'?
a dilation with a scale factor less than 1 and then a reflection
a dilation with a scale factor less than 1 and then a translation
a dilation with a scale factor greater than 1 and then a reflection
a dilation with a scale factor greater than 1 and then a translation
A dilation with a scale factor greater than 1 and then a translation is correct.
How does dilation work?Dilation of a figure will leave its sides to get scaled (multiplied) by the same number. That number is called the scale factor of that dilation.
Its also called scaling of a figure, but due to the involvement of coordinates, it involves a center of a dilation, which is like a pinned point that stays at the same place after dilation.
It's like we enlarge or shorten the size of the figure (or keep it same, when scale factor = 1).
Dilation totally depends on the scale factor.
We need to find the composition of similarity transformations maps A
LMN to AL'M'N'.
If the absolute value of the scale factor is more than 1, then it represents the enlargement and if the absolute value of the scale factor lies between 0 to 1, then it represents the compression.
Therefore, a dilation with a scale factor greater than 1 and then a translation is correct.
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Answer:
D.a dilation with a scale factor greater than 1 and then a translation.
9x^2-4=0 find two real solutions
Answer:
The two real solutions are [tex]x=\frac{12}{18} = 0.6667[/tex] and [tex]x=-\frac{12}{18} =-0.6667[/tex]
Step-by-step explanation:
The equation [tex]9x^{2} -4=0[/tex] is a quadratic function of the form [tex]ax^{2} +bx+c=0[/tex] that can be solved by using the Quadratic Formula.
[tex]x=\frac{-b±\sqrt{b^{2} -4ac} }{2a}[/tex]
The plus and minus mean that the equation has two solution.
In order to identify is the equation has two real solutions we use the discriminant equation [tex]b^{2} -4ac[/tex]. Depending of the result we got:
1. If the discriminant is positive, we get two real solutions.
2. if the discriminant is negative, we get complex solutions.
3. If the discriminant is zero, we get just one solution.
Solution:
The equation [tex]9x^{2} -4=0[/tex] has a=9, b=0, and c=-4
Using the discriminant equation to know if the quadratic equation has two real solutions:
[tex]b^{2} -4ac[/tex]
[tex]0^{2} -4(9)(-4)=144[/tex] The discriminant is positive which mean we get two real solutions.
Using the Quadratic Formula
[tex]x=\frac{-b±\sqrt{b^{2} -4ac} }{2a}[/tex]
[tex]x=\frac{-0±\sqrt{0^{2} -4(9)(-4)} }{2(9)}[/tex]
[tex]x=\frac{±\sqrt{144} }{18}[/tex]
[tex]x=±\frac{12}{18}[/tex]
then
[tex]x=\frac{12}{18} = 0.6667[/tex] and [tex]x=-\frac{12}{18} =-0.6667[/tex]
To solve the equation 9x^2-4=0, we simplify and take the square root of both sides, resulting in two real solutions: x = 2/3 and x = -2/3.
To find two real solutions to the equation 9x^2-4=0, we can approach this by simplifying it into a form that can use the square root method for solving. Here are the steps:
Add 4 to both sides of the equation: 9x^2 = 4.Divide both sides by 9: x^2 = 4/9.Take the square root of both sides: x = ±2√(4/9).Simplify the square root: x = ±2/3.Therefore, the two real solutions are x = 2/3 and x = -2/3.
In the diagram NM bisects ENL find ML
A. 2
B. 3
C. 6
D. 12
Answer:
Option C. 6
Step-by-step explanation:
we know that
If NM bisects the angle ENL
then
∠MNL=∠MNE
In the right triangle MLN
sin(∠MNL)=ML/MN -----> equation A
In the right triangle MEN
sin(∠MNE)=6/MN -----> equation B
equate equation A and equation B
ML/MN=6/MN
Simplify
ML=6
It is hard to calculate the volume of a mountain but several estimates put the volume of Mount Everest at around 2,413 cubic kilometers. The Dallas Cowboys Stadium (currently the largest football stadium in the U.S.) has a volume of 140 million cubic feet. How many Cowboy stadiums could fit inside of Mount Everest?
Estimate an answer to this question and explain your estimation process. Be sure to state what facts or ideas you used to help.
Answer:
About 609,000 Cowboy stadiums could fit inside of Mount Everest
Step-by-step explanation:
we have
The estimate volume of Mount Everest is at around [tex]2,413\ km^{3}[/tex]
The Dallas Cowboys Stadium has a volume of [tex]140,000,000\ ft^{3}[/tex]
step 1
Convert ft³ to km³
we know that
1 km=3,280.84 ft
so
[tex]140,000,000\ ft^{3}=140,000,000*(1/3,280.84)^{3}=0.003964\ km^{3}[/tex]
step 2
To find how many Cowboy stadiums could fit inside of Mount Everest, divide the volume of Mount Everest by the volume of the Dallas Cowboys Stadium
[tex]2,413/0.003964=608,729[/tex]
Round to the nearest Thousands
[tex]608,729=609,000[/tex]
The volume of Mount Everest is about 609,000 times greater than the volume of the Dallas Cowboys Stadium
To estimate how many Dallas Cowboys stadiums could fit inside Mount Everest, we converted the volume of the stadium to cubic kilometers and then divided Mount Everest's volume by this number, resulting in approximately 608,845 stadiums.
Explanation:Calculating the Volume of Mount Everest Compared to the Dallas Cowboys Stadium
To estimate how many Dallas Cowboys stadiums could fit inside of Mount Everest, we need to convert the volume of both structures to the same units and then perform a division.
We have the volume of Mount Everest as approximately 2,413 cubic kilometers. To convert the volume of the Dallas Cowboys Stadium from cubic feet to cubic kilometers, we use the conversion factor of 1 cubic kilometer equals 35.3147 million cubic feet:
Cowboys Stadium volume in cubic kilometers = 140 million cubic feet × (1 cubic kilometer / 35.3147 million cubic feet) = 3.9642 × 10-3 cubic kilometers.
Now, we can find how many Cowboys stadiums fit into Mount Everest:
Mount Everest volume / Cowboys Stadium volume = 2,413 cubic kilometers / 3.9642 × 10-3 cubic kilometers ≈ 608,845.
Therefore, approximately 608,845 Dallas Cowboys stadiums could fit inside of Mount Everest's volume.
Write the equation in standard form of the circle whose center is at (0, 0) and that is tangent to x + y = 6
Answer:
[tex]x^2 + y^2 =18[/tex]
Step-by-step explanation:
The standard equation of a circumference has the following formula.
[tex](x-h) ^ 2 + (y-k) ^ 2 = r ^ 2[/tex]
Where the point (h, k) is the center of the circle and r is the radius.
If in this case we know that the circle has center at point (0,0), then its equation will have the following form
[tex]x ^ 2 + y ^ 2 = r ^ 2[/tex]
The radius of the circumference will be the distance from the center of the circumference to the point where the circumference is tangent to the line [tex]Ax + Bx + C = 0[/tex]
The radio is:
[tex]r=\frac{|Ah + Bk +C|}{\sqrt{A^2+B^2}}[/tex]
In this case, the line is
[tex]x + y = 6[/tex]
And the center of the circumference is (0, 0)
So
[tex]A = 1\\B = 1\\C = -6\\h = 0\\k = 0[/tex]
The radio is:
[tex]r=\frac{|1*0 + 1*0 -6|}{\sqrt{1^2+1^2}}\\\\r=\frac{|-6|}{\sqrt{1^2+1^2}}\\\\r=\frac{6}{\sqrt{2}}[/tex]
Finally the equation of the circumference is:
[tex]x^2 + y^2 =(\frac{6}{\sqrt{2}})^2\\\\x^2 + y^2 =18[/tex]
Final answer:
The standard form equation of the circle centered at (0, 0) and tangent to the line x + y = 6 is x² + y² = 18, after determining the radius using the distance formula.
Explanation:
The question asks for the standard form equation of a circle centered at (0, 0) that is tangent to the line x + y = 6. To find the standard form of the circle, we first need to determine the radius of the circle, which is equal to the distance from the center of the circle to the tangent line. Since the center of the circle is at the origin (0,0), we can use the distance formula for a point to a line:
d = |Ax + By + C| / √(A² + B²), where A, B, and C are the coefficients from the line equation Ax + By + C = 0.
In this case, the line x + y = 6 can be rewritten as x + y - 6 = 0 (A = 1, B = 1, C = -6). Plugging these into the distance formula we get:
d = |1 · 0 + 1 · 0 - 6| / √(1² + 1²) = 6 / √2 which simplifies to √18.
The standard form equation of a circle with center at (h, k) and radius r is (x - h)² + (y - k)² = r². With a center at (0, 0) and a radius of √18, the equation becomes:
x² + y² = 18.
This is the standard form equation of the circle which is tangent to the line x + y = 6 at one point.
Evaluate the expression. Express the result in scientific notation.
(9.08 × 106) – (2.25 × 105)
To evaluate the expression (9.08 × 10⁶) - (2.25 × 10⁵), align the exponents and then subtract the base numbers, resulting in (8.855 × 10⁶) expressed in scientific notation.
To evaluate the expression (9.08 × 10⁶) - (2.25 × 10⁵) and express the result in scientific notation, we will align the exponents and then subtract the base numbers. Since the exponents are not the same, we need to adjust the smaller exponent to match the larger one.
First, we rewrite (2.25 × 10⁵) with a base of 10⁶, which becomes (0.225 × 10⁶). Now we can subtract:
(9.08 × 10⁶) - (0.225 × 10⁶) = (9.08 - 0.225) × 10⁶
Performing the subtraction, we get:
(8.855 × 10⁶)
Y intercept and x intercept definitions
Answer:
"The x-intercepts are where the graph crosses the x-axis, and the y-intercepts are where the graph crosses the y-axis."
Step-by-step explanation:
:)
Final answer:
The y-intercept is the point where a graph crosses the y-axis, while the x-intercept is the point where a graph crosses the x-axis.
Explanation:
The y-intercept is the point where a graph crosses the y-axis. It is represented by the coordinate (0, b), where b is the y-coordinate of the intercept. The y-intercept can be found by analyzing the equation of the line y = mx + b, where b is the y-intercept.
The x-intercept, on the other hand, is the point where a graph crosses the x-axis. It is represented by the coordinate (a, 0), where a is the x-coordinate of the intercept. To find the x-intercept, set y equal to 0 in the equation y = mx + b and solve for x.
Which has the least value 2 2/3,2.45,2 2/5
Answer:
2 2/5
Step-by-step explanation:
First, lets convert these all to decimals.
2 2/3 = 8/3 = 2.66666666.....
2.45 = 2.45
2 2/5 = 12/5 = 2.4
Thus, the smallest decimal here is 2.4, or, 2 2/5.
I hope this helps!
Answer:
the least value is 2 2/5
Step-by-step explanation:
If f(x)= x^2-1 and g(x)=2x-3, what is the domain of (fog)(x)
Answer:
[tex]\large\boxed{\text{The domain is the set of all real numbes}\to x\in\mathbb{R}}[/tex]
Step-by-step explanation:
[tex]f(x)=x^2-1,\ g(x)=2x-3\\\\(f\circ g)(x)-\text{instead of x in the function equation f(x) put}\ 2x-3:\\\\(f\circ g)(x)=(2x-3)^2-1\qquad\text{use}\ (a-b)^2=a^2-2ab+b^2\\\\(f\circ g)(x)=(2x)^2-2(2x)(3)+3^2-1=4x^2-12x+9-1\\\\(f\circ g)(x)=4x^2-12x+8\\\\\text{the domain is the set of all real numbes}\to x\in\mathbb{R}[/tex]
Write an equation of the line that has a slope of 3 and contains the point (2, 5) in point-slope form.
Answer:
y - 5 = 3(x - 2)
Step-by-step explanation:
Point Slope Form: y – y1 = m(x – x1)
y1 represents the y-coordinate
x1 represents the x-coordinate
m represents the slope
Determine the answer to 3 + (−5) and explain the steps using a number line.
Answer:
[tex]\boxed{ -2}[/tex]
Step-by-step explanation:
On a number line
Adding a positive number means moving to the right Adding a negative number means moving to the leftUsing the number line,
Add 3 + (-5)
Step 1. Find 3 on the number line
Start at 0 and move three units to the right (see Image below).
This takes you to 3.
Step 2. Add (-5)
Start at 3 and move five units to the left.
This takes you to -2.
[tex]\boxed{\textbf{3 + (-5) = -2}}[/tex]
The value of the expression 3 + (-5) is - 2
Given the value :
3 + (-5)
From the operation rule :
+ and - = -
Hence,
3 + (-5) = 3 - 5 = - 2
Using the number line analogy :
Positive values (+) lies to the right of a number line while negative (-) are positioned on the left.
To perform 3 + (-5) using a number line ;
From +3 taking 5 points backwards to the left (-5) ; takes us to the point - 2
Hence, the value of the expression 3 + (-5) = - 2
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The diagram is not drawn to scale
Find the value of x.
The value of x is 60.
How to find the value of x?The Midpoint theorem states that :
The line segment in a triangle joining the midpoint of two sides of the triangle is said to be parallel to its third side and is also half of the length of the third side
By Midpoint theorem
DE = 30
AC = x
DE = [tex]\frac{1}{2}[/tex] AC
30 = [tex]\frac{x}{2}[/tex]
x = 60
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Find the sum of the absolute deviations of the following data set.
8, 5, 15, 12, 10
Final answer:
The sum of the absolute deviations for the given data set is 14.
Explanation:
To find the sum of the absolute deviations of a data set, you need to find the absolute value of the difference between each data point and the mean, and then add them up. Here is the calculation for the given data set:
Absolute deviations: |8-10| + |5-10| + |15-10| + |12-10| + |10-10| = 2 + 5 + 5 + 2 + 0 = 14
So, the sum of the absolute deviations for this data set is 14.
if you are asked to solve a system of equations in which there is no linear equation to start with, you can sometimes begin by isolating and substituting a variable that is squared in both eqautions. true or false
Answer:
The correct answer option is: True.
Step-by-step explanation:
Its true that if there is no linear equation to start with, you can isolate and substitute a variable that is squared in both the equation.
For example, for the given non linear equation, start by dividing both sides by coefficient of the variable.
Once you do that and isolate a variable, continue solving by substituting that variable into the other equation.
Answer: true
Step-by-step explanation: A pex
Graph the linear equation. Find the three points that solve the equation then plot on the graph. -y=-x+1
Answer:
Step-by-step explanation:
The first step will be to make y the subject of the formula, by multiplying both sides of the equation by -1.
y = x - 1
This is simply the equation of a line with a slope of 1 and y-intercept (0,-1)
To determine the three points that solve the equation, we can let x be;
0, 1, 2
When x =0, y = 0-1 = -1
When x = 1, y = 1-1 = 0
When x = 2, y = 2 - 1 = 1
Therefore, we have the following three sets of points that can be used to graph the given linear equation;
(0, -1)
(1, 0)
(2, 1)
Find the attached for the graph
Find the interest earned and the future value of an annuity with annual payments of $1,400 for 18 years into an account that pays 4% interest per year.
Answer:
interest earned= 1436.143
the future value of an annuity= 2836.143
Step-by-step explanation:
Given Data:
Interest rate= 4%
time,t = 18 years
Annual payment, P= 1400
At the end of 18 years, final investment A= ?
As per the interest formula for interest
A= P(1+r)t
Putting the values in above equation
= 1400(1+0.04)^18
= 2836.143
Interest earned = A-P
= 2836.143-1400
= 1436.143 !
find the trinomial below 4x^2 + 12x + 9
Answer:
4x² + 12x + 18
Step-by-step explanation:
This would be the trinomial.
Answer:
if you mean to factor it, it would be, (2x + 3)(2x + 3) but if you do mean the trinomial, that is already the answer.
Step-by-step explanation:
4x^2 + 12x + 9
you can split 12x into 6x + 6x so now it's
4x^2 + 6x + 6x + 9
then simplify it into:
2(2x + 3) + 3(2x + 3)
then into:
(2x + 3)(2x + 3)
What's the area of this rectangle?
The area of this rectangle is 18 square units. What is the unit of measurement?
Answer:
Step-by-step explanation:so first you need to find the sides 6*3 so it is 24
Can someone please help me out
Answer:
5/2 or 5:2
Step-by-step explanation:
Answer:
6*5=30 to 2*6=12
Step-by-step explanation:
6:5 and 2:6 for smaller hexagon
Which of the following uses the Distributive Property to determine the product 12(185)
Answer:
The answer is D
Step-by-step explanation:
In D, all of the multiplacative parts of the problems add up to the factoring of 185 • 12, and the others don't. I really hope this helps!
Answer:
D. [tex]12\cdot 100 + 12 \cdot 80 + 12 \cdot 5[/tex]
Step-by-step explanation:
A possible solution of the expression is:
[tex]12\cdot (185)[/tex]
[tex]12\cdot (100 + 80 + 5)[/tex]
[tex]12\cdot 100 + 12 \cdot 80 + 12 \cdot 5[/tex]
The right answer is D.
What is the degree of vertex B and G?
Answer:
degree of vertex B = 2
degree of vertex g = 4
Step-by-step explanation:
Using given picture we need to find about what is the degree of vertex B and G.
In graph theory, we know that the degree (or valency) of a vertex of a graph is the number of edges incident to the vertex.
So we just need to count how many edges are incindent on vertex B and G.
From picture we see that number of edges incident on vertex B = 2
Hence degree of vertex B = 2
From picture we see that number of edges incident on vertex G = 4
Hence degree of vertex g = 4
5. Solve (2x - 1)2 = 8 using the quadratic formula.
The solution to the equation by using quadratic formula is [tex]x = \dfrac{1 + 2\sqrt{2}}{2} \ or \ \dfrac{1 - 2\sqrt{2}}{2}[/tex]
Solving quadratic equation using formula.
Quadratic equation can be solved by using the quadratic formula [tex]x = \dfrac{-b \pm \sqrt{b^2 -4ac}}{2a}[/tex]
The given equation (2x - 1)² = 8 can be written as 4x² - 4x - 7 = 0. where:
a = 4b = -4c = -7Replacing the values into the quadratic formula, we have:
[tex]x = \dfrac{-(-4) \pm \sqrt{(-4)^2 -4(4)(-7)}}{2(4)}[/tex]
[tex]x = \dfrac{4 \pm \sqrt{16 + 112}}{8}[/tex]
[tex]x = \dfrac{4 \pm \sqrt{128}}{8}[/tex]
[tex]x = \dfrac{4 \pm 8\sqrt{2}}{8}[/tex]
Divide the right hand side by 4;
[tex]x = \dfrac{1 \pm 2\sqrt{2}}{2}[/tex]
[tex]x = \dfrac{1 + 2\sqrt{2}}{2} \ or \ \dfrac{1 - 2\sqrt{2}}{2}[/tex]
Find the Quotient: 6/ 27L 600ML
Answer:
400mL/3l
Is the correct answer
Step-by-step explanation:
To find the quotient of 6 liters by 27 liters and 600 milliliters, convert both to milliliters and divide. The quotient is approximately 0.21739.
To find the quotient of 6 liters (L) divided by 27 liters and 600 milliliters (mL), we first need to convert the amounts to the same unit. Since there are 1,000 milliliters in a liter, we can convert 27 liters into milliliters:
27 L × 1,000 mL/L = 27,000 mL
Now we add the 600 mL:
27,000 mL + 600 mL = 27,600 mL
Rewrite the problem with both measurements in milliliters:
6,000 mL / 27,600 mL
We now divide 6,000 by 27,600:
6,000 mL / 27,600 mL = 0.21739 (rounded to five decimal places)
So, the quotient is approximately 0.21739.
A cylinder has a volume of 288 pie cubic meters and a height of 9 meters. What is the area of the base?
Answer:
32 m²
Step-by-step explanation:
V(cylinder) = Area(base)*height
288 = Area(base)*9
Area(base)= 288/9=32 m²
Answer: [tex]32\pi\ m^2[/tex]
Step-by-step explanation:
We know that the volume of cylinder is given by :-
[tex]\text{Volume}=\text{Area of base * height}[/tex]
Given: The volume of cylinder = [tex]288\pi\text{ cubic meters}[/tex]
Height of the cylinder= 9 meters
[tex]\Rightarrow\ 288\pi=\text{Area of base }\times9\\\\\Rightarrow\ \text{Area of base }=\dfrac{288\pi}{9}=32\pi[/tex]
Hence, the area of the base = [tex]32\pi\ m^2[/tex]
Help me answer this question please
Answer:
The answer is C.
Step-by-step explanation:
Just go to Desmos.com and plug it in.
For this case we have:
Let k> 0:
To graph[tex]y = f (x) + k,[/tex] the graph k units is moved up.
To graph [tex]y = f (x) -k[/tex], the graph moves k units down.
Let h> 0:
To graph [tex]y = f (x-h)[/tex], the graph moves h units to the right.
To graph [tex]y = f (x + h),[/tex] the graph moves h units to the left.
So, we have:
[tex]y = f (x) = \sqrt [3] {x}[/tex]
Shifted 1 unit down and 4 to the left means:
[tex]k = 1\\h = 4[/tex]
[tex]y = f (x) = \sqrt [3] {x + 4} -1[/tex]
Answer:
Option D
Ms. Redmon gave her theater students an assignment to memorize a dramatic monologue to present to the rest of the class. The graph shows the times, rounded to the nearest half minute, of the first 10 monologues presented. The next student presents a monologue that is about 0.5 minutes long. What effect will this have on the graph? The median will decrease. The mean will decrease. The median will increase. The mean will increase.
Answer:the awnser is:B the mean will decrease
Step-by-step explanation:
The effect it would have on the dot plot graph is that: B. The mean will decrease.
What is the Mean of a Dot Plot?The mean of a dot plot is found by simply adding up all data points on the dot plot and divide by the number of data points we have on the dot plot.
Mean of the first 10 monologues = (1.5 + 1.5 + 2 + 2.5 + 2.5 + 2.5 + 3 + 3.5 + 3.5 + 4)/10 = 2.65
Mean of the first 10 monologues + 0.5 minutes = (1.5 + 1.5 + 2 + 2.5 + 2.5 + 2.5 + 3 + 3.5 + 3.5 + 4 + 0.5)/11 = 2.45
Therefore, the effect it would have on the dot plot graph is that: B. The mean will decrease.
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Please help me with these !!!! asapppp!!!! they all go from 0-9 on the drop downs
Answer:
6x + 1
3x + 3
6x + 9
Step-by-step explanation:
1)
To find the missing number, compare both sides of the equation. If the variable terms are the same and the constant terms are different, then the equation has no solutions.
2x + 9 + 3x + x = _x +_
6x + 9 = _x + _
6x + 9 = 6x + 1
2)
To find the missing number, compare both sides of the equation. If the variable terms are the different and the constant terms are either different or same, then the equation has one solution.
2x + 9 + 3x + x = _x + _
6x + 9 = _x + _
6x + 9 = 3x + 3
3)
When equation is true for every possible value of x.
To find the missing number, compare both sides of the equation. If the variable terms are the same and the constant terms are same, then the equation has no solutions.
2x + 9 + 3x + x = _x + _
6x + 9 = _x + _
6x + 9 = 6x + 9
6x = 6x +9 -9
6x = 6x
6x/6 = x
x = x
Can somebody pls tell me which statement is true ?
Answer:
B
Step-by-step explanation:
Since the probability of an animal being blue isn't affected by the animal having two heads, the two events are independent.
if 6 squared x =1 what is the value of x
Question: 6^x = 1 (finding x)
Answer: x = 0
Explanation: Any non-zero expression raised to the power of 0 equals 1. Since we are trying to find 1, 0 would be an appropriate vale for x.
Please HELP !!
Each granola bar costs $1 write an expression that shows the total costs of the granola bars using the variable J
Answer:
Expression for the total cost is $1J.
Step-by-step explanation:
Given that each granola bar costs $1.
Now we need to write an expression that shows the total costs of the granola bars using the variable J.
So let's assume that the number of granola bars = J
then total cost of g granola bars = (J)($1) = $1J
Hence required expression for the total cost is 1J dollars.