An arithmetic progression is a progression where the next term is found by multiplying the previous by a constant number called the common ratio, for the given progression:
[tex]4,2,1[/tex]If we use 1/2 as a common ratio we get:
[tex]\begin{gathered} 2=\frac{4}{2} \\ 1=\frac{2}{2} \end{gathered}[/tex]Therefore this is an arithmetic progression and its common ratio is 1/2
In the picture shown b and F are midpoints solve for x
ANSWER:
x = 10
EXPLANATION:
Given:
Recall that the Midpoint Theorem states that the line segment joining the midpoints of any two sides of a triangle is parallel to the third side and equal to half of the third side.
We can go ahead and solve for x as seen below;
[tex]\begin{gathered} BF=\frac{1}{2}*AE \\ \\ 23=\frac{1}{2}*(5x-4) \\ \\ 23*2=5x-4 \\ \\ 46=5x-4 \\ \\ 5x=46+4 \\ \\ 5x=50 \\ \\ x=\frac{50}{5} \\ \\ x=10 \end{gathered}[/tex]Therefore, the value of x is 10
Which ordered pair must be a solution in the graph of the linear inequalitybelow?(-2,2)(0, -2)
SOLUTION:
We want to determine which ordered pair must be a solution in the graph of the linear inequality. The point picked must be in the shaded region to be a solution.
Going through the options, we see that, the only ordered pair that is a solution there is;
[tex](-5,1)[/tex]
What is the half-life of the goo in minutes? Find a formula for G(t), the amount of goo remaining at time t. How many grams of goo will remain after 68 minutes?
To solve this question on the half-life, we will use this expression:
[tex]\begin{gathered} G(t)=G_oe^{-kt} \\ \text{where G(t) is the remaining sample at time t.} \\ G_{o\text{ }}\text{ is the original sample} \\ K\text{ is a constant} \\ t\text{ is time} \end{gathered}[/tex]To proceed in solving, we will need to find the value of constant k
[tex]\begin{gathered} G(t)=G_oe^{-kt} \\ G(t)=17.25 \\ G_o=276 \\ t=255 \\ \text{Now substitute the parameters above into the formula:} \\ 17.25=276e^{-k(255)} \\ \frac{17.25}{276}=e^{-k(255)} \end{gathered}[/tex][tex]\begin{gathered} 0.0625=e^{-k255} \\ \ln 0.0625=-255k \\ \frac{\ln 0.0625}{-255}=k \\ 0.0109=k \end{gathered}[/tex]Now to get the half-life in minutes will be to get the time taken for the sample to go from 276g to 138g.
[tex]\begin{gathered} G(t)=G_oe^{-kt} \\ G(t)=138g \\ 138=276e^{-0.0109t} \\ \frac{138}{276}=e^{-0.0109t} \\ 0.5=e^{-0.0109t} \\ \ln 0.5=-0.0109t \\ \frac{\ln 0.5}{-0.0109}=t \\ 63.591\text{minutes = t} \end{gathered}[/tex]The half-life is 63.59 minutes.
The formula for G(t) at time t is:
[tex]G(t)=276e^{-0.0109t}[/tex]The amount of goo that will remain after 68 minutes is calculated using the formula above:
[tex]\begin{gathered} G(t)=276e^{-0.0109t} \\ t=68\text{ minutes} \\ G(t)=276e^{-0.0109(68)} \\ G(t)=276e^{-0.7412} \\ G(t)=131.5255\text{ grams} \\ G(t)\text{ = 131.53 grams (to 2 d.p)} \end{gathered}[/tex]The amount of goo remaining after 68 minutes is 131.53 grams.
I need help please, it’s my math assignment also can you add simple answers
a)
Step 1:
Draw the scatter diagram from the table
x represents days and y represent set up time
Step 2:
b)
Draw the scatter diagram
Step 3:
c)
Pick two points from the graph to find the linear equation
Points (2 , 16 ) and (6, 11)
[tex]\begin{gathered} \frac{y-y_1}{x-x_1}\text{ = }\frac{y_2-y_1}{x_2-x_1} \\ \frac{y\text{ - 16}}{x\text{ - 2}}\text{ = }\frac{11\text{ - 16}}{6\text{ - 2}} \\ \frac{\text{y - 16}}{x\text{ - 2}}\text{ = }\frac{-5}{4} \\ \frac{y-16}{x-2}\text{ = -1.25} \\ y\text{ - 16 = -1.25x + 2.5} \\ y\text{ = -1}.25x\text{ + 18.5} \end{gathered}[/tex]The equation is y = -1.25x + 18.5
A hotel swimming pool is made for semi circle and square. Find The perimeter of the swimming pool. Round your answer to the nearest tenth.
Combining the 4 semi-circles of the pool, we can make 2 circles, with a diameter of 10 yd.
The perimeter of a circle is calculated as follows:
[tex]P=\pi\cdot D[/tex]where D is the diameter.
Then, the perimeter of the swimming pool is:
[tex]\begin{gathered} P=2\cdot\pi\cdot10 \\ P=62.8yd^{} \end{gathered}[/tex]6. F(x) is the function that determines the absolute value of the cube of the input. Part 1. Evaluate: F(5) Part 2. Evaluate: F(-7) Part 3. Determine: F(5). F(-7) Or is the function defined by the following graph. The graph window is:
We have that F(x) is the function that determines the absolute value of the cube of the input, then we have that f(x) is:
[tex]f(x)=\lvert x^3\rvert[/tex]Part 1. Evaluate F(5): x = 5
[tex]f(5)=\lvert5^3\rvert=\lvert125\rvert=125[/tex]Part 2. Evaluate F(-7): x = -7
[tex]f(-7)=\lvert-7^3\rvert=\lvert-343\rvert=343[/tex]Part 3. Evaluate F(5)xF(-7)
[tex]f(5)\cdot f(-7)=125\cdot343=42875[/tex]Parabola in the form x^2=4pyIdentify Vertex, value of P, focus, and focal diameter.Identify endpoints of latus rectumWrite equations for the directrix and axis of symmetry X^2= -12y
Answer:
(a)
• The vertex of the parabola, (h,k)=(0,0)
,• The value of p = -3
• The focus is at (0,-3).
,• The focal diameter is 12
(b)The endpoints of latus rectum are (-1/12, -1/6) and (-1/12, 1/6).
(c)See Graph below
(d)
• I. The equation for the directrix is y=3.
,• II. The axis of symmetry is at x=0.
Explanation:
Given the equation of the parabola:
[tex]x^2=-12y[/tex]For an up-facing parabola with vertex at (h, k) and a focal length Ipl, the standard equation is:
[tex](x-h)^2=4p(y-k)[/tex]Rewrite the equation in the given format:
[tex]\begin{gathered} (x-0)^2=4(-3)(y-0) \\ \implies(h,k)=(0,0) \\ \implies p=-3 \end{gathered}[/tex]• The vertex of the parabola, (h,k)=(0,0)
,• The value of p = -3
The focus is calculated using the formula:
[tex]\begin{gathered} (h,k+p) \\ \implies Focus=(0,0-3)=(0-3) \end{gathered}[/tex]• The focus is at (0,-3).
Focal Diameter
Comparing the given equation with x²=4py, we have:
[tex]\begin{gathered} x^2=4ay \\ x^2=-12y \\ 4a=-12 \\ \implies a=-3 \\ \text{ Focal Diameter =4\mid a\mid=4\mid3\mid=12} \end{gathered}[/tex]The focal diameter is 12
Part B (The endpoints of the latus rectum).
First, rewrite the equation in the standard form:
[tex]\begin{gathered} y=-\frac{1}{12}x^2 \\ \implies a=-\frac{1}{12} \end{gathered}[/tex]The endpoints are:
[tex]\begin{gathered} (a,2a)=(-\frac{1}{12},-\frac{1}{6}) \\ (a,-2a)=(-\frac{1}{12},\frac{1}{6}) \end{gathered}[/tex]The endpoints of latus rectum are (-1/12, -1/6) and (-1/12, 1/6).
Part C
The graph of the parabola is given below:
Part D
I. The equation for the directrix is of the form y=k-p.
[tex]\begin{gathered} y=0-(-3) \\ y=3 \end{gathered}[/tex]The equation for the directrix is y=3.
II. The axis of symmetry is the x-value at the vertex.
The axis of symmetry is at x=0.
Solve the system by substitution. (If there is no solution, enter NO SOLUTION. If there are an infinite number of solutions, enter the general solution in terms of x, where x is any real number.)x − 0.2y = 2−10x + 2y = 10(x, y) =
Start multiplying the first equation for 10
[tex]\begin{gathered} 10(x-0.2y=2) \\ 10x-2y=20 \end{gathered}[/tex]add the resulting equation with the second equation
[tex]\begin{gathered} 10x-2y+(-10x+2y)=20+10 \\ 0=30\rightarrow false\text{ }0\ne30 \\ \end{gathered}[/tex]Answer:
There is no solution for the system
Аis a solid consisting of two polygons which are parallel to each otherand all points between them.O A. cubeO B. prismO C. pyramidO D. triangle
The prism is a type of polyhedron formed by two parallel faces that are identical polygons called bases. These figures are joined by the lateral faces that are parallelograms.
According to the previous definition we can conclude that the answer is:
B. Prism
while shopping at a 30% off sale, Robin was told that the sale price would saver her $6 on her purchase. Since the original price tag was missing, she had to calculate the price. what was the original price.
To do this, let x be the original price. Since the sale price would save you $ 6 on your purchase and this equates to 30% off, then using the rule of three you can find the original price, like this
[tex]\begin{gathered} \text{ \$6}\Rightarrow30\text{ \%} \\ x\Rightarrow100\text{ \%} \\ x=\frac{100\text{ \%}\cdot\text{ \$6}}{30\text{ \%}} \\ x=\text{ \$}\frac{600}{30} \\ x=\text{ \$20} \end{gathered}[/tex]Therefore, the original price was $20.
Verifying you have
[tex]\text{ \$20}\ast30\text{ \%= \$20}\cdot\frac{30}{100}=\text{ \$20}\cdot0.3=\text{ \$6}[/tex]Which was the $6 that Robin saved on his purchase.
Classify the polynomial as constant, linear, quadratic, cubic, or quartic, anddetermine the leading term, the leading coefficient, and the degree of thepolynomial.g(x) = - 2x^4 - 6
Given:
[tex]g(x)=-2x^4-6[/tex]To classify: The polynomial name, degree, leading term, and leading coefficient
Explanation:
Since the degree of the polynomial is the highest or the greatest power of a variable in a polynomial equation.
Here, 4 is the greatest power of a variable x.
So, the degree of the polynomial is 4.
As we know,
The leading term is the term containing the highest power of the variable.
So, the leading term is,
[tex]-2x^4[/tex]Since the coefficient of the term of the highest degree in a given polynomial is -2.
So, the leading coefficient is -2.
Since the degree of the polynomial is 4.
So, the given polynomial is a quartic polynomial.
Final answer: Option C. Quartic polynomial.
Which of the following options results in a graph that shows exponentialdecay?5 pointsO f(x) 0.4(0.2)^xf(x) = 4(4)^xf(x) = 0.7(1.98)^xOf(x) = 5(1+.1)^x
Answer
Option A is the answer.
f(x) = 0.4(0.2)ˣ
The value carrying the power of x is less than 1, so, this expression represents exponential decay.
Explanation
The key to knowing which expression is represents an exponential decay or exponential growth is the value of the number carrying the power of x.
If that number is greater than 1, then it represents exponential growth.
But, if that number is lesser than 1 (but greater than 0), then it represents exponential decay.
(2)ˣ represents exponential growth.
(0.5)ˣ represents exponetial decay.
f(x) = 0.4(0.2)ˣ
The value carrying the power of x is less than 1, so, this expression represents exponential decay.
f(x) = 4(4)ˣ
The value carrying the power of x is greater than 1, so, this expression represents exponential growth.
f(x) = 0.7(1.98)ˣ
The value carrying the power of x is greater than 1, so, this expression represents exponential growth.
f(x) = 5(1 + .1)ˣ
The value carrying the power of x is greater than 1, so, this expression represents exponential growth.
Hope this Helps!!!
log 2-log 5 can also be written as ?.
The formula for difference of two logarthimic terms are,
[tex]\log a-\log b=\log (\frac{a}{b})[/tex]Determine the expression for log 2 -log 5.
[tex]\log 2-\log 5=\log (\frac{2}{5})[/tex]Answer: log(2/5)
A woman invests $6300 in an account that pays 6% interest per year, compounded continuously.(a) What is the amount after 2 years? (Round your answer to the nearest cent.)$ (b) How long will it take for the amount to be $8000? (Round your answer to two decimal places.) yr
Given: A woman invests $6300 in an account that pays 6% interest per year, compounded continuously.
Required: a) To determine the amount after 2 years.
b) To determine how long it will take for the amount to be $8000.
Explanation: The amount, A after t years with an interest rate of r is given by-
[tex]A=Pe^{rt}[/tex]
Here,
[tex]\begin{gathered} P=6300 \\ r=\frac{6}{100} \\ =0.06 \\ t=2 \end{gathered}[/tex]Substituting the values, we get-
[tex]\begin{gathered} A=6300e^{0.06\times2} \\ =7103.23 \end{gathered}[/tex]Hence the amount after 2 years is $7103.23
Next, let t be the time it takes for the amount to be $8000-
[tex]\begin{gathered} 8000=6300e^{0.06t} \\ \frac{8000}{6300}=e^{0.06t} \\ \ln(1.2698)=0.06t \end{gathered}[/tex]Further solving for t as-
[tex]t=3.98\text{ years}[/tex]Hence, it takes 3.98 years for the amount to be $8000.
Final Answer: a) $7103.23
b) 3.98 years
Each expression represents the total number of dots in a pattern where n represents the step Select all the expressions that represent a quadratic relationship between the step number and the total number of dots. (If you get stuck, consider sketching the first few steps of each pattern as described by the expression.) A. I2 answer B. 2n C. non answer A D. nun E. n + 2 F.n=2 A &C • A, B, C B&C D. EF
We have the following:
We have that an option is quadratic when the same value is being multiplied twice, that is,
[tex]n\cdot n=n^2[/tex]Therefore, among the answers the only quadratic options are A and C.
all of the Patron in part shade and rewrite (x × y)^nas a product of two single powers
we have
(2*3)^5
we know that
(2*3)^5=(2^5)(3^5)
Rewrite each term as product of two single powers
so
(2^5)(3^5)=(2^3)(2^2)(3^3)(3^2)
Part c
we have
10^2/10^0
when divide, subtract the exponents
so
10^(2-0)
10^2
another way
Any number elevated to zero is equal to 1
so
10^0=1
substitute
10^2/1=10^2
Part f
we have
(2/3)^5
we know that
(2/3)^5=2^5/3^5
Select the conic section that represents the equation.4x2 - 25y2 = 100circleparabolaellipsehyperbola
We know that the equation of a circle is:
[tex](x-a)^2+(y-b)^2=r^2[/tex]the equation a a parabola is:
[tex]y=ax^2+bx+c[/tex]the equation
Five hundred students in your school took the SAT test. Assuming that a normal curve existed for your school, how many of those students scored within 2 standard deviations of the mean? (Give the percent and the number.)
In order to find the percentage of students within 2 standard deviations, let's look at the z-table for the percentages when z = -2 and z = 2.
From the z-table, we have that the percentage for z = -2 is 0.0228 and for z = 2 is 0.9772.
The percentage between z = -2 and z = 2 is given by:
[tex]0.9772-0.0228=0.9544[/tex]Therefore the percentage is 95.44%.
Now, calculating the number of students within this percentage, we have:
[tex]500\cdot0.9544=477.2[/tex]Rounding to the nearest whole, we have 477 students.
James bought a movie ticket for $4.05. Hepaid the movie ticket with quarters anddimes. If James used 18 coins in all, howmany quarters (q) and dimes (d) did he use?=q + d = 180.25q + 0.1d = 4.05+=ritorddia
q + d = 18
0.25q + 0.1d = 4.05
We will use substitution
Solving the first equation for q
q = 18 -d
Substituting this into the second equation
.25(18-d) + .1d = 4.05
Distribute
4.5 - .25d +.1d = 4.05
Combine like terms
4.5 - .15d = 4.05
Subtract 4.5 from each side
-.15d = -.45
Divide each side by -/15
-.15d/-.15 = -.45/-.15
d = 3
We have 3 dimes
Now we can find the number of quarters
q = 18-d
q = 18-3
q = 15
We have 15 quarters
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The population of Orange County is represented by the function f(x)=87,000(0.9)x, where x is the number of years since 2010.
The population of Greene County was 78,000 in 2010, and has decreased exponentially at a rate of 8% each year.
How do the populations of these counties compare in 2015?
Drag a value or word to the boxes to correctly complete the statements.
Put responses in the correct input to answer the question. Select a response, navigate to the desired input and insert the response. Responses can be selected and inserted using the space bar, enter key, left mouse button or touchpad. Responses can also be moved by dragging with a mouse.
In 2015, the population of Orange County was approximately Response area and the population of Greene County was approximately Response area. In 2015, Response area County was more populous.
The population of Greene County will be more than Orange County in 2015.
What is comparison?Comparing numbers, in maths, is defined as a process or method in which one can determine whether a number is smaller, greater, or equal to another number according to their values.
Given that, The population of Orange County is represented by the function f(x) = 87,000(0.9)x, where x is the number of years since 2010.
The population of Greene County was 78,000 in 2010, and has decreased exponentially at a rate of 8% each year.
Orange County population in 2015 = 87,000(0.9)^5 = 51372
Greene County population in 2015 = 78000(1+0.08)^5 = 51408
Hence, The population of Greene County will be more than Orange County in 2015.
For more references on comparison, click;
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I need help with this problem if anyone can help me please do Find the value of the variable
Answer:
u=11
Explanation:
The statement "The quotient of 44 and 4 is u" can be represented mathematically as:
[tex]u=44\div4[/tex]We can then solve the equation for u.
[tex]\begin{gathered} u=\frac{44}{4}=\frac{4\times11}{4} \\ \implies u=11 \end{gathered}[/tex]The value of u is 11.
Rewrite the fraction (4/1)
Answer:
4
Explanation:
Given the fraction 4/1, this can be rewritten as 4 because any number divided by 1 can also be written as the number itself, both are equivalent.
Help me please I don’t understand and I don’t get this
The solution:
Representing the given problem in a diagram, we have:
NEED HELP ASAPP!!!!!!
Answer:
second line
Step-by-step explanation:
no more than :
x≤ 52 (the dot is full, 52 is a value)
11. The table shows the distance, y, a car can travel in feet in x seconds. Speed or Car Time, x (seconds) 5 10 Distance, y (feet) 700 1,400 2,100 2,800 3,500 15 20 25 Based on the information in the table, which equation can be used to model the relationship between x and y? A. y = 140x B.y = 5x C. y = x + 140 D. y = x + 5
In this case, we'll have to carry out several steps to find the solution.
Step 01:
y = distance
x = time
equation = ?
Step 02:
y = k x
if y = 700ft , x = 5 seconds
700 = k * 5
700 /5 = k
140 = k
y = 140 x
The answer is:
y = 140 x
Stanley marked two points on the grid below to show the locations of the fiction section, point F, and the travel section, point T, in a bookstore.
EXPLANATION
We need to calculate the distance between the points (x₁,y₁)=(-8,-3) and (x₂,y₂)=(-3,8) applying the distance equation as shown as follows:
distance=
[tex]\text{Distance}=\sqrt[]{(x_2-x_1)^2+(y_2-y_1)^2}[/tex]Substituting terms:
[tex]\text{Distance = }\sqrt[]{(-3-(-8))^2+(8-(-3))^2}[/tex]Adding numbers:
[tex]\text{Distance}=\sqrt[]{(5)^2+(11)^2}=\sqrt[]{(25+121)}=\sqrt[]{146}[/tex]The shortest distance is sqrt(146)
graph the line y=-4x
Solution
x=-2 , y = 8
x=-1, y= 4
x=0, y=0
x= 1, y= -4
x= 2, y=-8
Segment XY measures 5cm. How long is the image of XY after a dilation with: A scale factor of a?
The image of the XY will be 5 times larger than the after dilation.
What is dilation?
resizing an object is accomplished through a change called dilation. The objects can be enlarged or shrunk via dilation. A shape identical to the source image is created by this transformation. The size of the form does, however, differ. A dilatation ought to either extend or contract the original form. The scale factor is a phrase used to describe this transition.
The scale factor is defined as the difference in size between the new and old images. An established location in the plane is the center of dilatation. The dilation transformation is determined by the scale factor and the center of dilation.
Segment XY mesured as 5cm
It will undergo dilation.
If X(0,0) and Y(x,y)
XY = √x²+y²
The factor we need to multiply, a
X'(0,0), Y'(ax,ay)
So the X'Y'=√a²x²+a²y²
X'Y'=a√x²+y²
X'Y'=aXY = 5a
Hence the image of the XY will be 5 times larger than the after dilation.
Learn more about dilation, by the following link
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if you travel 35 miles per hour for 4.5 hours hovú far will you travle
We need to multiply 4.5 hours by 35 miles per hour, as follows:
[tex]4.5\text{ hours}\cdot35\frac{miles}{hour}=157.5\text{ miles}[/tex]You will travel 157.5 miles
Add.(9s² - 3s) + (-6s - 9)
We have to add the expressions, grouping by similar terms:
[tex]\begin{gathered} \mleft(9s^2-3s\mright)+(-6s-9) \\ 9s^2-3s-6s-9 \\ 9s^2-9s-9 \end{gathered}[/tex]Answer: 9s²-9x-9