SOLUTION
[tex]\begin{gathered} 11x+b=2(5.5x+4) \\ 11x+b=11x+4 \\ b=11x-11x+4 \\ b=0+4 \\ b=4 \end{gathered}[/tex]The value of b is 4.
How to solve for x:27^x=9^x-4
In order to solve for x, we will need to apply a logarithm in both sides of the equation.
First, let's remember some properties of logarithm expressions:
[tex]\begin{gathered} \log (a^b)=b\cdot\log (a) \\ \log (a)+\log (b)=\log (a\cdot b) \\ \log (a)-\log (b)=\log (\frac{a}{b}) \end{gathered}[/tex]So we have:
[tex]\begin{gathered} 27^x=9^x-4 \\ (3^3)^x=(3^2)^x-4 \\ (3^x)^3=(3^x)^2-4 \end{gathered}[/tex]Let's substitute 3^x by y, then let's solve for y:
[tex]undefined[/tex]Suppose the graph of a polynomial function P(x) has an x-intercept at (c, 0). Write 4-6 sentences analyzing whether (c, 0) is also an x-intercept of the graphs that result from applying single transformations to P(x). For each transformation, elaborate on whether (c, 0) is always, sometimes, or never an x-intercept of the transformed graph, explaining your reasoning. For any transformations for which (c, 0) is only sometimes an x-intercept of the transformed graph, design specific functions to illustrate how the other x-intercepts of the original graph determine whether (c, 0) is an x-intercept of the transformed graph.
For example:
Let:
P(x) = x² - 1
P(x) has an x-intercept at x=1 or x=-1 because:
x² - 1 = 0
x² = 1
√(x²) = √(1)
x = ±1
When we talk about transformations of functions, we apply three fundamental processes:
Translation, Scaling, Reflection
Translation: allows us to move a function to the left, right, up or down.
Scaling: allows us to expand or narrow a function
Reflection: allows us to reflect the function with respect to the x or y axis.
Let's apply a scaling:
For example:
P(x) = 2 (x² - 1)
As you can see, the polynomial function compresses horizontally by a factor of 1/2, however its intercept remains the same, because:
2 (x² - 1) = 0
Solving for x:
x = ±1
Let's apply a translation:
For example:
P(x) = (x² - 1) - 4
In this case the x-intercept will be different, because:
(x² - 1) - 4 = 0
Solving for x:
x² = 5
√(x²) = √(5)
x = ±√(5) = ± 2.236
Explain why you cannot use the axes of symmetry to distinguish between the quadratic functions y=3x^2+12x+1 and y=x^2+4x+5.I'm not sure how to do this problem
Given a quadratic equation:
[tex]y=ax^2+bx+c[/tex]the expression to find the axis of symmetry is:
[tex]x=-\frac{b}{2a}[/tex]in this case, for the first equation, we have the following:
[tex]\begin{gathered} y=3x^2+12x+1 \\ axis\text{ of symmetry:} \\ \Rightarrow x=-\frac{12}{2(3)}=-\frac{12}{6}=-2 \\ x=-2 \end{gathered}[/tex]for the second equation, we get:
[tex]\begin{gathered} y=x^2+4x+5 \\ \text{axis of symmetry:} \\ \Rightarrow x=-\frac{4}{2(1)}=-\frac{4}{2}=-2 \\ x=-2 \end{gathered}[/tex]as we can see, both functions have the same axis of symmetry, that's why you cannot distinguish them. In general, several quadratic functions can have the same axis of symmetry, without being equivalent between each other.
Answer:
The axes of symmetry can be used to distinguish between the two functions because they are different. The first function has a y-intercept of (0,1), while the second function has a y-intercept of (0,5).
The four tables below show relationships in which the x values represent inputs and the y values represent thecorresponding outputs.QRsTyy2y.y-2-3-1-5-233413241453-33733345341054-5Which table represents a relationship that is not a function?AQBSCTDRSHOW HINI
The most appropriate choice for functions will be given by -
T is not a function.
Fourth option is correct
What is a function?
A function from A to B is a rule that assigns to each element of A a unique element of B. A is called the domain of the function and B is called the codomain of the function.
There are different operations on functions like addition, subtraction, multiplication, division and composition of functions.
In the first table
Q(-2) = -3, Q(1) = 3, Q(3) = -3, Q(5) = 3
Thus every element of domain has a unique image. Thus Q is a function
In the second table
R(-1) = -5, R(2) = 4, R(3) = 7, R(4) = 10
Thus every element of domain has a unique image. Thus R is a function
In the third table,
S(-2) = 3, S(1) = 3, S(3) = 3, S(5) = 3
Thus every element of domain has a unique image. Thus S is a function
In the first table
T(3) = 4, T(4) = 5, T(3) = -4, T(4) = -5
It can be seen that 3 and 4 has two images. So T is not a function.
So it can be seen that T is not a function.
To learn more about function, refer to the link:
https://brainly.com/question/22340031
#SPJ13
10 pointsQuestion 7. Contestants in a dance-a-thon rest for the same amount oftime every hour.A couple rests for 25 minutes in 5 hours. How long didthey rest in 8 hours? Please do not include units in your answer. (Enter anumber ONLY.) *Your answer
If the couples rest the same amount every hour, and you know that they rest for 25minutes in 5 hours, you can use cross multiplication to determine the amount of time they will rest in 8 hours:
5hours____25minutes
8hours____x minutes:
[tex]\frac{25}{5}=\frac{x}{8}[/tex]This means that the rate of the resting time and the hours is the same. To determine how much x is, multiply 25/5 by 8
[tex]\begin{gathered} 8(\frac{25}{5})=x \\ x=40 \end{gathered}[/tex]After 8 hours the couple will dance for 40 minutes.
3(x-4)=18 Need help solving this problem
Given equation is
[tex]3(x-4)=18[/tex]
Dividing both sides by 3, to eliminate 3 from the left side of the equation.
[tex]\frac{3(x-4)}{3}=\frac{18}{3}[/tex][tex]x-4=6[/tex]Adding 4 both sides to eliminate -4 from the left side of the equation, we get
[tex]x-4+4=6+4[/tex][tex]x=10[/tex]Hence the solution is x=10.
please try to be quick with your response. my brainly keeps crashing.
Given:
The surface area of the sphere is
[tex]36\pi in^2[/tex]Required:
To find the volume of the sphere.
Explanation:
The formula of surface area of the sphere is
[tex]\begin{gathered} SA=4\pi r^2 \\ \\ 36\pi=4\pi r^2 \\ \\ r^2=\frac{36\pi}{4\pi} \\ \\ r^2=9 \\ \\ r=3 \end{gathered}[/tex]Now the volume of the sphere is
[tex]\begin{gathered} V=\frac{4}{3}\pi r^3 \\ \\ =\frac{4}{3}\pi3^3 \\ \\ =36\pi in^3 \end{gathered}[/tex]Final Answer:
The volume of the sphere is
[tex]36\pi in^3[/tex]What is the equation for the line of best fit for the following data? Round theslope and y-intercept of the line to three decimal places.X2571216y30192092
Tyler rolled a six-sided number cube, recorded the results, and then rolled again. What is theprobability that the first roll was an odd number and the second roll was a number less than3?
NYou have an experiment where you could get the following answers, notice that I will suppose that each side represents a different number from 1 to 6
[tex]\lbrace1,2,3,4,5,6\rbrace[/tex]It means that when you roll the cube for the first time you could get any of this 6 numbers. You should also notice that you have three odd numbers and other three even. Then
[tex]P(X=odd)=\frac{|\lbrace1,3,5\rbrace|}{|\lbrace1,2,3,4,5,6\rbrace|}=\frac{3}{6}=0.5[/tex]Now, if you want to know the probability for the second event we have the following
[tex]P(X<3)=\frac{|\lbrace1,2\rbrace|}{|{}\lbrace1,2,3,4,5,6\rbrace|}=\frac{2}{6}=\frac{1}{3}[/tex]Now, the question for this time is what is the probability for both cases, it means
[tex]P(X=odd,and,X<3)[/tex]Notice that the cases are independent just because even when 1 is an odd number and at the same time it is less than 3, it will not affect the second role. Then
[tex]P(X=odd,and,X<3)=P(X=odd)P(X<3)=\frac{1}{2}(\frac{1}{3})=\frac{1}{6}[/tex]Then the probability that the first roll is and odd number and the second roll a number less than 3 is 1/6.
a.Write an inequality to represent the domain of the part shown. Explain your answer.bWrite an inequality to represent the range of the part shown. Explain your answer.
The domain of a portion of a function is the interval of x-values we take; in this case we notice that the graph takes values in the x-axis from -2 to 4. Since the circle in the graph are hollowed this means that the domain does not include the limits, therefore the domain is:
[tex]-2The range is the portion of the function is the interval of y-values it takes. We notice that the graph takes values in that axis from -1 to 2, therefore the range is:[tex]-13.Emanuel has 825 pictures in his phone. His memory is getting full, so he starts deleting 25pictures every day. Define the variable and write an algebraic expression to describe the numberof pictures left on his phone after any given number of days.ЕТРО
Let d be the number of days he took in deleting the picture
Since he started deleting 25 pictures per day, then;
Number of pictures he has deleted so far is 25 x d = 25d
Since there are 825 pictures in his phone, then number
Preview Mode: Your score will not be recordedPoints (4, 5) and (10,5) are vertices of a rectangle.The length of the rectangle is twice the width.The other vertices are located at (4, ___) and (10,.). What could these ordered pairs be?a. Type your answers in the box.B1
ANSWER
(4, 7) and (10, -7)
STEP-BY-STEP EXPLANATION
Given information
[tex]\text{The vertices of a rectangle are (4, 5) and (10, 5)}[/tex]step 1: Find the distance between the two points using the below formula
[tex]\begin{gathered} l\text{ = }\sqrt[]{(x1-x2)^2+(y1-y2)^2} \\ \end{gathered}[/tex]From the given points, you will see that both coordinates lie on the same y-axis
Then, we can find the length as
[tex]\begin{gathered} l\text{ = }\sqrt[]{(4-10)^2+(5-5)^2} \\ l\text{ = }\sqrt[]{(-6)^2\text{ + 0}} \\ l\text{ = }\sqrt[]{36} \\ \text{ = 6 units} \end{gathered}[/tex]Since the length of the triangle is twice the width
Therefore, l = 2w
l = 2(6)
l = 12 units
The y-coordinate of the other vertices will be
y = 5 - 12
y = -7
Therefore, other vertices are
(4, -7) and (10, -7)
Sid peeled 21 oranges every 28 hours. At that rate, how many would he peel in 24 hours?
He will peel 18 oranges in 24 hours
Here, we want to calculate the number of oranges that will be peeled in 24 hours
From the question, we can deduce the following;
21 oranges = 28 hours
x oranges = 24 hours
We then proceed to cross-multiply
[tex]\begin{gathered} 21\times24\text{ = x}\times28 \\ \\ x\text{ = }\frac{21\times24}{28} \\ \\ x\text{ = 18 oranges} \end{gathered}[/tex]mathhhhhhhhhhhhhhhhhh
Answer
Option C is correct.
A number half as much as 1000 minus 300 is given mathematically as
(1000 - 300)/2
Hope this Helps!!!
Find the area of the right triangle base = 13 height = 6 ft
Area of a triangle = (bxh)/2
In this case, base = 13 and height = 6
Area = (13 * 6)/2 = 39 square feet
Answer:
39 square feet
Two lines passing through the point (2 , 3) intersect each other at an angle of 60° . If slope of one line is 2, then find the equation of the other line ~ note : there are two possible slopes !
The circle graph shows how a family budgets its annual income. If the total annual income is $125,000, what amount is budgeted for Clothing?Housing29%Savings8%Leisure13%siX$?Insurance9%Auto12%Food15%Clothing14%SubmitPrivacContingContinue2021 McGraw-Hill Education. All Rights Reserved. Terms of UseHAHILiii
Notice that the budget for clothing is 14% of the total budget. Then, we can multiply the annual budget by 14% in its decimal form to get the following:
[tex]125,000(14\%)=125,000(0.14)=17,500[/tex]therefore, the amount budgeted for clothing is $17,500
find the circumference and area of each circle. Use 3.14 for π15. radius = 3in 16. diameter = 6cm17. diameter = 5ft
Answer
15) Radius = 3 inches
Circumference = 18.84 inches
Area = 28.26 square inches
16) Diameter = 6 cm
Circumference = 18.84 cm
Area = 28.26 cm²
17) Diameter = 5 ft
Circumference = 15.5 ft
Area = 19.625 ft²
Explanation
The circumference of a circle is given as
Circumference = 2πr
where
π = pi = (22/7) = 3.14
r = radius of the circle
In case the diameter is given, since the diameter is twice the size of the radius,
D = 2r
Circumference = πD
The Area of a circle is given as
Area = πr²
In terms of the diameter,
Area = (πD²/4)
So, we can answer the questions now
15) Radius = 3 inches
Circumference = 2πr
= 2π (3)
= 6π
= 18.84 inches
Area = πr²
= π(3)²
= 9π
= 28.36 square inches
16) Diameter = 6 cm
Circumference = πD
= π (6)
= 6π
= 18.84 cm
Area = (πD²/4)
= [π(6)²/4]
= 9π
= 28.36 cm²
17) Diameter = 5 ft
Circumference = πD
= π (5)
= 5π
= 15.7 ft
Area = (πD²/4)
= [π(5)²/4]
= (25π/4)
= 19.625 ft²
Hope this Helps!!!
Which expression is equivalent to 6^-3
Do you have any options available to choose from?
Answer: D
Step-by-step explanation:
Because, yes, trust me :DD
The radioactive substance uranium-240 has a half-life of 14 hours. The amount At of a sample of uranium-240 remaining (in grams) after t hours is given by the following exponential function.
Step 1
Given;
[tex]A(t)=5600(\frac{1}{2})^{\frac{t}{14}}[/tex]Required; To find the amount A(t) of a sample of uranium-240 remaining (in grams) after 13 hours and 60 hours
Step 2
Find the initial amount. To do this we set t=0
[tex]\begin{gathered} A(0)=5600(\frac{1}{2}_)^{\frac{0}{14}} \\ A(0)=5600grams \end{gathered}[/tex]Hence the equation remains valid
Step 3
Find the amount A(t) left after 13 hours
[tex]A(13)=5600(\frac{1}{2})^{\frac{13}{14}}[/tex][tex]\begin{gathered} =5600\cdot \frac{1^{\frac{13}{14}}}{2^{\frac{13}{14}}} \\ =\frac{5600}{1}\cdot \frac{1}{2^{\frac{13}{14}}} \\ =\frac{5600}{2^{\frac{13}{14}}} \\ =\frac{2^5\cdot \:175}{2^{\frac{13}{14}}} \\ =2^{\frac{57}{14}}\cdot\:175=2942.11858 \\ =2942grams \end{gathered}[/tex]Step 4
Find the amount A(t) left after 60 hours
[tex]\begin{gathered} A(60)=5600(\frac{1}{2})^^{\frac{60}{14}} \\ =5600\cdot \frac{1^{\frac{60}{14}}}{2^{\frac{60}{14}}} \\ =5600\cdot \frac{1}{2^{\frac{60}{14}}} \\ =\frac{5600}{1}\cdot \frac{1}{16\cdot \:2^{\frac{2}{7}}} \\ =\frac{5600}{16\cdot \:2^{\frac{2}{7}}} \\ =\frac{16\cdot \:350}{16\cdot \:2^{\frac{2}{7}}} \\ =\frac{350}{2^{\frac{2}{7}}} \\ =2^{\frac{5}{7}}\cdot \:175 \\ A(60)=287.11737 \\ A(60)\approx287grams \end{gathered}[/tex]Answers;
[tex]\begin{gathered} A(13)=2942grams\text{ to the nearest gram} \\ A(60)=287grams\text{ to the nearest gram} \end{gathered}[/tex]I need help with this word problem but only with the question "e"
Part e
we have the function
[tex]P(x)=-2x^2+32x-110[/tex]The given function represents a vertical parabola, open downward
The vertex represents a maximum
so
Convert the given equation into vertex form
step 1
Factor -2
[tex]P(x)=-2(x^2-16x)-110[/tex]step 2
Complete the square
[tex]\begin{gathered} P(x)=-2(x^2-16x+64-64)-110 \\ P(x)=-2(x^2-16x+64)-110+128 \\ P(x)=-2(x^2-16x+64)+18 \end{gathered}[/tex]step 3
Rewrite as perfect squares
[tex]P(x)=-2(x-8)^2+18[/tex]The vertex is the point (8,18)
That means
8 is the number of games in hundreds -------> 800 games
18 is the profit in ten thousand ------> 18*10,000=$180,000
so
The maximum profit is $180,000 for 800 gamesSelect the two values of x that are roots of this equation.x2 - 5x + 3 = 0OI B. X-A. x. 5+ y27B. x-5-Ec. x. 5-797D. x 5 + 5O C.
SOLUTION:
To find the roots of this given equation, we either make use of completing the square method or formula method because it is obvious that equation is not factorisable.
[tex]\begin{gathered} x\text{ = }\frac{-b\text{ }\pm\text{ }\sqrt[]{b^2\text{ - 4ac}}}{2a} \\ \\ x^2\text{ - 5x + 3 = 0} \\ a\text{ = 1, b = -5 and c = 3} \\ x\text{ = }\frac{-(-5)\text{ }\pm\sqrt[]{(-5)^2\text{ - 4 (1) (3)}}}{2\text{ (1)}} \\ \\ x\text{ = }\frac{5\text{ }\pm\sqrt[]{25-12}}{2} \\ \\ x\text{ = }\frac{5\text{ }\pm\sqrt[]{13}}{2} \\ \\ x\text{ =}\frac{5+\sqrt[]{13}}{2}\text{ and x = }\frac{5\text{ - }\sqrt[]{13}}{2} \end{gathered}[/tex]The correct options are options B and D.
Use the distributive property and the GCF of the addends to rewrite each sum as an equivalent expression that has two factors.28 + 4240 + 25 30 + 5475 + 90
We need to find the greatest common factor GCF of the two numbers, then first list the prime factors of each number:
a. 28: 2*2*7
42: 2*3*7
28 and 42 share one 2 and one 7 in common.
Multiply it to get the GCF: 2*7=14.
The GCF of 28 and 42 is 14.
Now, to use the distributive property, write the sum in the form: GCF(a+b) then:
[tex]28+42=14(2+3)[/tex]b. 40+25
40: 2*2*2*5
25: 5*5
They share one 5 in common.
The GCF of 40 and 25 is 5.
By using the distributive property:
[tex]40+25=5(8+5)[/tex]c. 30+54
30: 2*3*5
54: 2*3*3*3
They have one 2 and one 3 in common. Then 2*3=6.
The GCF of 30 and 54 is 6.
By using the distributive property:
[tex]30+54=6(5+9)[/tex]d. 75+90
75: 3*5*5
90: 2*3*3*5
They have one 3 and one 5 in common. So 3*5=15.
The GCF of 75 and 90 is 15.
By using the distributive property:
[tex]75+90=15(5+6)[/tex]help pleasefind all points (x) where the function g(x)= |x+5| - |x-9| is not differentiable…
Given the function:
[tex]g(x)=|x+5|-|x-9|[/tex]Using the absolute value rules
So, the function will be written as follows:
[tex]f(x)=\begin{cases}-14;x\le-5 \\ 2x-4;-5So, we will check the points x = -5, x = 9Because the function has corners at these points
So, f'(x) will be:
[tex]f^{\prime}(x)=\begin{cases}0;x\le-5 \\ 2;59\end{cases}[/tex]As shown, the middle function is not equal to the function on the sides
So, the answer will be:
g(x) is not differentiable at x = -5, 9
Sketch the right triangle and find the length of the side not given. If necessary, approximate the length to the nearest thousandth
Given the following:
Leg = 15
Leg = 20
We are to sketch a triangle and find the length of the side not given.
Therefore, the correct option is the third option which is 25
Hello! Thank you for helping me today, I need a little bit of assistance to understand the rest of this question please. (This is is not an active test, it is a book I am studying in order to take the ASVAB in a couple of weeks.)
Solution.
Let the height of the tree be h
[tex]\begin{gathered} Using\text{ the idea of similar triangle,} \\ \frac{4}{9}=\frac{h}{9+12} \end{gathered}[/tex][tex]\begin{gathered} \frac{4}{9}=\frac{h}{21} \\ h=\frac{21\text{ x }4}{9} \\ h=\frac{28}{3} \\ h=9\frac{1}{3}\text{ ft} \end{gathered}[/tex][tex]The\text{ height of the tree is 9 }\frac{1}{3}\text{ ft}[/tex]The correct option is C
are there any number pairs that satisfy both constrians. the sum is 12 and the difference is 5 . and is my answer correct
Given
There are a pair of numbers that satisfy both constraints
1) the sum is 12
2) the difference is 5
So, let the numbers are (x) and (y)
From the first constraint ⇒ x + y = 12
From the second constraint ⇒ x - y = 5
So, we can draw the following lines
As shown the point of intersection between the lines = (8.5, 3.5)
So, the answer will be the numbers pair = 3.5 and 8.5
Answer: one number is 8 and the other number is 4.
8 + 4 = 12
8 - 4 = 4
Step-by-step explanation:
Equation 1: Sum:
x + y = 12
Equation 2: Difference:
x - y = 4
Solution:
x + y = 12
x - y = 4
-------------
Add the two equations together:
2x = 16
Divide both sides by 2:
x = 8
Solve for y:
Use equation 1 substituting for x:
x + y = 12
8 + y = 12
Subtract 8 from both sides:
y = 4
what's the value of x?
To find a missig side in a right trianle use the Pythagorean theorem:
[tex]hypotenuse^2=leg1^2+leg2^2[/tex]In the give triangle the x is the hypotenuse.
[tex]\begin{gathered} \text{hypotenuse}=\sqrt[]{leg1^2+leg2^2} \\ \\ x=\sqrt[]{6^2+8^2} \\ \\ x=\sqrt[]{36+64} \\ \\ x=\sqrt[]{100} \\ \\ x=10 \end{gathered}[/tex]Then, the value of x is 103. Solve this system of equations. (7 points)5x+2y=73x - y = 2a. To solve the system using elimination, first multiply the bottom equation by 2. Write thenew system of equations. (1 point)b. What variable will be eliminated when the equations are combined after themultiplication? (1 point)c. Next, add the equations together. Your answer should be a single equation with onevariable. (1 point)
Given: the system of equation 5x+2y=7
3x-y=2
Find: (a) To solve the system using elimination, first multiply the bottom equation by 2. Write the new system of equations.
(b) What variable will be eliminated when the equations are combined after the multiplication?
(c). Next, add the equations together. Your answer should be a single equation with one variable.
(d) solve the equation for x.
(e) substitute x back into one of the equation to solve for y.
(f) what is the solution to the system of equation.
Explanation: 5x+2y=7
multiply seconf equation by 2, we get
6x-2y=4
the new system of equations are
5x+2y=7
6x-2y=4
(b) after multiplication by 2 , variable y will be eliminated.
(c) on adding both the given equation we get,
8x+y=9.................(1)
and from equation second we have the value of y is 3x-2
put the of y in equation (1) we get,
8x+3x-2=9
11x-11=0
(d) for to solve the equation for x , we multiply by 2 in second given equation , we get
5x+2y=7
6x-2y=4
on solving we get ,
11x=11
x=1
(e) put x=1 in first given equation we get,
5+2y=7
2y=2
y=1
(f) the solution of the equations is x=1 and y=1
Find the absolute change and the percentage change for the given situation. 260 is increase to 63.7
Absolute and Percentage Change
The absolute change is the difference between the final value and the initial value.
The percentage change is the same difference related to the initial value.
We know the initial value was 260. The final value was 637.
* The absolute change is the difference between those values:
Abs Change = 637 - 260 = 377
* The percentage change is the division of 377 by the original value:
Pct Change = 377 / 260 * 100%
Pct Change = 145%
We can say the initial value increased by 145%
