Answers
Given: An equation
[tex]4^{x-3}=8[/tex]Required: To draw the graph of the solution of the equation.
Explanation: The given equation is-
[tex]4^{x-3}=8[/tex]Solving,
[tex]\begin{gathered} (2^2)^{x-3}=2^3 \\ 2^{2x-6}=2^3 \end{gathered}[/tex]Now since the base on both sides are the same hence the exponents must also be equal i.e.,
[tex]\begin{gathered} 2x-6=3 \\ 2x=9 \\ \Rightarrow x=\frac{9}{2} \end{gathered}[/tex]Hence the graph of the equation can be drawn by taking the equations
[tex]\begin{gathered} y=4^{x-3} \\ y=8 \end{gathered}[/tex]Hence the graph is
Final Answer: Option C is correct.
Related Questions
(U.LL.2) A perfectly cube-shaped smelly candle has a volume of 125 cubic kilometers. What is the area of each side of the smelly candle?
Answers
25 square kilometers
Explanation
the volume of a cube is given by:
[tex]\begin{gathered} \text{Volume}=\text{side}\cdot\text{side}\cdot\text{side} \\ \text{volume}=(side)^3 \end{gathered}[/tex]Step 1
Let
volume = 125 cubic kilometers
Step 2
replace and solve for "side"
[tex]\begin{gathered} \text{Volume= side}^3 \\ 125km^3=side^3 \\ \text{cubic root in both sides} \\ \sqrt[3]{12}5km^3=\text{ }\sqrt[3]{side^3} \\ 5\text{ km= side} \end{gathered}[/tex]Step 3
now, we have the length of a side, to find the area, make
Area of a square is
[tex]\begin{gathered} \text{Area= side }\cdot side \\ \text{Area}=side^2 \end{gathered}[/tex]replace to find the area
Let side = 5 km
[tex]\begin{gathered} \text{Area}=(5km)^2 \\ \text{Area = 25 km}^2 \end{gathered}[/tex]
Find the unit price. If necessary, round your answer to the nearest cent. You would enter an answer like $0.49/pound, the value (like 0.49) in the first box and the appropriate unit (like pound) in the second boX $8.39 for 12 kg
Answers
For a determined product you can buy 12Kg for $8.39. To determine how much 1Kg of said product costs, you can apply cross multiplication to calculate it:
If 12 Kg cost $8.39
1 Kg costs $x:
[tex]\begin{gathered} \frac{8.39}{12}=\frac{x}{1} \\ \frac{8.39}{12}=x \\ x=0.699\cong0.70 \end{gathered}[/tex]The cost is $0.70/Kg
11. You want to tape five posters on a wall so that the spaces between posters are the same. You alsowant the spaces at the left and right of the group of posters to be three times the space between anytwo adjacent posters. The wall is 15 feet wide and the posters are 1.5 feet wide.a. Draw a diagram that represents theb. Write and solve an equation to find howsituation.to position the posters.
Answers
Let's use the variable x to represent the spaces between posters.
So the spaces at the left and right of the group will be 3x.
Drawing the diagram, we have:
Writing an equation to solve for x, we have:
[tex]\begin{gathered} 3x+3x+1.5+1.5+1.5+1.5+1.5+x+x+x+x=15 \\ 6x+7.5+4x=15 \\ 10x+7.5=15 \\ 10x=15-7.5 \\ 10x=7.5 \\ x=\frac{7.5}{10} \\ x=0.75 \end{gathered}[/tex]So the space between each pair of posters is 0.75 feet.
10. (09.02 MC)Which of the following tables shows the correct steps to transform x2 + 8x + 15 = 0 into the form (x - p)2 = q?[p and q are integers) (5 points)
Answers
To transform
[tex]x^2+8x+15=0[/tex]Make it a perfect square
since 8x/2 = 4x, then
We need to make 15 = 16 for 4 x 4 = 16, so add 1 and subtract 1
[tex]\begin{gathered} x^2+8x+(15+1)-1=0 \\ x^2+8x+16-1=0 \end{gathered}[/tex]Now we will make the bracket to the power of 2
[tex]\begin{gathered} (x^2+8x+16)-1=0 \\ (x+4)^2-1=0 \end{gathered}[/tex]Add 1 to both sides
[tex]\begin{gathered} (x+4)^2-1+1=0+1 \\ (x+4)^2=1 \end{gathered}[/tex]The answer is C
Solve the system by the method of your choice. Identify inconsistent systems and systems with dependent equations, using set notation to express solution sets
Answers
The given system of equations is
[tex]\begin{gathered} y=3x+5\rightarrow(1) \\ 5x-2y=-7\rightarrow(2) \end{gathered}[/tex]Substitute y in equation (2) by equation (1)
[tex]5x-2(3x+5)=-7[/tex]Simplify the left side
[tex]\begin{gathered} 5x-2(3x)-2(5)=-7 \\ 5x-6x-10=-7 \end{gathered}[/tex]Add the like terms on the left side
[tex]\begin{gathered} (5x-6x)-10=-7 \\ -x-10=-7 \end{gathered}[/tex]Add 10 to both sides
[tex]\begin{gathered} -x-10+10=-7+10 \\ -x=3 \end{gathered}[/tex]Divide both sides by -1
[tex]\begin{gathered} \frac{-x}{-1}=\frac{3}{-1} \\ x=-3 \end{gathered}[/tex]Substitute x in equation (1) by -3 to find y
[tex]\begin{gathered} y=3(-3)+5 \\ y=-9+5 \\ y=-4 \end{gathered}[/tex]The solution of the system of equations is {(-3, -4)}
Since the system has only one solution then it is an independent consistent system.
The radius of a circle is 7 in. Find its area in terms of pi
Answers
Answer:
49π
Step-by-step explanation:
πr^2 <---- The formula for the area of a circle.
let "a" represent area of the circle.
a = π × 7^2
Simplify by the use of the exponent.
7^2 = 49
Your answer:
49π
Find the volume of the triangular pyramid to the nearest whole number.HighlightA)181 in 3B)361 in 3722 inD)1,082 in 3what's the answer
Answers
the volume of a pyramid is
[tex]V=\frac{1}{3}Ah[/tex]where A is the area of the basis and h is the height of the pyramid.
[tex]A=\frac{12.3\text{ in }\times10\text{ in}}{2}=61.5in^2[/tex]Then the volume is
[tex]\begin{gathered} V=\frac{1}{3}(61.5in^2)(17.6in) \\ =360.8in^3 \end{gathered}[/tex]Then rounding the number, the answer is B).
Select the correct answer.378Convert4 to rectangular form.OA.Y = -1OB.y = 1O C.y =O D.O E.I = -1
Answers
The Solution.
Assuming the radius is 1.
[tex]x=\cos (\frac{3\pi}{4})=-\sin (\frac{3\pi}{4})[/tex]Therefore,
[tex]\begin{gathered} x=-y \\ or \\ y=-x \end{gathered}[/tex]So, the correct answer is option D
A square ABCD has the vertices A(n,n), B(n,-n), C(-n,-n), and D(-n,n). Which vertex is in Quadrant II?Answers:A.CB.DC.BD.A
Answers
Given:
A square ABCD has the vertices A(n,n), B(n,-n), C(-n,-n), and D(-n,n).
In quadrant II, the cordinates of the x have negative sign and coordinates of y axis have poistive sign.
Thus, the vertex is in Quadrant II is D(-n,n).
Flnd the value of x for the triangle or rectangle. Then find the length of the sides of the triangle or rectangle.Q1: Perimeter = 18 meters Q2: Perimeter = 23 feet
Answers
The perimeter of a rectangle is given by:
P = 2w + 2h
Where:
w = width = 2x
h = height = x
P = 18
Replacing the data into the equation:
18 = 2(2x) + 2(x)
18 = 4x + 2x
18 = 6x
Solving for x:
x = 18/6
x= 3
Therefore:
w = 2(3) = 6m
h = 3m
---------------------------------------------------------------------------------
P = x + 2x + (x + 3)
23 = 3x + x + 3
23 = 4x + 3
Solving for x:
23 - 3 = 4x
20 = 4x
20/4 = x
5 = x
Therefore its sides are:
x = 5 ft
2x = 2(5) = 10ft
x + 3 = 5 + 3 = 8ft
hello can you help me with this trigonometry question read carefully of how it has to be answered
Answers
Area of a circle = πr²
Replacing with radius = 8.4 in:
Area of a circle = π(8.4)²
Area of a circle = 221.6708 in²
This area corresponds to 2π radians. To find the area corresponding to 2.37 radians, we can use the next proportion:
[tex]\frac{2\pi\text{ rad}}{2.37\text{ rad}}=\frac{221.6708^{}}{x^{}}\text{ }[/tex]Solving for x:
[tex]\begin{gathered} 2\pi\cdot x=221.6708\cdot2.37 \\ x=\frac{525.359796}{2\pi} \\ x=83.6136\text{ sq. in} \end{gathered}[/tex]When asked to find f ( g ( x ) ), what should you do? plug f (x) into g (x)plug g (x) into f (x)multiply f (x) by g (x)none of the above
Answers
From the given question,
f(g(x)) means,
Plug g(x) into f(x)
Hence, the correct option is B
The figure on the left is a trapezoidal prism. The figure on the right represents its base. Find the volume of this prism. 13 ft 10 ft 10 ft 2 ft 13 ft 12 ft 13 ft 20 ft 13 ft 5 ft 10 ft 5 ft The area of the trapezoidal base is 8 ft2, the height is ft. Therefore, the volume is IN
Answers
volume of the trapezoidal prism is
[tex]V=A_b\times h[/tex]then, area of the trapezoidal base
[tex]\begin{gathered} A_b=\frac{1}{2}(b1+b2)h \\ A_b=\frac{1}{2}(10+20)\times12 \\ A_b=\frac{1}{2}(30)\times12 \\ A_b=\frac{360}{2}=180 \end{gathered}[/tex]area of the trapezoidal base = 180 ft^2
height = 2ft
so, the volume is:
[tex]\begin{gathered} V=180\times2 \\ V=360 \end{gathered}[/tex]volume = 360 ft^3
1277 concert tickets were sold for a total of $16,267. If students paid $11 and nonstudents paid $17, how manystudent tickets were sold?
Answers
Hello there. To solve this question, we'll have to remember some properties about system of equations.
Given that 1277 concert tickets were sold, for a total of $16,267, knowing that students paid $11 and non-students paid $17, we have to determine how many students tickets were sold.
Let's start labeling the variables we have. Say x is the number of tickets sold for students, while y is the number of tickets sold for non-students.
The total number of tickets sold can be found by adding how many students and non-students tickets were sold, i.e.
[tex]x+y=1277[/tex]To find the total amount collected, we have to multiply the number of each ticket sold by its respective fee, adding everything as follows:
[tex]11\cdot x+17\cdot y=16267[/tex]With this, we have the following system of equations:
[tex]\begin{cases}x+y=1277 \\ 11x+17y=16267\end{cases}[/tex]We can solve it using the elimination method. It consists in multiplying any of the equations by a factor (usually the easier equation) that when added to the other equation, one of the variables are cancelled out.
In this case, multiply the first equation by a factor of (-11)
[tex]\begin{cases}-11x-11y=-14047 \\ 11x+17y=16267\end{cases}[/tex]Add the two equations
[tex]\begin{gathered} -11x-11y+11x+17y=-14047+16267 \\ 6y=2220 \end{gathered}[/tex]Divide both sides by a factor of 6
[tex]y=370[/tex]Now we plug it back into the first equation in order to solve for x (i. e the number of tickets sold for students)
[tex]\begin{gathered} x+y=1277 \\ x+370=1277 \\ x=1277-370 \\ x=907 \end{gathered}[/tex]This is how many tickets were sold to students.
Which of the following expressions represents the simplified version of the expression below
Answers
we have the expression
[tex](5x^3y^2-3xy+2)+(2x^3y^2-3x^2y^2+4xy-7)[/tex]step 1
Combine like terms
so
[tex](5x^3y^2+2x^3y^2)+(-3xy+4xy)+(2-7))-3x^2y^2[/tex][tex](7x^3y^2)+(xy)+(-5)-3x^2y^2[/tex]therefore
the answer is the second optionFill in the blanks to make the question number since true
Answers
Sheliqua, this is the solution:
a. 13 divided by 5
13/5 = 2 3/5
b. 9/5
9 divided by 5
c. 7 divided by 8
7/8
d. 1 2/3
5/3
5 divided by 3
graphing a parabola of the form y=ax squared 2
Answers
The graph of the parabola given by the equation:
[tex]y=\frac{1}{4}x^2[/tex]has a vertex when y=0 which happens iff
[tex]\begin{gathered} \frac{1}{4}x^2=0 \\ x^2=0 \\ x=0 \end{gathered}[/tex]Therefore the graph is:
The vertex has coordinates (0,0). Now, two points to the left of the vertex that are on the parabola have coordinates (-2,1) and (-4,4). Two points that are to the right of the parabola have coordinates
A chemical company mixes pure water with their premium antifreeze solution to create an inexpensive antifreeze mixture. the premium antifreeze solution contains 90% pure antifreeze. the company want to obtain 180 gallons of a muxture that contains 45% pure antifreeze how many and how many gallons of the premium antifreeze solution must be mixed
Answers
Answer:
Both should be 90 gallons
Explanation:
Let the gallons of pure water used = x gallons
Since the company want to obtain 180 gallons of a mixture, the gallons of 90% pure antifreeze needed = (180-x) gallons
We therefore have that:
90% of (180-x) gallons = 45% of 180 gallons
[tex]\begin{gathered} 0.9(180-x)=0.45\times180 \\ 162-0.9x=81 \\ 0.9x=162-81 \\ 0.9x=81 \\ x=\frac{81}{0.9} \\ x=90 \end{gathered}[/tex]• The number of gallons of pure water used = 90 gallons
• The number of gallons of premium antifreeze solution
= 180-90
= 90 gallons.
I don’t know the answer for this one and others I need help
Answers
x = 1, y = 3
Explanation:The given system of equations is:
y = 4x - 1.......................(i)
y - 2x = 1..................(ii)
Substitute equation (i) into equation (ii)
4x - 1 - 2x = 1
4x - 2x = 1 + 1
2x = 2
x = 2/2
x = 1
Substitute x = 1 into equation (i)
y = 4x - 1
y = 4(1) - 1
y = 4 - 1
y = 3
The solution to the system of equations is x = 1, y = 3
I need help on 2 please Directions: Find the value of x. Round each answer to the nearest tenth.
Answers
The angle indicated is a right angle, so the triangle is a right triangle.
Thus, we can apply the Pythagora's Theorem:
[tex]a^2+b^2=c^2[/tex]Where c is the hypotenuse, the angle opposite to the right angle, and a and b are the legs.
x is the hypotenuse in this case, so:
[tex]\begin{gathered} 22^2+27^2=x^2 \\ x^2=484+729 \\ x^2=1213 \\ x=\sqrt[]{1213} \\ x=34.8281\ldots\approx34.8 \end{gathered}[/tex]A Ferris wheel has a radius of 12 meters and takes 16 seconds to complete one full revolution. The seat you are riding in, takes 4 seconds to reach the top which is 28 meters above the ground. Write a sine or cosine equation for the height of your seat above the ground as a function of time.
Answers
EXPLANATION
Given that the wheel has a radius of 12 meters and it takes 16 seconds to complete one full revolution, if we call t to the time in seconds and since the top of the wheel is 28 meters above the ground, the bottom is 4 meters above the ground.
Now, we need to consider that the equation that applies is the following:
[tex]height=16-12\cos \theta[/tex]As theta is the angle between the radius from the center of the wheel to the bottom and the rider's coordinate, we need to represent the angle as a function of the time. We have that it takes 16 second to complete one full revolution, this means that the wheel rotates 360 degrees in 16 seconds. Now, we can use the angular velocity: w= 360/16 = 22.5 degrees/s
Then, we need to represent the angular velocity in radians, as 360 degrees is 2π radians, the obtained angular velocity would be: w = 2π/16 = π/8 rad/s
Hence the appropiate equation as a function of the time would be as follows:
[tex]h=16-12\cdot\cos (\frac{\pi t}{8})[/tex]
A medicine is applied to a burn on a patient’s arm. The area of the burn in square centimeters decreases exponentially and is shown on the graph
Answers
EXPLANATION
The function that represents the exponential decay is as follows:
[tex]f(x)=ab^x[/tex]Where a=initial amount and b= decay coefficient
Since the initial amount is 8cm^2, the is the value of the coefficient a is 8.
[tex]f(x)=8b^x[/tex]Now, we need to compute the decay rate:
We can obtain this by substituting two given values, as for instance (0,8) and (1,6) and dividing them:
[tex]\frac{6}{8}=\frac{8}{8}\frac{b^1}{b^0}[/tex]Simplifying:
[tex]\frac{3}{4}=0.75=b[/tex]The value of b is 3/4:
[tex]y=8\cdot0.75^x[/tex]1) There will be 3/4 of the burn area each week.
2) The equation representing the area of the burn, after t weeks will be the following:
[tex]y=8\cdot(\frac{3}{4})^x[/tex]3) After 7 weeks, the area will be represented by the following expression:
[tex]y=8\cdot(\frac{3}{4})^7[/tex]Computing the power:
[tex]y=8\cdot\frac{2187}{16384}=1.068cm^2[/tex]
Find the slope and y-intercept of the line shown below.10-8-6-co +4-2--10-8-64-2-2- 2 4 6 8 10~ 60--4-X-6--8--10-
Answers
Looking at the graph
we have a horizontal line
the equation is
y=-5
The slope of a horizontal line is equal to zero
so
m=0
The y-intercept is the point (0,-5)
therefore
b=-5
The answer is
m=0b=-5Remember that
y=mx+b
substitute
m=0
b=-5
y=(0)(x)-5
y=-5
Select the correct answer.In triangle ABC, AB = 12, BC = 18, and m B = 75° what are the approximate length of side AC and measure of A?O AAC = 18.9;m SA = 66.99OB.OC.AC = 20.3 m A = 34.8°AC = 18.9: m A = 37.8°AC = 20.31 m A = 58.9°ODResetNext
Answers
Draw the triangle ABC.
Determine the length of side AC.
[tex]\begin{gathered} (AC)^2=(AB)^2+(BC)^2-2\cdot AB\cdot BC\cdot\cos B \\ =(12)^2+(18)^2-2\cdot12\cdot18\cdot\cos 75 \\ =356.190 \\ AC=\sqrt[]{356.19} \\ =18.87 \\ \approx18.9 \end{gathered}[/tex]So side AC is equal to 18.9 m.
Determine the measure of angle A.
[tex]\begin{gathered} \frac{AC}{\sin B}=\frac{BC}{\sin A} \\ \frac{18.9}{\sin75}=\frac{18}{\sin A} \\ \sin A=\frac{18}{18.9}\cdot\sin 75 \\ A=\sin ^{-1}(0.9199) \\ =66.9 \end{gathered}[/tex]So mesure of angle A is 66.9 degree.
The dot plot shows the hourly pay rate for ten employees at best books bookstore.
Answers
We will have the following:
The strongest case he can make is the mean hourly rate since Levi's current pay rate is well bellow the average hourly pay rate.
1. Write an equation of the line that is parallel to the linewhose equation is 4y + 9 = 2x and passes through thepoint (7,2)
Answers
First let's put the equation 4y + 9 = 2x in the slope-intercept form:
[tex]y=mx+b[/tex]Where m is the slope and b is the y-intercept. So we have that:
[tex]\begin{gathered} 4y+9=2x \\ 4y=2x-9 \\ y=\frac{2x-9}{4} \\ y=\frac{1}{2}x-\frac{9}{4} \end{gathered}[/tex]The slope of this equation is 1/2. In order to the second line be parallel to this line, it has to have the same slope. Also, since the second line passes through the point (7, 2), we have:
[tex]\begin{gathered} y=\frac{1}{2}x+b \\ (7,2)\colon \\ 2=\frac{1}{2}\cdot7+b \\ 2=\frac{7}{2}+b \\ b=2-\frac{7}{2}=\frac{4-7}{2}=-\frac{3}{2} \end{gathered}[/tex]So the second equation is:
[tex]y=\frac{1}{2}x-\frac{3}{2}[/tex]Hi, can you help me to find (Ir possible) the complement andsupplement of the angle of exercise
Answers
The angle is given 24 degree.
To determine the complement angle ,
[tex]90^{\circ}-24^{\circ}=66^{\circ}[/tex]To determine the supplement angle ,
[tex]180^{\circ}-24^{\circ}=156^{\circ}[/tex]I need help with this question Subtraction:3+(-4) = ?
Answers
Given:
We have to use subtraction
[tex]3+(-4)[/tex]To find: Solve the above expression?
Explanation:
Here we use the subtraction operation to solve the given expression.
We know the operator property,
[tex]\begin{gathered} (+)(-)=(-) \\ (-)(-)=(+) \\ (+)(+)=(+) \\ (-)(+)=(-) \end{gathered}[/tex]Therefore,
[tex]\begin{gathered} =3+(-4_) \\ \\ =3-4 \\ \\ =-1 \end{gathered}[/tex]Thus, 3+(-4) = -1.
Answer: 3+(-4) = -1.
given expression :4x-2y=11find the missing coordinate in ordered pair (-3,?)
Answers
Equations
We are given the equation:
4x - 2y = 11
And it's required to find the missing coordinate in the ordered pair (-3, ?).
The first coordinate is x=-3, thus we need to calculate the y-coordinate by solving the equation for y, using the value of x.
Substituting:
4(-3) - 2y = 11
Operating:
-12 - 2y = 11
Adding 12:
-2y = 23
Dividing by -2:
y = 23/(-2)
y = -23/2
The ordered pair is:
[tex](-3,-\frac{23}{2})[/tex]Find the area of a shaded region shown below, which was formed by cutting an isosceles trapezoid out of the top half of a rectangle. The width of the rectangle is 32 in, the height of the rectangle in 24 in. The leg of the isosceles trapezoid is 15 in.
Answers
Step 1: Redraw the diagram and label it.
From the figure, the hypotenuse of triangles A and B is 15 in and the height is 12 in. We can apply the Pythagoras theorem to find the base.
Let base of the triangle A and B be the adjacent.
Opposite = 12
Adjacent = ?
Hypotenuse = 15
[tex]\begin{gathered} Next,\text{ apply the Pythagoras theorem to find the adjacent.} \\ \text{Opposite}^2+Adjacent^2=Hypotenuse^2 \\ 12^2+Adj^2=15^2 \\ 144+Adj^2\text{ = 225} \\ \text{Collect like terms.} \\ \text{Adj}^2\text{ = 225 - 144} \\ \text{Adj}^2\text{ = 81} \\ F\text{ ind the square root of both sides.} \\ \sqrt[]{Adj^2\text{ }}=\text{ }\sqrt[]{81} \\ \text{Adj = 9 in} \end{gathered}[/tex]The area of the shaded region = Area of A + Area of B + Area of C
[tex]\begin{gathered} \text{Area of A = }\frac{Base\text{ x Heigth}}{2} \\ \text{Base = 9} \\ \text{Height = 1}2 \\ \text{Area of A = }\frac{9\text{ x 12}}{2} \\ =\text{ }\frac{108}{2} \\ =54in^2 \\ \text{Area of B = }\frac{Base\text{ x Height}}{2} \\ =\text{ }\frac{9\text{ x 12}}{2} \\ =\text{ }\frac{108}{2} \\ \text{= 54 in}^2 \end{gathered}[/tex][tex]\begin{gathered} \text{Area of rectangle C = Length }\times\text{ Breadth} \\ Lenght\text{ = 32} \\ \text{Breadth = 12} \\ \text{Area of C = 32 x 12} \\ =384in^2 \end{gathered}[/tex]Therefore,
Area of the shaded region = 54 + 54 + 384 = 492 inches square
Final answer
Area of the shaded region = 492 inches square