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We have to solve the equation with the square root method:
[tex]\begin{gathered} 2(x-4)^2-6=18 \\ 2(x-4)^2=18+6 \\ 2(x-4)^2=24 \\ (x-4)^2=\frac{24}{2} \\ (x-4)^2=12 \\ \sqrt[]{(x-4)^2}=\sqrt[]{12} \\ x-4=\pm\sqrt[]{12} \\ x=4\pm\sqrt[]{12} \\ x=4\pm2\sqrt[]{3} \end{gathered}[/tex]Answer: The solutions are:
[tex]\begin{gathered} x_1=4-2\sqrt[]{3} \\ x_2=4+2\sqrt[]{3} \end{gathered}[/tex]Related Questions
I need help on this I can’t remember how to do it
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Answer:
[tex]g(x)=7^{\frac{x}{3}}+1[/tex]Explanation:
The function f(x) is given as:
[tex]f(x)=7^x+1[/tex]If a function, f(x) is horizontally compressed by a factor of k units, the transformation rule is:
[tex]f(x)\to f(kx)[/tex]Therefore, if f(x) is transformed to g(x) through a horizontal compression by a factor of 1/3, the function g(x) is:
[tex]g(x)=7^{\frac{x}{3}}+1[/tex]Given the following angles of a regular polygon, 120°, (4*x+-3)°, (x+14)°, 45°, 135°, (x-31)°, and (x*6+20)°, what is the value of x?
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Since the polygon has seven angles we deduce it is a heptagon. In that case the sum of the interior angles must be equal to 900°. We can formulate the following equation accordingly.
120°+(4*x-3)°+ (x+14)°+ 45°+ 135°+ (x-31)°+ (x*6+20)° = 900°
120°- 3° +14° + 45° + 135° - 31° + 20 + 4x + x + x + 6x = 900° (Organizing)
300 ° + 12x = 900° (Operating like terms)
12x= 900° - 300° (Transposing 300° to the other side of the equation)
12x= 600° (Subtracting 300° from 900°)
12/12x= 600° / 12 (Dividing by 12 on both sides of the equation)
x= 50°
Answer is: x= 50°
Brady creates the graph below to keep track of the approximate height of the grass on hislawn over timeWhat is the dependent variable in the situation?Brady's Lawnthe number of days it takes for the grass togrow an inchthe height of the grass, in inchesthe number of inches the grass grows eachdayHeight of Grass (inches)the amount of time that has passed. In days2468 10 12 14 16 18 20Time (days)
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Answer:
The height of the grass, in inches
Explanation:
The dependent variable is the variable whose value changes whenever the other variable (independent) changes.
From the graph, the height of the grass (in inches) depends on the time in days.
Therefore, the dependent variable in this situation is the height of the grass, in inches
What is the measurement of the exterior angle in the diagram below?A. 100B. 30C. 70D. 88
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Find the unknown angle measure. 33 mZFGH: mZGFH: mzGHF: 33° х F 28 H
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m∠FGH =33º, m∠GFH =119º and m∠GHF= 28º
1) Since the sum of all interior angles of any triangle is always equal to 180º, we can write:
m∠f + m∠H + m∠G = 180º Plug it into that the following measures
x +33º +28º= 180º
x + 61º = 180º
x = 180 -66
x =119º
2) Then we can write:
m∠FGH =33º, m∠GFH =119º and m∠GHF= 28º
Question 18 of 30Use the formula below to solve the given problem. In the formula, drepresents the distance an object falls, in meters, and trepresents the timethat an object falls, in seconds. Round to the nearest tenth and do not includeunits in your answer.A screw from the space shuttle in outer space falls from the space shuttle.How far would the screw fall in 11 seconds?ſa=t•2.8Answer here
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SOLUTION
We were asked to find how far the screw will fall in 11 seconds.
How far simply means the distance. So we will find the distance using the formula they gave to us.
[tex]\begin{gathered} So\text{ from the formula }\sqrt[]{d}\text{ = t . 2.8, } \\ \sqrt[]{d}\text{ = t }\times\text{2.8, d = distance that we want to find, t = time = 11seconds} \end{gathered}[/tex][tex]\begin{gathered} \sqrt[]{d\text{ }}\text{ = 2.8t, when we multiply t by 2.8 } \\ \text{Now, we will take the square of both sides to remove the }\sqrt[]{\text{ }}\text{ } \\ (\sqrt[]{d})^2=(2.8t)^2 \\ d=(2.8\times11)^2 \\ d=30.8^2 \\ d\text{ = 948.64} \\ d\text{ = 948.6 to the nearest tenth} \end{gathered}[/tex]Therefore, the answer is 948.6 to the nearest tenth
The steps below show the incomplete solution to find the value of n for the equation 4n − 2n + 4 = −1 + 17:Step 1: 4n − 2n + 4 = −1 + 17 Step 2: 4n − 2n + 4 = 16 Step 3: 2n + 4 = 16Which of these is most likely the next step? (5 points)2n = 122n = 42n = 82n = 20
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In this case, we'll have to carry out several steps to find the solution.
Step 01:
Data:
4n − 2n + 4 = −1 + 17
Step 02:
We must apply the algebraic rules to find the solution.
Step 1: 4n − 2n + 4 = −1 + 17
Step 2: 4n − 2n + 4 = 16
Step 3: 2n + 4 = 16
2n + 4 = 16
2n = 16 - 4
2n = 12
The answer is:
2n = 12
Jaden and Lola are hosting events that are catered by the same company. Jaden plans to have 82 adults and 96 children attend, so the total projected cost of his meals is $5,664. Lola has 65 adults and 49 children on his guest list, so she will pay the caterer $4,002. How much does the caterer charge for each meal?
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Let's use the variable x to represent the cost of one adult meal, and y to represent the cost of one child meal.
If the cost of 82 adult meals and 96 children meals is $5,664, we can write the following equation:
[tex]82x+96y=5664[/tex]If the cost of 65 adult meals and 49 children meals is $4,002, we can write the equation:
[tex]65x+49y=4002[/tex]To solve this system, let's solve the second equation for y and then use its value in the first equation:
[tex]\begin{gathered} 65x+49y=4002 \\ 49y=4002-65x \\ y=\frac{4002-65x}{49} \\ \\ 82x+96y=5664 \\ 82x+96(\frac{4002-65x}{49})=5664 \\ 82x+7840.653-127.347x=5664 \\ -45.347x=-2176.653 \\ x=48 \\ \\ y=\frac{4002-65\cdot48}{49} \\ y=18 \end{gathered}[/tex]Therefore every adult meal costs $48 and every child's meal costs $18.
Describe the rotation:A) 180 degreesB) 90 degrees counterclockwise C) 90 degrees clockwise
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The image 1 is rotated 90 degree clockwise to get image 2.
Examine the figure below.If AABC is similar to ADEF, determine the measure of
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We have two similar triangles.
They will have proportional sides and equal measures.
Then, if we have to evaluate Then, we can write:
[tex]\begin{gathered} m\angle A=m\angle D \\ 3x+18=4x+2 \\ 3x-4x=2-18 \\ -x=-16 \\ x=16 \end{gathered}[/tex]Knowing x, we can calculate m[tex]\begin{gathered} m\angle A=3x+18 \\ m\angle A=3\cdot16+18=48+18=66\degree \end{gathered}[/tex]Answer: the measure of A is 66º
Need help with this homework Part 2) construct the line that is perpendicular to the directrix and passes through the focus. This line will be the axis of symmetry of the para bola what are the coordinates of the point of intersection,A, of the access of symmetry and directrix of the parabola
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After following the instructions in part A, the result is
In general, the equation of a horizontal line is y=a, with 'a' a constant. In our case, the line has to be 6 units below F; then y=4-6=-2. The equation of the directrix is y=-2
Part 2)
In Geogebra, go to Tools->Construct->Perpendicular Line; then, click on point F and line y=-2. A new line should appear on your screen, then go to Tools->Points->Intersect and select both lines. After naming the intersection point as 'A', the result is
The answer to part 2) is A=(6,-2)
Spread of Data Worksheet
1. Construct the box-and-whisker plot for the number of episodes in each season of the TV show "The
Office.
Season
1
2
3
4
5
6
7
8
9
Number of
Episodes
6
22
25
19
28
26
26
24
25
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The Box and Whisker Plot is shown in the graph below .
Box and Whisker Plot :
It is plotted to display variation in a set of data . In most cases, a histogram analysis provides a sufficient display, but a box and whisker plot can provide additional detail while allowing multiple sets of data to be displayed in the same graph.
How to construct a box and whisker plot ?
The left and right sides show the lower and upper quartiles of the data resp. . The box covers the interquartile interval where half the data is found .The vertical line that split the data in two is the median of data .
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An accountant charges a fee of $100 to complete a company's taxes. The accountant also charges an additional $35 per hour to complete the taxes. Which of the following equations can be used to describe this problem? y = 35 − 100x y = 35 + 100x y = 100 − 35x y = 100 + 35x
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We have that 100 is a fix amount and if x describes the additional charges per hour we have that the equations is 100 + 35x. The answer is y = 100 + 35x
this one is super hard
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Answer:
16, 767
Explanation:
The second term of the sequence is
23 * 3 = 69
the third term is
23* 3 *3 = 207
the fourth term is
23 * 3* *3 *3
the fifth term is
23 *3* *3 *3 *3
the sixth term is
23 *3* *3 *3 *3 * 3
the seventh term is
23 *3* *3 *3 *3 * 3* 3 = 16767
which is our answer!
select all the sets of the value that could be the side length of Triangle z.sides are 7,4,10
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We will determine if the sets are proportional, if they are, then those will be the sets of lengths that would belong to triangle z, that is:
a.
[tex]\frac{4}{8}=\frac{7}{11}=\frac{14}{10}\Rightarrow\frac{1}{2}\ne\frac{7}{11}\ne\frac{7}{5}[/tex]So, set a is not one.
b.
[tex]\frac{4}{10}=\frac{7}{17.5}=\frac{10}{25}\Rightarrow\frac{2}{5}=\frac{2}{5}=\frac{2}{5}[/tex]So, set b could be a set of lengths that belong to triangle z.
c.
[tex]\frac{4}{6}=\frac{7}{9}=\frac{10}{11}\Rightarrow\frac{2}{3}\ne\frac{7}{9}\ne\frac{10}{11}[/tex]So, set c is not one.
d.
[tex]\frac{4}{6}=\frac{7}{10.5}=\frac{10}{15}\Rightarrow\frac{2}{3}=\frac{2}{3}=\frac{2}{3}[/tex]So, set d could be a set of lengths that belong to triangle z.
e.
[tex]\frac{4}{8}=\frac{7}{14}=\frac{10}{20}\Rightarrow\frac{1}{2}=\frac{1}{2}=\frac{1}{2}[/tex]So, set e could be a set of lengths that beling to triangle z.
So, the options that could be candidate are: b, d & e.
Math help question one and two
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We can determine that the option D is better fit of equation model which calculated as follows :
First, insert the value x to the formula (y)
y = 0.07(100) + 0,94
y = 7 + 0,94
y = 7,94
Given the bone chips (x) is 100, then the bone tools (y) is 8.
The value of bone tools (y) which is 8 is the result of rounded of value (y) 7,94.
2. The answer for question no. 2 is B
The equation models the line of best fit for data is y = -0,35x + 31,6
We can prove it as follows :
First step is value of race (x) of the first column which given by 1 to the formula .
y = -0,35(1) + 31,6
y = -0,35 + 31,6
y = 31,25
Next, we check that given the value of the Time (y) of Race (x) value of 1 is 31,1.
Hence, it shows that the equation models the line of best fit for data is y = -0,35x + 31,6
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Place the following from least to greatest 9square root of 6square root of 101.53.14159
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[tex]\begin{gathered} \sqrt[]{6}=2.44\cdots \\ \sqrt[]{10}=3.16\cdots \end{gathered}[/tex]
Therefore, the given number ordered from least to greatest is:
[tex]1.5,\sqrt[]{6},3.14159,\sqrt[]{10},9[/tex]How is a dilation different from all other transformations in this unit?O A dilation changes both angle size and side lengths of the pre-image.O A dilation changes side lengths.O A dilation does not have a pre-image.A dilation is not a transformation.< Previous
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A dilation is a non-rigid transformation, which means it changes the size of the shape. Specifically, it changes the sides, not the angles.
Therefore, the answer is A dilation change side lengths.
5. Logan is cooking carrots as part of his dinner. He is in a rush so he wants them to cook as fast as possible. He decides to cut them into small pieces so they cook faster. Will this work? Use the dimensions of two pieces of carrot to justify your answer.
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Let's imagine a piece of carrot that has a shape of a cylinder, and the total surface area of the carrot is S.
If we cut the carrot in half, with a cut parallel to the cylinder base, we will have two smaller cylinders, but the total surface area will increase, since the "internal" part of the bigger cylinder will now be an external area for the new 2 pieces:
In the drawing, the green circles in the right image will add to the total surface area.
If only the base of the cylinder is touching the pan, the surface area will double (from pi*r² to 2*pi*r²), since we will have two pieces of carrot instead of one, with the same base area.
If a bigger surface area is in contact with the pan, the carrots will cook faster. Therefore the answer is YES.
Hi I want to double check if I’m right, thank you
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Solution
The whole shape is a trapezoid
a= 10 , b = 10 +7+7 = 24 , h = 9
Formula
[tex]A=\frac{1}{2}(a+b)h[/tex][tex]\begin{gathered} A=\frac{1}{2}(10+24)9 \\ A=\frac{1}{2}(34)9 \\ A=153units^2 \end{gathered}[/tex]The correct answer is 153
4. A cylinder has a volume of 198 cm^3,and itsbase has an area of 22 cm^2.What is theheight of the cylinder?Please hurry
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1) Let's find out the height of that cylinder, by plugging it into the formula:
[tex]\begin{gathered} V=\pi\cdot r^2\cdot h \\ 198\text{ =}\pi\cdot rh \\ \end{gathered}[/tex]2) The Base area is given by:
[tex]\begin{gathered} A_B=\pi\cdot r^2 \\ 22=\pi\cdot r^2 \\ \frac{22}{\pi}=\frac{\pi}{\pi}r^2 \\ r=\sqrt[]{\frac{22}{\pi}} \end{gathered}[/tex]So now let's plug that radius
[tex]undefined[/tex]A group of biologists is surveying the mice population in a forest. The equatio n=75 times 3t gives the total number of mice, n, t years after the survey began. What does the number 3 mean in the situationA: the common difference B: The original population of miceC: the common ratioD: the slop
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I think the equation should be
[tex]n=75\cdot3^t[/tex]where 3 is the common ratio of the exponential function
so the answer is C.
Janelle invests in a piece of art that cost 600 British Pounds. A study found that art appreciates in value at a rate of 3.97% per year. Assuming this pattern continues, how much, in British Pounds, will Janelle's piece of art be valued at after 10 years? Round your answer to the hundredths place.
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Step-by-step explanation:
The art piece originally costs £600.
And it appreciates at a rate of 3.97% each year.
And we want to find the value of the art after 10 years.
We can write an exponential function to model the situation. The standard exponential function is given by:
[tex]f(t)=a(r)^t[/tex]Where t is the time in years.
Since it appreciates at a rate of 3.97% each year, the value after each year will be (100% + 3.97%) or 103.97%.
103.97% = 1.0397. So, r = 1.0397:
[tex]f(t)=a(1.0397)^t[/tex]Our a is the initial value. Therefore:
[tex]f(t)=600(1.0397)^t[/tex]Then the value of the piece of art after 10 years is:
[tex]f(10)=600(1.0397)^{10}=885.58793\approx885.59[/tex]Hence, It will be worth about £885.59 after 10 years.
13. A table costs $439. It is on sale for 40%off. a How much do you save? b. What isthe sales price? Solve question#3 parts a &b.a. I saveb. The sales price isу
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A table costs 439, and it is on sale for 40%. That means we shall deduct 40% of 439 from the actual cost as follows;
[tex]\begin{gathered} \text{Sales}=\text{Cost}-\text{Discount} \\ \text{Sales}=439-(439\times\frac{40}{100}) \\ \text{Sales}=439-(439\times0.40) \\ \text{Sales}=439-175.60 \\ \text{Sales}=263.40 \end{gathered}[/tex]Therefore,
The savings is $175.60
The sales price is $263.40
Nick used a rope to make a rectangle and a circle below. If 10 cm rope was left, what was the original length of the rope? cm 10 cm 7 cm
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To find the original length of the rope, we must find the length of rope used in the rectangle and in the circle, and add it to the length of rope that was leftover.
The length of rope used in the rectangle would be the perimeter of the rectangle, the perimeter of the rectangle is the sum of all his sides.
Perimeter of a rectangle = side + side + side + side
[tex]\text{Perimeter rectangle= 10+7+10+7=34 cm}[/tex]The question gives us the perimeter of the circle, 20 cm this measure was the length of rope used in the circle.
[tex]\text{Perimeter circle= 20 cm}[/tex]Now the total length of the rope was: The sum of the perimeters of both rectangle and circle and the length of rope that was left.
Total length rope = 34 + 20 + 10 = 64 cm
Solve for 2. Enter the solutions from least to greatest.x^2 - 3x - 40 = 0lesser x = [ ]greater x = [ ]
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In this case, we'll have to carry out several steps to find the solution.
Step 01:
Data
x^2 - 3x - 40 = 0
x1 = ?
x2 = ?
Step 02:
Quadratic equation:
roots:
x² - 3x - 40 = 0
(x - 8)(x + 5) = 0
x1 = 8
x2 = -5
The answer is:
lesser x = -5
greater x = 8
Find the absolute value of -1818-181/18-1/18Find the opposite of -2525-251/25-1/25
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the absolute value of a number does not contain negative sign
so the absolute value of the given expression (-18) is,
= 18
thus, the answer is option A.
3
the opposite of -25 will be,
= -(-25)
= 25
thus the answer is for the second question is option A
For her cell phone plan heather pays 30 dollars per month plus 0.05 per text. She wants to keep her cell phone bill under 60 dollars per month. Which inequality represents the number of texts t heather can send each month while staying within her budget?
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The inequality represents the number of texts t heather can send each month while staying within her budget is t<600.
Given, heather pays 30 dollars per month plus 0.05 per text.
She wants to keep her cell phone bill under 60 dollars per month.
hence texts she can send = 0.5 × 600
= $30
hence for $30 heather can text upto 600 texts.
so, cell phone plans + text
= $30 + $ 30
= $60
so, the inequality represents the number of texts t heather can send each month while staying within her budget is t<600
Hence the inequality is t<600
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The engines of a plane are pushing itdue north at a rate of 300 mph, andthe wind is pushing the plane 20°west of north at a rate of 40 mph. Inwhat direction is the plane going?O[?]Round to the nearest tenth.
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STEP - BY - STEP EXPLANATION
What to find?
The direction in which the plane is going.
Given:
From the question given; the engines of a plane are pushing it due north at a rate of 300 mph, and the wind is pushing the plane 20° west of north at a rate of 40 mph.
We know that;
A complex number zı has a magnitude z1] = 2 and an angle 6, = 49°.=Express zy in rectangular form, as 21 == a +bi.Round a and b to the nearest thousandth.21 =+iShow Calculator
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Complex numbers can be written in two forms:
[tex]\begin{gathered} z=a+b\cdot i \\ z=r\cdot e^{i\theta} \end{gathered}[/tex]Where a and b are known as the real and the imaginary part and r and theta are the magnitude and the angle of the number. In this case we are given these last two quantities and we have to find a and b. One way to do this is recalling an important property of the exponential expression above:
[tex]e^{i\theta}=\cos \theta+i\sin \theta[/tex]Then the exponential form of a number is equal to:
[tex]z=r\cdot e^{i\theta}=r\cdot(\cos \theta+i\sin \theta)=r\cos \theta+i\cdot r\sin \theta[/tex]And since we are talking about the same number then this expression must be equal to that given by a and b:
[tex]a+i\cdot b=r\cos \theta+i\cdot r\sin \theta[/tex]Equalizing terms without i and those with i we have two equations:
[tex]\begin{gathered} a=r\cos \theta \\ b=r\sin \theta \end{gathered}[/tex]Now let's use the data from the exercise:
[tex]\begin{gathered} r=\lvert z_1\rvert=2 \\ \theta=\theta_1=49^{\circ} \end{gathered}[/tex]Then we have:
[tex]\begin{gathered} a=2\cdot\cos 49^{\circ} \\ b=2\cdot\sin 49^{\circ} \end{gathered}[/tex]Using a calculator we can find a and b:
[tex]\begin{gathered} a=1.312 \\ b=1.509 \end{gathered}[/tex]Then the answers for the two boxes are 1.312 and 1.509