Create a list of steps, in order, that will solve the following equation.5(x-3)² + 4 = 129Solution steps:
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We want to solve the equation
[tex]5\cdot(x-3)^2+4=129[/tex]To solve this equation, we must isolate the variable on one side of the equation. So, noticed that the term with the x has multiple things (it is raised to the second power, multiplied by five, etc) so we begin by subtracting 4 on both sides. (Step 1)
So we get
[tex]5\cdot(x-3)^2=129\text{ -4 =125}[/tex]Now we divide both sides by 5 (Step 2), so we get
[tex](x-3)^2=\frac{125}{5}=25[/tex]now we take the square root on both sides (Step 3). Then we get
[tex]\sqrt[]{(x-3)^2}=\sqrt[]{25}=5=x\text{ -3}[/tex]Finally, we add 3 on both sides (Step 4). Then we get
[tex]x=5+3=8[/tex]Related Questions
Joni took out a loan for $21,912. To pay it back, she will make 42 monthly paymentsof $931. How much will he pay in interest? Round answer to a whole number.
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Given:
Loan of $21,912
42 monthly payments of $931.
Find amount of interest.
First, find the total amount that Joni will pay.
[tex]42\times\$931=\$39,102[/tex]Next, subtract the result by the amount of loan
[tex]\$39,102-$\$21,912=$\$17,190[/tex]Therefore, Joni will pay $17,190 in interest.
Hi i have uploaded the question in the image. Equation no. 2 (ii).
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Let's determine if g(x) is a factor of f(x).
[tex]\text{ f(x) }=\text{ }x^3\text{ }-3x^2+4x-4[/tex][tex]\text{ g(x) = }x\text{ - 2}[/tex]Given that g(x) = x - 2, at x = 2, let's check the value of f(x) at x = 2, If f(x) = 0, then g(x) is a factor, otherwise, g(x) is not a factor of f(x).
We get,
At x = 2,
[tex]\begin{gathered} \text{ f(x) }=\text{ }x^3\text{ }-3x^2+4x-4 \\ \text{ f(2) = (2)}^3-3(2)^2\text{ + 4(2) - }4 \\ \text{ f(2) = 8 - 12 + 8 - }4 \\ \text{ f(2) = 16 - 1}6 \\ \text{ f(2) = 0} \end{gathered}[/tex]Therefore, g(x) is a factor of f(x).
3x=4 1/2 I need help to solve for x
Answers
We need to solve the equation:
[tex]3x=4\frac{1}{2}[/tex]First, notice that the mixed number 4 1/2 can be written as:
[tex]4\frac{1}{2}=4+\frac{1}{2}[/tex]Now, we can solve the equation for x by dividing both sides of the equation by 3. We obtain:
[tex]\begin{gathered} \frac{3x}{3}=\frac{\mleft(4+\frac{1}{2}\mright)}{3} \\ \\ x=\mleft(4+\frac{1}{2}\mright)\cdot\frac{1}{3} \\ \\ x=4\cdot\frac{1}{3}+\frac{1}{2}\cdot\frac{1}{3} \\ \\ x=\frac{4}{3}+\frac{1}{6} \\ \\ x=\frac{8}{6}+\frac{1}{6} \\ \\ x=\frac{9}{6} \\ \\ x=\frac{3}{2} \\ \\ x=1\frac{1}{2} \end{gathered}[/tex]Therefore, the solution is:
[tex]\mathbf{x=1\frac{1}{2}}[/tex]Answer:
Exact form:
x = 3/2
decimal form:
x = 1.5
mixed number form:
x = 1
1/2
Step-by-step explanation:
Find the area of the semicircle. Round to the nearest tenih. Use 3.14 for 3.8 yda. 22.7 yd²b. 23.9 yd²c. 45.3 yd²d. 11.9 yd²
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Answer:
[tex]A[/tex]Explanation:
Here, we want to calculate the area of the semi-circle
To get this, we have to calculate the area of the circle and divide by 2
Mathematically, we have that as follows:
[tex]A\text{ = }\frac{\pi r^2}{2}[/tex]where pi is 3.14 and r which is the radius of the circle is 3.8 yd
Mathematically, we calculate the area as follows:
[tex]A\text{ = }\frac{3.14\times3.8^2}{2}\text{ = 22.7 yd}^2[/tex]Question 2 (5 points) (04.01 LC) Simplify +5x+6 X+2
A x²+1
B x²-1
C X +3
D X-3
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[tex]\bf{\dfrac{x^{2} +5x+6 }{x+2} }[/tex]
Rewrite the term.
x² + 2x + 3x + 6
Group the terms into two fractional parts.
(x² + 2x + (3x + 6)
Factor the expression
x(x + 2) + 3 (x + 2)
[tex]\boldsymbol{\sf{\dfrac{(\not{x+2)(x+3)}}{\not{x+2}}=x+3 \to Option \ C }}[/tex]
[tex] \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \bold{\cfrac{x {}^{2} + 5 x + 6 }{x + 2} }[/tex]
Answer :
Note: To solve a problem like this, we must first determine which of the two numbers add 5 and multiply 6, we know that they are 2 and 3 and then we must Rewrite the expression using the above.
[tex] \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \bold{(x+2)(x+3)}[/tex]
Now, we must put a fraction since we can more easily solve the problem posed.
[tex] \: \: \: \: \: \: \: \: \: \: \: \: \: \: \bold{ \cfrac{(x + 2)(x + 3)}{x + 2} }[/tex]
Now the last thing we have to do is Cancel [tex]\bold{x+2}[/tex] to have a final result that is the following:
[tex] \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \bold{x+3}[/tex]
The diameter of a circle is 12 meters. What is the area of a sector bounded by a 102° arc?Give the exact answer in simplest form.
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Answer:
The area of the sector is;
[tex]\begin{gathered} 10.2\pi m^2 \\ or \\ 32.04m^2 \end{gathered}[/tex]Explanation:
The Area of a sector can be calculated using the formula;
[tex]A=\frac{\theta}{360}\times\pi r^2[/tex]Where:
A = area of the sector
Angle theta = the angle bounding the sector
r = radius
Given:
[tex]\begin{gathered} \theta=102^0 \\ r=\frac{\text{diameter}}{\text{2}}=\frac{12m}{2}=6m \\ r=6m \end{gathered}[/tex]substituting the given values, we have;
[tex]\begin{gathered} A=\frac{102}{360}\times\pi(6^2) \\ A=10.2\pi m^2 \\ A=32.04m^2 \end{gathered}[/tex]Therefore, the area of the sector is;
[tex]\begin{gathered} 10.2\pi m^2 \\ or \\ 32.04m^2 \end{gathered}[/tex]
For each row of the table, choose the equivalent expression
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Ok, so:
Let's make all operations and then choose the equivalent expression for each one.
Let's start in order:
a. 4/12 + 4/12 = 8/12
b. 1/12 + (3/12 + 3/12) = 7/12
c. 4/12 + 5/12 = 9/12
d. 2/12 + 2/12 + 2/12 = 6/12.
Notice that the last operations are the columns of the table.
So, let's do it the same with the upper rows:
e. 5/12 + 4/12 = 9/12
f. (1/12 + 3/12) + 3/12 = 7/12
g. 1/12 + 2/12 + 3/12 = 6/12
h. 15/12 - 7/12 = 8/12.
Now, let me draw the table to make this problem more understandable.
This is the order you have to put the answer:
Ezra is finding the perimeter of different-sized regular pentagons. There is a proportional relationship between the side length of the regular pentagon in inches, x, and the perimeter of the regular pentagon in inches, y. The equation that models this relationship is y=5x. What is the perimeter of a regular pentagon with a side length of 2 inches? Write your answer as a whole number or decimal.
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The perimeter of the regular pentagon Ezra is finding is 10m inches
How to find the perimeter of a regular pentagon with a side length of 2 inchesPerimeter refers to the total outside length of an object,
The equation given in the problem is
y = 5x
where
the side length of the regular pentagon in inches, x,
the perimeter of the regular pentagon in inches, y
if the side length is 5, we plug in 2 into the equation above
y = 5x
y = 5 * 2
y = 10 inches
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i need some help on this word problem please do it for me (12)
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The first thing we need to do is identify the important values, our variables, and our equations that model or describe our problem.
• A total of 560 tickets were sold.
• Tickets can be ,A,dult or ,S,tudent
[tex]A+S=560\to(1)[/tex]• The total of tickets sold $3166
,• The value of the Adult ticket is $8
,• The value of the Student ticket is $3.5
[tex]8A+3.5S=3166\to(2)[/tex]We can see that A and S correspond to the number of Adult or Student tickets sold. We solve the equations to find our numbers.
[tex]A=560-S\to\text{(1)}[/tex][tex]\begin{gathered} 8(560-S)+3.5S=3166 \\ 8\times560-8S+3.5S=3166 \\ S(3.5-8)=3166-4480 \\ -4.5S=-1314 \\ S=\frac{-1314}{-4.5} \\ S=292 \end{gathered}[/tex][tex]\begin{gathered} A=560-292 \\ A=268 \end{gathered}[/tex]In total, 292 Student tickets and 268 Adult tickets were sold.The baghrams make regular monthly deposits in a savings account. The graph shows the relationship between the numbers x of months and the amount y in dollars in the account.what is the equation for the deposit?A- y/x = $40/monthB- y/x = $25/monthC- y/x = $50/monthD- y/x = $75/month
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The two point throught which line passes are (2,100) and (4,200).
Determine the equation of line passes through the points.
[tex]\begin{gathered} y-100=\frac{200-100}{4-2}(x-2) \\ y-100=50(x-2) \\ y=50x-100+100 \\ y=50x \\ \frac{y}{x}=50 \end{gathered}[/tex]T
891 to which closer to hundred
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891 is closer to 900.
Consider the following:
800, 820, 840, 860, 880, 900
891 is found between 880 and 900
Thus, the hundred 891 is closer to is 900
Write an inequality for each of the following Mrs. Champlin needs to make at least 28 costumes for the school play
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ok
x = number of costumes
The inequality is:
[tex]\text{ x }\ge\text{ 28}[/tex]where "x" is the number of costumes
In the sentence given, they use the terms "at least", that means that the number must be equal or greater than 28.
In maths, there are five symbol that we can use in inequalities.
= means equal
< means less than
> means greater than
[tex]\begin{gathered} \ge\text{ means greater or equal than} \\ \leq\text{ means less or equal than} \end{gathered}[/tex]
In the sentence given, as they use at least, we must use greater or equal, it means it could be 28 or a greater number.
Can you please me with the question on the picture
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Solution
[tex]\begin{gathered} \text{Total marbles= 6+}5+4_{} \\ \text{Total marbles =15 marbles} \end{gathered}[/tex]6blue marbles
5 red marbles
4 white marbles
Part A
Formula
Not white means it blue or 5 = 11
[tex]P(\text{Blue given not white)}=\frac{P(B\text{ n W)}}{P(W)}=\frac{\frac{6}{15}\times\frac{6}{15}}{\frac{11}{15}}=\frac{6}{15}[/tex]Part B
Select the recursive and explicit formula for the Arnold family 2 answer
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ANSWER:
[tex]\begin{gathered} A\left(n\right)=a_{n-1}\times 2 \\ A\left(n\right)=0.05\cdot\left(2\right)^{n-1} \end{gathered}[/tex]STEP-BY-STEP EXPLANATION:
We have that the Arnolds family are going to save a nickel on the first day of the month and then double the amount each day.
One nickel is equal to $0.05, therefore, we can make an recursive formula, it is a geometric sequence where the initial value is 0.05 and the ratio is equal to 2, because it doubles every day, therefore:
[tex]A(n)=0.05\cdot(2)^{n-1}[/tex]Now, from the above we can deduce the explicit formula, since the next value will be double the previous value, therefore, the explicit formula would be:
[tex]A(n)=a_{n-1}\times2[/tex]Therefore, the correct answers are the 1st and 4th options.
An archer hits a bullseye 64% of the time. What is the probability the archer hitsthe bullseye exactly 4 times during 10 total attempts?a. 242b. .365C..077d. 168
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If the probability of hitting the bullseye is 64% (P(H) = 0.64), then the probability of not hitting the bullseye (P(H_bar)) is:
[tex]P(\bar{H})=1-P(H)=1-0.64=0.36[/tex]Now, if we have 10 attempts, and the archer hits 4 times, then he misses 6 times.
So we have 4 cases of hitting (P(H)) and 6 cases of not hitting(P(H_bar)), and the probability is the product of the probabilities of each case:
[tex]P=P(H)^4\cdot P(\bar{H})^6=(0.64)^4\cdot(0.36)^6=0.16777\cdot0,0021767=0\text{.}0003652[/tex]We also need to multiply this probability by a combination of 10 choose 4, because the 4 hits among the 10 attempts can be any of the 10, in any order:
[tex]C(10,4)=\frac{10!}{4!(10-4)!}=\frac{10!}{4!6!}=\frac{10\cdot9\cdot8\cdot7}{4\cdot3\cdot2}=210[/tex]So the final probability is:
[tex]P^{\prime}=P\cdot C(10,4)=0.0003652\cdot210=0.077[/tex]So the answer is C.
find the length of each chord. horizontal chord and vertical
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Consider the circle
we have the intersecting chords theorem, which states that
[tex]a\cdot b=c\cdot d[/tex]In our case we have a=x, b=12, c=6 and d=x+4. So we have
[tex]12\cdot x=6\cdot(x+4)[/tex]distributing on the right side we get
[tex]12\cdot x=6x+6\cdot4=6x+24[/tex]Subtracting 6x on both sides, we get
[tex]24=12x\text{ -6x=6x}[/tex]Dividing boht sides by 6, we get
[tex]x=\frac{24}{6}=4[/tex]So, the value of x is 4. Now we replace this value to find the length of each chord, so we have
x---->4
12---->12
x+4----->4+4=8
6----->6
What is the length of the hypotenuse of the right triangle with coordinates:(-2, -1), (-6,5), and (4, 3)?
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ANSWER:
10.2 units
STEP-BY-STEP EXPLANATION:
The first thing is to make a sketch of the triangle formed in the Cartesian plane, like this:
The hypotenuse is the side opposite the right angle, therefore, it would be the side from the point (-6, 5) to the point (4, 3).
We calculate the distance between these two points using the following formula:
[tex]d=\sqrt{\left(x_2-x_1\right)^2+\left(y_2-y_1\right)^2}[/tex]We replace and calculate the length of the hypotenuse:
[tex]\begin{gathered} d=\sqrt{\left(4-\left(-6\right)\right)^2+\left(3-5\right)^2} \\ d=\sqrt[]{(4+6)^2+(3-5)^2} \\ d=\sqrt[]{(10)^2+(-2)^2} \\ d=\sqrt[]{100+4} \\ d=\sqrt[]{104} \\ d\cong10.2 \end{gathered}[/tex]The length of the hypotenuse is 10.2 units.
I need help with a math assignment i linked the picture below with the question
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Answer:
[tex]P\text{ = 29x+5}[/tex]Explanation:
Here, we want to get the perimeter of the rectangle
Mathematically, that is:
[tex]P\text{ = 2(L + B)}[/tex]Where L is the length of the rectangle, given as 6.5x + 9 ft and B is the width of the rectangle which is 8x-6.5
Substituting these values into the formula, we have the perimeter of the rectangle as follows:
[tex]\begin{gathered} P=2(6.5x\text{ + 9 +8x-6.5)} \\ P\text{ = 2(14.5x+2.5)} \\ P\text{ = 29x+5} \end{gathered}[/tex]What is 5,421 rounded to the nearest hundred?A.4,000B.5,000C.5,4000D.5,200
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We have the following number:
[tex]5,421[/tex]By rounding down this number to the nearest hundred, we get
[tex]5,400[/tex]which corespond to option C
Jeff receive six dollars for each hour he babysits how much money will just make after six hours eight hours 10 hours in 12 hours right the function and then find each answer to the correct function table that matches this situation
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Jeff receive six dollars for each hour he babysits
Function:
f(x) = 6x
Where x is the number of hours
for 6 hours:
F(6) = 6(6) = 36
For 8 hours:
F(8)= 6(8) = 48
For 10 hours:
F(10)= 6(10)= 60
For 12 hours:
F(12)=6(12)=72
help me Plss Im begging you
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Answer:
2:1
Step-by-step explanation:
No of hydrogen atoms = 4
No of carbon atoms = 2
Ratio of hydrogen atoms to carbon atoms mean that the no of hydrogen atoms need to be divided by the no of Carbon atoms
that is 4/2 = 2/1 = 2 : 1
I need the answer as fast as you can give it to me
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Explanation
Given
[tex](256x^{16})^{\frac{1}{4}}[/tex]We can simplify the expression below;
[tex]\begin{gathered} =256^{\frac{1}{4}}\times x^{16\times\frac{1}{4}} \\ =\sqrt[4]{256}\times x^{\frac{16}{4}} \\ =4x^4 \end{gathered}[/tex]Answer:
Find the amount of interest and the monthly payment for the loan described.
Purchase of a living room set for $2,700 at 12% add-on interest for 3 years
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The amount of interest is $972 and monthly payment is $102.
What is Simple interest?Simple interest is based on the principal amount of a loan or the first deposit in a savings account.
Given that, a loan described as purchase of a living room set for $2,700 at 12% add-on interest for 3 years
SI = P*R*T/100
SI = 2700*12*3/100 = $972
Amount to be paid = $972+$2,700 = $3672
Amount to be paid monthly = $3672/3*12 = $102
Hence, The amount of interest is $972 and monthly payment is $102.
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write a linear equation that has m=4 and has an x intercept of (5,0)
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the equation is of the form y = mx + b, then
for b:
[tex]\begin{gathered} 0=4(5)+b \\ 0=20+b \\ 0-20=20+b-20 \\ b=-20 \end{gathered}[/tex]the equation is:
[tex]y=4x-20[/tex]please solve this for me
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The equation of the line in slope intercept form is y = -x + 6
How to write equation of a line in slope intercept form?The equation of a line in slope intercept form can be represented as follows:
y = mx + b
where
m = slopeb = y-interceptThe slope of the line can be found as follows:
using (6, 0) and (5, 1)
m = slope = 1 - 0 / 5 - 6
slope = 1 / -1
slope = -1
Therefore, let's find the y-intercept of the line using (0, 6).
y = -x + b
6 = -(0) + b
b = 6
Therefore, the equation of the line is y = -x + 6
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Back | Next Question 2 Indicate the answer choice that best completes the statement or answers the question. Determine if the two figures are congruent by using transformations. Explain your reasonin a. congruent; a rotation followed by a reflection Ob. congruent; a reflection followed by another reflection Oc. congruent; a reflection followed by translation O d. not congruent
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b. congruent; a reflection followed by another reflection
If grey shape is reflected across the x-axis and then the y-axis, or viceversa, white shape is obtained.
what property do we use to check that our factored form is equivalent to the standard form
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Lets solve an example:
[tex]\begin{gathered} y=x^2+6x+8 \\ \end{gathered}[/tex]this quadratic polynomial is in standard form. We can write the same polynomial in factored form as
[tex]y=(x+4)(x+2)[/tex]In the case of quadratic polynomials, a fast check is
that is, 4 plus 2 must be equal to 6 in the term 6x and
4 times 2 must be 8 in the constant term, which is 8.
can you please help me
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We have two types of crust, each of them with a different type of sauce and choice of toppings. The answer would be 54 single topping pizzas because we have two types of crust for 3 types of sauce 2*3 = 6
and 9 choices of toppings for each of them 6*9 = 54
A figure has an area of 100 units `2 what will the new area be after dilation with a scale factor of 2\5
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16 u²
1) If a figure has an area and it's been dilated of k= 2/5
2) Then we can sketch that situation, concerning to areas:
So, we can state this dilated figure is going to have an area of 16 u².
Hence, the answer is 16 u²
I need some help on finding the surface area. i don't know how to solve with a triangular base?
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The surface area(A) of a triangular pyramid can be found using the formula:
[tex]A\text{ = }\frac{1}{2}\text{ }\times\text{ a }\times\text{ b + }\frac{3}{2}\text{ }\times b\text{ }\times\text{ s}[/tex]Given the triangular prism:
Hence, we have:
a = 3.5 m
b = 4m
s = 11.1 m
Substituting the values into the formula:
[tex]\begin{gathered} A\text{ = }\frac{1}{2}\times3.5\text{ }\times4\text{ + }\frac{3}{2}\text{ }\times\text{ 4 }\times\text{ 11.1} \\ =\text{ 7 + 66.6} \\ =\text{ 73.6 m}^2 \end{gathered}[/tex]Hence, the surface area of the pyramid is 73.6 square meter