Please help me with this problem so my son can better understand I have attached an image of the problem
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We have to solve for c:
[tex](c+9)^2=64[/tex]When we have quadratic expressions, we have to take into account that each number has two possible square roots: one positive and one negative.
We can see it in this example: the square root of 4 can be 2 or -2. This is beacuse both (-2)² and 2² are equal to 4.
Then, taking that into account, we can solve this expression as:
[tex]\begin{gathered} (c+9)^2=64 \\ c+9=\pm\sqrt[]{64} \\ c+9=\pm8 \end{gathered}[/tex]We then calculate the first solution for the negative value -8:
[tex]\begin{gathered} c+9=-8 \\ c=-8-9 \\ c=-17 \end{gathered}[/tex]And the second solution for the positive value 8:
[tex]\begin{gathered} c+9=8 \\ c=8-9 \\ c=-1 \end{gathered}[/tex]Then, the two solutions are c = -17 and c = -1.
We can check them replacing c with the corresponding values we have found:
[tex]\begin{gathered} (-17+9)^2=64 \\ (-8)^2=64 \\ 64=64 \end{gathered}[/tex][tex]\begin{gathered} (-1+9)^2=64 \\ (8)^2=64 \\ 64=64 \end{gathered}[/tex]Both solutions check the equality, so they are valid solutions.
Answer: -17 and -1.
Related Questions
Im just needing a little bit more help with these type of problems ;/
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Answer:
Expected value = 2.21
Explanation:
The formula to obtain the expected value is given by:
[tex]E\mleft(X\mright)=\mu=∑xP\mleft(x\mright)[/tex]We will proceed to calculate the given scenario as given below:
[tex]\begin{gathered} E\mleft(X\mright)=\mu=∑xP\mleft(x\mright) \\ E(X)=(1\times0.31)+(2\times0.41)+(3\times0.07)+(4\times0.18)+(5\times0.03) \\ E(X)=0.31+0.82+0.21+0.72+0.15 \\ E(X)=2.21 \\ \\ \therefore E(X)=2.21 \end{gathered}[/tex]Therefore, the expected value of this scenario is 2.21
The graph represents a quadratic function. Write an equation of the function in standard form.
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A quadratic function in standard form with the given characteristics is (1/4) x² - 3x + 5.
Given that, the graph is passing through (2, 0), (10, 0) and (6, -4).
What is a quadratic function in standard form?The standard form of a quadratic equation is given as:
ax² + bx + c = 0 where a, b, c are real numbers and a ≠ 0.
Now, the equation passes through (2, 0)
y = ax² + bx + c
0 = 4a + 2b + c ----------------(1)
The equation passes through (6, -4)
y = ax² + bx + c
-4= 36a + 6b + c ----------------(2)
The equation passes through (10, 0)
y = ax² + bx + c
0 = 100a + 10b + c ----------------(3)
Using the Gauss elimination method to solve the system of equations we get,
a = 1/4, b = -3, and c = 5
The quadratic equation will be:
y = ax² + bx + c
y = (1/4) x² - 3x + 5
Therefore, a quadratic function in standard form with the given characteristics is (1/4) x² - 3x + 5.
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HELP ME PLEASE!!! Question 1Jim is planning his spring garden. He will construct a rectangular gardensurrounded by a chain link fence. The length of Jim's garden will be 8 feet morethan 3 times its width (w).(Drawing and labeling a diagram may be helpful)Part A: Write an expression in terms of w to represent the amount of chain linkfencing (the perimeter) Teeded to enclose Jim's garden.
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We have a rectangular garden.
The length L is 8 feet more than 3 times its width.
3 times the width is 3w, so we will add 8 to it and equal it to the length L:
[tex]L=8+3w[/tex]The perimeter will be 2 times the length plus 2 times the width. We can write it and transform it to an expression in terms only of w:
[tex]\begin{gathered} P=2L+2w \\ P=2(8+3w)+2w \\ P=16+6w+2w \\ P=16+8w \end{gathered}[/tex]The perimeter has a value of P=16+8w.
We can draw the diagram as:
Part B: If the perimeter of Jims garden is 88 feet, what would be the width of the garden?
We will use the equation we derived in Part A, and we have to replace P=88, in order to find w.
[tex]\begin{gathered} P=16+8w \\ 88=16+8w \\ 88-16=8w \\ 72=8w \\ w=\frac{72}{8} \\ w=9.75 \end{gathered}[/tex]The width is 9.75 feet.
If f (x)- VX-3, complete the following statement:x + 219) =
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Given that;
[tex]f(x)=\frac{3}{x+2}-\sqrt{x-3}[/tex]To get f(19), let's substitute 19 for x in the function f(x);
[tex]\begin{gathered} f(x)=\frac{3}{x+2}-\sqrt{x-3} \\ f(19)=\frac{3}{19+2}-\sqrt{19-3} \\ f(19)=\frac{3}{21}-\sqrt{16} \\ f(19)=\frac{1}{7}-4 \\ f(19)=-3\frac{6}{7} \end{gathered}[/tex]Therefore, the value of f(19) is;
[tex]f(19)=-3\frac{6}{7}[/tex]State the domain of the function.{-2,0, 1, 2, 3, 4){-4,0, 1, 2, 6){0, 1,2,3)(-2,4)
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D= {-2,0,1, 2,3,4}
1) Considering that the Domain is the set of entries of a function, on the x-axis, and examining that graph we can state
- The lowest value for that is given by x=-2
- The highest value for that is x= 4
- The points (-2,-4) (0,0), (1,1), (2,2), (3,1) and (4,6)
2) So, we can write the set, the Domain, after examining the options as:
D= {-2,0,1, 2,3,4}
Notice that we're considering the x-coordinates
3) So the answer is D= {-2,0,1, 2,3,4}
I have no idea what the answer is or how to do it,A certain state uses the following progressive tax rate for calculating individual income tax0-3000 2% tax rate3001-5000 3% tax rate5001-17,000 5% tax rate17,001 and up 5.75% tax rateCalculate the state income tax owed on a 60,000 per year salary
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SOLUTION
From the table given, the progessive income tax for salaries of $17,001 and above is 5.75% of the income.
So, for $60,000, it will also be 5.75% of the income.
This becomes
[tex]\begin{gathered} \frac{5.75}{100}\times60,000 \\ =3450 \end{gathered}[/tex]Therefore, the answer is $3,450
Lin is paid $90 for 5 hours of work. She used the following table to calculate how much she would be paid at this rate for 8 Hours of work. 1. What is the meaning of the 18 that appears in the table? 2. Explain how Lin used this table to solve the problem. 3. At this rate, how much would Lin be paid for 3 hours of work? For 2.1 hours of work. AMOUNTS EARNED ($) | TIME WORKED(hours)
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Let
y ------> the amount earned
x ----> the number of hours worked
In this problem we have a direct variation
A relationship between two variables, x, and y, represent a proportional variation if it can be expressed in the form y=kx
where
k is the constant of proportionality
k=y/x
In this problem the value of k is hourly rate
so
we have
For y=$90 -------> x=5 hours
substitute
k=90/5
k=$18 per hour
substitute in the linear equation
y=18x
so
Part 1) What is the meaning of the 18 that appears in the table?
18 is the hourly rate ( amount earned by a one hour of work)
Part 2) Explain how Lin used this table to solve the problem.
using the table
For x=8 hours
the value of y=$144
Verify with the equation
y=18x
y=18(8)=144 -----> is ok
Part 3) At this rate, how much would Lin be paid for 3 hours of work? For 2.1 hours of work.
For x=3 hours
substitute in the equation
y=18x
substitute the value of x
y=18(3)=$54
For x=2.1 hours
y=18(2.1)=$37.8
Nikki and four friends had lunch at their favorite restaurant. The total bill was $29.00, and they wanted to leave a 15% tip. Which amount of money is closest to the 15% tip? A $3.00 B $3.50C $4.00D $4.50
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Total bill = $29
Tip left = 15%
The valu of the tip = 15% of $29
[tex]\begin{gathered} \frac{15}{100}\text{ x 29} \\ \\ =\text{ \$4.35} \end{gathered}[/tex]The value of the tip = $4.35
Let us consider the options given
$4.35 - $3 = $1.35
$4.35 - $3.5 = $0.85
$4.35 - $4 = $0.35
$4.5 - $4.35 = $0.15
Looking t the deviation from the real value of the tip ($4.35), the least deviation is $0.15. Hence, we can conclude that $4.5 is the closest to the tip.
The answer is option D ($4.50)
What types of solutions will a quadratic equation have when the discriminant b2 − 4ac in the quadratic formula is negative?
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Explanation
When the discriminant is negative, this implies that
[tex]b^2-4ac<0[/tex]Answer: In this case, the equation has no real solutions;
Virginia is going to visit 5 cities this summer. She will choose from 8 different cities and the order in which she visits the cities does not matter. How many different city combinations are possible for the summer travelling?
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Find the value of x. Round tothe nearest tenth.27°Х34°11=x = [?]Law of Sines: sin AAsin Bbsin CIIaС
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Using the law of Sines
[tex]\frac{\sin A}{a}=\frac{\sin B}{b}=\frac{\sin C}{c}[/tex]Consider the given triangle
Let A = 27°, the a = 11
Let B = 34°, the b = x
Substitute the values into the sine rule formula
This gives
[tex]\frac{\sin27}{11}=\frac{\sin 34}{x}[/tex]Cross multiply
[tex]x\times\sin 27=11\times\sin 34[/tex]Divide both sides by sin 27
This gives
[tex]x=\frac{11\times\sin 34}{\sin 27}[/tex]Solve for x
[tex]\begin{gathered} x=\frac{11\times0.5592}{0.4540} \\ x=\frac{6.1512}{0.4540} \\ x=13.55 \end{gathered}[/tex]Therefore, the value of x is approximately 13.55
write the following basic forms in their single form
2√3
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The expression which represents the written form of the basic form expression; 2√3 as a single form is; √12.
What is the single form expression which is equivalent to the basic form expression; 2√3?It follows from the task content that the basic form expression be written as it's equivalent single form expression.
Since the given radical expression is; 2√3; it follows that the expression can be written as a single form expression as follows;
First, the square of 2, 2² is equal to 4;
Hence, by the converse;
2 = √4.
The given expression can therefore be written as; √4 • √3.
The expression above can therefore be written in its single form as; √(4 × 3) = √12.
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Find the vertical and horizontal lines that passes through the point (3,6).
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We have to find the vertical and horizontal lines that passes through the point (3,6).
A vertical line will be defined as x = constant. If it passes trough a point (x,1,y1), the line will be defined as a x=x1, so the point (x1,y1) belongs to the line.
The same goes for horizontal lines, but in this case the line is defined as y = constant.
For a point (x1,y1), the horizontal line that pass through the point will be y = y1.
Then, for point (x,y)=(3,6), the vertical and horizontal lines as:
x=3 and y=6.
Answer:
Vertical line: x = 3
Horizontal line: y = 6.
R’S’T’U is a dilation image of RSTU which is the correct description of the dilation?
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Statement Problem: R’S’T’U is a dilation image of RSTU which is the correct description of the dilation?
Solution:
R'S'T'U' is a dilation of RSTU by;
[tex]\frac{1}{3}[/tex]because it is reduced by that factor.
CORRECT OPTION: a reduction with scale factor
[tex]\frac{1}{3}[/tex]This chart shows the cost per pound of different fruits.
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From the given data, the cost per pound of apple, CP=$1.89≈$2.
We have to estimate the cost of n=3.2≈3 pounds(lb) of apple.
The cost of n=3 lb of apple can be calculated as,
[tex]\begin{gathered} T=CP\times n \\ =2\times3\text{ lb} \\ =6 \end{gathered}[/tex]Therefore, the cost of 3. pounds of apples is about $6.048.
The shortest side of a right triangle measures 5, and the longest side measures 13. Determine the measurement of the unknown side.
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The solution that we have that would have to do with the measurement of the unknown side would be 12.
How to solve for the unknown
The Pythagoras theorem says that the length of the suym of the square of a triangle is the same as the sum of the square of the other two sides.
From the definition that we have above.
We have the shortest side as 5.
The longest side as 13
Then we would have
13² - 5² = 25 - 169
= 144
Next we would have to take the square root of 144
= √144
= 12
Hence we would say that the length of the unknown is given as 12
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If Omar still needs 458How much does he need after saving for 5 weeks
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(a) Setting A(w)=458, we get:
[tex]800-18w=458.[/tex]Subtracting 800 from the above equation we get:
[tex]\begin{gathered} 800-18w-800=458-800, \\ -18w=-342. \end{gathered}[/tex]Dividing the above equation by -18 we get:
[tex]\begin{gathered} \frac{-18w}{-18}=\frac{-342}{-18}, \\ w=19. \end{gathered}[/tex]Therefore Omar has been saving for 19 weeks.
(b) Recall that to evaluate a function at a given value, we substitute the variable by the given value.
Evaluating A(w) at w=5 we get:
[tex]A(5)=800-18\cdot5.[/tex]Simplifying the above result we get:
[tex]\begin{gathered} A(5)=800-90 \\ =710. \end{gathered}[/tex]Answer:
(a) 19.
(b) $710.
Blue whales can weigh as much as 150 tons. Convert the weight to pounds.
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SOLUTION:
The conversion formula from tons to pounds is;
[tex]1\text{ }US\text{ }ton=2000\text{ }pounds[/tex]Thus, converting this to pounds, the Blue whale would weigh;
[tex]150\times2000=300,000\text{ }pounds[/tex]Thus, the whale weighs 300,000 pounds
Answer:
The answer is C: 150/y
Step-by-step explanation:
11. Jarrod's favorite movie is now on video at 15% off the originalprice. If he pays $17, what was the original price?
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original price = x
discount = 15%
price after discount = $17
Write an equation:
x (1-15/100) = 17
x (1-0.15 ) = 17
0.85x = 17
Solve for x:
x = 17/0.85
x = $20
y + 7x= 11; x= -1,0, 4
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We have an expression with 2 unknowns, and we have values for one unknown. We have to calculate then the other unknown value:
Expression:
[tex]\begin{gathered} y+7x=11 \\ y=11-7x \end{gathered}[/tex]Then, when x=-1
[tex]y=11-7x=11-7(-1)=11+7=18[/tex]When x=0
[tex]y=11-7(0)=11[/tex]When x=4
[tex]y=11-7(4)=11-28=-17[/tex]Find the exact area of a circle with a diameter of 12 in., expressed in terms of n.361 square inches61 square inches14471 square inches12 square inches241 square inches< Previous
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The area of a circle is given by:
[tex]A=\pi r^2[/tex]Since the radius is half the diameter we have that r=6. Then the area is:
[tex]A=\pi(6)^2=36\pi[/tex]Therefore, the answer is the first one.
want to graph xdont you need to find out what x is?-3x-6y=0
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We have a equation of a line in the form:
[tex]-3x-6y=0[/tex]This goes through the point (0,0).
With another point, we can graph the line.
For example, for x=2, we have:
[tex]\begin{gathered} -3(2)-6y=0 \\ -6-6y=0 \\ -6y=6 \\ y=-1 \end{gathered}[/tex]So the point (2,-1) belongs to the line.
We can graph the line passing through those points:
What is the equation of the circle with endpoints (5,7) and (1,3)
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Explanation:
endpoints (5,7) and (1,3)
The equation of circle formula:
[tex]\begin{gathered} (x-a)^2+(y-b)^2=r^2 \\ radius\text{ =r and (a, b) are the coordinates of the centre} \end{gathered}[/tex]To find the centre(a, b), we need to find the midpoint of the two given points:
[tex]\begin{gathered} \text{Midpoint = }\frac{1}{2}(x_1+x_2),\text{ }\frac{1}{2}(y_1+y_2) \\ \text{Midpoint = 1/2(5+1), 1/2(7+3)} \\ \text{Midpoint = 3, 5} \\ \text{centre = (a, b) =(3, 5)} \end{gathered}[/tex]The radius is the distance between the centre of the circle and any of the two points.
We will apply the distance formula:
[tex]\begin{gathered} dis\tan ce\text{ = }\sqrt[]{(y_2-y_1)^2+(x_2-x_1)^2} \\ (3,5)\text{ and (1, 3)} \\ \text{Distance =}\sqrt[]{(3-5)^2+(1-3)^2} \\ \text{Distance =}\sqrt[]{4+4} \\ \text{Distance =}\sqrt[]{8}\text{ = 2}\sqrt[]{2} \\ \text{radius = distance = 2}\sqrt[]{2} \end{gathered}[/tex]Using the equation of circle:
[tex]\begin{gathered} (x-3)^2+(y-5)^2=(2\sqrt[]{2)}^2 \\ (2\sqrt[]{2)}^2=\text{ }2\sqrt[]{2)}\times2\sqrt[]{2)}\text{ = 4(}\sqrt[]{2})^2\text{ = 4(2) = 8} \\ (x-3)^2+(y-5)^2=\text{ 8} \end{gathered}[/tex]个 == CR Algebra 1 B (GP) 21-22 / 8:Radical Expressions and Equations 104 6 2 -10-8-6 -4 - 2 0 N 4 6 8 10 2 -4 6 -8 -10 Match the graph with its function by translating the graph of y = Vx. 3. O y = √x-1+7 O y = x-7+1 = 7 O O y=√x+1+7 O y = x+7+1 Search the web and Windows a
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SOLUTION
The transformation of the function
[tex]y=\sqrt[]{x}[/tex]To give the graph in the question is as follows.
The graph is move to the left from the origin by 1 unit on the x-axis, which is to add 1 to x, we have
[tex]y=\sqrt[]{x+1}[/tex]Also,
The graph is the move upward along the y-axis by 7 unit, which is addition of 7 to the function
Then, the equations becomes
[tex]y=\sqrt[]{x+1}+7[/tex]Therefore
The function that produce the graph in the image is
y = (√x+1) + 7
State the domain and range for each graph and then tell if the graph is a function(write yes or no)
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For the point 1)
- The domain will be: (note that this is not an interval, it is a set of two points)
[tex]\mleft\lbrace-3,2\mright\rbrace[/tex]-The range is the set R of all real numbers (since the line extends to infinite)
-The first graph is NOT a function
For the point 2)
-The domain will be the interval
[tex](-5,5\rbrack[/tex]-The range is the interval:
[tex]\lbrack-2,2\rbrack[/tex]-The second graph is a function.
The diameter of the Milky Way is 2 x 10²⁰ meters. The radius of Earth is 6.37 x 10⁶meters. About how many times as great is the diameter of the Milky Way than the radius of Earth? The diameter of the Milky Way is about
Answers: 4.37 X 10¹⁴
3.1 X 10¹⁴
4.37 X 10¹³
3.1 X 10¹³
(blank) times as great as the radius of Earth.
Answers
Answer:
3.1 x [tex]10^{13}[/tex]
Step-by-step explanation:
[tex]\frac{2x10^{20} }{6.37x10^{6} }[/tex]
3/6.37 is about .31
When you are dividing with powers, you subtract the exponents
20 - 6 = 14
.31 x [tex]10^{14}[/tex] This is not in scientific notation because .31 is less than 1
3.1 x [tex]10^{-1}[/tex]x[tex]10^{14}[/tex] When we multiply powers with the same base we add the exponents
3.1 x [tex]10^{13}[/tex]
Square meters of ceiling Number of tiles 1 10.75 10 100.75 9.3 100 What is the value of the red X? Write your answer as an algebraic expression using variable "a".
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x = 9a + 1.75
slope = (100.75 - 10.75)/(10 - 9) = 90/9 = 9
offset: 10.75 = 9(1) + b
10.75 - 9 = b
1.75 = b
b = 1.75
y = mx + b
in this case: x = 9a + 1.75
If you borrow $100 for 3 years at anannual interest rate of 9%, howmuch will you pay altogether?
Answers
We are to determine the amount that you have pay back after borrowing a principal amount ( P ) for ( t ) number of years which is compounded annualy at rate ( R ).
You borrowed a principal amount of:
[tex]P\text{ = \$100}[/tex]The time duration for which we have borrowed the money for is:
[tex]t\text{ = 3 years}[/tex]The annual interest rate coumpounded each year is:
[tex]R\text{ = 9\% / year}[/tex]Step 1: Determine the simple interest that accumulated at the end of ( t ) years.
The folllowing formula is used to determine the simple interest that the borrower has to pay once the period of borrowing/lending is over i.e ( t ) years.
The simple interest is the proportional rate of interest ( R ) and the initial borrowed/loaned amount called principal amount ( P ).
[tex]\text{Simple Interest ( I ) = }\frac{P\cdot R\cdot t}{100}[/tex]Use the above simple interest formula ( I ) by plugging in the respective values as follows:
[tex]\text{Simple Interest ( I ) = }\frac{100\cdot9\cdot3}{100}\text{ = \$27}[/tex]Therefore, the total amount of interest that the borrower must pay as an extra ( over the borrowed amount ) is $27.
Step 2: Determine the total amount that is to be returned/paid to the lender
The total amoun that is to be paid by the borrower ( you ) to the lender is the principal amount borrowed ( P ) and the amount of interest accumulated for the contractual time period i.e ( I ).
[tex]\begin{gathered} \text{Total amount to be paid = P + I} \\ \text{Total amount to be paid = \$100 + \$27} \\ \text{Total amount to be paid = }127 \end{gathered}[/tex]Therefore, the amount that you need to pay altogether is:
[tex]\textcolor{#FF7968}{127}\text{\textcolor{#FF7968}{ dollars}}[/tex]Is this correct?
Or please provide an explanation.
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Answer:
The answer selected is correct
Step-by-step explanation:
When talking about balance, having -X (being X in the negative) , means owing X.
Dylan owes $19.25
Elise owes $42.75
Francesca owes $23
Jamaal owes $35.50
So naturally, Dylan owes the least.
I will show you the question
Answers
Given a coordinate plane
For each point, we will make a rotation about the origin
A: ( 9, 3) Clockwise by 90
The rule of rotation will be:
[tex](x,y)\rightarrow(y,-x)[/tex]So, the image of A will be A' = ( 3, -9)
B: ( -4, 7 ) counterclockwise 90
the rule of rotation will be:
[tex](x,y)\rightarrow(-y,x)[/tex]So, the image of B will be B' = ( -7, -4)
C: ( 6, -5) by 180
The rule of rotation will be:
[tex](x,y)\rightarrow(-x,-y)[/tex]so, the image of C will be C' = (-6, 5)
D: ( -8, -2) clockwise by 90
So, the image of D will be D' = ( -2, 8)