To solve the quadratic equation x² + 10x = 18 by completing the square, we rearrange the equation, complete the square, solve for x by taking the square root of both sides, and then isolate x. The two solutions are x = -5 + √43 and x = -5 - √43, which can be approximated if necessary.
To solve the equation x² + 10x = 18 by completing the square, we first need to move all terms to one side to get the equation in the form of ax² + bx + c = 0.
Subtracting 18 from both sides, we have x² + 10x - 18 = 0.
To complete the square, we take the coefficient of x, which is 10, divide it by 2 to get 5, and then square it to get 25. We add 25 to both sides of the equation and then subtract it right back to maintain the balance:
x² + 10x + 25 - 25 - 18 = 0
Now we group the perfect square trinomial and simplify:
(x + 5)² - 43 = 0
Next, we add 43 to both sides:
(x + 5)² = 43
Then we take the square root of both sides:
(x + 5) = √43
Subtract 5 from both sides to solve for x:
x = -5 ± √43
The solutions are x = -5 + √43 and x = -5 - √43.
Line segment BD is a diameter of circle E.
Circle E is inscribed with triangle B C D. LIne segment B D is a diameter. Line segments D C and C B are secants. Angle D B C is 51 degrees.
What is the measure of arc B C?
39°
78°
102°
129°
Answer:
78 degrees
Step-by-step explanation:
Mainly because the measure of the arcs intercepted by the interior angles equals 2 times those interior angles.
so arc DC = 2 * angle DBC = 2 * 51 degrees = 102 degrees.
We also see that because BD is a diameter the angle BCD that intercepts it is 90 degrees because half-circle arc BD = 2 * angle BCD
180 degrees = 2 * angle BCD
also we want arc BC.
we know that the total circle is the sum of all 3 arcs.
arc BC + (half-circle) arc BD + arc DC = 360 degrees
arc BC + 180 + 102 = 360 degrees.
arc BC = 360 - 180 - 102 = 78 degrees
NEED HELP ASAP!!!! WILL GIVE BRAINLIEST!!
Answer:
1st one the other 2 are linear
Answer:
the first one
Step-by-step explanation:
the other two are linear.
Find the value of z.
Answer:
[tex]60 \: degrees[/tex]
Step-by-step explanation:
[tex]180(n - 2)[/tex]
you have to put the number of sides for n
[tex]180(n - 2) \\ 180(6 - 2) \\ 180 \times 4 \\ = 720[/tex]
720 is the sum of interior angles. so to find the value of an angle you have to divide 720 by the number of angles.
[tex] \frac{720}{6} = 120 \: \: degrees[/tex]
we know that,
interior angle + exterior angle = 180 degrees
[tex]120 + z = 180 \\ z = 180 - 120 \\ z = 60 \: \: degrees[/tex]
hope this helps
brainliest appreciated
good luck! have a nice day!
Which angles are supplementary to eachother
Answer:
14 and 15
Step-by-step explanation:
Use a parameterization to find the flux ModifyingBelow Integral from nothing to nothing Integral from nothing to nothing With Upper S Bold Upper F times n d sigma of Bold Upper F equals z squared Bold i plus xj minus 4 z Bold k in the outward direction (normal away from the x-axis) across the surface cut from the parabolic cylinder zequals1minusysquared by the planes xequals0, xequals1, and zequals0.
Here is the correct interpretation of the question with the help of the text editor tool.
Use a parameterization to find the flux [tex]\int\limits \int\limits_s \ F. \ n \ d \sigma[/tex] of F = z²i + xj - 2zk in the outward direction
(normal away from the x-axis) across the surface cut from the parabolic cylinder z = 16 -y² by the planes x = 0 , x = 1, and z = 0 .
The flux is .
Answer:
[tex]-\frac{512}{3}[/tex]
Step-by-step explanation:
F(x,y,z) = (z² ,x , - 2z)
To find the flux across a surface : [tex]\int\limits \int\limits_s \ F. \ n \ dS = \int\limits \int\limits_D \ F. (r_u * r_v) \ dA[/tex]
The sphere z is given as = 16 -y², above x = 0 , x= 1, and z = 0
When z = 0 ⇒ 16 - y² = 0
⇒ y = ± 4
The parameterization is y=v⇒z= 16 -v² and x= u
⇒ r = (x,y, z) = ( u,v,16 - v²)
with 0 ≤ u ≤ 1 and -4 ≤ v ≤ 4
However the normal vector can now be determined as :
[tex]r_u = (1,0,0) , \ \ \ r_v = (0,1, - 2v)[/tex]
[tex]n = r_u*r_v = \left[\begin{array}{ccc}i&j&k\\1&0&0\\0&1&-2v\end{array}\right] = (0,2v,1)[/tex]
[tex]\int\limits \int\limits_s \ F. \ n \ dS = \int\limits \int\limits_D \ F. (r(u,v)) .(r_u*r_v)dA[/tex]
[tex]=\int\limits^1_0 \int\limits^4_{-4} [(16-v^2)^2 , u , -2 (16-v^2)](0,2v,1)dvdu[/tex]
[tex]=\int\limits^1_0 \int\limits^4_{-4} [2uv-2(16-v^2))dvdu[/tex]
[tex]=\int\limits^1_0 (uv^2 -32v+ \frac{2v^3}{3})^ ^4}__{-4}} du[/tex]
[tex]=\int\limits^1_0 (u(16-16)-32(8)+\frac{2}{3}(128))du[/tex]
[tex]= \int\limits^1_0 (-\frac{512}{3})du[/tex]
[tex]= - \frac{512}{3}(u)^ ^1}__0[/tex]
= [tex]-\frac{512}{3}[/tex]
The flux of a vector field across a surface is calculated by computing the surface integral of the vector field in the direction normal to the surface. This involves parametrizing the surface and taking antiderivatives based on the defined area. The direction of the flux is crucial as it determines the sign of the flux.
Explanation:To find the flux of the vector field upper Case Bold F across a surface, we need to compute the surface integral of upper Case Bold F in the given direction. For the given problem, the surface is defined by the parabolic cylinder z = 1 - y^2 and the planes x = 0, x = 1, z = 0. We parametrize this surface using two parameters x and y, with x ranging from 0 to 1, and y ranging from -1 to 1.
We then compute the surface integral by taking the antiderivative of the defined area with the boundaries of surface as the integral's bounds. This process might involve computation of multiple integrals if the surface is composed of multiple parts.
Note that the direction of the flux, which is normal away from the x-axis, is important for the calculation, as it determines the sign of the flux. The flux is positive if the angle between the vector field and the outward normal to the surface is less than 90 degrees, and negative otherwise.
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Store A sells a case of 18 bottles for $10. Store B sells a case of 12 bottles for $6. Which store sells the drinks for less?
Answer:
The answer is store A
Step-by-step explanation:
Since its simple to see 12 is divisible by 6. It equals 2. So the store sells each bottle for 2 dollars. Store A on the other hand is a little difficult but the same thing just divide 18 by 10 to get your outcome of 1.8
Can you guys create your own system of equations word problem, define the variable, write an equation, then solve it and make a sentence explanation on why you did what you chose
Thanks will give brainliest
Answer:
Using a system of equations, however, allows me to use two different variables for the two different unknowns.
number of adults: a
number of children: c
With these variables, I can create equations for the totals they've given me:
total number: a + c = 2200
total income: 4a + 1.5c = 5050
Now I can solve the system for the number of adults and the number of children. I will solve the first equation for one of the variables, and then substitute the result into the other equation:
a = 2200 – c
4(2200 – c) + 1.5c = 5050
8800 – 4c + 1.5c = 5050
8800 – 2.5c = 5050
–2.5c = –3750
c = 1500
Now I can back-solve for the value of the other variable:
a = 2200 – (1500) = 700
I have values for my two variables. I can look back at my definitions for the variables to interpret these values. To answer the original question, there were:
1500 children and 700 adults.
Final answer:
A word problem involving two people and their apples, where Alice has twice as many apples as Bob. The variables are defined, the equation is written, and the solution is found.
Explanation:
Word Problem:
Alice has twice as many apples as Bob. Together, they have 15 apples. Define the variable 'x' as the number of apples Bob has.
Equation:
Alice's apples: 2x
Bob's apples: x
2x + x = 15
Solution:
Combining like terms: 3x = 15
Dividing both sides by 3: x = 5
Sentence Explanation:
We defined the variable 'x' as the number of apples Bob has. Since Alice has twice as many apples, we expressed her number of apples as 2x. The total number of apples they have together is 15, so we created an equation by summing up both Alice's and Bob's apples. By solving for 'x', we found that Bob has 5 apples.
Please help me now plz
I will mark you brainliest
Answer:
x= 12 units.
Step-by-step explanation:
To solve this equation, we can find each half of the base using the Pythagorean theorem. We will use 'x' as denoting each HALF of the base:
45= 3²+x²
Subtracting from both sides will give us:
36= x²
x=6.
However, the base in this problem is '2x' because 'x' is HALF of the base.
2(6)= 12 units.
Jameson has $4,300 in credit card debt with 14% interest that he wants to pay off in 24 months. He will need to make monthly payments of $206.46 each month. Calculate the total cost of repayment and the interest Jameson will pay.
Answer:
The answer to this question can be defined as follows:
net paid interest = $ 655. 04
Total cost = $ 4955.04
Step-by-step explanation:
Given values:
loan amount = $ 4,300
monthly payment = $ 206.46
interest rate = 14 %
Time = 2 years
Solution:
yearly payment = one month amount × 12
1 year payment = $ 206.46 × 12
1 year payment = $2477.52
because Time is 2 year then payment is = $2477.52 *2
2 year payment = $ 4955.04
net interest paid = total payment - loan amount
= $ 4955.04 - $4300
= $ 655.04
total cost = $ 4955.04
net paid interest = $ 655.04
The total cost of repayment and the interest should be $4,955.04 and $655.04.
Calculation of the total cost and interest:Since
loan amount = $ 4,300
monthly payment = $ 206.46
interest rate = 14 %
Time = 2 years
Now
yearly payment = one month amount × 12
So,
= $ 206.46 × 12
= $2477.52
Now the two year payment should be
= $2477.52 *2
= $ 4955.04
Now
net interest paid = total payment - loan amount
= $ 4955.04 - $4300
= $ 655.04
hence, The total cost of repayment and the interest should be $4,955.04 and $655.04.
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Sally likes to collect coins.Sally got 37 coins from her brother 21 coins from her month era as well 22 coins from Benny however sally lost 32 coins before putting those coins into her piggy bank how many coins does sally have in her piggy bank
Answer: Sally has 48 in her piggy bank
Step-by-step explanation:
Hi, to answer this question, first, we have to add the coins given to Sally:
37 +21 +22 = 80
Since she lost 32 coins before putting those coins into her piggy bank, we have to subtract that number to the total number of coins collected.
80-32 = 48 coins
Sally has 48 in her piggy bank
Feel free to ask for more if needed or if you did not understand something.
what is the perimeter of this tile 4in 1in
Answer:
10 inches
Step-by-step explanation:
Assuming a rectangular tile
P = 2(l+w) where l is the length and w is the width
P = 2(1+4)
= 2(5)
= 10 inches
Answer:
10 in
Step-by-step explanation:
quadratic formula 2x^2+7x-15=0
Answer:
Step-by-step explanation:
I hope this was what you were looking for. Have a nice day!
Answer:
x= 3 /2 , x=−5
(2x−3)(x+5)=0
Step 2: Set factors equal to 0.
2x−3=0 or x+5=0
how many ounces are in 3 pounds
Answer:
48
Step-by-step explanation:
16*3
16 oz in a pound
how many 1/3 inch cubes can fit into a 2 inch cube?
Answer: 6
Step-by-step explanation: 2 / 1/3 = 6
Final answer:
To find out how many 1/3 inch cubes can fit into a 2 inch cube, calculate the volume of both cubes and divide the larger volume by the smaller. The result is 216 such cubes can fit into a 2 inch cube.
Explanation:
To determine how many 1/3 inch cubes can fit into a 2 inch cube, we first need to calculate the volume of the larger cube, which is 2 inches x 2 inches x 2 inches = 8 cubic inches. Next, we calculate the volume of the smaller cube which is (1/3 inch) x (1/3 inch) x (1/3 inch) = 1/27 cubic inch. To find how many smaller cubes fit into the larger one, we divide the volume of the larger cube by the volume of the smaller cube: 8 cubic inches / (1/27) cubic inch = 216. Therefore, 216 smaller cubes, each 1/3 inch on a side, can fit into a 2 inch cube.
Montel spends $ 0.75 each time he plays his favorite video game. If you have $ 10, write and solve an inequality to calculate how many video games you can play.
Brainliest and 25 points
Answer:
Inequality=0.75x∠10 Answer=13 or less
Step-by-step explanation:
Answer:
y=.75x (13 Times)
Step-by-step explanation:
y is the amount it will cost Montel to play the video game x amount of times, if Montel plays the game 2 times, 2x.75 is $1.50 so it would cost him $1.50 to play the game 2 times. However, we want to find how many times he can play with a $10 budget, so we must enter $10 as y and divide by .75 and we should get 13.33333. This means Montel will be able to play 13 times and will have 25 cents left over because 13 x .75 is $9.75
PLEASE HELP!!!!!! WILL MARK CORRECT ANSWER BRAINLIEST!!!!!!!!!!!!!!
Solve a triangle with b =7, c =10, and a=51 degrees. Round to the nearest tenth.
Answer:
a=7.8
<C=84.8°
<B=44.19
Step-by-step explanation:
Answer:
Step-by-step explanation:
What it means to "solve for a triangle" is to basically find ALL the missing parts, which in this case, are the lengths.
You are given the angles of the triangle, which we can use to help find the lengths.
By using sin, cos, and tan we can find the missing lengths
** quick side note, an easy way to remember how to use sin, cos, tan is SOH CAH TOA. In other words "for sine, multiply the opposite and hypotenuse, for cosine, multiply adjacent and hyp., and for tan, multiply opposite and adj.
start w/ solving for an angle (it doesn't matter which one but ill do A)
Bc you aren't given any side lengths, you have it a little easier by having to only use one method of SOH CAH TOA to solve. The method is sine
Using your calculator, type in sin(degree) or sin(51), and you should get
= 0.777145 OR 0.8
** make sure your calculator is is DEGREES not RADIANS
Now do this for the rest of the angles:
sin(7)= 0.1
sin(10)= 0.2
You have all the lengths (0.8, 0.1, 0.2) add them together to find the perimeter and if you want to find the area use Bh/2. But to find the area you must have a height, which you don't have
To find the height use formula: sqrt/( S(S-A)(S-B)(S-C)
A, B, C are the sides you've found using sine, and S is 1/2( A+B+C) or fast math is 0.55.
Plug in the values and solve :)
PLEASE HELP!!! exchange for my snpcht
A game show host offers to give you one penny on the first day, 2 pennies on the second day, 4 pennies the third day, and so on for the next 25 days.
Is this geometric or arithmetic?
How much money will you have at the end of the 25 days?
Answer:
it's geometric
Step-by-step explanation:
geometric equations change by a rate witch means you multiply to get to the next number in the sequence
arithmetic you add to get to the next number in the sequence
Answer:
Geometric
$335,544.31
Step-by-step explanation:
1, 2, 4, ..
This is Geometric progression with:
First term: 1
Common ratio: 4/2 = 2
S25 = 1(2²⁵-1)/(2-1) = 33,554,431
33,554,431 pennies or
33,554,431/100 = $335544.31
Help pls
Slope from graph
Find the surface area of the cube shown below.
Answer:
37.5 or 37 1/2
Step-by-step explanation:
The formula for finding surface area in a cube is A=6a^2
substituting 2.5 instead of a will result in this equation. A=6(2.5)^2
solving algebraically will then get you to your answer of 37.5
Answer:
S.A. = 37.5Step-by-step explanation:
Each cube has six faces. All faces are congruent and each of them is a square.
The fromula of an area of a square is:
[tex]A=s^2[/tex]
s - length of a side of a square
We have
[tex]s=2\dfrac{1}{2}[/tex]
Convert it to a decimal
[tex]s=2\dfrac{1}{2}=2.5[/tex]
Substitute to the formula of an area of a square:
[tex]A=(2.5)^2=(2.5)(2.5)=6.25[/tex]
The Surface Area of a cube:
[tex]S.A.=6A[/tex]
Substitute:
[tex]S.A.=6\cdot6.25=37.5[/tex]
It takes 8 hours for 4 men to paint a room.
How many men would be needed to paint the room in 2 hours?
Answer:
16 men would be needed to paint the room in 2 hours
Step-by-step explanation:
We can use proportion to solve the problem given, but first we need to determine whether it is a direct or indirect proportion.
If the number of men are increase, the time taken to do the work will decrease, If the number of men are decrease, the time taken to do the work will increase. Therefore, this is an indirect proportion.
We are going to arrange the data inversely.
Let x be the number of men needed to paint the room in two hours
8 hours = 2 hours
x = 4 men
Cross-multiply
2×x = 8×4
2x = 32
Divide both-side of the equation by 2
2x/2 = 32/2
x = 16 men
16 men would be needed to paint the room in 2 hours
Which algebraic expression has like terms? 9 n cubed minus 2 n + 3 minus 4 n squared 7 n cubed + 3 n minus 3 minus 6 n squared 7 n cubed + 4 n minus 3 n cubed minus 5 n squared 6 n cubed minus 4 n Superscript 4 Baseline + 6 n minus 5 n squared
Answer:
answer is c
Step-by-step explanation:
correct me if im wrong but it should be
Answer:
i believe its C
Step-by-step explanation:
Avery earned $68 at her job when she worked for 8 hours. What was her hourly pay rate in dollars per hour? Express your answer in simplest form.
Answer:
$8.5
Step-by-step explanation:
divide 68.00 by 8
Sunita creates a scale model of an aeroplane. The scale of the model is 5 cm to 13 m. Sunita's model has a wingspan of 24 cm. What is the wingspan of the real aeroplane?
To find the wingspan of the real aeroplane, we use the scale of 5 cm to 13 m and set up a proportion comparing the model's wingspan of 24 cm with the real wingspan, which results in a real wingspan of 62.4 m.
Sunita's scale model of an aeroplane has a wingspan of 24 cm, and the scale used is 5 cm to 13 m. To find the wingspan of the real aeroplane, we set up a proportion where 5 cm on the model represents 13 m in reality. The ratio would be:
Model scale: 5 cm
Real scale: 13 m = 1300 cm (since 1 m = 100 cm)
Now we find the corresponding real-life measurement for the 24 cm wingspan on the model:
(5 cm / 1300 cm) = (24 cm / Wingspan in cm)
To solve for the real wingspan, we cross-multiply and divide:
5 cm * Wingspan in cm = 1300 cm * 24 cm
Wingspan in cm = (1300 cm * 24 cm) / 5 cm
Wingspan in cm = 31,200 cm / 5 cm
Wingspan in cm = 6,240 cm
Converting back to meters (divide by 100 since 1 m = 100 cm):
Wingspan in m = 6,240 cm / 100 = 62.4 m
what is the value of p
13²=p
Answer:
169
Step-by-step explanation:
13 to the 2nd power is 169
hope this helps!!
p.s. could you please help me with my recent question??
What is the area of a regular hexagon with the radius of 8?
Answer:
The regular hexagon is made up of 6 equilateral triangles. Each has a side of 8 ft (the radius) Each area =8^2/4 sqrt 3 =16 sqrt 3 The hexagon's area =96sqrt3 sq ft
Step-by-step explanation:
I really need help with this, please help
Answer:
As the property of tangent line of circle, the 2 right triangles ABC and ADC are congruent.
=> AB = AD or j = k
j = 25x^2 + 100x + 9
k = 21x^2 + 100x + 18
=> 25x^2 + 100x + 9 = 21x^2 + 100x + 18
=> 4x^2 = 9
=> x^2 = 9/4 = (3/2)^2
=> x = 3/2 ( -3/2 value is not valid)
Hope this helps!
:)
The radius of a circle is 3.8 feet find the diameter
Answer:
7.6 feet
Step-by-step explanation:
The radius of a circle is halfway through. The diameter is the full way through. So what you do is multiply the radius by two. In this case, it's 3.8*2.
Answer:
7.6 ft
Step-by-step explanation:
The diameter of a circle is 2 times the length of the radius.
The formula to find the diameter is
d=2r
d= diameter
r= radius
Since the radius of this circle is 3.8, when multiplied by its self, it is 7.6 feet.
I hope this helped! :)
What is the value of x?
Answer:
x=2
Step-by-step explanation:
We will use the secant-secant Formula:
(whole secant) x (external part) = (whole secant) x (external part)
(1+x+4) * (x+4) = (11+x+1) * (x+1)
Combine like terms
(x+5) (x+4) = (x+12) (x+1)
FOIL
x^2 + 4x+5x + 20 = x^2 + x+ 12x + 12
Combine like terms
x^2 + 9 x + 20 = x^2 + 13 x + 12
Bring everything to the left
x^2 + 9 x + 20- (x^2 + 13 x + 12) = x^2 + 13 x + 12-( x^2 + 13 x + 12)
x^2 + 9 x + 20- (x^2 + 13 x + 12) =0
Distribute the minus sign
x^2 + 9 x + 20- x^2 - 13 x - 12 =0
Combine like terms
-4x +8 = 0
Subtract 8 from each side
-4x+8-8=0-8
-4x=-8
Divide each side by -4
-4x/-4 = -8/-4
x=2
1/6 6% 3/5 60% 6/100 which two values are equivalent to 0.6
Answer:
3/5 and 60%
Step-by-step explanation:
60% = 60/100= 3/5 =0.6
The two values which are equivalent to 0.6 are;
⇒ 3/5 , 60%
What is an expression?
Mathematical expression is defined as the collection of the numbers variables and functions by using operations like addition, subtraction, multiplication, and division.
Given that;
The numbers are,
⇒ 1/6 , 6%, 3/5, 6/100
Now,
Solve the numbers for the values are equivalent to 0.6 as;
A. 1/6 = 0.16
B. 6% = 6/100
= 0.06
C. 3/5 = 0.6
D. 60% = 60/100
= 0.6
E. 6/100 = 0.06
Thus, The two values which are equivalent to 0.6 are;
⇒ 3/5 , 60%
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Find the area of the shaded region. Round to the nearest tenth.
Answer:
3.5 square cm
Step-by-step explanation:
[tex]Area \: of \: both \: squares \\ = {2}^{2} + {3}^{2} \\ = 4 + 9 \\ = 13 \: {cm}^{2} \\ \\ Area \: of \: both \: right \: \triangle s \\ = \frac{1}{2} \times (2 + 3) \times 2 + \frac{1}{2} \times3 \times 3 \\ = 5 \times 1+ 1.5 \times 3 \\ = 5 + 4.5 \\ = 9.5 \: {cm}^{2} \\ \\ Area \: of \:shaded \: region \\ = Area \: of \: both \: squares\\ - Area \: of \: both \: right \: \triangle s \\ = 13 - 9.5 \\ \purple { \boxed{ \bold{Area \: of \:shaded \: region = 3.5 \: {cm}^{2} }}}[/tex]