Answer:
[tex]4x^2+72x+259=0[/tex]
Step-by-step explanation:
If [tex]x_1[/tex] and [tex]x_2[/tex] are the solutions to the quadratic equation, then this equation can be written as
[tex](x-x_1)(x-x_2)=0[/tex]
In your case,
[tex]x_1=-9+\dfrac{\sqrt{65}}{2}\\ \\x_1=-9-\dfrac{\sqrt{65}}{2}[/tex]
Then the equation is
[tex]\left(x-\left(-9+\dfrac{\sqrt{65}}{2}\right)\right) \left(x-\left(-9-\dfrac{\sqrt{65}}{2}\right)\right)=0\\ \\\left(x+9-\dfrac{\sqrt{65}}{2}\right)\left(x+9+\dfrac{\sqrt{65}}{2}\right)=0\\ \\x^2+9x+\dfrac{\sqrt{65}}{2}x+9x+81+\dfrac{9\sqrt{65}}{2}-\dfrac{\sqrt{65}}{2}x-\dfrac{9\sqrt{65}}{2}-\dfrac{65}{4}=0\\ \\x^2+18x+\dfrac{259}{4}=0\\ \\4x^2+72x+259=0[/tex]
The sum of two numbers is 60 and their quotient is 4. what are the two numbers
Final answer:
The sum of the two numbers is 60 and their quotient is 4. Using the substitution method, we find that the two numbers are 48 and 12.
Explanation:
Let's call the two numbers x and y. We're given that the sum of the two numbers is 60, so we can write the equation:
x + y = 60
We're also given that their quotient is 4, so we can write the equation:
x / y = 4
To solve this system of equations, we can use the substitution method. Solving the second equation for x, we get:
x = 4y
Substituting this value of x into the first equation, we get:
4y + y = 60
Combining like terms, we have:
5y = 60
Dividing both sides by 5, we find:
y = 12
Substituting this value of y back into the equation x = 4y, we get:
x = 4(12)
Simplifying, we find:
x = 48
So the two numbers are 48 and 12.
How many solutions does this system of equation have x+1=2y x-1=2y
Answer:
0
Step-by-step explanation:
These are two lines with equal slopes and different y intercepts so they will be parallel and will never intersect
What is the distance, on a coordinate plane, between the points G(2.-3) and D(2, 4)?
Answer:
Therefore ,the distance, on a coordinate plane, between the points G(2.-3) and D(2, 4) is [tex]GD = 7\ units[/tex]
Step-by-step explanation:
Given:
point G( x₁ , y₁) ≡ ( 2 ,-3)
point D( x₂ , y₂) ≡ (2 , 4)
To Find:
Distance between GD=?
Solution:
Distance Formula between two point is given by
[tex]l(GD) = \sqrt{((x_{2}-x_{1})^{2}+(y_{2}-y_{1})^{2} )}[/tex]
Substituting the values we get
[tex]l(GD) = \sqrt{((2-2)^{2}+(4-(-3))^{2} )}[/tex]
[tex]l(GD) = \sqrt{((0)^{2}+(4+3))^{2} )}=\sqrt{49}=7\\l(GD)=7\ units[/tex]
Therefore ,the distance, on a coordinate plane, between the points G(2.-3) and D(2, 4) is [tex]GD = 7\ units[/tex]
A total of $6000 was invested, part of it at 3% interest and the remainder at 8%. If the total yearly interest amounted to $380, how much was invested at each rate?
$ 2000 is invested at 3 % interest and $ 4000 is invested at 8 % interest
Solution:
Given that, total of $6000 was invested
Let "x" be the amount invested at 3 % interest
Then, (6000 - x) is the amount invested at 8 % interest
Given that,
The total yearly interest amounted to $380
Then, we can frame a equation as:
[tex]x \times 3 \% + (6000 - x) \times 8 \% = 380[/tex]
Solve the above expression for "x"
[tex]x \times \frac{3}{100} + (6000-x) \times \frac{8}{100} = 380\\\\0.03x + (6000-x) \times 0.08 = 380\\\\0.03x + 480 - 0.08x = 380\\\\-0.05x = -100\\\\\text{Divide both sides by -0.05 }\\\\x = 2000[/tex]
Thus, $ 2000 is invested at 3 % interest
(6000 - x) = 6000 - 2000 = 4000
$ 4000 is invested at 8 % interest
Please help me due today i really need help PWZZZZ someone i beg of u
Answer:
Step-by-step explanation:
8)Volume of cylinder = πr²h= π*3*3*10 =90π cubic inches
Volume of cone = 1/3πr²h = π*3*3*5/3= 15π cubic inches
Volume of rocket = 90π + 15π = 105π cubic inches
9) Matt made an error. radius = diameter/2 = 15/2= 7.5 cm.Instead using 7.5 in volume formula, he used diameter.
How do you do this math problem??
BRAINLEST for anyone who helps and explains!!
Answer:
It is angle k and angle l
Step-by-step explanation:
When opposite sides are given, especially for a right triangle, the longer the length the bigger the angle. The hypotenuse, which is across the right angle is always longest. The shortest side will always have the smallest angle. Check the image if it helps.
Sara's earnings vary directly with the number of hours she works. The data is shown in the graph. If x = number of hours worked, and y = earnings, which equation models Sara's direct variation?
A) y = 5x
B) y = 10x
C) y = 5 + x
D) y = 10 + x
Answer:
answer is y=10x
Step-by-step explanation:
multiply time by 10 to equal models sara's direct variaton.
The equation models Sara's direct variation if, Sara's earnings vary directly with the number of hours she works, which is y = 10x, so option B is correct.
What is a graph?A collection of objects is arranged in a graph, where some object pairings are conceptually "linked." Each pair of connected vertices is referred to as an edge, and the objects are represented by mathematical abstractions known as vertices.
Given:
Sara's earnings vary directly with the number of hours she works,
x = number of hours worked, and y = earnings,
The equation for the above statement can be written as shown below,
earnings = number of hours worked × salary
Assume the salary is a then,
y = ax
If she gets a salary of $10 then,
y = 10x
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0.48 = log x solve for x
Answer: x≈3
Step-by-step explanation:
0.48 = log x , this could also be written as :
[tex]log_{10}[/tex] x = 0.48 , that is
x = [tex]10^{0.48}[/tex]
x = 3.01995172
x≈ 3
The solution to the equation 0.48 = log x is approximately 3.02 after converting it from logarithmic form into exponential form and calculating 10 to the power of 0.48.
Explanation:To solve the logarithmic equation 0.48 = log x we have to rewrite this equation in exponential form. A logarithm log_b(x) = y in exponential form is represented as b^y = x. Considering that in your question it's not specified, this likely means a base of 10 is being used. Hence, the equation 0.48 = log x can be converted into exponential form: 10^0.48 = x.
Performing the calculation with a calculator (or by hand if you know how), we find x ≈ 3.02. Therefore, the solution for x in the given equation is approximately 3.02.
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Need t in degrees not just solve for t
An exterior angle is equal to the sum of the two opposite inside angles.
T + 31 = t + t-29
Simplify:
T + 31 = 2t -29
Add 29 to both sides:
T + 60 = 2t
Subtract 1t from both sides:
T = 60
You visit an animal rescue in Australia that serves primarily kangaroos and dingoes. You ask the zookeeper how many of each animal they have, and she decided to test your reasoning ability. She tells you that when she feeds the animals she counts a total of 116 feet where kangaroos have two feet and dingoes have 4 feet. She can also count a total of 34 heads. How many kangaroos and dingoes are at this animal rescue?
There are 10 kangaroos and 24 dingoes in this animal rescue.
Step-by-step explanation:
Given,
Total head count = 34 heads
∴ Kangaroos + Dingoes = 34
Let us assume,
Number of kangaroos as "x" and number of dingoes as "y"
The equation can be framed as x + y = 34
The number of feet for kangaroo = 2 feet
The number of feet for dingoes = 4 feet
The total number of feet = 116 feet
So, the equation can be framed as 2x + 4y = 116
Step 1 : Muliply the 1st equation by 2.
The new equation is 2x + 2y = 68
step 2 : Subtract the above equation with the second equation.
2x + 2y = 68
-2x - 4y = -116
-2y = -48
step 3 : Therefore, y =24. Substitute y=24 in the 1st equation.
x + 24 = 34
x = 34-24
x = 10
Kangaroos, x = 10 kangaroos
Dingoes, y = 24 dingoes
Final answer:
To find the number of kangaroos and dingoes, we can use a system of equations to solve for their values. Given the number of feet and heads, we can form equations to represent these quantities. Solving these equations simultaneously yields the solution of 10 kangaroos and 24 dingoes.
Explanation:
To solve this problem, we can use a system of equations. Let's denote the number of kangaroos as 'k' and the number of dingoes as 'd'. We are given two pieces of information:
1. The total number of feet is 116, where each kangaroo has 2 feet and each dingo has 4 feet. So, the equation would be: 2k + 4d = 116.
2. The total number of heads is 34. Since each animal has only one head, the equation would be: k + d = 34.
We can solve these equations simultaneously to find the values of k and d. Multiplying the second equation by 2, we get: 2k + 2d = 68. Subtracting this equation from the first equation, we have: (2k + 4d) - (2k + 2d) = 116 - 68. Simplifying, we get: 2d = 48. Dividing both sides by 2, we find that d = 24.
Substituting this value back into the second equation, we can find k: k + 24 = 34, k = 10.
Therefore, there are 10 kangaroos and 24 dingoes at the animal rescue.
use the method of completing the square to write the equations of the given parabola in this form:
(y-k)=a(x-h)^2
where a =0, (h,k) is the vertex, and x=h is the axis of symmetry.
Find the vertex of this parabola: y=-4x^2+8x-12
Answer:
The vertex is the point (1,-8)
Step-by-step explanation:
we have
[tex]y=-4x^{2} +8x-12[/tex]
Convert to vertex form
step 1
Group terms that contain the same variable, and move the constant to the opposite side of the equation
[tex]y+12=-4x^{2} +8x[/tex]
step 2
Factor the leading coefficient
factor -4
[tex]y+12=-4(x^{2} -2x)[/tex]
step 2
Complete the square. Remember to balance the equation by adding the same constants to each side
[tex]y+12-4=-4(x^{2} -2x+1)[/tex]
[tex]y+8=-4(x^{2} -2x+1)[/tex]
step 3
Rewrite as perfect squares
[tex]y+8=-4(x-1)^{2}[/tex]
therefore
The vertex is the point (1,-8)
A certain forest covers an area of 4500 km^2. Suppose that each year this area decreases by 8.75%. What will the area be after 5 years?
The area of forest after 5 years is 2846.93 square kilometer
Solution:
Given that, A certain forest covers an area of 4500 square kilometer
Suppose that each year this area decreases by 8.75%
To find: Area after 5 years
The decrease function is given as:
[tex]y = A(1-r)^t[/tex]
Where,
y is the value after t years
A = initial amount
r = decreasing rate in decimal
t is the number of years
Here in this sum,
A = 4500
t = 5 years
[tex]r = 8.75 \% = \frac{8.75}{100} = 0.0875[/tex]
Substituting the values in formula,
[tex]\begin{aligned}&y=4500(1-0.0875)^{5}\\\\&y=4500(0.9125)^{5}\\\\&y=4500 \times 0.632651\\\\&y=2846.93\end{aligned}[/tex]
Thus the area of forest after 5 years is 2846.93 square kilometer
1. Mr. Jackson buys a pair of shoes for $41.12. He
hands the clerk a $50 bill.
Answer:
Mr Jackson should get $8.88 back.
Step-by-step explanation:
$50 - $41.12 = $8.88
x times x + 3 to the power of 2 equals 48 , what is x ?
Answer:
I believe the answer to this question is: X=square root(39), and square root(-39).
Write an algebraic expression: X squared less than 15
Final answer:
An algebraic expression that represents 'x squared is less than 15' can be written directly as 'x² < 15', without additional mathematical operations.
Explanation:
The question asks for an algebraic expression that represents the inequality 'x squared is less than 15'. This is straightforward to write and does not require completing the square or solving a quadratic equation. The algebraic expression that correctly represents this inequality is simply x² < 15.
To explain further, the inequality suggests that the square of x (x²) must be less than the value 15. We do not need to perform any additional steps or manipulations like factoring or applying the quadratic formula, as the expression represents a basic inequality in its simplest form.
What is
AE?
Enter your answer in the box.
Answer:
[tex]AE=20\ units[/tex]
Step-by-step explanation:
we know that
If two triangles are similar, then the ratio of its corresponding sides is proportional and its corresponding angles are congruent
In this problem
Triangles AEB and DEC are similar by AA Similarity Theorem
so
[tex]\frac{AB}{DC}=\frac{AE}{DE}[/tex]
substitute the given values and solve for x
[tex]\frac{10}{4}=\frac{2x+10}{x+3}[/tex]
Multiply in cross
[tex]10x+30=8x+40\\10x-8x=40-30\\2x=10\\x=5[/tex]
Find the length side AE
[tex]AE=2x+10[/tex]
substitute the value of x
[tex]AE=2(5)+10=20\ units[/tex]
What is the product of (x-3) and (x+7)
Answer: (x−3)(x+7)
=(x+−3)(x+7)
=(x)(x)+(x)(7)+(−3)(x)+(−3)(7)
=x^2+7x−3x−21
=x^2+4x−21
The product of (x-3) and (x+7) is x² + 4x - 21
The product of (x - 3) and (x + 7) can be found as follows:
(x - 3)(x + 7)
open the bracket by multiplying
Therefore,
x(x) +x(7) - 3(x) - 3(7)
x² + 7x - 3x - 21
combine like terms
x² + 4x - 21
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Which of the following inequalities matches the graph?
A.) 3x - > 4
B.) 3x - 4y < 2
C.) 3x - 2y < 4
D.) The Correct inequality is not listed.
Answer:
c
Step-by-step explanation:
going negative stops at 4
CAN YALL HELP ME WITH THIS ONE PLEASE...
Answer:
x = 130°
Step-by-step explanation:
Segment AC tangent to circle O then ∠A = 90°
Segment BC tangent to circle O then ∠B = 90°
finally ,
x = 360 -(90+90+50) = 360-230 = 130
Answer:
x = 130°
Step-by-step explanation:
Evaluate C7, 5).
A. 21
B. 42
C. 1,008
=======================================
C(n, r) = (n!)/(r!*(n-r)!) is the combination formula
C(7, 5) = (7!)/(5!*(7-5)!)
C(7, 5) = (7!)/(5!*2!)
C(7, 5) = (7*6*5!)/(5!*2!)
C(7, 5) = (7*6)/(2!) ..... note the "5!" terms divided and canceled
C(7, 5) = (7*6)/(2*1)
C(7, 5) = 42/2
C(7, 5) = 21
19.25 as an equation
Graph the line y=Mx+b for the given values m=-2/3, b=-1
Answer:
See below for the graph:
Step-by-step explanation:
Find the equation of the line which has slope of -5 and y-intercept 7. Give your answer in the form y=mx+b
Answer:
y = - 5x + 7
Step-by-step explanation:
The equation of a line in slope- intercept form is
y = mx + b ( m is the slope and b the y- intercept )
Here m = - 5 and b = 7, thus
y = - 5x + 7 ← equation of line
Good morning ☕️
Answer:
y = -5x + 7Step-by-step explanation:
y=mx+b
m = slope = -5
b = y-intercept = 7
then the equation is : y = -5x + 7
:)
How much interest is earned in one year on $5000 at an interest rate of 3%
If we're talking about simple interest (and not compound interest), then
i = P*r*t
i = 5000*0.03*1
i = 150
$150 in simple interest is earned for the year----------
notes:
P = principal = amount invested or deposited = 5000r = 0.03 is the decimal form of 3%t = number of years that pass by = 1The interest earned in one year on $5,000 at an interest rate of 3% is $150. To find the interest earned on $5000 at 3% for one year, multiply the principal amount by the interest rate and time.
To calculate the interest earned with simple interest:
Interest = Principal x Rate x Time
Interest = $5000 x 0.03 x 1 year = $150
8-4 skills practice trigonometry
Answer:
what do you need?
Step-by-step explanation:
Answer:
4
Step-by-step explanation:
How many x-intercepts appear on the graph of this polynomial function?
f(x)= x4-5x2
The x-intercepts appear on this polynomial are 3 x intercepts.
Step-by-step explanation:
To find the x intercepts of the polynomial [tex]f(x)=x^{4} -5x^{2}[/tex] is by equating [tex]f(x)=0[/tex]
Thus, the equation becomes
[tex]\begin{array}{r}{x^{4}-5 x^{2}=0} \\{x^{2}\left(x^{2}-5\right)=0}\end{array}[/tex]
Equating, we get,
[tex]x^{2}=0,\left(x^{2}-5\right)=0[/tex]
[tex]x=0[/tex], [tex]\begin{aligned}x^{2}-5 &=0 \\x^{2} &=5 \\x &=\pm \sqrt{5}\end{aligned}[/tex]
Thus, the x-intercepts are [tex]x=0, x=\sqrt{5} , x=-\sqrt{5}[/tex]
Hence, the x-intercepts appear on this polynomial are 3 x intercepts.
Answer:
1 x-intercepts
Step-by-step explanation:
has same question on a test
You solved a linear system with two equations and two variables and got the equation -6=-6. How many solutions does the systems of equations have?
Answer:
The system of equations will have an infinite number of solutions.
Step-by-step explanation:
i) when we arrive at a solution of a linear system with two equations and two
variables and the solution of the equation does not give the value of any
variable but rather is in the form of an identity like the one given, that is
-6 = -6, then we can say that the two equations are exactly the same and
that the system of equations will have an infinite number of solutions.
Rayshawn has a certain amount of money if he spends $20 then he has 1/3 of the original amount how much money did Rayshawn have originally
Answer:
Rayshawn originally had $30.
Step-by-step explanation:
i) Rayshawn has a certain amount of money. Let us say this amount is $x.
ii) Rayshawn spends $20 which means that he is left with $(x - 20)
iii) it is also given that amount of money left after spending $20 is [tex]\dfrac{1}{3}[/tex] of the original amount, $x, the amount remaining is [tex]\dfrac{\$x}{3}[/tex].
iv) from the information given in ii) and iii) we get
$(x - 20) = [tex]\dfrac{\$x}{3}[/tex], Therefore we get 3x - 60 = x , therefore 2x = 60,
Therefore x = $30. Rayshawn originally had $30.
Therefore, Rayshawn had $60 initially.
If Rayshawn spends $20 and ends up with 1/3 of the original amount, we can deduce that $20 represents 2/3 of the original amount.
since 1 - 1/3 = 2/3. Thus, each part (1/3) of the original amount corresponds to $20. Consequently, to find the original amount, we multiply $20 by 3, yielding $60. Therefore, Rayshawn originally had $60. This conclusion emerges from understanding that after spending $20, Rayshawn retains 1/3 of his original funds, implying that the $20 spent was equal to 2/3 of his initial sum. Thus, the inverse operation, multiplying by 3, unveils the original amount. Therefore, Rayshawn had $60 initially.
A family buys 4 airline tickets online. The family buys travel insurance that cost $19 per ticket. the total cost is $688. Let x represent the price of one ticket. Write an equation for the total cost. then find the price of one ticket
Answer: 4x + 76 = 688, $153 per ticket
Step-by-step explanation:
there are 4 tickets but you don't know the price of the tickets. Let x represent the price. Insurance costs $19. They got insurance ($19) on all 4 tickets (19 x 4) to get a insurance total of $76.
To get the price of one ticket we need to solve the equation.
4x + 76 = 688
subtract 76 from both sides.
4x = 612
divide by 4.
x = 153
each ticket costs $153
Final answer:
The price of one airline ticket, without insurance, is $153. This was found by setting up an equation for the total cost (4 tickets plus insurance for each at $19 per ticket) and solving for the price of one ticket.
Explanation:
To solve the problem, we first set up an equation to represent the total cost for the family's purchase of 4 airline tickets with travel insurance. We let x represent the price of one ticket, and since the travel insurance costs $19 per ticket, the cost of insurance for one ticket can be represented as 19 + x. There are 4 tickets, so the total cost of insurance for four tickets is $19 multiplied by 4 (which equals $76). Therefore, the equation for the total cost is:
Total Cost = 4x (price of tickets) + $76 (cost of insurance for all tickets)
According to the question, the total cost for the family is $688. So we can set up the equation:
4x + 76 = $688
To find the value of x, we subtract 76 from both sides of the equation:
4x = $688 - $76
4x = $612
Now divide both sides by 4 to solve for x:
x = $612 / 4
x = $153
Therefore, the price of one ticket is $153.
Audrey needs 2.4 pounds if flour for birthday cakes and 3.75 pounds of flour for wedding cakes. if she plans on baking 72 birthday cakes and 5 wedding cakes, how many pounds of flour will she need?
Answer:
She will need 191.55 pounds of flour.
Step-by-step explanation:
Given:
Audrey needs 2.4 pounds if flour for birthday cakes and 3.75 pounds of flour for wedding cakes.
If she plans on baking 72 birthday cakes and 5 wedding cakes.
Now, to find pounds of flour will she need.
So, the pounds of flour for 72 birthday cakes:
[tex]2.4\times 72[/tex]
[tex]=172.8\ pounds.[/tex]
And, the pounds of flour for 5 wedding cakes:
[tex]5\times 3.75[/tex]
[tex]=18.75\ pounds.[/tex]
Now, to get the pounds of flour she need we add the pounds of flour to make 72 birthday cakes and 5 wedding cakes:
[tex]172.8+18.75[/tex]
[tex]=191.55\ pounds.[/tex]
Therefore, she will need 191.55 pounds of flour.