Solve for the roots in the following equation. Hint: Factor both quadratic expressions.
(4+5x²-36)(2x²+9x-5) = 0
Answers
Using the provided quadratic expression and factorizing it, The answer is x = ± √6.4 or x = ± 2.51 and x = 1 or x = -2.5 .
What is a equation?An equation is a statement of equality between two expressions. It typically includes numbers and mathematical operations such as addition, subtraction, multiplication, and division. For example, the equation 2x + 3 = 7 is a statement that the value of the expression 2x + 3 is equal to the value of 7. Equations can also include variables, which represent unknown values that can be solved for.
What are roots of the equation?Roots of an equation are the values of the variable that make the equation true. For example, the roots of the equation x^2 + 2x - 3 = 0 are -1 and 3, because (-1)^2 + 2(-1) - 3 = 0 and 3^2 + 2(3) - 3 = 0. In general, finding the roots of an equation can be a difficult task and may require the use of mathematical techniques such as factoring, graphing, or numerical methods. Roots are also known as solutions or zeroes of an equation. They can be found by setting the equation equal to zero and solving for the variable.
(4+5x²-36) = 0 or (2x²+9x-5) = 0
Solving the first factor:
4+5x²-36 = 0
5x²-32 = 0
5x² = 32
x² = 6.4
x = ± √6.4
x = ± 2.51 or -2.51
Solving the second factor:
2x²+9x-5 = 0
x²+4.5x-2.5 = 0
(x-1)(x+2.5) = 0
x = 1 or x = -2.5
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Related Questions
For the following data set, find Q1, Q2, Q3 and the interquartile range.
15, 12, 23, 15, 7, 8, 21, 10, 12, 14, 16, 24, 19
Answers
Answer: q1=11 q2=15 q3=20
Step-by-step explanation:
( 25 points!!!)pls answer this all plss
Answers
Answer:
1. the second one.
2. 7 faces
3. im not positive but I believe its 9
4. 24/3 = 8 30/7 30/7= 4 and 2/7
5. underline the second, third, and 4th
6. 195 minutes. 3 hours and 25 minutes
7. 768
8. 4/2, 20/5, 16/2, 30/3
9. 20
10. 6 7/10, 10 4/5, 15 8/20
11. 0.2
12. 0.2
13. Monday and Friday
14. 3rd also known as the rhombus
15. between 6,000 and 7,000
16. equal to
Step-by-step explanation:
I hope this helps :))
One end of a cable is attached to the top of a flagpole and the other end is attached 6 feet away from the base of the pole.
If the height of the flagpole is 6 feet, find the length of the cable.
Answers
i think it 134
sorry if it wrong
Suppose that 2 balls are chosen without replacement from an urn containing 5 white and 8 red balls. Let X1 equal 1 if the 1st ball selected is red, and let it equal 0 otherwise. Let X2 equal 1 if the 2nd ball selected is red, and let it equal 0 otherwise. (i) Give the joint probability mass function of X1 and X2. (ii) Are X1 and X2 independent
Answers
Answer:
The probability mass function :
P(X1 = 1, X2 = 1) = 5/13 * 4/12 = 5/39
P(X1 = 1, X2 = 0) = 5/13 * 8/12 = 10/39
P(X1 = 0, X2 = 1) = 8/13 * 5/12 = 10/39
P(X1 = 0, X2 = 0) = 8/13 * 7/12 = 14/39
Step-by-step explanation:
Given :
Number of white balls = 5
Number of red balls = 8
Total number of balls = (5 + 8) = 13
P(X1 = 1, X2 = 1) = 5/13 * 4/12 = (5/13 * 1/3) = 5/39
P(X1 = 1, X2 = 0) = 5/13 * 8/12 = (5/13 * 2/3) =10/39
P(X1 = 0, X2 = 1) = 8/13 * 5/12 = (2/13 * 5/3) =10/39
P(X1 = 0, X2 = 0) = 8/13 * 7/12 =(2/13 * 7/3) = 14/39
A blue rope is 3 times as long as a red rope. A green rope is 4 times as long as the blue rope. If the total length of the three ropes is 563.84 meters, what is the length of the blue rope?
Answers
Answer:
105.72 meters
Step-by-step explanation:
We can set up a system of equations to represent the information given in the problem, and then use algebra to solve for the length of the blue rope. Let x be the length of the red rope.
According to the problem statement:
blue rope = 3 * red rope = 3x
green rope = 4 * blue rope = 4 * 3x = 12x
we know that:
red rope + blue rope + green rope = 563.84
x + 3x + 12x = 563.84
then we can solve for x:
16x = 563.84
x = 35.24
So the length of the red rope is 35.24 meters.
The length of the blue rope is 3x = 3 * 35.24 = 105.72 meters.
Three people are sitting on a bus. Julian is seated 4 meters directly behind Elena and 3 meters directly left of Isabella. How far is Elena from Isabella?
Answers
Answer:
sq root of 21=7
Step-by-step explanation:
we need to use Pythagoras theorem
so distance(isa-jul)^2 +distance(ele-jul)^2= distance(isa-ele)^2
now just do the square root and there you go.
A high school football quarterback has a lifetime pass completion rate of p = 0.15. A random sample of 15 of his games is selected. Which is the best description of the shape for the sampling distribution of p hat ?
skewed left
skewed right
uniformly distributed
approximately Normal
man just help me
Answers
Answer: I think it’s skewed right
Step-by-step explanation:
Part A
GEOMETRY Consider a trapezoid that has one base that measures five feet greater than its height. The other base is one foot less than twice its height. Let x represent the height.
a. Write an expression for the area of the trapezoid.
A=(blank)x^2 +(blank)x ft^2
PART B Write an expression for the area of the trapezoid if its height is increased by 4 feet
A=(blank)x^2+(blank)x+(blank)ft^2
Answers
The area of the trapezoid is 1.5x² + 2x. If the height is increased by 4 feet, the new area would be 1.5x² + 8x
How to solve an equation?An equation is an expression that shows the relationship between two or more numbers.
Let x represent the height of the trapezoid.
a) One base of trapezoid measures five feet greater than its height. Hence:
First base = x + 5
The other base is one foot less than twice its height, hence:
Second base = 2x - 1
Area = (1/2)(sum of bases) * height = (1/2)(x + 5 + 2x - 1)(x) = 1.5x² + 2x
b) The height is increased by 4 feet. New height = x + 4
First base = (x + 4) + 5 = x + 9
Second base = 2(x + 4) - 1 = 2x + 7
Area = (1/2)(sum of bases) * height = (1/2)(x + 9 + 2x + 7)(x) = 1.5x² + 8x
The area of the trapezoid is 1.5x² + 2x.
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(x+8)² find the product, please
Answers
Answer:
Step-by-step explanation:
Answer:
Step-by-step explanation:
Someone help me please :(
Answers
9514 1404 393
Answer:
A. ∠EAG and ∠BAC
Step-by-step explanation:
Vertical angles share a vertex and have opposite rays for sides.
Rays AE and AB are opposite; rays AG and AC are opposite. These are the only pairs of opposite rays in the figure, so the vertical angles must be constructed from one of the rays of the first pair and one of the rays of the second pair. ∠EAG and ∠BAC are a pair of vertical angles.
The other pair is ∠EAC and ∠BAG.
If you can help me with these 4 questions I'll give you brainliest :))
Answers
Answer:
Mode: None
Range: 14
Median: 5.5
Mean: 6
Hope this helps!
Answer:
9. The mode is: There is no mode all the numbers occur once.
10. The range is: 14
11. The median is: 5.5
12. The mean is: 6
Al uses a box in the shape of a rectangular prism as shown in the diagram to for his coin collection.
What is the volume of this box?
192in³
275in³
37512 in³
425in³
Answers
Answer:
4 x 8.5 x 12.5 =425 (multiple hight x width x length)
The volume of the box is [tex]425in^{3}[/tex]
A college has an acceptance rate of about 21% if 8700 students apply about how many will be accepted
Answers
Answer:
1827
Step-by-step explanation:
Answer:
1827
Step-by-step explanation:
21% of 8700 = 1827
Mark as Brainliest
Visually estimate the location of the centroid of the region shown. Then find the exact coordinates of the centroid.
y=49-x², y = 0
Answers
Therefore exact coordinates of Centroid = (0,3/2)
Define Centroid.The centroid of a flat figure or solid figure, also known as the geometric center or center of figure, in mathematics and physics, is the arithmetic mean position of all the points on the figure's surface. Any n-dimensional Euclidean object is included by the same definition.
What is Triangle?A polygon having three edges and three vertices is called a triangle. It is one of the fundamental geometric forms. Triangle ABC is the designation for a triangle with vertices A, B, and C. In Euclidean geometry, any three points that are not collinear produce a distinct triangle and a distinct plane.
This region is a parabola opening downward, with vertex at (0, 49) and a range of y values from 0 to 49. The region is symmetric about the y-axis, This means that the x-coordinate of the centroid is at 0.
To find the y-coordinate:
Integral from -√(49) to √(49) of (49-x²) x dx = [x²(49-x²)/3] from -√(49) to √(49) = (492√(49))/3 = (98√(49))/3
The area is integral from -√(49) to √(49) of (49-x²) dx = [x(49-x²)/2] from -√(49) to √(49) = (49*(2√(49)) - (2/3)(49^(3/2)))/2 = (49*(2*√(49)) - (98√(49))/3)/2
Therefore Centroid = (0, (98√(49))/(49*(2*√(49)) - (98√(49))/3)) = (0,3/2)
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hey could anyone solve this for me and make sure its correct
Answers
the slope goes by several names
• average rate of change
• rate of change
• deltaY over deltaX
• Δy over Δx
• rise over run
• gradient
• constant of proportionality
however, is the same cat wearing different costumes.
to get the slope of any straight line, we simply need two points off of it, let's use those provided
[tex]R(\stackrel{x_1}{5}~,~\stackrel{y_1}{7})\qquad S(\stackrel{x_2}{15}~,~\stackrel{y_2}{31}) ~\hfill \stackrel{slope}{m}\implies \cfrac{\stackrel{\textit{\large rise}} {\stackrel{y_2}{31}-\stackrel{y1}{7}}}{\underset{\textit{\large run}} {\underset{x_2}{15}-\underset{x_1}{5}}} \implies \cfrac{ 24 }{ 10 } \implies \cfrac{12 }{ 5 }[/tex]
keeping in mind that perpendicular lines have negative reciprocal slopes
[tex]\stackrel{~\hspace{5em}\textit{perpendicular lines have \underline{negative reciprocal} slopes}~\hspace{5em}} {\stackrel{slope}{ \cfrac{12}{5}} ~\hfill \stackrel{reciprocal}{\cfrac{5}{12}} ~\hfill \stackrel{negative~reciprocal}{ {\Large \begin{array}{llll} -\cfrac{5}{12} \end{array}} }}[/tex]
Step-by-step explanation:
the slope of a line is the ratio
y coordinate change / x coordinate change
when going from one point on the line to another.
the perpendicular slope is simply turning that ratio fraction upside down and flips the sign.
(5, 7) to (15, 31)
x changes by +10 (from 5 to 15).
y changes by +24 (from 7 to 31).
the slope (or gradient) is therefore
+24/+10 = 12/5
the perpendicular slope or gradient is then
-5/12
what is between 3.25 and 3.26
Answers
Answer:
3.251, 3.252, 3.253, 3.254, 3.255.......3.259
Step-by-step explanation:
Answer:
3.251, 3.252, 3.253, 3.254, 3.255, 3.256, 3.257, 3.258 , and 3.259
Step-by-step explanation:
Consider the piecewise function.
f (x) = StartLayout Enlarged left-brace first row 2 x, x less-than 1 second row negative 4, x = 1 third row x + 8, x greater-than 1 EndLayout
The function has a discontinuity at x = 1. What are Limit of f (x) as x approaches 1 minus and Limit of f (x) as x approaches 1 plus?
Limit of f (x) = 2 as x approaches 1 minus. Limit of f (x) = 9 as x approaches 1 plus.
Limit of f (x) = 9 as x approaches 1 minus. Limit of f (x) = 2 as x approaches 1 plus.
Limit of f (x) = negative 4 as x approaches 1 minus. Limit of f (x) = negative 4 as x approaches 1 plus.
Limit of f (x) D N E as x approaches 1 minus. Limit of f (x) D N E as x approaches 1 plus.
Answers
Answer: A.
= 2
= 9
Step-by-step explanation:
edge2021
Answer:
A
Step-by-step explanation:
EDGE
Eric spent $21.85, including sales tax, on 2 jerseys and 3 pairs of socks. The jerseys cost $6.75 each and the total sales tax was $1.03. Fill in the table with the correct prices.
Item Cost
Cost of each jersey $
Cost of each pair of socks $
Cost of sales tax $
Answers
Answer
Cost of each jersey $6.75
Cost of each pair of socks $4.69
Cost of sales tax $1.03
Step-by-step explanation:
To find the cost of the socks you fist add $6.75 + $1.03 and you get $7.78.Then you subtract that by $21.85.After that you do $14.07 divided by 3 and you get $4.69.
Choose the system of equations which matches the following graph:
Question 11 options:
1)
x − 2y = 8
2x + 4y = 12
2)
x − 2y = 8
2x − 4y = 12
3)
x + 2y = 8
2x + 4y = 12
4)
x + 2y = 8
2x − 4y = 12
Thanks for helping me!
Answers
Answer:
3
Step-by-step explanation:
the equations of the lines are y= -1/2x+3(red) and y= -1/2x+4(blue)
rearrange the equations to find a match
1. y= -1/2x+ 4
y= -1/2x+3
2. y= 1/2x+4
y= 1/2x+3
3. y= -1/2x+4
y= -1/2x+3
4. y= -1/2+4
y= 1/2x-3
Quentin places 58 fish in several tanks. If he places 8 fish in each tank, how many fish are not placed in the tanks but in a small fish bowl ins
Answers
Answer: 2 fishes
Step-by-step explanation:
From the question, we are informed that Quentin places 58 fish in several tanks and that he places 8 fish in each tank. This means the amount of tanks that'll be used will be:
= 58/8
= 7 2/8
Since 7 tanks will be used and each tank contains 8 fishes, the number of fishes will be: = 7 × 8 = 56
Since there are 58 fishes and 56 fishes are in the tank, there'll be a remainder of (58 - 56) = 2 fishes which will be placed in the small fish bowl.
5x35 65x76 what the the total
Answers
The solution to the above math arithmetic is 5115.
Addition and subtraction are what?Finding the sum and difference of two integers are the two main addition and subtraction arithmetic procedures. They are both the other's polar opposite. An ordered group of integers with a shared difference between each word is known as an arithmetic sequence. The common difference, for instance, between the mathematical series 3, 9, 15, 21, and 27 is 6.
What exactly is an algebraic question?This grouping contains percent difficulties, decimal recognition, addition, subtraction, multiplication, and division as well as fraction and percent equivalences and estimate issues.
For instance, 5 + 6 = 11 and 11 - 6 = 5.
5x35 + 65x76=5115
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2 Justin had 3 rolls of ribbon. He used of a roll of ribbon to tie a parcel and 5 of another roll of ribbon to tie a present. How many rolls of ribbon did he use in all? How many rolls of ribbon did Justin have left?
Answers
Answer:1 roll of ribbon left
Step-by-step explanation:
A biology class examined some flowers in a local meadow. They saw 36 flowers, of which 25% were perennials. How many perennial flowers did the students see?
Answers
Answer: nine
Step-by-step explanation: 36 - 25 = 9 or 25% x 1 + 36 = 9
Answer:
9
Step-by-step explanation:
1 first split 36 by 4 because 25% is 1/4
2 once when divided you should get 9 because 9x4 is 36
Write an expression for the cost of a drink and popcorn for one person
Answers
Answer:
popcorn is usually around 5 dollars and a drink is 3 so: 5 x 3
Step-by-step explanation:
Answer:
drink (d) + popcorn (p) = total cost
Is it possible to scan a screenshot problem?
Answers
Answer:
Yes it's possible you just got to crop it to your liking
Answer: upload it’s to your drive on your computer
Step-by-step explanation:
What is the measure of missing angle F?
Answers
Answer:
84 (:
Step-by-step explanation:
Plss help me!! ASAP, first answer gets Brainlist! Here your choices, : Quadrant I, Quadrant II, Quadrant III, And Quadrant IV.
Answers
please please help middle school math I really need it I will give you brainliest I promise! PICTURE INCLUDED!
Answers
The starting point is in quad Q and the checkpoint is in P. The checkpoint is the starting point reflected across the Y axis.
HELP MAN PLEASE IM CRYING I NEED HELP I WILL DO ANYTHING
Answers
Answer:
see below
Step-by-step explanation:
OK, so volume of LxWxH. so for shape 1 it's 14x8x7=784
Its asking for base times height which is 112 so the blanks are 112 then 7 then 784
the second one is the same. the base is 81 times the height of 9 which is 729
so the blanks are 81 than 9 than 729
the third base is 20 times height of 11 which is 220
so the blanks are 20 than 11 than 220
Find the missing length indicated. Leave your answer in simplest radical form.
Please help due today!!
Answers
The triangle given by 9, unknown, and 15 and the triangle given by 15, unknown, and x are similar triangles and therefore 9:15 = 15:x
X is 25 in this case