The two x values that make up the equation's roots are:
x = [tex]\frac{5+\sqrt{13} }{2}[/tex]
x =[tex]\frac{5-\sqrt{13} }{2}[/tex]
These two items are the two answers to the problem.
what are equations?A mathematical definition of an equation is a claim that two expressions are equal and joined by the equals sign.
Two expressions are combined in an equation using an equal symbol ("="). The "left-hand side" and "right-hand side" of the equation are the two expressions on either side of the equals sign. Typically, we consider an equation's right side to be zero. As we can balance this by deducting the right-side expression from both sides' expressions, this won't reduce the generality.
from the question:
We can use the quadratic formula to determine the roots of the equation [tex]x^2 - 5x + 3 = 0.[/tex]
x = (-b ± [tex]\frac{b^2 - 4ac}{2a}[/tex])
where the quadratic equation's coefficients are a, b, and c.
With respect to our equation, we have:
a = 1, b = -5, and c = 3
These values are entered into the quadratic formula as follows:
x = (-(-5) ± [tex]\sqrt(-5)^2}[/tex] - 4(1)(3))) / 2(1)
x = (5 ± [tex]\frac{{13}}{2}[/tex])
The two x values that make up the equation's roots are:
x = [tex]\frac{5+\sqrt{13} }{2}[/tex]
x =[tex]\frac{5-\sqrt{13} }{2}[/tex]
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I just need my brain reworked on how to do this
The number of square feet of wallpaper that Austin will need for the large wooden storage boxes would be = 1,296 ft².
How to calculate the amount of wallpaper needed by Austin?To calculate the amount of wallpaper needed, we should find the area of the rectangular prism.
The formula for the area of rectangular prism = 2 (lh +wh + lw ).
Where;
Length (l) = 6ft
width (w) = 3ft
Height (h) = 6ft
area = 2( 6×6 + 3×6 + 6×3)
= 2( 36+18+18)
= 2( 72)
= 144 ft²
Therefore the amount of wallpaper needed = 144× 9 = 1296 ft².
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9feet to3 3/8inches ratio
Answer:
32 : 1
Step-by-step explanation:
dimensions of the parts of the ratio must be in the same units
convert 9 feet to inches
1 foot = 12 inches
then
9 feet = 9 × 12 = 108 inches
then ratio
9 feet : 3 [tex]\frac{3}{8}[/tex] inches
= 108 inches : 3 [tex]\frac{3}{8}[/tex] inches ( change mixed number to improper fraction )
= 108 : [tex]\frac{27}{8}[/tex] ( multiply both parts by 8 to clear the fraction )
= 864 : 27 ( divide both parts by 27 )
= 32 : 1
In a survey of 3,100 people who owned a certain type of car, 1,705 said they would buy that type of car again. What percent of the people surveyed were satisfied with the car?
55.0% of the people surveyed were satisfied with the car.
What is percentage, how to solve it?We must divide the value by the entire value to find the percentage, and then multiply the resulting number by 100.
Formula for percentages is (Value/Total value) x 100.
If two values are presented to us, we must determine the percentage difference between them.
Given that, 1,705 said they would buy that type of car again.
Thus, to find people who were satisfied with the car:
Percentage = (Number of satisfied people / Total number of people) x 100%
Percentage = (1,705 / 3,100) x 100% = 55.0%
Hence, 55.0% of the people surveyed were satisfied with the car.
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How to do a area problem
Answer: 205
Step-by-step explanation:
ok, the height of this thing is 22 so lets start whit the top. So the height of this thing is 17 not including the triangles at the top. And 22-17=5 so the height of these triangles is 5 and the base is 10 because if you dd the two 5s and subtract it from the whole base you get 10 and 10 x 7 is 70 /2 is 35 now for the rectangle in the middle the height is 7 and we alr know the base which is 10 so 7x10 is 70 70+35=105 ok now the last one 10 x 20= 200 +105= 205
Answer:
Area=295cm²
Step-by-step explanation:
please mark as brainliest
What is the best estimation of the equation 7 8 − 6 11 ? Drag the numbers into the boxes. Numbers may be used once, twice, or not at all. 1/42011/21/8 − =
For the equation 7/8 - 6/11, the best estimation is obtained as (1) - (1/2) = 1/2
To estimate 7/8 - 6/11, we need to find a common denominator for the two fractions.
One way to do this is to multiply the numerator and denominator of each fraction by the denominator of the other fraction.
So, we have -
(7/8) x (11/11) - (6/11) x (8/8)
= 77/88 - 48/88
= (77 - 48)/88
= 29/88
To simplify this fraction, we can look for common factors in the numerator and denominator.
The fraction 7/8 is almost 1 and the fraction 6/11 is almost 1/2.
Therefore, the best estimation of the equation 7/8 − 6/11 is -
(1) - (1/2) = 1/2
Therefore, the equation is obtained as (1) - (1/2) = 1/2.
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Find the degree of this polynomial.
8t5 + 5t4
Answer:
5
Step-by-step explanation:
The degree of a polynomial is the highest degree of its terms.
Identify the term with the largest exponent on the variable
Identify the degree of each terms
The degree of 8t5 is 5
The degree of 5t4 is 4
Degree of polynomial = 5
The sum of 4 consecutive integers is -326. Find the largest integer
[tex]x + (x+1) + (x+2) + (x+3) = -326\\[/tex]
[tex]4x + 6 = -326[/tex]
[tex]4x = - 326-6[/tex]
[tex]4x = -332[/tex]
[tex]x = -332/4 \implies x = - 83[/tex]
the integers are:
[tex]-83 < -82 < -81 < -80[/tex]
the largest integer is: -80
Graph the following functions and determine where F(x) = G(x). State the x values only. Select all that apply.
a. 6.767
b. 0
c. 2.922
d. -2
The x-coordinate at which F(x) = G(x) is 0.667. By graphing the functions, the answer has been discovered.
What does graphing a function mean?Making a graph of the pertinent function is the first step in graphing a function. The function equation will be satisfied by a curve if it reflects the function at that location.
According to the given information:We are given two functions as f(x) = log (2x) and g(x) = 3x - 2
The graph of the given functions has been plotted and attached below.
In the graph, the red line represents the log function i.e. f(x) and the blue line represents the linear function i.e. g(x).
From the graph, we can observe that the two functions meet at two points which are (0.667, 0) and (0, -2).
Hence, the x value where F(x) = G(x) is 0.667.
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Please help me anyone with this question ?!!!??!!
Answer:
Believe it's just a
Step-by-step explanation:
Because
The area of the triangle is 45.5 square units and the height of the triangle is given. What is the measurement of the base?
For the triangle which is mentioned above the measurement of the base will be 10 cm.
What is a Triangle?
With three sides, three angles, and three vertices, a triangle is a closed, two-dimensional object. A polygon also includes a triangle.
The area of a triangle is A=1/2b*h
Here, A is the area of triangle =45.5 square units
b will be the base(NEED TO FIND)
h will be the height = 9.1cm
Substituting, 45.5 = (1/2)×b×9.1
b= (45.5×2)/9.1
b= 10 cms
The base value will be: 10cms
The Complete Question: The area of the triangle is 45.5 square units and the height of the triangle is given as 9.1 cm. What is the measurement of the base?
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Find the value of k such that the line through (7, 1) and (k, 7) is parallel to the line y=3x.
The value of the k is 5
The slope of Parallel lines:The slope of a line is a measure of its steepness or inclination. It tells us how much the line rises or falls as we move horizontally along it.
Parallel lines will have the same slope. That means if two lines are parallel, they have the same steepness or inclination.
Here we have
Equation of the line is y = 3x --- (1)
Equation(1) is in the form y = mx + x
The slope of the line (1) = 3
Let y = m₁x + c is the line that is parallel to line (1)
Since the slope of the parallel lines are equal
=> y = 3x + c --- (2)
Given that the line passes through (7, 1)
=> 1 = 3(7) + c
=> c = - 21 + 1
=> c = - 20
Hence, the equation of the line is y = 3x - 20 --- (3)
It is given that the line will also pass through the point (k, 7)
=> 7 = 3k - 20
=> 3k = 27
=> k = 9
Therefore,
The value of the k is 9
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How much would it cost for a customer to purchase 20 subscriptions for each of their 20 employees after a free 30-day trial period, with each subscription costing $10 per month for a yearly commitment? Additionally, they will need 1 extra subscription for a different service for every two employees, with each of these subscriptions costing $5 per month for a yearly commitment. What would be the total cost for the customer for the entire year
The total cost for the customer for the entire year is $48,600.
How to the total cost for the customer for the entire yearThe customer wants to purchase 20 subscriptions for each of their 20 employees, so they need a total of 20 x 20 = 400 subscriptions.
Each subscription costs $10 per month for a yearly commitment,
so the cost for one subscription for a year would be $10 x 12 = $120.
Therefore, the total cost for 400 subscriptions for a year would be $120 x 400 = $48,000.
In addition, they need 1 extra subscription for a different service for every two employees, so they need 20 / 2 = 10 extra subscriptions.
Each extra subscription costs $5 per month for a yearly commitment, so the cost for one extra subscription for a year would be $5 x 12 = $60.
Therefore, the total cost for 10 extra subscriptions for a year would be $60 x 10 = $600.
Adding the cost of the extra subscriptions to the cost of the regular subscriptions, the total cost for the customer for the entire year would be $48,000 + $600 = $48,600.
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7. A standard dartboard has a radius of 170 mm and is split into 20 equal sections. What is the arc length of a single section on a dartboard rounded to the nearest millimeter?
The arc length of a single section on a dartboard rounded to the nearest millimeter is 53 mm.
What is equations ?
In mathematics, an equation is a statement that two expressions are equal. It typically involves one or more variables that can take on different values, and the goal is often to solve for the value(s) of the variable(s) that make the equation true.
According to given conditions :The total circumference of the dartboard is given by:
C = 2πr
where r is the radius of the dartboard.
Substituting the given values, we get:
C = 2π(170 mm)
C = 1068.18 mm
Dividing the circumference by the number of sections, we get the arc length of a single section:
Arc length = C/20
Arc length = 1068.18 mm/20
Arc length ≈ 53.41 mm
Rounding this to the nearest millimeter, we get:
Arc length ≈ 53 mm
Therefore, the arc length of a single section on a dartboard rounded to the nearest millimeter is 53 mm.
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Two containers designed to hold water are side by side, both in the shape of a cylinder. Container A has a diameter of 26 feet and a height of 20 feet. Container B has a diameter of 36 feet and a height of 19 feet. Container A is full of water and the water is pumped into Container B until Container A is empty.
no websites or links
After the pumping of Container A's water into Container B, the volume of water in Container B is 6,286 feet³.
What is the volume?The volume refers to the amount of space in a container.
The volume of a container can be determined using the following formula: πr²h, where:
π = pi = 22/7r = radius = diameter/2h = height.Container A:Diameter = 26 feet
Height = 20 feet
The volume of water in Container A = πr²h
r = radius = diameter/2
= 20/2 = 10 feet
Volume = 22/7 x 10 x 10 x 20
= 22/7 x 100 x 20
=6,285.7
= 6,286 feet³
Container B:Diameter = 36 feet
Height = 19 feet
Thus, the volume of Container B after the pumping, which is equal to the volume of water in Container A, is 6,286 feet³.
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Question Completion:After the pumping of Container A's water into Container B, what is the volume of water in Container B?
Keisha can ride her skateboard two and one half miles an hour how far can you ride in 3/4 of an hour
Answer:
1 and 7/8.
Step-by-step explanation:
Two and a half= 5/2
5/2 x 3/4 = 15/8 = 1 7/8
Determine whether the study is an experiment or an observational study, and then identify a major problem with the study.
In a survey, 1465 Internet users chose to respond to this question posted on a newspaper's electronic edition: "Is news online as satisfying as print and TV news?" 52% of the respondents said "yes."
Question content area bottom
Part 1
This is an
▼
experiment
observational study
because the researchers
▼
do not attempt to modify
apply a treatment to
the individuals.
Part 2
What is a major problem with the study?
A.
This is a convenience sample with voluntary response, which has a high chance of leading to bias.
B.
There is no blinding or replication, which has a high chance of leading to bias.
C.
The sample is not very large.
D.
The results apply only to Internet users.
This is an observational study because the researchers do not attempt to modify or apply a treatment to the individuals. Major problem with the study is A.
What is Statistics?Statistics is the discipline that concerns the collection, organization, analysis, interpretation, and presentation of data.
This is a convenience sample with voluntary response, which has a high chance of leading to bias.
The survey relies on self-selection, meaning that only those who were interested in responding to the question chose to do so.
This can result in a biased sample that does not accurately represent the population of all internet users.
Additionally, the sample size is not known to be representative or sufficient for generalization, and there is no control group or experimental design to establish cause and effect.
Hence, this is an observational study because the researchers do not attempt to modify or apply a treatment to the individuals.
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Gabe missed three less than twice as many points as his friend Noah on their test if they missed a total of 18 points how many did gabe miss
Noah missed 7 points on the test. And Gabe missed 2x - 3 = 2(7) - 3 = 11 points on the test. So, Gabe missed 11 points on the test.
What is Algebraic expression ?
Algebraic expression can be defined as combination of variables and constants.
Let x be the number of points that Noah missed on the test.
Then, the number of points that Gabe missed is 2x - 3, according to the problem.
The total number of points missed by both of them is given as 18.
So, we can write an equation based on the problem statement:
x + (2x - 3) = 18
Simplifying the equation, we get:
3x - 3 = 18
Adding 3 to both sides of the equation, we get:
3x = 21
Dividing both sides of the equation by 3, we get:
x = 7
Therefore, Noah missed 7 points on the test. And Gabe missed 2x - 3 = 2(7) - 3 = 11 points on the test. So, Gabe missed 11 points on the test.
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The solution to any system is where the graphs cross or touch?
true or false?
Where the graphs intersect or touch, the supplied statement is true, and that is the solution to any system.
What are the principles governing linear equations?One or two variables make up a linear equation. Neither the numerator nor the denominator of a fraction can be a variable in a linear equation raised to a power higher than 1. The lines that connect all the points on a coordinate grid when you identify the values that make a linear equation true are congruent.
A linear equation is what?An algebraic equation with simply a constant and a first-order (linear) term, such as y=mx+b, where m is the slope and b is the y-intercept, is known as a linear equation. The above is sometimes referred to as "linear equation of two variables," where y and x are the variables.
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Company A Company B
8/10/14/4 10/6/16/3
a. Calculate the single equivalent discount rate for each company?
Note: Do not round intermediate calculations. Round your final answers to the ne.
Company A
Company B
Single
equivalent
discount rate
%
%
The single equivalent discount rate for Company A is 19.28%, and for Company B is 23.18%.
How to find the percentage from the total value?
Suppose the value of which a thing is expressed in percentage is "a'
Suppose the percent that considered thing is of "a" is b%
Then since percent shows per 100 (since cent means 100), thus we will first divide the whole part in 100 parts and then we multiply it with b so that we collect b items per 100 items(that is exactly what b per cent means).
Thus, that thing in number is
[tex]\dfrac{a}{100} \times b[/tex]
We are given;
The measures of company A and B= 8/10/14/4 10/6/16/3
Now,
To calculate the single equivalent discount rate for each company, we can use the following formula:
Single equivalent discount rate = [(1 - (Discount % / 100)) ^ (365 / Average payment period) - 1] x 100
For Company A, the average payment period is:
(8 + 10 + 14 + 4) / 4 = 9
Using the formula, we can calculate the single equivalent discount rate for Company A:
Single equivalent discount rate = [(1 - (8/100)) ^ (365 / 9) - 1] x 100 = 19.28%
For Company B, the average payment period is:
(10 + 6 + 16 + 3) / 4 = 8.75
Using the formula, we can calculate the single equivalent discount rate for Company B:
Single equivalent discount rate = [(1 - (10/100)) ^ (365 / 8.75) - 1] x 100 = 23.18%
Therefore, by percentage the answer will be 19.28% and 23.18%.
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find the smallest number, which when is diminished by 7, is divisible by 18,72, and 86.
Answer: 1015
Step-by-step explanation: We will find the factors of all the given numbers by using the prime factorization method. Then we will multiply the factors with the highest degree to find the least common multiple of the given numbers.
The following figure has volume as indicated. Find the value of x.
V = 128
a) 8
b) 16/8
c) 4
d) 16
The value of x for the given cone will be 4. The correct option is C.
What is the volume of the cone?The area a cone takes up in a three-dimensional plane is known as its volume. A cone's base is circular, so it is made of a radius and a diameter.
Given that the volume of the cone is V = 128π and the height of the cone is h = 24 units.
The value of the radius x will be calculated as,
V = ( 1 / 3 )πr²h
128π = ( 1 / 3) π x r² x 24
r² = 16
r = 4 units
Therefore, the value of x will be 4 units.
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Find the volume of the solid
480 m³ is the volume of the given solid.
What is Volume?
The space that any three-dimensional solid occupies is known as its volume. These solids can take the form of a cube, cuboid, cone, cylinder, or sphere.
The dimensions of the trapezoidal prism are given in the diagram.
The dimensions of the cuboidal cavity are also given.
Volume of the solid = Volume of trapezoidal prism - Volume of cuboidal cavity
Volume of trapezoidal prism = (1/2)[Sum of parallel sides][h]×length
= (1/2)×[13+8]×[5]×10
= 525 m³
Volume of cuboidal cavity = l×b×h
= 10×3×1.5
= 45 m³
Volume of the solid = 525 - 45 m³
= 480 m³
The volume of the solid is 480 m³.
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Which of the diagrams below represents the contrapositive of the statement
"If it is a square, then it is a quadrilateral"?
not quadrilateral
not square
Figure A
OA. Figure A
OB. Figure B
not square
not
quadrilateral
Figure B
Figure B is the correct option which represents the the contrapositive of the statement "If it is a square, then it is a quadrilateral".
What is a contrapositive statement ?
A contrapositive statement is a statement formed by negating both the hypothesis and the conclusion of the original statement, and then switching them and negating the entire statement.
In other words, if the original statement is of the form "If A, then B", then the contrapositive statement is of the form "If not B, then not A". The contrapositive statement is logically equivalent to the original statement, which means that if the original statement is true, then the contrapositive statement is also true, and if the original statement is false, then the contrapositive statement is also false.
Finding the contrapositive statement -
We are given "if it is a square,then it is a quadrilateral ".
To determine the contrapositive of a conditional statement, we must switch the hypothesis and the conclusion and negate both.
The original statement is "If it is a square, then it is a quadrilateral." The hypothesis is "it is a square," and the conclusion is "it is a quadrilateral."
Contrapositive of our given statement is -
"if it is not a square,then it is not a quadrilateral "
Therefore, figure B is correct option.
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The youth center has installed a swimming pool on level ground. The pool is a right circular cylinder with a diameter of 24 feet and a height of 6 feet. To the nearest cubic foot, what is the volume of water that will be in the pool when it is filled with?
Rounding to the nearest cubic foot, the volume of water that will be in the pool when it is filled is approximately 2713 feet³.
What is volume?
Each thing in three dimensions takes up some space. The volume of this area is what is being measured. The space occupied within an object's borders in three dimensions is referred to as its volume. It is sometimes referred to as the object's capacity.
The first step is to find the radius of the cylinder.
Since the diameter is given as 24 feet, the radius is half of the diameter or 12 feet.
Next, we can use the formula for the volume of a cylinder -
V = πr²h
where V is the volume, r is the radius, and h is the height.
Substituting the given values, we get -
V = π(12)²(6)
= π(144)(6)
= 2712.96
≈ 2713 cubic feet
Therefore, the volume value is obtained as 2713 cubic feet.
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The scatterplot shows the number of students in each 8 different classrooms and the number of pencils needed for the entire school year.
Answer:
I think the answer is 50 pencils
Find the value of x
Answer:
x = 13
Step-by-step explanation:
We know that 5x, x+12, and 90 makes a straight line, which is 180 degrees
5x + x+12 + 90 = 180
Combine like terms.
6x+102=180
Subtract 102 from each side.
6x+102-102=180-102
6x = 78
Divide each side by 6
6x/6 = 78/6
x = 13
Answer:
x = 13
Step-by-step explanation:
Now we have to,
→ Find the required value of x.
We know that,
→ The angle of right angle is 90°.
Forming the equation,
→ (x + 12)° + (5x)° = 90°
Then the value of x will be,
→ (x + 12)° + (5x)° = 90°
→ x + 12 + 5x = 90
→ (x + 5x) + 12 = 90
→ 6x + 12 = 90
→ 6x = 90 - 12
→ 6x = 78
→ x = 78 ÷ 6
→ [ x = 13 ]
Hence, the value of x is 13.
Determine whether the pair of lines are parallel, perpendicular, or neither.
12x + 4y = 9
12x = 36y + 48
The pair of lines 12x + 4y = 9 and 12x = 36y + 48 are perpendicular.
Determining whether the pair of lines are parallel, perpendicular or neitherFrom the question, we are to determine whether the pair of lines are parallel, perpendicular or neither
To determine whether the pair of lines are parallel, perpendicular, or neither, we need to compare their slopes.
We can rewrite both equations in slope-intercept form, y = mx + b,
Where m is the slope of the line:
12x + 4y = 9
4y = -12x + 9
y = (-3/1)x + 9/4
12x = 36y + 48
12x - 48 = 36y
(1/3)x - 4/3 = y
The slope of the first line is -3/1, and the slope of the second line is 1/3.
Parallel lines have the same slope, so these lines are not parallel.
Perpendicular lines have slopes that are negative reciprocals of each other, meaning their slopes multiply to -1. Therefore, these lines are perpendicular.
Hence, the given pair of lines are perpendicular.
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complete the number pattern 9;27;81?
Answer:
the full numbers is 9, 27, 81, 243.
Answer:
243
Step-by-step explanation:
What is the product of 6 /square root 12 and 2/ square root 14 in simplest radical form?
The product of 6 √12 and 2√14 in simplest radical form is 24 √42 .
What is Radical?Radical - The √ symbol that is used to denote square root or nth roots. Radical Expression - A radical expression is an expression containing a square root.
We have to find the product of 6 √12 and 2√14 in simplest radical form.
So, 6 √12 x 2√14
= 12 x √12 x √14
= 12 x 2√3 x √14
= 24 x √3 x √14
= 24 √42
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At a restaurant, the bill comes to $76. If you decide to leave a 20% tip, how much total do you need to pay? Give your answer to the nearest dollar.
Answer:
$91
Step-by-step explanation:
bill = $76
tip = 20%
20% of bill = (20/100) * 76
= $15.2
total bill = $76 + $15.2
= $91.2
= $91