The roots of the quadratic equation x² - x - 56 = 0 is x = -7 or x = 8
What is Quadratic Equation?A quadratic equation is a second-order polynomial equation in a single variable x , ax² + bx + c=0. with a ≠ 0. Because it is a second-order polynomial equation, the fundamental theorem of algebra guarantees that it has at least one solution. The solution may be real or complex.
The roots of the quadratic equations are
x = [ -b ± √ ( b² - 4ac ) ] / ( 2a )
where ( b² - 4ac ) is the discriminant
when ( b² - 4ac ) is positive, we get two real solutions
when discriminant is zero we get just one real solution (both answers are the same)
when discriminant is negative we get a pair of complex solutions
Given data ,
Let the equation be represented as A
Now , the value of A is
x² - x - 56 = 0 be equation (1)
On simplifying the equation , we get
x² - 8x + 7x - 56 = 0
Taking the common terms in the equation , we get
x ( x - 8 ) + 7 ( x - 8 ) = 0
Now , on factorizing the equation , we get
( x + 7 ) ( x - 8 ) = 0
We have two factors which can solve the equation ,
when ( x + 7 ) = 0
Subtracting 7 on both sides of the equation , we get
x = -7
And , when ( x - 8 ) = 0
Adding 8 on both sides of the equation , we get
x = 8
Therefore , the roots of the equation are x = -7 and x = 8
Hence , the quadratic equation is solved
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Answer:
x = 8
x = -7
Step-by-step explanation:
To find the solutions of the quadratic equation x^2 - x - 56 = 0, we can use the quadratic formula:
x = (-b ± √(b^2 - 4ac)) / (2a)
In this equation, a = 1, b = -1, and c = -56. Plug these values into the formula and calculate the discriminant (the value inside the square root):
Discriminant (D) = b^2 - 4ac = (-1)^2 - 4(1)(-56) = 1 + 224 = 225
Now, calculate the two possible solutions:
x1 = (-(-1) + √225) / (2(1)) = (1 + 15) / 2 = 16 / 2 = 8
x2 = (-(-1) - √225) / (2(1)) = (1 - 15) / 2 = -14 / 2 = -7
So, the correct solutions to the equation x^2 - x - 56 = 0 are:
x = 8 (x = 0 is not a solution)
x = -7
Write an equation of the line that passes through (-3,3) and is perpendicular to the line 2y = 8x - 6
The equation of line that passes through (-3,3) and is perpendicular to 2y = 8x - 6 is y = (-1/4)x + 9/4.
What is the equation of line that passes through (-3,3) and is perpendicular to 2y = 8x - 6?The slope-intercept form is expressed as;
y = mx + b
Where m is slope and b is the y-intercept.
Given the equation of the original line.
Write in slope intercept form
2y = 8x - 6
y = 8x/2 - 6/2
y = 4x - 3
Using the slope intercept, slope m is 3.
The equation of a perpendicular line to 2y = 8x - 6 must have a slope that is the negative reciprocal of the original slope.
Slope of perpendicular line = -1 / ( 4 )
Slope of perpendicular line = -1/4
Plug the slope m = -1/4 and point (-3,3) into point-slope formula and simplify.
( y - y₁ ) = m( x - x₁ )
( y - 3 ) = (-1/4)( x - (-3) )
( y - 3 ) = (-1/4)( x + 3 )
y - 3 = (-1/4)x - 3/4
y = (-1/4)x - 3/4 + 3
y = (-1/4)x + 9/4
Therefore, the equation of the perpendicular line is y = (-1/4)x + 9/4.
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 A jar filled with maple syrup weighs 1.5 pounds. Two jars filled with honey weigh 3 pounds. What is the weight of the jar?
The weight of the jar after solving equation simultaneously is w=0.
Define system of linear equation.A set of two or more first-degree equations with two or more connected unknowns is known as a system of linear equations.
How to solve system of linear equation.A system of equations is solved by determining the value of each unknown until the system's equations are all satisfied. That is, it is necessary to find the values of the unknowns so that, when substituted, they will produce the suggested solution in both equations.
j+w=1.5
2j+w=3
Simultaneously solving gives
w=0
the weight of jar is 0.
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Given that cot 0 =
5
-, find csc 0.
√11
According to the given cosecant function the value of csc 0 is equal to 6/5.
What is the cosecant function?The sine function has a reciprocal called the cosecant function. The cosecant function is the hypotenuse divided by the opposite side, just like the sine function is the opposite side divided by the hypotenuse. The hypotenuse and legs are terms for the two sides that are not at the right angle.
It is given that:
[tex]cot\ 0=\sqrt{\frac{11}{5} }[/tex]
According to trigonometric identity,
[tex]csc^2\ alpha - cot^2\alpha = 1\\csc^2\ 0 -\frac{11}{25} =1\\csc^2\ 0 = \frac{36}{25} \\csc\ 0= \frac{6}{5}[/tex]
Therefore the value of csc 0 is equal to 6/5.
Complete question;
Given that [tex]cot\ 0=\sqrt{\frac{11}{5} }[/tex]
find csc 0.
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What are the more appropriate measures of center and spread for this data
set?
Except Option - A all satisfy the more appropriate measures of center and spread for the data that is median and IQR.
Given that,
We have to find what are the more appropriate measures of center and spread for data.
We know that,
Mean, median, and mode are the three central tendencies, and median is the more accurate indicator.
This is because
i) Extreme values affect the mean.
ii) If there are more outliers, the mean is in error.
iii) Means that are biassed to the right or left may not accurately reflect the nature of the data.
However, median is preferable to mean because it represents the center entry and is unaffected by extreme items or outliers.
Since extreme items will show higher standard deviation and some outliers may be misleading, IQR is a superior spread measurement tool. However, IQR provides an excellent idea.
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1. The sum of two angles is 85°, one angle is five more than the measure of the other angle. Write the equation that represents this scenario and find the measure of each angle. Be sure to show your
work.
On solving the provided question, we can say that - by equation angles will be, x + 5x = 85 => 6x = 85 => x = 14.1666666667
What is equation?An equation is a formula in mathematics that joins two statements with the equal symbol = to represent equality. The definition of an equation in algebra is a mathematical statement proving the equality of two mathematical expressions. In the equation 3x + 5 = 14, for instance, the terms 3x + 5 and 14 are separated by an equal sign. The link between two phrases on either side of a letter is expressed mathematically. There is often only one variable, which is also the symbol. instance: 2x - 4 Equals 2.
let one angle be = x
other angle be 5x
then, x + 5x = 85
6x = 85
x = 14.1666666667
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factor each square root
0.7 times square root of 300
-0.125 times square root of 192
Answer:
To factor the first expression, "0.7 times square root of 300", we can rewrite it as:
0.7 * sqrt(300)
The prime factorization of 300 is 2 * 2 * 3 * 5 * 5, so we can rewrite the expression as:
0.7 * sqrt(2 * 2 * 3 * 5 * 5)
Since the square root of a number is the same as the square root of that number's prime factorization, we can rewrite the expression as:
0.7 * sqrt(2) * sqrt(2) * sqrt(3) * sqrt(5) * sqrt(5)
Combining like terms, we get:
0.7 * 2 * sqrt(2) * sqrt(3) * sqrt(5)
= 1.4 * sqrt(2) * sqrt(3) * sqrt(5)
This is the fully factored form of the expression "0.7 times square root of 300".
To factor the second expression, "-0.125 times square root of 192", we can rewrite it as:
-0.125 * sqrt(192)
The prime factorization of 192 is 2 * 2 * 2 * 2 * 2 * 2, so we can rewrite the expression as:
-0.125 * sqrt(2 * 2 * 2 * 2 * 2 * 2)
Since the square root of a number is the same as the square root of that number's prime factorization, we can rewrite the expression as:
-0.125 * sqrt(2) * sqrt(2) * sqrt(2) * sqrt(2) * sqrt(2) * sqrt(2)
Combining like terms, we get:
-0.125 * 6 * sqrt(2)
= -0.75 * sqrt(2)
This is the fully factored form of the expression "-0.125 times square root of 192".
Answer:
for the second one the answer is - square root of 3
Step-by-step explanation:
i could only solve the second one sorry
A band expects to put 15 songs on their next CD. The band wriand records 60% more songs than they expect to put on the CD. During the editing process, 50% of the songs are removed. How many songs will there be on the final CD
Answer:
18 songs
Step-by-step explanation:
15 x 1.6 = 24
24 x 0.75 - 18
1.1.2 Quiz: What Is Health?
Question 2 of 10
In order to maintain wellness, the parts of the health triangle always need to
be
Select two responses.
and
A. working together
B. apart from one another
C. independent of one another
D. in balance
Answer:
The World Health Organization (WHO) defines health as 'a state of complete physical, mental and social wellbeing and not merely the absence of disease or infirmity'
PLEASE HELP!
An architect is designing a circular window to be installed in the
gable of a house. The metal window frame will be 1 foot wide and will be bordered by
the roof above and a wood beam below. The distance from the center of the window to the roof is 3 feet. What will be the circumference of the circular glass pane that will be
needed?
Exact Circumference = 4pi feet
Approximate Circumference = 12.56 feet (when using pi = 3.14)
======================================================
Explanation:
The larger circle has a 3 foot radius.
The inner circle has a 3-1 = 2 foot radius.
Let's find the circumference of the smaller inner circle, which represents the glass window and ignores the metal frame surrounding it.
C = 2pi*r
C = 2pi*2
C = 4pi
The exact circumference is 4pi feet. This is the perimeter around the circle.
If you wanted, you can use an approximation like pi = 3.14 to find that 4pi = 4*3.14 = 12.56 feet is the approximate circumference.
how to horizontally stretch a cubic fucnction
Answer:
Steps for How to Transform the Graph of a Cubic Function
Step 1: The standard form of a cubic function is y=a(x−h)3+k y = a ( x − h ) 3 + k , where a indicates a stretch or a shrink, h indicates a vertical shift, and k indicates a horizontal shift.
Step-by-step explanation:
A bag contains 9 tiles, each with a different number from 1 - 9. You chose a tile without looking, put it aside, choose a second tile without looking, put it aside, then choose a third tile without looking. What is the probability that you choose tiles with the numbers 1, 2, and 3 in that order?
Someone pls explain this. I know the answer is 1/504 but how do you get there?
The probability to choose tiles with the numbers 1, 2, and 3 in that order is a form of permutation and is equal to 1/504.
What are permutations?Permutations refer to the arrangements of objects in certain order or way.
The number of alternative arrangements in a set can be calculated mathematically using a permutation where the order of the configurations is important.
The probability to choose tiles with the numbers 1, 2, and 3 in that order is a form of permutation.
The probability is obtained as 1 / ₉P₃
where;
₉P₃ = 9! / (9 - 3)!
₉P₃ = 9! / 6!
9! = 9 * 8 * 7 * 6 * 5 * 4 * 3 * 2 * 1
6! = 6 * 5 * 4 * 3 * 2 * 1
₉P₃ = 504
Hence, the probability = 1/504
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Identify the slope and y-intercept of the line given by the equation: y = 1/3x - 2
Answer:
this is in the form of slope intercept. y = mx + b
m is the slope
and b is the y intercept
meaning that -2 is the y intercept
and 1/3 is the slope
(meaning on a graph you go up one, and over 3)
Step-by-step explanation:
A condominium owner pays property taxes of $2,000 per year. If taxes are figured
at a rate of $1.25 for every $100 in value, what is the value of his condominium?
Step-by-step explanation:
the tax rate gives us a ratio of tax amount to value.
this ratio (in our case 1.25/100) is constant for any value.
therefore, when we know how many $1.25 units are in $2000, we know that there are exactly as many $100 units in the value.
in other words, we multiply
1.25/100 × f/f
so that the numerator reaches the total of $2000 of taxes. and then the enumerator gives us the total value.
f = 2000 / 1.25 = 1600
so, we get
1.25/100 × 1600/1600 = 2000 / 160000
so, the value of the condominium is
value = $160,000
For polynomial function f, if f(3)=5 and f(5)=-2, what do we know about any roots of f(x)?
Answer:
There is a root between x=3 and x=5.
Step-by-step explanation:
Not entirely sure what this question wants, but from this you can tell that the function crossed the x-axis in the interval (3, 5). When x is 3, y is 5, and then when x is 5, y is -2.
Prove limit of function by using definition (delta-epsilon)
Answer:
Refer to step-by-step
Step-by-step explanation:
Prove the following, [tex]\lim_{x \to \ 2} 2^{x}=4[/tex], [tex]\lim_{z \to \ -1} 3^{x}=\frac{1}{3}[/tex], and [tex]\lim_{x \to \ 1} e^{x-1} = 1[/tex].
For part f:
Plug in the value of the limit, 2,
[tex](2)^{2} =4[/tex]
Thus we proved the limit.
For part g:
Plug in the value of the limit, -1,
[tex]3^{(-1)}[/tex]=>[tex]3^{-1}[/tex]=>[tex]\frac{1}{3^{1} }=\frac{1}{3}[/tex]
Thus we proved the limit.
For part h:
Plug in the value of the limit, 1,
[tex]e^{(1)-1}[/tex]=>[tex]e^{1-1}[/tex]=>[tex]e^{0}=1[/tex]
Thus we proved the limit.
PLEASE ANSWER
Write an equation in point-slope form passing through the given point and parallel to the given line:
(- 4, 4)
y = - 7/4x + 2
Answer:
y-4=-7/4(x+4)
Step-by-step explanation:
Point Slope Form: y-y*sub*1=m(x-x*sub*1)
Parallel lines have the same slope as the line to which they are parallel.
y-4=-7/4(x+4)
Hope this helps :)
What is the range of f(x) = 3* + 9?
O {yly<9}
O {yly>9}
O {yly> 3}
O {yly<3}
On solving the provided question, we can say that - the range [tex]|x + 1| = 0[/tex] [tex]x + 1 = 0 = > x = -1[/tex] and [tex]y = 3[/tex]
What is range?Finding the variable's greatest observed value (maximum) and deducting the least observed value will yield the range (minimum). Limits of variation or potential range: a variety of steel costs; several styles; The size or scope of an action or operation: insight. how far a weapon's projectile can or will travel. The number in a list or set between the lowest and maximum is referred to as a range. Line up all the numbers before locating the region. After that, take away (get rid of) the lowest number from the greatest number. The solution provides the list's range.
The regions where the absolute values are zero are known as the vertex points of an absolute value function.
[tex]|x + 1| = 0\\x + 1 = 0\\x = -1[/tex]
[tex]y = |-1 + 1| + 3\\y= 0 + 3\\y = 3[/tex]
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Let a = (2, 1, 0), b = (3, -1, 2), c = (4, 0, 3)
Find the volume of the parallelopiped with sides a, b and c.
The volume of the parallelopiped is 14 cubic units
What is the volume of a parallelopiped?The volume of a parallelopiped with vector sides a, b and c is given by
V = (a × b).c
Given that the parallelopiped has sides
a = (2, 1, 0)b = (3, - 1, 2) and c = (4, 0, 3)So, we have that
(a × b) = (2, 1, 0) × (3, -1, 2) = (2 × 3)i × i + (2 × -1)i × j + (2 × 2)i × k + (1 × 3)j × i + (1 × -1)j × j + (1 × 2)j × k + (0 × 3)k × i + (0 × -1)k × j + (0 × 2)k × k
Since
i × i = 0, j × j = 0, k × k = 0, i × j = k, j × i = -k, j × k = i, k × j = -i, k × i = j, i × k = -j,So,
(a × b) = (2, 1, 0) × (3, -1, 2) = (6) × 0 + (-2)k + -(4)j + 3i + (-1) × 0 + (2)i + -(3)j + -(0)i + (0) × 0
= 0 -2k - 4j + 3i + 2i - 3j - 0 + 0
= 5i -7j - 2k
= (5, -7, -2).
Since (a × b) = (5, -7, -2)
So, the volume of the parallelopiped is
V = (a × b).c
= (5, -7, -2).(4, 0, 3)
= 5 × 4 + (-7 × 0) + (-2 × 3)
= 20 - 0 - 6
= 14.
So, the volume is 14 cubic units.
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I need the answer to this question
Answer:
it is not factorable
Step-by-step explanation:
There are no factors of 24 that will make -4, so it is not factorable
Rick claims that the equation
×2 + 5x + 9 = 0 has no solution. Jenny claims that there are two solutions. Explain how Rick could be correct, and explain how Jenny could be correct.
Answer: Both Rick and Jenny could be correct because we do not know what "x" is.
Step-by-step explanation:
The purpose of the variable "x" is to substitute it for an unknown number. Since we do not know what "x" is we can not solve the equation. We can only add like terms.
I hope this helps :)
Find the length of side xx in simplest radical form with a rational denominator. 3
The length of x is 6 in simplest radical form.
What is a right-angled triangle?'A triangle in which one of the interior angles is 90° is called a right-angled triangle. The longest side of the right triangle, which is also the side opposite the right angle, is the hypotenuse and the two arms of the right angle are the perpendicular and the base.'
According to the given ,
Perpendicular = 3
Hypotenuse = x
We know,
sin∅ = 3/x
∅ = 30°
⇒ sin30 = 3/x
⇒ 1/2 = 3/x [ sin30 = /2 ]
⇒ x = 3 * 2
⇒ x= 6
Hypotenuse = 6
Applying Pythagoras theorem:
Hypotenuse² = Perpendicular² + Base²
6² = 3² + Base²
6² - 3² = Base²
Base² = 25
Base = √25
Base = 5
We can conclude the value of x to be 6.
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PLEASE HELP ME ASAP DUE TODAY NOW
Answer:
y = [tex]\frac{3}{4}[/tex]x + 3
Step-by-step explanation:
find the slope m
m = [tex]\frac{y2 - y1}{x2 - 21}[/tex]
m = [tex]\frac{3 - 0}{0 - - 4}[/tex]
m = [tex]\frac{3}{4}[/tex]
y = mx + b
find b
insert y1 and x1 into the equation
0 = [tex]\frac{3}{4}[/tex](-4) + b
0 = -3 + b
b = 3
y = [tex]\frac{3}{4}[/tex]x + 3
the width of a rectangle is 6n - 3.5 feet and the length is 3.5n + 7 feet
The perimeter of the rectangle is 19n + 7.
How to find the perimeter of a rectangle?A rectangle is a quadrilateral with opposite sides equal to each other and opposite sides parallel to each other.
The perimeter of a rectangle is the sum of the whole sides of the rectangle.
Therefore, let's find the perimeter of the rectangle with width of 6n - 3.5 ft and length of 3.5n + 7 ft. Hence,
perimeter of a rectangle = 2(l + w)
where
l = lengthw = widthTherefore,
w = 6n - 3.5
l = 3.5n + 7
Hence,
perimeter of a rectangle = 2(6n - 3.5 + 3.5n + 7)
perimeter of a rectangle = 2(6n + 3.5n - 3.5 + 7)
perimeter of a rectangle = 2(9.5n + 3.5)
perimeter of a rectangle = 19n + 7
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How do you do numb 3. please help
Step-by-step explanation:
first we need to identify the lines themselves.
the line from bottom left to top right is simply
y = x
the line is solid, so the points on the line are included.
the dotted line (the points on the line itself are not included) goes through
(0, 2) and (3, 0)
the y-intercept is therefore 2 (the y value when x = 0).
and for the slope
x changes by +3 (from 0 to 3).
y changes by -2 (from 2 to 0).
the slope is -2/+3 = -2/3
and the line is
y = (-2/3)x + 2
we see that the desired gray area is above both lines (">"), and we need to consider, whether the points in the lines are included or not.
so, the system of inequalities is
y >= x
y > (-2/3)x + 2
Helpp!! I’m stuck on this!!
What’s the answer pls?
Therefore ,option 3 is hence the appropriate choices. By the Side-Angle-Side Triangle Congruence Theorem, these triangles are congruent.
Triangle definitionAny three points in a plane can be connected to create triangles, which have three sides and three angles. They were one of the very first geometric shapes to be studied. They are particularly important because any polygon, whether it has four, five, six, or n sides, may be split into a triangle.
Here,
From the provided figure, it is clear that there are two triangles.
ABC and EFG are the triangles.
AB = EF
AC = FG
BC = EG
As a result, the triangles ABC and EFG are congruent according to the triangle's SSS theorem, and angle A is equal to angle D.
Therefore ,D and E are hence the appropriate choices. By the Side-Angle-Side Triangle Congruence Theorem, these triangles are congruent.
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Cones A and B both have volume 48pi cubic units, but have different dimensions. Cone A has radius 6 units and height 4 units. Find one possible radius and height for Cone B.
The possible radius and height for Cone B are 3 units and 16 units respectively
How to determine the radius and height of the cone
The formula for calculating the volume of a cone is expressed mathematically;
Volume = 1/3 πr²h
Given that;
π takes the value 3.1 4r is the radius of the coneh is the height of the coneFrom the information given, we have that;
Both cone A and B have volume of 48πCone A has 6 units and height of 4 unitsNow, let the height of cone B be 16 units
Substitute the value into the formula, we have;
48π = 1/ 3 × π × r² × 16
multiply the values, we have
48 = 16r²/3
cross multiply
16r² = 144
Divide both sides by 16
r² = 144/16
r² =9
Find the square root of both sides
r = 3units
Hence, the values are 3 units and 16 units
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There are 90 new houses being built in a neighborhood last month 2/5
of them were sold this month 1/3 of the remaining houses were sold.How many houses are left to be sold?
The number of houses left to be sold is 12
How to calculate the number of houses left to be sold?There are 90 new houses built in the neighbourhood
2/5 were sold last month
2/5 × 90
= 18 × 2
= 36
1/3 of the remaining were sold this month
1/3 × 36
=12
Hence there are 12 houses left to be sold
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Fill in the missing values to make the equations true. (a) log 5 + log 3 = log₁ 5 (b) log, log, 7 = log, 7 - (c) log, 4 = log, 2
Step-by-step explanation:
try this option:
[tex]a) \ log_{15}5+log_{15}3=log_{15}15;\\b) \ log_{1/2}log_{49}7=log_77;\\c) \ log_44=log_22.[/tex]
Evaluate x−25 when x=35.
Answer: 5
Step-by-step explanation:
1. Since you are told x=35. Plug it into x.
35-25
2. Simplify
35-25=5
Answer: 10
Step-by-step explanation:
x-25
substitute 35 for x
35-25 = 10