We must factorize the provided polynomial equation in order to obtain a linear and quadratic equation before we can discover the roots of the three-degree polynomial.
what are polynomials?A mathematical expression made up of coefficients and uncertainty that only makes use of additions, subtractions, multiplications, and positive integer powers of variables is known as a polynomial. The formula x2 4x + 7 denotes a single indeterminate x polynomial. An expression in mathematics known as a polynomial is made up of variables (also known as indeterminates) and coefficients that may be added, subtracted, multiplied, and raised to negative integer powers of non-variables. An algebraic statement with variables and coefficients is called a polynomial. An expression can only contain the operations addition, subtraction, multiplication, and non-negative integer exponents. Polynomials are the name for these expressions.
We must factorize the provided polynomial equation in order to obtain a linear and quadratic equation before we can discover the roots of the three-degree polynomial. The zeros of the three-degree polynomial are then easily ascertainable.
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What are exponents give examples?
Answer:
An exponent refers to the number of times a number is multiplied by itself.
Step-by-step explanation:
For example, 2 to the 3rd (written like this: 23) means: 2 x 2 x 2 = 8. 23 is not the same as 2 x 3 = 6. Remember that a number raised to the power of 1 is itself.
In the diagram, △OA′B′ is a scale drawing of △OAB . What is the length of AB ?
Answer:
2.4
Step-by-step explanation:
2/5=AB/6
=>AB=2.4
What is the value of exponential 2?
The value of exponential 2 is 2^2, or 4. This means two multiplied by itself two times or squared.
Exponential notation is a way of expressing a number, usually greater than 10, as a base number, the number 2 in this case, raised to a power, which in this case is 2. Therefore, exponential 2 is written as 2^2, which means two multiplied by itself two times or squared.
For example, if we wanted to find the value of exponential 8, we could easily calculate 2^8, or 256, which is much faster than multiplying 2 by itself 8 times. Exponential notation is also helpful when calculating exponents with variables.
For example, if we wanted to find the value of 3^x, we could use exponential notation to find the answer quickly. In summary, exponential notation is a useful tool for quickly finding the value of a number raised to a power.
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A rectangular box has the length of [tex]\sqrt{90}[/tex] inches, width of [tex]\sqrt{14}[/tex] inches, and height of [tex]\sqrt{70}[/tex] inches.
a. What is the volume of the box?
b. What is the area of the top of the box?
c. What is the ratio of the height of the box to the length of the box?
Don't answer in decimals.
The volume, surface area, and ratio of the height of the box to the length will be 296.98 cubic inches, 292.35 square inches, and 0.88, respectively.
What is a rectangular prism?A closed solid with two parallel rectangular bases joined by a rectangle surface is known as a rectangular prism.
A rectangular box has a length of √90 inches, a width of √14 inches, and a height of √70 inches.
The volume of the box is given as,
V = LBW
V = (√90) x (√14) x (√70)
V = 296.98 cubic inches
The area of the top of the box is given as,
SA = 2(LW + WB + BL)
SA = 2(√90 x √14 + √14 x √70 + √70 x √90)
SA = 292.35 square inches
The ratio of the height of the box to the length of the box is given as,
H / L = √70 / √90
H / L = 0.88
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Write an expression in simplest form to represent the area of the shaded region 3X 2 2X 3X 4X 
Answer:
6[tex]x^{2}[/tex] + 8x
Step-by-step explanation:
4x(3x + 2) = 12[tex]x^{2}[/tex] + 8x is the area of the big rectangle
2x(3x) = 6[tex]x^{2}[/tex] is the area of the small rectangle.
Subtract the small rectangle from the large rectangle to find the area of the shaded region
12[tex]x^{2}[/tex] + 8x - 6[tex]x^{2}[/tex]
6[tex]x^{2}[/tex] + 8x
whats the equation of the line in slope-intercept form
The equation in slope intercept form is
y = 5/2x + 5
What is Slope intercept form ?One of the most popular ways to describe a line's equation is in the slope intercept form of a straight line. When the slope of the straight line and the y-intercept are known, the slope intercept formula may be used to get the equation of a line ( the y-coordinate of the point where the line intersects the y-axis). The equation of a line is the equation that each point on the line fulfills.
The slope intercept form is a technique for figuring out a straight line's equation in the coordinate plane. Any point's coordinates on a straight line must fulfill a certain relation, which is known as the equation of a straight line.
Any location that is not on the line will not fulfill the coordinates.
This equation's solution is simple to find. A straight line's slope, or angle of inclination from the x-axis, and the intercept it makes with the y-axis are both necessary to determine the slope intercept form of the line.
Two points on the line are (-2,0) and (0,5)
The slope intercept form is
y = mx + c
so when y = 0 and x = -2
0 = -2(m) + c
or, 2m -c = 0 ..(i)
again when x= 0 y = 5
5 = 0*m + c
c = 5
so putting c= 5 in equation (i) we get
m = 5/2
so the equation in slope intercept form is
y = 5/2x + 5
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Moira needs a total of 214 hours to finish reading a book. Yesterday, she read for 178 hours. Supply the correct numbers to complete the equation that can be used to determine the number of hours, h, that Moira needs to read to finish the book.
h + =
An equation that can be used to determine the number of hours, h, that Moira needs to read to finish the book is h + 178 = 214.
How to write an equation to model this situation?In order to write an equation that model this situation, we would assign a variable to the number of hours that is needed to read to finish the book and the total number of hours respectively, and then translate the word problem into algebraic equation as follows:
Let the variable h represent the number of hours.Let the variable T represent the total number of hours.Next, we would translate the word problem into an algebraic equation based on the fact that she read for 178 hours yesterday as follows;
h + 178 = T
Substituting the given parameters into the algebraic equation, we have the following;
h + 178 = 214
Solving for h, we have the following;
h = 214 - 178
h = 36 hours.
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A banker loaned $5000 to one cutomer and $8000 to another. If the annual interet on the econd loan i %2 higher than the firt and the combined annual interet i $810, What i the interet rate for each loan?
The interest rate for first loan is 5% and for the second loan is 7%.
The amount of first loan = $5000
Let the rate of interest for first loan = r
The interest from first loan = ($5000 × r)/100
= 50 r
The amount of second loan = $5000
Let the rate of interest for second loan = r+2
The interest from first loan = ($8000 × (r+2))/100
= 80 r + 160
Total interest = 50 r + 80 r + 160
= 130 r + 160
As per the question statement combined annual interest = $810
810 = 130 r + 160
r = (810-160)/130
r = 5%
Rate of second loan = r+2 = 5+2
= 7%
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Inusah is x years old now if his age in 11 years time will be 3 times his age 7 years ago, how old is he now
===============================================
Work Shown:
x = his age now
x+11 = his age 11 years into the future
x-7 = his age 7 years ago
The equation to set up is
x+11 = 3(x-7)
since his age 11 years into the future is triple that of his age 7 years ago.
-------
Let's solve for x.
x+11 = 3(x-7)
x+11 = 3x-21
x-3x = -21-11
-2x = -32
x = -32/(-2)
x = 16
He is currently 16 years old.
11 years from now he'll be 16+11 = 27, and 7 years ago he was 16-7 = 9.
Note that 9*3 = 27 to help confirm the answer.
Answer:
16
Step-by-step explanation:
3(x-7)=x+11
Plug into equation and find value of x
What is the best way to show that the side lengths 8 feet, 16 feet, and 22 feet do NOT form a right triangle?
1. Substitute the values into the Pythagorean theorem and show that a false statement results.
2. Determine the sum of the side lengths and compare it to the Pythagorean theorem.
3.Calculate the difference between the horizontal and vertical coordinates of each pair of measurements to show the triangle is equilateral.
4.Use the coordinate plane to draw the triangle and show that it is an acute triangle.
Substitute the values into the Pythagorean theorem and show that a false statement results.
What is the best way to show that the side lengths 8 feet, 16 feet, and 22 feet do NOT form a right triangle?The best way to show that the side lengths 8 feet, 16 feet, and 22 feet do not form a right triangle is to substitute these values into the Pythagorean theorem and show that a false statement results.The Pythagorean theorem states that in a right triangle, the sum of the squares of the two shorter sides is equal to the square of the longest side.In this case, 8^2 + 16^2 = 64 + 256 = 320, which does not equal 22^2 = 484.This disproves the possibility of the triangle being a right triangle. As an alternative, one could also determine the sum of the side lengths and compare it to the Pythagorean theorem.In this case, the sum of the side lengths is 8 + 16 + 22 = 46, which again does not equal the square of the longest side.Both these methods show that the side lengths 8 feet, 16 feet, and 22 feet do not form a right triangle.To learn more about Pythagorean theorem refer to:
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Find the SP
Radio : cp =2,720, profit = 5 % sp
Cost is equal to Selling price plus Loss ( when selling price and loss is given )Therefore, the cost price (C.P.) is 350.
Find the C.P ?Cost is the same as the selling price plus the loss ( when selling price and loss is given ).
The Profit and Loss Percentage Formula
Profitability (P%) is calculated as (Profit /Cost Price) / 100.
Loss percentage (L%) Equals 100 divided by (Loss / Cost price).
S.P. = {(100 + P%)/100}
if SP > CP, then CP
If SP > CP, S.P. = (100 - L%)/100 CP
C.P. = {100/(100 + P%)}
if SP > CP, then SP
C.P. = SP (if SP > CP)/100/(100 - L%)
Loss percent = 10%
To find:
The C.P.
Solution:
Let x be the C.P.
We have,
S.P. = 315
Loss percent = 10%
S.P = C.P - 10% 0f C.P
315 = X- 0.1X
315 = 0.9 X
Divide both sides by 0.9.
315/0.9 =X
350 = x
Therefore, the cost price (C.P.) is 350.
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it's overlapping triangles, high school 10th grade math.
the statements need to be matched to the reasons.
In the overlapping triangles, the statements needed to be match to the reasons are explained below.
Properties of a triangle.A triangle is sometimes referred to as trigon because it is bounded by three straight sides, and has a measure of internal angles which add up to 180^o.
Considering the overlapping triangles given in the question, the statements to be matched to the reasons are given below:
STATEMENT REASON
1. ΔRTN ≅ ΔSTM Side-Angle-Side (SAS)
2. <T ≅ <T Betweenness
3. RN = SM Reflexive property
4. RM = SM, TM = TN Given
5. RT = ST Substitution
6. RM + TM = TN + SN CPCTE
7. RM + TM = SN + TM Addition property of equality
The match of statements with the reasons are required to proof that RN = SM
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How do you reflect a line over Y =- 2?
To reflect a line over the line y = -2, we can first graph the line and then apply a transformation. A reflection in the y = -2 line can be thought of as a reflection in the x-axis, followed by a translation 2 units upward.
The transformation for a reflection over the line y = -2 is given by (x, y) → (x, -y - 4). To reflect a point (x, y) over the line y = -2, we substitute the coordinates of the point into the transformation and solve for the reflected point.
For example, to reflect the point (3, 4) over the line y = -2, we would substitute the coordinates into the transformation to get (3, -4 - 4) = (3, -8).
To reflect a line, we can reflect each point of the line over the line y=-2 and plot the reflected points.
In conclusion reflecting a line over y=-2 is done by applying a transformation (x, y) -> (x, -y - 4) to each point of the line, this can also be thought of as reflecting the line over x-axis and then translating 2 units upward.
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A 500 g packet of Healthy Flakes costs €3.20.
A 750 g packet of Healthy Flakes costs €4.50.
Which size packet is the better buy?
Show all your calculations and explain your answer clearly.
The first packet by the second packet is the better size packet because the first packet is more expensive than the first packet.
what is unitary method ?The unit technique is a method of problem-solving that entails calculating the value of a single unit, multiplying that value, and then calculating the required value. To put it simply, the unit method is used to extract a single unit value from a specified multiple. One pen costs 400 rupees, thus 40 pens would cost 400 rupees. There might be a regular procedure for doing this out. merely one nation. anything containing a distinctive component. Mathematics of matrices or operators, linear algebra, mathematical analysis, and its adjoint and reciprocal are all equivalent.
given
The price of a 500 g packet of Healthy Flakes is €3.20.
Healthy Flakes come in packets of 750 g for €4.50.
A better size packet of 500 g costs €3.20. A two-pack of 750 g costs €166.66.
The first packet by the second packet is the better size packet because the first packet is more expensive than the first packet.
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HELPPPPPPPPPPPPPP
In Shawn's class, all the students have pets. Of those pets, 1/5 are cats. Of those cats, 2/3 are alley cats. What fraction of the pets are alley cats?
Answer: Would it just be 2/3? It says 2/3 are alley cats.
Step-by-step explanation:
Answer:
1/3 of them are alley cats
Step-by-step explanation:
Suppose DE is 500 yards, AB is 200 yards, and BC is 100 yards. What is the distance across the river (BD)?
The distance across the river (BD) is 800 yards
What is an equation?An equation is an expression that shows the relationship between two or more numbers and variables. Types of equation are linear, quadratic, cubic and so on.
From the image shown, triangle ABC and triangle ADE are similar triangles. For similar triangles, the ratio of corresponding sides are proportional to each other. Hence:
AD/AB = DE/BC
substituting values:
AD / 200 = 500/100
AD = 1000 yards
AD = AB + BD
substituting:
1000 = BD + 200
BD = 800 yards
The value of BD is 800 yards
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What are the 4 properties of solution?
The 4 properties of solutions are:
1) Consistency
2) Validity
3) Feasibility
4) Stability
PROPERTIES OF SOLUTIONSIn mathematics, a solution to an equation or system of equations is a set of values that can be substituted into the equation(s) to make the statement(s) true. The four properties of a solution are:
1) Consistency: A solution exists and is unique, or multiple solutions exist.
2) Validity: The solution(s) must satisfy the equation(s) and any constraints or boundary conditions.
3) Feasibility: The solution(s) must be within the domain of the equation(s) and any constraints or boundary conditions.
4) Stability: The solution(s) should be insensitive to small changes in the equation(s) or initial conditions.
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A relation is plotted as a linear function on the coordinate plane starting at point E at(0, 27)and ending at point F at (5, −8).
What is the rate of change for the linear function and what is its initial value?
Select from the drop-down menus to correctly complete the statements.
The rate of change for a linear function, also known as the slope, can be found by calculating the change in the y-coordinate (rise) divided by the change in the x-coordinate (run) between two points on the line. The slope of a line describes how steep the line is and whether it is increasing or decreasing.
In this case, the slope of the linear function can be found by using the coordinates of points E and F:
Slope = (y2 - y1) / (x2 - x1)
Slope = (-8 - 27) / (5 - 0)
Slope = -35/5
The slope of the linear function is -35/5 or -7.
The initial value of a linear function is the y-intercept, which is the point where the line crosses the y-axis. To find the y-intercept, we can use the slope and one point on the line (in this case point E (0,27)):
y = mx + b
27 = -7(0) + b
b = 27
The y-intercept of the linear function is 27.
So, the linear function starts at point E (0,27) with an initial value of 27, and has a rate of change or slope of -7.
Find the value of each variable in the following parallelogram
Answer:
a = 2
b = 7
Step-by-step explanation:
The given rectangle is a parallelogram.
WZ = XY10b + 1 = 9b + 8
Transfer like terms to the same side of the equation10b - 9b = 8 - 1
Add/Subtract like termsb = 7
2. WX = ZY
6a + 4 = a + 14
Transfer like terms to the same side of the equation6a - a = 14 - 4
Add/Subtract like terms5a = 10
Divide both sides by 5a = 2
Help me outtt please I reallyyyy need it
Answer:
Step-by-step explanation:
x36 + 24
x39x² + 24x - 28
x3(x2 + 9x - 28/3)
x3(x + 28/3)(x - 3)
you decide to buy a custom frame for painting which measures 6 by 14 inches. if the framing material cost 6$ per inch, what is the total(
The total cost of the rectangular frame is C = $240.
How to find the total cost?After a small search online, I found the original question, it is written at the end of the answer.
Remember that for a rectangle of length L and width W, the perimeter is given by:
P = 2*(L + W)
In this case, we know that the frame is 6 inches by 14 inches, then the perimeter will be:
P = 2*(6in + 14in)
P = 2*20in = 40in
And we know that the framing material costs $6 per inch, then the total cost of the frame will be:
cost = 40*$6 = $240
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After a small search online, I found that the complete question is:
"You decide to buy a custom frame for a painting which measures 4 by 6 inches. If the framing material costs $2 per inch, what is the total cost of framing material?"
find the area of shaded region
Answer:
119 cm²
Step-by-step explanation:
Area of shaded region:Area of white triangle:
base = 9 cm
height = 14 cm
[tex]\sf \boxed{Area \ of \ triangle = \dfrac{1}{2}*base *height}[/tex]
[tex]\sf =\dfrac{1}{2}*9*14\\\\ = 9*7\\\\= 63 \ cm^2\\[/tex]
Area of trapezium:
[tex]\sf \boxed{Area \ of \ trapezium =\dfrac{(a+b)*h}{2}}[/tex]
Here, a and b are the parallel sides of trapezium & h is the height.
a = 9 cm ; b = 17 cm and h =14 cm
[tex]\sf Area \ of \ trapezium = \dfrac{(9+17)*14}{2}[/tex]
[tex]= \dfrac{26*14}{2}\\\\\\=13*14\\\\= 182 \ cm^2[/tex]
Area of shaded region = area of trapezium - area of white triangle
= 182 - 63
= 119 cm²
Answer:
area of shaded region = 119 cm²
Step-by-step explanation:
the outer figure has one pair of parallel sides and is a trapezium.
the shaded area (A) is calculated as
A = area of trapezium - area of white triangle
the area of a trapezium is calculated as
area = [tex]\frac{1}{2}[/tex] h (b₁ + b₂ )
where h is the perpendicular height between the bases b₁ and b₂
here h = 14 , b₁ = 9 , b₂ = 17 , then
area = [tex]\frac{1}{2}[/tex] × 14 × (9 + 17) = 7 × 26 = 182 cm²
the area of the triangle is calculated as
area = [tex]\frac{1}{2}[/tex] bh ( b is the base and h the height )
here b = 9 and h = 14 , then
area = [tex]\frac{1}{2}[/tex] × 9 × 14 = 4.5 × 14 = 63 cm²
then area of shaded region (A) is
A = 182 - 63 = 119 cm²
213.5 miles in 3.5 hours. At that rate, how many miles will he travel in 7.2
hours?
Answer: 439.2 miles
Step-by-step explanation:
213.5/3.5=61
61*7.2=439.2 miles in total
Someone please help rn I’ll mark brainliest !!
The length of the side BD is; 8
The measure of the angle DAB is; ∠DAB = 53°
How to interpret Congruent Triangles?Two triangles are said to be congruent by any of the following postulates;
1) SSS (Side Side Side) Congruence Postulate.
2) SAS (Side Angle Side) Congruence Postulate.
3) ASA (Angle Side Angle) Congruence Postulate.
4) AAS (Angle Angle Side) Congruence Postulate.
5) HL (Hypotenuse Leg) Congruence Postulate
Now, for the given triangles that are congruent, we can say that;
∠ADC ≅ ∠ACB
∠DAB ≅ ∠CAB
BD ≅ BC
AC ≅ AD
Thus;
BD = 8
∠DAB 53°
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Question 4 In the equation y=3x+5 , the number represents the slope and the number represents the y-intercept. Question 4 In the equation y=3x+5 , the number represents the slope and the number represents the y-intercept.
The slope and the y-intercept of the line are 3 and 5 respectively.
What is the general equation of a straight line?The general equation of a straight line is -
y = mx + c
{m} - slope.
{c} - intercept along the y - axis.
Given is the equation of a straight line → y = 3x + 5
The equation of the straight line given is -
y = 3x + 5
We can compare and conclude that -
m = 3
c = 5
Therefore, the slope and the y-intercept of the line are 3 and 5 respectively.
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Compared to lat year, the population of Boom Town ha increaed by 25%. The population i now 6,000. What wa the population lat year
The population of the Boom town increased by 25% compared to last year, present population is 6000 then last year population is equal to 4800.
As given in the question,
Given population of the present year is equal to 6000
Let us consider 'x' be the last year population.
Increased in population compared to last year = 25%
Required equation is given by :
x + (25/100)x = 6000
⇒ (125 / 100 )x = 6000
⇒ x = ( 6000 × 100 ) / 125
⇒ x = 4800
Therefore, the population of the last year as per given data of the present year is equal to 4800.
The above question is incomplete, the complete question is:
Compared to last year, the population of Boom Town has increased by 25%. The population is now 6,000. What was the population last year?
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Is it 3 pair or 3 pairs?
It is "3 pairs" not "3 pair", because a pair is a set of two things, so if you have 3 of them it would be 3 sets of two things or 3 pairs.
The measures of the angles of a triangle are shown in the figure below. Solve for x. (3x)° 58° 80°
Answer:
x=14
Step-by-step explanation:
The angles inside a triangle add up to 180 degress all the time, therefore
58+80+3x=180
simplify
138+3x=180
subtract 138 from both sides of the equation
3x=42
divide both sides by 3
x=14
Solve 3x^2+16x-5 using quadratic equation
Using quadratic equation, the value of x is 5 and -1/3
How to calculate the value of x using quadratic equation?3x²+16x-5
3x² +16x -5= 0
Split the middle term using two factors
3x² -15x -x -5= 0
Take out the common factors
(3x-1)(x-5)= 0
3x+1= 0
3x= 0-1
3x= -1
x= -1/3
x-5= 0
x= 0+5
x= 5
Hence x = 5 and x= -1/3
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To assist faculty and students with
research, a school librarian must be
which of the following?
Professional librarians should be accessible to pupils, according to administrators
What are the main leadership roles performed by a school librarian?Professional librarians should be accessible to pupils, according to administrators. Although librarians wear many hats, their three primary responsibilities are to promote literacy, manage resources, and specialize in research. By identifying and acquiring library items based on the curriculum and student interests, school librarians, who are information specialists, build a resource base for the school. Additionally, they keep the library collection organised and up-to-date to encourage individual reading and lifelong learning. They could teach you the fundamentals of literature or perhaps do it for you. They can offer you facts or data that they have gleaned from years of experience.
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