There are three formulas that can be used to solve quadratic equations in class 10.
The first formula is the Quadratic Formula, which is used to solve any quadratic equation of the form ax² + bx + c = 0. This formula is used to find the two values of x that are the solutions to the equation. The second formula is the Completing the Square formula, which is used to solve any quadratic equation of the form ax² + bx + c = 0. This formula is used to rewrite the equation in the form (x + h)² = p , and then solve for the value of x. The third formula is the Factorization Method, which is used to solve any quadratic equation of the form ax² + bx + c = 0. This method is used to factor the equation into two linear factors, and then use either the Quadratic Formula or the Completing the Square formula to find the two values of x that are the solutions to the equation. All three of these formulas can be used to solve any quadratic equation of the form ax² + bx + c = 0.
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The diagram shows a hexagon inscribed in a circle.
Calculate the sum of the angles a, b and c.
Give a reason for your answer.
The sum of the angles, a, b and c is; 360° because, the sum measures 3 of all the equal angles in the regular hexagon.
What is the sum of all three angle Measures?It follows from the task content that the angle measures given in the task are a, b and c which are in a cyclic polygon (hexagon) in which case, the sum of all 6 angles in the hexagon is; 720.
Consequently, the sum of angle measures; a,b and c is; 720/2 = 360°.
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20 PIONTSSS TO WHOEVER ANDWER THIS QUESTION !!!
Answer:
The answer would be 36cm².
Step-by-step explanation:
⇒ Two prisms are similar.
⇒ Scale factor = 3:8
⇒ The ratio of the surface area is 9:64.
⇒ So S₁ : S₂ = 9:64
⇒ S₁ : 256 = 9:64
⇒ S₁ = 36cm²
This would mean that the answer is 36 centimeters ² (squared).
C = 75h + 125
The equation above gives the amount C, in dollars, an electrician charges for a job that takes h hours. Ms. Sanchez and Mr. Roland each hired this electrician. The electrician worked 2 hours longer on Ms. Sanchez's job than on Mr. Roland's job. How much more did the electrician charge Ms. Sanchez than Mr. Roland?
Ms. Sanchez paid 150 dollars more than Mr. Roland.
How much more did the electrician charge Ms. Sanchez than Mr. Roland?Let's say that the electrician worked for x hours in Mr. Roland's home, then worked for (x + 2) hours in Ms. Sanchez home.
Then we need to find the difference between the linear equations:
C(x + 2) - C(x) = (75*(x + 2) + 125) - (75*x + 125)
If we simplify that, we get:
75*x + 75*2 + 125 - 75*x - 125
= 75*2 = 150
This means that Ms. Sanchez paid 150 dollars more than Mr. Roland.
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If a line that passes through the
points (8, 10) and (4, -6) also passes through the point (b, 2b), then find the value of b?
To prove quadrilateral WXYZ is a parallelogram, Travis begins by proving △WZY ≅ △YXW by using the SAS congruency theorem.
Quadrilateral W X Y Z is shown. A diagonal is drawn from point W to point Y. Sides W Z and X Y are parallel and congruent.
Which reasons can Travis use to prove the two triangles are congruent? Check all that apply.
∠ZWY ≅ ∠XYW by the alternate interior ∠s theorem.
WY ≅ WY by the reflexive property.
∠ZWY ≅ ∠XWY by the corresponding ∠s theorem.
WX ≅ ZY by definition of a parallelogram.
WZ ≅ XY by the given.
The reasons Travis can use to prove both triangles are congruent by the SAS congruency theorem are:
∠ZWY ≅ ∠XYW by the alternate interior ∠s theorem.WY ≅ WY by the reflexive property.WZ ≅ XY by the given.What is the SAS Congruency Theorem?The SAS congruency theorem states that two triangles are congruent when they both have two pairs of corresponding congruent sides and a pair of corresponding congruent included angles.
Given the image below, we have the following proof with the statement and reasons in bracket:
WZ ≅ XY [given]
WY ≅ WY [reflexive property]
∠ZWY ≅ ∠XYW [by the alternate interior ∠s theorem]
△WZY ≅ △YXW [by the SAS congruency theorem]
Therefore, the reasons Travis can use are:
∠ZWY ≅ ∠XYW by the alternate interior ∠s theorem.WY ≅ WY by the reflexive property.WZ ≅ XY by the given.Learn more about the SAS congruency theorem on:
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Answer:
A. ∠ZWY ≅ ∠XYW by the alternate interior ∠s theorem;
B. WY ≅ WY by the reflexive property; & E. WZ ≅ XY by the given.
Step-by-step explanation: Trust Me! Answer is correct on Edge.
Good Luck! :)
Which reasons can Travis use to prove the two triangles are congruent? Check all that apply.
A. ∠ZWY ≅ ∠XYW by the alternate interior ∠s theorem B. WY ≅ WY by the reflexive property E. WZ ≅ XY by the given
help me please im in a rush
Answer:
The answers are in the image
Step-by-step explanation:
The solutions are in the image
You are out to dinner with 10 friends (meaning there are 11 of you). The bill total is $110. You all want to split the bill evenly. How would you write this as an improper fraction?
A 110/10
B 10/111
C 11/110
D 110/11
Answer:
110/11
A
Step-by-step explanation:
divide the bill by 11 people.
Answer:
D. 110/11
Step-by-step explanation:
110 Dollars
11 people to split it with
110/11 to find the total for each person
Simplify (5√3 − 2√5) the whole square
Answer:
95 - 20[tex]\sqrt{15}[/tex]
Step-by-step explanation:
(5[tex]\sqrt{3}[/tex] - 2[tex]\sqrt{5}[/tex] )²
= (5[tex]\sqrt{3}[/tex] - 2[tex]\sqrt{5}[/tex] )(5[tex]\sqrt{3}[/tex] - 2[tex]\sqrt{5}[/tex] )
each term in the second factor is multiplied by each term in the first factor, that is
5[tex]\sqrt{3}[/tex] (5[tex]\sqrt{3}[/tex] - 2[tex]\sqrt{5}[/tex] ) - 2[tex]\sqrt{5}[/tex] (5[tex]\sqrt{3}[/tex] - 2[tex]\sqrt{5}[/tex] ) ← distribute parenthesis
= 75 - 10[tex]\sqrt{15}[/tex] - 10[tex]\sqrt{15}[/tex] + 20 ← collect like terms
= 95 - 20[tex]\sqrt{15}[/tex]
Answer:
95 - 20√15
Step-by-step explanation:
I assume the expression is (5√3 − 2√5)^2 (?).
(5√3 − 2√5)*(5√3 − 2√5)
25√3^2 - 20√15 + 4√5^2
25*3 - 20√15 +4*5
75 - 20√15 +20
95 - 20√15
15 Points please me I'm in a rush
Using proportions, it is found that out of the next 1500 pizzas, she should expect 420 pan style pizzas.
What is a proportion?A proportion is a fraction of a total amount, and the measures are related using a rule of three.
The proportion of pan style pizzas is given as follows:
294/(284 + 313 + 159 + 294) = 0.28.
Hence, out of 1500 pizzas, this amount is equivalent to:
0.28 x 1500 = 420
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The graph of the function f(x) = (x +2)(x + 6) is shown below.
On a coordinate plane, a parabola opens up. It goes through (negative 6, 0), has a vertex at (negative 4, negative 4), and goes through (negative 2, 0).
What is true about the domain and range of the function?
The domain is all real numbers, and the range is all real numbers greater than or equal to –4.
The domain is all real numbers greater than or equal to
–4, and the r
Answer: The domain is all real numbers, and the range is all real numbers greater than or equal to –4.
Step-by-step explanation:
The domain is the set of inputs, and the range is the set of outputs.
Answer: Option A
Step-by-step explanation
The domain is the set of allowed x inputs of a function.
We can replace x with any number we want to get some output for y = f(x)
This tells us the domain is the set of all real numbers.
-----------
The range is the set of numbers y such that
In other words, we can have y = -4 or y > -4
This is because y = -4 is the lowest output possible, as indicated by the vertex point.
Which is the graph of the linear inequality 2x-3y < 12?
Answer:
First, transform the given equation into the slope-intercept form, y = mx + b.
2x - 3y < 12
3y > 2x - 12
y > [tex]\frac{2}{3}[/tex]x - 4
Since the equation is y > [tex]\frac{2}{3}[/tex]x - 4, first draw the graph of y = [tex]\frac{2}{3}[/tex]x - 4 with a dotted line (because it is >, not ≥) and shade the area above the dotted line.
 i need help putting it in expanded form and solving it
Answer:
4x^04x^04x^04x^1 which equals 256
Step-by-step explanation:
The 4 outside of the parentheses says take what you have outside of the parentheses and multiply it by itself that may times.
x raised to the zero is 1, so you are just left with 4x4x4x4 or 256
A shopkeeper has $680 in the denominations of $50, $20, $10 and $5 notes. The number of notes of each denomination is equal. What is the total number of notes?
The total number of notes is 32
The number of notes
Let the number of notes be x
$50 = x
$20 = x
$10 = x
$5 = x
Total number of notes = 4x
Let's find 'x'
50x + 20x + 10x + 5x = 680
85x = 680
x = 680/ 85
x = 8
We know that;
Total number of notes = 4x = 4 × 8 = 32 notes
Thus, the total number of notes is 32
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Next, you will make a scatterplot. Name a point that will be on your scatterplot and describe what it represents.
The point (12, 190) means that the temperature after 12 hours is 190 degrees Celsius
How to make a scatter plot?To do this, we make use of the following points
(12, 190), (14, 201), (15, 301), (16, 305), (18, 350), (20, 40), (25, 450)
Where x represents the number of hours and y represents temperature
See attachment for the scatter plot.
The description of a pointTo do this, we make use of the point (12, 190)
This means that the temperature after 12 hours is 190 degrees Celsius
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waheda purchased 8 textbooks each costing rupees 12 and 4 story books each question rupees 9 find the ratio of amounts she spent on the two types of books .
Answer:
8/3 or 2(2/3) Textbooks to storybooks
Step-by-step explanation:
Textbooks: (8 books)*(12 rupees/book) = 96 rupees
Storybooks: (4 books)*(9 rupees/book) = 36 rupees
Total is 132 rupees
Ratio: Textbook/Storybook = 96/36
96/36 = 8/3 or 2(2/3) Textbooks to storybooks
Find the missing value so that the two points have a slope of 1/2.
(9, 1) and (3, y)
Please explain
Answer: -2
Step-by-step explanation:
Substituting into the slope formula,
[tex]\frac{y-1}{3-9}=\frac{1}{2}\\\\y-1=-3\\\\y=-2[/tex]
Pls help me on 103 :((
Answer:
J) [tex]18cm^2[/tex]
Step-by-step explanation:
a square inscribed in a circle means that the radius of the circle is the same thing as a line drawn from the center of the square to a corner.
this will give you the side measurements for a triangle (look at the attached picture). now use the Pythagorean theorem to find the hypotenuse aka the side length of the square. then multiply it by itself.
Answer: H
Step-by-step explanation:
Finding the DiameterIf we draw a line through a diagonal of the square, two triangles are formed. The angle opposite the diagonal is 90°, as all angles are 90° in a square. One of the properties of a circle state that the angle in a semicircle is always 90°, which means that the diagonal formed a semi-circle.
A semi-circle only forms when a diameter is drawn in a circle, making the diagonal a diameter. This will be useful information, as we can calculate the side length of a square using the length of its diagonal.
A diameter is just twice the length of a radius, so the diagonal of the square would be 6 cm.
[tex]2*3=6[/tex]
Finding the Length of One SideThe diagonal also splits the square into two 45-45-90 triangles. These triangles have a special property that their hypotenuse is √2 times each leg, and all legs are the same length.
Therefore, we can calculate the length of a leg by dividing the hypotenuse by √2.
[tex]\frac{6}{\sqrt{3}}[/tex]
The length of one side of the square is [tex]\frac{6}{\sqrt{3}}[/tex]
Finding the AreaAs we already know the length of one side, we can just square it to get the area.
[tex](\frac{6}{\sqrt{3}})^2[/tex]
[tex]\frac{6^2}{(\sqrt{3})^2}[/tex] [Properties of Exponents]
[tex]\frac{36}{3}[/tex]
[tex]12[/tex]
Hence, the area of the square is 12 cm².
Full factor of 32a^3+ 12a^2
Answer:
4a²*(9a + 3)
Step-by-step explanation:
Factorize:Prime factorize 32 and 12. Then find GCF.
32a³ = 2 * 2 * 2 * 2 * 2 * a³
12a² = 2 * 2 * 3 * a²
GCF = 2 * 2 * a² = 4a²
32a³ + 12a² = (4a²*9a) + (4a²*3)
=4a²*(9a + 3)
A school system is reducing the amount of dumpster loads of trash removed each week. in week 5, there were 60 dumpster loads of waste removed. in week 10, there were 40 dumpster loads removed. assume that the reduction in the amount of waste each week is linear. write an equation in function form to show the amount of trash removed each week. f(x) = −4x 60 f(x) = 4x 60 f(x) = −4x 80 f(x) = 4x 80
The equation in function form is f(x)=-4x+80.
What is linear function?
A linear function is a function which forms a straight line in a graph. It is generally a polynomial function whose degree is utmost 1 or 0.
We can find the equation in function form as shown below:
We have given two points (5,60) and (10,40)
Slope of line
m = (40-60)/ (10-5)
m=-20/5
m=-4
Equation in slope intercept form
(y-y1) =m(x-x1)
(y-60) =-4(x-5)
y-60=-4x+20
y=-4x+20+60
y=-4x+80
y=f(x)
f(x)=-4x+80
Hence, the equation in function form is f(x)=-4x+80.
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(06.04 MC)
Find the perimeter of the image below:
Answer: 39 units
Step-by-step explanation:
Using the distance formula, we get that:
[tex]PT=\sqrt{10^2 + 4^2}=\sqrt{116}\\\\TS=\sqrt{7^2 + 0^2}=7\\\\SR=\sqrt{7^2 + 1^2}=\sqrt{50}\\\\RQ=\sqrt{6^2 + 5^2}=\sqrt{61}\\\\PQ=\sqrt{2^2 + 6^2}=\sqrt{40}[/tex]
So, the perimeter is
[tex]\sqrt{116}+7+\sqrt{50}+\sqrt{61}+\sqrt{40} \approx 39[/tex]
there are five chemistry instructors and six physics instructors at a college. if a committee of four instructors is selected,
The probability of at least one of them being a physics instructor is 120 ways to form the committee.
Probability of Independent Events: The 'At Least One' Rule?Sometimes, simply the occurrence of the event at least once matters when computing independent events. The "At Least One" Rule is used to describe this. The complement of the probability of the event never occurring will be used to calculate the probability of the event occurring at least once.
There are five chemistry instructors and six physics instructors at a college. If a committee of four instructors is selected.
Starting with 6, choose two because we require at least two professors. Let's move on to the remaining 8 individuals (there were initially 10, but now there are just 8): and select 3.
6 select 2; 8 select 3
15×56 =840
We then chose 5 individuals from a group of 10, at least 2 of whom were lecturers.
(9) = 20 options for selecting the professors. 3
(3) = 6 options for selecting the professors.
(9) (¹) = 20 × 6 = 120 ways.
Therefore, 120 ways to form the committee.
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Complete question:
There are five chemistry instructors and six physics instructors at a college. If a committee of four instructors is selected, find the probability of at least one of them being a physics instructor?
Manufacturers were subdivided into groups by volume of sales. Those with more than $100 million in sales were classified as large; those from $50 to $100 million as medium size; and those between $25 and $50 million, and so on. Samples were then selected from each of these groups. What is this type of sampling called
Stratified random sampling is used to subdivided into groups by volume of sales.
According to the statements
Manufacturers are subdivided into groups by volume of sales. and for this Stratified random sampling is used.
Stratified random sampling is the technique used divide the population can be partitioned into subpopulations.
Thus, Stratified random sampling is used to subdivided into groups by volume of sales.
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Which explains how to show that
X=-8/3
is a root of
9×^2+48×+64=0?
a. Graph
9x^2 + 48x + 64 = 0
to show that
x=-8/3
is where the parabola crosses the y axis.
b. Graph
9x^2 + 48x +64 = 0
to show that the parabola's vertex is just above the value
x=-8/3
c. Substitute
x=-8/3
back into
9x^2 + 48x + 64 =0
and simplify to show that a true statement
results.
d. Substitute
x=-8/3
back into
9x^2 + 48x + 64 = 0
and simplify to show the values of
a
c
remain perfect squares.
Answer:
c. Substitute
Step-by-step explanation:
A graph of the function on the left shows the parabola touches the x-axis at x = -8/3. That is, the vertex is on the x-axis. It crosses the y-axis at y = 64.
Show a value is a rootA given solution to an equation can be verified by substituting that value into the equation an showing the result is a true statement. Here, the value x=-8/3 is a root of the given equation because that value makes the equation true.
[tex]9\left(-\dfrac{8}{3}\right)^2+48\left(-\dfrac{8}{3}\right)+64=0\\\\9\left(\dfrac{64}{9}\right)-\left(\dfrac{48\cdot8}{3}\right)+64=0\\\\64-\dfrac{3\cdot2\cdot8\cdot8}{3}+64=0\\\\64-2\cdot64+64=0\\\\0=0\qquad\text{True}[/tex]
Solve for x in the equation: 8a = 2xy + b.
Step-by-step explanation:
Simplifying 8a = 2xy + b
Reorder the terms: 8a = b + 2xy
Solving 8a = b + 2xy
Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right.
Divide each side by '8'. a = 0.125b + 0.25xy
Simplifying a = 0.125b + 0.25xy
find the area of the following
Answer:
24000 ft²
Step-by-step explanation:
Triangle PRS:b = base = PR = 240 ft
2AS = 240 ft
[tex]\sf AS = \dfrac{240}{2}\\\\ AS = 120 \ ft[/tex]
h = height = AS = 120 ft
[tex]\sf \boxed{\bf \ Area \ of \ triangle = \dfrac{1}{2}b*h}[/tex]
[tex]\sf =\dfrac{1}{2}*240*120\\\\ = 120 * 120\\\\ = 14400 \ ft^2[/tex]
Triangle PRQ:b = PR = 240 ft
3BQ = 240 ft
[tex]\sf BQ = \dfrac{240}{3}\\\\ BQ = 80 \ ft[/tex]
[tex]\sf Area \ of \ triangle \ PRQ = \dfrac{1}{2}*240*80[/tex]
= 120 * 80
= 9600 ft²
Area of the quadrilateral PQRS = area of ΔPRS + area of ΔPRQ
= 14400 + 9600
= 24000 ft²
Which function has the domain as y=2 square root of x
Using it's concept, any function with domain [tex]x \geq 0[/tex] has the same domain as [tex]y = 2\sqrt{x}[/tex].
What is the domain of a function?The domain of a function is the set that contains all possible input values for the function.
Function [tex]y = 2\sqrt{x}[/tex] is defined for [tex]x \geq 0[/tex], hence any function with domain [tex]x \geq 0[/tex] has the same domain as [tex]y = 2\sqrt{x}[/tex].
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Please help me solve this random answers will be removed
Answer:
AB-46 cm
Step-by-step explanation:
Use law of cosines
AB^2 = 24^2 + 26^2 - 2 (24)(26)cos 134
AB= 46 cm
i need help with this page
9a). The measure of segment GH from the given information can be evaluated as one-fourth of the perimeter; 48/4 = 12 cm.
9b). The measure of <EJF is 90° as the angle EJF is a right angle made at the intersection of the rhombus diagonals.
9c). The measure of <EHG is 60° as the opposite angles in a rhombus are congruent and <EHG = 2 × <EHJ = 2 × 30 = 60°.
10a). The sides labelled in the rectangle are congruent by the rectangle diagonal congruence concept; it therefore follows that the required value of x is; 9x+ 20 = 10x +8; and x = 12.
10b). The angle measures as labelled in the rhombus are congruent as this follows from the fact that the diagonal is an angle bisector. Hence, 2x +15 = 5x +3; and x = 4.
What is congruence?The concept of congruence describes a similarly between 2 or more geometric figures or elements.
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Need help with this,30 points, please help very soon, thanks
A small airplane makes a 2400 kilometer trip in 7.30 hours and makes the returned trip in six hours. If the plane travels at a constant speed wind blows at a constant rate, find the airplanes airspeed and the speed of the wind.
The speed of the airplane is 360 km/h while the speed of the wind is 40 km/h.
What is an equation?An equation is an expression that shows the relationship between two or more variables and numbers.
Let a represent the speed of the airplane and b represent the speed of the wind, hence:
(a + b)6 = 2400
a + b = 400 (1)
Also:
(a - b)7.5 = 2400
a - b = 320 (2)
From eqn 1 and 2:
a = 360 km/h, b = 40 km/h
The speed of the airplane is 360 km/h while the speed of the wind is 40 km/h.
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find the value in the figure