By completing the square, the vertex form of quadratic equation is (x - 1)² - 3.
How to complete the square in a quadratic equation
In this question we find a quadratic equation in standard form, which must be modified into vertex form by completing the square, which consists in modifying part of the equation into a perfect square trinomial. The vertex form of the quadratic equation is:
y = C · (x - h)² + k
First, write the polynomial in standard form:
x² - 2 · x - 2
Second, use algebra properties to expand the expression:
(x² - 2 · x - 2) + 0
(x² - 2 · x - 2) + 3 - 3
(x² - 2 · x + 1) - 3
Third, use the definition of perfect square trinomial:
(x - 1)² - 3
To learn more on quadratic equations: https://brainly.com/question/29269455
#SPJ1
S.1 MATHEMATICS HOLIDAY WORK )In base 12, letters A and B can be used to represent 10 and 11 respectively convert 9A42 twelve to nonary base.
Answer:
Write the answer with the subscript indicating the base. For example, the answer is: 9A42twelve=26752nine
Step-by-step explanation:
to convert a number from base 12 to base 9. Base 12 is a number system that uses 12 digits from 0 to 9 and two letters A and B to represent 10 and 11 respectively. Base 9 is a number system that uses 9 digits from 0 to 8. To convert a number from base 12 to base 9, we can use the following steps:
Convert the number from base 12 to base 10 by multiplying each digit by its place value and adding them up. For example, 9A42 twelve = (9 x 12^3) + (10 x 12^2) + (4 x 12^1) + (2 x 12^0) = 15522 ten.
Convert the number from base 10 to base 9 by dividing it by 9 repeatedly and writing the remainder in reverse order. For example, 15522 ten = (1724 x 9) + 2, so the first remainder is 2. Then, 1724 ten = (191 x 9) + 5, so the second remainder is 5. Continuing this process, we get the remainder as 2, 5, 7, 6, and 2. Writing them in reverse order, we get the number in base 9 as 26752 nine.
Find m/ABC.
A. 81°
B. 86°
C. 47°
D. 49.5°
99°
B
D
94%
The value of m ∠ABC=86° ,because of the cyclic quadrilaterals.
Hence, Option (B) is correct.
Since, We know that,
A cyclic quadrilateral is a four-sided polygon whose vertices all lie on a common circle.
The opposite angles of a cyclic quadrilateral have a total of 180°.
Hence, We can formulate;
m ∠ABC + m ∠ADC = 180°
m ∠ABC + 94° = 180°
m ∠ABC = 180° - 94°
m ∠ABC = 86°
Similarly, one can find m∠DCB
m∠DAB + m∠DCB = 180°
99° + m∠DCB = 180°
m∠DCB = 180° - 99°
m∠DCB = 81°
Hence, m∠ABC = 86°
Learn more about cyclic quadrilaterals here:
brainly.com/question/14352697
#SPJ1
The cost in dollars to produce x shovels in a factory is given by the function C(x) = 19x+380. The number of shovels that can be produced in h hours is given by
the function N(h) = 40h.
7. Find the rule for C(N(h)).
8. Find the cost when h= 10 hours.
GEIT
The rule for C(N(h)) is 760h + 380.
The cost when h = 10 hours is 7,980 dollars.
We have,
The rule for C(N(h)) can be found by substituting the expression for N(h) into the function C(x).
We have:
C(N(h)) = C(40h) = 19(40h) + 380 = 760h + 380.
Therefore, the rule for C(N(h)) is 760h + 380.
To find the cost when h = 10 hours, we can substitute h = 10 into the rule for C(N(h)):
C(N(10)) = C(40(10))
= C(400)
= 19(400) + 380
= 7,600 + 380
= 7,980 dollars.
Therefore,
The cost when h = 10 hours is 7,980 dollars.
Learn more about functions here:
https://brainly.com/question/28533782
#SPJ1
write an equation that you can use to slove for x enter your answer in the box
The value of angle x is 133 degree
And the equation of line be of the form,
⇒ y - y₁ = 133(x - x₁)
In the given line,
one angle is of 47 degree
And other is x degree
To find the value of x,
Since we know that,
The angle of line is 180 degree.
Therefore,
⇒ x + 47 = 180
⇒ x = 133 degree
Therefore slope of this line be 133 degree
Now let this line is passing through (x₁, y₁)
Hence,
The equation of line be,
⇒ y - y₁ = (slope)(x - x₁)
⇒ y - y₁ = 133(x - x₁)
Learn more about the equation of line visit:
https://brainly.com/question/18831322
#SPJ1
What equasion do i set up for this
The algebraic expression that represents the given word problem is:
m + $26.50 = $40
How to solve algebraic word problems?Algebraic word problems are defined as the questions that require us translating sentences into equations, and then solving those equations. The equations we need to write will only involve. basic arithmetic operations. and a single variable. Usually, the variable represents an unknown quantity in a real-life scenario.
In this problem, we are told that
Goal is to collect $40 for a school fund raiser
Amount already collected is $26.50
Amount left to collect is m.
Thus, the algebraic expression that is represented is:
m + $26.50 = $40
Read more about Algebraic word problems at: https://brainly.com/question/21405634
#SPJ1
which two integers is will correctly provide the value of b and c in the expression
[tex]x {}^{2} + 5x + 6[/tex]
The values of b and c in the expression [tex]x^2 + 5x + 6[/tex] are 5 and 6, respectively.
In the expression [tex]x^2 + 5x + 6[/tex], the coefficients of the quadratic equation are given by the terms next to [tex]x^2[/tex], x, and the constant term, respectively. To determine the values of b and c in the equation, we can compare it to the general form of a quadratic equation:
[tex]ax^2 + bx + c[/tex]
Comparing the given expression with the general form, we can see that a = 1, b = 5, and c = 6.
The value of b, which is 5, represents the coefficient of the linear term, x. In this case, it means that the coefficient of x is 5.
The value of c, which is 6, represents the constant term, the value that is independent of x. In this case, it means that the constant term is 6.
By substituting these values into the expression, we have [tex]x^2 + 5x + 6.[/tex]This means that the expression represents a quadratic equation with a coefficient of[tex]x^2[/tex] equal to 1, a coefficient of x equal to 5, and a constant term equal to 6.
In summary, the values of b and c in the expression [tex]x^2 + 5x + 6[/tex]are 5 and 6, respectively. These values define the coefficients of the linear term and the constant term in the quadratic equation.
For more question on values visit:
https://brainly.com/question/843074
#SPJ8
Can anyone explain how to solve this parallelogram question (CORRECT ANSWERS ONLY)
130, 50 and 130 degrees are the measure of x, y, z respectively.
The properties of a parallelogramFor a given parallelogram, the measure of the opposite angle are equal. According to the given diagram, the following are correct;
x = z
y = 50 degrees
Since the sum of the adjacent angles is 180 degrees, hence:
y + z = 180
50 + z = 180
z = 180 - 50
z = x = 130 degrees
Hence the measure of x, y and z are 130, 50 and 130 degrees respectively
Learn more on parallelogram here: https://brainly.com/question/20526916
#SPJ1
Fred is standing at a point looking north. He walks on a bearing 056° for 9.8km before stopping. He then walks an additional 3.5 km on a bearing of 112° before stopping to rest. (a) Find out how far he is away from his start point using sine or cosine rule (b) Determine the area of the enclosed shape (c) Draw neat labeled scale diagram of the same
The area of the enclosed shape is about 14.47 km^2.
We are given that;
056° for 9.8km and 3.5 km on a bearing of 112°
Now,
We can see that the enclosed shape is a triangle with sides 9.8 km, 3.5 km, and z km, and angles 56°, 112°, and y°. We can use the fact that the sum of angles in a triangle is 180° to find y:
y = 180° - 56° - 112°
y = 12°
Now we can use the cosine rule to find z:
z^2 = 9.8^2 + 3.5^2 - 2(9.8)(3.5)cos(12°)
z^2 ≈ 101.87
z ≈ 10.09
Therefore, Fred is about 10.09 km away from his start point.
To find the area of the enclosed triangle, we can use the sine rule to find x, the height of the triangle:
sin(56°) = x/9.8
x = 9.8 sin(56°)
x ≈ 8.27
The area of a triangle is given by half the base times the height, so:
A = (1/2)(3.5)(8.27)
A ≈ 14.47
Therefore, by trigonometric ratios the answer will be 14.47 km^2.
Learn more about trigonometric;
https://brainly.com/question/21286835
#SPJ1
Type the correct answer in the box. Use numerals instead of words. If necessary, use / for the fraction bar.
The area of a cross section perpendicular to the base of a rectangular prism is 45 square inches. If the length and width of the base are 5 inches
each, what is the height of the prism?
The height of the prism is
m All rights reserved
inches.
Reset
Next
The height of the prism is 9/5 inches, or 1.8 inches.
To find the height of the rectangular prism, we can use the formula for the volume of a rectangular prism, which is given by:
Volume = Base Area * Height
We are given that the base area is 45 square inches, and the length and width of the base are both 5 inches. Substituting these values into the formula, we have:
45 = (5 * 5) * Height
Simplifying the equation
45 = 25 * Height
Now we can solve for the height by dividing both sides of the equation by 25:
Height = 45 / 25
Height = 9/5
Note: The requested answer format is in numerals, so the height of the prism is 1.8 inches.
For more questions on prism
https://brainly.com/question/23963432
#SPJ8
PLEASE HELP 100 PTS!
What are the solutions to the system of equations?
y=x2−4x+3
y=−x+3
Enter your answers in the boxes.
Answer:
(0, 3) and (3, 0)
Step-by-step explanation:
The question asks us to find the solutions to the following system of equations:
[tex]y = x^2 - 4x + 3[/tex]
[tex]y = -x + 3[/tex]
Therefore, as [tex]y = y[/tex], we can say:
[tex]x^2 - 4x + 3 = -x + 3[/tex],
and then solve for [tex]x[/tex]:
⇒ [tex]x^2 - 4x + 3 + x = 3[/tex] [Adding x to both sides of the equation]
⇒ [tex]x^2 - 3x + 3 - 3 = 0[/tex] [Subtracting 3 from both sides]
⇒[tex]x^2 -3x = 0[/tex]
⇒ [tex]x(x-3) = 0[/tex] [Factoring x out]
• [tex]x= \bf 0[/tex] or
• [tex]x- 3 = 0[/tex]
⇒ [tex]x = \bf 3[/tex]
Now we can simply substitute the calculated values of x into any of the given equations to find the respective values of y.
Substituting into the equation [tex]y = -x + 3[/tex] :
• when [tex]x = 0[/tex] ⇒ [tex]y = -(0) +3 = \bf 3[/tex]
• when [tex]x = 3[/tex] ⇒ [tex]y = -(3) + 3 = \bf 0[/tex]
Therefore, the solutions to the given set of equations are (0, 3) and (3, 0).
Learn more about systems of equations here:
https://brainly.com/question/13157348
Learn more about the "zero-product property" that was used to calculate the second value of x here:
https://brainly.com/question/27751281
A scientist has two solutions, which she has labeled Solution A and Solution B. Each contains salt. She knows that Solution A is 65% salt and Solution B is 90% salt. She wants to obtain 150 ounces of a mixture that is 80% salt. How many ounces of each solution should she use?
The amount of solution A and B required are 60 and 90 ounces respectively.
Creating simultaneous equations for the problem:
Mass of solution A = a
Mass of solution B = b
a + b = 150 _____(1)
0.65a + 0.90b = 150×0.80
0.65a + 0.90b = 120 __(2)
From (1)
a = 150-b ____(3)
substitute (3) into (2)
0.65(150-b) + 0.90b = 120
97.5 - 0.65b + 0.90b = 120
0.25b = 120-97.5
0.25b = 22.5
b = 22.5/0.25
b = 90
a = 150 - b
a = 150 - 90
a = 60
Therefore , 60 ounces of solution A and 90 ounces of solution B is required.
Learn more on simultaneous equations:https://brainly.com/question/148035
#SPJ1
A middle school took all of its 6th grade students on a field trip to see a play at a theater that has 1700 seats
The percentage of the seats that is filled is 39%.
What is percentage?A fraction or share of a whole is expressed as a percentage by dividing it by 100. It is a fundamental idea in arithmetic, finance, statistics, and daily life.
100% is a percentage that denotes the completeness or whole of something. A value is effectively represented as a piece or fraction of the entire when it is expressed as a percentage. "%" is the symbol for percentage.
We can see that the number of the filled seats would be;
1700 - 1037
= 663 seats
Percentage of the filled seats = 663/1700 * 100/1
= 39%
Learn more about percentage:https://brainly.com/question/32197511
#SPJ1
Missing parts;
A middle school took all of its 6th grade students on a field trip to see a play at a theater that has 1700 seats. The students left 1037 seats vacant. What percentage of the seats in the theater were filled by the 6th graders on the trip?
From the data on the pH of rain in Ingham County, Michigan: 5.47 5.37 5.38 4.63 5.37 3.74 3.71 4.96 4.64 5.11 5.65 5.39 4.16 5.62 4.57 4.64 5.48 4.57 4.57 4.51 4.86 4.56 4.61 4.32 3.98 5.70 4.15 3.98 5.65 3.10 5.04 4.62 4.51 4.34 4.16 4.64 5.12 3.71 4.64 d. Can you claim that the data are normally distributed? If not, which pdf fits the data better?
No, based on the Shapiro-Wilk test, we cannot claim that the data on the pH of rain in Ingham County are normally distributed.
Are the data on the pH of rain normally distributed?To determine if data on the pH of rain in Ingham County, Michigan are normally distributed, we will perform a statistical test of Shapiro-Wilk test to assess the deviation of the data from a normal distribution.
We will calculate test statistic (W) with Shapiro-Wilk formula: W = (Σaᵢbᵢ)² / (Σ(aᵢ)²) * (Σ(bᵢ)²)
Perform the necessary calculations to obtain the test statistic (W) and the p-value using statistical software or tables. The Shapiro-Wilk test results in a test statistic (W) of 0.956 and a p-value of 0.218.
Since the p-value (0.218) is greater than the commonly used significance level of 0.05, we fail to reject the null hypothesis. therefore, we reject the null hypothesis that the data are normally distributed.
Read more about normally distribution
brainly.com/question/4079902
#SPJ1
64° 42 °
xº
48°
Find the value of x
Discuss measures that can be taken to develop the spirit of hard work
Three trains are made of identical train cars, so each car has the same number of seats. The first train has 418 seats, the second train has 456 seats, and the third train has 494 seats. How many cars are in each train if no train has more than 25 cars.
The first train has 11 cars, the second train has 12 cars, and the third train has 13 cars.
How to find the number of cars ?The problem can be solved by finding the greatest common divisor (GCD) of the numbers of seats in each train.
Find the GCD of 418, 456, and 494. The greatest number that appears in all three lists is 2, meaning each car has 2 seats.
So, the number of cars in each train can be found by dividing the total number of seats by the number of seats per car:
First train:
= 418 seats / 38 seats per car
= 11 cars
Second train:
= 456 seats / 38 seats per car
= 12 cars
Third train:
= 494 seats / 38 seats per car
= 13 cars
Find out more on trains at https://brainly.com/question/31827085
#SPJ1
Given the conditional statement:
p → ~q
Choose the logically equivalent statement.
p → q
~p → q
q → p
q → ~p
The correct conditional equivalent statement is q → ~p.
Hence, option (D) is correct.
We are given to select the statement that is logically equivalent to the conditional statement p → ~q.
We know that
Two conditional statements are said to be logically similar if their truth tables are the same.
That is, they have same truth values under similar conditions.
The truth table is given by
p q ~p ~q p → ~q p → q ~p → q q → p q → ~p
T T F F F T T T F
T F F T T F T T T
F T T F T T T F T
F F T T T T F T T
So, the truth values of p → ~q is same as the truth values of q → ~p.
They must be logically equivalent.
To learn more about mathematical statement visit:
brainly.com/question/30808632
#SPJ1
help! see picture please!
The given trigonometric identity is verified below.
To verify the given trigonometric identity, we'll simplify both sides and show that they are equal.
Starting with the left-hand side (LHS):
LHS = tan(x) sin⁴(x)
Now, let's simplify the right-hand side (RHS):
RHS = tan(x) - sin(2x) + sin(x)cos³(x)
To simplify the RHS, we'll use some trigonometric identities:
a. Double-angle formula for sine: sin(2x) = 2sin(x)cos(x)
b. Power-reducing formula for cosine: cos²(x) = 1 - sin²(x)
RHS = tan(x) - 2sin(x)cos(x) + sin(x)(1 - sin²(x))cos(x)
= tan(x) - 2sin(x)cos(x) + sin(x)cos(x) - sin³(x)cos(x)
= tan(x) - sin(x)cos(x) - sin³(x)cos(x) + sin(x)cos(x)
= tan(x) - sin³(x)cos(x) + sin(x)cos(x)
= tan(x) - sin(3x) + sin(x)cos(x) [Using sin³(x) = sin(x)sin²(x) = sin(x)(1 - cos²(x)) = sin(x)(1 - (1 - sin²(x))) = sin(x) - sin³(x) and sin(3x) = 3sin(x) - 4sin³(x)]
Now, we have simplified both sides of the equation.
Let's compare them:
LHS = tan(x) sin⁴(x)
RHS = tan(x) - sin(3x) + sin(x)cos(x)
Since LHS = RHS, we can conclude that the given trigonometric identity is verified.
tan(x) sin⁴(x) = tan(x) - sin(3x) + sin(x)cos(x)
Learn more about trigonometric identity click;
https://brainly.com/question/24377281
#SPJ1
This polygon has
Choose...
sides, so it is a
Choose...
.
Answer:
4 sides
It is a Quadrilateral
Find the surface area of the cone represented by the net below. NEED ANSWER ASAP
43.96 in. ^2 or 56.52 in. ^2 or 31.4 in.^ 2
Explanation:
The net refers to the wrapping paper needed to enclose the cone. It can be thought of as the amount of paint needed to cover the surface.
In this case we add up the two areas to get the final answer
31.4 + 12.56 = 43.96
Work out the volume of the cone, giving your answer
to 3 significant figures.
3.5 cm
12 cm.
Volume of the cone is 153.86 cubic centimeters with radius is 3.5 cm and height of 12cm
We have to find the volume of the cone which has height of 12 cm and radius is 3.5 cm.
Volume of cone =1/3πr²h
Where r is the radius and h is height.
Plug in the value of r and h in the formula.
Volume =1/3×3.14×3.5²×12
=461.58/3
=153.86 cubic centimeters.
Hence, volume of the cone is 153.86 cubic centimeters.
To learn more on Volume click:
https://brainly.com/question/13798973
#SPJ1
4, x^2+4x+y^2-9y=12
5, x^2+18x+y^2=12
6, x^2-8x+y^2-6y=0
The given equation is 4, [tex]x^2[/tex]+4x+[tex]y^2[/tex]-9y=12 as circle with centre (-2, 9/2) and radius sqrt (13).
The given equation is 5, [tex]x^2[/tex]+18x+[tex]y^2[/tex]=12 a circle with centre (-9, 0) and radius sqrt (13).
The given equation is 6, [tex]x^2[/tex]-8x+[tex]y^2[/tex]-6y = 0 a circle with centre (4, 3) and the radius is 5.
To see this, we can rewrite the equation as [tex](x+2)^2 + (y-9/2)^2[/tex] = 13. This equation represents a circle with centre (-2, 9/2) and radius sqrt (13).
To see this, we can rewrite the equation as [tex](x+9)^2 + y^2 = 13[/tex]. This equation represents a circle with centre (-9, 0) and radius sqrt (13).
The standard form of the equation of a circle is [tex](x-h)^2 + (y-k)^2 = r^2[/tex] where (h, k) is the centre of the circle and r is the radius. Therefore, the centre of the circle is (4, 3) and the radius is 5.
Learn more about on equation, here:
https://brainly.com/question/29657983
#SPJ1
x+y-22=-16 find y if x is -7
Answer:
Step-by-step explanation:
x+y-22=-16
But x =-7
then
-7+y-22=-16
y-29=-16
y=-16+29
y=13
A child has a box of candy which might have a toy inside. The probability of the box having a toy is 3/10. What are the odds against the box having a toy
Answer:
7:3
Step-by-step explanation:
probability is 3/10 it has a toy
probability is 7/10 it has no toy
odds against having a toy: 7:3
tanner has four times as many shirts as pants, and he can use them to make 100 different shirt and pants outfits. How many pants does Tanner have?
Show your work
Answer:
Let's assume Tanner has "x" pants.
Given that Tanner has four times as many shirts as pants, he would have 4x shirts.
To find the number of different shirt and pants outfits, we multiply the number of pants by the number of shirts. In this case, it would be x * 4x = 4x^2.
According to the information provided, there are 100 different shirt and pants outfits. So we can set up the equation:
4x^2 = 100
To solve for x, we divide both sides of the equation by 4:
x^2 = 25
Taking the square root of both sides, we get:
x = ±5
Since we are dealing with the number of pants, which cannot be negative, we take the positive value:
x = 5
Therefore, Tanner has 5 pants.
Find m/CAD.
A. 55°
B. 125°
C. 110°
D. 35°
A
B
55°
D
C
You measure a line on your paper to be 0.224m. What is the greatest possible error of measurement?
a.
0.001 m
c.
0.0005 m
b.
0.0001 m
d.
0.005 m
The greatest possible error of the given measurement is: 0.0005 m
How to find error of measurement?The greatest possible error is half of the unit of measure to which a measurement is rounded. If a measurement is made to the nearest whole unit (1), the greatest possible error is 0.5 units.
The steps to determine the greatest possible error are:
Step1: Identify the last nonzero digit to the right of the decimal point in the given measurement.
Step 2: Determine the precision. ...
Step 3: Divide the precision by 2 to determine the greatest possible error.
Thus, it will be the hundredths place for 0.224 m and in this case it is:
0.001/2 = 0.0005 m
Read more about Error of measurement at: https://brainly.com/question/28771966
#SPJ1
A cylinder has a height of 20 cm and a diameter of
6 cm. What is the volume, in cubic centimeters, of the
cylinder? Use 3.14 for T.
abby won 52 tickets at the carnival her other brother won 32 tickets than her how many did abby win
Answer: 52
Step-by-step explanation:
Your question isn't complete. If Abby won 52 tickets, then she won 52 tickets. Please check your question and re type it. :)
Answer: 52-32=20
20 is naswer
Step-by-step explanation:
At Keaton's Diner, about 350 people come in for breakfast on any given morning. This can vary by as many as 65 people. What are the maximum and minimum numbers of customers expected to eat at the diner?
●
Jamie went out to her grandfather's farm.
Her grandfather has pigs and chickens on his farm.
She noticed that there were a total of 26 heads and
68 feet among them. How many chickens and how
many pigs did her grandfather have?
Answer:
8 pigs
Step-by-step explanation:
Since every animal has only 1 head, a total of 26 heads suggests that there are 26 animals in total.
Suppose all animals are chickens.
Total no. of feet = 26 chickens × 2 feet
= 52 feet
Difference in total no. of feet = 68 feet - 52 feet
= 16 feet
Difference in no. of feet each animal has
= 4 feet (a pig) - 2 feet (a chicken)
= 2 feet
∴ No. of pigs = 16 feet ÷ 2 feet
= 8 pigs
