A quadratic equation x² = 16 has two solutions, x = 4 and x = -4.
A quadratic equation has standard form:
ax² + bx + c = 0
There are several methods to solve a quadratic equation:
- using factorization
- by completing the square
The given quadratic equation is: x² = 16
Method 1: Using factorization
x² = 16
x² - 16 = 0
(x + 4) (x - 4) = 0
Hence, the solution is x = 4 and x = -4
Method 2: By completing the square
x² = 16
This is already a perfect square. Hence,
x = ±√16
x = ±4
Hence, the solution is x = 4 and x = -4
Conclusion: there are two solutions of x² = 16, x = 4 and x = -4
There was typos in your question, most likely your question was:
How many solutions does x² = 16 have?
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How to add fractions with unlike denominators
A rectangle with dimensions 7x4 was outlined on grid paper.
How many squares will a diagonal of this rectangle intersect?
(B) 9
(D) 11
(0) 10
A8
(E) 12
A diagonal of a rectangle will intersect the same number of squares as the length of the rectangle. The rectangle has a length of 7 squares and a width of 4 squares, so the diagonal will intersect 12 squares.
A diagonal of a rectangle will always intersect the same number of squares as the length of the rectangle. In this case, the rectangle has been outlined on a grid paper with dimensions of 7x4. This means that the length of the rectangle is 7 squares and the width is 4 squares. Therefore, the diagonal of this rectangle will intersect 12 squares in total. This is because the length of the rectangle is greater than the width and so the diagonal must intersect the entire length of the rectangle and all of the squares the width intersects. As a result, the diagonal of this rectangle will intersect 12 squares.
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What is the y intercept
Answer:
use y=mx+b. ... ...... ...
f(x) = 6x; f(x) = -24
Answer: X = -4
Step-by-step explanation:
Well, we are given two functions. We know that both of these functions are to be having the same value (they are both f(x) equations).
Therefore, we can create this equation:
6x = -24
We divide both sides by x to get:
x = -4
Find the area of the rectangle whoe ide are 12x to the power of 6 y quared and 5xy to the power of 7
The area of the rectangle is [tex]60x^{7y^{9} }[/tex] whoe ide are 12x to the power of 6 y quared and 5xy to the power of 7.
What is rectangle ?
A rectangle is a type of quadrilateral that has its parallel sides equal to each other and all the four vertices are equal to 90 degrees. Hence, it is also called an equiangular quadrilateral. Since, the opposite sides are equal and parallel, in rectangle, therefore, it can also be termed as a parallelogram.
The area of a rectangle is found by multiplying its length by its width. In this case, the length is given as [tex]12x^{6y^{2} }[/tex]and the width is given as [tex]5xy^{7}[/tex]. To find the area, we simply multiply these two values together:
Area = ([tex]12x^{6y^{2} }[/tex]) * ([tex]5xy^{7}[/tex]) = [tex]60x^{7y^{9} }[/tex]
So the area of the rectangle is [tex]60x^{7y^{9} }[/tex] whoe ide are 12x to the power of 6 y quared and 5xy to the power of 7.
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Ratnam hired a car from a car renting agency which charges a flat amount of Rs. x for travelling up to 40 kilometres and Rs. y per km for every kilometer travelled thereafter. How much should Ratnam pay the agency for a journey of 50 kilometres?
Ratnam will have to pay Rs. (x+50y) to the agency for a journey of 50 kilometers.
What are words problems?A word problem is a few sentences describing a 'real-life' scenario where a problem needs to be solved by way of a mathematical calculation.
Given that, Ratnam hired a car from a car renting agency which charges a flat amount of Rs. x for travelling up to 40 kilometers and Rs. y per km for every kilometer travelled thereafter.
We need to find how much should Ratnam pay the agency for a journey of 50 kilometers,
The amount for travelling a km is Rs. y
Therefore, for 50 km it will cost = 50y
Since, they are charging Rs. x as a flat amount,
Therefore, the total cost of travelling 50 km is = x+50y
Hence, Ratnam will have to pay Rs. (x+50y) to the agency for a journey of 50 kilometers.
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(NEED THE ANSWER RIGHT NOW!!!!)
A factory buys the boxes it needs in the form of flat nets. What advantages might the factory have in doing this?
Answer:
It could take up less space and be more convenient.
Answer:
none
Step-by-step explanation:
the advantage depends
How do latitudes and longitudes help in locating a point Class 6?
Latitudes and longitudes help in locating a point by providing a reference system for navigation.
They are used to pinpoint a specific location on the earth’s surface by providing coordinates. These coordinates are measured in degrees and minutes and are written in the form of a pair of numbers. Latitudes are measured in degrees north or south of the equator and are referred to as the lines of latitude. Longitudes are measured in degrees east or west of the prime meridian and are referred to as the lines of longitude. By using the coordinates of a point, the location can be accurately determined. This is especially useful for navigation, as it enables people to determine their position and travel to a specific destination.
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The triangles are similar. What is the value of x? enter your answer in the box. X = two right triangles. The larger triangle has the long leg labeled 96, the short leg labeled 28, and the hypotenuse labeled 6 x plus 28. The smaller triangle has the long leg labeled 24, the short leg labeled 7, and the hypotenuse labeled 25.
The value of x is 12.
The triangles which are similar have the same shape and measure of three angles are also same. The only thing that varies is their sides. However, the ratio of the sides of one triangle is equivalent to the ratio of the sides of another triangle, which is called here the scale factor.
By dividing the long sides and short sides, find the scale factor:
96 / 24 = 4
28 / 7 = 4
So, the large triangle is four times bigger than the small one.
Now applying the scale factor to calculate the hypotenuse:
The length of the smaller hypotenuse is 25, a scale that by 4 to get 25 * 4 =100
This means that the larger hypotenuse needs to equal 100 and the hypotenuse is labeled 6x +28:
6x+28 = 100
Subtract 28 from each side:
⇒6x = 72
Divide both sides by 6:
⇒x = 72/6
∴x = 12
So, the value of x is 12.
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describe and correct the error in graphing y={x+6 if x≤-3 and 1, if x>-2
In this function, y = x + 6, the points at x = -2 will be solid and in this function y = 1, there will be a circle at x = - 2. And the correct graph is given below.
What is a function?A function is an assertion, concept, or principle that establishes an association between two variables. Functions may be found throughout mathematics and are essential for the development of significant links.
The function is given below.
y = x + 6, x ≤ -2
y = 1, x > - 2
In this function, y = x + 6, the points at x = -2 will be solid and in this function y = 1, there will be a circle at x = - 2.
And the correct graph is given below.
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Which classification is correct for <2?
A. acute
B.right
C.straight
D.obtuse
Answer:
Option B
Step-by-step explanation:
Remember these facts about the following options:
An acute angle is less than 90 degrees.
A right angle is exactly 90 degrees.
A straight angle is more or less a straight line.
An obtuse angle is an angle greater than 90 degrees.
One of the most notable factors of a right angle is the fact that it takes the shape of an L, speaking of how the photo given takes the shape of an L we can immediately exclude options A, B, and D and say option B or
"right" is our answer.
Hope this helps.
What is real image class 10?
When the incident rays appear from a given object, then it is known as a real object. farther, the light rays emanating from the real object after reflection from the mirror, meet at a definite point, then the optically formed duplication of an object is known as an image.
There are two types of images are formed they are real image and virtual image. The real image indicates the representation of an actual object, produced when the light rays arising from a single source intersect at a particular (real) point.
On the opposite, the virtual image can be understood as the image produced due to the apparent separation of rays of light from a definite point.
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Jerome walks 90 feet from the base of a tree and looks up The ongle from the ground to the top of the free is 33° How tall is the t.ree?
Using Pythagorean theorem, The height of the tree is approximately 47.98 feet.
What does the Pythagorean theorem mean in everyday language?According to Pythagoras' Theorem, the square of a right-angled triangle's hypotenuse side is equal to the sum of the squares of its other two sides. The three sides of this triangle are known as the Perpendicular, Base, and Hypotenuse.
tan(angle) = opposite side / adjacent side
The opposite side is the height of the tree and the adjacent side is the distance from Jerome to the base of the tree (90 feet).
tan(33) = height / 90
height = tan(33) * 90
The height of the tree is approximately 47.98 feet.
Keep in mind this is an approximation as the angle in question is not a right angle and also the unit is not given so the final result is not accurate.
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if u answer it i will mark u brainiest. go to my other question to see the second graph
Answer: i dont kow
Step-by-step explanation:
Determine the null space of each of the following matrices:
2X4 matrix
(b)
1 2 -3 -1
-2 -4 6 3
3X3 matrix
(c)
1 3 -4
2 -1 -1
-1 -3 4
The Null spaces in matrix b is [tex]\left[\begin{array}{ccc}-2\\1\\0\\0\end{array}\right][/tex] , [tex]\left[\begin{array}{ccc}3\\0\\1\\0\end{array}\right][/tex]
The Null spaces for matrix C is [tex]\left[\begin{array}{ccc}0\\0\\0\end{array}\right][/tex]
For Null spaces we form an augmented matrix by appending a column of zeros to the right, and then put this matrix in reduced row-echelon form.
We convert the matrix equation back to an equivalent system. Add an equation for each free variable. Solve for each variable in terms of the free variables.
Then we collect terms into vectors and after that factor out variables on the right side. Thus, a basis for the null space is calculated. Detailed solution in the image.
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To paint a house, a company charges a flat rate of $500 for supplies, plus $50 for each hour of labour. How much would the painting company charge paint a house that needs 20 hours of labour? A house that requires 50 hours? 20 hours: $ Question B1 of 2 type your answer... 50 hours: $ Question Blank 2 of 2
Answer:
$1500
$3000
Step-by-step explanation:
let x = # of hours
$500 + ($50/hr)(20 hr) = $1500
$500 + ($50/hr)($50 hr) = $3000
Select the correct answer. how many moles are contained in 3.131 × 1024 particles? a. 5.199 mol b. 18.85 mol c. 0.5199 × 1023 mol d. 1.885 × 1047 mol
The particles contain 5.199 mol. The result is obtained by dividing the number of particles by the Avogadro number.
What is Avogadro number?Avogadro number is the number of particles contained in 1 mol of any substance. It is 6.022 × 10²³ particles/mol.
The number of particles of a substance can be expressed as
N = n × NA
Where
N = Number of particlesn = Number of molesNA = Avogadro numberThe number of particles of a substance is 3.131 × 10²⁴ particles. Find the number of moles!
With the Avogadro number, the number of moles would be
N = n × NA
3.131 × 10²⁴ = n × 6.022 × 10²³
n = (3.131 × 10²⁴) / (6.022 × 10²³)
n = 0.5199 × 10¹
n = 5.199 mol
Hence, there are 5.199 mol contained in the particles.
The answer is A.
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Could someone help with 9 and 10?
I’m lost :,)
Answer:
9.) -32 thousand ft per hour
10.) 9/4° per hour
Step-by-step explanation:
9.) To solve this problem, we first need to know the time that the plane landed, which is after 5 hours. Now, we need to find the altitude of the plane a four hours and thirty minutes, which is 16 thousand ft. Lastly, we need to know the formula for rate of change, which is change in y over change in x. Below is the work for how to solve the problem:
change in y / change in x = [tex]\frac{16-0}{4.5-5}[/tex]
[Note: four hours and thirty minutes is equal to 4.5 hours.]
[tex]\frac{16-0}{4.5-5} = \frac{16}{-0.5} =32[/tex]
So, the rate of change from four hours and thirty minutes to when the plane landed is -32 thousand ft per hour.
10.) You did number 10 for the most part, except that the denominator is 8 not 9-0. The reason for this is that is is 8 hours between 6am and 2pm, not 9. This means our final answer is 18/8, or 9/4° per hour.
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C) help please!! On picture question c.)
Answer:
A
Step-by-step explanation:
what is even going on at A
A sequence starts with: 312500, 62500, 12500, 2500
Calculate the next four terms!
My brain isnt working, please help
===================================================
Explanation:
The sequence appears to be geometric. Let's test that claim out.
Divide each term by the previous term.
r = term2/term1 = 62500/312500 = 0.2r = term3/term2 = 12500/62500 = 0.2r = term4/term3 = 2500/12500 = 0.2Each time we get the result 0.2, which is the common ratio r. It tells us this sequence is indeed geometric.
To get the next term in a geometric sequence, we multiply the last term 2500 by this common ratio.
term5 = r*term4 = 0.2*2500 = 500Follow similar steps for terms 6 through 8.
term6 = r*term5 = 0.2*500 = 100term7 = r*term6 = 0.2*100 = 20term8 = r*term7 = 0.2*20 = 4Terms 5 through 8 are 500, 100, 20, and 4 in that order.
Solve the following:-
[tex]\sf a-2 = -5[/tex]
Answer:
This equation is a simple algebraic equation. It can be solved by isolating the variable on one side of the equation.
a-2=-5
Add 2 to both sides:
a = -5+2
a = -3
So, the solution of the equation is a = -3
[tex] \tt \: a - 2 = - 5[/tex]
[tex] \: [/tex]
[tex] \tt \: a = - 5 + 2[/tex]
[tex] \: [/tex]
[tex] \large \underline{ \boxed{ \tt \color{red} a = - 3}}[/tex]
[tex] \: [/tex]
hope it helps! :)
Charlotte and her sister enjoyed a special dinner in a restaurant, and the bill was $53.86. If she leaves $6.46 for the server as her tip, what percent tip did she leave?
Charlotte and her sister enjoyed a special dinner in a restaurant, and the bill was $53.86. 11.99% tip did she leave.
Calculating the percent:Percent tip she give:
[tex]\frac{6.46}{53.86}[/tex] × 100
= 11.99 %
What percentage is it?A percentage, or percent, is a number smaller than or equal to 100. The term "per 100" refers to a percentage of a total amount. 45 percent, for instance, is 45 out of 100. Finding the share of a whole in terms of 100 is what percentage means. You can use online calculators or manually calculate it.
What is the purpose of percentages?Percentages are utilized extensively and in numerous contexts. Discounts in stores, interest rates at banks, inflation rates, and numerous media statistics are all expressed as percentages. Understanding the financial aspects of everyday life requires knowledge of percentages.
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What is the image of the point (-9,-6) after a rotation of 90 degrees counterclockwise about the origin?
The image of the point (-9, -6) after a rotation of 90 degrees counterclockwise about the origin is (6, -9).
A point in a 2D plane can be represented by its coordinates (x, y).
A rotation of 90 degrees counterclockwise about the origin can be represented by the transformation matrix:
[cos(90) -sin(90)]
[sin(90) cos(90)]
When we apply this transformation matrix to the point (-9, -6), we get the following:
[cos(90) -sin(90)][-9] = [0 * -9 + (-1) * -6] = 6
[sin(90) cos(90)][-6] = [1 * -9 + 0 * -6] = -9
Therefore, the image of the point (-9, -6) after a rotation of 90 degrees counterclockwise about the origin is (6, -9).
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A 4-pack of erasers costs $2.68. What is the unit price?
Answer: $0.67/eraser
Step-by-step explanation:
Simply divide the cost by the number of eraser in the pack which is 4 eraser.
Solution:
Let x (cost of an eraser)
x = 2.68/4
x = $0.67/eraser
QUESTION 2 2.1 Given the quadratic sequence: 20; 12; 10; 14;. 2.1.1 Determine an expression for the nth term of the pattern in the form T₁ = an² + bn+c. 2.1.2 The FIRST differences form an arithmetic sequence. Determine between which successive terms in the quadratic sequence, the FIRST difference will be 148. 2.1.3 Determine the smallest value of n for which S,> 10140 in the arithmetic sequence. 2.2. If Σ(r+b) = 10a, determine b in terms of a.
A sequence of the form a, a + d, a + 2d, a + 3d, a + 4d, etc. is an arithmetic sequence. The common difference of the sequence is d, and the number an is the first term. An arithmetic sequence's nth term is determined by the formula a = a + (n - 1)d.
What exactly is Bodmas math?Bracket, Of, Division, Multiplication, Addition, and Subtraction is referred to as BODMAS. A mathematical expression's order of operation is explained using the BODMAS. The acronym PEDMAS, which stands for Parentheses, Exponents, Division, Multiplication, Addition, and Subtraction, is sometimes used to refer to the BODMAS.
A geometric sequence is what?A geometric sequence is a set of numbers that follows a pattern in which the following term is determined by multiplying the previous one by a factor known as the common ratio, or r.
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1/2 plus 9 in fraction form
Answer:
9 1/2
Step-by-step explanation:
1/2 + 9
Answer:
19/2
Step-by-step explanation:
I am in 8th grade Ik wut the answer is bro
please help me with this question
What will be order of steps in solution?
let x = the possible number of wood pieces
24x ≤ 72
24x/24 ≤ 72/24
x ≤ 3 wood pieces
Answer:
4. x ≤ 3 wood pieces
[tex]\textsf{3.} \quad \dfrac{24x}{24}=\dfrac{72}{24}[/tex]
2. 24x ≤ 72
1. Let x = the possible number of wood pieces
Step-by-step explanation:
Step 1
Define the variable:
Let x = the possible number of wood piecesStep 2
Given that the wood the Carpenter bought is 72 inches long and he needs to cut it into pieces that are 24 inches long:
[tex]24x \leq 72[/tex]Step 3
To find the possible number of pieces the Carpenter can cut, divide both sides of the equation by 24:
[tex]\dfrac{24x}{24} \leq\dfrac{72}{24}[/tex]Step 4
Simplify both sides of the equation:
x ≤ 3 wood piecesGiven segment CB is parallel to segment ED. Find BD.
The length of segment BD on the triangle is given as follows:
BD = 12.5 units.
How to obtain the length of segment BD?The theorem used to solve this problem is given as follows:
A line parallel to one side of a triangle divides the other two proportionately.
The parallel lines in this problem are given as follows:
BC and DE.
Then the proportional segments are given as follows:
AB and AC.
Thus the proportional relationship that relates these side lengths is given as follows:
(x - 2)/3 = (x + 3)/5.
Applying cross multiplication, the value of x is obtained as follows:
3x + 9 = 5x - 10
2x = 19
x = 19/2
x = 9.5.
Then the length of BD is obtained as follows:
BD = x + 3 = 9.5 + 3 = 12.5.
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Write the first four terms of the sequence defined by an =
2, if n = 1
an-1-3, if n > 1
The first four terms of the sequence are:
a1 = 2
a2 = 2 - 3 = -1
a3 = -1 - 3 = -4
a4 = -4 - 3 = -7
The sequence defined by the rule an = 2, if n = 1; an-1-3, if n > 1, starts with the first term being 2. For all subsequent terms, the value of the previous term is subtracted by 3. Therefore, the second term of the sequence is -1 (2-3), the third term is -4 (-1-3) and fourth term is -7 (-4-3). This pattern of subtracting 3 from the previous term will continue for all subsequent terms in the sequence. The sequence can be represented by the function an = 2 - 3(n-1) for any natural number n.
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For 0 less-than x less-than startfraction pi over 2 endfraction, which expression is equivalent to startstartfraction sine (startfraction x over 2 endfraction) tangent (startfraction x over 2 endfraction) overover 1 minus cosine (x) endendfraction? a. startfraction 1 over startroot 2 (1 cosine x) endroot endfraction b. startfraction 1 over startroot 2 (1 minus cosine x) endroot endfraction c. (startroot startfraction 1 cosine (x) over 2 endfraction endroot) d. (startfraction 1 over 1 minus cosine (x) endfraction) e. (startfraction 1 cosine (x) over startroot 2 (1 minus cosine x) endroot endfraction) f. (startfraction 1 over 1 minus cosine (x) endfraction)
The single Trigonometric function is √2/2.
Trigonometric Function:
In mathematics, trigonometric functions (also called circular functions, trigonometric functions, angular functions) are real functions that relate the angles of a right-angled triangle to the ratio of the lengths of its two sides. They are widely used in all geometry-related sciences such as navigation, solid mechanics, celestial mechanics, and geodesy. They are one of the simplest periodic functions and are often used to study periodic phenomena using Fourier analysis.
The most commonly used trigonometric functions in modern mathematics are sine, cosine, and tangent. Their reciprocals are cosecane, secane, and cotangent, respectively, and are seldom used. Each of these six trigonometric functions has a corresponding inverse and a hyperbolic analogue.
According to the question:
Following are the solution to the given expression:
Given:
0 < x < π/2
[tex]\frac{sin \frac{x}{2} + cos \frac{x}{2} }{1-cos \frac{x}{2} }[/tex]
To find:
value=?
Solution:
0 < x < π/2
[tex]\frac{sin \frac{x}{2} + cos \frac{x}{2} }{1-cos \frac{x}{2} }[/tex]
Now,
Let x = π/2
[tex]\frac{sin \frac{x}{2} + cos \frac{x}{2} }{1-cos \frac{x}{2} }[/tex]
[tex]\frac{\frac{1}{\sqrt{2} * 1} }{1-0}[/tex]
[tex]\frac{1}{\sqrt{2} } * \frac{\sqrt{2} }{\sqrt{2} }[/tex]
[tex]\frac{\sqrt{2} }{2}[/tex]
Therefore, the answer is [tex]\frac{\sqrt{2} }{2}[/tex].
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