Answer:
3 1/2
Step-by-step explanation:
Rewriting our equation with parts separated
=6+1/4−2−3/4=6+1/4−2−3/4
Solving the whole number parts
6−2=4/6−2=4
Solving the fraction parts
1/4−3/4=−2/4 1/4−3/4=−2/4
Reducing the fraction part, 2/4,
−2/4=−1/2−2/4=−1/2
Combining the whole and fraction parts
4−1/2=3 1/2
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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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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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 piecesWhich equation is equivalent to ? x + 9 = x + 10 x + 9 = x2 + 20x + 100 x2 + 81 = x2 + 100 x2 + 81 = x2 + 20x + 100.
The equation (√x^2+81 = x+10 ) is equivalent to D: ( x^2 + 81 = x^2 + 20x + 100).
To prove that ( √x^2+81 = x+10 )is equivalent to ( x^2 + 81 = x^2 + 20x + 100 ), we will show that one equation is a consequence of the other.
First, we begin by squaring both sides of the equation ( √x^2+81 = x+10 ). This gives us ( x^2+81 = x^2+20x+100 ).
We can see that if ( √x^2+81 = x+10 ) is true, then (x^2 + 81 = x^2 + 20x + 100) must also be true because the left side of the equation is the square of the right side.
The other way around, if ( x^2 + 81 = x^2 + 20x + 100 ) is true, then we can take the square root of both sides and get (√x^2+81 = x+10 ).
So, the equation ( √x^2+81 = x+10 ) is equivalent to ( x^2 + 81 = x^2 + 20x + 100).
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The family minivan can hold 14 gallons of gas. During a trip to the Seattle Zoo, the van uses 8.4 gallons of gas. What percent of the total gas was used?
Answer: To find the percent of gas used, we need to divide the amount of gas used by the total amount of gas the van can hold and multiply by 100.
Percent of gas used = (Gas used / Total gas) * 100
Given that the van uses 8.4 gallons of gas and can hold 14 gallons of gas, we can substitute these values into the formula:
Percent of gas used = (8.4 / 14) * 100
By performing this calculation we can get that the percent of gas used was: 8.4/14 = 0.6 = 60%
So, 60% of the total gas was used during the trip to the Seattle Zoo.
Step-by-step explanation:
Answer:
60%
Step-by-step explanation:
8.4 divided by 14 = 0.6. Let 1 be the 100%. Since 0.6 is the same as 0.60, we remove the decimal and make it 60.
What should be added to the product of X and 2 to get X Class 8?
X should be subtracted from the product of X and 2 to obtain X, this can be represented as 2X - X = X, This operation is the inverse of addition, therefore it undoes the addition of X to 2X, resulting in the original number X.
To obtain the equation X from the product of X and 2, you would need to subtract X from the product. In other words, you would need to subtract the factor X from the product.
X × 2 - X = X
This can be simplified as
2X - X = X
So, X should be subtracted from the product of X and 2 to get X.
It is important to note that this is only true when X is not equal to zero, because if X is zero, any number multiplied by zero will give zero, and subtracting zero from zero will not give zero.
It can be seen that the operation of subtraction is the inverse of addition, therefore if you subtract X from 2X, you are essentially undoing the addition of X to 2X, which gives the original number X.
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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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At pizza Pi, 30 percent of the pizza made last week had extra cheese. If 150 pizzas were made, how many pizza had extra cheese
As 30% of the pizza were made, we will have 500 pizzas that as extra cheese.
How do we calculate the number of pizza that has extra cheese?At Pizza Pi, the number of Pizzas that had extra cheese last week = 150
The percentage of Pizzas that had extra cheese last week = 30%
Now, let us assume that number of Pizzas made last week = X. Then, we will write the equation as:
30X/100 = 150
30X = (150 * 100)
30X = 15000
X = 15000/30
X = 500. Therefore, it can be deducted that 500 pizzas were made last week .
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What is the name of the triangle whose all sides are of different measures?
The name of the triangle whose all sides are of different measures is Scalene triangle
What is a Scalene Triangle ?A scalene triangle is a triangle with three different side lengths and three different angle measurements. The total of all internal angles, however, is always equal to 180 degrees.
One of the three kinds of triangles that are categorized according to their sides is the scalene triangle. The isosceles triangle and the equilateral triangle are the other triangles depending on their sides. A triangle with scalene sides is one with distinct lengths on each side.
The following are a few of the scalene triangle's key characteristics:
It does not have equal sides.No equivalent angles exist.It lacks a symmetry line.No point symmetry exists.This triangle can have acute, obtuse, or right angles inside of it.The circumscribing circle's center will be within a triangle if all of the triangle's angles are less than 90 degrees (acute).The circumcenter will be outside the triangle in a scalene obtuse triangle.Obtuse, acute, or right triangles are all examples of scalene triangles.To learn more about triangles refer to :
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The name of the triangle whose all sides are of different measures is Scalene triangle
What is a Scalene Triangle ?A scalene triangle is a triangle with three different side lengths and three different angle measurements. The total of all internal angles, however, is always equal to 180 degrees.
One of the three kinds of triangles that are categorized according to their sides is the scalene triangle. The isosceles triangle and the equilateral triangle are the other triangles depending on their sides. A triangle with scalene sides is one with distinct lengths on each side.
The following are a few of the scalene triangle's key characteristics:
It does not have equal sides.No equivalent angles exist.It lacks a symmetry line.No point symmetry exists.This triangle can have acute, obtuse, or right angles inside of it.The circumscribing circle's center will be within a triangle if all of the triangle's angles are less than 90 degrees (acute).The circumcenter will be outside the triangle in a scalene obtuse triangle.Obtuse, acute, or right triangles are all examples of scalene triangles.
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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:
In a bag of Christmas treats,there are 3 red candy canes for every 5 gingerbread men. If there are a total of 40 treats, how many are candy canes?
Answer:
Candy canes are a classic Christmas treat, traditionally white with red stripes and flavored with peppermint. They have been popular since the 1600s and are thought to have originated in Germany. Today, 90 percent of all candy canes are sold between Thanksgiving and Christmas.
In a bag of Christmas treats, there are 3 red candy canes for every 5 gingerbread men. If there total is 40 treats, then the number of candy canes will be 24. This can be calculated by taking 40 divided by 8 (5+3) which equals 5, and then multiplying this by 3 which equals 15. Therefore, 24 candy canes are included in the bag of 40 Christmas treats.
Step-by-step explanation:
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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Given 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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Shen and Kaitlin each opened a savings account today. Shen opened his account with a starting amount of $770, and he is going to take out $30 per month.
Kaitlin opened her account with a starting amount of $935, and she is going to take out $45 per month.
Let x be the number of months after today.
(a) For each account, write an expression for the amount of money in the account after x months.
Amount of money in Shen's account (in dollars) =
Amount of money in Kaitlin's account (in dollars) =
(b) Write an equation to show when the two accounts would have the
same amount of money.
Jee ha aved $51 if we have aved five time a much money a Jee how much money ha Lee aved
Lee has saved $255. This can be found by multiplying Jee's aved amount of $51 by 5. Therefore, Lee has aved $255.
First, we need to calculate how much money Jee has aved. We know Jee has aved $51, so we multiply that by 5 to find out how much money Lee has aved.
51 x 5 = 255
Therefore, Lee has aved $255. Jee has aved $51, and if we multiply that amount by 5, we can calculate how much money Lee has aved. To find the answer, we first need to multiply 51 by 5. When we do this, we get the amount of money that Lee has aved, which is $255. This means that Lee has aved five times as much money as Jee has aved, which is $255. This can be found by multiplying Jee's aved amount of $51 by 5. Therefore, Lee has aved $255.
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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
Find the missing side length. Round to the nearest tenth if needed.
Answer:
b = 10.24 units.
Step-by-step explanation:
Pythagorean Theorem The Pythagorean Theorem explains the connection between a right triangle's three sides. The area of the square produced on the hypotenuse of any right triangle is equal to the sum of the areas of the squares formed on its legs: a2 + b2 = c2.a, is the shortest leg of the triangle or the opposite.b, is the adjacent leg of the triangle. This leg typically forms the right angle of the triangle.c, is the hypotenuse. This is the longest leg of the triangle. Applying the theorem[tex]a^{2} + b^{2} = c^{2}[/tex][tex]4^{2} + b^{2} = 11^{2}[/tex][tex]16 + b^{2} = 121[/tex][tex]b^{2} = 121-16[/tex][tex]b^{2} = 105[/tex][tex]\sqrt{b^{2}} = \sqrt{105}[/tex][tex]b = 10.24[/tex]The adjacent is 10.24 units long.
Please let me know if this helped!!!
What is the sin ratio of angle ~0 ? Start by finding the lengths of the sides of the triangle.
Answer:
sinΘ = [tex]\frac{4}{5}[/tex]
Step-by-step explanation:
given the point (3, 4 )
the x- coordinate indicates the horizontal length of the triangle, that is 3
the y- coordinate indicates the vertical length of the triangle, that is 4
the triangle is right and is a 3- 4- 5 , hypotenuse is 5
then
sinΘ = [tex]\frac{vertical}{hypotenuse}[/tex] = [tex]\frac{4}{5}[/tex]
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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X^2 - x=2
Solve for x
Answer:
To solve for x, you can start by moving the constant 2 to the other side of the equation by adding x to both sides:
x^2 - x = 2
x^2 - x + (1/4) = 2 + (1/4)
(x - 1/2)^2 = 9/4
x - 1/2 = +- (3/2)
x = -1/2 or x = 2
So the solutions for x are -1/2 and 2.
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.
C) help please!! On picture question c.)
Answer:
A
Step-by-step explanation:
what is even going on at A
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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Compute C7,5. (Enter an exact number.)
The permutation and combination C(n ,r) of
C(7,5) = 21.
Permutation
Permutation is the arrangement of objects, some or all of which are acquired at the same time, in a particular order. Consider ten numbers: 0, 1, 2, 3, 4, 5, 6, 7, 8, and 9. The number of different 4-digit PINs that can be formed from these 10 digits is 5040. P(10, 4) = 5040. This is a simple example of permutation. The permutation of 4 numbers out of 10 is equal to the factorial of 10 divided by the factorial of the difference between 10 and 4.
Combinations
Combinations are about grouping. Combinations can be used to calculate how many different groups can be formed from existing ones. Let's try to understand this with a simple example. Five students (William, James, Noah, Logan and Oliver) form teams of two.
According to the question:
C (n, r) = C( 7,5)
⇒ 7!/ 5! × 2!
⇒ 7 × 6 ×5!/ 5! × 2 ×1
⇒ 21.
Therefore, C(n ,r) = 21
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- 44 + 3.4
what does the question equal?
Answer:
-40.6
Step-by-step explanation:
Percy Verence breeds long-eared whistle mice. He has four in his incubator named Amin, Brenda, Carthik
and Dorothy. Amin weighs twice as much as Carthik, Brenda weighs 100g less than Carthik, Dorothy is 152g
grams. The mean weight of the mice is 238g.
How much does Carthik weigh?
Carthik weighs 225 grams, and the mean weight of the mice is 238g.
What is an equation?An equation is a expression that shows the relationship between numbers and variables.
Given that Dorothy weighs 152 g. Let x represent the weight of Amin, y represent that of Brenda and z represent Carthik.
Amin weighs twice as much as Carthik, hence:
x = 2z
x - 2z = 0 (1)
Brenda weighs 100g less than Carthik, hence:
y = z - 100
y - z = -100 (2)
The mean weight of the mice is 238g. hence:
(x + y + z + 152)/4 = 238
x + y + z = 800 (3)
Solving the 3 equations by elimination gives:
x = 450, y = 125 and z = 225
Carthik weighs 225 grams
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What is the area of the triangle??? Don’t pay attention to the stuff on the bottom of the screen lol
The area of the triangle is equal to 36 square units.
How to determine the area of a triangle
In this question we find a triangle whose base (b), in units, is parallel to x-axis and whose height (h), in units, is parallel to y-axis. The area formula for the triangle is shown below:
A = 0.5 · b · h
Where A is the area of th triangle, in square units.
If we know that b = 9 and h = 8, then the area of the triangle shown in the image is:
A = 0.5 · 9 · 8
A = 36
The triangle has an area of 36 square units. (Correct choice: B)
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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
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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What is the y intercept
Answer:
use y=mx+b. ... ...... ...