Answer:
x=4 and y=−2
Step-by-step explanation:
1. 3(−7x−8y=−12)
−4(4x−6y=28)
2. −21x−24y=−36
−16x+24y=−112
3. divide
4. Substitute 4 for x in−7x−8y=−12:
(−7)(4)−8y=−12
5. −8y−28+28=−12+28
divide 8 to 16
y=-2
Answer:
(4, -2)Step-by-step explanation:
Given system:
-7x - 8y = -12 4х - 6у = 28Simplify the second equation:
2x - 3y = 14Solve the system by elimination, multiply the first equation by 2 and the second equation by 7 and add up. Solve for y:
-7x(2) - 8y(2) + 2x(7) - 3y(7) = -12(2) + 14(7)-16y - 21y = -24 + 98-37y = 74y = -74/37y = -2Find x using the second equation:
2x - 3(-2) = 142x = 14 - 62x = 8x = 4Solution is (4, -2)
Is 7-¹ a negative number? Explain.
Answer:
No
Step-by-step explanation:
\(7^{-1}\) is a fraction
using the rule of exponents
• \(a^{-m}\) = \(\frac{1}{a^{m} }\)
then
\(7^{-1}\) = \(\frac{1}{7^{1} }\) = \(\frac{1}{7}\) ← that is a fraction
simplify without using a calculator :
[log_{x}(64) + log_{x}(4) - log_{x}(8)] ÷[log_{x}(1024)]
Since log(ab) = log(a) + log(b) and log(a/b) = log(a) - log(b) for any logarithm base, we have
\(\dfrac{\log_x(64) + \log_x(4) - \log_x(8)}{\log_x(1024)} = \dfrac{\log_x\left(\dfrac{64\times4}8\right)}{\log_x(1024)} = \dfrac{\log_x(32)}{\log_x(1024)}\)
Then using the change-of-base identity, we have
\(\dfrac{\log_x(32)}{\log_x(1024)} = \log_{1024}(32)\)
But we also know that 2¹⁰ = 1024 and 2⁵ = 32, so we can back up slightly and instead write
\(\dfrac{\log_x(32)}{\log_x(1024)} = \dfrac{\log_x(2^5)}{\log_x(2^{10})} = \dfrac{5\log_x(2)}{10\log_x(2)}\)
Then the logarithms cancel and you're left with 5/10 = 1/2.
PLEASE HELP!!!!!! I WILL GIVE BRAINLIST!!!!!!!!!!!
The local elementary school is creating a new playground for the students. A basketball court will take up 1/4 of the playground. A soccer field will take up another 3/8 of the new playground. How much of the playground will remain for swings and other equipment?
A) 1/3 of the playground
B)3/8 of the playground
C)5/8 of the playground
D)2/3 of the playground
Answer:
The Answer is B
Step-by-step explanation:
1/4 = 2/8
2/8 + 3/8 = 5/8
8/8 - 5/8 = 3/8
please give correct answer <3 :(
Answer:
216g^3
Step-by-step explanation:
6g^3 g^3
6g^3 = 6g * 6g * 6g = 216g^3
Answer:
\(216g^{3}\)
Step-by-step explanation:
6^3 x g^3=
6^3=216
216g^3
Enter the number that belongs in the green box. 4 51° 109°
The answer choice which belongs in the green box and is the longest side of the triangle as required is; 11.06.
What is the length of the longest side?It follows from the task content that since the sum of angles in a triangle is; 180°, the missing angle measure is; 180 - 51 - 109° = 20°.
Consequently, it follows from the sine law that;
4 / sin 20° = x / sin 109°
x = 4 sin 109° / sin 20°
x = 11.06.
Ultimately, the number that belongs in the green box is; 11.06.
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Please help me answer this question, thanks!
The maximum revenue possible in this situation is 15625/A dollars, where A is the coefficient in the quadratic equation.
To find the maximum revenue possible in this situation, we can use the concept of vertex or the vertex form of a quadratic equation.
The revenue equation is given by R = -Ax^2 + 250x, where A is a constant coefficient.
The maximum revenue occurs at the vertex of the parabolic curve represented by the equation. The x-coordinate of the vertex can be found using the formula x = -b / (2a), where a and b are the coefficients of the quadratic equation.
In this case, a = -A and b = 250. Plugging in these values, we get:
x = -250 / (2 * (-A))
= 125 / A
To find the maximum revenue, we substitute this value of x into the revenue equation:
R = -A * (125 / A)^2 + 250 * (125 / A)
= -A * (15625 / A^2) + (31250 / A)
= -15625 / A + 31250 / A
= 15625 / A
The maximum revenue is given by 15625 / A. The value of A is not specified in the question, so we cannot determine the exact maximum revenue without knowing the value of A. However, we can say that the maximum revenue increases as A decreases.
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You pay $2 to play a game in which you roll one fair die. If you roll a 5 on the first roll, you win $5. If you roll a 1 or a 2, you win $3. If not, you lose your money. Use this information to answer questions 1-2.
Find the expected value for this game? Round your answer to the hundredths place
Find the fair price for this game. Round your answer to the hundredths place
Answer:
The answer is 4
Step-by-step explanation:
MRK ME BRAINLIEST PLZZZZZZZ
Answer:
4
:P
Step-by-step explanation:
The word isometric can be broken into two parts. The prefix "iso-” means "of the same,” and "-metric” means "measure.” How does the meaning of the word isometric relate to determining if an isometric transformation occurred? Include the defining characteristics of angle measure and line segments in your response.
The term "isometric" has the Greek roots "isos," which means "same," and "metron," which means "measure." The definition of an isometric transformation is one in which the original figure and its transformed equivalent have the same shape, size, and orientation.
When we speak about geometric figures, the concept of shape, size, and orientation come into play.The defining characteristics of angle measure and line segments play a critical role in determining whether an isometric transformation has occurred. In geometry, angle measures are the measurements of angles in a geometric figure. An angle is formed by two line segments that share a common endpoint. It is a unit used to calculate the measure of a plane figure's interior or exterior, such as a polygon. In other words, the size of the angle doesn't change during an isometric transformation.Line segments are the building blocks of geometric figures. They are used to construct geometric figures such as polygons, triangles, and rectangles, among others. In an isometric transformation, the length of the line segments remains constant because the shape and size of the original figure and its transformed equivalent remain the same.In conclusion, the word "isometric" implies that the transformation has the same measurements of the original figure. It is a transformation that retains the original geometric figures' shape, size, and orientation. The defining characteristics of angle measure and line segments remain unchanged during the isometric transformation. This means that if an isometric transformation occurs, the original and transformed figures have the same measurements of angles and line segments.For such more question on isometric
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XZ is the perpendicular bisector of segment WY. Solve for k. Enter a NUMBER only.
The calculated value of k on the line is 9
How to determine the value of kFrom the question, we have the following parameters that can be used in our computation:
XZ is the perpendicular bisector of segment WY
This means that
WX = XY
substitute the known values in the above equation, so, we have the following representation
3k - 4 = 2k + 5
So, we have
3k - 2k = 4 + 5
Evaluate
k = 9
Hence, the value of k is 9
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A rope is being used to anchor a tree to the ground, as shown in the picture below. If the rope is 15 feet long and it is tied to the tree 12 feet above the ground, how far from the base of the tree is the rope tied to the ground???
Answer: 9
Step-by-step explanation:
Use the pythagorean thrm, a^2+b^2=c^2.
x^2+12^2=15^2 so x=sqrt(15^2-12^2)=9
Answer:
The answer to your problem is, B. 9 feet
Step-by-step explanation:
The pythagoras' theorem states that:
Hyp² = base² + perp²
Which can only be applicable for a right-angle triangle.
So by the ‘ Pythagoras' theorem ‘
Hyp² = base² + perp²
Base² = Hyp² - perp²
Base² = 15² - 12²
Base² = 225 - 144
Base² = 81
Base = 9
9 being the answer.
Thus the answer to your problem is, B. 9 feet
1) (b + a) = 4; use a = 1 and b = 3
2) c(b + b); use b = 1 and c = 5
3) 4+ pm; use m = 4 and p =3
4) 5+ pm; use m = 4 and p = 2
5) m(p + 2); use m = 5 and p = 2
6) h+j²; use h = 1 and j = 4
7) y-(x - 5); use x = 5 and y = 6
8) 4xy; use x = 5 and y = 2
9) n(p + 3); use n = 2 and p = 2
10) y +x+x; use x = 3 and y=5
11) 6+ a-b; use a = 4 and b = 4
The equations will be solved by putting the values of the variables in the bracket.
How to calculate the values?1. (b + a) = 4; use a = 1 and b = 3
( 1 + 3) = 4
2) c(b + b); use b = 1 and c = 5
5(1 + 1)
= 5 × 2 = 10
3) 4+ pm; use m = 4 and p =3
= 4 + (4 × 3)
= 4 + 12
= 16
4) 5+ pm; use m = 4 and p = 2
= 5 + (2 × 4)
= 5 + 8
= 13
5) m(p + 2); use m = 5 and p = 2
= 5(2 + 2)
= 5 × 4
= 20
6) h+j²; use h = 1 and j = 4
= 1 + 4²
= 17
7) y-(x - 5); use x = 5 and y = 6
= 6 - (5 - 5)
= 6 - 0
= 6
8) 4xy; use x = 5 and y = 2
= 4 × 5 × 2
= 40
9) n(p + 3); use n = 2 and p = 2
= 2(2 + 3)
= 10
10) y +x+x; use x = 3 and y=5
= 5 + 3 + 3
= 11
11) 6+ a-b; use a = 4 and b = 4
= 6 + 4 - 4
= 6
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Three out of eight students wore white shoes what percent of students did wore white shoes
Answer:
37.5 percent wore white shoes
Step-by-step explanation:
Diana y Juan están considerando abrir una cafetería. Semanalmente ellos gastarian
$1.348 en costos fijos de utilidades y mantenimiento. Cada almuerzo tiene un costo
de producción de $3.50. por lo que piensan vender cada almuerzo en $8.
a. ¿Cuántos almuerzos deben elaborar semanalmente si desean obtener una
ganancia de $775 para cada uno?
Answer:
Unidades a vender= 644 unidades
Step-by-step explanation:
Dada la siguiente información:
Costos fijos= $1.348
Costo unitario= $3,5
Precio de venta= $8
Ganancia deseada= 775*2= $1.550
Para calcular el número de unidades a vender, debemos usar la siguiente formula:
Unidades a vender= (costo fijo + ganancia deseada) / contribución marginal unitara
Unidades a vender= (1348 + 1550) / 4,5
Unidades a vender= 644 unidades
Short Response What is the cost of 15 tomatoes?
HOME GROWN VEGETABLES
Cucumbers 6 for $2
Peppers 12 for $9
Tomatoes 6 for $4
Answer:
60
Step-by-step explanation:
15x4= 60
Seventy-five 6th- grade students chose to watch a movie on the last day of school. This is 25% of the 6th-grade class. How many total students are in the 6th grade?
Put the steps in order to solve the literal equation for y in terms of x.
6x+2y+ 8 = 180
Answer:
x = \(\frac{172-2y}{6}\)
Step-by-step explanation:
6x + 2y + 8 = 180 ( subtract 8 from both sides )
6x + 2y = 172 ( subtract 2y from both sides )
6x = 172 - 2y ( divide both sides by 6 )
x = \(\frac{172-2y}{6}\)
7x + 2 = 5(x − 2)
Find X
Answer:
-6
Step-by-step explanation:
\(7x + 2 = 5(x - 2) \\ 7x + 2 = 5x - 10 \\ 7x - 5x = - 10 - 2 \\ 2x = - 12 \\ x = \frac{ - 12}{2} \\ x = - 6\)
Answer:
-6
Step-by-step explanation:
7x+2 =5x-10
7x-5x= -10-2
2x = -12
x= -12/2
x=-6
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Find a primitive Pythagorean triplet (a, b, c) where c=a+50.
Answer:
Pythagorean triple (PT) can be defined as a set of three positive whole numbers that perfectly satisfy the Pythagorean theorem: a2 + b2 = c2.
theorem: a2 + b2 = c2.
This set of numbers are usually the three side lengths of a right triangle. Pythagorean triples are represented as: (a, b, c), where, a = one leg; b = another leg; and c = hypotenuse.
There are two types of Pythagorean triples:
Primitive Pythagorean triples
Non-primitive Pythagorean triples
Primitive Pythagorean triples
A primitive Pythagorean triple is a reduced set of the positive values of a, b, and c with a common factor other than 1. This type of triple is always composed of one even number and two odd numbers.
For example, (3, 4, 5) and (5, 12, 13) are examples of primitive Pythagorean triples because each set has a common factor of 1 and also satisfies the
Step-by-step explanation:
Pythagorean theorem: a2 + b2 = c2.
(3, 4, 5) → GCF =1
a2 + b2 = c2
32 + 42 = 52
9 + 16 = 25
25 = 25
(5, 12, 13) → GCF = 1
a2 + b2 = c2
52 + 122 = 132
25 + 144 = 169
169 = 169.
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An angle measures 112° less than the measure of its supplementary angle. What is the measure of each angle?
Find all solutions of each equation on the interval 0≤ x <2pie
tan² x sec² x +2 sec²x - tan²x =2
The trigonometric equations has the following solutions: x = 0 + j · π or x = 0.352π + j · π or x = - 0.352π + j · π, where j is a non-negative whole number.
How to solve a trigonometric equation
In this problem we find the case of a trigonometric equation, whose solutions on the interval [0, 2π] must be found. This can be done by both algebra properties and trigonometric formulae. First, write the entire expression:
tan² x · sec² x + 2 · sec² x - tan² x = 2
Second, use trigonometric formulas to reduce the number of trigonometric functions:
tan² x · (tan² x + 1) + 2 · (tan² x + 1) - tan² x = 2
Third, expand the equation:
tan⁴ x + tan² x + 2 · tan² x + 2 - tan² x = 2
tan⁴ x + 2 · tan² x = 0
Fourth, factor the expression:
tan² x · (tan² x - 2) = 0
tan² x = 0 or tan² x = 2
tan x = 0 or tan x = ± √2
Fifth, determine the solutions to trigonometric equation:
x = 0 + j · π or x = 0.352π + j · π or x = - 0.352π + j · π, where j is a non-negative whole number.
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ITS EASY I PROMISE PLEASE NOW
Answer:
I'm pretty sure the answer is B
Step-by-step explanation:
Hope this helped :) Sorry if its wrong
Answer:
b
Step-by-step explanation:
I like to think of it as this:
If the circle is filled, it is \(\leq or \geq \\\) (more)
If not, it's < or >
The arrow points in the direction the line is going.
In this graph, the line is going to the left. So is the symbol.
Combine like terms.
9 + 12t – 6t
Question 3 options:
9 – 12t
21
21t
9 + 6t
The expression can be simplified to obtain as 9 + 6t.
What is an Algebraic expression?An algebraic expression can be obtained by doing mathematical operations on the variable and constant terms.
The variable part of an algebraic expression can never be added or subtracted from the constant part.
The given algebraic expression is 9 + 12t – 6t.
It can be simplified as follows,
9 + 12t – 6t
Here 9 is a constant.
And, the terms 12t and 6t have the same variable t.
Which implies they are like terms.
Since the like terms in an expression can be added to subtracted, the given expression can be simplified as below,
9 + 12t – 6t
⇒ 9 + 6t
Hence, the simplification of the given expression results as 9 + 6t.
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What are the coordinates of the vertices of the final image? A. P’(12, -6), Q’(8, -7), R’(4, -4), and S‘(7, -1) B. P’(12, 8), Q’(8, 9), R’(4, 6), and S‘(7, 3) C. P’(-12, 6), Q’(-8, 7), R’(-4, 4), and S‘(-7, 1) D. P’(12, 6), Q’(8, 7), R’(4, 4), and S’(7, 1)
Answer:
Given that the vertices of quadrilateral PQRS are P(6,3), Q(4,2), R(2,4) and S(4,5) and the quadrilateral is dilated with a scale factor of 2, about the origin.
Now, let's find the new vertices of the dilated image:
Vertex P is dilated by a scale factor of 2, its new coordinates will be (2 × 6, 2 × 3) = (12, 6). Therefore, the new vertex P' is at (12, 6).
Vertex Q is dilated by a scale factor of 2, its new coordinates will be (2 × 4, 2 × 2) = (8, 4). Therefore, the new vertex Q' is at (8, 4).
Vertex R is dilated by a scale factor of 2, its new coordinates will be (2 × 2, 2 × 4) = (4, 8). Therefore, the new vertex R' is at (4, 8).
Vertex S is dilated by a scale factor of 2, its new coordinates will be (2 × 4, 2 × 5) = (8, 10). Therefore, the new vertex S' is at (8, 10).
Therefore, the coordinates of the vertices of the final image are P’(12, 6), Q’(8, 4), R’(4, 8), and S’(8, 10).So, the correct option is D. P’(12, 6), Q’(8, 4), R’(4, 8), and S’(8, 10).
Step-by-step explanation:
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Select four statements from the invertible matrix theorem and show that all four statements are true or false
This learning module introduced the invertible matrix theorem. This theorem is a collection of 12 equivalent statements. This means that when one statement in the theorem is true, all statements in the theorem are true. Similarly, when one statement in the theorem is false, all statements are false. For your initial post, propose a specific n x n matrix A, where n >= 3. Select four statements from the invertible matrix theorem and show that all four statements are true or false, depending on the matrix you selected. Make sure to clearly explain and justify your work. Also, make sure to label your statements using the notation used in the notes (e.g., part (a), part (f), etc.).
Theorem (The Invertible Matrix Theorem): Let A be an n x n matrix. Then the following statements are equivalent:
A is an invertible matrix.
A is row equivalent to the n x n identity matrix.
A has n pivot positions.
The equation Ax = 0 has only the trivial solution.
The columns of A form a linearly independent set.
The linear transformation x à Ax is one-to-one.
There is an n x n matrix C such that CA = I.
There is an n x n matrix D such that AD = I.AT is an invertible matrix.
Answer:
A) A is an invertible matrix ( TRUE )
B) A is a row equivalent to the n x n identity matrix ( n = 3 ) ( TRUE )
C ) The equation Ax = 0 has only the trivial solution ( TRUE )
D ) The columns of A form a linearly independent set ( TRUE )
Step-by-step explanation:
Assuming a matrix A
\(\left[\begin{array}{ccc}1&2&1\\-1&0&3\\4&1&5\end{array}\right]\)
det A = 1 [ 0 -3 ] + 2 [12 + 5 ] + 1[-1]
= -3 + 34 -1 = 30 ≠ 0
THEREFORE det A = 30 ≠ 0
Attached is the detailed solution of the given statements above
how do I know if a fraction and decimal are equivalent
Answer:
To find the decimal equivalent of a fraction, divide the numerator by the denominator. Because the number in the numerator is smaller than the number in the denominator, you have to place the decimal point after it and add zeros. Then complete long division.
Marco wants to know how much the other students in his mathematics class study. He recorded the data he collected in
the following table.
Time spent studying per week (in hours)
2.0
5.0
1.0
2.5
2.5
3.5
0.0
4.5
2.5
4.0
3.5
3.0
2.0
1.5
4.0
2.0
0.5
3.0
1.0
3.0
3.5
1.5
1. Construct a histogram for the data.
Answer:
Step-by-step explanation:
This problem has been solved! You'll get a detailed solution from a subject matter expert that helps you learn core concepts.
express 11/4 as a mixed number 11/4=8/4+3/4+2and 3/4
Answer:
11/4 is an improper fraction. 11/4 as a mixed number is 2 3/4 or 2.75, look below for further information.
Step-by-step explanation:
To change 11/4 (an improper fraction) into a mixed number, we need to the denominator (bottom number) by the numerator (top number).
11 / 4 = 2.75
We can then change the 2.75 into 2 and 3/4. Think of a dollar, how many quarters do you need to make a full dollar? Four, and what is the cost of one quarter? 25 cents. 75 divided by 3 is 25. So we can say that 3/4 is equivalent to the decimal 0.75.
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solve for X. show your work. (x+2)(x+8)=0
Step-by-step explanation:
x = -2
x = -8
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what did he do wrong? pls help ill give brainliest
Answer:
Between step 4 and final answer, the incorrect square root is used as a multiplier
Step-by-step explanation:
Process should be
-5√11 + 15√(6 • 4)
-5√11 + 15√6 • √4
-5√11 + 15√6 • 2
-5√11 + 30√6
which holds the more capacity 0.75 litres or 350ml
Answer:
0.75 liters
Step-by-step explanation:
1000ml in 1 liter so 0.75*1000=750ml
750ml > 350ml