The solution to the system of equations is (3, 2)
System of equationGive the system of equation below
y = -x + 5
y=x-1
Equate both expression
-x+5 =x - 1
Equate
-x - x = -1 - 5
-2x = -6
x = 3
Since y = x - 1
y = 3 - 1
y = 2
Hence the solution to the system of equations is (3, 2)
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Find the difference by subtracting the polynomial 4a^3+6a^2-11a-3 from the polynomial 2a^3-4a^2-6a+1
The difference of the polynomials 4a^3+6a^2-11a-3 and 2a^3-4a^2-6a+1 is given as follows:
2a³ + 10a² + 5a - 4.
How to obtain the difference of polynomials?The difference of polynomials in this problem is defined as follows:
4a^3+6a^2-11a-3 - (2a^3-4a^2-6a+1)
To subtracted the polynomials, we combine the like terms, hence:
4a³ - 2a³ = 2a³.6a² - (-4a²) = 6a² + 4a² = 10a²-11a - (-6a) = -11a + 6a = -5a.-3 - 1 = -4.Hence the difference of the polynomials is given as follows:
2a³ + 10a² + 5a - 4.
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Algebra mathematic 8 class
Answer: 3a − 2/2a(3a + 1)(3a − 1)
Step-by-step explanation:
I simplified it and got 3a − 2/2a(3a + 1)(3a − 1)
Consider the matrices.
A=⎡⎣⎢4−3−578−2⎤⎦⎥ and B=⎡⎣⎢53−1−468⎤⎦⎥
What is the result of A−B?
The subtraction of the given martix B from A given as:
A - B = | -1 11 |
| -6 2 |
| -4 -10 |
Explain the term matix and its subtraction?When a matrix is subtracted, its equivalent elements from two or more other matrices are also subtracted. Data can be organized mathematically into rows and columns using matrices.A = | 4 7 | B = | 5 -4 |
| -3 8 | | 3 6 |
| -5 -2 | | -1 8 |
A - B = | 4 - 5 7 + 4 |
| -3 - 3 8 - 6 |
| -5 + 1 -2 - 8 |
A - B = | -1 11 |
| -6 2 |
| -4 -10 |
Thus, the subtraction of the given martix B from A given as:
A - B = | -1 11 |
| -6 2 |
| -4 -10 |
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What two numbers multiply to give you 56 and add up to give you negative -30
Answer:
The two numbers that multiply to give 56 and add up to give -30 are -8 and 7.
-8 * 7 = 56
-8 + 7 = -1
Use the drop-down menus to complete the statements to match the information shown by the graph.
Pool A is filling up slower than Pool B because slope of the graph of Pool A is less than that of the graph for Pool B.
The slope of the graph tells you the unit-rate in gallons per minute.
What is graph?Graphs are an essential type of computing tool in mathematics. The nodes and edges that make up a graph are referred to as its elements. Whether "directed" or "undirected," nodes can only move through a graph in a single direction (either direction may be traversed from node to node).
In contrast to a chart, a graph is a representation of linked values in a multidimensional space. Graphs are helpful for examining the various relationships among specific data points.
A graph's search algorithm seeks out the shortest route between any two nodes. The best path is determined by an algorithm that considers the weight of each path on a graph.
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Margaret has a monthly clothes budget of $50. She maps the amount of money she spends each month to the number of items of clothes she buys. what constraints are there on the domain?
Answer:The domain of Margaret's budget is the number of clothes she can buy.
The constraint on the domain is between 0 and the maximum number of clothes $50 can buy.
From the question, we understand that her budget is: $50.
The number of clothes she can buy is 0 or more.
And she cannot buy more than what $50 can afford.
This means that, the constraint on the domain is the amount of cloth she can purchase.
Step-by-step explanation:
becasue i know and i know i know
PENTAGONS
If ABCDE PQRST, find the
scale factor of ABCDE to PQRST and the
perimeter of each polygon.
The perimeters of ABCDE and PQRST are 65 and 91, respectively, and their respective scale factors are 5/7.
what is perimeter ?The perimeter of a form is its circumference. The interior space of a form is measured by area. The perimeter is the space around a shape's edge. Discover how to calculate the perimeter of various forms by multiplying their side lengths. The whole length of a shape's boundary is referred to in geometry as the perimeter of that shape. The length of each side and edge that surrounds a shape is added to find its perimeter. It is measured in linear distances such as centimeters, meters, inches, or feet.
given
the scale factor in the following format: a: b = 5/7 for ABCDE and PQRST
ABCDE's perimeter is equal to the total of its sides,
which is 65 (10 + 10 + 10 + 20 + 15).
the sum of all the sides of PQRST equals 91.
The perimeters of ABCDE and PQRST are 65 and 91, respectively, and their respective scale factors are 5/7.
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If x and y are positive integers less than 10, and 3x + 2y = 13, using a guess-and check method, what could be the value of y?
Find one of the two possible correct answers. Enter a number for y only!
Hint: Substitute numbers in for x and y and find a pair that works!
y = ____
Step-by-step explanation:
we can do even a little bit better than wild guessing and trying.
3x + 2y = 13
tells us that the sum of 2 terms is an odd number.
that means one term has to be odd and the other even, as only then their sum will be odd.
2y is because of the included factor 2 an even number. always.
so, 3x has to be odd.
and that means x has to be odd too. because an even number multiplied with any number is always even.
so, x can only be 1 or 3. because 3×5 = 15 (3×7 = 21, 3×9 = 27) and already too big for the sum 13.
so, for x = 1 we have
3×1 + 2y = 13
3 + 2y = 13
2y = 10
y = 5
for x = 3 we have
3×3 + 2y = 13
9 + 2y = 13
2y = 4
y = 2
so, the answer is either y = 2 or y = 5.
Find the sum of the equation
Recall swinging on a swingset as a kid. Assuming the chains or ropes for the swing were kept taut, the seat of the swing traced a circular arc. Now suppose you're on a swing hanging from ropes which are 6 ft long such that the seat is positioned 2 ft above the ground at rest. You swing forth to a terminal position /4 radians from your initial position at rest on the swing. At the height of your swing forth how high are you off the ground?
At the height of the swing forth, the swing seat would be at a maximum height of 2 + (6 * (1 - cos(pi/4))) = 4 feet above the ground.
What is cosine?
Cosine is a trigonometric function that relates the length of the adjacent side of a right triangle to the length of the opposite side to the hypotenuse. It is represented by "cos" and its formula is cos(x) = adjacent / hypotenuse. It is commonly used in mathematics, physics, and engineering to solve problems related to angles and vectors.
Cosine is a fundamental trigonometric function that is used in many areas of mathematics, physics, and engineering. The cosine of an angle is the ratio of the length of the adjacent side to the length of the hypotenuse in a right-angled triangle. It can also be defined as the dot product of the unit vector pointing in the direction of the angle and the unit vector pointing in the direction of the adjacent side. Cosine is periodic with a period of 2π and is always between -1 and 1, inclusive. It has many important properties and relationships with other trigonometric functions such as sine, tangent, and cotangent.
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Based on the correct answer from part A ( m/m times a1/1) + (1/1 times F/m) which of the following is the correct symbolic expression for a?
The correct symbolic expression for a is option C) [tex]\frac{ma_{1} +F}{m}[/tex]
A symbolic expression, also known as a mathematical expression, is a combination of numbers, variables, and mathematical operators (such as +, -, *, /) that can be evaluated to produce a numerical result.
Symbolic expressions can also contain functions, constants, and mathematical operations like logarithms, trigonometric functions, etc. They can be used to model physical phenomena or to solve mathematical problems.
A logarithmic function is a mathematical function that expresses the power (or exponent) to which a fixed number (the base) must be raised to produce a given value.
It is typically written in the form "logb(x)" where b is the base and x is the value being evaluated. The most common base used is 10 (common logarithm) or e (natural logarithm)
These expressions can be used to represent mathematical concepts, relationships, or equations.
Therefore, The correct symbolic expression for a is option C) [tex]\frac{ma_{1} +F}{m}[/tex].
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when using matrix bands on these teeth, the band should be trimmed to which of the following dimensions?
Height and contour: The matrix band should not extend more than 2 mm beyond the occlusogingival height of the crown of the tooth.
A dental matrix band can be defined as a properly shaped piece of metal, or other material, inserted. To support and give form to the restoration during placement, and hardening of the restorative material.
The primary function of a matrix band is to compensate for missing walls and thus provide containment of the filling material.
Matrix band systems have evolved over time and newer systems are made to give ease of use to operators and also cover for flaws and difficulties in older systems.
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What is the surface area of this shape?
Answer:
88 square cm
Step-by-step explanation:
Surface area of combined solids:Surface area of down rectangular prism:
l = 6cm ; w = 3 cm & h = 2 cm
[tex]\sf \boxed{Total \ surface \ area \ of \ rectangular \ prism = 2*(lw + wh+hl)}[/tex]
= 2*(6*3 + 3*2 + 2*6)
= 2* (18 + 6 + 12)
= 2 * 36
= 72 cm²
Lateral surface area of the top rectangular prism:
l = 3 cm
w = 1 cm
h = 4 - 2 = 2 cm
LSA = 2h( l + w)
= 2*2 *( 3 + 1)
= 4 * 4
= 16 cm²
Surface area of the shape = 72 + 16
= 88 cm²
Answer:
a = 88 cm2
Step-by-step explanation:
[tex]a=(4)(3)+2(4)(1)+2(5)(2)+2(3)(2)+(1)(3)+6(3)+5(3)=12+8+20+12+3+18+15[/tex]
[tex]a=88cm^{2}[/tex]
Hope this helps
b. As part of the assignment, you need to make a ratio table using the scale factor 0.5 nm
to 10 inches. A partially completed ratio table is shown. What value can be placed
where the question marks (?) are? Show all your work.
Nanometers Inches
? 5
0.5 10
1 20
3 ?
Answer: The ratio between the units of measurement of nanometers and inches is 0.5 nm to 10 inches. This means that for every 0.5 nanometers, the equivalent measurement in inches is 10 inches.
We can use this ratio to find the conversion of other values from nanometers to inches as well.
We know that 1 nm = 20 inches, we can multiply the value 1 by 20 to get 20 inches
So 3 nm will be 3 * 20 = 60 inches
so, the value that can be placed in the ratio table where the question marks (?) are would be 1 nm = 20 inches
and 3 nm = 60 inches.
Step-by-step explanation:
Michael has a bag of marbles. The frequency of selecting each color is recorded in the table below.
Outcome Frequency
Green 4
Black 6
Orange 5
Based on the given frequency, determine the experimental probability of selecting a black marble.
A. 0.27
B. 0.33
C. 0.40
D. 0.60
The required probability of selecting the black marble is given as 0.40. Option C is correct.
What is probability?Probability can be defined as the ratio of favorable outcomes to the total number of events.
Here,
Total number of marbles in the bag = 15
Number of black marble = 6 [from the table]
Now,
The experimental probability of selecting a black marble,
= Number of black marble/Total number of marbles
= 6/15 = 0.40
Thus, the required probability of selecting the black marble is given as 0.40. Option C is correct.
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Help me, please pls pls pls
In a classroom 1\6 of the students are wearing blue shirts,and 2/3 are wearing white shirts .There are 36 students in the classroom. How many students are wearing a shirt other than blue or white ?
Tom works in chilled food department in a supermarket all fresh juices should be kept at a certain temperature as shown on thermometer
The temperature change that is required is; A reduction in temperature by 8°C.
How to find the change in temperature?We are told that;
The freezer should be working at -18°C.
The temperature on the freezer marks -10°C.
Now, what we see here is basic arithmetic because we simply want to find the additional temperature that will make the current reading to be equal to the ideal temperature required for it to wor. Thus, what we will do is to simply subtract the current temperature from the ideal one to find out the temperature required to make it work well.
Thus;
Temperature change = -18 - (-10)
Temperature change = -18 + 10
Temperature change = -8°C.
We see that the freezer still needs its' temperature to be reduced by 8°C.
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Complete question is;
Tom works in the cold food department in a supermarket. The thermometer shows the temperature of one of the freezers. The freezer should be working at -18°C. The temperature on the freezer marks -10 The temperature should increase or decrease by how many °C?
PLEASE HELPPP <3
What is the domain of the square root function graphed below
The given graph function is a radical function. The domain of the function is [-4,∞). It can represent as x≥-4. Option A is the correct option.
What is a function?
A function from a set X to a set Y assigns exactly one element of Y to each element of X. The set X is known as the function's domain, and the set Y is known as the function's codomain. Originally, functions were the idealization of how a varying quantity depends on another quantity.
The graph starts at point (-4,0).
Then graph extended the upward direction vertically and the positive x-axis horizontally.
Since the graph extended the positive x-axis, thus x-coordinates of the points on the graph are also increasing.
The x-coordinate of the points on the graph are the domain of the graph.
Since (-4,0) is a point on the graph, thus the domain of the graph starts from -4.
The domain is [-4,∞).
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What is the first step in isolating the variable in this equation? (½)p + 75 = 100 A Subtract 75 from both sides. B Subtract ½ from both sides. C Divide both sides by 75. D Divide both sides by ½.
The first step in isolating the variable in this equation is to subtract 75 from both sides. Option A is correct.
The equation is the relationship between variables and represented as y = ax + b is an example of a polynomial equation.
here,
Given expression,
1/2p + 75 = 100
In order to isolate the variable our first step should be to subtract 75 from both sides
1/2P = 25
Then, multiply by 2 on both sides
P = 50
Thus, the first step in isolating the variable in this equation is to subtract 75 from both sides. Option A is correct.
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uhhh pls put the process of how u got the answer
Answer:
Here is a process on how to solve it:
Step-by-step explanation:
The midline theorem states that a seg that connects the midpoints of 2 sides is parallel and equal to 1/2 (50%) of the other side.
Look for the line that is drawn from one midpoint of another (you can see because it is usually drawn or you can see bisected segs) then multiply it by 2 to find the value of the other side.
Hope this helps!
169 divided, simplified
The number 169 is called the numerator or dividend, and the number 3 is called the denominator or divisor. The quotient of 169 and 3, the ratio of 169 and 3, as well as the fraction of 169 and 3 all mean (almost) the same: 169 divided by 3, often written as 169/3.
What is denominator or divisor?The number that is on top is called the numerator, and the number on the bottom is called the denominator (the prefix 'de-' is Latin for reverse) or divisor. These two numbers are always separated by a line, which is known as a fraction bar. This way of representing fractions is called display representation.
When we divide two numbers, the number that is being divided is the dividend, whereas the number by which we divide is the divisor. For example, 12 candies are to be divided among 3 children. So we have 12 ÷ 3. Here, 12 is the dividend, and 3 is the divisor.
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question- What is 169 when divided by 3 ? also write the remainder, and with decimal .
simplify the expression 5x^(2n-1)+(2x^(3n+1))^2
Hey there!
Given:
[tex]5x^(^2^n^-^1^)+(2x^(^3^n^+^1^))^2[/tex]
Simplified Solution:
[tex]5x^2^n^-^1+4x^6^n^+^2[/tex]
Hope this helps!
-6.2353535353535 as a fraction
6.2353535353535 as a fraction is 623535353535/1000000.
This fraction is written as a mixed number by dividing the numerator by the denominator to get 623,535,353,535/1,000,000. This can be further simplified to 623,535/1,000, which is the same as 623 5/8.
you have piano lessons every 7 days and tuba lessons every 3 days. Today you have both lessons . in how many days will you have both lessons on the same day again
Both lessons will be on the same day again after 21 days.
We will determine the least common multiple when two events occur simultaneously.
If I take tuba lessons every third day and piano lessons every seventh day,
Least common multiple of 3 and 7 will be,
Multiples of 3 = 1 × 3
Multiples of 7 = 1 × 7
Least common multiple (LCM) of 3 and 7 = 1 × 3 × 7
=21
Therefore, I will have both the lessons after 21 days.
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Use the graphs of f and g to describe the transformation from the graph of f to the graph of g.
The graph of g is a vertical translation 2 units up of the graph of f.
What is Graph?Graph is a mathematical representation of a network and it describes the relationship between lines and points.
Here, the two functions are f(x) = -2x
and Now, g(x) = f(x) + 2
g(x) we obtained by translating the graph f(x).
g(x) = -2x + 2
Implies f(x) is increased by 2 or graph translated 2 units upwards.
Thus, the graph f(x) is translated vertically upward by 2 units to g(x).
Hence, the graph of g is a vertical translation 2 units up of the graph of f.
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I need the answer please
Answer:ok
Step-by-step explanation:
ol
Write the inequality using interval notation
a movie theater can sell as little as 425 tubs of popcorn and as many as 800 tubs of popcorn on a friday night
Interval notation: [0, ∞). To arrange the intervals in interval notation, use brackets and parenthesis.
Write the inequality using interval notation ?To arrange the intervals in interval notation, use brackets and parenthesis.The number at the extremity of the interval is included when it is enclosed in brackets [or], and it is not included when it is enclosed in parentheses (or). We always use parentheses for infinite.For instance:Numbers higher than a and less than or equal to b are not included in this interval, so a x b applies.In this case, the expression x > 0 refers to numbers greater than or equal to zero.Since there is no upper bound specified, we must use a right parenthesis with an infinite symbol and a left bracket for zero in interval notation (since it includes the integer). Therefore, this is [0,] in interval notation.We first create a number line on which the extremes of the interval or intervals can be seen before graphing this.If one of them is an endless symbol, we must indicate that with an arrow, using a left arrow for - and a right arrow for. Then, we can use a bracket or parenthesis for the extremes.To learn more about interval notation refer
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After 16 years in an account with a 5.9% annual interest rate compounded continuously, an investment is worth a total of $37,950.24. What is the value of the principal investment? Round the answer to the nearest penny. $14,765.24 $14,859.72 $23,185.00 $23,090.52
Answer: We can use the formula A = Pert to find the value of the principal investment P
Where A is the future value of the investment, r is the annual interest rate, t is the number of years, and e is the mathematical constant approximately equal to 2.718
In this case,
A = 37950.24, r = 0.059, t = 16
We can plug in the given values into the formula and solve for P:
37950.24 = P * e^(0.059 * 16)
To find the value of P we will divide both sides by e^(0.059 * 16)
P = 37950.24 / e^(0.059 * 16)
using the calculator to find the value of e^(0.059 * 16) gives 1.966862298
P = 37950.24 / 1.966862298
The value of P is $19,169.99.
Rounded to the nearest penny $19170
Therefore, the answer is $19,170.00
Step-by-step explanation:
Evaluate the iterated integral by converting to polar coordinates_ J" La 6x2y dx dy a2 y2
The iterated integral by converting to polar coordinates is [tex]\frac{2a^{2} }{5}[/tex]
Evaluating an iterated integral by converting it to polar coordinates involves the following steps:
Identify the region of integration in the xy-plane.Convert the region of integration to polar coordinates. This typically involves finding the bounds for r and theta in terms of x and y.Write the iterated integral in terms of polar coordinates, with the outer integral being with respect to r and the inner integral being with respect to theta.Evaluate the integral by using the bounds found in step 2 and the appropriate substitution.Here, [tex]\int\limits^a_0 \int\limits^0_{-\sqrt{a^{2} - y^{2} } } {6x^{2} y} \, dx dy[/tex]
Now, converting it into the polar form:
[tex]\int\limits^\pi _\frac{\pi }{2} \int\limits^a_0} {6\cos^{2}\theta}\ {sin\theta\ r^{4} dr\ d \theta[/tex]
[tex]= \int\limits^\pi _{\frac{\pi}{2} } [\frac{6cos^2\theta}{5}\ r^5 sin\theta]^{a}_{0} \, d\theta[/tex]
[tex]= \int\limits^\pi _{\frac{\pi}{2} } [\frac{6\ a^2 \cos^2\theta sin\theta}{5}] \, d\theta[/tex]
[tex]= [-\frac{2a^{2} }{5}\ cos^{3}\theta ]^{{\pi} }_\frac{\pi}{2}[/tex]
[tex]= \frac{2a^{2} }{5}[/tex]
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The complete question is:
Evaluate the iterated integral by converting it to polar coordinates:
[tex]\int\limits^a_0 \int\limits^0_{-\sqrt{a^{2} - y^{2} } } {6x^{2} y} \, dx dy[/tex]
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