The solution for the given system of equations is (5.5, 4.333).The correct option is B
What is the general equation of a Straight line?The general equation of a straight line is -
[y] = [m]x + [c]
where -
[m] is slope of line which tells the unit rate of change of [y] with respect to [x].
[c] is the y - intercept i.e. the point where the graph cuts the [y] axis.
The equation of a straight line in point slope form can be also written as-
y - y1 =m (x - x1)
We have the following set of equations -
4x − 15y = −43
2x − 3y = −2
These are the equations of a straight line. Plotting the graphs and finding the point of intersection would give us the solution. It can be seen from the graph that the solution is given by coordinate - (5.5, 4.333).
Therefore, the solution for the system of equations is (5.5, 4.333).
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How do you find the sin of an acute angle?.
By using the Pythagorean identities we can find the sine of an acute angle.
What is angle ?
An angle is a measure of rotation about a point or a line. It is a geometric concept that describes the amount of rotation between two lines or planes. Angles are typically measured in degrees or radians.
What is acute angle ?
An acute angle is an angle that measures less than 90 degrees. It is an angle that is smaller than a right angle. Acute angles are commonly found in triangles and other geometric shapes. They are represented by the symbol "α" (alpha) in trigonometry.
What is Pythagorean identities?
The Pythagorean identities are a set of trigonometric identities that are based on the Pythagorean theorem. They relate the sine, cosine, and tangent of an angle to the ratios of the sides of a right triangle. The Pythagorean identities can be used to find the sine of an acute angle by relating it to the ratio of the opposite side to the hypotenuse of a right triangle.
Specifically, the identity [tex]sin^2(x) + cos^2(x) = 1[/tex] can be used to find the sine of an acute angle x by first finding the cosine of x and then subtracting it from 1.
The equation becomes [tex]sin(x) = \sqrt{1 - cos^2(x)}[/tex].
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After a certain number of people entered an empty room, 2/3 of the people who’d entered the room leave. After 2 more people leave, 1/4 of the original number of people who entered the room remain. What was the original number of people who entered the empty room?
Answer:
24
Step-by-step explanation:
Let x be the original number of people who entered the room
Since 2/3 of the people leave, 1/3 of the people remain = (1/3)x
If 2 more people leave, number of people remaining in the room = (1/3)x - 2
We know this to be 1/4 of the original number = (1/4)x
[tex]\rm{So\;\dfrac{1}{3}x - 2 = \dfrac{1}{4}x\\\\[/tex]
Multiply throughout by 12 to get rid of the denominator
[tex]\rm{So\;12 \left(\dfrac{1}{3}x - 2\right) = 12\left(\dfrac{1}{4}x\right)\\\\[/tex]
[tex]4x - 24 = 3x\\\\\implies x = 24\\\\[/tex]
Original number of people who entered the empty room = 24
)) Which sign makes the statement true? 10/
14 ? 5/6
In the given question of inequality, the greater than symbol makes the statement true, 14 > 5/6.
What is meant by inequality?A relationship between two expressions or values that is not equal to each other is known as inequality in mathematics. So inequality emerges from an imbalance.
"Less than or equal to," "less than," or "not equal to" are all ways to describe an inequality, which is a mathematical relationship between two expressions.
Both equations and inequalities are mathematical phrases created by connecting two expressions. The equal sign (=) in an equation denotes that the two expressions are regarded as equal. In contrast, an inequality indicates that the two phrases are not always equal by using the symbols >, <, or =.
Less than or equal to, larger than, less than, and more than or equal to are the four fundamental inequalities.
Therefore, the correct answer is option b) >.
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The complete question is:
Which sign makes the statement true?
-2 / 5 ___ -3 / 8
a) <
b) >
c) =
Find each product mentally show the steps you used 11x 27
Work Shown:
11 = 10+1
27*11 = 27*(10+1) = 27*10 + 27*1 = 270+27 = 297
I used the distribution rule a(b+c) = ab+ac
The 11 was broken up into 10+1 since 10 is easy to work with.
The area of a circle is 367 m². What is the circumference, in meters? Express your
answer in terms of .
The circumference of the circle is 67.9.
What is a circle?
A circle is a special kind of ellipse in which the eccentricity is zero and the two foci are coincident. A circle is also termed as the locus of the points drawn at an equidistant from the center. The distance from the center of the circle to the outer line is its radius. Diameter is the line which divides the circle into two equal parts and is also equal to twice of the radius.
The equation of circle in the plane is given as:
(x-h)^2 + (y-k)^2 = r^2
where (x, y) are the coordinate points
(h, k) is the coordinate of the center of a circle
and r is the radius of a circle.
and Area of circle = πr²
Circumference of circle=2πr
Now,
Given Area of circle=367m^2
as πr^2=367
r=√367/3.14
r=√116.7
r=10.8
Therefore, circumference of circle=2πr
=2*22/7*10.8
circumference of circle=67.9m.
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The circumference of the circle is 67.9.
What is a circle?
A circle is a special kind of ellipse in which the eccentricity is zero and the two foci are coincident. A circle is also termed as the locus of the points drawn at an equidistant from the center. The distance from the center of the circle to the outer line is its radius. Diameter is the line which divides the circle into two equal parts and is also equal to twice of the radius.
The equation of circle in the plane is given as:
(x-h)^2 + (y-k)^2 = r^2
where (x, y) are the coordinate points
(h, k) is the coordinate of the center of a circle
and r is the radius of a circle.
and Area of circle = πr²
Circumference of circle=2πr
Now,
Given Area of circle=367m^2
as πr^2=367
r=√367/3.14
r=√116.7
r=10.8
Therefore, circumference of circle=2πr
=2*22/7*10.8
circumference of circle=67.9m.
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What are the formulas in algebraic expressions Class 8?.
In class 8, students typically learn the following formulas in algebraic expressions:
The distributive property: This formula states that a(b + c) = ab + ac. This formula is used to simplify expressions by breaking down a product of a sum into separate products.
The commutative property: This formula states that a + b = b + a and a x b = b x a. This formula is used to change the order of the terms in an expression without changing its value.
The associative property: This formula states that (a + b) + c = a + (b + c) and (a x b) x c = a x (b x c). This formula is used to group the terms in an expression in a different way without changing its value.
The identity property: This formula states that a + 0 = a and a x 1 = a. This formula is used to simplify expressions by canceling out certain terms.
The inverse property: This formula states that a + (-a) = 0 and a x (1/a) = 1. This formula is used to simplify expressions by canceling out certain terms.
The order of operations: This formula, also known as PEMDAS (Parentheses, Exponents, Multiplication and Division, Addition and Subtraction), is used to determine the order in which mathematical operations should be performed.
Therefore, These are some of the basic formulas in algebraic expressions that students learn in class 8, they are important to understand and apply in solving algebraic equations and problems.
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please help 15 points
Answer:dddjdvjd
Step-by-step explanation:
mb i just need points\
Answer:
d = 63 degree
e = 96 degree
f = 21 degrees
Step-by-step explanation:
The angle d is the vertical angle theorem with 63 degrees; that is why d is 63 degrees.
The angle e is the vertical angle theorem with 96 degrees; that is why d is 63 degrees.
96 + 63 = 159 degrees
180 - 159 = 21 degrees
So, f = 21 degrees
hellpppp ive been here toooo long
Answer: To answer your question, since they played 35 games, that means that there were 12 wins, 14 draws, and they lost 9 games. I hope this helps! Sorry for the previous person, they just like to get points.
Step-by-step explanation:
P = 3W + D
50 = 3W + 14 subtract the 14 from both sides
36 = 3W divide both sides by 3
12 = W
please help me. i have no idea what to do
no idea either
but we are learning the same thing
Answer:
[tex]-2+2\sqrt{7} and -2-2\sqrt{7}[/tex]
Step-by-step explanation:
To find where x intersects x-axis, plug in y=0 and solve for x.
[tex](x+2)^2+(0-3)^2=37[/tex]
[tex](x+2)^2+(-3)^2=37[/tex]
[tex](x+2)^2+9=37[/tex]
[tex](x+2)^2=37-9[/tex]
[tex](x+2)^2=28[/tex]
[tex]x+2=\sqrt{28}[/tex]
x+2=±2[tex]\sqrt{7}[/tex] Simplify square root
x=-2±2[tex]\sqrt{7}[/tex]
Find the equation of the straight the line which passes through the point (3, 2) and cuts off equal intercepts on the axes.
Answer: The equation of a line can be written in the slope-intercept form y = mx + b, where m is the slope of the line and b is the y-intercept.
To find the equation of a line that passes through the point (3, 2) and cuts off equal intercepts on the x and y axes, we can use the following steps:
First, we need to find the slope of the line using the point (3, 2) and the fact that the line cuts off equal intercepts on the x and y axes. Since the line cuts off equal intercepts on the x and y axes, it means that it is a line of symmetry, which means that the slope of the line is zero.
Now we can use the point-slope form of a linear equation which is y-y1 = m(x-x1) and substitute the point (3,2) and the slope (0)
The equation of the line will be y = b where b is the y-intercept.
So the equation of the line which passes through the point (3, 2) and cuts off equal intercepts on the axes is y = 2
The line is a horizontal line passing through the point (3,2) and it cuts the x-axis at y = 2.
Step-by-step explanation:
pls help its due today!!!!
Answer: the table is proportional and the answer is 2/3
Step-by-step explanation: we can see that the top row goes up by 3 every time the bottom row goes up by 2
this gives us a ratio of 6 : 9
take the 6 and divide it by 3 we get 2
divide 9 by 3 and we get 3
this gives us the fraction 2/3 which is also an answer
gl :)
If ∠1 and ∠2 form a linear pair and m∠1 is eighteen less than twice m∠2, find the difference in the measures of the two angles.
Difference in the measures of two angles is 48°.
What are Linear Pair of Angles?Linear pair of angles are the pair of angles formed when two lines are intersected at a point.
Sum of the measures of angles of linear pair is supplementary or 180°.
Given that ∠1 and ∠2 form a linear pair.
m∠1 + m∠2 = 180°
Also, m∠1 is eighteen less than twice m∠2.
m∠1 = (2 × m∠2) - 18
Substituting second equation in first equation,
(2 × m∠2) - 18 + m∠2 = 180°
3 × m∠2 - 18 = 180
3 × m∠2 = 198
m∠2 = 198 / 3
m∠2 = 66°
m∠1 = (2 × 66) - 18 = 114°
Difference of the angles = m∠1 - m∠2 = 114° - 66° = 48°
Hence there is 48° difference in the measures of angles.
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what is 50% of 12?
what is 12% of $118.90?
what is 120% of 30?
what is 8.25% of $8,384.33?
Answer:
1. 6
2. $14.27
3. 36
4. $691.70
A rectangular prism has a height of 1/4 m and a square base with an area of 8 2/5m².
please help quick!! (47 mins) will give 15 pts
Answer:
E
Step-by-step explanation:
whiting a formula write a formula to find the number of sides n in a regular polygon given that the measure of one exterior angle is x
Answer:
To calculate the number of sides of the polygon, divide 360 by the amount of the exterior angle. For example, if the exterior angle is 60 degrees, then dividing 360 by 60 equals 6, which is the number of sides the polygon has.
solve for t.
8t = 24
Answer:
t=3
Step-by-step explanation:
8t=24
8x3=24
Answer:t=3 I hope this helps good luck
Step-by-step explanation:
8t=24
Divide both sides of the equation by 8
8t divide by 8 = 24 divided by 8
Any expression divided by itself equals 1
t=24 divided by 8
then do this
Calculate the quotient which is
T=3
Can you help me decribe how the placement of the decimal point change when you multiply a number I am a power of 10. How i thi the ame and different for diviion?
Multiplication: Decimal point moves right for every 10^n.
Division: Decimal point moves left for every 10^n.
When you multiply a number by a power of 10, the placement of the decimal point shifts to the right by the number of zeroes in the power of 10. For example, if you multiply 2.34 by 100 (102), the result would be 234.0, with the decimal point shifting two places to the right.
When you divide a number by a power of 10, the placement of the decimal point shifts to the left by the number of zeroes in the power of 10. For example, if you divide 234.0 by 100 (102), the result would be 2.34, with the decimal point shifting two places to the left.
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A muic tore mark up the intrument it ell by 30%. If the tore bought a guitar for $45, what will be it tore price? If the price tag on a trumpet ay $104, how much did the tore pay for it? If the tore paid $75 for a clarinet and old it for $100, did the tore mark up the price by 30%?. How much did the tore mark up the price? %
The markup percentage for the clarinet is 33.33%
The store buys a guitar at the price of $45
The price tag on the trumpet in the store is $104.
30% in decimal value is approximately 1.3 and so the price should either be multiplied or divided by it to know the store markup and margin.
The store's selling price for the guitar would be $45 x 1.3 = $58.50.
The store paid $104 / 1.3 = $80 for the trumpet.
The store marked up the clarinet by $100 - $75 = $25.
The markup percentage for the clarinet is ($25 / $75) x 100 = 33.33%.
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(sin30°+cos60°)(tan60°-sec30°)
To support a triangular kite, Hana
attaches thin strips of wood from each vertex
perpendicular to the opposite edge. She
then attaches the kite's string at the point
of concurrency. To calculate the point of
concurrency, she determines the coordinates
of each vertex on a coordinate plane. What
are the coordinates where the wood strips
cross? Round your answer to the nearest
hundredth.
The coordinates where the wood strips cross are (17.11,44). The solution is obtained using the concept of slope of line.
What is slope of line?
The change in y coordinate relative to the change in x coordinate is referred to as a line's slope in mathematics.
The symbols delta y and delta x stand for the net change in the y-coordinate and the net change in the x-coordinate, respectively.
We are given that Hana attaches thin strips of wood from each vertex perpendicular to the opposite edge.
Therefore, the point of concurrency will be in orthocenter.
We are given a triangle with coordinates X(0,0), Y(0,58), Z(36,44)
Now, we will find the slope
Slope(m) = [tex]\frac{y_{2}-y_{1} }{x_{2}-x_{1} }[/tex]
Slope of XY = (58-0)/0-0 = 0
Slope of YZ = (44-58)/(36-0) = -7/18
We know that slope of line perpendicular to XY is 0
Using point slope form, equation of the altitude perpendicular to XY is
⇒[tex]y-y_{1} = m(x-x_{1} )[/tex]
⇒y-44 = 0(x-36)
⇒y=44
Slope of line perpendicular to YZ is 18/7
Using point slope form, equation of the altitude perpendicular to YZ is
⇒y-0 = 18(x-0)/7
⇒y = 18x/7
Substitute the value of y in the above equation, we get
⇒44 = 18x/7
⇒x = 17.11
Hence, the coordinates where the wood strips cross are (17.11,44).
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How do you find the equation of a parabola from a graph in factored form?.
A quadratic equation's graph is referred to as a parabola in mathematics. Y = a(x - p)(x - q), where p and q are the parabola's x-intercepts, or the x-values at which the parabola crosses the x-axis.
It is the factored form of a parabola, also known as the intercept form of a parabola. We can locate the function's x-intercepts or zeros with the use of factored form.
It is referred to as being in factored form when a quadratic expression is represented as the sum of two linear factors plus a constant. To establish if a graph reflects a function, use the vertical line test. The graph is a function if a vertical line drawn across it is moved and only ever touches it at one point.
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The histogram shows the ages of all the workers in a London office. Given that 27 people are in the 40-55 age range, work out the total number of people in the office.
Using the same method, determine the histogram's total area: divide it into rectangles and use the calculation for a rectangle's area to arrive at a total area of 100.The answer 40.
Determine the histogram's total area:
The area below the 40 to 55 line in the histogram must first be located.By using the area of a rectangle, one can determine the area: side side.
This will reveal a 60-square-foot space.
Then, using the same method, determine the histogram's total area: divide it into rectangles and use the calculation for a rectangle's area to arrive at a total area of 100.
You must now apply the rule of three:
The number of people between the ages of 40 and 55 is 25, and that age range corresponds to 60, as indicated by the question's sentence, so:
60 ———- 24
100 ———- x
60•x = 24•100
60x = 2400
x = 2400/60
x = 40
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What is the degree of the polynomial 7x³ 5x 4x³ 2x²?.
The degree of the polynomial of 7x ³ 5x 4x ³ 2x ² is 3.
The largest power of a component in a polynomial expression is the polynomial's degree.
Just to clarify your position, a polynomial is an expression with more than two algebraic terms, typically the sum (or difference) of various terms with various powers of the same or distinct variables (s). It is a monomial linear combination.
The polynomial can be divided into those with single value and those with many variables (multivariable polynomial).
As was previously said, the higher power of the polynomial expression is the degree of the polynomial with one variable.
However, if a polynomial comprises more than one variable, the degree of the polynomial can be calculated by multiplying the powers of the additional variables by the terms in the polynomial expression.
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Which expression is equivalent to (5-2a³b-4)-1?
Answer:
2
Step-by-step explanation:
Since this is all raise to the -1, we put it under 1.
[tex]\frac{1}{5^{-2}a^{3}b^{-4} }[/tex] Pull the [tex]5^{-2}[/tex] and [tex]b^{-4}[/tex] from the bottom and put them on top to make them positive [tex]5^{2}[/tex] mean 5x5 or 25
[tex]\frac{25b^{4} }{a^{3} }[/tex]
Answer:
Option 2
Step-by-step explanation:
[tex]=(\frac{a^{3} }{5^{2} b^{4} } )^{-1}[/tex]
[tex]=\frac{1}{\frac{a^{3} }{5^{2} b^{4} } }[/tex]
[tex]=\frac{5^{2} b^{4} }{a^{3} }[/tex]
[tex]=\frac{25b^{4} }{a^{3} }[/tex]
Hope this helps
The output of a function i 6 more than 2 time the input find the input when the output i -10
The value of input is -8 when the output is -10.
What is function?A function is a mathematical relation between a set of inputs (also called independent variables) and a set of outputs (also called dependent variables). It assigns a unique output to each input in its domain. Functions are often represented by mathematical expressions, graphs, or tables. In computer science, functions are used to organize and structure code by breaking it down into smaller, more manageable tasks.
The function describes that the value of function is 6 more than 2 times tha input
so f(x) = 2x + 6
so this is required function according to the description.
given that output of the function is -10
so f(x) = -10
=> 2x+6 = -10
=> 2x = -16
=> x = -16/2
=> x = -8
so the value of input is -8 for which the output is 10.
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Suppoe there i a 1. 6°F drop in temperature for every thouand feet that an airplane climb into the ky. If the temperature on the ground i 57. 7°F, what will be the temperature when the plane reache an altitude of 5,000 ft?
The temperature when the plane reached an altitude of 5,000 ft will be 49.7°F.
According to the question,
For every thousand feet, the temperature drops 1.6°F.
So, 5000 feet (five thousand feet) the temperature drop
= (1.6 × 5)°F ( using multiplication)
=8°F
The temperature on the ground is 57. 7°F .
The temperature when the plane reached an altitude of 5,000 ft will be
= (57.7 - 8)°F (using subtraction)
=49.7°F
So, when the plane reaches an altitude of 5,000 ft, the temperature will be = 49.7°F.
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Is Y =- 2x 5 in standard form?.
The equation y = -2x + 5 is already in the standard slope intercept form.
The slope-intercept form is a way of expressing the equation of a straight line in algebraic terms. The equation of a line in slope-intercept form is typically written as:
y = mx + b
Where m represents the slope of the line and b represents the y-intercept, which is the point at which the line crosses the y-axis. The slope-intercept form is useful because it allows you to quickly identify the slope and y-intercept of a line, given its equation. The slope represents the rate of change of y with respect to x, and the y-intercept represents the initial value of y when x is equal to 0. By using slope-intercept form we can easily graph the line and also can find the equation of the line from the graph.
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A homeowner is financing the cost of new windows. Two lenders have approved the homeowner for a $12,000 loan. The terms of each loan are:
Offer 1: 4.5% annual simple interest, with a total account balance of $14,430 after a 54-month term
Offer 2: 3.75% annual interest compounded monthly for a 66-month term
Assuming no payments are made, what is the difference in the account balances at the end of the loan terms. Round your answer to the nearest penny.
$204.88
$313.98
$767.12
$795.34
The difference in the account balances at the end of the loan terms is $313.98.
What is the interest rate?The amount that the lender charges the borrower over and beyond the principal amount is referred to as the interest rate. A person who deposits money in a bank or other financial institution also earns additional income in terms of the recipient, known as interest, taking into account the time value of money.
Given A homeowner is financing the cost of new windows. Two lenders have approved the homeowner for a $12,000 loan.
principal = $12,000
Offer 1: 4.5% annual simple interest, with a total account balance of $14,430 after a 54-month term
Amount of offer 1 = $14,430
Offer 2: 3.75% annual interest compounded monthly for a 66-month term
the amount is given by,
A = [tex]p(1 + \frac{r}{n} )^{nt}[/tex]
nt = 66 months
n = 12
r = 3.75% = 0.0375
p = $12,000
substitute the values in the formula,
A = 12000(1 + (0.0375/12))⁶⁶
A = 12000(1.228665)
A = $14,743.98
Difference in amounts = $14,743.98 - $14,430
The difference in amounts = $313.98
Hence the difference in amounts is $313.98.
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What is the importance of knowing the concept of parallel and perpendicular lines?.
These concepts can be used in many buildings like skyscrapers because they may fall over if they are not parallel to the ground. In the case of a cabinet, you need the sides to be perpendicular to each other and to the top and bottom. Otherwise, the door may not open and close accurately.
The characteristics of parallel lines are;
1. The shortest distance between the lines that are parallel is the same at all points along the lines.
2. The lines are on the same plane.
3. As the plane is extended indefinitely, the lines do not intersect.
The characteristics of perpendicular lines are;
1. Perpendicular lines are lines that intersect at a point.
2. Where two lines are perpendicular, the slope of one line is the negative reciprocal of the other, such that the product of the slopes of two lines that are perpendicular is -1.
3. The angle formed at the intersection of perpendicular lines is 90°.
4. A horizontal and a vertical line on the same plane are perpendicular to each other.
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