Answer:
Remembering the 30-60-90 triangle rules is a matter of remembering the ratio of 1: √3 : 2, and knowing that the shortest side length is always opposite the shortest angle (30°) and the longest side length is always opposite the largest angle (90°).
What is the first step for solving the system using substitution results in an equation?.
The first step for solving the system using substitution results in an equation is solve one equation for either x or y.
The substitution method is a quick and easy way to algebraically solve a set of linear equations and determine the variables' solutions. According to what the name implies, this method entails determining the value of the x-variable in terms of the y-variable from the first equation and then substituting or replacing the value of the x-variable in the second equation.
We can solve and determine the value of the y-variable in this method. Finally, we may use any of the above equations to obtain x by substituting the value of y. This procedure can also be switched around so that we first solve for x before solving for y.
If we take an example ,
Equation 1: 3x + 2y = 11
Equation 2: -x + y = 3
Substituting y = 3+x in equation 1 is the first step in the equation.
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The power, P (watts), of a car engine is proportional to the square of its speed,
s (m/s).
When s= 25, P = 1400.
Work out the speed (to 1 DP) when the power is 1820 watts
m/s
Answer:
28.5 m/s
Step-by-step explanation:
Given that power is 1400 W when speed is 25 m/s, and power is proportional to the square of speed, you want the speed when the power is 1820 W.
ProportionSince power is proportional to the square of speed, the ratio of speed squared to power is a constant:
s²/P = 25²/1400 = x²/1820
where x is the unknown speed.
SolutionWe can find the value of x by multiplying by 1820 and taking the square root:
x² = 25²(1820/1400)
x = 25√(1820/1400) = 25√1.3 ≈ 28.5 . . . . m/s
The speed is 28.5 m/s when the power is 1820 watts.
to solve the equation below you need to divide by what number 2X = 8
Tiffany went shopping at Forever 21 and The Gap. She spent a total sum of $450 at the two stores. If the amount she spent at Forever 21 was four times as much as the amount she spent at The Gap, how much did she spend at each of the two stores?
According to the algebraic expression she spend at each of the two stores:
= 90 in the gap
= 360 in the Forever 21
What are expressions in algebra?Any mathematical statement with variables, numbers, as well as an arithmetic operation in between them is called an expression or an algebraic expression. For instance, the expression 4m + 5 has the terms 4m and 5 as well as the variable m of the supplied expression, all of which are separated either by arithmetic sign +.
According to the given information:Tiffany went shopping at Forever 21 and The Gap.
She spent a total sum of $450 at the two stores.
the amount she spent at Forever 21 was four times as much as the amount she spent at The Gap.
SO,
The amount she spent in Forever 21 = y
The amount she spent in Gap = 4x
4x + y = 450
5x + y = 450
= 450/5
= 90
She spent in the gap.
= 450- 90
= 360
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Where would the intensity of an earthquake be higher?.
The intensity of an earthquake generally higher near the epicenter.
Intensity is based on observed effects of ground motion on people, buildings and natural features. This varies from site to site within the fault region, depending on the observer's position relative to the earthquake epicenter. The seismic intensity of an earthquake decreases as the distance from the epicenter increases, and decreases as the distance from the epicenter increases. An epicenter is a point on the surface of the Earth directly above where an earthquake begins. Earthquakes with a moment magnitude of approximately 6.5 or less occur in a concentrated area directly below the epicenter. Therefore, apart from the effects of different rock types and different soil types, the greatest shaking occurs at the epicenter. Earthquakes with a moment magnitude greater than 6.5 cause faults at some distance from the epicenter. At these large sizes, it is common for fractures to reach the surface. In such cases, the maximum shaking may or may not occur at the epicenter..
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What is the limit of sum formula?.
The limit of sum formula is Sn=a(1−rn)1−r,for r≠1.
Consider a curve that lies above the x-axis. This graph's function is a continuous function with all of its values being non-negative, defined on the closed interval [a, b]. The definite integral ab f(x) dx of any such continuous function "f" is the region bound between the curve, the points "x = a" and "x = b," and the x-axis.
On the interval [a, b], the definite integral of a real-valued function f(x) with respect to a real variable x is written as,
[tex]\int\limits^b_a {f(x)} \, dx = F(b)-F(a)[/tex]
∫ = Integration symbol
a = Lower limit
b = Upper limit
f(x) = Integrand
dx = Integrating agent
A function may get close to two distinct limits. There are two scenarios: one in which the variable approaches its limit by values larger than the limit, and the other by values smaller than the limit.
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What is the mirror image of 4 46?.
The mirror image is (4, 46) is (4, -46)
The term mirror image is defined as it is like a reflection of it either because it is exactly the same or because it is the same but reversed.
Here we have given the point (4, 46) and here need to mirror image of the points.
The rule Mirror image of (x , y ) in the x - axis is written as ( x , -y)
Here we have the value of x as 4 and the value of y as 46.
Here we also know that it is defined as a reflected duplication of the number that appears almost identical but is reversed in the direction perpendicular to the mirror surface.
When we apply the values on the formula then we get the mirror image as (4, -46).
Complete Question:
What is the mirror image of the coordinate (4, 46)?
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Omar went to the college traveling 8 mph and returned home traveling 24 mph. If the total trip took 8
hours, how long did Omar travel at each speed?
hours at 8 mph
hours at 24 mph
The distance that light travels in 12.3 nanoseconds is 37.9 meters.
What is speed?
Speed is the rate of change of an object's position relative to a given frame of reference. It is a scalar quantity, meaning it has both magnitude and direction. Speed is usually measured in meters per second (m/s) or kilometers per hour (km/h). Speed is an important factor in many activities, including travel, sports, and transportation.
This can be calculated by multiplying the speed of light (3.0 x 108 m/s) by the time (12.3 nanoseconds), which yields a result of 37.9 meters. This answer is rounded to the correct number of significant figures, which is two.
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The triangle with coordinates (2,-3),(2,1),(-4,2) is reflected
across the y-axis and then translated by vector
(3,-2).
Part A
Find the new coordinates
Part B
What is the composition of functions for the
given sequence of transformations?
(x, y) → (
The new coordinates after reflection will be (4,2) (-2,1) (-1,-3).
A reflection is a type of transformation that involves flipping a shape, known as the preimage, across a line, known as the line of reflection, to produce a new shape (called the image). You can picture what would happen if you turned the form across the line to graph a reflection.
The general guidelines for the reflection over x-axis equation are as follows: The reflection equation of the new reflected graph will be y=f(x) y = f (x) given an equation, y=f(x) y = f (x). In other words, the function is just multiplied by 1, which results in a curve that crosses the x-axis.
The new coordinates after reflection will be -
(4,2) (-2,1) (-1,-3)
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What is the perfect square trinomial of 36?.
A perfect square trinomial is a polynomial of the form (x + b)^2 = x^2 + 2bx + b^2. It is called a "perfect square" because when it is multiplied out, the resulting polynomial is a square of a binomial.
To find the perfect square trinomial of 36, we need to find two numbers that when added, give us b and when multiplied give us b^2=36.
Those two numbers are 6 and -6, since 6*-6 = -36 = 36.
So, the perfect square trinomial of 36 is (x + 6)(x - 6) = x^2 - 36
Another way to find the perfect square trinomial is to take the square root of the constant term (36) and then add and subtract that value to the variable.
√36 = 6
then x^2 + 6x - 6x + 36 = x^2 - 36
So, the perfect square trinomial of 36 is x^2 - 36.
[tex]36[/tex] is the square of [tex]6[/tex]. The square of a binomial is called a perfect square trinomial. [tex]X^2+12x+36[/tex] is a perfect square trinomial.
What are the two properties of irrational numbers?.
Properties of irrational number:
The addition of an irrational number and a rational number gives an irrational number. Multiplication of any irrational number with any nonzero rational number results in an irrational number.Here, The definition of irrational number:
An irrational number is a type of real number which cannot be represented as a simple fraction. It cannot be expressed in the form of a ratio. If N is irrational, then N is not equal to p/q where p and q are integers and q is not equal to 0. Example: √2, √3, √5, √11, √21, π(Pi) are all irrational.
The following are the properties of irrational numbers:
The addition of an irrational number and a rational number gives an irrational number. Multiplication of any irrational number with any nonzero rational number results in an irrational number.Learn more about Irrational Number at:
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match each table to an equation that represents the relationship.
table a Equation 1 400 + x = y
table b Equation 2 x - 400 = y
table c Equation 3 x + y = 400
table d Equation 4 400 X x = y
The equation y = 400x represents the relationship as shown in the table.
The correct option is table d.
What is the proportional relationship?
A proportional relationship is a relationship between two expressions, where changes in one expression mean some constant change in another expression as well. Generally, it is represented as x/y = k, where x and y are two expressions and k is constant.
Given:
A table is shown in the attached image.
To find the relationship:
We will find the common ratio,
y/x = k, where k is the proportionality constant,
400/1 =400
800/2 = 400
1200/3 = 400.
That means, the equation is,
y = 400x
Therefore, y = 400x is the equation.
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The complete question is given in the attached image.
HELP ME ASAP!!! PLS!!
The Chu family can hike 3 miles per hour. How long will it take them to hike 15 miles?
A- 3.75 hours
B- 4 hours
C- 4.5 hours
D- 5 hours
Answer:
D- 5hrs
Step-by-step explanation:
If the family can hike 3 miles per hour,
for 15 miles: 15/3 = 5 hours.
Every hour they cover 3 miles per hour, so to cover 15 miles, they will take 5 hours
Answer:
D. 5 hours
Step-by-step explanation:
3 miles per 1 hour so 3/1
15 miles per x hours so 15/x
3/1 = 15/x or 3 = 15/x
get x by itself so
3 divided by 3 and 15 divided by 3
x = 5 hours
you invested 52,400 at 7% compounded annually for 10 years what is your total return on this investment
Answer:
$50678.73
Step-by-step explanation:
Answer:
103,078.73.
Step-by-step explanation:
Amount after n years = P(1 + r/100)^n where P is amount invested, r is the percentage rate and n = number of years.
So, here we have:
Total after 10 years = 52400(1 + 7/100)^10
= 52400 * 1.967151357
= 103,078.73.
Erika i purchaing a new cooler from outdoor World. The cooler cot $125. If Erika ha a coupon for 15% off, and ha another coupon for $15 off, which coupon hould he ue?
Erika should use the coupon which gives her a discount of 15% as it will bring down the cost of the cooler to $106.25.
Given,
The initial cost of the cooler = $125
Erika has two options: (i) 15% off coupon
(ii) $15 off coupon
Cost of the cooler that Erika gets from option (i):
[tex]= 125 - \frac{15}{100} * 125\\= 125 - 18.75\\= 106.25\\[/tex]
Cooler costs $106.25 to Erika from option (i).
Cost of the cooler that Erika gets from option (ii):
[tex]= 125 -15\\=110[/tex]
Cooler costs $110 to Erika from option (ii).
We can clearly see, $106.25 < $110
Therefore, Erika should use the coupon which gives her a discount of 15%.
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Sam ued to be 175cm tall. He i now 7% taller. To the nearet centimeter,how tall i Sam now
Sam is now 187cm tall. When we say that Sam is now 7% taller, it means that his new height is 7% greater than his original height.
To find out how much taller he is, we can calculate 7% of his original height using the percentage formula:
percentage of original value = (part / whole) * 100
In this case, the part is the increase in height, and the whole is the original height. To find the part, we can rearrange the formula to:
part = (percentage / 100) * whole
So, to find the increase in height, we can substitute the values we know:
increase in height = (7 / 100) * 175 cm
This simplifies to:
increase in height = 12.25 cm
Now that we know how much taller Sam is, we can add this increase to his original height to find his new height:
new height = original height + increase in height
new height = 175 cm + 12.25 cm = 187.25 cm
So, Sam is now 187.25 cm tall. This number is rounded to the nearest centimeter, so his new height is 187cm tall.
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For 5-8, use the diagram to complete each sentence.
(diagram attached)
5. An exterior angle of the triangle is ________.
6. The remote interior angles of the triangle to the exterior angle 1 are ________ and ________.
7. The sum of the measure of angles 2 and 3 is equal to the measure of ________.
8. The sum of the measure of angles 1 and 4 is _______.
By using the diagram, each of the sentence should be completed as follows;
An exterior angle of the triangle is ∠1.The remote interior angles of the triangle to the exterior angle 1 are ∠2 and ∠3.The sum of the measure of angles 2 and 3 is equal to the measure of ∠1.The sum of the measure of angles 1 and 4 is 180°.What is the exterior angle theorem?In Mathematics, the exterior angle theorem can be defined as a theorem which states that the measure of an exterior angle in a triangle is equal in magnitude to the sum of the measures of the two remote or opposite interior angles of that triangle.
By applying the exterior angle theorem, we can reasonably infer and logically deduce that the sum of the measure of both angle 2 and angle 3 in the given triangle is equal to the measure of angle 1 (∠1);
∠2 + ∠3 = ∠1
By applying the Linear Pair Postulate to the two angles formed at a point, we have the following:
∠1 + ∠4 = 180°
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maya reads 6 3/4 chapters in 1 7/8 hours
what is the unit rate in chapters per hour?
write your answer as a fraction or a mixed number in simplest form
Answer:To find the unit rate in chapters per hour, we need to divide the number of chapters read by the amount of time it took to read them.
6 3/4 chapters / 1 7/8 hours = (64+3)/(18+7) chapters/hours
= (25/8) chapters/hours
To simplify this fraction, you can divide both the numerator and denominator by their greatest common factor which is 1.
25/8 chapters/hours = (25/8) chapters/hours
So the unit rate in chapters per hour is 25/8 chapters per hour.
Step-by-step explanation:
I need help with this question, please
The credit utilization ratio would be 11.7%.
What is credit utilization?
The credit utilization ratio is a measure of how much of a person's credit limit is being used. It is calculated by dividing the total credit card balances by the total credit limit.
In Mary's case, the total credit card balances are $150 + $200 = $350
The total credit limit is $2000 + $1000 = $3000
To find the credit utilization ratio, we divide the total credit card balances by the total credit limit:
$350 / $3000 = 0.117 or 11.7%.
Hence, the credit utilization ratio would be 11.7%.
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In the expression 5 x y over 7 what value of y would make a product greater than 5 ?
Answer:
y > 7x
Step-by-step explanation:
(5xy)/7 [5 x y over 7]
["what value of y would make a product greater than 5 ?"] can be written as:
(5xy)/7 > 5
Rearrange to find y:
(5xy)/7 > 5
(5xy) > 35
y > 35/5x
y > 7x
Find the distance between the points C(0, 0) and D(8, 3).
8.3
011
√73
√55
Answer: Number 3, which is √73
Step-by-step explanation:
Use the distance formula:
Distance (d)
= √(8 - 0)2 + (3 - 0)2
= √(8)2 + (3)2
= √73
= Number 3 :>
factorise
12x*2 + 15xy-9x
Answer:
see picture
Step-by-step explanation:
Factorise for 12[tex]x^{2}[/tex]+15xy-9x is 3x (4x+5y−3)
Solution steps:
The first step is to factor out 3.
So,
3 (4[tex]x^{2}[/tex]+5xy-3x)
The second step is to consider 4[tex]x^{2}[/tex]+5xy−3x. Factor out x.
So,
x (4x+5y−3)
The third step is to rewrite the complete factored expression.
3x (4x+5y−3)
Evaluate:
3x (4x+5y−3)
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What distance on the map (in centimeters) represents an actual distance of 4 kilometers
The distance on the map, in centimeters, that represents an actual distance of 4 kilometers, is 3. 2 cm
How to find the distance ?The map is such that the scale is 4 cm on the map, equals 5 km on the ground.
If we have a distance of 4 km therefore, the distance on the map would be:
= ( Distance on ground x scale on map ) / Kilometers on scale
= ( 4 x 4 ) / 5
= 16 / 5
= 3. 2 cm
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Full question is:
Scale of a map says that 4 cm represents 5 km. What distance on the map (in centimeters) represents an actual distance of 4 kilometers?
Solve the system of equations using any method. Describe the method used.
The solutions of the system are x = 1, y = 2 and z = -1.
And we solve the system with the help of Jordan-canonical form.
What is matrix?A collection of numbers lined up in rows and columns to form a rectangular array is called a matrix. The elements, or entries, of the matrix are the numbers.
Given:
A system of equations,
x + y - 2z = 5
-x + 2y + z = 2
2x + 3y - z = 9
In the matrix form;
[tex]\left[\begin{array}{ccc}1&1&-2\\-1&2&1\\2&3&-1\end{array}\right] \left[\begin{array}{c}x\\y\\z\end{array}\right] = \left[\begin{array}{c}5\\2\\9\end{array}\right][/tex]
[tex]\left[\begin{array}{ccc}1&1&-2\\0&0&-10/3\\0&1&3\end{array}\right] \left[\begin{array}{c}x\\y\\z\end{array}\right] = \left[\begin{array}{c}5\\10/3\\-1\end{array}\right][/tex]
That means,
x = 1, y = 2 and z = -1.
Therefore, the solutions of the system are x = 1, y = 2 and z = -1.
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What is the inverse equation of the function, y = 3x - 6? y -1 = y -1 = x + 6 x -1 = 3 y - 6 y -1 = 3 x + 6.
The best answer (and only correct answer) among the options given is: option [C]: y⁻¹ = (x+6) / 3 .
What is the inverse function?
The inverse function returns the original value for which a function gave the output. If you consider functions, f and g are inverse, f(g(x)) = g(f(x)) = x.
Given the original function: y = 3x - 6 ;
To find the "inverse equation" of said function; we change the "x" to a y"; and the "y" to an "x"; and rewrite:
x = 3y − 6 ;
Now, rewrite in "slope-intercept form" ; or y = mx + b ;
that is, with y as "single, isolated" variable on the left-hand side of the equation (with an "implied coefficient of positive one", only); then an "equal sign, then "mx + b" ; in which: "m" is the coefficient of the variable, "x"; and in which "m" refers to the "slope"; and "b" refers to the 'y-intercept".
So, we have the inverse function:
x = 3y − 6 ; we want to write in slope-intercept form;
Add "6" to each side of the equation:
x + 6 = 3y − 6 + 6 ;
x + 6 = 3y ;
Rewrite as: 3y = x + 6 ;
Divide EACH side of the equation by "3" ; to isolate "y" one side of the equation; specifically, the left-hand side of equation; and to write in "slope-intercept form:
3y / 3 = (x + 6) / 3 ;
to get:
y = (x + 6) / 3 ;
y = (x/3) + (6/3) ;
y = (x/3 ) + 2 ;
or; write as: y = (1/3)x + 2 ;
Now, let us examine the answer choices given:
Note that all the answer choices begin with "y-1" ;
(except "answer choice: [B]" , which begins with "x-1"). This seems confusing; however, in reality, this does not mean, "y minus 1"; or "x minus 1". Rather, it mean y⁻¹ or x⁻¹ as notation for the "inverse" (not to be confused with the exponent notation. The confusion stems from the fact that it can be difficult to make such notations on the "Brainly" system.
That being said, we can write the aforementioned "rewritten equations" (see above in THIS VERY ANSWER) as:
y⁻¹ = (x + 6) / 3 ;
y⁻¹ = (x/3) + (6/3) ;
y⁻¹ = (x/3 ) + 2 ;
or; write as: y⁻¹ = (1/3)x + 2
That being said:
Therefore, the best answer (and only correct answer) among the options given is: option [C]: y⁻¹ = (x+6) / 3 .
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given g(x)=-x^2+10x-3 find the following,
g(9)
g(-1)
Step-by-step explanation:
g(x) = - x² + 10x - 3
To get the g(9) substitute X in the equation for 9
g(9) = - 9² + 10(9) -3
g(9) = 81 + 90 - 3
g(9) = 171 - 3
g(9) = 168
Similarly to get g(-1)
g(-1) = - (-1)² + 10(-1) - 3
g(-1) = - 1 - 10 - 3
g(-1) = - 14
What are the examples of logarithmic equation?.
The examples of logarithmic equation are 625 = [tex]5^{4}[/tex] and 4 = [tex]log_{5}625[/tex], 100000 = [tex]19^{5}[/tex] and 5 = [tex]log_{19}100000[/tex] .
To generate a given number, a base must be raised to a particular exponent, power, or logarithm. The time needed to multiply numbers with numerous digits was drastically decreased thanks to the logarithms, which were developed in the 17th century to speed up calculations.
For more than 300 years, they served as the foundation for numerical labor, but the development of mechanical adding machines in the late 19th century and computers in the 20th century made them obsolete for large-scale calculations.
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A rental car company charges $24 per day to rent a car and $0.10 for every mile
driven. Xin wants to rent a car, knowing that:
• She plans to drive 200 miles.
.
. She has at most $140 to spend.
Write and solve an inequality which can be used to determine d, the number of days
Xin can afford to rent while staying within her budget.
Inequality:
Answer:
24 a b c d
Step-by-step explanation:
whyats the answert
Answer:[tex]d\leq 5[/tex]
[tex]24d+20\leq 140[/tex]
Step-by-step explanation: First You do 200x0.10 which equals 20. then you put the cost per day first so 24 per day + the cost of all miles which is 20 at most means she can also spend less then 380 so we use the greater than equal symbol.
State if the triangles in each pair are similar. If so, state how you know they are similar and complete the similarity statement.
Thank you!
Answer: Similar by SAS, and ABC ~ AVU
Step-by-step explanation:
AV = 77 - 66 = 11
AU = 42 - 36 = 6
6/36 = 1/6
11/66 = 1/6
Therefore, these two triangles ABC and AVU are similar by SAS similarity.
ABC ~AVU :>
What is the degree of polynomial 5x2 4x2 7x?.
The degree of the polynomial 5x2 + 4x2 - 7x is 3.
5x2 and x2 are the same power value is 4 and 7x contain the power value 1 so the difference of the degree of polynomial we find is 3. When they don't already, unite all the different phrases in the expression to make it simpler.
The phrases that are not associated with a variable, like 3 or 5, are referred to as constant terms. The terms associated with the variable are known as coefficients. Either intentionally disregard these terms or check them off the list while looking for the degree of a polynomial.
The polynomial is represented in standard form in this manner. First should be the phrase with the highest exponent, and last should be the word with the lowest exponent. This will enable you to determine which term's exponent has the highest value.
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