Answer:
b = √(c^2 - a²)
Step-by-step explanation:
Start with the given c = √a^2 + b^2. Squaring both sides, we get:
c² = a² + b².
We want to iosolate b² and then b.
So: subtract a² from both sides, resulting in:
c² - a² = b²
Taking the square root of both sides, we get:
√b² = √(c² - a²)
and so:
b = √(c^2 - a²)
To solve the Pythagorean theorem equation for b, isolate b on one side by first squaring both sides. Move the a^2 term to the other side of the equation, then take the square root of both to solve for b. The solution is b = √(c^2 - a^2).
Explanation:The formula mentioned, c = √a^2 + b^2, represents the application of the Pythagorean theorem for right-angled triangles. To solve this equation for b, you would have to isolate b on one side. Start by squaring both sides of the equation, which gives: c^2 = a^2 + b^2. Then, move a^2 to the other side of the equation to isolate b^2 assuming c^2 > a^2. This gives you: b^2 = c^2 - a^2. Then, take the square root of both sides, which gives: b = √(c^2 - a^2).
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PLEASE HELP ME
3x - 8y = 29
3x + y = -2
Question 4 options:
(0.5, -3.5)
(0, -2)
(0.75, -2.25)
(0, -3.75)
Answer:
Solution to pair of linear equations
Step-by-step explanation:
Subtract second equation from the first
[tex]3x-8y=29\\3x+ y=-2\\[/tex]
subtraction eqn 2 from 1 we get
[tex](3x-3x)+(-8y-y) = (29-(-2))\\-9y=31\\y=-\frac{31}{9} \\y= - 3.44[/tex]
In order to find the value of x we will put this value of y in anyof the above equation and solve it for x
[tex]3x-\frac{31}{9} = -2\\3x=-2+\frac{31}{9} \\3x=\frac{-18+31}{9} \\3x=\frac{13}{9} \\x=\frac{13}{9*3} \\x=\frac{13}{27} \\x=0.4814[/tex]
The Correct answer which is solution two the above linear pair of equations is
x=0.4814
y=-0.344
1. An angle in a right triangle is identified as θ. If the tangent of θ equals one, what must be true about the triangle side lengths?
A. The side adjacent to theta is half the length of the hypotenuse.
B. The side opposite to theta is longer than the adjacent side.
C. The sides opposite and adjacent to theta are the same length.
D. The side adjacent to theta is longer than the adjacent side.
Answer: Option C
"The sides opposite and adjacent to theta are the same length."
Step-by-step explanation:
By definition the tangent of an angle [tex]\theta[/tex] is written as:
[tex]tan(\theta) = \frac{opposite}{adjacent}[/tex]
Where:
"opposite" is the side opposite the [tex]\theta[/tex] angle
"adjacent" is the side that contains the angle [tex]\theta[/tex] and the angle of 90 °.
In this case we know that
[tex]tan(\theta) = \frac{opposite}{adjacent} = 1[/tex]
If [tex]\frac{opposite}{adjacent} = 1[/tex] then [tex]opposite = adjacent[/tex]
Finally the answer is the option C
"The sides opposite and adjacent to theta are the same length."
Answer:
C. The sides opposite and adjacent to theta are the same length.
Step-by-step explanation:
Given : tanθ = 1
recall tanθ = [tex]\frac{opposite}{adjacent}[/tex]
the only way for [tex]\frac{opposite}{adjacent}[/tex] to equal 1, is that the numerator is the same value as the denominator,
hence the answer is
C. The sides opposite and adjacent to theta are the same length.
Graph the solution to the following system of inequalities in the coordinate plane.
Answer:
see below
Step-by-step explanation:
The first equation is in slope-intercept form, so you can see that the boundary line has a slope of -2 and goes through the point (x, y) = (0, -4). Since the comparison is "<", the line is dashed and shading is below it.
The second equation is that of a vertical boundary line at x=-3. It is solid, because the comparison includes the "equal" case. Shading is to the right of it, where x values are greater than -3.
PLS HELP SHOW ALL YOUR WORKING OUT
BRAINLIEST
BRAINLIEST
find the value of a^n b^n if n=3,a=100,and b=1/4
Answer:
= (100)^3(1/4)^3
= 15,625 i think im not that good at math but i passed
Step-by-step explanation:
Hi there! My name is Zalgo and I am here to help you out on this gracious day. If n=3, a=100 and b=1/4, the equation should look like "100^3 * 1/4^3". The answer would be 15625.
I hope that this helps! :D
"Stay Brainly and stay proud!" - Zalgo
One angle of a triangle measures 76" more than the smallest, while a third angle is twice the smallest. Find the
measure of each angle
The triangle has angles of
degrees
Answer:
26,102,52
Step-by-step explanation:
Let x be the smallest angle
x+76 is the second angle
2x is the third angle
The sum of all three angles is 180 degrees
x+ (x+76) + 2x = 180
Combine like terms
4x+76 = 180
Subtract 76 from each side
4x+76-76 = 180-76
4x =104
Divide by 4
4x/4 =104/4
x =26
x+76 =26+76 =102
2x = 2*26 = 52
The ratio of money in Obi's wallet to Rudy's wallet one day was 5:2. Obi spent ?20 that day. Obi now had ?8 less than Rudy. How much did they have initially altogether?
Answer:
Altogether, they had ?28
Step-by-step explanation:
Had Obi spent only ?12, they would have been even. Thus ?12 is the same as 5-2 = 3 "ratio units". So, each "ratio unit" is worth ?12/3 = ?4.
Then Obi started the day with 5·4 = 20, and Obi started the day with 2·4 = 8. Obi ended with 0, which is 8 less than Rudy.
Altogether, they started with 20 + 8 = 28 of whatever a ? is.
Answer:
Money they have initially altogether = 28
Step-by-step explanation:
The ratio of money in Obi's wallet to Rudy's wallet one day was 5:2.
Money Obi has = 5 r
Money Rudy has = 2 r
Obi spent 20 that day and bi now had 8 less than Rudy
5r -20 = 2r - 8
3r = 12
r = 4
Initial money they have
Obi = 5r = 5 x 4 = 20
Rudy = 2 x 4 = 8
Altogether they have 20+8 = 28
Money they have initially altogether = 28
Solve the following equation for . A. y = 3 B. y = 18 C. y = 6 D. y = 36
Your answer is D. y = 36
We can find this by just rearranging the equation firstly:
2 + √4y - 3 = 11
√4y - 1 = 11
√4y = 12
Now we can simplify √4y, because 4 2², so you get 2√y :
2√y = 12
√y = 6
We can now square both sides to get the equation as "y ="
y = 36
I hope this helps! Let me know if you have any questions :)
One side of a triangle is 2 feet shorter than the second side. The third side is 4 feet shorter than the second side. The perimeter of a triangle is 15 feet. Find the length of each side.
The length of first side is 5 feet, the length of second side is 7 feet, the length of third side is 3 feet.
What is perimeter?The perimeter is the sum of measurement of all sides of a triangle. It is done by a ruler.
How to calculate perimeter?let the second side be x
according to question first side will be (x-2) feet and the third side will be (x-4) feet.
We know that the perimeter is equal to the sum of all sides of a triangle.
so
x+x-2+x-4=15
3x=6=15
3x=21
x=7
The length of first side=7-2=5 feet
The length of second side=7 feet
The length of third side=3 feet
Hence the sides of the triangle is 5 feet, 7 feet, and 3 feet.
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Michael has never taken a foreign language class, but is doing a story on them for the school newspaper. The school offers French and Spanish. Michael has a list of all 25 kids in the school enrolled in at least one foreign language class. He also knows that 18 kids are in the French class and 21 kids are in the Spanish class. If Michael chooses two kids at random off his list and interviews them, what is the probability that he will be able to write something about both the French and Spanish classes after he is finished with the interviews? Express your answer as a fraction in simplest form.
Answer:
112/125
Step-by-step explanation:
If we know all 25 are in at least one foreign language class then we can assume that exactly 4 of the 18 kids in French only take French to add up to 25 and this means that the 14 left take both classes. Now we can create three fractions for each case which are 7/25 (Spanish only) 4/25 (French only) and 14/25 (Both) and we can know say that if he goes down the route of getting a Spanish only as his first he needs one of the 18 other students the chances of this happening are 7/25 * 18/25 = 126/625 the same thing is done with the French only and we get 4/25 * 21/25 = 84/625 and then we have the possibility of just getting a student that does both which is 14/25 or 350/625. now we add them all together to get 560/625 which is simplified to 112/125.
Hope this helps please mark brainliest :)
Ms. Clint is comparing the sales of sweaters and gloves at her store for the past ten winter weeks. Select the true statement based on the graph.
Answer:
i would say b
Step-by-step explanation:
Answer:
The correct option is B.
Step-by-step explanation:
The given graph represents the sales of sweaters and gloves at her store for the past ten winter weeks.
If the scatter points lie near to a straight line and the slope of the line is positive, then there is a strong positive linear correlation between two variables.
r=1 means strong positive correlation.
r=0 means no correlation.
r=-1 means strong negative correlation.
From the figure it is clear that the scatter points lie near to a straight line and the slope of the line is positive. So, there is a positive linear correlation between the sales of sweaters and gloves.
Therefore the correct option is B.
Omar is painting a 24-square-foot wall. The wall is divided into squares that each measure 1 /4 square foot. How many squares is the wall divided into?
Answer:
96 squares
Step-by-step explanation:
The number of squares is ...
(wall area)/(square area) = (24 ft²)/(1/4 ft²) = 24×4 = 96 . . . . squares
Answer:
96 squares
Step-by-step explanation:
HELP ME PLEASE MATH
Which graph represents the following system of inequalities?
y > 5x-1, because it is just a greater than sign, the shaded area would be to the left of a dotted line.
y ≤ x +3, because the sign is less than or equal to, the line is solid and the shaded area would be to the right.
Combine the shaded areas would make Graph B. the correct answer.
Given the following system of equations:
−4x + 8y = 16
2x + 4y = 8
What action was completed to create this new equivalent system of equations?
−2x + 4y = 8
2x + 4y = 8
A.Multiply the second equation, 2x + 4y = 8, by −1.
B.Multiply the first equation, −4x + 8y = 16, by −1.
C.Divide the second equation, 2x + 4y = 8, by 2.
D.Divide the first equation, −4x + 8y = 16, by 2.
Answer:
D.Divide the first equation, −4x + 8y = 16, by 2.
Step-by-step explanation:
All you have to do is look at the effect of the proposed action on the constant on the right to tell which answer choices are incorrect.
A: you would get -8 on the right. Neither equation has that.B: you would bet -16 on the right. Neither equation has that.C: you would get 4 on the right. Neither equation has that.D: you would get -2x +4y = 8, matching the first equation of the new system exactly.Answer:
D.Divide the first equation, −4x + 8y = 16, by 2.
Step-by-step explanation:
−4x + 8y = 16
2x + 4y = 8
Take the first equation and divide it by 2
−4x/2 + 8y/2 = 16/2
-2x + 4y = 8
At how many points does the graph of the function below intersect the x-
axis?
y = 4x^2 - 6x + 1
Answer:
Option B is correct.
Step-by-step explanation:
y=4x^2-6x+1
Solving the quadratic equation:
4x^2-6x+1
[tex]x=\frac{-b\pm\sqrt{b^2-4ac}}{2a}[/tex]
a=4, b=-6 and c=1
[tex]x=\frac{-(-6)\pm\sqrt{(-6)^2-4(4)(1)}}{2(4)}\\x=\frac{6\pm\sqrt{36-16}}{8}\\x=\frac{6\pm\sqrt{20}}{8}\\x=\frac{6+\sqrt{20}}{8} \,\,and\,\, x=\frac{6-\sqrt{20}}{8}[/tex]
So, it has 2 solutions,
Option B is correct.
Celine has a bottle that contains 20% milk and the rest water. The bottle has 1 liter of water. Part A: Write an equation using one variable that can be used to find the total number of liters of milk and water in the bottle. Define the variable used in the equation and solve the equation. Hint: 0.2x represents the number of liters of milk in the bottle. (5 points) Part B: How many liters of milk are present in the bottle? Show your work. (5 points)
Answer:
A) 0.2x +1 = x . . . . x is the volume of liquid in the bottle (liters)
B) 0.25 liters of milk are in the bottle
Step-by-step explanation:
It is often convenient to define a variable as the answer to the question. Here, the question says "find the total number of liters of milk and water in the bottle", so that is the definition of our variable, x.
A) The problem statement tells us that 20% of the liquid is milk, so that amount is 0.2x (as the hint says). Then the sum of milk volume and water volume is the total volume:
0.2x + 1 = x . . . . . . . an equation in one variable that can find total volume
We can solve this equation by subtracting 0.2x, then dividing by the coefficient of x.
1 = 0.8x
1/0.8 = x = 1.25 . . . the total number of liters of milk and water is 1.25
__
B) The number of liters of milk is 0.2x, so is 0.2·1.25 = 0.25
There are 0.25 liters of milk in the bottle.
please help asap urgent brainliest
Answer:
24 units cubed
Step-by-step explanation:
Volume is just length x width x height
so the width is 2 units and the height is 2 units and the length is 6 units: 2 x 2 = 4
4 x 6 = 24 units cubed
One unit cube = 1 by 1 by 1.
In the long picture, we have 2 by 2 by 6.
Volume = 2 x 2 x 6
Volume = 4 x 6
Volume = 24 units^3
4. Which relation is a function?
A.{(0; -9), (-9, -2), (0, -3)}
B.{(0, -9), (-9,0), (-3, -3)}
C.{(0, -9), (-2, -3), (-2, 0), (-3,-2)}
D.{0,-9, -2, -3}
Answer:
It's B.
Step-by-step explanation:
That is B because there are no duplicate x-values in the ordered pairs.
D is a set of numbers, not a function.
In this triangle, cosA/cosB is equal to what? (the triangle is below)
Answer:
CosA/CosB =1
CosA = Adjacent side/Hypotenuse
=AC/AB = 3/4.24
Cos B = Adjacent side/Hypotenuse
= BC/AB = 3/4.24
CosA/CosB = (3/4.24)/(3/4.24) = 1
The value of CosA/CosB = 1
Answer:
1
Step-by-step explanation:
trust lol
Brainliest!, write an algebraic expression to represent the verbal expression
the cube of the quotient of a number and 24
Answer:
(n/24)^3
Step-by-step explanation:
If "n" represents "a number," then "the quotient of a number and 24" means ...
(n/24)
The cube of that is ...
(n/24)^3
Need help with a math question
ANSWER
P'(2,7)
EXPLANATION
When we reflect a point in the y-axis, we negate the x-coordinates.
The rule for reflection across the y-axis is
[tex](x,y)\to (-x,y)[/tex]
The given point, P has coordinates (-2,7)
To obtain the coordinates of the image P', we negate the x-coordinate of P(-2,7).
[tex]P( - 2,7) \to \: P'( - - 2,7)[/tex]
[tex]P( - 2,7) \to \: P'(2,7).[/tex]
Answer:
(2, 7)
Step-by-step explanation:
Under a reflection in the y- axis
a point (x, y) → (- x, y)
Hence
P(- 2. 7) → P'(2, 7)
what is the measure of STY in oo below? 130 310 230 50
ANSWER
B. 310°
EXPLANATION
The sum of angles in a circle is 360°
From the diagram, the measure of arc SY is 50°
The measure of arc STY plus the measure of arc SY is 360°
To find the measure of arc STY, we subtract 50° from 360° to get:
Measure of arc STY
[tex] = 360 \degree - 50 \degree[/tex]
This simplifies to
[tex]310 \degree[/tex]The correct answer is B 310°
Answer:
The correct answer is option B. 310°
Step-by-step explanation:
From the figure we can see that, a circle with center o.
And an arc SY with central angle 50°
To find the measure of arc STY
From the figure we can write,
arc SY + arc STY = 360
measure of arc STY = 360 - measure of arc SY
= 360 - 50 - 310°
Therefore the correct answer is option B. 310°
An air conditioning unit promises to have a cooling capacity of 6,000 British thermal units (Btu). The unit has a maximum variance of y Btu. If x is the air conditioning unit’s actual capacity, which graph could be used to determine variance levels that would cause a unit to be rejected because of its cooling capacity?
Answer:
ITS 100% A
Step-by-step explanation:
Answer:
Option 2.
Step-by-step explanation:
Let as consider x be the air conditioning unit's actual capacity and y is the maximum variance in British thermal units (Btu).
It is given that an air conditioning unit promises to have a cooling capacity of 6,000 British thermal units (Btu).
We need to find the graph that could be used to determine the variance levels that would cause a unit to be rejected because of its cooling capacity.
It means the maximum variance is less than or equal to absolute difference of actual capacity and 6,000.
[tex]y\leq |x-6000|[/tex]
The related equation of this inequality is
[tex]y=|x-6000|[/tex]
It is a V-shaped curve with vertex (6000,0) and y-intercept (0,6000).
The related curve is a solid V-shaped curve because the points on curve included in the solution set.
The shaded region lie below the curve because the sign of inequality is ≤.
Therefore the correct option is 2.
find f’(x).
1. f(x)=x^2-5x+1
2. f(x)=10/x
Answer:
1) 2x-5 2) -10/x^2
Step-by-step explanation:
Use power rule and constant rule for the first one:
1) f(x)=x^2-5x^1+1 (x^n)'=nx^(n-1) and (c)'=0
f'(x)=2x^1-5(1)x^0+0
f'(x)=2x-5(1) x^0=1
f'(x)=2x-5
Use just power rule for last one after a rewrite
2) f(x)=10/x
f(x)=10x^(-1) now use power rule
f'(x)=-10x^(-2) =-10/x^2
Solve the formula I = Prt, in general, to find the principal, P.
By substitution of formula, the expression of principle P is P = I/(r*t) .
What is substitution of formula ?Substitution of formula is a method to find any parameter from the given expression by substituting the required value from the expression or equation mentioned.
Given expression is I = Prt .
Substituting the parameter of principle(P) from the above expression -
P = I/(r * t)
Thus, by substitution of formula, the expression of principle P is P = I/(r*t) .
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A parabola with a vertical axis has its vertex at the origin and passes through point (7,7). The parabola intersects line y = 6 at two points. The length of the segment joining these points is
A. 14
B. 13
C. 12
D. 8.6
E. 6.5
Answer:
[tex]\boxed{\text{B. 13}}[/tex]
Step-by-step explanation:
1. Find the equation of the parabola
The vertex is at (0, 0), so the axis of symmetry is the y-axis.
The graph passes through (7, 7), so it must also pass through (-7,7).
The vertex form of the equation for a parabola is
y = a(x - h)² + k
where (h, k) is the vertex of the parabola.
If the vertex is at (0, 0),
h = 0 and k = 0
The equation is
y = ax²
2. Find the value of a
Insert the point (7,7).
7 = a(7)²
1 = 7a
a = ⅐
The equation in vertex form is
y = ⅐x²
3. Calculate the length of the segment when y = 6
[tex]\begin{array}{rcl}6 & = & \dfrac1{7}x^{2\\\\42 & = & x^{2\\x & = & \pm \sqrt{42}\\\end{array}[/tex]
The distance between the two points is the length (l) of line AB.
A is at (√42, 6); B is at (-√42, 6).
l = x₂ - x₁ = √42 – (-√42) = √42 + √42 = 2√42 ≈ 2 × 6.481 ≈ 13.0
[tex]\text{The length of the segment joining the points of intersection is }\boxed{\mathbf{13.0}}[/tex]
Use the Rational Zeros Theorem to write a list of all possible rational zeros of the function. f(x) = 2x3 + 8x2 + 7x - 8
Answer:
The list is -1,1,-2,2,-4,4,-8,8,-1/2,1/2
Step-by-step explanation:
Possible rational zeros are the constant factors/leading coefficient factors
So factors of -8: -1,1,-2,2,-4,4,-8,8
So factors of 2: -1,1,-2,2
Now put every number in the first list over every number in the second list:
The possible rational zeros are:
-1/1=-1
1/1=1
-2/1=-2
2/1=2
-4/1=-4
4/1=4
-8/1=-8
8/1=8
-1/2
1/2
I didn't write any number twice.... like -8/2 is just -4 which I already wrote
The list is -1,1,-2,2,-4,4,-8,8,-1/2,1/2
Answer:
±1/2, ±1, ±2, ±4 and ±8
Step-by-step explanation:
The Rational Zeros Theorem is defined as when a polynomial has all coefficients integer, then any rational zeroes of the polynomial have to be in the form ±p/q, where q is the coefficient of the highest power of the variable and p is declared as the constant term.
Furthermore, a rational "zero" is for a polynomial. when the polynomial is p(x), a "zero" is a value of x when p(x) = 0
Secondly, we have to know what a "rational zero" is. A "rational zero" is a zero that its number is rational. Some polynomials have some rational zeros and some irrational zeros, and some only have zeros that are rational numbers.
By applying this theorem, all possible factors of the constant term must be considered . In this example they are 1, 2, 4, and 8. After that Then you consider all possible factors of the coefficient of the highest power of the variable. we take the x³ term, whose coefficient is 2. the the possible factors of 2 are 1 and 2.
Therefore, the possible list of rational zeroes are given below
±1/1 = ±1
±1/2
±2/1 = ±2
±2/2 = ±1
±4/1 = ±4
±4/2 = ±2
±8/1 = ±8
±8/2 = ±4
By removing the duplicates, we arrive at the following,
±1/2, ±1, ±2, ±4 and ±8
Suppose that y varies inversely with x, and y = 2 when x = 4. What is an
variation?
Answer:
xy=8
Step-by-step explanation:
The equation for inverse variation is
xy = k where k is the constant of variation
4*2 = k
8=k
The equation is
xy=8
Define what an inverse function is in terms of domain and range.
and
Define what a function is in terms of domain and range.
Answer:
Step-by-step explanation:
Let's start with a function first. The domain of a function is all the x values that are covered by the graph of the function; the range is all the y values that are covered by the graph of the function.
In order to graphically find the inverse of a function, you literally switch the x and y variables and replot them. For example if a point on your function is
(3, -1), then the point on its inverse is (-1, 3). Because of this, you interchange the domains and the ranges. Therefore, the domain of a function is the range of its inverse, and the range of a function is the domain of its inverse.
The domain of the inverse function f⁻¹(x) will be (c, d) and the range of the inverse function f⁻¹(x) will be (a, b).
What are domain and range?The domain means all the possible values of x and the range means all the possible values of y.
Let the function be f(x).
Let the domain of the function f(x) is (a, b) and the range of the function f(x) is (c, d).
The inverse function of f(x) will be f⁻¹(x).
Then the domain of the inverse function f⁻¹(x) will be (c, d) and the range of the inverse function f⁻¹(x) will be (a, b).
More about the domain and range link is given below.
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Identify the slope and y-intercept of the line: PLEASE HELP ME IT WOULD ME SO MUCH THANK YOU!!!!!
y =– (¾)x - 2
Answer:
slope: -3/4y-intercept: -2 . . . . or point (0, -2)Step-by-step explanation:
Slope-intercept form is ...
y = mx + b
Comparing your equation to this pattern, you can see that your equation is already in this form, with ...
m = -3/4b = -2In this form, the coefficient of x (which is m) is the slope of the line. Thus your slope is -3/4. The added constant (which is b) is the y-intercept, the value of y when x=0. Your y-intercept is -2. Expressed as the coordinates of a point, the y-intercept is (x, y) = (0, -2).