Answers
Then use Pythagorean Theorem to find BD (the hypotenuse of right triangle DCB). So Pythag here would be:
[tex]BC^2+DC^2=BD^2[/tex]
See attached picture for full work.
Related Questions
Find the domain of the function :
Can you show the steps
Answers
a domain for a rational is any values of "x" that are safe, namely will not make the denominator undefined, there are a few other constraints, but this is the only one in this case.
so, what values "x" cannot take on safely? well, we can find out what makes the denominator to 0, by simply, yeap, you guessed it, zeroing it out, let's do so,
[tex]\bf 5x+2=0\implies 5x=-2\implies x=-\cfrac{2}{5}[/tex]
so, if ever "x" becomes -2/5, our handy dandy fraction will go poof.
so the domain is all real numbers for "x", EXCEPT -2/5, or in Set Builder notation, {x | x ∈ ℝ; x ≠ -⅖}
Which equation is NOT true?
A. 15x + 55 = 6x + 4x
B. 15x + 55 = 26x
C. 25x + 55 = 180
D. m ∠S = 6x + 4x
Answers
Answer:
C
Step-by-step explanation:
Answer:
A. 15x + 55 = 6x + 4x
Step-by-step explanation:
Process of elimination the rest are true so this one is not. The angles of one side are supplementary with these angles which means they are not congruent.
10. simplify the rational expression by rationalizing the denominator.( 1 point ) 4√150/√189x
Answers
[tex]\bf \cfrac{4\sqrt{150}}{\sqrt{189x}}\cdot \cfrac{\sqrt{189x}}{\sqrt{189x}}\implies \cfrac{4\sqrt{150}\sqrt{189x}}{(\sqrt{189x})^2}\implies \cfrac{4\sqrt{(150)({189x})}}{189x}[/tex]
[tex]\bf \cfrac{4\sqrt{28350x}}{189x}\qquad \begin{cases} 28350=2\cdot 3\cdot 3\cdot 3\cdot 3\cdot 5\cdot 5\cdot 7\\ \qquad 2\cdot 3^2\cdot 3^2\cdot 5^2\cdot 7\\ \qquad 2\cdot (3^2)^2\cdot 5^2\cdot 7\\ \qquad 2\cdot (3^2\cdot 5)^2\cdot 7\\ \qquad 2\cdot (45)^2\cdot 7\\ \qquad 14\cdot 45^2 \end{cases}\implies \cfrac{4\sqrt{14\cdot 45^2}}{189x} \\\\\\ \cfrac{4\cdot 45\sqrt{14}}{189}\implies \cfrac{180\sqrt{14}}{189x}\implies \cfrac{20\sqrt{14}}{21x}[/tex]
The Nichols family consists of 8 children and 2 adults. The family minivan can safely transport a total of 7 family members, including an adult driver.
Which number line illustrates the capacity of the Nichols minivan as an inequality?
Answers
x: number of people who will use the family minivan.
We have then:
"The family minivan can safely transport a total of 7 family members, including an adult driver":
x <= 7
Answer:
x <= 7
A number line that illustrates the capacity of the Nichols minivan as an inequality is:
option C)
Write a quadratic equation whose solutions are 2i and -2i.
Answers
Answer:
answer= 2i
Step-by-step explanation:
A rectangular wall has a length of 12ft and a width of 8ft. The wall has two rectangular windows. Each window has a width of 3ft and a height of 5ft. Andrea chooses a point on the wall at random to test a new paint color. What is the probability she could choose a point on a window
Answers
Jack and Jane are married and both work. However, due to their responsibilities at home, they have decided that they do not want to work over 65 hours per week combined. Jane is paid $14 per hour at her job, and Jack is paid $7 per hour at his. Neither of them are paid extra for overtime, but they are allowed to determine the number of hours per week that they wish to work. If they need to make a minimum of $770 per week before taxes, what is the maximum amount of hours that Jack can work per week according to these limits?
Answers
Answer:
20
Step-by-step explanation:
Item 11 Solve y=4x+8x for x.
Answers
To solve the equation y = 4x + 8x for x, isolate x by combining like terms on the right side and dividing both sides by 12. The solution is x = y/12.
Explanation:To solve the equation y = 4x + 8x for x, we need to isolate x on one side of the equation.
We can start by combining the like terms on the right side:
12x = y
To find the value of x, divide both sides of the equation by 12:
x = y/12
So the solution to the equation is x = y/12.
To solve the equation y = 4x + 8x for x, combine like terms to get y = 12x and then divide both sides by 12 to find x = y/12.
Explanation:The student's question requires us to solve the given equation for x. The original equation provided is y = 4x + 8x. To solve for x, we first combine like terms on the right side of the equation.
Combine like terms: y = 4x + 8x becomes y = 12x.Divide both sides of the equation by 12 to isolate x: x = y/12.The solution for x is x = y/12. This is a straightforward algebraic manipulation that involves combining like terms and using division to solve for the unknown variable.
The monthly rent of Marilyn's house went from $500 to $400, if p is the percent decrease in the rent, which proportion can be used to calculate p?
Answers
Answer:
D
Step-by-step explanation:
doing the test right now
I really need this answer to be correct
Answers
if
11,15,21,22,23,27,30 before 22 is the median
if
11,15,21,22,23,27,30 after 22 is still the median
The median is unchanged
What is the y-intercept of the line whose equation is y = x - 3?
Answers
Answer:
-3
Hope this helps! Please mark as brainliest.
Which ordered pair is a solution of y = x + 12?
(24, 12)
(9, 21)
(–12, –24)
(0, –12)
Answers
For bananas are to be selected from a group of seven in how many ways can this be done
Answers
15 is 10 % of what number
Answers
15*10=150
15 is 10% of 150
A ball is thrown upward from the top of a building. The function below shows the height of the ball in relation to sea level, f(t), in feet, at different times, t, in seconds: f(t) = −16t2 + 48t + 160 The average rate of change of f(t) from t = 3 seconds to t = 5 seconds is _____ feet per second.
Answers
The Average rate of change of f(t) from t = 3 seconds to t = 5 seconds is - [tex]v_{avg} = -80\;ft/s[/tex]
We have a equation -
[tex]f(t) = -16t^{2} +48t+160[/tex]
that calculates the height of the ball from sea level in feet at different times.
We have to find the average rate of change of f(t) from t = 3 seconds to t = 5 seconds.
What is Average velocity?The rate of change of displacement per unit time is called average velocity. Mathematically -
[tex]v_{avg} = \frac{d_{2} - d_{1} }{t_{2} - t_{1} }[/tex]
We have -
[tex]f(t) = -16t^{2} +48t+160[/tex]
For time t = 3 seconds, f(t) is -
[tex]f(3) = -16(3)^{2} + 48(3) + 160\\f(3) = -144 +144 +160\\f(3) = 160\; feets\\[/tex]
For time t = 5 seconds, f(t) is -
[tex]f(5) = -16(5)^{2} + 48(5) + 160\\f(5) = -400+240+160\\f(5) = -400 + 400\\f(5) = 0 feet[/tex]
The formula for average velocity is -
[tex]v_{avg} = \frac{d_{2} - d_{1} }{t_{2} - t_{1} }[/tex]
According to question -
[tex]t_{2} = 5s[/tex] and [tex]t_{1} = 3s[/tex]
[tex]d_{2} = f(5) = 0 feet[/tex] and [tex]d_{1} = f(3)=160[/tex]
Substituting the values in the formula of average velocity, we get -
[tex]v_{avg} = \frac{0 - 160}{5 - 3} \\v_{avg} = \frac{-160}{2\\} \\v_{avg} = -80\;ft/s[/tex]
Hence, average rate of change of f(t) from t = 3 seconds to t = 5 seconds is [tex]v_{avg} = -80\;ft/s[/tex].
To solve more questions on calculating the average rate of change of height with time, visit the following link -
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Let logba=3 logbc=2 logbd=5 what is the value of logba^3d^4/c^2
Answers
[tex]\log_ba=3;\ \log_bc=2;\ \log_bd=5[/tex]
[tex]\log_b\dfrac{a^3d^4}{c^2}=\log_b(a^3d^4)-\log_bc^2=\log_ba^3+\log_bd^4-\log_bc^2\\\\=3\log_ba+4\log_bd-2\log_bc=3\cdot3+4\cdot5-2\cdot2=9+20-4=25[/tex]
Answer:
25
Step-by-step explanation:
If the sum of two numbers is 20 and one of those numbers is three times the other, what is the smaller number?
Answers
y = bigger number
y = 3x
x+y = 20
x+3x = 20
4x = 20
x = 5
The smaller number is 5.
Given a possible triangle ABC with a=5, b=11, and A=23 degrees, find a possible value for angle b. Round to the nearest tenth. A. 10.2° B. 11.2° C. 59.3° D. no solution Please select the best answer from the choices provided
Answers
Sine (A) / a = Sine (B) / b
Substituting values we have:
Sine (23) / 5 = Sine (B) / 11
Clearing we have:
(Sine (23) / 5) * (11) = Sine (B)
B = Asine ((Sine (23) / 5) * (11))
B = 59.27 degrees
Rounding off we have:
B = 59.3 degrees
Answer:
C. 59.3 °
What is the answer for this equation?
36^-x+3=(1/216)^x+1
Answers
also photomath is a good app to use for math ☺️
hoped this helped
Please answer ASAP!!! How many vertical asymptotes does the graph of this function have ?
Answers
Answer:
The answer is 1.
Got it from Apex
Step-by-step explanation:
WILL GET BRAINLIEST
Which does NOT represent the interior angle measures of a triangle? A.5°, 75°, 100°B.10°, 80°, 90°C.20°, 60°, 100°D.45°, 45°, 45°E.50°, 50°, 80°
Answers
5° + 75°+ 100° = 180°
10°+ 80°+ 90° = 180°
20° + 60° + 100° = 180°
45° + 45° + 45° = 135°
50° + 50° + 80° = 180°
So D does not represent interior angle measures of a triangle.
Hope this Helps!!
Please help due tomorrow! Math
Answers
7,9,11,..
This is an arithmetic sequence which follows an explicit formula given by:
an=a+(n-1)d
where:
a=first term
d=common difference
but
a=7 and d=9-7=2
thus
an=7+(n-1)2
an=7+2n-2
an=2n-5
Thus the number of seats in nth row is:
an=2n-5
Select ALL the expressions that are equivalent to the polynomial below.
(4x+5)(-3x-1)
(-16x^2 + 10x - 3) + (4x^2 - 29x - 2)
3(x - 5) - 2(6x^2 + 9x + 5)
2(x - 1) - 3(4x^2 + 7x + 1)
(2x^2 - 11x - 9) - (14x^2 + 8x - 4)
(-15x^2 + 9x - 10) + (3x^2 - 10x - 5)
(4x^2 - 13x - 7) - (16x^2 + 9x - 5)
Answers
(4x + 5) (- 3x-1)
Rewriting we have:
-12x ^ 2 - 4x - 15x - 5
-12x ^ 2 - 19x - 5
The equivalent polynomials for this case are given by:
(-16x ^ 2 + 10x - 3) + (4x ^ 2 - 29x - 2)
2 (x - 1) - 3 (4x ^ 2 + 7x + 1)
(2x ^ 2 - 11x - 9) - (14x ^ 2 + 8x - 4)
Answer:
(-16x ^ 2 + 10x - 3) + (4x ^ 2 - 29x - 2)
2 (x - 1) - 3 (4x ^ 2 + 7x + 1)
(2x ^ 2 - 11x - 9) - (14x ^ 2 + 8x - 4)
Consider the following graph of a piecewise-defined function.
When x<-2, f(x)=
A: -3
B: 5
C: 2
When -2
A: x+2
B: 2x+2
C: 2x
When x>3, f(x)=
A: -3
B: 5
C: 2
Answers
a] When x<-2, the value of f(x) will be f(x)=5
Answer: B:5
b] when x≥3, the value of f(x) will be f(x)=-3
Answer: A: -3
Answer:
When x<-2, f(x) = 5
When -2<x<3, f(x)= 2x+2
When x>3, f(x)= -3
Step-by-step explanation:
brainly The point (−4, 2) is on the terminal side of angle Θ, in standard position. What are the values of sine, cosine, and tangent of Θ? Make sure to show all work. (10 points)
Answers
The length of the hypotenuse = sqrt20 = 2 sqrt5
sine = 2 / 2 sqrt5 = 1 / sqrt5
cosine = -4 / 2 sqrt5 = -2/sqrt5
A shipping container is in the shape of a right rectangular prism with a length of 13.5 feet, a width of 10.5 feet, and a height of 2.5 feet. The container is completely filled with contents that weigh, on average, 0.33 pound per cubic foot. What is the weight of the contents in the container, to the nearest pound?
Answers
Total weight=(volume of the container)*(weight per cubic volume)
volume of the container
=length*width*height
=13.5×10.5×2.5
=354.375 ft³
weight per cubic volume=0.33 pound per cubic ft
Total weight=354.375×0.33=116.94375 pounds~117 pounds
The weight of the contents in the container, to the nearest pound, is 117 pounds.
To calculate the weight of the contents, we first find the volume of the container, then multiply it by the weight per cubic foot.
Step 1: Calculate the volume of the container.
Volume = length × width × height
Volume = 13.5 ft × 10.5 ft × 2.5 ft
Volume = 354.375 cubic feet
Step 2: Calculate the weight of the contents.
Weight = Volume × Weight per cubic foot
Weight = 354.375 cubic feet × 0.33 pounds per cubic foot
Weight ≈ 116.8725 pounds
Rounded to the nearest pound, the weight of the contents is 117 pounds.
First, we find the volume of the container by multiplying its length, width, and height together. The formula for the volume of a rectangular prism is length × width × height. In this case, the dimensions are given as 13.5 feet for the length, 10.5 feet for the width, and 2.5 feet for the height.
Next, we multiply the volume of the container by the weight per cubic foot of the contents to find the total weight. The average weight per cubic foot is given as 0.33 pounds.
Finally, we round the calculated weight to the nearest pound to match the desired precision. In this case, the weight of the contents is rounded to 117 pounds.
Complete question:
A shipping container is in the shape of a right rectangular prism with a length of 13.5 feet, a width of 10.5 feet, and a height of 2.5 feet. The container is completely filled with contents that weigh, on average, 0.33 pound per cubic foot. What is the weight of the contents in the container, to the nearest pound?
Sin (2x -9)= Cos (x +30) to solve for x
Answers
f(x) = sin(2x -9°) -cos(x +30°)
in the range 0° ≤ x ≤ 360°
Solutions are x ∈ {23°, 129°, 143°, 263°).
_____
You can make use of a couple of trig identities to rearrange this equation.
cos(x) = sin(x+90°)
sin(a) -sin(b) = 2*cos((a+b)/2)*sin((a-b)/2)
So
sin(2x -9°) -sin(x +120°) = 2*cos((3x +111°)/2)*sin((x -129°)/2) = 0
The cosine factor will be zero for
(3x +111°)/2 = n*180° +90°
3x -69° = n*360°
x = 23° +n*120° . . . . . . for any integer n
The sine factor will be zero for
(x -129°)/2 = n*180°
x = 129° +n*360° . . . . . for any integer n
Combined, these solutions give the ones listed above in the range 0..360°.
Solve the system of equations -4x + 3y = -2 y = x - 1
Answers
Plug in x-1 to the first equation and solve.
-4x+3(x-1)=-2
-4x+3x-3=-2
-x=1
X=-1
You then plug x into one of the original equations and solve
Y=-1-1
Y=-2
Answer:(-1,-2)
The solution to the system of equations -4x + 3y = -2 and y = x - 1 is x = -1 and y = -2.
What is the solution to the system of equations?Given the system of equations in the question:
-4x + 3y = -2
y = x - 1
Solve the system of equations by substituting the expression for y from the second equation into the first equation:
-4x + 3y = -2
Plug in y = x - 1:
-4x + 3( x - 1 ) = -2
Simplifying, we get:
-4x + 3x - 3 = -2
Solve for x:
-x = -2 + 3
-x = 1
x = -1
Now, plug x = -1 into equation 2 and solve for y:
y = x - 1
y = -1 - 1
y = -2
Therefore, the solution is x = -1 and y = -2.
Learn more about system of equations here: brainly.com/question/30319215
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please help asap 48 pts
Answers
-2y multiplied by -2y = 4y^2
3x Times 5x = 15x^2
3x Times -2y = -6xy
-2y times 5x = -10xy
-6xy plus -10xy = -16xy
I need help
Simplify 4z2 + z2 + 6a.
4z2 + 7a
5z2 + 6a
3z2 + 6a
11az2
Answers
This is because there is an imaginary 1 in front of the second term that you have to remember to use when combining like terms.