Answer:
[tex]u = \frac{y - (xd) { }^{2} }{3x {}^{2} } [/tex]
Step-by-step explanation:
3u=y/x^2-d^2
3u=y-(xd)^2/x^2
u=y-(xd)^2/3x^2
Solve each of the following:
a) x² + 4x – 77 = 0
b) x(x + 4) = -2(3x + 8)
Please show your work
Answer:
a.) x=7 or x=-11
b.) x=−2 or x=−8
Step-by-step explanation:
a) x² + 4x – 77 = 0
Step 1: Factor left side of equation.
(x−7)(x+11)=0
Step 2: Set factors equal to 0.
x−7=0 or x+11=0
x=7 or x=−11
b.) x(x + 4) = -2(3x + 8)
Step 1: Simplify both sides of the equation.
x^2+4x=−6x−16
Step 2: Subtract -6x-16 from both sides.
x^2+4x−(−6x−16)=−6x−16−(−6x−16)
x^2+10x+16=0
Step 3: Factor left side of equation.
(x+2)(x+8)=0
Step 4: Set factors equal to 0.
x+2=0 or x+8=0
x=−2 or x=−8
Answer:
a) {-11, 7}.
b) {-8, -2}
Step-by-step explanation:
a) x^2 + 4x - 77 = 0
To factor this we need 2 numbers whose product is -77 and sum is + 4.
They are + 11 and - 7, so:
( x + 11)(x - 7) = 0
x + 11 = 0 or x - 7 = 0
x = -11, 7.
b) x(x + 4) = -2(3x + 8)
x^2 + 4x = -6x - 16
x^2 + 4x + 6x + 16 = 0
x^2 + 10x + 16 = 0
(x + 2)(x + 8) = 0
x = -8, -2.
Determine the constant of variation for the direct variation given. (0, 0), (3, 12), (9, 36)
12
4
3
Answer:
4
Step-by-step explanation:
y = kx
Use point (3, 12).
12 = k * 3
k = 12/3 = 4
y = 4x
Answer: 4
Divide y by x:
12/3 = 4
36 / 9 = 4
The constant of variation is 4
plzzz helppp only a hour due today
Answer:
A or C
Is my best I got stuck A or C
Answer:
[tex]\text{C. about }72.05\:\mathrm{cm^2}[/tex]
Step-by-step explanation:
This is a very fun problem that requires the use of multiple concepts to solve.
Concepts/formulas used:
The measure of an inscribed angle is half the measure of the arc it formsThere are 360 degrees in a circleThe sum of the interior angles of a triangle add up to 180 degreesLaw of Sines is given by [tex]\frac{\sin A}{a}=\frac{\sin B}{b}=\frac{\sin C}{c}[/tex] All radii of a circle are exactly half all diameters of the circleThe area of a circle with radius [tex]r[/tex] is given by [tex]A=r^2\pi[/tex]The measure of an inscribed angle is equal to half the measure of the arc it forms. In circle Z, [tex]\angle XVY[/tex] is an inscribed angle that forms arc XY. Since XY is 40 degrees, angle XVY must be [tex]40\div 2=20^{\circ}[/tex].
Similarly, [tex]\angle VYX[/tex] is also an inscribed angle and forms arc XV. Notice how arc XY and arc XV form arc VY, which is half the circumference of the circle, since segment VY is a diameter of the circle. Since there are 360 degrees in a circle, arc VY must be 180 degrees. Therefore, we have:
[tex]\widehat{XY}+\widehat{XV}=180^{\circ},\\\widehat{XV}+40^{\circ}=180^{\circ},\\\widehat{XV}=140^{\circ}[/tex]
Now we can find the measure of angle VYX, using our knowledge that the measure of an inscribed angle is half the measure of the arc it forms.
[tex]m\angle VYX=\frac{140}{2}=70^{\circ}[/tex]
Now, we have two angles of triangle VXY. Since the sum of the interior angles of a triangle add up to 180 degrees, the third angle, [tex]\angle VXY[/tex], can be found:
[tex]\angle VXY+\angle VYX+\angle XVY=180^{\circ},\\\angle VXY+20^{\circ}+70^{\circ}=180^{\circ},\\\angle VXY+90^{\circ}=180^{\circ},\\\angle VXY=90^{\circ}[/tex]
We can now use this angle and the Law of Sines to find the length of segment VY. The Law of Sines works for any triangle and is given by [tex]\frac{\sin A}{a}=\frac{\sin B}{b}=\frac{\sin C}{c}[/tex] (the ratio of any angle and its opposite side is maintained throughout all angles of the triangle).
Since angle VXY's opposite side is VY and angle VYX's opposite side is VX, we have the following proportion:
[tex]\frac{\sin 70^{\circ}}{9}=\frac{\sin 90^{\circ}}{VY}[/tex]
Recall that [tex]\sin 90^{\circ}=1[/tex]. Cross-multiply:
[tex]9\sin 90^{\circ}=VY\sin 70^{\circ},\\9=VY\sin 70^{\circ},\\VY=\frac{9}{\sin 70^{\circ}}[/tex]
This is the diameter of the circle. By definition, all radii are half the diameter. Therefore, the radius of the circle is [tex]\frac{9}{\sin 70^{\circ}}\cdot \frac{1}{2}=\frac{9}{2\sin 70^{\circ}}[/tex].
The area of a circle with radius [tex]r[/tex] is given by [tex]A=r^2\pi[/tex]. Substitute [tex]r=\frac{9}{2\sin 70^{\circ}}[/tex] to get the area of circle Z:
[tex]A=(\frac{9}{2\sin 70^{\circ}})^2\pi,\\A\approx (4.78879997614)^2\pi,\\A\approx 22.9326052115\pi,\\A\approx \boxed{72.05\:\mathrm{cm^2}}[/tex]
Which of the expressions below is equivalent to
4x²
12x2 - 4
X
x²
3x²
3x
4
1
12x
1
12
A
B
D
Answer:
The choose (B)
[tex] \frac{4 {x}^{2} }{12 x^{2} - 4 } \\ \frac{4 {x}^{2} }{4(3 {x}^{2} - 1)} \\ \frac{ {x}^{2} }{3 {x}^{2} - 1} [/tex]
Can you answer this math homework? Please!
Answer:
Height is equal = Y = 1.8 X + 3.1 = 2.3 X + 1.9
=> 2.3 X - 1.8 X = 3.1 - 1.9
=> 0.5 X = 1.2
=> x = 1.2/0.5 = 2.4
Time = 2.4 weeks
Step-by-step explanation:
Answer:
2.4
Step-by-step explanation:
(⅔)-⁴ (two over three to the power minus 4)
I need answer asap pleaseeeee
Answer:
81/16
Step-by-step explanation:
(⅔)-⁴
81/16
= 5.0625
10. Two planes are flying one directly behind the other. Both planes are at an alttude of 1.7 miles. The angle
of depression to the airport from the plane closer to the airport is 58. The angle of depression to the
airport from the plane farther from the airport is 37. What is the distance between the two planes to the
nearest tenth of a mile?
A 1.0
B 23 -
C 12
D Not here
Margaret took a trip to Italy. She had to convert US dollars to euros to pay for her expenses there. At the time she was traveling, the conversion rate was represented by the function , where n is the number of dollars and E(n) is the equivalent value in euros. Later, she traveled to Dubai and converted her remaining euros into the local currency, UAE dirhams. At that time, the conversion rate was represented by the function , where x is the number of euros and D(x) is the equivalent value in dirhams. Which function can be used to convert n dollars directly to dirhams?
The conversion rate US dollars to Euros is represented with the function:
E(n)=0.72n
n- number of dollars
E(n) - Euros as a function of US dollars
The conversion rate Euros to Dirhams is :
D(x)=5.10x
x- number of Euros
D(x)- Dirhams as a function of Euros
We are trying to find D(x) in terms of n.
D(x) = 5.10x
x can be rewritten as E(n)
D(x) = 5.10(E(n))
D(x) = 5.10(E(n))
D(x) = 5.10(0.72n)
D(x) = 3.672n
According to this the following statement is true:
A) (D x E)(n) = 5.10(0.72n)
Solve for x. X/5-x/6=1/3 x = 10 x = 1/90 x = 1/10
Answer:
x=10
Step-by-step explanation:
I hope this will help you
A student bought 84 pencils. If he sharpened 35 pencils, what is the ratio of the unsharpened pencils to the sharpened pencils?
Hello!
Sharpened => 35
Unsharpened => 84-35 = 49
49:35= 7:5Good studies!
Answer:
7: 5
Step-by-step explanation:
unsharpened to sharpened
First we need to determine the number of unsharpened
84 - 35 =49
There are 35 sharpened
49:35
Divide each by 7
49/7 : 35/7
7: 5
12. (05.02 LC) Look at the figure below: an image of a right triangle is shown with an angle labeled y If sin y° = 7 over q and tan y° = 7 over r, what is the value of sec y°? (4 points) sec y° = q over r sec y° = 7r sec y° = 7q sec y° = r over q
Answer:
[tex]sec~y=\frac{q}{r}[/tex]
Step-by-step explanation:
[tex]tan ~y=\frac{7}{r} \\\\\frac{sin~y}{cos~y} =\frac{7}{r} \\\\sin~y=\frac{7}{r} cos~y\\sin ~y=\frac{7}{q} \\\frac{7}{q} =\frac{7}{r} cos~y\\sec~y=\frac{7}{r} \times \frac{q}{7} =\frac{q}{r}[/tex]
The tangent is equal to the product of the sine and secant. The value of sec y is q over r, then the correct option is A.
What is a right-angle triangle?It is a type of triangle in which one angle is 90 degrees and it follows the Pythagoras theorem and we can use the trigonometry function. The Pythagoras is the sum of the square of two sides is equal to the square of the longest side.
If sin y = 7/q and tan y = 7/r.
Then the value of sec y will be
We know that the identity
[tex]\sec x =\dfrac{\tan x}{\sin x}[/tex]
Then we have
[tex]\rm \sec y = \dfrac{7/r}{7/q} \\\\\\\sec y = \dfrac{q}{r}[/tex]
The value of sec y is q over r.
More about the right-angle triangle link is given below.
https://brainly.com/question/3770177
What is the value of y?
Answer:
C, 40 degrees
Step-by-step explanation:
All the angles of a triangle add to 180 degrees according to the Triangle Sum Theorem.
Since all angles sum to 180, we can set all the values to add to 180.
We have:
[tex]2y+y+10+50=180[/tex]
Combining like terms, we have:
[tex]3y+60=180[/tex]
Subtracting 60 from both sides gets us
[tex]3y=120[/tex]
Dividing by 3 from both sides equals
[tex]y=40[/tex]
Answer:
I think the value of y is 40
Step-by-step explanation:
Here, 2y+ y+ 10+50=180°( sum of all angles of triangle)or, 3y+ 60=180or, 3y=180-60or, 3y=120or, y= 120÷3:.y= 40What is the interquartile range of the following data set? 78,90,456,676,111,381,21
Answer
The IQR of the data set is 368.
Explanation
To find the interquartile range, you first need to find the median of the data set. Then, you find the median of the median and subtract them. This might be a little confusing but I'll walk through everything.
First, put the data set in order from least to greatest; 21 78 90 111 381 456 676. Find the median. The median of this data set is 111, since it is the middle number when the data set is ordered from least to greatest.
To find the Q1 and Q3 of the set, you have to find the median of the median.
The set right now is 21 78 90 111 381 456 676. Remove the 111 (if there were an even amount of numbers in the set, you wouldn't remove the 111 and you would just split the data set in half). Now you have two sets: 21 78 90 and 381 456 676. The median of the first set is 78 (this is the Q1) and the median of the second set is 456 (this is the Q3).
To find the interquartile range, subtract the Q1 from the Q3. 456-78=368.
Solve the inequality and write the solution in interval notation:
x-6/x+5 <0
(-5, 6)
[-5, 6)
(-infinity,-5) U [6,infinity)
(-infinity,-5] U (6,infinity)
Answer:
A
Step-by-step explanation:
Firstly x cannot be -5 because the expression on th left would be undefined so it's only between choices a and c.
Create a number line with makes the expression on left 0 and undefined...so at 6 and -5 this happens.
-------(-5)--------(6)---------
Let's test the 3 intervals by choosing a value from that interval to see if all numbers from that interval will make the expression on left less than 0.
Number before -5 is -6:
(-6-6)/(-6+5)=-12/-1=12 >0 so this interval is not a part of our solution.
Number between -5 and 6 is 0:
(0-6)/(0+5)=-6/5<0 so this interval is a part of our solution
Number after 6 like 7:
(7-6)/(7+5)=1/12>0 so this interval is not a part of our solution.
The winner is everything between-5 and 6 so answer is A.
Solve the following inequality: |x + 1| <_3
<_ = greater than or equal to
Answer:
x <= -4 or x >= 2
Step-by-step explanation:
so, it actually says
|x+1| >= 3
so, then, this is valid for all x >= 2 (then x+1 is 3 or higher), and for all x <= -4 (then x+1 is -3 or lower, and |x+1| is still 3 or higher)
Ilhan needs to write in function notation and evaluate this equation at the given value of the
independent variable. What answer should she get? 6x + y = 3; x=3
Answer:
it should be the second one I hope this help
PLS HELP ME ITS EASY JUST WANT TO MAKE SURE IM RIGHT Calculate the answer to the correct number of significant figures: (1.705 + 0.5067) / (0.2 * 1.243) = ______.
8.897
8.8966
8.9
9
8.90
Answer:
8.90
Step-by-step explanation:
this and the other answers are the rounded ones
write a fraction of the probability of rolling a multiple two
Answer: 1/2
Step-by-step explanation:
there are 6 sides all together and 3 of those are multiples of two. this fraction is 3/6 but that can be simplified to 1/2
Answer:
1/2
Step-by-step explanation:
For this we will be assuming a die size of six. With that in mind, all even numbers are divisible by two. There are a total of three numbers on a six sided die, those being two, four, and six. We then put this number over the total possibilities, which would be six. It is good form to simplify, which we can. We take three out from our 3/6 to leave us with 1/2.
What is the initial value of 34.2 x 3^x
Initial value is your y intercept, and to find that you just need to substitute 0 for x. Anything to the power of 0 is just 1. So you get 34.2(1), which means that your initial value is 34.2.
HELP?p?P?p?p?p?P?P?p?p?p?p?P?p?p?p?p?p?p?pp?p?p?P
Answer:
Yes, its a rational number.
Step-by-step explanation:
Rational numbers can be whole numbers, fractions, and decimals, and in this case it is a decimal.
Hope this helped!
Answer: yes
Step-by-step explanation:
yes 1.86 is a rational number
please help with these two questions!!
6√5 + 3√6 = 6√5 + 3√6 [cannot be simplified]
; roots do not contain any perfect squares, and the roots are not similar.
6√5(3√6) = 18√30 [can be simplified]
; although roots do not contain any perfect squares, the product rule can be applied to create a singular expression.
B) Construct a Rhombus MARS where MR = 6.8 cm & AS = 7 cm. Write the measurement of each side of Rhombus.
Answer:
Length = 4.88
Step-by-step explanation:
Given
[tex]MR = 6.8cm[/tex]
[tex]AS = 7cm[/tex]
First, we calculate the lengths of each side of the rhombus.
Diagonals of a rhombus are bisected at right-angled.
So, the lengths (x,y) of the right-angled triangle formed are:
[tex]x = \frac{1}{2}MR = \frac{1}{2} * 6.8 = 3.4[/tex]
[tex]y = \frac{1}{2}AS = \frac{1}{2} * 7 = 3.5[/tex]
The length of the sides (z) is calculated using:
[tex]z^2 = x^2 + y^2[/tex]
[tex]z^2 = 3.4^2 + 3.5^2[/tex]
[tex]z^2 = 11.56 + 12.25[/tex]
[tex]z^2 = 23.81[/tex]
Take square roots
[tex]z = \sqrt{23.81[/tex]
[tex]z = 4.88[/tex] --- approximated
Sally is serving lemonade to four friends. She is serving 4/7 cup per person.
Estimate how much lemonade she needs. Then calculate exactly how much she needs. What is the difference between the estimate and actual amount?
pls help, :)
Answer:
oi ngl levi is hawt I like your pfp ^^
Step-by-step explanation:
my name is Riley
Prachi was 555 kilometers east of her home when she began driving farther east at 707070 kilometers per hour. Let f(n)f(n)f, (, n, )be Prachi's distance from her home at the beginning of the n^\text{th}n th n, start superscript, start text, t, h, end text, end superscript hour of her drive. fff is a sequence. What kind of sequence is it
Answer:
The answer is "[tex]\bold{f(n) = 70n + 5}[/tex]"
Step-by-step explanation:
The complete question is defined in the attached file Please find it.
She started driving further east, 70 kilometers an hour, 5 km east of her home. Allow f(n) at the outset of its nth hour drive to just be Prachi's length from home.
F is a series of arithmetic.
Construct the series with an explicit formula.
[tex]\bold{f(n) = 70n + 5}[/tex]
Answer:
Arithmetic and it is f(n)=5+70(n-1)
Step-by-step explanation:
Khan Academy
Solve the inequality.
-14> x-32
A. x>18
B. x< 46
C. x<-46
D. x < 18
Answer:
Option D
Step-by-step explanation:
-14 > x - 32
Add 32 to both sides;
18 > x OR x < 18
Each side of a pentagon is 10 cm greater than the previous side. If the perimeter of this pentagon is 500 cm, find the lengths of the sides.
Answer: See explanation
Step-by-step explanation:
The perimeter of a pentagon is gotten through the summation of its five sides. Let the first side be represented by x. Since each side of a pentagon is 10 cm greater than the previous side, then the sides will be:
First side = x
Second side = x + 10
Third side = x + 10 + 10 = x + 20
Forth side = x + 30
Fifty side = x + 40
Therefore,
x + (x + 10) + (x + 20) + (x + 30) + (x + 40) = 500
5x + 100 = 500
5x = 500 - 100
5x = 400
x = 400/5
x = 80
Therefore, the lengths will be:
First side = x = 80cm
Second side = x + 10 = 80 + 10 = 90cm
Third side = x + 20 = 80 + 20 = 100cm
Forth side = x + 30 = 80 + 30 = 110cm
Fifty side = x + 40 = 80 + 40 = 120cm
Find the values of the variables and please give the reasons
180 ÷3 = 60 ° (angles on a straight line equals to 180 ° )
a+b+60 =180°
a+ b= 180 ° - 60° = 120°
(a+b) are 2 variables
so 120 ÷2 =60 °
therefore a and b =60 °
c +b+ 60° = 180° ( co - interior angles are supplementary angles )
c+60° +60° =180°
c +120° =180°
c =180°-120°
c=60 °
d=60° (alternate angles are equal )
or
c+b+d=180°
60° +60° + d = 180°
d=180°-120°
d=60°
Colin drove 45 minutes to the airport. He arrived 90 minutes before his flight departed, and then he spent 70 minutes in the air. Once he landed, Colin spent 20 minutes gathering his luggage, and then he drove 35 minutes to his hotel. What must be true of any expression that represents the total time that Colin spent traveling from his house to the hotel?
Please help ASAP!!!!
========================================================
Explanation:
The two points mentioned in bold are midpoints of segments AB and AC respectively.
To find the coordinates of a midpoint, you add up the x coordinates and divide by 2. Do the same with the y coordinates.
For example, points A and B are at (7,6) and (1,-2)
If we add up the x coordinates and divide by 2, then we get (7+1)/2 = 4. Do the same for the y coordinates to get (6+(-2))/2 = 2. So that's how (4,2) is the midpoint of segment AB. You'll use similar logic to find that (8,2) is the midpoint of segment AC.
A slight alternative is that once you find one midpoint is (4,2), you can draw a horizontal line until you reach (8,2). We're using the idea that the midsegment is parallel to BC which is also horizontal.
Multiply the binomials:
(y+2)•(y+9)
Answer:
y² + 11y + 18
Step-by-step explanation:
y² + 9y + 2y + 18
y² + 11y + 18
