Answer:
Assuming that you meant 4+√19 is C.
Step-by-step explanation:
[tex]x^2-8x-3=x^2-2(4)x-3=x^2-2(4)x+16-3-16\\(x-4)^2-19\\(x-4)^2-19=0\\(x+4)^2=19\\x+4=\sqrt{19} \\x=-4+-\sqrt{19}[/tex]
please help with this
Answer:
158m^3
Step-by-step explanation:
First, let's figure out the total amount of water in the tank.
It measures 4.5m by 6m by 8m. The volume of a rectangular prism is V=lwh.
Therefore, the volume is:
[tex]V=(4.5)(6)(8)=216 m^3[/tex]
We are told is it filled to the brim, so we can conclude that there are 216 cubic meters of water in the tank.
We used 58 cubic meters of water, so we simply need to subtract that from 216:
[tex]216m^3-58m^3=158m^3[/tex]
There is still 158 cubic meters of water left in the tank.
Answer:
158 m^3
Step-by-step explanation:
Volume of the tank
= 4.5 * 6 * 8
= 216 m^3.
So amount left in the tank
= 216 - 58
= 158 m^3.
Please help ASAP!
Rearrange the equation so x is the independent variable. -5x - 4y = -8
Answer:
Hey there!
Original Equation
-5x-4y=-8
Multiply by -1
5x+4y=8
Subtract 4y
5x=8-4y
Divide by 5
x=(8-4y)/5
Let me know if this helps :)
Answer:
x = -4/5y + 8/5
Step-by-step explanation:
So to single out x we use the communicative property,
its the moving of numbers and variables to each side of the equation.
So we have,
-5x - 4y = -8
+4y
-5x = 4y - 8
Divide -5 by both sides,
x = -4/5y + 8/5
Thus,
the equation rearanged is x = -4/5y + 8/5.
Hope this helps :)
What is the length of DF?
Answer:
7.06
Step-by-step explanation:
17/8 = 15/DF
DF = 7.06
1. What is the value of x? Show all of your work.
Answer:
9 cm
Step-by-step explanation:
Pythagorean's Theorem: a^2+b^2=c^2
x^2+6^2=117 (the square root of 117, squared)
X^2+36=117
x^2=117-36
x^2=81
x=9
Answer:
x = 9 cm
Step-by-step explanation:
Use the Pythagorean Theorem to find the length of the missing side.
a² + b² = c²
a² + (6)² = (√117)²
a² + 36 = 117
a² = 81
a = √81
a = 9
X is equal to 9 cm.
Hope this helps.
Which of the following geometric series converges?
All three series converge, so the answer is D.
The common ratios for each sequence are (I) -1/9, (II) -1/10, and (III) -1/3.
Consider a geometric sequence with the first term a and common ratio |r| < 1. Then the n-th partial sum (the sum of the first n terms) of the sequence is
[tex]S_n=a+ar+ar^2+\cdots+ar^{n-2}+ar^{n-1}[/tex]
Multiply both sides by r :
[tex]rS_n=ar+ar^2+ar^3+\cdots+ar^{n-1}+ar^n[/tex]
Subtract the latter sum from the first, which eliminates all but the first and last terms:
[tex]S_n-rS_n=a-ar^n[/tex]
Solve for [tex]S_n[/tex]:
[tex](1-r)S_n=a(1-r^n)\implies S_n=\dfrac a{1-r}-\dfrac{ar^n}{1-r}[/tex]
Then as gets arbitrarily large, the term [tex]r^n[/tex] will converge to 0, leaving us with
[tex]S=\displaystyle\lim_{n\to\infty}S_n=\frac a{1-r}[/tex]
So the given series converge to
(I) -243/(1 + 1/9) = -2187/10
(II) -1.1/(1 + 1/10) = -1
(III) 27/(1 + 1/3) = 18
If the quadratic formula is used to solve 2x2-3x - 1 = 0, what are the solutions?
1-3 + fin 3 - i7)
4.
4.
0 -3-17 3 - 171
4
4
이
13 +17 3 - (1)
4
4
Answer:
x = (3 +/- sqrt(17) / 4.
Step-by-step explanation:
x = [-(-3) +/- sqrt((-3)^2 - 4*2*-1)] / 4
x = (3 +/- sqrt(17) / 4.
For the given term, find the binomial raised to the power, whose expansion it came from: 15(5)^2 (-1/2 x) ^4
A. (5+1/2 x)^6
B. (Y- 1/2 x) ^6
C. (5- 1/2 x) ^6
D. (-5 + (- 1/2 x))^6
Answer:
C. [tex](5-\frac{1}{2})^6[/tex]
Step-by-step explanation:
Given
[tex]15(5)^2(-\frac{1}{2})^4[/tex]
Required
Determine which binomial expansion it came from
The first step is to add the powers of he expression in brackets;
[tex]Sum = 2 + 4[/tex]
[tex]Sum = 6[/tex]
Each term of a binomial expansion are always of the form:
[tex](a+b)^n = ......+ ^nC_ra^{n-r}b^r+.......[/tex]
Where n = the sum above
[tex]n = 6[/tex]
Compare [tex]15(5)^2(-\frac{1}{2})^4[/tex] to the above general form of binomial expansion
[tex](a+b)^n = ......+15(5)^2(-\frac{1}{2})^4+.......[/tex]
Substitute 6 for n
[tex](a+b)^6 = ......+15(5)^2(-\frac{1}{2})^4+.......[/tex]
[Next is to solve for a and b]
From the above expression, the power of (5) is 2
Express 2 as 6 - 4
[tex](a+b)^6 = ......+15(5)^{6-4}(-\frac{1}{2})^4+.......[/tex]
By direct comparison of
[tex](a+b)^n = ......+ ^nC_ra^{n-r}b^r+.......[/tex]
and
[tex](a+b)^6 = ......+15(5)^{6-4}(-\frac{1}{2})^4+.......[/tex]
We have;
[tex]^nC_ra^{n-r}b^r= 15(5)^{6-4}(-\frac{1}{2})^4[/tex]
Further comparison gives
[tex]^nC_r = 15[/tex]
[tex]a^{n-r} =(5)^{6-4}[/tex]
[tex]b^r= (-\frac{1}{2})^4[/tex]
[Solving for a]
By direct comparison of [tex]a^{n-r} =(5)^{6-4}[/tex]
[tex]a = 5[/tex]
[tex]n = 6[/tex]
[tex]r = 4[/tex]
[Solving for b]
By direct comparison of [tex]b^r= (-\frac{1}{2})^4[/tex]
[tex]r = 4[/tex]
[tex]b = \frac{-1}{2}[/tex]
Substitute values for a, b, n and r in
[tex](a+b)^n = ......+ ^nC_ra^{n-r}b^r+.......[/tex]
[tex](5+\frac{-1}{2})^6 = ......+ ^6C_4(5)^{6-4}(\frac{-1}{2})^4+.......[/tex]
[tex](5-\frac{1}{2})^6 = ......+ ^6C_4(5)^{6-4}(\frac{-1}{2})^4+.......[/tex]
Solve for [tex]^6C_4[/tex]
[tex](5-\frac{1}{2})^6 = ......+ \frac{6!}{(6-4)!4!)}*(5)^{6-4}(\frac{-1}{2})^4+.......[/tex]
[tex](5-\frac{1}{2})^6 = ......+ \frac{6!}{2!!4!}*(5)^{6-4}(\frac{-1}{2})^4+.......[/tex]
[tex](5-\frac{1}{2})^6 = ......+ \frac{6*5*4!}{2*1*!4!}*(5)^{6-4}(\frac{-1}{2})^4+.......[/tex]
[tex](5-\frac{1}{2})^6 = ......+ \frac{6*5}{2*1}*(5)^{6-4}(\frac{-1}{2})^4+.......[/tex]
[tex](5-\frac{1}{2})^6 = ......+ \frac{30}{2}*(5)^{6-4}(\frac{-1}{2})^4+.......[/tex]
[tex](5-\frac{1}{2})^6 = ......+15*(5)^{6-4}(\frac{-1}{2})^4+.......[/tex]
[tex](5-\frac{1}{2})^6 = ......+15(5)^{6-4}(\frac{-1}{2})^4+.......[/tex]
[tex](5-\frac{1}{2})^6 = ......+15(5)^2(\frac{-1}{2})^4+.......[/tex]
Check the list of options for the expression on the left hand side
The correct answer is [tex](5-\frac{1}{2})^6[/tex]
Find the length of x.
Micah is handing out miniature chocolate bars and butterscotch hard candies for Halloween. He wants tohave a total of 7 pounds of candy, but he doesn't want to spend more than $11.00 total on the candy. If miniature chocolate bars costs $1.80 per pound, and butterscotch hard candies costs $1.00 per pound, how many pounds of each type of candy should he buy?
Answer:
5 pounds of miniature chocolate and 2 butterscotch hard candies
Step-by-step explanation:
5 x $1.80 =$9 for 5 pounds of candy
2 x $1.00 =$2 for 2 pounds of candy
2 + 5 =7 pounds
7 pounds of candy using $11.00
HElp Find the line of symmetry for the parabola whose equation is y = 2x∧2 - 4x + 1.
x = 2
x = -1
x = 1
Answer:
x = ---------- = 1
Step-by-step explanation:
The formula for the axis of symmetry is x = -b/(2a). In this case b = -4 and a = 2, and so the axis of symmetry is
-(-4)
x = ---------- = 1
2(2)
Answer:
x=1
Step-by-step explanation:
because I said so
write a system of equations for the problem, and then solve the system. if a plane can travel 340 miles per hour with the wind only 260 miles per hour against the wind, find the speed of the wind and the speed of the plane in still air. please show step by step
Answer:
The speed of plane = 40 m/s
The speed of the wind = 300 m/s
Step-by-step explanation:
Let the speed of the plane = Y
And the speed of the wind = X
If the plane then travel 340 miles per hour with the wind, that means the plane and the wind are moving in the same direction. Therefore,
X + Y = 340 ..... ( 1 )
Also, 260 miles per hour against the wind. That is, the plane is moving opposite to the direction of the wind. Therefore,
X - Y = 260 ..... ( 2 )
Solve the two equations simultaneously by addition. That will eliminate Y
X + Y = 340
X - Y = 260
2X = 600
X = 600/2
X = 300 m/s
Substitutes X in equation (1)
300 + Y = 340
Make Y the subject of formula by collecting the like terms
Y = 340 - 300
Y = 40 m/s
Therefore, the speed of the plane is 40 m/s. While the speed of the wind is 300 m/s.
this squared based pyramid is cut horizontally at a height of 15cm to leave this frustum base area=10cm
Answer:
583.33 cm³
Step-by-step explanation:
From the image attached, the total height (H) of the pyramid is 30 cm, the height of the frustrum (h) = 15 cm, the Frustrum base = lower base = B = 10 cm . To find the length of the upper base (b), we use:
[tex]\frac{b}{H-h}=\frac{B}{H}\\ b=(H-h)\frac{B}{H}\\b=(30-15)\frac{10}{30}=5\\b=5\ cm[/tex]
The volume of the frustrum is given by:
[tex]V=\frac{1}{3}h(B_1+B_2+\sqrt{B_1B_2} )\\ Where\ B_1\ is \ the\ area \ of\ the\ upper\ base= 5cm*5cm=25cm^2\\B_1\ is \ the\ area \ of\ the\ lower\ base= 10cm*10cm=100cm^2\\V=\frac{1}{3}(10)(25+100+\sqrt{25*100} )=583.33\\V=583.33\ cm^3[/tex]
2. Kelsea needs a test average of at least 90 to get an "A-" this marking period in math. Her three test grades
are 87,91 and 86. What score must she get on her fourth test to receive at least an A- ?
Define variable:
Equation:
Solution:
can someone check this please :)
Answer:
Equation: 87 + 91 + 86 + x = 360
Solution: 264 + x = 360
x = 360 - 264
x = 96
Step-by-step explanation:
1. Let's review the information given to us to answer the question correctly:
First three Kelsea's test grades : 87, 91 and 86
2. What score must she get on her fourth test to receive at least an A- ?
Define variable: x that represents the grade needed by Kelsea on her fourth test to receive at least an A-
Equation: 87 + 91 + 86 + x = 360
Solution: 264 + x = 360
x = 360 - 264
x = 96
Now you can understand if the previous work you did is correct
please help me with this
Answer:
Step-by-step explanation:
Open box is in rectangular shape. cuboid that is open in the top
l = length = 30 - (2.5 + 2.5 ) = 30 - 5 = 25 cm
h = 2.5 cm
w = width = 30 - (2.5 + 2.5) = 30 - 5 = 25 cm
Surface Area = 2lh + 2wh + lw
= 2*25*2.5 + 2* 25*2.5 + 25*25
=125 + 125 + 625
= 875 square cm
Volume = lwh
= 25*25*2.5
= 1562.5 cubic cm
A painter leans a 25-foot ladder against the wall. The bottom of the ladder is 20 feet from the base of the wall. The painter then moves the bottom of the ladder 13 feet closer to the wall. How much higher is the top of the ladder on the wall?
Answer:
9 ft
Step-by-step explanation:
a²+b²=c²
20²+b²=25²
400=b²=625
b²=625-400
b²=225
b=15 (the distance up the wall the ladder is to begin with)
20-13=7
7²+b²=25²
49+b²=625
b²=625-49
b²=576
b=24 (The distance up the wall the ladder is after moving it)
24-15=9
The lengths of the sides of a triangle are in the ratio of 6:6:5. The perimeter of the triangle
is 34 centimeters. Find the length of each side of the triangle.
Hello!
Answer:
12 cm, 12 cm, 10 cm.
Step-by-step explanation:
Given:
Perimeter, or P = 34 cm
Ratio of sides = 6 : 6 : 5
To find the length of each side, we can use a variable in the ratio to find the perimeter:
34 = 6x + 6x + 5x
Combine like terms:
34 = 17x
Solve for x:
34/17 = 17x/17; x = 2
Plug in this value of "x" into each expression for the side-lengths:
6(2) = 12 cm
6(2) = 12 cm
5(2) = 10 cm
Therefore, the lengths of each side of the triangle are 12 cm, 12 cm, 10 cm.
Hope this helped you! :)
Answer:
12, 12 and 10 cm.
Step-by-step explanation:
6 + 6 + 5 = 17
So one side = 6/17 * 34 = 12 cm
One other side is also 12 cm
The third side = 5/17 * 34 = 10 cm.
Please help me answer my questions...
Answer:
80$
Step-by-step explanation:
total amount of needed=200
Total =Tef +Angelina+Jason
200=90+30+Angelina
Angelina=200-120
Angelina=80$
plz help me plz if u get it correct i will mark brainlist if i can
Jackson is attending a lacrosse game that is halfway through the first quarter.
4) What fractional part of the game is leh?
3) If 74 minutes of playing time have past, how many total minutes of playing
time are there in the game?
6) How many minutes of playing time are left in the game?
(okay so I have to draw the picture so someone please help meh :p)
Answer:
7/8 of the game is left. The game lasts for 592 minutes.
Step-by-step explanation:
It is halfway through the first quarter so it is 1/8. So that's 7/8 part of the game left. if 74 minutes of playing time has past, then you do 74*8 so that's 592 minutes.
Answer:
4) 1/8
3)74x8=592
6)592-74= 518
Step-by-step explanation:
What is the value of x? (Use only the digits 0 - 9 and the decimal point, if needed, to write the number.)
x + 12.66 = 18
Answer: 5.34
Step-by-step explanation: 18 - 12.66 = 5.34
five sixths of a number equals 200. What is the number?
Answer: 240
Step-by-step explanation:
5/6x=200
(6/5)5/6x=200(6/5)
1x=40(6/1)
x=40(6)
x=240
Please answer quickly.
Answer:
Option 4
Step-by-step explanation:
=> [tex]\frac{4}{5} x^{-9}y^6z^8[/tex]
If there is any variable having a negative exponent, we should move it to its opposite side (Denominator to numerator and vice versa) So that it's exponent become positive.
=> [tex]\frac{4y^6z^8}{5x^9}[/tex]
Answer: D) [tex]\frac{4y^6z^8}{5x^9}[/tex]
Step-by-step explanation:
(4/5)x^-9y^6z^8 = [tex]\frac{4x^{-9}y^6z^8}{5}[/tex]
Any negative exponent can be taken to the other side of the fraction to be positive. Thus,
[tex]\frac{4x^{-9}y^6z^8}{5}[/tex] = [tex]\frac{4y^6z^8}{5x^9}[/tex]
Hope it helps <3
What is the Domain and Range *DON'T FORGET PARENTHESES AND BRACKETS*
Answer:
Domain: (-5,-4,-3,-2,-1,0,1,2,3,4,5)
Range: (0,1,2,3,4, -1, -2)
Step-by-step explanation:
Domain means all of the x-axis values on the graph, so for example in (-2,0), -2 would be part of the domain and 0 part of the range. Therefor, what you would do would be take all of the plots and put all x values as the domain and all y values as the range. Hope this helped!
help please. Find the length of x.
Answer:
x=10
Step-by-step explanation:
The triangles are similar so we can use ratios to solve
6.5 (6.5+6.5)
------ = -----------------------
5 x
6.5 (13)
------ = -----------------------
5 x
Using cross products
6.5x = 65
Divide by 6.5
6.5x/6.5 = 65/6.5
x = 10
Martin uses 8 5/8 of a gallon of paint to cover 4/5 of a wall. What is the unit rate at which Martin paints in walls per gallon?
Answer: 32/345 wall per gallon
Step-by-step explanation:
Rate is defined as ratio between two quantities with different units.
Gallons of paint used by Martin = 8 5/8 gallons = 69/8 gallons
Portion of wall Martin wishes to pint = 4/5 wall
Rate at which Martin paints the wall:
= Portion of wall covered / paint used
=
4/5 / 69/8 = 32/345 wall per gallon
Answer:
Martin paints 0.093 walls per gallon of paint
Step-by-step explanation:
1. Let's review the information provided to us to answer the question correctly:
Amount of paint used by Martin = 8 5/8 of a gallon
Ratio of wall painted by Martin with 8 5/8 of a gallon = 4/5
2. What is the unit rate at which Martin paints in walls per gallon?
Let's convert the mixed fractions to decimals this way:
8 5/8 = 8 + 0.625 = 8.625
4/5 = 0.8
Now, let's use the Direct Rule of Three, this way:
Gallons Walls
8.625 0.8
x 1
Solving for x :
0.8x = 8.625 * 1
x = 8.625/0.8
x = 10.78125
x = 10.8 (rounding to next tenth) gallons
For painting a wall, we will use 10.8 gallons of paint. Now, we can calculate the unit rate at which Martin paints in walls per gallon, this way:
Gallons Walls
10.8 1
1 x
Solving for x :
10.8x = 1
x = 1/10.8
x = 0.09259
x = 0.093 (rounding to the next hundredth) walls per gallon of paint
Select the correct answer from each drop-down menu.
The given equation has been solved in the table.
Step
Statement
1
= 15
- - 6 =
- - 6 + 6 = 15 +
+4
- = 21
N
3
4.
2
-2 - 21
5
y = -42
Use the table to complete each statement.
In step 2, the
In step 4, the
property of equality was applied.
property of equality was applied.
V
Reset
Next
Answer:
Step 2: addition property of equality
Step 4: multiplication property of equality
Step-by-step explanation:
=>In step 2, from step 1, where you have [tex] -\frac{y}{2} - 6 = 15 [/tex] , to make -6 cross over to the other side of the equation, the addition property of equality was applied. That would ensure the equation remains balanced. Thus, 6 is added to both sides of the equation.
[tex] -\frac{y}{2} - 6 + 6 = 15 + 6 [/tex]
[tex] = -\frac{y}{2} = 21 [/tex]
=>In step 4, the multiplication property of equality was used as both sides of the equation were multiplied by -2, to balance the equation and also solve for y.
Answer:
Step 2 > addition
Step 4 > multiplication
Step-by-step explanation:
how do you solve these problems?
Answer:
Step-by-step explanation:
Hello,
a. The area of region P is the area of the rectangle 1 * e minus the
[tex]\displaystyle \int\limits^0_1 {e^x} \, dx=[e^x]^{1}_{0}=e-1[/tex]
So this is e - (e-1) = e - e + 1 = 1
b. The area of region P is the area of the rectangle 1 * e minus P and minus the
[tex]\displaystyle \int\limits^0_1 {e^{-x}} \, dx=[-e^{-x}]^{1}_{0}=-e^{-1}+1[/tex]
So this is
[tex]e - 1 - (-e^{-1}+1) = e-1+e^{-1}-1=e+e^{-1}-2[/tex]
This is around 1.08616127...
Hope this helps.
Do not hesitate if you need further explanation.
Thank you
Help ASAP!! This one's is difficult for me to understand!! Help me please!
Answer:
Ok so im in 7thgrade so ima try to help answer is x= 8x9
Plz Help me solve this
Answer:
Step-by-step explanation:I think the answer is 12?
is 3 over the square root of 27 rational or irrational
Answer:
rational (I think
Step-by-step explanation: