Answer:
Take 5^x as y.
Now the question becomes a simple equation.
y + 20y - 125 = 0.
21y = 125.
Thus, y = 125/21.
Now resubstituting we get,
5^x = 125 /21.
Taking log on both sides,
xlog5 = log 125 - log 21
x = (log125/log5) - (log21/log 5)
x= 3- 1.89
find m<SPT in degrees
Answer: 60°
Step-by-step explanation:
∠UQR = 180°
∠UQR = ∠UQ + ∠QR
180° = 115° + ∠QR
65° = ∠QR
∠QRT = 180°
∠QRT = ∠QR + ∠RS + ∠ST
180° = 65° + ∠RS + 55°
180° = 120° + ∠RS
60° = ∠RS
John has a cylindrical propane tank that measures 8" in diameter and 8" tall If John
buys a new cylindrical propane tank that is twice as wide and half as tall as his
current tank, how much larger will the volume of the new tank be?
Answer:
2 times as large
Step-by-step explanation:
For the original cylinder, we can say that the volume of a cylinder is equal to V= πr²h. For this cylinder, we can say that V = π * radius² * height. The radius is equal to 1/2 of the diameter, so the original radius is 8/2 = 4. Therefore, the volume of the original cylinder is V = π * radius² * height = π * 4² * 8 = π * 16 * 8 = π * 128
For the new cylinder, "twice as wide" means that the diameter is twice as big as the original one. Half the height means that the height is halved. The new diameter is therefore 8 * 2 = 16 (meaning that the new radius is 16/2=8) while the new height is 8/2 = 4. The new volume is thus
V = π * radius² * height = π * 8² * 4 = π * 64 * 4 = π * 256
To see how much larger the new tank volume is, we can divide (new tank volume) by (old tank volume), resulting in
π * 256 / (π *128) = 2
Multiply and simplify the following complex numbers (-4-5i)•(1-i)
Answer:
Step-by-step explanation:
(-4 - 5i)⋅(1 - i) = (-4)(1) + (-4)(-i) + (-5i)(1) + (-5i)(-i)
= -4 + 4i - 5i + 5i²
= -4 - i -5
= -9 - i
The given line segment has a midpoint at (-1, -2).
What is the equation, in slope-intercept form, of the
perpendicular bisector of the given line segment?
ch
4
3
O y=-4x - 4
O y = -4x - 6
O y=x-4
2
1
х
5 4 -3 -2 -11
61,-2)
Oy=+x-6
234
(3.-1).
-3
(-5, 3)
w5
Answer:
y = -4x -6
Step-by-step explanation:
The given segment has a rise if 1 for a run of 4, so a slope of ...
m = rise/run = 1/4
The desired perpendicular has a slope that is the negative reciprocal of this:
m = -1/(1/4) = -4
A point that has a rise of -4 for a run of 1 from the given midpoint is ...
(-1, -2) +(1, -4) = (0, -6) . . . . . . . the y-intercept of the bisector
So, our perpendicular bisector has a slope of m=-4 and a y-intercept of b=-6. Putting these in the slope-intercept form equation, we find the line to be ...
y = mx +b
y = -4x -6
The equation of the line in slope intercept form is y = -4x -6
What is a linear equation?A linear equation is in the form:
y = mx + b
Where y,x are variables, m is the rate of change and b is the y intercept.
Two lines are perpendicular of the product of the slope is -1
The line passes through the point (-5, -3) and (3, -1). Hence:
Slope = (-1 - (-3)) / (3 - (-5)) = 1/4
The slope of the line perpendicular to this line is -4 (-4 * 1/4 = -1).
The line passes through (-1, -2), hence:
y - (-2) = -4(x - (-1))
y + 2 = -4(x + 1)
y = -4x -6
The equation of the line in slope intercept form is y = -4x -6
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At a store An orange costs 18 cents A pineapple costs 27 cents An apple costs 15 cents How much does a strawberry cost??
Answer:
A strawberry cost 30 cents
Step-by-step explanation:
Given:
Orange= 18 cents
Pineapple = 27 cents
Apple = 15 cents
Strawberry = ?
From the given:
Orange has 6 letters multiplied by 3
=6 * 3
=18 cents
Pineapple has 9 letters multiplied by 3
=9 * 3
=27 cents
Apple has 5 letters multiplied by 3
= 5 * 3
= 15 cents
Therefore, cost of the strawberry=
Strawberry has 10 letters. Multiply the 10 letters by 3
That is,
10 × 3
= 30 cents
An airplane travels 1200 miles in 4 hours with the wind. The same trip takes 5 hours against the wind. What is the speed of the plane in still air and what is the wind speed?
Answer:
Speed of plane in still air is 270 mph
Wind speed is 30 mph
Step-by-step explanation:
Check the picture.
The speed of the plane in still air is 270 mph and the speed of the wind will be 30 mph.
What is the distance formula?The distance traveled by an object is the product of the speed of an object and the time taken.
Distance = speed x time
An airplane travels 1200 miles in 4 hours with the wind. The same trip takes 5 hours against the wind.
Let the speed of the plane be x
The speed of wind be y
Distance covered with the wind = (x + y)t
1200 = (x + y)4
(x + y) = 1200/4
(x + y)= 300 .....(a)
Distance covered against the wind = (x - y)t
1200 = (x - y)5
(x - y) = 1200/5
(x - y) = 240 .......(b)
By solving both the equation
(x + y)= 300
(x - y) = 240
Therefore the values will be x= 270mph and y = 30 mph
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Solve for y: 1/3y+4=16
Hey there! I'm happy to help!
We want to isolate y on one side of the equation to see what it equals. To do this, we use inverse operations to cancel out numbers on the y side and find the correct value.
1/3y+4=16
We subtract 4 from both sides, canceling out the +4 on the right but keeping the same y-value by doing the same to the other side.
1/3y=12
We divide both sides by 1/3 (which is multiplying both sides by 3) which will cancel out the 1/3 and tell us what y is equal to.
y=36
Now you know how to solve basic equations! Have a wonderful day! :D
What is the value of this expression when g = -3.5?
8 − |2g − 5|
Answer:
-4
Step-by-step explanation:
Replace g by -3.5
● 8- | 2g - 5 |
● 8 - | 2*(-3.5)-5 |
● 8 - |-7-5|
● 8 - | -12|
The absolute value turns the number inside the | | into a positive value
-12 is negative so |-12| = 12
●8 -12
● -4
Suppose that you are standing 150 feet from a building and the angle of elevation to the top of the building is 42°. What is the building's height?
Answer:
135.06 feet
Step-by-step explanation:
Since the side of the building makes a right triangle with the ground and you know one side length and the degree angle between you and the top of the building we can use trigonometric function to find the height of the building. So since we know one side other than the hypotenuse we can use tangent to solve. Tangent is the opposite side over the adjacent side of the known angle.
opposite side = x
adjacent side = 150 feet
angle = 42°
tan(42°) = x/150 feet
150 feet * tan(42°) = x
x = 135.06 feet
About how many feet are in 3.6 kilometers? 1 m = 39.37 in
Answer:
11811 feet
Step-by-step explanation:
Hope it helps!
There are about 11,812 feet in 3.6 kilometers.
To convert kilometers to feet, we need to use the conversion factor:
1 kilometer = 3,280.84 feet.
Now, to find how many feet are in 3.6 kilometers,
we can multiply 3.6 by the conversion factor:
So, 3.6 kilometers x 3,280.84 feet/kilometer
= 11,811.504 feet.
Thus, Rounded to a whole number, there are about 11,812 feet in 3.6 kilometers.
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State whether each ratio forms a proportion.
1) 6:3, 18:9 2) 3:4, 30:40 3) 14/18,28/36 4) 2/5,5/2
Answer: Please Give Me Brainliest, Thank You!
#1, #2, #3 do, but #4 doesn't
Step-by-step explanation:
#1
18/9=2
6/3=2
#2
30/3=10
40/4=10
#3
28/14=2
36/18=2
Find the exact value by using a half-angle identity.
tan seven pi divided by eight
9514 1404 393
Answer:
1 -√2
Step-by-step explanation:
[tex]\tan(x/2)=\dfrac{1-\cos(x)}{\sin(x)}\\\\\tan\left(\dfrac{1}{2}\cdot\dfrac{7\pi}{4}\right)=\dfrac{1-\cos\dfrac{7\pi}{4}}{\sin\dfrac{7\pi}{4}}=\dfrac{1-\dfrac{1}{\sqrt{2}}}{-\dfrac{1}{\sqrt{2}}}=\boxed{1-\sqrt{2}}[/tex]
tan(7π/8) = 1 -√2
Does coordinate x or coordinate y represent a greater number?
Answer:
Y
Step-by-step explanation:
You see that (x,3) and (2,7) are on the exact same x-value, which is 2. Y, on the other hand, is on the same y-value as (4,3), so it's going to be 4. 4 > 2, so your answer is y.
Y represents the greater number.
We see that (x,3) and (2,7) are on the exact same x-value, which is 2. Y, on the other hand, is on the same y-value as (4,3), so it's going to be 4. 4 > 2, so your answer is y.
What is an example of a coordinate?A set of values that display an actual role. On graphs it is also a pair of numbers: the first variety indicates the gap along, and the second variety indicates the distance up or down. As an example, the factor (12,5) is 12 units long, and five units up.
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Translate and solve: 54 greater than x is greater than 216
Answer:
x >162
Step-by-step explanation:
x+54 > 216
Subtract 54 from each side
x+54-54 > 216 - 54
x >162
Answer:
[tex]\huge \boxed{{x>162}}[/tex]
Step-by-step explanation:
[tex]x+54 > 216[/tex]
[tex]\sf Subtract \ 54 \ from \ both \ parts.[/tex]
[tex]x+54 -54> 216-54[/tex]
[tex]x>162[/tex]
Find the solution set of the inequality and the number: 12 − 6x > 24 A. , C. ≤, D. ≥, E. =
Answer:
x < -2
Step-by-step explanation:
12 − 6x > 24
Subtract 12 from each side
12-12 − 6x > 24-12
-6x > 12
Divide each side by -6, remembering to flip the inequality
-6x/-6 < 12/-6
x < -2
Answer:
x < -2
Step-by-step explanation:
12 − 6x > 24
12 - 12 − 6x > 24 - 12
-6x > 12
-6x/(-6) < 12/(-6)
x < -2
Lexie, a bowler, claims that her bowling score is more than 140 points, on average. Several of her teammates do not believe her, so she decides to do a hypothesis test, at a 5% significance level, to persuade them. She bowls 18 games. The mean score of the sample games is 155 points. Lexie knows from experience that the standard deviation for her bowling score is 17 points. H0: μ=140; Ha: μ>140 α=0.05 (significance level) What is the test statistic (z-score) of this one-mean hypothesis test, rounded to two decimal places?
Answer:
The test statistic is [tex]t = 3.744[/tex]
Step-by-step explanation:
From the question we are told that
The population mean is [tex]\mu = 140[/tex]
The The level of significance is [tex]\alpha = 0.05[/tex]
The sample size is n = 18
The null hypothesis is [tex]H_o : \mu = 140[/tex]
The alternative hypothesis is [tex]H_a : \mu > 140[/tex]
The sample mean is [tex]\= x = 155[/tex]
The standard deviation is [tex]\sigma = 17[/tex]
Generally the test statistics is mathematically represented as
[tex]t = \frac{\= x - \mu }{ \frac{ \sigma}{ \sqrt{n} } }[/tex]
substituting values
[tex]t = \frac{ 155 - 140 }{ \frac{ 17 }{ \sqrt{18} } }[/tex]
[tex]t = 3.744[/tex]
A random sample of 11 students produced the following data, where x is the hours spent per month playing games, and y is the final exam score (out of a maximum of 50 points). The data are presented below in the table of values.
x y
14 46
15 49
16 37
17 42
18 37
19 31
20 25
21 23
22 20
23 15
24 12
What is the value of the intercept of the regression line, b, rounded to one decimal place?
Answer:
b = - 3.7
Step-by-step explanation:
here are the data values:
x y XY X²
14 46 644 196
15 49 735 225
16 37 592 256
17 42 714 289
18 37 666 324
19 31 589 361
20 25 500 400
21 23 483 441
22 20 440 484
23 15 345 529
24 12 288 576
now we are required to find the summation (total) of all values of X, Y, XY and X².
∑X = 209
∑Y = 337
∑XY = 5996
∑X² = 4081
The formular for finding b is given as:
b = n∑XY - (X)(Y) / n∑X² - (∑X)²
= 11(5996) - (209)(337) / 11(4081) - (209)²
= 65956 - 70433 / 44891 - 43681
= -4477/ 1210
= -3.7
The question asked us to find the value of b but we can go further to find the equation of the regression line:
a = ∑Y - b∑X / n
= 337 - (-3.7)(209)/ 11
=1110.3/11
= 100.94
the equation is:
Y = 100.94 - 3.7X
I hope you find my solution useful!
=
Try to get to every number from 1 to 10 using four 4's and any number of arithmetic operations (+, −, ×, ÷). You may also you parentheses.
Answer:
Step-by-step explanation:
1. 4/4+4-4=1
2. 4/4+4/4=2
3. 4+4/4-4=3
4. 4 × (4 − 4) + 4=4
5. (4 × 4 + 4) / 4=5
6. 44 / 4 − 4=6
7. 4+4-4/4=7
8. 4+4+4-4=8
9. 4+4+4/9=9
10. 44 / 4.4=10
Answer:
1 = (4 x 4)/(4 x 4) or (4 + 4)/(4 + 4) or (4 / 4) x (4 / 4) or (4 / 4)/(4 / 4)
2= (4 x 4)/(4 + 4) or 4 / ((4+4)/4)
3= (4 + 4 + 4)/4 or (4 x 4 - 4)/4
4 = 4 - (4 - 4)/4
5 = (4 x 4 + 4)/4
6 = 4 + (4 + 4)/4
7 = 4 - (4/4) + 4
8 = 4 + (4 x 4)/4
9 = 4 + 4 + (4/4)
10 - I tried the best. You might need ! or sqrt operator to get 4.
Updated:
I forgot we could use 4, 44, 444, or 4444, so that 10 could be expressed as:
10 = (44 - 4)/4
Simplify the slope of bd
Answer:
[tex] \boxed{ - 1}[/tex]Step-by-step explanation:
The co-ordinates of B = ( 0 , a ) ⇒ ( x₁ , y₁ )
The co-ordinates of D = ( a , 0 )⇒( x₂ , y₂ )
Let's find the slope of BD
Slope = [tex] \mathrm{ = \frac{y2- y1}{x2 - x1} }[/tex]
[tex] \mathrm{ = \frac{0 - a}{a - 0} }[/tex]
[tex] \mathrm{ = \frac{ - a}{a} }[/tex]
[tex] \mathrm{ = - 1}[/tex]
[tex] \mathcal{HOPE \: I \: HELPED !}[/tex]
[tex] \mathcal{BEST \: REGARDS !}[/tex]
The angles of a quadrilateral are (3x + 2), (x-3), (2x+1), and 2(2x+5). Find x.
Answer:
3x+2+x-3+2x+1+2(2x+5)=360
10x+10=360
x=35
find value of x and YZ if Y is between X and Z
XY=2x+1, YZ =6x, and XZ=81
Answer:
10
Step-by-step explanation:
Applying the segment addition theorem, the value of x = 10
YZ = 60
What is the Segment Addition Theorem?The segment addition theorem states that if a point, C, lies between two endpoints of a segment, A and B, then: AC + CB = AB.
Given:
XY = 2x+1
YZ = 6x
XZ = 81
Thus:
XY + YZ = XZ (segment addition theorem)
2x + 1 + 6x = 81
Find x
8x = 81 - 1
8x = 80
x = 10
Find YZ:
YZ = 6x
Plug in the value of x
YZ = 6(10)
YZ = 60
Therefore, applying the segment addition theorem, the value of x = 10
YZ = 60
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what are the coordinates of A,B and C
Answer:
Please display full question . your question is incomplete ..
Answer:
Step-by-step explanation:
Please display a picture
x^2+y^2≤ 4y, x^2+y^2≤4x
Answer:
0 what is the question man what
Brian needs to paint a logo using two right triangles. The dimensions of the logo are shown below. What is the difference between the area of the large triangle and the area of the small triangle?
Answer:
7.5 cm²
Step-by-step explanation:
Dimensions of the large ∆:
[tex] base (b) = 3cm, height (h) = 9cm [/tex]
[tex] Area = 0.5*b*h = 0.5*3*9 = 13.5 cm^2 [/tex]
Dimensions of the small ∆:
[tex] base (b) = 2cm, height (h) = 6cm [/tex]
[tex] Area = 0.5*b*h = 0.5*2*6 = 6 cm^2 [/tex]
Difference between the area of the large and the small ∆ = 13.5 - 6 = 7.5 cm²
On the first day of a two-day meeting, 10 coffees and 10 doughnuts were purchased for a total of $20.00. Since nobody drank the coffee and all the doughnuts were eaten, the next day only 2 coffees and 14 doughnuts were purchased for a total of $13.00. How much did each coffee and each doughnut cost?
Answer:
1.25 dollars- the value of each coffee
0.75 dollars- the value of each doughnut
Step-by-step explanation:
Suppose that value of one coffee is x dollars, when one doughnut costs y dollars. The value o 10 coffee is 10x, when 10 doughnuts cost 10y. The sum is 10x+10y and it is 20.
10x+10y= 20 (we can divide each part by 10)
x+y=2
2coffee cost 2x, 14 doughnuts cost 14y
2x+14y=13 (it can be divided by two)
x+7y=6.5
We have the system of equations x+y=2, x+7y=6.5
Subtract the first equation from the second one (the left side of the first equation from the left side
x+7y - (x+y)= 6.5-2
6y=4.5
y=4.5/6= 3/4 = 0.75 dollars- the value of each doughnut
x=2-0.75=1.25 dollars- the value of each coffee
A school is holding a raffle to raise money to buy new books for the library. The school plans on awarding 18, $200 prizes, 120 $25 prizes and 270 $5 prizes. Is $10 enough to charge per ticket if they only sell 1000 tickets?
Answer:
Yes
Step-by-step explanation:
18 × 200 = 3600
120 × 25 = 3000
270 × 5 = 1350
in total 7950
tickets = 10 × 1000 = 10000
7950 < 10000
p(a) = 0.60, p(b) = 0.20, and p(a and b) = 0.15 what is p(a or b) choices: A. 0.12, B. 0.65, C. 0.40, or D. 0.80 (Note- This is on AP3X)
Answer:
[tex]p(a\ or\ b) = 0.65[/tex]
Step-by-step explanation:
Given
[tex]p(a) = 0.60[/tex]
[tex]p(b) = 0.20[/tex]
[tex]p(a\ and\ b) = 0.15[/tex]
Required
[tex]p(a\ or\ b)[/tex]
The relationship between the given parameters and the required parameters is as follows;
[tex]p(a\ and\ b) = p(a) + p(b) - p(a\ or\ b)[/tex]
Substitute values for the known parameters
[tex]0.15 = 0.60 + 0.20 - p(a\ or\ b)[/tex]
[tex]0.15 = 0.80 - p(a\ or\ b)[/tex]
Collect Like Terms
[tex]p(a\ or\ b) = 0.80 - 0.15[/tex]
[tex]p(a\ or\ b) = 0.65[/tex]
Hence;
[tex]p(a\ or\ b) = 0.65[/tex]
the ordered pairs belonging to the relation
S = {(x, y): 2x = 3y}
Answer:
{(0, 0), (1, ⅔), (2, 4/3), (3, 2)…}
Quick! Andrew has to play 15 games in a chess tournament. At some point during the tournament he has won half of the games he has played, he has lost one-third of the games he has played and two have ended in a draw. How many games has Andrew still to play?
[tex]x[/tex] - the number of the games he played
[tex]\dfrac{x}{2}[/tex] - the number of the games he won
[tex]\dfrac{x}{3}[/tex] - the number of the games he lost
[tex]x=\dfrac{x}{2}+\dfrac{x}{3}+2\Big|\cdot6\\6x=3x+2x+12\\x=12[/tex]
[tex]15-12=3[/tex]
so, he has still 3 games to play
Follow the instructions on the image
Answer:
k=3
Step-by-step explanation:
Assuming the centre of dilation is 0,0, we can use the formula (kx,ky) to determine it.
Here,
The co-ordinates of pre-image=(0,1),(-1,-1) & (1,-1)
The co-ordinates of image=(0,3),(-3,-3) & (3,-3)
Now,
(kx,ky)=(0,3)
(k*0,k*1)=(0,3)
Equating,
k=3
You can use the other coordinates to further solidify your answer.