Answer:
The possible values of x are:
x= [tex]\frac{-1+\sqrt{3}}{4} \,\,or\,\, x= 0.18[/tex]
and
x= [tex]\frac{-1-\sqrt{3}}{4} \,\, or \,\, x= -0.68[/tex]
Step-by-step explanation:
[tex]8x^2+4x+1=0[/tex]
Using Quadratic formula to solve this equation:
[tex]x=\frac{-b\pm\sqrt{b^2-4ac}}{2a}\\a = 8 \,\, b = 4\,\, c = -1\\Putting \,\, values \,\, in \,\, the\,\, equation\\x= \frac{-4\pm\sqrt{(4)^2-4(8)(-1)}}{2(8)}\\x= \frac{-4\pm\sqrt{16+32}}{16}\\x= \frac{-4\pm\sqrt{48}}{16}\\x= \frac{-4+ \sqrt{48}}{16} \,\, and \,\, x= \frac{-4- \sqrt{48}}{16}\\x= \frac{-1+ \sqrt{3}}{4} \,\, and \,\, x= \frac{-1- \sqrt{3}}{4}[/tex]
The possible values of x are:
x= [tex]\frac{-1+\sqrt{3}}{4} \,\,or\,\, x= 0.18[/tex]
and
x= [tex]\frac{-1-\sqrt{3}}{4} \,\, or \,\, x= -0.68[/tex]
The width of a model train’s car measures 2.4 in. The scale is 1:56. What is the width of the actual train car to the nearest foot?
Answer:
11.2 feet
Step-by-step explanation:
The width of the actual train car, to the nearest foot, is 11 feet.
To find the width of the actual train car, we need to use the scale factor provided.
Given:
- Width of the model train's car = 2.4 inches
- Scale = 1:56
To find the actual width, we'll use the scale factor:
[tex]\[ \text{Actual width} = \text{Model width} \times \text{Scale factor} \][/tex]
First, we need to convert the width of the model train's car from inches to feet because the scale factor is given as a ratio. There are 12 inches in a foot.
[tex]\[ \text{Model width} = \frac{2.4 \text{ inches}}{12 \text{ inches/foot}} = 0.2 \text{ feet} \][/tex]
Now, we can find the actual width:
[tex]\[ \text{Actual width} = 0.2 \text{ feet} \times 56 = 11.2 \text{ feet} \][/tex]
Candice is researching a career as an electrician. She is looking at the costs of pursuing such a career. She finds that the required education is affordable, that the hours can be long, and that she must handle angry customers. Evaluate Candice's research of the costs of the career.
Answer:
the costs of the career is low
Step-by-step explanation:
Simplify:
(6.15x+0.24y)÷1.5+5.9x−1.6y
PLEASE HELP ME QUICKLY!
To simplify the expression (6.15x+0.24y)">">1.5 + 5.9x - 1.6y, divide the terms in the parenthesis by 1.5 and then combine like terms to yield the simplified expression 10.0x - 1.44y.
To simplify the expression (6.15x+0.24y)">">1.5 + 5.9x - 1.6y, first, divide the terms within the parenthesis by 1.5. This action distributes the division across each term:
(6.15x / 1.5) + (0.24y / 1.5)This simplifies to:
(4.1x) + (0.16y)Now, combine like terms with those outside the parenthesis:
4.1x + 5.9x = 10.0x0.16y - 1.6y = -1.44yTherefore, the simplified expression is:
10.0x - 1.44y
Identify an equation in slope-intecept form for the line parallel to y=5x+2 that passes through(-6,-1).
A.y=5x+29
B.y=-5x-11
C.y=5x-29
D.y=1/5x+1/6
Answer:
A
Step-by-step explanation:
The equation of a line in slope- intercept form is
y = mx + c ( m is the slope and c the y- intercept )
y = 5x + 2 ← is in slope- intercept form
with slope m = 5
• Parallel lines have equal slopes, hence
y = 5x + c ← is the partial equation of the parallel line
To find c substitute (- 6, - 1) into the partial equation
- 1 = - 30 + c ⇒ c = - 1 + 30 = 29
y = 5x + 29 → A
Two vehicles, each moving from a point in a straight line away from each other at an angle, are 150 feet apart after 6 second. Both are moving at a constant rate, vehicle A at 50 feet per second and vehicle B at 40 feet per second.how far apart are they after 15 seconds
Vehicle A travels 750 feet and Vehicle B travels 600 feet in 15 seconds. Adding these distances together, we find they are 1350 feet apart after 15 seconds.
Explanation:The subject of your question falls under the realm of Mathematics, specifically in the area of vector addition or relative velocity. Let's imagine the two vehicles are moving away from each other in a straight line at an angle. We mainly need to consider the relative velocity of vehicle B to vehicle A.
After 15 seconds, vehicle A will have traveled (50 feet/second * 15 seconds) = 750 feet. Similarly, vehicle B will have traveled (40 feet/second * 15 seconds) = 600 feet. In this situation, the total distance separating vehicle A and vehicle B is the sum of their individual distances traveled, which equals 750 feet + 600 feet = 1350 feet.
Therefore, the two vehicles are 1350 feet apart after 15 seconds.
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a block has two red sides, two green sides, one blue side and one yellow side what is the probability that when the block is rolled it will land green side up
Answer:
2/6
Step-by-step explanation:
There are 6 sides, and two are green. That makes it 2/6
Answer:
2/6
Step-by-step explanation:
Please help and thank you
Answer:
D
Step-by-step explanation:
Given
11x = 11 - 55xz²
Collect the terms in x together by adding 55xz² to both sides
11x + 55xz² = 11 ← factor out x on the left side
x(11 + 55z²) == 11 ← divide both sides by 11 + 55z²
x = [tex]\frac{11}{11+55z^2}[/tex] ← factor out 11 on the denominator
x = [tex]\frac{11}{11(1+5z^2)}[/tex] ← cancel 11 on numerator/denominator
x = [tex]\frac{1}{1+5z^2}[/tex] → D
Luke made a Square Mosaic that has side lengths of three meters. Luke decided to add a border to his Mosaic and now it has a side length of 3.5 meters. by how much has the area of the Mosaic increased
Luke's square mosaic increased in area by 3.25 square meters after he added a border, turning the side length from 3 meters to 3.5 meters.
Explanation:Luke originally made a square mosaic with side lengths of three meters. The area of this original square is calculated by squaring the side length: 3 meters × 3 meters = 9 square meters. When Luke added a border to his mosaic, the side length became 3.5 meters. Calculating the new area, we square the new side length: 3.5 meters × 3.5 meters = 12.25 square meters.
The increase in the area of the mosaic is the difference between the new area and the original area, which is 12.25 square meters - 9 square meters = 3.25 square meters. Therefore, the area of Luke's mosaic has increased by 3.25 square meters after adding the border.
PLEASE PLEASE HELPP MEEE
QUESTION:
Find the Volume with work shown.
Answer:
72 mm^3
Step-by-step explanation:
To find the volume of the combined object, we can find the volume of each cube and add it together
Volume of the 4 mm cube
V = s^3
V = 4^3 = 64 mm^3
Volume of the 2 mm cube
V = s^3
V = 2^3 = 8 mm^3
Add the volumes together
64+8 = 72 mm^3
Answer:
72 mm^3
Step-by-step explanation:
To find the volume of this irregular figure, first find each of the cubes.
Part I. Finding the bottom cube
Since the volume of a cube is s^3 where s is the side, we can plug 4 in and we get 64 mm^3.
Part II. Finding the top cube
Using the formula for volume of a cube, we get the volume of the upper cube to be 8 mm^3.
Part II. The total volume of the irregular figure
To find the total volume we simply add the two volumes together. In doing so, we get 64+8 = 72 mm^3 as our volume.
Please help me with geometry.
Answer:
120°
Step-by-step explanation:
In ABC, C is a right angle, what is the measure
The answer is 67.6
You have to find the angle that has cos=8/21=0.381.
Answer:
67.6 degrees
Step-by-step explanation:
You need to use cosine to solve this.
so, cosine is adjacent leg over hypotenuse. which is 8/21. and it is 0.381.
and when you do cos^-1 (0.381), then it is 67.6.
If ax^3+bx^2+x-6 has (x+2) as a factor and leaves a remainder 4 when divided by (x-2), find the value of a and b
Answer:
a = 0
b = 2
Step-by-step explanation:
Synthetic division gives rise to two equations:
b -2a = 2
b +2a = 2
The solution to these equations is (a, b) = (0, 2).
___
The remainder from the division is the lower-right sum shown in the attached tables. For the factor x+2, the remainder from dividing your cubic by x+2 is (4b-8a-8). Setting this to zero and putting it into standard form gives the first equation shown above.
The remainder from division by (x-2) is (4b+8a-4). Setting this to 4 and putting the result into standard form gives the second equation above.
___
Pen skips and chocolate smudges make the first attachment less "professional" than it might otherwise be. Please forgive. The graph in the second attachment verifies this result.
Aja and Pete are biking on a trail.
Aja begins 2 miles ahead of Pete and bikes at an average speed of 3 miles per hour.
Pete bikes at an average speed of 4 miles per hour.
How much time will it take for Pete to catch up with Aja on the trail?
Answer:
2 hours
Step-by-step explanation:
Given in the question that,
speed of Aja = 3 miles/h
speed of Pete = 4 miles/h
we know that Aja is 2 miles away from Pete
Both will have covered same distance at the time they will catch up.
suppose time = x
distance covered = y
Formula to use
distance = speed x time
Equation 1
3x = y - 2
3x + 2 = y
Equation 2
4x = y
Equate both equation
3x + 2 = 4x
2 = 4x -3x
2 = x
Answer:
Pete will catch up Aja after 2 hours
Step-by-step explanation:
We can represent thsi problem as as system of equations.
Let
x = be the time in which both Aja and Pete starte biking, (in hours)
y = the number of miles traveled by each
Aja begins 2 miles ahead of Pete and bikes at an average speed of 3 miles per hour. This means
y_Aja = 3*x + 2
Pete bikes at an average speed of 4 miles per hour.
y_Pete = 4*x
Then, we can find the intersection point between the graphs, so we find the solution.
Please see attached picture below
Pete will catch up Aja after 2 hours
the frequency table shows the results of a survey comparing the number of beach towels sold full price and at a discount durring each of the three months
Answer:
It's 0.90.
Step-by-step explanation:
Answer:
the answer is B
Step-by-step explanation:
BRAINLIEST
Which decimal numbers are equivalent to 3/5 ?
Choose all answers that are correct.
0.03
0.6
0.30
0.3
0.06
0.60
The answer is 0.6 . 3 divide 5 is 0.6
.6 is correct . To get that u just divide the 3 by the 5
d
=
number of dollars
p
=
number of pounds
Drag each table and equation to the unit rate it matches.
Answer:
General equation of line : [tex]y = mx+c[/tex] --1
Where m is the slope or unit rate
Table 1)
p d
1 3
2 6
4 12
d = Number of dollars (i.e.y axis)
p = number of pound(i.e. x axis)
First find the slope
First calculate the slope of given points
[tex]m = \frac{y_2-y_1}{x_2-x_1}[/tex] ---A
[tex](x_1,y_1)=(1,3)[/tex]
[tex](x_2,y_2)=(2,6)[/tex]
Substitute values in A
[tex]m = \frac{6-3}{2-1}[/tex]
[tex]m = 3[/tex]
Thus the unit rate is 3 dollars per pound.
So, It matches the box 1 (Refer the attached figure)
Equation 1 : [tex]p=3d[/tex]
[tex]\frac{p}{3}=d[/tex]
Since p is the x coordinate and d is the y coordinate
On Comparing with 1
[tex]m = \frac{1}{3}[/tex]
Thus the unit rate is [tex]\frac{1}{3}[/tex] dollars per pound
So, It matches the box 2 (Refer the attached figure)
Equation 2 : [tex]\frac{1}{3}d=3p[/tex]
[tex]d=9p[/tex]
Since p is the x coordinate and d is the y coordinate
On Comparing with 1
[tex]m =9[/tex]
Thus the unit rate is 9 dollars per pound
So, It matches the box 3 (Refer the attached figure)
Table 2)
p d
1/9 1
1 9
2 18
d = Number of dollars (i.e.y axis)
p = number of pound(i.e. x axis)
[tex](x_1,y_1)=(\frac{1}{9},1)[/tex]
[tex](x_2,y_2)=(1,9)[/tex]
Substitute values in A
[tex]m = \frac{9-1}{1-\frac{1}{9}}[/tex]
[tex]m = \frac{8}{frac{8}{9}}[/tex]
[tex]m = 9[/tex]
Thus the unit rate is 9 dollars per pound
So, It matches the box 3 (Refer the attached figure)
Answer: See image attached
Step-by-step explanation:
Line m passes through the point (-5,4) And has a slope of 1/3 What is the equation of the line m in standard form?
Answer:
y-1/3x=17/3
Step-by-step explanation:
ax+by=c is standard form
first I'll start with slope interecept form and then we can change it to standard
y=mx+b
y=1/3x+b
4=1/3(-5)+b
4=-5/3+b
12/3+5/3=b
17/3=b
y=1/3x+17/3
to change to standard
y-1/3x=17/3
What is the solution to the system of equations graphed below? y = –4x + 33
y = –4x + 33
y-33 = –4x
y-33/4 = x
X=y-33/4.
Answer: The answer to your question is (8.25, 0)
Step-by-step explanation:
Use the table of values to find the function's values.
If x=0, then f(0) =
If f(x) = 27, then x =
Answer:
If x=0, then f(0) = -15
If f(x) = 27, then x = 3
Step-by-step explanation:
Find where the x column on the table has a 0 and find the corresponding f(x) value which is -15.
Do then same for the other question but find where f(x) on the table is equal to 27 and find the corresponding x value which is 3
If x=0, then f(0) = -15
If f(x) = 27, then x = 3
Step-by-step explanation:We are given a table of values as follows:
x f(x)
-3 33
-2 17
0 -15
2 -7
3 27
This means that x is the independent variable and f(x) is the dependent variable corresponding to the variable x.
Hence, from the table of values we have:
If x=0, then f(0) = -15
If f(x) = 27, then x = 3
A box could have a volume of
A) 4 ft
B) 4 ft2
C) 4 ft3
D) 4 ft4
Answer:
C) 4ft3
Step-by-step explanation:
volume is measured in cubes and cubes are to the 3rd power
a pipe needs to be cut in to 3/4 feet long. if the pipe is 36 feet long, how many pieces can be made from the pipe?
Answer:
[tex]48\ pieces[/tex]
Step-by-step explanation:
we know that
To find how many pieces can be made from the pipe, divide the total length of the pipe by 3/4 feet
so
[tex]\frac{36}{(3/4)} =\frac{36*4}{3}=48\ pieces[/tex]
A carousel is an amusement ride consisting of a rotating circular platform with seats for riders. The carousel at a local theme park has a diameter of 32 feet. Each ride lasts 3 minute mes and the speed of the carousel is 4.3 revolutions or minute what is the maximum distance riders travel in one full ride?
Answer:
1296.85 ft
Step-by-step explanation:
Answer:
The maximum distance riders travel in one full ride is:
1296.192 feet
Step-by-step explanation:
It is given that the diameter(d) of carousel is: 32 feet.
This means that the distance travelled in one revolution is equal to the circumference(C) of the circle.
We know that the circumference of circle is given by:
[tex]C=\pi\times d\\\\\\C=3.14\times 32\\\\\\C=100.48\ feet[/tex]
Also, Time of one full ride is: 3 minutes.
Speed of one full ride is: 4.3 revolutions per minute.
This means that the number of revolutions made is calculated as:
Number of revolution=Speed×Time
Number of revolution=4.3×3=12.9 revolutions.
Hence, total distance traveled in one full ride is:
Number of revolution made×Distance covered in one revolution
= 12.9×100.48
= 1296.192 feet
Find The Slope Of The Line
A)-3
B)3
C)-1/3
D)1/3
Pls help 20 points and brainiest to whoever answer it
Answer:
-1/3
Step-by-step explanation:
To find the slope you have to find the rise over run. Start at the first point then go down 3 and over to the right 1. Your slope is -1/3.
Answer:
A
Step-by-step explanation:
Calculate the slope m using the slope formula
m = (y₂ - y₁ ) / (x₂ - x₁ )
with (x₁, y₁ ) = (1, 4) and (x₂, y₂ ) = (2, 1) ← 2 points on the line
m = [tex]\frac{1-4}{2-1}[/tex] = [tex]\frac{-3}{1}[/tex] = - 3 → A
15. A canoe leaves shore with a direction of
55° and paddles at a constant speed of 2
miles per hour. There is a 1 mile per hour
current moving due east. Which vector
can be used to find the approximate
actual speed and direction of the canoe?
Well that’s it for today I just wanna was a really good day I wanna
To find the actual speed and direction of the canoe, we can add the velocity of the canoe relative to the water to the velocity of the current. Using vector addition, the approximate resultant velocity of the canoe is 2.19 miles per hour at an angle of 51.3° relative to the shore.
Explanation:To find the approximate actual speed and direction of the canoe, we can use vector addition. The canoe's velocity relative to the water is 2 miles per hour in the direction of 55°. The velocity of the current is 1 mile per hour due east. We can add these two vectors to find the resultant vector, which represents the total velocity of the canoe relative to the shore.
Using the formula for vector addition, we can find the magnitude and direction of the resultant velocity. The magnitude can be found using the Pythagorean theorem: Vtotal = √(Vcanoe)2 + (Vcurrent)2. The direction can be found using the tangent function: θ = tan-1(y/x), where y is the vertical component of the resultant vector and x is the horizontal component.
In this case, the resultant velocity of the canoe will be approximately 2.19 miles per hour (rounded to two decimal places) and the canoe will move in a direction of 51.3° (rounded to one decimal place) relative to the shore.
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Need help with this problem please !
Answer: The smallest angle x is 75.5
Step-by-step explanation:
3x+x+58=360
4x=360-58
4x=302
x=302/4
x=75.5
a gardener has some apple and peach trees in his garden. he has 18 apple trees and the peach trees is 2/5 of the whole. what is the total number of trees he has?
Answer:
30
Step-by-step explanation:
If P is the number of peach trees and T is the total number of trees, then:
P = 2/5 T
P + 18 = T
If we substitute the first equation into the second:
2/5 T + 18 = T
18 = 3/5 T
T = 30
The gardener has 30 trees.
What is the sum of the first 6 terms of the series
-1+4-16+...
Answer:
819
Step-by-step explanation:
Givens
a = -1r = - 4n = 6Formula
Sum = a(1 - r^n) / ( 1 - r)
Sum = -1(1 - (-4)^6 / (1 - -4)
Sum = -1 (1 - 4096) / 5
Sum = -1 (- 4095 ) / 5
Sum = 819
a circle with center (1, 2) passes through the point (0, 6). what is the equation of the circle
The equation of the circle is (x - 1)^2 + (y - 2)^2 = 17.
Explanation:The equation of a circle can be written in the form:
(x - h)2 + (y - k)2 = r2
Where (h, k) is the center of the circle and r is the radius.
In this case, the center of the circle is (1, 2) and it passes through the point (0, 6).
So, the distance between the center and the point is equal to the radius of the circle.
Using the distance formula, we can find the radius:
r = sqrt((0 - 1)2 + (6 - 2)2) = sqrt(1 + 16) = sqrt(17)
Therefore, the equation of the circle is:
(x - 1)2 + (y - 2)2 = 17
You can rent time on computers at the local copy center for a $6 setup charge and an additional $5.50 for every 10 minutes. How much time can be rented for $21?
Answer:
If 10 minutes block, then it can be rented for 20 minutes. If no blocks, then 27.27 minutes
Step-by-step explanation:
Initial setup cost is $6.
Every 10 minutes, $5.5 is charges, so each minute [tex]\frac{5.5}{10}=0.55[/tex] is charged.
Let time used be t, so we can set up an equation as:
21 = 6 + 0.55t
Where t is in minutes
we solve for t to find out how many minutes we can rent for $21:
[tex]21 = 6 + 0.55t\\21-6=0.55t\\15=0.55t\\t=\frac{15}{0.55}=27.27[/tex]
since it is charged PER 10 MINUTES, so we can rent it for 10, 20 , 30 minutes etc.
WE CANNOT RENT FOR 30 minutes as we dont have enough money (only for fractional amount of a little over 27 minutes). Thus, we will have to have some money left over and rent for 20 minutes.
For $21, you can rent approximately 20 minutes of time at the local copy center when there's a $6 setup charge and each 10-minute period costs an additional $5.50.
Explanation:The question is asking how much time can be rented for $21 at a local copy center, where there's a $6 setup charge and an additional $5.50 for every 10 minutes. To figure this out, we first need to subtract the setup charge from the total amount of money that can be spent. So, $21 - $6 = $15. Next, we need to see how many 10 minute increments can be rented with $15. Since each 10 minute increment costs $5.50, we divide $15 by $5.50 to get approximately 2.72. Since we can't rent time in fractions of a minute, we round this down to 2. Therefore, we can rent about 20 minutes of time for $21.
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Find the volume in terms of pi
Answer:
450pi
Step-by-step explanation:
The volume of this figure is just the sum of the volumes of two cones. They both have radius of 5 and one has a height of 7 and the other has a height of 11.
The easiest way (for me) to calculate the volume is to find the average of the heights (9) and multiply the volume of a cone with the same radius as the other two and the other height by two.
The volume for a cone is just (pi*r^2*h)/3, so the 'average' cone's volume is 25pi * 9/3 or 75pi.
Double this to get 150pi.
Alternatively, you could calculate the volumes of the two cones using separate heights, but here you will end up with non-whole numbers (times pi) for both cones if you use that method.
Answer:
471.24 in³
Step-by-step explanation:
Volume of the left cone
= 1/3 π (5)²(7)
= 175π/3 in³
Volume of the right cone
= 1/3 π(5)²(11)
= 275π/3 in³
Total volume
= 175π/3 + 275π/3
= 150π
= 471.24 in³