Solve for x. − 6 ≥ 10 − 8x.
Answer:
2</x or x>/2
Step-by-step explanation:
-6>/10-8x
-10 -10
-16>/-8x
divide both sides by -8
2</x or x>/2
the reason the sign is bc u r dividing by a - number.
Answer:
x ≥ 2
Step-by-step explanation:
-6 ≥ 10 - 8x
Subtract 10 on both parts.
-6 - 10 ≥ 10 - 8x - 10
-16 ≥ -8x
Divide both parts by -8 remembering to reverse sign.
-16/-8 ≤ (-8x)/-8
2 ≤ x
Switch parts.
x ≥ 2
Help me with 2a and 2b please
Answer:
Step-by-step explanation:
A∩B={x| x∈a and x∈B}
a) A∩B={4,6}
b) A∩B={ 4,9}
c) A∩B={yellow,green}
If a football player passes a football from 4 feet off the ground with an initial velocity of 36 feet per second, how long will it take the football to hit the ground? Use the equation h = −16t2 + 6t + 4. Round your answer to the nearest hundredth.
Answer:
0.723 seconds
Step-by-step explanation:
Let h = 0
0 = -16t² + 6t + 4
Let’s solve by completing the square.
Subtract 4 from both sides.
-4 = -16t² + 6t
Since the coefficient of -16t² is -16, divide both sides by -16.
1/4 = t² - 3/8t
The coefficient of (-3)/8t is (-3)/8. Let b=(-3)/8.
Then we need to add (b/2)² = 9/256 to both sides to complete the square.
Add 9/256 to both sides.
73/256 = t² - 3/8t + 9/256
Factor right side.
73/255 = (t-3/16)²
Take the square root on both sides.
±√(73/255) = t-3/16
Add 3/16 to both sides.
3/16 ± √(73/255) = t
The answer has to be positive, not negative.
0.72254626884 = t
0.723 ≈ t
Answer:
Rounding to the nearest hundredth, it is 0.72
A prism has a volume of 405 cubic inches. A prism has a length of 15 inches, height of h, and width of 4.5 inches. Which is the correct substitution for finding the height of the prism? V = l w h. 405 = 15 + 4.5 + h. V = l w h = 15 times 4.5 times 405 V = l w h = 15 times 4.5 times 15 V = l w h. 405 = 15 times 4.5 times h
Answer:
d) 405 = 15 times 4.5 times h
The height of the prism 'h' = 6 inches
Step-by-step explanation:
Explanation:-
Given Volume of prism
V = 405 cubic inches
Given length of the prism
L = 15 inches
Given width of the prism
W = 4.5 inches
The volume of the prism
V = l w h
405 = 15 ×4.5× h
405 = 67.5 h
Dividing '67.5' on both sides , we get
h = 6 inches
Final answer:-
The height of the prism 'h' = 6 inches
Answer: V = l w h. 405 = 15 times 4.5 times h
Step-by-step explanation:
Given the following :
Volume of prism = 405 in^3
Length = 15 inches
Height = h
Width = 4.5 inches
Recall :
The volume of a prism is the product of the Base and the height.
That is;
Volume = Base × height
However, Base of prism is given by the area of the base shape of the prism.
From our parameters Base shape of the prism is a rectangle.
Therefore, Area of rectangle = Length × width
= 15 inches × 4.5 inches = 67.5 inch^2 = Base of prism
Therefore, Volume of prism equals ;
Volume = 15 × 4.5 × h
Volume = 405in^3
Volume = Base × height
405 = 15 × 4.5 × h
The circumference of a circular field is 285.74 yards. What is the diameter of the field? Use 3.14 for it and do not round your answer.
yards
x
?
Answer:
The diameter is 91.
Step-by-step explanation:
The formula for circumference is 2*pi*radius(you can use circumference = diameter*pi too). Plug 285.74 into it. Divide both sides by 3.14, and you get 2*radius(aka the diameter) = 91
Answer:
91 yards
Step-by-step explanation:
The circumference of a circle can be found using the following formula:
c=π * d
We know that the circumference is 285.74 yards and we are using 3.14 for pi. Substitute 285.74 in for c and 3.14 for pi.
285.74= 3.14 *d
We want to find the diameter. Therefore, we need to get the variable d by itself. d is being multiplied by 3.14 The inverse of multiplication is division. Divide both sides of the equation by 3.14
285.74/3.14= 3.14*d/3.14
285.74/3.14=d
Divide
91=d
d= 91 yards
The diameter of the field is 91 yards.
Tom brown decided to purchase a new bike on an installment loan.The bike was $300.00He agreed to pay $30 a month for 12 months . What is the finance charge in dollars
Answer:
The answer is $60. $30 × 12 = $360 – $300 = $60.
Step-by-step explanation:
△ABC is an isosceles triangle with legs AB and AC. △AYX is also an isosceles triangle with legs AY and AX. Triangle A Y X is shown. Line segment B C is drawn from side A Y to A X to form triangle A B C. The proof that △ABC ~ △AYX is shown. Statements Reasons 1. △ABC is isosceles with legs AB and AC; △AYX is also isosceles with legs AY and AX. 1. given 2. AB ≅ AC and AY ≅ AX 2. definition of isosceles triangle 3. AB = AC and AY = AX 3. definition of congruency 4. AY • AC = AX • AC 4. multiplication property of equality 5. AY • AC = AX • AB 5. substitution property of equality 6. 6. division property of equality 7. 7. division property of equality 8. ? 8. ? 9. △ABC ~ △AYX 9. SAS similarity theorem Which statement and reason are missing in the proof?
Explanation:
Here is our take on the proof shown in the problem statement. The missing statements and reasons are shown in bold.
Statements Reasons
1. △ABC is isosceles with legs AB and AC; △AYX is also isosceles with legs AY and AX. 1. given
2. AB ≅ AC and AY ≅ AX 2. definition of isosceles triangle
3. AB = AC and AY = AX 3. definition of congruency
4. AY • AC = AX • AC 4. multiplication property of equality
5. AY • AC = AX • AB 5. substitution property of equality
6. AY • AC/AX = AB 6. division property of equality
7. AC/AX = AB/AY 7. division property of equality
8. Corresponding sides are proportional 8. Definition of proportional
9. △ABC ~ △AYX 9. SAS similarity theorem
_____
The reason given in statements 6 and 7 suggest you need to divide something. For SAS similarity, you need to show corresponding sides are proportional. The missing steps are to get to the point where you can say that.
Answer:
I think its A. ∠A ≅ ∠A; reflexive property
Step-by-step explanation:
Can anyone please explain
what a function mean? (in maths:graph,etc) i haven't learnt this but it might be useful for future references
Answer:
For example, the position of a planet is a function of time. ... A function is a process or a relation that associates each element x of a set X, the domain of the function, to a single element y of another set Y (possibly the same set), the codomain of the function.
Step-by-step explanation:
Select the correct answer.
Use the power of a product property to answer the question.
Which expression equals (
Answer:
7^1/3 * y^1/3
Step-by-step explanation:
(7y) ^ 1/3
We know that (ab) ^c = a^c * b^c
7^1/3 * y^1/3
Answer:
7^1/3 * y^1/3
Step-by-step explanation:
7^1/3 * y^1/3
The graph of the parent function f(x) = x3 is translated to form the graph of g(x) = (x − 4)3 − 7. The point (0, 0) on the graph of f(x) corresponds to which point on the graph of g(x)?
Answer:
The point (0, 0) in the graph of f(x) corresponds to the point (4, -7) in the graph of g(x)
Step-by-step explanation:
Notice that when we start with the function [tex]f(x)=x^3[/tex], and then transform it into the function: [tex]g(x)=(x-4)^3-7[/tex]
what we have done is to translate the graph of the function horizontally 4 units to the right (via subtracting 4 from the variable x), and 7 units vertically down (via subtracting 7 to the full functional expression).
Therefore, the point (0, 0) in the first function, will now appeared translated 4 units to the right (from x = 0 to x = 4) and 7 units down (from y = 0 to y = -7).
then the point (0, 0) after the translation becomes: (4, -7)
Answer:4, -7
Step-by-step explanation:
A study of an association between which ear is used for cell phone calls and whether the subject is left-handed or right-handed began with a survey e-mailed to 5000 people belonging to an otology online group, and 717 surveys were returned. (Otology relates to the ear and hearing.) What percentage of the 5000 surveys were returned? Does that response rate appear to be low? In general, what is a problem with a very low response rate? Of the 5000 surveys, nothing% were returned. This response rate ▼ appears does not appear to be low.
Answer:
Of the 5000 surveys, 14% were returned. This response rate APPEARS to be low.
Step-by-step explanation:
Given:
Total sample collected = 5000
Survey returned = 700
i) What percentage of the 5000 surveys were returned?
To find percentage returned, we have:
[tex] = \frac{700}{5000} * 100 = 14 percent [/tex]
Percentage returned = 14%
ii) Does that response rate appear to be low?
Yes, the response is significantly low as only 14% is returned out of expected 100%
iii) In general, what is a problem with a very low response rate?
The problem with in low response rate in general is that it causes the result to be biased as biased samples of those interested in a particular aspect may have been gotten.
Therefore, of the 5000 surveys, 14% were returned. This response rate APPEARS to be low.
PLLLLLLLLLLLLLLLEEEEEEEEEAAAAAAAASSSSSSSE HEEEEEEEEELP As soon as a new car that costs $25,000 is driven off the lot, it begins to depreciate at a rate of 24.9% annually. About how much money is the car worth after the second year?
Answer:
The value of the car after two years is $14,100.025
Step-by-step explanation:
Here, we want to calculate the value of a car after its second year, given the depreciation percentage.
To get the value of the car year after year at the fixed percentage level, what we do is to set up an exponential equation;
V = I(1-r)^t
where V is the present value
I is the initial value = $25,000
r is the rate = 24.9% = 24.9/100 = 0.249
t is the number of years = 2 in this case
So we substitute these values in the depreciation case and have;
V = 25000(1-0.249)^2
V = 25000(0.751)^2
V = $14,100.025
Find the area of the composite figure in square mm. Round your
answer to the nearest square milimeter. (Enter only a number as
your answer.)
Answer:
521
Step-by-step explanation:
Composite figure.
Draw a straight down from C to line segment AB. This forms a triangle.
Now, the area of this figure=
Area of semicircle+area of rectangle+ area of triangle.
Rectangle area formula = l times w
Length - 20
Width =14
14 times 20 = 280
Area of rectangle = 280
Semicircle area = area of circle/2
Area of circle = π[tex]r^2[/tex]
Diameter =20= 2r
r=10
π[tex]r^2[/tex]= π 10^2 =100π
100 times 3.14 =314
314/2 = 157
Area of semicircle = 157
Area of triangle= bh/2
Triangle's base= 32-20=12
Triangles height = 14
14 times 12 = 168
168/2 = 84
Area of triangle: 84
Area of semicircle+area of rectangle+ area of triangle.
157+280+84 =521
1. A car bought for $20,000. Its value depreciates by 10% each year for 3 years. What is the car's worth after3 years?
2. Find the perimeter of a circle whose radius is 3.5cm. (Take pi = 22/7)
3. The volume of a cone is 1540cm³. If its radius is 7cm, calculate the height of the cone. (Take pi = 22/7)
4. What is the coefficient of b in the expression b² - 5b +18
5. Expand (x +2) (9 - x)
7. Find x and y in the simultaneous equations. x + y = 4 3x + y = 8
8. Factorize a² +3ab - 5ab - 15b²
9. The bearing of a staff room from the assembly ground is 195degrees, what is the bearing of the assembly ground from the staff room?
Step-by-step explanation:
68$53++83(-$(7(3($++$
Which of the following expressions are equivalent to -9/6?
the correct answer is:
A. 9/-6
Please can someone help!
Answer:
51 mph
Step-by-step explanation:
→ The first thing we need is a formula which links speed, distance and time so,
Speed = Distance ÷ Time
Speed = mph
Distance = metres/miles
Time = hours
→ Since we want to work out the average speed of the entire journey we need to first work out the total distance and total time. Using the first sentence of the paragraph, it says that the car travels at an average speed of 45 mph for 40 minutes, we can rearrange the formula to work out the distance so,
Speed = Distance ÷ Time
→ Rearrange to get distance as subject
Distance = Speed × Time
→ Substitute in the values
Distance = 45 × 40
→ Remember that the time is hours but we substituted in minutes so we divide the time value by 60
40 ÷ 60 = 0.666666667
→ Substitute in the time value multiplied by the speed
Distance = 45 × 0.666666667 = 30
⇒ 30 metres/miles is overall distance for the first part of the journey
→ Now we have to work out the distance for the second part of the journey. State the distance formula.
Distance = Speed × Time
→ Substitute in the values into the distance formula
Distance = 60 × 25
→ Remember that the time is hours but we substituted in minutes so we divide the time value by 60
25 ÷ 60 = 0.416666667
→ Substitute in the time value multiplied by the speed
Distance = 60 × 0.416666667 = 25
⇒ 25 metres/miles is overall distance for the second part of the journey
→ Now we have to add the distance of both the journeys together
25 + 30 = 55
→ Then we add the times of the journey together
40 minutes + 25 minutes = 65 minutes
→ Convert 65 minutes into hours
65 ÷ 60 = 1.08333 hours
→ Substitute both values into the speed = distance ÷ time formula
Speed = 55 ÷ 1.08333 = 50.76923077
→ The question says to round it to the nearest whole number so,
50.76923077 = 51 mph
What is the sum of the measures, in degrees, of the interior angles of an 18-
sided polygon?
A. 2880
B. 3600
C. 3240
D. 3060
Answer:
Option (D)
Step-by-step explanation:
Sum of interior angles of a polygon is represented by the expression,
Sum of interior angles = n(n - 1)×180°
Here n is the number of sides of a polygon
If n = 18,
Sum of 18 sided polygon = (18 - 1) × 180°
= 7 × 180°
= 3060°
Therefore, sum of interior angles of a 18 sided polygon will be 3060°.
Option (D) will be the answer.
Answer:
2880
Step-by-step explanation:
SUM=_-2=
18-2=16
16*180 = 2880 OR
18*160 = 2880 degrees
What are two integers whose sum is -2 and product is -80?
Answer:
We can write:
x + y = -2
xy = -80
We can rewrite the first equation as x = -y - 2 and then plug that into the second equation to get (-y-2) * y = -80 → -y² - 2y = -80 → y² + 2y - 80 = 0 → (y - 8)(y + 10) = 0 → y = 8, -10. Substituting these values into the first equation we get x = -10, 8 so the answer is (x₁, y₁) = (-10, 8) or (x₂, y₂) = (8, -10).
The windows of a downtown office building are arranged so that each floor has 6 fewer windows than the floor below. If the ground floor has 52 windows, how many windows are on the 8th floor?
Answer:
10
Step-by-step explanation:
This is an arithmetic sequence. The common difference is -6, and the first term is 52.
a = 52 − 6(n − 1)
When n = 8:
a = 52 − 6(8 − 1)
a = 52 − 42
a = 10
What is the solution to this equation?
4x-3 + 2x= 33
O A. x= 15
B. x = 18
O c. x = 5
O D. x = 6
Answer:
4x – 3 + 2x = 33
6x = 36
x = 6
D. x = 6
Write the expression in standard form. -3 + yi = x + 6i
Answer:
The expression in standard form is -3 + 6i
Step-by-step explanation:
Writing complex equation in standard form we have;
-3 + yi = x + 6i
We transfer the real and imaginary parts to be on different sides of the equation as follows;
yi - 6i = x + 3
We factorize the imaginary part;
i(y-6) = x + 3
We note that the real portion on the left hand side of the equation is zero, therefore, we have;
i(y-6) + 0= x + 3
x + 3 = 0
Therefore, x = -3
Substituting the value of x in the first equation, we have;
-3 + yi = -3 + 6i
Comparing gives;
y = 6
The expression in standard form is -3 + 6i.
What is the slope of the line that passes through the points (-3,2) and (6, -9)?
Answer:
-11/9 is the slope
Step-by-step explanation:
Use the formula and u will find this is the answer, hope this helped!
Y2 - Y1 / X2 - X1
(-9 - 2) / (6 - (-3))
<!> Brainliest is appreciated!
Answer:
-11/9
Step-by-step explanation:
In order to find the slope from 2 points, use the following formula: [tex]m=\frac{y_{2} - y_{1} }{x_{2}-x_{1} }[/tex]
Plug in each of the numbers into their corresponding areas. Basically, we are subtracting the y values together and dividing it with the difference of the x values:
[tex]\frac{-9-2}{6-(-3)}[/tex]
The negatives cancel out and become postive, so the denominator will then read to be 6+3:
[tex]\frac{-9-2}{6+3}[/tex]
[tex]-\frac{11}{9}[/tex]
The graph of f(x) =7x is reflected across the x-axis. write a function g(x) to describe the new graph. G(x)=___
To reflect a function across the x axis, we just stick a negative in front. This will make all point's y coordinates to go from positive to negative or vice versa. If the original function already has a negative out front, then remove it.
Please help urgently
Answer:
203.5Solution,
Onions less than 60 grams = 2 --> Pickling
Onions greater than 120 grams = 5 + 3 = 8 --> Market
Onions between 60 and 120 = 13---> Processing
Total frequency = 2 + 8 + 13 = 23
Now,
[tex]x = \frac{13}{23} \times 360[/tex]
[tex]x = 203.48[/tex]
[tex]x = 203.5[/tex]
Hope this helps ..
Good luck on your assignment...
Answer:
x=190°
Step-by-step explanation:
find the frequency of the given numbers dividing by their numbers
onions less than 60g=(2+2/2)=²/9
onions greater than 120g=(5+3/2)= 4 (4+3/2). =3.5/9
To convert into degrees so that they can fit in the bar graph multiply the frequencies by 360 that is:
picking=²/9×360=80°
market=3.5/9×360=90°
x=360°-90°-80°
x=190°
confirmation
pie chart° add up to 360°
picking=80°
market=90°
x=190°
190°+80°+90°=360°
the cube of the difference of 4 times x and 6 divided by 2 times the sum of x and 1
4(1 - 6)2
25 + 1
(41 – 6)
2(1 + 1)
413 - 6
2(1 + 1)
(41 - 6)
21 + 1
Answer:
[tex]\dfrac{(4x-6)^3}{2}(x+1)[/tex]
Step-by-step explanation:
Maybe you want your verbiage written as a mathematical expression.
"the difference of 4 times x and 6" is (4x -6). "the sum of x and 1" is (x+1).
No other grouping is indicated, so we have ...
[tex]\boxed{\dfrac{(4x-6)^3}{2}(x+1)}[/tex]
A item in a shop is increased in price by 20% and then decreased in price by 20% a month later.
Is there an overall increase or
decrease in price and by how
much?
please give the method too
Answer:
Decrease of 4% ($4).
Step-by-step explanation:
Suppose the initial price was $100. An increase of 20% will make the price $120.
Now we decrease it 20% which brings it to 120 - 0.20 * 120
= 120 - 24
= $96.
So that's an overall decrease of $4 or 4%.
D. Is no solution please help
Answer:
B
Step-by-step explanation:
I can't really see the problem, however I believe B is the only one that shows an infinite number of solutions.
Answer:
B
Step-by-step explanation:
It is too blurry BTW but B is correct
Find the pattern and fill in the missing numbers: 0, …, 9, 18, 30, 45, ...
it is 9
and it is also 54
Answer:
3 and 63.
Step-by-step explanation:
The sequence formula is [tex]\frac{3n(n+1)}{2}[/tex].
Resulting in a sequence of 0, 3, 9, 18, 30, 45, 63.
What is the solution to this equation?
4x + 2(x + 6) = 36
O A. x = 7
B. x = 5
O c. x = 4
D. x = 8
Simplifying
4x + 2(x + 6) = 36
Reorder the terms:
4x + 2(6 + x) = 36
4x + (6 * 2 + x * 2) = 36
4x + (12 + 2x) = 36
Reorder the terms:
12 + 4x + 2x = 36
Combine like terms: 4x + 2x = 6x
12 + 6x = 36
Solving
12 + 6x = 36
Solving for variable 'x'.
Move all terms containing x to the left, all other terms to the right.
Add '-12' to each side of the equation.
12 + -12 + 6x = 36 + -12
Combine like terms: 12 + -12 = 0
0 + 6x = 36 + -12
6x = 36 + -12
Combine like terms: 36 + -12 = 24
6x = 24
Divide each side by '6'.
x = 4
Simplifying
x = 4
If a toy rocket is launched vertically upward from ground level with an initial velocity of 120 feet per second, then its height h after t seconds is given by the equation h(t) = -16t^2 + 120t. How long will it take the rocket to return to the ground? Group of answer choices
Answer:
[tex]Time = 7.5\ seconds[/tex]
Step-by-step explanation:
Given
[tex]Equation:\ h(t) = -16t^2 + 120t[/tex]
[tex]Initial\ Velocity = 160ft/s[/tex]
Required:
Determine the time taken to return to the ground
From the equation given; height (h) is a function of time (t)
When the rocket returns to the ground level, h(t) = 0
Substitute 0 for h(t) in the given equation
[tex]h(t) = -16t^2 + 120t[/tex]
becomes
[tex]0 = -16t^2 + 120t[/tex]
Solve for t in the above equation
[tex]-16t^2 + 120t = 0[/tex]
Factorize the above expression
[tex]-4t(4t - 30) = 0[/tex]
Split the expression to 2
[tex]-4t = 0\ or\ 4t - 30 = 0[/tex]
Solving the first expression
[tex]-4t = 0[/tex]
Divide both sides by -4
[tex]\frac{-4t}{-4} = \frac{0}{-4}[/tex]
[tex]t = \frac{0}{-4}[/tex]
[tex]t =0[/tex]
Solving the second expression
[tex]4t - 30 = 0[/tex]
Add 30 to both sides
[tex]4t - 30+30 = 0+30[/tex]
[tex]4t = 30[/tex]
Divide both sides by 4
[tex]\frac{4t}{4} = \frac{30}{4}[/tex]
[tex]t = \frac{30}{4}[/tex]
[tex]t = 7.5[/tex]
Hence, the values of t are:
[tex]t =0[/tex] and [tex]t = 7.5[/tex]
[tex]t =0[/tex] shows the time before the launching the rocket
while
[tex]t = 7.5[/tex] shows the time after the rocket returns to the floor