Answer:
a. [tex]T = 17s[/tex]
b. [tex]D = 72cm[/tex]
Step-by-step explanation:
Given
Direct Variation
[tex]Distance(D)\ \alpha\ Time (T)[/tex]
D = 264 cm when T = 11 s
Calculating (a)
First, the constant of variation (k) as to be calculated;
Since, there exist a direct proportion; then,
[tex]D\ \alpha\ T[/tex]
[tex]D = kT[/tex]
Make k the subject of formula
[tex]k = \frac{D}{T}[/tex]
D = 264 cm when T = 11 s; So
[tex]k = \frac{264}{11}[/tex]
[tex]k = 24[/tex]
So: Solving for (a)
[tex]D = 408[/tex]
Substitute 408 for D and 24 for k in [tex]D = kT[/tex]
[tex]408 = 24 * T[/tex]
Divide both sides by 24
[tex]\frac{408}{24} = T[/tex]
[tex]T = \frac{408}{24}[/tex]
[tex]T = 17s[/tex]
Hence, time to move a distance of 408cm is 17s
Calculating (b)
[tex]T = 3[/tex]
Substitute 3 for T and 24 for k in [tex]D = kT[/tex]
[tex]D = 24 * 3[/tex]
[tex]D = 72cm[/tex]
Hence, distance covered in 3 seconds is 72cm
The university bought a total of 2200 computers they bought three kinds of computers HP IBM and dell the ratio of the number of HP computers to IBM to dell is 2/3 and 6 each HP computer cost $750 each. Computer cost 90% of the price of the HP computer if the university spent a total 1650000 what is the cost of each IBM computer
Complete question :
The University but a total of 2200 computers they bought three kinds of computers HP, IBM and dell. The ratio of theNumber of HP computers to IBM to dell is 2:3:6 each HP computer cost $750 each dell computer cost 90% of the price of an HP computer if the University spent a total of $1,650,000 what is the total cost of each IBM computer
Answer:
$900
Step-by-step explanation:
Given that :
Total amount of computers purchased = 2200
Number of brands purchased = 3;
HP, IBM and DELL
The ratio of theNumber of HP computers to IBM to dell is 2:3:6
Cost per HP = $750
Cost per Dell = 90% of HP = 0.9 × $750 = $675
Total amount spent = $1,650,000
2:3:6 = (2+3+6) = 11
Number of IBM computers purchased :
(3/11) * 2200 = 600 IBM
(2/11) * 2200 = 400 HP
(6/11) * 2200 = 1200 DELL
TOTAL Cost of HP = (400 × $750) = $300,000
TOTAL cost of Dell = (1200 * $675) = $810,000
TOTAL cost of IBM :
$1,650,000 - ($300,000 + $810,000)
$1,650,000 - $1,110,000 = $540,000
Cost of each IBM:
540,000 / 600 = $900
I need help on how to explain my answer.
Answer:
(1,-1)
Step-by-step explanation:
(1,-1) because if you subtract 5-6 you get -1 and 2-1 you get 1.
Answer:
if F where to move down 6 points then it would be 2, -1.
then if it where to move left 1 unit the coordinants for F prime would be
(1, -1)
A particle is thrown vertically upwards with velocity 20 metre per second find a the distance travelled by the particle in first 3 second and displacement of the particle in 3 seconds
Step-by-step explanation:
[tex]\huge\underline\bold\blue{ƛƝƧƜЄƦ}[/tex]
[tex]\huge\underline\bold\green{Gïvëñ}[/tex]
[tex]\small\underline\bold\red{ v=0}[/tex]
[tex]\small\underline\bold\blue{ v = u+gt}[/tex]
[tex]\small\underline\bold\blue{0=20-10t}[/tex]
[tex]\small\underline\bold\blue{t = 2 sec}[/tex]
[tex]\huge\underline\bold\yellow{distance in first 2 second }[/tex]
s = s(t=0 to 2 second) + s(2second to 3 second)
s = (ut+1\2(at)^2+ (ut+1\2at^2)
s = 20×2-1\2×10×4+1\2×10×1
s = 25
[tex]\huge\underline\bold\blue{Displacement}[/tex]
s = 20 - 5 = 15
Hope it helps
A cabinet is 6 feet high, 3 feet wide and 2 feet long. The entire outside of the cabinet is being painted, except for the bottom. What is the surface area being painted?
Answer:
66ft²Step-by-step explanation:
The cabinet is rectangular shaped. Using the formula for calculating the surface area of a reactangular bos to solve the problem.
Surface area = 2(LW+WH+LH) where;
L is the length of the cabinet
W is the width of the cabinet
H is the height of the cabinet.
If the entire outside of the cabinet is being painted, except for the bottom, then the surface area of the painted area will be expressed as;
S = LW+2WH+2LH
Given L = 2 feet, W = 3 feet and H = 6 feet
S = 2(3)+2(3*6)+2(2*6)
S = 6+2(18)+2(12)
S = 6+36+24
S = 66 feet²
Hence the surface area of the painted part is 66ft²
It costs 4.75 for a pack of 25 pencils. Find the unit price in dollars per pencil. If necessary, round your answer to the nearest cent.
Answer:
0.19
Step-by-step explanation:
the easiest way to solve for this is 4.75/25 (division). This is assuming I read this right and your asking the price of each individual pencil
0.19 dollars is the unit price.
As we can see that a pack of 25 pencils costs 4.75 dollars
So the cost for 1 pencil would be 4.75/25
=0.19
What does the pack mean?A group of friends or a group of something
What is a pack example?An example of to pack is putting collectibles in a box to be stored away. An example of to pack is putting your child's lunch in a lunch box for them to take to school.
An example of to pack is placing what you'll need for a weekend trip in a piece of luggage.
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.
Solve 2x^2+16x+34=0?????
Answer:
2([tex]x^{2}[/tex]+8x+17)
Step-by-step explanation:
Factor out 2 of the equation.
Answer:
For real numbers: no solution
For complex numbers: [tex] x = -4 \pm 4i [/tex]
Step-by-step explanation:
2x^2 + 16x + 34 = 0
Divide both sides by 2.
x^2 + 8x + 17 = 0
There are no two numbers whose product is 17 and whose sum is 8, so this polynomial is not factorable.
We can use the quadratic formula.
[tex] x = \dfrac{-b \pm \sqrt{b^2 - 4ac}}{2a} [/tex]
We have a = 1; b = 8; c = 17
[tex] x = \dfrac{-8 \pm \sqrt{8^2 - 4(1)(17)}}{2(1)} [/tex]
[tex] x = \dfrac{-8 \pm \sqrt{64 - 68}}{2} [/tex]
[tex] x = \dfrac{-8 \pm \sqrt{-64}}{2} [/tex]
If you have not learned imaginary or complex numbers, stop here. Since the discriminant is negative, there is no real solution.
If you have learned complex numbers, then we continue.
[tex] x = \dfrac{-8 \pm 8i}{2} [/tex]
[tex] x = -4 \pm 4i [/tex]
is 8.3 greater than 83 tenths?
Answer:
NO
Step-by-step explanation:
They are equal
83 tenths divided by 10 is 8.3
Hope this helps :-)
Joe earned $10 in allowance this week and $2 for each extra chore he did. Let (c) represent the number of extra chores Joe did this week. Which of the following expressions best represents Joe's income for the week? a. 10 + 2c b. 10 + 2 c. 10 + c + 2 d. 10c + 2
Answer:
10 + 2c (i think)
Step-by-step explanation:
You do the $10 for his cores plus $2x The Amount of extra chores he did
Find the area of the shape.
Your question has been heard loud and clear.
Alright , so basically , the area of a circle formula = pi * R squared
R = radius = 4 units
Pi = 3.14
So , Area = 3.14 into 4 = 12.56 units
So Area of the circle = 12.56 units
Thank you
Answer:
The area is 50.24
Step-by-step explanation:
Here is the equation to find the area of a circle (π=3.14):
A=πr²
A=3.14·4²
A=3.14·16
A=50.24
Which of the following statements is true?
A) Two similar triangles must be congruent.
B) Two congruent triangles must be similar.
C) Two triangles having ye same area must be congruent.
D) Two triangles having the same perimeter must be similar.
Answer:
A or C
Step-by-step explanation:
Look at this graph:
What is the slope?
Simplify your answer and write it as a proper fraction, improper fraction, or integer.
Answer: 1/3
Step-by-step explanation:
Two points on this graph are (40, 80) and (70, 90). These points can be used to find the slope. The formula for slope is (y2-y1)/(x2-x1).Plugging our numbers into the formula: (80-90)/(40-70) = (-10)/(-30) = 1/33 and one half times two eleventh’s divided by two and one third times eleven equals...
Convert the following to standard notation.
1.5 x 10
Answer:
15
Step-by-step explanation:
1.5*10 =15
Answer:
15.
Step-by-step explanation:
1.5 x 10 is expanded notation, so you just solve it (by multiplying) to convert it into standard notation.
Josh and David collect pecans for their mother to make a pecan pie. Josh collects 3.25 pounds of pecans, and David harvest 4 3/8 pounds. How many more pounds of pecans does David collect than Josh?
Answer:
1 1/8
Step-by-step explanation:
So the first step is to convert all of them to fractions, so 3.25 become 3 1/4
Next, we do 4 3/8- 3 1/4
We convert 1/4 to 2/8
So, it's now 4 3/8- 3 2/8
The answer is 1 1/8
1. Triangle ABC with coordinate points A(-2,3); B(-1,0); C(5,-4) is rotated 90 degrees clockwise. What
are the new image points for triangle A'B'C'?
Answer: A'(3,2), B'(0,1) and C'(-4, -5).
Step-by-step explanation:
When we rotate (a,b) 90 degrees clockwise, the new point will be (b,-a).
i.e. rotation rule for 90 degrees clockwise : (x,y) → (y,-x)
Given: Triangle ABC with coordinate points A(-2,3); B(-1,0); C(5,-4) is rotated 90 degrees clockwise.
Then, the new image points for triangle A'B'C' will be :
A(-2,3) → A'(3,-(-2)) =A'(3,2)
B(-1,0)→ B'(0,-(-1)) = B'(0,1)
C(5,-4) → C'(-4, -5)
Hence, the new image points for triangle A'B'C' are A'(3,2), B'(0,1) and C'(-4, -5).
Five times the sum of a number and 4 is -15.
number is 3.8
subtract 4 from -15 then divide by five
Please explain with working!!! Find the set of values of x that satisfy the inequality 9x^2-15x<6
Answer:
[tex]\displaystyle -\frac{1}{3} < x < 2[/tex]
Step-by-step explanation:
We want to solve the quadratic inequality:
[tex]9x^2-15x<6[/tex]
In order to solve a quadratic inequality, find its zeros. That is, let the inequality sign be an equal sign and solve for x. We do this because it denotes when the graph crosses the x-axis: that is, when it is positive and/or negative. This yields:
[tex]9x^2-15x=6[/tex]
Solve for x:
[tex]\displaystyle \begin{aligned} 9x^2-15x-6 &= 0\\ 3x^2 - 15 -6 &= 0 \\ (3x+1)(x-2) &= 0\end{aligned}[/tex]
By the Zero Product Property:
[tex]\displaystyle 3x + 1 = 0 \text{ or } x - 2 = 0[/tex]
Hence:
[tex]\displaystyle x = -\frac{1}{3}\text{ or } x = 2[/tex]
Now, we can test intervals. The three intervals are: all values less than -1/3, values between -1/3 and 2, and all values greater than 2.
To test the first interval, let x = -1. Substitute this into our original inequality:
[tex]\displaystyle \begin{aligned}9(-1)^2 -15(-1) \, &?\, 6 \\ 9+15 \, &? \, 6 \\ 24&> 6 \xmark \end{aligned}[/tex]
The resulting symbol is "greater than," which is not our desired symbol.
To test the interval between -1/3 and 2, we can let x = 0:
[tex]\displaystyle \begin{aligned} 9(0)^2 - 15(0) \, &? \, 6 \\ (0) - (0) \, &? \, 6 \\ 0 &< 6\, \checkmark\end{aligned}[/tex]
The resulting symbol is indeed less than. So, the interval (-1/3, 2) is a part of our solution.
Finally, to test the third interval, let x = 3. Then:
[tex]\displaystyle \begin{aligned} 9(3)^2 - 15(3) \, &? \, 6 \\ (81) - (45) \, &? \, 6 \\ 36 &> 6\end{aligned}[/tex]
Again, this is not our desired symbol.
In conclusion, our only solution is the interval:
[tex]\displaystyle \left(-\frac{1}{3}, 2\right)[/tex]
Or as an inequality:
[tex]\displaystyle -\frac{1}{3} < x < 2[/tex]
Write an equivalent expression for the following.
-3(ab +6ba) -(4+b)
Emma wants to know how much her dog weighs. She held her dog and stepped on the scale. Their combined weight is 118.6 pounds. Emma weighs 85.4 pounds, so how many pounds does her dog weigh?
Answer:
33.2
Step-by-step explanation:
If he pays $46.80 for one year. He receives one magazine each month for 12 months. Find the dollars he pays for each
magazine
Answer:
Each magazine costs 3.90
Step-by-step explanation:
Take the total cost and divide by the number of magazines
46.80/12
3.90
Answer:
3.90$ per magazine is paid
Given the points A(-1, 2) and B(7, 14), find the coordinates of the point P on directed line segment stack A B with bar on top that partitions stack A B with bar on top in the ratio 1:3. Show your work.
Answer:
(1, 5)
Step-by-step explanation:
The desired point is the weighted average of the end point coordinates. The weights are the reverse of the relative line segment lengths.
P = (3A +1B)(3+1) = (3(-1, 2) +(7, 14))/4 = (-3+7, 6+14)/4 = (1, 5)
The point of interest is (1, 5).
Every negative integer J is less than or equal to its inverse
Answer:
Here we have the statement:
" Every negative integer J is less than or equal to its inverse"
First, remember that when we are talking about negative numbers, the ones that are closer to 0 are the larger ones.
For example, if we have -1 and -5
-1 is closer to zero, then:
-1 > -5
Now we have a negative integer J.
The smallest negative integer is -1
it's inverse is 1/-1 = -1
Then, if j = -1:
j = 1/j
-1 = 1/-1 = -1
and if j < -1 (-2, -3, -4, -5.......)
then for example, for j = -2
1/-2 = - (1/2)
and (-1/2) is a number between -1 and 0
So it is closer to zero than -2
then:
(-1/2) > -2.
Then, concludin, if IjI > 1, we have always that 0 > 1/j > -1 > j.
12. What value of c would make x = 4 in the
equation 5 + cx = 13 ?
Using the graph provided, find f(x)=2
Answer:
so x=3
Step-by-step explanation:
f(x) = 2
We want to find the x value when y =2
Going across where y = 2
Then go down to find the x value x=3 when y = 2
f(3) =2
so x=3
HELP PLZ WILL GIVE BRAINLIEST
Answer:
x = 31 °
Step-by-step explanation:
90 = 58 + x
x = 90 - 58
x = 31 °
Answer:
x° = 32°
Step-by-step explanation:
∠BAC = ∠IAK = 58° (Vertically opposite angles)
∠GCJ = ∠ACB = x° (Vertically opposite angles)
Angles of a Δ ABC = 180°
Δ ABC = 90° + 58° + x° = 180°
⇒x° = 180° - 90° - 58 °
⇒x° = 32°
Find an equation of the line that passes through the given point and has the indicated slope m.
Answer:
y = -5.5
Step-by-step explanation:
The only lines that have a slope of 0 are horizontal lines. Horizontal lines are always in the form y = c where c is a constant. Basically, on a horizontal line, no matter what x is, y will always be the constant c. Therefore, the x coordinate of our given point does not matter and we only have to look a the y-coordinate, which is -5.5. Therefore, the equation is y = -5.5.
1.25+3/4+4/10+2 x 3/8+ 1.6
Answer:
(3x/4) + 4
Step-by-step explanation:
convert al to decimal and then add
1.25 + 0.75 +0 .4 + 2x 0.375 + 1.6
90 POINTS PLEASE HELP Choose one problem below and use trigonometry to solve for the missing side x of the right triangle
Answer:
x = 13.28
Step-by-step explanation:
basic trig ratios: using tanФ = opp/adj.
tan(38) = x / 17
x = tan(38) * 17
x = 13.28
to get more idea of the subject, read below:
The cotangent (cot)
The cotangent is the reciprocal of the tangent. It is the ratio of the adjacent side to the opposite side in a right triangle.
tan(A) = opp/adj = a/b
cot(A) =adj/opp = b/c
Answer:
[tex]\Huge \boxed{x \approx 13.28}[/tex]
[tex]\rule[225]{225}{2}[/tex]
Step-by-step explanation:
The triangle is a right triangle.
We can use trig functions to solve for the problem.
[tex]\sf \displaystyle tan (\theta)=\frac{opposite}{adjacent}[/tex]
[tex]\sf \displaystyle tan (38)=\frac{x}{17}[/tex]
Multiplying both sides by 17.
[tex]\sf \displaystyle 17 \cdot tan (38)=\frac{x}{17} \cdot 17[/tex]
[tex]\sf x= 13.28185565...[/tex]
The measure of x is approximately 13.28.
[tex]\rule[225]{225}{2}[/tex]
k squared - 13k+36
[tex]18n + 20n - 378[/tex]
Answer:
k^2-13+36
38n-378
Step-by-step explanation:
k^2-13k+36
k^2-13+36
The above expression can't be simplified further because they are not like terms.
18n+20n-378
38n-378
Hope this helped ;) ❤❤❤
Sue buys a certain brand of cereal that costs $12 per box. Sue changes to a super-saving brand of the same size. The equation shows the price, y, as a function of the number of boxes, x, for the new brand. y = 8x Part A: How many more dollars is the price of a box of Sue's original brand of cereal than the price of a box of the super-saving brand? Show your work. Part B: How much money does Sue save each month with the change in cereal brand if she buys 4 cereal boxes each month? Show your work. (10 points) PLEASEEEEEE help
Answer:
part A : $4
part B : $16
Sue buys a certain brand of cereal that costs = $12 per box.
She changes to a super-saving brand of the same size.
The equation showing price y as a function of the number of boxes, x is for the new brand.
y = 8x
for x = 1, y = 8
So for 1 box super-saver cereal brand costs $8.00
Part A. - So saving per box = 12 - 8 = $4
Part B. - Money saved in 1 box = $4
Therefore, money saved in 4 boxes = 4 × 4 = $16
HOPE THIS HELP YOU FRIEND
The price of the Sue's original box is $4 more than the super saving brand's box. Sue saves $16 per month if she buys 4 cereal boxes each month.
How to form mathematical expression from the given description?You can represent the unknown amounts by the use of variables. Follow whatever the description is and convert it one by one mathematically. For example if it is asked to increase some item by 4 , then you can add 4 in that item to increase it by 4. If something is for example, doubled, then you can multiply that thing by 2 and so on methods can be used to convert description to mathematical expressions.
For this case, we're specified that:
Price of original cereal box = $12 per box.Price of super saving box = y = 8x, where x is the number of boxes.putting x= 1, we get y = 8. Thus, for each box of super saving brand, Sue pays $8.
The difference between both box's price is: 12 - 8 = 4 dollars.
Also, as Sue saves 4 dollars on each box of cereal, and she buys 4 boxes of cereal, then if she buys the boxes of super saving brands, then she saves 4 dollars per box for 4 boxes, whose total is 4 times 4 = 16 dollars.
Thus, the price of the Sue's original box is $4 more than the super saving brand's box. Sue saves $16 per month if she buys 4 cereal boxes each month.
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