Answer:
Ted is 6 years old
Leon is 7 years old
Andrew is 8 years old
Step-by-step explanation:
Ted+Leon=13 ⇒T+L=13 ⇒L=13-T
Leon+Andrew=15 ⇒L+A=15 ⇒A=15-L ⇒A=15-(13-T) because Leon =13-Ted
A=2+T
Ted+Andrew=14
T+A=14 ( substitute Andrew age from A=2+T)
T+2+T=14
2T=12
T=12/2=6 (Ted is 6 years old)A=2+T=2+6=8 ( Andrew is 8 years old)Leon=13-T=13-6=7 ( Leons is seven years old)check: Ted+Leon=13 ⇒ 6+7=13
Leon + Andrew=15 ⇒7+8=15
Andrew+Ted=14 ⇒ 6+8=14
what is the value of sin 12 - cos 78
Answer:
0
Step-by-step explanation:
[tex]\sin(12\º) - \cos(78\º)[/tex]
Consider the cofunction identity:
[tex]$\boxed{\sin(\theta)=\cos \left(\frac{\pi}{2} - \theta \right)} $[/tex]
[tex]$\boxed{\sin(\theta)=\cos \left(90\º - \theta \right)} $[/tex]
[tex]\sin(12\º)=\cos(90\º - 12\º)=\cos(78\º)[/tex]
[tex]\therefore \cos(78\º) - \cos(78\º) = 0[/tex]
The value of Sin 12-cos 78 is 0
What are trigonometric functions?In mathematics, trigonometric functions are real functions that relate an angle of a right-angled triangle to ratios of two side lengths. The six trigonometric functions are Sine, Cosine, Tangent, Secant, Cosecant, and Cotangent.
Given here: sin 12 - cos 78 = Sin(90-12)-cos78 but we know sine of any angle = the cosine of any complementary angle
Thus we have Sin78-Cos78=0
Hence, The value of Sin 12-cos 78 is 0
Learn more about trigonometric functions here:
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Viola has 185 cans of soda. Dixie has 17 cans of soda less than viola. How many cans
of soda does Dixie have?
Can someone please convert this into a algebraic expression?
Answer:
168
Step-by-step explanation:
No of cans of soda Dixie has = 185 - 17 = 168
Another way:
Let Dixie has x cans of soda
Therefore,
Viola has = (x + 17) cans
According to the given information:
x + 17 = 185
x = 185 - 17
x = 168
Ray created the list of factors for 48 below.
48: 1, 2, 3, 4, 6, 7, 8, 12, 16, 24, 48
Which number should be removed from his list to make the list accurate?
O 3
07
O 16
O 48
please help!!
kinda disrespectful someone didn't answer this but anyway..
Without an explanation your answer is 7
W/ an explanation:
___________________________________
7 should be removed from the list because all the other numbers can multiply to 48
1 x 48 ✔
2 x 24 ✔
3 x 16 ✔
4 x 12 ✔
6 x 8 ✔
7 x ? ❌
Thus, 7 is left with nothing to multiply by besides itself which would give you 47 but the number we have the list of is 48. So 7 is your number to remove from the list.
How do you know when to add or subtract?
The lengths of XY and YZ add up to the length of XZ:
XY + YZ = XZ
We know that XZ = 10 + 1/5 = 51/5, and XY = 4 + 2/3 = 14/3, so
14/3 + YZ = 51/5
Subtract 14/3 from both sides to solve for YZ:
YZ = 51/5 - 14/3
Find a common denominator; the least common multiple of 5 and 3 is 15, so multiply the first fraction by 3/3 and the second one by 5/5 to get
YZ = 153/15 - 70/15
YZ = (153 - 70)/15
YZ = 83/15
We have 80 = 75 + 8, so that
YZ = 83/15 = (75 + 8)/15 = 75/15 + 8/15 = 5 + 8/15
3
The sum of two consecutive whole numbers is
91. What are the numbers?
Represent your numbers as follows.
X ⇒ first number
X + 1 ⇒ second number
Since their sum is 91, we have x + (x + 1) = 91.
Solving from here, simplify on the left side to get 2x + 1 = 91.
Subtract 1 from both sides to get 2x = 90.
Now divide both sides by 2 and x = 45.
So if x = 45, then x + 1 must be 46.
So our numbers are 45 and 46.
Answer:
5423875
Step-by-step explanation:
Variations problem Help please
Answer:
9
Step-by-step explanation:
12-5=7 so...
2+7 = 9
y = 9
I need to know what -(6h + 7) + 8 = -19 is
Answer:
10/3
Step-by-step explanation:
-1(6h + 7) = -6h - 7
-6h - 7 + 8 = -6h + 1
-6h + 1 = -19
-1 -1 - Subtract 1 from both sides.
-6h = -20
-6 -6 - Divide both sides by negative 6
h = 10/3
Answer:
h = 10/3
Step-by-step explanation:
-(6h + 7) + 8 = -19
Subtract 8 from each side
-(6h + 7) + 8-8 = -19-8
-(6h + 7) = -27
Divide by a negative
6h+7 = 27
subtract 7
6h+7-7 = 27-7
6h = 20
Divide by 6
6h/6 = 20/6
h = 10/3
Cori saved $15 every week for 6 months. Then she
spent 60% of the money for a new bike. How much
money did she have left?
Answer:
$144
Step-by-step explanation:
15*4=60
60*6=360
360*0.6=216
360-216=144
djdsklsa;jska da;kja849381-09
━━━━━━━━━━━━━━━ ♡ ━━━━━━━━━━━━━━━
849381 - 9 = 849372
━━━━━━━━━━━━━━━ ♡ ━━━━━━━━━━━━━━━
Simplify the expression:
(12x - 3+ 2x) + (5 + 3x? - 2x)
Helppp and how do did u simply it!!
Answer:
20[tex]x^{2}[/tex] + 109x -15
Step-by-step explanation:
12x * 5 = 60x
12x * 3x = 36x
12x * -2x= -24[tex]x^{2}[/tex]
-3 * 5 = -15
-3 * 3x = -9x
-3 * -2x = 6x
2x * 5 = 10x
2x * 3x =6x
2x * -2x= -4[tex]x^{2}[/tex]
60x + 36x -9x + 6x + 10x + 6x = 109x
24[tex]x^{2}[/tex] - 4
-15
Hope this helpss
Three people are sitting on a bus. Bridget is directly behind Sophia and directly left of Alan. If Sophia and Bridget are 3 feet apart, and Alan and Sophia are 9 feet apart, what is the distance between Bridget and Alan? If necessary, round to the nearest tenth.
Answer:
The distance between Bridget and Alan is 9.48 ftStep-by-step explanation:
kindly find attached a rough sketch of their sitting position which forms a right triangle
We can proceed by using Pythagoras therm to solve for the distance between Bridget and Alan which is the hypotenuse
[tex]C^= A^2+B^2\\\\C= \sqrt{A^2+B^2}[/tex]
From the problem statement
A, which is the opposite is = 3 ft
B, which is the adjacent = 9 ft
C, is the hypotenuse= ?
Substituting into the expression we have
[tex]C= \sqrt{3^2+9^2} \\\\C= \sqrt{9+81}\\\\C= \sqrt{90}\\\\ C= 9.48 ft[/tex]
To the nearest tenth the distance is 9.48 ft
Answer:
2.6 meters
Step-by-step explanation: That the most unnecessary math ever, thank you to who ever decided to come up with the Pythagorean theorem.
The type of person to write the name on scratch paper...
:)
Solve for R. P=R−C What is R equal to?
Answer:
R = P+C
Step-by-step explanation:
P = R-C
+C +C
R = P+C
8/5x+4 + 16/5x = 6(4/5x+3) – 20
find x
Answer:
First of all, you are going to add
5
x
to each side. This will give you a new equation of
8
x
=
16
. The reason you add 5 is because you want to get rid of the -5x on the right. When you add 5 it changes to 0x. Anything times 0 equals 0. The next step is to divide both sides by 8. The reason you divide is to get x alone. When you divide 8x by 8, you get 1x. 1 times anything equals what the other thing is. For example, 1 times 4 is 4. This will give you your answer of
x
=
2
Up and down represents_________ and left to right represents_________.
Answer:
y-axis and x-axis
Step-by-step explanation:
To solve 2x+9=21, what is the first step?
Answer:
The first step is to subtract 9 from each side
Step-by-step explanation:
2x+9=21
The first step is to subtract 9 from each side
2x+9-9 = 21-9
2x = 12
Then divide by 2 on each side
2x/2 = 12/2
x = 6
Answer:
That would be to collect like terms
Step-by-step explanation:
Further explanation
[tex]2x+9=21\\\\Collect\: like\: terms\\2x = 21-9\\\\Simplify\\2x = 12\\\\Divide\:both\:sides\:of\:the\:equation\:by\:2\\\frac{2x}{2} = \frac{12}{2} \\Simplify\\\\x =6[/tex]
The monthly cost of driving a car depends on the number of miles driven. Lynn found that in May it cost her $375 to drive 380 mi and in June it cost her $455 to drive 700 mi. (a) Express the monthly cost C as a function of the distance driven d, assuming that a linear relationship gives a suitable model. C(d)
Answer:
idk
Step-by-step explanation:
i need help with #6
Answer: The whole equation is simplified down to -20.
Step-by-step explanation:
Here's how I got my answer:
Equation is 4p^2 + 7q^3
All you need to do is plug in the values they have given you. If you apply them, you get:
4 (-3)^2 + 7 (-2)^3
Which simplifies to:
4 (9) + 7 ( -8)
Simplify furthermore:
36 + (-56)
Which gives you:
-20
given directed line segment ab find the coordinates of p such thats the ratio of ap to pd is 2:1
Answer:
The point P on line AB such that the ratio of AP to PB is 2:1 is P = (0, 3)
Step-by-step explanation:
The dimension of the graph can be taken as 1 box = 1 unit
Therefore;
The coordinates of the point A = (-2, -7)
The coordinates of the point B = (1, 8)
For the a point P that gives the ratio AP to PB = 2:1 is given as follows;
The fraction of AP to AB = 2/(2 + 1)×AB = 2/3 × AB
Which gives;
The coordinate of the point P = (-2 + 2/3×(1 - (-2)), -7 + 2/3×(8 - (-7)))
P = (0, 3)
Therefore;
The coordinates of P such that the ratio of AP to PB is 2:1 is P = (0, 3).
At Alexandra's Orchards, 99% of the trees are apple trees. Across town at Zachary's Orchards, 558 out of 563 trees are apple trees. Which orchards have a greater percentage of apple trees?
Answer:
Zachary's Orchards
Step-by-step explanation:
We are already given the percent of trees at Alexandra's Orchards, so nothing to do here, yet.
Zachary's Orchards we could find by dividing the trees over the total.
558/563 = .9911
Multiply by 10 in order to get a whole number
.9911 * 10 = 99.11
Hence, Zachary's Orchards have a greater percentage
Anam is thinking of a prime number it is between 40 to 60 the differnce between is digit is 3 what prime number is anum thinking of?
Answer:There are two possible answers. 41 and 47
Step-by-step explanation: These both have a difference of 3 between the digits. Other prime numbers between 40 and 60: 43, 53, 57, 59 have differences of 1, 2, and 4.
last month jensen earned $270 for h hours of working. this month, she earned the same rate for 15 hours of working. write an expression to show how much jensen earned his month
At the end of a dice game, James has -5 points and Richard has 15 points. What is the difference in their scores? A. -20 B. 10 C. 20 D. -10
C) 20 points
Step-by-step explanation:James - 5
Richard + 15
What is the difference in their scores ?
+ 15 - (- 5) =
= 15 + 5
= 20 points
Answer:
a is the answer because the question had said that to find out the difference
Variations question help please
Answer:
y = 156
Step-by-step explanation:
The equation for direct variation is
y = kx
65 = k*5
Divide each side by 5
65/5 = k
13 =k
The equation is y = 13x
Let x = 12
y = 13*12
y = 156
A softball has a diameter of 3.8in. How many softballs will fit inside of a storage unit that is 6 feet wide,10 feet wide, and 8 feet high?
Answer:
29090
Step-by-step explanation:
First of all, we will have to calculate the volumes of a soft ball and the volume of box.
Then we will divide the volume of box with volume of softball to find the number of balls that can be stored in the box.
Diameter of softball = 3.8 in
Radius of softball = 1.9 in = 0.158 ft
Volume of a sphere = [tex]\frac{4}{3}\pi r^3[/tex]
[tex]\Rightarrow \dfrac{4}{3}\pi (0.158)^3=0.0165\ ft^3[/tex]
Volume of cuboid box = Length [tex]\times[/tex] Width [tex]\times[/tex] Height = 6 [tex]\times[/tex] 10 [tex]\times[/tex] 8 = 480 [tex]ft^3[/tex]
Number of softballs that can fit inside the storage = [tex]\frac{480}{0.0165}[/tex] = 29090
What percentage of the UKs population is 14.1 million people?
The UK has a population of 66.65 million. What do 14.1 million people make up a percentage of?
Answer:
≈21.16%
Step-by-step explanation:
Population = 66.65 M
14.1 M make up:
14.1/66.65*100% ≈21.16%A rectangular garden has a perimeter of 578 yds.
The length is one more than three times the width.
Find the dimensions of the garden.
Answer:
Width (w) = 72 yds
Length (L) = 217 yds
Step-by-step explanation:
Let L represent the length.
Let w represent the width.
From the question given above:
Perimeter (P) = 578 yds.
Length (L) is one more than three times the width (w). This can be written as. Follow:
three times the width (w) = 3w
Therefore, the length (L) is given by:
L = 1 + 3w
Next, we shall determine the value of length (L) and width (w). This can be obtained as follow:
Recall:
Perimeter of rectangle is given by:
P = 2(L + w)
P = 2L + 2w
Perimeter (P) = 578 yds.
Length (L) = 1 + 3w
Width (w) = w
P = 2L + 2w
578 = 2(1 + 3w) + 2w
Clear bracket
578 = 2 + 6w + 2w
578 = 2 + 8w
Collect like terms
578 - 2 = 8w
576 = 8w
Divide both side by 8
w = 576/8
w = 72
Therefore, the width is 72 yds
L = 1 + 3w
w = 72
L = 1 + 3(72)
L = 1 + 216
L = 217
Therefore, the length is 217 yds.
The dimensions of the garden is given below:
Width (w) = 72 yds.
Length (L) = 217 yds.
7/8 greater than or less than 2/4
Answer:
greater than
Step-by-step explanation:
7/8 is greater than 4/8
Scientist measured a Madeira cockroach and found it to be 3.438 centimeters long. Between which two cockroaches would the Madeira cockroach belong?
Answer:
Oriental and American cockroach
Step-by-step explanation:
The question is not complete. The complete question is:
The length of the oriental, American and Australian cockroaches are 3.432 cm, 3.576 cm and 3.583 cm respectively. Scientist measured a Madeira cockroach and found it to be 3.438 centimeters long. Between which two cockroaches would the Madeira cockroach belong?
Answer: From the question, the Australian cockroach is the longest cockroack with a length of 3.583 cm followed by the American cockroach of length 3.576 cm and lastly the Oriental cockroach of length 3.432 cm.
If the Madeira cockroach is to be placed, its length is greater than that of the Oriental cockroach but less than that of the American cockroach hence it would be placed between the Oriental and American cockroach. The lengths from lowest to highest is:
3.432 cm 3.438 cm 3.576 cm 3.583 cm
I have an order to administer nitroglycerin 10mcg/min continuous infusion. The bottle of nitroglycerin available is 50mg in 250 ml of D5W. At what rate would you set the IV pump to infuse at
Answer:
The IV pump infusion rate = 0.05ml per minute
Step-by-step explanation:
available concentration = 50 mg per 250 ml of D5W
This means that
250 ml of D5W contains 50 mg
note that
mg = milligram
mcg = microgram
250 ml = 50mg
1ml = 50/250 mg
1ml = 0.2mg
Next, let us convert from milligram (mg) to microgam (mcg) since the unit of administration is in mcg.
1 mg = 1000 mcg
∴ 0.2 mg = 1000 × 0.2
= 200mcg
Therefore the available concentration 200mcg/ml
required concentration/min = 10
since 1 ml = 200mcg
1 mcg = (1 ÷ 200) ml
1 mcg = 0.005 ml
∴ 10 mcg = 0.005 × 10 = 0.05 ml
10 mcg is contained in 0.05 ml of the solution
Therefore, the IV pump infusion rate = 0.05ml per minute
Tim took his friends to the movies. He stared with $40 and bought 3 movie tickets that each cost x dollars. He also bought one tub of popcorn that cost $5.75. Which of the following expression(s) represent the amount of money Tim has left? *
(A) 40-x-x-x-5.75
(B) 40-3-5.75 34.25-3x
(C) 40-3X-5.75 0
(D) -3x+34.25 31.253
Answer:
40 - x - x - x - 5.75 OR 40 - 3x - 5.75 OR 34.25 - 3x
Step-by-step explanation:
To find the amount of money Tim has left, we will simply write an expression that starts with the total he started with subtracting each expense.
$40
- $x
- $x
- $x
- $5.75
________________________
$40 - $x - $x - $x - $5.75
= $ (40 - 5.75) - 3(x)
= $ 34.25 - 3x
So you can choose one of three of these expressions:
(1) 40 - x - x - x - 5.75
(2) 40 - 3x - 5.75
(3) 34.25 - 3x
Cheers.