A submarine hovers at 66 and 2/3 yards below sea level. If it ascends 24 and 1/8 yards and then descends again 78 and 3/4 yards, what is the submarine’s new position, in yards, below sea level?
Answer:
The submarine's new position is [tex]-121\frac{7}{24}\text{ yards}[/tex] below sea level.
Solution:
Given that a submarine hovers at [tex]66\frac{2}{3}[/tex] yards below sea level. This means that the position of submarine is negative
Therefore, we get [tex]-66\frac{2}{3}[/tex]
Also given that it ascend [tex]24\frac{1}{8}[/tex] yards
So we have to add [tex]-66\frac{2}{3}[/tex] and [tex]24\frac{1}{8}[/tex]
[tex]\rightarrow -66\frac{2}{3} + 24\frac{1}{8}\\\\\text{Convert mixed fractions to improper fractions }\\\\\rightarrow -\frac{66 \times 3+2}{3} + \frac{24 \times 8+1}{8} = \frac{-200}{3} + \frac{193}{8}\\\\\rightarrow \frac{-200 \times 8}{3 \times 8} + \frac{193 \times 3}{8 \times 3}\\\\\text{Simplify the above expression }\\\\\rightarrow \frac{-1600}{24} + \frac{579}{24} = \frac{-1021}{24}[/tex]
The submarine descends again 78 and 3/4 yards
This means we need to subtract [tex]-78\frac{3}{4}\text{ yards from } -\frac{1021}{24}\text{ yards}[/tex]
[tex]\rightarrow \frac{-1021}{24} -(78\frac{3}{4})\\\\\rightarrow \frac{-1021}{24} - \frac{78 \times 4 + 3}{4}\\\\\rightarrow \frac{-1021}{24} - \frac{315}{4} = \frac{-1021}{24} - \frac{315 \times 6}{4 \times 6}\\\\\rightarrow \frac{-1021 -1890}{24} = \frac{-2911}{24}\\\\\text{Simplify the expression }\\\\\rightarrow \frac{-2911}{24} = -121\frac{7}{24}[/tex]
Therefore, the submarine's new position is [tex]-121\frac{7}{24}\text{ yards}[/tex] below sea level.
Answer:
The answer-121 and 7/24
Hope this helps
:D
If I'm wrong sorry
And sorry that I'm super late
draw triangle abc where:
AB has the length 3.9cm (this is drawn for you)
angle CAB is 50
and
angle ABC is 63
Step-by-step explanation:
We are asked to draw a triangle.
The information we are given with is AB is a line segment with length 3.9 cm.
∠CAB = 50°.
∠ABC = 63°.
With the given details we need to draw triangle using given angles. We need protractor and ruler to draw the triangle.
Step 1: Draw the line segment of length 3.9 cm using ruler and mark as AB.
Step 2: Using protractor, we need to mark the angle. Keep the center of the protractor at the A and mark with a point at 50°.
Step 3: Draw a line from a passing through the marked point.
Step 4: Repeat step 2 with marking at 63° and step 3 on the other side.
Step 5: Mark the intersection point as C.
Ajar contains a mixture of 10 black balls, 8 red balls, and 2 white balls all the same size. What is the probability of
drawing either a red, black, or white ball in one draw?
Answer:
10 black- 10/20 - 50%
8 red- 8/20 - 40%
2 white - 2/20 -10%
Step-by-step explanation:
The total number of balls = 10 + 8 + 2 = 20 balls
probability of black balls = 10/20 = 50%
probability of red balls = 8/20 = 40%
probability of white balls = 2/20 = 10%
the three probabilities:
probability that the ball is one of the three colors = (10/20) + (8/20) + (2/20)
= 1 = 100%
-3(3x-2)=24 helppppppppppp
Answer:
x=-2
Step-by-step explanation: I gotchu
1. You first apply the -3 to (3x-2) which makes the equation -9x+6=24
2. Then, to isolate "-9x", you subtract 6 from both sides to make the equation -9x=18
3. Lastly, to isolate "x", you divide both sides by -9 which would make x=-2
Graph the system of linear inequalities. y≥2/3 x-3 y<-4x+7
Answer:
The answer is given in the graph attached.
Step-by-step explanation:
i) The answer is given in the graph attached.
PLEASE HELP
-
I need someone to check my answers for me, if anything is wrong please explain where I messed up so I can fix it. It is solving systems - word problems. If it helps, I've also listed the copyright holder for the worksheet.
©️ Gina Wilson (All Things Algebra), 2012
Please help me out!
The Town Recreation Department ordered 76 baseballs and 24 bats.
Given that, the total number of baseballs = 100, the total purchase = $822, cost of each baseball = $4.50 and the cost of each bat = $20.
What are simultaneous equations?In mathematics, a set of simultaneous equations, also known as a system of equations or an equation system, is a finite set of equations for which common solutions are sought.
Let the number of baseballs be x and the number of bats be y.
Now, the total number of items = The number of baseballs + The number of bats
⇒ 100=x+y ------(I)
Total amount = 4.50x+20y
⇒ 4.50x+20y = 822 ------(II)
Solve the obtained equations:
Put x=100-y in the equation 4.50x+20y = 822
We get, 4.50(100-y)+20y = 822
⇒ 450-4.50y+20y=822
⇒ 15.5y=372
⇒ y=372/15.5
⇒ y= 24
So, x+y =100
⇒ x=100-24=76
Therefore, the Town Recreation Department ordered 76 baseballs and 24 bats.
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The question picked from the figure given:
The Town Recreation Department ordered a total of 100 baseballs and bats for the summer baseball camp. Baseballs cost $4.50 each and bats cost 20 each. The total purchase was $822. How many of each item was ordered?
ANSWER QUICK
What are the values of a, b, and c in the quadratic equation 0=1/2x^2-3x?
Answer:
[tex]a=\dfrac{1}{2}\\ \\b=-3\\ \\c=0[/tex]
Step-by-step explanation:
The general form of the quadratic equation is
[tex]ax^2+bx+c=0[/tex]
You are given the quadratic equation
[tex]0=\dfrac{1}{2}x^2-3x[/tex]
It can be rewritten in standard form as
[tex]\dfrac{1}{2}x^2-3x=0[/tex]
Hence,
[tex]a=\dfrac{1}{2}\\ \\b=-3\\ \\c=0[/tex]
Add the two expressions.
3z−4 and 2z + 5
Enter your answer in the box.
Answer:
5z+1
Step-by-step explanation:
(3z-4)+(2z+5)
3z-4+2z+5
3z+2z-4+5
5z-4+5
5z+1
Answer:
5z+1
Step-by-step explanation:
3z-4+2z+5
Group like terms
3z+2z+5-4
Simplify
5z+1
what is 10x minus 35 factored
Answer:
5
(
2
x
+
7
)
Step-by-step explanation:
Answer: 5 (2x-7)
Step-by-step:
PLS I NEED ASAP WILL GIVE BRAINLIEST
Which equation is linear?
y=2x+2
2
y=2x^+2
3
y=2x^+2
4
y=2x^+2
For this case we have that by definition, a linear equation is of the form:
[tex]ax + b = 0[/tex]
The variable (s) involved in the equation always have exponent 1.
Some examples of linear equations are:
[tex]x + 5 = 3y\\y + 6 = 3x\\y = 2x + 2[/tex]
Answer:
In a linear equation the variables have exponent 1.
[tex]y = 2x + 2[/tex]
Alegbra, K12 Question. Answer needed ASAP --- Brainliest to the correct answer!
Good evening ,
Answer:
-1Step-by-step explanation:
From the table :
f(x) = g(x) only when x = -1 then -1 is the only solution
f(-1) = 9 = g(-1)
note : the equation could have some other solutions not shown in the table
:)
Find the next two terms of this sequence
112, 28, 7, ...........
Answer:
1.75, 0.4375
Step-by-step explanation:
Note there is a common ratio between consecutive terms, that is
r = 28 ÷ 112 = 7 ÷ 28 = 0.25
Thus the sequence is geometric.
To obtain a term in the sequence multiply the previous term by 0.25
7 × 0.25 = 1.75
1.75 × 0.25 = 0.4375
The next 2 terms in the sequence are 1.75, 0.4375
Write the ratio in simplest form.
8 min : 12 min
Answer:
2:3
Step-by-step explanation:
Answer:
2min :3min
Step-by-step explanation:
8 min divided by 4 =2
12 min divided by 4 =3
If k(x) = 5x – 6, which expression is equivalent to (k + k)(4)?
HELP PLS
Answer:
The third dot
Step-by-step explanation:
I did this question before :)
There are 5 5/4 of milk left in a carton. Write 5 5/4 an improper fraction. Explain what the improper fraction represents in this situation
Answer:
25/4 This improper fraction represents how much milk is left in the carton.
Step-by-step explanation:
5×4=20
20+5=25
25/4
Suzanna walked two over seven of a mile in two over five of an hour. What is her unit rate in miles per hour?
two sevenths over two fifths = one and two fifths miles per hour
two fifths over two sevenths = one and two fifths miles per hour
two sevenths over two fifths = five over seven mile per hour
two fifths over two sevenths = five over seven mile per hour
Get brainlest if aswered in the first 1 min.\
Two sevenths over two fifths = five over seven mile per hour
The unit rate is 5 over 7 miles per hour
Solution:
Given that, Suzanna walked two over seven of a mile in two over five of an hour
We have to find the unit rate in miles per hour
Unit rate means number of miles covered in 1 hour
From given information,
Two over seven of a mile in two over five of an hour
Which means,
[tex]\frac{2}{7} \text{ miles } = \frac{2}{5} \text{ hour }[/tex]
[tex]\text{ So she covered } \frac{2}{7} \text{ miles in } \frac{2}{5} \text{ hour }[/tex]
To find for number of miles covered in 1 hour, divide the [tex]\frac{2}{7} \text{ by } \frac{2}{5}[/tex]
[tex]\text{Unit rate in miles per hour } = \frac{\frac{2}{7}}{\frac{2}{5}}\\\\\text{Unit rate in miles per hour } = \frac{2}{7} \times \frac{5}{2} = \frac{5}{7}[/tex]
Two sevenths over two fifths = five over seven mile per hour
Thus unit rate is 5 over 7 miles per hour
Answer:
two sevenths over two fifths = five over seven mile per hour
Step-by-step explanation:
two sevenths over two fifths = five over seven mile per hour
A math teacher wants to buy 25 new scientific calculators for the classroom. Acme and Zenith makes two different type of calculators. Acme calculators cost $15 each. Zenith calculators cost $12 each. The math teacher has $330 to spend. How many of each calculators can she buy?
Answer: 10 Acme and 15 Zenith.
She can buy 10 Acme and 15 Zenith calculators.
What is the system of equations?One or many equations having the same number of unknowns that can be solved simultaneously called as simultaneous equation. And simultaneous equation is the system of equation.
Given:
A math teacher wants to buy 25 new scientific calculators for the classroom.
Acme and Zenith makes two different type of calculators.
Acme calculators cost $15 each.
Zenith calculators cost $12 each.
The math teacher has $330 to spend.
Let x represents the number Acme calculators and y represents Zenith.
Now, we have the system of equations,
x + y = 25
So, y = 25 - x
And 15x + 12y = 330
Substituting the value of y,
15x + 300 - 12x = 330
3x = 330 - 300
3x = 30
x = 10
So, y = 15
Therefore, 10 Acme and 15 Zenith calculators.
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What is the algebraic expression to 6 less than twice a number
Answer:
it would be 2x-6
Step-by-step explanation:
since you don't know what the value of "the number" is you would put a variable, x. and there is 2 of this number.
then 6 less would be -6 of this variable.
Five times a number , subtracted from twenty ,is triple the number. find the number .
Let's label the number you're trying to find x. You have to set up a system of equations.
1. Five times a number can be labeled as 5x.
2. Subtracted from 20 gives us 5x-20.
3. The problem says this is the same as simply tripling the original number. So set the first equation equal to 3x.
4. 5x-20=3x
5. Move like terms onto the same side. We can do this by subtracting 3x from both sides and adding 20 to both sides.
6. 5x-3x=20
7. 2x=20
8. Divide both sides by 2 to get x by itself.
Answer: x=10
The number is 2.5.
Let the number is = x.
According to the question:
20 - 5x = 3x
Add 5x.
20 = 5x + 3x
20 = 8x
Divide by 8.
x = 20/8 = 2.5
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How to solve 7(x+2y)=
Answer:
7x + 14y
Step-by-step explanation:
7(x + 2y)
Multiply 7 by the values inside the parenthesis (x + 2y)
7x + 14y
Hope this helps :)
(-3,4) is one of many solutions to the inequality:
2x+y ≥ -2
True or false
Answer:
True
Step-by-step explanation:
Answer:
True
Step-by-step explanation:
(-3,4) it shows that -3 =x and 4 =y
2x + y ≥ -2
Inserting both values into the equation
2(-3) + 4
-6 +4
-2
Answer confirms equation
What is 6350.384 rounded to the nearest tenth
Answer:6350.4
Step-by-step explanation:
What is the perimeter of this red polygon?
Answer:
Answer: The perimeter of the red polygon is 26 cm.
Step-by-step explanation:
Answer:
Tangents from an external point are equal. This can be used to find the perimeter
Perimeter = 22+22+22+22+27+27+98+98
= 338 in.
Hope this helps!
Teresa, Charlie, and Justin served a total of 153 orders Monday at the school cafeteria. Justin served 4 times as many orders as Charlie. Teresa served 9 more orders than Charlie. How many orders did they each serve?
Teresa served 33 orders and Charlie served 24 orders and Justin served 96 orders
Solution:
Let "a" be the orders served by Teresa
Let "b" be the orders served by Charlie
Let "c" be the orders served by Justin
Teresa, Charlie, and Justin served a total of 153 orders
Therefore,
a + b + c = 153 -------- eqn 1
Justin served 4 times as many orders as Charlie
Orders served by Justin = 4( orders served by Charlie )
c = 4b ---------- eqn 2
Teresa served 9 more orders than Charlie
orders served by Teresa = 9 + orders served by Charlie
a = 9 + b ----------- eqn 3
Let us solve eqn 1 and eqn 2 and eqn 3
Substitute eqn 2 and eqn 3 in eqn 1
9 + b + b + 4b = 153
9 + 6b = 153
6b = 153 - 9
6b = 144
b = 24
Substitute b = 24 in eqn 3
a = 9 + 24
a = 33
Substitute b = 24 in eqn 2
c = 4(24)
c = 96
Thus Teresa served 33 orders and Charlie served 24 orders and Justin served 96 orders
A gym instructor has a total of 60 hand weight in her studio. Some of the hand weights are 3 pound weights and the rest are 5 pound weights. If there are 10 more 5-lb weights than 3-lb weights, then how many of each kind does she have?
Answer:
35 5-lb weights25 3-lb weightsStep-by-step explanation:
Let t and f represent the numbers of three- and five-pound weights. The problem statement tells us ...
f + t = 60
f - t = 10
Adding these two equations, we get ...
(f +t) +(f -t) = (60) +(10)
2f = 70 . . . . . eliminate parentheses
f = 35 . . . . . . divide by 2
She has 35 5-lb weights, and 25 3-lb weights.
(u-4)5 please solve this
Answer:
5u - 20
Step-by-step explanation:
(u - 4)5
Multiply
5u - 20
Hope this helps :)
-4, -9, -14. What is a formula for the nth term if the given sequence in explicit formula
Answer: the formula is
(-4) + (-5) = -9
(-9) + (-5) = -14
Step-by-step explanation:
Answer:
an = 1 − 5n
Explanation:
a1 = 1 − 5 (1) = −4
a2 = 1 − 5 (2) = −9
a3 = 1 − 5 (3) = −14
Which best describes the complement of spinning any number less than 3?
Answer:
The complement of spinning any number less than 3, is spinning a number equal to or greater than 3.Explanation:
The complement of a subset is the subset of elements that are not in the given subset.
You must know which numbers the spinner has.
Assuming the spinner has the numbers 1, 2, 3, 4, the complement of spinning any number less than 3, is spinning a number that is not less than 3.
Then, that is spinning a number that is equal to or greater than 3.
The numbers that are equal to or greater than four, for a spinner that has the numbers 1, 2, 3, and 4 are 3 and 4.
Thus, the complement of spinning any number less than 3 is spinning a three or a four.
Answer:
C
Step-by-step explanation:
25x2-8x=12x-4
Can someone please help me on this ?????
Answer: X=2.7
Step-by-step explanation:
25*2-8x=12x-4
50-8x = 12x-4
subtract 50 from both sides
-8x = 12x-54
subtract 12x from both sides
-20x= -54
divide both sides by -20
X=2.7
Answer:x=2/5
Step-by-step explanation:
25x2-8x=12x-4
25x2-8x-12x+4=0
25x2-20x+4=0
25x2-10x-10x+4=0
5x(5x-2)-2(5x-2)=0
(5x-2)(5x-2)=0
5x-2=0 and 5x-2=/
5x=2 and 5x=2
X=2/5
BICYCLING The bicycle path at the
park is a loop that covers a distance
of m miles. Dot biked 2 loops each on
Monday and Wednesday and 3 loops
on Friday. On Sunday, Dot biked
10 miles. Write an expression in
simplest form that represents the
total distance that Dot biked this
week.
Dot bikes 7m+10 miles this week.
Step-by-step explanation:
Distance of one loop = m miles
Distance of 2 loops = 2m
Distance of 3 loops = 3m
Distance covered on Sunday = 10 miles
Total distance = Monday + Wednesday + Friday + Sunday
Total distance = 2 loops + 2 loops + 3 loops + 10 miles
Total distance = 2m + 2m + 3m + 10
Total distance = (7m+10) miles
Dot bikes 7m+10 miles this week.
Keywords: addition, distance
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The equation of a given circle in. general form is x^2+y^2+12y+27=0. Write the equation in standard form, (x-h)^2+(y-k)^2=r^2, by completing the squares in the equation. Show your work in the table.
Answer:
Center (h, k) = (0, 6)
Radius, r = 3 units
Step-by-step explanation:
The given equation of the circle is: [tex]$ x^2 + y^2 + 12y + 27 = 0 $[/tex]
STEP I: Move the constant term to the right hand side.
To do that we subtract 27 on both the sides, we get:
[tex]$ x^2 + y^2 + 12y = -27 $[/tex]
STEP II: Divide the co - effecient of 'x' by 2 and square it.
Here there is no 'x' term. Its co-effecient is 0.
STEP III: Add the result on both sides.
Since, we got 0 in the previous step, there would no change in the equation
STEP IV: We repeat the process for 'y'.
Here, the co-effecient of 'y' is: 12.
Dividing by 2 and squaring it will yield:
[tex]$ \frac{12}{2} = 6; \hspace{5mm} 6^2 = 36 $[/tex]
STEP V: Adding 36 to both the sides of the equation, it becomes:
[tex]$ x^2 + y^2 + 12y + 36 = -27 + 36 $[/tex]
[tex]$ \implies x^2 + y^2 + 12y + 36 = 9 $[/tex]
We have arrived at perfect squares.
STEP VI: Write in the form of perfect squares.
[tex]$ (x - 0)^2 + (y - 6)^2 = 3^2 $[/tex]
STEP VII: Compare it with the standard form.
[tex]$ (x - h)^2 + (y - k)^2 = r^2 $[/tex]
We get: The centre of the circle: (h, k) = (0, 6) and
the radius of the circle, r = 3 units.