The depth of the personal submarine is -14.9 meter.
What is an integer?An integer is a whole number that can be positive, negative, or zero and is not a fraction. Integer examples include: -5, 1, 5, 8, 97, and 3,043. 1.43, 1 3/4, 3.14, and other numbers that are not integers are some examples.
Given that,
The submarine descends 20.6 meters and then ascends 5.7 meters. it means 20.6 is a negative number and 5.7 is a positive number.
Now,
To find the depth adding the -20.6+5.7
-20.6+5.7
-14.9
Hence, The depth of the personal submarine is -14.9 meter
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(X) 1.10.PS-7
Simplify the expression. Write the answer in scientific notation.
(7×10¯²) (9×10¯²)
(7×10¯²) (9×10¯²) = ¯
(Simplify your answer. Use scientific notation. Use the multiplication symbol in the r
Enter you
The scientific notation is 6.3 × [tex]10^{-3}[/tex]
The expression is ( 7 ×[tex]10^{-2}[/tex] )( 9 × [tex]10^{-2}[/tex])
Calculate the product or quotient
=63 × ([tex]10^{-2}[/tex] ×[tex]10^{-2}[/tex])
Simplify using the exponent rule with the same base [tex]a^{n} . a^{m}[/tex] = [tex]a^{n + m}[/tex]
=63 × [tex]10^{-2-2}[/tex]
=63 ×[tex]10^{-4}[/tex]
= 6.3 × [tex]10^{-3}[/tex]
Therefore the scientific notation is 6.3 ×[tex]10^{-3}[/tex].
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If f(x) = (x-4)(x+3), determine the x-intercepts of each function.
a) y=f(x)
b) y=-2f(x)
c) y=f(-1/2x)
d) y=f(-(x+1))
a) The x-intercepts of y=f(x) is (-3,0) (4,0)
b) The x-intercepts of y=-2f(x) is (-3,0) (4,0)
c) The x-intercepts of y=f(-1/2x) is (-1/8,0) (1/6,0)
d) The x-intercepts of y=f(-(x+1)) is (-5,0) (2,0)
What is x-intercept?A line's x-intercept is the distance in x coordinates from the line's intersection with the x-axis at its origin. A location on the graph where y is 0 is known as the x-intercept. The x-intercept of a line that is perpendicular to the y-axis is undefined.
Here to determine the x-intercept put y=0,
Given f(x)=(x-4) (x+3)
a) y=(x-4) (x+3)
Replacing y by 0 we get,
(x-4) (x+3) =0
x=-3, 4
Therefore, x-intercepts of y=f(x) is (-3,0) (4,0)
b) y = -2(x-4) (x+3)
Replacing y by 0 we get,
-2(x-4) (x+3) =0
x=-3, 4
Therefore, x-intercepts of y=-2f(x) is (-3,0) (4,0)
c) y= (-[tex]\frac{1}{2x}[/tex]-4) (-[tex]\frac{1}{2x}[/tex]+3)
Replacing y by 0 we get,
(-[tex]\frac{1}{2x}[/tex]-4) (-[tex]\frac{1}{2x}[/tex]+3) =0
By solving the above equation
(-[tex]\frac{1}{2x}[/tex]-4) =0 and (-[tex]\frac{1}{2x}[/tex]+3) =0
-1/2x=4 and -1/2x=-3
x=-1/8 and x=1/6
Therefore, x-intercepts of y=f(-1/2x) is (-1/8,0) (1/6,0)
d) y=(-(x+1)-4) (-(x+1) +3)
Replacing y by 0 we get,
(-(x+1)-4) (-(x+1) +3) =0
By solving the above equation
(-(x+1)-4) =0 and (-(x+1) +3) =0
-(x+1) =4 and -(x+1) =-3
x=-5, 2
Therefore, x-intercepts of y=f(-(x+1)) is (-5,0) (2,0)
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The Smith twins, Joe and John, have a car collection.
The number of cars is represented by x.
The number of cars in Joe's collection is 2 times the number in John's collection.
The total number in both is 78. What is x, the number in John's collection?
A. 26 Cars
B. 54 Cars
C. 39 Cars
D. 78 Cars
Answer:
Step-by-step explanation:
x = 39
C. 39 Cars
Determine which answer in the solution set will make the equation true.
2p + 9 = 4p − 13
S: {−11, 0, 11, 22}
Answer:
11
Step-by-step explanation:
If you input the number and then solve, you should get that #=#
2(11)+9=4(11)-13
22+9=44-13
31=31
Answer: 11
Step-by-step explanation: 2(11)+9=4(11)-13, 22+9=44-13, 31=31
Given A-
2 2
1 3
what is A-¹?
The inverse of matrix A = [tex]\left[\begin{array}{cc}2&2&1&3\\\end{array}\right][/tex] is [tex]A^{-1} = \frac{1}{4}[/tex] [tex]\left|\begin{array}{cc}3&-2&-1&2\\\end{array}\right|[/tex]
The given matrix is A = [tex]\left[\begin{array}{cc}2&2&1&3\\\end{array}\right][/tex]
The inverse of a matrix is given by
[tex]A^{-1} = \frac{1}{|A|} adjA[/tex] ...(1)
Now, determinant of matrix A is
|A| = [tex]\left|\begin{array}{cc}2&2&1&3\\\end{array}\right|[/tex]
= (3)(2) - (2)(1)
= 6 - 2
= 4
Now, adjoint A will be
[tex]A_{11}[/tex] = 3
[tex]A_{12}[/tex] = -1
[tex]A_{21}[/tex] = -2
[tex]A_{22}[/tex] = 2
AdjA = [tex]\left|\begin{array}{cc}3&-2&-1&2\\\end{array}\right|[/tex]
Now, substituting the values of |A| and AdjA in equation (1), we get
[tex]A^{-1} = \frac{1}{4}[/tex] [tex]\left|\begin{array}{cc}3&-2&-1&2\\\end{array}\right|[/tex]
Therefore, [tex]A^{-1} = \frac{1}{4}[/tex] [tex]\left|\begin{array}{cc}3&-2&-1&2\\\end{array}\right|[/tex]
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F(x)=3x^2-4x+8G(x)=2x-5 use the functions above to find the value of g(f(-2)) I don’t understand how to do this
Given,
[tex]f(x)=3x^2-4x+8,\text{g(x)=2x-5}[/tex]To find g(f(-2)). we first find the value of f(-2).
The value of f(-2) is,
[tex]\begin{gathered} f(-2)=3(-2)^2-4(-2)+8 \\ \text{ =3(4)+8+8} \\ \text{ =12+8+8} \\ \text{ =28} \end{gathered}[/tex]So now to find the value of g(f(-2)),
[tex]g(f(-2))=g(28)[/tex]So the value of g(28) is,
[tex]\begin{gathered} g(28)=2(28)-5 \\ \text{ =56-5} \\ \text{ =51} \end{gathered}[/tex]So the value of g(f(-2)) is 51.
35 = u/5 + 12 solve for u and simplify the answer as much as possible
Answer:
u = 115
Step-by-step explanation:
35 = u/5 + 12
35 - 12 = u/5
(35 - 12) * 5 = u
u = (35 - 12) * 5
u = 115
is 12x17=6x34 true or is it flase i cant do it
A robot can complete 5 tasks in 3/4 hour. each task is the same. how long does it take the robot to complete one task
The robot will take 0.15 hours to complete one task.
What is the unitary method of problem solving?
A single unit's value can be determined from the values of multiple units, and multiple units' values can be determined from the values of single units using the unitary technique. The unitary technique involves first determining the value of a single unit, followed by the value of the necessary number of units. In the unitary method, the value of a unit quantity is determined before the values of other units are determined. Direct variation and inverse variation are its two different forms of variations. When there is a direct variation, an increase or decrease in one quantity will result in an equivalent rise or fall in the other. If we increase one quantity in inverse variation, the value of another quantity will drop.
Given, time taken by robot to complete five tasks = 0.75 hours
Thus, time taken by robot to complete one task = (0.75/5) = 0.15 hours
Therefore, the robot will take 0.15 hours to complete one task.
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A straight road makes an angle of 15 degrees with the horizontal. When the angle of elevation of the sun is 57 degrees, a vertical pole at the side of the road casts a shadow 75 feet long directly down the road, as shown in the figure. Approximate the length of the pole. Round to the nearest hundredth.
The length of the pole is 19.15 feet.
What is the angle of elevation?The angle of elevation is the angle created when an observer looks at an object placed above its height in relation to the eye level or the horizontal line. An angle of elevation is, for example, the angle created between the line of sight and the horizontal line when a man on Earth observes the Sun.
Given:
Angle made by straight road = 15°
Angle of elevation of the sun = 57°
Length of the shadow = 75 feet
∠ACB = 90° - 57° = 33°
∠CAB = 57° - 15° = 42°
Using Sine Law to find BC i.e.length of the pole.
[tex]\frac{BC}{sin A} = \frac{AB}{sin C}[/tex]
[tex]\frac{BC}{sin 42} = \frac{75}{sin 33}[/tex]
[tex]BC= \frac{75sin 42}{sin 33}[/tex]
BC ≅ 19.15 feet (to the nearest hundredth.)
Hence, the approximate length of the pole is 19.15 feet.
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What number does
2(x+3)²
3(x-1)²
represent WHEN x = 3?
Answer:
72 and 12
Step-by-step explanation:
substitute x = 3 into the expressions
2(x + 3)²
= 2(3 + 3)²
= 2(6)²
= 2 × 36
= 72
--------------------
3(x - 1)²
= 3(3 - 1)²
= 3(2)²
= 3 × 4
= 12
On your own sheet of paper, use long division to find the quotient of 5,550 ÷ 39. What is the remainder?
Answer: Quotient 142
Remainder 12
Step-by-step explanation:
The quotient is 142 and the remainder is 12.
The long division method is as follows :
[tex]142[/tex]
[tex]39\sqrt{5550}[/tex]
-39
165 (3rd 5 taken down )
-156
90 ( 0 taken down )
-78
12
step 1 : take the first two digits (55) of the divident , now multiply 39 with such a number that the product of those two must not go above 55 but should be closest to it.
step 2 : write the number on top and subtract the answer from 55.
step 3 : Now bring down the third 5 and write it after the answer of the subtraction. So the number becomes 165.
step 4 : Again multiply 39 with such a number that the product of those two must not go above 165 but should be closest to it.
step 5 : write that number on top after the previous number and subtract the answer from 165.
step 6 : Now bring down the 0 and write it after the answer of the subtraction. So the number becomes 90.
step 7 : Again multiply 39 with such a number that the product of those two must not go above 90 but should be closest to it.
step 8 : write that number on top after the previous number and subtract the answer from 90.
We have to repeat these steps until all the digits from the divident are used and the remainder comes out to less than the divisor.
Here all the digits of divident are used and the remainder (12) is also less than the divisor (39), so we stopped.
Hence the quotient is 142 and the remainder is 12.
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A car journey is m
miles long.
One kilometre is equivalent to x
miles.
The car uses one litre of fuel to travel a distance of f
kilometres.
Fuel for the car costs p
pence per litre.
Which of the following expressions gives the cost of fuel for this journey, in pounds?
The expression gives the cost of fuel for this journey is option H mp / 100 fx
Given,
The total distance of a car journey = m miles
One kilometer = x miles
The amount of petrol needed to travel a distance of f kilometers = 1 liter
Cost of the fuel = p pence/ liter
Now we have to find the expression which gives the cost of fuel for this journey in pounds.
1 pound = 100 pence
So,
The distance in miles we can travel with 1 liter of petrol = fx
Total liter of petrol needed for the journey = m/fx
Total cost of petrol for the journey = mp / fx100
That is,
The expression gives the cost of fuel for this journey is option H mp / 100 fx
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The question is incomplete. Completed question is given below:
A car journey is m miles long.
One kilometre is equivalent to x miles.
The car uses one litre of fuel to travel a distance of f kilometres.
Fuel for the car costs p pence per litre.
Which of the following expressions gives the cost of fuel for this journey, in pounds?
(There are 100 pence in one pound.)
A. 100fmpx
B. 100fmp/x
C. 100mpx/f
D. 100mp/fx
E. fmpx/100
F. fmp/100x
G. mpx/100f
H. mp/100fx
PLEASE HURRYYYY
The segment contains points S(a, b) and T(c, d). Which formula should be used to find the midpoint of the segment?
The table shows the percent of each type of movie in Brayden's collection. What is the ratio of Action movies to all of the movies in Brayden's collection?
Movie Type Percent of Collection
Comedy 20%
Action 40%
Drama 15%
Science Fiction 25%
Select all that apply.
A.
2 : 5
B.
3
20
C.
2
3
D.
2
5
E.
3 : 20
the ratio of action movies to all movies is 2: 5 .
In mathematics, a ratio illustrates how frequently one number appears in another. On a fruit tray, the ratio would be eight to six if there were eight oranges and six lemons.
Ratios can be lowered by dividing each quantity by the sum of all the common factors between the numbers (much like fractions are).When the ratio's numbers are the smallest practical integers, the fraction is said to be in its simplest form.The ratio's antecedent and consequent are frequently referred to as A and B, respectively.Let Brayden has x number of movies in total.
Total number of action movies in his collection = 40% of x = 0.4 x
Other movies = 1 - 0.4x = 0.6 x
Ratio of action movies to all movies = 0.4x : x = 2: 5
Therefore the ratio of action movies to all movies is 2: 5 .
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If g(x) = -x, for what value of x does
g(x) = -9?
Answer:
x = 9
Step-by-step explanation:
given g(x) = - x and g(x) = - 9 , the equate right sides
- x = - 9 ( multiply both sides by - 1 )
x = 9
Consider the matrices.
What matrix results from B + A?
Enter your answer by filling in the boxes.
Answer:
Step-by-step explanation:
[tex]\displaystyle\\A=\left[\begin{array}{ccc}-1&6\\-2&2\\4&9\\-5&-11\end{array}\right] \ \ \ \ \ \ \ \ \ B=\left[\begin{array}{ccc}-4&-1\\-8&8\\2&-7\\-6&5\end{array}\right] \\\\A+B=B+A\ (commutativity)\\\\\Rightarrow B+A=\left[\begin{array}{ccc}-4+(-1)&-1+6\\-8+(-2)&8+2\\2+4&-7+9\\-6+(-5)&5+(-11)\end{array}\right] \\\\\\ \Rightarrow B+A=\left[\begin{array}{ccc}-5&5\\-10&10\\6&2\\-11&-6\end{array}\right][/tex]
What is the equation in slope-intercept form of a line that passes through the point (−2, −6) and has a slope of 12?
Answer:
y = 12x + 18
Step-by-step explanation:
Equation of line in slope-intercept form: y =mx +b
Here, m is the slope and b is the y-intercept.
m = 12
Substitute m =12 in the above equation,
y = 12x + b
This line passes through (-2,-6). So, plugin the point in the above equation.
-6 = 12*(-2) + b
-6 = -24 + b
-6 + 24 = b
b = 18
Equation of the line:
[tex]\sf \boxed{\bf y = 12x + 18}[/tex]
The population of a city increases by 3.1% per year. If this year's population is
290,000, what will next year's population be, to the nearest individual?
Answer:
the next year population is 122,689
Step-by-step explanation:
The computation of the next year population is as follows:
= This year population × increase percentage
= 119,000 × (1 + 0.031)
= 119,000 × 1.031
= 122,689
Hence, the next year population is 122,689
The above formula is applied so that the correct value of the population could come
and the same is relevant
John's commute to work is 20kmhr while Sheri's commute is 500mmin.
Who has the fastest commute to work in mihrif 1.61km=1mi?
By 6.2 miles per hour, Sheri commutes more quickly.
We are given that,
John travels to work = 20km/hr
Sheri travels to work = 500m/min converting this into km/hr we get ,
1.61km/hr or 1 mile
John travels to work at the following rate:
[tex]\frac{20 km}{1 hr} * \frac{1 mile}{1.61km} = 12.42 miles/hr[/tex]
Sheri travels work at the following rate:
[tex]\frac{500m}{1min} *\frac{1km}{1000 m}*\frac{1mile}{1.61km}*\frac{60min}{1hr}=18.63 miles/hr[/tex]
Computing the difference between the two,
18.63 miles/hr - 12.42 miles/hr = 6.21 miles/ hr ≈ 6.2 miles/ hr
thus, by 6.2 miles per hour, Sheri commutes more quickly.
What are conversions in maths?
An amount that is multiplied or divided between one set of units and another is known as a conversion factor. In the event that a conversion is necessary, it must be carried out with the proper conversion factor to produce an equivalent value. For instance, when translating between inches and feet, 12 inches equals one foot.
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3.if the m∠1 is 57° , find the measure of ∠6.
Show your work
123°
180°-57°=<6=123°
If the height of a cone is three
times of the radius of the base and its volume is
343 cm³, then find the radius of the base of the cone
As a result, the cone's volume is equal to three times its radius √343/π .
How to understand the concept of mensuration?The word "mensuration" literally means "to measure." It is typically employed when dealing with geometric shapes when it is necessary to calculate different physical values like perimeter, area, volume, or length. Mensuration is the term for measuring these amounts.
According to the given data:So with respect to the information provided to us :
Height of a cone =3* radius of the base
let height be h and radius be r
h=3r
The Formula for volume of cone is:
V=1/3hπr²
Putting the value we get:
343=1/3*π*r²*3r:
r= √343/π
Therefore ,
the volume of the cone whose height is three times its radius is:
√343/π
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Question 12
REASONING Given: 2a²
a
= 72. Conjecture: a = 6. Write a counterexample.
A counterexample to show that 2a^2 = 72 where a = 6 is that a = -6 will still arrive at 72
What is counterexample?This is a term that counters a statement. we can therefore say that counterexample is one that proves a statement to be false.
How to write the counterexamplegiven data
2a² = 72
Conjecture: a = 6
The counterexample is a = -6
substituting a = -6 into the given equation
= 2a²
= 2 * ( -6 )^2
= 2 * ( 36 )
= 72
Since a = -6 gave same answer of 72 as a = 6 then a = -6 is the counterexample
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Would the image be categorized as a function or as a relation? Use at least one sentence to explain your answer.
Answer:
This is a relation, not function.Step-by-step explanation:
The attached graph is NOT a function, since it doesn't pass the vertical line test.
If a vertical line cuts the graph more than once, then this relation is not a function.
i give brainlest can somebdy pls help me
After evaluating the given fraction, the resultant answer is (C) 1¼.
What are fractions?An element of a whole is a fraction. The number is represented mathematically as a quotient, where the numerator and denominator are split. Both are integers in a simple fraction. A fraction appears in the numerator or denominator of a complex fraction. The numerator of a proper fraction is less than the denominator. There are three main categories of fractions in mathematics. Proper fractions, incorrect fractions, and mixed fractions are these three types. The expressions with a numerator and a denominator are called fractions.So, 8 ÷ 6⅖:
Now, evaluate as follows
8 ÷ 6⅖8 ÷ 30+2/58 ÷ 32/58/1 × 5/325/4Which can also be written as 1¼.
Therefore, after evaluating the given fraction, the resultant answer is (C) 1¼.
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Evaluate the quantity of x cubed minus 2x squared plus 3x minus 7 end quantity divided by the quantity of x minus 1 end quantity period. x squared minus x plus 2 minus 5 divided by the quantity x minus 1 end quantity x squared minus 2x plus 2 minus 9 divided by the quantity x minus 1 end quantity x squared minus x plus 4 minus 9 divided by the quantity x minus 1 end quantity x cubed minus 2x plus 2 minus 5 divided by the quantity x minus 1 end quantity
Answer:
(x^3 + 3x^2 - 2x + 7)/x- 2
Expand the numerator in the above expression
(x^3 + 5x^2 - 2x^2 + 8x - 10x - 16 + 23)/(x - 2)
Rearrange the terms of the numerator in the above expression
(x^3 + 5x^2 + 8x - 2x^2 - 10x - 16 + 23)/(x- 2)
Factorize the numerator in the above expression
[x(x^2 + 5x + 8) - 2(x^2 + 5x + 8) + 23]/(x - 2)
Factor out x^2 + 5x + 8
[(x -2)(x^2 + 5x + 8) + 23]/(x - 2)
Split the fractions
(x -2)(x^2 + 5x + 8)/(x - 2) + 23/(x - 2)
Divide the common factors
(x^2 + 5x + 8) + 23/(x - 2) hope this help btw your welcome
Answer:
The answer is really option A. x^2 - x +2-5/x-1
Step-by-step explanation:
I just took the test and got it right :)
Help please i forgot about this
Whats the product of 3 plus 4
whats 5 times 8
In a Sports league each team has 36 players and 3 coaches. There are also a number of team assistants. The ratio of team assistants to players is 1/6. What is the ratio of coaches to assistants?
Answer:
1/2
Step-by-step explanation:
We know that each team has the following:
36Players + 3Coaches + ?Assistants = Sports League
We know that the ratio of assistants to players is 1/6, rewrite the equation accordingly:
36Players + 3Coaches + 6Assitants = Sports League
Now find the ratio of coaches to assistants:
3Coaches / 6Assistants = 1/2
how do i multiply these ? (5x-6.9)(2x+12.2)
Answer:
10x^2 + 47.2x - 84.18
Step-by-step explanation:
You distribute both terms in the first set of parentheses (5x-6.9) to the terms in the second set (2x+12.2) So when you're doing it 5x gets multiplied by 2x and 12.2 and -6.9 gets multiplied by 2x and 12.2. Then you simplify as much as possible
Given mn, find the value of x.
Answer:
(2x+5)° (8x+5)°
Submit Answer
m
00
Step-by-step explanation:
2x+(-8x) +5-5
-5=0. u Wii collect like terms and if u do that that's the answer if am wrong let me know