Answer:
A. -5
Explanation:
For (3x + 15)/(6 - x) to be equal to zero. Set the equation to 0.
Doing so:
(3x + 15)/(6 - x) = 0
3x + 15 = 0(6 - x)
3x + 15 = 0
3x = -15
x = -15/3
x = -5
Therefore, the value of x is -5 to equal to zero.
11. Calculate the weight on earth of an object with a mass of 48 kg. Gravitational acceleration (a) = 9.81 m/s ² Show all steps and formulae used. (3) ✓
Answer:
470.88 N
Step-by-step explanation:
F = ma
48 ( 9.81) = 470.88 N ( 105.958 lbs)
Write a rule to describe each translation
Answer:
slide - translate
Step-by-step explanation:
you slided them both as neither of the figures changed
find Y if AB bisects DAC and CB bisects ACE
Answer:
L1 and L2 are parallel
BAC = 58° as it is given in the question that AB bisects DAC
similarly BCE = y°
angle B = 90° ( from figure)
Y + 58° + 90° = 180 ( angle Sum property of a triangle).
Y + 148° = 180°
Y = 180 - 148
Y = 32°
please help. Show with steps please.
Solve the compound inequality.
0 < 5-2x/3 <5
Answer: The answer is x < 5/2 and x > -5.
Step-by-step explanation:
First you need to separate the inequality and keep x on one side to maintain consistency. For instance the problem-
[tex]\frac{5-2x}{3} > 0\\\frac{5-2x}{3} < 5\\[/tex]
Now solve as normal.
*Note: When dividing a side or multiplying a side by a negative number, the sign of the inequality switches (this will be shown when I do the equation if it doesn't make since how I word it).
[tex]5-2x > 0*3\\5-2x < 5*3[/tex]
[tex]-2x > 0-5\\-2x < 15-5[/tex]
[tex]x < \frac{-5}{-2} =x < \frac{5}{2} \\x > \frac{10}{-2} =x > -5[/tex]
So, x < 5/2 and x > -5.
If anything is confusing about the procedure just leave a comment, and I'll try to explain further.
Find f(g(x)) for the functions f(x)=5sqrt(x+1)-2 and g(x)=x^2-1
The value of the composite function f(g(x)) is 5x + 2
Composite functionsComposite functions are functions inside another function. Given the following functions:
f(x) = 5√x+1 - 2
g(x) = x² - 1
Determine the composite function f(g(x))
f(g(x)) = f(x² - 1)
f(x² - 1) = 5√x² - 1+1 - 2
f(x² - 1) = 5√x² + 2
f(x² - 1) = 5x + 2
Hence the value of the composite function f(g(x)) is 5x + 2
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What is the area of the triangle?
24 square units
32 square units
48 square units
96 square units
Answer:
24 square units
Step-by-step explanation:
1) the area can be calculated using the formula:
A=0.5*a*h, where a- base, h-height;
2) if a=8, h=6, then the required area is:
A=0.5*8*6=24 [units²].
Answer: 24 square units
Step-by-step explanation:
The base: 8
The height: 6
The area: 8 x 6 / 2 = 24
/ stands for divided by
The radius of a circle is 3ft. What is the circumference of the circle? Use 3.14 for pie.
RATS is a parallelogram. M
Answer:
Answer:
x = 12
Step-by-step explanation:
m∠S + m∠T = 180
8x + 7x = 180
15x = 180
x = 12
does this help?
A sells an article to B at profit of 20% and B sells it to C at a profit of 25%. If C buys it for Rs.225, what did A pay for it?
Answer:
A pay 120 for itLet the cost price be X
A Sells to B
profit = 20%
= cost price + 20%
= X + 20/100 of X
= 6x/ 5
B sells to C
profit = 25%
= Cost price + + 25%
= cost price + 25%
= 6x/5 + 25/100*6x/5
= 6x/5.+ 3x/10.
= 3x/2
3x/2 = 225.
3x = 450
x = 150.
sp = C. p + profit
S. p - profit = C. p
X - X/5
4x/5
4(150)/5.
120
Need help with this please!! :)
What is the solution to the equation shown below?
-1/3(6x+6)+21=3y
Answer:
A or 19/5
Step-by-step explanation:
To solve first we isolate are variables so we distubte to get -2y-2+21=3y then we add 2y to the opposite side to get -2+21=5y. Then we add -2+21 to get 19 so are equation is 19=5y. Next we just divide 19 by 5 to get y=(19/5) or option A
he table shows the height of water in a pool as it is being filled. A table showing Height of Water in a Pool with two columns and six rows. The first column, Time in minutes, has the entries, 2, 4, 6, 8, 10. The second column, Height in inches, has the entries, 8, 12, 16, 20, 24. The slope of the line through the points is 2. Which statement describes how the slope relates to the height of the water in the pool? The height of the water increases 2 inches per minute. The height of the water decreases 2 inches per minute. The height of the water was 2 inches before any water was added. The height of the water will be 2 inches when the pool is filled.
The height of water increases by 2 inches per minute option first "The height of the water increases 2 inches per minute" is correct.
What is the slope?The ratio that y increase as x increases is the slope of a line. The slope of a line reflects how steep it is, but how much y increases as x increases. Anywhere on the line, the slope stays unchanged (the same).
[tex]\rm m =\dfrac{y_2-y_1}{x_2-x_1}[/tex]
We have given a table:
Time height
2 8
4 12
6 16
8 20
10 24
The slope of the line = (12-8)/(4-2) = 4/2 = 2
The value of the slope is positive we can say, the height of water increases as time passes.
Thus, the height of water increases by 2 inches per minute option first "The height of the water increases 2 inches per minute" is correct.
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the answer is A: The height of the water increases 2 inches per minute.
hope this helped :)
Which is the equation of the line with slope 0 passing through the point (-3, -1)?
factorise 4ab +6bn-2a-3n
Answer:
(2b - 1)(2a + 3n)
-----------------------------------------------
Given polynomial
4ab + 6bn - 2a - 3nFactorize it as below:
4ab + 6bn - 2a - 3n =
(4ab - 2a) + (6bn - 3n) = Regroup
2a(2b - 1) + 3n(2b - 1) = Factorize each group using common factors
(2b - 1)(2a + 3n) Factorize using common factor
Answer:
[tex](2b-1)(2a+3n)[/tex]
Step-by-step explanation:
Given expression:
[tex]4ab+6bn-2a-3n[/tex]
Factorize the first two terms and the last two terms separately:
[tex]\implies 2b(2a+3n)-1(2a+3n)[/tex]
Factor out the common term (2a + 3n):
[tex]\implies (2b-1)(2a+3n)[/tex]
Which number produces a rational number when added to 1/2?
Answer:
Another rational number.
Step-by-step explanation:
For example, [tex]\pi[/tex] is incorrect because It is a irrational number
you must add another rational number to 1/2 to make the sum rational.
Rational number are numbers that can be converted into a fraction.
all natural numbers, whole numbers, integers, are rational.
and all rational and irrational numbers are real numbers
The graph shows that is translated horizontally and vertically to create the function .
On a coordinate plane, 2 exponential functions are shown. f (x) approaches y = 0 in quadrant 2 and increases into quadrant 1. It goes through (negative 1, 0.5) and crosses the y-axis at (0, 1). g (x) approaches y = 2 in quadrant 2 and increases into quadrant 1. It goes through (0, 2) and (2, 3).
What is the value of h?
−2
−1
1
2
According to the function transformations, the value of h is -2
How to determine the value of h?The complete question is in the attachment
The functions are given as:
[tex]f(x) = (2.5)^x[/tex]
[tex]g(x) = (2.5)^{x-h[/tex]
From the question, we understand that the function f(x) is translated to the left to get g(x)
From the attached graph, we can see that the function h(x) is 2 units to the left of f(x).
This transformation is represented by:
(x, y) => (x + 2, y)
So, we have:
x - h = x + 2
Evaluate the like terms
h = -2
Hence, the value of h is -2
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Answer:H=-2
Step-by-step explanation:
Question 5 of 50
Perpendicular lines are best defined as which of the following?
OA. Lines that intersect
O B. Lines that meet to form a right angle
OC. Lines that are not coplanar
O D. Lines that never intersect
A
if the ratio of three angles of a triangle is 2:3:4 find the size of the largest angle
A man wants to cut down a tree in his yard. To ensure that the tree doesn’t hit anything, he needs to know the height of the tree. He measures the distance from the tree at 14 m and the angle of elevation to the tree at 88°. What is the height of the tree to the nearest tenth of a meter
Answer:
400.9 m
Step-by-step explanation:
Find the reciprocal of the sum of the reciprocals of 1/-5 and -1/6
Answer:
-1/11
Step-by-step explanation:
A reciprocal means the reverse of a number. So the numerator becomes a one and the number goes in the denominator (for example 2 becomes 1/2). Or vice versa: the one becomes the denominator and the denominator becomes the numerator (for example 1/2 becomes 2/1 which is 2).
The reciprocal of -1/5 is -5.
The reciprocal of -1/6 is -6.
The sum of both reciprocals: -5 + -6 = -11
The reciprocal of the sum -11 is -1/11.
Which ordered pair is on the graph of the equation 4x + 3y = 13?
(1, 6)
(0, –3)
(1, –3)
(4, –1)
ABC is an isosceles triangle, with AB = AC. find X
Answer:
67.13°
Step-by-step explanation:
First separate triangles then you use Pythagoras theorem to get the third side and then apply the sine rule
The following are scores for students in Ms. Kennedy's math class.What is the range of the scores?
451
560
600
422
603
514
A 109
B 149
C 178
D181
Answer:
The answer will be D. 181
Step-by-step explanation:
603 - 422 = 181
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Generalize A system of linear equations has exactly one solution. What can you say about the slopes of the lines when the equations are graphed? How do you know? Generalize A system of linear equations has exactly one solution . What can you say about the slopes of the lines when the equations are graphed ? How do you know ?
If a system of linear equations has exactly one solution then the slopes of both the lines should be different.
Given A system of linear equations has exactly one solution.
Linear equation is a type of equation when when plotted on the graph gives a straight line. The slope is the ratio of the vertical change to the horizontal change between two distinct points on a line.
let two equations be who have one solution
2x+3y=7
5x+6y=1
solving them
x=7-3y/2
put the value of x in second equation
5(7-3y)/2+6y=1
35-15y/2+6y=1
35-15y+12y=2
-3y=-33
y=11
put the value of y in x=7-3y/2
x=7-3*11/2
x=7-33/2
x=-26/2
x=-13.
There is only one solution which is (-13,11)
Taking equations and convert them into standard form
first
y=7/3-2/3x
second
y=1/6-5/6x
The standard form is y=a+bx where b is slope
from the above equations we can find that the slope of first equation is -2/3 and the slope of second equation is -5/6. In this way we are able to conclude that slopes should be different for one solution.
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15 In the figure, O is the centre of the circle. The diameter of the circle, AB, is 14 cm, and
is the same as the length of each side of the square PQRS. Find
Answer:
56cmsquared
Step-by-step explanation:
if you look clearly at that question that diagram which has the coloured part out of that small square comes a quarter circle.
now take that quarter circle and get its area .
then put a dotted line such that they'll be formation of a triangle in that quarter circle.
then get the area of that quarter triangle in minus it from the area of the quarter circle.
and you'll get the area of 1 shaded part because you had subdivided those shaded parts by the dotted line you had kept earlier in order to emerge with a triangles
after that what multiply what you got by two to get the whole shaded part then finalize by multiplying by two because two shapes were shaded.
good day
Which pair of equations below represents two lines that are not parallel?
Select one:
a.
y = 2x + 8 and y = 2x + 8
b.
y = ( 1 / 6 ) x + 1 /2 and y = (1 / 6 ) x + 2
c.
y = ( 1 / 6 ) x + 8 and y = 6x + 4
d.
y = ( 1 / 2 ) x + 9 and y = ( 1 / 2) x + 4
The pair of equations (c) y = (1 / 6) x + 8 and y = 6x + 4 are not parallel
How to determine the pair of equations?A linear equation is represented as:
y = mx + b
Where m is the slope of the line
Two lines are said to be parallel if their slopes are the same
i.e. y = mx + b and y = mx + c
Using the above as a guide, the option (c) represents lines that are not parallel, because they do not have the same slope
Hence, y = (1 / 6) x + 8 and y = 6x + 4 are not parallel
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If a = 7, b = 2 and c = 3, evaluate: a-bc.
Answer: 1
Step-by-step explanation:
[tex]a-bc=7-2(3)=7-6=\boxed{1}[/tex]
Let’s say you bought a car for $16,500. The car is expected to last 8 years and then it can be sold for scrap for $500. The value at the end of the life of the car is sometimes called the “salvage value” or “residual value.” Part A: If we assume that the relationship between the value of the car and the year is linear, how much will the value of the car depreciate each year? Explain your strategy. Part B: Complete the table of values. Years of Ownership Value of the Car 0 1 2 Part C: Create a sketch of the data points on your paper. Be sure to label the graph thoroughly. Would it make sense to connect the points? 3) Consider all of the information you have collected in Question 2. Part A: Write an equation for the value of the car in terms of the year. Part B: What is the slope of the line? Explain what the slope means in this context. 4) Are the value of the car and the number of years since the car was purchased proportional? Justify your response. 5) Look at the changes in the value of the car and the corresponding changes in the years of ownership. Are the changes proportional? How do you know? 6) Examine the proportionality of these two equations: � = 2� + 3 � = 2� Which is an example of a linear equation that is also proportional? Justify your
Answer:
value of car depreciate each year = $2000
y + 2000x = 16,500
slope of line = -2000
No, not proportional
Step-by-step explanation:
Value of depreciation of an object is given by :-
Depreciation = [tex]\frac{ total Cost-scrap value}{estimated life}[/tex]
according to question ;
total cost = $16500
scrap value = $500
estimated life = 8 years
therefore,
depreciation = [tex]\frac{16500 - 500}{8}[/tex] = [tex]\frac{16000}{8}[/tex] = $2000
now,
let the value of car after 'x' years be 'y'
therefore linear equation showing the relation of x and y is
y + 2000x = 16500
The graph of a linear equation is a line.
If c = 0 in a linear equation (so y = mx), then the equation is a proportional linear relationship between y and x.
If c ≠ 0, then y = mx + c is a non-proportional linear relationship between y and x.
here equation is of type,
y = mx +c, thus it is not linear.
also in the equation y = mx +c,
'm' is the slope of line
therefore by comparing the equation,
y +2000x = 16500
y = -2000x + 16500
slope is - 2000
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Find the perimeter of the following shape, given its curves are made from parts of circles.
Give your answers in terms of .
4cm
4cm
4cm
The diagram is not drawn to scale.
help me pleaseeeeeeeeeeee i need the answer fast because it is limited
i will mark as brainiest
Answer:
D
Step-by-step explanation:
Original area = x * x = x^2
New area = x ( x +3.5) = x^2 + 3.5x <====the underlined is the increase in area
