Answer: This can be done by properly interpreting the words into appropriate signs and digits.
Please check below for explanation of WORD PROBLEMS.
Step-by-step explanation: In mathematics, as you move to a higher level, you would encounter more of word problems than simply figures and signs. This simply means, you would be presented with series of statements that should be interpreted and hence an equation would be derived and then solution proffered. First it is really important to note that an equation only exists when the expression on one side is equal to that on the other side. Equally important are the following expressions;
(1) Sum refers to addition (plus)
(2) Difference refers to subtraction (minus)
(3) Product refers to multiplication (times) and
(4) Quotient refers to division (divide)
(5) The same as refers to equal to
Hence, interpreting the expression is largely determined by the use of any of the above expressions and the slightest error in interpreting negates everything afterwards.
So on the one hand, one set of statements will usually tell you that, "so and so is the same as" this and that. This is interpreted as "so and so" is equal to "this and that."
A simple example would help to illustrate this;
Illustration:
(a) Four times a number added to a dozen would result in seven times that same number.
Solution; Let the number be x. Four times a number means 4 times x, which gives you 4x.
Added to a dozen means you add 4x to a dozen, that is 4x + 12.
This would result in seven times that same number. Simply put, what you just did above (4x + 12) would result in or would be equal to 7 times x which is 7x. This now gives you,
4x + 12 = 7x.
Therefore to determine each of the two expressions of an equation is largely dependent on properly interpreting the words into the appropriate signs and figures (that is, plus, minus, times, divide and equal to).
Given that ABCD is a rhombus, find the value of x.
Answer:
C
Step-by-step explanation:
The diagonals of a rhombus are perpendicular bisectors of each other.
Thus the angle at the intersection of the diagonals is 90°
The sum of the 3 angles in a triangle = 180°
Sum the angles in the lower triangle and equate to 180, that is
90 + x + x + 40 = 180
2x + 130 = 180 ( subtract 130 from both sides )
2x = 50 ( divide both sides by 2 )
x = 25 → C
The value of x is 25.
What are some of the properties of a rhombus?
All four sides are equal.Diagonals bisect each other at 90°.Given
ABCD is a rhombus,
∠CAD = x°,
∠BDA = (x + 40)°.
Find the equation in x
Let the point where the diagonals intersect be E.
Then, using the property of the rhombus ∠AED = 90°.
We know, in a triangle that the sum of all the three interior angles equals 180°. So, we get,
∠AED + ∠BDA + ∠CAD = 180°
⇒ ∠BDA + ∠CAD = 180° - ∠AED
= 180° - 90° = 90° (∠AED = 90°)
Put the given values of these angles,
(x + 40)° + x° = 90°.
This is the equation to be solved to obtain x.
Solve for x
(x + 40)° + x° = 90°
⇒ (2x)° = 90° - 40° = 50°
⇒ x° = (50 / 2)°
⇒ x = 25.
The required value of x is 25.
Learn more about the properties of a rhombus here
https://brainly.com/question/12189679
#SPJ2
What is the domain of g(x)?
Answer:
-2 ≤x≤5
Step-by-step explanation:
The domain is the inputs
The lowest value of x is -2 and every value of x is valid up to 5
-2 ≤x≤5
On Monday the price of a company’s stock is $30 per share. On Tuesday, the stock price drops $3, on Wednesday it rises $7, on Thursday it rises $3, and on Friday it drops $4. Write a mathematical statement that represents the situation and determine the price at the end of the week.
Answer:
The price at the end of the week is $33.
Step-by-step explanation:
We are given that on Monday the price of a company’s stock is $30 per share. On Tuesday, the stock price drops $3, on Wednesday it rises $7, on Thursday it rises $3, and on Friday it drops $4.
The price of a company’s stock on Monday = $30 per share
So, the mathematical statement that represents the situation is given by;
Price of company’s stock on Monday = $30
On Tuesday, the stock price drops $3, so the price of company’s stock on Tuesday = Price of company’s stock on Monday - Drop in price on Tuesday
= $30 - $3 = $27
On Wednesday, the stock price rises $7, so the price of company’s stock on Wednesday = Price of company’s stock on Tuesday + Rise in price on Wednesday
= $27 + $7 = $34
On Thursday, the stock price rises $3, so the price of company’s stock on Thursday = Price of company’s stock on Wednesday + Rise in price on Thursday
= $34 + $3 = $37
On Friday, the stock price drops $4, so the price of company’s stock on Friday = Price of company’s stock on Thursday - Drop in price on Friday
= $37 - $4 = $33
Hence, the price at the end of the week is $33.
Solve x^4 -3x^2 +2=0 using substitution. U=
Answer:
U = x^2
hope this helped!
Answer:
x^2
Step-by-step explanation:
The person above me is spitting mad facts and da TRUTH and also UNUS ANNUS
th
Write an explicit formula for An, the nth
term of the sequence 15, 23, 31, ....
Answer:
a₁ = 15 and common difference = 8 so the formula is:
aₙ = 15 + (n - 1) * 8
= 8n + 7
can i have help thanks
Answer:
∠ BOC = 42°
Step-by-step explanation:
Since OA and OC are perpendicular , that is at 90° to each other, then
∠ AOB + ∠ BOC = 90 , substitute values
5x + 8 + 6x - 6 = 90
11x + 2 = 90 ( subtract 2 from both sides )
11x = 88 ( divide both sides by 11 )
x = 8
Thus
∠ BOC = 6x - 6 = 6(8) - 6 = 48 - 6 = 42°
Work of the size of one exterior angle
Answer:
<x = 36°
Step-by-step explanation:
In a regular decagon, Every interior angles is equal to 144.
So,
<x + 144 = 180 [Angles on a straight line]
<x = 180-144
<x = 36°
please help me whats the answer for jim has 100 cards there is a whole number from 1 to 100 on each card no cards have the same number jim puts a star on every card has a multiple of 3 on it he puts a circle on every card that has a multiple of 7 on it what number are on the cards that have both a star and a circle on them the final line on your answer must list only these numbers
Answer:
4
Step-by-step explanation:
Multiples of 7 and 3 are 21, 42, 63, 84
Hope this helps.
Answer:
21, 42, 63, 84
Step-by-step explanation:
Cards with both star and circle are multiples of both 3 and 7, ie 3*7= 21
21, 21*2= 42, 21*3= 63, 21*4= 84
So 21, 42, 63 and 84 are the required numbers
x square + 4 x - 12 all over x squared - 2x
Answer:
[tex]\frac{x+6}{x}[/tex]
Step-by-step explanation:
=> [tex]\frac{x^2+4x-12}{x^2-2x}[/tex]
=> [tex]\frac{x^2+6x-2x-12}{x(x-2)}[/tex]
=> [tex]\frac{x(x+6)-2(x+6)}{x(x-2)}[/tex]
=> [tex]\frac{(x-2)(x+6)}{x(x-2)}[/tex]
Cancelling (x-2)
=> [tex]\frac{x+6}{x}[/tex]
2x + 3y = 13
4x - y = -2
Answer:
x=1/2. y=4
Step-by-step explanation:
4(2x+3y=13)=8x+12y=52
2(4x-y=-2)=8x-2y=-4
subtract equation one from equation two to get
14y=56 then u will divide bothe sides by 14. for x u substitute y in equation one
Answer:
x = 1/2 y = 4
Step-by-step explanation:
Equation 1
2x + 3y = 13
Equation 2
4x - y = -2
Multiply equation 2 by 3
12x - 3y = -6
Add equation 1 to 3
14x = 7
x = 7/14
x = 1/2
Substitute x into equation 1
2(1/2) + 3y = 13
3y = 13 -1
3y = 12
y= 12/3
y = 4
x =1/2 y = 4
Hope this helps.
Which symbol would make the statement TRUE?
-3/4
-0.75
A. <
B. >
C. =
D. none of the above
Answer: C
Step-by-step explanation: -3/4 is equal to -.75 ,
Elijah uses 2 pints of stain on each table that he makes . How many tables can he paint with 1 gallon of stain ? sets
Answer:
4 sets
Step-by-step explanation:
1 gallon contains 8 pints. It takes 2 pints per table, so we should divide 8 by 2.
By doing this, we get 4, therefore he can stain 4 sets of tables with a gallon of stain.
What is one value that makes the fraction (4x-8)/(x^2+x-42) undefined? Plz help me I'll mark brainliest! And plz explain how you did it plz ty!
Answer:
x = 6
Step-by-step explanation:
To make a fraction undefined, the denominator would have to be equivalent to zero. If that is so, x^2 + x - 42 would have to equal 0, and we would have to solve for the value of x;
[tex]x^2 + x - 42 = 0,\\Factored Equation = \left(x-6\right)\left(x+7\right),\\\left(x-6\right)\left(x+7\right) = 0,\\\\Zero Factor Principle, \\x - 6 = 0, and, x + 7 = 0\\\\x = 6, x = - 7\\\\Solution = Either, 6 / - 7[/tex]
We can take x to be either 6 or - 7, but as the question asks us to state only one value, I will take x = 6.
what are the y-intercept and axis of symmetry of this quadratic function??
Answer: The answer is B I believe
Step-by-step explanation:
Answer:
y-intercept : (0,5), D
axis of symmetry : x = 3, E
What is the units digit of $7^7$ when expressed as an integer?
Answer:
3
Step-by-step explanation:
Answer:
3
Step-by-step explanation:
Just stick it into a calculator lol
Decrease £248 by 30%
Answer:
173.6
Step-by-step explanation:
0.7(248)
173.6
Answer:
£ 173.6
Step-by-step explanation:
£248 *0.30= 74.4
£248 -74.4 =173.6
The sequence of the differences, 2, 4, 8, 16, 32, … is a geometric sequence with:
Answer:
The first term as 2.
Pattern: Multiply the previous term and 2 to get the next term.
Step-by-step explanation:
The pattern is every term is 2× the previous term.
The sequence of the differences, 2, 4, 8, 16, 32, … is geometric. The pattern is every term is 2 times the previous term.
What is geometric series?The geometric series is a series in which the ratio of two consecutive numbers is constant.
The sequence of the differences, 2, 4, 8, 16, 32, … is geometric.
So, The ratio of two consecutive numbers is constant.
r = 4/2 = 2
r = 8/4 = 2
Thus, The pattern is every term is 2 times the previous term.
Learn more about geometric series;
https://brainly.com/question/13041183
#SPJ2
What is the axis of symmetry of the quadratic function y = 2(x + 3)2 + 5?
x = –5
x = –3
x = 5
x = 3
Answer:
-3
Step-by-step explanation:
m 1 = a) 40 b) 130 c) 50
Answer:
A) 40
Step-by-step explanation:
The angle adjacent 40 is complementary to it, meaning that it must have a measure of 90-40=50 degrees. This angle is a vertical angle with the one inside the triangle, meaning that it also has an angle of 50 degrees. Now that you know two of the angles in the triangle and you know that all of the interior angles of a triangle add up to 180 degrees, you can find angle 1:
[tex]\angle 1=180-90-50=40^{\circ}[/tex]
Hope this helps!
Answer:
<1 = 40
Step-by-step explanation:
Corresponding angles are equal and <1 and 40 are corresponding angles on parallel lines
straight line graphs: find the equation of the lines shown
Answer:
1. y = -2n + 9
2. y = (1/2)x + 1/2
Step-by-step explanation:
1.
The equation of a line is denoted by y = mx + b, where m is the slope and b is the y-intercept.
Slope is calculated by taking two coordinates and dividing the difference of the y-coordinates by the difference of the x-coordinates. The y-intercept is where the line intersects the y-axis.
Let's choose any two points on the line: (4, 1) and (3, 3). Then:
slope = m = (3 - 1) / (3 - 4) = 2 / (-1) = -2
Now, we can also see that at the point (0, 9), the line intersects the y-axis, so that means b = 9.
The equation is thus y = -2n + 9.
2.
Let's again choose any two points to find the slope: (1, 1) and (3, 2). Then:
slope = m = (2 - 1) / (3 - 1) = 1/2
We can see that the line crosses the y-axis at the point (0, 1/2), so that means b = 1/2.
The equation is thus y = (1/2)x + 1/2.
~ an aesthetics lover
Answer:
1. y = -2x + 9
2. y = (1/2)x + 1/2
Step-by-step explanation:
There was a mistake on the last one so I would like to correct it it is
y= -2x+9
The other one said -2n its -2x
The snail moved 6 inches in 120 minutes. What was the average speed of the snail in inches per minute
20 of an inch per minute
1
O z of an inch per minute
O2 inches per minute
O 20 inches per minute
Answer:
The answer is; the snail moved 1 inch every 20 minutes.
Step-by-step explanation:
120 divided by 6 is 20
Answer:
A) 1 Over 20 of an inch per minute
Step-by-step explanation:
I took this test and got 100
Anybody know this ? Please help :(
Answer:
D
Step-by-step explanation:
5.50. 5.50+0.25= 5.75, 5.75+0.25= 6.00, 6.00+0.25= 6.25, 6.25+0.25= 6.50
Option D is the answer:
5.50, 5.75, 6.00, 6.25, 6.50...
Brainliest will be given i need answer ASAP please.
Simplify 84,375/325 to its lowest multiple Example 16/4 = 4/1
Answer:
3375/13
Step-by-step explanation:
it's found though this equation [tex]\frac{84375/25}{325/25}[/tex]
Answer:
[tex]3375/13[/tex]
Step-by-step explanation:
[tex]84,375/325[/tex]
Divide the numerator and denominator by 25.
[tex]3375/13[/tex]
[tex]=259.615385[/tex]
apply the distributive property to factor out the greatest common factor for 9+12n I need an expression too
Answer:
3(3+4n)
Step-by-step explanation:
The volume of the cylinder is 230 cubic units. What is the volume of the
cone? Round to the nearest enth if necessary.
Answer:
Step-by-step explanation:
The formula for determining the volume of a cylinder is expressed as
Volume = πr²h
Where
r represents the radius of the cylinder
h represents the height of the cylinder
π is a constant
The formula for determining the volume of a cone is expressed as
Volume = 1/3πr²h
Where
r represents the radius of the cone
h represents the height of the cone
This means that the volume of the cone is 1/3 × volume of cylinder. Since the volume of the given cylinder is 230 cubic units, then
Volume of cone = 1/3 × 230 = 76.7 cubic units
Mr. Bloop can high jump 5.75 feet. How far short is that of Charles Austin's record of 7 ft 10 in?
Answer:
5.75 feet is the same as 5 ft 9 inches (because 12 in = 1 ft and 0.75 * 12 = 9 so its 9 in). 7 ft 10 in - 5 ft 9 in = 2 ft 1 in.
Is the following statement true or false? The intersection of a plane and a ray can be a line segment.
Answer:
False
Step-by-step explanation:
Is the following statement true or false?
The intersection of a plane and a ray can be a line segment.
It is false. Correct one is the point.Please answer asap thanks
Answer:
V = 200 pi units ^3
Step-by-step explanation:
The volume of a cone is given by
V = 1/3 pi r^2 h
V = 1/3 pi ( 10 ^2) (6)
V = 1/3 pi (100) *6
V = 200 pi
What is the value of x when y=31
Answer:16
Step-by-step explanation:
32/16=2
8*2=16
Hope that helps :D
Answer:
16
Step-by-step explanation:
Direct variation
y = kx
16 = k*8
Divide each side by 8
16/8 = 8k/8
2 = k
The equation is y =2x
y =2x
Let y =32
32 = 2x
Divide by 2
32/2 = x
16 =x
Important!!!
That is the distance between (-5, 4) and (-1, 4)?
-5 units
-4 units
4 units
5 units
Answer:
4 units
Step-by-step explanation:
Since the y value is the same, we only have to look at the x value
-1 - -5
-1 +5
4
The distance is 4 units
Answer:
4 units
Step-by-step explanation:
if you graph these 2 points, they'll be on the same line of the graph separated by 4 units