In mathematics, the reciprocal, or multiplicative inverse, of a number x is the number which, when multiplied by x, yields 1. It is denoted 1/x or x-1.
A girl is twice as old as her sister. Five years hence, the product of their ages (in years) will be 375. Find their present ages. A girl is twice as old as her sister. Five years hence, the product of their ages (in years) will be 375. Find their present ages.
Answer: girls=20, sister=10
Step-by-step explanation:
Let x = the girl's sister's age (present)
Let 2x= the girl's age (present)
-------------------------------------------------------------
According to the question
(x+5)(2x+5)=375
Expand parentheses by FOIL (First Outer Inner Last)
2x²+5x+10x+25=375
Combine like term (5x and 10x)
2x²+15x+25=375
Subtract 375 on both sides
2x²+15x+25-375=375-375
2x²+15x-350=0
Find the factors (cross factor)
(x-10)(x+17.5)=0
x=10 or x=-17.5 (rej) ⇔ the age can't be negative
the girl's age is 20, and her sister's age is 10.
a colony is a statement far away from the government that rules it true or false
How are the solutions of an inequality different from the solutions of an equation?
Answer:
Step-by-step explanation:
+
there were 8 lunchboxes on the first table.there were 6 lunchboxes on the second table. how many more lunchboxes were on the first table then on the second table?
Answer:
2 lunchboxes more.
Step-by-step explanation:
Its 2 lunchboxes more as the question asked how many MORE lunchboxes the first table has then the second table so its bassically 8 - 6 = 2
Find the value of x.
A pair of intersecting lines is shown. The angle above the point of intersection is labeled left parenthesis 7 x minus 8 right parenthesis degrees. The angle directly opposite below the point of intersection is labeled left parenthesis 6 x plus 11 right parenthesis degrees.
A. –19
B. 125
C. 19
D. 55
The value of x is 19. Therefore, option C is the correct answer.
From the given figure, the two angles are (7x-8)° and (6x+11)°.
What is the vertical angle theorem?Vertical angles are a pair of non-adjacent angles formed by the intersection of two straight lines. In simple words, vertical angles are located across from one another in the corners of the "X" formed by two straight lines. They are also called vertically opposite angles as they are situated opposite to each other.
Now, (7x-8)° = (6x+11)° (Vertically opposite angles are equal)
⇒ 7x-6x = 11+8
⇒ x = 19°
The value of x is 19. Therefore, option C is the correct answer.
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The graph of y = –0.2x2 is the graph of y = x2.
Answer:
the answer is correct, "D"
Step-by-step explanation:
(wider than and opens in the opposite direction of) just took the test, made a 90%
y = -0.2*x^2 is a vertical dilation of scale factor 0.2 followed by a reflection over the x-axis of y = x^2
How to relate these two graphs?
We have two functions:
f(x) = x^2
g(x) = -0.2*x^2
The transformations used are:
Reflection over the x-axis.
For a function f(x), a reflection over the x-axis is written as:
g(x) = -f(x).
Vertical dilation.
For a function f(x), a vertical dilation of scale factor k is written as:
g(x) = k*f(x).
So here we can see that we have a vertical dilation of scale factor 0.2, followed by a reflection over the x-axis.
g(x) = -0.2*f(x).
So, g(x) opens in the opposite direction than f(x), and grows slower (because of the dilation).
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The path of water from a hose on a fire tugboat can be approximated by the equation y=-0.0055x^2 +1.15x + 5, where y is the height above the ocean and x is the distance from the tugboat. When the water is 6 ft above the ocean how far is it from the tugboat
Answer:
The water is 208.22ft from the tug boat
Step-by-step explanation:
The governing equation is [tex]y=-0.0055x^2 +1.15x + 5[/tex]
y is the height above the ocean
x is the distance from the tugboat
if y= 6ft, the equation will now become
[tex]6=-0.0055x^2 +1.15x + 5[/tex]
we can arrange this properly to form a quadratic equation by grouping like terms.
[tex]-0.0055x^2 +1.15x -1=0[/tex]
solving quadratically we have two values of x as 208.22ft and 0.873 ft.
We can take a more realistic value as a solution to our problems:
208.22ft
Tina has 1/2 of a pan of cornbread left from a dinner party. She eats 1/2 of the leftover part the next night. How much of the whole pan does tina eat? Write and solve this equation
Answer:
Tina ate 3/4 of the whole pan of cornbread.
Step-by-step explanation:
Let the amount of cornbread in the initial pan be x.
After the dinner party, Tina has 1/2 of x left; That is 1/2x
If she eats 1/2 of the leftover, that will be 1/2 of 1/2x that is eaten. This will be 1/4x that is eaten.
To find the potion of the whole pan that Tina ate, we will add the potion she ate during the party to the portion of the leftover she ate the next night.
That will be 1/2x + 1/4x =3/4x
Therefore, Tina ate 3/4 of the whole pan of cornbread.
A jar contains 16 black balls,13 blue balls and 2 red balls in a bag. A ball is drawn in random. Find the probability of drawing a black ball? Find the probability of drawing a blue ball? Find the probability of not drawing a red ball?
Answer:
black: 16/31 blue: 13/31 red 2/31
16 black, 13 blue, 2 red
16+13+2 = 31 total
16/31 is the probability of picking black
13/31 is the probability of picking blue
2/31 is the probability of picking red, so 29/31 is the probability of not picking red (since 31-2 = 29 are not red out of 31 total)
20. Rolando drives at least 40 miles but less than 60 miles each week.
Part A. Write and then graph the compound inequality representing all of the possible distances Rolando could
drive for 8 weeks. (7 points)
Answer:
Step-by-step explanation:
60 miles
A rectangular prism has a volume of 170 cubic centimeters. The length of the prism is 5 centimeters, and the height of the prism is 17 centimeters. What is the width of the prism. Enter the answer in the box .
Answer:
The width of the prism is 2 cm
Step-by-step explanation:
The given parameters are;
The volume of the prism = 170 cm³
The length of the prism = 5 cm
The height of the prism = 17 cm
The volume of the prism is given by the relationship v = Length, l × Height, h × Width, w
Therefore;
The volume of the prism = 5 cm × 17 cm × w = 170 cm³
Which gives;
w = 170 cm³/(5 cm × 17 cm) = 170 cm³/(85 cm) = 2 cm
∴ The width of the prism = 2 cm.
The width of the prism is 2cm given length of the prism is 5 centimeters, and the height of the prism is 17 centimeter.
The formula for calculating the volume of a rectangular prism is expressed as:
V = LWH where:
L is the lengthW is the widthH is the heightGiven the following:
V = 170cm³
L = 5cm
H = 17cm
Required
Width
Substitute the given values into the formula:
170 = 5 * 17 * W
170 = 85W
W = 170/85
W = 2cm
Hence the width of the prism is 2cm
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5x
2x
7x
4x
Equation
X=
Answer:
look this for the solution
If anybody is good at math please help me out.
Step-by-step explanation:
The general equation of a straight line graph is y = mx + c, where m is the gradient of the line and c is the y-intercept.
Gradient = (2 - (-18)) / (3 - (-2)) = 20/5 = 4.
So y = 4x + c.
When x = 3, y = 2. (Given in the question)
This means that 2 = 4(3) + c, hence c = -10.
The answer is y = 4x - 10.
Did you know that chickens sometimes eat vegetables and fruits? A farmer likes to give the chickens apples to share. The farmer observes that 3 chickens eat 5 apples. What is the ratio of the number of chickens to apples? 5:2 5:3 2:5 3:5
Answer:
3:5
Step-by-step explanation:
Answer:
its 3:5
Step-by-step explanation:
Is -5/3 rational or irratuonal
Click on the graph until the graph of a line with undefined slope appears.
Answer:
The graph with the vertical line.
Step-by-step explanation:
All vertical lines have an undefined slope. Horizontal lines have zero slope, and diagonal lines have a slope.
When calculating a slope for a vertical line, you would have to divide by zero. The quotient of any number and 0 are undefined, as you cannot divide by zero. This is what makes vertical lines have an undefined slope.
Hope this helps.
I have a math question g=mB-2qB and I have to solve for B
Answer:
[tex]B = \frac{g}{m-2g}[/tex]
Step-by-step explanation:
Given
[tex]g = mB - 2qB[/tex]
Required
Solve for B
[tex]g = mB - 2qB[/tex]
Factorize the expression
[tex]g = B(m - 2q)[/tex]
Divide both sides by m - 2g
[tex]\frac{g}{m-2g} = \frac{B(m - 2q)}{m-2g}[/tex]
[tex]\frac{g}{m-2g} = B[/tex]
Reorder
[tex]B = \frac{g}{m-2g}[/tex]
Kyle is installing new baseboards and carpet in his rectangular living room. He measured the length as 24.25 feet and the width as 16.4 feet. Select Yes or No for each statement.
Answer:
answer is yes,yes, no
Step-by-step explanation:
The area of the rectangular carpet is equivalent to 397.7 ft².
What is the area of rectangle? What is equation modelling? What is a mathematical equation and expression?The area of a rectangle is equivalent to -
Area = Length x Breadth
[A] = [L] x [B]
Equation modelling is the process of writing a mathematical verbal expression in the form of a mathematical expression for correct analysis, observations and results of the given problem.A mathematical expression is made up of terms (constants and variables) separated by mathematical operators.A mathematical equation is used to equate two expressions.Given is that the length of the carpet is 24.25 feet and the width is 16.4 feet.
The area of the rectangle is equivalent to -
A = L x B
A = 24.25 x 16.4
A = 397.7 ft²
Therefore, the area of the rectangular carpet is equivalent to 397.7 ft².
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11( 8r+ 3) - 2(-9 + 6r)
Answer:
r = -51/76
Step-by-step explanation:
11( 8r+ 3) - 2(-9 + 6r)
76 r + 51
r = -51/76
Hoped I helped! Please put me as brainliest!
Using the fact that [tex]a - b = -1(b-a)[/tex] simplify the following: [tex]\frac{3}{1-x} - \frac{2}{x-1}[/tex]
Answer:
[tex]\frac{5}{1-x}[/tex]
Step-by-step explanation:
Given
[tex]\frac{3}{1-x}[/tex] - [tex]\frac{2}{x-1}[/tex]
= [tex]\frac{3}{1-x}[/tex] - [tex]\frac{2}{-1(1-x)}[/tex]
= [tex]\frac{3}{1-x}[/tex] + [tex]\frac{2}{1-x}[/tex]
= [tex]\frac{5}{1-x}[/tex]
Dr. Ames earns an annual salary of $265,000. If social security is 8% of your income, then how much will Dr. Ames pay each year in social security? $13,250 $21,200 $15,900 $18,40063
Answer:
The correct answer is b.
Step-by-step explanation:
Giving the following information:
Annual salary= $265,000
Social security is 8% of his income.
To calculate the annual expending on social security, all we have to do is multiply the annual salary for the expend percentage.
Annual expense= 265,000*0.08
Annual expense= $21,200
find value of (-1/2)∧-6
Answer:
64.
Step-by-step explanation:
(-1/2)∧-6
= 1 / (-1/2)^6
= 1 / 1/64
= 64.
please help!!
Which system of inequalities is represented by the graph?
Answer:
The third option
y < -2x +2
y < or = 1/2x -1
y > or = -4
Step-by-step explanation:
Solved on Desmos graphing calculator ;)
Solve the following equation for X... -3x + 12 = 24
Answer:
the answer is -4
Step-by-step explanation:
-3x+12=24
-12 -12
-----------------
-3x=12
12 divided by-3= -4
x= -4
Answer:
x=-4
Step-by-step explanation:
move the constant
-3x=24-12
-3x=12
divide both side by -3
ANSWER=-4
(6 + 8x)8
help pls don’t kno the answer
Answer:
8(6+8x)= 48+ 64x
hope this helps uh
2 ABC Company has a large piece of equipment
that cost $85,600 when it was first purchased 6
years ago. The current value of the equipment is
$30,400. What is the average depreciation of the
equipment per year?
F. $ 5,800
G. $ 9,200
H. $15,200
J. $27,600
K. $42,800
Answer:5,800
Step-by-step explanation:
The average depreciation of the equipment per year is $9200.
What is depreciation?The monetary value of an asset decreases over time due to use, wear and tear or obsolescence, this is called as depreciation.
Now it is given that,
Cost of the equipment = $85,600
current value of the equipment is given as $30,400
Duration for which the equipment was used = 6 years
Now the depreciation of the equipment is given as,
Total depreciation in the price of the equipment
= Cost of the equipment - current price of the equipment
So, total depreciation = $85,600 - $30,400 = $55,200
Now,
Average yearly depreciation = Total depreciation ÷ Years used
Average depreciation = 55,200/6
⇒Average depreciation = $9200
Therefore, average depreciation of the equipment per year is $9200.
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Tell if is: < or >
Answer:
-2>-5
4/7<3/5
-1.3>-1.333333
Step-by-step explanation:
soolve the abslut value of |2x-1|=3
Answer: x = 2 or x = -1
Step-by-step explanation: When you are solving an absolute value equation, you can split the problem up into two separate equations.
The first equation will look just like the original problem,
except for the absolute value signs (2x - 1 = 3).
The second equation will look just like the first,
but the right side will be changed to a negative (2x - 1 = -3).
Now solve each equation from here to get x = 2 or x = -1
Find two numbers with a sum of 65. Twice the smaller number is 10 more than the larger number.
Answer:
Step-by-step explanation:
Let x be the smaller number. What is the larger number if we know that sum of the two numbers is
ur answer ? ur answer
Select the correct answer. Which statement about an electromagnet is true? A. It doesn’t function without a source of current. B. The core is made from a nonmagnetic material. C. It uses moving magnets to create an electric field. D. It creates a permanent and strong magnetic field.
Answer:I’m going to say it’s A I apologize if it’s wrong
Step-by-step explanation:
Magnets are magnetic fields that compares together when attracted close to one another so that’s Why I’m choosing A because it’s close to what I think