The unknown number is 8.
Let the unknown number be x.
According to the given question.
We have a phrase "Triple a number decreased by 25 is equivalent to five less than half the same number".
Therefore, the equation for the phrase "Triple a number decreased by 25 is equivalent to five less than half the same number" is given by
3x - 25 = x/2 - 5
To find the unknown number we have to solve the above equation for x.
Therefore,
3x - 25 = x - 10/2
⇒ 6x - 50 = x - 10
⇒ 6x - x = -10 + 50
⇒ 5x = 40
⇒ x = 40/5
⇒ x = 8
Hence, the unknown number is 8.
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PLEASE HELP!
Beth is solving this equation: 1/3 + 3 = 3/x
She says “I can multiply both sides by x and get the linear equation 1 + 3x = 3, whose solution is x = 2/3 ."
Which of the following statements makes this a correct argument, or shows that it is incorrect? Select all that apply.
You cannot multiply both sides by x because you do not know what x is.
After multiplying both sides by x you need to subtract 1 from both sides.
You can assume x does not equal 0 because both sides are undefined is x = 0.
The equation is not linear, so you cannot use the methods normally used for solving linear equations.
Answer:
x= 0.9
step-by-step explanation:
LCM=3x
use the lcm to multiply each term
3x×1/3+3x×3=3x×3/x
cancel out
x+9x=9
10x=0
divide both side by the coefficient of x
10x/10=9/10
x=0.9
the world record for the most number of speed skips is 60 seconds is 332 skips if the record holder skipped at a constant ratio of seconds to skips how many makes in 15 seconds
The record holder skips 83 times in 15 seconds
We refer to a ratio as constant if the number we multiply by remains constant throughout the series.
By comparing two amounts of the same units, the ratio can be used to calculate how much of one item is included in the other. There are two different categories for ratios. The first is a part-to-part ratio, whereas the second is a part-to-whole ratio.
The World record for the most number of skips is 332 in 69 seconds.
Let's assume the record holder skipped at a constant ratio.
The proportion, if s is the number of skips:
skips / seconds = s / 15 = 332/60
s / 15 = 332 / 60
s = 332( 15/60 )
s = 332/4
s = 83
She skipped 83 times in the space of 15 seconds.
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10. A Cube-root function with a reflection across the y-axis; a vertex of (4,0).
We need to know about cube-root function and reflection to solve this problem. The function is f(x)=[tex]-\sqrt[3]{x-4}[/tex]
A cube-root function is the inverse of a cubic function, a cubic function can be given by f(x)=[tex]x^{3}[/tex], the inverse of this is a cube-root function which can be given by f(x)=[tex]\sqrt[3]{x}[/tex] with vertex at (0,0). The general formula for a cube root function is given be
f(x)=a[tex]\sqrt[3]{x-h} +k[/tex] where a is the measure of how horizontally compressed the graph is and (h,k) is the vertex of the graph. In the question we have to find a cube root function which has been reflected about the y-axis, which means our a will be negative. The vertex of the graph is at (4,0) so (h,k) is (4,0). Thus the cube root function we need is
f(x)=-[tex]\sqrt[3]{x-4}[/tex]
Therefore we found the cube root function that has been reflected about y-axis and the vertex at (4,0) to be f(x)=[tex]-\sqrt[3]{x-4}[/tex]
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Factoring All Methods
Answer:
5(3n - 4)(3n - 10)
Step-by-step explanation:
15n² - 110n + 200 ← factor out 5 from each term
= 5(3n² - 22n + 40) ← factor the quadratic
consider the factors of the product of the coefficient of the n² term and the constant term which sum to give the coefficient of the n- term.
product = 3 × 40 = 120 and sum = - 22
the factors are - 12 and - 10
use these factors to split the n- term
3n² - 12n - 10n + 40 ( factor the first/second and third/fourth terms )
3n(n - 4) - 10(n - 4) ← factor out (n - 4) from each term
(n - 4)(3n - 10)
then
15n² - 110n + 200 = 5(n - 4)(3n - 10)
Answer:
Hello,
Step-by-step explanation:
[tex]15n^2-110n+200=15(n^2-\dfrac{22}{3}x +\dfrac{40}{3} )\\[/tex]
1. I am thinking about 2 numbers with sum=22/3 and product=40/3.
Those numbers are 4 and 10/3 since 4*10/3=40/3 and 4+10/3=22/3
[tex]15(n^2-\dfrac{22}{3}x +\dfrac{40}{3} )=15(n-\dfrac{10}{3} )(n-4)=5*(3n-10)(n-4)[/tex]
2.
[tex]15(n^2-\dfrac{22}{3}x +\dfrac{40}{3} )=15(n^2-2*\dfrac{11}{3} x+(\dfrac{11}{3})^2 -\dfrac{121}{9} +\dfrac{120}{9})\\\\=15((n-\dfrac{11}{3})^2 -\dfrac{1}{9})\\\\=15( n-\dfrac{11}{3} -\dfrac{1}{3})*(n-\dfrac{11}{3} +\dfrac{1}{3})\\=15(n-\dfrac{10}{3})(n-4)\\\\=5(3n-10)(n-4)\\[/tex]
3.
Using discriminant ...
Gabriel finds some dimes and quarters in his change purse. How many coins does he have if he has 11 dimes and 8 quarters? How many coins does he have if he has dd dimes and qq quarters?
Answer:
8 quarters equal 2 dollars 11 dimes is a dollar and 10 cents so 3 dollars and 10 cents
Step-by-step explanation:
Madelyn read 45 pages in 1 1/3 hours . At what rate , in pages per hour , did she read?
Madelyn reads at the rate of 33.75 pages per hour.
Here rate is defined as the number of pages read per hour. Rate or unit rate is defined as the quantity that is done in 1 unit of time(second, minute or hour). Distance per time is called speed. Velocity per time is called acceleration.
Here it is given Madelyn reads 45 pages in [tex]1\frac{1}{3}[/tex] hours.
Now to find the unit rate we have to divide the number of pages read in the total time taken to read 45 pages.
Unit rate= [tex]45\div 1\frac{1}{3}[/tex]
[tex]=45\div \frac{4}{3}\\=\frac{135}{4} \\=33.75[/tex]
Madelyn reads at the rate of 33.75 pages in 1 hour .
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Match the angle with its classification
Answer:angels
Step-by-step explanation:bea
Question 4 A woman borrowed $2,000,000.00 from bank at a rate of 15% per annum simple interest for 2 years. a) Find i) the interest for the 2 years; how much she paid in all to the after the 2 years. ii) b) She used the $2,000,000.00 to purch fridge and sold it at a profit of 45%.Find the selling price of the fridge.
Part i) Simple interest = $600,000.00.
Part ii) Selling price = $2,900,000.00.
What is defined as the simple interest?Simple interest is a simple and quick method to approximate the interest on a loan. Simple interest is calculated by multiplying this same daily interest rate by the principal multiplied by the number of days between payments.Part i) The formula for simple interest is;
SI = PRT/ 100
P = principal amount = $2,000,000.00.
R = rate of interest = 15%
T = time in years = 2 years.
Put the value in the formula;
SI = ( $2,000,000 × 2 × 15)/100
On simplification;
SI = 600,000
Thus, the simple interest at the end of 2 years is $600,000.oo
Part ii) the selling price
Selling price = cost price + profit
Selling price = cost price + 45%of cost price
Cost price = $2,000,000.00
45%of cost price = 45× $2,000,000.00/100
45%of cost price = 900,000.00
Selling price = $2,000,000.00 + 900,000.00
Selling price = $2,900,000.00.
The the selling price of the fridge is found as $2,900,000.00.
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Find the sum of all multiple 3 between 5 and 64
Answer:
690
Step-by-step explanation:
The multiples of 3 between 5 and 64 are 6+9+12+15+18+21+24+27+30+33+36+39+42+45+48+51+54+57+60+63 which gives you 690.
Hope this helps, have a good day! :D
Answer: ∑=690
Step-by-step explanation:
Let's use the formulas for an arithmetic progression:
[tex]a_1=6 \ \ \ \ \ a_n=63\ \ \ \ d=3\\a_n=a_1+(n-1)d\\63=6+(n-1)3\\63=6+3n-3\\63=3+3n\\63-3=3+3n-3\\60=3n\\[/tex]
Divide both parts of the equation by 3:
[tex]20=n[/tex]
Thus,
[tex]\displaystyle\\\sum=\frac{a_1+a_n}{2} n\\\\\sum=\frac{6+63}{2}20 \\\\\sum=\frac{69*20}{2} \\\\\sum=69*10\\\\\sum=690[/tex]
8. A total of $36,000 is to be invested, some in bonds and some in certificates of deposit (CDs). If the amount invested in
bonds is to exceed that in CDs by $5,000, how much will be invested in each type of investment?
The amount invested in CDs is $
The amount invested in bonds is $
Using a system of equations, it is found that:
The amount invested in CDs is $20,500.The amount invested in bonds is $15,500.What is a system of equations?A system of equations is when two or more variables are related, and equations are built to find the values of each variable.
For this problem, the variables are given as follows:
Variable x: amount invested in CDs.Variable y: amount invested in bonds.The total invested is of $36,000, hence:
x + y = 36000.
The amount invested in bonds is to to exceed that in CDs by $5,000, hence:
x = y + 5000.
Replacing in the first equation:
y + 5000 + y = 36000.
2y = 31000
y = 15,500.
x = y + 5000 = 20,500.
Hence:
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HURRY PLS!!
A company orders 22 boxed lunches from a deli for $273.90. If each boxed lunch costs the same amount, how much do 16 boxed lunches cost?
Answer:
Step-by-step explanation:
1 box costs x amount
18 boxes cos 223.20
Cross multiply
223.20 * 1 = 18 x
Divide by 18
223.20 / 18 = 18x / 18
x = 12.40
Cost of 1 box is 12.40
Answer:
It should be 199.20 for 16 boxes
Step-by-step explanation:
I divided 273.90 by 22 which came out to 12.45
so then i multiplied 12.45 by 16 and it gave me 199.20
what are the answers ?! help pls !!! this is a timed T-T
Answer:I would say c
Step-by-step explanation: because it is the only one that makes sense
Dice have 6 sides, with values 1, 2, 3, 4, 5, and 6. which expression randomly rolls one dice, directly yielding one of those values?
(rand() % 6) + 1 is the expression randomly rolls one dice, directly yielding one of those values.
What is dice?Small objects (polyhedrons) used as playing pieces for dice games and other gambling-related activities. The cube, the most popular type of die, has one to six tiny dots on each side (spots). The spots are positioned in the following traditional patterns: 1 and 6, 2 and 5, 3 and 4, so that spots on opposite sides always sum up to 7. The poker and crown and anchor dice, as well as many other types of dice with 4, 5, 7, 8, 10, 12, 16, and 20 sides, are examples of dice with different configurations of spots or other face designs. The majority of the time, dice are employed to generate a random outcome (usually a number or a mixture of numbers), and the mathematical probabilities depend on the physical characteristics and quantity of dice thrown.
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The freezing point of water in degrees Celsius is 0 while in degrees Fahrenheit it is 32. The boiling point of water is 100 degrees Celsius and 212 degrees Fahrenheit. Given that the function F is linear, use this information to find an equation for F
The function F to be used to convert the temperature is; F = ⁹/₅C + 32
How to Solve Algebra Word Problems?
From the given information, we can tag the coordinates as;
(32,0) and (212,100)
Thus, the slope is calculated as;
m = (100-0)/(212-32)
m = 100/180
m = 5/9
The intercept is;
c = y - mx
c = 0 - (5/9)(32)
c = 0 - 160/9
c = -160/9
The line equation is;
y = 5/9 x + (-160/9)
y = 5/9 x - 160/9
y = 5/9 (x - 32)
Let x = F and y = C and we have;
F = ⁹/₅C + 32
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Find the value of x²+8x+12 when x = -9
Answer:
165
Step-by-step explanation:
x² + 8x + 12 =
= (9)² + 8(9) + 12
= 81 + 72 + 12
= 153 + 12
= 165
Answer:
-165
Step-by-step explanation:
(-9)2+8×-9+12
-81-72+12
-81-84
-165 answer.
5a + 2b = 40 solve for b
Answer:
5a-40=-2b
5a-40/-2=-2b/-2
-5a/2+20=b
CAN ANYONE PLS PLS PLS HELP ME THIS IS A DISASTER AND I WIL GET PUNISHED IF NO DONE.
12. −7.5 • −2³/4
19
Answer:
-9.5
Step-by-step explanation:
What is the slope of the line that passes through the points (-4,5) and (-7,8) ? write your answer in the simplest form
Answer:
[tex]\frac{-3}{3}[/tex]
Step-by-step explanation:
So we going to put them in the Rise Over Run fomula which is [tex]\frac{5-8}{-4-(-7)}[/tex] and we simplifying this which give us [tex]\frac{-3}{3}[/tex]
How many posts does it take to support a straight fence 300 feet long if a post is placed every 25 feet?
12 posts are required to support a straight fence 300 feet long if a post is placed every 25 feet.
The given question can be solved using division. We are given that 25 feet is covered by 1 post. So, we will simply find the number of posts that will cover the 300 feet long fence. Now, calculating the number of posts as shown in steps below -
Number of post that covers 25 feet = 1
So, 300 feet will be covered by number of posts = (1÷25)×300
Performing multiplication and division to find the number of posts required to cover 300 feet long fence
Number of posts required to cover 300 feet long fence = 12 posts
Hence, 12 posts are required to cover 300 feet long fence.
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A router is located in the school library which is 1.5 meters away from the a student lounge. the range of the router, which services the wifi connection of the school has a diameter of 3.5 meters with it as the center. can student staying on the lounge connect to the said wifi
The distance between the center of the circle to any point in the circle is called the radius of the circle. The student staying in the lounge connected to the said wifi will be in the range of the wifi.
What is a circle?A circle is a curve sketched out by a point moving in a plane so that its distance from a given point is constant; alternatively, it is the shape formed by all points in a plane that are at a set distance from a given point, the center.
The distance between the center of the circle to any point in the circle is called the radius of the circle, while the diameter is twice this distance.
Given that the range of the router, which services the wifi connection of the school has a diameter of 3.5 meters. Therefore, the radius of the wifi will be,
Radius = Diameter/2 = 3.5 meters / 2 = 1.75 meters
Now, it is also given that a router is located in the school library which is 1.5 meters away from the student lounge. Therefore, the distance between the school library and the lounge is less than the radius of the range of the wifi.
Thus, the student staying in the lounge connected to the said wifi will be in the range of the wifi.
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The sum of eight and half
of a number
We get the expression for the statement "The sum of eight and half of a number" as (16 + x) / 2.
We are given a statement:
The sum of eight and half of a number.
We have to form an expression for the same.
An expression means a combination of numbers and variables.
Let the number be a variable say x.
Now we need the half of a number.
1 / 2 of x = x / 2
Now we need the sum of 8 and x / 2.
So, it will be:
8 + x / 2
= (16 + x) / 2
Therefore, we get the expression for the statement "The sum of eight and half of a number" as (16 + x) / 2.
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Uber charges $3 plus $0.75 per mile driven. lyft charges $5.00 plus $.50 per mile driven. write the equations for both companies
The linear equation for both Uber and Lyft will be Y = 0.75x + 3 and
Y = 0.5x + 5 .
A linear equation is an algebraic equation of the form y = mx+b. Involving only a constant and a first-order (linear) term, where m is the slope and b is the y-intercept. Occasionally, the above is called a "linear equation of two variables," where y and x are the variables.
Here we have,
Uber charge $3 fix on every trip and additional charges on per mile $0.75
So, linear equation be
Y = 0.75x + 3 where, x = no. of mile covered
Similarly, lyft charge $5 fix and $0.5 as an additional
So, linear equation be
Y = 0.5x + 5 where, x = no. of mile covered
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What is Euclidian Geometry?
Answer:
Euclidean geometry is a mathematical system attributed to ancient Greek mathematician Euclid, which he described in his textbook on geometry: the Elements. Euclid's approach consists in assuming a small set of intuitively appealing axioms, and deducing many other propositions from these.
Step-by-step explanation:
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There is a safety fence around a circular pool with a gate. The gate is 150 cm wide.
20 m
gate
150 cm
What is the length of the fence not including the gate?
m
Please, help me. I have no idea.
Janet weights 20 pounds more than anna if the sum of their weights is 250 lb how much does each girl weigh
Anna's weight is 115 pounds and Janet's weight is 135 pounds.
What is weight?The weight of the object is the force acting on it due to gravity in science and engineering. Weight is defined as a vector quantity in some standard textbooks, as the force of gravity acting on the object. Others define weight as just a scalar quantity, the magnitude of gravity.To find the wight of Anna and Janet:
It is assumed:
Janet is 20 pounds heavier than Anna.This means that if Anna weighs x pounds,Janet's age is then (x+20) pounds.Also,
Their combined weight is 250 pounds.So,
x+x+20 = 2502x+20=250Subtraction of both sides by 20 yields:
2x = 250-202x = 230By dividing both sides by 2, we get:
x = 115So, Anna's weight is 115 pounds and Janet's weight is 115+20=135 pounds.
Therefore, Anna's weight is 115 pounds and Janet's weight is 135 pounds.
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write the value of this expression as a fraction 14/33 x 55/8 x 12/35
Answer: 1
Step-by-step explanation:
[tex]\displaystyle\\\frac{14}{33} *\frac{55}{8} *\frac{12}{35} =\\\\\frac{14*55*12}{33*8*35}=\\\\\frac{2*7*5*11*3*4}{3*11*2*4*5*7}=\\\\\frac{1}{1}=\\\\1[/tex]
Nylah and harper share £2700.harper gets twice as much money as nylah.
How much does hamper receive?
Give your answe in pounds (£)
Harper will receive £1800 as his own share of the total money
How to calculate the amount of harper that Nylah will receive ?Nylah and harper both share £2700
let x represent Nylah share
let 2x represent harper share
x + 2x= 2700
3x= 2700
divide both sides by the coefficient of x which is 3
3x/3= 2700/3
x= 900
Since harper share is 2x, let's substitute 900 for x
2(900)
= 1800
Hence harper share is £1800
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Pls help me im stuck
