Step-by-step explanation:
Given that,
The hypotenuse of a right triangle is 15 cm
Let x is the length of the other leg. So, the length of the first leg is 2x.
Using Pythagoras theorem for the right angle triangle such that,
hypotenuse² = base²+height²
Let base is x and height is 2x
So,
[tex]15^2=x^2+(2x)^2\\\\225=x^2+4x^2\\\\225=5x^2\\\\x^2=45\\\\x=3\sqrt{5} \ cm[/tex]
Hence,
Base = [tex]3\sqrt{5} \ cm[/tex]
Height = [tex]2\times 3\sqrt{5} \ cm=6\sqrt5\ cm[/tex]
Hyoptenuse = 15 cm (given)
If f(x) = х2 – 2х + 3, thеn find
f(-3).
Answer:
[tex]\huge\boxed{\sf f(-3) = 18}[/tex]
Step-by-step explanation:
[tex]\sf f(x) = x^2 - 2x + 3[/tex]
Put x = -3
[tex]\sf f(-3) = (-3)^2 -2(-3) + 3\\f(-3) = 9 + 6 + 3\\f(-3) = 18[/tex]
one number is 7 more than twice the other number. if the sum of the two numbers is 19, find the two numbers
Answer:
4 and 15
Step-by-step explanation:
Let the two numbers be a and b.
The sum of the two is 19. Therefore:
[tex]a+b=19[/tex]
One number (let's use a) is 7 more than twice the other. Thus:
[tex]a=7+2b[/tex]
Solve for the system of equations. Substitute the second equation into the first:
[tex]a+b=19\\(7+2b)+b=19[/tex]
Subtract 7 from both sides:
[tex]2b+b=12[/tex]
Combine like terms:
[tex]3b=12[/tex]
Divide by 3:
[tex]b=4[/tex]
So, b is 4.
And since they add up to 19, this means that a is:
[tex]a+b=19\\a+4=19\\a=15[/tex]
So our numbers are 4 and 15
And we are done :)
Answer:
the equation is: 2x+7+x=43
the 2 numbers are: 12 and 31.
The sum of three consecutive integers is 162 . What are the integers?
Answer:
53 54 55
Step-by-step explanation:
Consecutive Integers are integers that go one after the other unless explained otherwise, so 53, 54 and 55 add up to 162.
ANSWER
X=52
x+2=54
x+4=56
these are the three consecutive integers
ILL GIVE YOU BRAINLIST ! Marlene is given 7 feet of fabric to design a dress. She uses 6 1/9 feet of fabric. How much fabric is left?
Answer:
This question is a lot easier than it seems. What you have to do here is subtract 6 1/9 from 7.
This will give you 0.8 of the fabric left, or 8/9.
You know that there is a strong correlation between the consumption of ice cream and body weight. The Pearson's r = 0.78. You also know that the average consumption of ice cream per week is five grams with a standard deviation of 1.5 grams. The average weight is 65 kg with a standard deviation of 15 kg. What is the formula of the regression line?
ŷ = 26 + 7.8x
ŷ = 7.8 + 26x
ŷ = -502 + 0.078x
ŷ = 0.078 - 502x
Find the distance between the two points in simplest radical form.
(3,7) and (9,9)
Answer:
The answer is
[tex]2 \sqrt{10} \: \: units[/tex]Step-by-step explanation:
The distance between two points can be found by using the formula
[tex]d = \sqrt{ ({x1 - x2})^{2} + ({y1 - y2})^{2} } \\ [/tex]where
(x1 , y1) and (x2 , y2) are the points
From the question the points are
(3,7) and (9,9)
The distance between them is
[tex]d = \sqrt{ ({3 - 9})^{2} + ({7 - 9})^{2} } \\ = \sqrt{ ({ - 6})^{2} + ({ - 2})^{2} } \\ = \sqrt{36 + 4} \\ = \sqrt{40} [/tex]We have the final answer as
[tex]2 \sqrt{10} \: \: units[/tex]Hope this helps you
An executive invests 29,000, some at 8% and the rest at 7% annual interest. If he receives an annual return of $2,230, how much is invested at each rate?
Answer:
Amount invested in A (8%) = $20,000
Amount invested in B (7%) = $9,000
Step-by-step explanation:
Given:
Total amount invested = $29,000
Interest rate A = 8% = 0.08
Interest rate B = 7% = 0.07
Annual return = $2,230
Find:
Amount invested in each
Computation:
Assume;
Amount invested in A = x
Amount invested in B = 29,000 - x
So,
Interest receive from A = x × 0.08
Interest receive from A = 0.08 x
Interest receive from B = (29000 - x) × 0.07
Interest receive from B = 2,030 - 0.07 x
Annual return = Interest receive from A + Interest receive from B
2,230 = 0.08 x + 2,030 - 0.07 x
x = 20,000
Amount invested in A = $20,000
Amount invested in B = 29,000 - $20,000
Amount invested in B = $9,000
PLSSS HELP MARKING BRAINLIST PLSSSS GUYS NO ONE IS GOING TO HELP ME?
Answer:
top
question 1 is 25
question 2 is 0.2
------------------------------
bottom
question 3 is the second graph
the last question is the first graph
Step-by-step explanation:
Given a standard day, at what altitude is the true airspeed of an aircraft approximately twice of what the airspeed indicator reads
Answer:
40000ftMSL
Step-by-step explanation:
We know that airspeed is measured using a pilot tube
And the air pressure is a function of density given as
Pressure= 1/2 xdensityx V²
So at 40,000ftMSL
Is this is replaced for V in the equation then the density of air will be 1/4 that of sea level
So since we are deriving velocity from pressure and pressure is 1/4 so the velocity Will be half of its pressure since velocity is squared from The equation above
Gasoline at a particular gas station costs $2.78 per gallon. If Cory buys $18 of gas, how many gallons did he buy?
Answer:
Cory bought 6.474 gallons of gasolline.
Step-by-step explanation:
The total cost of gasoline ([tex]C[/tex]), measured in dollars, is given by the following expression:
[tex]C = n\cdot c[/tex]
Where:
[tex]n[/tex] - Amount of gasoline, measured in gallons.
[tex]c[/tex] - Unit cost, measured in dollars per gallon.
Given that [tex]C = \$\,18[/tex] and [tex]c = \$\,2.78\,\frac{1}{gal}[/tex], the amount of gasoline is cleared and calculated:
[tex]n = \frac{C}{c}[/tex]
[tex]n = \frac{\$\,18}{\$\,2.78\,\frac{1}{gal} }[/tex]
[tex]n = 6.474\,gal[/tex]
Cory bought 6.474 gallons of gasolline.
Use the table below to answer the following questions. a. Plot the points (x,y) in this table on a graph (except when x is 5)
Answer:no answers sorry
Step-by-step explanation:
No answers sorry
Given the following exponential function, identify whether the change represents growth or decay, and determine the percentage rate of increase or decrease. y=570(0.98)^x
Answer:
decay2% decreaseStep-by-step explanation:
The growth factor is the base of the exponent: 0.98. Its relation to the rate of change is ...
growth factor = 1 + rate of change
0.98 = 1 + (-0.02)
So, the rate of change is -0.02 = -2%. Since the rate of change is a 2% decrease, it represents decay.
what is. - 3 7/8 × - 4 3/5 help please
Answer: 1/ 40 x (-155x-184)
Answer:
[tex]:\quad \frac{713}{40}=17\frac{33}{40}[/tex]
Step-by-step explanation:
[tex]-3\frac{7}{8}\times \:-4\frac{3}{5}\\\mathrm{Convert\:mixed\:numbers\:to\:improper\:fractions}:\quad 3\frac{7}{8}=\frac{31}{8}\\-\frac{31}{8}\times \:-4\frac{3}{5}\\\mathrm{Convert\:mixed\:numbers\:to\:improper\:fractions}:\quad 4\frac{3}{5}=\frac{23}{5}\\-\frac{31}{8}\times \:-\frac{23}{5}\\\mathrm{Apply\:rule}\:-\left(-a\right)=a\\=\frac{31}{8}\times \frac{23}{5}\\\mathrm{Multiply\:fractions}:\quad \frac{a}{b}\times \frac{c}{d}=\frac{a\:\times \:c}{b\:\times \:d}\\[/tex]
[tex]=\frac{31\times \:23}{8\times \:5}\\\\=\frac{713}{40}\\\\\mathrm{Convert\:improper\:fractions\:to\:mixed\:numbers}:\\\quad \frac{713}{40}=17\frac{33}{40}[/tex]
Suppose that on each play of a game, a gambler either wins 1 with probability p or loses 1 with probability 1–p (or q). The gambler keeps betting until she or he is either up a total of n or down a total of m. What is the probability the gambler will quit an overall winner? You must consider both cases when p = 0.5 and when p ≠ 0.5
Answer:
Step-by-step explanation:
From the given information,
Considering both cases when p = 0.5 and when p ≠ 0.5
the probability that the gambler will quit an overall winner is:
[tex]P = \dfrac{1 - (\dfrac{1-p}{p} )^K}{1- (\dfrac{1-p}{p})^N } \ \ \ is \ p \neq 0.5 \ and\ K/N = \dfrac{1}{2}[/tex]
where ;
N.k = n and k = m
Hence, the probability changes to:
[tex]P = \dfrac{1 -(\dfrac{1-p}{p})^m}{1 -(\dfrac{1-p}{p})^{m+n}}[/tex] is p ≠ 0.5 and k/N = [tex]\dfrac{m}{m+n}[/tex] is P = 0.5
f(x) = (10/x)^3 what is the value of f(2)?
What are the greatest and the least
6-digit numbers that have a 9 in the hundreds place and 3 fewer
hundred thousands than hundreds?
Answer:
Greatest = 699,999
Least = 600,900
Step-by-step explanation:
6 digit numbers
9 in the Hundred place
3 fewer hundred thousands than hundred
9 - 3 = 6
Hundred thousand = 600,000
Hence, greatest 6 digit number
Hth__TTh__Th__H__T__U
6____9____9___9__9__9
600,000 + 90,000 + 9,000 + 900 + 90 + 9
= 699,999
Hence, least 6 digit number
Hth__TTh__Th__H__T__U
6____0____0___9__0__0
600,000 + 00000 + 0000 + 900 + 00 + 0
= 600,900
The length of a rectangle is one more than four times its width. If the perimeter of the rectangle is 62 meters, find the dimensions of the rectangle.
Answer:
Length = 25 meters
Width = 6 meters
Step-by-step explanation:
62 = 2(a+b)
a = 4b + 1
a = length
b = width
then:
62 = 2((4b+1)+b)
62/2 = 4b+b+1
31 = 5b + 1
31 - 1 = 5b
30 = 5b
b = 30/5
b = 6m
a = 4b + 1
a = 4*6 + 1
a = 24 + 1
a = 25m
Check:
62 = 2(6+25)
62 = 2*31
ayyyyyyyyyyyyyyyyyyyyyyyyyyyyyy please help me
The least expensive type life insurance is ______
Answer:
Whole life policies
Step-by-step explanation:
Whole life policies are the least expensive way to meet your life insurance needs. The advantages of whole life insurance policies are that they provide long-term coverage, the rates are fixed, and they have a savings or cash value feature.
2/9 * 5/6
Multiply. Write the answer as a fraction in simplest form.
Answer:
5 / 27
Step-by-step explanation:
The school paper charges $1.50 for an ad, plus 25 cents per word. Carl wants to spend only $12.00 on the ad.
What is the maximum number of words that can be in his ad?
Answer:
42 words
Step-by-step explanation:
To solve just solve 0.25x +1.50 = 12.00 for x
How many solutions exist for 2 |x - 1| = 8?
A. 0
B. 1
C. 2
D. 3
Answer:
I believe the correct answer is C.
Step-by-step explanation:
So to get 0 solutions the absolute value would have to equal a negative number. To get 1 solution the absolute value would have to equal 0. To get 2 solutions the absolute value would have to equal a positive number.
2 |x - 1| = 8
divide by 2
|x - 1| = 4
The absolute value equals a positive so it has 2 solutions.
x(2x + 3) + (x - 3)(x - 4)
Answer:
3x²-4x+12
Step-by-step explanation:
Answer:
[tex]=3x^2-4x+12[/tex]
Step-by-step explanation:
So we have the expression:
[tex]x(2x+3)+(x-3)(x-4)[/tex]
To simplify, distribute the left side and the right:
[tex]=x(2x)+x(3)+(x-3)(x)+(x-3)(-4)[/tex]
Distribute:
[tex]=(2x^2+3x)+(x^2-3x)+(-4x+12)[/tex]
Combine like terms:
[tex]=(2x^2+x^2)+(3x-3x-4x)+(12)[/tex]
Simplify:
[tex]=3x^2-4x+12[/tex]
A triangle has a base of 16 inches and a height of 18 inches. What is its area?
Answer:
The answer is
144 square inchesStep-by-step explanation:
Area of a triangle is given by
[tex]A = \frac{1}{2} bh[/tex]where
b is the base
h is the height
From the question
b = 16 inches
h = 18 inches
Substitute the values into the above formula and solve for the area
That's
[tex]A = \frac{1}{2} \times 16 \times 18 \\ = 8 \times 18 \: \: \: \: \: \: [/tex]We have the final answer as
144 square inchesHope this helps you
in 2016 the average Raleigh driver spent 18 hours in traffic jams, which accounted for 6% of their total driving time. How many hours did the average Raleigh driver spend behind the wheel in 2016
Answer: 300 hrs
The time spent behind the wheel by the average Raleigh driver in 2016 is 300 hrs
Step-by-step explanation:
Given that;
Raleigh driver spent 18 hours in traffic jams
And it accounts for 6% of their total driving time
Now
let total driving time be = x hrs
so
6% of total driving time = 18 hrs
6/100 × x = 18hrs
6x = 1800 hrs
x = 1800/6
x = 300 hrs
∴ The time spent behind the wheel by the average Raleigh driver in 2016 is 300 hrs
Evaluate the expression for x = 5 and y = 3.
3x – 4y2
A. 9
B. 27
C. 39
D. 81
find the difference of 5.95 and 4.7
Answer:
1.25 is your answer.
a cylinder container can hold 2.45l of water. it radius is 4.00cm. what is the the volume of it in cm3
Answer:
Step-by-step explanation:
Ion know
On a number line suppose point E has a coordinate of 1, and EG=11 What are the possible coordinates of G?
Answer:
- 10 and 12
Step-by-step explanation:
On a typical number line, we have basically two directions that we can move on. Either to the left where the numbers are negative, of to the right where the numbers are positive.
Given that point E has a coordinate of 1 on a number line, and we are told that the distance between E and another point on the number line is 11 (EG), the possible coordinates of point G are two (either we are moving to the right or to the left). Therefore, possible coordinates of G are:
1 - 11 = -10 (to the left)
1 + 11 = 12 (to the right)
Which expression is equivalent to : (-4x-3y-5)2