300 people went on a trip. 20% chose hiking. how many people chose hiking?
A rope is broken up into 3 pieces. The first piece is three times bigger than the second piece and the third piece is eight feet more than the first piece. How big is each piece if the sun of all pieces is 64 feet ?
When completing the square on the equation c^2 + 11c = 12, the resulting solution is
Answer:
Attached file is the solutions
Step-by-step explanation:
which is the most appropriate Venn diagram...
The most appropriate Venn diagram is known to be option b in the image shown.
What is a common multiple?A Common multiples are known to be the multiples that are said to be common to two or that have more numbers in them.
The Least Common Multiple ( LCM ) is known to be a term that connote the Lowest Common Multiple ( LCM ) and also that has the Least Common Divisor ( LCD).
From the image shown the lowest multiples are 5², 2⁶, 3 while the greatest common factor is 2⁶.
Option B is correct because the greatest common factor which is 2⁶ can only be found in the middle and this was gotten when you add:
2³ . 2³
Collect like terms
2 ³⁺³
2⁶
Therefore, the greatest common factor which is 2⁶
To get the Least Common Multiple, one need to add all the factors in the Venn diagram which are therefore:
5², 2³ . 2³, 3
=5², 2 ³⁺³, 3
=5², 2⁶, 3
Therefore, The most appropriate Venn diagram is known to be option b in the image shown.
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Marsha deposited $9,500 into a savings account 2 years ago. The simple interest rate is 2%. How
much money did Marsha earn in interest?
Substitute the values into the equation.
Interest=$years
Answer:
$380Step-by-step explanation:
GivenDeposit amount P = $9500Interest rate r = 2%Time t = 2 years
Use interest formula:
I = PrtSubstitute given values and calculate:
$9500*0.02*2 = $380Answer:
$ 380
Step-by-step explanation:
We can use the below formula to find the simple interest.
Simple interest = P r t ÷ 100
Here,
P ⇒ Principal ⇒ $ 9500
r ⇒ rate ⇒ 2%
t ⇒ time ⇒ 2 years
Let us solve it now.
Simple interest = P r t ÷ 100
Simple interest = 9500 × 2 × 2 ÷ 100
Simple interest = 38000 ÷ 100
Simple interest = $ 380
The short leg of a 90-45-45 triangle is 5. What is the long leg and the hypotenuse?
The long leg and the hypotenuse of the isosceles right triangle will be 7.07 units.
What is a Pythagoras theorem?The Pythagoras theorem states that the sum of two squares equals the squared of the longest side.
The Pythagoras theorem formula is given as
H² = P² + B²
The short leg of a 90-45-45 triangle is 5.
The right triangle is an isosceles right triangle. Then the two side will be same.
Then the long leg and the hypotenuse will be
H² = 5² + 5²
H² = 25 + 25
H² = 50
H = 7.07 units
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What is the simplified form of 12x/900x²y4z6?
O 30y²|xz³|
O 30x²y2z4
O 360xy²|xz³|
O 360xy²|z³|
Answer:
[tex]360xy^2|xz^3|[/tex]
Step-by-step explanation:
Given expression:
[tex]12x \sqrt{900x^2y^4z^6}[/tex]
[tex]\textsf{Apply radical rule} \quad \sqrt{ab}=\sqrt{a}\sqrt{b}:[/tex]
[tex]\implies 12x \sqrt{900}\sqrt{x^2}\sqrt{y^4}\sqrt{z^6}[/tex]
Replace 900 with 30² :
[tex]\implies 12x \sqrt{30^2}\sqrt{x^2}\sqrt{y^4}\sqrt{z^6}[/tex]
[tex]\textsf{Apply radical rule} \quad \sqrt{a^2}=a, \quad a \geq 0:[/tex]
[tex]\implies 12x \cdot 30|x|\sqrt{y^4}\sqrt{z^6}[/tex]
[tex]\implies 360x|x|\sqrt{y^4}\sqrt{z^6}[/tex]
(We need to use the absolute value of √x² since the x term was originally to the power of 2, which means the value of x² is always positive since the exponent is even).
[tex]\textsf{Apply exponent rule} \quad \sqrt{a^m}=a^{\frac{m}{2}}:[/tex]
[tex]\implies 360x|x|\cdot y^{\frac{4}{2}}\cdot z^{\frac{6}{2}}[/tex]
Simplify:
[tex]\implies 360xy^2|xz^3|[/tex]
(We need to use the absolute value of z³ since the z term was original to the power of 6, which means the value of z⁶ is always positive since the exponent is even).
I opened a grocery account at my bank with $100. Every week thereafter, I withdraw $45 from the account to pay for groceries. If x is the number of weeks I've had the account, then y is the amount in the account. Find an equation of a line in the form y = mx + b that describes my grocery account balance.
Answer:
y=-45x + 100
Step-by-step explanation:
The slope-intercept form is y=mx+b where m is the slope and b is the y-intercept or in other words the initial amount (when x is 0). Since you start off with 100 dollars the y-intercept is going to be 100 since after 0 weeks (when you opened the account) you put 100 dollars in... so you should have 100 dollars. The slope is going to be -45 since you are withdrawing 45 each week so the value is going to be decreasing by 45 every week. If you put that together you get y=-45x+100
You are given the steps for using a compass and a straightedge to construct a line perpendicular to a given line through a point not lying on the given line. Arrange the steps in the proper sequence.
Place the compass needle on the external
point R. Make the compass width greater
than the distance from R to the given line.
Draw an arc cutting the given line at
two points. Mark and label the points
of intersection P and Q.
Draw a line from the external point R to
the point where the arcs intersect, S.
Line RS is perpendicular to line PQ and
passes through the external point R.
Move the compass needle to P and make an
arc below the line. Keep the compass width,
and move the compass needle to Q. Draw an
arc below the line crossing the other arc.
Mark and label the point of intersection S.
The proper steps for the construction are given as 1, 2 4, and then 3.
Write the steps for construction?The proper steps for the construction are;
1. Place the compass needle on the external point R. Make the compass width greater than the distance from R to the given line.
2. Draw an arc cutting the given line at two points. Mark and label the points of intersection P and Q.
3. Move the compass needle to P and make an arc below the line. Keep the compass width, and move the compass needle to Q. Draw an arc below the line crossing the other arc. Mark and label the point of intersection S.
4. Draw a line from the external point R to the points where the arcs intersect, S. Line RS is perpendicular to line PQ and passes through the external point R.
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If f(x) = 5x - 1, then f-1 (x)
Step-by-step explanation:
[tex]f(x) = 5x - 1[/tex]
[tex] \: [/tex]
[tex]y = 5x - 1[/tex]
[tex]5y - 1 = x[/tex]
[tex]5y = x + 1[/tex]
[tex]y = \frac{x + 1}{5} [/tex]
[tex] {f}^{ - 1} (x) = \frac{x + 1}{5} [/tex]
The graph of f(x) = x2 is translated to form g(x) = (x – 5)2 + 1. On a coordinate plane, a parabola, labeled f of x, opens up. It goes through (negative 2, 4), has a vertex at (0, 0), and goes through (2, 4). Which graph represents g(x)? On a coordinate plane, a parabola opens up. It goes through (2, 10), has a vertex at (5, 1), and goes through (8, 10). On a coordinate plane, a parabola opens up. It goes through (2, 8), has a vertex at (5, negative 11), and goes through (8, 8). On a coordinate plane, a parabola opens up. It goes through (negative 8, 10), has a vertex at (negative 5, 1), and goes through (negative 2, 10). On a coordinate plane, a parabola opens up. It goes through (negative 8, 8), has a vertex at (negative 5, negative 11), and goes through (negative 2, 8).
The transformation of a function may involve any change. When the graph of f(x) is transformed into 5 units to the right and one unit up, then the function g(x) is obtained.
How does the transformation of a function happen?The transformation of a function may involve any change.
Usually, these can be shifted horizontally (by transforming inputs) or vertically (by transforming output), stretched (multiplying outputs or inputs) etc.
If the original function is y = f(x), assuming the horizontal axis is the input axis and the vertical is for outputs, then:
Horizontal shift (also called phase shift):
Left shift by c units, y=f(x+c) (same output, but c units earlier)Right shift by c units, y=f(x-c)(same output, but c units late)Vertical shift
Up by d units: y = f(x) + dDown by d units: y = f(x) - dStretching:
Vertical stretch by a factor k: y = k \times f(x)Horizontal stretch by a factor k: y = f(x/k)Given the function f(x)=x², which is transformed to g(x)=(x-5)²+1, therefore, the graph of both the functions are given below.
When the graph of f(x) is transformed into 5 units to the right and one unit up, then the function g(x) is obtained.
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A piecewise function is represented by the graph below.
On a coordinate plane, a piecewise function has 2 lines. The first line is made up of 2 lines. One line goes from (negative 5, 3) to (negative 1, negative 1) and then goes up to a closed circle at (1, 1). The second line has an open circle at (1, 2) and then continues up through (3, 4).
What is the domain for the piece of the function represented by f(x) = x + 1?
x < –1
–1 ≤ x ≤ 1
1 ≤ x < 2
x > 1
Because we have an open circle at (1, 2), and then the line continues up, we conclude that the domain is:
D: x > 1.
What is the domain for the piece of the function represented by f(x) = x + 1?
Here we know that:
"The second line has an open circle at (1, 2)"
This means that the value x = 1 is not on the domain of the second line, and we know that the line "then continues up through (3, 4)"
(notice that these are two points on the line y = x + 1).
So we conclude that x = 1 is the lower bound of the domain of that line (and we can't tell that there is an upper bound).
Then we can just write the domain as:
D: x > 1.
So the last option is the correct one.
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If $5000 is invested at a rate of 3% interest
compounded quarterly, what is the value of
the investment in 5 years? (Use the formula
A = P (1 + =)",
, where A is the amount accrued, P
is the principal, r is the interest rate, n is
the number of times per year the money is
compounded, and t is the length of time, in years.)
The value of the investment in 5 years is $5805.9
What is Interest ?Interest is the amount earned over years for the amount invested.
It is given that
Principal = $5000
Rate = 3%
Compounded Quarterly
Time = 5 years
Amount = ?
The Amount is given by the formula
Amount = P( 1 + (r/n))ⁿˣ
Here n = t = time period for which the investment has been done.
Amount = 5000( 1+(3/4 * 100)⁴ˣ⁵
Amount = 5000 (1.16)
Amount = $ 5805.9
Therefore , The value of the investment in 5 years is $5805.9
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is the square root of 10 a rational number
Answer:
No
Step-by-step explanation
The square root of 10 is irrational because it isn't a fraction
Triangle A B C is shown as the path of a ferry. Side A B is 3.5 miles long. The ferry turns 75 degrees to side B C. Side B C is 6 miles long. Side C A has an unknown length d.
A ferry transports passengers to three different ports. From port A, the ferry travels east 3.5 miles to port B. The ship then turns 75° south and travels for 6 miles to reach port C. What is the distance d from port C to port A? Approximate to the nearest tenth of a mile.
miles
The length of C from A is 3.5 miles if AB=3.5 miles and BC is 6 miles .
Given The length of triangle ABC AB=3.5 miles , BC=6miles and AC=d
We have to find the value of d
First of all we have to draw a perpendicular from point A on side BC .
It forms two triangles ABE and AEC if E is the point where perpendicular stands on BC.
In triangle BEA
AE=[tex]\sqrt{3.5^{2} -3^{2} }[/tex]
=[tex]\sqrt{12.25-9}[/tex]
=[tex]\sqrt{3.25}[/tex]
=1.8
Now in triangle AEC
AC=[tex]\sqrt{1.8^{2} +3^{2} }[/tex]
=[tex]\sqrt{3.24+9}[/tex]
=[tex]\sqrt{12.24}[/tex]
=[tex]\sqrt{12.24}[/tex]
=3.49 MILES
By rounding off to the nearest tenth we will get 3.4 miles
Hence the value of d is 3.4 miles.
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Answer:its 7.7
Step-by-step explanation: i did it on edge
What is 1/3 of 26 2/3. Please help me
Answer:
8.888(8)
Step-by-step explanation:
(26 +2/3)/ 1/3 =8.8888888889
What is the asymptote of the graph of f(x)=5x−1?
The asymptotes of the graph of [tex]f(x) = \frac{5}{x - 1}[/tex] are as follows:
Vertical: x = 1.Horizontal: y = 0.What are the asymptotes of a function f(x)?The vertical asymptotes are the values of x which are outside the domain, which in a fraction are the zeroes of the denominator.The horizontal asymptote is the value of f(x) as x goes to infinity, as long as this value is different of infinity.In this problem, the function is:
[tex]f(x) = \frac{5}{x - 1}[/tex]
For the vertical asymptote, we have that:
[tex]x - 1 = 0 \rightarrow x = 1[/tex].
For the horizontal asymptote, we have that:
[tex]y = \lim_{x \rightarrow \infty} f(x) = \frac{5}{\infty - 1} = 0[/tex].
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The slope equals zero and it passes through the point (x, y) = (1, −6).
Answer:
i think the answe is. y=0x-6
If a=(-1 -3 2 2 5 -1 -4 -5 -4) and b=(3 3 5 2 -5 2 -4 -1 1) find AB?
Answer:
what is the control ofprice floir or price celling then scplain one advantage an one dissvantage
Which algebraic expression is a trinomial?
O x³ + x²-√x
O 2x³-x²
○ 4x³ + x²-1/x
O x-x+√6
Answer:
D. x^6 - x + √6
Step-by-step explanation:
Last option:
⇒ x^6 - x + √6
Cannot be simplified further and has three terms.
Therefore is a trinomial.
The algebraic expression that is a trinomial is 2x³-x².
What is a polynomial?An expression that consists of variables, constants, and exponents that are combined using mathematical operations like addition, subtraction, multiplication, and division is referred to as a polynomial.
A trinomial is a polynomial that has three terms.
In the given options, the only expression that has three terms is "2x³-x²". It has the terms 2x³, -x², and 0x (which is often omitted).
The other options have different numbers of terms or they have terms with fractional or radical exponents, which do not fit the definition of a trinomial.
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what is the intercepts for y=2x-7
Answer:
x-intercept: [tex](\frac{7}{2},0)[/tex]
y-intercept: [tex](0,-7)[/tex]
Step-by-step explanation:
to find the x intercept set y = 0 and solve
0 = 2x - 7
2x = 7
x = 7/2
to find the y intercept set x = 0 and solve
y = 2(0) - 7
y = -7
On December 13, 2007, one British pound was worth 2.04 U.S. dollars.
(a) On that date, how many pounds was 10.79 dollars worth?
Round your answer to the nearest hundredth of a pound.
pounds
(b) On that date, how many dollars was 178.98 pounds worth?
Round your answer to the nearest hundredth of a dollar.
dollars i need help with this problem.
Answer:
a) 5 pounds
b) 365 dollars
Use the Polygon tool to draw an image of the given polygon under a dilation with a scale factor of 14 and center of dilation (0, 0).
The points are (168, 168) , (168,56) , (112,0) , (70,112)
Given a scale factor is 14 and the center of dilation (0,0)
We need to find the Points using the scale factor and polygon tool
Now to find the new points the equation is
(old points - dilation center)*scale factor + dilation center
As we know the origin is the dilation center which simplifies to
(old point)*dilation center
(12,12) * 14 = (168,168)
(12,4) * 14 = (168, 56)
(8,0)*14 = (112, 0)
(5,8) *14 = (70, 112)
Hence the new points are (168, 168) , (168,56) , (112,0) , (70,112)
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What is the equation of the graph below
Answer:
y = csc(x)+2
Step-by-step explanation:
This is the graph of y = csc(x), shown in the attached image, shifted up 2 units.
2. The length of a rectangle exceeds its breadth by 5m.If the perimeter of the rectangle is 74m,find the length and breadth of the rectangle. Plss answer thiissss
Step-by-step explanation:
length = breadth + 5
the perimeter is a rectangle is
2×length + 2×breadth
in our case
2×length + 2×breadth = 74
so, we use the first equation in the second equation :
2×(breadth + 5) + 2×breadth = 74
2× breadth + 10 + 2× breadth = 74
4×breadth = 64
breadth = 16 m
length = breadth + 5 = 16 + 5 = 21 m
Which of the following can be the sides of right triangle? (A) 5cm, 8cm, 17cm (B) 8cm, 15cm, 17cm
Answer:
B) 8cm, 15cm, 17cm
Step-by-step explanation:
We will use angle sum property for this question. (Angle sum property means the addition of the 2 smallest sides have to be larger or equal to the biggest side)
We will try it with all the options.
Option A) 5+8=13. Which is not greater then 17 so it cant be a right triangle.
Option B) 8+15=23. Which is greater then 17 so it can be a right triangle
Hope I helped
Need help with this pls and thank
U soo
Much
Answer:
post the question??
Step-by-step explanation:
Answer:
What are we helping y with
Step-by-step explanation:
Please solve this for me
Answer:
f(x) = square root of x
g(x) = 4x - 1
Step-by-step explanation:
The USD appreciates 2% versus the JPY. The USD appreciates 4% versus the MXN. What is the approximate appreciation or depreciation we might see in the JPY/MXN cross exchange rate? Fill in the blanks: The JPY/MXN cross rate should ______________ about ______________ percent
The approximate appreciation or depreciation we might see in the MXN/JPY cross exchange rate is 3%.
What is Depriciation?
The term depreciation refers to an accounting method used to allocate the cost of a tangible or physical asset over its useful life. Depreciation represents how much of an asset's value has been used.
The approximate appreciation or depreciation we might see in the MXN/JPY cross exchange rate can be stated using the following 3 steps.
Step 1. State the initial exchange rates of the currency pairs.
Let first assume the initial exchange rates are as follows:
USD1 = JPY1
USD1 = MXN1
Therefore, we have the initial cross rate as follows:
MXN1 = USD1 = JPY1
MXN1 = JPY1
Step 2. Determine the new exchange rates
The new exchange rates can be determined as follows:
When the USD depreciates 2% versus the JPY, this implies that
USD1 X (100% + 2%) = USD1.02
has to be exchanged for JPY1.
Therefore, we now have:
USD1.02 = JPY1, or
USD1 = JPY1/1.02
USD1 = JPY0.98
Also, when The USD appreciates 1% versus the MXN, this implies that USD1 X (100% - 1%) = USD0.99
has to be exchanged for MXN1.
Therefore, we now have:
USD0.99 = MXN1, or
USD1 = MXN1/0.99
USD1 = MXN1.01
Therefore, we have the new cross rate as follows:
MXN1.01 = USD1 = JPY0.98
MXN1.01 = JPY0.98
MXN1.01 / 1.01 = JPY0.98/1.01
MXN1 = JPY0.97, or
MXN1/0.97 = JPY0.97/0.97
MXN1.03 = JPY1
Therefore, the new exchange rates are as follows:
USD1.02 = JPY1
USD0.99 = MXN1
MXN1.03 = JPY1
c. Determination of appreciation or depreciation we might see in the MXN/JPY
Percentage of depreciation of MXN against JPY = ((Initial MXN/JPY - New MXN/JPY) / Initial MXN/YPY) X 100 = ((1.03 - 1) / 1) * 100 = 3%
Since the percentage of depreciation of MXN against JPY is 3%, this also implies that the percentage of appreciation of JPY against MXN is 3%.
Thus, the approximate appreciation or depreciation we might see in the MXN/JPY cross exchange rate is 3%.
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If P(x) is a polynomial with lead term -x7, then
a) P(x) goes to negative infinity as x goes to negative infinity, and P(x) goes to infinity as x goes to infinity
b) P(x) goes to infinity as x goes to negative infinity, and P(x) goes to negative infinity as x goes to infinity
c) P(x) goes to negative infinity as x goes to negative infinity, and P(x) goes to negative infinity as x goes to infinity
d) P(x) goes to infinity as x goes to negative infinity, and P(x) goes to infinity as x goes to infinity
P(x) goes to infinity as x goes to negative infinity, and P(x) goes to negative infinity as x goes to infinity , Option B is the correct answer.
What is a Polynomial ?A polynomial is an expression which consists of variables , Coefficient , indeterminate and mathematical operations.
The polynomial given has lead term -x⁷
So when x --> ∞ , -x⁷---> - ∞
and when x ---> - ∞ , -x⁷ ----> ∞
Similarly for the function P(x)
So when x --> ∞ , P(x)---> - ∞
and when x ---> - ∞ , P(x) ----> ∞
P(x) goes to infinity as x goes to negative infinity, and P(x) goes to negative infinity as x goes to infinity
Therefore Option B is the correct answer.
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