Step-by-step explanation:
A=P(1+R)
A/P=1+R
(A/P)-1=r
(3000000/20000)-1=r
149=r
[tex]\textbf{Answer:}[/tex]
[tex]r\approx 0.13345[/tex]
[tex]\textbf{Step-by-step explanation:}[/tex]
[tex]\text{Your formula is missing something: t}[/tex]
[tex]\text{It should read }A=P(1+r)^t[/tex] [tex]\text{Where A is the final amount, P is the principal, r is rate in decimal, and t is time in years}[/tex]
[tex]\text{Given that A=3000000, P=20000, and t=40, we can subsitute and solve}[/tex]
[tex]A=P(1+r)^t[/tex]
[tex]\text{subsitute}[/tex]
[tex]3000000=20000(1+r)^{40}[/tex][tex]\text{ now solve for r}[/tex]
[tex]\text{Divide both sides by 20000}[/tex]
[tex]150=(1+r)^{40}[/tex]
[tex]\text{Take the 40th root of both sides }(\sqrt[40]{})[/tex]
[tex]\sqrt[40]{150}=1+r[/tex]
[tex]\text{subtract 1 from both sides}[/tex]
[tex]\sqrt[40]{150}-1=r[/tex] [tex]\text{ or in approximate form, }[/tex][/tex]r\approx 0.13345[/tex]
I’m stuck, please help ASAP. Will give brainliest!
Answer:
C) 35 Degrees
Step-by-step explanation:
To find the degree of an exterior angle, subtract the larger arc, DE, degree by the smaller arc, BC, and then divide by 2! Which is 35. 118-48/ 2 = 35.
Shelly biked 21 miles in 4 hours.
What is Shelly's average speed in miles per hour?
Answer: 5.25 miles per hour.
Step-by-step explanation:
21/4 = 5.25
Hello There!
WHAT WE KNOW Shelly biked 21 miles in 4 hours. We know that Shelly's average speed = 5.25 miles / hour because "21 divided by 4 equals 5.25"
What is the answer for 27^x=9^x-4
Answer:
x = -8
Step-by-step explanation:
We are given the following expression which we are to solve for [tex]x[/tex]:
[tex] 2 7 ^ x = 9 ^ { x - 4 } [/tex]
For this expression, we will make the bases same on both sides of the equation and then equate the exponents equal to each other.
[tex](3^3)^x = (3^2)^{x-4}[/tex]
Multiplying the exponents and equating them to get:
[tex] 3 x = 2 ( x - 4 ) [/tex]
[tex] 3 x = 2 x - 8 [/tex]
[tex] 3 x - 2 x = - 8 [/tex]
x = -8
For this case we must solve the following equation:
[tex]27 ^ x = 9 ^ {x-4}[/tex]
We rewrite:
[tex]27 = 3 * 3 * 3 = 3 ^ 3\\9 = 3 * 3 = 3 ^ 2[/tex]
So:
[tex]3^{3(x)}=3^{2(x-4)}[/tex]
Since the bases are the same, the two expressions are only equal if the exponents are also equal. So, we have:
[tex]3 (x) = 2 (x-4)\\3x = 2x-8[/tex]
Subtracting 2x on both sides:
[tex]3x-2x = -8\\x = -8[/tex]
Answer:
[tex]x = -8[/tex]
[tex]\frac{x}{2}[/tex] = -7 solve for x
All you need to do to solve this is multiply 2 to both sides. This will cancel out 2 from the denominator and isolate x...
2([tex]\frac{x}{2}[/tex]) = -7 * 2
x = -14
Hope this helped!
~Just a girl in love with Shawn Mendes
Hello There!
The Answer is -14
If we substitute -14 in the equation as x, -14 ÷ 2 ≈ -7
A negative number divided by a positive number gives us a negative number.
A taxi company charges passengers $1.75 for a ride, no matter how long the ride is, and an additional $0.40 for each mile traveled. The rulec
= 0.40m + 1.75 describes the relationship between the number of miles m and the total cost of the ride c.
a. What is the charge for a 1-mile ride?
b. What is the charge for a 2.7-mile ride?
A. $2.15; $2.83
B. $0.40; $5.13
C. $1.75; $2.15
D. $0.40; $1.08
Answer:
A
Step-by-step explanation:
For a 1 mile ride, plug in 1 into m.
Total = 0.40(1) + 1.75
= 0.40+1.75 = 2.15.
Because no other answer but A has 2.15, you're answer is A
Answer:A
Step-by-step explanation:
Dan spends 2/5 of his wages on rent and 1/2 on food. If he makes £540 per week, how much money does he have left?
Answer:
Dan has £54 left
Step-by-step explanation:
Dan's weekly wages are £540.
Then his spending includes (2/5)w + (5/10()w, or (9/10)w, and this is subtracted from Dan's wages: £540 - (expenses)
£540 - (9/10)(£540) = £54
Dan has £54 left after having spent 9/10 of his weekly wages on rent and food.
A taxi driver charges a $5 flat fee to enter the car and $0.50 per mile .what is the total cost of a taxi ride ?
The total cost of a taxi ride includes a $5 flat fee plus $0.50 for every mile traveled. The total cost can be calculated using the formula: Total cost = $5 flat fee + ($0.50 × number of miles). For instance, a 10-mile trip would cost $10.
Explanation:The total cost of a taxi ride is dependent on the distance traveled in miles. The taxi driver charges a $5 flat fee to enter the car and $0.50 per mile. To find the total cost, you can use the equation:
Total cost = Flat fee + (Cost per mile × Number of miles traveled)
For example, if you traveled 10 miles, the total cost would be:
Total cost = $5 + ($0.50 × 10) = $5 + $5 = $10
This formula will give you the total expense for any number of miles traveled in the taxi.
help? find the area of the regular polygon round to the nearest tenth.
Answer:
[tex]A=779.4\ cm^{2}[/tex]
Step-by-step explanation:
we know that
The area of a regular hexagon is equal to the area of six equilateral triangles
Applying the law of sines
The area of six equilateral triangles is equal
[tex]A=6[\frac{1}{2}b^{2}sin(60)][/tex]
where
b is the side length of the regular hexagon
we have
[tex]b=10\sqrt{3}\ cm[/tex]
[tex]sin(60\°)=\sqrt{3}/2\ cm[/tex]
substitute
[tex]A=6[\frac{1}{2}(10\sqrt{3})^{2}(\sqrt{3}/2)][/tex]
[tex]A=450\sqrt{3}=779.4\ cm^{2}[/tex]
What is the answer to this question?
Answer:
(0,2/3)
Step-by-step explanation:
I would go for elimination on this one.
This will require we manipulate at least one equation.
I'm going to multiply bottom equation by -2: -2x-12y=-8
So we have
2x+3y=2
-2x-12y=-8
---------------add the two equations
0 -9y=-6
-9y=-6
y=6/9=2/3
2x+3y=2
2x+3(2/3)=2
2x+2=2
2x=0
x=0
(0,2/3)
Answer: The Answer is A X=0 Y=2/3
Step-by-step explanation:
2x+3y=2
X+6y=4
step one: substitute in the value of x into the equation
2x +3y = 2
x= 4-6y
Step two: Solve with the X substitution
2(4-6y) +3y = 2
You get Y= 2/3
Step three: plug in 2/3 for X
X= 4-6(2/3)
You get 0
therefore: X = 0 and Y=2/3
A cash register contains 10$ bills and 20$ bills total value of 340 if there are 23 bills total then how many of each does the register contains
Answer:
There are 12 bills of 10$ and 11 bills of 20$
Step-by-step explanation:
Let
x ------> number of 10$ bills
y -----> number of 20$ bills
we know that
x+y=23 -----> x=23-y -----> equation A
10x+20y=340 ----> equation B
substitute equation A in equation B and solve for y
10(23-y)+20y=340
230-10y+20y=340
10y=340-230
y=110/10=11
Find the value of x
x=23-y ----> x=23-11=12
therefore
There are 12 bills of 10$ and 11 bills of 20$
the function f(x)= sqrt x is translated left 5 units and up 3 units to create the function g(x). what is the domain of g(x)?
Answer:
x ≥ -5
Step-by-step explanation:
If we have a translation to left c units, we write " x + c " in the function, and
If we have a translation to right c units, we write " x - c" in the function
If we have vertical translation up b units, we "add b to the function", and
If we have vertical translation down b units, we "subtract b to the function"
The parent function is [tex]f(x)=\sqrt{x}[/tex]
Since translation left 5 units and up 3 units, we can write:
[tex]f(x)=\sqrt{x+5} + 3[/tex]
The domain is affected by the square root sign and we know the number under the square root CANNOT be negative, so we can say:
x + 5 ≥ 0
x ≥ -5
This is the domain.
The domain of the function g(x), which is the translated version of f(x) = √x, is all x ≥ -5 after being shifted left 5 units and up 3 units.
Explanation:The function g(x) resulting from translating f(x) = √x left 5 units and up 3 units is expressed as g(x) = √(x+5) + 3. Because we cannot take the square root of a negative number in the set of real numbers, the domain of f(x) is all x ≥ 0. After the translation, the domain of g(x) will also be shifted 5 units to the left. Therefore, the domain of g(x) is all x ≥ -5, as this is the new point where the function starts to produce real number outputs.
2.3 +0.02(x + 20) - 4.8= -9
Answer:
x = -345
Step-by-step explanation
2.3 + .02x + .4 - 4.8 = -9
2.7 - 4.8 + .02x = -9
-2.1 + .02x = -9
.02x = 6.9
x = -6.9 / .02
x = -345
Answer: x = -345
Step-by-step explanation:
2.3 + .02(x + 20) - 4.8 = -9
2.3 + (.02x + .4) - 4.8 = -9
-2.1 + .02x = -9
+2.1 +2.1
.02x = -6.9
.02/.02 -6.9/.02
x = -345
Solve 2x - 8 < 7.
{x | x < 1/2}
{x | x > 1/2}
{x | x < 15/2}
{x | x > 15/2}
The solution to the inequality is [tex]\( \{ x \,|\, x < \frac{15}{2} \} \),[/tex] indicating all real numbers less than [tex]\( \frac{15}{2} \).[/tex]
To solve the inequality [tex]\(2x - 8 < 7\)[/tex], we'll isolate x by adding 8 to both sides and then dividing both sides by 2.
Here's the step-by-step calculation:
Starting inequality:
[tex]\[ 2x - 8 < 7 \][/tex]
Add 8 to both sides:
[tex]\[ 2x - 8 + 8 < 7 + 8 \][/tex]
[tex]\[ 2x < 15 \][/tex]
Divide both sides by 2:
[tex]\[ \frac{2x}{2} < \frac{15}{2} \][/tex]
[tex]\[ x < \frac{15}{2} \][/tex]
So, the solution to the inequality is [tex]\(x < \frac{15}{2}\).[/tex]
Now, let's express the solution set in set-builder notation. The solution set for x consists of all real numbers less than [tex]\( \frac{15}{2} \)[/tex]. This can be written as:
[tex]\[ \{ x \,|\, x < \frac{15}{2} \} \][/tex]
So, the correct option is:
[tex]\[ \boxed{\{ x \,|\, x < \frac{15}{2} \}} \][/tex]
Evaluate 4(x - 3) + 5x - x2 for x = 2.
Answer:
The value of the expression for x=2 is 2.
Step-by-step explanation:
Consider the provided expression.
[tex]4(x - 3) + 5x - x^2 [/tex]
We need to find the value of expression for x=2.
Substitute the value of x=2 in provided expression and simplify as shown.
[tex]4(2 - 3) + 5(2) - 2^2 [/tex]
[tex]4(-1) + 10 - 4 [/tex]
[tex]-4 + 6 [/tex]
[tex]2 [/tex]
Hence, the value of the expression for x=2 is 2.
The numerical value of the expression 4(x - 3) + 5x - x² when x = 2 is 2.
What is the value of the expression when x = 2?Given the expression in the question:
4(x - 3) + 5x - x²
x = 2
To evaluate the expression 4(x - 3) + 5x - x² for x = 2, repalce all the occurences of x in the expression with 2 and simplify:
4(x - 3) + 5x - x²
Plug in x = 2:
4(2 - 3) + 5(2) - (2)²
Subtract 3 from 2:
4(-1) + 5(2) - (2)²
Take the square of 2:
4(-1) + 5(2) - 4
Multiply 4 and -1:
-4 + 5(2) - 4
Multiply 5 and 2:
-4 + 10 - 4
Add the 3 numbers:
2
Therefore, the value of the expression is 2.
Learn more about algebraic expressions here: https://brainly.com/question/28959918
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If 2x+y = 6 and x−6=y, what is the value of x?
(A) 0 (B) 2 (C) 3 (D) 4 (E) 6
Answer:
x = 4
Step-by-step explanation:
2x + y = 6 ... (i)
x - 6 = y ... (ii)
y = 6 - 2x ... (i)
y = x - 6 ... (ii)
So,
6 - 2x = x - 6
x + 2x = 6 + 6
3x = 12
x = 12/3 = 4
How do you do this problem
1. You have a piece of land where you want to grow a garden. You only
have 20 yards of fencing to surround the garden. Work through the steps
below to figure out the maximum space you can create to grow plants.
A) you decide to make the width 2 yards
What is the length? ___ yards
Check: is the perimeter 20? _____
What is the area? ____ square yards
Apartment rentals in Fairview run approximately $0.90 per square foot. Jillian has determined that she can afford $630 per month for rent. What is the largest apartment, in square feet, she should consider at the given rate?
Answer:
700 square feet
Step-by-step explanation:
We can simply divide 630 by 0.9 to find the value:
[tex]\frac{630}{0.90}=700[/tex]
Checking, if she goes for 700 sq ft at $0.90 per square feet, she would need:
700 * 0.90 = $630
Yes, that's the max, so 700 sq. feet apartment is what she can afford.
A field is 910 yards by 300 yards. What is the greatest number of rectangle lots of 120 yards by 65 yards that can be places on the field?
Let R = greatest number of rectangular lots.
R = (910 • 300)/(120 • 65)
R = 273,000 ÷ 7800
R = 35
Which of the following equations is an example of inverse variation between
the variables x and y?
A. Y=x+5
B. Y=5x
C. Y=5/x
D. Y=x/5
[tex]\bf \qquad \qquad \textit{inverse proportional variation} \\\\ \textit{\underline{y} varies inversely with \underline{x}}\qquad \qquad y=\cfrac{k}{x}\impliedby \begin{array}{llll} k=constant\ of\\ \qquad variation \end{array} \\\\[-0.35em] \rule{34em}{0.25pt}\\\\ k=5\qquad \qquad y=\cfrac{5}{x}[/tex]
Answer:
C. Y=5/x
Step-by-step explanation:
Inverse variation is given by
xy = k where k is a constant
Divide each side by x
xy/x = k/x
y = k/x where k is a constant
Let k=5
y = 5/x is an equation that is inverse variation
Which outcome is represented by X?
rolling a two and the coin landing on tails
rolling a three and the coin landing on tails
rolling a two and the coin landing on heads
rolling a three and the coin landing on heads
Answer:
A. rolling a two and landing on tails
Juan is hiking up a mountain starting at an elevation of 800 feet. Every hour, he is 2000 feet higher in elevation.
Which function, h(t), where t is time in hours, represents Juan's height over time?
1. h(t)=2800t
2. h(t)=800t+2000
3. h(t)=2000t
4. h(t)=2000t+800
Answer:
4. h(t)=2000t+800
Step-by-step explanation:
800 is his starting elevation we dont not multiply it
every hour he gains 2000ft in elevation and t shows the hours 2000ft * t (hours) + 800
rectangle q has an area of 2 square units thea drew scaled version and labled it rectangle r what scale factor did thea use to go from q to r
Pre-Image < Image, then the scale factor is k >1.
Pre-Image > Image, then the Scale factor will be lies between,
0 < k < 1.
Scale factor of a rectangleIt exists given that Rectangle Q has an area of 2 square units.
Thea Drew a scaled version of Rectangle Q and labeled it as R.
As you must keep in mind If we draw a scaled copy of the pre-image, then the two images.
Therefore, Pre-image and Image are similar.
Consider the Scale factor of transformation = k
Rectangle Q = Pre - image,
Rectangle R= Image
If, Pre-Image < Image, then the scale factor is k >1.
But If, Pre-Image > Image, then the Scale factor will be lies between,
0 < k < 1.
To learn more about the Scale factor of a rectangle
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Find the radius of K
Answer:
6 ft.
Step-by-step explanation:
solution :
360 degree = pie r².
1 degree =pie r²/360
50degree=5pie r²/36
5pie = 5 pie r²/36
r²=36
r=6
Therefore radius = 6 ft.
A line passes through the given points. Write an equation for the line in
point-slope form. Then rewrite the equation in slope-intercept form.
(4, -2), (9, -8)
4-9=5
-2--8=6
y=mx+b
slope/mx=6/1
base/y intercept=5
Answer: The equation for the line in point-slope form :[tex] (y+2)=\dfrac{-6}{5}(x-4)[/tex]
The equation in slope-intercept form : [tex]y=\dfrac{-6}{5}x+\dfrac{14}{5}[/tex]
Step-by-step explanation:
The equation of a line in point slope form passing through points (a,b) and (c,d) is given by :-
[tex](y-b)=\dfrac{d-b}{c-a}(x-a)[/tex]
Now, the point slope form passing through points (4, -2) and (9, -8) is given by :-
[tex](y-(-2))=\dfrac{-8-(-2)}{9-4}(x-4)\\\\\Rightarrow (y+2)=\dfrac{-6}{5}(x-4)[/tex]
The equation for the line in point-slope form :[tex] (y+2)=\dfrac{-6}{5}(x-4)[/tex]
Further if we simplify the equation , we get
[tex] y+2=\dfrac{-6}{5}x+\dfrac{24}{5}\\\\\Rightarrow\ y=\dfrac{-6}{5}x+\dfrac{24}{5}-2\\\\\Rightarrow\ y=\dfrac{-6}{5}x+\dfrac{14}{5}[/tex]
The equation in slope-intercept form : [tex]y=\dfrac{-6}{5}x+\dfrac{14}{5}[/tex]
Lucinda wants to make $6.00 on every arrangement of flowers she sells. If it costs her $10.00 to prepare an
arrangement, by what percentage will she mark up the price?
a.60%
b.70%
c.59%
d.167%
Answer:60%
Step-by-step explanation:
Final answer:
Lucinda will mark up the price of her flower arrangements by 60% to make a $6.00 profit on each one, which costs her $10.00 to prepare. The correct answer is option a.
Explanation:
Lucinda wishes to make a profit of $6.00 on each flower arrangement she sells, on top of the $10.00 it costs her to prepare one. To calculate the percentage markup, we use the formula: Markup Percentage = (Profit / Cost) × 100%. In Lucinda's case, the profit is $6.00 and the cost is $10.00.
So, the calculation will look like this:
Markup Percentage = ($6.00 / $10.00) × 100% = 0.6 × 100% = 60%.
Therefore, Lucinda will mark up the price by 60% to achieve her desired profit. The correct answer to the question is option a.
Find the area of rectangle ABCD with vertices A(-4, 0), B(2, 2), C(3, -1), and D(-3, -3)
Answer:
18 square units.
Step-by-step explanation:
graph the square or find the difference then multiply the base by the hight.
is 1 greater than 5/3
Answer: No
Step-by-step explanation: 5/3 is greater than 1 because 1 is the same as 3/3 and 5/3 is greater than 3/3 making 5/3 greater than 1.
what is the slope of the line y=-2x+3
Answer: The slope is -2
Step-by-step explanation:
It is important to remember that the equation of the line in Slope-Intercept form is the following:
[tex]y=mx+b[/tex]
Where "m" is the slope of the line and "b" is the y-intercept.
In this case you can observe that the given equation of the line [tex]y=-2x+3[/tex] is written in Slope-Intercept form.
Therefore, you can identify that the slope "m" is:
[tex]m=-2[/tex]
And the y-intercept "b" is:
[tex]b=3[/tex]
Find the value of y and
simplify completely.
y =
?
Answer:
y=9.01
Step-by-step explanation:
In this question you apply the Pythagoras Theorem to generate relationships which will enable you to form equations and solve for the unknown.
The Pythagoras Theorem states that when you have a right-angle triangle and squares are made at each of the three sides, the sum of squares of the two small sides will equal the square of the longest side.
It is expressed as a²+b²=c² where;
a and b are the shortest sides of the triangle, where b is the heightc is the longest side of the triangle/hypotenuseIn the question we can use three triangles to form expressions using this theorem
First triangle
That one with a height of y, short side of 3 and hypotenuse of zThe relationship you can form is;
[tex]3^2+y^2=z^2\\9+y^2=z^2\\y^2=z^2-9------------------------(1)[/tex]
In this equation you make y² the subject of the formula
Second Triangle
The second triangle is that with a base of 27 as the (a), a height of y as the (b) and the hypotenuse of x as the (c)Hence the relationship you can form is
[tex]27^2+y^2=x^2\\729+y^2=x^2\\y^2=x^2-729[/tex]
In this equation you make y² the subject of the formula
Third Triangle
The third triangle is that one with a base of z as (a) , x as (b) which is the height and 30(3+27) as the (c) which is the hypotenuseThe relationship you can form is;
[tex]z^2+x^2=30^2\\x^2=30^2-z^2---------------------(3)[/tex]
Here x² is the subject of the formula
Equations
[tex]y^2=z^2-9\\y^2=x^2-729\\x^2=900-z^2[/tex]
Substitute equation 3 in equation 2
[tex]y^2=x^2-729-------------2\\\\x^2=900-z^2-------------3\\\\y^2=900-z^2-729\\\\y^2=171-z^2---------------4[/tex]
Substitute equation 4 in equation 1
[tex]y^2=171-z^2---------------4\\\\y^2=z^2-9------------1\\\\z^2-9=171-z^2\\\\2z^2=171+9\\\\z^2=180\\\\z=\sqrt{180} \\\\z=9.487\\\\z=9.5[/tex]
Use the value of z in equation 1 to get value of y
[tex]z^2-3^2=y^2\\\\9.5^2-9=y^2\\\\90.25-9=y^2\\\\81.25=y^2\\\\\sqrt{81.25} =y\\\\y=9.01[/tex]