Answer: 22
Step-by-step explanation: 2x2 + x -41= -15
* 4 + x -41= -15
* x -37= -15
* x= 22
A park, in the shape of a quadrilateral ABCD has angle B=900 , AB=9m, BC=40m, CD=15m, DA=28m. How much area does it occupy?
Given:
In quadrilateral ABCD, angle B=90° , AB=9m, BC=40m, CD=15m, DA=28m.
To find:
The area of the quadrilateral ABCD.
Solution:
In quadrilateral ABCD, draw a diagonal AC.
Using Pythagoras theorem in triangle ABC, we get
[tex]AC^2=AB^2+BC^2[/tex]
[tex]AC^2=9^2+40^2[/tex]
[tex]AC^2=81+1600[/tex]
[tex]AC^2=1681[/tex]
Taking square root on both sides, we get
[tex]AC=\sqrt{1681}[/tex]
[tex]AC=41[/tex]
Area of the triangle ABC is:
[tex]A_1=\dfrac{1}{2}\times base\times height[/tex]
[tex]A_1=\dfrac{1}{2}\times BC\times AB[/tex]
[tex]A_1=\dfrac{1}{2}\times 40\times 9[/tex]
[tex]A_1=180[/tex]
So, the area of the triangle ABC is 180 square m.
According to the Heron's formula, the area of a triangle is
[tex]Area=\sqrt{s(s-a)(s-b)(s-c)}[/tex]
where,
[tex]s=\dfrac{a+b+c}{2}[/tex]
In triangle ACD,
[tex]s=\dfrac{28+15+41}{2}[/tex]
[tex]s=\dfrac{84}{2}[/tex]
[tex]s=42[/tex]
Using Heron's formula, the area of the triangle ACD, we get
[tex]A_2=\sqrt{42(42-28)(42-15)(42-41)}[/tex]
[tex]A_2=\sqrt{42(14)(27)(1)}[/tex]
[tex]A_2=\sqrt{15876}[/tex]
[tex]A_2=126[/tex]
Now, the area of the quadrilateral is the sum of area of the triangle ABC and triangle ACD.
[tex]A=A_1+A_2[/tex]
[tex]A=180+126[/tex]
[tex]A=306[/tex]
Therefore, the area of the quadrilateral ABCD is 306 square meter.
Use Lagrange multipliers to find the maximum and minimum values of the function subject to the given constraint. f(x,y)= e^xy; X^3+y^3=16
Answer:
f(x,y) = [tex]e^{xy}[/tex] is maximum at x = 2 and y = 2 and f(2,2) = [tex]e^{4}[/tex]
Step-by-step explanation:
Since f(x,y) = [tex]e^{xy}[/tex] and x³ + y³ = 16, Ф(x,y) = x³ + y³ - 16
df/dx = y[tex]e^{xy}[/tex], df/dy = x[tex]e^{xy}[/tex], dФ/dx = 3x² and dФ/dy = 3y²
From the method of Lagrange multipliers,
df/dx = λdΦ/dx and df/dy = λdΦ/dy
y[tex]e^{xy}[/tex] = 3λx² (1) and x[tex]e^{xy}[/tex] = 3λy² (2)
multiplying (1) by x and (2) by y, we have
xy[tex]e^{xy}[/tex] = 3λx³ (4) and xy[tex]e^{xy}[/tex] = 3λy³ (5)
So, 3λx³ = 3λy³
⇒ x = y
Substituting x = y into the constraint equation, we have
x³ + y³ = 16
x³ + x³ = 16
2x³ = 16
x³ = 16/2
x³ = 8
x = ∛8
x = 2 ⇒ y = 2, since x = y
So, f(x,y) = f(2,2) = [tex]e^{2 X2}[/tex] = [tex]e^{4}[/tex]
We need to determine if this is a maximum or minimum point by considering other points that fit into the constraint equation.
Since x³ + y³ = 16 when x = 0, y is maximum when y = 0, x = maximum
So, 0³ + y³ = 16
y³ = 16
y = ∛16
Also, when y = 0, x = maximum
So, x³ + 0³ = 16
x³ = 16
x = ∛16
and f(0,∛16) = [tex]e^{0X\sqrt[3]{16} } = e^{0} = 1[/tex].
Also, f(∛16, 0) = [tex]e^{\sqrt[3]{16}X0 } = e^{0} = 1[/tex].
Since f(0,∛16) = f(∛16, 0) = 1 < f(2,2) = [tex]e^{4}[/tex]
f(2,2) is a maximum point
B. The difference between the cash price and the initial deposit in hire purchase is known as ?
Hire Purchase agreement
[tex]{correct me if i am wrong}}[/tex]
The difference between the cash price and the initial deposit in hire purchase is known as [tex]_\( \text{Principal} \)_[/tex].
In hire purchase transactions, buyers can acquire goods by making an initial down payment and paying the remaining amount in installments. The difference between the total cost of the item and the initial deposit is a crucial concept known as the [tex]_\( \text{Principal} \)_[/tex] in mathematical terms. Let's explore this in detail.
In the context of hire purchase, the total cost of the item is often referred to as the cash price. It represents the actual value of the item without considering any interest or finance charges. On the other hand, the initial deposit, also called the down payment, is the amount paid upfront by the buyer to secure the item.
Now, let's introduce some variables to help us understand this concept mathematically:
- Let CP be the cash price of the item.
- Let D be the initial deposit made by the buyer.
The difference between the cash price and the initial deposit is given by:
[tex]\[ \text{Principal} = CP - D \][/tex]
The Principal is the amount that remains to be paid off in installments, and it serves as the basis for calculating the subsequent monthly or periodic payments in a hire purchase agreement.
The Principal is critical because it determines the total amount the buyer will end up paying for the item. It also affects the duration of the hire purchase agreement, as the buyer's installments are typically spread over a specific number of months or years.
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if p(a) contain 8 elements then set a contain which element
Answer:
3 elements
because 2^3=8
Answer:
3 elements
because 2^3=8
Step-by-step explanation:
plz answer if you know it....
Sales tax is charged on the subtotal (amount before tax).
First, find the subtotal by adding up all of the amounts.
4(675) + 2(110) + 5(41) + 6(135) + 230(2.50)
2700 + 220 + 205 + 810 + 575
Total = 4510
Next, we need to find 7% of 4510. That number is the sales tax.
0.07 x 4510 = 315.70
Sales Tax = $315.70
Total Amount (with tax) = $4825.70
Hope this helps!! :)
7. You are mixing some concrete for a home project, and you've calculated according to the
directions that you need six gallons of water for your mix. But your bucket isn't calibrated, so you
don't know how much it holds. On the other hand, you just finished a two-liter bottle of soda. If you
use the bottle to measure your water, how many times will you need to fill it?
Answer:
11.4 bottles for US gal.
13.6 bottles for Imperial gal.
Step-by-step explanation:
1 US gallon = 3.8 L
6 US Gallons = 6*3.8 L = 22.8 L = 11.4 bottles
1 Imperial gallon = 4.54 L
6 Imperial gallons = 6*4.54 L = 27.24 L = 13.6 bottles.
247 1372 as a number
Answer:
Do you mean in words?
Step-by-step explanation:
then it is
Two million,four hundred and seventy one thousand,three hundred and seventy two.
12. The bus left at 9.30 a.m and
reached Their destination at 1.00 p.m. How long did
the bus take to reach their destination?
Answer:
3.5 hours
Step-by-step explanation:
1300 - 0930 = 330 = 3.5 hours
work out the size of angle x.
Answer:
actually I would have solved it but don't know the angle you're talking about
The average age of Iowa residents is 37 years. Amy believes that the average age in her hometown in Iowa is not equal to this average and decided to sample 30 citizens in her neighborhood.Using the alternative hypothesis that µ ≠ 531, Amy found a t-test statistic of 1.311.What is the p-value of the test statistic?
Answer:
The p-value of the test is 0.2.
Step-by-step explanation:
Using the alternative hypothesis that µ ≠ 531, Amy found a t-test statistic of 1.311.
Alternative hypothesis means that e have a two-tailed hypothesis test.
Sample 30 citizens. Amy found a t-test statistic of 1.311.What is the p-value of the test statistic?
Thus, we have a two-tailed test with 30 - 1 = 29 degrees of freedom and t = 1.311. So, using a t-distribution calculator, the p-value of the test is 0.2.
tell whether or not the measurements below form a triangle:
1. 4, 5, 10
2. 12, 26, 20
3. 2, 3, 5
Answer:
Below.
Step-by-step explanation:
If the sum of any 2 sides are less than or equal to the third side then there's no triangle
1. N0 because 4 + 5 < 10
2. YES
3. NO because 2 + 3 = 5.
Answer:
Step-by-step explanation:
1 . 4,5,10 : this measurement does not form a triangle because the sum of two sides is not greater than the third side (longest side)
4 + 5 > 10
9 > 10 (this is not satisfied)
2. 12,26,20 :this measurement forms a triangle beacuse the sum of two sides is greater than the third side
12 + 26 > 20
38 > 20
3 .
2,3,4 : this measurement does not form a triangle because the sum of two sides is not greater than the third side.
2 + 3 > 5
5 > 5 (this is not satisfied)
Which choice shows the coordinates of C'if the trapezoid is reflected across the y-axis?
Answer:
The coordinate of C is (5, 3). The trapezoid is reflected across the y-axis. When it is reflected over y-axis only the sign of the x coordinate change and y coordinate remains the same. Hope this will helpful.
Dax borrowed Nu 5000 from the bank to buy a computer. she paid the money back at the end of 1 year.she was charged 12 percent simple interest for the year. what amount did Dax pay in interest.how much did Dax have to pay back
Answer:
Interest = Nu 600
Amount = Nu 5600
Step-by-step explanation:
P = Nu 5000
R = 12%
T = 1
[tex]Interest = \frac{PRT}{100} = \frac{5000 \times 12 \times 1}{100} = Nu \ 600[/tex]
[tex]Amount = P + Interest = 5000 + 60 0 = Nu \ 5600[/tex]
HELPP FASTTT PLEASEE HELP MEEE!!!!
1-2
x+1
1. If f(x) = find f-'(x)=
2
2
Y +1
y-1
b. 2y-1
c. 2x +1
d.
a.
e. 2x -1
2.
2
Answer:
1) 2x-1
2) 8 , 11, 11.3
Step-by-step explanation:
1) To figure out the inverse of a function , first change the F(x) to y
y = [tex]\frac{x+1}{2}[/tex]
Then switch the x and y
x = [tex]\frac{y+1}{2}[/tex]
Solve for y. Multiply by 2 both sides. Subtract 1 from both sides.
2) Use distance formula : d = [tex]\sqrt{(x_{2}-x_{1}) ^{2} + (y_{2}-y_1)^{2} }[/tex]
the first two are easy because the same x value. so just calculate Δy
-2 - 6 = -8 When you square it it becomes positive 64 and square root it and it becomes 8.
the next is a Δx. same method. 8-(-3) = -11 Square and square root and you get 11.
last one use the formula. substitute values of x's and y's into equation and solve for d.
The prices of a term of notebooks are between $2 and $5. If
you plan to spend $10 on notebooks, calculate the least
number of notebooks you can buy in this situation.
notebooks
Answer: Number “2”
Step-by-step explanation: I took the ck-12 Applications with Inequalities
Use algebra to solve 3x+4 = 1/x
The exact solutions are x=
Х
Answer:
Ignore the A before the ±, it wouldn't let me type it correctly.
[tex]x=\frac{2±\sqrt{7} }{3}[/tex]
Step-by-step explanation:
3x + 4 = 1 ÷ x
3x + 4 - 4 = 1 ÷ x - 4
3x = 1 ÷ x - 4
[tex]3x=\frac{1}{x} +\frac{x(-4)}{x}[/tex]
[tex]3x=\frac{1+x(-4)}{x}[/tex]
[tex]3x=\frac{1-4x}{x}[/tex]
[tex]x(3x)=x(\frac{1-4x}{x})[/tex]
x · 3x = - 4x + 1
3x² = - 4x + 1
3x² - (- 4x + 1) = 0
3x² + 4x - 1 = 0
Ignore the A before the ±, it wouldn't let me type it correctly.
[tex]x=\frac{-b±\sqrt{b^{2}-4ac } }{2a}[/tex]
a = 3
b = 4
c = - 1
[tex]x=\frac{-4±\sqrt{4^{2}-4((3)(-1)) } }{2(3)}[/tex]
[tex]x=\frac{-4±\sqrt{16-4((3)(-1)) } }{2(3)}[/tex]
[tex]x=\frac{-4±\sqrt{16+12 } }{2(3)}[/tex]
[tex]x=\frac{-4±\sqrt{28 } }{2(3)}[/tex]
[tex]x=\frac{-4±\sqrt{(2)(14) } }{2(3)}[/tex]
[tex]x=\frac{-4±\sqrt{(2)(2)(7) } }{2(3)}[/tex]
[tex]x=\frac{-4±\sqrt{2 } \sqrt{2}\sqrt{7} }{2(3)}[/tex]
[tex]x=\frac{-4±2\sqrt{7} }{2(3)}[/tex]
[tex]x=\frac{-4±2\sqrt{7} }{6}[/tex]
Two separate equations
[tex]x=\frac{-4+2\sqrt{7} }{6}[/tex]
[tex]x=\frac{2+\sqrt{7} }{3}[/tex]
[tex]x=\frac{-4-2\sqrt{7} }{6}[/tex]
[tex]x=\frac{2-\sqrt{7} }{3}[/tex]
Which expression is equivalent to xy^2/9?
Answer:
[tex]xy^\frac{2}{9} = x*\sqrt[9]{y^2}[/tex]
Step-by-step explanation:
Given
[tex]xy^\frac{2}{9}[/tex]
Required
The equivalent expression (see attachment)
We have:
[tex]xy^\frac{2}{9}[/tex]
Split
[tex]xy^\frac{2}{9} = x*y^\frac{2}{9}[/tex]
Apply the following laws of indices
[tex]y^\frac{m}{n} = \sqrt[n]{y^m}[/tex]
So, we have:
[tex]xy^\frac{2}{9} = x*\sqrt[9]{y^2}[/tex]
Hence (d) is correct
Answer:
Its D.
Step-by-step explanation:
Just took the quiz on EDGE2022
The curve y=9-6/x and the line y+x=8 intersect at two points. Find the coordinates of the two points
Answer: (2,6) (-3,11)
Step-by-step explanation:
At the intersection, y=9- 6/x and y+x = 8 are equal to each other
y + x = 8 is the same as y=8-x
Sub this into y = 9 - 6/x
8 - x = 9 - 6/x
Multiply everything by x:
8x - x^2 = 9x - 6
x^2 + x - 6 = 0
(x-2)(x+3) = 0
x = 2 (so y = 9 - 6/x so y = 9 - 6/2 =6)
x = -3 (so y = 9-6/x so y = 9-6/-3 = 11)
The coordinates of two points will be ; (2,6) and (-3,11).
It is given that the curve y = 9 - (6 / x) and line y + x = 8.
Find the coordinates of two points.
What is the general equation of line ?
General equation is given by ; y = mx + c.
At the intersection,
y = 9 - 6/x ----------- (Equation 1)
and y + x = 8 are equal to each other.
y + x = 8 can be written as y = 8-x.
Substitute this into Equation 1.
8 - x = 9 - ( 6/x )
Multiply both sides by x ;
8x - [tex]x^{2}[/tex] = 9x - 6
[tex]x^{2}[/tex] + x - 6 = 0
This can be written as ;
(x-2) (x+3) = 0
So we get values of x ;
i.e., x = 2 , -3
For , x = 2
y = 9 - 6/x
⇒ y = 9 - (6/2)
⇒ y = 6
For , x = - 3
⇒ y = 9 - (6/x)
⇒ y = 9 - (6/ -3)
⇒ y = 11
Thus , the coordinates of two points will be ; (2, 6) and (-3,11).
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Caroline is going to invest in an account paying an interest rate of 5.2% compounded continuously. How much would Caroline need to invest, to the nearest dollar, for the value of the account to reach $940 in 6 years?
Answer:
688
Step-by-step explanation:
For delta math
pls help asap!!!!!!!!
Answer:
It is possible, because the two shortest sides have to add up to be more than the longest side, and 8 + 12 = 20, which is more than the longest side of 17.
So yes, I agree with Bear.
how many solutions does this system have?
Answer:
B. One
Step-by-step explanation:
Multiply the first equation by 2 and then add both equations to get rid of [tex]x[/tex]:
[tex]\begin{cases}2x+8y=18,\\-2x+y=0\end{cases}[/tex]
Adding both equations:
[tex]8x+y=18,\\9y=18,\\y=2[/tex]
Substituting [tex]y=2[/tex]:
[tex]-2x+2=0,\\-2x-2,\\x=1[/tex]
Therefore the only solution to the system of equations is (1, 2) and the system has one solution.
What is the length of the line segment joining the points A(3, - 5) and B(-5,1)?
Given the quadriceps function ,y=ax2+bc+c what happens to the graph when "a" is a positive?
Answer:
When "a" is positive, the parabola opens upwards and the vertex is the minimum value.
Step-by-step explanation:
-3x2 + 5x- 7 = 0 is not in general form.
True
False
The answer is true because it is not a general form
A tepee is designed to have a diameter of 10 ft and a volume of 393 ft. At
what height, h, should the support poles cross to assemble the tepee
correctly? Use 3.14 for 1 and round your answer to the nearest foot.
Answer:
15 ft.
Step-by-step explanation:
The tepee is a cone and its volume
= 1/3 pi r^2 h where r = radius and h = height.
The radius r = 1/2 * 10 = 5 ft.
So we have the equation:
393 = 1/3*3.14* 5^2 * h
h = 393 / (1/3*3.14*25)
= 15.02 ft.
Write an equation for the line parallel to y = -7x + 15 that passes through the point P(9,-6).
Answer:
y = -7x + 57
Step-by-step explanation:
If the line is parallel, it will have the same slope. So, this line will also have a slope of -7.
Use y = mx + b, plug in the slope and given point, and solve for b:
y = mx + b
-6 = -7(9) + b
-6 = -63 + b
57 = b
Plug in the slope and y intercept into y = mx + b:
y = mx + b
y = -7x + 57
So, the equation is y = -7x + 57
r negative 7 divided by s negative 1
Unfortunately that's an impossible question because we have no idea what the variable is. Sorry buddy. You're on ur own there
The circumference of a circle is 19 pi m. What is the area, in square meters? Express your answer in terms of pi
Answer:
90.25πm^2
Step-by-step explanation:
circumference = 2 pie r
then , 19 pie meter = 2 pie r
so radius r = 19 /2 m
therefore ,
area of circle = pie r ^ 2
= 90.25 pie meter square
Answer:
circle circumference formula is 2 pi R
and area of circle pi R ²
19 pi is 2×9.5×pi
so the radius is 9.5
and area is pi 9.5² m² = 90,25 pi m²
Please help me
Thank you.
Answer:
(8, -1)
General Formulas and Concepts:
Algebra I
Reading a coordinate planeCoordinates (x, y)Solving systems of equations by graphingStep-by-step explanation:
Where the 2 lines intersect is the solution to the systems of equations. The systems of equations intersect at (8, -1).
how to simplify this equation ?
(3xy) (9y)
Answer:
27 xy^2
Step-by-step explanation:
(3xy) (9y)
Multiply
3*9 =27
xy*y = xy^2
Combine
27 xy^2