Which of the following is the equation of a line in slope-intercept form for a
line with slope = and yintercept at (0, -1)?
O A. y - x-
1
B. y = 4x-1
O c. y= |x-1
O D. y=x+1

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.

Answer:

(8, -1)

General Formulas and Concepts:

Algebra I

Step-by-step explanation:

Where the 2 lines intersect is the solution to the systems of equations. The systems of equations intersect at (8, -1).

Answer:

The population of this problem would be the 3 million viewers and the sample would be the 0.2 million that voted.

hope this helps!

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.

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.

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]

[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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The answer is true because it is not a general form

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.

Answer:

688

Step-by-step explanation:

For delta math

Answer:

actually I would have solved it but don't know the angle you're talking about

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.

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

Answer:

27 xy^2

Step-by-step explanation:

(3xy) (9y)

Multiply

3*9 =27

xy*y = xy^2

Combine

27 xy^2

Answer:

5.1 ; 8.29 ; 2.879

Step-by-step explanation:

Given :

Number of Computer Sold X

Probability P(x)

0

0.1

2

0.2

5

0.3

7

0.2

9

0.2

Mean = E(X) = Σ(x*p(x)

E(X) = (0*0.1) + (2*0.2) + (5*0.3) + (7*0.2) + (9*0.2)

E(X) = 5.1

Variance, Var(X) = Σx²p(x) − E(X)²

Var(X) = [(0^2*0.1) + (2^2*0.2) + (5^2*0.3) + (7^2*0.2) + (9^2*0.2)] - 5.1^2

Var(X) = 34.3 - 26.01 = 8.29

Standard deviation ; Std(X) = √Var(X) = √8.29 = 2.879

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

Answer:

3.5 hours

Step-by-step explanation:

1300 - 0930 = 330 = 3.5 hours

Answer:

When "a" is positive, the parabola opens upwards and the vertex is the minimum value.

Step-by-step explanation:

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

Answer:

Increasing the number of people allows more variety and diversity, which makes the sample more accurate.

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

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.

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.

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]

Answer: Number “2”

Step-by-step explanation: I took the ck-12 Applications with Inequalities

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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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!! :)

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)