What are the x- and y-intercepts of the graph of 5x – 4y = 20?

Answer:

b

Step-by-step explanation:

2/3 * 2/3 = 4/9

2/3 * 3/2 = 1

2/3 * 3/4 = 1/2

2/3 * 4/4 = 2/3

[tex]6x^2 +17x -3\\\\=6x^2 +18x-x-3\\ \\=6x(x+3)-(x+3)\\ \\=(x+3)(6x-1)\\\\\text{The length and width of the rectangle are}~ (6x-1)~ \text{and}~ (x+3)[/tex]

Answer:

[tex]\textsf{length}=6x - 1[/tex]

[tex]\textsf{width}=x+3[/tex]

Step-by-step explanation:

Area of a rectangle = length × width

Given area:  [tex]A=6x^2+17x-3[/tex]

Therefore,  [tex]6x^2+17x-3=\sf length \cdot width[/tex]

To find the length and width, we need to factorize the given expression for area.

To factor a quadratic in the form [tex]ax^2+bx+c[/tex]

[tex]6x^2+17x-3 \implies a=6, b=17, c=-3[/tex]

[tex]ac=6 \cdot -3=-18[/tex]

[tex]d+e=17[/tex]

So we are looking for a pair of numbers that multiply to -18 and sum to 17.

Factors of 18: 1, 2, 3, 6, 9, 18

Therefore, the two numbers (d and e) that multiply to -18 and sum to 17 are:

18 and -1

Rewrite [tex]17x[/tex] as [tex]+18x-x[/tex]:

[tex]\implies 6x^2+18x-x-3[/tex]

Factor first two terms and last two terms separately:

[tex]\implies 6x(x+3)-1(x+3)[/tex]

Factor out common term [tex](x+3)[/tex]:

[tex]\implies (6x-1)(x+3)[/tex]

As length > width,

[tex]\textsf{length}=6x - 1[/tex]

[tex]\textsf{width}=x+3[/tex]

Answer:

The origin is at (0,0) its where the x and y coordinate intersect.

Step-by-step explanation:

what was the question here?

Answer:

3x - 5 fits the equation perfectly

Step-by-step explanation:

if we put the following value in X we get,

x processing y

3. 3*3 - 5. 4

5. 3*5 - 5. 10

7. 3*7 -5. 16

9. 3*9 - 5. 22

11. 3*11 - 5. 28

Answer:

It's a function because when you simplify it becomes y=-x-3. the only reason it wouldn't be a function would be if the equation were to be x = a random number that is not a variable. The equation would not pass the vertical line test which is the requirement to see if an equation is a function.

Simply put, it's a function.

Answer:

1 liter

Step-by-step explanation:

100 milliliters = 0.10566882 quarts

500 milliliters = 0.52834411 quarts

1 liter = 1.05668821 quarts

10 liters = 10.5668821 quarts
______________________________

From this, we can see that 1 liter is closest to a quart.

hope this helps!

Answer:

Option C, [tex]36x^2 + 60x + 25[/tex]

Step-by-step explanation:

Step 1:  Determine the perfect square

According to online, "When an expression has the general form a²+2ab+b², then we can factor it as (a+b)². For example, x²+10x+25 can be factored as (x+5)². This method is based on the pattern (a+b)²=a²+2ab+b², which can be verified by expanding the parentheses in (a+b)(a+b)"

The only one that seems to work is Option C so lets factor it.

[tex]36x^2 + 60x + 25[/tex]

[tex](6x + 5)(6x + 5)[/tex]

[tex](6x + 5)^2[/tex]

Yup!  We can see that Option C would give us a perfect square

Answer:  Option C, [tex]36x^2 + 60x + 25[/tex]

Step-by-step explanation:

If we have f(x) and it's inverse, and we compose them

we will get

[tex]f {}^{ - 1} (f(x) = x[/tex]

So here we compose

[tex]( \frac{1}{ \frac{1 + x}{x} - 1} )[/tex]

[tex]( \frac{1}{ \frac{1}{x} + 1 - 1} [/tex]

[tex] \frac{1}{ \frac{1}{x} } [/tex]

[tex]x [/tex]

So the composition is x, so they are inverses.

Answer:

P(A|B) = 0.5

Step-by-step explanation:

A: set of prime numbers ={1,2,3}

B: set of divisors of 3 ={1,3}

P(A)=P(1)+P(2)+P(3)= 0.1+0.1+0.3 =0.5

P(B)=P(1)+P(3)=0.1+0.3=0.4

P(A|B) means: probability of A knowing that B

In other words we have to find the probability that a prime outcome occurs knowing that it is a divisor of 3

Its formula is given by:

P(A|B) = P(AintersectionB) /P(B)

A intersection B: outcome is prime and a divisor of 3 at the same time. (common elements between sets A and B)

A int B= {1,3}

P(AintB)= P(A)xP(B) = 0.5x0.4=0.2

Now back to the formula:

P(A|B) =P(AintB) / P(B)

=0.2/0.4=0.5

HOPE THIS HELPS :)

Step-by-step explanation:

Median: 35000

Mean: 383333.33333333 (round it)

Mode: 10000, 20000, 30000, 40000, 200000, 2000000 (all the numbers)

Answer:

  a. exception: C; obtuse angle with a different measure

  b. corresponding angles are congruent; corresponding sides are proportional

  c. corresponding angles are congruent among the similar triangles; they are not congruent when the triangles are not similar

  d. corresponding sides are porportional; they are not proportional when the triangles are not similar

Step-by-step explanation:

As you know, similar triangles have congruent corresponding angles, and proportional corresponding sides. This gives them the same shape, but they may be of differenent sizes.

__

Figure C appears to have a larger smallest angle and a smaller largest angle than the rest of the figures. Its long side relative to its second-longest side appears to be shorter, consistent with a smaller largest angle.

__

The similar triangles have congruent corresponding angles and proportional corresponding sides.

__

See (b) regarding similar triangles. Non-similar triangles have different angles.

__

See (b) regarding similar triangles. Non-similar triangles have different side proportions.

Answer:

Skewed right

Step-by-step explanation:

There is a 'tail' towards the right.

The polynomial of least possible degree having the graph as given is; f(x) = x³-8x²+x +42.

It follows from the graph that the roots of the polynomial are; -2, 3 and 7.

On this note, the factors of such polynomial are;

Hence; (x+2)(x-3)(x-7) = f(x)

Read more on polynomials;

https://brainly.com/question/2833285

Answer:

1620

Step-by-step explanation:

(-18)×(-10)×9= 1620

Answer:

B. 100 units

Step-by-step explanation:

What I did was I couunted the lines at the bottum and since it was 10 then I counted up  and that was 10 so you would do 10x10 get 100 units.

best answer of this equation is 10.772

Answer: 10.772

Step-by-step explanation:

Isolate the variable by dividing each side by factors that don't contain the variable.

exact form:

x= 10 4/3

--------- (its a fraction)

2

decimal form: 10.77217345....

after that round to the nearest thousandth.

[tex]x=\frac{1+4f-\sqrt{16f^{2}+8f+25 } }{2}[/tex]

since there are 36 inches in 1 yard, 12 yards will have 12(36) = 432 inches.

Answer:

3 and 4

Step-by-step explanation:

30/8=3.75

3.75 lies between 3 and 4

Hey there!

30/8

= 30 ÷ 2 / 8 ÷ 2

= 15 / 4

≈ 3 3/4

≈ 3.75

It falls in between three (3) and four (4). But, fun fact it rounds to up to four (4)

Good luck on your assignment & enjoy your day!

~Amphitrite1040:)

Answer:

832.5²

Step-by-step explanation:

Base x height ÷ 2 is the formula to find a triangles area.

45 x 37= 1665 then 1665 ÷ 2 = 832.5 dont forget to add the ²

Answer:

832.5²

Step-by-step explanation:

Answer:

See below.

Step-by-step explanation:

A(1, 4)

B(3, 0)

C(-3, -2)

We find the coordinates of he midpoints using the midpioint formula.

D([1 + 3]/2, [4 + 0]/2) = D(2, 2)

E([1 + (-3)]/2, [4 + (-2)]/2) = E(-1, 1)

We find the slopes using the slope formula.

slope of BC:

m_BC = (-2 - 0)/(-3 - 3) = -2/(-6) = 1/3

slope of DE:

m_DE = (1 - 2)/(-1 - 2) = -1/(-3) = 1/3

Since the slopes of BC and DE are equal, the lines are parallel.

To calculate hydronium concentration from pH, type on you calculator

10 to the power of negative pH value

10^-5.5 = 3•10^6 mol/L

Since there are 3 hydrogens in every hydronium molecule,

There are 9 • 10^6 hydrogens in that liter of acid.

Answer

91.67inch^3

Step-by-step explanation:

The volume of a cone can be calculated using below formula

V= 1/3 π.r^2h

Where h= height of the cone

r= radius of the cone

V= volume of the cone

Given :

height= 11 inches

radius= 5 inches

π= 3.14

Then substitute into the formula we have

V= 1/3 × 3.14× 5^2 ×11

V= 91.67inch^3

Therefore volume of the cone is 91.67inch^3

Answer:

-a^3 -3a^2

Step-by-step explanation:

(fg) (x) = x^2 (x-3)

= x^3 - 3x^2

(fg) (-a) = (-a)^3 -3 (-a)^2

= -a^3 -3a^2

[tex]y < \frac{1}{2} x - 2 \\ [/tex]

Answer:

Discriminant

[tex]b^2-4ac\quad\textsf{when}\:ax^2+bx+c=0[/tex]

[tex]\textsf{when }\:b^2-4ac > 0 \implies \textsf{two real roots}[/tex]

[tex]\textsf{when }\:b^2-4ac=0 \implies \textsf{one real root}[/tex]

[tex]\textsf{when }\:b^2-4ac < 0 \implies \textsf{no real roots}[/tex]

Given equation: [tex]kx^2+2x+(1-k)=0[/tex]

[tex]\implies a=k,\:b=2,\:c=(1-k)[/tex]

[tex]\begin{aligned}\implies b^2-4ac & =(2)^2-4(k)(1-k)\\ & =4-4k(1-k)\\ & =4-4k+4k^2\\ & = 4k^2-4k+4 \end{aligned}[/tex]

Complete the square:

[tex]\begin{aligned}\implies 4k^2-4k+4 & =4(k^2-k+1)\\ & = 4\left[k^2-k+\left(\dfrac{-1}{2}\right)^2+1-\left(\dfrac{-1}{2}\right)^2\right]\\ & = 4\left[\left(k-\dfrac12\right)^2+\dfrac34\right]\\ & = 4\left(k-\dfrac12\right)^2+3\end{aligned}[/tex]

[tex]\textsf{As }\left(k-\dfrac12 \right)^2 \geq 0 \implies 4\left(k-\dfrac12 \right)^2+3\geq 3[/tex]

Therefore, the roots are always real.

Step-by-step explanation:

1.581 × 10² like this ? : )