find the slope and y-intercept of the line y=7x-9

Answer:

See below ↓↓

Step-by-step explanation:

Important facts given [needed to solve]

Solving :

Interest paid

Answer:

Eleanor has made an error in Step 1

She clearly intended to multiply both sides by 2, but forgot to multiply the [tex]-9x[/tex] part of the RHS.

Step 1 should be:   [tex]x+18=8(2x-6)-18x[/tex]

Correct solution

Given:   [tex]\dfrac12(x+18)=4(2x-6)-9x[/tex]

Step 1:  [tex]x+18=8(2x-6)-18x[/tex]

Step 2:  [tex]x+18=16x-48-18x[/tex]

Step 3:  [tex]x+18=-48-2x[/tex]

Step 4:  [tex]66=-3x[/tex]

Step 5:  [tex]x=-22[/tex]

S casts a "shadow" on the x-y plane given by the set

[tex]S' = \left\{(x,y) ~:~ -1 \le x \le 1 \text{ and } x^2 \le y \le 1\right\}[/tex]

Each cross section is a square whose side length is determined by the vertical distance between y = 1 and y = x², which is |1 - x²|. But since -1 ≤ x ≤ 1, this distance simplifies to 1 - x².

The volume of an infinitesimally thin section is then (1 - x²)² ∆x (where ∆x represents its thickness), and so the volume of S is

[tex]\displaystyle \int_{-1}^1 (1-x^2)^2 \, dx = \int_{-1}^1 (1 - 2x^2 + x^4) \, dx[/tex]

The integrand is even, so this integral is equal to twice the integral over [0, 1] :

[tex]\displaystyle \int_{-1}^1 (1-x^2)^2 \, dx = 2 \int_0^1 (1 - 2x^2 + x^4) \, dx = 2 \left(1 - \frac23 + \frac15\right) = \boxed{\frac{16}{15}}[/tex]

Answer:

Pls help me with my questions

Step-by-step explanation:

Answer:

Vertex is (-1/3, -1/3) and the axis of symmetry is x = -1/3

Hope this helps :)

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Answer:

Multiply the number of cups of cream by two and a half.

[tex]\sqrt{ { (x2 - x1)}^{2} + {(y2 - y1)}^{2} } \\ \\ = \sqrt{( {5 - ( - 1)}^{2} + {( - 9 - ( - 1)}^{2} )} \\ \\ = \sqrt{ {(5 + 1)}^{2} + {( - 9 + 1)}^{2} } \\ \\ = \sqrt{ {(6)}^{2} + {( - 8)}^{2} } \\ \\ = \sqrt{36 + 64} \\ \\ = \sqrt{100} \\ \\ = 10 \: units[/tex]

Step-by-step explanation:

[tex] \sin(θ) = \frac{2}{5} [/tex]

We know that

[tex] { \sin ^{2} (θ) } + \cos^{2} (θ) = 1[/tex]

Using that we get

[tex] \cos^{2} (θ) = 1 - \sin^{2}( θ) = 1 - { \frac{2}{5} }^{2} [/tex]

[tex] = 1 - \frac{4}{25} [/tex]

[tex] \frac{21}{25} [/tex]

hence

[tex] \cos(θ ) = \frac{ \sqrt{21} }{5} [/tex]

Step-by-step explanation:

please mark me as brainlest

Answer:

the answer is 60 yards for the triangle

Answer

Since 3 is greater than 0 we know that 7.835 is greater than 7.8. We follow the same process to find that 7.35 is less than 7.358. Then we can put the number

There you go I hope that helps and have a great day

Step-by-step explanation:

1) x+13+90 = 180

or, x = 180 - 103

    x = 77

2) x+74+90 = 180

or, x = 180 - 164

    x = 16

3)  x+62+45 = 180

or, x = 180 - 107

    x = 73

Answer:

-c is the blank and a+b is variables of real numbers.

Step-by-step explanation:

A real number is a value of a continuous quantity that can represent a distance.

However equality is a relationship between two quantities or, more generally two mathematical expressions, asserting that the quantities have the same value, or that the expressions represent the same mathematical object.

The tan θ and cos θ values of 17π/12 are illustrations of trigonometry ratios

The values of tan θ and cos θ are 2 + √3 and (√2 - √6)/4, respectively

We have:

θ = 17π/12

Express as sum

θ = 9π/12 + 8π/12

Simplify

θ = 3π/4 + 2π/3

The above becomes

tan(17π/12) = tan(3π/4 + 2π/3)

Using the sum formula, we have:

tan(A + B) = [tan(A) + tan(B)]/[1 - tan(A)tan(B)]

Substitute known values

tan(3π/4 + 2π/3) = [tan(3π/4) + tan(2π/3)]/[1 - tan(3π/4)tan(2π/3)]

Evaluate the expression

tan(3π/4 + 2π/3) = [-1 - √3]/[1 - (-1)(-√3)]

Evaluate the product

tan(3π/4 + 2π/3) = [-1 - √3]/[1 - √3]

Rationalize

[tex]tan(\frac{3\pi}4 + \frac{2\pi}3) = \frac{-1 - \sqrt3}{1 - \sqrt3} * \frac{1 + \sqrt3}{1 + \sqrt3}[/tex]

Evaluate the product

[tex]tan(\frac{3\pi}4 + \frac{2\pi}3) = \frac{-(1 + \sqrt3)^2}{1 - 3}[/tex]

This gives

[tex]tan(\frac{3\pi}4 + \frac{2\pi}3) = \frac{-(1 + 3 + 2\sqrt 3)}{-2}[/tex]

[tex]tan(\frac{3\pi}4 + \frac{2\pi}3) = \frac{-(4 + 2\sqrt 3)}{-2}[/tex]

Divide

[tex]tan(\frac{3\pi}4 + \frac{2\pi}3) = 2 + \sqrt 3[/tex]

So, we have:

tan(17π/12) = 2 + √3

We have:

θ = 17π/12

Express as difference

θ = 9π/4 - 5π/6

The above becomes

cos(17π/12) = cos(9π/4 - 5π/6)

Using the difference formula, we have:

cos(A - B) = cos(A)cos(B) + sin(A)sin(B)

So, we have

cos(17π/12) = cos(9π/4)cos(5π/6) + sin(9π/4)sin(5π/6)

Evaluate

[tex]cos(\frac{17\pi}{12}) = \frac{\sqrt 2}{2} * - \frac{\sqrt 3}{2} + \frac{\sqrt 2}{2} * \frac 12[/tex]

Evaluate

[tex]cos(\frac{17\pi}{12}) = \frac{\sqrt 2}{2} (- \frac{\sqrt 3}{2} + \frac 12)[/tex]

Evaluate the difference

[tex]cos(\frac{17\pi}{12}) = \frac{\sqrt 2}{2} (\frac{1 - \sqrt 3}{2})[/tex]

Expand

cos(17π/12) = (√2 - √6)/4

Hence, the values of tan θ and cos θ are 2 + √3 and (√2 - √6)/4, respectively

Read more about trigonometry ratios at:

https://brainly.com/question/11967894

Answer:

P(M &C) = 0.24

Step-by-step explanation:

Chemistry book will be denoted by C

Mathematics book will be denoted by M

5C2 = 10

There are 10 possible ways in which she can choose two books from the 5 books.

The probability of choosing a chemistry book:

P(C) = 2/5

The probability of choosing a mathematics book:

P(M) = 3/5

Probability of choosing a chemistry book and a mathematics book:

P(M &C) = (2/5) × (3/5)

P(M &C) = 0.24 or 24%

The probability that she pulls out a math book and a chemistry book will be 0.24.

The term probability refers to the likelihood of an event occurring

Given that;

Julia has 2 chemistry books and 3 math books.

Now,

Since, Julia has 2 chemistry books and 3 math books.

Hence, Total number of books = 2 + 3 = 5

So, The probability to choosing a chemistry book = 2/5

And, The probability to choosing a math book = 3/5

Thus, The probability that she pulls out a math book and a chemistry book is,

⇒ 2/5 × 3/5

⇒ 6/25

⇒ 0.24

Learn more about the probability visit:

https://brainly.com/question/13604758

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Answer:

8x+10y=-8

Step-by-step explanation:

5x+3x=8x

4y+6y=10y

-14+6=-8

Answer:

e

Step-by-step explanation:

Answer:

a, e

Step-by-step explanation:

a would round to 110,000 because 113,450 rounded to the ten thousand round down to 110,000

95,678 would round up to 100,000 not 110,000

104,298 would round down to 100,000 not 110,000

94,560 would round down to 90,000

106,789 would round up to 110,000 because 6 rounds up because 5 and up is rounded up

[tex]\qquad\qquad\huge\underline{{\sf Answer}}♨[/tex]

According to angle sum property of a quadrilateral, Sum of all angles of a quadrilateral measures 360°

So, let's solve for x ~

[tex]\qquad \tt \dashrightarrow \:68 + 126 + 106 + x = 360[/tex]

[tex]\qquad \tt \dashrightarrow \:300+ x = 360[/tex]

[tex]\qquad \tt \dashrightarrow \:x = 360 - 300[/tex]

[tex]\qquad \tt \dashrightarrow \:x = 60 \degree[/tex]

Answer:

45 fireflies

Step-by-step explanation:

Because,

Sheri caught 70 and Robert caught 35.

150-35-70= 35

35+10 is equal to 45.

Following the rules given is the right answer

Answer:

2854.5 in^3

Step-by-step explanation:

4/3 π(8.8)^3

4/3π(681.472)

908.63π = 2854.5 in^3

Answer: (-4, -6)

Step-by-step explanation:

Solving by graphing

[] See attached

    () The only point in the required range is point (-4, -6)

Solving by plugging-in

        I will figure out what the correct option is by plug them into the first equation. Since only one of these options is true, I do not need to do the second equation.

[✗] Let's check point (4, 10)

    () 10 < (1/4)4 - 4

       10 < 1 - 4

       10 < -3 is false, so this answer is incorrect

[✗] Let's check point (-4, 5)

    () 5 < (1/4)-4 - 4

       5 < -1 -4

       5 < -5 is false, so this answer is incorrect

[✗] Let's check point (-4, -4)

    () -4 < (1/4)-4 - 4

       -4 < -1 -4

       -4 < -5 is false, so this answer is incorrect

[✓] Let's check point (-4, -6)

    () -6 < (1/4)-4 - 4

       -6 < -1 - 4

       -6 < -5 is true, so this answer is correct      

Answer:

Step-by-step explanation:

The angle formed by two secants is half the difference of intercepted arcs.

Correct choice is C

Let that be y

Option C

Pythagorean Theorem:

[tex]a^2 + b^2 = c^2[/tex]

Since 10 and 24 are the legs, "x" has to be the hypoteneuse.  "a" and "b" are the legs (10 and 24).

Now, replace the values in.

[tex]10^2+24^2 = x^2[/tex]

[tex]x^2 = 100+576\\x^2 = 676\\x = 26[/tex]

Hope this helped! :)

Answer:

D. marginal credit is right one

Step-by-step explanation:

for me it is best as a first step to combine this all to one big fraction, and then simplify the whole expression.

you do know that when multiplying the same variable with exponent we simply add the exponents. and she we divide the same variable with exponents, we subtract them from each other (as the overlapping exponent parts cancel each other out).

(3ac³f³)/(8a²bcf⁴) × (12ab²c)/(18ab³c²f) =

= (3×12a²b²c⁴f³)/(8×18a³b⁴c³f⁵) =

= (3×12c)/(8×18ab²f²) = 12c / (8×6ab²f²) =

= 2c / (8ab²f²) = c / (4ab²f²)

Answer:

The correct answer is Choice C.

Step-by-step explanation:

I drew a diagram of all the triangles to compare the statements given to each other

I marked the triangle sides with lines to show congruency in length.

One line for AB = DF

Two lines for AB = GI

Three lines for BC = HI

Four lines for DE = HI

The angles are all marked for the last sentence we are given.

The first and third triangles are the only ones similar. This is because of SAS congruence as given in the Diagram. AB = GI, angle B = angle I, BC = IH

The second triangle is different from the rest, and even if we tried to rotate it ad compare it, it would still be wrong.

Answer:

14[tex]w^{8}[/tex] + 63[tex]w^{4}[/tex]

Step-by-step explanation:

7w³ (2[tex]w^{5}[/tex] + 9w) ← multiply each term in the parenthesis by 7w³

= 14[tex]w^{8}[/tex] + 63[tex]w^{4}[/tex]

[ using rule of exponents

[tex]a^{m}[/tex] × [tex]a^{n}[/tex] = [tex]a^{(m+n)}[/tex] ]

Answer:

7w⁴ (2w⁴ + 9)

Step-by-step explanation:

Given

Let's simplify.

Answer:

yes

Step-by-step explanation:

The equation of the line is written in the slope-intercept form, which is: y = mx + b, where m represents the slope and b represents the y-intercept.