What is the point-slope form of the
equation for the line with a slope of
-2 that passes through (1, 4)?
A y + 1 = -2(x + 4)
B y-1=-2(x-4)
C y + 4 = -2(x + 1)
D y - 4 = -2(x - 1)​

Suppose [tex]x=3.1\overline6[/tex]. Then [tex]10x=31.\overline6[/tex], and [tex]100x=316.\overline6[/tex].

Now,

[tex]100x-10x=316.\overline6-31.\overline6=316-31[/tex]

[tex]\implies90x=285[/tex]

[tex]\implies x=\dfrac{285}{90}=\boxed{\dfrac{19}6}[/tex]

Answer:

Step-by-step explanation:

Givens

Height = h = 4cm

b = ?

Area = 40 cm^2

Formula

Area = 1/2 * h * b

Solution

40 cm^2 = 1/2 * 4 * b      Combine the right

40 cm^2 = 2 * b              Divide by 2

40 cm^2 /2 = 2b/2         Do the division

20 cm = b

Answer D

Answer:

Step-by-step explanation:

[tex]\text{Domain:}\\\\x-4\neq0\ \wedge\ x-2\neq0\ \wedge\ x^2-6x+8\neq0\\\\x\neq4\ \wedge\ x\neq2\ \wedge\ x^2-4x-2x+8\neq0\\\\x\neq4\ \wedge\ x\neq2\ \wedge\ x(x-4)-2(x-4)\neq0\\\\x\neq4\ \wedge\ x\neq2\ \wedge\ (x-4)(x-2)\neq0\\\\x\neq4\ \wedge\ x\neq2\ \wedge\ x-4\neq0\ \wedge\ x-2\neq0\\\\\boxed{D:x\neq4\ \wedge\ x\neq2}[/tex]

[tex]\dfrac{1}{x-4}+\dfrac{x}{x-2}=\dfrac{2}{x^2-6x+8}\\\\\dfrac{1(x-2)}{(x-4)(x-2)}+\dfrac{x(x-4)}{(x-4)(x-2)}=\dfrac{2}{(x-4)(x-2)}\\\\\dfrac{x-2+x(x-4)}{(x-4)(x-2)}=\dfrac{2}{(x-4)(x-2)}\iff x-2+x(x-4)=2\\\\x-2+(x)(x)+(x)(-4)=2\\\\x-2+x^2-4x=2\qquad\text{subtract 2 from both sides}\\\\x^2-3x-4=0\\\\x^2-4x+x-4=0\\\\x(x-4)+1(x-4)=0\\\\(x-4)(x+1)=0\iff x-4=0\ \wedge\ x+1=0\\\\x-4=0\qquad\text{add 4 to both sides}\\x=4\notin D\\\\x+1=0\qquad\text{subtract 1 from both sides}\\x=-1\in D[/tex]

Answer:

∠XBA=43°

Step-by-step explanation:

we know that

If ray BA bisect angle ∠XBY

then

∠XBA=∠XBY/2

we have

∠XBY=86°

substitute

∠XBA=86°/2=43°

Answer:

C and E

Step-by-step explanation:

Recall that according to the complex conjugate theorem, if P(x) is a polynomial function with real coefficients, and a+bi is an imaginary root of P(x), then its conjugate (i.e a-bi) must also be a root.

Here we see that 2 of the given roots are imaginary : i and 2+i

by the theorem given above, the conjugates of these must also be roots

i.e -i and 2-i

Answer:

(x - 10)(x + 10)

Step-by-step explanation:

x² - 100 ← is a difference of squares and factors in general as

a² - b² = (a - b)(a + b)

Hence

x² - 100

= x² - 10² = (x - 10)(x + 10)

Answer:

The reciprocal of [tex] \frac { 7 } { 9 } [/tex] is [tex] \frac { 9 } { 7 } [/tex].

Step-by-step explanation:

We are asked about the reciprocal of the given fraction [tex] \frac { 7 } { 9 } [/tex].

We know that in mathematics, a reciprocal is the multiplicative inverse of a number.

For example, in case of a fraction, its reciprocal will be its inverse which means that we swap the places of numerator and denominator.

So the reciprocal of [tex] \frac { 7 } { 9 } [/tex] will [tex] \frac { 9 } {7 } [/tex].

Fractions are always set up with numerator on top and denominator on bottom like so:

[tex]\frac{numerator}{denominator}[/tex]

To take the reciprocal of a number you must switch the places of numerator and denominator.

Reciprocal of [tex]\frac{7}{9}[/tex] is [tex]\frac{9}{7}[/tex]

Hope this helped!

~Just a girl in love with Shawn Mendes

Answer:

Choice B. sin(B)=cos(90-B)

Step-by-step explanation:

That cofunction identity is the one you looking for...choice B.

If you aren't convinced or don't know that identity, then maybe this will help:

90-B is actually the same thing as saying A for this right triangle since A+B=90.

So choice B basically says sin(B)=cos(A)

Well let's find both sin(B) and cos(A)

sin(B)=b/c

cos(A)=b/c

Those are the same ratios!

So they are equal!

Answer:

option B

Step-by-step explanation:

from the given options

a)      sin (B)  = sin (A)

b)      sin (B ) = cos (90° - B)

        cos (90° - B ) = Sin B

c)       cos  (B ) =  sin(180° - B)

         sin(180° - B) = sin (B)

d)        cos (B)  = cos(A)

so, we can clearly see from the above solution that option B is correct.

As 90° - B is in first quadrant and in first quadrant sign of cos dose not change  and 90 is multiple of odd so 'cos' changes to 'sin'

Answer:

x = - 1, x = [tex]\frac{1}{8}[/tex]

Step-by-step explanation:

Given

8x² + 7x - 1 = 0 ← in standard form

Consider the factors of the product of the x² term and the constant term which sum to give the coefficient of the x- term

product = 8 × - 1 = - 8 and sum = + 7

The factors are + 8 and - 1

Use these factors to split the x- term

8x² + 8x - x - 1 = 0 ( factor the first/second and third/fourth terms )

8x(x + 1) - 1(x + 1) = 0 ← factor out (x + 1) from each term

(x + 1)(8x - 1) = 0

Equate each factor to zero and solve for x

x + 1 = 0 ⇒ x = - 1

8x - 1 = 0 ⇒ 8x = 1 ⇒ x = [tex]\frac{1}{8}[/tex]

Answer:

x

=

1

8

,

−

1

x=1/8,-1 I solved using  the quadratic formula

Step-by-step explanation:

answer: 4x² + 9x - 28.

multiply the factors together:

4x times x = 4x²

4x times 4 = 16x

-7 times x = -7x

-7 times 4 = 28

therefore, (4x-7) times (x+4) = 4x² + 16x -7x = 28

next, you must condense and simplify your answer:

16x -7x equals 9x

your final answer should be 4x² + 9x - 28.

Answer:

The answer is B aka 4x² + 9x - 28.

Step-by-step explanation:

For this case we must find an expression equivalent to:

[tex]\sqrt [5] {13 ^ 3}[/tex]

By definition of properties of powers and roots we have:

[tex]\sqrt [n] {a ^ m} = a ^ {\frac {m} {n}}[/tex]

Then, rewriting the expression:

[tex]13 ^ {\frac {3} {5}}[/tex]

Answer:

Option D

[tex]13 ^ {\frac {3} {5}}[/tex]

Your answer would be [tex]\frac{1}{w^{35} }[/tex]

This is because (w^5)^-7 expands to give w^-35 because you multiply the exponents. When you have a negative exponent, this can also be written as a reciprocal, i.e. x^-2 = 1/x². This means that we can write w^-35 as 1/(w^35), which doesn't include any negative exponents.

I hope this helps! Let me know if you have any questions :)

The answer without using negative exponents  [tex](w^{5})^{-7}[/tex] is  [tex]\frac{1}{w^{35} }[/tex] .

The following properties of exponents are -

Given expression is [tex](w^{5})^{-7}[/tex] .

Using the properties of exponents, we have -

= [tex]w^{-35}[/tex]

= [tex]\frac{1}{w^{35} }[/tex]  which does not have any negative exponents.

Thus, the answer without using negative exponents  [tex](w^{5})^{-7}[/tex] is  [tex]\frac{1}{w^{35} }[/tex] .

To learn more about properties of exponents, refer -

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Answer:

60.7143% decrease  or 60%

Step-by-step explanation:

The percent of change from 56 to 22 is 60%.

The percent of change from 56 to 22 is 60%.

Problem-solving is the act of defining a problem; figuring out the purpose of the trouble; identifying, prioritizing, and selecting alternatives for an answer; and imposing an answer.

Problem-solving starts with identifying the issue. As an example, a trainer may need to parent out a way to improve a scholar's overall performance on a writing talent test. To do that, the instructor will overview the writing exams looking for regions for improvement.

Learn more about Problem-solving here: brainly.com/question/13818690

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Answer:

A. (55 x 5) - (40 x 5)

Step-by-step explanation:

You are solving how much miles (further along) would the second car be after 5 hours.

The first car averages 40 miles per hour. 5 hours later, it will have averaged about 200 miles in 5 hours (40 x 5 = 200).

The second car averages 55 miles per hour. 5 hours later, it will have averaged about 275 miles in 5 hours (55 x 5 = 275)

Subtract: 275 - 200 = 75

The second car would have averaged 75 more miles than the first car.

~

Answer:

A. (55 x 5) - (40 x 5)

Step-by-step explanation:

The "speedier" car goes 55 mph * 5 hrs = 55*5 miles

The "slower" car goes 40mph * 5   hrs = 40*5 miles

The distance between them is

55  *5 - 40*5

Answer:

B

Step-by-step explanation:

5x + 3y = 15

5x = -3y +15

x = -3/5y +3

Answer:

The correct option is B) x = negative three fifths y + 3

Step-by-step explanation:

Consider the provided equation.

5x + 3y = 15

We need to solve the above equation for x.

Subtract both the side by 3y.

[tex]5x + 3y-3y = 15-3y[/tex]

[tex]5x= 15-3y[/tex]

To find the value of y, isolate the variable y:

Divide both the sides by 5.

[tex]\frac{5x}{5}= \frac{15}{5}-\frac{3y}{5}[/tex]

[tex]x= 3-\frac{3y}{5}[/tex]

[tex]x= -\frac{3y}{5}+3[/tex]

Hence, the correct option is B) x = negative three fifths y + 3

Answer:

Matt is correct

Step-by-step explanation:

we know that

If two lines are parallel, then their slopes are the same

In this problem we can have two cases

case 1) The two equations are equal, in this case the system has infinite solutions

case 2) The two equations have the same slope but different y-intercept, in that case the system has no solution.

therefore

Matt is correct

Matt is correct. Whether lines with the same slope are parallel or the same line depends on the y-intercepts. If y-intercepts are the same, lines are identical and have infinitely many solutions. If y-intercepts differ, lines are parallel and there's no solution.

Matt is correct in this scenario. While it is true that lines with the same slope are either parallel or the same line, determining whether they are the same line or parallel lines requires examining the y-intercepts. If the y-intercepts are the same, then the lines are identical, and there are infinitely many solutions to the system of equations. However, if the y-intercepts are different, the lines are parallel and there is no solution to the system. So, slope, parallel lines, and y-intercept are crucial concepts in solving this problem.

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Answer:

9 < x

Step-by-step explanation:

5x - 47< 3(12x - 108) – 2​

Distribute

5x - 47< 36x - 324 – 2​

Combine like terms

5x - 47< 36x-326

Subtract 5x from each side

5x-5x - 47< 36x-5x-326

- 47< 31x-326

Add 326 to each side

326 - 47< 31x-326+326

279 < 31x

Divide by 31 on each side

279/31 < 31x/31

9 < x

Answer:

The turning point is (-2,10)

Step-by-step explanation:

we have

[tex]y=6-4x-x^{2}[/tex]

This is a quadratic equation (vertical parabola) open downward

we know that

The turning point of a quadratic equation is the vertex

so

Convert the quadratic equation into vertex form

[tex]y-6=-4x-x^{2}[/tex]

[tex]y-6=-(x^{2}+4x)[/tex]

[tex]y-6-4=-(x^{2}+4x+4)[/tex]

[tex]y-10=-(x^{2}+4x+4)[/tex]

[tex]y-10=-(x+2)^{2}[/tex]

[tex]y=-(x+2)^{2}+10[/tex] ----> equation in vertex form

The vertex is the point (-2,10)

therefore

The turning point is (-2,10)

The turning point of the parabola described by the equation y=6-4x-x^2 is at the point (-2, 10), which is a maximum since the parabola opens downwards.

To find the turning point of the curve given by the equation y=6-4x-x^2, we first need to rewrite the equation in the form of the vertex of a parabola, which is given by y=a(x-h)^2+k, where (h,k) is the coordinate of the turning point or vertex. Noting that there is a mistake in the information provided since the second derivative would actually be y" = -2, and not 6x - 12, indicating that we have a concave down parabola with a maximum point, not a point of inflection. We can complete the square to rewrite the function in vertex form.

Start by completing the square: y = -x^2 - 4x + 6 can be rewritten as y = -(x^2 + 4x) + 6. Adding and subtracting 4 inside the parenthesis (which is the square of half the coefficient of x), we get y = -(x^2 + 4x + 4 - 4) + 6, which simplifies to y = -(x + 2)^2 + 10. Thus, the vertex or turning point is at (-2, 10).

This shows the turning point of the parabola is at the point (-2, 10), which is a maximum since the parabola opens downwards as reflected by the negative coefficient of the x^2 term. This can be visualized on the graph of the function as the highest point on the curve. Remember that a quadratic equation represents a parabola in a Cartesian coordinate system.

Answer:

True

Step-by-step explanation:

The domain of a function is the complete set of possible values of the independent variable 'x'. Therefore, the graph of funtion is defined as the set of all points (x, f(x)) where 'x' is the domain of f(x).

Hence, the statement is TRUE

Answer:

True (Please give brainliest)

Step-by-step explanation:

Answer:

3n=5d and 3n = 5d and 3n + 6 = 2d + 4

Step-by-step explanation:

Answer:  The correct option is

(A) [tex]5n=3d~~~\textup{and}~~~3n+6=2d+4.[/tex]

Step-by-step explanation:  Given that the numerator and denominator of a fraction are in the ratio of 3 to 5. When the numerator and denominator are both increased by 2, the fraction is equal to \dfrac{2}{3}.

We are to select the system of equations that could be used to solve the problem.

Since n denotes the numerator and m denotes the denominator of the given fraction, so we have

[tex]\dfrac{n}{d}=\dfrac{3}{5}\\\\\\\Rightarrow 5n=3d,[/tex]

and

[tex]\dfrac{n+2}{d+2}=\dfrac{2}{3}\\\\\\\Rightarrow 3(n+2)=2(d+2)\\\\\Rightarrow 3n+6=2d+4.[/tex]

Thus, the required system of equations is

[tex]5n=3d~~~\textup{and}~~~3n+6=2d+4.[/tex]

Option (A) is CORRECT.

Answer:

No, the power multiplied to 8.64 should havean exponent of zero.

HOPE THIS WILL HELP YOU

Answer:

No, The power multiplied to 8.64 should have an 0 exponent.

Option 2 is correct

Step-by-step explanation:

Nick found the quotient of 8.64 and 1.25 × 10⁵.

Quotient of two number is form of division.

If quotient of a and b then expression is [tex]\dfac{a}{b}[/tex]

Correct steps:

[tex]\Rightarrow \dfrac{8.64\times 10^0}{1.25\times 10^5}[/tex]

[tex]\Rightarrow (8.64\div1.25)\times 10^{0-5}[/tex]

[tex]\Rightarrow 6.912\times 10^{-5}[/tex]

Nick steps:

[tex]\Rightarrow \dfrac{8.64\times 10^1}{1.25\times 10^5}[/tex]  wrong step

[tex]\Rightarrow (8.64\div1.25)\times 10^{1-5}[/tex]

[tex]\Rightarrow 6.912\times 10^{-4}[/tex]

The power multiplied to 8.64 should have an 0 exponent.

Therefore, Nick was wrong.

Answer:

P = 1.44 Watts

Step-by-step explanation:

We know that the relation between voltage and current in a simple circuit with a resistor is

V = I.R

Where

V = the voltage of the source

I = current of the circuit

R = resistance

The power is defined as

P = V.I

Which is the same as

P = V.(V/R)

P = (24 v)^2 / (400 ohm)

P = 1.44 Watts

Answer: i cant read that m8 take a better picture

Step-by-step explanation:

Answer:

associative property of multiplication

Step-by-step explanation:

If we have 3 numbers x, y and z the associative property of multiplication says that:

[tex]x (yz) = z (xy) = (xz)y[/tex]

This means that the result will be the same regardless of the order in which the multiplication takes place.

In this case we have the following equality

[tex]2(xy) = (2x)y[/tex]

Note that the property used is the associative property of multiplication

Answer: [tex]\bold{-\dfrac{8}{3}}[/tex]

Step-by-step explanation:

[tex]\sum \limits_{n=1}^{\infty}-4\bigg(\dfrac{-1}{2}\bigg)^{n-1}\implies a_1=-4, r=-\dfrac{1}{2}\\\\\\\text{Use the formula for the sum of an infinite geometric series:}\\S=\dfrac{a_1}{1-r}\\\\\\.\ =\dfrac{-4}{1-(-\frac{1}{2})}\\\\\\.\ =\dfrac{-4}{\frac{3}{2}}\\\\\\.\ =-4\times \dfrac{2}{3}\\\\\\.\ =\large\boxed{-\dfrac{8}{3}}[/tex]

Answer:

The corresponding side lengths of the figure will be proportional based on the scale factor.

Step-by-step explanation:

A dilation can either be an enlargement or reduction.  If the scale factor is less than one then the figure will be a reduction.  If the scale factor is one or larger then the figure will be an enlargement.  Since a dilation is basically multiplying the figure will always be proportional to the original figure.

Answer:

m < b = 70, m < c = 110 and m < d = 70 degrees.

Step-by-step explanation:

The opposite angle a ( angle c) = a = 110 degrees  (Property of a parallelogram).

The angle on the same line as a ( that is angle b) = 180 - 110 = 70 degrees.

(Property of a parallelogram).

Finally angle d which is opposite angle b = 70 degrees.

Final answer:

In parallelogram ABCD with angle A being 110 degrees, angle C is also 110 degrees as opposite angles are equal. Angles B and D are 70 degrees each since consecutive angles in a parallelogram are supplementary and add up to 180 degrees.

Explanation:

To find the measures of the angles B, C, and D in the parallelogram ABCD with angle A being 110 degrees, we can use the properties of parallelograms. Specifically, opposite angles in a parallelogram are equal, and consecutive angles are supplementary (add up to 180 degrees).

Since angle A is 110 degrees, angle C, being opposite to angle A, also measures 110 degrees. Now, to find the measures of angles B and D we know that:

Angle A and angle B are consecutive, so they add up to 180 degrees. Therefore, angle B equals 180 degrees - 110 degrees which is 70 degrees.

Similarly, angle C and angle D are consecutive, so angle D also measures 180 degrees - 110 degrees, giving us 70 degrees for angle D as well.

Thus, the measures of angles B, C, and D in parallelogram ABCD are 70 degrees, 110 degrees, and 70 degrees, respectively.

To determine the first five terms of the given recursive sequence, we begin with the first term, a1 = -10, and use the provided recurrence relation to calculate each subsequent term. The first five terms of the sequence are -10, -33, -125, -493, and -1965.

The student has presented a recursive sequence with the first term stated as – 10 and a recursive formula to find any subsequent term, an, defined as an = 4an-1 + 7 for n ≥ 2.

To find the first five terms of the sequence, we'll apply the formula starting with a1 and proceed to each next term.

First term, a1: – 10

Second term, a2: 4(– 10) + 7 = – 40 + 7 = – 33

Third term, a3: 4(– 33) + 7 = – 132 + 7 = – 125

Fourth term, a4: 4(– 125) + 7 = – 500 + 7 = – 493

Fifth term, a5: 4(– 493) + 7 = – 1972 + 7 = – 1965

Therefore, the first five terms of the sequence are – 10, – 33, – 125, – 493, and – 1965.

The attachment should answer some of your guys “what does k=?” Questions