Find the y-intercept and the slope of the line.
-8x -4y =5

Answers

Answer 1

Answer:

[tex]\sf m = -2\\\\y-intercept =\dfrac{-5}{4}[/tex]

Step-by-step explanation:

Slope and y-intercept of the line:

     Write the equation in slope y-intercept form: y =mx +c

Here, m is the slope and c is the y-intercpet.

To isolate y, add 8x to both side,

            -8x - 4y = 5

                   -4y  = 8x + 5

Now, divide the entire equation by (-4),

                        [tex]\sf \dfrac{-4y}{-4}=\dfrac{8x}{-4} + \dfrac{5}{-4}\\\\\\y = -2x -\dfrac{5}{4}[/tex]

Now, compare with y = mx +c

          [tex]\boxed{\sf m= -2}\\\\\\\boxed{\sf y-intercept=\dfrac{-5}{4}}[/tex]

 

Answer 2

Answer:

y-intercept = -5/4

slope = -2

Step-by-step explanation:

To quickly find the slope and y-intercept of a given linear equation, we can express it in the following form, called the slope-intercept form:

[tex]\boxed{y = mx + c}[/tex],

where:

m ⇒ slope

c ⇒ y-intercept

In order to take the given equation into the slope-intercept form, we have to  make y the subject of the equation:

[tex]-8x - 4y = 5[/tex]

⇒ [tex]-4y = 8x + 5[/tex]                 [Adding 8x to both sides of the equation]

⇒ [tex]y = -\frac{1}{4}(8x + 5)[/tex]              [Dividing both sides of the equation by -4]

⇒ [tex]y = -2 x - \frac{5}{4}[/tex]

Comparing the above equation with the slope-intercept form, we can see that m = -2 and c = -5/4.

Therefore, y-intercept = -5/4, and slope = -2.

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Related Questions

subtract these polynomials

(3x^-2x+5)-(x+3=

Answers

2x² -2x+2 is the  polynomial we obtained after subtraction

The given polynomials are (3x²-2x+5)-(x²+3)

Three times of x square minus two times of x plus five minus x square plus three

We have to subtract the polynomials

3x²-2x+5 -x² - 3

Combine the like terms

2x² -2x+2

Hence, the polynomial we obtained after subtraction is 2x² -2x+2

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Please help. Any unnecessary answers will be reported.

If n! = (2^8)(3^4)(5^2)(7), then what is n? Note that n! = n × (n - 1) × (n - 2) × ... × 1.

Answers

Answer:

n = 10

Step-by-step explanation:

Factorial is denoted by an exclamation mark "!" placed after the number. It means to multiply all whole numbers from the given number down to 1.

Therefore, n! represents the product of all positive integers from 1 to n.

[tex]\boxed{n!=n \times(n-1) \times(n-2) \times ... \times 1}[/tex]

Given expression:

[tex]n! = (2^8)(3^4)(5^2)(7)[/tex]

The expression for n! has been given as the product of prime factors.

As n! represents the product of all positive integers from 1 to n, begin by writing out the positive integers from 1 in ascending order as the product of primes (using exponents where possible):

[tex]\begin{array}{|c|c|c|c|c|c|c|c|c|c|c|c|c|c|}\cline{1-14}\vphantom{\dfrac12}n&1&2&3&4&5&6&7&8&9&10&11&12&13\\\cline{1-14}\vphantom{\dfrac12}\sf Product\;of\;primes&1&2&3&2^2&5&3\cdot 2&7&2^3&3^2&5 \cdot 2&11&2^2\cdot 3&13\\\cline{1-14}\end{aligned}\;\;\sf etc.[/tex]

If we examine the prime products of the given expression, we can see that largest prime number 7 appears only once. Therefore, n must be less than 14, since the next time 7 appears as a prime factor is when 2 · 7 = 14.

The prime number 5 appears twice in the given expression.

From the above table, we can see that the first two times the number 5 is present is (1) on its own, and (2) as a factor of 10. Therefore, n must be equal to or more than 10.

The prime number 3 appears four times in the given expression.

From the above table, we can see that the first four times the number 3 is present is (1) on its own, (2) as a factor of 6, (3) & (4) as both factors of 9.

The 5th time prime number 3 is present is as a prime factor of 12. Therefore, n must be less than 12, else 2⁵ would be a factor of n!.

Therefore, we have determined that 10 ≤ n < 12.

As 11 is a prime number and does not appear in the given expression for n!, we can conclude that n = 10.

We can check this by calculating the given expression and 10!:

[tex]\begin{aligned}n! &= (2^8)(3^4)(5^2)(7)\\&=256 \cdot 81\cdot25\cdot7\\&=20738\cdot25\cdot7\\&=518400\cdot7\\&=3628800\end{aligned}[/tex]

[tex]\begin{aligned}10!&=10 \cdot 9 \cdot 8 \cdot 7 \cdot 6 \cdot 5 \cdot 4 \cdot 3 \cdot 2 \cdot 1\\&=90 \cdot 8 \cdot 7 \cdot 6 \cdot 5 \cdot 4 \cdot 3 \cdot 2 \cdot 1\\&=720 \cdot 7 \cdot 6 \cdot 5 \cdot 4 \cdot 3 \cdot 2 \cdot 1\\&=5040 \cdot 6 \cdot 5 \cdot 4 \cdot 3 \cdot 2 \cdot 1\\&=30240 \cdot 5 \cdot 4 \cdot 3 \cdot 2 \cdot 1\\&=151200 \cdot 4 \cdot 3 \cdot 2 \cdot 1\\&=604800 \cdot 3 \cdot 2 \cdot 1\\&=1814400 \cdot 2 \cdot 1\\&=3628800 \cdot 1\\&=3628800\end{aligned}[/tex]

Therefore, this proves that n = 10.

The Question is in the Picture, use the Pythagorean theorem to solve and show your work please

Answers

Answer:

y=8

Step-by-step explanation:

Please do #1 and show work

Answers

The solution to the integration of the function given, ∫√(5x - 1) dx, is:

[tex]\frac{2}{15}(5x-1)^{3/2} + C[/tex]

Understanding Integration

To solve the integral of:

√(5x - 1) dx

we can use a u-substitution.

Let u = 5x - 1, then:

du = 5 dx

dx = du/5

Now we can rewrite the integral in terms of u:

∫√(5x - 1) dx = ∫√u * (du/5)

Simplifying the integral:

(1/5) ∫√u du

Integrating √u:

(1/5) * (2/3) * u^(3/2) + C

Where C is the constant of integration

Substituting back u = 5x - 1:

(2/15) * (5x - 1)^(3/2) + C

Therefore, the solution to the integral of √(5x - 1) dx is:

[tex]\frac{2}{15}(5x-1)^{3/2} + C[/tex]

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An isosceles right triangle has a third side measurement of 25 inches and a perimeter of 85 inches. The leg of the dilated triangle measures 6 inches. What is the perimeter of the dilated triangle?

Answers

In an isosceles right triangle, the two legs are equal in length. Let's assume that the length of each leg of the original triangle is "x" inches. Since it's an isosceles right triangle, the hypotenuse is also "x" inches.

Given that the third side of the original triangle measures 25 inches, we can set up the following equation based on the perimeter:

x + x + 25 = 85

Simplifying the equation:

2x + 25 = 85

Subtracting 25 from both sides:

2x = 60

Dividing both sides by 2:

x = 30

So, the length of each leg of the original triangle is 30 inches.

Now, let's consider the dilated triangle. We are told that the leg of the dilated triangle measures 6 inches. Let's assume the scale factor of the dilation is "k."

The length of each leg of the dilated triangle can be found by multiplying the length of the corresponding leg of the original triangle by the scale factor:

Leg of dilated triangle = k * Leg of original triangle

Leg of dilated triangle = k * 30

Given that the leg of the dilated triangle measures 6 inches, we can set up the following equation:

k * 30 = 6

Dividing both sides by 30:

k = 6/30

Simplifying:

k = 1/5

So, the scale factor of the dilation is 1/5.

Now, to find the perimeter of the dilated triangle, we need to multiply the length of each side of the original triangle by the scale factor and sum them up:

Perimeter of dilated triangle = 2 * (k * 30) + k * 25

Plugging in the values:

Perimeter of dilated triangle = 2 * (1/5 * 30) + 1/5 * 25

Simplifying:

Perimeter of dilated triangle = 2 * 6 + 5

Perimeter of dilated triangle = 12 + 5

Perimeter of dilated triangle = 17 inches

Therefore, the perimeter of the dilated triangle is 17 inches.

Which of the following is not a condition for a geometric setting?

The trials are independent

The probability of success is the same for each trial

There are a fixed number of trials

The variable of interest is the number of trials required to reach the first success

There are only 2 outcomes for each trial

Answers

There are a fixed number of trials is not a condition for a geometric setting

In a geometric setting, we are dealing with a sequence of independent trials, where each trial can result in either a success or a failure.

The key concept in a geometric setting is the number of trials needed until the first success occurs.

The trials are independent  is essential in a geometric setting.

It means that the outcome of one trial does not affect the outcome of subsequent trials.

The probability of success is the same for each trial is also crucial in a geometric setting.

It implies that the probability of achieving a success does not change from trial to trial.

There are a fixed number of trials is not specific to a geometric setting.

The variable of interest is the number of trials required to reach the first success is fundamental to a geometric setting.

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sin( 3pi/4 ) =
O A. 1/2
OB. -√2/2
O C. √3/2
O D. √2/2

Answers

Answer:

sin(3pi/4 ) = -√2/2

So, B.

The accompanying diagram shows a revolving door with three panels, each of which is 4 feet long. What is the width, w, of the opening between x and y, to the nearest tenth of a foot?

Answers

The width, w, of the opening between x and y, is 6.9 ft.

We have,

From the diagram,

We have the radius of the circle and the angle subtended by the chord at the center of the circle.

So,

We can also use the formula.

= 2 x radius x sin(angle/2)

This is the length of the chord.

Now,

radius = 4 ft

angle = 360/3 = 120

Substituting the values.

= 2 x radius x sin(angle/2)

= 2 x 4 x sin (120/2)

= 2 x 4 x sin 60

= 2 x 4 x √3/2

= 4 x √3

= 4 x 1.732

= 6.928

Rounding to the nearest tenth.

= 6.9 ft

Thus,

The width, w, of the opening between x and y, is 6.9 ft.

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please help! thank uu ~ :)

Answers

Answer:

Unlikely.

Step-by-step explanation:

Possibility Formula: [tex]\frac{Desired Outcome}{Total Possible Outcoes}[/tex]

We want to roll a 5. On a standard six-sided die, then the odds of that happening is [tex]\frac{1}{6}[/tex]

[tex]\frac{1}{6}[/tex] is unlikely.

I WILL GIVE BRAINLIEST, square root of x, find the domain of x

Answers

The domain for the square root function is the set of all whole numbers

Calculating the domain of the square root function

From the question, we have the following parameters that can be used in our computation:

Function type = square root function

Equation: square root of x

This means that

f(x) = √x

The domain for x in the function is the set of input values the function can take

In this case, the square root function can take any whole number as its input

This means that the domain for f(x) is the set of all whole number

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Quentin deposited $1,264 into a savings account that earns 2.75% simple interest annually. What will Quentin’s account balance be at the end of 2.5 years? Assume he makes no additional deposits during that time period.

Answers

Answer:

I love math

Step-by-step explanation:

The formula for simple interest is:

I = P * r * t

where:

I = interest earned

P = principal amount

r = interest rate (as a decimal)

t = time (in years)

In this case, we know that:

P = $1,264

r = 2.75% = 0.0275 (as a decimal)

t = 2.5 years

So, we can plug in these values and solve for I:

I = 1,264 * 0.0275 * 2.5 = $87.55

Therefore, the interest earned over 2.5 years is $87.55. To find the ending balance, we need to add the interest earned to the principal:

Ending balance = $1,264 + $87.55 = $1,351.55

So, Quentin's account balance will be $1,351.55 at the end of 2.5 years.

How do you find the length of an arc expressed in terms of pi?

Answers

To find the length of an arc expressed in terms of pi, you need to use the formula L = (n/2) * (C), where L is the length of the arc, n is the number of pi radians in the arc, and C is the circumference of the circle. If the circle has a radius of r, then the circumference is C = 2 * pi * r. Therefore, we can rewrite the formula as L = (n/2) * (2 * pi * r) = n * r * pi. This formula tells us that the length of an arc expressed in terms of pi is equal to the radius of the circle times the number of pi radians in the arc.

1.The volume of a triangular prism is 204cm3 . If its height is 17cm, then find the area of its base.





Answers

Answer:

12 cm ^2

Step-by-step explanation:

Using the formula

V=ABh

Solving forAB

AB=V

h=204

17=12cm²

If tanA = 60/11 and sinB = 45/53 and angles A and B are in Quadrant I, find the value of tan(A-B)

Answers

Based on the information, it should be noted that the value of tan(A-B) is 234/583.

How to calculate the value

Given:

tanA = 60/11

sinB = 45/53

A and B are in Quadrant I

We can use the following identity to find tan(A-B):

tan(A-B) = (tanA - tanB)/(1 + tanA*tanB)

Substituting the given values, we get:

tan(A-B) = (60/11 - 45/53)/(1 + (60/11)*(45/53))

= (15/53)/(295/583)

= 234/583

Therefore, the value of tan(A-B) is 234/583.

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PLEASE HELP

Which of the following graphs shows an angle that would have an equivalent cosine ratio to the graph shown?

Answers

Answer: 150 deg

Step-by-step explanation:

cosine is negative in quadrants 2 and 3. the current angle, 210, is in quad 3. It will have an equal cosine value in quad 2.

that angle will be -210 degrees. in positive terms that is 360-210 = 150 degrees.

thus the answer which shows 150 degrees is correct.

in general:

[tex]cos(x) = cos(-x)[/tex]

I need help can someone help me

Answers

The two figures are congruent because a reflection and a translation are used to map Figure 1 onto Figure 2.

The angle corresponding to angle M is given as follows: <S.

What are transformations on the graph of a function?

Examples of transformations are given as follows:

Translation: Lateral or vertical movements.Reflections: A reflection is either over one of the axis on the graph or over a line.Rotations: A rotation is over a degree measure, either clockwise or counterclockwise.Dilation: Coordinates of the vertices of the original figure are multiplied by the scale factor, which can either enlarge or reduce the figure.

For this problem, the two transformations are:

Reflection, as the orientation changed.Translation, as the position changed.

These two are rigid motions, keeping the side lengths constant, hence the figures are congruent.

Angle S is corresponding to angle M, as they are the angles at the "pointed" vertex of the figure.

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f+90+42=180 what is the answer of this

Answers

Answer:

hello

the answer is:

f = 180 - 42 - 90 = 48

Solve for X
20x+30
28x-10

Answers

Answer:

[tex]\huge\boxed{\sf x = 5}[/tex]

Step-by-step explanation:

Statement:Corresponding angles are equal.Solution:

20x + 30 = 28x - 10 (Corresponding angles)

Add 10 to both sides

20x + 30 + 10 = 28x

20x + 40 = 28x

Subtract 20x from both sides

40 = 28x - 20x

40 = 8x

Divide both sides by 8

5 = x

OR

x = 5

[tex]\rule[225]{225}{2}[/tex]

p: 10 > 7 q: 10 > 5
p →q

F F → T
T F → F
F T → T
T T → T

Answers

Answer: if it's true that 10 > 7 (P), then it's also true that 10 > 5 (Q).

Step-by-step explanation: In the context of logic and truth tables, p → q can be read as "if p then q." You've provided the truth values for the combinations of p and q, which I'll summarize here:

If p and q are both False (F), then p → q is True (T).

If p is True (T) and q is False (F), then p → q is False (F).

If p is False (F) and q is True (T), then p → q is True (T).

If p and q are both True (T), then p → q is True (T).

Given your propositions:

P: 10 > 7

Q: 10 > 5

P is True because 10 is indeed greater than 7. Q is also True because 10 is greater than 5.

Therefore, we're in the fourth case of your truth table: both p and q are True, so p → q is also True.

Write the equation of the hyperbola

Answers

Using the center and distance between co-vertex and center, the equation of the hyperbola is written below

[tex]\frac{(y + 3)^2}{49} - \frac{(x - 10)^2}{144} = 1[/tex]

What is the equation of hyperbola

A hyperbola, in analytic geometry, is a conic section that is formed when a plane intersects a double right circular cone at an angle such that both halves of the cone are intersected.

The equation of hyperbola is given as;

[tex]\frac{(y - k)^2}{a^2} - \frac{(x - h)^2}{b^2} = 1[/tex]

where (h,k) is the center of the hyperbola, a is the distance between a vertex and the center, and b is the distance between a co-vertex and the center.

In this case, the center is (10,−3), a=7, and b=12. Therefore, the equation of the hyperbola is

The equation of the hyperbola is;

[tex]\frac{(y + 3)^2}{49} - \frac{(x - 10)^2}{144} = 1[/tex]

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PLEASE HELPPP IM CONFUSEDDDD

Answers

Answer: C: (-4,-3)

Step-by-step explanation:

You have the correct answer selected!

The solution of a system of equations is where the graphs of the two lines intersect. we can read that point to be (-4,-3), so thats the answer :)

the answer is C (-4, -3)

Ratios are often represented by the symbol. For example, 5 : 4 might mean 5 eggs are needed for every 4 batches of cookies. Select all of the ratios that are equivalent to the ratio 12:3. 6:1 1:4 4:1 246 15:6 120 : 30​

Answers

The ratios that are equivalent to the ratio 12:3 are 4:1 and 120:30.

We have,

To determine the ratios that are equivalent to the ratio 12:3, we need to find ratios that have the same value when simplified.

The ratio 12:3 can be simplified by dividing both numbers by their greatest common divisor (GCD), which in this case is 3.

Dividing 12 by 3 gives us 4, and dividing 3 by 3 gives us 1. Therefore, the simplified ratio is 4:1.

Now let's check the given options:

6:1 - This ratio is not equivalent because it is different from the simplified ratio 4:1.

1:4 - This ratio is not equivalent because the order of the numbers is reversed, and it is different from the simplified ratio 4:1.

4:1 - This ratio is equivalent to the original ratio 12:3. When simplified, both ratios result in 4:1.

246 - This is not a ratio and cannot be compared to the original ratio 12:3.

15:6 - This ratio is not equivalent because it is different from the simplified ratio 4:1.

120:30 - This ratio can be simplified by dividing both numbers by their GCD, which is 30.

Dividing 120 by 30 gives us 4, and dividing 30 by 30 gives us 1.

Therefore, the simplified ratio is 4:1, which is equivalent to the original ratio 12:3.

Thus,

The ratios that are equivalent to the ratio 12:3 are 4:1 and 120:30.

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Complete the square to put
y=3x²-24x + 56 in vertex form.
a) y = 3(x-8)² +4
b) y=3(x-7)² +5
c) y = 3(x-6)² +6
d) y = 3(x - 5)² +7
e) y = 3(x-4)² +8

Answers

Answer would be E! Hope that was helpful!

In ΔWXY, w = 320 inches, y = 740 inches and ∠Y=169°. Find all possible values of ∠W, to the nearest 10th of a degree.

Answers

Using the law of sines, we have:

$dfrac{sinangle W}{320}=dfrac{sin169°}{740}$

Multiplying both sides by 320, we have:

$sinangle W=dfrac{320sin169°}{740}$

Using a calculator, we find that $sinangle W approx 0.7555$. Taking the inverse sine of both sides, we have:

$angle W approx sin^{-1}(0.7555)$

There are two possible values for $angle W$: $angle W approx 49.5°$ and $angle W approx 130.5°$ (since $sin^{-1}(0.7555) approx 49.5°$ and $angle W = 180° - sin^{-1}(0.7555) approx 130.5°$).

Therefore, the two possible values of $angle W$ are approximately 49.5° and 130.5°.

i need help can everyone please help me

Answers

Since AC is the angle bisector of ∠BAD, the flowchart proof should be completed as follows;

Statement                                 Reason

AC bisects ∠BAD                      Given

∠BAC ≅ ∠DAC                         Definition of an angle bisector.

∠BCA ≅ ∠DCA                         Congruent angles of a triangle (SAS).

AC ≅ AC                                   Reflexive property

ΔABC ≅ ΔADC                         AAS postulate

What is an angle bisector?

In Mathematics and Geometry, an angle bisector can be defined as a type of line, ray, or segment, that typically bisects or divides a line segment exactly into two (2) equal and congruent angles.

By applying the angle bisector theorem to the given triangle, we have the following statements and justifications:

AC bisects ∠BAD       Given

∠BAC ≅ ∠DAC           Definition of an angle bisector.

Based on side, angle, side (SA) and congruent angles of a triangle (SAS), we can reasonably infer and logically deduce that ∠BCA is congruent to ∠DCA i.e ∠BCA ≅ ∠DCA.

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NO LINKS!!!

answer all 4!!!

WILL GIVE BRAINLIEST!!

Answers

Answer:

tan T = 12/5

sin A = 12/13

sec Z = 97/65

m<H = 54.5°

Step-by-step explanation:

In general:

sin A = opp/hyp

cos A = adj/hyp

tan A = opp/adj

sec A = 1/cos A = hyp/adj

tan T = 48/20

tan T = 12/5

AB = √(100 + 576)

AB = 26

sin A = 24/26

sin A = 12/13

XZ = √(72² + 65²)

XZ = 97

sec Z = 97/65

tan H = 7/5

H = tan^-1 7/5

m<H = 54.5°

Find the equation of the line.
Use exact numbers.

Answers

Answer:

y = 3x + 3

Step-by-step explanation:

the equation of a line in slope- intercept form is

y = mx + c ( m is the slope and c the y- intercept )

calculate m using the slope formula

m = [tex]\frac{y_{2}-y_{1} }{x_{2} -x_{1} }[/tex]

with (x₁, y₁ ) = (- 1, 0) and (x₂, y₂ ) = (0, 3) ← 2 points on the line

m = [tex]\frac{3-0}{0-(-1)}[/tex] = [tex]\frac{3}{0+1}[/tex] = [tex]\frac{3}{1}[/tex] = 3

the line crosses the y- axis at (0, 3 ) ⇒ c = 3

y = 3x + 3 ← equation of line

I really need help doing this. please help me.

Answers

The bisector angle is angle PQT which is equal to angle RQT.

What is angle bisector?

Angle bisector or a bisector angle is a type of angle obtained after dividing the initial angle into two equal parts.

The bisected angle can be obtained using a pair of compass and a pencil attached to it.

To bisect the given angle RQP; we will take the following steps;

place the compass on exactly point Qexpand the radius of the compass such that the pencil attached to the compass will be in between R and P.strike an arc with the pencil clock wisestrike another arc with the pencil anti clock wise such that the two arc intersects.draw a line from point Q to intersect the two arcs.label the point of intersection of the two arcs Tangle PQT is equal to angle RQT

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un edificio de 5 metros proyecta una sombra de 4 metros determina la altura que tiene una casa que proyecta una sombra 2 metros

Answers

The height of a house that has a shadow projection of 2 meters is given as follows:

2.5 meters.

How to obtain the height of the house?

The height of a house that has a shadow projection of 2 meters is obtained applying the proportions in the context of the problem.

The proportional relationship between the height of the building and the height of the shadow is given as follows:

5/4 = x/2

Hence we apply cross multiplication to obtain the height of the house, as follows:

4x = 10

x = 10/4

x = 2.5.

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Name the quadrant in which angle 0 must lie for the following to be true.

Answers

Answer:

d

Step-by-step explanation:

Other Questions
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