Mathematics High School

Are the lines parallel, perpendicular, or neither?

5x + 2y = 10
15x + 4y = -4

Answers

Answer 1
5x+2y=10, 2y=-5x+10, y=-2.5x+5

15x+4y=-4, 4y=-15x-4, y=-3.75x-1

-2.5 != -3.75

And -2.5m=-1, m=0.4, 0.4 !=-3.75

So the slopes are not equal and they are also not negative reciprocals of one another.

Thus the lines are neither parallel nor perpendicular.

Related Questions

The rectangle below has an area of x^2-15x+56 x ​2 ​​ −15x+56 x, start superscript, 2, end superscript, minus, 15, x, plus, 56 square meters and a length of x-7x−7x, minus, 7 meters. what expression represents the width of the rectangle

Answers

The expression that represents the width of the rectangle is x - 8

Area of a rectangle:area = lw

l = length

w = width

area = x² + 15x + 56

length = x - 7

Therefore,

x² - 15x + 56 = (x - 7) w

divide both sides by x - 7

w = x² - 15x + 56 / x - 7

w = (x - 7)(x - 8) / x - 7

w = x - 8

learn more on rectangle here: https://brainly.com/question/4529723

Can someone help me

Answers

2.89-2.84 = 0.05 cent increase

0.05/2.84 = 0.0176

0.0176 = 1.8% increase

price increase = (new number - original number) / original number....* 100
                       = (2.89 - 2.84) / 2.84...* 100
                      = 0.05 / 2.84....* 100
                      = 0.0176 ...* 100
                      = 1.76  rounds to 1.8% <===

Solve cos x +sqrt2 = -cos x for x over the interval (0,2pi) .

Answers

Final answer:

The equation cos x + sqrt(2) = -cos x is solved by combining like terms and isolating cos x, resulting in the solutions x = 3π/4 and 5π/4 over the interval (0,2π).

Explanation:

To solve the equation cos x + sqrt(2) = -cos x for x over the interval (0,2π), first combine like terms by adding cos x to both sides of the equation, resulting in:

2 cos x + sqrt(2) = 0

Isolate cos x by subtracting sqrt(2) from both sides:

2 cos x = -sqrt(2)

Divide both sides by 2 to solve for cos x:

cos x = -sqrt(2)/2

The value of cos x = -sqrt(2)/2 corresponds to angles in the second and third quadrants. So, the solutions for x in the interval (0,2π) are:

x = 3π/4, 5π/4

Use Gauss-Jordan elimination to solve the following linear system: 5x – 2y = –2 –x + 4y = 4 A. (–6,–5) B. (2,0) C. (0,1) D. (–1,0)

Answers

Im pretty sure its A.

The answer is C.(0,1)

5x - 2y = -2 -x + 4y = 4

5(0) - 2(1) = -2 -(0) + 4(1) = 4

Identify the cross section shown.

circle


trapezoid


rectangle


pentagon

Answers

The cross section shown in the picture below include the following: B. rectangle.

In Mathematics and Euclidean Geometry, a rectangle refers to a type of quadrilateral or polygon in which its opposite sides are equal and all the angles that are formed are right angles.

Generally speaking, a circle has no edge or sides. A trapezoid is a type of quadrilateral that has one pair of parallel sides and one pair of non-parallel sides. Additionally, a pentagon is a regular polygon that comprises 5 sides.

By critically observing the cross section shown in the picture below, we can logically deduce that it represents a rectangle because its opposite sides are equal.

The sum of 2 numbers is 7. if one number is subtracted from the other, the result is -1. find the numbers

Answers

Let the two numbers be x and y.

Given,

x + y = 7

x = 7 - y

Also given,

x - y = -1

7 - y - y = -1

-2y = -8

y = 4

x = 7 - y = 7 - 3 = 4

Hence, the numbers are 3 and 4.

What is the equation of the line?

Answers

First find the slope of the line. Slope is defined as the change in y over the change in x.

[tex]m = \frac{y_2 - y_1}{x_2 - x_1}[/tex]

Find two ordered pairs and plug them into the slope formula.

After looking at the graph, I found two points: (0, 1) and (4, 4)

[tex]\frac{4 - 1}{4 - 0} = \frac{3}{4}[/tex]

Now find where the line intersects the y-axis.

After looking at the graph, I found out that the line intercepts the y-axis at
(0, 1)

Now build the slope-intercept equation.

General form: y = mx + b
Where m is the slope and b the y-intercept

So, the answer is y = 3/4m + 1

You invest an initial $2,000 in an account that has an annual interest rate of 6%, compounded daily. How much money will you have in the account after 15 years? Round your answer to the nearest whole number.

Answers

The formula is
A=p (1+r/k)^kt
A future value?
P present value 2000
R interest rate 0.06
K compounded daily 365
T time 15 years
A=2,000×(1+0.06÷365)^(365×15)
A=4,918.84

A surface on which all points are at the same potential is referred to as

Answers

equipotential, equi=equal

Find the greatest common factor of the following monomials 28g5h2 12g6h5
Also explain step by step how to solve these problems please

Answers

28g^5h^2 and 12g^6h^5

first, we find the GCF of the coefficients 28 and 12. What is the highest number that will go into both 28 and 12 evenly ? That number is going to be 4.

now, we look at our variables....to find the GCF of the variables, pick the lowest exponent.
another words, the lowest exponent of ur variable h is h^2...and the lowest exponent of ur variable g is g^5

therefore, the GCF of these monomials is : 4h^2g^5

A line passes through the point (-8,3) and has a slope of 5/4.

Write an equation in slope-intercept form for this line.

Answers

y = mx + b
3 = 5/4(-8) + b
3 = -10 + b
b= 13


equation

y = 5/4x + 13
y - y1 = m(x - x1)
y - 3 = (5/4) ( x + 8)
y - 3 = 5/4x + 10
add 3 to both sides
y = 5/4 x + 13

The initial temperature of a cup of tea is 200ºF. The surrounding temperature is 70ºF, and the value of the constant k is 0.6.
Applying Newton's cooling model, the temperature of the tea after 2 hours will be ___
ºF. round to the nearest integer.

Answers

Newton's Law of Cooling states that the change of the temperature of an object is proportional to the difference between its own temperature and the ambient temperature over time.

Therefore when expressed mathematically, this is equivalent to:

dT = - k (T – Ts) dt

dT / (T – Ts) = - k dt

Integrating:

ln [(T2– Ts) / (T1– Ts)] = - k (t2 – t1)

Before we plug in the values, let us first convert the temperatures into absolute values R (rankine) by adding 460.

R = ˚F + 460

T1 = 200 + 460 = 660 R

Ts = 70 + 460 = 530 R

ln [(T2– 530) / (660 – 530)] = - 0.6 (2 - 0)

T2 = 569.16 R

T2 = 109 ºF

Answer: After 2 hours, it will be 109 ºF

Answer:

109 degrees

Step-by-step explanation:

For the polynomial 8x3y2 – x?y2 + 3xy2 – 4y3 to be fully simplified and written in standard form, the missing exponent on the

Answers

A polynomial in standard form has terms arranged with the highest exponent on leftmost side and the lowest exponent on the right end. The variables are also arranged alphabetically.

Therefore, the exponent of the x-term must be 2 for the polynomial to be fully simplified and written in standard form.

Answer: 2

Step-by-step explanation: this answer is 100% correct for edge.nuity

Given the function f(x) = log3(x + 4), find the value of f−1(3

Answers

First of all, find f ⁻¹ (x), or the inverse function like so:
y = log(3x + 12)
e^y = 3x + 12
3x = e^y - 12
x = 1/3 (e^y - 12)
Now, swap x and y:
f ⁻¹ (x) = y = 1/3 (e^x - 12)

Secondly and finally, substitute 3 into this eq'n:
f ⁻¹ (3) = 1/3 (e³ -12) = 2.695.....
so 2.695 (to 4 sig.figs/ 3 d.ps)
or if asked for an exact answer then it is just: 1/3 (e³ -12), which can be simplfied to 1/3e³ - 4.

Answer:

23

Step-by-step explanation:

Given : [tex]f(x) = log_3(x + 4)[/tex]

To Find: [tex]f^{-1}(3)[/tex]

Solution:

[tex]y = log_3(x + 4)[/tex]

Replace y with x and x with y

[tex]x = log_3(y + 4)[/tex]

[tex]3^x = y + 4[/tex]

[tex]3^x-4 = y [/tex]

So, [tex]f^{-1}(x)=3^x-4[/tex]

Now substitute  x= 3

[tex]f^{-1}(3)=3^(3)-4 [/tex]

[tex]f^{-1}(3)=27-4 [/tex]

[tex]f^{-1}(3)=23[/tex]

Hence the value of [tex]f^{-1}(3)[/tex] is 23

I need help with #18 c-i

Answers

c - one is -4 due to that when y=0 the x coordinate shows -4, the other is when 4-x^2=0, and the square root of 4 is 2

d - x intercepts

e - it's 4 due to that 4 is shown where x=0 on the graph

f - y intercept

g - Since x>0, we do 4-x^2. x=1, and 1^2=1, so 4-1=3. 1 is x and 3 is f(x), or y, so the coordinates are (1,3)

h - Since it's <0, -1+4=3, and since 3 is the output the coordinates are (-1,3)

i - Since -3 <0, we do -3+4=1

What is the image of point (0,3) for mapping (x,y) (x-2,y-3)

Answers

When it asks for the image, that means what are your new coordinates after doing the rules they give you. In this, the rule is to subtract 2 from your x value and subtract 3 from the y value. So you subtract 2 from 0 and subtract 3 from 3. This will give you the values to use for the x and y of your answer:)

Can you use the ASA Postulate or the AAS Theorem to prove the triangles congruent?

Answers

Answer:

ASA only

Step-by-step explanation:

Given is a picture of two triangles with one side and one angle congruent.

Comparison of these two triangles given

side = side

one angle = one angle (given)

Second angle = second angle (Vertically opposite angles)

Thus we find here that two angles and one corresponding side are congruent.

HEnce we say that these two triangles are congruent by ASA theorem

ASA theorem can be applied here because the equal side is between the two congruent angles.  

Instead if the side is not between the congruent angles but corresponding side then we can only use AAS

SO here ASA is correct.

Answer:

ASA only

Step-by-step explanation:

We are given that  two triangles in which

An angle of triangle is equal to its corresponding angle of second triangle.

One side of a triangle is equal to one side of other triangle.

ASA  postulate: It states that two angles and included side of one triangle are congruent to its corresponding angles and corresponding side of other triangle , then the two triangles are congruent.

AAS postulate: It states that two angles and non- included side of one triangle are congruent to its corresponding two angles and its corresponding side of another triangle, then the triangles are congruent by AAS postulate.

In triangle AOB and COD

[tex]\angle AOB= \angle COD[/tex]  (Vertical angles are equal )

[tex]\angle ABO=\angle CDO[/tex] ( Given )

[tex]OB=OD[/tex] (Given )

[tex]\triangle AOB\cong \triangle COD[/tex] ( ASA Postulate )

Answer: ASA only

Quadrilateral ABCD is a parallelogram. ,  bisects , and . What is the best name for quadrilateral ABCD?

A.

rectangle

C.

isosceles trapezoid

B.

rhombus

Answers

C. Isosceles trapezoid

Using the graph, find this information about the child’s movement in the vertical (y) direction:
1. the best trigonometric function to start with
2. the amplitude
3. the period
4. any horizontal displacement of the graph.
5. any vertical displacement of the graph.

Type your response here:

Answers

1. The sine and cosine function are sinusoidal waves such that they form waves when you graph them on a cartesian plane. The only difference between them is that the crest comes first followed by the trough in the sine function. The opposite is true for the cosine function. The graph in the picture is a sine function.

2. The amplitude is the measure from crest to crest, or from trough to trough. The amplitude in the graph is 1.5.

3. The period is the reciprocal of amplitude. Therefore,itis 1/1.5 or 2/3.

4. There is no horizontal displacement because the wave only moves in a vertical direction.

5. The vertical displacement is from crest to trough which is 1 unit.

When a line has an undefined slope what will any two points on the line have in common

Answers

y-coordinate
Good luck and have a nice day.
I think it y or k coordinate most likely y coordinate
 

Two containers, one for 3 liters and one for 5 liters, how would you measure 4 liters

Answers

Fill the 5-liter container, pour water from that into the 3 liter container until that is full,  You will now have 2 liters left in the 5 liter container.

Empty the 3-liter container, and then transfer the 2 liters from the 5-liter container into it.

Now fill the 5-liter container again, then pour water carefully from the 5-liter container into the 3-liter container until it is full - exactly one more liter.

The 5-liter container now has 4 liters in it.

A dresser contains six pairs of shorts one each in the colors, red, black, blue, green, khaki, and gray. The dresser also contains four shirts one each in the colors black, navy, red, gray. Melanie has to get dressed in the dark, so she grabs A pair of shorts and a T-shirt at random. What is the probability that she selects a green pair shorts and a gray T-shirt?

(First of all, Melanie, you should really get a lamp. And second why is it you own more shorts than shirts?)

Answers

Answer: 1/24

---------------------------------------------------------------------
---------------------------------------------------------------------

Work Shown:

A = selects green pair of shorts
B = selects gray t-shirt

P(A) = probability of selecting green shorts
P(A) = (number of green shorts)/(number of shorts total)
P(A) = 1/6
P(B) = probability of selecting gray t-shirt
P(B) = (number of gray t-shirts)/(number of t-shirts total)
P(B) = 1/4

P(A and B) = probability of selecting green shorts AND gray t-shirt
P(A and B) = P(A)*P(B) ... since A and B are independent events
P(A and B) = (1/6)*(1/4)
P(A and B) = (1*1)/(6*4)
P(A and B) = 1/24

Note: The fraction 1/24 is approximately equal to 0.041667

A gardener has 27 pansies and 36 daisies. He plants an equal number of each type of flower in each row.What is the greatest possible number of pansies in each row?

Answers

There are 27 pansies.
The factors of 27 are (3,9)
Therefore,
Either (a) plant 3 pansies in 9 rows, or
           (b) plant 9 pansies in 3 rows.

There are 36 daisies.
The factors of  36 are (3,12), (6,6) or (9,4).
Therefore
Either (a)  plant 3 daisies in 12 rows, or
           (b) plant 12 daisies in 3 rows, or
           (c) plant 6  daisies in 6 rows, or
           (d) plant 9 daisies in 4 rows, or
           (e) plant 4 daisies in 9 rows.

Because each row has an equal number of pansies and daisies, the only common arrangements are
(a) 9 pansies and  12 daisies in 3 rows, or
(b) 3 pansies and 4 daisies in 9 rows.

To have the greatest number of daisies in each row means planting 9 pansies and 12 daisies in 3 rows.

Answer: 
The greatest number of pansies per row is 9.
Plant 9 pansies and 12 daisies in 3 rows.

For large parties, a restaurant adds a 15% service charge to the bill. how much would be added to a bill of $638.40?

Answers

In restaurants, especially the fine dining ones, the bill includes a service charge. This payment is intended for the service given by the restaurant crew to make your experience in their premises worthwhile. 

The service charge accounts for a fixed percentage of your total expenses. If your total expenses amount to $638.40, then the service charge would be equal to 638.4(0.15) = $95.7. Therefore, $95.7 will be added to your original bill.

Answer:

Service charge  added to a bill of $638.40 is $95.76 .

Step-by-step explanation:

As given

For large parties, a restaurant adds a 15% service charge to the bill.

Bill of the parties  is  $638.40 .

15% is written in the decimal form

[tex]= \frac{15}{100}[/tex]

= 0.15

Thus

Service charge = 0.15 × Bill of the parties .

                          = 0.15 × $638.40

                           = $ 95.76

Therefore service charge  added to a bill of $638.40 is $95.76 .

Evaluate. 5.4 - 1.3

Answers

5.4-1.3=4.1 is ur answer.
5.4 - 1.3= 4.1 is your answer

A student performed the following steps to find the solution to the equation x^2-2x-8=0. Where did the student go wrong?

Step 1. Factor the polynomial into (x-4) and (x-2)
Step 2. x-4=0 and x-2=0
Step 3. x=4 and x=3

A. The student did not make any mistakes, the solution is correct
B. in step 1
C. in step 2
D. in step 3

Answers

In step 1, because you want to find factors that multiply to -8 and add to -2. So the correct factorization is (x-4)(x+2). The student got the minus sign wrong.

(Then in step 3 the x=3 is also very wrong, but that looks more like a typo).
(Also, it should be x-4=0 OR x+2=0, there is no x for which both factors are 0 at the same time!)

Which is a counterexample that disproves the conjecture? After completing several multiplication problems, a student concludes that the product of two binomials is always a trinomial.

Answers

When you make the product of a binomial of the kind x + a times other binomial that is of the kind x - a, you obtain another binomial (not a trinomial), so any example with that form will be a counterexample that disproves the conjecture:

(x + a) * (x - a) = x^2 - a^2

For example, (x +3) * (x - 3) = x^2 - 9. So, not always the product of two binomials is a trinomial.

Find the angle between the given vectors to the nearest tenth of a degree. u = <-5, 8>, v = <-4, 8>

Answers

Answer: 5.4 degrees

Step-by-step explanation:

look up online "how to find the angle between 2 vectors, and it'll show you how"

Evaluate f(x) when x=9

Answers

if x = 9 then f(x) = 12

answer
12
that is in the range 9≤x<13

f(x) in that range is equal to 12

so f(9)=12

The variable Z is inversely proportional to X. When X is 6, Z has the value 2. What is the value of z . When x = 13
Round to at least the thousandths place if needed.

Answers

Given that z is inversely proportional to x, then:
z α 1/x
hence;
z=k/x
where:
k is the constant of proportionality; 
when x=6, z=2
therefore;
2=k/6
hence;
k=2*6=12

Therefore:
z=12/x
the value of z when x=13 will be:
z=12/13
the answer is 12/13

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