What do the following two equations represent? 4x-2y=-5 and -2x+3y=-3
Choose 1 answer:
A) equal lines
B) parallel lines
C) perpendicular lines
D) none of the above

*40 points*

8.3524 equals the expression c - 2ab if a = 2.4 b = 0.237 c = 9.49

Step-by-step explanation:

The given is:

We need to find the value of the expression c - 2ab

∵ The expression is c - 2ab

∵ a = 2.4

∵ b = 0.237

∵ c = 9.49

- Substitute the values of a , b and c in the expression to find its value

∴ 9.49 - 2(2.4)(0.237) = 9.49 - 2(0.5688)

∴ 9.49 - 2(2.4)(0.237) = 9.49 - 1.1376

- Subtract the two numbers

∴ 9.49 - 2(2.4)(0.237) = 8.3524

8.3524 equals the expression c - 2ab if a=2.4 b=0.237 c=9.49

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Both Henry and Colin have a ratio of 4, so Colin gets the same amount as Henry, so we know Colin has 56.

Brian's ratio is 5, so for every 4 Colin gets, brian gets 5 ( 1 more).

Divide Colin's quantity by 4 :

56/4 = 14

Brain gets 14 more.

Answer:

210 people.

Step-by-step explanation:

Here is the correct question: At a school fair, 70% of the people are under 16 years old. One third of the people  remaining are teachers. If there are 21 teachers at the fair, how many people are there at the fair?

Now, solving to find total number people in the fair.

Lets assume total number of people in the fair is "x".

As given, there is 70% of total number of people are under 16 year old.

∴ People under 16 year old= [tex]70\% of x= \frac{7x}{10}[/tex]

Next, finding the number of remaining people.

∴ Number of remaining people= [tex]x-\frac{7x}{10} = x-0.7x[/tex]

Number of remaining people is 0.3x

As given, One third of the people  remaining are teachers.

∴ Number of teachers= [tex]\frac{1}{3} \times 0.3x= 0.1x[/tex]

As given there are 21 teachers at the fair.

⇒ [tex]0.1x= 21\ teachers[/tex]

∴ x= [tex]\frac{21}{0.1} = 210[/tex]

Hence, total number of people in the fair are 210.

Answer:

-1/16

Step-by-step explanation:

Answer:

x = 12

Step-by-step explanation:

both (x+5) and (2x-7) are corresponding angles formed by an intersection between a transversal and 2 parallel lines.

hence they are equal in value

x+5 = 2x-7

x - 2x = -7 - 5

-x = -12

x = 12

Answer: x=12

Step-by-step explanation:

Answer:

Step-by-step explanation:

Curved surface Area = 2πrh

Area of its bases = 2πr²

6* Area of its bases = 4 * Curved surface Area

6 * 2πr² = 4 *2πrh

r²  / r = 4 * 2* π*12 / 6 * 2 * π   { substituting h =12 cm}

r = 4*2

r = 8 cm

Curved surface Area = 2πrh

= 2 * 3.14 * 12 * 8

= 602.88 Sq. cm

Answer:

603.42

Step-by-step explanation:

Curved Surface Area = 2πrh sq.cm

Area of the base = πr² sq. cm

Sum area of the base = πr² + πr² = 2πr² sq.cm

                               A.T.Q

4(2πrh) = 6x2πr²

8πrh = 12πr²

2h = 3r

r = 8 cm

Curved Surface Area = 2πrh

2x22/7x8x12

4224/7

603.42

Answer:

Step-by-step explanation:

You would require the table with the number of males and females who prefer either pink or yellow lemonade at the state fair.

                      Pink Lemonade         Yellow Lemonade       TOTAL

Male                    156                                104                          260

Female                  72                               48                          120

TOTAL                 228                               152                         380

P(pink lemonade | female) = 72 / (48 + 72) = 72 / 120 = 0.6

P(pink lemonade) = (156 + 72) / (156 + 72 + 104 + 48) = 228 / 380 = 0.6

Therefore, The event "prefers pink lemonade" and "female" are independent because P(pink lemonade | female) = P(pink lemonade) = 0.6

Answer:

P(pink lemonade | female) = P(pink lemonade) = 0.6.

Step-by-step explanation:

The equation of line perpendicular to 4y = x-8 passing through (3,-3) is:

[tex]y = -4x+9[/tex]

Step-by-step explanation:

Given equation of line is:

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

We have to convert the given line in slope-intercept form to find the slope of the line

So,

Dividing both sides by 4

[tex]\frac{4y}{4} =\frac{x-8}{4}\\y = \frac{1}{4}x-\frac{8}{4}\\y = \frac{1}{4}x-2[/tex]

Let m1 be the slope of given line

Then

[tex]m_1 = \frac{1}{4}\\[/tex]

Let m2 be the slope of line perpendicular to given line

As we know that produt of slopes of two perpendicular lines is -1

[tex]m_1.m_2 = -1\\\frac{1}{4} . m_2 = -1\\m_2 = -1*4\\m_2 = -4[/tex]

The slope intercept form of line is given by:

[tex]y = m_2x+b[/tex]

Putting the value of slope

[tex]y = -4x+b[/tex]

to find the value of b, putting (3,-3) in equation

[tex]-3 = (-4)(3) + b\\-3 = -12 +b\\b = -3+12\\b = 9[/tex]

Putting the value of b in the equation

[tex]y = -4x+9[/tex]

Hence,

The equation of line perpendicular to 4y = x-8 passing through (3,-3) is:

[tex]y = -4x+9[/tex]

Keywords: Equation of line, slope

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Final answer:

The result is the equation f(x) = -4x + 9 in function notation.

Explanation:

To find the equation of a line that is perpendicular to another and passes through a given point, follow these steps:

Therefore, the equation of the line in function notation is f(x) = -4x + 9.

36km per hour

Step-by-step explanation:

Answer:

c

Step-by-step explanation:

Answer:

1

Step-by-step explanation:

rise over run 4/4=1

Paulo's family has 1 hour and 45 minutes before the trip to Scenic Lake Park after their arrival at the reunion.

The question asks how long Paulo's family has before the trip to Scenic Lake Park if they arrived at a family reunion at 8:30 A.M. and the trip is scheduled to start at 10:15 A.M. To solve this, we need to calculate the time difference between 8:30 A.M. and 10:15 A.M.

Here's how you calculate the time difference:

Answer:

  0

Step-by-step explanation:

When any number or expression is divided by one of its factors, the remainder is zero.

Answer:

$37.33 dollars

Step-by-step explanation:

16 x 7/3= 112/3

d=37.33

Answer:

this should be correct.

Answer:

Solutions are -10 and 26

Step-by-step explanation:

( - the abolute sign I'm using

( x - 8 ) + 2 = 20

( x - 8 ) = 18

x - 8 = 18 (postive case)

x - 8 + 8 = 18 + 8

x = 26

( x - 8 ) = 18

x - 8 = -18 (negative case)

x - 8 + 8 = -18 + 8

x = -10

Answer:

Step-by-step explanation:

The vertex is of the form (h, k).  The general equation of a quadratic in vertex form is

[tex]y=(x-h)^2+k[/tex]

where h is the x coordinate of the vertex and k is the y coordinate of the vertex.  The important thing to remember is that the "x -" part of the formula is constant, it doesn't change.  So if our expression inside the parenthesis is

(x + 3), it is understood to be (x - (-3)) which indicates movement to the left.  The "+ k" part is not taken literally.  If we have a + 2 at the end of our equation we are moving up 2; if we have a -1 at the end, we are moving down 1.  Our vertex then is located at (-3, -1)

Answer:

5x + 32 < 50

Step-by-step explanation:

On a particular airline, bags checked in must weigh less than 50 pounds. Betty packed 32 pounds of clothes and five gifts that weigh the same amount.

If each gift weighs w pounds, then the weight of five gifts will be 5w pounds and an additional 32 pounds of clothes will make it total (32 + 5w) pounds.  

Now, this total weight has to be less than 50 pounds.

Therefore, the inequality equation that can be used to find the possible weight of each gift, w is  

5x + 32 < 50 (Answer)

The sale price of the service is $25.50.

Given that,

We need to find out the sale price

So, the sale price is

= $30 - (15% of $30)

= $30 - $4.50

= $25.50

Therefore we can conclude that the sale price of the service is $25.50.

Learn more: brainly.com/question/20418815

Answer:

2

Step-by-step explanation:

Answer: Option B.

Step-by-step explanation:

For this exercise it is important to remember that, by definition, a relation is a function if and only if each input value has an unique output value.

The input values are the values of the variable "x" and the output values are the values of the variable "y".

You can observe in the table shown in the picture, that the input value -2 has two different output values:

[tex]x=-2,y=3\\\\x=-2,y=-13[/tex]

Notice that the input vale -1 has two different output values too:

[tex]x=-1,y=-1\\\\x=-1,y=-9[/tex]

Therefore, based on this, you can conclude that the information given in the table is a relation but not a function.

Final answer:

To find the third angle of a triangle, add the two known angles and subtract from 180 degrees. In this case, the third angle measures 90 degrees since the sum of the two given angles is 90 degrees.

Explanation:

When determining the measure of the third angle in a triangle, we utilize the fundamental property that the sum of all angles in a triangle equals to 180 degrees. Given that two of the angles measure 18° and 72°, we can find the third angle by subtracting the sum of these two angles from 180°.

The calculation is as follows:

Therefore, the measure of the third angle in the triangle is 90 degrees.

Answer:

the answer is x=2

I used math-way

Answer:

Yes, because there are no repeated input values.

Step-by-step explanation:

*This would not be a function IF any input value (x-value) was repeated. In functions, x-values CANNOT be repeated, but y-values CAN be repeated.

I hope this helps!

- sincerelynini

Answer:

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

Step-by-step explanation:

you can use process of elimination on this one just distribute the equations:

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

6x^2-15x+4x-10 <------ Combine like terms

6x^2-11x-10

Final answer:

Factor completely [tex]6x^2[/tex] - 11x - 10 to find the equivalent binomials involves finding two numbers that multiply to -60 and add to -11. In this case, the numbers are -15 and +4, and using factor by grouping, the correct factorization is (3x + 2)(2x - 5).

Explanation:

When asked to factor the expression [tex]6x^2[/tex] − 11x − 10 completely, we're looking for two binomial expressions that multiply together to produce the original quadratic equation. To do this, we seek two numbers that multiply to give [tex]6x^2[/tex] times -10 (which is -[tex]60x^2[/tex]) and add to give -11x. Factoring is a method to express an equation as a product of its factors.

Let's find two such numbers: -15 and +4. These numbers give a product of -60 and a sum of -11, which fits our criteria. Now we replace the middle term (-11x) with -15x+4x to use factor by grouping.

Original equation: [tex]6x^2[/tex] − 11x − 10
Rewritten with new terms: [tex]6x^2[/tex] − 15x + 4x − 10
Factor by grouping: ([tex]6x^2[/tex] − 15x) + (4x − 10)
Factor out common terms: 3x(2x − 5) + 2(2x − 5)
Factor out the common binomial: (2x − 5)(3x + 2)

The completely factored form of the quadratic equation is (3x + 2)(2x − 5).

Answer:

16 hours and 20 minutes.

Step-by-step explanation:

Please consider the complete question.

Rita's family is moving to Grand Junction to Dallas, which is 980 miles. The moving van averages 60 miles each hour. About how many hours does the van take to reach Dallas?

To find the time taken by van to reach Dallas, we will divide total distance by speed.

[tex]\text{Time}=\frac{\text{Distance}}{\text{Speed}}[/tex]

[tex]\text{Time taken to reach Dallas}=\frac{980\text{ Miles}}{60\frac{\text{ Miles}}{\text{Hour}}}[/tex]

[tex]\text{Time taken to reach Dallas}=\frac{980\text{ Miles}}{60}\times \frac{\text{ Hour}}{\text{Miles}}[/tex]

[tex]\text{Time taken to reach Dallas}=\frac{98}{6}\text{ Hour}[/tex]

[tex]\text{Time taken to reach Dallas}=16.3333\text{ Hour}[/tex]

Let us convert 0.3333 hours into minutes by multiplying 0.3333 by 60.

[tex]0.3333\times 60=19.998\approx 20[/tex]

Therefore, it will take 16 hours and 20 minutes for the van to reach Dallas.

Final answer:

To calculate the time it takes for the van to reach Dallas, divide the distance from Grand Junction to Dallas by the average speed of the van.

Explanation:

To calculate the time it takes for the van to reach Dallas, we need to divide the distance from Grand Junction to Dallas by the average speed of the van.

The distance from Grand Junction to Dallas is not provided in the question, so we cannot calculate the exact time taken. However, if we are given the distance, we can use the formula:

Time = Distance / Speed

For example, if the distance is 300 miles, and the van's average speed is 60 miles per hour, then the time taken would be:

Time = 300 / 60 = 5 hours

The question asks for equivalent expressions to 3-8/3-4. After clarifying and simplifying the expression, we determined that the equivalent expressions are 3-12 (A) and 13/12 (F).

The question is asking us to determine which expressions are equivalent to 3−83−4. First, let's clarify this expression. The symbols − and − can stand for subtraction or negative signs, making the expression ambiguous. However, we can interpret this as a subtraction problem with mixed numbers, which would be processed as 3 minus 8 thirds minus 4. Converting the mixed numbers to improper fractions, we get: 3−(8/3)−4 which simplifies to (9/3)−(8/3)−(12/3). This simplifies to 1/3−(12/3), or 1/3− 4, which then further simplifies to −(⅔).

When we look for equivalent expressions, we have the following options:

Question:

Set up a right triangle model for this problem and solve by using a calculator. Follow the models above,

A photographer stands 60 yards from the base of a lighthouse and observes that the angle between the  ground and the top of the lighthouse is 41° How tall is the lighthouse?

Answer:

The height of lighthouse is 52.2 yards

Solution:

Given that photographer stands 60 yards from the base of a lighthouse and observes that the angle between the  ground and the top of the lighthouse is 41 degree

The diagram is attached below

Consider a right angled triangle ABC

AB is the height of the lighthouse

BC is the distance between the base of a lighthouse and Photographer

As per given, BC = 60 yards

Angle between the  ground and the top of the lighthouse is 41 degree

Angle ACB = 41 degree

To find: height of lighthouse i.e AB = ?

We know that,

[tex]tan(\angle ACB) = \frac{Perpendicular}{Base}[/tex]

Here Base is BC and perpendicular is AB

[tex]\tan 41^{\circ}=\frac{A B}{B C}[/tex]

Substituting the values,

[tex]\begin{aligned}&\tan 41^{\circ}=\frac{A B}{60}\\\\&0.8692=\frac{A B}{60}\\\\&A B=0.8692 \times 60=52.157 \approx 52.2\end{aligned}[/tex]

Thus the height of lighthouse is 52.2 yards

Answer:

0.55 would be the decimal form

Step-by-step explanation: