Find all solutions of the equation 4x^2−144=0 by factoring the left hand side and using the zero factor property.

Answer:

  ray

Step-by-step explanation:

A ray is a line that extends in one direction from its end point.

Answer:

The answer to your question is: 35 questions worth 2 points and 15 questions worth 3 points.

Step-by-step explanation:

Data

Number of questions = 50

Total points = 115

x = questions worth 2 points

y = questions worth 3 points

Process

write to equations

(1)  ---------------    x + y = 50

(2) --------------    2x + 3y = 115

Solve them by substitution

           x = 50 - y

         2 (50 - y) + 3y = 115

          100 - 2y + 3y = 115

           3y -2 y = 115 - 100

                     y = 15

           x = 50 - 15

            x = 35

Answer:

4660194 metric ton

126802560 gallon

Step-by-step explanation:

1 cm = 0.01 m

6 km = 6000 m

8 km = 8000 m

Volume = 0.01 m x 6000 m x 8000 m =  480000 m³

480000 m³ = 480000000 kg of water (density of water = 1000kg/m³)

103 kg = 1 metric ton

480000000 kg = 480000000 / 103 = 4660194 metric ton

1 m³ = 264.17 gallon

480000 m³ = 480000 x 264.172 = 126802560 gallon

A total of 480,000 metric tons of water fell on the city, which is equivalent to approximately 126,802,560 gallons of water.

To calculate the amount of water in metric tons that fell on the city, we need to first determine the volume of the rainfall which can be calculated by taking the product of the rainfall's depth (1.0 cm), and the area of the city (6 km x 8 km).

Firstly, convert all dimensions into the same unit. Let's use meters: 1.0 cm = 0.01 m, 6 km = 6000 m, 8 km = 8000 m. Therefore, the volume equals 0.01 m x 6000 m x 8000 m = 480,000 m³.

The mass of the water is then found by multiplying the volume by the density of water. Given that the density of water is 1 g/cm³ (or 1000 kg/m³, which is more useful here, as mass needs to be in kg), this calculation gives us a mass of 480,000,000 kg = 480,000 metric tons.

To convert this to gallons, we use the fact that 1 m³ = 264.172 gallons. Therefore, 480,000 m³ = 480,000 x 264.172 = 126,802,560 gallons.

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Answer:

D

Step-by-step explanation:

There are 1.61 km in 1 mi.

10 mi × (1.61 km/mi) = 16.1 km

Answer:

Step-by-step explanation:

You may recognize that you are given two relationships between two unknowns. You can write equations for that.

You are asked for numbers of adult tickets and of student tickets. It often works well to let the values you're asked for be represented by variables. We can choose "a" for the number of adult tickets, and "s" for the number of student tickets. Then the problem statement tells us the relationships ...

  a + s = 800 . . . . . . 800 tickets were sold

  12.50a + 7.50s = 8600 . . . . . . . revenue from sales was 8600

(You are supposed to know that the revenue from selling "a" adult tickets is found by multiplying the ticket price by the number of tickets: 12.50a.)

___

You can solve these two equations any number of ways. One way is to do it by elimination. We can multiply the first equation by 12.50 and subtract the second equation:

  12.50(a +s) -(12.50a +7.50s) = 12.50(800) -(8600)

  5s = 1400 . . . . simplify. (The "a" variable has been eliminated.)

  s = 280 . . . . . . divide by 5

Then the number of adult tickets can be found from the first equation:

  a + 280 = 800

  a = 520

280 student tickets and 520 adult tickets were sold.

520 adult tickets and 280 student tickets were sold.

To solve this problem, we need to set up a system of two linear equations using the given information and then solve for the number of adult and student tickets sold.

Let x be the number of adult tickets sold, and y be the number of student tickets sold.

Given information:

- Total number of tickets sold: [tex]x + y = 800[/tex]

- Total receipts: [tex]12.50x + 7.50y = 8600[/tex]

We have a system of two equations with two unknowns:

[tex]x + y = 800[/tex]

[tex]12.50x + 7.50y = 8600[/tex]

We can solve this system using the substitution method or the elimination method.

Using the substitution method:

From the first equation, [tex]y = 800 - x[/tex]

Substituting this into the second equation:

[tex]12.50x + 7.50(800 - x) = 8600[/tex]

[tex]12.50x + 6000 - 7.50x = 8600[/tex]

[tex]5x = 2600[/tex]

[tex]x = 520[/tex]

Substituting [tex]x = 520[/tex] into the first equation:

[tex]y = 800 - 520 = 280[/tex]

Therefore, 520 adult tickets and 280 student tickets were sold.

By setting up a system of linear equations based on the given information and solving them using algebraic methods, we can find the number of adult and student tickets sold that satisfy the conditions of the total number of tickets and the total receipts.

Answer:

  D' = (4, -1)

Step-by-step explanation:

Translation down by 2 units subtracts 2 from the y-coordinate. The x-coordinate remains unchanged. You can see this in the descriptions of C and C':

Likewise:

__

The translated segment is still a horizontal segment, now at y=-1 instead of at its previous position of y=1.

[tex]\bf \sqrt{5x-9}+1=x\implies \sqrt{5x-9}=x-1\implies 5x-9 = (x-1)^2 \\\\\\ 5x-9=\stackrel{\mathbb{FOIL}}{x^2-2x+1}\implies 5x=x^2-2x+10\implies 0=x^2-7x+10 \\\\\\ 0=(x-5)(x-2)\implies x= \begin{cases} 5\\ 2 \end{cases}[/tex]

Answer:

One ml is equal to a cm3, then

m=2.67g/cm3*30.5cm3

m=81.435g

If we divide this quantity by 1000 to pass this to Kg we get:

m=81.435/1000=0.081435kg

Step-by-step explanation:

Remember the formula of density is density=mass/volume, if we solve for mass we get:

mass=density*volume

The correct answer is:

Option C: 5(2x^5+x^2−3)

A Quick Check:

5*2x^5 is 10x^5

5*x^2 is 5x^2

and 5*-3 is -15

making the equations match

The factored form of the expression 10x⁵ + 5x² - 15 is 5(x⁵ + x² - 3).

A factor is a number that completely divides another number. To put it another way, if adding two whole numbers results in a product, then the numbers we are adding are factors of the product because the product is divisible by them.

Given, A polynomial of degree five which is 10x⁵ + 5x² - 15.

Now, The HCF of 10, 15, and 5 is 5, and the HCF of x⁵, x², and x⁰ is x⁰ = 1.

Therefore,

10x⁵ + 5x² - 15.

= 5x⁰(x⁵ + x² - 3).

= 5(x⁵ + x² - 3).

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Answer: 4,85 meters

Step-by-step explanation:

Using energy we get the velocity when the man gets to the bottom of the hill

mgh=1/2 m v^2

Then the velocity is the squareroot of two times the mass times the gravity constant =9,598 m/s2

Using energy again, we can get the velocity on the edge of the ledge (using the second mass, the one of the man plus the backpack)

1/2 M1 V1^2=1/2 M2 V2^2

We get V2=8,24 m/s2

Then we have to analyze the jump, horizontally, with constant velocity, and vertically, with constant acceleration equals to the gravity constant.

To get the time we analyze the vertical move

Y=1/2 g t^2

t=59 seconds

To get the horizontal distance we use

X= v t

X=4,85 meters.

Answer:

23

Step-by-step explanation:

or 2.8 but try 23 frist

The percentage of increase of total number of students on the honor roll is obtained as 22.97%.

A percentage is a value that indicates 100th part of any quantity.

A percentage can be converted into a fraction or a decimal by dividing it by 100.

And to convert a fraction or a decimal into percentage, they are multiplied by 100.

The number of boys and girls on the honor code last year is given as 132 and 90.

Then, the total number is 132 + 90 = 222.

When, the number of boys increased by 25%, it can be obtained as,

⇒ 132 + 25% × 132 = 165

And, the number of girls increased by 20% can be obtained as,

⇒ 90 + 20% × 90 = 108

Now, the total number of students is 165 + 108 = 273.

The percent increase can be obtained as follows,

Change in the total number ÷ Initial number × 100

⇒ (273 - 222) ÷ 222 × 100 = 22.97%

Hence, the percent value of the increase in the number is 22.97%.

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Answer:

Option A - 342 feet

Step-by-step explanation:

Given : Janice puts a fence around her rectangular garden. The garden has a length that is 9 feet less than 3 times its width.

To find : What is the perimeter of Janice fence if the area of her garden is 5,670 square feet?

Solution :

Let the width of the garden be w=x feet.

The garden has a length that is 9 feet less than 3 times its width.

The length of the garden be l=3x-9 feet

The area of the garden is A=5670 square feet.

The formula of area of garden is [tex]A=l\times w[/tex]

[tex]5670=(3x-9)\times x[/tex]

[tex]5670=3x^2-9x[/tex]

[tex]3x^2-9x-5670=0[/tex]

[tex]x^2-3x-1890=0[/tex]

[tex]x^2-45x+42x-1890=0[/tex]

[tex]x(x-45)+42(x-45)=0[/tex]

[tex](x-45)(x+42)=0[/tex]

[tex]x=45,-42[/tex]

Reject x=-42 as measurement cannot be negative.

The width of the garden is w=45 feet.

The length of the garden is l=3(45)-9=135-9=126 feet.

The perimeter of the garden is [tex]P=2(l+w)[/tex]

[tex]P=2(126+45)[/tex]

[tex]P=2(171)[/tex]

[tex]P=342[/tex]

The perimeter of Janice fence is 342 feet.

Therefore, Option A is correct.

The perimeter of Janice's fence is: [tex]\[ {342 \text{ feet}} \][/tex]

To determine the perimeter of Janice's garden, let's follow these steps:

Step 1: Define Variables

Let ( w ) be the width of the garden in feet.

The length ( l ) of the garden is given by: [tex]\[ l = 3w - 9 \][/tex]

Step 2: Set Up the Area Equation

The area of the rectangular garden is given as 5,670 square feet:

[tex]\[ \text{Area} = l \times w \][/tex]

[tex]\[ 5670 = (3w - 9) \times w \][/tex]

Step 3: Solve the Quadratic Equation

Expand and simplify the equation:

[tex]\[ 5670 = 3w^2 - 9w \][/tex]

Rearrange it to standard quadratic form:

[tex]\[ 3w^2 - 9w - 5670 = 0 \][/tex]

Step 4: Factor or Use the Quadratic Formula

Divide through by 3 to simplify:

[tex]\[ w^2 - 3w - 1890 = 0 \][/tex]

Solve using the quadratic formula [tex]\( w = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a} \)[/tex]:

[tex]\[ a = 1, \, b = -3, \, c = -1890 \][/tex]

[tex]\[ w = \frac{-(-3) \pm \sqrt{(-3)^2 - 4 \cdot 1 \cdot (-1890)}}{2 \cdot 1} \][/tex]

[tex]\[ w = \frac{3 \pm \sqrt{9 + 7560}}{2} \][/tex]

[tex]\[ w = \frac{3 \pm \sqrt{7569}}{2} \][/tex]

[tex]\[ w = \frac{3 \pm 87}{2} \][/tex]

This gives two potential solutions:

[tex]\[ w = \frac{90}{2} = 45 \][/tex]

[tex]\[ w = \frac{-84}{2} = -42 \][/tex]

Since width cannot be negative:

[tex]\[ w = 45 \][/tex]

Step 5: Find the Length

Substitute ( w = 45 ) into the length equation:

[tex]\[ l = 3(45) - 9 \][/tex]

[tex]\[ l = 135 - 9 \][/tex]

[tex]\[ l = 126 \][/tex]

Step 6: Calculate the Perimeter

[tex]\[ P = 2l + 2w \][/tex]

[tex]\[ P = 2(126) + 2(45) \][/tex]

[tex]\[ P = 252 + 90 \][/tex]

[tex]\[ P = 342 \][/tex]

Thus, the perimeter of Janice's fence is: [tex]\[ {342 \text{ feet}} \][/tex]

The answer is 240000

Step-by-step explanation:

When you round 620 to the nearest hundred,you will get 600

and when you round 374 to the nearest hundred,you will get 400

multiplying the product after rounding them will give 600×400

=240000

The estimated product when 620 and 374 are rounded to the nearest hundred and multiplied is 240000.

Product is the output obtained when two numbers are multiplied.

The product has to be obtained of numbers 620 and 374

Rounding to nearest hundred

620 can be written as 600

374 can be written as 400

=> 600 * 400

= 240000

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Answer:

 the quantities do NOT vary directly

Step-by-step explanation:

A graph showing a proportional relationship is a straight line through the origin. This graph goes through (0, 100), so does NOT show a proportional relationship. y does NOT vary directly with x.

Answer:

13665.6 deaths per year

Step-by-step explanation:

We can determine certain statistics based on the information. If 15567 patients where discharge and 245 deaths were recorded, the total number of patients were:

[tex]=15567+245=15812[/tex]

If 75 deaths occured in the first 48 hours we have a death rate of:

[tex]=75/48=1.56[/tex]

1.56 deaths per hour.

We want the death rate per year. If we have the death rate per hour we can determine the death rate per year:

[tex]1.56\cdot{24}\cdot{365}=13665.6[tex]

13665.6 deaths per year

The correct net death rate for the year is [tex]\(\frac{172}{15567}\).[/tex]

To calculate the net death rate for the year, we need to consider the total number of deaths that occurred and the total number of discharges. The net death rate is calculated by dividing the number of deaths by the number of discharges.

 From the given statistics, we have:

- Total discharges: 15,567

- Total deaths: 245

 However, we need to adjust the total deaths to account for the deaths that occurred under 48 hours and the medical examiner's cases, as these might not be included in the net death rate calculation.

- Deaths under 48 hours: 75

- Medical examiner's cases: 8

 The deaths under 48 hours and the medical examiner's cases are typically excluded from the net death rate calculation because they may not reflect the quality of care provided by the hospital. Therefore, we subtract these from the total deaths:

Adjusted deaths = Total deaths - Deaths under 48 hours - Medical examiner's cases

Adjusted deaths = 245 - 75 - 8

Adjusted deaths = 162

 Now, we can calculate the net death rate:

Net death rate =[tex]\(\frac{\text{Adjusted deaths}}{\text{Total discharges}}\)[/tex]

Net death rate = [tex]\(\frac{162}{15567}\)[/tex]

This gives us the net death rate for the year based on the adjusted number of deaths."

the result of subtracting[tex]\( (4x^2 - x) \)[/tex]  from [tex]\( -3x^2 \) is \( \boxed{-7x^2 + x} \).[/tex]

To subtract [tex]\( (4x^2 - x) \) from \( -3x^2 \)[/tex], we need to distribute the negative sign to each term inside the parentheses and then perform the subtraction.

Given:

[tex]\( -3x^2 - (4x^2 - x) \)[/tex]

Step 1: Distribute the negative sign inside the parentheses:

[tex]\( -3x^2 - 4x^2 + x \)[/tex]

Step 2: Combine like terms:

[tex]\( (-3x^2 - 4x^2) + x \)[/tex]

[tex]\( = -7x^2 + x \)[/tex]

Therefore, the result of subtracting[tex]\( (4x^2 - x) \)[/tex]  from [tex]\( -3x^2 \) is \( \boxed{-7x^2 + x} \).[/tex]

Answer:

C - 4x4+14x2y+49y2

Step-by-step explanation:

Just took the test

To determine which option is a factor of the given expression, we need to check each option individually. After checking, we find that option 2, 2x^2 + 7y, is a factor.

To determine which of the given options is a factor of the expression 24x^6 - 1029y^3, we need to check each option individually.

Option 1: 24 - We can verify if 24 is a factor by dividing 24x^6 - 1029y^3 by 24 and checking if there is no remainder.

Option 2: 2x^2 + 7y - We can substitute values for x and y and simplify the expression to see if it equals zero for any values.

Option 3: 4x^4 + 14x^2y + 49y^2 - We can substitute values for x and y and simplify the expression to see if it equals zero for any values.

After checking each option, we can determine that option 2, 2x^2 + 7y, is a factor of the expression 24x^6 - 1029y^3.

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Answer:

Let the number of hours traveled by train be "x".

The x = the number of hours traveled by plane.

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

Equation:

train distance + plane distance = 1300 miles

50x + 275x = 1300

x(325) = 1300

x = 4 hours

---

The trip took 8 hrs.

Step-by-step explanation:

Trust me

Answer:

The answer to your question is: time = 4 hours

Step-by-step explanation:

Data

Total distance = 1300 miles

train v = 50 mi/h      time is the same        distance = x

plane v = 275 mi/h                                      distance = 1300 - x

t = ?

Formula

v = d/t

Process

Train  t = d/v           t = x / 50

Plane  t = d/ v         t = (1300 - x) / 275

                   x / 50   =  (1300 - x) / 275

                  275 x  = 50 (1300 - x)

                  275 x = 65000 - 50x                   solve for x

                  275x + 50x = 65000

                  325x = 65000

                  x = 65000/325

                  x = 200

   Time with train

                                t = 200 / 50 = 4 hours

Time with plane

                               t = (1300 - 200) / 275

                               t = 1100 / 275 = 4 hours

Answer:

Step-by-step explanation:One of the things you can use for that is RAP so here's how this goes:

R:A skier is trying to decide whether or not to buy a season ski pass. A daily pass costs ​$61. A season ski pass costs ​$400. The skier would have to rent skis with either pass for ​$25 per day. How many days would the skier have to go skiing in order to make the season pass less expensive than the daily​ passes?

A:what do we want to know?(Understand the problem)

How many days would the skier have to go skiing in order to make the season pass less expensive than the daily passes

What do we already know?

A daily pass costs $61,A season ski pass costs $400,The skier would have to rent skis with either pass for ​$25 per day.

what is the plan??

Carry out the plan.Show work for your solution

Hopefully I helped a little

                                       blessings,lilabear

Answer:

(3,7) for the first line, and (12,0) for the second one.

Step-by-step explanation:

Hi Isabella,

1) The Midpoint of a line, when it comes to Analytical Geometry, is calculated as Mean of two points it follows:

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

2) Each segment has two endpoints, and their midpoints, namely:

a) (1,-9) and its midpoint (2,-1)

b) (-2,18) and its midpoint (5,9)

3) Calculating. You need to be careful to not sum the wrong coordinates.

So be attentive!

The first line a

[tex]2=\frac{1+x_{2} }{2}\\  4=1+x_{2}\\  4-1=-1+1+x_{2} \\ x_{2}=3\\-1=\frac{y_{2}-9}{2}\\-2=y_{2}-9\\+2-2=y_{2}-9+2\\ y_{2}=-7[/tex]

So (3,7) is the other endpoint whose segment starts at (1,-9)

The second line b endpoint at (-2,18) and its midpoint (5,9)

[tex]5=\frac{-2+x_{2} }{2} \\ 10=-2+x_{2} \\ +2+10=+2-2+x_{2}\\ x_{2}=12 \\ \\ 9=\frac{18+y_{2} }{2} \\ 18=18+y_{2} \\ -18+18=-18+18+y_{2}\\ y_{2} =0[/tex]

So (12,0) it is the other endpoint.

Take a look at the graph below:

Answer:(3,7) for the first line, and (12,0) for the second one.

Step-by-step explanation:

Hi Isabella,

1) The Midpoint of a line, when it comes to Analytical Geometry, is calculated as Mean of two points it follows:

Step-by-step explanation:

Answer:

The Andrew equitation is 4 times more bigger than Peter equation.

Step-by-step explanation:

(16x-8x=40) is:

4*(4x-2=10)=(16x-8=40)

Answer:

The answer to your question is: 4.2 x 10⁻²

Step-by-step explanation:

Information: (3 x 10⁶) x (1.4 x 10⁻⁸)

                    3 x 1.4 = 4.2                                   we just multiply the integers

                   10⁶ + 10⁻⁸ = -2                                then we add 6 and -8

                   4.2 x 10⁻²                                   now join the results and -2 will be a power of ten.

Answer:

  91.8 ft

Step-by-step explanation:

So we can talk about the diagram, let's name a couple of points. The base of the tree is point T, and the top of the tree is point H. We want to find the length of TH given the length AB and the angles HAT and ABT.

The tangent function is useful here. By its definition, we know that ...

  TA/BA = tan(∠ABT)

and

  TH/TA = tan(∠HAT)

Then we can solve for TH by substituting for TA. From the first equation, ...

  TA = BA·tan(∠ABT)

From the second equation, ...

  TH = TA·tan(∠HAT) = (BA·tan(∠ABT))·tan(∠HAT)

Filling in the values, we get ...

  TH = (24.8 ft)tan(87.3°)tan(9.9°) ≈ 91.8 ft

The height h of the tree is about 91.8 ft.

Answer:

12x²√2z

Step-by-step explanation:

Given to simplify

3√32x⁴z

This can be written as

3* √32 *√x⁴ *√z--------------------------break down into terms

3*√16*√2*√x⁴*√z------------------------identifying perfect squares

3 * 4* √2 * x² *√z---------------------------collect like terms

12 * x² * √2 * √z-----------------------multiplication

12x² *√2z------------------------puting terms under same root together

12x²√2z

The answer will be 13

since he give you the C and X

you just need to add them and then subtract them from 90 degree

51+26-90=13

I hope this will helps you.

Answer:

Step-by-step explanation:

1. The magnitude of the multiplier is 6, so the magnitude of the new vector is 6×(15 m) = 90 m. The sign on the multiplier is negative, so the new vector will be in the opposite direction of East. It will be 90 m West.

__

2. The components can be found from ...

  (8.9 m/s)(cos(-40°), sin(-40°)) ≈ (6.82, -5.72) m/s

__

One or both of the components will usually be irrational if the angle is a rational number of degrees not a multiple of 90°. Here, we have rounded to 2 decimal places.

Answer:

18 quarters

30 pennies

15 dimes

Step-by-step explanation:

Let number of quarters be q, number of pennies be p, number of dimes be d

The value of pennies is 0.01, the value of quarters is 0.25 and value of dimes is 0.10.

Jack has 63 pennies, dimes, and quarters worth $6.30:

We can write:

p + q + d = 63

0.01p + 0.25q + 0.10d = 6.30

Also, the number of dimes is three less than the number of quarters:

We can write:

d = q - 3

Now we have written 3 equations. Replacing 3rd equation in 1st gives us:

p + q + (q-3) = 63

p + 2q -3 = 63

p + 2q = 66

Solving for p:

p = 66 - 2q

Now we can use this and the 3rd equation and replace p and d with q:

0.01p + 0.25q + 0.10d = 6.30

0.01(66-2q) + 0.25q + 0.10(q-3) = 6.30

Solving for q, gives us:

[tex]0.01(66-2q) + 0.25q + 0.10(q-3) = 6.30\\0.66-0.02q+0.25q+0.10q-0.3=6.30\\0.36+0.33q=6.30\\0.33q=5.94\\q=18[/tex]

There are 18 quarters

Since, p = 66 - 2q, there are:

p = 66 - 2 (18) = 30 pennies

Also,

d = q - 3, so d = 18 - 3 = 15 dimes

Hence, there are:

18 quarters

30 pennies

15 dimes

I think it 8 I think this is the right answer

Answer:

g(3) = 34

Step-by-step explanation:

To evaluate g(3) substitute x = 3 into g(x), that is

g(3) = 4(3)² - 3(3) + 7 = (4 × 9) - 9 + 7 = 36 - 9 + 7 = 34

Answer:

k=3

I mean the third choice

Step-by-step explanation:

f(x) = x-1

The required value of k is 3. Option C is correct.

Given that,
To find the value of k in the data set such that the data set represents a linear function.

Functions are the relationship between sets of values. e g y=f(x), for every value of x there is its exists in a set of y. x is the independent variable while Y is the dependent variable.

Here,
The slope of the function,
x, f(x) = (7,6) and (9,8)
Slope = 8 - 6 / 9 - 7
Slope = 2 / 2 = 1

Equation,
y + 3 = 1 (x + 2)
y = x - 1
Now at x = 4 : f(x) = k
k = 4 - 1
k = 3

Thus, the required value of k is 3. Option C is correct.

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Answer:

[tex]y = - 2000x + 14000[/tex]