Mariah started to find the solutions of x2 + 4x + 1 = 0. Her work is shown below. x2 + 4x + 1 = 0 x2 + 4x = –1 x2 + 4x + 4 = –1 + 4 (x + 2)2 = 3 Which describes the solutions of the equation?

since -2 and 3 are both rational, the sum and difference are both rational
since -2 and /3 are both rational, the sum and difference are both rational
since -2 is rational and /3 is irrational, the sum and difference are irrational.
Since /2 is rational and /3 is irrational, the sum and difference are irrational.

Answer:

3. 9.2 mL; 4. 0.25 mL

Step-by-step explanation:

3. 12 mL syringe

The arrow points to the first division between 9 mL and 10 mL.

There are five divisions, so

5 divisions = 1.0 mL or

 1 division = 0.2 mL

The reading is  

9.0 mL + 0.2 mL = 9.2 mL

4. 0.5 mL syringe

The arrow points to the fifth division between 0.20 mL and 0.30 mL.

There are 10 divisions, so

10 divisions = 0.10 mL or

   1 division = 0.01 mL

 5 divisions = 0.05 mL

The reading is  

0.20 mL + 0.05 mL = 0.25 mL

Answer:

45.6 ft

Step-by-step explanation:

The room is a rectangle. The perimeter of a rectangle is

perimeter = 2L + 2W

perimeter = 2(12.62 ft) + 2(10.2 ft)

perimeter = 25.24 ft + 20.4 ft

perimeter = 45.64 ft

Since 10.2 ft has only 3 significant digits, the answer must also have only 3 significant digits.

Answer: perimeter = 45.6 ft

Answer:

ANS IS 2m

Step-by-step explanation:

we can solve it by using coordinate geometry

Answer:

Height of the bottom seats is 2 meter.

Step-by-step explanation:

It has been given in the question seats are located on a slope having gradient [tex]\frac{1}{2}[/tex]

We have to find the height h of the bottom seats.

Since gradient = [tex]tan\theta=\frac{1}{2}[/tex]

Therefore, from the figure attached,

[tex]tan\theta =\frac{(12-h)}{20}[/tex]

[tex]\frac{1}{2}=\frac{(12-h)}{20}[/tex]

12 - h = [tex]\frac{20}{2}[/tex]

12 - h = 10

h = 12 - 10

h = 2 m

Therefore, height of the bottom seats if 2 m.

7.0717 million

Lets see:

1 million = 1.000.000

So, 7.0717 million = 7.071.700

7.071.700 can be read as "seven million seventy one thousand and seven hunred"

If you wanna split it you can split in

seven million = 7 million

seventy one thousand = 71 thousand

seven hundred = 7 hundred

Answer:

  the weight of a bag of beans

Step-by-step explanation:

You have an equation representing the total weight of a box, 15 bags of beans, and a bag of rice. You want to know the meaning of the variable b in the equation ...

  0.6 +15b +4 = 25.6

Each term in the equation is the weight of something.

The first term (0.6) is the weight of the empty box.

The second term (15b) is the weight of 15 bags of beans. In this context, we assume the meaning of 'b' is the weight of 1 bag of beans.

The third term (4) is the weight of a bag of rice.

The term on the right of the equal sign (25.6) is the total of the other weights.

The unknown value in the equation is the value of 'b', the weight of a bag of rice. When we solve for that value, we get ...

  4.6 +15b = 25.6

  15b = 21

  b = 21/15 = 7/5 = 1.4

When this value is multiplied by bags, the result is pounds. That means the units of 'b' are "pounds per bag", the weight of one bag of rice.

The solution (b=1.4) represents the weight of one bag of rice.

The solution to the given equation represents the weight of one bag of beans. The variable 'b' represents this weight in the equation, and by solving, we can find this value.

The equation 0.6+15b+4=25.6 represents a situation where a cardboard box, which is empty weighs 0.6 pounds, is filled with 15 bags of beans and a 4-pound bag of rice, leading to a total weight of 25.6 pounds. Here, the variable 'b' represents the weight of one bag of beans. To find this value, we rearrange the equation and isolate 'b', leading to the equation b=(25.6-0.6-4)/15. We then calculate the righthand side to get the weight of a bag of beans. The solution to the equation is the weight of one bag of beans.

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Answer:

The possible dimensions of the region are

52 ft by 16 ft

32 ft by 26 ft

Step-by-step explanation:

Let

x -----> the length of the rectangular region

y ----> the width of the rectangular region

we know that

The perimeter of a rectangle is equal to

[tex]P=2(x+y)[/tex]

Remember that

A kennel owner wants to subdivide  this region into three smaller rectangles of equal  length

so

we also have to take into account the divisions

[tex]P=2(x+y)+2y[/tex]

[tex]P=2(x+2y)[/tex]

we have

[tex]P=168\ ft[/tex]

[tex]168=2(x+2y)[/tex]

simplify

[tex]84=(x+2y)[/tex] -----> [tex]x=84-2y[/tex] -----> equation A

The total area to be enclosed is 832 ft^2

The area is equal to

[tex]A=xy[/tex]

so

[tex]832=xy[/tex] ----> equation B

substitute equation A in equation B

[tex]832=(84-2y)y[/tex]

[tex]832=84y-2y^2[/tex]

[tex]2y^2-84y+832=0[/tex]

Solve the quadratic equation by graphing

The solution are y1=16 ft, y2=26 ft

see the attached figure

For

[tex]y=16\ ft\\x=84-2(16)=52\ ft[/tex]

For

[tex]y=26\ ft\\x=84-2(26)=32\ ft[/tex]

therefore

The possible dimensions of the region are

52 ft by 16 ft

32 ft by 26 ft

Answer:

The combined length is 61 inches

Step-by-step explanation:

we know that

To find out the combined length of all the pieces Meg measured, multiply each measure by the number of pieces and then sum all the values

Let

x -----> the combined length

we know that

we have

1 piece of 3 inches

2 pieces of 5 inches

3 pieces of 6 inches

3 piece of 7 inches

1 piece of 9 inches

so

[tex]x=(1)(3)+ (2)(5)+(3)(6)+(3)(7)+(1)(9)\\x=3+10+18+21+9\\x=61\ in[/tex]

therefore

The combined length is 61 inches

Answer:

(6y + 1) (6y - 1)

Step-by-step explanation:

The binomial can be factored using the difference of squares formula.

:)

Completely validate answer:)

Answer:

Babatunde weigh on the Moon would be 124.8 N

Step-by-step explanation:

* The wight of an object on the earth is mg , where m is the the

  mass of the object in kg and g is the acceleration of gravity which

  is 9.8 m/s²

* The mass of an object on earth is the same as the mass of the

  same object on the moon but the weight of the object on the

  earth is different from the weight of the same object on the

  moon because the gravity on the earth different from on the moon

* The wight on the moon is mg , where m is the the mass of the

  object in kg and g is gravitational field strength on the Moon

  which is 1.6 N/kg

∵ Babatunde has a mass of 78 kg

∵ The mass on the moon = the mass on the earth

∵ On the moon the gravitational field strength is 1.6N/kg

∵ Weight = mg

∴ Babatunde weigh = 78 × 1.6 = 124.8 N

* Babatunde weigh on the Moon would be 124.8 N

Babatunde's weight on the Moon is calculated by multiplying his mass (78 kg) by the Moon's gravitational field strength (1.6 N/kg), resulting in 124.8 newtons.

To calculate Babatunde's weight on the Moon, we use the formula for weight, which is the product of mass and gravitational field strength. On Earth, the average acceleration due to gravity is approximately 9.8 m/s², and on the Moon, it is about 1.6 N/kg. Babatunde's mass on Earth is 78 kg. Therefore, to calculate his weight on the Moon, we multiply his mass by the Moon's gravitational field strength.

Weight on the Moon = Mass × Gravitational field strength on the Moon

Weight on the Moon = 78 kg × 1.6 N/kg

Weight on the Moon = 124.8 N

Babatunde would weigh 124.8 newtons on the surface of the Moon, significantly less than his weight on Earth due to the Moon's lower gravitational pull.

Answer:

3x^3 + 3x^2 − 30x − 48

Step-by-step explanation:

3( x + 2 )( x^2 − x − 8 )

= ( 3( x + 2 ))( x^2 + − x + − 8 )

= ( 3( x + 2 ))( x^2 ) + ( 3( x + 2 ))( −x ) + ( 3( x + 2 ))( −8 )

= 3x^3 + 6x^2 − 3x^2 − 6x − 24x − 48

3x^3 + 3x^2 − 30x − 48

Answer:

The correct option is A) [tex]3x^3+3x^2-30x-48[/tex]

Step-by-step explanation:

Consider the provided expression.

[tex]3\left(x+2\right)\left(x^2-x-8\right)[/tex]

Distribute 3 as shown

[tex]\left(3x+6\right)\left(x^2-x-8\right)[/tex]

Distribute parentheses as shown.

[tex]3xx^2+3x\left(-x\right)+3x\left(-8\right)+6x^2+6\left(-x\right)+6\left(-8\right)[/tex]

[tex]3x^2x-3xx-3\cdot \:8x+6x^2-6x-6\cdot \:8[/tex]

[tex]3x^3-3x^2-24x+6x^2-6x-48[/tex]

Add and subtract like terms

[tex]3x^3+3x^2-30x-48[/tex]

Hence, the correct option is A) [tex]3x^3+3x^2-30x-48[/tex]

Answer:

multiplied

Step-by-step explanation:

Answer:

If a scale factor is greater than 1, then your figure gets bigger.

Step-by-step explanation:

For scale factors, you are multiplying the scale factor to get the desired outcome. If the scale factor is greater than 1, you are multiplying by a whole number, which would be ≥ the original number. If the scale is 1, then it would be = too the original number. If the scale factor is a fraction, then the figure would be scaled down.

~

Answer:

m = 21/16 or 1.325

Step-by-step explanation:

1. 9m/12 - m/12 = 7/8 (find common denominator)

2. 8m/12 = 7/8 (subtract)

3. 64m = 84 (cross multiply)

4. m = 84/64 (solve for m)

5. m = 21/16 (simplify fraction)

~1.325

The value of m is 21/16 or 1.3125.

Given,

3m/4 - m/12 = 7/8

We have to solve for m step by step.

We have,

3m/4 - m/12 = 7/8

Step 1.

Find LCM between 4 and 12 and make 3m/4 and m/12 into one fraction.

LCM of 4 and 12 = 12

( 3 x 3m - m ) / 12 = 7 / 8

( 9m - m ) / 12 = 7 / 8

8m / 12 = 7 / 8

Step 2.

Multiply both sides by 12.

12 x 8m/12 = 12 x 7/8

8m = ( 12 x 7 ) / 8

8m = 84 / 8

Step 3.

Dividing 8 into both sides.

8m/8 = 84 / (8 x 8)

m = 84 / 64

m = 4 x 21 / 4 x 16

m = 21 / 16 or m = 1.3125

Thus the value of m is 21/16 or 1.3125.

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Answer:

2Hours and 30 mins. 2 1/2

Step-by-step explanation:

3x60=180 since there is 60 minutes in an hour There is no possible ways to get an exact number.

Answer:

2.5 hours

Step-by-step explanation:

Just divide your total number of minutes by 60, which is how many minutes are in an hour to receive your answer of 2.5!

Answer:

for a

the integer 1 will be represented by 1 pm the same day

for b

-2 will be represented by 10 am

for C:

12 midnight will be represented by 0

for D:

the integer 10 will be represented by that .

Using a number line, integers can be used to represent the following given day time in hours as shown in the diagram below:

a. Integer 1 represents 1 P.M.

b. Integer -2 represents 10 A.M.

c. Integer -12 represents 12 midnight.

d. Integer 10 represents 10 P.M.

Recall:

Integers on a number line has been shown below to illustrate how they can represent measure of time in hours if 12 noon is integer 0.

From the image given showing the integers on a number line, the following integers and their respective day time they represent are:

a. Integer 1 represents 1 P.M.

b. Integer -2 represents 10 A.M.

c. Integer -12 represents 12 midnight.

d. Integer 10 represents 10 P.M.

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Answer:

a) Order: 0.947 < 0.97 < 1.268 < 1.5

b)Smallest total rainfall = 0.947 meters in Ithaca

c)  100 years total rainfall = [tex]126.8 \text{ meters} = 1.268\times 10^2[/tex]

Step-by-step explanation:

We are given the following data in the question:

                  City:  Rochester    Ithaca    Sara-Toga     New-York

Rainfall(meters):     0.97            0.947          1.5             1.268

a)  Order:

0.947 < 0.97 < 1.268 < 1.5

Ithaca < Rochester < New-York < Sara-Toga

Smallest total rainfall = 0.947 meters in Ithaca

Expanded form: [tex]0.947 = 9\times \frac{1}{10} + 4\times\frac{1}{100} + 7\times \frac{1}{1000}[/tex]

Word form:  seven thousandths and ninety four hundredths.

b) Round off to nearest tenths

 Rochester - 1.0 meters

Ithaca - 0.9 meters  

Sara-Toga - 1.5 meters  

New-York - 1.3 meters

c) [tex]\text{Rainfall in 100 years} = \text{Annual rainfall}\times 100 = 1.268\times 100 = 126.8 \text{ meters}[/tex]

d) 100 years total rainfall = [tex]126.8\text{ meters} = 1.268\times 10^2 = 0.1268\times 10^3[/tex]

The points shifted because we have to multiply 1.268 by 100. This would again result in shifting the point towards right.

Final answer:

The rainfall totals ordered from least to greatest are Ithaca, Rochester, New York City, Saratoga Springs. Rounded to the nearest tenth, New York City would receive 126.8 meters of rain in 100 years, represented as 1.268 x 10^2 with the base ten exponent indicating multiplication by 100.

Explanation:

Ordering Rainfall Totals and Mathematical Operations

To answer the student's question regarding the average annual rainfall totals for cities in New York:

Ordering from least to greatest: Ithaca (0.947 meters), Rochester (0.97 meters), New York City (1.268 meters), Saratoga Springs (1.5 meters). The smallest total rainfall (Ithaca) in word form is nine hundred forty-seven thousandths and in expanded form is 0.9 + 0.04 + 0.007.

Rounding to the nearest tenth: Rochester (1.0 meters), Ithaca (0.9 meters), New York City (1.3 meters), Saratoga Springs (1.5 meters).

Rainfall in 100 years: New York City's rainfall of 1.268 meters every year would result in 126.8 meters of rain in 100 years.

Equation with exponent: The equation to express the total 100-year rainfall for New York City is 1.268 meters x 100 years. Using an exponent, this is written as 1.268 x 102. The digits shift two places to the left because the base ten exponent indicates the value should be multiplied by 100.

The figures above are based on the provided data and standard mathematical operations such as ordering, rounding, and multiplication with exponents.

$300*e^(0.09*3) = $392.99.

the answer is $392.99

Answer:

11

Step-by-step explanation:

So, we can say that

3 × X - 3 = 30

3 × X = 30+3

3 × X = 33

X = 33/3

X = 11

Answer:

we know that

By alternate interior angles

m∠PRD=m∠APR -------> equation

m∠PRD=120°

so

m∠APR=120°

m∠APR=m∠APQ+m∠QPR ---------> equation

m∠APQ=62°

m∠QPR=x°

Substitute the values in the equation 120=62+x

x=120-62

x=53

therefore

the answer is

The measure of angle x is equal to 53 degrees

Because the lines are parallel the lower outside angle given as 155 is equal to the opposite angle, which is made up of X and 62.

To find X subtract 62 from 115:

X = 115 - 62

X = 53

Answer: 0.86 0.875 0.9

Step-by-step explanation: 7/8 is 8.75 in decimal form, so above would be the answer from least to greatest.

Answer: 0.86, 7/8, 0.9 is least to greatest

Step-by-step explanation:

Answer:

four hundred and fifty six thousand six hundred and ninety eight

Answer:

611 miles max

Step-by-step explanation:

250 = 0.09x + 195

-195               -195

  55    = 0.09x

/0.09     /0.09

x=611.11111111111

because of the context of the question, you'd have to round up

x = 611

Hope this helps! If you have any questions ask! :)

Answer:

-3w = 9

w = -3

yes, it is an identity

Answer:

B - 16466

C - 13362

total value - 35170

Step-by-step explanation:

to find B add 11124 to 5342 (11124+5342=16466)

to find C subtract 3104 from 16466 (16466-3104=13362)

total value - add them all together

Answer:

A

Step-by-step explanation:

Answer:

38.5182

Step-by-step explanation:

54 • 0.7133 is 38.5182.

Answer:

Quadrant IV

Step-by-step explanation:

The points (x,y) such that

y < 0 and x>0, i.e. quadrant IV of the plane.

QUESTION:To decrease an amount by 7% what single multiplier would you use?

ANSWER: You want 7% less than 100%, so the answer is (100%-7%)=93% =0.93.

Hope this helped! Enjoy! :)

Answer:

Input

Independent variable

Step-by-step explanation:

we know that

Independent variables, are the values that can be changed or controlled in a given model or equation

Dependent variables, are the values that result from the independent variables

we have the function

[tex]d(t)=50t[/tex]

In this problem

This is a proportional relationship between the variables d and t

The function d(t) represent the dependent variable or the output

The variable t represent the independent variable or input

Answer:

Independent variable

Step-by-step explanation:

Given is a function

[tex]d(t) = 50t[/tex]

We have to find the independent and dependent variable in this equation

In scientific analysis, the independent variable is one which is changed to get some results for tests.  Dependent variable is one which changes according to changes in independent variable

Here we find the term t is independent as it can be changed independently and d(t) can be analysed for various values of t

Thus the dependent variable [tex]d(t)[/tex] a function of t is tested for various values of independent variable t.