The sum of two numbers is 14. When one number is added to twice the other number, the result is 25. Find the numbers

Answer:

see the explanation

Step-by-step explanation:

we know that

A Rational Number is a number that can be made by dividing two integers

we have

[tex]\frac{\sqrt{2}}{8}[/tex]

[tex]\sqrt{2}[/tex] ----> is not a integer

so

The given number cannot be rewritten as the quotient of two integers

therefore

The given number is irrational

Student A is incorrect because is a irrational number and not all fractions are rational

Student B reasoning is incorrect, because there are fractions that have as numerator an irrational number and can be rational numbers

example

[tex]\frac{\sqrt{2}}{3\sqrt{2}}=\frac{1}{3}[/tex] ----> is a rational number and the numerator is a irrational number

Student A incorrectly claims √2/8 is rational because it can be written as a fraction. Student B is correct, stating that √2/8 is irrational because √2 is irrational, and dividing it by 8 doesn't change its irrationality.

Let's evaluate the reasoning of both students A and B and correct any errors:

Student A:

Student A's reasoning is incorrect. They claim that √2 / 8 is rational because it can be written as a fraction. However, being able to write a number as a fraction doesn't necessarily make it rational. The key point is whether the number can be expressed as a ratio of two integers, and in this case, √2 cannot be expressed as a simple fraction. √2 is known to be an irrational number, and when you divide an irrational number by 8, the result remains irrational.

Student B:

Student B's reasoning is correct. They state that √2 / 8 is irrational because √2 is irrational. This is accurate. The division of an irrational number by a rational number does not change its irrationality. Therefore, √2 / 8 is indeed an irrational number.

In summary, Student B provides the correct reasoning, while Student A's reasoning is flawed.

Learn more about rational and irrational number here:

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Answer:

15-2w-2=2(w-15)-1

15-2w-2=2w-30-1

-2w-2w=-30-1-15+2

0=-44

No solution

This is because -44 can never equal 0

Step-by-step explanation:

Answer: b

Step-by-step explanation:

ok, lets see the answers one for one.

a) in this case, t can be 4, if t= 4 then t + 1 = 5 and the inequality is false.

b) in this case, the maximum vale of t is 2, then 2 + 1 = 3, the inequality is true here, and all the other numbers in the set is smaller than 2, then all this set keeps the inequality true.

c and d) both sets allow to take, for example, t= 10, wich makes the inequality false.

now in this type of exercises, you should se the biggest and lowest number that keeps the inequality true, in this case the biggest is 2, because 2 + 1 = 3, and there is no lowest limit because any negative number + 1 will be less than 3. With those limits then you can figure the set of valid solutions with all the numbers in between.

Final answer:

The solution to the inequality 3 ">=" t + 1 is option b) {t | t ">=" 2}, which means that t is any number less than or equal to 2.

Explanation:

Before solving the inequality 3 ">=" t + 1, first, let's isolate the variable t. To do that, we subtract 1 from both sides of the inequality:

3 - 1 ">=" t + 1 - 1

2 ">=" t

This can be read as 't is less than or equal to 2' or 't must be any number that is 2 or smaller.' Therefore, the correct answer is:

{t | t ">=" 2}

When comparing with the question options, it is clear that option b) matches our solution.

Thus, option b) {t | t ">=" 2} is the correct answer to the inequality given in the question.

Answer:

a. Number of flour cups needed = 4 cups

b. Number of cookies that can be baked = 240 cookies

Explanation:

We are given that:

1 cup of flour is needed to make 2 dozen cookies

To solve the two parts of this question, we will simply use cross multiplication

Part a:

1 cup of flour .......................> 2 dozen cookies

x cups of flour ....................> 8 dozen cookies

[tex]x = \frac{8*1}{2} = 4[/tex] cups

Therefore, 4 cups of flour are required to make 8 dozen cookies

Part b:

1 cup of flour .................> 2 dozen cookies

10 cups of flour ............> y dozens of cookies

[tex]y=\frac{10*2}{1} = 20[/tex] dozens of cookies

This means that, 10 cups of flour can make 20 dozen cookies

However, here we are asked about the number of cookies, not the number of dozens

We know that 1 dozen contains 12 parts

This means that:

1 dozen cookies = 12 cookies

Therefore:

20 dozens cookies = 20 × 12 = 240 cookies

Hope this helps :)

Answer:

c.) 4 2/3

Step-by-step explanation:

look at the screenshot below it'll explain the answer

Answer: Andy has 30 dollars left

Step-by-step explanation: 38 - 5 - 3 = 30

Answer:

$30

Step-by-step explanation:

Answer:

6.5

Step-by-step explanation:

Answer:

7 buses

Step-by-step explanation:

when doing a problem like this you have to divide the larger group of people by the smaller group

78 divided by 12 = 6.5

if u answered this multiplication problem correctly you would get 6.5 but u cannot put .5 people on a bus lol. so therefore u are not done yet... so u need to round up

here's a poem to help with ur rounding...

Find a place look next door

4 or less let it rest

5 or more raise the score!!!

so in conclusion your answer would be 7!

Answer:

1,840 units squared

Step-by-step explanation:

Answer:

all work is pictured and shown

Answer:

x = [tex]\displaystyle\frac{11}{4}[/tex] or 2 [tex]\displaystyle\frac{3}{4}[/tex]

Step-by-step explanation:

1. Subtract both sides of the equation by [tex]\displaystyle\frac{1}{4}[/tex].

[tex]\displaystyle\frac{1}{4} - \frac{1}{4}  + x = 3 - \frac{1}{4}[/tex]

x = [tex]\displaystyle\frac{11}{4}[/tex]

2. (Optional Step) Convert the improper fraction to a mixed number

x = [tex]\displaystyle\frac{11}{4}[/tex]

↓

[tex]x = 2\displaystyle\frac{3}{4}[/tex]

Answer:

(12,10)

Step-by-step explanation:

Answer: 9

Step-by-step explanation:

6 divided by 2/3 = 9

In 6 cups of cereal, there are 9 servings of 2/3 cup.

To find out how many 2/3-cup servings are in 6 cups of cereal, we need to divide the total cups of cereal by the size of each serving. In this case, we divide 6 by 2/3. To divide a whole number by a fraction, we can multiply the whole number by the reciprocal of the fraction. The reciprocal of 2/3 is 3/2, so we have 6×3/2 = 9 cups in total. Therefore, there are 9 servings of 2/3 cup in 6 cups of cereal.

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Answer:

Step-by-step explanation:

Hello:

the equation is : y = ax+b

the slope is a : a×(2) = -1......( perpendicular to a line with a slope of 2 for : y=2x+1)

a =-1/2          y=(-1/2)x+b

the line that passes through (6, 2) : 2 = (-1/2)(6)+b

b = 5

the equation is :  y  = (-1/2)x+5

You can use the fact that perpendicular lines have slopes such that their multiplication ends up as -1.

The equation of the line perpendicular to line y = 2x + 1 and passing through (6,2) point coordinate is given as

[tex]y = -\dfrac{1}{2}x + 5[/tex]

Suppose that first straight line has slope 's'

Let another straight line be perpendicular to this first line.

Let its slope be 'a'

Then due to them being perpendicular, they have their slopes' multiplication as -1

or

[tex]s \times a = -1\\\\a = -\dfrac{1}{s}[/tex]

If the slope of a line is m and the y-intercept is c, then the equation of that straight line is given as:

[tex]y = mx + c[/tex]

The first line y = 2x + 1 is in slope intercept form and its slope is s = 2

Now, let the second line which is perpendicular to this line and passing through (6,2) coordinate be

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

Then as both lines are perpendicular, thus

[tex]a = -\dfrac{1}{s} = -\dfrac{1}{2}[/tex]

Thus, equation of second line is

[tex]y = -\dfrac{1}{2}x + c[/tex]

Since this line passes through coordinate (6,2), thus, this point coordinate should satisfy the equation of line as an equation is true for all points the graph represented by it passes through.

Thus,

[tex]y = -\dfrac{1}{2}x + c[/tex]

[tex]2 = -\dfrac{1}{2} \times 6 + c\\\\2 = -3 +c\\\\c=2+3 = 5[/tex]

Thus, equation of the second line is

[tex]y = -\dfrac{1}{2}x + 5[/tex]

Thus,

The equation of the line perpendicular to line y = 2x + 1 and passing through (6,2) point coordinate is given as

[tex]y = -\dfrac{1}{2}x + 5[/tex]

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Answer:

20 square units

Step-by-step explanation:

we know that

The area of rectangle is equal to

[tex]A=LW[/tex]

In this problem

[tex]L=WX=ZY\\W=WZ=XY[/tex]

the formula to calculate the distance between two points is equal to

[tex]d=\sqrt{(y2-y1)^{2}+(x2-x1)^{2}}[/tex]

Find the distance WX

we have

W(-3,1), X(3,3)

substitute the values in the formula

[tex]d=\sqrt{(3-1)^{2}+(3+3)^{2}}[/tex]

[tex]d=\sqrt{(2)^{2}+(6)^{2}}[/tex]

[tex]d_W_X=\sqrt{40}\ units[/tex]

Find the distance XY

we have

X(3,3),Y(4,0)

substitute the values in the formula

[tex]d=\sqrt{(0-3)^{2}+(4-3)^{2}}[/tex]

[tex]d=\sqrt{(-3)^{2}+(1)^{2}}[/tex]

[tex]d_X_Y=\sqrt{10}\ units[/tex]

Find the area of rectangle

[tex]A=(WX)(XY)[/tex]

substitute the values

[tex]A=(\sqrt{40})(\sqrt{10})=20\ units^2[/tex]

Answer:

c

Step-by-step explanation:

Answer: 35 miles

Step-by-step explanation:

Answer:

Step-by-step explanation:

60

Answer: 8/3

Step-by-step explanation: To add like fractions, or fractions that have the same denominator, simply add the numerators and keep the original denominator.

Answer:

(11/3)x=(2/9)

Step-by-step explanation:

1) Three and two thirds can be simplified to 11/3

2) A number can be rewritten as "x"

(11/3)x=(2/9)

The measure of ∠ACD is 150°. So the answer is D.150°.

The ∠ACD is an exterior angle of triangle ABC. We can use the fact that the sum of the measures of the interior angles of a triangle is 180° to solve for the measure of ∠ACD.

Identify the interior angles of triangle ABC: We are given the measures of two interior angles: ∠A = 33° and ∠B = 117°.

Find the sum of the interior angles of triangle ABC: ∠A + ∠B + ∠C = 180°

Substitute the known values and solve for ∠C: 33° + 117° + ∠C = 180°

Combine like terms: 150° + ∠C = 180°

Isolate ∠C: ∠C = 180° - 150°

Calculate the measure of ∠C: ∠C = 30°

Find the measure of ∠ACD: Since ∠ACD is an exterior angle of triangle ABC and ∠C is an interior angle, we know that ∠ACD and ∠C are supplementary angles. Therefore, their measures add up to 180°.

Calculate the measure of ∠ACD: ∠ACD = 180° - ∠C = 180° - 30° = 150°

Therefore, the measure of ∠ACD is 150°. So the answer is D. 150°.

Answer:

Write the formula for one measurement, then solve the formula for the different measurement you want to find and use this new formula to find that measurement.

Step-by-step explanation:

 We can understand this through an example.

If we need to find the lenght of a rectangle whose width is 4 feet and whose perimeter is 28 feet, we can use a formula for one measurement to write a formula for a different measurement:

 - We need to write the formula for the perimeter of a rectangle:

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

Where "l" is the lenght and "w" is the width.

- Since we know the width and the perimeter of the rectangle and we need to find the lenght, we can solve for "l":

[tex]P=2l+2w\\\\P-2w=2l\\\\l=\frac{P-2w}{2}[/tex]

Now we get a new formula for calculate a differente measurement (the lenght of the rectangle).

- Substituting values, we get:

[tex]l=\frac{28ft-2(4ft)}{2}=10\ ft[/tex]

Answer: Steroids Linked to Higher Heart Disease Risk. High Doses May Raise Risk of Heart Attack, Stroke, Study Shows. By Miranda Hitti. Nov. 15, 2004 -- Taking high doses of steroids (glucocorticoids) seems to increase the risk of heart disease including heart attack, heart failure, and stroke, according to new research.

Step-by-step explanation:

Answer:

high dosages of steroids can cause heart disease and increase the risk of heart attack, heart failure, and stroke.

Step-by-step explanation:

Answer:

[tex]y= \frac{-5}{2}x-1[/tex]

Step-by-step explanation:

the line equation is  5x + 2y = 12

Solve for y to find out slope m

y=mx+b

[tex]5x + 2y = 12[/tex]

Subtract 5x from both sides

[tex]2y =-5x+12[/tex]

Divide both sides by 2

[tex]y=\frac{-5}{2} x+6[/tex]

slope = -5/2

Slope of parallel lines are same . So slope of parallel line is [tex]\frac{-5}{2}[/tex]

m=-5/2 , point (-2,4)

[tex]y-y_1= m(x-x_1)[/tex]

[tex]y-4= \frac{-5}{2}(x+2)[/tex]

[tex]y-4= \frac{-5}{2}x-5[/tex]

Add 4 on both sides

[tex]y= \frac{-5}{2}x-1[/tex]

Answer:

Answer is A

Step-by-step explanation:

Trust the process

Answer:1\2=0.5

3\4=0.75

Step-by-step explanation:you can make fractions into decimals which would be closer to number just look up on Google ✌

Answer:

The bedroom closet will measure 2 feet by 3 feet.

Step-by-step explanation:

A blueprint of a bedroom has a scale of 1/4 inch is equivalent to 1 foot

[tex]\frac{1}{4}[/tex] inch= 1 foot

We need to convert 1/2 inch is how many foot

[tex]\frac{\frac{1}{2}}{\frac{1}{4} } =\frac{1}{2} \cdot \frac{4}{1} =2[/tex]

We need to convert 3/4 inch is how many foot

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

1/2 inch is 2 feet

3/4 inch is 3 feet

The bedroom closet will measure 2 feet by 3 feet.

Step-by-step explanation:

[tex]\sqrt{a}=b\iff b^2=a,\ \text{for}\ a\geq0\ \text{and}\ b\geq0.\\\\a.\ \sqrt{16}=4\ \text{because}\ 4^2=16\\\\b.\ \sqrt{169}=13\ \text{because}\ 13^2=169\\\\c.\ \sqrt{64}=8\ \text{because}\ 8^2=64\\\\d.\ \sqrt{400}=20\ \text{because}\ 20^2=400[/tex]

Answer:

Step-by-step explanation:

√16 =  √4² = 4

√169=√13² = 13

√64 = √8² = 8

√400 = √20² = 20

Answer:

¾ = x

Step-by-step explanation:

Since 3 - 0 gives us the 3, we do this:

[tex]0 = -|8x - 6|[/tex]

0 = -8x + 6 >> Distributive Property

-6 - 6

___________

-6 = -8x

__ ___

-8 -8

¾ = x

I am joyous to assist you anytime.

Answer:

The length of the longer rope piece is 14 ft

Step-by-step explanation:

Let

x -----> the longer piece

y ----> the shorter piece

we know that

The sum of the longer piece plus the shorter piece must be equal to the length of the original piece

x+y=21

y=(21-x) -----> equation A

3x-7=5y ----> equation B

substitute equation A in equation B and solve for x

[tex]3x-7=5(21-x)\\3x-7=105-5x\\5x+3x=105+7\\8x=112\\x=14\ ft[/tex]

therefore

The length of the longer rope piece is 14 ft

Answer:

12

Step-by-step explanation:

divide 100 by 8

Answer:

The answer to your question is:  zero

Step-by-step explanation:

# of protons = 3     they are in the nucleus (blue)

# of electrons = 3   they are in red

Charge = protons + electrons

Charge = +3 + (-3)

Charge = +3 - 3

Charge = 0    

Good evening ,

Answer:

B. g(x)= -x² - 4

___________________

Step-by-step explanation:

The graph of g is downward facing then we must have (-) before the x²

Since, The vertex of parabola g is on point (0 ,-4) then we have to subtract 4.

:)

Answer:

4410 cards, 9 albums

Step-by-step explanation:

Number of cards in a box = 315

Number of boxes = 14

b) Total number of cards =  Number of boxes × Number of cards in 1 box

=[tex]315\times 14 = 4410[/tex]

a) Carmella estimated she had 3,000 cards so she bought a 6 album of 500 cards.

No, 6 albums are not enough as she estimated wrong number of cards. There are total of 4410 cards but she estimated it to be 3000 cards.

c) Total number of albums required = [tex]\displaystyle\frac{\text{Total number of cards}}{\text{Number of card 1 album can hold}}[/tex]

[tex]=\frac{4410}{500} = 8.82 \approx 9[/tex]

Thus, she will require 9 albums to put all her cards.