The expression 21m−49n factored using the GCF is

3 : 4 = 2700 : 3600

sum the parts of the ratio : 3 + 4 = 7

divide 6300 by 7 to obtain 1 part

[tex]\frac{6300}{7}[/tex] = 900 ← 1 part

3 parts = 3 × 900 = 2700

4 parts = 4 × 900 = 3600

note that 2700 + 3600 = 6300

No. If red balls = 4, Total no. Of balls = 7

Prob of getting first red = 4/7

Second red = 4/7

Third red = 4/7

As all balls are taken out with replacement ,therefore total no. Of red balls remain same

Probability of drawing all red = 4/7×4/7×4/7

=64/343

ANSWER

The image point is [tex](1,-6)[/tex].

EXPLANATION

For a reflection in then line [tex]y=x[/tex], we simply swap the x and y coordinates.

Thus, in general the mapping for the reflection in the line [tex]y=x[/tex], is

[tex]P(x,y)\rightarrow P'(y,x)[/tex].

Hence,

[tex]P(-6,1)\rightarrow P'(1,-6)[/tex].

See graph.

The reflection of the point (-6,1) over the line y=x results in the point (1,-6).

In the context of coordinate geometry, reflection over a line, specifically y=x, requires that we swap the x and y coordinates of a given point. So, when we have the point (-6,1), it is reflected to become (1,-6) over the line y=x. Hence, "this operation fundamentally changes the position of the point".

https://brainly.com/question/18376051

#SPJ3

Answer:

The amount of minutes Grace has to use her cell phone this month is 59 minutes

Step-by-step explanation:

Let

x -----> amount of minutes Grace has to use her cell phone this month

we know that

The average usage during the four months is equal to the sum of the minutes used in the four months divided by four (the number of months)

so

[tex]55=\frac{42+62+57+x}{4}[/tex]

Solve for x

Multiply by 4 both sides to remove the fraction

[tex]55(4)=(42+62+57+x)[/tex]

[tex]220=(161+x)[/tex]

[tex]x=220-161[/tex]

[tex]x=59\ min[/tex]

therefore

The amount of minutes Grace has to use her cell phone this month is 59 minutes

Final answer:

A student's math problem involving an algebraic equation to find a number has been solved by isolating and solving variables, resulting in the number 12.

Explanation:

To solve the equation where ten times a number decreased by seven equals 101 plus that same number, we would set up the following equation:

10x - 7 = 101 + x

Now, we solve for x:

First, subtract x from both sides of the equation to get all the x terms on one side:

9x - 7 = 101

Next, add 7 to both sides of the equation to isolate the term with x:

9x = 108

Finally, divide both sides by 9 to solve for x:

x = 12

Hence, the number we are looking for is 12.

A. is this answer to this question.

The value of inequality is t ≤ -14  which means t will have all value less then and equals to -14 In number line.

What is number line ?

Number line is virtual representation of numbers along with coordinates axis with number equally spaced with equal number of interval.

Here the given inequality is :

−5t ≥ 70

Now, to solve for t we divide both side by -5 :

−5t/-5 ≥ 70/-5

t ≤ -14  

It should be noted that negative -5 reverse the inequality sign.

Therefore, the value of inequality is t ≤ -14  which means t will have all value less then and equals to -14 In number line.

check and know more about inequality here :

https://brainly.com/question/21209456

#SPJ5

Answer:

Its orientation may change and the measures of its angles stay the same.

Step-by-step explanation:

Answer:

When a figure is translated its orientation may change and the measures of its angles keeps the same measure.

Step-by-step explanation:

Whenever we translate a figure, we move a figure into some orientation given by this same vector. But the angles will remain the same since there is no distortion.

Just as the picture below

3 hours because if u have 175 dollers and u spend 100 so now u have 75. 75 -20 is 55. then 55 - 20 is 35. then 35 - 20 is 15 so then you have 15 dollers to spare. so 3

You can represent this problem as a linear equation 100 + 20x = 175. Solving for x gives you 3.75, hence with $175, you can rent the jet ski for 3.75 hours.

To solve this problem, you need to set up a linear equation. Let's represent the number of hours of the jet ski rental as x. The jet ski rental company charges a $100 rental fee plus $20 per hour, so we can write this as a equation: 100 + 20x = 175.

Next, we need to solve for x. First, subtract 100 from each side of the equation, you obtain 20x = 75. Then, divide each side by 20 to solve for x. You'll find that x = 3.75. Therefore, with $175, you can rent the jet ski for 3.75 hours.

https://brainly.com/question/32634451

#SPJ3

Answer:

he would have to sell 30 cakes

Step-by-step explanation:

if you take the amount it actually cost to make it and the amount he is selling them for you would first do

1.80 - 3.00 = 1.20$

after you get 1 dollar and 20 cents you would divide it by 36 dollars to get 30

to check your answer do 30 x 1.20 = 36.00

- 6x - 1

distribute parenthesis and collect like terms

- 2x - 3 - 4x + 2

= (- 2x - 4x) + (-3 + 2) = - 6x - 1

Answer:

True ,if they are adjacent and share a vertex and one side

Answer:

1/10

Step-by-step explanation:

There are three simple fractions in this problem:  3/5, -1/4 and 7/10.  Rules of order require that the division (-1/4) divided by 7/10 be carried out first; the correct product is  -10/28, or -5/14.  Then we have 3/5 + (-5/14).

Here the LCD is 70.  Then 3/5 + (-5/14) becomes 42/70 - 35/70, which simplifies to 1/10.

Answer:

1/10

Step-by-step explanation:

4(x + 1) = 12(3 - x)

Distributive property on both sides.

4x + 4 = 36 - 12x

Add 12x to both sides.

16x + 4 = 36

Subtract both sides by 4.

16x = 32

Divide both sides by 16.

x = 2

Let x = the width

then

2x = the length

:

The box dimensions: 2x by x by 4

Given the surface area:

2(2x*x) + 2(2x*4) + 2(x*4) = 220

:

4x^2 + 16x + 8x = 220

A quadratic equation:

4x^2 + 24x - 220 = 0

simplify, divide by 4

x^2 + 6x - 55 = 0

Factor

(x+11)(x-5) = 0

The positive solution is what we want here:

x = 5 ft is the width

then

2(5) = 10 ft is the length

:

Find the volume

10 * 5 * 4 = 200 cu/ft is the volume

Final answer:

The volume of the box is 192 cubic feet, calculated using the dimensions provided in the question.

Explanation:

The volume of the box is 192 cubic feet.

To find the volume, we need to calculate the dimensions of the base rectangle. Since the base and top are twice as long as they are wide, the larger square will have sides of 8 feet. With a height of 4 feet, the volume can be calculated as V = length*width*height. Plugging in the values, we get V = 8*4*4 = 192 cubic feet.

So remember that the degree of the polynomial will indicate how many solutions there are, real or complex. Since the degree of the polynomial is 2, this means that there is a maximum of 2 real solutions in this equation.

Next, we are going to apply the difference of squares rule to this polynomial, which is [tex]x^2-y^2=(x+y)(x-y)[/tex] . In this case:

[tex]x^2-9=(x+3)(x-3)\\(x+3)(x-3)=0[/tex]

Now, we are going to apply the Zero Product Property, which states that if a × b = 0, this means that either a or b = 0 or a and b = 0. In this case, a = x + 3 and b = x - 3. Solve each as such:

[tex]x+3=0\\x=-3\\\\x-3=0\\x=3[/tex]

In short, there are 2 real solutions: x = 3 and x = -3.

The equation [tex]x^2-9=0[/tex] has two real solutions which are x=3 and x=-3. The solutions are obtained by applying the quadratic formula, which indicates that every equation containing an unknown squared will have two solutions.

The equation[tex]x^2-9=0[/tex] is a quadratic equation. For any quadratic equation in the form ax²+bx+c = 0, the solutions or roots can be calculated using the quadratic formula: -b ± √(b² - 4ac) / 2a.

In this specific equation, [tex]x^2-9=0[/tex]can be rewritten as x²-9+9 = 9, which simplifies to x² = 9. The solutions can then be obtained using the principal square root or the negative square root, resulting in x = ± √9. Therefore, the two real solutions are x = 3 and x = -3.

It's important to note that every equation containing an unknown squared will have two solutions, which can be both meaningful or only one of them can be reasonable depending on the context of the problem.

https://brainly.com/question/34196754

#SPJ11

The height of a baseball thrown from the catcher to first base is modeled by the function [tex]h(t) = -0.09t^2 + 0.72t + 6[/tex], where h is the height of the ball measured in feet and t is the time since being thrown, measured in seconds

To find out height of the ball at 10 seconds, we plug in 10 for t

[tex]h(t) = -0.09t^2 + 0.72t + 6[/tex]

[tex]h(10) = -0.09(10)^2 + 0.72(10) + 6[/tex]

h(10)=4.2 feet

the height of the ball at 10 seconds= 4.2 feet

Given the function [tex]p(x)=x^2+4x-12.[/tex]

Part A.

To write the expression that defines [tex]p(x-6)+5,[/tex] you have to substitute x-6 instead of x into the function expression and then add 5 to the function:

[tex]p(x-6)+5=((x-6)^2+4(x-6)+12)+5,\\\\p(x-6)+5=x^2-12x+36+4x-24+12+5,\\\\p(x-6)+5=x^2-8x+29.[/tex]

Part B.

1 transformation is translation 6 units to the right (p(x-6) determines this transfromation).

2 transformation is translation 5 units up (+5 determines this transformation).

Answer:

k=2

Step-by-step explanation:

We have got a right triangle LNO with sides = m,4 and 8

By Pythagorean theorem

m^2=4^2 +8^2

Or m^2 = 80  ... i

IN triangle NOM, 4^2 +k^2 = l^2

i.e. 16+k^2 = l^2... i

In triangle LNM, m^2+l^2 = (8+k)^2

Substitute for m^2 as 80,

i.e. 80+l^2 = 64+k^2 +16k  ... iii

From i, l^2 = 16+k^2

Substitute in iii

80+16+k^2 = 64+k^2 +16k

16k = 32 or k =2

Im assuming that to be the case, so:-

11/12 + 1 3/4

= 11/12 + 7/4

= 11/2 + 21 / 12

= 32 / 12

= 2 2/3 OZ.    (Choice D).

Mary mixed Quatities of 2 2/3 ounces of paint by adding 11/12 oz of red paint and 1 3/4 oz of white paint.

To find out how many ounces of paint Mary mixed, we need to add the amounts of red and white paint.

First, let's add the red paint: 11/12 oz.

Next, let's add the white paint: 1 3/4 oz.

To add fractions, we need a common denominator. In this case, the common denominator is 12, so we can rewrite 1 3/4 as 7/4: 7/4 oz.

Now, let's add the two amounts: 11/12 + 7/4.

To add fractions with different denominators, we need to find a common denominator. In this case, the common denominator is 12. Multiply the numerator and denominator of the first fraction by 1 (12/12) and the numerator and denominator of the second fraction by 3 (3/3).

So, 11/12 + 7/4 is equal to (11/12) + (21/12) = 32/12.

We can simplify 32/12 to 2 8/12, and further simplify it to 2 2/3 oz.

Therefore, Mary mixed 2 2/3 ounces of paint.

https://brainly.com/question/13676317

#SPJ2

Answer:

In the picture

Step-by-step explanation:

First You do 30.75 x 12 This is because he said every month for a year and a year has 12 months The answer to 30.75 x 12 is 369 Now  all you have to do is 550 - 369 = 181.      

Hope this helps :D

I think the answer you're looking for is $9.50.

513 / 54 = 9.5

Sue made $9.50 an hour.

To find the mass of each cube, divide the total mass of the box by the number of cubes. The mass of each cube in Box A is 33.21 grams, while the mass of each cube in Box B is 90 grams.

To determine the mass of each cube, we need to divide the total mass of the box by the number of cubes.

Mass of each cube in Box A = Total mass of Box A / Number of cubes in Box A = 1760 grams / 53 cubes = 33.21 grams per cube.

Mass of each cube in Box B = Total mass of Box B / Number of cubes in Box B = 1620 grams / 18 cubes = 90 grams per cube.

A triangle is the answer.

Answer:

ok the answer is

Step-by-step explanation:

69 gooba, go watch it NOW

Answer:

2500 + 215d

Step-by-step explanation:

Total revenue from all booths is the sum of the revenue from the food booths and from the games booths. The food booth revenue for each booth is 100 + 5d, where d is the number of days the fair lasts. There are 15 food booths, so the total revenue from them is ...

... (food booth revenue) = 15(100 +5d)

The games booth revenue for each booth is 50 + 7d, where d is the number of days the fair lasts. There are 20 games booths, so the total revenue from them is ...

... (games booth revenue) = 20(50 +7d)

Then the total revenue is

... total revenue = (food booth revenue) + (games booth revenue)

... = 15(100 +5d) + 20(50 +7d) . . . . . . use the expression for revenue from each

... = 1500 +75d + 1000 +140d . . . . . . eliminate parentheses

... = 2500 + 215d . . . . . . . . . . . . . . . . collect terms

Answer:

Step-by-step explanation:

As we move up the list -- as we push the digits one place right -- the number has been divided by 10 because each place to the right is worth 10 times less. ... As we move down the list -- as we push the digits to the left through the decimal point -- each number has been multiplied by 10

Dividing by 10 shifts each digit one place to the right due to our base-ten counting system. Each time we divide by 10, the number is broken into 10 equal parts, thereby moving its digits one place to the right. The same principle applies when dealing with larger powers of 10 and is often employed in scientific notation.

The reason why dividing by 10 shifts each digit one place to the right relates directly to the base-ten number system we use, which relies on powers of ten. Whenever we divide by 10, we are asking how many times the number can be broken into 10 equal parts, thus moving its digits one place to the right.

For instance, if we take the number 250 and divide it by 10, the result is 25. We've essentially shifted the digits one place right. Similar to this when we are dealing with decimal numbers, the shift occurs with the decimal point. If we had 25.0 and divided by 10, the result would be 2.5

The same principle applies to larger powers of 10. If you divide by 100 (which is 10^2), you shift each digit two places to the right, and so on.

Another way to consider it is using scientific notation, which often uses powers of 10 to simplify large or small numbers. A number like 1,230,000,000 is written as 1.23 × 10⁹ in scientific notation. When we divide this number by 10, the exponent decreases by 1 to become 1.23 × 10⁸, effectively shifting each digit one place to the right.

https://brainly.com/question/30586279

#SPJ3

the volume is 408

l times w times h

simplify 9[3+4}

using bodmass

=9{7}

63