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Three consecutive integers such that the first plus 4 times the second total 210 more than the third are 52, 53, 54

Integers that are listed in a consistent counting pattern are referred to as consecutive integers. There are no numbers missed while listing consecutive integers in a sequence, so the difference between them is always fixed. The difference between each successive integer, for instance, can be written as -4, -3, -2, -1, 0, 1, 2, 3, and so on.

Let the three numbers be x, x+1, x+2

As per given question,

⇒ x + 4(x + 1) + = 210 + x + 2

⇒ x + 4x + 4 = 210 + x + 2

⇒ 4x + 4 = 212

⇒ 4x = 208

⇒ x = 52

∴ The three consecutive integers will be 52, 53, 54

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Answer:

-6

Step-by-step explanation:

x= 21/3

x=7

using this value,

22-4x= 22-4*7

=22-28

=-6

If r = -6,  s= -2, v=10  and w = 3 then the response of the expression vs(r-s)÷2+rw is option (d) 22

The expression is

vs (r-s) ÷ 2 + rw

To find the response, we have to substitute the values in the expression

The values of the term

r = -6

s = -2

v = 10

w = 3

Substitute the values in the given expression

= 10×-2(-6-(-2)) ÷ 2 + (-6)×3

Do the arithmetic operations in bracket

= 10×-2(-4) ÷ 2 + (-6)×3

Do the multiplication

= 80 ÷2 - 18

Do the division

= 40 - 18

= 22

Hence, if r = -6,  s= -2, v=10  and w = 3 then the result of the expression vs(r-s)÷2+rw is option (d) 22

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They have [tex]30[/tex] pennies. So the option A is correct.

The ratio of pennies to dimes they have is [tex]3:5[/tex].

They have a [tex]2:3[/tex] ratio of dimes to quarters.

They have [tex]75[/tex] quarters.

We have to find the how many pennies they have.

The ratio of pennies to dimes [tex]=3:5[/tex]

We can write it as

Pennies : Dimes[tex]=3:5[/tex]

The ratio of dimes to quarters [tex]=2:3[/tex]

We can write it as

Dimes : Quarter [tex]=2:3[/tex]

When we see both ratio then we can notice that the ratio of dimes is different in both ratio.

So firstly we equal the ratio of dimes.

We can equal the ratio of dime in the ratio of pennies to dimes by multiplying with [tex]2[/tex] in both ratio and in the ratio of dimes to quarters by multiplying [tex]5[/tex] on both side.

Now we get after multiplying in the ratio.

Pennies : Dimes[tex]=3\times2:5\times2[/tex]

Pennies : Dimes[tex]=6:10[/tex]

Dimes : Quarter [tex]=2\times5:3\times5[/tex]

Dimes : Quarter [tex]=10:15[/tex]

The number of quarter is [tex]75[/tex].

They given in the ratio which means there have any number in the multiple of ratio. That which we can get real value from the ratio.

So we used [tex]x[/tex] as a multiple of ratio.

If we see in the ration of Dimes and Quarter the ratio of quarter is [tex]15x[/tex].

Now the value of quarter

[tex]15x=75[/tex]

Now the value of [tex]1[/tex] quarter

Divide by [tex]15[/tex] on both side.

[tex]\frac{15}{15}x=\frac{75}{15}[/tex]

[tex]x=5[/tex]

Hence, the value of [tex]x[/tex] is [tex]5[/tex].

Now we have to find the value of pennies.

In the ratio we can see that the ratio of pennies is [tex]6[/tex].

We can find the value of pennies by multiplying with [tex]5[/tex].

After multiplying we get [tex]30[/tex].

Hence, they have [tex]30[/tex] pennies. So the option A is correct.

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Answer: A

Step-by-step explanation:

According to the scale the model mountain would be 39.04 inches.

Scale factor is the ratio of an object's original scale to that of a new object that is a representation of it but in a variety of sizes (bigger or smaller).

For instance, by increasing each side by, say, 2, we can expand the size of a rectangle with sides of 2 cm and 4 cm. The second figure will mimic the first figure, but every dimension of the second rectangle will be double that of the first figure. In this instance, the scale factor will be indicated by the number 2.

We now that 48800 feet = 48800 × 12 inches = 585600 inches

Scale = 1:15,000

height of model = 585600 ÷ 15000 = 39.04 inches

Hence the length of the model is 39.04 inches.

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We want to know which equation is most likely represented by the circle graphed.

For doing so, we remember the general equation of a circle:

In the equation, (h,k) is the center of the circle, and r is the radius. Thus, if we obtain the center and the radius of the circle, we will be able to obtain its equation. The center is on the point (-1, -6), as we see on the figure:

And the radius (the distance from the center to a point of the circle) is 4:

Replacing on the formula, we obtain that the equation that represents the circle graphed is:

The number of tiles needed to cover the floor is 60 tiles.

Given Information,

The floor area of the passage = 2.4 m²

Length of a side of square tile = 200mm

Length of the side is in mm which needs to be converted in its standard form which is meters.

Therefore, the length of side = 200/1000 m

                                                = 0.2 m

Area of the square tile = 0.2 x 0.2

                                      =  0.04 m²

Let the number of tiles be x.

∴ Number of tiles = [tex]\frac{Area of passage}{Area of each tile}[/tex]

 x = 2.4/0.04

 x = 60

∴ The number of tiles needed to cover the floor is 60 tiles.

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Answer: Uhhhh there are no names for me to choose from- but it's basically any shape with straight lines and is closed. hope this helps

Step-by-step explanation:

Answer:

 y = 2x - 20

Step-by-step explanation:

where m is slope and b is y-intercept.

  y + 1 = 2(x - 3)

Write this equation in y = mx + b form.

 y + 1 = 2x - 2*3

y + 1 =2x - 6

      y = 2x - 6 - 1

      y = 2x - 7

m =2

Parallel lines have same slope.

 Slope of the required line = 2

  y = 2x + b

The point (9,-2) passes through the line. Substitute in the above equation and find the value of 'b'.

          -2 = 9*2 + b

        -2   = 18 + b

    -2 - 18 = b

        [tex]\sf \boxed{b = -20}[/tex]

Equation of the required line:

            y = 2x - 20

Nisha solved an equation given, and she made a mistake in the third step. The correct option is c. step 3.

An error in math is a mistake in solving any arithmetic equation or calculation. It can be calculating wrong or left a step.

Given;

Step 1: 7 b + 3.2 b - 5 = 18.92

Step 2:  10.2 b - 5 = 18.92   (Combining like terms in left side)

Step 3:  10.2b = 23.92   (Adding 5 on both sides)

Step 4:  b = 3.64 (Dividing both sides by 10.2)

But in step 3, she did not add 5 on both sides.

5.2 b = 18.92 incorrect. The correct equation is 10.2b = 23.92

Therefore, the correct option is c. Step 3.

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Peter threw a water balloon out of the top of a 15-yard-tall structure. The Option b is correct because it asks the domain so the option a and c are wrong from the graph can we know 0≤x≤8.

Given that,

Peter threw a water balloon out of the top of a 15-yard-tall structure.

The water balloon's height is plotted as a function of x, or the building's distance from the location in yards.

We have to find which one most domain reflects the situation's context.

The Option b is correct because it asks the domain so the option a and c are wrong from the graph can we know 0≤x≤8.

Therefore, Option b is correct.

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Answer:

A hope it helps follow please

Step-by-step explanation:

hope you have a great day today

Answer: Therefore, the value of k is -20

Step-by-step explanation:A=-26-3= -29

                                             B=-3x+2

                                             C = -2x + 7    

                                       A+B+C= -29 -3x +2 -2x +7

                                       A+B+C= -29 +2+7 -3x -2Xx

                                       A+B+C= -20-5x    

Answer:

true

Step-by-step explanation:

Answer:

110 is the answer

Step-by-step explanation:

I can't not just under 30 letters so I'm doing this so I can actually submit this so u can see this answer so dont mind this part right here

The equation of the line passing through the point (-6, 4) and (-2, 2) is y = -(1/2)x + 1

An equation is an expression that shows the relationship between two or more numbers and variables.

The standard form of a linear equation is:

y = mx + b

Where m is the slope and b is the y intercept.

The equation of a line passing through the point (-6, 4) and (-2, 2) is:

y - 4 = [(2 - 4)/(-2 - (-6))](x - (-6))

y - 4 = -(1/2)(x + 6)

y - 4 = -(1/2)x - 3

y = -(1/2)x + 1

The equation of the line is y = -(1/2)x + 1

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the green would be 15% of the counters

The number of counters that are green is 162 and the percentage of counters that are green is 42 %

What is an Equation?

Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.

It demonstrates the equality of the relationship between the expressions printed on the left and right sides.

Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.

Given data ,

The total number of counters = 400

The number of counters that are red = 3/8 of total number of counters

                                                              = ( 3/8 ) x 400

                                                              = 3 x 50

                                                              = 150 counters

The number of counters that are yellow = 82 counters

So , the number of counters that are green =
Total number of counters - number of counters that are red - number of counters that are yellow

The number of counters that are green = 400 - 150 - 82

                                                                  = 168 counters

Now , the percentage of counters that are green =
( number of counters that are green / total number of counters ) x 100

The percentage of counters that are green = ( 168 / 400 ) x 100

                                                                        = 168 / 4

                                                                        = 42 %

Hence , the number of counters that are green is 168 and the percentage of counters that are green is 42 %

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Suplementsry angles are

Form a sum of 180°

Then in figure

Suplements for angle 3 are, Angles 2 and 4

Because <3 + <4 = 180°

and also

<3 + <2 = 180 °

Then answer is

Option B) Angle 4

The number of times as much as her brother is Jackie now on the phone is 1 2/5 times.

From the information, Jackie used to be on the phone 3 1/2 times as much as her brother and her parents threatened to take away the phone, so she cut down to 2/5 of the time she used to be on the phone.

Therefore, the times that she's using as much as her brother will be:

= Original times × Fraction cut

= 3 1/2 × 2/5

= 7/2 × 2/5

= 7/5

= 1 2/5 times.

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Answer:

1 1/4 hours

Step-by-step explanation:

3/2 x5/6

15/12

1 3/12

1 1/4

Hopes this help please mark brainliest

The factors of the given functions are ( x+ 1 ) and  ( 2x + 5 )

Given : The two functions are f(x) = 2x² += 5x -5 and g(x) = -2x - 10

In questions like these where we have to equate the two functions. We first have to do the obvious step that is equate the two values and then after that we are supposed to bring the like terms to one side because this will make the calculation both easy and less time consuming .

So as mentioned above

f( x ) = g ( x )

2x² + 5x -5 =  -2x - 10

Now bring the like variables together ;

2x² + 7x = -10 + 5

this implies the equation becomes

2x² + 7x = - 5

which can also be written as

2x² + 7x + 5 = 0

Now we can solve it further by splitting the middle term

and we will get:

2x² + 5x + 2x + 5 = 0

Taking out the common factors '

x( 2x + 5 ) + 1 ( 2x + 5) = 0

( x+ 1 ) ( 2x + 5 ) = 0

Thus the two factors are ( x+ 1 ) and ( 2x + 5 )

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Answer:

Answers below

Step-by-step explanation:

For 28 Students 300-90-(6*28) the answer is 42.

For 29 Students 300-90-(6*29) the answer is 36.

For 30 Students 300-90-(6*30) the answer is 30.

The greatest number of students that can go on the field trip for $300 is 35.

I've gotten this answer by doing 300-90-(6*35) which equals to 0.

If a computer with a cash price of $1,900 at $150.00 down and $87.50 per month for 24 months. a. The total installment price is $2250, b. The carrying charges, and (c) the number of months needed to save the money at the monthly rate to buy the item for its cash price is 22 months.

a. Total installment price:

Total installment price = 150 + 87.50 (24)

Total installment price =150 + 2100

Total installment price =2250

b. Carrying charges :

Carrying charges = Total installment price - Cash price

Carrying charges = 2250 -1900

Carrying charges = 350

c. Number of months needed:

Number of months needed = Cash price / 87.50 per month

Number of months needed = 1900 / 87.50 per month

Number of months needed = 21.7 months

Number of months needed = 22 months (Approximately)

Therefore installment price is 2250, charges is 350 and the number of months is 22.

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Answer:

12 should be 1 as in 1 foot. 1' 1/4"

Step-by-step explanation:

The system of equations containing equations  y = 5/2 x + 2 and 2y = 5 x + 4 will have infinitely many solutions.

What is system of equations?

A finite collection of equations for which we searched for the common solutions is referred to in mathematics as a system of equations, sometimes known as a set of simultaneous equations or an equation system. Similar to single equations, a system of equations can be categorized. In everyday life, systems of equations are used to model problems when the unknown values can be represented by variables.

Given equations:

y = 5/2 x + 2

2y = 5 x + 4

We will use the substitution method, to get the values of x and y:

2 ( 5/2 x + 2 ) = 5 x + 4

5 x + 4 = 5 x + 4

0 · x = 0

x , y ∈  R

Therefore, this system of equations will have infinitely many solutions.

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Complete question

How many solutions does the following system of equations have?

y = 5/2x + 2,

2y = 5x + 4.

Side of the cube = 2 cm

Width of the rectangular prism = 9 cm

Length of the rectangular prism = 9cm

Height of the rectangular prism = 4 cm

Now,

The volume of total water (submerged cube)

= width of the rectangular prism x length of the rectangular prism x height of the cube

= 9 x 9 x 2 = 162 cm^3

As we know that 1 cm^3 = 1ml

So,

162 cm^3 = 162 ml

Hence the volume of water required to fill the prism such that the cube is submerged is 162 ml.

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Answer:

Step-by-step explanation:

b

Answer:

1.62, 15/20, 16.2%

Step-by-step explanation:

Let us consider all the answers out of one. In percentages, 100% always equals 1. (If you ate 100% of a cookie, you would have eaten 1 cookie), 16.2% is much less than 100% and not even half of 100%.

16.2%<0.5

Following the same logic, imagine there are 20 cookies this time. 15/20 would be 15 out of the 20 cookies which is more than half.

15/20>0.5

Finally, 1.62 is greater than 1

1.62>1

You can tell I'm hungry rn lol, also I would appreciate if you could give Brainliest, I'm kind of on a streak

Answer:

x = -5

Step-by-step explanation:

f(x) = -x-4

Let f(x) = 1

Find x

1 = -x-4

Add 4 to each side

1+4 = -x-4+4

5 = -x

Multiply each side by -1

-5 =x

x = -5

Answer:

x  = -5

Step-by-step explanation:

Given that,

f ( x ) = - x - 4

If, f ( x ) = 1,

Let us find the value of x.

For that, replace f ( x ) with 1.

f ( x ) = - x - 4

1 = - x - 4

First, add x to both sides.

x + 1 = -4

Now, subtract 1 from both sides.

x = -4 - 1

x = -5