An engineer designed a new bridge and drew the scale drawing shown below. 6 Inches If the engineer used the scale 3 inch = 40 feet, how long is the actual bridge the engineer designed?​

Answer:

Task

Kipton has a digital scale. He puts a marshmallow on the scale and it reads 7.2 grams. How much would you expect 10 marshmallows to weigh? Why?

Kipton takes the marshmallows off the scale. He then puts on 10 jellybeans and then scale reads 12.0 grams. How much would you expect 1 jellybean to weigh? Why?

Kipton then takes off the jellybeans and puts on 10 brand-new pink erasers. The scale reads 312.4 grams. How much would you expect 1,000 pink erasers to weigh? Why?

IM Commentary

The purpose of this task is to help students

Recognize that in a multi-digit number, a digit in one place represents 10 times as much as it represents in the place to its right and 1/10 of what it represents in the place to its left (5.NBT.1)

By setting the task in the context of weighing objects and bundles of 10, 100, and 1,000 objects, it helps students visualize that bundling 10 units of a given place value will create 1 unit of the next highest place value. For example, taking 10 of an item that weighs 4.2 grams will result in 42 grams because it is 10 groups of 4 grams that weights 40 grams all together, and 10 groups of 0.2 grams that weigh 2 grams all together. The task allows students to explore both the structure of our place value system and how we use that to efficiently multiply and divide powers of 10.

Though this task is written as questions to be discussed or answered by students, the parts of this task are most valuable as a set of scenarios to be infused throughout a unit on place value. The teacher can actually bring in a digital scale and go through a series of explorations with students. It might be natural to start with students weighing one object and making predictions about how much 10 or 100 of these objects would weigh. From there, the teacher may want to have students start weighing sets of 10 or 100 objects and work backwards to think about the weight of 1 object.

The digital scale has several advantages: the weight will always appear in decimal form, thereby making it perfect for students to start reasoning about shifts in decimal place value from a more intuitive place. Moreover, the digital scale will not always show the expected answer. For example, something that weighs 3.5 grams alone might weigh 35.4 grams (rather than 35 grams) when taken as a group of 10. This slight difference provides an excellent opportunity to talk about rounding error. It also requires students to think beyond the rules of sliding a decimal point to the right when multiplying by powers of 10.

If students were still developing the rules for multiplying and dividing by powers of 10, this task would also incorporate MP8, Look for and express regularity in repeated reasoning. It also incorporates parts of MP6, Attend to precision, in that a higher-level discussion will push students to reason why one marshmallow might weigh 7.2 grams, but 10 marshmallows might weigh 7.19 grams. See the solution for part (a) for further elaboration.

Solution

Solution:

10 marshmallows should weigh 72 grams. Students might use repeated addition, multiplication or reason that each digit’s place value will be multiplied by a factor of 10:

10×(7+0.2)(10×7)+(10×0.2)70+272===

If students have had practice using digital scales in class, some students might respond with guesses that are close such as 73 grams or 72.4 grams because the original 7.2 grams may have been rounded to the nearest tenth. If, for example, the original actual weight were 7.24 grams, then the weight of ten marshmallows on a scale that rounds to the nearest tenth of a gram would be 72.4 grams.

1 jellybean should weigh 1.2 grams. Students may come to the solution a number of ways.

Students might notice that dividing 12 by 10 could be expressed in fraction form 1210. Students might further reason that

1210=1010+210

or 1.2.

Students might alternately reason that 12÷10 is the same as

(10÷10)+(2÷10)=1+0.2=1.2

Students might also use the rule that they are beginning to develop about sliding the decimal point one place to the left to divide by 10.

1,000 pink erasers should weigh about 31,240 grams. Students may come to the solution a number of ways:

A student might reason that first, it would be necessary to find out what 100 erasers would weigh by multiplying by a factor of 10 and then further multiplying by another factor of 10 to find out what 1,000 erasers would weigh. This is represented by

312.4×10×10

In this solution method, the student reasoned that multiplying by a factor of 10 and then another factor of 10 would be the same as multiplying by a factor of 100:

312.4×10×10312.4×100100×(300+10+2+0.4)30,000+1,000+200+4031,240====

Another student might want to find the weight of a single eraser. If 10 erasers weigh 312.4 grams, then one eraser must weigh 31.24 grams. From there the student could multiply the weight of one eraser by a factor of 1,000:

1000×(30+1+0.22+0.04)30,000+1,000+200+4031,240==

Step-by-step explanation:

You would expect 1,000 pink erasers to weigh 31,240 grams.

If 10 erasers weigh 312.4 grams, and to get 1,000 you multiply by 100, if you multiply 312.4 by 100 you get 31240.

Or if you use rates

[tex]\frac{312.4}{10} =\frac{31240}{1000}[/tex]

(when you multiply by 100)

Answer:

x=u+k

Step-by-step explanation:

Answer:

x = k+u

Step-by-step explanation:

u = x - k

+k       +k

u + k = x

Hope this helps!

Answer: 4

Step-by-step explanation: 4 was the biggest denominator in that equation. so if we multiply by 4 on all the terms, all the denominators will go away. we will not have any more fractions!

Answer:

50 employees

Step-by-step explanation:

The total number of employees the business has will have to be made up the full-time employees and part-time employees.

The number of full-time employees = 15

Let the total number of  employees = x

[tex]15 = 30 percent of x[/tex]

[tex]15 = 30/100 \times x\\x=1500/30 = 50[/tex]

The company has a total of 50 employees

Answer:

They will both have paid the same amount after 4 months

Step-by-step explanation:

Assume that they will pay the same amount after x months

∵ Billy pays $30 for his new phone

∵ He only pays $12.50 each month

→ Find how much he will pay in x month

∴ He will pay → 30 + 12.50x

∵ Annie got her new phone for free

∵ She only pays $20 a month

→ Find how much she will pay in x month

∴ She will pay → 20x

∵ They will pay the same amount

→ Equate their expressions above

∴ 20x = 30 + 12.50x

→ Subtract 12.50x from both sides

∵ 20x - 12.50x = 30 + 12.50x - 12.50x

∴ 7.50x = 30

→ Divide both sides by 7.50

∴ x = 4

∴ They will both have paid the same amount after 4 months

Answer:

the first one and last one are true

Step-by-step explanation:

Answer:

17

Step-by-step explanation:

Use the Pythagorean Theorem, [tex]a^{2} +b^{2} =c^{2}[/tex]

In this situation, you would use the equation as [tex]8^{2} +15^{2} =x^{2}[/tex]

Answer:

42.3

Step-by-step explanation:

3.6(3)+4.5(7)

10.8+31.5

42.3

Answer:

Step-by-step explanation:

Line x = 0 is parallel to y-axis

Line parallel to given line is also parallel to y-axis. It passes through point (-2, 3), so its equation is:

Answer:

0.6

Step-by-step explanation:

Brainliest please

Answer:

it's the first answer

Step-by-step explanation:

literally every other answer is ruled out because D is the greatest variable and can't be smaller than anything else

Answer:

Slope = 4.000/2.000 = 2.000

Slope = 2.000/2.000 = 1.000

Step-by-step explanation:

the first answer is for the first problem and the second answer is for the second problem. Hoped it helped i tried my best.

Answer:

there are 120 apples in each basket and 5 are left over

Step-by-step explanation:

Answer:

The two number are :

x = 1411

y = 1079

Step-by-step explanation:

Let the two numbers = x and y

The sum of two numbers is 2490

x + y = 2490..... Equation 1

If 6.5 percent of one no. is equal to 8.5 percent of the other,

Hence:

6.5% of x = 8.5% of y

0.065x = 0.085y

Make x the subject of the Formula

x = 0.085y/0.065

x = 1.308y

We substitute 1.308y for x Equation 1

x + y = 2490..... Equation 1

1.308y + y = 2490

2.308y = 2490

y = 2490/2.308

y = 1078.8561525

y = 1079

x + y = 2490..... Equation 1

x = 2490 - y

x = 2490 - 1079

x = 1411

So you want to go to your calculator type 42 divided by zero, and you should get a 52.5.

Answer:

Option B

Step-by-step explanation:

Slope = Change in y / Change in x

Slope = (8 - 2) / {6 - (-4)}

Slope = 6 / (6 + 4)

Slope = 6 / 10

Slope = 3 / 5

So option B is your answer

Answer: 3/49 as a decimal is 0.06122

Answer:

The solutions are:

-28.25, -14.5, -2.25

Step-by-step explanation:

Given compound inequality is:

[tex]-17.5\leq \frac{2x+4}{3} <17.5[/tex]

The compound inequalities are broken down into two inequalities to find the solution

The two inequalities will be:

[tex]\frac{2x+4}{3} \geq -17.5[/tex]   AND   [tex]\frac{2x+4}{3}<{17.5}[/tex]

Solving both inequalities one by one

[tex]\frac{2x+4}{3} \geq -17.5\\2x+4 \geq -52.5\\2x \geq -52.5-4\\2x \geq -56.5\\\frac{2x}{2} \geq \frac{-56.5}{2}\\x \geq -28.25\\\frac{2x+4}{3} < 17.5\\2x+4 < 52.5\\2x < 52.5-4\\2x \geq 48.5\\\frac{2x}{2} \geq \frac{48.5}{2}\\x < 24.25[/tex]

The solution is:

-28.25 ≤ x < 24.25

We have to see which options lie in the solution range.

The solutions are:

-28.25, -14.5, -2.25

Answer: i think A, but might not be sry

Step-by-step explanation:

Answer:

PAIN

Step-by-step explanation:

Answer:

3x+48

add 3+45=48

Step-by-step explanation:

Hope this helps! Please consider marking brainliest! I hope you have an amazing day. Always remember, your smart and you got this! -Alycia :)

Answer:

3(x+16)

Step-by-step explanation:

45+3=48

3x/3=x

48/3=16

3(x+16)

Given:

Point is T(-3,8).

To find:

The coordinates of T' after [tex]R(y-axis)\circ R(x-axis)[/tex].

Solution:

We know that, [tex]R(y-axis)\circ R(x-axis)[/tex] means the figure reflected across the x-axis then reflected across y-axis.

If a figure reflected across x-axis, then

[tex](x,y)\to (x,-y)[/tex]

[tex]T(-3,8)\to T_1(-3,-8)[/tex]

If a figure reflected across y-axis, then

[tex](x,y)\to (-x,y)[/tex]

[tex]T_1(-3,-8)\to T'(-(-3),-8)[/tex]

[tex]T_1(-3,-8)\to T'(3,-8)[/tex]

Therefore, the required point is T'(3,-8).

Answer:

40 square cm

Step-by-step explanation:

Answer:40 square cm

Step-by-step explanation:

Answer:

I think the answer is 6 sorry if i'm wrong

Step-by-step explanation:

Answer:

48.75

Step-by-step explanation:

Answer:

so one thing you can do is to put the standard form into slope-intercept form

so 6x+y= -4 into y=-6x -4

now, you put a point on (0,-4)

(x,y)

now the slope is -6/1 so you rise (go down) -6 points and run (sideways) 1