1. y = x2 + 2x – 8

Axis of Symmetry:

Vertex:

Domain:

Range:

Answer:

c

Step-by-step explanation:

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

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:

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:

[tex]a=9[/tex]

Step-by-step explanation:

In this problem, you can use the Pythagorean Theorem ([tex]a^{2} +b^{2} =c^{2}[/tex]) to find what a is. The steps are shown below:

Steps (variables a, b, and c are in italics):

-You can rearrange the formula from the Pythagorean Theorem, which is[tex]a^{2} +b^{2} =c^{2}[/tex] to only get a because we want to know what a is.

Rearranged: [tex]a=\sqrt{c^{2}-b^{2} }[/tex] or [tex]a=-\sqrt{c^{2}-b^{2} }[/tex]  It has to ways/options for a because when finding the square root of a number, it can be either positive or negative. But in this problem, it’s going to be positive because we’re finding the length of something.

-Since we know what c and b are, you can plug them into the new formula:

[tex]a=\sqrt{15^{2}-12^{2} }[/tex]

-Simplify it:

[tex]a=\sqrt{225-144}[/tex]

-Subtract inside the radical:

[tex]a=\sqrt{81}[/tex]  Then simplify it to get [tex]a=9[/tex].

You can check your answer by putting a back into the original Pythagorean Theorem formula ([tex]a^{2} +b^{2} =c^{2}[/tex]):

Steps

-Plug a, b, and c into the formula [tex]a^{2} +b^{2} =c^{2}[/tex]:

[tex](9)^{2} +(12)^{2} =(15)^{2}[/tex]

-Simplify to get:

[tex]81+144=225[/tex]

-Add:

[tex]225=225[/tex]  This is very true. So our answer is correct.

ANSWER: [tex]a=9[/tex]

Sorry for the long explanation, but I hope you understand and that this helps with your question! :)

Answer:

Step-by-step explanation:

lets make is short and simple

Pythagorean theorem: a² + b² = c²

a² + 12² = 15²

a² = 15² - 12²

a = √81

a = 9

Answer:

the first one and last one are true

Step-by-step explanation:

Answer:

40 square cm

Step-by-step explanation:

Answer:40 square cm

Step-by-step explanation:

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:

x=3 C

Step-by-step explanation:

5x-13=-3x+11

8x-13=11

8x=24

x=3

Answer:

the answer is x=3

Step-by-step explanation:

i hope this help you

Answer:

1

Step-by-step explanation:

f(4)=4-2x+5

4-2(4)+5

4-8+5

1

Answer:

x=1

Step-by-step explanation:

4-2x+5

x=4 so substitute the x with 4.

4-2(x)+5

=1

Answer:

It would be a obtuse triangle instead

Step-by-step explanation:

By using pythagorean and theorem (a^2 + b^2 = c^2)

So it would be 13^2___2^2 + 12^2

When you square them, you get 169___4 + 144

144 + 4 = 148, which is less than 169

SO it would be 169>148

So no, not a right triangle

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:

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

Step-by-step explanation:

Answer:

y = + 4

Step-by-step explanation:

I used an online algebra calculator to check my answer, so you can trust that this is correct.

Answer:

y=x+4

Step-by-step explanation:

2y=2x+8

Divide everything by 2y

y=x+4

Answer:

According to the calculation, Wayra mage a mistahe in step 2 where she added 13 and 6 together instead of multiplying to get 78.

She also make a mistake in step 2 where he subtracted 5z from 4z to get z instead of -z

Step-by-step explanation:

Given the equation solved by Wayra expressed as;

Step 1: 13(z+6) = 4(z-3)-5z

She is find the value of z from the equation;

Step 2: Open the parenthesis using the distributive property;

13(z+6) = 4(z-3)-5z

13z + 13(6) = 4z - 4(3) - 5z

13z + 78 = 4z - 12 - 5z

Step 3: Simplify

13z + 78 = 4z - 5z - 12

13z + 78 = -z -12

Step 4: Collect the like terms;

13z + z = -12 - 78

Step 5: Simplify the result

14z = -90

Step 6: Divide both sides by 14

14z/14 = -90/14

z = 6.428

According to the calculation, Wayra mage a mistahe in step 2 where she added 13 and 6 together instead of multiplying to get 78.

She also make a mistake in step 2 where he subtracted 5z from 4z to get z instead of -z

Answer:

42.3

Step-by-step explanation:

3.6(3)+4.5(7)

10.8+31.5

42.3

Answer:

first year $20 second year $20.80 Third year $21.63

Step-by-step explanation: This is for an extra money per year so after the first year that is how much extra money he gets every year.

Answer:

Step-by-step explanation:

if we have 137 students, and out of this number 7 were in cars

137-7=130 students in buses

there are 5 buses

130/5=26

26 students in each bus

Answer:

-9/7 bc the perpendicular is the inverse of the former slope

Step-by-step explanation:

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:

7

Step-by-step explanation:

5x4=20

20/2=10

17-10=7

Answer:

your answer is 7

Step-by-step explanation:

17-5×4÷2

P- parenthesis

E- Exponents

M- Multiplication

D- Divide

A- Add

S- Subtract

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:

x = 6

∠2 = 75

Step-by-step explanation:

In the given triangle two sides are equal and so it is an isosceles triangle. So, the angles opposite to equal sides are equal

11x + 9 + 11x + 9 + 30 = 180   {Angle sum property of triangle}

      11x + 11x + 9 +9 +30 = 180

                     22x + 48   = 180

                            22x    = 180 - 48

                               22x = 132

                                   x = 132/22

                                  x = 6

∠2 = 11*6 + 9 = 66 +9 = 75

Answer:

C.) 1 5/b boxes

Number of boxes left over

= 3 - 1/2 - 2/3

Convert each  fraction to one in terms of the LCM:

= 18/6 - 3/6 - 4/6

= 11/6

= 1 5/6 boxes.

The solution is Option B.

The number of boxes of crackers left with Eloise is 1 5/6 boxes of crackers

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 ,

Let the number of boxes of crackers left with Eloise be = A

Now , the total number of boxes of crackers be = 3 boxes

The number of boxes of crackers ate on Saturday = 1/2

The number of boxes of crackers ate on Sunday = 2/3

So , the equation will be

Number of boxes of crackers left with Eloise A =  total number of boxes of crackers - number of boxes of crackers ate on Saturday - number of boxes of crackers ate on Sunday

Substituting the values in the equation , we get

Number of boxes of crackers left with Eloise A = 3 - 1/2 - 1/3

On simplifying the equation , we get

Number of boxes of crackers left with Eloise A = 5/2 - 2/3

Number of boxes of crackers left with Eloise A = ( 15 - 4 ) / 6

Number of boxes of crackers left with Eloise A = 11/6

Number of boxes of crackers left with Eloise A = 1 5/6 boxes

Therefore , the value of A is 1 5/6 boxes

Hence , the number of boxes left is 1 5/6 boxes of crackers

To learn more about equations click :

https://brainly.com/question/19297665

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Answer:

PAIN

Step-by-step explanation:

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