4. Write a number story to show 917 + 67 = . Solve the problem.​

He is correct.

The further away ( to the left) from 0 a negative number is the smaller it is.

Billy correctly determined that −3/4 is smaller than −1/4 by plotting them on a number line. Numbers further to the left on the number line are smaller, and thus −3/4 is less because its absolute value is greater than that of −1/4 when both are negative.

Billy is correct in determining that −3/4 is smaller than −1/4. On a number line, negative numbers to the left are smaller than those to the right. Since −3/4 is further to the left than −1/4, it is indeed the smaller number. Comparing fractions with negative signs can initially be challenging, but remembering that the further left a number is on the number line, the smaller it is, can help clarify comparisons.

When plotting fractions on a number line, it is helpful to consider the absolute value of those fractions. The absolute value of −3/4 is 3/4, and the absolute value of −1/4 is 1/4. Since 3/4 is greater than 1/4, the negative version, −3/4, will be further to the left than −1/4 and therefore less than −1/4.

Answer: B

Step-by-step explanation:

The common factor missing from both sets of parentheses in the polynomial 10x^3 + 35x^2 - 4x - 14 when factored by grouping is (2x + 7).

To factor the polynomial 10x3 + 35x2 - 4x - 14 by grouping, we must first split the polynomial into two pairs that have a common factor. We can pair the terms as follows: (10x3 + 35x2) and (-4x - 14).

Factoring out the greatest common factor from each pair, we get:

5x2(2x + 7)

-2(2x + 7)

Now, we can observe that both pairs contain the common factor (2x + 7). So, the polynomial can be re-written using this common factor:

5x2(2x + 7) - 2(2x + 7)

Drawn out completely, the factored form of the polynomial using the distributive property (also known as factoring by grouping) thus becomes:

(5x2 - 2)(2x + 7)

Given expression is:

By substituting the value of "b" in the given expression, we get

→ [tex]a + \frac{3}{4} = 21[/tex]

→       [tex]a = 21 - \frac{3}{4}[/tex]

By taking L.C.M, we get

             [tex]= \frac{84-3}{4}[/tex]

             [tex]= \frac{81}{4}[/tex]

Thus the response above is correct.

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Answer:

3/6 or 1/2 or 50:50 there all right

Step-by-step explanation:

I am guessing that by simple dice you mean a 6 sided die and we know that 6 sided dice goes up to 6 and there are 3 prime number up to 6 which are 2 3 5 so if 3 out of 6 numbers are prime it is half of the dice so there is a 50/50 chance you role a prime number

Answer:

x=1/2

Step-by-step explanation:

4x-5(x-2)=12x+4-x

4x-5x+10=12x-x+4

-x+10=11x+4

-x-11x+10=4

-12x+10=4

-12x=4-10

-12x=-6

12x=6

x=6/12

simplify

x=1/2

Answer: x = 1/2

Explanation :

First write the equation as you see it:

4x-5(x-2)=12x+4-x

Next do the math in the parentheses:

4x-5x+10=12x-x+4

Combine the x’s:

-12x+10=4

Switch the 10 and put it on the other side:

-12x=4-10

Change to negative to positive:

12x=6

Divide:

x=6/12

Simplify

x=1/2

Thus, you answer is x = 1/2

Hope this helps! :)

Answer:

$1.95 is 15% of 13 dollars

Answer:

13 - 15% (1.90) = 11.10

Step-by-step explanation:

13 - 15% (1.90) = 11.10

Answer:

9 tables

Step-by-step explanation:

Let x be the number of chairs sold and y be the number of tables sold.

Chairs are sold for $100 each, then x chairs cost $100x.

Tables are sold for $550 each, then y tables cost $550y.

Every day, the store can ship at most 21 pieces of furniture, then

[tex]x+y\le 21[/tex]

Store must sell no less than $5,700 worth of chairs and tables, then

[tex]100x+550y\ge 5,700[/tex]

If 10 chairs were sold, then [tex]x=10.[/tex] Substitute this value into both inequalities:

1. [tex]10+y\le 21\Rightarrow y\le 11[/tex]

2. [tex]100\cdot 10+550y\ge 5,700\Rightarrow 550y\ge 4,700\Rightarrow y\ge \dfrac{470}{55}=8\dfrac{6}{11}[/tex]

Hence, [tex]8\dfrac{6}{11}\le y\le 11[/tex]

The minimum number of tables that the the store must sell in order to meet the requirements is 9 tables

Answer:{ 9, 10, 11 }

Step-by-step explanation:

Answer:

[tex]\frac{11}{36}[/tex] yard

Step-by-step explanation:

Length of string Mrs. Ruiz has = [tex]\frac{11}{12}[/tex] yard

Mrs. Ruiz needs to hang 3 banners using the string.

Having known that each banner uses same length of string to be hung we can divide total length of sting into 3 equal parts.

So, we can divide [tex]\frac{11}{12}[/tex] yard by 3 as

⇒ [tex]\frac{11}{12}\div 3[/tex]

Changing the division sing to multiplication by taking reciprocal of divisor.

⇒ [tex]\frac{11}{12}\times \frac{1}{3}[/tex]

We can now multiply numerators and denominators.

⇒ [tex]\frac{11}{36}[/tex] yard

∴  Mrs. Ruiz must used  [tex]\frac{11}{36}[/tex] yard of string for each banner.

Answer:

The kinetic energy of the roller coaster is 1600000 J.

Step-by-step explanation:

Given:

Mass of the roller coaster is 8000 Newton's and speed 20.0 meters/seconds.

Now, we need to find the kinetic energy [tex]E_{k}[/tex] of the roller coaster.

So, Mass of roller coaster (m) = 8000 N.

Velocity of roller coaster (v) = 20.0 m/s.

Now, putting the formula of kinetic energy:

[tex]E_{k} = \frac{1}{2}\times m\times v^{2}[/tex]

[tex]E_{k}=\frac{1}{2} \times 8000\times 20^{2}[/tex]

[tex]E_{k}=\frac{1}{2} \times 8000\times 400[/tex]

[tex]E_{k}=\frac{1}{2} \times 3200000[/tex]

[tex]E_{k}=1600000[/tex]

Therefore, the kinetic energy of the roller coaster is 1600000 J.

Step-by-step explanation:

A box of cereal states that there are 93 calories in a three fourths-cup serving. What is the unit rate for calories per cup?

126.7 ~= 127 calories

How many calories are there in 2 cups of the cereal?

127 *2 = 254 calories.

The unit rate for calories per​ cup is 124 calories and 2 cups of the​ cereal contain 248 calories.

The unitary method is a technique for solving a problem by first finding the value of a single unit, and then finding the necessary value by multiplying the single unit value.

Given is a box of cereal which states that there are 93 calories in a

(3/4)th of a cup serving.

We can write -

3/4 cup serving contain → 93 calories

1 cup serving will contain → (93 x 4)/3 which is equivalent to 124 calories

Similarly, we can calculate for 2 cups of serving as -

1 cup → 124 calories

2 cups → (2 x 124) = 248 calories

Therefore, the unit rate for calories per​ cup is 124 calories and 2 cups of the​ cereal contain 248 calories.

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Answer:

[tex]AB=DC=32\ units[/tex]

[tex]AD=BC=24\ units[/tex]

Step-by-step explanation:

we know that

In a parallelogram, opposite sides are parallel and congruent

In this problem we have a parallelogram

so

[tex]DC=AB[/tex]

[tex]AD=BC[/tex]

substitute the given values

[tex]5x-18=2x+12[/tex]

[tex]5x-2x=12+18[/tex]

[tex]3x=30[/tex]

[tex]x=10[/tex]

Find the length of side AB

[tex]AB=2x+12[/tex]

substitute the value of x

[tex]AB=2(10)+12=32\ units[/tex]

Find the length of side CB

[tex]BC=3x-6[/tex]

substitute the value of x

[tex]BC=3(10)-6=24\ units[/tex]

therefore

[tex]AB=DC=32\ units[/tex]

[tex]AD=BC=24\ units[/tex]

x equals 22

____________________________________________

The Segment Postulate states the following:

Given two end points A and B, a third point C lines on the segment AB if and only if the distances between the points satisfy the equation:

[tex]\overline{AB}=\overline{AC}+\overline{CB}[/tex]

____________________________________________

From the figure:

[tex]\overline{AC}=8+x \\ \\ \overline{CB}=10 \\ \\ \overline{AB}=40[/tex]

Our goal is to find x:

[tex]\overline{AB}=\overline{AC}+\overline{CB} \\ \\ Substituting \ values: \\ \\ 40=(8+x)+10 \\ \\ 18+x=40 \\ \\ Subtracting \ 18 \ from \ both \ sides: \\ \\ 18-18+x=40-18 \\ \\ \boxed{x=22}[/tex]

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The equation for Louis's purchase is: [tex]x+y=8[/tex]

The equation for Kate's purchase is: [tex]y+z=9[/tex]

The equation for Biff's purchase is: [tex]x+y+z=13.50[/tex]

Step-by-step explanation:

First of all we have to define variables for each item involved in the purchase

Let x represent burger

y represent soda

z be the slice of pizza

Then

"Louis bought a burger and soda for $8"

[tex]x+y=8[/tex]

"Kate purchased a slice of pizza and soda for $9"

[tex]y+z=9[/tex]

"Biff purchased a burger, a slice of pizza and a soda for $13.50"

[tex]x+y+z=13.50[/tex]

The equation for Louis's purchase is: [tex]x+y=8[/tex]

The equation for Kate's purchase is: [tex]y+z=9[/tex]

The equation for Biff's purchase is: [tex]x+y+z=13.50[/tex]

Keywords: Linear Equations, Variables

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Answer:

x=110

Step-by-step explanation:

66*20=6*2*x

1320=12x

x=1320/12

x=110

Answer:

B

Step-by-step explanation:

A.) If you plug in 5 for t, you'd get -5 squared + 10(5) - 16

Which would equal 25 + 50 - 16 = 59

Answer a says t is less than 5, so for example let's plug in 4. You'd get a lower number, which means its decreasing. A is wrong

B.) Now let's plug in 8 for t.

-8 squared = 64.

64 + 10(8) - 16 = 144 - 16 = 128

Your answer here is positive, and B states is t > 8. Any number above 8 is going to give you a positive number and it is increasing

Answer:

B. t>8

Step-by-step explanation:

Answer:

132 inches

Step-by-step explanation:

first convert yards(yd) to feet(ft)

3yd* (3ft / 1 yd)  (yds cancel)

3 * 3ft = 9ft

9ft + 2ft = 11ft

11ft * (12in / 1ft) (ft cancel)

11 * 12in = 132in

Answer:

110 inches

Step-by-step explanation:

1 yard = 36 * 3 = 108 + 2 = 110

Answer:

x = 7,y = 8

Step-by-step explanation:

(20 + x + y )/ 5 = x

4x = 20 + y

x ≥ 6

y ≥ 6

if x = 6, y = 4 No

if x = 7, y = 8 Yes!

Answer:

6

Step-by-step explanation:

you take 18 and divide it by 3

The completed table shows that the product of wavelength and frequency (k) is approximately constant for X-rays, radio waves, green light, and UV rays. Here are the final values for a, b, c, and d: [tex]a = \frac{1}{3} \times 10^{8} \, \text{m/s} , \ b = \frac{1}{3} \times 10^{8} \, \text{m/s} , \ c = \frac{1}{3} \times 10^{8} \, \text{m/s} , \ d = \frac{2}{15} \times 10^{-8} \, \text{m/s}.[/tex]

To determine if wavelength varies inversely with frequency, we can use the formula [tex]\(k = \text{wavelength} \times \text{frequency}\).[/tex]. Rearranging this formula to solve for k, we get [tex]\(k = \frac{1}{\text{frequency}} \times \text{wavelength}\)[/tex].

Now, we can calculate the values of k for each type of radiation:

[tex]\[a = \frac{1}{3 \times 10^{18}} \times (1 \times 10^{-10}) = \frac{1}{3} \times 10^{-28} \, \text{m/s}.\]\[b = \frac{1}{3 \times 10^9} \times (1 \times 10^{-1}) = \frac{1}{3} \times 10^{-10} \, \text{m/s}.\]\[c = \frac{1}{5 \times 10^{11}} \times (600 \times 10^{-6}) = \frac{1}{3} \times 10^{-8} \, \text{m/s}.\]\[d = \frac{1}{7.5 \times 10^{14}} \times (4 \times 10^{-7}) = \frac{4}{30} \times 10^{-21} \, \text{m/s}.\][/tex]

Now we express the values in terms of [tex]\(10^8\)[/tex]:

[tex]\[a = \frac{1}{3} \times 10^{-20} \, \text{m/s} = \frac{1}{3} \times 10^{8} \, \text{m/s}.\]\[b = \frac{1}{3} \times 10^{-2} \, \text{m/s} = \frac{1}{3} \times 10^{8} \, \text{m/s}.\]\[c = \frac{1}{3} \times 10^{0} \, \text{m/s} = \frac{1}{3} \times 10^{8} \, \text{m/s}.\]\[d = \frac{4}{30} \times 10^{-13} \, \text{m/s} = \frac{2}{15} \times 10^{-8} \, \text{m/s}.\][/tex]

So, the completed table is as follows:

[tex]\[a = \frac{1}{3} \times 10^{8} \, \text{m/s}.\]\[b = \frac{1}{3} \times 10^{8} \, \text{m/s}.\]\[c = \frac{1}{3} \times 10^{8} \, \text{m/s}.\]\[d = \frac{2}{15} \times 10^{-8} \, \text{m/s}.\][/tex]

Answer:

about $2,557

Actual cost : $2556.97

Step-by-step explanation:

well since all of them are .99 if you round to the hundreths it make another dollar cause it will force the .9 to become 1.0

so it be 1450 for the refrigerator, 490 for the dishwasher, and 617 for the electric range.

add those numbers to get about $2,557

Answer:

[tex]\frac{72}{q}[/tex] number of cheerleaders, she would expect to forget their bows.

Step-by-step explanation:

Kaley estimates that 2 out of every q cheerleaders will forget to bring their bows for practice.

So, if there are q cheerleaders then 2 of them will forget to bring their bows.

Then if there are 1 cheerleader then [tex]\frac{2}{q}[/tex] of them will forget to bring their bows.

Finally,  if there are 36 cheerleaders then [tex]\frac{2 \times 36}{q} = \frac{72}{q} [/tex] of them will forget to bring their bows.

Therefore, [tex]\frac{72}{q}[/tex] number of cheerleaders, she would expect to forget their bows. (Answer)

Answer:

B

Step-by-step explanation:

You could plug in the point given with another point but for simplicity, you can count how far away you are from the vertex. (Since the y intercept is at 0,0)

Go up 3 spots from the vertex, and then go one spot to the right. Ay now you're at (1,3)

You went up 3 and right 1, which translates to simply 3

Correct option:

[tex]2x^2+3x-13x-1[/tex]

A quadratic function is given by the form:

[tex]f(x)=ax^2+bx+c \\ \\ Being \ a,b,c \ any \ real \ constants[/tex]

On the other hand, a quadratic equation is given by the form:

[tex]ax^2+bx+c=0 \\ \\ Being \ a,b,c \ any \ real \ constants[/tex]

And a quadratic expression is given by the form:

[tex]ax^2+bx+c \\ \\ Being \ a,b,c \ any \ real \ constants[/tex]

As you can see, when talking about the term quadratic the higher degree of the polynomial is 2. The options are:

[tex]1. \ 6x^4-5x^3+3x^2-7x-8 \\ \\ 2. \ 5x^3+3x^2-7x-8 \\ \\ 3. \ 2x^2+3x-13x-1[/tex]

So the only option that meets our requirement is:

[tex]2x^2+3x-13x-1[/tex]

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Answer:

2x^2+3x-13x-1

Step-by-step explanation:

Answer:

-1 1/2

The drawing will help

Answer:

-15

Step-by-step explanation:

9 divided by 10 is 0.9 and -3 divided by 5 is -0.06

and 0.9 divided by -0.06 is

Answer:

A deck=52

Probability of selecting black cards 26/52

26/52*3/52

Step-by-step explanation:

Correct me if I am wrong.

Answer:

q = 8

Step-by-step explanation:

Given the 2 equations

p + q = 36 → (1)

p - q = 20 → (2)

Add the 2 equations term by term

2p = 56 ( divide both sides by 2 )

p = 28

Substitute p = 28 into (1)

28 + q = 36 ( subtract 28 from both sides )

q = 8

If p + q = 36, and p -q = 20, then q = B

The given question is an example of an algebraic equation that involves the use of BODMAS and the substitution method.

Let

From equation (1)

Let p = 36 - q.

Then we can substitute the value of p into equation (2)

p - q = 20

36 - q - q = 20

36 - 2q = 20

collecting the like terms

-2q = 20 - 36

- 2q = - 16

Divide both sides by (-2)

q = -16/-2

q = 8

Therefore, we can conclude that the value of q = 8

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Answer: x=-1,-2

Step-by-step explanation:

X^2+3x+2=0

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

x=-1,-2

Answer:

See explanation

Step-by-step explanation:

    Statement                              Reason

1. [tex]\overline{PS}\perp \overline{SQ}[/tex]                           Given

2. [tex]m\angle PSQ = 90^{\circ}[/tex]          Definition of perpendicular lines

3. [tex]\triangle PSQ[/tex] is right triangle   Definition of right triangle

4. [tex]\overline{RQ}\perp \overline{SQ}[/tex]                          Given

5. [tex]m\angle RQS = 90^{\circ}[/tex]          Definition of perpendicular lines

6. [tex]\triangle RQS[/tex] is right triangle   Definition of right triangle

7. [tex]m\angle PSQ=m\angle RQS[/tex]       Substitution property of equality

8. [tex]\overline {SQ}\cong \overline {QS}[/tex]    Reflexive property

9. [tex]\overline {PQ}\cong \overline {RS}[/tex]                        Given

10. [tex]\triangle PSQ\cong \triangle RQS[/tex]               HL postulate

[tex]\bf \left( \cfrac{1}{~~\begin{matrix} 2 \\[-0.7em]\cline{1-1}\\[-5pt]\end{matrix}~~} \right)(~~\begin{matrix} 2 \\[-0.7em]\cline{1-1}\\[-5pt]\end{matrix}~~x)(x+8)\implies x(x+8)\implies x^2+8x[/tex]

Answer:

[tex]x^{2} +8x[/tex]

Answer:

11.39

Step-by-step explanation:

-3.86+6.82=2.96

abs(2.96)=2.96

----------------------

4.02-12.45=-8.43

abs(-8.43)=8.43

-----------------------

1(2.96)+8.43=2.96+8.43=11.39