Solve the following inequality.
AlGEBRA 1 QUESTION:

Answer:

Step-by-step explanation:

Answer:

k > 7

Step-by-step explanation:

Given the inequality statement:  4k - (5 + 3k) > 2

Distribute -1 into (5 + 3k):

4k -5 - 3k > 2

Next,  add like terms:

k - 5 > 2

Add 5 to both sides of the inequality:

k - 5 + 5 > 2 + 5

k > 7

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Answer:

\(k>7\)

Step-by-step explanation:

\(4k-\left(5+3k\right)>2\)

\(-\left(5+3k\right)\)

\(-5-3k\)

\(4k-5-3k\)

\(4k-3k=k\)

\(k-5\)

\(k-5>2\)

Add 5 to both sides

\(k-5+5>2+5\)

\(k>7\)

Answer:

(a) 2.79 seconds after its release the bag will strike the ground.

(b) At a velocity of 73.28 ft/second it will hit the ground.

Step-by-step explanation:

We are given that a balloon, rising vertically with a velocity of 16 feet per second, releases a sandbag at the instant when the balloon is 80 feet above the ground.

Assume the acceleration of the object is a(t) = −32 feet per second.

(a) For finding the time it will take the bag to strike the ground after its release, we will use the following formula;

                        \(s=ut+\frac{1}{2} at^{2}\)

Here, s = distance of the balloon above the ground = - 80 feet

          u = intital velocity = 16 feet per second

          a = acceleration of the object = -32 feet per second

          t = required time

So,  \(s=ut+\frac{1}{2} at^{2}\)

      \(-80=(16\times t)+(\frac{1}{2} \times -32 \times t^{2})\)

       \(-80=16t-16 t^{2}\)

       \(16 t^{2} -16t -80 =0\)

          \(t^{2} -t -5 =0\)

Now, we will use the quadratic D formula for finding the value of t, i.e;

           \(t = \frac{-b\pm \sqrt{D } }{2a}\)

Here, a = 1, b = -1, and c = -5

Also, D = \(b^{2} -4ac\) = \((-1)^{2} -(4 \times 1 \times -5)\) = 21

So,  \(t = \frac{-(-1)\pm \sqrt{21 } }{2(1)}\)

      \(t = \frac{1\pm \sqrt{21 } }{2}\)

We will neglect the negative value of t as time can't be negative, so;

\(t = \frac{1+ \sqrt{21 } }{2}\) = 2.79 ≈ 3 seconds.

Hence, after 3 seconds of its release, the bag will strike the ground.

(b) For finding the velocity at which it hit the ground, we will use the formula;

                       \(v=u+at\)

Here, v = final velocity

So,  \(v=16+(-32 \times 2.79)\)

      v = 16 - 89.28 = -73.28 feet per second.

Hence, the bag will hit the ground at a velocity of -73.28 ft/second.

Answer:

The percent would be 10 Im guessing

Step-by-step explanation:

Hope this helped :)

After selling some of the walnut cakes, the number of walnut cake remaining is 48. The number of walnut cake sold is 40.

Baker Jack baked 160 cakes. 55 percent of them were walnut cakes and the rest were almond cakes.

Therefore,

the number of walnut cakes = 55% of 160

the number of walnut cakes = 55 / 100 × 160

the number of walnut cakes = 8800 / 100

the number of walnut cakes = 88

Therefore,

the number of almond cakes = 160 - 88 = 72

After selling some of the walnut cakes, the percentage of the walnut cakes become 40%.

Therefore, the number of walnut cakes after sales is as follows:

let

x = number of walnut cake sold

40% of (88 - x + 72 ) = 88 - x

40 / 100 (160 - x) = 88 - x

6400 - 40x / 100 = 88 - x

cross multiply

6400 - 40x = 8800 - 100x

6400 - 8800 = -100x + 40x

-2400 = -60x

x = 2400 / 60

x = 40

Therefore,

number of walnut cake remaining = 88 - 40 = 48  

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The amount of gas that is left in the tank if there is only 1 / 8 of the tank is 1.5 gallons

The car tank can accommodate 12 gallons of gas .

Her fuel gauge says that there is 1 / 8 of the tank left in the car tank.

Therefore, the amount of gas that is left in the tank is calculated as follows:

amount left in the tank = 1 / 8 × 12

amount left in the tank = 12 / 8

amount left in the tank = 6 / 4

amount left in the tank = 3 / 2

amount left in the tank = 1.5 gallons

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3/8 divided by 1 3/5 is 3/8 ÷ 1 3/5 = 15/64.

What is the fraction?

A fraction is a numerical quantity that represents a part of a whole or a ratio between two quantities. It is expressed as one integer divided by another integer, with a horizontal line separating the two numbers. The number above the line is called the numerator and the number below the line is called the denominator.

To divide a fraction by another fraction, you need to multiply the first fraction by the reciprocal of the second fraction.

First, we need to convert the mixed number to an improper fraction:

1 3/5 = (5*1 + 3)/5 = 8/5

Now we can find the reciprocal of 8/5:

reciprocal of 8/5 = 5/8

So, 3/8 ÷ 1 3/5 can be rewritten as:

3/8 ÷ 8/5 = 3/8 * 5/8

Multiplying the numerators and denominators:

3/8 * 5/8 = (35)/(88) = 15/64

Therefore, 3/8 divided by 1 3/5 is 3/8 ÷ 1 3/5 = 15/64.

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Answer:

  55

Step-by-step explanation:

We can use the given relations to write an equation that can be solved for my age 25 years from now.

__

Let x represent my age in 25 years. The age relationships can be summarized as ...

We know 10 years ago my dad was 4 times my age, so we have ...

  4(x -35) = 3x -85

  4x -140 = 3x -85 . . . eliminate parentheses

  x = 55 . . . . . . . . . . . add 140-3x

I will be 55 in 25 years from now.

_____

Additional comment

10 years ago, I was 20 and my dad was 80. Now, I'm 30 and my dad is 90. In 25 years, I'll be 55.

Step-by-step explanation:

To find the percent increase, divide the increase by the original price.

P1 = price yesterday

P2 = price today

To find percent increase

\( \frac{(p2 - p1)}{p1} \)

Or to answer the question,

P1 = 9.74

P2 = 9.87

\( \frac{(9.87 - 9.74)}{9.74} = 0.013347\)

Or 1.33%

Answer:

I think the answer is 11i

there is the correct answer.

Answer:

1.) A = (1/2bh) 4 + lxw

= 1/2 x 7 x 13 x 4 + 7 x 7

182 + 49 = 231cm2

l think u can use the formula to find the area of the other pyramids

According to the solving Sam will spend $585.00 of the money he collects on cleaning materials.

%, a relative figure signifying hundredths of any amount. Since one percent (symbolised as 1%) is equal to one hundredth of something, 100 percent stands for everything, and 200 percent refers to twice the amount specified. percentage. Mathematical percentile is a related topic.

Sam collects $150.00 each day for 6 days, so the total amount he collects is:

$150.00/day x 6 days = $900.00

The shelter will use 35% of the money he collects to buy pet food. To find out how much money will be used to buy pet food, we can multiply the total amount Sam collects by 35% (or 0.35):

$900.00 x 0.35 = $315.00

So, $315.00 of the money that Sam collects will be used to buy pet food. To find out how much money will be used to buy cleaning supplies, we can subtract the amount used to buy pet food from the total amount collected:

$900.00 - $315.00 = $585.00

$585.00 of the money that Sam collects will be used to buy cleaning supplies.

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Answer:

drag  the sum to 0

Step-by-step explanation:

\(\large{\underline{\underline{\pmb{\frak {\color {red}{Question:}}}}}}\)

\( \sf \red{what \: is \: the \: distance \: the \: points(51) \: and ( - 3 - 5)}\)

\(\large{\underline{\underline{\pmb{\frak {\color {blue}{Answer:}}}}}}\)

Here,

\(x_{1}\) = 5. \(x_{2}\) = - 3

\(y_{1}\) = 1. \(y_{2 }\) = - 5

We know, Distance formula

\( \red \dag \boxed{\sqrt{ (x_{2} - x_{1} )^{2} + (y_{2} - y_{1} )^{2} } } \red \dag\)

\( \sqrt{( - 3 - 5 )^{2} + ( - 5 - 1)^{2} } \\ \\ \leadsto \sqrt{( - 8)^{2} + ( - 6)^{2} } \\ \\ \leadsto \sqrt{64 +36 } \\ \\ \leadsto \sqrt{100} \\ \\ \leadsto10 \: units\)

Therefore, the required answer is 10 units.

I've written units because measurement is not given.

\( \boxed{ \frak \red{brainlysamurai}}\)

Answer:

200

Step-by-step explanation:

1,800,000/9,000 = 200

Para confirmar:

200 x 9,000 = 1,800,000

The answer is 3,240

Explanation:

To calculate the total income tax, it is necessary to calculate what is the 15% of 8000, and 17% for the remaining money, which is 12.000 (20,000 - 8,000= 12,000). Considering the statement specifies the 15% is paid for the first 8,000 and from this, the 17% is paid. Now to know the percentages you can use a simple rule of three, by considering 8000 and 12000 as the 100%. The process is shown below:

1. Write the values

\(8000 = 100\)

\(x = 15\) (the percentage you want to know)

2. Use cross multiplication

\(x =\frac{8000 x 15 }{100}\)

\(x = 1200\)

This means for the first 8000 the money Rafael needs to pay is 1,200

Now, let's repeat the process for the remaining money (12,000)

\(12000 = 100\\\\\)

\(x = 17\)

\(x = \frac{12000 x 17}{100}\)

\(x = 2040\)

Finally, add the two values \(1200 + 2040 = 3240\)

Answer:

Step-by-step explanation:

Since order does not matter \(_{12}C_3\\ \\ \frac{12!}{3!9!}\\ \\ 220\)

Answer:55 degrees

Step-by-step explanation: We  are dealing with a right angle which is also the same as a complementary angle that adds up to 90 degrees.

The following equation can be obtained from the right angle

(x-20)+x=90

Simplifying like terms

2x-20=90

We want to solve for x this means we want to get x  terms on its own.

We need for -20 to disappear the only way to do this is to add 20. What we do to one side we must do to the other.

2x-20+20=90+20

2x=110

To solve for x we need to divide both sides by 2

2x/2=110/2

x=55 degrees

Answer:

y=2

Step-by-step explanation:

add 5 to 0 then divide 5 with 2

Quartile deviation in Statistics can be defined as the statistic that measures the dispersion. Here, the Dispersion is the state of getting dispersed or spread. Statistical dispersion means the extent to which numerical data is likely to vary about an average value. In other words, dispersion helps to understand the distribution of the data Suppose Q1 is the lower quartile, Q2 is the median, and Q3 is the upper quartile for the given data set, then its quartile deviation can be calculated using the following formula.

QD = (Q3 – Q1)/2

In the next section, you will learn how to calculate these quartiles for both ungrouped and grouped data separately.

For an ungrouped data, quartiles can be obtained using the following formulas,

Q1 = [(n+1)/4]th item

Q2 = [(n+1)/2]th item

Q3 = [3(n+1)/4]th item

Where n represents the total number of observations in the given data set.

Also, Q2 is the median of the given data set, Q1 is the median of the lower half of the data set and Q3 is the median of the upper half of the data set.

The given data is that is first quartile is lowest off 25% of the numbers and second quartile. It is between 0% and 50% of two median. And thought quartile is the rope percent two 75% ward court trial is the highest 25% of numbers. For example, spores, the distribution spores, the distribution of math scores not so of course in a class of 19 students of 19 students in ascending order is with 39 60 6 to 5 65, 68, 69, 70 72, 75, 75, 76, 77 81, 84, 87, 90 95, 98. No postmark the median and Q two which is in this case in this Case is the 10th value and value that is 70 five. You won is the central. Mhm point between the smallest to score smallest school and median in this case. Do you want Falls between the two post and fifth school? That is 68. The average of fifth and six score is fifth plus sixth way two. That is 68 plus 69/2 which is equal to 68.5. No Q three is middle value between 23 and I used to score is 84. No Q three Is 82 plus 84/2. That is 83. No. Do you want the hosts as that? 25% of the scores ah less then 68 and 75% of the of course are greater and you do the median is the 50th percentile and shows that, and shows that 50% of the scores are less than 75 and 50% of the scores are above 75 and finally, you're three the 75th percentile. It reveals that 25% of the scores, odd greater than 75%, are less than it would be full.

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Answer:  The answer has one solution:

_______________________________

      →  x = 1 ;   y =  -4 ;  or, write as:  [1, -4].

_______________________________

Step-by-step explanation:

_______________________________

Given:

  y  =  - 1x – 3

  y  =   -7x + 3 ;

_______________________________

    -1x – 3  =   -7x + 3  ;  Solve for "x" ;

Add:  " +1x" ; and add " +3 " ;  to Each Side of the equation:

Subtract " 1x " ; and Subtract " 1 " ; from Each Side of the equation:

   -1x  + 1x  – 3  + 3  =  -7x  + 1x + 3 + 3 ;

         to get:  

             0  =  -6x + 6

          ↔  -6x + 6 = 0 ;

Now, subtract " 6 " from Each Side of the equation:

                -6x + 6 – 6  = 0 – 6  ;

       to get:

               -6x = -6 ;

Now, divide Each Side of the equation by " -6 ";  

      to isolate "x" on one side of the equation;

      & to solve for "x" ;

              -6x /-6  =  -6/-6 ;

      to get:

                x = 1 .

_______________________________

Now, let us solve for "y" ;  

We are given:  

 y =  -x – 3  ;

Substitute our solved value for "x" ; which is:  " 1 " ; for " x " ; into this given equation; to obtain the value for " y " :

 y =  -x – 3  ;

    =  -1  – 3  

 y =   - 4 .

_______________________________

Let us check our answers by plugging the values for "x" and "y" ;

" 1 " ; and " -4 "; respectively);  into the second given equation; to see if these values for " x " and " y"  ; hold true:

Given:   y  =    - 7x  +  3 ;

           →  -4   =?  -7(1) + 3 ??  ;

           →  -4   =?   -7   + 3  ??  ;

           →  - 4 =?   -4 ?? ;

           →  Yes!

_______________________________

The answer has one solution:

      →  x = 1 ;   y =  - 4 ;  or, write as:  [1, -4 ].

_______________________________

Hope this is helpful!  Best wishes!

_______________________________

The number of bears that the researcher should be expected to see in the larger central Pennsylvania forest with about 1,000 total animals is given as follows:

95 bears.

To obtain the number of bears in the larger forest, first we must obtain the proportion in the smaller forest.

The proportion is given by the number of bears divided by the total number of animals, both of these amounts given by the bar graph presented at the end of the answer.

The number of bears is given as follows:

20.

The total number of animals is given as follows:

20 + 70 + 30 + 90 = 210.

Meaning that the proportion of bears is of:

20/210.

Hence, out of 1000 animals, the expected number of bears is of>

20/210 x 1000 = 20000/210 = 95 bears.

The bar graph is given by the image presented at the end of the answer.

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Answer:Total units would be: 3+4 = 7. value of 1 unit = 28/7 = 4. ratio would be 3(4) & 4(4) = 12 & 16

Step-by-step explanation:

No, the rank of the product of two n by n square matrices A and B, denoted as AB, cannot be less than n-1 if both A and B have ranks of n-1.

According to the Rank-Nullity theorem, for any matrix M, the sum of its rank and nullity is equal to the number of columns in M. In this case, the number of columns in AB is n, so the sum of the rank and nullity of AB must be n.

If rank(A) = rank(B) = n-1, it means that both A and B have nullity 1. The nullity of a matrix is the dimension of its null space, which consists of all vectors that get mapped to the zero vector when multiplied by the matrix. Since both A and B have rank n-1, their null spaces consist only of the zero vector.

Now, considering AB, if the rank of AB were less than n-1, it would mean that the nullity of AB is greater than 1.

However, this would violate the Rank-Nullity theorem since the sum of the rank and nullity of AB must be n, which is the number of columns.

Therefore,  if rank(A) = rank(B) = n-1, the rank of AB cannot be less than n-1.

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Answer:

Step-by-step explanation:

The given hexagon has interior angles

x,x,x, x/2, x/2, x/2 for a total of S1=4.5x.

We also know that the sum of interior angles of any polygon of n sides is

S2=180(n-2)

For a hexagon, S2 = 180(6-2) = 720°.

Equating S1 and S2

4.5x = 720

x = 720/4.5 = 160.

Therefore substitute x in the given angles to get

{160°,160°.160°,80°,80°,80°}

Answer:

Number 1

Step-by-step explanation:

-5(m + 1) ≤ 23

Distribute

-5m - 5 ≤ 23

-5m ≤ 23 + 5

-5m ≤ 28

-m ≤ 28/5

Since we divide by a negative the ≤ flips to ≥

m ≥ -28/5

Hope this helps :3

Answer: below :p

Step-by-step explanation:

First problem is irrational since square roots are part of the irrational group.

Second problem is rational since the decimal is repetitive or repeating in an infinite 363636.