Complete the square for the function f(x) = x² - 10 + 21. What is the minimum point on a graph of this function?
(1, -4)
(-5, -1)
(-4,5)
(5, -4)

The width of rectangle is [tex]2\frac{1}{4}[/tex] cm and length is [tex]5\frac{5}{12}[/tex] cm.

Step-by-step explanation:

Let,

Width of rectangle = w

Length of rectangle = [tex]w+3\frac{1}{6}=w+\frac{19}{6}[/tex]

Perimeter of rectangle = [tex]15\frac{1}{3}=\frac{46}{3}[/tex] cm

Perimeter = 2(Length + Width)

[tex]\frac{46}{3}=2(w+\frac{19}{6}+w)\\\\\frac{46}{3}=2(2w+\frac{19}{6})\\\\\frac{46}{3}=4w+\frac{19}{3}\\\\4w+\frac{19}{3}=\frac{46}{3}\\\\4w=\frac{46}{3}-\frac{19}{3}\\\\\ 4w=\frac{46-19}{3}\\\\4w=\frac{27}{3}\\\\4w=9[/tex]

Dividing both sides by 4

[tex]\frac{4w}{4}=\frac{9}{4}\\\\w=\frac{9}{4}[/tex]

Width of rectangle = [tex]\frac{9}{4}=2\frac{1}{4}\ cm[/tex]

[tex]Length = w+\frac{19}{6}=\frac{9}{4}+\frac{19}{6}\\\\Length = \frac{27+38}{12}=\frac{65}{12}\\\\Length=5\frac{5}{12}\ cm[/tex]

The width of rectangle is [tex]2\frac{1}{4}[/tex] cm and length is [tex]5\frac{5}{12}[/tex] cm.

Keywords: rectangle, perimeter

Learn more about perimeter at:

#LearnwithBrainly

Final answer:

The width of the rectangle is 9.92 cm (approx.) and the length is 13.09 cm, calculated using the given perimeter and the relationship between the width and length, both rounded to three significant figures.

Explanation:

The question asks to find the width and length of a rectangle given that the length is 3 1/6 cm longer than the width and the perimeter is 15 1/3 cm. To solve this, first express the perimeter as an equation involving width (w) and length (l):

Perimeter (P) = 2l + 2w

Since the length is 3 1/6 cm longer than the width, we can express the length as:

l = w + 3 1/6

Substitute the value of l in the perimeter equation:

15 1/3 = 2(w + 3 1/6) + 2w

Convert mixed numbers into improper fractions for easier computation:

46/3 = 2(w + 19/6) + 2w

Expand and solve for w:

46/3 = (4w + 19/3)

3(46) = 4w(3) + 19

138 = 12w + 19

119 = 12w

w = 119/12

w = 9.916666...

To match our significant figures requirement, we report the width of the rectangle as 9.92 cm to three significant figures. Now calculate the length:

l = w + 3 1/6

l = 9.92 + 3.1666...

l = 13.0866...

Again, matching our significant figures requirement, the length is reported as 13.09 cm to three significant figures.

Answer:

[tex]y=-2x+3[/tex]

Step-by-step explanation:

Given the slope of line [tex]m[/tex] is [tex]-2[/tex].

And y-intercept is [tex](0,3)[/tex]

We can write the equation of line by using the slope-intercept form.

The slope-intercept from is

[tex]y=mx+b[/tex]

Where [tex]m[/tex] is the slope of line. And [tex]b[/tex] is the y-intercept.

In our problem y-intercept is given as [tex]b=3[/tex].

Plugging these we get,

[tex]y=-2x+3[/tex]

Answer:

3n + 5

Step-by-step explanation:

You can't add 5 to 3n. So in 5 years he will 3n + 5.

José's age in 5 years will be 3n + 5, where 3n represents his current age.

If José's present age is 3n, and we want to find out how old he will be in 5 years, we need to add 5 to his current age expressed as 3n. This can be done with a simple algebraic expression:

Age in 5 years = Current Age + 5 = 3n + 5

Without the value of n, we can't calculate his exact future age, but we know that in 5 years, his age will be 5 years older than it is now.

Answer:

work is shown and pictured

Answer:

The final simplification is (32p^-15).

Step-by-step explanation:

Given:

(2p^-3)^5 we have to simplify.

Property to be used:(Power rule)

Power rule states that: [tex](a^x)^y=a^x^y[/tex] ...the exponents were multiplied.

Using power rule.

We have,

⇒[tex](2p^-3)^5[/tex]          

⇒[tex](2^5)(p^-3^*5)[/tex]     ...taking exponents individually.

⇒[tex]32(p^-^1^5)[/tex]         ...[tex]2^5=2*2*2*2*2=32[/tex]

⇒[tex]32p^-^1^5[/tex]

So our final values are 32p^-15

[tex]\frac{x^2}{4}-\frac{10x}{2}+25[/tex]

Solution:

Given expression is [tex](\frac{1}{2}x-5)^2[/tex].

Simplify the expression using algebraic formula [tex](a-b)^2=a^2-2ab+b^2[/tex]

[tex](\frac{1}{2}x-5)^2=(\frac{x}{2}-5)^2[/tex]

               [tex]=(\frac{x}{2})^2-2(\frac{x}{2})5+5^2[/tex]

               [tex]=\frac{x^2}{4}-10(\frac{x}{2})+25[/tex]

               [tex]=\frac{x^2}{4}-\frac{10x}{2}+25[/tex]

[tex](\frac{1}{2}x-5)^2=\frac{x^2}{4}-\frac{10x}{2}+25[/tex].

Hence, the simplified form of  [tex](\frac{1}{2}x-5)^2[/tex] is [tex]\frac{x^2}{4}-\frac{10x}{2}+25[/tex].

5 jars of jam and 3 packages of bread mix are in gift basket

Solution:

Let "x" be the number of jars of jam

Let "y" the number of packages of bread mix

Cost of 1 jars of jam = $ 6

Cost of 1 package of bead mix = $ 5

There are 8 items in the basket

Therefore,

number of jars of jam + number of packages of bread mix = 8

x + y = 8 ---------- eqn 1

A gift basket that contains jars of jam and packages of bread mix costs $45

Therefore, we frame a equation as:

number of jars of jam x Cost of 1 jars of jam + number of packages of bread mix x Cost of 1 package of bead mix = 45

[tex]x \times 6 + y \times 5 = 45[/tex]

6x + 5y = 45 --------- eqn 2

Let us solve eqn 1 and eqn 2

From eqn 1,

x = 8 - y --------- eqn 3

Substitute eqn 3 in eqn 2

6(8 - y) + 5y = 45

48 - 6y + 5y = 45

y = 48 - 45

Substitute y = 3 in eqn 3

x = 8 - 3

Thus 5 jars of jam and 3 packages of bread mix are in gift basket

Answer:

B is the answer

Answer:

I=60

Step-by-step explanation:

So

P=$250

R=6%

T=4

So to get the answer we would need to multiply everything to get the interest so the answer would be 60 because 250 times 6% equals to 15 then we would multiply 15 by 4 and then get out answer of $60 interest.

Answer:

OPTION B:   229.28 $

Step by-step explanation:

Whenever a deposit is made the balance increases and when a withdrawal is made the balance is decreased.

So, to compute the balance on Friday, assuming that he hasn't deposited on Friday, we add all the deposits and subtract all the withdrawals.

On Monday he has 225 $. He withdraws 27.25 $. So, the balance would be: 225 - 27.25 = 197.75

On Tuesday he deposits money. So, the balance would be 197.75 + 75.5

= 273.25

On Wednesday he deposits and withdraws. So, it would be

273.25 + 32.19 - 61 . 95 = 243.49

On Thursday, he withdraws. So, the balance would be: 243.49 - 14.21

= 229.28 $ which will be the balance on Friday.

Hence, OPTION B is the answer.

The percent increase is 0.53%

The percentage increase in the number of Greywolf is 90% and this can be determined by using the unitary method.

Given :

The following steps can be used in order to determine the percentage increase in the number of Greywolf:

Step 1 - The unitary method can be used in order to determine the percentage increase in the number of Greywolf.

Step 2 - According to the given data, there are previously 20 Greywolf in a wildlife park which is 100%.

Step 3 - So, let the percentage of 38 Greywolf be 'x'. So, the value of 'x' can be calculated as:

[tex]x = \dfrac{38}{20}\times 100[/tex]

[tex]x = 190\%[/tex]

Step 4 - So, the percentage increase in the number of Greywolf is:

[tex]{\rm Percentage \; Increase} = 190-100[/tex]

[tex]{\rm Percentage \; Increase} = 90\%[/tex]

The percentage increase in the number of Greywolf is 90%.

For more information, refer to the link given below:

https://brainly.com/question/1202726

Answer: 1 1/3

Step-by-step explanation: 0.33 repeating and in general is equal to 1/3

To solve the mixture problem, we set up an equation based on the total weight and another based on the total cost, then solve the system of equations algebraically to find out how many pounds of peanuts and raisins are needed.

The question involves creating a cost-based blend of two items, peanuts and raisins, to produce a mixture with a target cost per pound. This is a typical algebraic mixture problem, commonly encountered in high school math. To solve this problem, we want to find out how many pounds of peanuts and raisins are needed to make a 50-pound mixture that costs $1.47 per pound when peanuts cost $1.20 per pound and raisins cost $2.10 per pound.

Let's denote the weight of peanuts as P pounds and the weight of raisins as R pounds. The total weight of the mixture is given as 50 pounds, which gives us the equation:

P + R = 50

Next, we need to consider the total cost of the mixture. The cost of the peanuts is P times $1.20, and the cost of the raisins is R times $2.10. Since the mixture should have an overall cost of $1.47 per pound, our cost equation becomes:

1.20P + 2.10R = 1.47 × 50

From our first equation, we can express R as 50 - P, and substitute it into our second equation to find the value of P. After solving these linear equations, we will obtain the exact quantities of peanuts and raisins required to make the desire mixture.

Answer: 5/11,5

Step-by-step explanation:

Multiply equation one by -4

Multiply equation two by 2

Then, it becomes

-8x - 28y = 28

-8x - 6y = 38

Subtract equation two from equation one .

It becomes -22y = -10

Divide both sides by 22, you have y= 5/11

NOW substitute y=5/11 into equation two to get X.

-4x -3(5/11) =19

-4x = 19 + 15/11

-4x = 20

Divide both sides by -4

X = -5

To solve the system of equations, the elimination method was used, resulting in the solution of the equations as an ordered pair (-6 16/77, 5/11).

To solve the system of equations 2x + 7y = -7 and -4x - 3y = 19, one can use the elimination method. This involves manipulating the two equations to eliminate one of the variables, allowing the other variable to be found. We can multiply the first equation by 2 to align the coefficients of the 'x' terms and then add the equations to cancel out the 'x' terms.

Multiply the first equation by 2: 4x + 14y = -14.

Add this to the second equation: (4x + 14y) + (-4x - 3y) = -14 + 19.

This simplifies to 11y = 5, and solving for 'y' gives y = 5/11.

Substitute 'y' back into the first original equation: 2x + 7(5/11) = -7.

Solve for 'x', which gives x = -6 16/77.

So, the solution to the system of equations, expressed as an ordered pair, is (-6 16/77, 5/11).

Answer: area for circle is  πr² so πr² =28.26 and we can sub 3.14 as pi

3.14*r²=28.26 we can divide by 3.14 to get r² on it's own

r²=28.26/3.14

then we root both sides to get r on it's own

28.26/3.14=9 √9=3

and the diameter is double the radius 3*2=6 so the diameter is 6

Step-by-step explanation:

Answer:

X=9

Step-by-step explanation:

In the picture above.

Answer:

Contour lines. Hope this helps!

speed of a boat when it goes downstream is 336/12 = 28 mi/h

speed of a boat when it goes upstream is 336/14 = 24 mi/h

Let v is speed of the boat in still water and x is speed of the current. Then,

v + x = 28

v - x = 24

Solve the system for v and x and get v = 26 mi/h, x = 2 mi/h

Answer:

1 4/12

Step-by-step explanation: What you need to do first is make them improper fractions with the same denominator.

1 1/6 = 7/6       1 4/12 = 16/12.       Now you can make them have the same denominator. 7/6 = 14/12 and 16/12. So 1 and 4/12 is bigger.

Answer: x=13

Step-by-step explanation:

Replace u wit y = 3x+14

6x-6(3x+14)=-24

6x-18-84 = -24

6x-102=-24

Add -102 on both sides

6x=78

Divide 6 on both side and have your answer

Answer:

Step-by-step explanation:

I've already answered this question.

Maricel's code will adjust the shot by 12º

Answer:

The correct angle will be 12.5 degrees.

Answer:

I believe 27%

Step-by-step explanation:

Total juniors = 8

Total students = 30

So 8 out of 30 as a percentage = 26.67

Hope this helps! :)

Answer:

Step-by-step explanation:

the average can be found by adding up all ur numbers and dividing by how many numbers u have

so her average test score is : (88 + 80) / 2 = 168/2 = 84 <==

To find Maddie's average test score, add up her scores (88+80=168) and divide by the number of tests (2). This gives us an average of 84.

The subject of this question is Mathematics, specifically the concept of calculating averages. To calculate Maddie's average test score, you'll need to add up the scores she received and then divide the sum by the number of tests she took.

In this case, Maddie earned an 88 on her first test and an 80 on her second test. You would add these two scores together (168), then divide by 2 (since she took 2 tests), which gives us an average of 84.

So, Maddie's average test score is 84.

https://brainly.com/question/31930809

#SPJ3

Answer:

Step-by-step explanation:

31) Y = -3x² + 18 x -25 = -3*x² + -3*-6x -25

  = -3(x² -6x) - 25

( (a-b)² =a² - 2ab + b²;   here a = x; 2ab = -6x = -2*x*3; and so b = 3)

  = -3(x² -6x + 9 - 9) - 25  

 { when we add and subtract 9, the equation will not change}

= -3[(x -3)² - 9] -25

= -3(x - 3)² - (-3)*9 - 25

= -3(x - 3)² + 27 -25

= -3(x - 3)² + 2

32) y= -3x² - 18x - 25

    = -3 (x² + 6x )-25

  = -3 (x² + 6x + 9 - 9) -25

= -3 [ (x+ 3)² - 9] -25

=-3 (x + 3)² - (-3)*9 - 25

= -3(x + 3)² + 27 - 25

= -3(x+3)² +2

Answer:

The correct answer is He made a mistake in his calculations when substituting the ordered pair into the equation 5x – 2y = 6 and simplifying.

Step-by-step explanation:

I just took the test ;) good luck on yours

Answer:

He made a mistake in his calculations when substituting the ordered pair into the equation 5x – 2y = 6 and simplifying.

Step-by-step explanation:

Answer:

[tex]10.3\ in^3[/tex]

Step-by-step explanation:

Orange has the shape of a ball.

The volume of a ball with radius r inches is

[tex]V=\dfrac{4}{3}\pi r^3\ in^3[/tex]

The radius of one of the oranges is 1.35 inches.

Hence, its volume is

[tex]V=\dfrac{4}{3}\cdot \pi \cdot (1.35)^3\approx \dfrac{4}{3}\cdot 3.14\cdot 2.460375=10.30077\ in^3 \approx 10.3\ in^3[/tex]

Answer:

10.3 in^3

Step-by-step explanation:

Frank will plant a total of 5y + 9 vegetable seeds across his two gardens.

Frank has two gardens where he plans to plant vegetable seeds. In one garden, he will plant y vegetable seeds. In the other garden, he will plant 4y+9 seeds. To find the total number of seeds Frank is going to plant, we need to add together the number of seeds for each garden.

The total number of seeds is:

Total seeds = y + (4y + 9)

Combine like terms:

Total seeds = y + 4y + 9

Total seeds = 5y + 9

Thus, Frank will plant a total of 5y + 9 vegetable seeds across both gardens.

Answer:

4/9 or 0.444...

Step-by-step explanation:

[tex] \frac{7}{9} - \frac{1 \times 3}{3 \times 3} [/tex]

[tex] \frac{7}{9} - \frac{3}{9} [/tex]

[tex] \frac{4}{9} [/tex]

Answer: 4/9

Step-by-step explanation: Since our denominators in this problem are 9 and 3, and 9 factors as 3 x 3, they have a common factor of 3 so we find their least common denominator by multiplying the 3 that comes from the 3's that match up times the 3 that doesn't match up so we have 3 x 3 or 9.

In order to get a common denominator of 9 for both our fractions, we multiply top and bottom of the the second fraction by 3 and we have 7/9 - 3/9 which simplifies to 4/9. So 7/9 - 1/3 is 4/9.

I have also attached my work in the image provided.

Answer:

Step-by-step explanation:

0.4 × 3.2

Convert to fraction

0.4 = 4/10 = 2/5 & 3.2 = 32/10 = 16/5

0.4 × 3.2 = 2/5 × 16/5 = 32/25 = 1.28

Without conversion you press ur calculator and you get 1.28