Max can mow a lawn in 45 minutes. Jan takes twice as long to mow the same lawn. If they work together, how long will it take them to mow the lawn?

Answer:

f(x)=-3(x+1)^2+27

Step-by-step explanation:

Forst, simplify the expression by pulling out -3, but leave 24 out.

=-3(x^2+2x)+24

Then complete the square of the equatio inside the parenthesis (remember to subtract from the outside what you add to the inside times -3).

=-3(x^2+2x+1)+24+3

=-3(x+1)^2+27

The equation is now in vertex form.

from that, we now know that the vertex is (-1,27).

Set this equation equal to 0 to find the x intercepts:

0=-3(x+1)^2+27

-27=-3(x+1)^2

9=(x+1)^2

3 and -3=x+1

x=2 and -4

For this case we have a quadratic equation, [tex]x ^ 2 + 28x-60 = 0[/tex], of the form [tex]ax ^ 2 + bx + c = 0[/tex]

Where:

[tex]a = 1\\b = 28\\c = -60[/tex]

We can solve the equation by factoring, that is, we bias two numbers that multiplied give as a result -60 and added as a result 28.

These numbers are:

[tex]+30\ and\ -2\\+ 30-2 = + 28\\+ 30 * -2 + -60[/tex]

Then, the factorization is given by:

[tex](x-2) (x + 30) = 0[/tex]

The roots are:

[tex]x_ {1} = 2\\x_ {2} = - 30[/tex]

Answer:

[tex]x_ {1} = 2\\x_ {2} = - 30[/tex]

Answer:

Option C is Correct

Step-by-step explanation:

Given:

[tex]\sqrt{648}= \sqrt{2^a.3^b}[/tex]

We need to check the values of a and b such that the given equation remains true

1. a= 3 and b=2

[tex]\sqrt{648}= \sqrt{2^3.3^2}\\25.4 = \sqrt{72}\\25.4 \neq 8.4[/tex]

So, Option A is incorrect

2. a=2 and b= 3

[tex]\sqrt{648}= \sqrt{2^2.3^3}\\25.4 = \sqrt{108}\\25.4 \neq 10.3[/tex]

So, Option B is incorrect

3. a=3, b=4

[tex]\sqrt{648}= \sqrt{2^3.3^4}\\25.4 = \sqrt{648}\\25.4= 25.4[/tex]

So, Option C is correct.

4. a= 4, b=3

[tex]\sqrt{648}= \sqrt{2^4.3^3}\\25.4 = \sqrt{432}\\25.4 \neq 20.7[/tex]

So, Option D is incorrect.

Jack incorrect plotted the third quartile.

Explanation:

A box plot has 5 data descriptions. The option that Jack marked incorrectly is Median.

A box plot has 5 data descriptions:

In the given box plot, the median is plotted wrongly, because the median of the box plot is not 3.9.

Hence, the option that Jack marked incorrectly is Median.

Learn more about Box-plot:

https://brainly.com/question/1523909

#SPJ2

Answer:

32

Step-by-step explanation:

To find the lcm of 8 and 32 by listing

multiples of 8 are : 8, 16, 24, 32, 40, ....

multiples of 32 : 32, 64, 96, ....

The least common multiple of 8 and 32 is 32

Answer:

Final answer is [tex]\frac{80}{3}[/tex].

Step-by-step explanation:

We have been given an infinite geometric series.

Now we need to find it's sum.

common ratio [tex]r=-\frac{1}{5}[/tex].

plug n=1 to get the first term

[tex]a_n=32\left(-\frac{1}{5}\right)^{\left(n-1\right)}[/tex]

[tex]a_1=32\left(-\frac{1}{5}\right)^{\left(1-1\right)}[/tex]

[tex]a_1=32\left(-\frac{1}{5}\right)^{\left(0\right)}[/tex]

[tex]a_1=32\left(1\right)[/tex]

[tex]a_1=32[/tex]

Now plug these values into infinite sum formula

[tex]S_{\infty}=\frac{a_1}{1-r}=\frac{32}{1-\left(-\frac{1}{5}\right)}=\frac{32}{1.2}=\frac{320}{12}=\frac{80}{3}[/tex]

Hence final answer is [tex]\frac{80}{3}[/tex].

The sum of the infinite geometric series given in the problem is 26.6

7.

A geometric series is a sequence of terms in which each term is obtained by multiplying the previous term by a constant ratio. It is a specific type of series where the terms follow a geometric progression.

Formally, a geometric series is expressed as:

a, ar, a[tex]r^2[/tex], a[tex]r^3[/tex], ...

To solve the geometric series sum of the form:

S = a + ar + a[tex]r^2[/tex] + a[tex]r^3[/tex] + ...,

where a is the first term and r is the common ratio, we can use the formula for the sum of an infinite geometric series:

S = [tex]\frac{a}{1 - r}[/tex].

In this case, the given series is:

S = 32[tex]\times \frac{-1}{5}^(^n^ -^ 1^)[/tex],

Comparing this to the standard geometric series form, we can identify that the first term a is 32, and the common ratio r is [tex]\frac{-1}{5}[/tex].

Substituting these values into the formula, we get:

S =  32[tex]\times \frac{-1}{5}^(^n^ -^ 1^)[/tex],

S = [tex]\frac{32}{(1 +\frac{1}{5})}[/tex],

S = [tex]\frac{32}{\frac{6}{5} }[/tex],

S = 32 [tex]\times \frac{5}{6}[/tex],

S = [tex]\frac{160}{6}[/tex]

S = [tex]\frac{80}{3}[/tex] = 26.67.

Therefore, the sum of the given geometric series is 80/3 or approximately 26.67.

Learn more about geometric series here:

https://brainly.com/question/30264021

#SPJ6

Answer:

Assuming you mean baseball in stead of basketball, if must be the 5th floor.

Step-by-step explanation:

"The girl on the fifth floor thinks soccer is boring" implies that on the 5th floor lives the football or baseball fan. However, it cannot be the football fan since it is already known that she lives on 6th.

So the baseball fan, which is Jean, lives on 5th.

Answer:

63,8%

Step-by-step explanation:

Assuming the sample is a good representation of the people from the United States.

Since there were 1,000 surveyed... and 638 of them were wearing glasses,  that makes a proportion of 638 out of  1,000 people, or 63,8 / 100 people... so 63.8%

I would say the sample is not representative of the reality.... because I don't think so many people wear glassed.

Answer:

[A.] and [D.]

Step-by-step explanation:

Before we even solve to see which options are true and false, write the polynomial in descending order.

To do this, break the polynomial into terms.

1. -2xy^5

2. 3x^7

3. -10x^3y^6

4. 8x^6

5. 4

To write this in descending order, look at the exponents or degrees.

We have 5 terms [So A. is already a correct option choice] so look at the exponents or degrees for each term

1. -2xy^5  [degree: 6 (x has an exponent, 1)]

2. 3x^7 [degree: 7]

3. -10x^3y^6 [since there are 2 exponents, add them together (degree: 9)]

4. 8x^6 [degree: 6]

5. 4 [degree: 1 (even though it doesn't look like it, 4 actually has an exponent, 1, along with other numbers like 1, 2, 3, 4, 5 etc.)]

-10x^3y^6 has the largest degree, then 3x^7, then 8x^6 and -2xy^5, and lastly 4.

Now, rewrite the polynomial

-2xy^5 + 3x^7 -10x^3y^6 + 8x^6 + 4 = -10x^3y^6 + 3x^7 + 8x^6 -2xy^5 + 4

We already established A.) is a correct answer.

B.) is not correct since our leading term is -10x^3y^6 and -10 would be the leading coefficent.

C.) Is not correct since the degree of the polynomial is 9, since the highest degree is 9

D.) Is correct since 4 has no variables attached to it

E.) Is not correct since the polynomial was not in descending form, we had to do it for them.

Thus, A.) and C.) are the correct answers.

I hope this helps! Let me know if I did something wrong or you have any questions! Thanks! :)

You appear to be missing side A. Here is the equation for that:

a = √(c² - b²)

So do c squared (13 squared) - b squared (12 squared)

= 25

However, the answer is not c squared - b squared, but the SQUARE ROOT of c squared - b squared.

In other words, we want the square root of 25, so your answer is...

Answer:

Step-by-step explanation:

d. 1/4

width of clip is 1/4 to the 1 inch

The width of the paper clip to the nearest eighth of an inch is 1/2 inch.

The smallest subdivision or unit that a scale's digital display can display is a scale division. It's a phrase that's frequently used synonymously with readability or resolution. The scale's capacity can be calculated by dividing it by its readability.

We have to find the width paper clip.

Here, the scale is having 4 division each of marked as 1/4.

So, the paper clip covers

= 1/4 + 1/4

= 2/4

= 1/2

Thus, the width of paper clip in 1/2 inch.

Learn more about Scale division here:

https://brainly.com/question/30259099

#SPJ2

ANSWER

a=-32

EXPLANATION

If C(a,1) is on the line that passes through A(3, 7), and B(-4, 9), then the three points are collinear.

This implies that, when we find the slope using any two points, we should get the same result.

[tex] \frac{9 - 1}{ - 4 - a} = \frac{9 - 7}{ - 4 - 3} [/tex]

We simplify to obtain;

[tex] \frac{8}{ - 4 - a} = \frac{ - 2}{ - 7 } [/tex]

[tex]\frac{8}{ - 4 - a} = \frac{ 2}{ 7 } [/tex]

We cross multiply to get;

[tex]8 \times 7 = 2( - 4 - a)[/tex]

This implies that,

[tex]56 = - 8 - 2a[/tex]

[tex]56 + 8= - 2a[/tex]

[tex]64 = - 2a[/tex]

Divide both sides by -2

[tex]a = \frac{64}{ - 2} [/tex]

[tex]a = - 32[/tex]

Answer:

a=-32

Step-by-step explanation:

Answer:

A and B

Step-by-step explanation:

A. -9<-4  ....TRUE

B. |-10| >| 2 |  => 10 > 2 ...TRUE

C. | -3 | < | 2 |   => 3 > 2  ....FALSE

D. 6< - 12 ....FALSE

Answer A and B

Answer:

log 64

Step-by-step explanation:

Using the rules of logarithms

• log [tex]x^{n}[/tex] ⇔ nlogx

• logx + logy ⇔ log xy

Given

2 log 4 + log 2 + log 2

= log 4² + log (2 × 2)

= log 16 + log 4

= log (16 × 4) = log 64

Answer:

A, log 64

Step-by-step explanation:

your answer A, log 64 is correct. i will explain why below:

2 log 4, log 2 and log 2 have the same bases (10), meaning they are able to be added easier. but before we add, we use the Power Rule of Logarithms on 2 log 4

the Power Rule says that we can move an exponent in a logarithm to the front then solve. this also applies to the reverse, as we can move 2 back as an exponent of 4 and solve

2 log 4 ---> log 4² < simplify the exponent and we get log 16

we can now use the Product Rule of Logarithms where log x + log y = log(xy)

we can use that on the first two terms of the addition

log 16 + log 2 ----> log (16 × 2) = log 32

now we can apply the other log 2 to the rule but instead with log 32

log 32 + log 2 ---> log (32 × 2) = log 64

our answer is log 64

Answer:

Step-by-step explanation:

[tex]\dfrac{x}{2x-3}-\dfrac{8-3x}{4x^2-9}=0\\\\\bold{DOMAIN:}\\\\2x-3\neq0\ \wedge\ 4x^2-9\neq0\\\\2x-3\neq0\qquad\text{add 3 to both sides}\\2x\neq3\qquad\text{divide both sides by 2}\\\boxed{x\neq1.5}\\\\4x^2-9\neq0\qquad\text{add 9 to both sides}\\4x^2\neq9\qquad\text{divide both sides by 4}\\x^2\neq2.25\\x\neq\pm\sqrt{2.25}\\\boxed{x\neq-1.5\ \wedge\ x\neq1.5}[/tex]

[tex]\dfrac{x}{2x-3}-\dfrac{8-3x}{4x^2-9}=0\\\\\dfrac{x}{2x-3}-\dfrac{8-3x}{(2x)^2-3^2}=0\qquad\text{use}\ a^2-b^2=(a-b)(a+b)\\\\\dfrac{x}{2x-3}-\dfrac{8-3x}{(2x-3)(2x+3)}=0\\\\\dfrac{x(2x+3)}{(2x-3)(2x+3)}-\dfrac{8-3x}{(2x-3)(2x+3)}=0\\\\\dfrac{x(2x+3)-(8-3x)}{4x^2-9}=0[/tex]

[tex]\text{The fraction is equal to 0 if the numerator is equal to 0. Therefore}\\\\\dfrac{x(2x+3)-(8-3x)}{4x^2-9}=0\iff x(2x-3)-(8-3x)=0\\\\\text{use the distributive property}\\\\(x)(2x)+(x)(3)-8-(-3x)=0\\\\2x^2+3x-8+3x=0\qquad\text{combine like terms}\\\\2x^2+(3x+3x)-8=0\\\\2x^2+6x-8=0\qquad\text{divide both sides by 2}\\\\x^2+3x-4=0\\\\x^2+4x-1x-4=0\\\\x(x+4)-1(x+4)=0\\\\(x+4)(x-1)=0\iff x+4=0\ \vee\ x-1=0\\\\x+4=0\qquad\text{subtract 4 from both sides}\\x=-4\in D\\\\x-1=0\qquad\text{add 1 to both sides}\\x=1[/tex]

Answer:

The estimated cost for the labor is less than or equal to [tex]\$150.77[/tex]

Step-by-step explanation:

Let

n -----> the estimated cost for the labor

we know that

The inequality that represent this situation is equal to

[tex]49.23+n\leq 200[/tex]

Solve for n

[tex]n\leq 200-49.23[/tex]

[tex]n\leq \$150.77[/tex]

Answer:

9

Step-by-step explanation:

Because every number next to 64 is over

let's firstly convert the mixed fractions to improper fractions and then subtract, bearing in mind that the LCD of 4 and 2 is 4.

[tex]\bf \stackrel{mixed}{8\frac{3}{4}}\implies \cfrac{8\cdot 4+3}{8}\implies \stackrel{improper}{\cfrac{35}{4}}~\hfill \stackrel{mixed}{7\frac{1}{2}}\implies \cfrac{7\cdot 2+1}{2}\implies \stackrel{improper}{\cfrac{15}{2}} \\\\[-0.35em] ~\dotfill\\\\ \cfrac{35}{4}-\cfrac{15}{2}\implies \stackrel{\textit{using the LCD of 4}}{\cfrac{(1)35~~-~~(2)15}{4}}\implies \cfrac{35-30}{4}\implies \cfrac{5}{4}[/tex]

Answer:

Step-by-step explanation:

She makes $325 a week, so go to the 8th row, for weekly income of $300 to $400.  She claims 2 exemptions, so go to the third column labeled 2.  The value is 2.  That means the $2 is withheld from her paycheck on top of the 6.25% for FICA.  The total is therefore:

$2 + (0.0625) ($325)

$22.3125

Rounded to the nearest cent, that's $22.31.

Answer:

The measure of angle y is 90°

Step-by-step explanation:

we know that

The inscribed angle is half that of the arc it comprises.

so

m∠y=(1/2)[180°] -----> because the diameter divide the circle into two equal parts

so

m∠y=90°

m∠x=(1/2)[148°]

m∠x=74°

Answer:

Y = 90

Step-by-step explanation:

Answer:

40%

Step-by-step explanation:

4÷10x100=40

As you have 10 players total and 4 players scored between 31 and 40 points

Answer:

B, C, F, H

Step-by-step explanation:

Just search up how to solve equations

Answer: B. x+2=10

C. x-4=4

F. 3x=24

H. [tex]\dfrac{x}{8}=1[/tex]

Step-by-step explanation:

To check whether 8 is a solution of the given equation or not , we need to substitute the value of 8 in the place of x check whether equation is truw or not.

A. [tex]x+6=2[/tex]

At x= 8, we have

[tex]8+6=2\Rightarrow\ 14=2[/tex] , which is not true , it means 8 is not a solution of this equation.

B. x+2=10

At x= 8, we have

[tex]8+2=10\Rightarrow\ 10=10[/tex] , which is true , it means 8 is a solution of this equation.

C. x-4=4

At x= 8, we have

[tex]8-4=4\Rightarrow\ 4=4[/tex],  which is true , it means 8 is a solution of this equation.

D. x-2=10

At x= 8, we have

[tex]8-2=10\Rightarrow\ 6=10[/tex] , which is not true , it means 8 is not a solution of this equation.

E. 2x=4

At x= 8, we have

[tex]2(8)=4\Rightarrow\ 16=4[/tex] , which is not true , it means 8 is not a solution of this equation.

F. 3x=24

At x= 8, we have

[tex]3(8)=24\Rightarrow\ 24=24[/tex],  which is true , it means 8 is a solution of this equation.

G. [tex]\dfrac{x}{2}=16[/tex]

[tex]\dfrac{8}{2}=16\Rightarrow\ 4=16[/tex], which is not true , it means 8 is not a solution of this equation.

H. [tex]\dfrac{x}{8}=1[/tex]

At x= 8, we have

[tex]\dfrac{8}{8}=1\Rightarrow\ 1=1[/tex],  which is true , it means 8 is a solution of this equation.

Hence, the required equations :

B. x+2=10

C. x-4=4

F. 3x=24

H. [tex]\dfrac{x}{8}=1[/tex]

Answer:

w = 4 m

Step-by-step explanation:

The volume (V) of a cuboid is

V = lwh ( l is length, w is width and h is height )

Given V = 144 m³, then

lwh = 144 ( substitute l = 3 and h = 12 )

3 × w × 12 = 144

36w = 144 ( divide both sides by 36 )

w = 4

The volume of a rectangular prism is given by the product of its dimension: let w, h, l be the width, height and length of the prism, we have

[tex]V = whl[/tex]

In your case, everything is given except the width:

[tex]144 = w\cdot 3 \cdot 12 \iff 144 = 36w \iff w = \dfrac{144}{36} = 4[/tex]

The Answer is in the picture below...

the area of the pool and deck can be calculated by using the expression [tex]500 + 90x + 4x^2[/tex]

The dimension of the pool are:

25 ft long and 20 ft wide

We know that the deck extends x ft away from every side of the pool.

Thus, the total length of the pool and deck together is 25 + 2x ft, and the total width is 20 + 2x ft

Area of rectangle can be found using the formula:

[tex]Area = length \times breadth[/tex]

Putting in values we get:

[tex](25 + 2x) \times (20 + 2x)[/tex]

On simplifying we get:

[tex](25 + 2x) (20 + 2x) = 500 + 50x + 40x + 4x^2 \\\\(25 + 2x) (20 + 2x) = 500 + 90x + 4x^2[/tex]

Thus the area of the pool and deck can be calculated by using the expression [tex]500 + 90x + 4x^2[/tex] ft²

Step-by-step explanation:

Firstly to facilitate the conversion we need to convert mph to km/h.

50 m= 0.05 km

1 mph= 0.001 km/h

2 mph= 0.002 km/h

For the girl

D=0.05 km

S= 0.002 Km/h

T= 25 h

For the Boy

D=0.05

S= 0.001

T= 50 h

Now to find after how many time they will meet each other, we simply have to add the two times.

So,

25 h + 50 h= 75 h

ANS: 75 h

Add 6 to both sides

-102 + 6 = -2(6 - 7x)

Simplify -102 + 6 to -96

-96 = -2(6 - 7x)

Divide both sides by -2

-96/-2 = 6 - 7x

Two negatives make a positive

96/2 = 6 - 7x

Simplify 96/2 to 48

48 = 6 - 7x

Simplify 48 - 6 to 42

42 = -7x

Divide both sides by -7

-42/7 = x

Simplify 42/7 to 6

-6 = x

Switch sides

Answer: x = -6

Hello There!

The Y-intercept Of this line is -4 because it’s subtracting 4 that’s me as it’s going down on y axis

a. addition

b. multiplication

c. division

d. distributive property

Answer:

six plus y

five times j

h divided by eight / h over eight

x plus seven times four

Step-by-step explanation:

Answer:

B, C, E

Step-by-step explanation:

trust me ;)

The correct statements are true about the curve are as follows;

The variance of the data set is 49.

The median is 64.

The data point 50 is two standard deviations away from the mean.

The standard deviation of a random variable, sample, statistical population, data set, or probability distribution is the square root of its variance.

The correct statements are true about the curve are as follows;

1. The variance of the data set is;

σ ² = 7²

σ ² = 49

The variance of the data set is, 49.

2. The median is the middle value of the data set.

The median is 64.

3. The data point 50 is two standard deviations away from the mean.

Learn more about standard deviation here;

brainly.com/question/11863959

#SPJ5

Answer:

900 sq ft

Step-by-step explanation:

The area of a trapezoid is (Base 1 + Base 2) * height/2. So to plug the numbers in...

(30+60)20/2

90*20/2

1800/2

900 sq ft

The correct answer is: 708 square feet

the area of the full shape is 900^2 feet and the area of the door is 192^2 feet therefore 900 - 192 = 708.