last year, Mr. Petersen's rectangular garden had a width of 5 meters and an area of 20 square meters.
This year, he wants to make the garden three times as long and two times as wide.
a
Solve for the length of last year's garden using the area formula. Then, draw and label the
measurements of this year's garden
Last Year
This Year
20
square
meters

Answer:

The slope is -2.

Step-by-step explanation:

m=(y2-y1)/(x2-x1)=(8-6)/(1-2)=2/-1=-2

Answer:

[tex]y\le\dfrac{1}{2}x+2[/tex]

Step-by-step explanation:

On a coordinate plane, a solid straight line has a positive slope and goes through (negative 4, 0) and (0, 2). This line has the equation

[tex]y-0=\dfrac{2-0}{0-(-4)}(x-(-4))\\ \\y=\dfrac{1}{2}(x+4)\\ \\y=\dfrac{1}{2}x+2[/tex]

The origin belongs to the shaded region, so its coordinates must satisfy the inequality. Since

[tex]\dfrac{1}{2}\cdot 0+2=2\ge 0,[/tex]

then the correct inequality is

[tex]y\le\dfrac{1}{2}x+2[/tex]

Answer:

A

y ≤ [tex]\frac{1}{2}[/tex]x + 2

Step-by-step explanation:

Answer:

False

Step-by-step explanation:

Answer:

False

Step-by-step explanation:

The multiples of 16: 16,32,48,64,80,96,112,128,144,160,176,192,208,224,240,256,27

Factors of 24

The factors of 24.: 1,2,3,4,6,8,12,24,

Answer:

[tex](0, log_{b}(-k)), k < 0[/tex]

Step-by-step explanation:

[tex]y = \log_{b}(a - k)[/tex]

To find the y-intercept, set a = 0 and solve for y.

[tex]y = \log_{b}(0 - k)\\y = \log_{b}(-k)[/tex]

This equation is undefined for k ≥ 0.

There is a y-intercept only if k < 0. Only then can the argument of the log function be positive.

The y-intercept is at

[tex]\mathbf{(0, log_{b}(-k)), k < 0}[/tex]

For example, if b = 2 and k = -3, log₂(3) = 1.585

The intercept is at (0, 1.585).

Answer:

(d) negative 12 s squared + 11 s t minus 2 t squared    is the PRODUCT.

Step-by-step explanation:

Here, the given expression is:

(negative 3 s + 2 t)(4 s minus t)   =  (- 3s + 2t) (4s - t)

Now, by DISTRIBUTIVE PROPERTY:

   A(B-C) = AB - AC

Simplifying the given expression ,we get:

[tex](- 3s + 2t) (4s - t)  = -3s(4s-t) + 2t(4s -t)\\= -3s(4s) -3s(-t) + 2t(4s) + 2t(-t)  = -12s^2 + 3st + 8 st - 2t^2\\= -12s^2 + 11st - 2t^2\\\implies (- 3s + 2t) (4s - t)  =   -12s^2 + 11st - 2t^2[/tex]

Now, the resultant expression can also be written as

[tex]-12s^2 + 11st - 2t^2[/tex]  =  negative 12 s squared + 11 s t minus 2 t squared.

Hence, the option (4) is the correct option.

Answer:

option 4 is the answer

Step-by-step explanation:

Answer:

cot(x)

Step-by-step explanation:

csc(x) = 1/sin(x)

cos(x)*csc(x) = cos(x)*1/sin(x)

cos(x)*csc(x) = cos(x)/sin(x)

cos(x)*csc(x) = cot(x)

----

abbreviations

csc = cosecant

cos = cosine

sin = sine

cot = cotangent

To simplify cos x csc x, we can replace csc x with 1/sin x based on the trigonometric identity. This will give us cos x/sin x, which is the same as cot x based on the trig identities.

The question is asking us to simplify the expression cos x csc x. To do this, we can use the trigonometric identity sin = 1/csc, which tells us what csc x is in terms of sin x.

So if that is the case, we can rewrite csc x as 1/sin x and replace csc x in the original expression giving us cos x * (1/sin x) or equivalently cos x/sin x.

And if we look at our trigonometric identities again, we can find that cos x/sin x is the same as cot x, our final simplified expression.

https://brainly.com/question/11659262

#SPJ3

Answer:

Step-by-step explanation:

Equation 1:  3a + 1o =5     3(1) + 1(2) = 5

Equation 2:  1a + 1o =3      2(1) + 1(2) = 3

Solution: apples are $1.00 each and oranges are $2.00 each

Answer: 53, 54, 55, and 56

Step-by-step explanation: This problem states that the sum of 4 consecutive numbers is 218 and it asks us to find the numbers.

4 consecutive numbers can be represented as followed.

X ⇒ first number

X + 1 ⇒ second number

X + 2 ⇒ third number

X + 3 ⇒ fourth number

Since the sum of our 4 consecutive numbers is 218, we can set up an equation to represent this.

X + X + 1 + X + 2 + X + 3 = 218

On the left side of the equation, we can combine our x's and our numbers.

4x + 6 = 218

      -6     -6   ← subtract 6 from both sides of the equation

4x = 212

÷4    ÷4   ← divide both sides of the equation by 4

 X = 53

X ⇒ first number   = 53

X + 1 ⇒ second number   = 54

X + 2 ⇒ third number   = 55

X + 3 ⇒ fourth number   = 56

Therefore, our 4 consecutive numbers are 53, 54, 55, and 56.

Answer:

None.

Step-by-step explanation:

18+36=54

A) 29+16=45

B) 6/3+12=2+12=14

C) 7(2+4)=7(6)=42

D) 2+36=38

Answer:

6 inches

Step-by-step explanation:

p=l+l+w+w

p=2+2+1+1

p=6

Answer:

6 in

Step-by-step explanation:

Answer:

Critical value is -1.98.

Step-by-step explanation:

Given:

The value of alpha is, [tex]\alpha=0.024[/tex]

Now, in order to find the critical value, we need to subtract alpha from 1 and then look at the z-score table to find the respective 'z' value for the above result.

The probability of critical value is given as:

[tex]P(critical)=1-\alpha=1-0.024=0.976[/tex]

So, from the z-score table, the value of z-score for probability 0.976 is 1.98.

Now, in a left tailed test, we multiply the z value by negative 1 to arrive at the final answer. We do so because the area to the left of mean in a normal distribution curve is negative.

So, the z-score for critical value 0.024 in a left tailed test is -1.98.

The critical value for α = 0.024 in a left-tailed test is -1.98.

To find this value, we locate α = 0.024 in the z-table. The z-table is a table that shows the probability of obtaining a z-score less than or equal to a certain value.

The z-score is a measure of how many standard deviations a particular data point is away from the mean of the population.

Here is the critical value for α = 0.024 in a left-tailed test: -1.98

In this case, we are looking for the z-score that corresponds to a probability of 0.024. This z-score is -1.98. Therefore, if our test statistic is less than or equal to -1.98, we will reject the null hypothesis.

For more questions on critical value

https://brainly.com/question/31529419

#SPJ3

Answer:

t=1.6

Step-by-step explanation:

Answer:

3 quarts

Step-by-step explanation:

There are 4 quarts in a gallon

3×4=12

12-9= 3

Answer:

The slope for the given points is - 2  , and  y- intercept is 5

Step-by-step explanation:

Given points as :

( - 1 , 7 )  and  ( 0 , 5 )

Now slope of line in points form as

Slope = m = [tex]\dfrac{y_2-y_1}{x_2-x_1}[/tex]

or, m =  [tex]\dfrac{5 - 7}{0 + 1}[/tex]

or, m = - 2

so, Slope of line is - 2

Now equation of line is given as

y - [tex]y_1[/tex] = m × ( x -  [tex]x_1[/tex] )

or, y - 7 = ( - 2 ) × ( x + 1)

or, y - 7 = - 2 x - 2

Or, equation of line is

y = - 2 x + 5

Now, for y - intercept , x = 0

So, from line equation

y = - 2 × 0 + 5

Or, y = 0 + 5

∴ y = 5

Hence The slope for the given points is - 2  , and  y- intercept is 5  Answer

Answer:

375

Step-by-step explanation:

Jim earns a total of $4500 over 12 weeks. To find out how much he makes weekly, divide the total earnings by the number of weeks, which is $4500 divided by 12, resulting in Jim earning $375 per week.

To calculate how much Jim makes in one week, we can divide his total earnings over the 12-week period by the number of weeks. Jim earns a total of $4500 over 12 weeks, so we can use the following equation where M stands for the amount Jim earns each week:

M = Total Earnings÷ Number of Weeks

M = $4500÷ 12

By performing the division, we find that Jim earns $375 per week. This is done by dividing 4500 by 12:

M = $375

Therefore, Jim makes $375 each week doing yardwork.

Answer:

680$

Step-by-step explanation:

If this is a 64% discount, the price 244.80 is 36% of the original price

244.8 = 36%    -Divide by 36 on both sides

6.8 = 1%            - Times by a hundred

680 = 100%

The original price is 680$

To find the original price of the sofa given a 64% discount, divide the sale price by the discount percentage and subtract it from 100%.

To find the original price, we need to determine what the discount percentage represents in terms of the original price. Since the sale price is 64% of the original price, the discount is 100% - 64% = 36%. Let's represent the original price as x:

36% of x = $ 244.80

To solve this equation, we can convert 36% to the decimal form by dividing it by 100: 36/100 = 0.36. Now we can solve for x:

0.36x = $ 244.80

Dividing both sides of the equation by 0.36, we get:

x = $ 244.80 / 0.36 = $ 680

Therefore, the original price of the sofa was $ 680.

https://brainly.com/question/34046204

#SPJ3

The division of 3.78 by 0.9 equals 4.2 after rounding to the nearest tenth. The given problem is an arithmetic division question typically encountered in mathematics. The keyword 3.78 is the number being divided by 0.9.

The division question posed: 3.78 divided by 0.9, is a simple arithmetic problem. To solve, we will perform the division calculation directly. First, we divide 3.78 (the dividend) by 0.9 (the divisor). This yields a quotient of approximately 4.2. Thus, 3.78 divided by 0.9 equals 4.2 when rounded to the nearest tenth. This division problem would be typically encountered in arithmetic, a branch of mathematics that deals with numbers and numerical computation.

https://brainly.com/question/32066115

#SPJ2

Answer:

y = -0.5x -2

Step-by-step explanation:

We have to find a line perpendicular to the line y = -2x -3.

Let the required line will have slope m so ,

-2m = 1

m = -0.5.

So, the required line will have the slope -0.5.

Now, let the line be y = -0.5x + c.

This line is passing through (-2,-1), So putting this point in the line we will get

-1 = 1 + c

c = -2 .

So, the required line is

y = -0.5x -2.

Answer:

A'B'= 34 units long.

Step-by-step explanation:

The length A'B' will be 2 times the length of AB.

AD = sqrt( (8-0)^2 + (8- -7)^2 )

= sqrt 289

= 17

So A'B' = 34 .

An average of 291 backpacks were given out the past five years.

Step-by-step explanation:

Number of bags for last 5 years;

278, 310, 320, 242, 303

No. of terms = 5

Average = [tex]\frac{Sum\ of\ the\ terms}{No.\ of\ terms}[/tex]

[tex]Average=\frac{278+310+320+242+303}{5}\\Average=\frac{1453}{5}\\Average=290.6[/tex]

Rounding off to nearest whole number

Average = 291

An average of 291 backpacks were given out the past five years.

Keywords: average, addition

Learn more about addition at:

#LearnwithBrainly

Good evening ,

Answer:

x^2+16x-71 = (x+8)²-135

Step-by-step explanation:

x^2+16x-71 = (x+8)²-8²-71

                 = (x+8)²-(64+71)

                 = (x+8)²-135.

:)

Answer:

my mistake sorry

Step-by-step explanation:

Answer:

Any [a,b] that does NOT include the x-value 3 in it.

Either an [a,b] entirely to the left of 3, or

an  [a,b] entirely to the right of 3

Step-by-step explanation:

The intermediate value theorem requires for the function for which the intermediate value is calculated, to be continuous in a closed interval [a,b]. Therefore, for the graph of the function shown in your problem, the intermediate value theorem will apply as long as the interval [a,b] does NOT contain "3", which is the x-value where the function shows a discontinuity.

Then any [a,b] entirely to the left of 3 (that is any [a,b] where b < 3; or on the other hand any [a,b] completely to the right of 3 (that is any [a,b} where a > 3, will be fine for the intermediate value theorem to apply.

After 14 weeks, both Megan and Conner will have saved the same amount.

Step-by-step explanation:

Amount Megan have = $50

Amount saved each week = $5.50

Amount Conner have = $18.50

Amount saved each week = $7.75

Let,

x be the number of weeks.

According to given statement;

M(x) = 50+5.50x    Eqn 1

C(x) = 18.50+7.75x   Eqn 2

For amount to be same;

Eqn 1 = Eqn 2

[tex]50+5.50x=18.50+7.75x\\50-18.50=7.75x-5.50x\\31.50=2.25x\\2.25x=31.50\\[/tex]

Dividing both sides by 2.25

[tex]\frac{2.25x}{2.25}=\frac{31.50}{2.25}\\x=14[/tex]

After 14 weeks, both Megan and Conner will have saved the same amount.

Keywords: functions, division

Learn more about linear equations at:

#LearnwithBrainly

Answer:

D. [tex]\displaystyle (0,5, 0,5)[/tex]

Step-by-step explanation:

C(3, −3) and A(−2, 4)

Just by looking at the graph, we can CLEARLY see that answer choice D is EXACTLY halfway in between the two given endpoints.

I am joyous to assist you anytime.

Answer: 1/8

Step-by-step explanation: To write a percent as a fraction in lowest terms, first remember that a percent is a ratio that compares a number to 100.

So here, 12.5% can be written as the ratio 12.5 to 100 or 12.5/100.

To write 12.5/100 in lowest terms, first multiply the numerator and the denominator by 10 to get rid of the decimal. When we do this, we get the fraction 125/1000.

Now, we divide the numerator and the denominator of 125/1000 by the greatest common factor of 125 and 1,000 which is 125 and we end up with the equivalent fraction which is 1/8.

Therefore, 12.5% is equivalent to 1/8.

Answer:

y = 43x − 25

Step-by-step explanation:

Evaluate the function at x=1:

f(x) = 12x³ + 3x² + x + 2

f(1) = 12 + 3 + 1 + 2

f(1) = 18

Find the slope of the tangent line at x=1:

f'(x) = 36x² + 6x + 1

f'(1) = 36 + 6 + 1

f'(1) = 43

Point-slope form:

y − y₀ = m (x − x₀)

y − 18 = 43 (x − 1)

Convert to slope-intercept form:

y − 18 = 43x − 43

y = 43x − 25

Graph:

desmos.com/calculator/giumpkkphr

To find the linear approximation for the function f(x) = 12x^3 + 3x^2 + x + 2 at x = 1, we can use the equation for the linear approximation. First, we need to find the derivative of the function and then plug in the values into the formula. The linear approximation is f(1).

To find the linear approximation for the function f(x) = 12x^3 + 3x^2 + x + 2 at x = 1, we can use the equation for the linear approximation:

() ≈ () + '()( − )

First, we need to find '(), which is the derivative of the function. Taking the derivative of f(x) gives us:

'() = 36^2 + 6 + 1

Next, we plug in x = 1 into the first equation:

(1) ≈ (1) + '(1)(1 − 1)

Simplifying, we have:

(1) ≈ (1)

So, the linear approximation for f(x) at x = 1 is f(1).

Answer:

0

Step-by-step explanation:

5y-2=3

5y=3+2

5y=5

y=5/5=1

9y-9=9(1)-9=9-9=0

Assuming that the correct expression is 2(x - 3)= 2(4x -12)

(2 * x) + (2 * −3) = (2 * 4x) + (2 * −12)

2x - 6 = 8x − 24

2x − 6 − 8x = 8x − 24 − 8x

−6x − 6 = −24

−6x − 6 + 6 = −24 + 6

−6x = −18

-6x/-6 = -8/-6

x = 3 (Answer)

______

Best Regards,

Wolfyy :)

Answer:

3 minutes

5 minutes.

Step-by-step explanation:

It is given that, Amelia can wash 8 plates in 24 minutes.

So, if this rate remains constant then 1 plate will be washed in [tex] \frac{24}{8} = 3[/tex] minutes.

Again, it is given that, Amelia bakes 12 cookies in 60 minutes.

So, if this rate also remains constant then she will bake 1 cookie in [tex] \frac{60}{12} = 5[/tex] minutes. ( Answer )