The length of a rectangle is 5 cm more than the width and the perimeter is at least 61cm. What are the smallest possible dimensions for the rectangle? (Hint: Perimeter = 2L +2W)
Explanation pleaseeee

Answer:

5.7 meters

Step-by-step explanation:

Image a rectangle being cut diagonally in half, that would lead to two triangles. We can use the pythagorean theorem to find the missing side.

7 is the hypotenuse and 4 is the side length

4^2+x^2=7^2

16+x^2=49

sqrx=sqr(49-16)

x=sqr33

x=5.74

Rounded to the nearest tenth is 5.7

Answer:

10

Step-by-step explanation

50 divided by 10 is 5 so

50 times 2 which is 100 divided by 10 is 10

Answer:

The last option

Step-by-step explanation:

When you have a fraction as a power, the denominator goes to the root, so in this case, it becomes root 4. The base, 5, goes to the outside, and the numerator 1, goes beside the x.

Hope this helps!

Answer:

Approximately [tex]58.28\; \rm m \cdot s^{-1}[/tex].

Step-by-step explanation:

The velocity of an object is the rate at which its position changes. In other words, the velocity of an object is equal to the first derivative of its position, with respect to time.

Note that the arrow here is launched upwards. (Assume that the effect of wind on Mars is negligible.) There would be motion in the horizontal direction. The horizontal position of this arrow will stays the same. On the other hand, the vertical position of this arrow is the same as its height: [tex]y = 62\, t - 1.86\, t^2[/tex].

Apply the power rule to find the first derivative of this [tex]y[/tex] with respect to time [tex]t[/tex].

By the power rule:

Therefore:

[tex]\begin{aligned}\frac{dy}{d t} &= \frac{d}{d t}\left[62 \, t - 1.86\, t^2\right] \\ &= 62\,\left(\frac{d}{d t}\left[t\right]\right) - 1.86\, \left(\frac{d}{d t}\left[t^2\right]\right) \\ &= 62 \times 1 - 1.86\times\left(2\, t) = 62 - 3.72\, t\end{aligned}[/tex].

In other words, the (vertical) velocity of this arrow at time [tex]t[/tex] would be [tex](62 - 3.72\, t)[/tex] meters per second.

Evaluate this expression for [tex]t = 1[/tex] to find the (vertical) velocity of this arrow at that moment: [tex]62 - 3.72 \times 1 =58.28[/tex].

Answer:

58.28 m/s

Step-by-step explanation:

y = 62t - 1.86t²

Speed, S = dy/dt = 62 - 2(1.86)t

S = 62 - 3.72t

When t = 1

S = 62 - 3.72 = 58.28 m/s

Answer:

The present age of the woman is 37 years and her daughter is 7 years

Step-by-step explanation:

two years ago a woman was 7 times old as her daughter, but in 3 years time she would be 4 times old as the girl. how old are they now

Two years ago a woman wad 7 times as old as her daughter

Let her daughter=x-2

The woman=y-2

x-2

7(y-2)=7y-14

x-2=7y-14

x-7y=-14+2

x-7y= -12 (1)

but in 3 years time she would be 4 times as old as the girl.

x+3

y+3

x+3

4(y+3)=4y+12

x+3=4y+12

x-4y=12-3

x-4y=9. (2)

x-7y= -12 (1)

x-4y=9. (2)

Subtract (1) from (2)

4y-(-7y)=9-(-12)

-4y+7y=9+12

3y=21

y=21/3

y=7

Substitute

y=7 into (1)

x-7y= -12

x-7(7)=-12

x-49=-12

x= -12+49

=37

The present age of the woman is 37 years and her daughter is 7 years

Step-by-step explanation:

If a line segment AB of length 6.6cm is drawn, bisecting it perpendicularly at N, we have two lines AN and NB of length 3.3cm each.

Because the line is bisected perpendicularly, the angles formed at the point of bisection are 90 degrees.

Answer:

D. 4(2x² + 4x - 6); 130.0 inches

Step-by-step explanation:

Margot is sewing a ribbon on a seam along the perimeter of a square pillow. The side length of the pillow is 2x²+1 inches. She plans to make a similar pillow, including the ribbon, whose side length is 4x−7 inches. What expression can be used for the length of ribbon that she needs for both pillows, and what is the length if x = 3.5?

2x2+4x−6; 22.0 inches

2x2+4x−6; 32.5 inches

4(2x2+4x−6;) 88.0 inches

4(2x2+4x−6;) 130.0 inches

Perimeter of a square = 4 * side length

1- First square pillow

length = 2x²+1 in

Perimeter of first pillow = 4 * (2x²+1) in

Second square pillow

length = 4x-7 in

Perimeter of second pillow = 4(4x-7) in

Total ribbon length required = perimeter of first square pillow + perimeter of second square pillow

Total ribbon length required = 4(2x²+1) + 4(4x-7)

Factorise

4 is the common factor

=4(2x²+1)+(4x-7)

=4(2x²+1+4x-7)

=4(2x²+4x-6)

Total ribbon length required=4(2x²+4x-6)

If x=3.5

Total ribbon length required=4(2x²+4x-6)

=4{2(3.5)²+4(3.5)-6}

=4{2(12.25)+14-6)

=4(24.5+14-6)

=4(32.5)

=130.0 inches

Answer:

40

Step-by-step explanation:

We can split this figure into two figures, a square and a trapezoid. The square, as shown has a side length of 4. That means that the area of the square is 16. The trapezoid, has base lengths of 2 and 4, and a height of 8. We can plug that into the area of a trapezoid formula:

[tex]\frac{2+4}{2}(8)[/tex]

Two plus 4 is 6, and 6 divided by 2 is 3. Three times 8 is 24.

24 plus 16 (the area of the square) is equal to 40, which is the area of the shape.

Answer:

-1

Step-by-step explanation:

Answer:

Well, we can write a really simple quadratic polynomial as:

P(x) = a*(x - c1)*(x - c2)

Where a is a constat, and c1 and c2 are the roots, here we have:

c1 = 5 and c2 = -3

P(x) = a*(x -5)(x + 3) = a*x^2 + a*x*3 - a*5*x - a*15

then the quadratic polynomial can be:

P(x) = a*x^2 + a*(3 - 5)*x - a*15

P(x) = a*x^2 - 2*a*x - a*15

Where a can be any real number.

Answer:

4000 rupees

Step-by-step explanation:

20000×10×2/100

= 4000 rupees

Answer:

$44.1

Step-by-step explanation:

March>>>>$40

for April: $40 × 5/100= $2 which is the 5% of $40.

Meaning for April Siti got $42

Then for May: $42 × 5 /100= $2.1 meaning she got $44.1 for May.

Answer:

The expression that could help calculate the price of the TV is;

$P - 20% of $P

Step-by-step explanation:

Here, we want to write an expression that corresponds to the price of a television set that is on sale at a price which is 20% off the regular price.

From the question, we can see that the regular price is $P

So now we are having 20% off;

This corresponds to;

20/100 * p = p/5 = 0.2p

So in the expression form, we can have;

$P - 20% of $P

Answer: 17 hours

Step-by-step explanation:

Given that On each of the last 2 days, he worked 2 hours more than the mean number of hours he worked per day during the first 8 days. That is he worked additional 4 hours for the two days.

Let the total hours for the 8 days = E

The mean = E/8 = 0.125E

For the two last days, he worked

( 0.125E + 2 ) × 2 = 0.25E + 4

If he worked 69 hours in all, then

E + 0.25E + 4 = 69

Collect the like terms

1.25E = 69 - 4

1.25E = 65

E = 65/1.25

E = 52.

Now find the mean of the first 8 days

Mean = 52 / 8 = 6.5 hours

Nam works during the last 2 days together for:

(6.5 + 2)×2

8.5 × 2 = 17 hours

Answer:

Step-by-step explanation:

sorry it should be the second one for the interval notations

Answer:

[tex]n=10[/tex]

Step-by-step explanation:

[tex]\frac{4^8}{(4^2)^-^3}\ / 4^4=4^n[/tex]

Simplify, remember, an exponent raised to the power of another exponent is equal to the product of the two exponents,

[tex]\frac{4^8}{(4^2)^-^3}\ / 4^4=4^n[/tex]

[tex]\frac{4^8}{4^-^6}\ / 4^4=4^n[/tex]

Now bring the term in the denominator (number under the fraction bar) to the numerator (number over the fraction bar). This can be done by multiplying the exponent of the denominator by (-1).

[tex]\frac{4^8}{4^-^6}\ / 4^4=4^n[/tex]

[tex]4^8(4^(^-^1^)^(^-^6^))\ / 4^4=4^n[/tex]

Simplify,

[tex]4^8(4^6)\ / 4^4=4^n[/tex]

Remember, multiplying two numbers of the same base is the same as adding their exponents, apply this property here,

[tex]4^8(4^6)\ / 4^4=4^n[/tex]

[tex]4^1^4\ / 4^4=4^n[/tex]

Dividing two numbers of the same base is the same as subtraction their exponents,

[tex]4^1^4\ / 4^4=4^n[/tex]

[tex]4^1^0=4^n[/tex]

Thus, the following statement can be made,

[tex]4^1^0=4^n[/tex]

[tex]n=10[/tex]

Answer:

128

Step-by-step explanation:

3a² - 4b

plug in values

3(-6)² - 4(-5)

use PEMDAS and simplify (-6)² first

3(36) -4(-5)

multiply

108 + 20

add

128

hope this helps :)

Answer:

Sin

Step-by-step explanation:

Sin < = opposite/hypotenuse

Answer:

7.2

Step-by-step explanation:

Since the angle is equal, 24/(x+8.7)=13.1/8.7. x=7.2

Answer:

x ≈ 7.2

Step-by-step explanation:

Δ MNO and Δ MKL are similar, so the corresponding sides are in proportion, that is

[tex]\frac{MN}{MK}[/tex] = [tex]\frac{MO}{ML}[/tex] , substitute values

[tex]\frac{13.1}{13.1+10.9}[/tex] = [tex]\frac{8.7}{8.7 +x}[/tex]

[tex]\frac{13.1}{24}[/tex] = [tex]\frac{8.7}{8.7+x}[/tex] ( cross- multiply )

13.1(8.7 + x) = 208.8 ← distribute left side

113.97 + 13.1x = 208.8 ( subtract 113.97 from both sides )

13.1x = 94.83 ( divide both sides by 13.1 )

x = [tex]\frac{94.83}{13.1}[/tex] ≈ 7.2 ( to the nearest tenth )

Answer:

Step-by-step explanation:

2x ( -3y - 4) + 8 ( -3y - 4 )

= -6xy - 8x - 24y - 32

Hope this helps

plz mark as brainliest!!!

Answer:

Step-by-step explanation:

Use FOIL method

(2x + 8)(-3y -4) = 2x*(-3y) + 2x*(-4) + 8*(-3y) + 8*(-4)

                       = -6xy - 8x - 24y - 32

Answer:

=2x+3/4=5.50

x=19/8 or 2 3/8

hope this helps

Step-by-step explanation:

Answer:

b y=2.4x -1.8

Step-by-step explanation:

the equation y=2.4x -1.8 represents 2.4 from it

Answer:

Step-by-step explanation:

[tex]sin^3xcosx+sinxcos^3x\\=sinx cosx(sin^2x+cos^2x)\\=sinx ~cosx(1)\\=sin~x~cos~x[/tex]

Answer:

see explanation (please confirm if I read you problem correctly)

Step-by-step explanation:

150 kilometers

60 kph

tank is 20 liters

6 km/l

150/6 = 25 liters needed

$60/l

you will need to get 5 more liters of fuel

total cost 25 x .60 =  $15

Answer:

AHHHHH I think its two hours

Step-by-step explanation:

she...? can drive 120 Kilometers before she runs out of fuel since the car's tank has 20 liters of fuel at the beginning of the drive, and its fuel efficiency is 6 kilometers per liter. and that means she can drive 2 hours

Answer:

0

Step-by-step explanation:

Chalice with purified water = 4

With spoiled milk = 5

With flat soda = 6

Probability of Jones drinking from a chalice with purified water after Donovan had drank from 3 = 1/3

Probability = required outcome / Total possible outcomes

Total possible outcomes = (4 + 5 + 6) = 15

After Donovan drinks 3 :

Total possible outcomes = (15 - 3) = 12

If the probability of Jones choosing a chalice with purified water is 1/3 then :

(Required outcome / Total possible outcomes) =1 /3

(Required outcome / 12) = 1 / 3

Required outcome * 3 = 12

Required outcome = 12 / 3

Required outcome = 4

Therefore, since initial number of chalice with purified water is 4,

4 - 4 = 0

Then Donovan did not drink from a chalice containing purified water.

Answer:

y = - 140

Step-by-step explanation:

The statement

y varies jointly as x & z is written as

to find y when x = 7 and z = -5 we must first find the relationship between the variables

when y = - 180

z = 15

x = - 3

- 180 = k(15)(-3)

-180 = - 45k

Divide both sides by - 45

k = 4

The formula for the variation is

when

x = 7

z = -5

y = 4(7)(-5)

y = 4(-35)

Hope this helps you

The equation that could best represent the line of best fit for the given data is; y = 0.625x

The formula for the equation of a line in slope intercept form is;

y = mx + c

where;

m is slope

c is y-intercept which is the point where the line intersects the y-axis

Now, in this question, we see that the line intersects the y-axis at 0. Thus;

y-intercept; c = 0

Now, let us find the slope from the formula;

m = (y₂ - y₁)/(x₂ - x₁)

Using the first and penultimate coordinate which are;

(0, 0) and (8, 5), we have;

m = (5 - 0)/(8 - 0)

m = 0.625

Thus, the equation is;

y = 0.625x

Read more about Scatter plot equation at; https://brainly.com/question/6592115

#SPJ1

Answer:

y=0.625x

Step-by-step explanation:

plato

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Answer:

[tex]Average = 12\frac{4}{7}\ lb[/tex]

Step-by-step explanation:

Given

Number of jars = 14

Weights = 2, 2, 2, 1, 11, 12, 12, 2, 24, 22, 24, 3, 37, 22  in pounds

Required

What is the weight of each jar if the sea glass is evenly distributed

What this question implies is that, the average weight of the sea glass is calculated;

[tex]Average = \frac{Sum\ of\ weights}{Number\ of\ jars}[/tex]

[tex]Average = \frac{2+ 2+ 2+ 1+ 11+ 12+ 12+ 2+ 24+ 22+ 24+ 3+ 37+ 22}{14}[/tex]

[tex]Average = \frac{176}{14}[/tex]

[tex]Average = 12\frac{8}{14}[/tex]

Divide the numerator and denominator by 2

[tex]Average = 12\frac{4}{7}[/tex]

Hence, the weight of each jar would be [tex]12\frac{4}{7}\ lb[/tex]