The base of an open rectangular box is of length (2x + 5) cm and width x cm.
The area of this base is 58 cm
The height of the open box is (x - 2) cm.
a) Show that 2x + 5x -58 = 0
) Solve the equation 2x + 5x -58 = 0, giving your answers correct
to 2 decimal places
D) Hence calculate the volume of the box, stating the units of your answer.

Answer:

35/87

Step-by-step explanation:

To find the probability, we must find (total number of favorable outcomes)/ (total number of outcomes). We thus need to find the total number of outcomes. As people have only answered "yes" or "no", the total number of outcomes is 208+140 = 348.

The total number of favorable outcomes, or what we're looking for, is 140 (140 people responded that they had run a red light). Thus, our fraction is 140/348, or 35/87

Answer:8

Step-by-step explanation:

0.5*10=5

3+5=8

a. Montserrat runs 7.5 kilometers in her 10th training week.

b. by her 15th training week, Montserrat will have run a total of 78.75 kilometers.

To find how many kilometers Montserrat runs in her 10th training week, we can use the arithmetic sequence formula to find the nth term:

[tex]a_n = a_1 + (n - 1) * d[/tex]

where:

[tex]a_n[/tex] is the nth term (the number of kilometers in the nth week),

[tex]a_1[/tex] is the first term (the number of kilometers in the first week, which is 3 km),

n is the number of weeks (in this case, 10), and

d is the common difference (the amount by which the distance increases each week, which is 0.5 km).

[tex]a_{10} = 3 + (10 - 1) * 0.5\\a_{10} = 3 + 9 * 0.5\\a_{10} = 3 + 4.5\\a_{10 }= 7.5 km[/tex]

So, Montserrat runs 7.5 kilometers in her 10th training week.

b. Next, to calculate the total number of kilometers Montserrat will have run by her 15th training week, we use the sum of the first n terms formula:

[tex]S_n = (n / 2) * (a_1 + a_n)[/tex]

where:

[tex]S_n[/tex] is the sum of the first n terms (the total number of kilometers run by the nth week),

[tex]a_1[/tex] is the first term (3 km),

[tex]a_n[/tex] is the nth term (which we found to be 7.5 km in her 10th week),

n is the number of weeks (15 in this case).

[tex]S_{15} = (15 / 2) * (3 + 7.5)\\S_{15} = 7.5 * 10.5\\S_{15} = 78.75 km[/tex]

So, by her 15th training week, Montserrat will have run a total of 78.75 kilometers.

To know more about training:

https://brainly.com/question/28942187

#SPJ3

Answer:

The answer is below

Step-by-step explanation:

The endpoints of AB are A(2, 3) and B(8, 1). The perpendicular bisector of AB is CD, and point C lies on AB. The length of CD is (root of 10) units.

The coordinates of point C are (-6, 2) (5, 2) (6, -2) (10, 4) . The slope of is -3 -1/3 1/3 3 . The possible coordinates of point D are (4, 5) (5, 5) (6, 5) (8, 3) and (2, 1) (4, -1) (5, -1) (6, -1) .

Solution:

Since CD is the perpendicular bisector of AC, hence line CD is perpendicular to AB and divides line AB into two equal parts.

Point C(x, y) is the midpoint of AB.

hence:

x = (2 + 8) / 2 = 5

y = (3 + 1)/2 = 2

The coordinates of point C = (5, 2)

The slope of line AB is:

slope of AB = (1 - 3) / (8 - 2) = -1/3

Since CD is perpendicular to AB, hence the product of the slope of AB and the slope of CD is -1

slope of AB * slope of CD = -1

slope of CD * -1/3 = -1

slope of CD = 3

Line CD has slope of 3 and pass through C(5, 2). The equation of line CD is:

y - 2 = 3(x - 5)

y = 3x - 13

The possible coordinates of point D are (6, 5) and (4, -1), because this point lie on line CD.

Answer:

Step-by-step explanation:

[tex]carry\: on \: learning[/tex]

Answer:

Try to glue it back together

Step-by-step explanation:

I heard gorilla glue works, but be careful and don't get the glue on your body. If that happens it can cause irritation and call posion control immediately.

Answer:

y >= x/2 - 1

Step-by-step explanation:

the slope (rise/run) is 1/2 and the y-intercept is -1 so in point-slope form

y = x/2 - 1 but everything above the line (unshaded part) is valid so y is equal to or greater than.

Answer:

2 + y > 16

Step-by-step explanation:

the sum of 2 and y is greater than 16

                   2 + y           >                   16

2 + y > 16

Answer:

C. 12x² + 8x + 25

Step-by-step explanation:

A. 12x² + 15

B. 20x² + 25

C. 12x² + 8x + 25

D. 24x² + 16x + 50

Hypotenuse = 8x²

Height = 4x² + 15

Base = 8x + 10

Perimeter of the triangle = hypotenuse + height + base

= 8x² + (4x² + 15) + (8x + 10)

= 8x² + 4x² + 15 + 8x + 10

Perimeter of the triangle = 12x² + 8x + 25

C. 12x² + 8x + 25

Answer:The answer is C

Answer:

x≈95,6

Step-by-step explanation:

x= cos 15⁰ x 99 ≈95,6

Answer:

π × d

Step-by-step explanation:

The relationship between the diameter and circumference is that the circumference is equal to π multiplied by the diameter. This means that our answer is π × d, or the third option

Answer:

1. reflection- a figure is flipped over

2. translation- a figure is slide

3. rotation- a figure is turned

☆ Bio fertilizer :- Biofertilisers are organisms that enrich the nutrient quality of the soil. The main source f biofertilizers are bacteria, fungi and cyanobacteria.

Answer: 4

2x2+3(2)−6

lets make sure we do OOO (order of operations correctly)

2x2+3(2)−6

4+3(2)−6

4+6−6

10−6

4

Step-by-step explanation:

Step-by-step explanation:

a)50°

b)75°

c)125°

d)d=40°

Answer:

Step-by-step explanation:

A)180-(60+70)=50

C)180-30=150 150/2=75

B)180-(35+20)=125

D)2d+d+60=180

3d+60=180

3d=120 ; d=40 ; 2d=40×2=80

Answer:

what do you mean for this question. What do you need help on?

Answer:

21 x 3.1 / 2 = 32.55

Step-by-step explanation:

Answer:

[tex]x = \frac{7}{2}[/tex]

Step-by-step explanation:

[tex]6^{x-1} = 36 \sqrt6\\\\6^{x-1} = 6^2 \times 6^{\frac{1}{2}}\\\\6^{x-1} = 6^{2 + \frac{1}{2} }[/tex]                        [tex][ \ a^x \times a^ y = a^{x+ y} \ ][/tex]

[tex]x - 1 = 2 + \frac{1}{2}[/tex]                          [tex][ \ b^x = b^y => x = y \ ][/tex]

[tex]x = 2 + \frac{1}{2} + 1\\\\x = 3 + \frac{1}{2} \\\\x = \frac{6+ 1}{2} \\\\x = \frac{7}{2}[/tex]

Answer:

x = 3.5

Step-by-step explanation

Using the rules of exponents

[tex]a^{m}[/tex] × [tex]a^{n}[/tex] ⇔ [tex]a^{(m+n)}[/tex] and [tex]\sqrt{a}[/tex] = [tex]a^{\frac{1}{2} }[/tex]

Then

36[tex]\sqrt{6}[/tex] = 6² × [tex]6^{\frac{1}{2} }[/tex] = [tex]6^{(2+0.5)}[/tex] = [tex]6^{2.5}[/tex]

Thus

[tex]6^{x-1}[/tex] = [tex]6^{2.5}[/tex]

Since the bases on both sides are equal, both 6, equate the exponents

x - 1 = 2.5 ( add 1 to both sides )

x = 3.5

Answer:B

Step-by-step explanation:

simple, there is one point of intersection or where the lines meet

Answer:

B:  One solution

Step-by-step explanation:

The graphs show that the two lines intersect at one point.  This point represents the ONE solution of this system of equations.

If the lines did not intersect, the system would have no solution.

If the lines coincide, the system would have infinitely many solutions.

Answer:

B: The retiree has a pension savings of $51,000

Step-by-step explanation:

Answer:

7x

or 7*x

Step-by-step explanation:

Answer:

5

Step-by-step explanation:

the answer is on the picture

[tex]\implies {\blue {\boxed {\boxed {\purple {\sf {x\:=\:33}}}}}}[/tex]

[tex]\large\mathfrak{{\pmb{\underline{\red{Step-by-step\:explanation}}{\red{:}}}}}[/tex]

[tex]x = 42 - 9[/tex]

➼[tex]\:x = 33[/tex]

Therefore, the value of [tex]x[/tex] is 33.

[tex]\sf\pink{Thank\:you. \:ヅ}[/tex]

Answer:

x =33

Step-by-step explanation:

x = 42-9

We are solving for x, which is already isolated

42-9 = 33

x = 33

Check 33+9 = 42

Answer:

25 in and 9 cm

Step-by-step explanation:

Using Pythagoras' identity

The square on the hypotenuse is equal to the sum of the squares on the other 2 sides.

let x be the missing side

A

x² = 7² + 24² = 49 + 576 = 625 ( take square root of both sides )

x = [tex]\sqrt{625}[/tex] = 25

B

x² + 12² = 15²

x² + 144 = 225 ( subtract 144 from both sides )

x² = 81 ( take square root of both sides )

x = [tex]\sqrt{81}[/tex] = 9

Answer:

A) [tex]\sqrt{7^{2} +24^{2} }[/tex] = 25

B) [tex]15^{2} -12^{2} = B^{2}[/tex]

   [tex]B^{2} =81\\[/tex]

B = 9

Step-by-step explanation:

The answer to your question is 137

Answer:

The rate (or speed) of the wind is 40 meters per minute.

Step-by-step explanation:

Let's define:

S = speed (or rate) of the duck alone

S' = speed (or rate) of the wind.

When the duck travels with the wind, its speed is:

(S + S')

While when the duck travels against the wind, its speed is:

(S - S')

Also, remember the relation:

Distance = Speed*Time

ok, we know that the duck can travel a distance of 2400 m in 10 minutes with the wind, then:

2400m = (S + S')*10 min

And against the wind, it can travel 2/3 of that distance, then we can write:

(2/3)*2400m = (S - S')*10 min

Then we have a system of 2 equations:

2400m = (S + S')*10 min

(2/3)*2400m = (S - S')*10 min

We want to find the speed of the wind, then we want to find the value of S'.

To solve this, we first need to isolate S in one of the equations.

Let's isolate S in the first one:

2400m = (S + S')*10 min

2400m/10min = (S + S')

240 m/min = S + S'

240 m/min - S' = S

Now we can replace this in the other equation:

(2/3)*2400m = (S - S')*10 min

(2/3)*2400m = ( 240 m/min - S' - S')*10 min

Now let's solve this for S'

(2/3)*2400m/10min = 240 m/min - 2*S'

(2/3)*240 m/min = 240 m/min - 2*S'

2*S' = 240 m/min - (2/3)*240 m/min

2*S' = (1/3)*240 m/min

2*S' = 80 m/min

S' = (80 m/min)/2

S' = 40 m/min

The rate (or speed) of the wind is 40 meters per minute.

Answer: x = 34

Step-by-step explanation:

2x+3+3x+7=180

5x+10=180

5x=170

x = 34

Answer:

Ox-12

Step-by-step explanation:

Answer:

A

Step-by-step explanation:

(4x - 6) - (3x + 6)              Remove the brackets

4x - 6 - 3x - 6                   Collect like terms

4x - 3x - 6 -6

x - 12

The answer   is A

Step-by-step explanation:

Finding the (maximum) respective prime powers would yield the answer. Also we need not ... Is perfectly divisible by 720^n? ... So we can say that for any positive value of n it not divisible.