Simplify 0.4(5a-3.2b+7)

The actual distance between the opposite corners of the school hall is; 10√34 m

The scale drawing showing the corners of the hall has been drawn and attached.

Now, from the attached scale drawing it was drawn with the scale;

1 cm to represent 5 m.

Now, the distance between the opposite corners of the hall measuring 50 m and 30 m is indicated as D on the scale drawing. Thus, to find the distance between the opposite corners, we will use Pythagoras theorem to get;

D² = 30² + 50²

D² = 900 + 3500

D² = 4400

D = √4400

D = 10√34 m

Thus, the actual distance between the opposite corners of the school hall is; 10√34 m

Complete question is;

Make a scale drawing of a rectangular school hall which is 50 m long and 30 m wide using a scale of 1 cm to 5 m. From your scale drawing, find the actual distance between the opposite corners of the hall.

Read more about Scale Drawing at; https://brainly.com/question/15891755

#SPJ1

Answer:

  138.37 g

Step-by-step explanation:

Mass is the product of density and volume.

  M = ρV = (0.685 g/mL)(202 mL) = 138.37 g

[tex]\\ \tt{:}\dashrightarrow \ell=\dfrac{\Theta}{180}\pi r[/tex]

[tex]\\ \tt{:}\dashrightarrow \Theta=\dfrac{180\ell}{\pi r}[/tex]

[tex]\\ \tt{:}\dashrightarrow \Theta=\dfrac{180(13)}{5\pi}[/tex]

[tex]\\ \tt{:}\dashrightarrow \Theta=149^{\circ}[/tex]

[tex]\\ \tt{:}\dashrightarrow \Theta=149(60)[/tex]

[tex]\\ \tt{:}\dashrightarrow \Theta=8940'[/tex]

The angle subtended at the center of a circle of radius 5 cm by a length of 13 cm is 149.1°.

Given that,

The angle is subtended at the center of a circle of radius 5 cm by a length of 13 cm.

Here, Lenght of an arc = 13 cm

The radius of an arc = 5 cm

Used the formula for the angles (θ);

Length of an arc = 2πrθ / 360°

Substitute all the values, we get;

13 = 2 × 3.14 × 5 × θ / 360°

Solve for θ;

13 × 360° = 31.4 × θ

4,680° = 31.4 × θ

θ = 4,680°/31.4

θ = 149.1°

To learn more about the circle visit:

https://brainly.com/question/24810873

#SPJ7

Answer:

3 consecutive no.s are

5×6×7=210

sum of them is= 5+6+7

=18

So, I hope. it helps !!

Answer:

The slope is -3.

Step-by-step explanation:

The slope is the Rise/Run between the two points.  The change in y for every change in x.  Take the two points and calculate the:

RISE = (-6 - 3) = -9

RUN = (8 - 5) = 3

Rise/Run, or slope, is = -9/3 or -3

I graphed a line with slope of -3 and then added 18 to force the line to intersect the two given points.

The value of output, h, when the input, x, is -18 for the given equation is 14

From the given question, we are to determine the value of the output, h, when the input x is -18

The given equation written properly is

h = 17 + x/6

Now, to determine the value of output, h, we will put in the value of x into the equation

h= 17 + x/6

The given value of x is -18

Thus, putting the given value of x into the equation, we get

h= 17 + x/6

h= 17 + -18/6

h = 17 + -3

h = 17 - 3

NOTE: + × - = -

h = 14

∴ h is 14 when x is -18

Hence, the value of output, h, when the input, x, is -18 for the given equation is 14

Learn more on Solving an equation here: https://brainly.com/question/20725347

#SPJ1

The logarithmic equation is:

log₂128 = x

So the correct option is the third one

Here we have the expression.

2ˣ = 128

Now, if we apply the natural logarithm to both sides, we can get:

ln(2ˣ) = ln(128)

Because of the property of natural logarithms, we can write the left side as:

ln(2ˣ) = x*ln(2) = ln(128)

Now, if we isolate x, we get:

x = ln(128)/ln(2)

And remember that:

ln(k)/ln(n) = logₙ(k)

Then we can rewrite the logarithmic equation as:

x = log₂(128)

Which is the third option.

If you want to learn more about logarithmic equations, you can read:

https://brainly.com/question/236421

#SPJ1

Answer:

Use the distance formula on both points AC and AB.

Distance formula is this:

\begin{gathered}d=\sqrt{(x2-x1)^2+(y2-y1)^2} \\\\d=\sqrt{(1--5)^2+(8--7)^2} \\\\d=\sqrt{(6)^2+(15)^2} \\\\d=\sqrt{36+225} \\\\d=\sqrt{261} \\\\\end{gathered}d=(x2−x1)2+(y2−y1)2d=(1−−5)2+(8−−7)2d=(6)2+(15)2d=36+225d=261

Distance for AC  is  16.16

Now do the same with the numbers for AB and get the distance of 5.39

2. To get the area, use the formula 1/2 x base x height

AB is the base and AC is the height.

1/2 x 16.16 x 5.39 = 43.55

the answer is 43.5

The zeros represent the number of monthly memberships where no profit is made; x = 6, x = 44.

The function we have is: [tex]f(x) = -x^{2} +50x-264[/tex]

That models the profit in dollars, where [tex]x[/tex] is the number of memberships sold.

In order to get the zeros we'll use the quadratic formula:

[tex]x_{1,2} =\frac{-b+-(b^{2}-4ac) }{2a} \\[/tex]

For,

[tex]a=-1,b=50,c=-264: x^{1,2} =\frac{-50+-\sqrt[]{50^{2} -4(-1)(-264)} }{2(-1)} \\x_{1} =\frac{-50+\sqrt[]{50^{2} -4(-1)(-264)} }{2(-1)} =\frac{-50+\sqrt[]{50^{2} -4*1*264} }{2(-1)}=\frac{-50+\sqrt[]{1444} }{-2} =6\\x_{2} =\frac{-50+\sqrt[]{50^{2} -4(-1)(-264)} }{2(-1)} =\frac{-50-\sqrt[]{50^{2} -4*1*264} }{2(-1)}=\frac{-50-\sqrt[]{1444} }{-2} =44\\[/tex]

So, the zeroes are [tex]x=6, x=44[/tex].

Therefore, the zeros represent the number of monthly memberships where no profit is made; x = 6, x = 44.

Know more about a function here:

https://brainly.com/question/25638609

#SPJ4

The complete question is given below:

A yoga studio sells monthly memberships. The function f(x) = −x2 + 50x − 264 models the profit in dollars, where x is the number of memberships sold.

Determine the zeros, and explain what these values mean in the context of the problem.

x = 6, x = 44; The zeros represent the number of monthly memberships that produce a maximum profit.

x = 6, x = 44; The zeros represent the number of monthly memberships where no profit is made.

x = 25, x = 361; The zeros represent the number of monthly memberships where no profit is made.

x = 25, x = 361; The zeros represent the number of monthly memberships that produce a maximum profit.

Answer:

The answer is: x = 6, x = 44; The zeros represent the number of monthly memberships when no profit is made.

Answer:

Step-by-step explanation:

190/x=100/63

(190/x)*x=(100/63)*x       - we multiply both sides of the equation by x

190=1.5873015873016*x       - we divide both sides of the equation by (1.5873015873016) to get x

190/1.5873015873016=x

119.7=x

x=119.7

now we have:

63% of 190=119.7

You are requesting a number, as the question clearly states. So, a number should be the response. However, because 63 and 190 are not stated and might indicate a variety of things, we must make an assumption in order to provide a response.

We will thus assume that 63 is a percentage and that 190 is a number in order to respond to the question, "What number is 63 of 190?"

We multiply 63 by 190 and then divide the result by 100 to obtain the solution. Here is the calculation and response to your query:

⇒ 63 x 190 = 11970

⇒ 11970 / 100 = 119.7

Assuming you meant 63 percent of 190, the answer to the question "What number is 63 of 190?" is 119.7, as shown and computed above.

Thank you,

Eddie

The probability of rolling a sum of six or two even numbers.

is P = 1/3

Here we are rolling two dice, and each dice has 6 possible outcomes, then the total number of outcomes is:

6*6 = 36

Now, the outcomes that given a sum of 6 are:

dice 1    dice 2.

1              5

5              1

2              4

4              2

3             3

We have 5 outcomes there.

The outcomes where both numbers are even are:

dice 1    dice 2.

2             2

2             4

4             2

4             4

4            6

6             2

6             4

6             6

We have 8 outcomes here (such that 2 are in the ones we counted before).

Then the total number of outcomes that either add to 6 or have both even numbers are:

5 + 8 - 2 = 12

Then 12 out of 36 outcomes either add to 6 or have both even numbers, this means that the probability is:

P = 12/36 = 1/3

If you want to learn more about probability:

https://brainly.com/question/25870256

#SPJ1

The solutions for the given system are (3,2), (3,-2), (-3,2) and (-3,-2).

The quadratic function can represent a quadratic equation in the Standard form: ax²+bx+c=0 where: a, b and c are your respective coefficients. In the quadratic function the coefficient "a" must be different than zero (a≠0) and the degree of the function must be equal to 2.

The solution of these equations represents the points at which the parabolas intersect.

2x²+8y²=50 (1)

x²  + y²= 13 (2)

Multiplying the equation 2 by -2, you have:

2x²+8y²=50 (1)

-2x² -2 y²= -26(2)

Sum both equations, you have: 6y²= 24. Now, you can find y.

6y²= 24

y²=4

y=±2

If y=2, from equation 2, you have

x²  + y²= 13

x²  + 2²= 13

x²  + 4= 13

x² =13-4

x² =9

x=±3

Read more about the solution to the system of equations here:

https://brainly.com/question/6566909

#SPJ1

The plastic containers should be used by the company to minimize the cost because it will cost $5.40 more to use the wooden containers.

A mathematical word problem is a question that is stated as one or more sentences and calls on students to use their understanding of arithmetic operations to solve a "real-life" problem.

As you are aware, word problems can include almost any operation, including addition, subtraction, division, and even many operations at once.

From the given information:

If the company uses a wooden container shaped-liked rectangular prism, the will need to use (7560/180) containers.

= 42 containers of wooden containers.

If the company uses a plastic cylindrical container, they will need to use (7560/126) containers.

= 60 containers of plastic containers.

To determine the container that the company should use that will minimize the cost:

Therefore, we can conclude that the company should use plastic containers because it will cost $5.40 more to use wooden containers.

Learn more about word problems here:

https://brainly.com/question/13818690

SPJ1

Answer:

B. The plastic containers should be used because it will cost $5.40 more to use the wooden containers.

Step-by-step explanation:

right angles. .... . . . . ......

Answer:

x + 4y = 7

Step-by-step explanation:

the equation of a line in slope- intercept form is

y = mx + c ( m is the slope and c the y- intercept )

calculate m using the slope formula

m = [tex]\frac{y_{2}-y_{1} }{x_{2}-x_{1} }[/tex]

with (x₁, y₁ ) = (- 1, 2 ) and (x₂, y₂ ) = (3, 1 )

m = [tex]\frac{1-2}{3-(-1)}[/tex] = [tex]\frac{-1}{3+1}[/tex] = - [tex]\frac{1}{4}[/tex] , then

y = - [tex]\frac{1}{4}[/tex] x + c ← is the partial equation

to find c substitute either of the 2 points into the partial equation

using (- 1, 2 )

2 = [tex]\frac{1}{4}[/tex] + c ⇒ c = 2 - [tex]\frac{1}{4}[/tex] = 1 [tex]\frac{3}{4}[/tex] = [tex]\frac{7}{4}[/tex]

y = - [tex]\frac{1}{4}[/tex]x + [tex]\frac{7}{4}[/tex] ← in slope- intercept form

multiply through by 4 to clear the fractions

4y = - x + 7 ( add x to both sides )

x + 4y = 7 ← equation in standard form

equation of line in two point form is needed here.

Answer:

b

Step-by-step explanation:

Answer:

B. Monday

Step-by-step explanation:

Monday, Tuesday, Wednesday, Monday, Tuesday, Wednesday, Monday

hope it helps

Answer:

14×7=98 so multiply the same into 14×8=112

Answer:

112 watermelons

Step-by-step explanation:

7/8 = 7÷7/8÷7 = 1/1.14285714286

1 x 98/ 1.14285714286 x 98

98/112

Answer:

As the number of files increases, the storage space used increases.

Answer:

D. 13

Step-by-step explanation:

54 ÷ 3 = 18 (your age in 5 years)

18 - 5 = 13 (your age now)

Answer:

11.8 units

Step-by-step explanation:

The circle equation is given as:

The circle equation is given as:(x - 2)^2 + (y + 6)^2 = 35

The circle equation is given as:(x - 2)^2 + (y + 6)^2 = 35A circle equation is represented as:

The circle equation is given as:(x - 2)^2 + (y + 6)^2 = 35A circle equation is represented as:(x - a)^2 + (y - b)^2 = r^2

The circle equation is given as:(x - 2)^2 + (y + 6)^2 = 35A circle equation is represented as:(x - a)^2 + (y - b)^2 = r^2Where

The circle equation is given as:(x - 2)^2 + (y + 6)^2 = 35A circle equation is represented as:(x - a)^2 + (y - b)^2 = r^2WhereDiameter = 2r

The circle equation is given as:(x - 2)^2 + (y + 6)^2 = 35A circle equation is represented as:(x - a)^2 + (y - b)^2 = r^2WhereDiameter = 2rBy comparing both equations, we have

The circle equation is given as:(x - 2)^2 + (y + 6)^2 = 35A circle equation is represented as:(x - a)^2 + (y - b)^2 = r^2WhereDiameter = 2rBy comparing both equations, we haver^2 = 35

The circle equation is given as:(x - 2)^2 + (y + 6)^2 = 35A circle equation is represented as:(x - a)^2 + (y - b)^2 = r^2WhereDiameter = 2rBy comparing both equations, we haver^2 = 35Take the square root of both sides

The circle equation is given as:(x - 2)^2 + (y + 6)^2 = 35A circle equation is represented as:(x - a)^2 + (y - b)^2 = r^2WhereDiameter = 2rBy comparing both equations, we haver^2 = 35Take the square root of both sidesr = 5.9

The circle equation is given as:(x - 2)^2 + (y + 6)^2 = 35A circle equation is represented as:(x - a)^2 + (y - b)^2 = r^2WhereDiameter = 2rBy comparing both equations, we haver^2 = 35Take the square root of both sidesr = 5.9Multiply by 2

The circle equation is given as:(x - 2)^2 + (y + 6)^2 = 35A circle equation is represented as:(x - a)^2 + (y - b)^2 = r^2WhereDiameter = 2rBy comparing both equations, we haver^2 = 35Take the square root of both sidesr = 5.9Multiply by 22r = 11.8

The circle equation is given as:(x - 2)^2 + (y + 6)^2 = 35A circle equation is represented as:(x - a)^2 + (y - b)^2 = r^2WhereDiameter = 2rBy comparing both equations, we haver^2 = 35Take the square root of both sidesr = 5.9Multiply by 22r = 11.8Hence, the diameter of the circle is 11.8 units

Answer: 8,9.

Step-by-step explanation:

[tex](x-2)^2+(y+6)^2=20\\Circle \ equation\\\boxed {(x-a)^2+(y-b)^2=r^2}\\r^2=20\\r*r=\sqrt{20}*\sqrt{20}\\ r=\sqrt{20}\\ r=\sqrt{4*5}\\ r=2\sqrt{5} \\ D=2r\\D=2*2\sqrt{5}\\ D=4\sqrt{5}\\ D\approx8,9.[/tex]

Answer:

A.  y = 1/3x^2

Step-by-step explanation:

The red graph is stretched horizontally by a factor 1/3  to give the blue graph

Answer:

x=16

Step-by-step explanation:

6= x/4 + 2

Subtract 2 from both sides.

4= x/4

Multiply 4 to both sides.

x=16

Hope this helps!

Answer:

salary=120000

1/4×120000=30000= money spent

remainder=120000- 30000

= 90000

money spent on clothing =1/2×90000

=45000

Explanation: If his salary is $120,000 and 1/4 is used on food he has a remaining of $80,000. He uses 1/2 on clothing so he has a remainder of $40,000 so now we know that he used $40,000 on clothing

Answer: $40,000

Hope this helps you! :D

The simplified form of the expression 7^x+1 + 7^x / 2×7^x as given in the task content follows from the laws of indices and is equal to; 4.

It follows from the task content that the expression whose simplified form is to be determined is given as; 7^x+1 + 7^x / 2×7^x.

On this note, it follows from the law of indices that; 7^x+1 = 7× 7^x.

Hence, we have; 7^x(7+1 ) / 2×7^x.

And upon simplification, we have; 8/2 = 4.

Consequently, we may conclude that the simplified form of the expression as given in the task content is; 4.

Read more on laws of indices;

https://brainly.com/question/10339517

#SPJ1

Answer:

B

Step-by-step explanation:

Answer:

4

Step-by-step explanation:

18 + 18 = 36

So you got 36 cuz you times by two so you times the same for x

which is

2 x 2 = 4

Answer:

4

Step-by-step explanation:

We can set up a proportion.

18:2 = 36: x

If we multiply 18 by 2, and multiply 2 by 2, we can get 18:2 = 36:4, so x is equal to 4

One fourth of m minus six is equal to two times the sum of m and 9:

This is self-explanatory, please comment if something is unclear.

Drew has 50 marbles; red, green and blue.

Equation for this:

He has six more red marbles than blue marbles:

Equation for this:

He has four fewer green marbles than blue marbles:

Equation for this:

Substitute r and g into first equation and solve for b:

Drew has 16 blue marbles.

Using the total weight the number of red, green and yellow colour are 2, 4 and 3 respectively.

The total number of reds, yellows, and greens on a scale is 9.

The reds weighed 3 pounds each, the yellows weighed 6 pounds each, and the greens weighed 5 pounds each. The total weight is 44

pounds. There are 2 more greens than reds.

Therefore,

let

x = number of reds

number of greens = x + 2

y = number of yellow

Therefore,

x + x + 2 + y = 9

2x + y = 7

3x + 6y + 5(x + 2) = 44

3x + 6y + 5x + 10 = 44

8x + 6y = 34

Hence,

2x + y = 7

8x + 6y = 34

8x + 4y = 28

8x + 6y = 34

2y = 6

y = 6 / 2

y = 3

2x + 3 = 7

2x = 7 - 3

2x  = 4

x = 4 / 2

x = 2

Therefore,

the number red colour = 2

the number of green colour = 2 + 2 = 4

the number of yellow colour = 3

learn more on total weight here: https://brainly.com/question/4310004

#SPJ1