For questions 5-8, evaluate the expression for x = 6 and y =17

5. 4x + 5y

6. 2x + (20 - y )

7. x ÷ 3 + y

8. 4y ÷ 2 + ( 8x + 10)​

Answer:

The Proof for  "Equal chord of a circle subtends equal angle at the Center".

Step-by-step explanation:

Consider a Circle with center as C,

Radius AC ,BC ,DC and EC

Chord AB = Chord CD

To Prove:

"Equal chord of a circle subtends equal angle at center".

i.e ∠ACB = ∠ECD

Proof:

In  Δ ABC and Δ DEC

Chord AB ≅ Chord DE     .….{Given}

AC ≅ DC                           …..{Radius of Same Circle}

BC ≅ EC                           ….{Radius of Same Circle}

Δ ABC ≅ Δ DEC               ….{By Side-Side-Side Congruence Postulate}

∴∠ACB ≅ ∠ECD  ...{Corresponding Parts of Congruent Triangles are Congruent or CPCTC} ....Proved

i.e Equal chord of a circle subtends equal angle at the Center.

Answer:

180 chickens and 40 pigs

Step-by-step explanation:

We are given;

We are required to determine the number of chickens and pigs in the farm;

To answer the question we need to know the following;

Assuming the number of chickens is x and the number of pigs is y

Then we can form two equations;

We can solve the two equations simultaneously to find the number of chickens and pigs;

x + y = 220

2x + 4y = 520

Multiplying the first equation by 2, we get

2x + 2y = 440

2x + 4y = 520

Eliminating x, we get;

- 2y = -80

    y = 40

Solving for x;

x = 220 - y

  = 220 - 40

x  = 180

Therefore, there are 180 chickens and 40 pigs at the farm

The new pressure is 2 Kpa

Solution:

At constant temperature, the pressure of a sample of gas is inversely proportional to its volume

Therefore,

[tex]\text{ pressure of a sample of gas} \propto \frac{1}{\text{volume}}[/tex]

Let "p" be the pressure of sample gas

Let "v" be the volume

Then we get,

[tex]p \propto \frac{1}{v}\\\\p = k \times \frac{1}{v}\\\\p = \frac{k}{v} ---------- eqn 1[/tex]

Where, "k" is the constant of proportionality

I have some oxygen in a 2.28 liter container with a pressure of 5 kPa

Substitute v = 2.28 and p = 5 in eqn 1

[tex]5 = \frac{k}{2.28}\\\\k = 5 \times 2.28\\\\k = 11.4[/tex]

I move all of it to a 5.7 liter container at the same temperature

Substitute k = 11.4 and v = 5.7 in eqn 1

[tex]p = \frac{11.4}{5.7}\\\\p = 2[/tex]

Thus new pressure is 2 kPa

There is 32.69% decrease.

Step-by-step explanation:

Given,

Old value = 52 million

New value = 35 million

Change = New value - Old value

Change = 35 - 52 = -17

The negative sign indicates the decrease.

Percent decrease = [tex]\frac{Change}{Old\ value}*100[/tex]

Percent decrease = [tex]\frac{17}{52}*100[/tex]

Percent decrease = [tex]\frac{1700}{52}\\[/tex]

Percent decrease = 32.69%

There is 32.69% decrease.

Keywords: percentage, division

Learn more about division at:

#LearnwithBrainly

Answer:

Jenny spent 1 hour swimming in the morning.

Jenny pasó 1 hora nadando por la mañana.

Step-by-step explanation:

Translated:

Jenny is on the summer swimming team and her practice is 4 hours per day, in a week. The schedule is the same every day. The team swims in the morning and again in the afternoon 2 hours. If she swims 12 hours a week, how much does she swim every morning?

We know that she swims 4 hours per day, mornings and evenings.

We know that one specific week she swam for 12 hours total in that week.

Let as denote the number of hours swam in a day as [tex]x[/tex].

Then we can say that in that week for 12 hours total and 4 hours swimming per day, we have:

[tex]4x=12\\x=\frac{12}{4}\\x=3[/tex]hours per day swam for that week.

Now since we know for a fact that 2 hours are spend swimming in the evening then we can subtract this from the total of 3 hours as

[tex]3-2=1[/tex] hour of swimming in the morning.

So we can conclude that on the week that Jenny swam for 12 hours total, she spent 1 hour swimming in the morning and 2 hours swimming in the evening.

En Espagnol:

Entonces podemos concluir que la semana en que Jenny nadó durante 12 horas en total, pasó 1 hora nadando por la mañana y 2 horas nadando por la noche

To find the new number of counters in each bag, subtract 5 from bag a and add 5 to bag b.

The subject of this question is mathematics. In this question, we are given two bags, bag a and bag b, which contain 7x and 2x counters respectively. Five counters are taken from bag a and put in bag b.

To find the new number of counters in each bag, we subtract 5 from bag a and add 5 to bag b:

https://brainly.com/question/34484346

#SPJ3

Good evening

Answer:

Step-by-step explanation:

Look at the photo below for the details.

:)

Answer:

x = 5 or x = -2

Step-by-step explanation:

See the attached image for the working out.

[tex]\huge\text{Hey there!}[/tex]

[tex]\mathsf{\dfrac{3}{8}\times\dfrac{4}{5}}\\\\\\\mathsf{= \dfrac{3\times4}{8\times5}}\\\\\\\mathsf{= \dfrac{12}{40}}\\\\\\\mathsf{= \dfrac{12\div4}{40\div4}}\\\\\\\mathsf{= \dfrac{3}{10}}\\\\\\\\\\\\\huge\text{Therefore, your answer is: \boxed{\mathsf{\dfrac{3}{10}}}}\huge\checkmark[/tex]

[tex]\huge\text{Good luck on your assignment \& enjoy your day!}[/tex]

~[tex]\frak{Amphitrite1040:)}[/tex]

Final answer:

A total of 63 cars raced over the two days: 36 cars on Saturday (4 races × 9 cars) and 27 cars on Sunday (3 races × 9 cars).

Explanation:

The student is asking to calculate the total number of cars that raced over two days. There were 4 car races on Saturday and 3 on Sunday, with 9 cars racing in each race. To find the total number of cars that raced, you would multiply the number of races each day by the number of cars in each race and then add those two products together.

For Saturday: 4 races × 9 cars per race = 36 cars

For Sunday: 3 races × 9 cars per race = 27 cars

Adding the cars from Saturday to the cars from Sunday gives us the total: 36 cars + 27 cars = 63 cars.

Therefore, over the two days, a total of 63 cars raced.

Answer:

Area of the wall without the doorway = 67.5 - 21 = 46.5 [tex]feet^{2}[/tex]

Step-by-step explanation:

i) let length of smaller side of trapezoidal wall, a = 22 feet

ii) let length of longer side of trapezoidal wall, b = 23 feet

iii) height of trapezoidal wall, h = 3 feet

iv) area of trapezoidal wall = [tex](\frac{a + b}{2} )\times h[/tex] = [tex](\frac{22 + 23}{2} )\times 3[/tex] = 22.5 [tex]\times[/tex] 3 = 67.5 [tex]feet^{2}[/tex]

v) area of door = 7 [tex]\times[/tex] 3 = 21 [tex]feet^{2}[/tex]

vi) Area of the wall without the doorway = 67.5 - 21 = 46.5 [tex]feet^{2}[/tex]

Answer:

738

Step-by-step explanation:

984 ÷ 100 = 9.84

9.84 × 75 = 738

75/100

Answer:

Step-by-step explanation:

interior angle = sum of interior angles/total no. of angles

= 540/5 = 108

Answer:

He will pay $64

Step-by-step explanation:

Using the attached image, for the head of household earning $36,558, he's bound to pay $4,866 considering that his age bracket is in the last line of the image ($36,550-$36,600). However, since he has already paid $4,802 then he hasn't paid it all. He remains with a balance of $4,866-$4,802=$64

Therefore, he's supposed to pay additional $64

Answer:

23/25

Step-by-step explanation:

Just figure out what goes in both of these numbers and i think of it as making a Fraction getting skinny so I simplify until I can't get any Skinner, and as I reduced I got 23/25 or 0.92.

I hope this help, This is just how to think about it you should try it, it really helps me!

Answer: [tex]60\ cm^3[/tex]

Step-by-step explanation:

You can observe in the picture attached that the box is a rectangular prism.

The volume of a rectangular prism can be found with this formula:

[tex]V=lwh[/tex]

Where "l" is the length, "w" is the width and "h" is the height.

You know that the lenght of each side of those cubes is 1 centimeter. Therefore, you can multiply the number of cubes on each side of the box by 1 centimeter in order to find the lenght, the width and the height of the box:

 [tex]l=(4)(1\ cm)=4\ cm\\\\w=(3)(1\ cm)=3\ cm\\\\h=(5)(1\ cm)=5\ cm[/tex]

Now you can substitute the lenght, the width and the height of the box into the formula shown at the beginning of the explanation:

[tex]V=(4\ cm)(3\ cm)(5\ cm)[/tex]

Finally, evaluating, you get that the volume of the box is:

[tex]V=60\ cm^3[/tex]

Answer: 1

Step-by-step explanation:

i think u just have to divide

Answer:54.3915

Step-by-step explanation:

Price:63.99

Off:15%

Price after 15% off:

{63.99*(100-15)}/100

={63.99*85}/100

=5439.15/100

=54.3915

Answer:

31/7 = 4 3/7.....3/7 is less then 1/2....so the closest integer is 4

Step-by-step explanation:

Please mark me brainlist if this helped

Answer:Integer Part: 67

Fractional Part: 60

Step-by-step explanation: This is how to round 67.6 to the nearest whole number. In other words, this is how to round 67.6 to the nearest integer.

67.6 has two parts. The integer part to the left of the decimal point and the fractional part to the right of the decimal point:

Answer:67

Step-by-step explanation:

When you round 67.6 to the nearest whole number you take the  6 off and get 67

Answer:

look below

Step-by-step explanation:

To write a fraction or mixed number as a decimal, divide the numerator by the denominator. So, for example, if you had 5/2, then you'd do 5÷2, which gives you 2.5. Hope that helped!

The equation of the line perpendicular to y=1/2x-9 passing through the point (7,10) is y=-2x+24.

To find the equation of a line that is perpendicular to another line, we need to determine the slope of the given line and use the negative reciprocal of that slope for our new line. The line given is y = ½x - 9, so the slope (m) is ½. The slope of the perpendicular line will be the negative reciprocal of ½, which is -2.

The next step is to use the point given, (7,10), and the slope of the perpendicular line to write the equation in point-slope form, which is y - y1 = m(x - x1). Plugging in our values we get: y - 10 = -2(x - 7).

Finally, we can rearrange this into slope-intercept form, y = mx + b, by simplifying and solving for y:

Therefore, the equation of the line perpendicular to y = ½x - 9 that passes through the point (7,10) is y = -2x + 24.

We have to trade 5 bunnies for a donkey.

Solution:

To calculate how many bunnies could be exchanged for a donkey, we have to multiply the exchange rates of each animal/bird.

One bunny = 3/4 chickens (0.75 chicken),

One chicken = 2/5 pigs (0.4 pigs)

One pig = 2/3 donkeys (0.67 donkeys).

On multiplying all of the above rates we get,

0.75*0.4*0.67=0.2

Since we now know a bunnies worth is 0.2 donkey

Therefore, (1/0.2=5) 5 bunnies to trade for a donkey.

Answer:

Step-by-step explanation:

It should be 2.3 because dividing by decimals is almost the same as dividing by normal numbers you just change the decimal point when you are done dividing.

Answer:

C. 6.2y can be combined with -3/8y.

Step-by-step explanation:

6.2y can be combined with -3/8y because both numbers have the same variable x. All of the other choices have different variable that are not like terms.

Answer:

The Discount would save $2.25 of the final purchase.

Step-by-step explanation:

If the cake originally costs $9, 25% of that would be $2.25 off the final purchase. So the discount would save $2.25

Answer:

With the discount, you are saving $2.25 on the cake that you want.

Answer:

Option (c) is correct.

68% of the data points lie between 10 and 18.

Step-by-step explanation:

Given :  a normal distribution with a standard deviation of 4 and a mean of 14

We have to choose the  sentence that correctly describes a data set that follows a normal distribution with a standard deviation of 4 and a mean of 14.

Since, given 68% data.

We know mean of data lies in middle.

And standard deviation is distribute equally about the mean that is 50% of values less than the mean  and 50% greater than the mean.

So, 68% of data lies

mean - standard deviation = 14 - 4 = 10

mean + standard deviation = 14 + 4 = 18

So, 68% of the data points lie between 10 and 18.

The correct sentence for a normal distribution with a standard deviation of 4 and a mean of 14, is that 68% of the data points lie between 10 and 18.

The correct answer is C.

About 68% of the data in a normal distribution lie within one standard deviation of the mean.

● 14−4=10 is one standard deviation below the mean, and

14+4=18 is one standard deviation above it.

Thus, the range of 68% of the data values is between 10 and 18. Option C, which states that "68% of the data points lie between 10 and 18," thus accurately sums up the dataset.

Answer:$2,000

Step-by-step explanation:

Answer:

see explanation

Step-by-step explanation:

The sum of the 3 angles in a triangle = 180°

Subtract the sum of the given angles from 180 for B

B = 180° - (90 + 40)° = 180° - 130° = 150°

--------------------------------------------------------------

sin40° = [tex]\frac{opposite}{hypotenuse}[/tex] = [tex]\frac{a}{21}[/tex]

Multiply both sides by 21

21 × sin40° = a, thus

a ≈ 13.5 ( to the nearest tenth )

--------------------------------------------------------------

cos40° = [tex]\frac{adjacent}{hypotenuse}[/tex] = [tex]\frac{b}{21}[/tex]

Multiply both sides by 21

21 × cos40° = b, thus

b ≈ 16.1 ( to the nearest tenth )

The height scale is 75

Solution:

Given that, you are trying to enlarge an image that is 4 centimeters tall and 10 centimeters wide onto a billboard that is 3 meters tall and 8 meters wide

In this problem, we have:

Height of enlarged image = 3 m

Height of original image = 4 centimeter

We have to find the height scale

Convert 4 cm to meter

Use the following conversion factor

1 cm = 0.01 m

Therefore,

4 cm = 0.04 m

Thus, we have got,

Height of original image = 0.04 m

Height of enlarged image = 3 m

Therefore, the height scale is given by the following ratio:

[tex]Height\ scale = \frac{\text{height of enlarged height}}{\text{height of original image}}[/tex]

[tex]Height\ scale = \frac{3}{0.04} = 75[/tex]

So, the height scale is 75

Answer:

75cm

Step-by-step explanation:

i got the question right