A scout troop consists of 10 boys and 10 girls. The total weight of their backpacks is 600 pounds. All the boys have to carry backpacks that weigh the same amount. All the girls, too, must carry bags of equal weight, but the girls' backpacks are 1.5 times lighter than the boys' backpacks. How heavy is one boy's backpack?

Answer:

x=20

<B=150°

Step-by-step explanation:

Opposite Interior Angles

8x-10=3x+90

8x-3x=90+10

5x=100

x=20

<B=3x+90

=3(20)+90

=60+90=150

Answer:

x=20

<B = 150

Step-by-step explanation:

The angles are alternate interior angles and when the lines are parallel, alternate interior angles are equal

8x-10 = 3x+90

Subtract 3x from each side

8x-10 -3x = 3x+90-3x

5x-10 = 90

Add 10 to each side

5x-10 +10 = 90+10

5x = 100

Divide by 5

5x/5 = 100/5

x = 20

<B = 3x+90

    = 3*20 +90

    = 60+90

    = 150

Answer:

x > - 8 or x < 2

Step-by-step explanation:

Given

- 8 < 2(x + 4) or - 3x + 4 > x - 4

Solve each part separately

- 8 < 2(x + 4) ← divide both sides by 2

- 4 < x + 4 ( subtract 4 from both sides )

- 8 < x , thus

x > - 8

OR

- 3x + 4 > x - 4 ( subtract x from both sides )

- 4x + 4 > - 4 ( subtract 4 from both sides )

- 4x > - 8

Divide both sides by - 4, reversing the symbol as a result of dividing by a negative quantity

x < 2

Solution is x > - 8 or x < 2

Answer:

-2x

Step-by-step explanation:

-2x-7+9-2

Combine like terms

-2x +0

-2x

Answer:

-2x

Step-by-step explanation:

from the question

-2x-7+9-2=

step 1

collect the like terms

we have,

-2x-7+9-2

-2x + 2 -2

-2x + 0

-2x

therefore the answer to the question -2x-7+9-2 is equal to -2x

Answer:

y = 4

Step-by-step explanation:

Move all terms not containing  y  to the right side of the equation.

-y = -4

Multiply each term in  − y  =  − 4  by  − 1

y = 4

Hope this can help you

Answer:

[tex]\boxed{\sf 200 \ feet^2}[/tex]

Step-by-step explanation:

The 3D shape is a square-based pyramid.

The surface area of a square-based pyramid is given as:

[tex]\sf SA=2 \times (base \ length) \times (slant \ height) + (base \ length)^2[/tex]

Plug in the values.

[tex]\sf SA=2 \times 10 \times 5 + 10^2[/tex]

[tex]\sf SA=100 + 100[/tex]

[tex]\sf SA=200[/tex]

Answer:

(2b, 2b + 7).

Step-by-step explanation:

y = x + 7 and x = 2b ,

therefore y = 2b + 7.

Answer:

(2b, 2b + 7)

Step-by-step explanation:

Answer:

answer is d

Step-by-step explanation:

Answer:

Amount received by wife = RS 24000

Amount received by father = RS 16000

Step-by-step explanation:

His income is RS 80000

He gave 30% of his income to his wife

That's

[tex] \frac{30}{100} \times RS \: \: 80000[/tex]

Which is RS 24000

He gave 20% of his income to his father

That's

[tex] \frac{20}{100} \times RS \: \: 80000[/tex]

Which is RS 16000

Hope this helps you

Answer:

1306.90≅  1307 rounded to the nearest tens

Step-by-step explanation:

r= radius = 13 cm

l is the slant height =19 cm

surface area of the cone= area of the circle + area of the curved of the cone

SA=πrl +πr²

SA=π(13)(19) +169π

SA= 247π +169π= 416π=1306.90≅  1307 rounded to the nearest tens

Answer:

Step-by-step explanation:

333 times 555=184815

777 times 444=344988

now add 184815+344988=529803

Full question :

The Tasty Sub Shop Case:

A business entrepreneur uses simple linear regression analysis to predict the yearly revenue for a potential restaurant site on the basis of the number of residents living near the site. The entrepreneur then uses the prediction to assess the profitability of the potential restaurant site.

And

The QHIC Case:

The marketing department at Quality Home Improvement Center (QHIC) uses simple linear regression analysis to predict home upkeep expenditure on the basis of home value. Predictions of home upkeep expenditures are used to help determine which homes should be sent advertising brochures promoting QHIC’s products and services.

Discuss the difference in the type of prediction in both cases and provide rational of the reasons that these predictions were used.

Answer and explanation:

In the first case, The Tasty Sub Shop Case, the entrepreneur aims to utlilize the predicted values from his regression analysis in ascertaining profit of his potential business. He does this using the values from number of residents in the area(independent variables) to predict the revenue for his business(dependent variables). His predictions using the number of residents in the area are largely because the residents in the area are his target consumers and are the ones to buy food from his restaurant and increase his revenue.

In the other case, the marketing department in QHIC utilizes the predicted values in determining their customers who need to be aware of their products. They get the predicted values(home upkeep expenditure and dependent variable) by plotting their relationship with home value(independent variable) and then use predicted values of home upkeep expenditures in determining their customers who they will market their products to. They do this because predicting home upkeep expenditures will enable them determine what homes can afford or will need their products and services.

one utilizes his predictions at ascertaining profit while the other uses his predictions in determining potential customer base to market products to. The first case is making a revenue/ profitability prediction while the other is making a market prediction

Answer:

Step-by-step explanation:

A(0,0) ∧  B(3,0)  ⇒  AB = 3

A(0,0) ∧  C(0,4)  ⇒  AC = 4

From Pythagorean theorem:

AB² + AC² = AB²

3² + 4² = AB²

AB² = 9+16 = 25

AB = 5

Perimeter:  

               AB + AC + BC = 3 + 4 + 5 = 12

Answer:

1.3

Step-by-step explanation:

5.2/4 = 1.3

To check, 1.3 multiplied by four is 5.2.

Answer:

It’s 1.3

Step-by-step explanation:

Make meeee brainliest

Answer:

216,004

Step-by-step explanation:

so 5(14-2)third power + 8/2,

that would be

5(12)third power + 8/2

(60) third power + 4

216,000 + 4

Step-by-step explanation:

w=3

4w^2-7w-8

4*3^2-7*3-8

4*9-21-8

4*9-29

36-29

7

hope this helps

Answer:

7

Step-by-step explanation:

Answer:

y = 6x - 2

Step-by-step explanation:

slope-intercept form: y = mx + b

Note that:

m = slope = 6

b = y-intercept = -2

x = (x , y)

y = (x , y)

Plug in the corresponding numbers to the corresponding variables:

y = 6x + (-2)

y  = 6x - 2

y = 6x - 2 is your answer.

~

Answer:

y = 6x-2

Step-by-step explanation:

The slope intercept equation  form of a line is

y = mx+b where m is the slope and b is the y intercept

y = 6x-2

Answer:

Step-by-step explanation:

When you draw out that picture (and very good description, btw!) basically what you have is a right triangle that has a base of 32 and a hypotenuse of 45. The right angle is one of the base angles and x is the vertex angle. We need to find the vertex angle before we can find the angle of depression from the second bird to the watcher. The side of length 32 is opposite the angle x, and 45 is the hypotenuse, so the trig ratio we need is the only one that directly relates side opposite to hypotenuse, which is the sin ratio:

[tex]sin(x)=\frac{32}{45}[/tex] and

sin(x) = .711111111

Go to your calculator and hit the 2nd button then the sin button and on your screen you will see:

[tex]sin^{-1}([/tex]  

and after that open parenthesis enter in your decimal .711111111 and hit equals. You should get an angle of 45.325. That's angle x. But that's not the angle of depression. The angle of depression is the one complementary to angle x.

Angle of depression = 90 - angle x and

Angle of depression = 90 - 45.325 so

Angle of depression = 44.67 or 44.7 degrees.

Answer:

Its 45.3!!!

Step-by-step explanation:

Answer:

1.5p + 3p + 2.5p

Step-by-step explanation:

This expression, 1.5p + 3p + 2.5p, will represent the amount of money received when p people buy one of each food item.

Since the price of each is the coefficient for p, this will represent how much money will be gained from each food item. All 3 terms will be added together to represent the total amount of money gained from selling all 3 items.

Answer:

1 st pattern 48+122 = 170

2 nd pattern 8½+3½ = 5

so, 3rd pattern 41+13= 54 (B)

41+13=54 this is the ans

Problem 1.

Yes it is true that vertical angles are congruent, but that's not what your teacher is asking. Instead, your teacher is asking basically how the term "congruent" is defined.

Two segments are congruent if they are the same length. Two angles are congruent if they are the same measure. Two triangles are congruent if they have the same angles and sides.

So in short, "congruent" just means "same". You can think of having mirror copies.

==========================================

Problem 2.

Angles 2 and 4 are one pair of vertical angles. They are opposite one another in this X shape formed by the two lines. The other pair of vertical angles are angle 1 and angle 3.

Angle 2 is given to be 76 degrees, so this means angle 4 is this measure as well.

Angle 1 = 180 - (angle 2) = 180 - 76 = 104, which is also the measure of angle 3 as well. I'm using the idea that the adjacent angles form a straight angle. This is known as a linear pair (ie the angles form a straight line).

==========================================

Problem 3.

If all three angles are the same (all 60 degrees), then we have an equilateral triangle. We could say it's equiangular, but it's also equilateral as well meaning all 3 sides are the same length. "equi" means "equal", "angular" means what you'd expect, and "lateral" means "side".

If only two angles are equal with the third one different, then we have an isosceles triangle. An isosceles triangle is one where only two sides are the same length.

If none of the angles are the same, then we have a scalene triangle. As you probably expect, none of the sides are the same length with a scalene triangle.

----

If all three angles are less than 90 degrees, then the triangle is acute

If one angle is 90 degrees, then we have a right triangle

If one angle is over 90 degrees (but less than 180), then the triangle is obtuse

---

Often you'll see the terms of the previous two sections combined. For instance, we could have an isosceles right triangle. Or we might have an obtuse scalene triangle. Any equilateral triangle is acute (as all three angles are less than 90).

To solve this problem we have to understand what congruent angles are and then find the angles that are congruent to one other in this given question.

Congruent angles are angles that are equal to one another and in the given question, we were given m<2 = 76 degrees.

Data;

If we look critically at the angles, we can use opposite angle theorem here to predict angles that are congruent to another here.

angles 2 and angle 4 are congruent to one another while angle 1 and angle 3 are congruent to one another.

This implies that

Let's solve for other angles.

But the some of angles at a point is equal to 360°

Applying that theorem here,

[tex]m > 1=x\\m > 2 = 72^0\\m > 3 = x\\m > 4 = 72^0[/tex]

Let's substitute the values and solve.

[tex]x+ x + 72+72 = 360\\2x + 144 = 360\\2x = 360 - 144\\2x = 216\\x = \frac{216}{2} \\x = 108^0[/tex]

This can be further summarized as

Learn more on corresponding angles here;

https://brainly.com/question/2009183

#SPJ2

Answer:

110 feet per second

Step-by-step explanation:

You would mutiply your speed in miles per hour by 5,280. That's the number of feet in a mile and your result is your speed in feet per hour.

75 x 5,280 = 396,000 feet per hour

Then you would divide your speed by 60 and that result is your speed in feet per minute.

396,000 / 60 = 6,600 feet per minute

Lastly, you would divide that speed by 60 and the result is your speed in feet per second.

6,600 / 60 = 110 feet per second

The conversion of 75 miles per hour to feet per second is approximately 110 feet per second.

We can do this by using conversion factors that relate the two units. Specifically, we can use the fact that 1 mile equals 5,280 feet and 1 hour equals 3,600 seconds.

To convert miles per hour to feet per second, we need to multiply the value in miles per hour by a conversion factor that will cancel out the "miles" unit and replace it with "feet," and another conversion factor that will cancel out the "hours" unit and replace it with "seconds."

So, first we convert miles per hour to feet per hour by multiplying 75 miles/hour by 5,280 feet/mile.

This gives us:

= 75 miles/hour x 5,280 feet/mile

= 396,000 feet/hour

Next, we convert feet per hour to feet per second by dividing by 3,600 seconds/hour.

This gives us:

=396,000 feet/hour ÷ 3,600 seconds/hour

= 110 feet/second

Therefore, 75 miles per hour is approximately equal to 110 feet per second.

To know more about unit conversion check:

https://brainly.com/question/17540215

#SPJ2

Answer:

The slope is 4/1

Step-by-step explanation:

for every 4 units you go up on the y-axis, you go 1 unit on the x-axis.

Answer:

[tex]\huge \boxed{\mathrm{Option \ C}}[/tex]

Step-by-step explanation:

Length of arc formula = θ/360 × 2[tex]\pi[/tex]r

The angle is 210 degrees.

The radius is 7 ft.

210/360 × 2[tex]\pi[/tex](7)

Simplify the expression.

210/360 × 14[tex]\pi[/tex]

2940/360[tex]\pi[/tex]

49/6[tex]\pi[/tex]

The length of the arc of circle having radius 7 feet is 49π/6 which is option C.

An arc is a part of circumference of a circle which is formed from two radius of the circle. The length of arc is equal to Θr in which r is radius and Θ is angle in radian form.

We have been given the radius of the circle be 7 feet and angle be 210°.

The length of arc will be Θr in which r is the radius and Θ is the angle in radian form.

First we have to convert angle in radian form=210*π/180=7π/6.

Length of arc=7π/6*7

=49π/6

Hence the length of the arc of circle having radius 7 feet is 49π/6 which is option C.

Learn more about arc at https://brainly.com/question/2005046

#SPJ2

Answer:

question 11: A

question 12: B

Step-by-step explanation:

Thanks calculator :)

Answer:

11. less than

12.less than

hope this helps

Step-by-step explanation:

Answer:

Step-by-step explanation:

Since the triangle is a right angled triangle we can use the Pythagoras theorem to find the missing side

Using the Pythagoras theorem

That's

[tex] {a}^{2} = {b}^{2} + {c}^{2} [/tex]

From the question

x is the hypotenuse or the longest side of the triangle

Substituting the values into the above formula we have

[tex] {x}^{2} = {9}^{2} + {7}^{2} [/tex]

[tex] {x}^{2} = 81 + 49[/tex]

[tex] {x}^{2} = 130[/tex]

Find the square root of both sides

We have the final answer as

Hope this helps you

Answer:

$76

Step-by-step explanation:

The amount changed is the total amount of the whole entire thing.

Therefore, we use absolute value or simply find the difference.

21 - (-55) = 76

So the bank account changed $76 over the 2 days.

Answer:

[tex]\huge\boxed{2k-13}[/tex]

Step-by-step explanation:

[tex]\sf -3(2+4k)+7(2k-1)\\Expanding \ brackets\\-6-12k+14k-7\\Combining \ like \ terms\\-12k+14k-6-7\\2k -13[/tex]

Answer:

f(1) = 45

f(n) = f(n-1)*(4/5)

Step-by-step explanation:

f(1)

= 45(4/5)^(1-1)

= 45(4/5)^(0)          use law of exponents

= 45*1

= 45

f(1) = 45

f(n) = f(n-1)*(4/5)

Answer:

See explanation

Step-by-step explanation:

a) 15:20 - 12:35 = 14:80 - 12:35 = 2 hours and 45 minutes

b) 13:05 - 10:15 = 12:65 - 10:15 = 2 hours and 50 minutes

c) 6:50 - 4:30 = 2 hours and 20 minutes

d) 1:15pm - 9:55am = 13:15 - 9:55 = 12:75 - 9:55 = 3 hours and 20 minutes

Answer:

a) 15:20 - 12:35 = 14:80 - 12:35 = 2 hours and 45 minutes

b) 13:05 - 10:15 = 12:65 - 10:15 = 2 hours and 50 minutes

c) 6:50 - 4:30 = 2 hours and 20 minutes

d) 1:15pm - 9:55am = 13:15 - 9:55 = 12:75 - 9:55 = 3 hours and 20 minutes

Step-by-step explanation:

Answer:= -12+4x

Step-by-step explanation:

Distribute -4 through the parentheses

8+4x=20

Calculate the difference

-12+4x