the ratio of 6th graders to 7th graders at a basketball game is 4:1. if there are eight 6th 7th graders how many 6th graders are there

Answer:

x= 1

Step-by-step explanation:

- = negative. so negative 2 blank + 7 equals 14.

x is 1 because the more you add positively to a negative number the close it gets to zero. negative 21 + 7 is negative 14 but I you got an 8ntegr the n it would be 14.

The graph of the function -2x + 7y = 14 is attached

From the question, we have the following parameters that can be used in our computation:

-2x + 7y = 14

We start by making the variable y the subject

-2x + 7y = 14

So, we have

7y = 2x + 14

Divide through by 7

y = 2/7x + 2

And it also means that the equation is a linear equation

A linear equation is represented as

y = mx + c

Where

m = slope

i.e. m = 2/7

Hence, the equivalent equation to plot is y = 2/7x + 2

See attachment for graph

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Answer:

17.2°

Step-by-step explanation:

using the tangent ration in the right triangle

tan y° = [tex]\frac{opposite}{adjacent}[/tex] = [tex]\frac{19.1}{14.1}[/tex], hence

y = [tex]tan^{-1}[/tex]([tex]\frac{19.1}{14.1}[/tex]) ≈ 53.6°

tan x° = [tex]\frac{14.1}{19.1}[/tex], hence

x = [tex]tan^{-1}[/tex]([tex]\frac{14.1}{19.1}[/tex]) ≈ 36.4°

y - x = 53.6° - 36.4° = 17.2°

Answer:

D) y -x = Approximate 17.1 degree.

Step-by-step explanation:

Given : Triangle .

To find :  Approximate value of y - x.

Solution : We have given a right angle triangle with

Opposite side = 19.1 in.

Adjacent side = 14 .1 in.

Tan( y ) = [tex]\frac{Opposite}{adjacent}[/tex].

Plug the values

Tan( y ) = [tex]\frac{19.1}{14.1}[/tex].

tan(y) = 1.354.

Taking tan inverse both sides.

y = [tex]tan^{-1}(1.354)[/tex].

y = 53.55 degree.

Now, by the sum of angle of triangles is 180 degree.

Angle c + angle y + angle  x = 180.

Plug the variable

90 + 53.55 + x = 180.

83.55 + x = 180

On subtracting both sides by 83.55

x = 36.45 degree

Then ,

y - x = 53 .55 - 36 . 45

y - x = 17.2

Approximate 17.1 degree

Therefore, D) y -x = Approximate 17.1 degree.

Statement: Two planes intersect to form a point

This is false. Two planes intersect to form a single straight line.

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

Statement: two lines intersect to form a point

This is true assuming the two lines have different slopes

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

Because the first statement is false, the overall argument is false.

Final answer:

The intersection of two planes is a line, not a point, which makes the statement false. Two lines intersecting in a point is true provided they are not parallel.

Explanation:

The statement that the intersection of two planes is a point is false. According to geometric principles, specifically the line of intersection of two planes, when two planes intersect, they do so along a line, not just a single point. This line of intersection is represented by the points where their respective great circles cross. The intersection of two lines, however, is indeed a point, provided that the lines are not parallel. This is in agreement with Theorem 1, which states that two straight lines of a plane have either one point or no point in common; similarly, two planes have no point in common or a straight line in common.

Relevant Theorems on Intersections

Theorem 1 and Theorem 2 outline the foundational concepts regarding intersections in geometry. Understanding these theorems helps explain why two intersecting planes result in a line and not a single point.

Graham and Max will meet at the same altitude after approximately 22 minutes.

Explanation:

To find out how many minutes it will take Graham and Max to meet at the same altitude, we need to set up an equation.

Let's assume that after t minutes, Graham and Max will meet at the same altitude. This means that the altitude of Graham is equal to the altitude of Max.

Equation: 14,040 - 50t = 12,500 + 20t

To find t, we can solve this equation:

14,040 - 50t = 12,500 + 20t

Subtract 20t from both sides: 14,040 - 70t = 12,500

Subtract 12,500 from both sides: 14,040 - 12,500 - 70t = 0

Combine like terms: 1,540 - 70t = 0

Subtract 1,540 from both sides: -70t = -1,540

Divide by -70 on both sides: t = -1,540/-70

Simplify: t ≈ 22 minutes

Therefore, it will take approximately 22 minutes for Graham and Max to meet at the same altitude.

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Answer:

35q-384 = 225q-189

Step-by-step explanation:

since its 384 subtracted from 35 times q it will be 35q-384 and then it says "is" which is an equal sign (=) and then q times 225 which is 225q decreased by 189 which is 225q-189 so it will be 35q-384 = 225q-189

Answer:the answer would be a i just did it but correct me if i was wrong

Step-by-step explanation:

Answer:

b. $3,000.00

Step-by-step explanation:

Daniel buys one bond each with a par value of $1,000 from Grath Oil, Ombor Medical Supplies, and Dwyn Horticulture.

Grath Oil bonds are selling at 120.514

Ombor Medical Supplies bonds are selling at 90.773

Dwyn Horticulture bonds are selling at 101.180.

These values have nothing to do here as we only have to find the face value.

The face value of 1 bond is $1000 so, the face value of 3 bonds will be = [tex]1000\times3=3000[/tex] dollars.

[tex]a-the\ side\ of\ square\\a^2-the\ area\ of\ square\\\\a+3-the\ one\ side\ of\ rectangle\\a-2-the\ second\ side\ of\ rectangle\\(a+3)(a-2)-the\ area\ of\ rectangle\\\\\text{The equation:}\\\\(a+3)(a-2)=a^2+30\qquad\text{use distributive property}\\\\(a)(a)+(a)(-2)+(3)(a)+(3)(-2)=a^2+30\\\\a^2-2a+3a-6=a^2+30\qquad\text{subtract}\ a^2\ \text{from both sides}\\\\a-6=30\qquad\text{add 6 to both sides}\\\\\boxed{a=36}\\\\Answer:\ \boxed{36\ cm}[/tex]

Answer:

The solution of the inequality is [tex](-2.5,\infty)[/tex].

Step-by-step explanation:

The given inequality is

[tex]-3x<7.5[/tex]

If an inequality divided by a negative number,then the sign of inequality change. Divide both sides by -3.

[tex]\frac{-3x}{-3} >\frac{7.5}{-3}[/tex]

[tex]x >-2.5[/tex]

Therefore the solution of the given inequality is all real numbers greater than -2.5.

In interval notation it can be defined as

[tex](-2.5,\infty)[/tex]

Answer:

x > −2.5

Step-by-step explanation:

i got the correct answer

Answer:

20% was evaporated

Step-by-step explanation:

Formula:

((New value-old value)/(old value))*100

((2-2.5)/(2.5))*100 = 20

Answer:

20% of the water evaporated

Step-by-step explanation:

We know that 500,000 evaporated because 2,500,000-2,000,000 is 500,000.

100% - 2,500,000

500,000 - x%

2,500,000/500,000 = 100/x

x=(500,000)(100)/2,500,000

x= 20%

20% of the water evaporated.

The uppercase T means "transpose". A matrix transpose is where you swap the rows and columns. Anything that is row becomes a column, and vice versa. What this means is that instead of a row vector, you end up with a column vector. The dimensions are important so you can properly multiply matrices.

Answer:

C. b^27

Step-by-step explanation:

By the definition of exponents

[tex](b^9)^3=b^9*b^9*b^9[/tex]

And since for any real numbers [tex]r,x,[/tex] and [tex]y[/tex]

[tex]r^x*r^y=r^{(x+y)}[/tex]

This makes

[tex](b^9)^3=b^9*b^9*b^9=b^{{9+9+9}}=\boxed{b^{27}}[/tex]

Which is choice C.

Alternatively, we could use the identity

[tex](r^x)^y=r^{xy}[/tex]

in which case

[tex](b^9)^3=b^{(9*3)}= \boxed{b^{27}}[/tex]

which is the same answer.

Answer:b²⁷

Step-by-step explanation:

Answer:

a. x+y=10, 2x+3y=24

b.this systems of equations have a unique solution since there is only one value for x and one value for y where each equation is present in. There is no same slope or y-intercept

c. 4 magnet gift boxes

Step-by-step explanation:

Answer:

D. multiplication property

Step-by-step explanation

Am not so sure but i think its that

Answer:

Tate has 7x pennies.

Step-by-step explanation:

Tate has 2x pennies because Mia has x pennies and Tate has twice the pennies of Mia so

5+2x= 7x

Look at the picture.

This is isosceles triangle. Therefore, the angles at the base are congruent.

m∠ BAC = m∠ABC.

We know, the sum of the measures of the angles in a triangle is equal 180°.

Therefore:

m∠BAC + m∠ABC + m∠ACB = 180°

2m∠ABC + 120° = 180°     subtract 120° from both sides

2m∠ABC = 60°     divide both sides by 2

m∠ABC = 30°

m∠MCB = 90° → ΔMCB is a right triangle (30 - 60 - 90).

The sides of that triangle are in proportion: 1 : √3 : 2.

Therefore MC : BC : MB = 1 : √3 : 2

MC = 12 → BC = 12√3 and MB = 2 · 12 = 24

ΔCDB is the right triangle (30 - 60 - 90) too.

Therefore CD : BD : BC = 1 : √3 : 2

CD = 1/2 BC → CD = 1/2(12√3) = 6√3

BD = CD√3 → BD = 6√3(√3) = 6(3) = 18

AB = 2BD therefore your answer is:

AB length is 24 cm

Given length CM = 12 cm

and length CB = 12 sqrt 3

sin 60 ° = CB / BM

1/2 sqrt 3 = 12 sqrt 3 / BM

BM = 1/2 sqrt 3 * 12 sqrt 3

BM = 18 cm

sin 30 ° = CM / MA

1/2 = 12 / MA

MA = 1/2 * 12

MA = 6 cm

So, the length of AB is BM + MA = 18 cm + 6 cm = 24 cm

A triangle is the name of a shape made from three sides in the form of a straight line and three angles. The mathematician Euclid who lived around 300 BC found that the sum of the three angles on a triangle on a flat plane was 180° degrees. This allows us to calculate the magnitude of one angle when the other two angles are known.

According to the length of the sides:

According to the biggest angle:

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Details

Class: Middle/High School and College

Subject: Mathematics

Keyword: degrees, angles, triangle

Answer:

[tex]n=241[/tex]

Step-by-step explanation:

We are given

[tex]5x^2+nx+48[/tex]

Let's assume it can be factored as

[tex]5x^2+nx+48=(5x-s)(x-r)[/tex]

now, we can multiply right side

and then we can compare it

[tex]5x^2+nx+48=5x^2-5rx-sx+rs[/tex]

[tex]5x^2+nx+48=5x^2-(5r+s)x+rs[/tex]

now, we can compare coefficients

[tex]rs=48[/tex]

[tex]5r+s=-n[/tex]

[tex]n=-(5r+s)[/tex]

now, we can find all possible factors of 48

and then we can assume possible prime factors of 48

[tex]48=-+(1\times 48)[/tex]

[tex]48=-+(2\times 24)[/tex]

[tex]48=-+(3\times 16)[/tex]

[tex]48=-+(4\times 12)[/tex]

[tex]48=-+(6\times 8)[/tex]

Since, we have to find the largest value of n

So, we will get consider larger value of r because of 5r

and because n is negative of 5r+s

so, we will both n and r as negative

So, we can assume

r=-48 and s=-1

so, we get

[tex]n=-(5\times -48-1)[/tex]

[tex]n=241[/tex]

91.8 ft above sea level

Answer:

The answer is approximately about 23.5 feet about the ground touching the wall.

Step-by-step explanation:

The ladder makes a right triangle with the wall and ground, therefore you use pythagorean theorem. If you draw what is being described, you can see that the 24 ladder is the hypotenuse or "c", while the ground and wall are "a" and "b" for the equation.

you set it up like so:

√(24²-5²) = a²

which will result in √(551) or ≈23.5 feet

The number of feet above the ground where the ladder touches the wall is 23.47 ft.

The information above forms a right angle triangle. The base of the right angle triangle is 5 ft and the hypotenuse of the right angle triangle is 24 ft.

Let's find the height of the triangle to know how many feet above the ground where the ladder touches the wall.

Using Pythagoras theorem,

where

c =hypotenuse

a and b are either adjacent side or opposite sides.

Therefore,

b² = 24² - 5²

b² = 576 - 25

b = √551

b = 23.4733891886

b ≈ 23. 47 ft.

Therefore, the feet above the ground where the ladder touches the wall is 23.47 feet.

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Answer:

y = 3.5x

Step-by-step explanation:

The equation for a straight line is  

y = mx +b

We know that when

x₁ = 2, y₁ = 7 and when

x₂ = 5, y₂ = 17.5

Step 1. Determine the slope

m = (y₂ - y₁)/(x₂ - x₁)       Substitute values

m = (17.5 – 7)/(5 – 2)    Remove parentheses

m = 10.5/3

m = 3.5

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

Step 2. Determine the y-intercept.

y = 3.5x + b     Insert x₁ and y₁

7 = 3.5×2 + b

7 = 7 + b          Subtract 7 from each side

b = 0

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

Step 3. Write the equation

y = mx + b

y = 3.5x + 0

y = 3.5x

The equation is y = 3.5x.

Answer:

Slope (m) = 0.2 and y-intercept (b) = 3.5.

Step-by-step explanation:

We are given weather equation y=0.2x +3.5 for finding the amount of accumulated snow y in inches x hours after 5 P.M. on a certain day.

We need to identify the slope and y- intercept of the graph of the equation .

Let us compare given equation y=0.2x +3.5 by slope-intercept form y=mx+b, we get

Slope (m) = 0.2 and y-intercept (b) = 3.5.

Answer:

y= 2x-4   ,   y= -1/2x +3    , y= -2/3x+2

Step-by-step explanation:

slope intercept form: y=mx+b

y-2x=-4

add 2x to both sides

y= 2x-4

y-3= -1/2x

add 3 to both sides

y= -1/2x +3

2x+3y=6

subtract 2x from both sides

3y= -2x+6

divide both sides by 3

y= (-2x+6)/3

y= -2/3x+2

NOTES:

Slope-Intercept form is y = mx + b  ; where m is the slope and b is the y-intercept.

To convert an equation into slope-intercept form, solve for y

******************************************************************************************

Answer: y = 2x - 4

Step-by-step explanation:

y - 2x = -4

  +2x    +2x  

y       = 2x - 4

********************************************************************************************

Answer: y = [tex]-\frac{1}{2}x[/tex] + 3

Step-by-step explanation:

y - 3 = [tex]-\frac{1}{2}x[/tex]

  +3          +3  

y       = [tex]-\frac{1}{2}x[/tex] + 3

********************************************************************************************

Answer: y = [tex]-\frac{2}{3}x[/tex] + 2

Step-by-step explanation:

2x + 3y = 6

-2x         -2x  

        3y = -2x + 6

        ÷3    ÷3  ÷3  

          y = [tex]-\frac{2}{3}x[/tex] + 2

f(2) This means that x is 2, so you can plug in 2 for "x" in the equation

f(x) = 3x - 12

f(2) = 3(2) - 12

f(2) = 6 - 12

f(2) = -6

Your answer is D

Answer:

D. -6

Step-by-step explanation:

Hi!!! You have to substitute 2 for f(x) & for the x next to 3!!!

f(x) = 3x- 12

f(2) = 3(2) - 12

= 6 - 12

= 6 -12

= -6

[tex]1/4(20-4a)=6-a \ /\cdot4\\20-4a=24-4a\\-4a+4a=24-20\\0=4\\false[/tex]

Answer:

22.5 miles

Step-by-step explanation:

first divide 75 by sixty and that will be your traveled per minute then multiply that by 18 and that is you answer. Good luck, please mark me brainliest.

Constant speed is the speed of the object witch does not changes with the time. With constant speed the body traveled the same distance for the each time interval. The distance traveled by the car in 18 minutes is 22.5 miles.

The car traveled with the constant speed is 75 miles in 60 minutes.

Constant speed is the speed of the object witch does not changes with the time. With constant speed the body traveled the same distance for the each time interval.

As the car traveled with the constant speed is 75 miles in 60 minutes. Let x the total miles traveled by  the car in one minutes is.

[tex]x=\dfrac{75}{60}[/tex]

[tex]x=\dfrac{5}{4}[/tex]

Thus the the total miles traveled by the car in one minutes is 5/4 miles. Let n be the total miles traveled by the car in 18 minutes. Thus,

[tex]x=\dfrac{5}{4}\times 18[/tex]

[tex]x=\dfrac{45}{2}[/tex]

[tex]x=22.5[/tex]

Hence the distance traveled by the car in 18 minutes is 22.5 miles.

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Answer:

3.00 = original price * (1-.4)

or

3 = original price*.6

Step-by-step explanation:

We know the cost after the discount.

Price after discount = original price - original price * discount rate

Factoring out the original price

Price after discount = original price (1- discount rate)

We know the price after discount = 3.00  and the discount rate =.40

Substituting these values in

3.00 = original price * (1-.4)

3 = original price*.6

Divide each side by .6

3/.6 = original price

5.00 = original price

Answer:

x = 10

Step-by-step explanation:

First, we need to isolate all the x's on one side. To do this we need to move the -20 over to the other side making it a +20:

3.5x + 1/2x = 40 + 20 - 2x

Add the x's and the 40 and 20:

4x = 60 - 2x

Move the -2x over to the other side making it a +2x:

4x + 2x = 60

6x = 60

Divide both sides by 6:

x = 10

So x = 10

Answer:

10

Step-by-step explanation:

3.5(x) + -20 + 1/2(x) = 40 - 2x

3.5x - 20 + x/2 = 40 - 2x

3.5x + x/2 + 2x = 40 + 20

6x = 60

x = 60/6

    = 10

Answer:

[tex]\frac{1}{81}[/tex]

Step-by-step explanation:

Law of exponent

[tex]a^{-m} = \frac{1}{a^{m} }[/tex]

1) Applying the above rule, we have

[tex]9^{-2} = \frac{1}{9^{2} }[/tex]

= [tex]\frac{1}{9*9}[/tex]

= [tex]\frac{1}{81}[/tex]