In a basketball tournament, Team A scored 5 fewer than twice as many points as Team B. Team C scored 80 more points than Team B. The combined score for all three teams was 983 points. Write an equation to represent this scenario using the variable b to represent Team B's total points. Translate the scenario.

Answers

Answer 1

Answer:

(2b - 5) + b + (b + 80) = 983

Step-by-step explanation:

Given that,

Total score of three teams = 983

Since the teams' scores are given in reference to team B's score, let 'b' be the score of team B.

So,

The scores of Team A = (2 * b) - 5

The scores of Team B = b

The scores of Team C = (b + 80)

Thus,

The equation for determining the total points of Team B would be:

(2b - 5) + b + (b + 80) = 983

On solving,

(2b - 5) + b + (b + 80) = 983

⇒ 2b + b + b = 983 + 5 - 80

⇒ 4b = 908

⇒ b = 908 ÷ 4

⇒ b = 227

Team B's score = 227

Team A's score = (2 * 227 - 5)

= 449

Team C's score = 227 + 80

= 307

Total ⇒ 449 + 227 + 307 = 983

Hence proved.


Related Questions

What is -3 over 9 in standard form

Answers

Answer:

-1/3

Step-by-step explanation:

-3/9

= -1/3

Help PLEASE eeeeeeeeeeeeeeeee

Answers

Answer:

0.6 is the answer please

James' truck uses 8 gallons of gas per day. He filled his tank up with 36 gallons of gas. How many days will James be able to drive using 36 gallons of gas?

Answers

Answer:

4.5

Step-by-step explanation:

36 ÷ 8 = 4.5

James will be able  to drive for 4.5 days.

Mark me as brainliest please

James will be able to drive [tex]=4\frac{1}{2}[/tex] days.

What is arithmetic maths ?

Arithmetic is the fundamental of mathematics that includes the operations of numbers like addition, subtraction, multiplication and division.

We have,

James' truck uses gas per day [tex]=8[/tex] gallons

Tank has gas [tex]=36[/tex] gallons

Now,

According to the question,

Number of days James will drive [tex]= \frac{Total\ gas}{Gas\ used\ per\ day}[/tex]

                                                        [tex]=\frac{36}{8}[/tex]

Number of days James will drive[tex]=4\frac{1}{2}[/tex] days

Hence, we can say that James will be able to drive [tex]=4\frac{1}{2}[/tex] days.

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convert 4 seconds to hour​

Answers

Answer:

0.00111111 hrs

Step-by-step explanation:

Have a nice day

Answer:

4/3600 = .001111 hr

Step-by-step explanation:

4 seconds * 1 hour            *    1 minute            =    4/3600 = .001111 hr

                    60 minutes          60 seconds

What is the recursive formula for this geometric sequence?
-4, -24, -144, -864, ...
= -4
O A.
an =
2n-1 • 30
OB.
la = -4
ar = 2n-16
fa
= -6
C.
= 2n-1 • 30
= -6
O D.
lan
ar = 2n-1.4

Answers

Answer:

a1 = -4

an = an-1 * 6

Step-by-step explanation:

-4, -24, -144, -864, ...

First find the common ratio

Take the second term and divide by the first term

-24/-4 = 6

The common ratio is 6

The recursive formula is

a1 = -4

an = an-1 * 6

Please help me with this on the image

Answers

Answer:

hope this may help u

q. no (a)= 60%

(b)=55%

Answer:

a) [tex]\frac{6}{10}[/tex] = [tex]\frac{3}{5}[/tex]  = .6 or 60%

b) [tex]\frac{11}{20}[/tex]  = .55 or 55%

Step-by-step explanation:

Count the boxes.

[tex]\frac{shaded}{total}[/tex]

Divide and multiply by 100

what is the surface area of a sphere if the volume is 3000 pi

Answers

Answer:

228.95 cm2 / 229 cm2

Step-by-step explanation:

Volume of a sphere is given by;

V = (4/3)πr3

So in this question we have to find the radius of the sphere to enable us find the surface area.

Therefore let's find the radius using the volume formula;

3000π = (4/3)πr3

Divide through by (4/3)π

r3 = 2250

r =3√2250 (cube root of 2250)

r = 13.104cm2

Since we have gotten the radius, let's calculate the surface area using the formula;

A = (4/3)πr^2

= (4/3) × π × 13.104^2

= 228.95 π cm2 or 229 cm2

what is 8/9 divide 2/3?

Answers

Answer:

4/3

Step-by-step explanation:

8/9 ÷ 2/3

Simplify the complex fraction.

4/3

Step-by-step explanation:

8/9 ÷ 2/3

Simplify

4/3 is the correct answer

Determine the period

Answers

Answer:

3 units

Step-by-step explanation:

The period of a wave is the time taken to complete a cycle of motion of the wave

In the given figure, the graduations of the x-axis, which is the usually time axis = 1 unit

At the origin, (0, 0), the vertical displacement of the wave = 0

The maximum value of the wave function is between x = 0 and x = 1

The minimum value of the wave function is between x = 2 and x = 3

At the point (3, 0) the value of the wave function is again 0, and a cycle of the wave is completed

Therefore, the period of the wave = 3 units of the x-variable

PLS HELP QUESTION ATTACHED

Answers

Answer:

A

Step-by-step explanation:

the -1 represents the graph going down by 1

Show Workings.
Question is in attached image.​

Answers

Answer:

A.]A chord of a circle of diameter 40 cm subtends an angle of 70° at the centre of the circle.

Solution given;

diameter [d]=40cm

centre angle [C]=70°

(a) Find the perpendicular distance be tween the chord and the centre of the circle.

Answer:

we have

the perpendicular distance be tween the chord and the centre of the circle=[P]let

we have

P=d Sin (C/2)

=40*sin (70/2)

=22.9cm

the perpendicular distance be tween the chord and the centre of the circle is 22.9cm.

(b) Using = 3.142, find the length of the minor arc.

Solution given;

minor arc=[tex]\frac{70}{360}*πd=\frac{7}{36}*3.142*40[/tex]

=24.44cm

the length of the minor arc. is 24.44cm.

B.]In the diagram, XZ is a diameter of the cir cle XYZW, with centre O and radius 15/2 cm.

If XY = 12 cm, find the area of triangle XYZ.

Solution given:

XY=12cm

XO=15/2cm

XZ=2*15/2=15cm

Now

In right angled triangle XOY [inscribed angle on a diameter is 90°]

By using Pythagoras law

h²=p²+b²

XZ²=XY²+YZ²

15²=12²+YZ²

YZ²=15²-12²

YZ=[tex]\sqrt{81}=9cm[/tex]

:.

base=9cm

perpendicular=12cm

Now

Area of triangle XYZ=½*perpendicular*base

=½*12*9=54cm²

the area of triangle XYZ is 54cm².

Answer:

Question 1

a)

d = 40 cm ⇒ r = 20 cm

Let the perpendicular distance is x.

Connecting the center with  the chord we obtain a right triangle with hypotenuse of r and leg x with adjacent angle of 70/2 = 35°.

From the given we get:

x/20 = cos 35°x = 20 cos 35°x = 16.383 cm (rounded)

b)

The minor arc is 70° and r = 20

The length of the arc is:

s = 2πr*70/360° = 2*3.142*20*7/36 = 24.437 cm (rounded)Question 2

Since XZ is diameter, the opposite angle is the right angle, so the triangle XYZ is a right triangle.

r = 15/2 cm ⇒ XZ = d = 2r = 2*15/2 = 15 cm

Find the missing side, using Pythagorean:

[tex]YZ = \sqrt{XZ^2 - XY^2} = \sqrt{15^2-12^2} = \sqrt{81} = 9[/tex]

The area of the triangle:

A = 1/2*XY*YZ = 1/2*12*9 = 54 cm²

Select the correct answer.
What is the value of x in the triangle?

Answers

Answer:

The answer is A. 21

Hope it helps.

Step-by-step explanation:

• • •

6 – x + = 6 minus StartFraction 3 Over 4 EndFraction x plus StartFraction 1 Over 3 EndFraction equals StartFraction one-half EndFraction x plus 5.X + 5 2 3 6 12

Answers

Answer:

x = 16/15

Step-by-step explanation:

Given:

6 - 3/4x + 1/3 = 1/2x + 5

Collect like terms

6 + 1/3 - 5 = 1/2x + 3/4x

(18+1-15)/3 = (2x+3x)/4

4/3 = 5/4x

x = 4/3 ÷ 5/4

x = 4/3 × 4/5

x = (4 * 4) / (3 * 5)

x = 16/15

Please help!

A line intersects the points (-2, 8) and
(4, 12). Find the slope and simplify
completely.
Help Resource
Slope
[?]
= +
Hint: m =
y2-yi
X2-X1
Enter

Answers

Answer:

2/3

Step-by-step explanation:

We can use the slope formula

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

 = (12-8)/(4 - -2)

  (12-8)/(4+2)

  4/6

   2/3

(Hurry giving brainliest) Which idea does Arnold need to correct? In specular reflection, reflected rays move in the same direction. In scattering, light strikes particles in the atmosphere. In diffuse reflection, reflected rays move in different directions. In scattering, long wavelengths are scattered the most.

Answers

Answer:

D. In scattering, long wavelengths are scattered the most.

Step-by-step explanation:

Scattering of light is the effect observed when there is an interaction between light energy and some particles. This occurs often in the earth's atmosphere which consists of different sizes of particles that interacts with the sunlight.

In scattering, light of shorter wavelengths are scattered by small sized particles compared to those with longer wavelengths. Example is the scattering of the sunlight by the atmospheric particles where colors with short wavelengths are scattered the most.

Arnold need to correct the statement; In scattering, long wavelengths are scattered the most. To read; In scattering, short wavelengths are scattered the most.

Answer:

D on edgen

Step-by-step explanation:

Choose the one that is FALSE. *
A. 1/4 = 2/8
B. 3/4 = 10/12
C. 5/10 = 1/2
D. 10/12 = 5/6

Answers

Answer:

B. 3/4 = 10/12

Step-by-step explanation:

A. 1/4*2/2  = 2/8

B. 3/4*3/3 = 9/12  not10/12

C. 5/10*5/5 = 1/2

D. 10/12 divided by 2/2 = 5/6

Which of the following is a correct tangent ratio for the figure? A) tan (24) 76 B) tan(76°) °= 2 C) tan(76°) = D) tan(8") = 24 76​

Answers

Given question is incorrect; here is the complete question.

"Which of the following is a correct tangent ratio for the figure attached"

A) tan(76°) = [tex]\frac{24}{8}[/tex]

B) tan (76°) = [tex]\frac{8}{24}[/tex]

C) tan (24°) = [tex]\frac{76}{8}[/tex]

D) tan (8°) = [tex]\frac{24}{76}[/tex]

Option A will be the correct option.

   From the figure attached,

Given triangle is a right triangle.Measure of one angle = 76°Measure of two sides of the triangle are 24 and 8units.

By applying tangent ratio of angle having measure 76°.

tan(76°) = [tex]\frac{\text{Opposite side}}{\text{Adjacent side}}[/tex]

             = [tex]\frac{24}{8}[/tex]

    Therefore, Option (A) is the correct option.

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Solve. -7x+1-10x^2=0

Answers

Answer:

[tex]-7x+1-10x^2=0[/tex]

[tex]-10x^2-7x+1=0[/tex]

[tex]quadratic\:equation:-[/tex] [tex]ax^2+bx+c=0[/tex]

[tex]solutions:-\\\\x_{1,\:2}=\frac{-b\pm \sqrt{b^2-4ac}}{2a}[/tex]

[tex]For \\A=-10\\B=-7\\C=1[/tex]

[tex]x_{1,\:2}=\frac{-\left(-7\right)\pm \sqrt{\left(-7\right)^2-4\left(-10\right)\cdot \:1}}{2\left(-10\right)}[/tex]

[tex]\sqrt{\left(-7\right)^2-4\left(-10\right)\cdot \:1}=\sqrt{89}[/tex]

[tex]x_{1,\:2}=\frac{-\left(-7\right)\pm \sqrt{89}}{2\left(-10\right)}[/tex]

[tex]x_1=\frac{-\left(-7\right)+\sqrt{89}}{2\left(-10\right)},\:x_2=\frac{-\left(-7\right)-\sqrt{89}}{2\left(-10\right)}[/tex]

[tex]\frac{-\left(-7\right)+\sqrt{89}}{2\left(-10\right)}=-\frac{7+\sqrt{89}}{20}[/tex]

[tex]\frac{-\left(-7\right)-\sqrt{89}}{2\left(-10\right)}=\frac{\sqrt{89}-7}{20}[/tex]

[tex]x=\frac{\sqrt{89}-7}{20}[/tex]

OAmalOHopeO

Oscar bought 15 gallons of water at $1.98 per gallon. He wants to divide this water in bottles of 1/8 gallon each. What is the cost of a bottle of water?

Answers

Answer:

Step-by-step explanation:

juans pencil box measures 6 cm long. if the length of the diagonal is 10 cm what is the width of the pencil box

Answers

Answer:

8 cm

Step-by-step explanation:

We can use the Pythagorean theorem to solve since we have a right triangle

a^2 +b^2 = c^2 where a and b are the legs and c is the hypotenuse

a^2 +6^2 = 10^2

a^2 +36 = 100

a^2 = 100-36

a^2 = 64

Taking the square root of each side

sqrt(a^2) = sqrt(64)

a =8

Answer:

8 cm

Step-by-step explanation:

Use the Pythagorean theorem- [tex]a^{2} +b^{2} =c^{2}[/tex]

leg a: 6cm

leg b: unknown

hypotenuse: 10cm

Therefore [tex]6^{2} +x^{2} =10^{2} = 36+x^{2} =100[/tex]

Subtract 36 to 100 to isolate the [tex]x^{2}[/tex].    [tex]x^{2} =64[/tex]

Square root both sides and get your answer of 8cm

This drawing would be a step in finding which point of concurrency in a triangle?

Answers

Answer:

B. Orthocenter

Step-by-step explanation:

The orthocenter of a triangle is the point of intersection of the three altitudes (the perpendicular from a vertex to the side facing the vertex) of a triangle

The steps used in constructing the orthocenter includes the steps for drawing of the perpendicular to the sides of the triangle from a point which is the vertex opposite the side of the triangle

Therefore, in the given diagram, a perpendicular to the side KS is drawn from the (vertex) point W, by drawing an arc with center at W that intersects the side KS at two points. Rom the points of intersection of the arc drawn from W intersects KS, with the compass, two arcs are drawn to intersect at a point from which a line drawn to W, is perpendicular to KS

Therefore;

The correct option is B. orthocenter

What is the measure of ∠
A. 6°

B. 42°

C. 60°

D. 49°

Answers

Answer:

<XYZ is equal to 49°

Step-by-step explanation:

Set the two expressions equal to each other so 7x+7=5x+19. Subtract 5x from 7x and 7 from 19 which is equal to 2x=12 that means x is 6. then plug 6 into (7x+7) which is equal to 49.

which statement must be true about line TU?

Answers

line tu is parallel to rs

Answer:

line TU has no slope in the diagram above

Evaluate the expression 3(5 + 2)(7 - 2) using order of operations.

Answers

The answer is 36. Do the parentheses first and then multiply by 3

Answer:

105

Step-by-step explanation:

The order of operations is written as PEMDAS. These letters stand for:

-Parentheses

-Exponents

-Multiplication

-Division

-Addition

-Subtraction

We follow these steps in order to solve expressions efficiently. Now, we are going to use PEMDAS to evaluate the expression 3(5+2)(7-2) step by step.

3(7)(5)  The first step is to simplify the numbers in the parentheses.

There are no exponents, so we skip to the next step, multiplication.

(3*7)(5)

21(5)

105

PEMDAS is no longer needed because 105 has come out to be our answer.

I hope this helps you out! Have an an awesome day :3

On Monday morning at 8:00 a.m. the temperature is – 14 o C. Over the
next 6 hours the temperature rises 6 o C. Between 2:00 p.m. on Monday
and 8:00 a.m. on Tuesday the temperature drops 9 o C. Over the next 6
hours the temperature rises only 4 o C. What is the temperature at 2:00
p.m. on Tuesday?

Answers

Answer : the temperature is -13 degrees Celsius

Which statement is true regarding the angles in the figure below?

Triangle E D F. A diagonal line is drawn from point D to form an angle.
Angle D is an exterior angle because it shares a side with the triangle.
Angle D is an exterior angle because it is not inside the triangle.
Angle D is an exterior angle because it is formed by one side of the triangle and by extending another side of the triangle.
Angle D is not an exterior angle.

Answers

An exterior angle is an angle supplementary to one of the interior angles.  

In other words, an exterior angle is the angle between one of the sides, and the extension of an adjacent side.

In the given diagram, the angle D is measured from one of the sides, but not to the extension of an adjacent side.

Therefore angle D is not an exterior angle.

Option D is the correct one!

An exterior angle is an angle supplementary to one of the interior angles.  

We have given that,

Triangle E D F. A diagonal line is drawn from point D to form an angle.

Angle D is an exterior angle because it shares a side with the triangle.

Angle D is an exterior angle because it is not inside the triangle.

Angle D is an exterior angle because it is formed by one side of the triangle and by extending another side of the triangle.

Angle D is not an exterior angle.

What is the exterior angle?

an exterior angle is an angle between one of the sides and the extension of an adjacent side.

In the given diagram, the angle D is measured from one of the sides, but not to the extension of an adjacent side.

Therefore angle D is not an exterior angle.

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which of the following equations are perpendicular

Answers

I think it’s the third one but I’m not %100 sure

True or False?
k = 3 over 4 is a solution to the inequality 12k + 2 < 12.
True
False

Answers

Answer:

False.

Step-by-step explanation:

...................

We know that k is 3/4. We can plug in 3/4 into k. 12(3/4) + 2 < 12. This gives us 36/48. 36/48 simplified is 3/4. Our equation is currently 3/4 + 2 < 12. We need common denominators to add 3/4 and 2. 2 with a denominator of 4 is is 8/4. 3/4 + 8/4 is 11/4. 11/4 < 12. 11/4 as a mixed number is 2 3/4. 2 3/4 as a decimal is 2.75. 2.75 < 12. 2.75 is less than 12. This is true.

Can I know the answer for the above questions

Answers

Answer:

Step-by-step explanation:

Calculate the answer to the correct number of significant figures: (1.705 + 0.5067) / (0.2 * 1.243) = ______.


8.897


8.8966


8.9


9


8.90

Answers

Answer:

8.9

Step-by-step explanation:

they said to the sig. figure so since it's 8.8966, so the answer will be 8.9

The answer to the correct number of significant figures is 8.897, the correct option is A.

What are Significant Figures?

Significant figures is a positional notation, these are the digits that are required to understand the quantity of something.

The expression is

⇒(1.705 + 0.5067) / (0.2 * 1.243)

=2.2117/0.2486

=8.89662

≈ 8.897

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