How many solutions does this system of equation have x+1=2y x-1=2y

Answer:

x = 6

Step-by-step explanation:

Given ∠ 1 = ∠ 2 then the segment is an angle bisector and the ratios of sides to base are equal, that is

[tex]\frac{3}{x-4}[/tex] = [tex]\frac{x}{4}[/tex] ( cross-  multiply )

x(x - 4) = 12 ← distribute left side

x² - 4x = 12 ( subtract 12 from both sides )

x² - 4x - 12 = 0 ← in standard form

(x - 6)(x + 2) = 0 ← in factored form

Equate each factor to zero and solve for x

x - 6 = 0 ⇒ x = 6

x + 2 = 0 ⇒ x = - 2

However, x > 0 , thus x = 6

The answer for P(A∪B) is 40/45 (or) 8/9.

Step-by-step explanation:

Given,

The number of students that play only stringed instruments (A) = 35 students.

The number of students that play only brass instruments (B) = 10 students.

The number of students that play both of the instruments = 5 students.

The number of students that play none of the instruments = 5 students.

Probability = Number of required events / Total events

To find the total number of students,

TOTAL = A + B - both + neither.

TOTAL = 35 + 10 - 5 + 5 = 45 students.

P(A∪B) = P(A) + P(B) - P(A∩B)

Probability of A, P(A) = 35 students / 45 students = 35/45

Probability of B, P(B) = 10 students / 45 students = 10/45

Probability of A∩B (both), P(A∩B) = 5 students / 45 students = 5/45

P(A∪B) = (35/45) + (10/45) - (5/45)

             = 40/45

P(A∪B)  = 8/9

Answer:

30 miles/1 hour is the unit rate.

Step-by-step explanation:

This is the unit rate because unit rates are a number over 1 unit. 30 miles/1 hour fulfills that, and the others are 2 and 3 hours.

Answer:

4

Step-by-step explanation:

its a parabola that opens upward, the zeros are x=4 and x=3

Answer:

[tex]y=4000*(1.05)^t[/tex]

Step-by-step explanation:

The graduating class grows by 5% each year, this means after 1 year the number of students graduating will be 105% of 4000, or

[tex]4000*\frac{105}{100} =4000*1.05[/tex]

And after 2 years it will be

[tex](4000*1.05)*1.05[/tex]

and so on. Thus, after [tex]t[/tex] years the number of students [tex]y[/tex] will be

[tex]\boxed{ y=400*(1.05)^t}[/tex]

An exponential function to model the number of students y in the graduating class t years  after 2008 is y = 4000(1.05)^t

The standard exponential function is expressed as:

y = ab^x

If a college with a graduating class of 4000 students in the year 2008 predicts that its graduating class  will grow 5% per year, hence the required exponential equation will be:

y = 4000(1.05)^t

Learn more on exponential function here: https://brainly.com/question/12940982

The question involves converting the model depth from centimeters to meters, which typically requires dividing by 100. However, without a specific scale or additional detail, the direct conversion of 32cm would be 0.32 meters.

The student's question is about converting the depth of a model water tower, provided in centimeters, to its actual depth in meters without giving a specific depth in the question. This concept usually involves understanding the scale of models and how to apply proportional reasoning to determine actual sizes. However, without a specific scale or the actual depth given in the question, we can't calculate the actual depth.

Generally, to convert from centimeters to meters directly, we divide the length in centimeters by 100, because 1 meter equals 100 centimeters. For example, if a model tower's depth is 32cm, to find this depth in meters, you would divide 32 by 100, which equals 0.32 meters.

Answer:

0.214 * 0.32 = 0.06848 (3 + 2 = 5 decimal places)

0.7 * 0.11 = 0.077 (1 + 2 = 3 decimal places)

Step-by-step explanation:

Let's remember that multiplying decimals is the same as multiplying whole numbers except that you have to put the decimal point in the answer. When you multiply decimals, the decimal point is placed on the product so that the number of decimal places in the product is the sum of the decimal positions of the factors.

Example:

214 * 32 = 6,848

0.214 * 0.32 = 0.06848 (3 + 2 = 5 decimal places)

7 * 11 = 77

0.7 * 0.11 = 0.077 (1 + 2 = 3 decimal places)

Answer:

slope = [tex]\frac{11}{3}[/tex]

Step-by-step explanation:

Calculate the slope m using the slope formula

m = (y₂ - y₁ ) / (x₂ - x₁ )

with (x₁, y₁ ) = (5, 4) and (x₂, y₂ ) = (2, - 7)

m = [tex]\frac{-7-4}{2-5}[/tex] = [tex]\frac{-11}{-3}[/tex] = [tex]\frac{11}{3}[/tex]

Answer:

  (8π -8√3) cm²

Step-by-step explanation:

The area of a circle with radius 4 cm is given by ...

  A = πr² = π(4 cm)² = 16π cm².

The red shaded portion is part of a semicircle. That semicircle will have an area half that of the circle, so ...

  A/2 = 8π cm²

__

The triangle OCB is an equilateral triangle, so the angle at B is 60°. The side AC is then √3 times side BC*, so is 4√3 cm. The area of triangle ABC is then ...

  A = (1/2)AC·BC = (1/2)(4√3 cm)(4 cm) = 8√3 cm²

This area is subtracted from that of the semicircle to obtain the red shaded area:

  red area = semicircle area - triangle area

  red area = (8π -8√3) cm²

____

* AC can be found either from the Pythagorean theorem (√(8²-4²)), using trig functions (4tan(60°)), or using your knowledge of 30°-60°-90° triangles.

Answer:

2300-x(250) is the best i could think of hope it helps

Step-by-step explanation:

We need to represent the value of a TV whose value decreases yearly.

The required equation is [tex]y=2300-250x[/tex]

The cost of the TV set is $2300.

The decrease in value is $250 per year.

Let [tex]x[/tex] be the number of years that has passed after buying the TV

and [tex]y[/tex] be the cost of TV after [tex]x[/tex] years have passed.

The linear equation that represents the situation is [tex]y=2300-250x[/tex]

Learn more:

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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 A

A = 180° - (90 + 48)° = 180° - 138° = 42°

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

tan48° = [tex]\frac{opposite}{adjacent}[/tex] = [tex]\frac{18}{a}[/tex]

Multiply both sides by a

a × tan48° = 18 ( divide both sides by tan48° )

a = [tex]\frac{18}{tan48}[/tex] ≈ 16.2 ( to the nearest tenth )

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

sin48° = [tex]\frac{opposite}{hypotenuse}[/tex] = [tex]\frac{18}{c}[/tex]

Multiply both sides by c

c × sin48° = 18 ( divide both sides by sin48° )

c = [tex]\frac{18}{sin48}[/tex] ≈ 24.2 ( to the nearest tenth )

Answer:

[tex]\frac{3}{5} \ of \ an\ hour\ elapses[/tex]

Step-by-step explanation:

Given hours is from 4:56 P.M. to 5:32 P.M.

Now, finding the part of an hour elapases.

We know the starting time is 4 minutes to 5:00 P.M and end time is 32 minutes past 5 P.M.

∴ Total times elapses= [tex]4\ minutes + 32\ minutes= 36\ minutes[/tex]

Hence, 36 minutes elapses out of an hour.

Remember; 1 hours= 60 minutes

Next, finding the fraction of an hour elapses.

[tex]Part\ of\ an\ hour\ elapses= \frac{36}{60}[/tex]

∴ [tex]Part\ of\ an\ hour\ elapses= \frac{3}{5} \ hour[/tex]

Hence, [tex]\frac{3}{5} \ of \ an\ hour\ elapses[/tex]  from 4:56 P.M. to 5:32 P.M.

Answer:

Step-by-step explanation:

y - y1 = m(x - x1)

slope m = 3/2, y1 = -7, x1 = 4

y + 7 = 3/2(x - 4)

y + 7 = 3x/2 - 6

y = 3x/2 - 6 - 7

y = 3x/2 - 13

Answer:

y=-1/2x+2

Step-by-step explanation:

y = mx + p

m=slope = -1/2

p= y-intercept = 2

Answer:

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

Step-by-step explanation:

The segment for - 2 ≤ x ≤ 2 is a straight line

The equation of a line in slope- intercept form is

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

To calculate m use the slope formula

m = (y₂ - y₁ ) / (x₂ - x₁ )

with (x₁, y₁ ) = (- 2, 3) and (x₂, y₂ ) = (2, 1) ← the endpoints of the line

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

Note the line crosses the y- axis at (0, 2) ⇒ c = 2

y = - [tex]\frac{1}{2}[/tex] x + 2 ← equation for - 2 ≤ x ≤ 2

Answer: [tex]\angle GFH[/tex]

Step-by-step explanation:

A Transversal is defined as a line that intersect two or more lines.

For this exercise it is important to know that when a Transversal cut two parallel lines, several angles are formed. These are grouped in pairs.

One of those pairs are called "Alternate exterior angles".

Alternate exterior angles are those non-adjacent angles that are located outside the parallel lines and on opposite sides of the Transversal.

Alternate exterior angles are congruent, which means that they have equal measure.

In this case you know that the Transversal [tex]CH[/tex] cuts the parallel lines [tex]AD[/tex] and [tex]EG[/tex].

Therefore, based on the explanation given before, you can identify in the picture given in the exercise that the angles [tex]\angle ABC[/tex] and [tex]\angle GFH[/tex] are Alternate exterior angles.

Answer:

The equation of the required straight line is y = 4x + 1.

Step-by-step explanation:

The equation of all the straight lines that are parallel to the straight line y = 4x - 3 is given by  

y = 4x + c .............. (1)  

where, c is any real constant and c ≠ - 3.

{Since parallel straight lines have the same slope and different y-intercept }

Now, we have to find the value of c such that the parallel straight line passes through the point (-1,-3).

Now, putting x = - 1 and y = - 3 in equation (1) we get,

- 3 = 4(- 1) + c

⇒ c = 1

Therefore, the equation of the required straight line is y = 4x + 1. (Answer)

Answer:

I believe it is 1/4

Sorry if I am wrong

the answer is 1/4

this is from apx :))

Answer:

whats the question?

Step-by-step explanation:

Answer:

x intercept is 15 and y intercept is -3.75

Step-by-step explanation:

The first thing is to form equation with the given tow point using the formula

y-y1/x - x1 = y2 - y1/ x2 - x1

y + 5/x + 5 = -2 + 5/7 + 5

y + 5/x + 5 = 3/ 12

3x + 15 = 12y + 60

12y - 3x = -45

On x intercept y = 0

x = 15

On y intercept x = 0

y = -3.75

Answer:

My best guess is 384 ft

Step-by-step explanation:

Tangent 38° = opposite side / adjacent side

Tangent 38° = 300 ft / x ft

The value of x from the equation is 383.98 ft. Thus, the engineer is 383.98 ft.

Rounding it up gives us 384 ft.

Answer:

384 ft.

Step-by-step explanation:

We know the opposite side of the triangle and we need the adjacent side.

So tan 38 = opposite / adjacent

= 300 / x

x = 300 tan 38

x = 383.98 feet.

Answer:

-2 degrees celcius

Step-by-step explanation:

-6/3

Answer:

Each day, the temperature rises plus -6 Celsius

The solution is [tex](1,1)[/tex]

Step-by-step explanation:

The system of linear equation is

[tex]y=-3x+4[/tex] and [tex]y+\frac{1}{3} y=\frac{4}{3}[/tex]

Using substitution method, let us substitute [tex]y=-3x+4[/tex] in the equation

[tex]y+\frac{1}{3} y=\frac{4}{3}[/tex]

[tex]-3 x+4+\frac{1}{3}(-3 x+4)=\frac{4}{3}[/tex]

Multiplying the term [tex]-3x+4[/tex] by [tex]\frac{1}{3}[/tex], we get,

[tex]-3 x+4-x+\frac{4}{3}=\frac{4}{3}[/tex]

Subtracting both sides by [tex]\frac{4}{3}[/tex],

[tex]-3x+4-x=0[/tex]

Simplifying, we get,

[tex]\begin{aligned}-4 x+4 &=0 \\-4 x &=-4 \\x &=1\end{aligned}[/tex]

Now, substitute [tex]x=1[/tex] in [tex]y=-3x+4[/tex]

[tex]y=-3(1)+4\\y=-3+4\\y=1[/tex]

Thus, the solution is [tex](1,1)[/tex]

Answer:

y = -3x + 4

x + 1/3y = 4/3

Substitute the first expression into the second equation for y:

x + 1/3(-3x + 4) = 4/3

x - x + 4/3 = 4/3

4/3 = 4/3

Thus, all real numbers are solutions.

Step-by-step explanation:

HOPE THIS HELPS, GOOD-LCK, and Brainliest, also let me know if i am wrong.

By setting up a system of equations from the given scenarios, we find that the cost of a burrito platter is $32 and the cost of a taco platter is $26.

To solve Carmen's problem about the cost of burrito and taco platters, we need to set up a system of equations based on the information given.

We know she spent $58 on one burrito platter and one taco platter and $90 on two burrito platters and one taco platter.

Let's denote the cost of a burrito platter as B and the cost of a taco platter as T.

Step 1: Establish the Equations

The first scenario gives us the equation: B + T = 58.
The second scenario gives us the equation: 2B + T = 90.

Step 2: Solve the Equations

From the first equation, we can express T in terms of B: T = 58 - B.

Therefore, the cost of a burrito platter is $32 and the cost of a taco platter is $26.

[tex]F(x)+G(x)=3x^2+2x-2.[/tex]

Solution:

Given data: [tex]F(x)=3x^2+1[/tex] and [tex]G(x)=2x-3[/tex]

To find F(x) + G(x):

Adding two functions which gives another function.

Substitute F(x) and G(x), we get

[tex]F(x)+G(x)=(3x^2+1)+(2x-3)[/tex]

                    [tex]=3x^2+1+2x-3[/tex]

                    [tex]=3x^2+2x-3+1[/tex]

                    [tex]=3x^2+2x-2[/tex]

[tex]F(x)+G(x)=3x^2+2x-2[/tex]

Hence, [tex]F(x)+G(x)=3x^2+2x-2.[/tex]

Answer:

4/5

Step-by-step explanation:

.8 is the same as 8/10

8/10 simplifies to 4/5 as both the numerator and denominator can be divided by 2

Answer:

Step-by-step explanation:

0.8 = 8/10 = 4/5

Answer:

103

Step-by-step explanation:

You start with long division 4 goes into 4 1 time and then 0 cause you have nothing else drop the 12 and then 4 goes into 12 3 times 103

Answer:

103

Step-by-step explanation:

If you solve it using partial quotients, it would be eaisier to demonstrate than using another method like standard division.

Hope this helps!

-Coconut;)

Answer:

[tex]x = \$187n[/tex]

Step-by-step explanation:

let x be the total cost in dollars for two days for the n members

Given:

The first day the members paid $70 for transportation plus $15 per ticket to the planetarium.

The second day they paid $90 for transportation plus $12 per ticket to the geology museum.

We need to write an an expression to represent the total cost in dollars for two days for the n members of the club.

Solution:

First day each member pay $70 for transportation and $15 for ticket,

[tex]Cost\ per\ member\ for\ the\ first\ day = transportation\ cost+ticket\ cost[/tex]

[tex]Cost\ per\ member\ for\ the\ first\ day = 70+15[/tex]

[tex]Cost\ per\ member\ for\ the\ first\ day = \$85[/tex]

Therefore, cost for n members for the first day.

[tex]Cost\ for\ n\ member\ for\ the\ first\ day = \$85n[/tex]

Similarly for the second day each member pay $90 for transportation and $12 for ticket,

[tex]Cost\ per\ member\ for\ the\ second\ day = transportation\ cost+ticket\ cost[/tex]

[tex]Cost\ per\ member\ for\ the\ second\ day = 90+12[/tex]

[tex]Cost\ per\ member\ for\ the\ second\ day = \$102[/tex]

Therefore, .

[tex]Cost\ for\ n\ member\ for\ the\ second\ day = \$102n[/tex]

Now, we write an expression to represent the total cost in dollars for two days for the n members of the club, so cost for n members for two days is equal to sum of the two days expenses for n members.

[tex]Cost\ for\ n\ member\ for\ the\ two\ day = \$85 + \$102n[/tex]

[tex]x = \$85n + \$102n[/tex]

[tex]x = \$187n[/tex]

Therefore, total cost for two days for the n members [tex]x = \$187n[/tex]

Answer:

30

Step-by-step explanation:

the required ans 30 or the valuse is 30