What are the solutions of -1/2x + 4 = x+1

Answer:

48 tickets

Step-by-step explanation:

I just had this question on a test and got it right! So this is how i did it:

if the advance price is $4, and you sell 40 tickets in advance, you do 40 times 4.

40 x 4 = 160

so you subtract the $160 from 400 and then that brings you $240 dollars left.

*these 240 dollars will be tickets bought at the door*

to determine the amount of tickets that need to be bought left, you need to do 240 divided by 5.

and that will give you a total of:

a least amount of 48 tickets

The least number of tickets the club needs to sell at the door to reach the president’s goal, 48.

A word problem is a few sentences describing a 'real-life' scenario where a problem needs to be solved by way of a mathematical calculation.

Given that, Tickets to a play cost $4 in advance and $5 at the door. The theater club president wants to raise at least $400 from the ticket sales. If the club sells 40 tickets in advance,

Since, the cost if advance ticket is $4 and they already sold 40,

Therefore, collected cost = 4 × 40 = $160

Now, cost to collect yet = 400 - 160 = $240

Cost of tickets at the door = $5

Therefore, tickets to be sold to meet the goal = 240/5 = 48

Hence, the least number of tickets the club needs to sell at the door to reach the president’s goal, 48.

Learn more about word problems, click;

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Answer: (D) 4

Step-by-step explanation:

Average rate of change means slope (m) from point a to point b.

when x = 5, y = -2  →  coordinate (5, -2)

when x = 7, y = 6  → coordinate (7, 6)

slope (m) = [tex]\dfrac{6-(-2)}{7-5} = \dfrac{8}{2}=4[/tex]

Answer:

Step-by-step explanation:

Where is line B?

The inequality 20x ≤ 300 represents the number of 20-pound bags of soil a 300-pound capacity wheelbarrow can carry. Solving the inequality, we find x ≤ 15, meaning the wheelbarrow can carry up to 15 bags of soil without exceeding its weight limit.

To represent the problem as an inequality, let's say the number of bags of soil the wheelbarrow can carry is represented by x. Each bag of soil weighs 20 pounds, and the wheelbarrow can carry up to 300 pounds. So, the inequality would be 20x ≤ 300.

To solve the inequality, we divide both sides by 20: x ≤ 300/20. Therefore, x ≤ 15. This means the wheelbarrow can carry up to 15 bags of soil without exceeding its 300 pounds weight limit.

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Answer:

x = 11

Step-by-step explanation:

∠CAB = ∠DCA = 33° ( alternate angles )

∠ACB = 180 - 5x ( straight angle )

the sum of all 3 angles in a triangle = 180°, hence

33 + 180 - 5x + 2x = 180

- 3x + 213 = 180 ( subtract 213 from both sides )

- 3x = - 33 ( divide both sides by - 3 )

x = 11

Answer:

both 17 and 19 are right triangles because they both have a right angle

Step-by-step explanation:

Answer:

m <  −4/3

Step-by-step explanation:

−5(3m−2)>30

Simplify both sides of the inequality.

−15m+10>30

Subtract 10 from both sides.

−15m+10−10>30−10

−15m>20

Divide both sides by -15.

−15m/−15  >  20/−15

m<−4/3

[tex]-5(3m-2)>30\qquad\text{use distributive property}\\\\(-5)(3m)+(-5)(-2)>30\\\\-15m+10>30\qquad\text{subtract 10 from both sides}\\\\-15m>20\qquad\text{change the signs}\\\\15m<-20\qquad\text{divide both sides by 15}\\\\m<-\dfrac{20}{15}\qquad\text{simplify}\\\\m<-\dfrac{20:5}{15:5}\\\\\boxed{m<-\dfrac{4}{3}}[/tex]

[tex]1)\\p\%=\dfrac{p}{100}\\\\13\%=\dfrac{13}{100}=0.13\\\\13\%\ of\ 20\ is\ 0.13\cdot20=2.6\\\\2)\\\underbrace{7\cdot7\cdot7\cdot7\cdot7}_{5}=7^5\\\\3)\\Use:\\a^n\cdot a^m=a^{n+m}\\\\\dfrac{a^n}{a^m}=a^{n-m}\\\\12.\ 6^2\cdot6^{-4}=6^{2+(-4)}=6^{2-4}=6^{-2}\\\\13.\ 2^{-3}\cdot2^{-2}=2^{-3+(-2)}=2^{-5}\\\\14.\ \dfrac{4^4}{4^2}=4^{4-2}=4^2}\\\\15.\ \dfrac{8^3}{8^{-2}}=8^{3-(-2)}=8^{3+2}=8^5[/tex]

Answer:

b

Step-by-step explanation:

We need to find the median of:-

73 75 87 65 69 62 81 64 68 101 74 71 89 87

First, we need to arrange the numbers in ascending order as below:-

62, 64, 65, 68, 69, 71, 73, 74, 75, 81, 87, 87, 89, 101

Since there are a total of 14 numbers, let's split it up into two halves (each of seven numbers)

62, 64, 65, 68, 69, 71, 73           |||             74, 75, 81, 87, 87, 89, 101

The median would be the mean of the two middle numbers i.e. the mean of 73 and 74

Median = [tex]\frac{73+74}{2}[/tex]

= [tex]\frac{147}{2}[/tex]

= 73.5

So, about half of the students spent less than 73.5 minutes doing homework and about half spent more than 73.5 minutes on homework

Answer:

Option b is the correct choice.

Step-by-step explanation:

We have been given a data set about minutes spent on doing homework the previous night by 14 seniors.

To find the median of data set, first of all we will arrange our data values from least to greatest order.  

62, 64, 65, 68, 69, 71, 73, 74, 75, 81, 87, 87, 89, 101.

Since our data set has an even number (14) of data points, therefore, median will be the average of middle two points, that is 7th and 8th term.

[tex]\text{Median}=\frac{\text{7th term + 8th term}}{2}[/tex]

[tex]\text{Median}=\frac{73+74}{2}[/tex]

[tex]\text{Median}=\frac{147}{2}[/tex]

[tex]\text{Median}=73.5[/tex]

Therefore, median of our given data set is 73.5.

Since median of a data set separates the higher half from the lower half of a data sample. So about half of the students spent less than 73.5 minutes doing homework and about half spent more than 73.5 minutes on homework.

Therefore, option b is the correct choice.

Answer:

218 feet per minute

Step-by-step explanation:

To find this, first subtract the initial amount (20) from the depth he soon reaches (3290). This will leave you with the amount of 3270 which is the distance the pilot whale went.

To find the feet per minute, divide by new depth by 15 in order to get the final answer of 218 feet per minute.

Hope this helps!

Answer:

The answer is

n=5 3/5

Step-by-step explanation:

first collect the like terms:

2-1/2n=3n+16

then...

3n-1/2=16-2

==2 1/2n = 14

===n=5 3/5

Answer:

10b + 5 is your answer

Step-by-step explanation:

Simplify the expression as much as possible. Combine terms with the same amount of variables.

6b + 4b = 10b

10b + 5

10b + 5 is your answer

~

Answer:

$89.25

Step-by-step explanation:

If one week is 29.75, then you can infer that each week separately would be the same amount. With this information, you can form this equation:

y = 29.75x

X would be the number of weeks while y would be the final amount based off the number of weeks.

If you substitute x with 3, then you should get the final answer of 89.25.

Hope this helps!

Answer:

The solution of the equation 9x=7(x+2) is:

Option D) 7

Step-by-step explanation:

9x=7(x+2)

Eliminating the parentheses applying distributive property:

9x=7(x)+7(2)

Multiplying:

9x=7x+14

Grouping the x's on the left side of the equation: Subtracting 7x both sides of the equation:

9x-7x=7x+14-7x

Subtracting:

2x=14

Solving for x: Dividing both sides of the equation by 2:

2x/2=14/2

Dividing:

x=7

Solution: x=7 (option D)  

[tex]Domain:\\\\x+3\geq0\ \wedge\ 2x-1\geq0\\\\x\geq-3\ \wedge\ x\geq0.5\\\\D:x\in[0.5;\ \infty)[/tex]

[tex]\sqrt{x+3}-\sqrt{2x-1}=-2\qquad\text{square of both sides}\\\\(\sqrt{x+3}-\sqrt{2x-1})^2=(-2)^2\qquad\text{use}\ (a-b)^2=a^2-2ab+b^2\\\\(\sqrt{x+3})^2-2(\sqrt{x+3})(\sqrt{2x-1})+(\sqrt{2x-1})^2=4\qquad\text{use}\ (\sqrt{a})^2=a\\\\x+3-2\sqrt{(x+3)(2x-1)}+2x-1=4\qquad\text{combine like terms}\\\\3x+2-2\sqrt{(x+3)(2x-1)}=4\qquad\text{subtract 3x + 2 from both sides}\\\\-2\sqrt{(x+3)(2x-1)}=2-3x\qquad\text{square of both sides}\\\\\left(-2\sqrt{(x+3)(2x-1)}\right)^2=(2-3x)^2[/tex]

[tex]4(x+3)(2x-1)=2^2-2(2)(3x)+(3x)^2\qquad\text{use distributive property}\\\\(4x+12)(2x-1)=4-12x+9x^2\\\\(4x)(2x)+(4x)(-1)+(12)(2x)+(12)(-1)=4-12x+9x^2\\\\8x^2-4x+24x-12=4-12x+9x^2\\\\8x^2+20x-12=4-12x+9x^2\qquad\text{subtract }\ 9x^2\ \text{from both sides}\\\\-x^2+20x-12=4-12x\qquad\text{add 12 and}\ 12x\ \text{from both sides}\\\\-x^2+36x=16\qquad\text{change the signs}\\\\x^2-36x=-16\\\\x^2-2(x)(16)=-16\qquad\text{add}\ 16^2\ \text{to both sides}[/tex]

[tex]\underbrace{x^2-2(x)(16)+16^2}_{(a-b)^2=a^2-2ab+b^2}=16^2-16\\\\(x-16)^2=256-16\\\\(x-16)^2=240\iff x-16=\pm\sqrt{240}\\\\x-16=\pm\sqrt{16\cdot15}\\\\x-16=-\sqrt{16}\cdot\sqrt{15}\ \vee\ x-16=\sqrt{16}\cdot\sqrt{15}\\\\x-16=-4\sqrt{15}\ \vee\ x-16=4\sqrt{15}\qquad\text{add 16 to both sides}\\\\x=16-4\sqrt{15}\notin D\ \vee\ x=16+4\sqrt{15}\\\\\boxed{x=4(4+\sqrt{15})}[/tex]

Answer:

n = -4

Step-by-step explanation:

2 - 1/2n = 3n + 16

First isolate n

2 - 16 = 3n + 1/2n

-14 = 3 1/2n

n = -4

Answer:

n=-4

Step-by-step explanation:

2-.5n=3n+16 REWRITTEN

2=3.5n+16    ADDITION PROPERTY OF EQUALITY

-14=3.5n       SUBTRACTION PROPERTY OF EQUALITY

n=-4              DIVISION PROPERTY OF EQUALITY

Answer:

18 L

Step-by-step explanation:

(a) Millilitres shipped

There are 750 mL/bottle.

Vol. shipped = 24 × 750

Vol. shipped = 18 000 mL

=====

(b) Litres shipped

1 L = 1000 mL

Vol. shipped = 18 000 × 1/1000

Vol. shipped = 18 L

Answer: 7.16cm

Step-by-step explanation:

R=C/2pi

R=45/pi2

R=45/2 = 22.5pi

The radius of a circle with a circumference of 45pi centimeters is 22.5 centimeters.

To find the radius of a circle with a circumference of 45pi centimeters, we can use the formula for circumference:

C = 2(pi)r

Given that the circumference is 45pi, we can substitute this value into the formula:

45pi = 2(pi)r

Now, we can solve for r:

r = 45/2 = 22.5 centimeters

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Answer:

This property would be the Associative property of addition.

the answer is C) 2. the 8 is in the ones place, 2 is in the tenths, and 1 is in the hundreths.

Answer: the answer is (A)

Step-by-step explanation:

Answer: 15 There would be 15 blue jays out of all the other birds

please mark as brainliest

Step-by-step explanation:

Answer:

Step-by-step explanation:

Its 4:7

Final answer:

Plotting the integer 850 and its opposite involves marking the points on a coordinate system. The point 850 is plotted 8.5 units to the right of the origin, and its opposite, -850, is plotted 8.5 units to the left, assuming a scale where each unit represents 100.

Explanation:

To plot an integer and its opposite, let's use the number 850 and its opposite, -850, as an example. A plot in mathematics typically refers to marking points on the coordinate system, which consists of two intersecting lines, usually perpendicular, called axes. The horizontal axis is known as the x-axis, and the vertical axis is the y-axis.

To plot the integer 850, you first need to establish a scale suitable for the values you intend to plot. In this example, if each unit on your plot represents 100, then the point representing 850 would be placed 8.5 units to the right of the origin (0,0). Conversely, to plot the opposite of 850, which is -850, you would move 8.5 units to the left of the origin.

In coordinate form, the point 850 can be represented as (850,0), and its opposite, -850, would be (-850,0). This illustration shows how to plot integers and their opposites on a simple two-dimensional graph.

Answer:

The correct answer is D.

Step-by-step explanation:

just multiply the original function by the factor 3.

check the picture below.

Answer:

(C) 12.5mm

Step-by-step explanation:

It is given that a pyramid having slant height AC is to be determined. From the given information, we get

AB=12mm, BC=3.5mm and we have to find out the value of AC.

Thus, using the Pythagoras theorem, we have

[tex](AC)^2=(AB)^2+(BC)^2[/tex]

Substituting the given values, we have

[tex](AC)^2=(12)^2+(3.5)^2[/tex]

[tex](AC)^2=144+12.25[/tex]

[tex](AC)^2=156.25[/tex]

[tex]AC={\sqrt{156.25}}[/tex]

[tex]AC=12.5mm[/tex]

Therefore, the value of the slant height is 12.5mm.

Hence, option C is correct.

Answer:

D) (1,5)

Step-by-step explanation:

You have to substitute so...

(-1,0):

y = 3x + 2

0 = 3(-1) + 2

0 = -3 +2

0 = -1

(-1,0) is NOT a solution.

(0,3):

y= 3x + 2

3 = 3(0) + 2

3 = 0 +2

3 = 2

(0,3) is NOT a solution.

(1/3,1):

y = 3x + 2

1 = 3(1/3) + 2

1 = 1 + 2

1 = 3

(1/3,1) is NOT a solution.

(1,5):

y = 3x + 2

5 = 3(1) + 2

5 = 3 + 2

5 = 5

(1,5) IS a solution.

A. They are not similar because their corresponding angles are not congruent.

Their angles are not the same.

The 1st triangle is a scalene triangle (a triangle that has 3 unequal sides and angles)

The 2nd triangle is an isosceles triangle (a triangle that has 2 congruent/equal sides and 2 congruent angles)

Answer:

Step-by-step explanation:

Answer: Choice C) 115 degrees

Focus on the parallel lines G and L, which are the top and bottom most horizontal lines. Notice that the transversal cut forms the alternate exterior angles 2 and 11. The angles are on the outside or exterior of the "train tracks" of the parallel lines. Also, they are on opposite sides of the transversal line. So that is how we can consider them to be alternate exterior angles.

Similar to alternate interior angles, alternate exterior angles are congruent if we have a transversal cutting a pair of parallel lines.

So in short, angle 2 and angle 11 are congruent. We are given angle 2 to be 115 degrees. Angle 11 is also 115 degrees.