Mylar balloons cost $1.25 each l, and latex balloons cost $0.75 each. What equations can be used to find the number of each type of balloon in a bunch of 18 balloons that costs $19?
A)1.25m+0.751=18
B)m+1=18; 1.25m= 0.751
C)1.25m-m=18;0.751-1=19
D)m+1=18;1.25m+0.751=19

To determine the original price before a 30% discount resulted in a sale price of $206.50, we calculate the sale price as 70% of the original price, leading to the original price being $295.00.

If the discount is 30% and the sale price is $206.50, we need to determine the original price before the discount. To do this, we first understand that the sale price represents 70% of the original price, because a 30% discount has been applied. Thus, to find the original price, we can set up the following equation where original price × 70% = $206.50.

Converting 70% to decimal form, we get 0.70. The equation then becomes original price × 0.70 = $206.50. To find the original price, we divide both sides of the equation by 0.70:

Original price = $206.50 / 0.70

Original price = $295.00

Therefore, the original price of the item before the 30% discount was applied is $295.00.

Answer:

f(2) = 0

Step-by-step explanation:

Evaluate the function at x = 2.

f(x) = -3x^2 + 6x

f(2) = -3(2^2) + 6 * 2

f(2) = -3(4) + 12

f(2) = 0

Answer:

[tex]x_{1} = -1 - \sqrt{\frac{2}{3}}  ; x_{2} = -1 +\sqrt{\frac{2}{3}}[/tex]

Step-by-step explanation:

-6x -1 + 5x² = 8x²     Move all terms to the right-hand side

0 = 8x² - 5x² + 6x +1     Combine like terms

3x² + 6x + 1 = 0

Apply the quadratic formula

[tex]x = \frac{-b\pm\sqrt{b^2-4ac}}{2a}[/tex]

a = 3; b = 6; y = 1

[tex]x = \frac{-6\pm\sqrt{6^2 - 4\times 3 \times1}}{2\times 3}[/tex]

[tex]x = \frac{-6\pm\sqrt{36-12}}{6}[/tex]

[tex]x = \frac{-6\pm\sqrt{24}}{6}[/tex]

[tex]x = \frac{-6\pm \sqrt{4\times6}}{6}[/tex]

[tex]x = \frac{-6\pm 2\sqrt{2}}{6}[/tex]

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

[tex]x_{1} = -1 +\sqrt{\frac{{2}}{3}}; x_{2} = 1 -\sqrt{\frac{{2}}{3}}[/tex]

The graph below shows the roots at x₁ =-1.816 and x₂ = -0.184.

Answer:

2550 m  

Step-by-step explanation:

Change in elevation = 400 – (-2150)

Change in elevation = 400 + 2150

Change in elevation = 2550 m

Answer:

x=2.49

Step-by-step explanation:

3(x−0.50)=5.97

Distribute the 3

3x - 3*.5 = 5.97

3x -1.5 = 5.97

Add 1.5 to each side

3x -1.5+1.5 = 5.97+1.5

3x = 7.47

Divide each side by 3

3x/3 = 7.47/3

x=2.49

To convert the slope-intercept form of a line, y = 6x - 4, to standard form, subtract 6x from both sides of the equation. The resulting standard form is -6x + y = -4.

You asked about writing the equation y = 6x - 4 in standard form. The standard form for the equation of a line in mathematics is usually given as Ax + By = C, where A, B, and C are constants, and A should ideally be a positive integer. To convert the given equation into standard form, we want to rearrange it so that both x and y are on the same side of the equation and the constant is on the other side.

Here are the steps to convert y = 6x - 4 to standard form:

Therefore, the standard form of the equation is -6x + y = -4.

First you have to find out the cost of the ticket. To do so you have to Divide 15  and 6. Which equals $2.50. So each ticket is $2.50 dollars. Now you have to multiple 2.50 times 9. which equals 22.5. So your total answer is $22.50 dollars

Answer:

aproximatley 6 units

Step-by-step explanation:

Answer:

A) -56

Step-by-step explanation:

B) First, you have to ignore the plus sign, and recognize that the second negative number means you are subtracting that number.

If this is correct, please like the comment so others can know, too!

Final answer:

Mr. Jimerson will earn $27.60 per hour after receiving a 15% raise on his original $24 per hour salary, resulting in a $3.60 increase per hour.

Explanation:

Mr. Jimerson earns $24 per hour working and qualifies for a 15% raise in salary. To calculate his new hourly salary after the raise, first determine the amount of the raise by finding 15% of his current hourly wage. Since 15% can be written as 0.15, we multiply his current wage by 0.15 to find the raise amount.

0.15 × $24 = $3.60

Next, add this raise amount to his original hourly wage to find his new salary:

$24 + $3.60 = $27.60 per hour

Therefore, Mr. Jimerson's salary after the raise will be $27.60 per hour.

The calculation shows that 13 crates weigh 170 pounds less than 15 crates.

To find out how much less 13 crates of apples weigh than 15 crates of apples, we need to first determine the weight of the two different amounts of crates.

We know that one crate weighs 85 pounds.

So, for 15 crates, we multiply 15 by 85 to get the total weight:

= 15 crates x 85 pounds per crate = 1275 pounds

Next, we calculate the weight for 13 crates:

= 13 crates x 85 pounds per crate = 1105 pounds

Now, we subtract the weight of 13 crates from the weight of 15 crates:

= 1275 pounds - 1105 pounds = 170 pounds

Therefore, 13 crates of apples weigh 170 pounds less than 15 crates of apples.

Perpendicular lines are two coplanar lines that intersect at a 90-degree angle, option B in the question.

Perpendicular lines are defined as two coplanar lines that intersect at a 90 degree angle. This means that the correct answer to the given question is B. It's important to understand that when lines are perpendicular, they create four right angles at the point where they intersect. Various geometrical theorems relate to the properties of perpendicular lines, for example:

Theorem 15 states that if two planes are perpendicular, a line drawn in one perpendicular to their intersection is perpendicular to the other plane.

Theorem 14 explains that if a line is perpendicular to two intersecting lines at their intersection, it is perpendicular to all lines on their plane that pass through this point.

Theorem 11 describes that if two equal lines in a plane are erected perpendicular to a given line, the line joining their extremities will make equal angles with them.

In advanced contexts, such as the geometry of spacetime, perpendicularity can be defined differently, often using the concept of the dot product being zero to identify perpendicular vectors.

Hello,

So Y variable is what you would start with.

20 <= he'll start off with for a

40 <= what he'll start off with for b

And X variables would be the # of hours you're working.

10 <= meaning every hour worked is worth 10 dollars

5 <= meaning every hour worked will be paid 5 dollars

So let's just say for option a he works two hours

(Option A)

10 (2) + 20

20 + 20

= 40

(Option B)

5 (2) + 40

10 + 40

50

As for your equations

Y = 10x + 40

Y= 5x + 40

Answer:

Yes, x + 12

Step-by-step explanation:

Simplify the following:

3 x - 2 x + 12

Grouping like terms, 3 x - 2 x + 12 = (3 x - 2 x) + 12:

(3 x - 2 x) + 12

3 x - 2 x = x:

Answer: x + 12

Answer:

Yes, it is.

Step-by-step explanation:

3x + 12 - 2x =

Use the commutative property of addition to change the order of the addition.

= 12 + 3x - 2x

Use the distributive property of addition over multiplication in reverse (which is factoring).

= 12 + x(3 - 2)

Do the operation: 3 - 2 = 1

= 12 + x * 1

Simplify x * 1 to just x.

= 12 + x

Use the commutative property of addition.

= x + 12

There you have x + 12 from 3x + 12 - 2x by using properties and operations.

Answer:

≈ $2.92 per visit

Step-by-step explanation:

10 times each month

so 12 months = 12 x 10 = 120

an annual fee of $350

$350 / 120 ≈ $2.92

Answer:

Converse of triangle proportionality theorem

Step-by-step explanation:

We are given that in a triangle ABC, D and E are some points in AB and AC respectively.

D and E divide AB and AC such that

AD/DB =AE/DC

To prove that DE is parallel to third side BC>

This can be proved using converse of triangle proportionality theorem

REcollect the triangle proportionality theorem that

If a line is parallel to a side of a triangle which intersects the other sides into two distinct points, then the line divides those sides in proportion

So converse is is a line intersects the other sides make proportional intercepts then the line is parallel to the third side.

Answer:

The answer is Converse of the Pythagorean theorem

Step-by-step explanation:

Answer:

x=9

Step-by-step explanation:

These two angles are equal because they are corresponding angles and the two lines are parallel.

13x-7 = 11x+11

Subtract 11x from each side

13x-11x -7 = 11x-11x+11

2x-7 = 11

Add 7 to each side

2x-7+7 = 11+7

2x = 18

Divide each side by 2

2x/2 = 18/2

x =9

Answer:

[tex]\frac{sin(3a)-cos(3a)}{sin(a)+cos(a)} =2sin(2a)-1[/tex]

Step-by-step explanation:

we are given

[tex]\frac{sin(3a)-cos(3a)}{sin(a)+cos(a)} =2sin(2a)-1[/tex]

we can simplify left side and make it equal to right side

we can use trig identity

[tex]sin(3a)=3sin(a)-4sin^3(a)[/tex]

[tex]cos(3a)=4cos^3(a)-3cos(a)[/tex]

now, we can plug values

[tex]\frac{(3sin(a)-4sin^3(a))-(4cos^3(a)-3cos(a))}{sin(a)+cos(a)} [/tex]

now, we can simplify

[tex]\frac{3sin(a)-4sin^3(a)-4cos^3(a)+3cos(a)}{sin(a)+cos(a)} [/tex]

[tex]\frac{3sin(a)+3cos(a)-4sin^3(a)-4cos^3(a)}{sin(a)+cos(a)} [/tex]

[tex]\frac{3(sin(a)+cos(a))-4(sin^3(a)+cos^3(a))}{sin(a)+cos(a)} [/tex]

now, we can factor it

[tex]\frac{3(sin(a)+cos(a))-4(sin(a)+cos(a))(sin^2(a)+cos^2(a)-sin(a)cos(a)}{sin(a)+cos(a)} [/tex]

[tex]\frac{(sin(a)+cos(a))[3-4(sin^2(a)+cos^2(a)-sin(a)cos(a)]}{sin(a)+cos(a)} [/tex]

we can use trig identity

[tex]sin^2(a)+cos^2(a)=1[/tex]

[tex]\frac{(sin(a)+cos(a))[3-4(1-sin(a)cos(a)]}{sin(a)+cos(a)} [/tex]

we can cancel terms

[tex]=3-4(1-sin(a)cos(a))[/tex]

now, we can simplify it further

[tex]=3-4+4sin(a)cos(a))[/tex]

[tex]=-1+4sin(a)cos(a))[/tex]

[tex]=4sin(a)cos(a)-1[/tex]

[tex]=2\times 2sin(a)cos(a)-1[/tex]

now, we can use trig identity

[tex]2sin(a)cos(a)=sin(2a)[/tex]

we can replace it

[tex]=2sin(2a)-1[/tex]

so,

[tex]\frac{sin(3a)-cos(3a)}{sin(a)+cos(a)} =2sin(2a)-1[/tex]

Answer:

To prove : sin(3a)-cos(3a)/sin(a)+cos(a) = 2sin(2a)-1                                      

Step-by-step explanation:

\frac{\sin3a-\cos3a}{\sin a+\cos a}=2\sin 2a-1\\\cos3a=4\cos^{3}a-3\cos a\\\sin 3a=3\sin a-4\sin ^{3}a\\substituting the value, we get\\L.H.S= \frac{3\sin a-4\sin ^{3}a-[4\cos ^{3}a-3\cos a]}{\sin a+\cos a}\\\frac{3(\sin a+\cos a)-4(\sin ^{3}a+4\cos ^{3}a)}{\sin a+\cos a}\\\frac{3(\sin a+\cos a)-4[(\cos a+\sin a)(\cos ^{2}a+\sin ^{2}a-\sin a\cos a)]}{\sin a+\cos a}\\\frac{3(\sin a+\cos a)-4[(\cos a+\sin a)(1-\sin a\cos a)]}{\sin a+\cos a}\\\frac{(\sin a+\cos a)[3-4(1-\sin a\cos a)]}{\sin a+\cos a}\\\frac{(\sin a+\cos a)[3-4+4\sin a\cos a]}{\sin a+\cos a}\\\frac{(\sin a+\cos a)(-1+4\sin a\cos a)}{\sin a+\cos a}\\-1+4\sin a\cos a\\-1+2\sin 2a\\2\sin 2a-1=R.H.S

Since, sin(2a)= 2sin(a)cos(a)

2sin(2a)= 4sin(a)cos(a)

Answer:

0 solutions

Step-by-step explanation:

same slope, different y intercepts so they never intersect

Answer:

As both slopes are equal, and the values of b are different it means that the two lines are parallel and the system of equations does not have any solution. (Please see the picture below)

Step-by-step explanation:

1. First write the system of equations:

[tex]y=6x+2[/tex]

[tex]3y-18x=12[/tex]

2. Solve y for the second equation:

[tex]3y-18x=12[/tex]

[tex]3y=18x+12[/tex]

[tex]y=\frac{18x+12}{3}[/tex]

[tex]y=6x+4[/tex]

3. Re write both equations in the form y=mx+b, where m is the slope and b is the value of y when x=0 :

[tex]y=6x+2[/tex]

[tex]y=6x+4[/tex]

As both slopes are equal, and the values of b are different it means that the two lines are parallel and the system of equations does not have any solution.

Answer:

q1 = 3x^2 + 6x + 16

Step-by-step explanation:

2 || 3    0     4    -  32

           6    12       32

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

     3    6    16         0

q(x) + r(x)/(x - 2)

r(x) = 0

q(x) = 3x^2 + 6x + 16

This does not factor down any further unless you have take complex number. The only real root isw

x = 2

Just in case you have done complex numbers

x2 = -1 + 2.0817i

x3 = -1 - 2.0817i

Answer:

(4,2)

Step-by-step explanation:

Answer:

3x = t and it costs 15 dollars in total with x = 5.

Step-by-step explanation:

The 3 represents her friends and x represents the cost of one ticket. The variable t represents the total cost or tickets. If x equals 5, then it would be 15 because of 3x.  

Hope it helps :)

Answer:$52.50

Step-by-step explanation:

It would be $0.68.

To find it, divide the cost by the weight. So, the equation would be 3.40/5 or 3.40 divided by 5.

The cost per pound of potato would be $0.68.

The unitary method is a method for solving a problem by the first value of a single unit and then finding the value by multiplying the single value.

We are given that  5 pound bag of potatoes cost $3.40

Then the cost per pound of potato .

We have to divide the cost by the weight.

So, the equation would be;

3.40 divided by 5.

3.40/5 = 0.68

The cost per pound of potato would be $0.68.

Learn more about the unitary method, please visit the link given below;

https://brainly.com/question/23423168

#SPJ2

Answer:

All the real numbers between [tex]\pm 90^\circ[/tex] including [tex]\pm 90^\circ[/tex].

Step-by-step explanation:

T(p) models the average yearly temperature based on degree latitude of the location.

Since the lines of latitude runs from East to West and extending from [tex]-90^\circ[/tex] to [tex]+90^\circ[/tex], they can be included in the domain.

Also, the degrees of latitude can be fractional units, positive units, or negative units. Therefore, the domain appropriate for this function is All the real numbers between [tex]\pm 90^\circ[/tex] including [tex]\pm 90^\circ[/tex].

Answer:

D = all real numbers between ± 90, inclusive

Step-by-step explanation:

Degrees of latitude can be fractional units, positive units, or negative units.

Answer:

y = [tex]\frac{96}{5}[/tex]

Step-by-step explanation:

given that y and x are proportional then the equation relating them is

y = kx ← k is the constant of proportionality

to find k use the given condition y = 12 when x = 5

k = [tex]\frac{y}{x}[/tex] = [tex]\frac{12}{5}[/tex]

y = [tex]\frac{12}{5}[/tex] x ← equation of proportionality

when x = 8, then

y = [tex]\frac{12}{5}[/tex] × 8 = [tex]\frac{96}{5}[/tex]

Answer:

Option B. 5.5 ft²

Step-by-step explanation:

Perimeter of the square piece of land = length of fence required

4(length of a side of the square) = 24 ft

Length of a side = 6 ft

Area of the square land = (Side)²

= 6²

= 36 square ft

Area of the side walk = Area of the square - [Area of two triangles separated by the sidewalk]

= 36 - [[tex]\frac{1}{2}(\text{Area of the square})+\frac{1}{2}(\text{Base})\tmes (\text{height})[/tex]]

= 36 - [[tex]\frac{36}{2}+\frac{1}{2}(6-1)(6-1)[/tex]]

= 36 - (18 + 12.5)

= 36 - 30.5

= 5.5 ft²

Therefore, Option B. is the correct answer.