At a restaurant, Hamburgers cost $2.50 each and French Fries cost $1.20 each. If I went to this restaurant, and bought $8.60 worth of food,
write an equation which models how many hamburgers and french fries I purchased.
Let H represent Hamburgers
Let F represent French Fries.
Answer:
2.50h+1.20f=8.60
Step-by-step explanation:
Since the total cost of food costs $8.60, add together the costs of however many burgers and however many fries you bought. 2.50 and 1.20 are multiplied by the amount of food you purchase
Write an equation that represents the line.
Use exact numbers.
Answer:
y = -2x -3
Step-by-step explanation:
To write an equation we need two points that the line cuts through.
we then use the formula: Gradient = Rise/Run
the points chosen are (0,-3) and (1,-5)
Gradient = (-5--3)/(1-0)
= -2
to write the equation we need one known point, gradient and one unknown point say (x,y).
we therefore use the formula for gradient/slope
G = Rise/Run
-2 = y+3/x-0
-2x = y + 3
y = -2x -3
Answer:
y = - 2x - 3
Step-by-step explanation:
the equation of a line in slope- intercept form is
y = mx + c ( m is the slope and c the y- intercept )
calculate m using the slope formula
m = [tex]\frac{y_{2}-y_{1} }{x_{2}-x_{1} }[/tex]
with (x₁, y₁ ) = (0, - 3) and (x₂, y₂ ) = (1, - 5) ← 2 points on the line
m = [tex]\frac{-5-(-3)}{1-0}[/tex] = [tex]\frac{-5+3}{1}[/tex] = [tex]\frac{-2}{1}[/tex] = - 2
the line crosses the y- axis at (0, - 3 ) ⇒ c = - 3
y = - 2x - 3 ← equation of line
The mass of Mars is 6.42 x 1023 kilograms. The mass of Mercury is 3.3 x 1023 kilograms.
Answer:
Im unaware what you are asking?
Step-by-step explanation:
hmmmm
Given the figure below, find the values of x and z.
zº
X
(15x + 35).
100°
Find Z pleasee
ANSWER: x = 3
z = 100
2334567Happy Paws charges $19.00 plus $2.50 per hour to keep a dog during the day. Woof Watchers charges$10.00 plus 53.75 per hour. Complete the equation and solve it to find for how many hours the total costof the services is equal. Use the variable h to represent the number of hours.The equation isThe total cost of the services will be equal athours.
Let h be the hours and y the total charge. Then, for Happy Paws, we have
[tex]y=2.50h+19[/tex]and for Woof Watches, we have
[tex]y=3.75h+10[/tex]Then, we need to solve these equations.
Solving by elimination method.
If we multiply by -1 the first equation, we have the equivalent system of equations:
[tex]\begin{gathered} -y=-2.50h-19 \\ y=3.75h+10 \end{gathered}[/tex]If we add both equations, we obtain
[tex]0=(3.75-2.50)h+10-19[/tex]because y-y=0. Then, it yields,
[tex]0=1.25h-9[/tex]If we move -9 to the left hand side as -9, we have
[tex]\begin{gathered} 9=1.25h \\ h=\frac{9}{1.25} \\ h=7.2 \end{gathered}[/tex]Hence, to find the total cost, we must substitute this values into one of the 2 equations. If we choose the first one, we obtain
[tex]\begin{gathered} y=2.50(7.2)+19 \\ y=18+19 \\ y=37 \end{gathered}[/tex]Then, the answers are:
The equation is
[tex]2.50h+19=3.75h+10[/tex]and, the total cost of the services will be equal at 7.2 hours
hellppppp meeee pleaseeee
Answer:
a) x+4
b) a = 1, b = 10
Step-by-step explanation:
a) You can read the lenght of AB, which is 4 + x
b) The lenght of AD is 6+x
The area of the rectangle ABCD is lenght AB * lenght CD,
so (4+x)*(6+x) = 24 + 6x + 4x + x^2 = x^2 + 10x +24
Since this must equal 28, it follows that
x^2 + 10x + 24 = 28,
so 1*x^2 + 10x = 4
(note that 1*x^2 is just x^2)
so a = 1 and b = 10
Given m/n find the value of x
Answer:
x = 49°
Step-by-step explanation:
x = 49°
since m and n are parallel to each other
with T an oblique vector
forming a Z shape
to make this true
Use the figure to find the measures of the numbered angles.
Applying the angle relationships, the measures of the numbered angles are:
m∠1 = 145°
m∠2 = 145°
m∠3 = 35°
m∠4 = 35°
m∠5 = 145°
m∠6 = 145°
m∠7 = 35°
How to Find the Measures of Angles Using Angle Relationships?The position of angles when a transversal intersects parallel lines determines the type of angle relationships that exist between the angles, and also their measure.
Based on angle relationships, the angle measures in the image are solved as follows:
m∠1 = 180 - 35 [linear pair angle relationship]
m∠1 = 145°
m∠2 = m∠1 [vertical angles]
m∠2 = 145°
m∠3 = 35° [vertical angles]
m∠4 = 35° [corresponding angles]
m∠5 = m∠2 [alternate interior angles]
m∠5 = 145°
m∠6 = m∠5 [vertical angles]
m∠6 = 145°
m∠7 = m∠4 [vertical angles]
m∠7 = 35°
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Mrs. McKinnon was making t-shirts. One of the designs had the instructions to make points at the following locations and then draw lines to connect the points in order: A(-5, 5); B (-5, 1); C(2,1); and D (2, 5).
Use graph paper to plot the points.
Connect them in order: A to B, B to C, C to D, and then D back to A. What shape is created?
Answer:
It's basically a quadrilateral, it has no name for it.
Step-by-step explanation:
start off by graphing the points
the number in the front is the x axis and the number after is the y axis
Ex: (-4,3) = (X,Y)/ X is horizontal going left to right & Y is vertical going up and down.
Which value represents |12|? A. -12 B. -6 C. 6 D. 12
Answer: 12
Step-by-step explanation: Because the absolut value of something will always be positive.
Answer:
The value for |12| is D. 12
Find a cubic model for the set of values. (-2,-7)(-1,0)(0,1)(1,2)(2,9)
The required cubic model would be y = 1 + x³ for the given set of values.
What is the cubic model?The cubic model function takes the form:
y = a + bx + cx² + dx³,
where a, b, c, and d are real integers that represent the cubic regression model's coefficients As you can see, we simulate how the value of y changes as x changes.
x₁ = -2, y₁ = -7
x₂ = -1, y₂ = 0
x₃ = 0, y₃ = 1
x₄ = 1, y₄ = 2
x₅ = 2, y₅ = 9
Computing the values in the regression models to get the values of coefficients to which the graph has attached.
y = a + bx + cx² + dx³
Fitted coefficients:
a = 1
b = 0
c = 0
d = 1
Cubic model:
y = 1 + x³
Hence, the required cubic model would be y = 1 + x³ for the given set of values.
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Solve u² = -121, where u is a real number. Simplify your answer as much as possible.
Simplifying the answer
What is Real number ?
The value of a continuous quantity that can represent a distance along a line is a real number. René Descartes first used the word "real" in this meaning in the 17th century when he made a distinction between the real and imaginary roots of polynomials.
Solve : u² = -121
putting square root on both side
√u² = √ (-121)
u = (-11)
u = 11i
Since, there is no real square root of -121
If i is the imaginary unit then i = -1 and we find that
11i is square root of -121
Hence, the simplify answer for u² = -121 is 11i
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Given the equations y=x+7 and y=x^2+4 how many times do they intercept?
According to the following graph, the equations y=x+7 and y=x²+4 will intercept 2 times at the points (-1.3, 5.7) and (2.3, 9.3).
Intercept:
The point where the line or curve crosses the axis of the graph is known as intercept.
That is, if a point crosses the x-axis, then it is known as the x-intercept. Similarly, if a point crosses the y-axis, then it is called as the y-intercept.
Given,
Here we have the equation y=x+7 and y=x²+4.
Now, we need to find the number of times the equation is intercepts.
First, we have to plot the graph for the given equations,
Then based on that one we have easily identify the intercepting points in order to get the results.
In the following graph, the blue line represents the equation y=x²+4 and the red line represents the equation y = x + 7.
While we looking into the graph we have identified that the two lines are intersecting at two point they are (-1.3, 5.7) and (2.3, 9.3).
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what is 7.6 x 10^4 in standard form?
Answer: 76,000
Step-by-step explanation:
You move the decimal point to the right 4 times because of the positive exponent.
A and B together can do a piece of work in 12 days; B and C together can do it in 15 days. If A is twice as good a workman as C, in how many days will A alone need to finish the work.
Answer:
it's 21 something like that
Step-by-step explanation:
im 14
what is 14+7.2n=11+7.5n (whole number)
Hello!
Let's solve:
[tex]\text{Copy down the equation}\\14+7.2n=11+7.5n\\\\\\\text{Move all the variables to one sides and constants to the other}\\14-11=7.5n-7.2n\\7.5n-7.2n = 14-11\\0.3n = 3\\\\\\\text{Divide both sides by 0.3}\\\dfrac{0.3n}{0.3} =\dfrac{3}{0.3} \\\\n = 10[/tex]
Answer: 10
Hope that helps!
Ax+By=C form with slope of 14 over 13 with points (5,6) and (-8,-8)
[tex]\displaystyle\\Answer:\ -\frac{14}{13} x+y=\frac{8}{13}[/tex]
Step-by-step explanation:
Ax+By=C the slope is 14/13 (5,6) (-8,-8)
The slope m equil 14/13
[tex]\displaystyle\\By=mx+C\\\\By=\frac{14}{13} x+C\ \ \ \ (1)[/tex]
Substitute the coordinates of the points into equation (1) and obtain a system of equations:
[tex]\displaystyle\\\left \{ {{B(6)=\frac{14}{13}(5)+C } \atop {B(-8)=\frac{14}{13}(-8)+C }} \right.\\\\\left \{ {{6B=\frac{70}{13} +C\ \ \ \ \ \ \ (2)} \atop {-8B=-\frac{112}{13}+C\ \ \ (3) }} \right.[/tex]
Multiply both parts of the equation (3) by -1:
[tex]\displaystyle\\\left \{ {{6B=\frac{70}{13}+C \ \ \ \ (4)} \atop {8B=\frac{112}{13}-C }} \right.[/tex]
Add these equations :
[tex]14B=\frac{182}{14}\\\\ 14B=14[/tex]
Divide both parts of the equation by 14:
[tex]B=1[/tex]
Hence, let's substitute the value of B into equation (4):
[tex]\displaystyle\\6(1)=\frac{70}{13}+C \\\\6=\frac{70}{13}+C\\6-\frac{70}{13} =\frac{70}{13} +C-\frac{70}{13}\\\\\frac{6*13-70}{13}=C\\\\\frac{78-70}{13}=C\\\\\frac{8}{13}=C\\[/tex]
[tex]\displaystyle\\Thus,\ C=\frac{8}{13}\\\\ So,\ 1(y)=\frac{14}{13} x+\frac{8}{13} \\ -\frac{14}{13} x+y=\frac{8}{13}[/tex]
The area of one surface of a cube is 19,600 sq. cm. If the cube is filled with water how many bottles of 4 litres each can be filled from it?
686 bottles of 4 liters each can be filled from this cube.
We can solve this problem by following a few steps.
As we know that a cube has 6 surfaces and each surface has a geometrical shape of a square. We also know that each side of a square is the same.
So, the surface area of a square ≡ Side × Side.
Let's assume the side as z
Now, the area of this square ≡ z × z = z²
∴ z² = 19600, as per the question.
We have to solve the equation, z² = 19600 Or, z = 140 ( by doing root both sides)
Now we know the side of the cube, then the volume of this cube is z³.
As, we know the volume of a cube ≡ side × side × side, as the height of a cube is also identical.
Volume of the cube = 140³ = 2,744,000 cc
1000 cc is considered as 1 liter. Therefore, this cube consists of, 2,744,000/1000 = 2744 liter of water.
Each bottle consists of 4 liters of water. Then we can fill, 2744/4 = 686 bottles of water.
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its so so so hard heplp !!
3. Is x^5 + x² + x? a polynomial? Explain why or why not.
ANSWER:
A polynomial is an algebraic expression of ordered addition, subtraction, and multiplication made up of variables, constants, and exponents.
Polynomials are made up of finite terms. Each term is an expression that contains one or more of the three elements they are made of variables, constants, or exponents.
In this case, for each term, the variable is x, the constant is 1, and the exponents are 5, 2, and 1, respectively.
This means that we have a sum of monomials, that is, that the expression is a polynomial.
Five rays share a common endpoint. Set up an equation to find the value of x.
The equation that can be set up is, 2x° + 3x° + 36.5° + 36.5° + 2x° = 360°.
The value of x is: x = 41.
What are Angles around a Point?Angles that are formed around an endpoint but several rays will have a sum of 360 degrees when each of the angles formed around the endpoint is added together.
The diagram shows the angles that are formed by the five rays at a common endpoint. The angles are, 2x°, 3x°, 36.5°, 36.5°, and 2x°.
The sum of all these angles formed will give us 360 degrees. Therefore, the equation that would be created to find the value of x would be written as:
2x° + 3x° + 36.5° + 36.5° + 2x° = 360° [equation set up to find x]
Combine like terms
7x° + 73° = 360°
Subtract 73 from each side
7x° + 73° - 73° = 360° - 73° [subtraction property of equality]
7x = 287
Divide both sides by 7:
7x/7 = 287/7 [division property of equality]
x = 41
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simplify the expression 22(5) − 8
Answer:The answer to the expression is 102.
Step-by-step explanation:
Answer:
102
Step-by-step explanation:
22(5)-8=102
Multiply and divide (left to right) 22(5) : 110
= 110 - 8
Add and subtract ( left and right) 110 - 8 : 102
Rewrite this sentence
The brick old red depressing building was filled with students
Answer: Students filled the brick old red depressing building.
Step-by-step explanation:
Write an equation of the line passing through point P(-2, 6) that is parallel to the line x =-5 X Graph the equations of the lines to check that they are parallel.
The equation of the line passing through the point P(-2,6) that is parallel to the line x = -5 is x = -2 .
In the question ,
it is given that
the required line is parallel to x [tex]=[/tex] -5
means the line x [tex]=[/tex] -5 , is a vertical line parallel to y axis , it makes an angle of 90° with the x axis .
so , slope will be tan(90°) = 1/0
hence the slope of the required line is 1/0.
The equation of the line passing through point P(-2,6) and with slope = 1/0 , is
y-6 = (1/0)*(x-(-2))
0 = 1 * (x + 2)
0 = x + 2
x = -2
the graph is drawn below .
Therefore , The equation of the line passing through the point P(-2,6) that is parallel to the line x = -5 is x = -2 .
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A 8 letter Code word is selected. What is the probability that there are no repeated letters?
Probability of selecting eight letter word without repetition of letter is 0.3016.
There are total 26 letters in English alphabets. A 8 letter Code word is selected. We have to take care of repetition of letters as be are not allowed to repeat the letters.
Any letter being chosen should have an equal probability of 1/26. So, we have a probability of 1 to get a non-repeated letter while choosing the first letter.
For first letter the probability is = 26/26
For second letter the probability is = 25/26
For third letter the probability is = 24/26
For fourth letter the probability is = 23/26
For 5th letter the probability is = 22/26
For 6th letter the probability is = 21/26
For 7th letter the probability is = 20/26
For 8th letter the probability is = 19/26
To get an eight letter code that has no repeated letters, all these events have to occur.
Probability of selecting eight letter word without repetition of letters = (26/26) (25/26) (24/26) (23/26) (22/26) (21/26) (20/26) (19/26)
Probability of selecting eight letter word without repetition of letters = 0.3016
So, 0.3016 is the probability of selecting eight letter word without repetition of letters.
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Tina says, "The difference between any 2 consecutive square numbers is always odd." Is she correct? Yes No
Answer:
Yes
Step-by-step explanation:
Because they are consecutive, one is odd and one is even.
The square of an odd number is always odd
The square of an even number is always even
The difference between an odd number and an even number is always odd
Therefore, the difference between any 2 consecutive square numbers is always odd
the product of a number and -3 increased by 16 is 31
-2 1/3+ 1 4/7 what is the solution of this equation?
Answer:
[tex]-\frac{16}{21}[/tex]
Step-by-step explanation:
lets organize the equation so it becomes easier to see
[tex]-2\frac{1}{3} + 1\frac{4}{7}[/tex]
switch the spots so that it becomes even easier to read (this does not affect the result in any way)
[tex]1\frac{4}{7}-2\frac{1}{3}[/tex]
now make them both improper fractions
[tex]\frac{11}{7} -\frac{7}{3}[/tex]
and make them both have the same denominator (21)
[tex]\frac{33}{21} -\frac{49}{21}[/tex]
and solve
([tex]33-49= -16[/tex])
[tex]\frac{33}{21} -\frac{49}{21} =\frac{-16}{21}[/tex]
can we simplify [tex]\frac{-16}{21}[/tex]? does 16 and 21 have a common factor?
No.
so our result is
[tex]-\frac{16}{21}[/tex] or 0.761904762
P=2W+2L (solve for L)
please help me❗️❗️
Answer:
L = 1/2(p) - w
Step-by-step explanation:
a) Flip the equation.
2l + 2w = p
b) Add -2w to both sides.
2l + 2w + −2w = p +-2w
2l = p − 2w
c) Divide both sides by 2.
2L/2 = p - 2w/2
L = 1/2(p) - w
Thenegative interval(3) of the functiony=-X²+1 are
We are given the following function
[tex]y=-x^2+1[/tex]We are asked to find the negative interval of this function.
A negative interval means that where the y values of the function are negative.
Let us have a look at the graph of this function.
As you can see,
For x = 0, the interval is positive.
For x = 1 and x = -1 the y value is 0 (we don't consider 0 as either positive or negative that's why 0 is not included in the negative or positive interval)
The y values of the function are negative for
x > 1 and x < -1
Therefore, the negative interval of the function y = x² + 1 is
[tex]1