The perimeter of a rectangle is 64 feet. The length is two more than double the
width. Find the dimensions of the rectangle.
(Remember Perimeter of rectangle = 2L+ 2w)
Answer:
To solve this problem, we can set up the following equation:
2L + 2W = 64
We are told that the length of the rectangle is two more than double the width, so we can write the following equation:
L = 2W + 2
Substituting this equation into the first equation, we get:
2(2W + 2) + 2W = 64
Simplifying this equation, we get:
6W + 4 = 64
Subtracting 4 from both sides, we get:
6W = 60
Dividing both sides by 6, we get:
W = 10
The width of the rectangle is 10 feet.
To find the length of the rectangle, we can substitute this value back into the equation L = 2W + 2 to get:
L = 2(10) + 2
= 20 + 2
= 22
The length of the rectangle is 22 feet.
Therefore, the dimensions of the rectangle are 10 feet by 22 feet.
Step-by-step explanation:
show that x^4-1=0 has four solutions
Step-by-step explanation:
Why can't I plus x² to each side of the inequality x²+4x > -x² ?
(Note: one adds things; one does not plus them.)
You can easily add x² to both sides here:
(x² + 4x) + x² > (-x²) + x², or
2x² + 4x > 0, or
x² + 2x > 0, or
x(x + 2) > 0.
For this to be true, x > 0 and x+2 > 0; or else x < 0 and x+2 < 0.
Case 1: x > 0 and x+2 > 0.
Rewrite this as x > 0 and x > -2.
This is true for all x > 0.
Case 2: x < 0 and x+2 < 0.
Rewrite this as x < 0 and x < -2.
This is true for all x < -2.
The solution set for the inequality, in interval notation, is then (-∞,-2) ∪ (0,∞).
done its a good question btw ....
the phone company charges $33 for having a smartphone plus $9.95 a month for 2gb. IF mark has only $146.43 to spend on a phone, how many months can he have the phone? inequalities
The number of months Mark can have the phone is given by the equation
A = 11.4 months
What is an Equation?Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.
It demonstrates the equality of the relationship between the expressions printed on the left and right sides.
Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.
Given data ,
Let the number of months be represented as = A
Now , the equation is
Now , the total amount with Mark = $ 146.43
The initial amount for the smartphone = $ 33
The amount per month for 2GB is = $ 9.95
So , the amount for A months = $ 9.95 ( A )
So , the equation will be
Initial amount for the smartphone + the amount for A months = total amount with Mark
Substituting the values in the equation , we get
33 + 9.95 ( A ) = 146.43 be equation (1)
On simplifying the equation , we get
Subtracting 33 on both sides of the equation , we get
9.95 ( A ) = 113.43
Divide by 9.95 on both sides of the equation , we get
A = 11.4 months
Therefore , the value of A is 11.4 months
Hence , the number of months is 11.4 months
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What are the features of the quadratic function ƒ(x) = (x – 3)(x + 7)?
Answer:
See below
Step-by-step explanation:
I guess if you look at the zeroes/x-intercepts, we got (3,0) and (-7,0) as zeroes.
Additionally, we can calculate the minimum by expanding the function:
[tex](x-3)(x+7)=x^2+4x-21[/tex]
[tex]\displaystyle x=-\frac{b}{2a}=-\frac{4}{2(1)}=-2\\\\f(-2)=(-2)^2+4(2)-21=4+8-21=12-21=-9[/tex]
So the minimum of the function is (-2,-9)
Also, our y-intercept is (0,-21)
Just need the answer to this question. No explanation needed
The distance of the ship from lighthouse found using sine law at both locations are 14.12 miles and 4.8 miles.
What is sine law?
The sine law asserts that the ratio of a triangle's side length to the sine of its opposing angle, which is constant for all three sides.
From the given figure we can find θ = 30 - 10 = 20°
According to sine law, we can write the following equation,
[tex]\frac{9.6}{sin \theta} = \frac{x}{sin \angle ABL} = \frac{y}{sin \angle LAB} \\[/tex]
From the figure, we get that ∠LAB= 10° (alternate angles)
∠LBC = 30°
∠ABL = 180 - 30 = 150°
θ = 20°
Substituting above values in the equation we get ,
[tex]\frac{9.6}{sin 20} = \frac{x}{sin 150} = \frac{y}{sin 10} \\\\\frac{9.6}{0.34} = \frac{x}{0.5} = \frac{y}{0.17}[/tex]
Solving the above we get,
x = 14.12
y = 4.8
Therefore the ship began 14.12 miles from the lighthouse and after travelling 9.6 miles south it is at 4.8 miles from the lighthouse.
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Can someone answers this
Answer: ( see image )
Step-by-step explanation:
Complete the table using the function c = 12m - 17.
Step-by-step explanation:
c = 12m - 17
m = 2
c = 12×2 - 17 = 24 - 17 = 7
m = 4
c = 12×4 - 17 = 48 - 17 = 31
m = 8
c = 12×8 - 17 = 96 - 17 = 79
2 alien spaceships are traveling toward each other from space stations that are 7100 km apart at speed of 110000 km
It would take 116.18 seconds for the space stations that are 7100 km apart at speed of 110000 km to meet
How to solve an equation?An equation is an expression that shows the relationship between two or more numbers.
The speed of an object is the ratio of the total distance travelled to the total time taken. It is given by:
Speed = distance / time
Distance = Speed * time
The spaceships are moving at 110000 km/h
The distance covered by each in x hours is:
Distance = 110000 * x = 110000x
Since they are 7100 km apart, hence:
110000x + 110000x = 7100
220000x = 7100
x = 0.03227 hours = 116.18 seconds
It would take 116.18 seconds for the spaceships to meet.
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what is the value of q³?!
Answer:
-6
Step-by-step explanation:
You seem to want the value of q₃ in the matrix Q⁻¹.
Matrix inverseThe inverse matrix, Q⁻¹, is the transpose of the cofactor matrix, divided by the determinant. That makes q₃ = -q₂₁/det(Q):
q₃ = -(-2/3)/((-1(-1/9) -(-2/3)(-1/3))
q₃ = (2/3)/(1/9 -2/9) = (6/9)/(-1/9)
q₃ = -6
__
Additional comment
The transpose of the cofactor matrix of a 2×2 matrix is the original with the diagonal terms swapped, and the off-diagonal terms negated. Basically, the only math involved in computing the inverse is finding the determinant, and dividing by it.
The ratio 81:108 in the simplest form
The ratio 81:108 can be simplified to 9:13. To find the simplest form of the ratio, you can divide both numbers by the greatest common factor. The greatest common factor of 81 and 108 is 9, so you can divide both numbers by 9 to get the simplified ratio of 9:13.
[NEED HELP ASAP] How do I find the surface area of the shape in the picture?
When calculating the surface area of a 3D shape, it is important to remember to include the area of all the components that make up the shape.
How do I find the surface area of the shape in the picture?The surface area of the shape in the picture is approximately 300.4 cm².To calculate this, use the formula for the surface area of a triangular prism, which is SA = 2(bhl) + 2(bh + la).In this case, b = a = 4 cm, h = 12 cm, and l = s = 4.6 cm, so the calculation is SA = 2(4 x 12 x 4.6) + 2(4 x 4.6 + 4 x 12) = 300.4 cm².To calculate the surface area of the shape in the picture, you need to first calculate the area of the rectangle, triangle and circle.The rectangular portion has a height of 12 cm and a length of 4 cm, so the area is 48 cm^2.The triangle has a height of 12 cm and a base of 4 cm, so the area is 24 cm^2. The circle has a radius of 4.6 cm, so the area is 66.48 cm^2. Therefore, the total surface area of the shape is 138.48 cm^2. To calculate the surface area, you need to add the area of each of the components.For example, the area of the rectangle is 48 cm^2, the area of the triangle is 24 cm^2, and the area of the circle is 66.48 cm^2.The total surface area of the shape is then the sum of all these components, which is 138.48 cm^2.In this example, the rectangular portion, triangle and circle each had to be calculated separately in order to find the overall surface area.To learn more about the surface area of a of the prism refer to:
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please answer quickly :)
Answer:
The solution is (-1, 0)-----------------------------------
Given lines:
y = - 2x - 2 and y = x + 1Plot both of the lines using the graphing calculator by adding the equations, then find the graphical solution as the intersection of the lines.
See attached.
The solution is (-1, 0).
ABC~A'B'C'. Their scale factor is 7:9. If the perimeter of smaller ABC is 42, then the
perimeter of A'B'C' is.
Pls hurry!!
Answer:
54
Step-by-step explanation:
ratio is 7:9
7=42
9=?
9×42÷7
Question 4 of 10
Find the difference. Enter your answer in the box below as a fraction, using
the slash mark (/) for the fraction bar.
8-7
14 14
There is a 2/17 difference between 16/17 and 14/17 as 17 is the shared denominator of both fractions.
what is fractions ?A whole can be represented by any number of equal parts, or fractions. The number of units of a particular size is expressed as a fraction in standard English. 8, 3/4. Fractions are included in wholes. Numbers are expressed in mathematics as the ratio of the numerator to the denominator. In simple fractions, each of these is an integer. A complicated fraction contains a fraction in either the numerator or denominator. There is a difference between the numerators and denominators of true fractions. A sum that is a fraction of a whole is referred to as a fraction. You can evaluate it by dissecting the whole into smaller pieces. For example, 12 is used to represent one-half of a full number or item.
Given,
To get the difference between 16/17 and 14/17, discover their common denominator first.
17 is the shared denominator of both fractions.
To solve, multiply the result by the numerator of the fractions, then divide the sum by the common denominator:
16 - 14/17 (16 - 14) = 2/17 is the solution.
Therefore, there is a 2/17 difference between 16/17 and 14/17.
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Click an item in the list or group of pictures at the bottom of the problem and, holding the button down, drag it into the correct position in the answer box. Release your mouse button when the item is place. If you change your mind, drag the item to the trashcan. Click the trashcan to clear all your answers.
Click and place the simplified expression after its original expression.
b) The completed construction of a regular hexagon is shown below. Explain why ACF is a 30º-60º-90º triangle. (10 points)
[tex] \div 7841562130. = 98[/tex]
Answer:
123459c
Step-by-step explanation:
round
Jen has some buttons. She gets
23 more buttons from her mom.
Now she has 65 buttons.
How many buttons did
Jen have to begin with?
Answer:
x + 23 = 65
x = 42
She had 42 buttons to begin with.
Given that f(x)=√x, describe the function of g(x)
shown on the graph.
The function is represented by the equation
g(x)=√x +
The function g(x) has a domain x²
The function g(x) has a range y ≥
Answer: It's not possible to accurately describe the function g(x) without more information about the equation or the graph. The equation provided is g(x)=√x + , which is incomplete, it does not have a value assigned for the "+" operator, it could be added to any number, for example, g(x)= √x + 1, or g(x)= √x+5, and so on.
Additionally, the statement that the function g(x) has a domain x² and range y ≥ , is not a valid mathematical notation or statement. The domain of a function is the set of all input values (x-values) for which the function is defined, it's usually a set of real numbers or interval, like [-∞,+∞], (a,b) or [a,b], for example.
And range is the set of all output values (y-values) of a function, it's also usually a set of real numbers or interval.
I would suggest if you can provide me with the complete function of g(x) and more detailed information about the graph. I can help you better understand its features and properties.
Step-by-step explanation:
How do I write an equation for this relationship (where y represents the number of blocks and x represents the stage number).
The equation of the line is y = 4x + 1 , where the slope of the line is m = 4
What is an Equation of a line?The equation of a line is expressed as y = mx + b where m is the slope and b is the y-intercept
And y - y₁ = m ( x - x₁ )
y = y-coordinate of second point
y₁ = y-coordinate of point one
m = slope
x = x-coordinate of second point
x₁ = x-coordinate of point one
The slope m = ( y₂ - y₁ ) / ( x₂ - x₁ )
Given data ,
Let the equation of line be represented as A
Now , the value of A is
Let the number of blocks be y
Let the stage number be x
Let the first point be represented as P = P ( 1 , 5 )
Let the second point be represented as Q = Q ( 2 , 9 )
Now , the slope of the line between the points be
Slope m = ( y₂ - y₁ ) / ( x₂ - x₁ )
Substituting the values in the equation , we get
Slope m = ( 9 - 5 ) / ( 2 - 1 )
Slope m = 4
Now , the equation of line is y - y₁ = m ( x - x₁ )
Substituting the values in the equation , we get
y - 5 = 4 ( x - 1 )
On simplifying the equation , we get
y - 5 = 4x - 4
Adding 5 on both sides of the equation , we get
y = 4x + 1
Therefore , the value of A is y = 4x + 1
Hence , the equation of line is y = 4x + 1
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In Exercises 7-8, find the domain of the function.
7. f(x) = x-5/x + 2
8. h(x) = 4x²
On solving the provided question, we can say that - the value of the function is = x-5/x + 2 => x= 2 => -3/4
what is function?The topic of numbers, formulae and associated structures, forms and the areas where they exist, quantities and their variations, and spaces where they exist are all included in the field of mathematics. An association between a collection of inputs, each of which has an output, is known as a function. A function is, to put it simply, a relationship between inputs and outputs, where each input has a single, specific outcome. A domain and a codomain, or scope, are assigned to each function. Typically, f is used to represent functions (x). input is x. Four different sorts of functions are available. Based on the following items: One-to-one functions, many-to-one functions, on functions, one-to-one functions, and within functions.
x-5/x + 2
x= 2
-3/4
ans also 4x² = 4 *2*2 = 16
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Judi is making a rope ladder. She uses 1/2 yard of for each step. How many yards of rope can she make for step?
The number of yards of rope she can make for the step is 3 yards
How to determine the number of yards of rope she can make for the step?From the question, we have the following parameters that can be used in our computation:
Yards of rope per step = 1/2 yards per step
Total number of steps = 6 steps
The number of yards of rope she can make for the step can then be calculated using the following equation
The number of yards of rope = Total number of steps * Yards of rope per step
Substitute the known values in the above equation, so, we have the following representation
The number of yards of rope = 1/2 * 6
Evaluate
The number of yards of rope = 3
Hence, the number of yards of rope is 3
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Complete question
Judi is making a rope ladder. she uses 1/2 yard of rope for each step. how many steps can she make with 6 yards of rope?
Find the equivalent measures. Express as a decimal
(a) 250 cm =
The answer is 2.50. This, 250% in deciaml form is 2.50, in improper fraction form is 52 and as a mixed number it is 2 12. 2 1 2.
Given points A (1, 5) and B (-7, -5), which of the following coordinates is the midpoint of AB? (-3, 0) (-4, 0) (-2, 0) (4, 0) (2, 0)
Using formula of midpoint of a line, the coordinate of the midpoint is (-3, 0)
What is Midpoint of LineThe midpoint of a line is a point that is equidistant from both endpoints of the line. It can be found by taking the average of the x-coordinates of the two endpoints, and then taking the average of the y-coordinates of the two endpoints. For example, if the two endpoints of a line are (x₁, y₁) and (x₂, y₂), then the midpoint of the line is:
Midpoint = ((x₁ + x₂) / 2, (y₁ + y₂) / 2)
The formula of midpoint of a line is given as;
M(x, y) = (x₂ + x₁) / 2, (y₂ + y₁) / 2
Substituting the values into the formula;
M(x, y) = (-7 + 1) / 2, (-5 + 5) / 2
M(x , y) = -6/2, 0/2
M(x, y) = -3, 0
The coordinate of midpoint is (-3, 0)
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Prove that limx→2 2^x=4 using the formal definition of limit.
Answer:
Refer to step-by-step
Step-by-step explanation:
Prove that, [tex]\lim_{x \to \22} 2^{x}=4[/tex]
Plug in the value of 2 into the limit.
[tex](2)^{2}=4[/tex]
Thus we proved the limit.
Can somebody help me? I need help please
By using concept of angle relationship, we get x equal to 27°.
What are angle relationships defined as?We compare the position, measurement, and congruence of two or more angles when we talk about angle relationships. For instance, two pairs of vertical angles are created when two lines or line segments intersect.
∠BAF+∠EAF=180°
∠EAF=180° - 138°
∠EAF=42°
Since, ∠EAF and ∠BAC are vertically opposite angle,
Hence,
∠EAF = ∠BAC =42°
Again,
∠EAD+∠DAC+BAC=180°
4x+30°+42°=180°
4x=180°-72°
4x=108°
x=27
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What is the differences between solving an equation and solving an inequality?
The equation includes equal to sign and the inequality includes the sign of greater than and equal to sign.
What is inequality?Inequality is defined as the relation which makes a non-equal comparison between two given functions.
when we have to solve an equation, it does not has an equal sign and inequalities.
When we have to solve an inequality equations usually are exact answers.
The equation includes equal to sign and the inequality includes the sign of greater than and equal to sign.
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Miguel rode his bike to work which was 15 miles from home. However he was too tired to ride back so he got a ride in a
car from a co-worker. He spent a total of 2 hours traveling. The average speed of traveling by car was 3 times faster
than on his bike. What was Miguel's average speed on his bike and in the car?
Answer:
Bike: 10 miles per hour
Car: 30 miles per hour
Step-by-step explanation:
He spent: 2h/(1+3) = 0,5h by car and 0,5h x 3 = 1,5h by bike
The car is: 15 miles/ 0,5h = 30 miles/h
The bike is: 15 miles/ 1,5h = 10 miles/h
PLEASE HELP FRACTION S EASY!! A construction worker is making concrete by mixing sand, gravel, and cement in water. For each pound of sand, he uses pounds of gravel. For each pound of gravel, he uses pound of cement. He is making enough concrete that he needs to use 3 pounds of sand.
How many pounds of cement does he use?
The pound of cement used based on the information will be C. 2 pounds.
How to illustrate the fraction?A fraction simply means a piece of a whole. In this situation, the number is represented as a quotient such that the numerator and denominator are split. In this situation, in a simple fraction, the numerator as well as the denominator are both integers.
In this case, for each pound of sand, he uses 1 2/3 pounds of gravel and for each pound of gravel, he uses 2/5 pound of cement.
The pound of cement used will be:
Gravel = 1 2/3 × 3
= 5 pounds
Cement used will be:
= 2/5 × 5.
= 2 pounds.
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Given that M =
2x 2
93
calculate the value(s) of x for which [M] = 0.
Please help me, I need help asap !! I can’t figure it out