The length of the original square must be equal to 3 inches.
Length of the Original SquareTo find the length of the original square, we have to first assume the unknown length is equal x and then use formula of area of a square to determine it's length.
Since the new length is stretched by 5in, the new length would be.
[tex]l = (x + 5)in[/tex]
The area of a square is given as
[tex]A = l^2[/tex]
But the area is equal 64 squared inches; let's use substitute the value of l into the equation above.
[tex]A = l^2\\l = x + 5\\A = 64\\64 = (x+5)^2\\64 = x^2 + 10x + 25\\x^2 + 10x - 39 = 0\\[/tex]
Solving the quadratic equation above;
[tex]x^2 + 10x - 39 = 0\\x = 3 or x = -13[/tex]
Taking the positive root only, x = 3.
The side length of the original square is equal to 3 inches.
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Hello. I think I have the right answer. These types of questions have been giving me problems
EXPLANATION
Using a composite figure to approximate the area of the figure will give us the needed surface,
The area of the composite is approximately the area of the squares:
Area of square:
A= base * height = 1.0*1.0 = 1 cm^2
Since we have approximately 22 squares inside the figure, the approximate area will be as follows:
[tex]Area_{composite\text{ figure}}=22*1cm^2=22cm^2[/tex]Therefore, the solution is approximately 22 square units.
A birthday cake has a diameter of 9 inches. A wedding cake has a diameter of 14 inches. What is thedifference in area between the top surfaces of the two cakes?
90.32 square inches
Explanation
Step 1
the area of the circle is given by:
[tex]\text{Area}=\frac{\pi}{4}\cdot diameter^2[/tex]Step 2
find the areas
birthday cake
[tex]\begin{gathered} \text{Area}_b=\frac{\pi}{4}\cdot9^2 \\ \text{Area}_b=\frac{81\pi}{4} \\ \text{Area}_b=\frac{254.46}{4} \\ \text{Area}_b=63.61\text{ square inches} \end{gathered}[/tex]Now, the wedding cake
[tex]\begin{gathered} \text{Area}_w=\frac{\pi}{4}\cdot14^2 \\ \text{Area}_w=\frac{\pi}{4}\cdot196\text{ square inches} \\ \text{Area}_w=49\cdot\pi\text{ square inches} \\ \text{Area}_w=153.93\text{ square inches} \end{gathered}[/tex]Step 3
finally, find the difference
[tex]\begin{gathered} \text{difference}=153.93\text{ square inches-63.61 inches} \\ \text{difference}=90.32 \end{gathered}[/tex]so, the answer is 90.32 square inches
In an office building, 54 office are currently being rented, this represent 30% of the total units. how many offices are in the building
given that,
54 offices are currently rented
and it represent 30% of the total unit
to get the total offices in the building
let the total offices be x
30% of x = 54
30/100 X x = 54
cross multiply
30x = 5400
dividing both sides by 30
30x/30 = 5400/30
x = 5400/30
x = 180
therefore the total offices in the building is 180
Identify the domain and range and tell whether the relation is a function
For a function, every element in the domain must have a unique image in the range.
On checking the domain and range provided in the question, we can see that there are two images for the range when the domain equals -2:
[tex](-2,3)\text{ and (}-2,7)[/tex]Therefore, the given domain and range violate the property of a function.
The relation is NOT a function.
Line segment AB is on square ABCD. Segment EF on equilateral triangle EFG is 12 units longer than AB. Square ABCD and triangle EFG have equal perimeters. What is the length of AB?
The length of segment AB as required in the task content is; 36.
What is the length of segment AB?It follows from the task content that the length of the line segment AB which is a side of the square ABCD is to be determined.
Since the perimeters of triangle EFG and square ABCD are equal as given;
Let the length of segment AB = x.
Therefore, EF = x + 12.
Therefore, the perimeter of the equilateral triangle = 3(x +12).
While the perimeter of square ABCD is; 4x.
Therefore, since the perimeters are equal;
3(x + 12) = 4x
3x + 36 = 4x
36 = x.
On this note, thee Length of line segment AB is; 36.
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Mrs. Smith has 12 times as many markers as colored pencils. The total number of markers and colored pencils is 78. How many markers does Mrs. Smith have?ok...answers given so far are not helpful in explaining process.
Let:
x = Colored markers
y =
Three friends rented a kayak. It cost $4 per hour per person to rent the kayak, plus $2 for each life jacket, and $3 to park the car. It cost $57 in all. How many hours did they spend kayaking? Write an equation and solve.
Answer:
13 hours
Step-by-step explanation:
Let y = the total cost
let x = hours
y = 4x + 5 5 = the one time fee of the jacket and the parking
57 = 4x + 5 Subtract 5 from both sides
52 = 4x Divide both sides by 4
13 = x
Hello! I need some help with this homework question, please? The question is posted in the image below. Q5
ANSWER:
STEP-BY-STEP EXPLANATION:
We can determine the domain and range of the function, knowing that the domain is the interval of values in x and the range is the interval of values in y.
Therefore:
[tex]\begin{gathered} D=\lbrack-5,5\rbrack \\ R=\mleft[-5,\frac{25}{17}\mright] \end{gathered}[/tex]When a function is inverted, the domain and range are inverted, therefore:
[tex]\begin{gathered} D=\mleft[-5,\frac{25}{17}\mright] \\ R=\lbrack-5,5\rbrack \end{gathered}[/tex]Which means that the inverted function goes from -5 to 25/17 in x and from -5 to 5 in y.
In addition to this we must take into account that when the inverse function is done, in most cases a reflection is made in y = x.
The only graph that meets all of the above is graph A
Large Small
3
Blue 17
Red 8 12
Find: P(Red and Small)
Remember to reduce your answer.
Enter
Using mathematical operations, we know that P(Red and Small) is 4/3.
What exactly are mathematical operations?A mathematical function known as an operation converts zero or more input values into a precisely defined output value.The quantity of operands affects the operation's arity.The order of operations refers to the rules that define the sequence in which we should perform the operations necessary to solve an expression.Parentheses, Exponents, Multiplication, Division, and Addition Subtraction are also known as PEMDAS (from left to right).So, simple form of P(Red and Small):
Red balls: 8 (large) + 12 (Small) = 20 red ballsSmall balls: 3 (Blue small balls) + 12 (Red small balls) = 15 small ballsThen, P(Red and Small):
20/154/3Therefore, using mathematical operations, we know that P(Red and Small) is 4/3.
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A school is organising a fun runThe fun run involves a 4
1
2
mile run around the field, then a 3
2
5
mile run back to the school. Find the total distance of the fun run.Give your answer as a mixed number in its simplest form.
The total distance of the fun run is 7 9/10 miles and it can be written in the simplest fraction form.
Fraction:
The fraction is the part of the whole thing.
For example, a cake is divided into four equal pieces, then each piece is represented by ¼.
Given,
A school is organizing a fun run. The fun run involves a 4 1/2 mile run around the field, then a 3 2/5 mile run back to the school.
Now, we need to find the total distance of the fun run and we have to write it as simplest form.
First we have to convert the given fraction into simplest fraction then we get,
=> 4 1/2 = 9/2
=> 3 2/5 = 17/5
Now , we have to add these to fraction in order to get the total distance,
=> 9/2 + 17/5
The fractions have unlike denominators. First, find the Least Common Denominator and rewrite the fractions with the common denominator.
LCD(9/2, 17/5) = 10
Multiply both the numerator and denominator of each fraction by the number that makes its denominator equal the LCD. This is basically multiplying each fraction by 1.
=> 45/10 + 34/10
=> 79/10
While we convert this into mixed number then we get,
=> 79/10 = 7 9/10
Therefore, the total distance is 7 9/10 miles.
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Find an equation of the tangent line to the graph of y = B(x) at x = 25 if B(25) = −1 and B ′(25) = − 1 5 .
The most appropriate choice for tangent to a curve will be given by-
[tex]3x + 2y = 73[/tex] is the required equation of tangent.
What is tangent to a curve?
Tangent to a curve at a point is the straight line that just touches the curve at that point.
Equation of tangent to a curve at a point [tex](x_1, y_1)[/tex] is given by
[tex]y - y_1 = \frac{dy}{dx}|_{(x_1,y_1)} (x - x_1)[/tex]
Here,
y = B(x), B(25) = -1, B'(25) = -1.5
Equation of tangent =
[tex](y - (-1)) = -1.5(x - 25)[/tex]
[tex]y + 1=-1.5x +37.5\\y + 1 = -\frac{3}{2}x + 37.5\\2y + 2 = -3x + 75\\3x+2y = 75-2\\3x+2y=73[/tex]
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A student is trying to solve the set of two equations given below:Equation A: x + z = 6Equation B: 3x + 2z = 1Which of the following is a possible step used in eliminating the z-term
Answer:
multiply equation A by -2
Which expression uses the commutative property to make it easier to evaluate
Let's begin by listing out the given information:
The commutative property states that for addition, the order in which we add numbers does not change their sum & for multiplication, the order in which we multiply does not change their product.
Mathematically expressed as:
[tex]\begin{gathered} x+y+z=y+z+x \\ x\cdot y\cdot z=y\cdot z\cdot x \end{gathered}[/tex]Therefore, the commutative property of this is:
[tex]\begin{gathered} \frac{4}{3}\cdot\frac{1}{5}\cdot18=\frac{4}{3}\cdot18\cdot\frac{1}{5} \\ \Rightarrow\frac{4}{3}\cdot18\cdot\frac{1}{5} \\ \end{gathered}[/tex]Therefore, Option D is the correct answer
name a 2 digit odd number that is composite
We should know that:
All the odd integers which are not prime are odd composite numbers. Examples of composite odd numbers are 9, 15, 21, 25
4y+3+6xWhat is the numerical coefficient of the first term?What is the constant term?
We are given the following expression:
[tex]4y+3+6x[/tex]The numerical coefficient is the number that multiplies a variable, in this case, the first variable is "y" and the numerical coefficient is 4.
The constant in an expression is the number that does not multiply any variable, in this case, the constant is 3.
find the circumference of the circle L. Write your answer as a decimal, rounded to the nearest hundredth. the circumference is blank feet
Let us call C the circumference of the circle.
We know that the ratio of angle to circumference must be
[tex]\frac{106}{360}=\frac{1.25}{C}[/tex]cross multipication gives
[tex]106(C)=360\cdot1.25[/tex]Dividing both sides by 106 gives
[tex]C=\frac{360\cdot1.25}{106}[/tex][tex]C=4.25[/tex]which is our answer!
Equation of line passing thru point -6,-3 and perpindicular to JK -2,7 and 6,5
Equation of the line passing through the point (-6,-3) and perpendicular to the line passing through (-2,7) and (6,5) is y = 4x -19.
First we will find the slope of the line passing through (-2,7) and (6,5).
Slope of the line = (5-7)/(6-(-2)) = -2/8 = -1/4.
We know that,
Product of the slopes of two perpendicular lines = -1.
Let the equation of the line we have to find be y = mx + c.
Slope will be m.
Hence, we can write,
m*(-1/4) = -1
m = -1*(-4/1)
m = 4
Putting (6,5) and m = 4 in y = mx + c , we get
5 = 4*(6) + c
5 = 24 + c
c = 5 - 24 = -19
Hence, the equation of the line is:-
y = 4x -19
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5. Prove triangle ABD is congruent to triangle CDB. DC|AB D
My Marjorie made for rates and 6 hours and 6 wreaths and 9 hours what is the constant of proportionality
The constant of proportionality is computed as follows:
[tex]k=\frac{\text{number of wreaths}}{\text{ number of hours}}[/tex]Assuming that 6 wreaths correspond to 9 hours, the constant of proportionality is:
[tex]k=\frac{6\text{ wreaths}}{9\text{ hours}}=\frac{2}{3}\frac{wreath}{hour}[/tex]Identify the composition that is represented by:r (90, O). T (-2, 4)A translation left 2, up 4 and then a reflection of 90°O A rotation of 90° and then a translation left 2, up 4.A reflection of 90° and then a translation left 2, up 4.O A translation of left 2, up 4 and then a rotation of 90°.
ANSWER:
A rotation of 90° and then a translation left 2, up 4.
STEP-BY-STEP EXPLANATION:
Since r (90, 0) is the first and means a 90 ° rotation and that T (-2, 4) is a translation of 2 units to the left (because it is negative) and 4 units up (because it is positive) , the answer is the option "A rotation of 90° and then a translation left 2, up 4."
a bottle of ketchup holds 0.95 liters how maney milliliters does it hold?
Explanation:
The relation between liters and milliliters is:
[tex]1\text{ liter}=1000\text{ milliliters}[/tex]we have to multiply the liters by 1000
Answer:
The answer is 950 milliliters
(4, 2); slope = 3 writing linear equations given point and slope
The standard equation of a line in point-slope form is expressed as;
y-y0 = m(x-x0) where;
m is the slope
(x0, y0) is the point on the line
Given
(x0, y0) = (4, 2)
From the coordinate;
x0 = 4 and y0 =2
slope m = 3
Substitute the given parameters into the equation as shown;
y-2 = 3(x-4)
Hence the linear equations given the point and slope id expressed as y-2 = 3(x-4)
A car is purchased for 19,00. Each year it loses 25% of its value. After how many years will the car be worth 5800. dollars or less? Write the smallest possible whole number answer
5 years
Explanation
Given
Cost price = $ 19,000
Depreciation yearly is % 25
What to find
Time to depreciate to $ 5, 800 or less
Step- by - Step Solution
After first year St
[tex]\begin{gathered} 25\%\text{ }of\text{ 19,000} \\ \\ \frac{25}{100}\times\text{ 19,000 = 4,750} \\ \\ 19,000\text{ - 4750 = 14, 250} \end{gathered}[/tex]After the year the second year
[tex]\begin{gathered} \frac{25}{100}\text{ }\times\text{ 14, 250 = 3,562.5} \\ \\ 14,250\text{ - 3,562.5 =10, 687.5} \end{gathered}[/tex]After Third year
[tex]\begin{gathered} 25\%\text{ of 10,687.5} \\ \\ \frac{25}{100\text{ }}\times\text{ 10, 687.5 = 2,671.875} \\ \\ 10,687.5\text{ - 2,671.875 = 8,015.625} \\ \end{gathered}[/tex]After Fourth year
[tex]\begin{gathered} 25\%\text{ of 8,015.625} \\ \\ \frac{25}{100}\times\text{ 8,015.625 = 20003.906} \\ \\ 8\text{,015.625 - 20,003.906 = 6011.719} \end{gathered}[/tex]After Fifth year
[tex]\begin{gathered} 25\%\text{ of 6011.719} \\ \\ \frac{25}{100}\times\text{ 6011.719 = 1502.930} \\ \\ 6011.719-1502.930\text{ = 4508.789} \end{gathered}[/tex]Therefore after 5 years the car be worth 5800. dollars or less Therefore after 5 years the car be worth 5800. dollars or less
a coral reef grows 0.15 m every week. how much does it grow in 13 weeks? in centimeters
Given:
A coral reef grows 0.15 m every week.
Coral reefs grow 13 times 0.15m for 13 weeks.
[tex]=13\times0.15m[/tex][tex]=1.95\text{ m}[/tex]We need to convert m into cm.
[tex]1m=100cm[/tex]Multiply 1.95m by 100, we get
[tex]1.95\times100=195cm[/tex]Hence a coral reef grows 195cm in 13 weeks.
A total of $5000 is invested: part at 5% and the remainder at 15%. How much is invested at each rate if the annual interest is $540?
Answer
The amount invested at
Step-by-step explanation:
The total amount invested is $5000
Let x be the investment at 5%
Let y be the investment at 15%
Mathematically, this can be expressed as
x + y = 5000 -- equation 1
Since the first part of the investment is invested at 5% and the second part is at 15%
0.05x + 0.15y = 540 --------- equation 2
The systems of equations can be solved simultaneously using the substitution method
x + y =5000 ----- equation 1
0.05x + 0.15y = 540 ------ equation 2
Isolate x in equation 1
x = 5000 - y
Substitute the value of x into equation 2
0.05(5000 - y) + 0.15y = 540
Open the parenthesis
250 - 0.05y + 0.15y = 540
Collect the like terms
-0.05y + 0.15y = 540 - 250
0.1y = 290
Divide both sides by 0.1
0.1y/0.1 =290/0.1
y = $2900
Recall that equation 1 is
x + y = 5000
y = $2900
x = 5000 - y
x = 5000 - 2900
x = $ 2100
Hence, the investment at 5% is $2100 and the investment at 15% is $2900
When you multiply possible options in each scenario to get the total number of combinations, this is referred to as the fundamental _____ principle.
Fundamental counting principle.
It is also called the counting rule, applying this principle we can know the number of outcomes by multiplying the options of each event together.
Elana has 80 unit squares. What is the volume of the largest cube she can build with them? Need to show work to explain to my son, having a hard time with this.
Answer: The largest cube has volume of 64 cubic units, and the sides are 4 units long.
Step-by-step explanation:
Elena has 80 unit cubes and she has to build the largest cube using the unit cubes she has
Unit cube has a dimension of 1 unit on each side (Cube has all sides equal)
To make the largest cube, she needs to calculate the maximum volume which is near 80 units of cubes
Therefore,
We have a cube with each side 4 units whose volume is 64 and a cube with each side 5 units whose volume is 125
Elena has only 80 unit cubes to build the maximum-sized cube
Therefore she will be able to build a cube with each side as 4 units with a volume of 64 units with 16 spare cubes
I need help answering this if you can show your work to the be good
Let:
x = Number of sodas purchased
y = Number of hamburgers purchased
The food truck charges $3 for sodas, so the total cost for sodas will be:
3*x=3x
also, it charges $8 for each hamburger, hence, the total cost for hamburgers will be:
8*y = 8y
Since Jack wants to spend no more than $30, the total cost must be less or equal than $30:
[tex]\begin{gathered} \text{Total cost }\leq\text{ 30} \\ \text{Total cost = total cost for sodas+total cost for hamburgers} \\ 3x+8y\le30 \end{gathered}[/tex]Point B is located at -2. Points C and D are each 8 units away from point B. Where are C and D located?
They are located 8 units away, so one has to be away in the left direction and the other one in the right direction
[tex]\begin{gathered} \text{ - 2 - 8 = -10 } \\ \text{ - 2 + 8 = 6} \end{gathered}[/tex]So, C and D are located at -10 and 6
Let f(x) = 2x
. Suppose that a new function g(x) is created by taking the
graph of f(x) and performing the following transformations:
• Reflection in the x-axis
• Reflection in the y-axis
• Vertical stretch by a factor of 3
• Translation up 2 units
• Translation right 3 units. [3, 2 marks]
a) Find a possible equation for g(x).
Assume that a new function g(x) is created by taking the graph of f(x) and performing the following transformations: vertical stretch by a factor of 3
What is meant by Reflection?A reflection is the shape's mirror image. The line of reflection is formed when an image reflects through a line. A figure is said to reflect another figure when every point in one figure is equidistant from every point in another figure. The reflected image should be the same shape and size as the original, but it should face in the opposite direction. Translation can also occur as a result of changes in position. The original image is referred to as the pre-image, and its reflection is referred to as the image. The pre-image and image are represented by ABC and A'B'C', respectively. The coordinate system may be used in the reflection transformation (X and Y-axis).To learn more about Reflection, refer to:
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