The width of the plywood = 23/8 ft
The two rectangular pieces of plywood had equal widths.
The length of first rectangular piece = 6 ft
The length of second rectangular piece = 5 1/2 ft = 11/2 ft
The two pieces are joined to make a single rectangular stage.
Then the total length of the stage = 6 + 11/2 = 23/2 ft
Now area of the rectangular stage = 66 1/8 = 529/8 square feet.
⇒ length x width = 529/8
⇒ 23/2 x width = 529/8
⇒ width = 529/8 x 2/23 = 23/4 ft
Let 'x' be the width of a rectangular plywood.
Then 2x = width of the stage
⇒ 2x = 23/4
⇒ x = 23/8 ft
Hence width of the plywood = 23/8 ft
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1 (a). Determine if each of the following is true or false. Explain your reasoning.i. There are 12 cubic inches in a cubic foot.ii. There are 144 squares inches in a square foot. iii. If I triple the length and width of a rectangle, then the area increase by a factor of 3.iv. If I triple the length and width and height of a cube, then the volume increases by a factor of 27.
1 cubic foot is equivalent to 1728 cubic inches, this is why the statement is false.
(ii)1 square foot is equivalent to 144 square inches, so the second statement is also false.
(iii)The third statement is also false because if we triple both dimensions of a rectangle, the area will be increased by a factor of 9.
[tex]A=3w\times3l=9wl[/tex](iv)This statement is true because when we multiply 3x3x3 we actually get a factor of 27
[tex]V=3w\times3l\times3h=27\text{wlh}[/tex]4y+3z=19
-x+z=27
x-3y=-19
Solve the system of equations
Answer:
x = -262/13, y = -5/13, z = 89/13
Step-by-step explanation:
Solve the following system:
{3 z + 4 y = 19 | (equation 1)
z - x = 27 | (equation 2)
-3 y + x = -19 | (equation 3)
Swap equation 1 with equation 2:
{-x + 0 y + z = 27 | (equation 1)
0 x + 4 y + 3 z = 19 | (equation 2)
x - 3 y + 0 z = -19 | (equation 3)
Add equation 1 to equation 3:
{-x + 0 y + z = 27 | (equation 1)
0 x + 4 y + 3 z = 19 | (equation 2)
0 x - 3 y + z = 8 | (equation 3)
Add 3/4 × (equation 2) to equation 3:
{-x + 0 y + z = 27 | (equation 1)
0 x + 4 y + 3 z = 19 | (equation 2)
0 x + 0 y + (13 z)/4 = 89/4 | (equation 3)
Multiply equation 3 by 4:
{-x + 0 y + z = 27 | (equation 1)
0 x + 4 y + 3 z = 19 | (equation 2)
0 x + 0 y + 13 z = 89 | (equation 3)
Divide equation 3 by 13:
{-x + 0 y + z = 27 | (equation 1)
0 x + 4 y + 3 z = 19 | (equation 2)
0 x + 0 y + z = 89/13 | (equation 3)
Subtract 3 × (equation 3) from equation 2:
{-x + 0 y + z = 27 | (equation 1)
0 x + 4 y + 0 z = -20/13 | (equation 2)
0 x + 0 y + z = 89/13 | (equation 3)
Divide equation 2 by 4:
{-x + 0 y + z = 27 | (equation 1)
0 x + y + 0 z = -5/13 | (equation 2)
0 x + 0 y + z = 89/13 | (equation 3)
Subtract equation 3 from equation 1:
{-x + 0 y + 0 z = 262/13 | (equation 1)
0 x + y + 0 z = -5/13 | (equation 2)
0 x + 0 y + z = 89/13 | (equation 3)
Multiply equation 1 by -1:
{x + 0 y + 0 z = -262/13 | (equation 1)
0 x + y + 0 z = -5/13 | (equation 2)
0 x + 0 y + z = 89/13 | (equation 3)
Collect results:
Answer: {x = -262/13, y = -5/13, z = 89/13
wo horses start a race at the same time. Horse A gallops at a steady rate of 32 feet per second and Horse B gallops at a steady rate of 28 feet per second. After 5 seconds, how much farther will Horse A have traveled? Explain or show your reasoning.
Answer:
Step-by-step explanation:
Multiply 32 by 5 = 160
Multiply 28 by 5 =140
subtract 140 from 160
Answer Horse A would have traveled 20 feet farther the Horse B
There are 4 consecutive integers with a sum of –278. What is the greatest of the 4 integers?
The greatest of the 4 consecutive integers with a sum of -278 is -68
Let n, n + 1, n + 2 and n + 3 be four consecutive integers.
The sum of four consecutive integers is -278.
⇒ n + (n + 1) + (n + 2) + (n + 3) = -278
⇒ n + n + n + n + 1 + 2 + 3 = -278
⇒ 4n + 6 = -278
⇒ 4n = -278 - 6
⇒ 4n = -284
⇒ n = -284/4
⇒ n = -71
So, the consecutive integers would would be:
n = -71
n + 1 = -70
n + 2 = -69
n + 3 = -68
here, the greatest of the 4 integers is -68
Therefore, the greatest of the 4 consecutive integers with a sum of -278 is -68
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Write an equation for the line parallel to the given line that contains C.
C(4,6); y=x+7
The equation of the parallel line is….
The equation of the parallel line is y = x + 2.
What is Equation of line?
The equation of line with slope m and y intercept at point b is given as;
y = mx + b
Given that;
The point = C(4, 6)
And, equation of line is y = x + 7
Since, Slope of Parallel lines are always same.
So, The slope of the given line is calculated as;
y = x + 7
m = dy/dx = 1
Thus, Slope of parallel lines is 1.
Since, The equation of line is passes through point C (4, 6).
So, The equation of line with slope(m) 1 and point C(4, 6) is;
y - 6 = 1 (x - 4)
y - 6 = x - 4
y = x - 4 + 6
y = x + 2
Thus, The equation of the parallel line is y = x + 2.
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Given the function f(x) = 8x + 7, find each of the following. f(1), f(-9), f(0)
IN THE PLACE OF X YOU INSERT THE NUMBER GIVEN AS F(X<<<) AND SIMPLIFY .
[tex]f(1) = 8(1) + 7 \\ f(1) = 8+ 7 \\ f(1) = 15[/tex]
[tex]f( - 9) = 8( - 9) + 7 \\ f( - 9) = - 72 + 7 \\ f( - 9) = - 65[/tex]
[tex]f(0) = 8(0) + 7 \\ f(0) = 0 + 7 \\ f(0) = 7[/tex]
GOODLUCK !!
Danielle earns $36.80 for 4 hours of yardwork. How much does Danielle earn for 10 hours of yardwork
What is the least common denominator of 1/2x+1=1/4x-6
Answer:
The least common denominator for 1/2 and 1/4 is 4.
1/2 --> 2/4
Step-by-step explanation:
Hope this helps!
Pls brainliest, tysm!
which measurements are equivalent to 3 yards
The equivalent measures to 3 yards are;
108 inches and ; 6 ft 36 inches
Here, we want to get the values of the measurements that are equivalent to 3 yards
To do this, we need to know how to convert between the various measure types
We proceed as follows;
Mathematically, 1 yard is 36 inches; also, 1 yard is 3 feet
So, 3 yards is (3*36) = 108 inches
Also, 3 yards is (3*3) = 9 feet
Also, 1 ft is 12 inches;
So, 6 ft 12 inches is 7 feet
108 inches is as seen above, so 3 yards equal this
3 yards is not 108 feet as calculated above
6 ft 36 inches
36 inches is 3 ft; so by addition; 6 ft 36 inches is 9 ft
So, the correct answers here are 108 inches and 6 ft 36 inches
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The left side of the two-column proof should be filled as follows:
Statements Reasons_______________
k||i Given
m∠4 = m∠5 Alternate Interior Angles Theorem
What are parallel lines?Parallel lines can be defined as two (2) lines that are always the same (equal) distance apart and never meet.
What is the Alternate Interior Angles Theorem?The Alternate Interior Angles Theorem states that when two (2) parallel lines are cut through by a transversal, the alternate interior angles that are formed are congruent. Also, these angles are generally referred to as alternate interior angles.
Additionally, there are four (4) special angle relationships that are typically formed when two parallel lines are intersected by a transversal and these include the following:
Corresponding angles.Same-side interior angles.Alternate interior angles.Alternate exterior angles.Read more on alternate interior angle here: https://brainly.com/question/16638047
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jenny believes that spending one hour studying for economics will increase her grade by 20 points. studying for a second hour will increase her grade by 10 points. she also believes that studying for an hour for history will increase her grade by 15 points, but spending a second hour will increase her grade by only 5 points. jenny has two hours to study. if jenny wants to maximize her scores, what should she do?
If Jenny studies one hour both for economics and history she can gain 10+15=25 points
What is meant by Increasing?Increasing: Growing larger or greater. Therefore, if the derivative of a function is positive, then the function is increasing. Let's consider our example of g(x) = x2. The derivative of g(x) = x2 is g'(x) = 2x. Since we are multiplying x by the positive number 2, it's easy to see that g ' is positive when x is positive and negative when x is negative.
Jenny will receive 15 points if she simply studies economics, which equates to 10 points in the first hour and 5 points in the second.
Jenny will earn 20 points if she exclusively studies history, which equates to 15 points in the first class and 5 points in the second.
Jenny should study economics for one hour, which will get her 10 points, and history for one hour, which will gain her 15 points, for a total of 25 points in the two hours
So we concluded that if Jenny studies one hour both for economics and history she can gain 10+15=25 points
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The graph below represents the number
of containers and liters of water contained
in the containers. What is the constant of
proportionality?
Keenan travels 14 miles per hour. How long does it take him to travel 70 miles? Your answer should be in hours, accurate to at least the
nearest tenth.
Answer: 5 Hours
Step-by-step explanation:
14 miles x 5 hours = 70miles in 5 hours.
Hope this helps!
PLEASE HELP ME I DON'T UNDERSTAND
Answer:
(0, 3)
Step-by-step explanation:
-x+2y=6
-x=6+2y
x=-6+2y
-6+2y+2y=6
-6+4y=6
4y=12
y=3
-x+2(3) = 6
-x+6=6
-x=0
x=0
Answer: 0, 3
The temperature of a day at the end of winter starts in the morning at -2 degrees Fahrenheit. The weather report notes that the temperature increases 10 degrees
by midday. At 5:00 pm, the temperature has doubled since midday. What was the temperature at 5:00 pm?
A 24 degrees
B16 degrees
C-16 degrees
D10 degrees
Answer:
B. 16 degrees
Step-by-step explanation:
First, we find temperature at miday:
- 2 (Temperature at morning) + 10 (Increase in temperature by midday) = 8 degrees (Temperature at midday)
Now, for temperature at 5:00 pm:
8 x 2 (At 5 pm temperature is double since midday) = 16 degrees (Temperature at 5:00 pm)
Answer:
B 16 degrees
Step-by-step explanation:
Find the temperature
We start at -2
We increase 10 degrees by noon
-2 + 10 = 8
at 5pm the temperature doubles
8*2 = 16
Write the plural form of the noun. 1. menu 2. speech 3. theory 4. era Math Write the given number in word form. 9. standard form: 290.1 word form: 10. standard form: 7,035.486 word form: 5. lady 6. mailbox 7. patio 8. apostrophe
Menus, speeches, theories, eras, ladies, mailboxes, patios, apostrophes are the plural forms of all the specified nouns as provided in the question.
What is Word form?The written format or the word format of any number provided is called as its word form.
In this question, we are asked to find out the word form of 290.1 and 7,035.486.
290.1 in word form can be written as Two Hundred and ninety point one.
7,035.486 in word form can be written as Seven thousand and thirty-five point four eight six.
What is Plural form?Any word or noun that has to be described such that it is present more than one in number is represented by its plural form. Almost all of the noun words have their plural forms.
The plural forms of the asked nouns have been specified as above already.
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A rancher is filling a trough for her horses. The trough already contains 25 gallons of water, and the rancher is adding 11 gallons per minute. How long will it take for the trough to have 80 gallons of water?
The time for the trough to have 80 gallons of water is 5 minutes.
What is an equation?A mathematical equation is the statement that illustrates that the variables given. In this case, two or more components are taken into consideration to describe the scenario.
Let the number of minutes be represented as m.
The trough already contains 25 gallons of water, and the rancher is adding 11 gallons per minute. This will be:
25 + 11m =80
Collect like terms
11m = 80 - 25
11m = 55
Divide
m = 55 / 11
m = 5
Therefore, there will be 5 minutes.
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Starting from the origin, what movements do you need to plot the ordered pair (2, -3)?
Here, x coordinate is 2 and y coordinate is -3, so we have to first move two units on right thereafter we will move three units downward.(for better understanding please see the attached graph).
A coordinate plane is formed by the intersection of a horizontal number line and a vertical number line. The number lines intersect at the origin and separate the coordinate plane into four regions called quadrants.
An ordered pair is used to locate a point in a coordinate plane.
ordered pair(P) = (2,-3).
Hence, x coordinate is 2 and y coordinate is -3. we have to first move two units on right thereafter we will move three units downward.
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Which 3 measurements could be the dimensions of a right triangle?
(a² + b² = c²)
Answer:
5, 12, 13
Step-by-step explanation:
let a = 5 , b = 12 , c = 13 , then
5² + 12² = 25 + 144 = 169
13² = 169
so a² + b² = c²
Answer:
3, 4, 5
Step-by-step explanation:
In a right triangle, we have 2 legs and a hypotenuse. The hypotenuse equals c, while the other 2 legs are a and b.
Lets say a = 3, b = 4, and c = 5
The formula is a² + b² = c²
3² + 4² = 5²
9 + 16 = 25
25 = 25
Therefore, 3, 4, and 5 can be dimensions of a right triangle.
A giant tortoise can travel 0.17 miles in 1 hour. At this rate, how long would it take the tortoise to travel 1.1 miles?
It would take the tortoise
hours.
(Type an integer or decimal rounded to one decimal place as needed.)
...
Answer:
1.07
friend me? anyone
Answer:
6.5 hours
Step-by-step explanation:
distance = rate times time
1.1 = .17t t stands for time Divide both side by .17
my calculator shows 6.47058823527 We need to round to one decimal place
time = 6.5 hours or 6 1/2 hours
I need the blank angles answers with the reason of justification please
Answer:
We had this question last week let me check my book real quick.
Evaluate the following equation when x = {1, 2, 3, 4, 5} by filling in the table with the correct values for the function f (x) = (-3)^x
Step-by-step explanation:
In x you can put the value which can given in question.
A shipping container is in the form of a right rectangular prism, with dimensions of 30 ft by 8 ft by 7 ft 3 in. If the container holds 1096 cubic feet of shipped goods, what percent is empty?
As per the volume of a rectangular prism, it is found that 34.76% of the container is empty.
Volume of a rectangular prism
The volume of the rectangle prism is calculated by multiplying the length, breadth and height of the prism.
The formula for the volume of rectangle prism is
V = l x w x h
where
l represents the length
w represents the width
h represents the height
Given,
A shipping container is in the form of a right rectangular prism, with dimensions of 30 ft by 8 ft by 7 ft 3 in.
Here we need to find if the container holds 1096 cubic feet of shipped goods, what percent is empty
According to the given question,
Let us consider the length is 30ft, Width is 8ft and Height is 7ft.
Here the value 3ft refers the depth.
That one is also multiplied with the volume.
Therefore, the volume of the container is
=> 8 x 7 x 30
=> 1680
Therefore, the volume of the container is 1680 cubic feet.
So, here we have to percentage of the empty space for that we have to find the difference of them and convert it into percentage,
=> 1680 - 1096
=> 584
The percent of empty space is,
=> x% of 1680 = 584
=> x% = 584/1680
=> x% = 0.3476
=> x = 34.76
Therefore, 34.76% of rectangular prism container is empty.
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Just the bottom part that’s all :)
To transform is to alter. So, changing any given geometric shape would be considered a geometric transformation.
What does one transformation mean?
A 180° rotation about the origin characterizes the sole transformation. Translation, rotation, reflection, and dilation are the four primary categories of transformation.
The term "Geometric" transformation refers to a group of picture transformations where the geometry of the image is modified without changing the actual pixel values. In general, various actions can be performed on it, but the actual pixel values will not change.
Students get the opportunity to consider fundamental mathematical concepts in novel ways thanks to geometric transformations (e.g., functions whose domain and range are R2). Students can view mathematics as a connected field by using geometric transformations as a framework.
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Shawn borrows $600 to be paid back in one year with 8% simple interest. How much interest will Shawn pay?
Answer:
48
Step-by-step explanation:
0.08 × 600 =48
for the percent you move the decimal forward twice.
1.if the m∠7 = 115° , find the measure of ∠2
Show your work
Answer: The measure of is 115°.
Step-by-step explanation:
Now, assuming those angles are supplementary, then
m<7 + m<2 + 180
Because, supplementary angles sum 180\°, due to their position on a straight angle.
We know by given that m<7 = 115 , replacing this value, we have
115 + m<2 + 180
m<2 = 180 - 115
m<2 + 65
Step-by-step explanation:
What is the y-intercept?
At one store Roberto bought 10 packages of batteries. Each package had 24 batteries. At another store, he bought 10 packages of batteries, but each
PLEASE HELP ME!!! *correct answer will get brainlist*
PLEASE HELP ASAP! What is the rate of change (slope) and the initial value (y-axis) for this table? PLEASE ANSWER BOTH Y AXIS AND SLOPE! And please give an explanation if possible
Answer:
24 and 11
Step-by-step explanation:
See attached worksheet.