A square with side lengths 12 feet. 4 2 feet by 2 feet squares are cut out of each corner of the square.
Find the Area of the Space.[tex] \mathbb{SOLUTION:} [/tex][tex] \bold{A = Length \: x \: Width} [/tex][tex] \bold{A = 12 \: ft \: x \: 4.2 \: ft } [/tex][tex] \blue{\bold{A = 50.4 \: ft} }[/tex][tex] \bold{ A\red{ = 50.4 } \: x \: 2 \: ft} [/tex][tex] \boxed{ \bold{ A = 100.80 ft²}}[/tex]"If the 2 is quantity use multiply it again"
••••••••••••••••••••••••••••••••••••••••••••••••NOTE:The way to solve a square area is by measuring the length and width of your area then multiplying those two numbers together to get the area in feet squared (ft2).
"Problem has been solve"
(ノ^_^)ノ
[tex]\large\bold{SOLUTION} \\ [/tex]
GIVEN :-
A square with side lengths 12 feet.4.2 feet by 2 feet squares are cut out of each corner of the square .FIND :-
Find the area of the space that needs to be covered .By finding the area of the space that needs to be covered we must use multiplication and multiply the given measurements .
[tex] \bold{Formula:}[/tex]
[tex] \qquad \boxed{ \bold{ \: \: Area = Length \times Width \: \: }}[/tex]
Now let's start solving :-
[tex] \quad \sf \implies{Area = Length \times Width} \\ [/tex]
[tex] \quad \sf \implies{Area = 12ft \times 4.2ft} \\ [/tex]
[tex] \quad \sf \implies{Area = 12feet \times 4.2ft = \pmb{50.4 ft}} \\ [/tex]
[tex] \quad \sf \implies{Area = 50.4ft \times 2ft = \pmb{100.80ft^2}} \\ [/tex]
Therefore, the area of the space that needs to be covered is 100.80ft² .
[tex] \underline{ \rule{185pt}{3pt}}[/tex]
What is m∠C?
Enter your answer in the box.
Answer:
60
Step-by-step explanation:
Total degree of triangle interior angles is 180
So x+2x+3x=180
6x=180
x=30
Measurement of angle C is 2x which is 60 degree
Timothy is 13 5/6 years old. Camden is 1 1/3 years younger than Timothy and Jane is 1 1/4 years younger than Camden. How old is Jane?
Answer:
Jane is 11 1/4 years old.
Step-by-step explanation:
Subtract all of the numbers given.
[tex]13\frac{5}{6} -1\frac{1}{3} -1\frac{1}{4}[/tex].
To subtract this, we need to find a common denominator.
A common denominator in this situation is 12. To do this multiply the 5 and the 6 of 5/6 by 2. Multiply the 1 and the 3 of 1/3 by 4. And multiply the 1 and the 4 1/4 by 3.
The new expression will look like this:
[tex]13\frac{10}{12} -1\frac{4}{12} -1\frac{3}{12}[/tex].
Now we can subtract.
[tex]13\frac{10}{12} -1\frac{4}{12} -1\frac{3}{12}=11\frac{3}{12}[/tex]
Reduce the answer.
[tex]11\frac{3}{12}=11\frac{1}{4}[/tex]
In decimal form 11.25
Hope this helps!
If not, I am sorry.
HELP ME PLEASEEE
Beatrice writes down every expression that appears in this problem set, one after the other, linking them with
+ signs between them. She is left with one very large expression on her page. Is that expression a polynomial expression? That is, is it algebraically equivalent to a polynomial?
What if she wrote - signs between the expressions instead?
What if she wrote × signs between the expressions instead?
Is that expression a polynomial expression?
yes because they are terms linked into one expression.
What if she wrote - signs between the expressions instead?
it would still be considered a polynomial.
What if she wrote × signs between the expressions instead?
no because it would be one huge term
Complete the tasks to subtract the polynomials vertically. (1.3t3 0.4t2 – 24t) – (0.6t2 8 – 18t) what is the additive inverse of the polynomial being subtracted?
The difference of the polynomials is [tex]1.3t^{3}-0.2t^{2}-6t-8[/tex] and the additive inverse of the polynomial being subtracted is [tex]-0.6t^{2} +8+18t[/tex].
The given polynomials are [tex](1.3t^{3}+0.4t^{2} -24t )[/tex] and [tex]0.6t^{2} +8-18t[/tex].
We need to find the additive inverse of the polynomial being subtracted.
What is additive inverse?In mathematics, the additive inverse of a number a is the number that, when added to a yields zero. This number is also known as the opposite, sign change, and negation.
Now, [tex](1.3t^{3}+0.4t^{2} -24t )-(0.6t^{2} +8-18t)[/tex]
[tex]=1.3t^{3}+0.4t^{2}-0.6t^{2}-24t+18t-8[/tex]
[tex]=1.3t^{3}-0.2t^{2}-6t-8[/tex]
The additive inverse of the polynomial being subtracted is [tex]-0.6t^{2} +8+18t[/tex].
Therefore, the difference of the polynomials is [tex]1.3t^{3}-0.2t^{2}-6t-8[/tex] and the additive inverse of the polynomial being subtracted is [tex]-0.6t^{2} +8+18t[/tex].
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Please help!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!! i will give u brainliest
Answer: The answer is x = +/- [tex]\sqrt{y+1}[/tex].
Step-by-step explanation: You can solve this by simply rearranging the equation to make x by itself.
-[tex]x^{2}[/tex] = -y - 1
Then cancel out the -1 by dividing it through to obtain.
[tex]x^{2} =y+1[/tex]
The final step is to square root both sides to get rid of the exponent.
x = [tex]\sqrt{y+1}[/tex]
This should be the answer since square roots have a +/-.
5. Walker is reading a book that is 792 pages. He reads
15 pages a day during the week, and 25 pages a day
during the weekend. After 5 weeks of reading, how
many pages does Walker still have left to read before
he finishes the book?
Let r represent the pages left to read.
Equation:
Walker has
to read.
pages left
To form equations from word problems, we can derive mathematical operations as well as variables from the given information.
In this case, each time Walker reads a certain number of pages, we subtract that from the total number of pages left to know how many pages is left to read.
Solving the QuestionLet r represent the pages left to read.
792 pages in total
⇒ r = 792Walker reads 15 pages a day during the week and 25 pages a day during the weekend.
There are 5 weekdays, and he reads 15 pages each of those days. ⇒ r = 792 - 5×15There are 2 weekend days, and he reads 25 pages each of those days.5 weeks have passed
Multiply the terms representing the number of pages he reads a week by 5, for 5 weeks.r = 792 - (5×15 + 2×25)×5
Point T is located at (6, –2) and point S is located at (1, 13). What are the coordinates of the point that is `\frac{4}{5}` of the way from T to S?
The coordinates of the point that is 4/5 of the way from T to S is (2,10)
How to determine the coordinates of the point?The given parameters are:
T = (6,-2)
S = (1,13)
Location = 4/5
The location 4/5 means
Ratio, m : n = 4 : 1
The coordinate is then calculated as:
[tex](x,y) = \frac{1}{m +n} * (mx_2 + nx_1,my_2 + ny_1)[/tex]
This gives
[tex](x,y) = \frac{1}{4 +1} * (4 * 1 + 1 * 6 , 4 * 13 + 1 * -2)[/tex]
Evaluate
[tex](x,y) = \frac{1}{5} * (10 , 50)[/tex]
This gives
(x,y) = (2,10)
Hence, the coordinates of the point that is 4/5 of the way from T to S is (2,10)
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8.
(05.04 LC)
The amount of money in tips earned by four restaurant servers waiting on 10 tables is represented by the following data sets.
Alyssa {3, 6, 2, 8, 12, 14, 5, 7, 7, 8}
Bryant {9, 2, 7, 50, 0, 5, 2, 8, 6, 8}
Camila {1, 9, 10, 3, 0, 12, 10, 9, 8, 2}
Devon {4, 2, 8, 15, 20, 7, 5, 0, 6, 2}
Which data set has the greatest interquartile range? (1 point)
Alyssa
Bryant
Camila
Devon
Camila's data set has the greatest interquartile range and the value of IQR = 8 option third is correct.
What is the range?It is defined as the difference between the maximum value in the data set to the minimum value in the data set.
We have:
The amount of money in tips earned by four restaurant servers waiting on 10 tables is represented by the following data sets:
Alyssa {3, 6, 2, 8, 12, 14, 5, 7, 7, 8}
Bryant {9, 2, 7, 50, 0, 5, 2, 8, 6, 8}
Camila {1, 9, 10, 3, 0, 12, 10, 9, 8, 2}
Devon {4, 2, 8, 15, 20, 7, 5, 0, 6, 2}
The IQR for Alyssa:
IQR = Q3 - Q1
IQR = 8 - 5 = 3
The IQR for Bryant:
IQR = Q3 - Q1
IQR = 8 - 2 = 6
The IQR for Camila:
IQR = Q3 - Q1
IQR = 10 - 2 = 8
The IQR for Devon:
IQR = Q3 - Q1
IQR = 8 - 2 = 6
Thus, Camila's data set has the greatest interquartile range and the value of IQR = 8 option third is correct.
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A piece of copper wire of length 200 m has a diameter of 1.2 mm.
(a) Find the volume of the wire.
(b) If the density of copper is 8.9 g/cm3, find the mass of the wire.
The volume of the copper wire is 226.080 cm³ and the mass of the wire is 2,012.112 g/cm³.
Given that, the length of copper wire=200 m=200000 mm and the diameter of the copper wire=1.2 mm.
We need to find the volume of the copper wire.
What is the formula to find the volume of the cylinder?The formula to find the volume of a cylinder is πr²h.
Now, the volume of the copper wire=πr²h=[tex]\frac{22}{7} \times (0.6)^{2} \times 200000=2,26,080[/tex] mm³=226.080 cm³
If the density of copper is 8.9 g/cm³, find the mass of the wire.
We know that [tex]Density=\frac{Mass}{Volume} }[/tex].
⇒8.9 g/cm³=[tex]\frac{Mass}{226.080}[/tex]
⇒Mass=2,012.112 g/cm³
Therefore, the volume of the copper wire is 226.080 cm³ and the mass of the wire is 2,012.112 g/cm³.
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The median height of 11 footballers is 1.85m.
Only one footballer has a height of 1.85m
How many footballers have a height under 1.85m
William can pack 60 toys in 4 hours. Find the unit rate with which he packs toys.
O14 toys/hour
O13 toys/hour
15 toys/hour
16 toys/hour
What is the area of the triangle pictured?
A. 612 in2
B. 540 in2
C. 555 in2
D. 531 in2
Answer:
D. 531[tex]in^{2}[/tex]
Step-by-step explanation:
I suppose these are rectangles and not triangles.
Area of Rectangle = Length x Breadth
Area of Large Rectangle = 21 x 18
= 378[tex]in^{2}[/tex]
Area of Small Rectangle = 17 x 9
= 153[tex]in^{2}[/tex]
Total Area = Area of Large Rectangle + Area of Small Rectangle
= 378 + 153
= 531[tex]in^{2}[/tex]
does someone mind helping me with this question? Thank you!
Answer:
[tex]\bf -20[/tex]Step-by-step explanation:
[tex]\bf 2(xy-7)[/tex] [tex]\bf when[/tex] [tex]\bf x=-1/y=3[/tex]
Substitute with x and y with 3:-
[tex]\bf 2\left(\left(-1\right)(3)-7\right)[/tex]
First, Multiply -1 and 3 = -3
[tex]\bf 2(-3-7)[/tex]
Subtract 7 from -3 = -10
[tex]\bf 2(-10)[/tex]
Multiply 2 and -10 = -20
[tex]\bf -20[/tex]
______________________Find the greatest common factor of these two expressions.
28y^7x^2 and 8y^8v^4x^6
Answer:
4y⁷x²
Step-by-step explanation:
Finding GCF:Prime factorize each expression.
28y⁷x² = 2 * 2 * 7 * y⁷ * x²
8y⁸v⁴x⁶ = 2 * 2 * 2 * y⁸ * v⁴ * x⁶
GCF = 2 * 2 *y⁷*x²
= 4y⁷x²
What is an important similarity between the uniform and normal probability distributions?
The important similarity between the uniform and normal probability distributions is that the mean and the median of both distributions are equal
How to determine the important similarity?In a normal probability distribution, we have:
Mean = Median
In a uniform probability distribution, we have:
Mean = Median
This means that:
In both distributions, the mean and the median are equal
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The function f(x) is shown in this graph.
The function g(x) = -6x + 3.
-5
Compare the slopes and y-intercepts.
what is the angle between a=7i+3j and b=4i-j
[tex]a\cdot b=(7)(4)+(3)(-1)=25\\\\|a|=\sqrt{7^{2}+3^{2}}=\sqrt{58}\\\\|b|=\sqrt{4^{2}+(-1)^{2}}=\sqrt{17}\\\\\cos \theta=\frac{25}{\sqrt{58}\sqrt{17}}\\\\\theta=\cos^{-1} \left(\frac{25}{\sqrt{58}\sqrt{17}} \right) \approx 37.235^{\circ}[/tex]
Alex defeated 10 gyms today! She started with four hundred and forty coins and now has five hundred and forty coins
Find the Percent of increase
The percentage increase is 22.72%
How to determine the percentage increase?The given parameters are:
Initial = 440 coins
Final = 540 coins
The percentage increase is calculated as:
%Increase = (Final - Initial)/Initial * 100%
So, we have:
%Increase = (540 - 440)/440 * 100%
Evaluate the difference
%Increase = 100/440 * 100%
Evaluate the quotient
%Increase = 0.2272 * 100%
Evaluate the product
%Increase = 22.72%
Hence, the percentage increase is 22.72%
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Analyze the diagram below and complete the instructions that follow.
Solve for y.
11
21
24
42
The value of y is 11 if the measure of the angle (x + 6y) is 90 degree and x = 24 option first is correct.
What is a perpendicular line?Lines that intersect at a right angle are named perpendicular lines. Lines that are always the same distance apart from each other known as parallel lines.
We have a perpendicular line shown in the picture.
The measure of the angle (4x - 6) is equal to 90 degree.
4x - 6 = 90
4x = 96
x = 24
Similarly, the measure of the angle (x + 6y) is equal to 90 degree:
x + 6y = 90
Plug x = 24
24 + 6y = 90
y = 11
Thus, the value of y is 11 if the measure of the angle (x + 6y) is 90 degree and x = 24 option first is correct.
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the answer choices is A. x B. z C. w D.y pls help me, I greatly appreciate all the help I'm getting
The graphed that represents the new function with the same slope and y-intercept is: graph Y.
What is the Slope and Y-intercept of a Function?Slope = rise/run along a line.
Y-intercept is the y-value of the point on the y-axis that the line intercepts.
Slope of the function given = rise/run = 2/1 = 2
2 multiplied by 1/2 = 2/2 = 1.
Y-intercept of the given function is: 1
1 increased by 3 units is: 1 + 3 = 4
The slope of graph Y = rise/run = 2/2/ = 1
The y-intercept is also 4
Therefore, the answer is: Graph Y
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Describe and correct the error in solving the absolute value inequality.
The steps are shown below: -5<x<1
What is inequality?A statement of an order relationship—greater than, greater than or equal to, less than, or less than or equal to—between two numbers or algebraic expressions.
Given:
|x +2 | <-3
If we take the module is positive,
x+2 -2 < -3-2
x < -5
If we take the module is negative,
-( x+2) < -3
-x -2 < -3
-x -2 +2 < -3 +2
-x< -1
x>1
Combining the inequalities,
-5<x<1
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Find the measure of ZDCF. C F mDF = 49 G E MEG = 127 Find the measure of angle DCF
Answer:
Step-by-step explanation:
Comment
If two secants intersect outside a circle (as these two do) then the angle at which they meet is 1/2 the difference between the intersected arcs. Put much simpler <DCF = 1/2 (arc EG - arc DF)
Givens
Arc EG = 127
Arc DF = 49
Solution
<DCF = 1/2(127 - 49)
<DCF = 1/2(78)
<DCF = 39
which expresion is equivalent to the given expresion
(3m-4)³(3m³)
The equivalent expression of [tex](3m^{-4})^3 * (3m^3)[/tex] is [tex]729m^{-9}[/tex]
How to determine the equivalent expression?The expression is given as:
[tex](3m^{-4})^3 * (3m^3)[/tex]
Expand the brackets
[tex]27m^{-12} * 27m^3[/tex]
Apply the law of indices
[tex]729m^{-12+3}[/tex]
Evaluate the sum
[tex]729m^{-9}[/tex]
Hence, the equivalent expression of [tex](3m^{-4})^3 * (3m^3)[/tex] is [tex]729m^{-9}[/tex]
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halp
What is the relationship between \blueD{\angle a}∠astart color #11accd, angle, a, end color #11accd and \greenD{\angle b}∠bstart color #1fab54, angle, b, end color #1fab54?
Answer:
D. None of the above.
Step-by-step explanation:
Supplementary angles must add up to 180 degrees.
Complementary angles must add up to 90 degrees.
Vertical angles are opposite of each other.
Hope this helps!
If not, I am sorry.
Drag each response to the correct location on the table. Each response can be used more than once, but not all responses will be used.
Consider the two exponential equations shown. Identify the attributes for each equation to complete the table.
8.9%
250 89%
W
40 =
Decay
250 (0.89)
Initial Value::
Growth or Decay::
Growth/Decay Rate::
11%
F
40
Growth
250 =
111%
40(1.11)
Initial Value:
Growth or Decay:
Growth/Decay Rate::
The equation is y = 250(0.89)^x and the decay rate is 11%.
How to calculate the values?The initial value will be:
= 250(0.89)^x
= 250(0.89^0)
= 250
The decay rate will be:
= 1 - 0.89
= 0.11
= 11%
In conclusion, the equation is y = 250(0.89)^x and the decay rate is 11%.
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Measure the height of the palm tree indirectly using a mirror that is placed on the ground a certain distance away from the tree. The distance from the
mirror to the base of the palm tree is 2.5 m and the distance from the mirror to the person's foot is 0.5 m. The person is 1.78 m tall.
Answer:
(b) 8.9 m
Step-by-step explanation:
The mirror ensures that angle 1 is congruent to angle 2, so the triangles in the diagram are similar. The ratios of height to mirror distance are proportional.
__
setupThe height of the object is proportional to its distance from the mirror, so we have ...
(tree height)/(tree-to-mirror) = (person height)/(person-to-mirror)
(tree height)/(2.5 m) = (1.78 m)/(0.5 m)
solutionMultiplying this proportion by 2.5 m, we find ...
tree height = (2.5 m)(1.78/0.5) = 8.9 m
The height of the palm tree is 8.9 meters.
Please help fast!!!
Multiply and reduce to lowest terms. Convert into a mixed number if necessary.
5 x 2/3 =
x= help me please thank u :)
Step-by-step explanation:
the product of segments theorem :
products of segments of intersecting chords are equal.
the 2 chords helping us are
the "4 + 25" chord.
the "x + x" chord (that connects then outwards to the 20 segment).
so, based on that theorem
4 × 25 = x × x
100 = x²
x = sqrt(100) = 10
Question 2(10 pos
A football quarterback has 2 more chances to throw a touchdown before his team is forced to punt the ball. He mates the receiver the first trew of the time When his fest throw is incomplete he misses the receiver on the second throw 10% of the tame What is the probability of not throwing me ball to a receiver on either throw?
The chance of not throwing the ball to a receiver on either throw is 0.0375, or 3.75 per cent.
What is probability?Probability is defined as the ratio of the number of favourable outcomes to the total number of outcomes in other words the probability is the number that shows the happening of the event.
This is event A when he misses the first throw. P(A) = 25%, or 0.25 Because event B takes place only after event A. When he misses on the second throw, event B occurs. P(B/A) = 15% or 0.15
P(A[tex]\cap[/tex]B) = P(A) P(B/A) P(A[tex]\cap[/tex]B)
P(A[tex]\cap[/tex]B) = (0.25)x(0.15) P(ANB)
P(A[tex]\cap[/tex]B) = 0.0375
Therefore the chance of not throwing the ball to a receiver on either throw is 0.0375, or 3.75 per cent.
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Giving my all points away! What is the Value of log5512, when log 2 = 0.3010 and log 3 = 0.4771?
[tex]\\ \rm\Rrightarrow log_5512[/tex]
[tex]\\ \rm\Rrightarrow log_52^9[/tex]
[tex]\\ \rm\Rrightarrow 9log_52[/tex]
Use change of base[tex]\\ \rm\Rrightarrow 9\dfrac{log2}{log5}[/tex]
[tex]\\ \rm\Rrightarrow 3.876[/tex]
If your question is something different let me know by which I can change my answer
Answer:
3.876 (3 d.p.)
Step-by-step explanation:
Given:
[tex]\log_{10}2=0.3010[/tex][tex]\log_{10}3=0.4771[/tex]Please note: The question gives two values of log base 10 which should be used to help find the value of [tex]\log_5512[/tex]
Log Law: Change of Base
[tex]\log_ba=\dfrac{\log_xa}{\log_xb}[/tex]
Change the given expression to log base 10:
[tex]\implies \log_5512=\dfrac{\log_{10}512}{\log_{10}5}[/tex]
Replace 512 with 2⁹, and 5 with 10/2:
[tex]\implies \dfrac{\log_{10}{2^9}}{\log_{10}\frac{10}{2}}[/tex]
[tex]\textsf{Apply the Power Log law}: \quad \log_ax^n=n\log_ax[/tex]
[tex]\implies \dfrac{9\log_{10}{2}}{\log_{10}\frac{10}{2}}[/tex]
[tex]\textsf{Apply the Log Quotient law}: \quad \log_a\frac{x}{y}=\log_ax - \log_ay[/tex]
[tex]\implies \dfrac{9\log_{10}{2}}{\log_{10}10-\log_{10}2}[/tex]
[tex]\textsf{Apply log law}: \quad \log_aa=1[/tex]
[tex]\implies \dfrac{9\log_{10}{2}}{1-\log_{10}2}[/tex]
Given:
[tex]\log_{10}2=0.3010[/tex]Substitute this into the expression and simplify:
[tex]\implies \dfrac{9(0.3010)}{1-0.3010}[/tex]
[tex]\implies \dfrac{2.709}{0.699}[/tex]
[tex]\implies 3.876\:(\sf 3\: d.p.)[/tex]