How to draw A Area Model For 29×56
Answers
First, notice that:
[tex]29\text{ x }56=1624[/tex]now, we can write 29 as 20 + 9 and 56 as 50 + 6, so, we can draw the following rectangles:
Then, if we calculate the area of each of the rectangles, we get the following:
then, if we add all the areas together, we get:
[tex]1000+120+450+54=1120+504=1624[/tex]which is the same result as 29 x 56
Related Questions
A rectangle has a diagonal of length 10 cm and a base of length 8 cm . Find its height
Answers
Given:
The length of diagonal of rectangle is d = 10 cm.
The length of base is b = 8 cm.
Explanation:
The relation between length, height and diagonal of rectangle is given by pythagoras theorem. So
[tex]d^2=l^2+h^2[/tex]Substitute the values in the equation to obtain the value of h.
[tex]\begin{gathered} (10)^2=(8)^2+h^2 \\ 100=64+h^2 \\ h=\sqrt[]{100-64} \\ =\sqrt[]{36} \\ =6 \end{gathered}[/tex]So the height of rectangle is 6 cm.
Answer: 6 cm
A rectangular parking lot has length that is 3 yards less than twice its width. If the area of the land is 299 square yards, what are the dimensions of the land?The parking lot has a width of square yards.
Answers
Answer:
• Width = 13 yards
,• Length = 23 yards
Explanation:
Let the width of the parking lot = w yards.
The length is 3 yards less than twice its width.
[tex]\implies\text{Length}=(2w-3)\text{ yards}[/tex]The area of the land = 299 square yards.
[tex]w(2w-3)=299[/tex]We then solve the equation above for w.
[tex]\begin{gathered} 2w^2-3w=299 \\ \implies2w^2-3w-299=0 \end{gathered}[/tex]Factor the resulting quadratic expression.
[tex]\begin{gathered} 2w^2-26w+23w-299=0 \\ 2w(w-13)+23(w-13)=0 \\ (2w+23)(w-13)=0 \end{gathered}[/tex]Solve for w.
[tex]\begin{gathered} 2w+23=0\text{ or }w-13=0 \\ 2w=-23\text{ or }w=13 \\ w\neq-\frac{23}{2},w=13 \end{gathered}[/tex]Since w cannot be negative, the parking lot has a width of 13 yards.
Finally, find the length of the parking lot.
[tex]\begin{gathered} 13l=299 \\ l=\frac{299}{13}=23\text{ yards} \end{gathered}[/tex]The length of the parking lot is 23 yards.
I will attach a picture to this question so you can understand it better.
Answers
Here are the given information:
1. 7 red beads for every 4 blue beads
2. total of 44 beads (red and blue)
Find: the number of red beads
Solution:
We can solve this in two ways. We can solve this using proportion or we can solve this by counting.
Let's start counting first. Let's say 7 red beads and 4 blue beads is 1 set. So, for every set, we already have 7 + 4 = 11 beads in total.
First set = 7 red bead + 4 blue beads = 11 beads
Second set = 7 red bead + 4 blue beads = 11 beads
Third set = 7 red bead + 4 blue beads = 11 beads
Fourth set = 7 red bead + 4 blue beads = 11 beads
If we add all the 4 sets, we have a total of 44 beads. If we add all the RED beads only, we get 7 red beads x 4 sets = 28 red beads.
Therefore, Lily used 28 red beads.
Now, using proportion, we can have this equation:
[tex]\frac{7\text{red beads}}{4\text{blue bead}}=\frac{x\text{ red beads}}{(44-x\text{ red)blue beads}}[/tex]where x = the total number of red beads and we got 44 - x as the number of blue beads.
The next thing that we need to do here is to solve for x.
1. To solve for x, do cross multiplication first.
[tex]7(44-x)=4x[/tex]2. Multiply 7 to the numbers inside the parenthesis.
[tex]308-7x=4x[/tex]3. Add 7x on both sides of the equation.
[tex]\begin{gathered} 308-7x+7x=4x+7x \\ 308=11x \end{gathered}[/tex]4. Lastly, divide both sides by 11.
[tex]\begin{gathered} \frac{308}{11}=\frac{11x}{11} \\ 28=x \end{gathered}[/tex]As we can see, the value of x = 28. Lily used 28 red beads.
f(x) = x + 4 and g(x) = x - 1Step 3 of 4: Find (f 3)(x). Simplify your answer.Answer(f)(x) =
Answers
For this problem, we are given two functions, we need to determine the composite between these two expressions.
The two functions are:
[tex]\begin{gathered} f(x)=x+4\\ \\ g(x)=x-1 \end{gathered}[/tex]This composite is the product of the two functions, therefore we have:
[tex]\begin{gathered} (f\cdot g)(x)=(x+4)\cdot(x-1)\\ \\ (f\cdot g)(x)=x^2-x+4x-4\\ \\ (f\cdot g)(x)=x^2+3x-4 \end{gathered}[/tex]The answer is x²+3x-4.
2(3 + v) =
Please help solve this problem and thank you
Answers
Answer:
6 +2v
Step-by-step explanation:
This is distributive property. That means you will multiply each term inside the parentheses by the term on the outside of the parentheses.
2(3 + v)
2(3) + 2(v)
6 +2v
!!!!!!!!!
A population of 2000 is decreasing by 4% each year. In how many years the population will be reduced in half?
Answers
the initial amount is 2000
the rate of change is 4%
t=time in years
Therefore we have the next exponential decay function
[tex]\begin{gathered} y=2000(1-0.04)^t \\ y=2000(0.96)t \end{gathered}[/tex]Half of the population is y=1000 so we need to find find the value of t
[tex]1000=2000(0.96)^t[/tex]we need to isolate the t
[tex]\frac{1000}{2000}=0.96^t[/tex][tex]\frac{1}{2}=0.96^t[/tex]Using logarithms
[tex]\begin{gathered} \ln (\frac{1}{2})=\ln (0.96^t) \\ \ln (\frac{1}{2})=t\ln (0.96^t) \end{gathered}[/tex][tex]t=\frac{\ln (\frac{1}{2})}{\ln (0.96^{})}=16.98\approx17[/tex]ANSWER
in 17 years the population will be reduced in half
Determine whether 17y = 3x − 19 is quadratic or not. Explain.No; there is no x2 term, so a = 0.No; there is no x-term, so b = 0.No; there is no constant term, so c = 0.Yes; it can rewritten in the form y = ax2 + bx + c.
Answers
The standard form of quadratic equation is given as,
[tex]ax^2+bx\text{ + c = 0 where a }\ne\text{ 0}[/tex]The equation is given as,
[tex]17y\text{ = 3x - 19}[/tex]Therefore,
[tex]\text{From the given equation x}^2\text{ is not present and also a = 0.}[/tex]Thus the given equation is not a quadratic equation.
Yoko plans to watch 2 movies each month. Write an equation to represent the total number of movies n that she will watch in m months.
Answers
Answer:
2m because 2 times the months will tell us how many she has watched for example in 2 months she will watch 4 because 2*2 is 4
Mark is roofing an old gymnasium that measures 270’x390’, and needs to calculate how many “squares “ he will need.(1 “square=100 ft square). The gym’s roof is a standard gable roof with 3’ of overhang on all sides. The roof angle measures 22.55 degrees from horizontal. How many squares of roofing does mark need ?
Answers
First, because of the roof having an inclination, we need to calculate the lenght of the surface we want to roof. The width will be the same.
Let's take a look at the situation:
Since we're on a right triangle, we can say that:
[tex]\cos (22.25)=\frac{G}{R}[/tex]Solving for R,
[tex]\begin{gathered} \cos (22.25)=\frac{G}{R}\rightarrow R\cos (22.25)=G \\ \\ \Rightarrow R=\frac{G}{\cos (22.25)} \end{gathered}[/tex]Since we already know that the lenght of the gym's floor is 390',
[tex]\begin{gathered} R=\frac{390^{\prime}}{\cos (22.25)} \\ \\ \Rightarrow R=421.38^{\prime} \end{gathered}[/tex]We get that the lenght of the surface we want to roof is 421.38'
Now, let's take a look at the surface we want to roof:
Since the roof is a standard gable roof with 3’ of overhang on all sides, we add 6' to each dimension:427
Our total roofing area would be:
[tex]427.38^{\prime}\cdot276^{\prime}=117956.88ft^2[/tex]We then divide this total area by the area of one of our "squares":
[tex]\frac{117956.88}{100}=1179.56[/tex]We round to the nearest integer from above, since we can't buy a fraction of a square.
(this is called ceiling a number)
[tex]1179.56\rightarrow1180[/tex]Therefore, we can conclude that Mark needs 1180 squares of roofing.
John has two apples, he gives Jane 251. How many apples does John have? Please help 2nd grade is so hard.
Answers
Find the links of the sides of these special triangles
Answers
From the triangle, we express the tangent of 60° as:
[tex]\tan 60\degree=\frac{Z}{7}[/tex]But tan(60°) = √(3), then:
[tex]\begin{gathered} \frac{Z}{7}=\sqrt[]{3} \\ \Rightarrow Z=7\sqrt[]{3}\text{ ft} \end{gathered}[/tex]Hello! I need some assistance with this homework question, pleaseQ12
Answers
Answer:
A(-1,4) and B(2,0)
Step-by-step explanation:
The quadratic parabola equation is represented as;
[tex]\begin{gathered} y=a(x-h)^2+k \\ \text{where,} \\ (h,k)\text{ is the vertex of the parabola} \end{gathered}[/tex]Therefore, if the given vertex (2,-5) and the other given point (-1,-1), substitute into the equation and solve for the constant ''a'':
[tex]\begin{gathered} -1=a(-1-2)^2-5 \\ -1=9a-5 \\ 9a=4 \\ a=\frac{4}{9} \end{gathered}[/tex]Hence, the equation for the parabola:
[tex]f(x)=\frac{4}{9}(x-2)^2-5[/tex]Now, for the line since it is a horizontal line, the equation would be:
[tex]g(x)=5[/tex]Then, for (f+g)(x):
[tex]\begin{gathered} (f+g)(x)=\frac{4}{9}(x-2)^2-5+5 \\ (f+g)(x)=\frac{4}{9}(x-2)^2 \end{gathered}[/tex]Then, the graph for the composite function and the points that lie on the graph:
A(-1,4) and B(2,0)
what is the value of 6 3/4 (-11.5)
Answers
We are given the following expression
[tex]6\frac{3}{4}(-11.5)[/tex]As you can see, a mixed number is being multiplied with a negative decimal number.
First, convert the mixed number to a simple fraction then multiply with the decimal number
[tex]6\frac{3}{4}=\frac{6\cdot4+3}{4}=\frac{24+3}{4}=\frac{27}{4}[/tex]Now multiply it with the negative decimal number
[tex]\frac{27}{4}(-11.5)=-\frac{310.5}{4}=-77.625[/tex]So the resultant decimal number may be written back into the mixed form as
[tex]-77.625=-77\frac{5}{8}[/tex]Therefore, the result of the given expression is -77 5/8
Find the third side in simplest radical form: 25 24
Answers
Here, we want to get the length of the third side
Mathematically, we can get this by the use of Pythagoras' theorem
It states that the square of the length of the hypotenuse equals the sum of the squares of the two other sides
Let the missing side be s
From the diagram, we have the hypotenuse as 25 (the hypotenuse is the longest side and it is the side that faces the right angle
We have this as;
[tex]\begin{gathered} 25^2=s^2+24^2 \\ s^2=25^2-24^2 \\ s^2\text{ = 625-576} \\ s\text{ = }\sqrt[]{49} \\ s\text{ = 7} \end{gathered}[/tex]Which describes the product when two fractions greater than 0 and less than 1 are multiplied?
Answers
When you multiply two numbers, one of them greater than 0 and the other one lower than 1. The result is a number that is lower than the first one, that is, a number lower than the number greate than 0.
Select the correct answer from each drop-down menu.
Given: Kite ABDC with diagonals AD and BC intersecting at E
Prove: AD L BC
A
C
E
LU
D
B
Determine the missing reasons in the proof.
Answers
The missing reasons are
ΔCDA ≅ ΔBDA by SSS [side side side]
ΔCED ≅ ΔBED by SAS [side angle side]
What is Kite?
A kite is a quadrilateral having reflection symmetry across a diagonal in Euclidean geometry. A kite has two equal angles and two pairs of adjacent equal-length sides as a result of its symmetry.
Given,
ABCD is a kite, with the diagonal AD and BC
We have,
AC = AB
and
CD = BD [Property of Kite]
In ΔACD and ΔABD
AC = AB
and
CD = BD [Property of Kite]
AD = AD [Common]
By rule SSS Criteria [Side Side Side ]
ΔACD ≅ ΔABD
∴ ∠CDA = ∠BDA [CPCT]
Now,
In ΔCDE and ΔBDA
CD = BD
∠CDE = ∠BDE
DE = DE [Common]
By rule SAS Criteria [Side Angle Side]
ΔCDE ≅ ΔBDA
∴ CE = BE [CPCT]
Hence, AD bisects BC into equal parts
The missing reasons are
ΔCDA ≅ ΔBDA by SSS [side side side]
ΔCED ≅ ΔBED by SAS [side angle side]
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Suppose that a regression line for some data transformed with logarithmspredicts that when x equals 4, log(y) will equal 2.671. What does theregression line predict y will equal when x equals 4?
Answers
Explanation:
The information that we have is that when the value of x is 4
[tex]x=4[/tex]The logarithm of y is 2.671
[tex]log(y)=2.671[/tex]The question is:
What does the regression line predict y will equal when x =4?
That means we need to solve for y in
[tex]log(y)=2.671[/tex]To find the predicted y-value.
To solve for y, we make 10 the base of the two sides of the equation as shown in the following expression:
[tex]10^{log(y)}=10^{2.671}[/tex]Due to the properties of logarithms, on the left side, we will be left only with 'y'
[tex]y=10^{2.671}[/tex]And finally, solving the operations on the right-hand side, the result is:
[tex]y=468.813[/tex]Answer:
[tex]y=468.813[/tex]URGENT!! ILL GIVE
BRAINLIEST!!!!! AND 100 POINTS!!!!!
Order the numbers from least to greatest
Answers
Answer:
-1, √4/5, -6/5, √3, 2, -3√9, 2√125
Step-by-step explanation:
Amy's cookie shop had expenses of the following: flour $45.00sugar $92.00butter $53 she earns $12 per dozen. what is her profit,if she sells 9 dozen?what is the total dollar amount for expenses?what is the total dollar amount for earnings or revenue?
Answers
If she earns $12 per dozen, the following will be the profit if she sells 9 dozen:
[tex]9\cdot12=108[/tex]Profit would be $108.
*The dollar amount of expenses would be:
[tex]e=\frac{190\cdot108}{12}\Rightarrow e=1710[/tex]The expenses would be $1710 if she were to sell 9 dozen.
*The total amount of revenue would be $108 for the 9 dozen sold.
Which is 56,900,000 in scientific notation?o 5.69 x 10⁷o 56.9 x 10⁷o 5.69 X 10⁶o 56.9 X 10⁶
Answers
Answer:
5.69 x 10⁷
Explanation:
A number is said to be in the scientific notation when it is written as a product of a number between 1 and 10 and a power of 10.
The number 56,900,000 in scientific notation is 5.69 x 10⁷.
The correct choice is A.
Which of the following expressions is equivalent to 2-3?A -2-31B-23C231D- 2-3
Answers
2 - 3
the correct answer is letter C
If we follow the rules of the exponents, the power is negative so we change the negative sign writing the numerator in the denominator,
21. Juanita is packing a box that is 18 inches long and 9 inches high. The total volume of the box.1,944 cubic inches. Use the formula V = lwh to find the width of the box. Show your work
Answers
The width of the box is 12 inches
Explanations:
The formula for calculating the volume of a rectangular box is expressed as:
[tex]V=\text{lwh}[/tex]where:
• l is the ,length ,of the box
,• w is the ,width, of the box
,• h is the ,height ,of the box
Given the following parameters
• length = 18 inches
,• heigh = 9 inches
,• volume = 1,944 cubic inches
Substitute the given parameters into the formula to calculate the width of the box as shown:
[tex]\begin{gathered} 1944=18\times w\times9 \\ 1944=162w \end{gathered}[/tex]Divide both sides by 162 to have:
[tex]\begin{gathered} 162w=1944 \\ \frac{\cancel{162}w}{\cancel{162}}=\frac{1944}{162} \\ w=12\text{inches} \end{gathered}[/tex]Hence the width of the box is 12 inches
The Neckware association of America reported that 3% of ties sold in the United States are bow ties. If 4 customers who purchased a tie randomly selected,find the probability that at least 1 purchased a bow tie
Answers
Pr (people with bow ties) = 3% = 0.03
p = 0.03
Pr (people without bow tie) = 1 - 0.03 = 0.97
q = 0.97
n = 4 customers
[tex]Pr(at\text{ least 1 purchased a bow tie) = 1 - Pr(none purchased a bow tie)}[/tex]To find the probability that at least 1 purchased a bow tie, we will use a binomial probability formula:
[tex]p(x=^{}X)=^nC_xp^xq^{n\text{ - x}}[/tex][tex]\begin{gathered} \text{Pr(none purchased a bow tie) = p(x = 0)} \\ \text{p(x = 0) = }^4C_0\times p^0\times q^{4\text{ - }0} \\ \text{p(x = 0) = 1 }\times\text{ 1}\times q^4=(0.97)^4 \\ \text{p(x = 0) = }0.8853 \\ \\ \text{Pr(none purchased a bow tie) = }0.8853 \end{gathered}[/tex][tex]\begin{gathered} Pr(at\text{ least 1 purchased a bow tie) = 1 - 0.8853} \\ Pr(at\text{ least 1 purchased a bow tie) = 0.1147} \end{gathered}[/tex]What are examples of vertical stretch and compression and horizontal stretch and compression?
Answers
Examples of vertical stretch and compression and also horizontal stretch/vertical compression are explained below considering x² and
sin(x) function.
What is vertical stretch/vertical compression ?
A vertical stretch is derived if the constant is greater than one while the vertical compression is derived if the constant is between 0 and 1.Vertical stretch means that the function is taller as a result of it being stretched while vertical compress is shorter due to it being compressed and is therefore the most appropriate answer.example : If the graph of x² is is transformed to 2x² Then the function is compressed Vertically.
If the graph of x² is is transformed to x²/2 Then the function is stretch Vertically.
What is horizontal stretch/vertical compression ?
We know that if f(x) is transformed by the rule f(x+a) then the transformation is either a shift ''a'' units to the left or to the right depending on a is positive or negative respectively this phenomenon is horizontal stretch and compression.example : If the function y = sin(x) is transformed to y = sin(2x) Then the function is compressed horizontally.
example : If the function y = sin(x) is transformed to y = sin(x/2) Then the function is stretch horizontally.
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In the picture below, measure 1 is 5x-14 degrees and measure 3 is 2x+10 degrees. Find measure 2.
Answers
SOLUTION:
Step 1:
In this question, we have the following:
In the picture below, measure 1 is (5x-14) degrees and measure 3 is (2x+10) degrees.
Find the measure of 2.
Step 2:
From the diagram, we can see that angles 1 and 3 are vertically opposite and they are also equal.
Based on this fact, we can see that:
[tex]\begin{gathered} \angle\text{1 = }\angle3 \\ (\text{ 5 x- 14 ) = ( 2x + 10 )} \\ \text{collecting like terms, we have that:} \\ 5x\text{ - 2x = 10 + 14} \\ \text{3 x = 24} \end{gathered}[/tex]Divide both sides, we have that:
[tex]\begin{gathered} x\text{ =}\frac{24}{3} \\ \text{x = 8 } \end{gathered}[/tex]Then, we put x = 8 into the equation for Angle 1 , we have that:
[tex]\angle1=(5x-14)=5(8)-14=40-14=26^0[/tex][tex]\angle3=(2x+10)=2(8)+10=16+10=26^0[/tex]Hence, we can see that Angles 1 and 3 are equal.
Step 3:
From the diagram, we can see that:
we can see that angles 2 and 4 are vertically opposite and they are also equal.
Recall that angles 1 and 3 are also vertically opposite and they are also equal.
Therefore, we can see that:
[tex]\begin{gathered} \angle2\text{ = p} \\ \angle4\text{ = p} \\ \angle1\text{ = }26^0 \\ \angle3=26^0 \\ \text{Then, we have that:} \\ p+p+26^0+26^{\text{ 0 }}=360^0\text{ ( Sum of angles at a point)} \\ 2p+52^0=360^0 \\ 2p=360^0-52^0 \end{gathered}[/tex]Divide both sides by 2, we have that:
[tex]\begin{gathered} 2p=308^0 \\ p\text{ =}\frac{308^0}{2} \\ p=154^0 \end{gathered}[/tex]CONCLUSION:
[tex]\begin{gathered} \operatorname{Re}call\text{ that }\angle2\text{ = p} \\ \text{Then, we have that:} \\ \angle2=154^0 \end{gathered}[/tex]find the missing lenghts, the triangle in each pair are similar.
Answers
Since the triangles are similar, we have that
[tex]\frac{50}{40}=\frac{x}{52}[/tex]then
[tex]x=\frac{52\times50}{40}=65[/tex]then the answer will be D) 65- 2/3 (x+12)+2/3 x=-5/4 x+2
Answers
We will have the following:
[tex]-\frac{2}{3}(x+12)+\frac{2}{3}x=-\frac{5}{4}x+2\Rightarrow-\frac{2}{3}x-8+\frac{2}{3}x=-\frac{5}{4}x+2[/tex][tex]\Rightarrow-\frac{2}{3}x+\frac{2}{3}x+\frac{5}{4}x=2+8\Rightarrow\frac{5}{4}x=10[/tex][tex]\Rightarrow5x=40\Rightarrow x=8[/tex]So, the value of x is 8.
Do the side measures 35 mm, 53 mm and 70 mm create a triangle?Yes, there are infinitely many triangles that can be created.No, it is impossible to create a triangle with the given measures.Yes, there is a unique triangle that can be created.Yes, there are two triangles that can be created.
Answers
Hello!
Let's call these sides a, b, and c:
• a = 35mm
,• b = 53mm
,• c = 70mm
To be a triangle, it must satisfy the existence condition of triangles, that is:
Let's check each of them:
[tex]\begin{gathered} |b-c|Answer:
Yes! There are infinitely many triangles that can be created.
A person invests $9000 at 3% interest compound annually for 4 years and then invests the balance (the $9000 plus the interest earned) in an account at 7% interest for 8 years. find the final value of the investment.
Answers
Answer:
$17,404.5
Explanation:
To calculate the balance after t years, we can use the following equation:
[tex]A=P(1+r)^t[/tex]Where P is the initial investment and r is the rate.
So, we can calculate the balance after 4 years, replacing t by 4, r by 3%, and P by $9000. Therefore the balance is:
[tex]\begin{gathered} A=9000(1+0.03)^4 \\ A=9000(1.126)_{} \\ A=10129.579 \end{gathered}[/tex]Now, we can use this quantity to calculate the final value of the investment. So, replacing P by 10129.579, r by 7%, and t by 8 years, we get:
[tex]\begin{gathered} A=10129.579(1+0.07)^8 \\ A=10129.579(1.718) \\ A=17404.503 \end{gathered}[/tex]Therefore, the final value of the investment is $17,404.5
The oldest child in a family of four children is three times as old as the youngest. The two middle children are 19 and 23 years old. If the average age of the children is 28.5, how old is the youngest child?
Answers
Answer:
18 years old
Solution:
Let x represent the age of the youngest child.
So the age of the oldest = 3x
If the ages of the two middle children are 19 and 23, and the average age of the four children is 28.5, let's go ahead and find x;
[tex]\begin{gathered} \frac{(x+19+23+3x)}{4}=28.5 \\ 4x+42=114 \end{gathered}[/tex]Let's go ahead and subtract 42 from both sides;
[tex]4x=72[/tex]Dividing both sides by 4, we'll have;
[tex]x=\frac{72}{4}=18[/tex]Therefore, the youngest is 18 years old.
