The shape below is made of two rectangles joined together.
9 cm
5 cm
8 cm
5 cm
Find the total area of the shape.
Optional working
Answers
Answer:
a=7, b=3
Step-by-step explanation:
Subtracting, we get the area of QRXY is 63 cm².
Using the area formula of a rectangle, we get 9a=63, and thus a=7.
Using the area formula again on triangle PXYS, 7b=21, and thus b=3.
The value of side 'a' is 7cm and side b is 3 cm.
What is an area?The space occupied by any two-dimensional figure in a plane is called the area. The space occupied by the rectangle in a two-dimensional plane is called the area of the rectangle.
It is given that the area of PQRS is 84 square cm and the area of PSYX is 21 square cm.
The area of QRXY is calculated as,
Area QRXY = 84 - 21
Area QRXY = 63 square cm
The side a will be calculated as,
a x 9 = 63
a = 63 / 9
a = 7 cm
The side of b will be,
b x 7 = 21
b = 21 / 7
b = 3 cm
Therefore, the value of side 'a' is 7cm and side b is 3 cm.
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Related Questions
Which value of a will make the following equation true?
(p²)4p³ = pll
a=0
a=2
O No value of a will work.
O a = 1
Answers
so u need to know
[tex] {p}^{a} \times {p}^{b} = {p}^{a + b} [/tex]
and
[tex] { ({p}^{a} )}^{b} = \: {p}^{a \times b} [/tex]
question :
[tex] { ({p}^{a} )}^{4} \times {p}^{3} = {p}^{11} [/tex]
so we can tell :
[tex] {p}^{(a \times 4) +3 } = {p}^{11} [/tex]
then
[tex](a \times 4 )+ 3 = 11[/tex]
[tex]a = 2[/tex]
the answer is a=2
The sum of measures of the angles of a triangle is 180. The sum of the measures of the second and third angles is three times the measure of the first angle. The third angle is 21 more than the second. Let x,y, and z represent the measures of the first, second, and third angles, respectively. Find the measures of the three angles.
Answers
The measure of all the three angles of a triangle will be 45°, 57° and 78° respectively.
What is Triangle?
A triangle is a three sided polygon , which has three vertices and three angles, whose sum is equal to 180 degree.
Given that;
The sum of measures of the angles of a triangle is 180.
The sum of the measures of the second and third angles is three times the measure of the first angle.
The third angle is 21 more than the second.
Now,
Let the measures of all the three angles are x , y and z.
Since, The sum of measures of the angles of a triangle is 180.
So, we can formulate;
x + y + z = 180° .... (i)
The sum of the measures of the second and third angles is three times the measure of the first angle.
So, we can formulate;
y + z = 3x ... (ii)
The third angle is 21 more than the second.
So, we can formulate;
z = 21 + y ... (iii)
Substitute value of z in equation (ii);
y + 21 + y = 3x
3x = 2y + 21
x = 2/3 y + 7
So, We can substitute x = 2/3y + 7 , y = y and z = 21 + y in equation (i), we get;
x + y + z = 180°
2/3 y + 7 + y + 21 + y = 180
2/3y + 2y + 28 = 180
8/3 y = 180 - 28
8/3 y = 152
y = 152 × 3 / 8
y = 57°
Hence, x = 2/3y + 7
x = 2/3 × 57 + 7
x = 2 × 19 + 7
x = 45°
And, z = 21 + y
z = 21 + 57
z = 78°
Thus, The measure of all the three angles of a triangle will be 45°, 57° and 78° respectively.
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What is 1+1? Express in number form.
Answers
The number form of (1 + 1) will be (1 + 1) only.
What is number form?When a person who experiences number forms thinks of numbers, a mental map of the numbers automatically and unconsciously appears. Numbers are translated into specific spatial locations, and this translation may vary from person to person. In his book The Visions of Sane Persons, Sir Francis Galton first described and named number forms (Galton 1881a). They have been classified as a type of synesthesia in later studies (Seron, Pesenti, and Nol 1992; Sagiv et al. 2006).So, 1 + 1 in number form:
Given (1 + 1) is 2 when we do the sum of it, the number form of 2 will be:
1 + 1Therefore, the number form of (1 + 1) will be (1 + 1) only.
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0.51 + 6.1 = 6.61 because 0.51 is precise to the hundredth digit, so theanswer must also be rounded to the nearest hundredth.A. TrueB. False
Answers
When two decimal numbers are added, the result is precise to the one that has the least precision.
For example,
0.51 + 6.1
Here 0.51 is precise to the hundredth place and 6.1 is precise to the tenth place.
So, the result will be precise to the tenth place since this was the least precision in the operation.
0.51 + 6.1 = 6.6
help meeeeeeeeee pleaseee
Answers
The domain of the line in the graph is x∈R.
What is a domain?The set of all potential inputs for a function is its domain. For instance, the domain of f(x)=x² and g(x)=1/x are all real numbers with the exception of x=0. Additionally, we can define special functions with more constrained domains. Consider the function y = f(x), which has the independent variable x and the dependent variable y. A value for x is said to be in the domain of a function f if it successfully allows the production of a single value y using another value for x.So, the domain the line is:
From the given graph, we know that y = every time.Which means, in the given graph, y = x = 10.
This also means:
y = x = 9y = x = 11y = x = 10The values of x can go to infinity.
Then the domain will be x∈R.Therefore, the domain of the line in the graph is x∈R.
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Theo is saving $8 per week for a vacation he is taking. He started off with some money in savings, but less than $8. At the end of his weeks savings, he had a total of $52. How much money did theo start of with?
Answers
To find the money at start let us use an equation
Since he puts $8 per week
Then his rate is 8
Since he has a total of $52 after some weeks
We must find the nearest number to 52 in table 8
Since 6 * 8 = 48 the nearest number to 52 in table 8
Then he did that for 6 weeks
52 = 8(6) + x
Let us find x
52 = 48 + x
Subtract 48 from both sides
52 - 48 = 48 - 48 + x
4 = x
He started with $4
Which value of x is in the domain of f(a)V-14?A. X = 13B. X=0C. X = 20D. X= -1SUBMIT
Answers
the answer is C x=20
6 ft
11 ft
How do I solve this problem
Answers
Answer:
the answer is 66
Step-by-step explanation:
multiply
6. A newborn baby eats 8 times a day. At each feeding, he
eats 2.5 ounces of formula. How many ounces would the
baby eat in 1 week?
Answers
Answer:
140 ounces
Step-by-step explanation:
(8)(2.5)(7) = 140 ounces
What does x equal?
x(x + 10) = 0
Answers
Answer:
x=-10, you would get this by fixing the equation like this (x+10) (x+) =0 then you would have to -10 on both sides and you get -10 as your answer
Solve the system by the substitution method. *8x – 3y = -22y = 5x + 19 (-5,6) (4,-3) (0,-5) (-3,4)
Answers
8x - 3y = -22
y = 5x + 19
Substituting the second equation into the first one:
8x - 3(5x + 19) = -22
8x - 3*5x - 3*19 = -22
8x - 15x - 57 = -22
-7x = -22 + 57
x = 35/(-7)
x =
Fill in the missing amounts (do not use commas or decimal points.)
A$
B$
C$
D$
E$
F$
Answers
The missing amount is A. 790 B. 20 C. 90 D. 75 E. 20 F. 275
Subtract non-cash assets from total current assets. This number represents the cash amount on the balance sheet. Below is a simple way to calculate income, capital, and total cost of income: Net Income = Ending Equity Starting Equity from the Balance Sheet Total Expenses = Net Income Net Income.
Everything a company owns must come from debt-equity owners or equity so the equation must be balanced. Equity equals the balance sheet total minus all liabilities. All these figures are on the company's balance sheet. For homeowners, equity is the value of the home minus any outstanding mortgage debt or liens.
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find the intervals for the function Y=f(x) whose graph is given below is increasing and where it is decreasing and find the value of the absolute minimum
Answers
In this problem we have a vertical parabola open upward
the vertex represents the absolute minimum
Looking at the graph
the vertex is the point (1,-3)
therefore
the function is increasing at the interval (1, infinite)
the function is decreasing at the interval (-infinite, 1)
the absolute minimum is (1,-3)
Figure NN is the result of a transformation on Figure MM. Which transformation would accomplish this?
Answers
The transformation that is used is a translation of 3 units upwards.
Numerous different coordinate systems can be used to describe geometrical figures.
The connection between several systems is defined by coordinate transformations, which offer formulas for the coordinates in one system in terms of the coordinates in another system. For example, if the polar axis on a plane is the positive x axis and the origins of the Cartesian coordinates (x, y) and the polar coordinates (r), respectively, are the same. The transformation of the coordinates from the polar to the Cartesian coordinate system is x = r cos α and y = r sin α.From the diagram of the graph we can see that the transformation that is used is translation of 3 units upwards.
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1. Classify each angle pair as corresponding, alternate interior, alternate exterior,
same side interior, linear pair.
a) <1 and <5
b) <15 and <7
c) <11 and <1
d) <4 and <10
e) <8 and <13
f) <3 and <4
Answers
∠1 and ∠5 are a pair of corresponding angles.
∠15 and ∠7 are corresponding angles.
∠4 and ∠10 are a pair of alternate interior angles.
∠8 and ∠13 are a pair of co-interior angles.
∠3 and ∠4 are a pair of linear angles.
What are corresponding angles?
When two parallel lines are intersected by another line, comparable angles are the angles that are created in matching corners or corresponding corners with the transversal (i.e. the transversal).
What are alternate interior angles?
When a transversal connects two coplanar lines, alternate interior angles are created. They are located on the transverse sides of the parallel lines, but on the inner side of the parallel lines. At two different locations, the transversal passes through the two lines that are coplanar. These angles indicate whether or not the two provided lines are parallel to one another. When a transversal intersects two parallel lines, the angles that are created inside are equal to the alternate pairings of that transversal. Alternate interior angles are what they are termed.
What are alternate exterior angles?
The pair of angles on the outside of the two parallel lines but on the other side of the transversal are known as alternate exterior angles.
What are linear pair of angles?
When two lines cross at one point, a linear pair of angles is created. If the angles follow the intersection of the two lines in a straight line, they are said to be linear. A linear pair's total angles are always equal to 180°. These are also referred to as additional angles.
Following the above literature,
∠1 and ∠5 are a pair of corresponding angles since angles are created in matching corners or corresponding corners with the transversal.
∠15 and ∠7 are corresponding angles since angles are created in matching corners or corresponding corners with the transversal.
∠4 and ∠10 are a pair of alternate interior angles.
∠8 and ∠13 are a pair of co-interior angles.
∠3 and ∠4 are a pair of linear angles since pair's total angles are always equal to 180°.
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Stella measured a line to be 12.4 inches long. If the actual length of the line is 9.6 inches, then what was the percent error of the measurement, to the nearest tenth of a percent?
Answers
measured 12.4 inches but it is 9.6, the error is 12.4 - 9.6 = 2.8 inches
2.8 inches in percentage with tespect to 9.6:
100 (2.8/9.6) = 280/9.6 = 29.2 %
Answer:
Error is 29.2% of the actual lenght (9.6)
What is the slope of the line passing through the points (-1, 7) and (4, -1)? 0 2 0-2 please answer quickly if you can
Answers
Answer:
answer in image
Step-by-step explanation:
1,1,2,6,24,_,_,_,_,Explain and fill the sequence, write the explicit and recursive formula for the sequence
Answers
Given the sequence:
1, 1, 2, 6, 24
Let's fill in the sequence.
Here, we can see that the nth term is equal to the pprevious term multiplied by n.
First term: 1 x 1 = 1
Second term: 1 x 2 = 2
Third term: 2 x 3 = 6
Fourth term: 6 x 4 = 24
Fifth term: 24 x 5 = 120
Sixth term: 120 x 6 = 720
Seventh term: 720 x 7 = 5040
8th term: 5040 x 8 =40320
Hence, the sequence is:
1, 1, 2, 6, 24, 120, 720, 5040, 40320
The explicit formula of the sequence is:
[tex]a_n=a_{n-1}\ast n[/tex]For example to find the 6th term, we have:
[tex]\begin{gathered} a_6=a_{6-1}\ast6 \\ \\ a_6=a_5\ast6 \\ \\ a_6=120\ast6 \\ \\ a_6=720 \end{gathered}[/tex]We can see the 6th term is 720.
For the recursive formula, we have:
[tex]\begin{cases}a_1=1 \\ \\ n\ge2_{} \\ \\ a_n=a_{n-1}\ast n\end{cases}[/tex]ANSWER:
Sequence: 1, 1, 2, 6, 24, 120, 720, 5040, 40320
Explicit formula:
[tex]a_n=a_{n-1}\ast n[/tex]
Recursive formula:
[tex]\begin{cases}a_1=1 \\ \\ n\ge2_{} \\ \\ a_n=a_{n-1}\ast n\end{cases}[/tex]
consider the following functions which all have a value of 30 does each equation represent growth or decay
Answers
The general equation forms representing growth or decay is;
[tex]\begin{gathered} F=I(1+r)^{t\text{ }}orF=I(1-r)^t \\ F\text{ is future value} \\ I\text{ is initial value} \\ r\text{ is growth rate} \\ t\text{ is time} \\ (1-r)\text{ represents decay} \\ (1+r)\text{ represents growth} \end{gathered}[/tex]So let us consider the equations;
a) f(t) = 30(1.04)^t
f(t) = 30(1+0.04)^t
It is growth as it is greater than 1 and the growth rate is 0.04 = 4/100 = 4%
b) p(x) = 30(0.65)^x
P(x) = 30(1-0.35)^x
it is decay as it is less than 1
Growth rate is 0.35 = 35/100 = 35%
c) A(x) = 30(1.10)^x
A(x) = 30(1 + 0.1)^x
it is growth as it is greater than 1
0.1 = 10/100 = 10%
d) h(t) = 30(0.98)^t
h(t) = 30(1-0.02)^t
It is decay since it is less than 1
growth rate is;
0.02 = 2/100 = 2%
e) s(t) = 30(0.77)^t
s(t) = 30(1-0.23)^t
it is decay as it is less than 1
0.23 is growth rate = 23/100 = 23%
f) B(t) = 30(1.2)^t
B(t) = 30(1+0.2)^t
It is growth since it is greater than 1
0.2 = 20/100 = 20%
Betty's Auto Wash earns revenues of $14 per customer. After serving 6 customers, how much revenue will Betty's Auto Wash have?
Answers
Given data:
The given revenue earn per customer is $14.
The expression for the given statement is,
1 customer= $14
Multiply the above expression by 6 on both sides.
6(1 customer)=6($14)
6 customers=$84
Thus, revenue earn by 6 customers is $84.
Find the area of the figure given to the right. The hexagon is regular. Round to the nearest whole number.
Answers
We can divide the hexagon into 6 equilateral triangles, and call the side 'x'. I will draw the situation:
Every line is x because the hexagon is regular (all sides have the same length). Therefore we can find x, because two times x is 18'':
[tex]2x\text{ = 18}[/tex][tex]x\text{ = 9 inches}[/tex]The hexagon has the same area of 6 equilateral triangles with the side equal to x. The formula of the area of an equilateral triangle is:
[tex]Area\text{ = }\frac{x^2\sqrt[]{3}}{4}[/tex]Therefore the area of the hexagon will be:
[tex]\text{AreaHexagon = 6}\times\frac{x^2\sqrt[]{3}}{4}^{}[/tex][tex]\text{AreaHexagon = 6}\times\frac{9^2\sqrt[]{3}}{4}^{}[/tex][tex]\text{AreaHexagon }\cong210.44\text{ square inches}[/tex]Rounding it will be 210 square inches.
The approximate volume in milliliters, y, for a volume of x fluid ounces is equal to 29.57 times the value of x. Which table represents this relationship?
Answers
Step-by-step explanation:
volumes of liquor because these are the ones which have volume and cm can be changed to millimeters
The Heights(in inches)and the weight (in pounds)of a simplified women are recorded. round your answer to one decimal place ×=height. y=weight 66. 122 67. 13269. 15368. 13865. 125a) calculate the slope of B1 and the y-intercept Bl0) of the regression line. Write the regression equation.y= _____ x+_____b) Interest interpret the values of B1 and B0. For it each increase of 1 inches the estimate weight increase by_______ pounds. When x=0 inches weight the estimate weight is________ pounds
Answers
For the linear regression the dependent and independent variables are:
y: "weight of a woman" (measured in pounds)
x: "height of a woman" (measured in inches)
You have to calculate the estimated linear regression equation:
[tex]y^{}=b_{0\text{ }}+b_1x[/tex]Where
b₀ is the estimate of the y-intercept
b₁ is the estimate of the slope
To calculate both by hand you have to use the following formulas:
[tex]b_1=\frac{\sum ^n_1x_iy_i-\frac{(\sum^n_1x_i)(\sum^n_1y_i)}{n}}{\sum ^n_1x^2_i-\frac{(\sum ^n_1x_i)^2}{n}}[/tex][tex]b_0=y_{\text{bar}}+bx_{\text{bar}}[/tex]y bar and x bar are the sample means for the weight and height
n is the number of women observed, in this case the sample size is
n=5 women
Next calculate the needed summatories, i.e. add each obervation from the corresponding variables
∑xi= 335
∑xi²= 22455
∑yi=670
∑xiyi=44962
ybar=∑yi/n= 670/5=134 pounds
xbar=∑xi/n= 335/5=67 inches
Replace the values in the formulas:
Slope:
[tex]b_1=\frac{44962-\frac{335\cdot670}{5}}{22455-\frac{(335)^2}{5}}=7.20\text{ }\frac{pounds}{In}[/tex]y-intercept
[tex]b_0=134-7.20\cdot67=-348.4\text{pounds}[/tex]The estimated linear equation is:
y=-348.4+7.20x
b)
The y-intercept of the linear regression indicates the value of the estimated mean of the variable y when x equals zero.
The slope of the linear regresion insicates the change of the estimated mean of the variable y when the variable x increases one unit.
So in terms of this exercise you can interpret the y-intercept as:
-348.4pounds is the estimated average weight of women when their height is zero inches.
→ Note that this interpretation has no logical meaning, at least not one applicable in real life, but for the regression is a valid mathematical result and interpretation.
And the slope can be interpreted as:
7.2pounds/inches is the modification of the estimated average weight of weomen when their height increases 1 inch.
A line passes through the point (−10, 4) and has a slope of 3/2. Write an equation in slope-intercept form for this line.
Answers
The equation of the line in slope intercept form is y = 3/2x + 19
What are linear equations?Linear equations are equations that have constant average rates of change.
Note that the constant average rates of change can also be regarded as the slope or the gradient
How to determine the equation of the line?The given parameters are
Slope, m = 3/2
Points, (x1, y1) = (-10, 4)
A linear equation is represented as
y = slope * x + y-intercept
i.e.
y = m(x - x1) + y1
So, we have
y = 3/2(x + 10) + 4
Expand
y = 3/2x + 15 + 4
Evaluate the like terms
y = 3/2x + 19
Hence. the linear equation is y = 3/2x + 19
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I need urgent help with this math problem, please help me!
Answers
Answer:
See below
Step-by-step explanation:
The MONTHLY payment for each loan is just the interest and principal paid for each month
I just used the first line of each amortization:
First one 26 + 196 = $ 222 per month
Second one 26 + 127 = $ 153 per month
Sorry if the numbers are incorrect....the image is very fuzzy....
but this is the method for the answer .
Check each answer to see whether the student evaluated the expression correctly. If the answer is incorrect, cross out the answer and write the correct answer. Algebraic expressions 7p+5 when p=12Student answer7(12) +5 = 7(17) =119
Answers
Given the expression:
[tex]7p+5[/tex]We will find the value of the expression when p = 12
so, substitute with p = 12
[tex]7(12)+5=84+5=89[/tex]So, the student answer is incorrect
The correct answer will be 89
Simplify: qp - 8m - m +1 - m; usee m= -3, p = 9, and q = 570-297616None of these answers are correct.
Answers
Answer:
76
Step-by-step explanation:
We are given the following expression:
qp - 8m - m + 1 - m
It can see simplified combining commom terms as:
qp + m(-8 - 1 - 1) + 1
Which is
qp - 10m + 1
Replacing m by -3, q by 5 and p by 9
5*9 - 10*(-3) + 1 = 45 + 30 + 1 = 76
1. In 2014, the population of Florida was 19,580,000. Write the 2014 population of Florida in scientific notation.
Answers
The population of Florida in scientific notation 1.958 x [tex]10^{7}[/tex]
What is Scientific notation?
Numbers that are either too large or too little to be conveniently stated in decimal form can be expressed using scientific notation. It can also be referred to as standard form in the UK, standard index form, or scientific form.
Given,
19,580,000
We know that,
19580000 = 1.9580000(10000000)
10000000 = [tex]10^{7}[/tex]
Substitute
1.9580000([tex]10^{7}[/tex])
or, 1.958 x [tex]10^{7}[/tex]
Hence, The 2014 population of Florida in scientific notation is equal to 1.958 x [tex]10^{7}[/tex]
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a wildfire organization wants to fence off an area of a beach. The organization can only fence 100 yd². what length (x) and width (y) should the organization use the Least amount of fencing as possible
Answers
It is given that the total area of the beach is 100 yd².
We have to find the length x and the width y that the organization shoul use to use the least amount of fencing as possible. it means that we have to find the dimensions for which parameter is leasr.
The perimeter of a rectangle is:
[tex]P=2\times(l+w)[/tex]In option 1, the length is 50 yards and the width is 20 yards. then the perimeter will be (using the previous formula) equal to 140.
In option too the perimeter will be 130.
in option 3 the perimeter will be 134.44
and, in option 4 it will be 146.36
therefore the least perimeter is 130 when the length is 40 yd and the width is 25 yd.
solve for k=prt for p
