The area of the lawn is 2.5 times greater than the area of the garden.
What is Heron's formula in math?Heron's formula for finding the area of a triangle in terms of the lengths of its sides.
In symbols, if a, b, and c are the lengths of the sides: Area = √s(s - a)(s - b)(s - c) where s is half the perimeter, or (a + b + c)/2.
Given vertices W(-100,-70), X(-100,0),Y(0,0), and Z(-60,-70) of a backyard,
We have to find distances WX, XY, YZ, ZW and XZ:
1. WX= √(-100+100)²+(0+70)²
=√0+4900
=70
2. XY= √(0+100)²+(0-0)²
=100 units.
3. YZ= √(-60-0)²+(-70-0)²
=√3600+4900
= √8500= 10√85
4. ZW= √(-60+100)²+(-70+70)²
=√40²+0
=40 units
5. XZ= √(-60+100)²+(-70+0)²
=√40²+70²
=√6500=10√65
Then:
1. the area of WXZ
[tex]\sqrt{(70+40+10\sqrt{65}) /2 * ({70+40+10\sqrt{65}) /2 -70* {(70+40+10\sqrt{65}) /2 -40[/tex]*[tex]\sqrt{(70+40+10\sqrt{65}) /2 -10\sqrt{65}[/tex]
=1400 feet²
Area of XYZ= [tex]\sqrt{(100+10\sqrt{65}+10\sqrt{85}) /2 * (100+10\sqrt{65}+10\sqrt{85}) /2 -100* {(100+10\sqrt{85}+10\sqrt{65}) /2[/tex]-[tex]\sqrt{-10\sqrt{85}*(10+10\sqrt{85} +10\sqrt{65}) /2 -10\sqrt{65}[/tex]
=3500 feet²
Then, ar(WXZ)/ ar (XYZ)= 3500/1400=2.5 times.
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The oblique prism below has an isosceles right triangle
base.
x
(x+2)
(x+3)
Mark this and return
53:21
What expression represents the volume of the prism, in
cubic units?
01/2+2²
028+22²
02 +2
O²+37²2²
Save and Exit
Submit
Next
The volume of the prism, in cubic units is V = 1/2*x³ + x²
The figure and options are in the figure attached
What is an Oblique Prism ?An oblique prism is a polyhedron figure , with a rectangular base and triangular side faces .
It is given that
The oblique prism below has an isosceles right triangle base.
In the figure attached, the oblique prism is shown.
The volume of the prism is given by
V = b*h
h is the height and b is the Area of the base
It is given that the base is an isosceles right triangle, its area is:
Area of a Triangle = (1/2) base * height
here the base and height is x
b = 1/2*x²
The height of the prism is (x + 2).
Then, the volume is:
V = 1/2*x²*(x + 2)
V = 1/2*x³ + x² cu. units
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What is the height??
[tex]\bold{\huge{\underline{ Solution }}}[/tex]
Here, we have given
One isosceles triangle that means the given triangle having two sides equal. The dimensions of the triangle are 21cm, 21 cm and 16 cm.Consider the given triangle as ABC . In ΔABC, AD acts as a median. It means Angle ADB = 90°
Therefore,
By using Pythagoras theorem,
It states that the sum of the squares of base and perpendicular height is equal to the square of the hypotenuse.That is,
[tex]\bold{ ( Hypotenuse) ^{2} = (Perpendicular) ^{2} + (base) ^{2}}[/tex]
Subsitute the required values
[tex]\sf{ AC^{2} = AB^{2} + BC^{2}}[/tex]
[tex]\sf{ (21)^{2} = (h) ^{2} + (16)^{2}}[/tex]
[tex]\sf{ 441 = (h)^{2} + 256}[/tex]
[tex]\sf{ (h)^{2} = 441 - 256}[/tex]
[tex]\sf{ h^{2} = 185}[/tex]
[tex]\sf{ h = \sqrt{185}}[/tex]
[tex]\bold{ h = 13.6 \: cm}[/tex]
Hence, The required height of the given isosceles triangle is 13.6 cm.
[ Note :- you can also solve this problem by using Heron's Formula but it's too lengthy to solve that's why I have used simple method ]
four students are trying to determine what number must replace the question (x^2)^7=x^4*x^8 in order to make it true
Joe said the answer is 6. Sam said it is impossible to answer.
Peter said the answer is 32. Alex said the answer is 16.
Who is correct? Explain why.
Let's solve ourselves instead of believing anyone
[tex]\\ \rm\Rrightarrow (x^2)^7=x^4x^8[/tex]
a^m+a^n=a^m+n[tex]\\ \rm\Rrightarrow x^{14}=x^{4+8}[/tex]
[tex]\\ \rm\Rrightarrow x^{14}=x^{12}[/tex]
[tex]\\ \rm\Rrightarrow x^{14}-x^{12}=0[/tex]
[tex]\\ \rm\Rrightarrow x^{12}(x^2-1)=0[/tex]
[tex]\\ \rm\Rrightarrow x^2-1=0[/tex]
[tex]\\ \rm\Rrightarrow x^2=1[/tex]
[tex]\\ \rm\Rrightarrow x=\pm 1[/tex]
0 is also a solutionAnswer:
Joe is correct
Step-by-step explanation:
Given equation:
[tex](x^2)^?=x^4 \cdot x^8[/tex]
The exponent outside the bracket is a question mark and the students are trying to determine the value of the question mark.
For ease of answering, let y be the unknown number (question mark):
[tex]\implies (x^2)^y=x^4 \cdot x^8[/tex]
First, simplify the equation by applying exponent rules to either side of the equation:
[tex]\textsf{Apply exponent rule} \quad (a^b)^c=a^{bc}\quad\textsf{to the left side}:[/tex]
[tex]\implies (x^2)^y=x^4 \cdot x^8[/tex]
[tex]\implies x^{2y}=x^4 \cdot x^8[/tex]
[tex]\textsf{Apply exponent rule} \quad a^b \cdot a^c=a^{b+c} \quad \textsf{to the right side}:[/tex]
[tex]\implies x^{2y}=x^4 \cdot x^8[/tex]
[tex]\implies x^{2y}=x^{4+8}[/tex]
[tex]\implies x^{2y}=x^{12}[/tex]
Now, apply the exponent rule:
[tex]x^{f(x)}=x^{g(x)} \implies f(x)=g(x)[/tex]
Therefore,
[tex]x^{2y}=x^{12}\implies 2y=12[/tex]
Finally, solve for y:
[tex]\implies 2y=12[/tex]
[tex]\implies 2y \div 2 = 12 \div 2[/tex]
[tex]\implies y=6[/tex]
Therefore, Joe is correct as the unknown number is 6.
Find the area of the shaded region in terms of pi
Answer:
[tex]13\frac{1}{3} \pi[/tex]
Step-by-step explanation:
First, find the area of the small circle whose radius is 3cm.
[tex]A = \pi r^{2} \\A = \pi (3^{2})\\A = \pi (9)\\A = 9\pi \\[/tex]
Next, find the area of the large circle. First, you need to find the radius of the large circle by adding the 3 and 4.
Radius of large circle.
3 + 4 = 7 cm
Area of large circle:
[tex]A = \pi r^{2} \\A = \pi (7^{2})\\A = \pi (49)\\A = 49\pi \\\\[/tex]
Now subtract the area of the small circle from the large circle since the shaded area doesn't include the small circle.
[tex]49\pi -9\pi =40\pi[/tex]
Finally find the shaded area. To do this first find what degree of the circle is shade by dividing 120 by 360.
120/360 = 1/3
Now multiply the area by 1/3, or you can divide it by 3
[tex]\frac{40\pi }{3} =13\frac{1}{3} \pi[/tex]
HELP MEE ,20 POINTS !!!!
Celina says that each of the following expressions is actually a binomial in disguise:
5abc-2a^2+6abc
5x^3∙2x^2-10x^4+3x^5+3x∙(-2) x^4
(t+2)^2-4t
5(a-1)-10(a-1)+100(a-1)
(2πr-πr^2 )r-(2πr-πr^2)∙2r
Celina says true that each of the following expressions is actually a binomial expression.
What is binomial?The binomial is a polynomial of two-term only. For example, x + 5 where x and 5 are the two separate terms.
Celina says that each of the following expressions is actually a binomial in disguise:
a. 5abc - 2a² + 6abc = 11abc - 2a²
The is a binomial expression.
b. 5x³∙2x² - 10x⁴ + 3x⁵ + 3x∙(-2) x⁴ = 7x⁵ - 10x⁴
The is a binomial expression.
c. (t+2)² - 4t = t² + 4
The is a binomial expression.
d. 5(a - 1) - 10(a - 1) + 100(a - 1) = 95a - 95
The is a binomial expression.
e. (2πr - πr² )r - (2πr - πr²)∙2r = -2πr² + πr³
The is a binomial expression.
Celina says true that each of the following expressions is actually a binomial expression.
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Select ALL the correct answers. Observe the expression below and select the true statement(s). The "6" in the third term is a coefficient. The "7" in the third term is a coefficient. The "9" in the second term is a constant. The "y" in the third term is a factor. The "4" In the first term is a constant. The "x" in the first term is an exponent. 4r + 9 = y(6x + 7)
An expression is defined as a set of numbers, variables, and mathematical operations. The statements that are true are 1, 3, and 5.
What is an Expression?In mathematics, an expression is defined as a set of numbers, variables, and mathematical operations formed according to rules dependent on the context.
For the given expression 4x + 9 - y(6x + 7), the following things are can be written,
4 and 6 are coefficients.9 and 7 are constants.x and y are variables.Thus, the statements that are true are:
The 6 in the third term is a coefficient.The 9 in the second term is a constant.The y in the third term is a factor.Hence, the statements that are true are 1, 3, and 5.
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Through aregular hexagonal prism whose base edge is 8cm whose height 12 cm ahole in the shape of aright prism with its end being arhombus with diagonals 6cm and 8cm is drilled find total surface area of remaining solid and the volume
Answer:
96 cm2, 48 cm2
Step-by-step explanation:
Basically you times the first two questions and then the other 2, that leads you with the answer
MATH!!! 15 points;))) find the surface area of the composite figure
please answer correctly and check over your work...
The area of a 2D form is the amount of space within its perimeter. The surface area of the composite figure is 76.8 ft².
What is an area?The area of a 2D form is the amount of space within its perimeter. It is measured in square units such as cm2, m2, and so on. To find the area of a square formula or another quadrilateral, multiply its length by its width.
The surface area of the composite figure,
Surface area = 2(3.6×2) + (4×2) + 3(3.6×4) + 2(5.6)
= 14.4 + 8 + 43.2 + 11.2
= 76.8
Hence, the surface area of the composite figure is 76.8 ft².
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A parabola opens upward. The parabola goes through the point (3, -1), and the vertex is at (2, -2). write the equation of the parabola
The value of a is 1/4 and the equation of the parabola is (x-2)² = (y+2)
What is a Parabola ?A parabola is a u shaped curve. It is a plane curve whose all points are at a fixed distance form a point called focus.
(x-h)² = 4a(y-k)
It is given that the parabola goes through the point (3, -1), and the vertex is at (2, -2).
Therefore
(x -2)² = 4a(y +2)
The parabola passes through the point (3,-1)
(3-2)² = 4*a(-1+2)
1 = 4 a
a = 1/4
The equation of the parabola is
(x-2)² = (y+2)
Therefore The value of a is 1/4 and the equation of the parabola is (x-2)² = (y+2)
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what type of function is this?
Answer:
It's a sech x function
Step-by-step explanation:
Explanation is in attached file
^ What is the product of 3x(x²+4)? ´0x²+3x+4 O 3x³+4 O 3x³ + 12x O 3x² + 12x
Answer:
3x³ + 12x
Step-by-step explanation:
→ Multiply 3x by x²
3x³
→ Multiply 3x by 4
12x
Which measurements could create more than one triangle?
A. Angles measuring 85°, 45°, and 60°
B. Angles measuring 95°, 35°, and 50⁰
C. Sides measuring 8 cm and 15 cm and an included angle measuring 60°
D. Sides measuring 5 inches, 7 inches, and 13 inches
Answer:
A.
Step-by-step explanation:
The sum of angles of a triangle is 180. if you add 85+45+60 you get 190. That is more than 180.
help i need it quick!!
Answer:
47°
Step-by-step explanation:
45+88= 133
180-133=47
Which table represents a linear function?
X
X
y
1
1
1
2
2
1
2
3
4
34
O
122
1/7/2
O
y
1
121314
X
1
2
3
4
X
1
2
3
14
O
y
7
9
13
21
y
0
6
16
30
the third one
Step-by-step explanation:
50% if £80 pls helppp
Answer:
50%×€80
50/100×80
€40
Step-by-step explanation:
please mark me as brainlest
Answer:
£40
Step-by-step explanation:
▪︎ Method I:
£80 - 100%
£x - 50%
x = (£80 * 50%) / 100% = £40
▪︎ Method II:
50% is one half
Therefore, 50% of £80 is £80 / 2 = £40
Use the hundredth grids to model the question.
Two 10 by 10 grids are shown. In the first grid, 8 columns and 9 squares are shaded brown and 1 column and 1 square are shaded blue. The second grid is entirely shaded blue.
Which is the sum of 0.89 and 1.11?
A.
1.00
B.
1.89
C.
1.90
D.
2.00
The sum of 0.89 and 1.11 will be 2. Then the correct option is D.
What is Algebra?The analysis of mathematical representations is algebra, and the handling of those symbols is logic.
Two 10 by 10 grids are shown.
In the first grid, 8 columns and 9 squares are shaded brown and 1 column and 1 square is shaded blue.
The second grid is entirely shaded blue
Then the sum of 0.89 and 1.11 will be
⇒ 0.89 + 1.11
⇒ 2.00
Then the correct option is D.
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answer this question asap
Answer:
the first option
Step-by-step explanation:
f(c)= 1/3p + 5/3
make r the subject of the formula in V= ⅓π r²h
Answer:
switch the position
1/3πr²h=v
multiply all through by 3
3•1/3πr²h=3•v
3 will cancel out 3
πr²h=3v
divide both sides by πh
r²=3v/πh
root both sides
r=±√3v/πh
1. Triangle STU is shown on the coordinate plane below. Triangle STU is transformed using the rule (x, y) -> (x+4, y-2). In the image of the transformation, triangle S'T'U', what is the x-coordinate of S'?
Using translation concepts, considering S(2,-1), the x-coordinate of S' is given by 6.
What is a translation?A translation is represented by a change in the function graph, according to operations such as multiplication or sum/subtraction in it's definition.
In this problem, the rule is given by:
(x, y) -> (x+4, y-2).
Considering S(2,-1), 4 is added to the x-coordinate in the translation, hence:
2 + 4 = 6.
The x-coordinate of S' is given by 6.
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Write the equation for g(x)
The equation of the function, g(x) from the task content is; g(x) = -x/25 + 203/25.
What is the equation of the function g(x)?From observation of the function, f(x), it follows that the slope of f(x) is 25. Hence, it follows that the slope of g(x) is; -1/25 since both functions are perpendicular to each other.
Therefore, the equation for g(x) is;
-1/25 = (y-8)/(x-3)
25y -200 = -x +3
Hence, y = -x/25 + 203/25.
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Teri was 10 km race she has completed 74% of the way race when the winner crosses to finish there are approximately 2.48 miles in 4 km how many more miles does Terry need to run when the winner crosses the finish line answer to the nearest 10th
The distance Terry needs to run when the winner crosses the finish line is 1. 6 miles.
How to find the distance Terry needs to run?
The race was a 10 km race and she has completed 74% of the race when the winner crosses the finish line.
Therefore, the number of more miles Terry need to cover can be calculated as follows:
74 / 100 × 10 = 740 / 100 = 7.4 km
He has covered 7.4 km.
The distance remaining to cover = 10 km - 7.4 km = 2.6 km
Therefore,
4km = 2.48 miles
2.6 km = ?
cross multiply
The distance remaining to cover(miles) = 2.6 × 2.48 / 4
The distance remaining to cover(miles) = 6.448 / 4
The distance remaining to cover(miles) = 1.612
The distance remaining to cover(miles) = 1.6 miles
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I saw this in a newspaper – it was a puzzle for adults, fully grown humans, but I think you will find it easy.
All the digits from 1 to 9 are used in this grid, but only once. Can you work out their positions in the grid so that each of the six different sums work?
Two of the numbers have been inserted in order to get you started. Just identify the other seven numbers.
(NOTE: perform operations in the order they appear, e.g., 3+4×5=35 (not 23))
a=
b=
c=
d=
e=
f=
Answer:
d=9
Step-by-step explanation:
any other idea
helpp plss
The following table shows how the average constituency changes for two regional governing boards, joshua and salinas, when a new representative is added to each board.
joshua's
average
constituency salinas's
average
constituency
joshua receives
new board
member 1232 1520
salinas receives
new board
member 1448 1333
(a) determine the relative unfairness of an apportionment that gives a new board member to joshua rather than to salinas. round to the nearest thousandth.
(b) determine the relative unfairness of an apportionment that gives a new board member to salinas rather than to joshua. round to the nearest thousandth.
(c) using the apportionment principle, determine which regional governing board should receive the new board member.
joshua
salinas
The relative unfairness of an apportionment that gives a new board member to joshua rather than to salinas will be
How to calculate the values?The relative unfairness of an apportionment that gives a new board member to joshua rather than to salinas will be:
= (1520 - 1232)/1232
= 288/1232
= 0.234
The relative unfairness of an apportionment that gives a new board member to salinas rather than to Joshua will be:
= (1448 - 1333)/1333
= 115/1333
= 0.086
The regional governing board that should receive the new board member is Salinas.
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13) Circle O is shown with point A, B, C, and D on Circle O.
If x = 50, what is the value of y and the angle measurement of angle AOB?
y = _____
m
(25) (50) (100) (not enough information)
The value of y is 50
The angle measurement of angle AOB is 100°
Circle Geometry
From the question, we are to determine the value of y and the measure of angle AOB
From one the circle theorems, we have that
Angles in the same segment are equal
In the given diagram, x° and y° are angles in the same segment
∴ x° = y°
From the given information,
x = 50
∴ y = 50
Hence, the value of y is 50
Also, from another circle theorem,
Angle at the center is twice the angle at the circumference
∴ ∠AOB = 2x° = 2y°
Then,
∠AOB = 2×50°
∠AOB = 100°
Hence, the angle measurement of angle AOB is 100°
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Which are applications of mathematics in music? Select all that apply.
identifying measurements
calculating beats per minute
calculating the time signature
finding ratios of note frequencies
mapping marching band performances
Answer:
calculating beats per minute
Mr Ellis invests £800 into an account that pays 3.4% compound interest per year how much will be in the account after two years
The amount after 2 years will be 855.3248
What is Interest?Interest, in its most simple form, is calculated as a percent of the principal.
Given:
P= £800 , r= 3.4%, t= 2 year
For, compounded annually
=800*(0.034+1)²
=800* 1.034*1.034
=800* 1.069156
=855.3248
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a negative number raised to an odd power is ____ negative ?
Answer:
always negative?
Step-by-step explanation:
-2^3=-8
Answer:
It is negative
Step-by-step explanation:
since you are multiplying the negative no. by itself an odd no. of times, your answer will be negative, b/c a negative no. multiplied an odd no. of times will be negative, and if it is multiplied an even no. of times it will be positive.
According to the box-and-whisker plot shown above, what are the following:
6. The median?
7. The first quartile?
8. The third quartile?
9. The minimum value?
10. The maximum value?
I need help i put the plot i need help 6 threw 10
Answer:
6. 80
7. 60
8. 100
9. 40
10. 110
Step-by-step explanation:
A box and whisker plot is a visual representation of the 5-number summary of a data set. The features of the plot are, left-to-right, the minimum, first quartile, median, third quartile, maximum.
You are being asked to identify the numerical value associated with each of these features.
__
The left whisker extends to the minimum of 40.
The left end of the box identifies the first quartile as 60.
The line in the middle of the box is the median, 80.
The right end of the box identifies the third quartile as 100.
The right whisker extends to the maximum of 110.
__
Additional comment
We hope you can rearrange the order of these numbers to suit the order in which the questions ask for them.
For the complex number z = (5sqrt(3))/4 - 5/4 * i what is the polar form
Answer: 3
Step-by-step explanation:
The required polar form of the equation is [tex]Z = 5/2cos30 - 5/2sin30i.[/tex]
For the complex number z = (5sqrt(3))/4 - 5/4 * i the polar form is to be determined.
The number that constitutes real and imaginary numbers are called complex numbers. The standard form of complex number = a + bi
[tex]z = 5\sqrt{3}/4 - 5/4i[/tex]
the polar form complex numbner can be given as
[tex]z = rcos\theta +rsin\theta i[/tex] - - - - - -(1)
where r = [tex]\sqrt{a^2+b^2}[/tex]
and [tex]\theta=tan^-\frac{b}{a}[/tex]
Since a = 5√3/4 and b = -5/4
[tex]r = \sqrt{(5\sqrt{3}/4)^2+(5/4)^2}[/tex]
r = 10/4
r = 5/2
Now,
[tex]\theta=tan^-\frac{b}{a}[/tex]
[tex]\theta=tan^-\frac{-5/4}{5\sqrt{3}/4 }\\\theta=tan^-\frac{1}{\sqrt{3} }\\\theta=tan^-(-tan30)\\\theta=-30[/tex]
Now the polar form is given by substituting the values of r and [tex]\theta[/tex] in equation 1
Here,
[tex]z = 5/2cos30 +5/2sin(-30)i\\z = 5/2cos30-5/2sin30 i[/tex]
Thus, the required polar form of the equation is [tex]Z = 5/2cos30 - 5/2sin30i.[/tex]
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Sid has a water dispenser in his refrigerator as shown in the figure.
PLS HELP!
A prism has a length of 4 inches, height of 14 inches, and width of 8 inches.
Sid would like to have three water dispensers in his refrigerator. How much cubic space will all three dispensers take up in Sid’s refrigerator?
448 in.3
896 in.3
1,200 in.3
1,344 in.3
Answer:
c. I'm sorry if I'm wrong
Step-by-step explanation: