The system of equations that models the given situation is given as follows:
x + y = 25.15x + 25y = 475.What is a system of equations?A system of equations is when two or more variables are related, and equations are built to find the values of each variable.
In this problem, the variables are given as follows:
Variable x: Number of single lawns cut.Variable y: Number of front and back lawns cut.He had 25 customers, hence:
x + y = 25.
He charges $15 for a single lawn and $25 for a front and back lawn, and made a total of $475, hence:
15x + 25y = 475
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A cube has side length 3 inches. A sphere has a radius of
3 inches. (Lesson 5-16)
a. Before doing any calculations, predict which solid has greater surface
area to volume ratio.
b. Calculate the surface area, volume, and surface area to volume ratio for
each solid.
I predict that the solid with the greater surface area to volume ratio would be the cube.
The volume of the cube is 27in³
The surface area of the cube is
The ratio of surface area to volume for the cube is 2.
The volume of the sphere is 113.14 in³
The surface area of the sphere is 113.14 in²
The ratio of surface area to volume is 1.
What is the surface area and volume of each solid?The volume of a cube = side length³
3³ = 27 in³
The surface area of a cube = 6a²
a = side length
6 x (3²) = 54 inches²
Ratio of surface area to volume = 54 / 27 = 2
The volume of the sphere= 4/3πr³
4/3 x 22/7 x 3³ = 113.14 in³
The surface area of the sphere = 4πr²
4 x 22/7 x 3² = 113.14 in²
Ratio of surface area to volume = 113.14 / 113.14 = 1
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A regular polygon with n sides has n(n-3)/2 diagonals. Find the number of sides of a regular polygon that has 44 diagonals.
[tex]\dfrac{n(n-3)}{2}=44\\\\n(n-3)=88\\n^2-3n-88=0\\n^2+8n-11n-88=0\\n(n+8)-11(n+8)=0\\(n-11)(n+8)=0\\n=11 \vee n=-8[/tex]
Therefore, the number of sides is 11.
In the solid figure below, what is the volume of the bottom section of the figure?
48
24
36
12
The volume of the bottom section of the figure is:
V = 48 cm³
How to get the volume of the bottom section?Remember that for a rectangular prism of length L, width W, and height H, the volume is V.
V = L*W*H
For the bottom section the dimensions are:
Length = 6cm
Width = 4cm
Height = 4cm - 2cm = 2cm
Replacing these in the volume equation we get:
V = (6cm)*(4cm)*(2cm) = 48cm³
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Answer:
Step-by-step explanation:That’s t up to you STOP CHEATING!!
Find the angle of CD. Round to the nearest tenth. 12.7 cm 45.5° 9/06 cm mCD= [?]°
Using the information in the diagram, the measure of [tex]\overset{\LARGE\frown}{CD}[/tex] is 89.0°
Calculating the angle subtended by an arcFrom the question, we are to determine the measure of [tex]\overset{\LARGE\frown}{CD}[/tex]
Consider the right triangle
The measure of [tex]\overset{\LARGE\frown}{CD}[/tex] is twice the measure of the unknown angle
Let the unknown angle in the right triangle be x
∴ The measure of [tex]\overset{\LARGE\frown}{CD}[/tex] = 2x
Then,
x + 90° + 45.5° = 180° (Sum of angles in a triangle)
x = 180° - 90° - 45.5°
x = 44.5°
Thus,
The measure of [tex]\overset{\LARGE\frown}{CD}[/tex] = 2×44.5°
The measure of [tex]\overset{\LARGE\frown}{CD}[/tex] = 89°
Hence, the measure of [tex]\overset{\LARGE\frown}{CD}[/tex] is 89.0°
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Evaluate:
[tex]\bf{\sum^{10}_{n-1}\:8(\cfrac{1}{4})^{n-1}[/tex]
[tex]\bf{\overline{\underline{\overline{\underline{Please\:show\;work!}}}}[/tex]
Let S be the given sum, so
[tex]S = 8 + 8 \left(\dfrac14\right) + 8 \left(\dfrac14\right)^2 + \cdots + 8 \left(\dfrac14\right)^9[/tex]
[tex]\displaystyle S = 8 \left(1 + \dfrac14 + \frac1{4^2} + \cdots + \frac1{4^9}\right)[/tex]
Multiply both sides by 1/4.
[tex]\displaystyle \frac S4 = 8 \left(\frac14 + \frac1{4^2} + \frac1{4^3} + \cdots + \frac1{4^{10}}\right)[/tex]
Subtract this from S to eliminate all the but the first term in S and the last term in S/4 :
[tex]\displaystyle S - \frac S4 = 8 \left(1 - \frac1{4^{10}}\right)[/tex]
Solve for S :
[tex]\displaystyle \frac{3S}4 = 8 \left(1 - \frac1{4^{10}}\right)[/tex]
[tex]\displaystyle S = \frac{32}3 \left(1 - \frac1{4^{10}}\right) = \boxed{\frac{349,525}{32,768}}[/tex]
[tex]\huge\fbox\purple{question}[/tex]
#Write the member of the following sets=
a)V={vowels of English alphabets}
b){cube numbers between 0 to 50
c)M={y:y is a multiple of 3 less than 20}
#a
V={Vowels of English alphabets}
V={a,e,i,o,u,A,E,I,O,U}#b
C={cube numbers between 0 to 50}
C={0,1,8,27}#c
M={y:y is a multiple of 3 less than 20}
M={0,3,6,9,12,15,18}please help, 30 points, will give brainly
Answer:
∠ABC = 39°
Step-by-step explanation:
Since ED bisects ∠CBD :
∠EBD = ∠CBE = 30°
Now, ∠ABD = ∠ABC + ∠CBE + ∠EBD = 99°
Solving :
99° = ∠ABC + 30° + 30°∠ABC = 99° - 60°∠ABC = 39°In trapezoid ABCD, Line AB is parallel to CD. If AE=5.2, AC=11.7 and CD=10.5, what is the length of AB to the nearest tenth?
In trapezoid ABCD ,length of AB is equals to 8.4units(nearest tenth).
What is trapezoid?" Trapezoid is defined as the quadrilateral whose one pair of opposite side is parallel."
According to the question,
Given
Length of AE=5.2
Length of AC=11.7
Length of CD=10.5
As shown in figure
In trapezoid ABCD,
AB is parallel to CD, AC is the transversal.
AC and BD intersect at point E.
In ΔABE and ΔCDE,
∠BAE ≅∠ECD
∠ABE ≅∠EDC
By AA theorem,
ΔABE ~ ΔCDE
Therefore,
[tex]\frac{AE}{EC}=\frac{AB}{CD}[/tex]
AE + EC = AC
⇒ 5.2 + EC = 11.7
⇒ EC = 11.7 - 5.2
⇒ EC = 6.5units
Substitute the value in the given proportion we get,
[tex]\frac{5.2}{6.5}=\frac{AB}{10.5}[/tex]
⇒ [tex]AB = \frac{(10.5)(5.2)}{6.5}[/tex]
⇒[tex]AB = 8.4[/tex] units
Hence, in trapezoid ABCD ,length of AB is equals to 8.4units(nearest tenth).
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help me, please ist question 1
Answer:
432
Step-by-step explanation:
To find the volume of a rectangular prism you multiply, L × W × H
L = 6 W = 8 H =9 you plug that in 6 × 8 × 9= 432
so the volume is 432in²
write (4 x 100) + (3 x 10) + (6 x 1/10) + (7 x 1/100) in standard form.
Answer:
430.67
Step-by-step explanation:
(4 x 100) + (3 x 10) + (6 x 1/10) + (7 x 1/100)l
(400) + (30) + (6×0.1) + (7×0.01)
400 + 30 + 0.6 + 0.07
430.67
Which expression has the same value as the one below?
8 + 4 + (negative 9)
12 + (negative 9)
Negative 12 + 9
Negative 4 + (negative 9)
4 + (negative 9)
Answer:
A. 12 + (negative 9)
Step-by-step explanation:
8 + 4 - 9 = 3
12 - 9 = 3
-12 + 9 = -3
-4 - 9 = -13
4 - 9 = -5
this means that 8 + 4 - 9 = 12 - 9
making A the right expression
Which of the following is most likely the next step in the series?
A.
Answer:
D.
Step-by-step explanation:
If you look at the pattern, the first shape (square) has four sides. Then, you have 5 sides, and finally, 6 sides.
Thus, a pattern of 4, 5, 6. So, the next shape must have 7 sides, leaving the only possible answer as D.
If y=3x+5 and z=x^2+2x-5, what is yz?
Work Shown:
yz = y(x^2+2x-5)
yz = y(x^2) + y(2x) + y(-5)
yz = x^2( y ) + 2x( y ) - 5( y )
yz = x^2( 3x+5 ) + 2x( 3x+5 ) - 5( 3x+5 )
yz = x^2*3x + x^2*5 + 2x*3x + 2x*5 - 5*3x - 5*5
yz = 3x^3 + 5x^2 + 6x^2 + 10x - 15x - 25
yz = 3x^3 + 11x^2 - 5x - 25
For each inequality, decide whether the solutions is represented by x < 2.5 or x >2.5
1. -4x + 5 > -5. 2. -25 > -5(x + 2.5)
#1
-4x+5>-5-4x>-5-5-4x>-104x<10x<2.5#2
-25>-5(x+2.5)25<5(x+2.5)x+2.5>5x>2.5Answer:
1. x < 2.5
2. x > 2.5
Step-by-step explanation:
Question 1
Given inequality:
-4x + 5 > -5
Subtract 5 from both sides:
⇒ -4x + 5 - 5 > -5 - 5
⇒ -4x > -10
Divide both sides by -4 (remembering to flip the sign as we are dividing by a negative):
⇒ -4x ÷ -4 > -10 ÷ -4
⇒ x < 2.5
Question 2
Given inequality:
-25 > -5(x + 2.5)
Expand the brackets:
⇒ -25 > -5x - 12.5
Add 12.5 to both sides:
⇒ -25 + 12.5 > -5x - 12.5 + 12.5
⇒ -12.5 > -5x
Divide both sides by -5 (remembering to flip the sign as we are dividing by a negative):
⇒ -12.5 ÷ -5 > -5x ÷ -5
⇒ 2.5 < x
⇒ x > 2.5
rearrange the equation so b is the independent variable
a - 7 = 3(b+2)
a = ?
i really need help will give brainliest
Answer:
You would put 11y-22+7y-6+3x+12+5x and that will give you the answer. Hope this helps!
can someone help me with this question? thank ou!
Answer:
11
Step-by-step explanation:
2x-13=9
2x=9+13
2x=22
x=11
What is 5829×3782?
I will give you brainliest for right answer
Answer:
22045278
Step-by-step explanation:
5 8 2 9
3 7 8 2
11 6 5 8
4 6 6 3 2 0
4 0 8 0 3 0 0
1 7 4 8 7 0 0 0
2 2 0 4 5 2 7 8
Answer:
22045278
Step-by-step explanation:
It seems tricky, but if you break it down step by step it will make it a lot easier.
Hope it helped and you can do it!!
OA. Graph D
OB. Graph B
OC. Graph A
OD. Graph C
A
C
& I
of
B
D
SUBMIT
Answer:
My sister is doing this, I if remember correctly graph B?
Determine whether triangles EFG and PQR are congruent
Plsss help
Answer:
B
Step-by-step explanation:
Because it flipped over the x axis
Spot the coordinates
E(-3,1)P(-3,-1)F(1,1)Q(1,-1)G(4,4)R(4,-4)Yes it's reflection along x axis
.(x,y)=(x,-y)Option B
which of the following are accepted without proof in a logical system?check all that apply
a. postulates
b. theorems
c. conjectures
d. axioms
B postulates and C axioms are accepted without proof in a logical system.
What is Theorem?A theorem is a statement that can be proven true using standard mathematical operations and reasoning. A theorem, in general, is an embodiment of a general principle that is part of a larger theory. A proof is the process of demonstrating that a theorem is correct.
A conjecture is a proposition or conclusion based on insufficient knowledge for which no demanding proof exists.A statement that is said to be universal truth is referred to as an axiom.A postulate is a proposition that is said to be true in the absence of logical proof.A theorem is a statement with a logical proof that relies on previously confirmed statements.Learn more about theorem here:
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a pair of dice is rolled what is the probability of getting a sum of seven or eleven
Answer:
Step-by-step explanation:
this year you earned $75500. Last year you earned $72400. What the rate of change on your earnings since last y?
Which statement describes the vertical asymptotes of the graph of f(x)=x^2-64/8x-64
O The graph has no vertical asymptote.
O The graph has a vertical asymptote at x = 8 only.
O The graph has a vertical asymptote at x = -8 only.
O The graph has vertical asymptotes at both x = 8 and x = -8.
The graph has no vertical asymptote
===========================================================
Explanation:
Let's simplify the function by factoring each piece.
[tex]f(x) = \frac{x^2-64}{8x-64}\\\\f(x) = \frac{(x-8)(x+8)}{8x-64}\\\\f(x) = \frac{(x-8)(x+8)}{8(x-8)}\\\\f(x) = \frac{x+8}{8}\\\\[/tex]
In the 2nd step, I used the difference of squares rule to factor the numerator. In the 4th step, the (x-8) terms cancel.
The simplified version doesn't have any variables in the denominator. This indicates the denominator is always 8, and never 0. So it's impossible to divide by zero in this simplified form. Consequently it means this graph has no vertical asymptotes.
However, there is a hole at x = 8 because this input causes a division by zero error in the original non-simplified function. Why? Because the calculator will use PEMDAS to evaluate the expression after replacing every copy of x with 8. It likely won't attempt to simplify like shown in the steps above. This is what causes the hole at x = 8.
The value x = -8 is perfectly fine in either the original function or the simplified one. It doesn't cause the denominator to be zero.
What is limit of startroot x squared minus 8 endroot as x approaches negative 3? –5 1 startroot 2 endroot startroot negative 14 endroot
The limit of [tex]\lim_{x \to -3}\sqrt{ x^2-8}[/tex] as x approaches negative 3 is 1
Limit of a functionThe limit of the function given in question can also be written as:
[tex]\lim_{x \to -3}\sqrt{ x^2-8}[/tex]
To determine the required limit, we will simply substitute the value of x into the function as shown:
[tex]\lim_{x \to -3}\sqrt{ x^2-8}=\sqrt{ (-3)^2-8}\\\lim_{x \to -3}\sqrt{ x^2-8}=\sqrt{9-8}=1\\[/tex]
Hence the limit of [tex]\lim_{x \to -3}\sqrt{ x^2-8}[/tex] as x approaches negative 3 is 1
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Answer: the answer is b. 1
Step-by-step explanation: just got it right on edge
I want pictures of how you took the answer
The value of x in both case is 17 and 10.
What is complementary and supplementary angle?If the sum of two angles is 180 degrees then they are said to be b angles, which form a linear angle together. Whereas if the sum of two angles is 90 degrees, then they are said to be complementary angles, and they form a right angle together.
1. As the given angle is 90 degree i.e., complementary angle.
So,
22+4x=90
4x= 90-22
4x= 68
x= 17
2. As the figure for the linear pair i.e., supplementary angle
So,
110+7x=180
7x=70
x=10
Hence the value of x in both case is 17 and 10.
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help me thank you ill give brainlyies
Answer:
-5 degrees is colder than -3 degrees farienheight.
Step-by-step explanation:
Let's take this and eliminate every answer-
"The lowest temperature is -3 degrees."
-5 is lower than -3.
"The highest temperature is -5 degrees."
-5 degrees is the lowest temperature, not the highest!
"-5 is warmer than 3 degrees."
-5 is the LOWEST TEMPERATURE.
This leaves us with "-5 is colder than -3 degrees," which is correct because -5 is the smallest temperature and therefore, it is the coldest.
From a hot-air balloon, Ian measures a 30^{\circ}
∘
angle of depression to a landmark that’s 1250 feet away, measuring horizontally. What’s the balloon’s vertical distance above the ground? Round your answer to the nearest tenth of a foot if necessary.
The balloon’s vertical distance above the ground is 721.7 f
Angle of elevation and depressionIn order to determine the balloon's vertical distance, we will use the SOH CAH TOA identity
Given the following parameters
Angle of depression = 30 degrees
Horizontal distance =1250 feet
Required
vertical distance H
Using the SOH CAH TOA identity
tan 30 = H/1250
H = 1250tan30
H = 721.7 feet
Hence the balloon’s vertical distance above the ground is 721.7 feet
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Answer:
721.7
Step-by-step explanation:
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the atlanta braves are offering bobblehead to every 10th person who enters your fundraiser. the nashville predators are offering a free ticket to every 15th person who enters the fundraiser. how many attendees must come before someone receives both bobblehead and a ticket?
In this situation, attendee number thirty will be the first one o receive both the bobblehead and the ticket.
Which attendees will receive the bobblehead and the ticket?Bobblehead:
Attendee number 10Attendee number 20Attendee number 30Ticket:
Attendee number 15Attendee number 30What can be concluded?It can be concluded the attendee number 30 will be the first one to receive both the ticket and the bobblehead.
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9x?=3/2+ 3/2 + 3/2 10 pts for correct answer
A fraction is a way to describe a part of a whole. The fraction that can replace the question mark is 1/2.
What is a Fraction?A fraction is a way to describe a part of a whole. such as the fraction ¼ can be described as 0.25.
The fraction that can replace the question mark is,
9 × ? = (3/2) + (3/2) + (3/2)
9 × ? = 3(3/2)
9 × ? = 9/2
9 × ? = 9/2
? = 9/(2×9)
? = 1/2
Hence, the fraction that can replace the question mark is 1/2.
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It’s just fill in the blank please help LOL
Answer and explanation:
vertex: (3,25) The vertex is the minimum/maximum of a parabola where the direction it's moving in changes. For this question, that point is (3,25).
zeroes: x=6 and x=0 The zeroes of an equation are the points that y=0. Since it doesn't look like they want the full coordinate points, I would list x=6 for the point (6,0) and x=0 for the point (0,0).
y-intercept: x=0 The y-intercept is the point at which the graph crosses the y-axis, which here happens at (0,0), or x=0.
Highest point: 25 The highest point is the maximum of the graph, meaning it's the highest y-value that the graph has. Here, this is 25 (it's also the y-value for the vertex).
Time: 3 seconds The time it takes for Simon to reach the highest point is just the x-value of the vertex, so 3.
Total air time: 6 seconds This value is the total time that the y-value of the graph is above 0. To find this, you must subtract the x-values of the zeroes from each other. Since 6-0=0, Simon is in the air for 6 total seconds.
Hope this helps! :)