Answer:
31/10
Step-by-step explanation:
Scott is 5 years old. His Aunt Mary
is 4 times as old. In how many
years will Scott be half as old as
his aunt will be at that time?
Right now, Scott is 5.
His Aunt Mary is 4*5 = 20
We can solve this algebraically if your teacher requires to.
In x years, Scott will be half as old as his Aunt right now (which is 20).
5+x= 20/2
5+x=10
x=5
In 5 years Scott will be half as old as his aunt was.
Which part of the algebraic expression 7a - 4 is the constant?
7a4
4
7 a
O7
Given the equation, what is the center and radius of the circle?
(x-7) ^2 + (Y-4) ^2= 64 ^2
We are given the equation of circle (x - 7)² + (y - 3)² = 64² , but let's recall the standard equation of circle i.e (x - h)² + (y - k)² = r², where (h, k) is the centre of the circle and r being the radius ;
So, consider the equation of circle ;
[tex]{:\implies \quad \sf (x-7)^{2}+(y-4)^{2}=(64)^{2}}[/tex]
On comparing this equation with the standard equation of Circle, we will get, centre and radius as follows
Centre = (7, 4)Radius = 64 units4sin45 degrees cos 15degrees=1+square root 3
[tex]\text{R.H.S}\\\\=4\sin 45^{\circ} \cos 15^{\circ} \\\\=4\sin 45^{\circ} \cos (45^{\circ}-30^{\circ})\\ \\=4 \sin 45^{\circ} \left(\cos 45^{\circ} \cos 30^{\circ} +\sin 45^{\circ} \sin 30^{\circ} \right)\\\\=4 \left(\sin 45^{\circ} \cos 45^{\circ} \cos 30^{\circ} +\sin^2 45^{\circ} \sin 30^{\circ} \right)\\[/tex]
[tex]=4\left[\dfrac 1{\sqrt 2} \cdot \dfrac 1{\sqrt 2} \cdot \dfrac{\sqrt 3}2 +\left( \dfrac 1{\sqrt 2} \right)^2 \cdot \dfrac 12 \right]\\ \\=4\left(\dfrac{\sqrt 3}4 +\dfrac 14\right)\\\\=4\cdot \dfrac 14 \left(1+\sqrt 3\right)\\\\=1+\sqrt 3\\\\=\text{L.H.S}[/tex]
What is the solution to the equation x + 14 = 63? (Input a whole number only.) (3 points) Blank 1:
Hey there!
This is a one-step equation, meaning that we can solve it in one step.
This is the step:
Subtract 14 from both sidesGoal:
To find out the value of xSubtract 14:
x+14-14=63-14
the 14's on the left cancel:
x=49
Hence, the answer is
[tex]\boxed{\boxed{\bold{x=49}}}[/tex]
Hope everything is clear.
Let me know if you have any questions!
#LearningDoesn'tEnd
:-)
[tex]\rule{200}{2}[/tex]
A triangle has an angle measuring 90., an angle measuring 20., and a side that is 6 units long. The 6-unit side is in between
the 90 and 20. angles.
Is this a picture of the above triangle?
yes - true
no-false
Will give branliest
Yes :- true
as in the diagram 6 units in between the 20° and 90° and third angle will be 180-110 = 70°
Triangle with angle 90 and 20 degree possible as it Satisfies the angle sum property.
What is Angle Sum Property?The total of a triangle's three internal angles is 180 degrees, as stated by the angle sum feature of a triangle. A closed shape with both inner and exterior angles, a triangle is created by three line segments.
Given:
angles= 20 and 90 degree
Using Angle Sum property
20 + 90 + <3 =180
<3 = 180 - 110
<3 =70
Hence, the Triangle with angle 90 and 20 degree possible as it Satisfies the angle sum property.
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i need help quick.......
[tex]\text{Radius of circle, r} =\dfrac 62 = 3~ m \\\\\text{Area of circle} = \pi r^2 = \pi \cdot 3^2 = 3.14 \times 9 =28.26~m^2[/tex]
A building that is 150 ft tall casts a shadow of 20 feet long.
At the same time a tree casts a shadow of 2 ft. How tall is
the tree?
a. 15
b. 20
c. 25
d. 30
Answer:
a.15 feet
Step-by-step explanation:
150 divided by 20 is 7.5
7.5 times 2 is 15
Please help this is due
[tex]\text{Area of equilateral triangle ABC}\\ \\=\dfrac{\sqrt 3}{4} BC^2\\\\=\dfrac{\sqrt 3}4 \cdot 12^2\\\\=\dfrac{144\sqrt 3}{4}\\\\=36\sqrt 3[/tex]
What is the volume of this object?
Answer:
19
Step-by-step explanation:
(Assuming that each cube is 1 unit), the volume is 5 + 6 + 8 which equals 19
$5000 principal earning 4% compounded annually, 4 years
Answer: $7401.22
Step-by-step explanation: it’s right just trust me
[tex]\underline{\boxed{\blue{\Large{\bf{Challenge}}}}}[/tex]
If 'P and 'Q' are two points whose coordinates are (at^2, 2at) and (a/t^2, 2a/t) respectively and S is the point(0, 0). Show that 1/SP + 1/SQ is independent of 't'.
Note:-
Plagarised/spam/short answers will be deleted on the spot.
Answer with all steps and proper explanation .
Step-by-step explanation:
Given point are: P(at², 2at)
Q(a/t², 2a/t)
S(0, 0)
Now, the distance between A(x₁y₁) and B(X₂, y₂)
then AB = √{(x₂ - x₁)² + (y₂ - y₁)²} units
(i) The distance between S and P:
(x₁, y₁) = (0, 0) ⇛x₁= 0, y₁ = 0
(x₂, y₂ ) = (at², 2at) ⇛x₂ = at², y₂ = 2at
SP = √{at² - 0)² + (2at - 0)²}
= √{(at²)² + (2at)²}
= √{a²t²*² + 4a²t²}
= √{a²t⁴ + 4a²t²}
= √{a²t²(t²+4)}
SP = at√(t² + 4)→→→Eqn(1)
(ii) The distance between S and Q :
(x₁, y₁) = (0, 0) ⇛x₁= 0, y₁ = 0
(x₂, y₂ ) = (a/t², 2a/t) ⇛x₂ = a/t², y₂ = 2a/t
SQ = √[{(a/t²) - 0} + {(2a/t) - 0}
= √{(a/t²)² + (2a/t)²}
= √{(a²/t²*²) + (4a²/t²)}
= √{(a²/t⁴) + (4a²/t²)}
= √{(a² + 4a²t²)/t⁴}
= √[{a²(1 + 4t²)}/t⁴]
SQ = (a/t²)√(1 + 4t²) →→→ Eqn(2)
Now,
(1/SP) + (1/SQ) = [1/{at√(t² + 4)}] + [1/{(a/t²)√(1 + 4t²)}]
= (1/at)[1/{√(t² + 4)}] + (t²/a)[1/{(√1 + 4t²)}]
= (1/a)[[1/{t√(t² + 4)}] + [t²/{√(1 + 4t²)}]]
(1/SP) + (1/SQ) = 1/a is not independent of 't'
If suppose S = (a, 0) then
SP = √{(at² - a)² + (2at - 0)²}
= √{a²(t² - 1)² + (2at)²}
= a√{(t² - 1)² + 4t²}
= a√{(t² + 1)²}
SP = a(t² + 1)
1/SP = 1/{a(t² + 1)} →→→Eqn(1)
And
SQ = √[{(a/t²) - a}² + {(2a/t) - 0}²]
= √[a²{(1/t²) - 1}² + a²(2/t)²]
= a√[{(1 - t²)²/t⁴} + (4/t²)]
= a√[{(1 - t²)² + 4t²}/t⁴]
( a/t²)√(1 + t²)²
SQ = (a/t²)(1 + t²)
1/SQ = 1/{(a/t²)(1 + t²)} = t²/{a(1 + t²)} →→→Eqn(2)
Therefore, (1/SP) + (1/SQ)
= 1/{a(t² + 1)} + t²/{a(1 + t²)}
= (1 + t²)/a(1 + t²)
= 1/a
1/a is independent of 't'.
What is the area of this trapezoid?
15 ft
Enter your answer in the box
18 ft
37 ft
Ft^2
Answer: I am pretty sure it's 18 feet.
Step-by-step explanation:
What is the measure of m? n 20 m 5 m.
m = 5 V Give your answer in simplest form. Enter
Answer:
m = 5[tex]\sqrt{5}[/tex]
Step-by-step explanation:
To find the measure of m we use the following Euclidian theorem:
m^2 = 5*(5+20)
m^2 = 125 find the root for both sides
m = 5[tex]\sqrt{5}[/tex]
Which is the correct graph of y=2/x^2-4 ?
Ann got a prepaid debit card with $15 on it. For her first purchase with the card, she bought some bulk ribbons at a craft store. The price of the ribbon was 17 cents per yard. If after that purchase there was $10.41 left on the card, how many yards of ribbon did Ann buy?
Since the price of the ribbon is 17 cents per yards, the number of yards of ribbon Ann bought is 27 yards.
How to find the length(yard) from the cost(dollars)She has 15 dollars in her debit card.
She bought bulk ribbons at a craft store.
The price of the ribbon is 17 cents per yards. Therefore,
17 cents = 0.17 dollars
Hence,
Amount debited from her account = 15 - 10.41 = $4.59
Therefore, she spent a total of $4.59 .
The yards of ribbon bought = 4.59 / 0.17
The yards of ribbon bought = 27
Therefore, Ann bought 27 yards of bulk ribbon.
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In the rectangular pyramid below, l=30, w=20, and h=28. What is the length of s?
Answer:
A=lw+l(w
2)2+h2+w(l
2)2+h2=30·20+30·(20
2)2+282+20·(30
2)2+282≈2127.25933
Your answer is 2127.259
I think it will help you
If "s" represents the slant height in the rectangular pyramid with dimensions l = 30, w = 20, and h = 28, then the length of "s" is approximately 29.75 units.
To find the length of "s" in the rectangular pyramid, we first need to understand the terminology used to describe the different dimensions of a pyramid.
In a rectangular pyramid, "l" usually represents the length of the base, "w" represents the width of the base, and "h" represents the height of the pyramid (the perpendicular distance from the base to the apex or top vertex of the pyramid).
However, there is no standard notation for the length of the slant height (s) in a rectangular pyramid. In this context, the term "s" could represent either the slant height or some other unknown dimension of the pyramid.
If "s" represents the slant height of the pyramid, we can use the Pythagorean theorem to find its value. The slant height, "s," is the hypotenuse of a right triangle formed by one of the triangular faces of the pyramid and the height and half the width of the base.
Using the given dimensions:
l = 30 (length of the base)
w = 20 (width of the base)
h = 28 (height of the pyramid)
Let's find the value of "s" using the Pythagorean theorem:
[tex]s^2 = h^2 + (w/2)^2\\s^2 = 28^2 + (20/2)^2\\s^2 = 28^2 + 10^2\\s^2 = 784 + 100\\s^2 = 884\\[/tex]
Now, take the square root of both sides to find the value of "s":
s ≈ √884
s ≈ 29.75 (rounded to two decimal places)
So, if "s" represents the slant height in the rectangular pyramid with dimensions l = 30, w = 20, and h = 28, then the length of "s" is approximately 29.75 units.
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Given ∠4≅∠14, which lines, if any, must be parallel based on the given information? Justify your conclusion. a∥b, Converse of the Same-Side Interior Angles Theorem a∥b, Converse of the Alternate Interior Angles Theorem a∥b, Converse of the Corresponding Angles Theorem not enough information to make a conclusion Two horizontal, parallel lines, line c and line d, where line c is above line d. These lines are intersected by two diagonal parallel lines, line a and line b. Line a is to the left of line b. The angles created by each intersection are numbered. From top left, going clockwise, the angles where line a intersects line c are labeled eleven, ten, nine, and twelve. The angles where line b intersects line c are labeled seven, six, five, and eight. The angles where line a intersects line d are labeled fifteen, fourteen, thirteen and sixteen. The angles where line b intersects line d are labeled three, two, one and four.
Answer:
a∥b, Converse of the Alternate Interior Angles Theorem
A team t-shirt costs $3 per adult and $2 per child. On a certain day, the total number of adults (a) and children (c) who bought shirts was 100, and the total money collected was $275. Which of the following options represents the number of children and the number of adults who purchased team shirts that day, and the pair of equations that can be solved to find the numbers?
Answer:
D.)25 children and 75 adults
Equation 1: a + c = 100
Equation 2: 3a + 2c = 275
Step-by-step explanation:
A team t-shirt costs $3 per adult and $2 per child.
Let the number of children be = c
Let the number of adults be = a
A team t-shirt costs $3 per adult that is 3a and $2 per child that is 2c, also given is that the total money collected is $275, so equation becomes:
On a certain day, the total number of adults (a) and children (c) who bought shirts was 100, equation becomes:
Now to know the number of children and adult, we can check by plugging in the values from options provided.
25 children and 75 adults = 25(2)+75(3)=50+225 =275
How do you solve this
2x + 3 = 12
[tex]======================================[/tex]
In order to solve this equation, we should first subtract 3 from both sides:
[tex]\pmb{2x=12-3}[/tex]
Which equals
[tex]\pmb{2x=9}[/tex]
Divide both sides by 2
[tex]\pmb{x=\displaystyle\frac{9}{2} }[/tex]
[tex]======================================[/tex]
note:-Hope everything is clear; if you need any more explanation/clarification, kindly let me know, and I will comment and/or edit my answer :)
Answer:
If you are trying to find slope this is how you solve it.
Step-by-step explanation:
2x+3=12
-2x -2x
3=-2x+12
÷3 ÷3 ÷3
y=-2/3x+4
So if you are trying to find the slope it is -2/3x and the y intercept is 4.
9×4 - 10 fours - ? fours
Answer:
9×4 - 10 fours - 26 fours
Step-by-step explanation:
9×4 - 10 fours - 26 fours
. Quinn is building a table. The top is an isosceles trapezoid, with bases that are 1.5 meters and 2 meters, and a height of Imeter. What is the area of the table top?
The family soent 125$ in may for electric bills, in june the bill increased by 12% bc they used the ac more often. Write a equation to calculate their total electricity bill in june. Let y equal the total cost
Answer:
125x 12 and divide the answer
Step-by-step explanation:
Answer:
125x 12 and divide the answer
Step-by-step explanation:
There are several ways to reduce how much does it cost to run an air conditioner. The two main ones are:Buying an air conditioner with a high energy efficiency rating (EER, SEER, CEERratings are valid specifications).Reducing the number of hours per day that you use a given air conditioner.Note: It’s recommended to estimate how much electricity does an air conditioner use before buying a specific unit.On average, running an air conditioner costs between $0.06 and $0.88 per hour. Let’s calculate how much does air conditioning cost per month (running 8h per day):
What are the solutions to the system of equations graphed below?
A. (-2, 0) and (6,0)
B. (-3, -3) and (0,6 )
C. (-3,3) and (6,0)
D. (-2,0) and (2,0)
Answer:
looking at the straight line, it touches the axis at (-2,0) and (6,0)
Step-by-step explanation:
Simplify the given expressions below.
I) 4x + 8 - 2x + 7
2) 2n ×5 ×2a
3) 6a power 5 over 3a power 2 ×2a
please work it out and clear
Step-by-step explanation:
1) [tex] \Rightarrow \: \sf \: 4x + 8 - 2x + 7[/tex]
Combine like terms
[tex] \rightarrow \: \sf \: ( 4x - \textcolor{green}{2}x) + (7 + \textcolor{green}{8})[/tex]
Add 4x and 2x , 7 + 8
[tex] \rightarrow \sf \: 2x + 15[/tex]
~Done~
2) [tex] \Rightarrow \sf 2n ×5 ×2a[/tex]
[tex] \rightarrow \sf \:( 2n) (5) (2a)[/tex]
[tex] \rightarrow \sf \: 20an[/tex]
~Done~
Lisa, Kim and Bridget flew total of 7800 miles on Southwest airlines last year. Lisa flew 1500 miles. Kim flew 2200 miles. How many miles did Bridget fly?
Answer:
Bridget flew 4100 miles.
Step-by-step explanation:
L + K + B = 7800
1500+2200+B=7800
3700 + B = 7800
Subtract 3700.
B = 4100
Bridget flew 4100 miles.
Jason measured rainfall for a science project. Last week it rained 3 1/8 inches in all. This week it rained 1 7/8 inches on one day and 2 3/4 inches on another. How many more inches did it rain this week than last week? Explain how you found your answer.
Answer:
1 1/2 inches
Step-by-step explanation:
To find how much more a second number is than a first number, the first is subtracted from fhe second. Here, we want to know how much more the second week total is than the first, so we subtract the first week's total from the second week's total.
__
We find the second week's total by adding up the values associated with the different days in the second week.
second week's total = 1 7/8 +2 3/4 = (1 +2) +(7/8 +6/8) = 3 13/8 = 4 5/8
Then the difference is ...
second week's total - first week's total
= 4 5/8 -3 1/8 = (4 -3) +(5/8 -1/8) = 1 4/8 = 1 1/2
It rained 1 1/2 inches more this week than last week.
Which of the following best describes the graph below
Answer:
i believe its A
Step-by-step explanation:
Answer:
B. The graph is not a function.
Step-by-step explanation:
We are given the graph of a relation. It is required to determine whether the graph represents a function or not. 'If a vertical line passing through the graph of the relation cuts the graph at at-most one point, then the given graph represents a function else not'. So, if we plot the vertical line 'x = 3' in the figure, we see that, The vertical line drawn crosses the graph at two points A and B as shown below. Thus it would be B
What numbers could replace each letter to make both of the number sentences true?
Answer:
N = 9 & P = 4
Step-by-step explanation:
N* N = 81
N * N = 9*9
N = 9
N * P = 36
Substitute N = 9,
9* p = 36
P = 36 ÷ 9
P = 4
what is the value of n in the equation -1/2(2n+4)+6= -9+4(2n+1)
Answer:
n=1
Step-by-step explanation:
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