Step-by-step explanation:
Let me start off by saying that 1 unit side is absolutely useless.
You can translate the 6 unit side downwards, so now we have a right isosceles triangle of 2 equal sides which are 6
The hypotenuse is given here by x.
Applying the Pythagorean theorem i can then say;
[tex]x {}^{2} = 6 {}^{2} + 6 {}^{2} [/tex]
[tex]x {}^{2} = 36 + 36[/tex]
[tex]x {}^{2} = 72[/tex]
[tex]x = \sqrt{72} = 6 \sqrt{2} = 8.485[/tex]
x=8.5
rounded to the nearest 10 :)
The local museum had 350 members only 20% of the members visit on any given Saturday what number usually on Saturday k
Answer:
70
Step-by-step explanation:
20% of 350 =
= 20% * 350
= 0.20 * 350
= 70
Which value of x makes the equation 6 ( x − 2 ) = 3 − 9 x true?
Answer:
x = 1
Step-by-step explanation:
6(x - 2) = 3 - 9x
We want to find x so that LHS = RHS/
6x - 12 = 3 - 9x
6x + 9x = 3 + 12
15x = 15
x = 1
Not 100% sure!
The value of x that makes the equation true is x = 1.
What is an expression?An expression in mathematics is a combination of numbers, variables, and mathematical operations (such as addition, subtraction, multiplication, and division) that represents a value or quantity.
We can solve for x by simplifying the equation using the distributive property and combining like terms:
6(x - 2) = 3 - 9x
6x - 12 = 3 - 9x (distribute 6)
6x + 9x = 3 + 12 (add 9x and 12 to both sides)
15x = 15 (combine like terms)
x = 1 (divide both sides by 15)
Therefore, the value of x that makes the equation true is x = 1.
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A small rectangular package has a area of 9x square units and a height of 5 units. A large rectangular package has an area of 6 square units a d a height of 3x units more than the small box. What equation could be used to determine the volume of the large rectangular box?
The equation to determine the volume of the rectangular box is:
V = 6 * (5 + 3x)
Given that the area of the large rectangular package is 6 square units and its height is 3x units more than the small box,
To determine the volume of the large rectangular package, multiply its area by its height.
Volume of the large rectangular package = Area of the large rectangular package * Height of the large rectangular package
The area of the large rectangular package is given as 6 square units, so we substitute it into the equation:
Volume of the large rectangular package = 6 * Height of the large rectangular package
Now, the height of the large rectangular package is 3x units more than the small box. The height of the small box is 5 units, so we add 3x to it:
Height of the large rectangular package = 5 + 3x
Substituting this into the equation:
Volume of the large rectangular package = 6 * (5 + 3x)
Hence, the equation to determine the volume of the large rectangular package is: Volume = 6 * (5 + 3x)
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You want to determine how quickly messages can spread on a social media website. On the first day, you
create a message that is shared with 2 people. On the second day, each of those people share it with 3 people.
On third day, everyone who received the message shares it with 3 more people, and so on. Write an equation
that represents the nth term of the geometric sequence. Then find as.
The equation that represents the nth term of the geometric sequence is 6 x 3^N = X.
Equations
Given that you want to determine how quickly messages can spread on a social media website, and on the first day, you create a message that is shared with 2 people, and on the second day, each of those people share it with 3 people, and on the third day, everyone who received the message shares it with 3 more people, and so on, to write an equation that represents the nth term of the geometric sequence, the following calculation must be made:
2 x 3 x (3 x (3 x (3 x( 3 x ...)))) = X2x3x3^N = X6x3^N = XTherefore, the equation that represents the nth term of the geometric sequence is 6 x 3^N = X.
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P is inversely proportional to q^3, when p has the value 27, q has the value 3. i) find the formula which expresses p in terms of q. P= r is directly proportional to q, when r has the value 10, q has the value 2. ii) prove that r=kp^n and so find the value of k and n.
Answer:
Step-by-step explanation:
i) If p is inversely proportional to q³, this is expressed as p ∝ q³
p = k/q³ where q is the proportionality constant.
Given p = 27 and q = 3
Substitute this values into the formula
27 = k/(3)³
27 = k/27
k = 27×27
k = 729
Substitute k = 1 into the formula
p = 729/(q)³
Hence the formula which expresses p in terms of q is p = 729/q³
ii) If r is directly proportional to q, it is expressed as r ∝ q
r = kq
If r = 10 and q = 2
Substitute
10 = 2k
k = 10/2
k = 5
The equation becomes
r = 5q... 1
From 1) p = 729/q³
q³ = 729/p
q = 9/³√p
q = 9/p^1/3....2
Substitute equation 2 into 1
r = 5(9/p^1/3)
r = 45p^-1/3
Compare r = 45p^-1/3 with r = kp^n
k = 45 and n = -1/3
A 2-column table with 4 rows. The first column labeled Elevation (meters) has entries 500, 1000, 1500, 2000. The second column labeled Temperature of air (degrees Celsius) has entries 11. 8, 8. 5, 5. 3, 2. 0. As elevation increases, temperature decreases. At which elevation will sound travel fastest? 500 meters 1,000 meters 1,500 meters 2,000 meters.
At an elevation of 500m, the sound will travel fastest.
Elevation Temp
500m 11.8°C
1000m 8.5°C
1500m 5.3°C
2000m 2.0°C
Why do sounds travel at a faster rate at high temeratures?We know that air molecules at higher temperatures have more energy and can vibrate faster and allow sound waves to travel more quickly because the more is the medium, the more quickly sound waves propagate.
So, when the given temperature is maximum i.e. 11.8°C, the sound will travel fastest. The elevation corresponding to 11.8°C is 500m.
So, Sound will travel fastest at 500m elevation.
Therefore, At an elevation of 500m, the sound will travel fastest.
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Leila purchased a snack-size roll of candy tarts, and found that only 1/7 of them were grape-flavored. Suppose Leila later
buys a king-size roll of candy tarts that contains 40 pieces. How many of that roll can she expect to be grape-flavored?
HELP PLEASE!!!!!
Answer:
6 candy tarts
Step-by-step explanation:
Based on Leila's observations, we would expect all boxes of candy tarts to have 1/7 grape-flavoured ones. If we have a box of 40, we can find the expected number of grape flavoured nady tarts by multiplying 40 and 1/7.
40 × 1/7 = 5.714285714
You can round this to 6 candy tarts
help i need help! please help
Anwser: its the secend answer
Step-by-step explanation: have had the smae question
Make a number line and mark the points that represent the following values of x.
−5≤x≤34
The expression −5 ≤ x ≤ 34 is an inequality expression
How to draw the number lineThe expression is given as:
−5 ≤ x ≤ 34
This can be split as follows:
−5 ≤ x and x ≤ 34
The inequalities used in the expression are less than or equal to.
This means that the endpoints of the inequality are inclusive of the values of x.
So, the value of x starts from -5, and it ends at 34
See attachment for the number line
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Please help! Problem is below! What is the length of CD to the nearest tenth of a centimeter? All angles are right angles and right triangles are formed.
Part A
What is the approximate area of each cross section of the cone and pyramid?
Type the correct answer in each box. Use numerals instead of words.
Both areas of the circle (cross section for cone) and the square(cross section for pyramid) was found using the
Area of Circle = πr^2Area of Square = Length * WidthArea of Flat ShapesNo Images were provided in this question, however, the cross section of a cone and a pyramid will result to the shapes of a circle and a square respectively when we slice them horizontally
Hence the area of the cross section of the cone can be estimated using the expression for the area of a circle
Area of Circle = πr^2
Also, the area of the cross section of the pyramid can be estimated using the expression for the area of a square
Area of Square = Length * Width
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The area of a rectangle is 54 square meters. The width is 9 meters long.
Answer:
A) [tex]9 *l=54[/tex]
Step-by-step explanation:
The area of a rectangle is w*l=A, where w is the width and l is the length.
In this question, we are given 2 of the variables. We are told that the width is 9 and the area is 54. So, to find the equation that represents this situation, simply plug in the values.
This gives [tex]9 *l=54[/tex].Then, if needed we can find the length of the rectangle. Through the division property of equality, we know that dividing both sides of the equation maintains the equality of the equation. So, we can divide both sides by 9 to isolate the variable.
This means that [tex]l=6[/tex].What is the width rounded to the nearest whole number? (width = 13.62 ft)
Answer:
14
Step-by-step explanation:
Our goal is to round it so we only have an integer part using the following rules:
If the first digit in the fractional part of 13.62 is less than 5 then we simply remove the fractional part to get the answer.
If the first digit in the fractional part of 13.62 is 5 or above, then we add 1 to the integer part and remove the fractional part to get the answer.
The first digit in the fractional part is 6 and 6 is 5 or above. Therefore, we add 1 to the integer part and remove the fractional part to get 13.62 rounded to the nearest whole number as:
14
Darren arrived at school at 8:00 a.m. and left at 2:30 p.m. Dean arrived at school at 8:15 a.m. and left at 3:15 p.m. How much longer was Dean at school than Darren
Answer:
Dean was at school for 30 minutes more than Darren.
Step-by-step explanation:
8:15-3:15 is 7 hours. 8:00-2:30 is 6 hours 30 minutes. The difference between the two is half an hour.
Hope this helps!!
guys i NEED HELP NOW! ansewr this ( 2 1/4) x (-8)
Answer:
-18
Step-by-step explanation:
If you turn 2 1/4 into an improper fraction, you get 9/4
Turn -8 into an improper fraction, you get -8/1
Equation: 9/4*-8/1
You can cross cancel the 4 and the 8 so your equation becomes 9/1*-2/1 which becomes 9*-2
Multiply and you get -18 :)
For what values of a are the following expressions true? a +5 = −5−a ,a +5 = a + 5
Answer:
Step-by-step explanation:
PLEASE HELP!!! URGENT!!! ASAP!!! WILL GIVE BRAINLIEST!!! JUST PLEASE LEND ME A HELPING HAND!
anyone know the answer
Answer: 0.1 goes in the blank because the hundredths is improper
Step-by-step explanation:
Rewrite in simplest terms: -2(5d-9f)+7f-10(-9f-7d)
Answer:
= 5 ( 12d + 23f )
Step-by-step explanation:
-2(5d-9f)+7f-10(-9f-7d
Open parenthesis
= -10d + 18f + 7f + 90f + 70d
Collect like terms
= -10d + 70d + 18f + 7f + 90f
= 60d + 115f
Factorise
= 5 ( 12d + 23f )
Therefore,
-2(5d-9f)+7f-10(-9f-7d) in its simplest form is 5 ( 12d + 23f )
Natalie is shopping for new clothes and does not want to spend more than $65. She buys one dress for $26 and wants to buy a few shirts that cost $13 each. Which inequality can she use to determine the number of shirts she can buy, x?
Answer:
easy
Step-by-step explanation:
65=26=13x
you should be able to solve it from there, its legit just subtracting then dividing.
the adjacent side of a parrallelogram are 12 and 7cm.if the angle between them is 150 degrees.find the area of the parallelogram
Answer:
area of parallelogram= 59.39 cm square
A plant is already 12.00 meters tall, and it will grow 15 centimeters every month. The plant's height, H (in meters), after x months is given by the following. H= 12.00 +0.15x What is the plant's height after 40 months?
Answer:
495cm
Step-by-step explanation:
so for a second forget about the already 12 meters. Multiply 15 by the amount of months, in this case 40 so 12x40= 480. Then add the 15, so its 495cm tall
I’ve tried a couple different things and are still stuck some help would be great
Answer:
12×7×4+1=337
Step-by-step explanation:
if u did anything else it would be smaller and u can't use all multiplication because 12×7×4×1=336
(07.02 MC) what is the value of y in the equation 3(3y - 15) = 0?
Answer:
[tex]y = 5[/tex]
Step-by-step explanation:
Given equation:
[tex]3(3y - 15) = 0[/tex]
Divide both sides by 3:
[tex]\implies \dfrac{3(3y - 15)}{3} = \dfrac{0}{3}[/tex]
[tex]\implies 3y-15 = 0[/tex]
Add 15 to both sides:
[tex]\implies 3y-15 +15= 0+15[/tex]
[tex]\implies 3y=15[/tex]
Divide both sides by 3:
[tex]\implies \dfrac{3y}{3}=\dfrac{15}{3}[/tex]
[tex]\implies y=5[/tex]
Answer:
The value of y is 5.
Step-by-step explanation:
First, we will distribute 3 on (3y - 15) This means 3(3y) - 3(15) = 0. Now, we will multiply 3 by what is inside the parentheses for each value. This gives us 9y - 45 = 0. After that, we will add 45 to both sides, which leaves us with 9y = 45. Finally, we will divide 45 by 9 to give us the y value, 5. I hope this helped (:
List the Slope of this Equation: Y=-7/2x+3
The slope is -7/2
Y = mx + b
m stands for the slope (numerical coefficient for x)
find the measure of x
Answer:
3
Step-by-step explanation:
Answer:
X=3
Step-by-step explanation:
If f(–2) = 0, what are all the factors of the function f (x) = x cubed minus 2 x squared minus 68 x minus 120? use the remainder theorem.
Then all factors of the function f(x) = x³ – 2x² – 68x – 120 is (x + 2), (x + 6), and (x – 10).
What is a factorization?It is the method to separate the polynomial into parts and the parts will be in multiplication. And the value of the polynomial at this point will be zero.
If f(–2) = 0, that mean one root is –2.
The function f(x) = x³ – 2x² – 68x – 120
We have the one factor is (x + 2)
Then the function can be written as
f(x) = (x + 2)(x² – 4x – 60)
f(x) = (x + 2)(x² – 10x + 6x – 60)
f(x) = (x + 2)[(x(x – 10) + 6(x – 10)]
f(x) = (x + 2)(x – 10)(x + 6)
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Answer:
C
Step-by-step explanation:
edge2022
What is the domain of the function y = l n (StartFraction negative x 3 Over 2 EndFraction).
The domain of the provide function where the function is defined is x less than the number three.
What is the domain of the function?Domain of a function is the set of all the possible input values which are valid for that function.
The function given in the problem is,
[tex]y=\ln\left(\dfrac{-x+3}{1}\right)[/tex]
The above function is the function of logarithm. For the logarithmic function, it is defined for all the real numbers except 0.
Thus, the function should be greater than zero as,
[tex]\left(\dfrac{-x+3}{1}\right) > 0\\(-x+3) > 0\\-x > -3[/tex]
Change the sign of both side, by changing the inequality,
[tex]x < 3[/tex]
Thus, the domain of the provide function where the function is defined is x less than the number three.
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Answer:
x<3
Step-by-step explanation:
edge 2022
If a point is on the perpendicular bisector, then...
O It will cut the segment into two parts
O it forms a 90 degree angle all by itself.
O it is pretty
O It is equidistant from the endpoints
Elizabeth invested $7,800 in an account paying an interest rate of 7\tfrac{1}{8}7 8 1 % compounded monthly. Mason invested $7,800 in an account paying an interest rate of 7\tfrac{3}{8}7 8 3 % compounded continuously. To the nearest dollar, how much money would Elizabeth have in her account when Mason's money has doubled in value?
Answer:
$339
Step-by-step explanation: