Answer:
[tex] {x}^{2} + 8x + 16 = 18[/tex]
[tex] {(x + 4)}^{2} = 18[/tex]
x + 4 = +3√2, so x = -4 + 3√2
A 7-pack of raffle tickets costs $6.58. What is the unit price?
Answer: 1.06 rounded
Step-by-step explanation:
7/6.58 = 1.06 rounded
Hope it helps I'm running out of time!!
Have a nice day!!!!
the side length of a cube is 2y. express the volume of the cube in y.
Answer:
The cube's volume can be represented as 8y^3 when expressed in terms of y.
Step-by-step explanation:
The side length of a cube is given as 2y. To express the volume of the cube in y, we can use the formula for the volume of a cube which is given as V = s^3, where s is the length of one side of the cube.
Substituting 2y as the length of the side of the cube, we get:
V = (2y)^3
Simplifying, we get:
V = 8y^3
Therefore, the volume of the cube expressed in terms of y is 8y^3.
2. One of Kara's birthday balloons has a leak. The amount of air in the balloon can be modeled by the
function A(t) = 1.48 (0.87), where A(t) is the number of cubic feet of air in the balloon t seconds
after the leak begins.
a. According to the model, by what percentage is the balloon losing air each second?
Therefore, according to the model, the balloon is losing air at a rate of 13% per second.
What is function?In mathematics, a function is a rule that maps each element in one set, called the domain, to a unique element in another set, called the range. A function can be represented by an equation, a graph, or a table. Functions are commonly used to describe relationships between variables, such as how the area of a square changes as its side length increases. They are a fundamental concept in calculus, linear algebra, and many other branches of mathematics.
Here,
The function A(t) = 1.48(0.87)ⁿ represents the amount of air in the balloon t seconds after the leak begins.
To find the percentage at which the balloon is losing air each second, we need to find the percentage decrease in the amount of air for every one second of time passing.
To do this, we can calculate the ratio of the amount of air at time t=1 second to the amount of air at t=0 seconds, and then find the percentage decrease:
A(1) / A(0) = [1.48(0.87)¹] / [1.48(0.87)⁰] = 0.87
The ratio is 0.87, which means that the balloon is losing 13% of its air each second (since 1 - 0.87 = 0.13, which is 13% expressed as a decimal).
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An astronomer knows the distances from herself to stars AAA and BBB, as well as the distance between them. The distances are 450450450, 400400400, and 909090 light years (\text{l. Y. }l. Y. Start text, l, point, y, point, end text) respectively.
If the astronomer's telescope is currently pointed at star AAA, how many degrees must she rotate her telescope to see star BBB?
Do not round during your calculations. Round your final answer to the nearest degree
The astronomer must rotate her telescope 86.829° to see star BBB. Rounding to the nearest degree, the astronomer must rotate her telescope 87°.
We can use the law of cosines to solve this problem. The law of cosines states that for a triangle with sides A, B, and C, A2 = B2 + C2 - 2BCcos(θ), where θ is the angle opposite side C.
In our case, A = 450450450, B = 400400400, and C = 909090. We know that angle θ is the angle we need to find, so we can rearrange the equation to solve for θ.
θ = cos-1(A2 - B2 - C2)/(-2BC)
θ = cos-1((450450450)2 - (400400400)2 - (909090)2)/(-2(400400400)(909090))
θ = cos-1(-9.65 × 10-12)/(-2.8 × 1012)
θ = cos-1(-3.4 × 10-13)
θ = 86.829°
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Estimate 15 times 34 by rounding each number to the nearest
Two cakes and three-quarters of another cake were eaten at a party.
how do you write this amount as a fraction?
Answer:
[tex]2\frac{3}{4}[/tex]
Step-by-step explanation:
because 2 is whole
then 3/4 is just there
so we put them together
brainliest please
Answer:
Step-by-step explanation:
Why is it not possible to make a right triangle using lengths of 4 feet, 8 feet, and 10 feet?
question 8 options: you want to develop a three-sigma -chart. you know the mean of the means is 30 and the average range is 5 based on several samples of size 10. what is the lcl of the -chart? round your answer to two decimal places.
As per the given average, the value of LCL is 20.49.
The average range is the average of the differences between consecutive samples. In your case, you have several samples of size 10, and the average range is 5. This means that on average, the range (maximum value minus minimum value) of each sample is 5.
The mean of the means is simply the average of all the sample means. In your case, the mean of the means is 30.
To calculate the LCL, you use the formula: LCL = mean of the means - 3 x average range / d2, where d2 is a constant that depends on the sample size. For a sample size of 10, d2 is 2.704.
Substituting the values, we get: LCL = 30 - 3 x 5 / 2.704 = 20.49
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A motor racing circuit has length 55 miles. A straight section of the circuit has length 14 miles. What fraction of the circuit is the straight section? Give your answer in its simplest form.
A full glass of water can hold 1/6 of a bottle. How many glasses of water can be filled with 3 1/2 bottles of water?
Answer:
21
Step-by-step explanation:
[tex]\frac{x}{6}=\frac{7}{2} \\x=21[/tex]
Answer:
21 glasses------------------------------
Let the number of glasses be g.
Then g glasses can be filled with 3 1/2 bottles of water.
Set up equation to represent this and solve for g:
(1/6)g = 3 1/2(1/6)g = 7/2g = 7/2 : 1/6 g = 7/2 * 6g = 7*3g = 21LET'S FIND THE QUOTIENTS!:
(4m² + 5m - 6 ) ( m + 2)
HELPPPPP!!!
Answer:
4[tex]m^{3}[/tex] +13m² + 4m - 12
Step-by-step explanation:
Use FOIL type method:
(4m^2 +5m - 6)(m+2)
= (4m^2)(m) + (5m)(m) - (6)(m) + (4m^2)(2) + (5m)(2) - (6)(2)
= 4m^3 +5m^2 +8m^2 -6m +10m -12
combine like terms:
= 4m^3 +13m^2 + 4m -12
Use substitution to solve the system 5r+2w=68, r=3w
Answer:
4
Step-by-step explanation:
5r+2w=685(3w)+2w=6815w+2w=6817w=68w=68/17w=4Answer: w=4
Step-by-step explanation:
1). 5(3w)+2w=68
2). 15w+2w=68
3). 17w=68
4). 17w/17=68/17
5). w=4
HOW CAN I SOLVE THIS ASAP??
1. What is the area of ABCD?
2.What is the length of diagonal BD?
Answer:
1. 28.88
2. 7.6
Step-by-step explanation: Not sure if these answers are correct, but this is what I got.
Step-by-step explanation:
so, I understand this is a rhombus, yes ?
I will base my answer on that assumption.
the area of a rhombus is
p×q/2
p, q being the diagonals.
so, all 4 sides are equally long (5 cm).
the angle(s) between the diagonals is (are) 90°.
opposing angles are equally sized (B = D, A = C), and they are split in half by the diagonals.
and always remember : the sum of all angles in a triangle is always 180°.
so,
b1 = b2 = d1 = 50°.
a1 = a2 = c1 = c2 = 180 - 90 - 50 = 40°.
law of cosine :
c² = a² + b² - 2ab×cos(C)
with c being the side opposite of angle C. a, b are the kthe 2 sides.
that applies to all 3 sides and angles.
BD² = 5² + 5² - 2×5×5×cos(c1 + c2) =
= 25 + 25 - 50×cos(80) = 50 - 50×cos(80) =
= 41.31759112....
BD = 6.427876097... cm ≈ 6.43 cm
AC² = 5² + 5² - 2×5×5×cos(b1 + b2) =
= 25 + 25 - 50×cos(100) = 50 - 50×cos(100) =
= 58.68240888...
AC = 7.660444431... cm ≈ 7.66 cm
the area of ABCD is a described
AC × BD / 2 = 24.62019383... cm² ≈ 24.62 cm²
Please help me I'm stuck.
[tex]\cfrac{89.40~~ - ~~\stackrel{ \textit{minus the tax of each} }{0.50-0.50-0.50-0.50-0.50-0.50}}{6}\implies \cfrac{86.40}{6}\implies \stackrel{ each }{14.40}[/tex]
PLEASE PLEASE HELP IT IS DUE TONIGHT!!!
I need help with number 9.
USE MATH WAY IT HELPS ALOT
Which graph shows the solution to the equation below?
log Subscript 3 Baseline (x + 2) = 1
On a coordinate plane, a curve starts in quadrant 3 and curves up into quadrant 1 and approaches y = 3. It crosses the x-axis at (1, 0). A horizontal straight line is at y = 1.
On a coordinate plane, a curves starts in quadrant 4 and curves up into quadrant 1 and approaches y = 3. It crosses the x-axis at (1, 0). A horizontal straight line is at y = negative 1.
On a coordinate plane, a curve starts in quadrant 3 and curves up into quadrant 1 and approaches y = 1. It crosses the x-axis at (negative 1, 0). A horizontal straight line is at y = 1.
On a coordinate plane, a curves starts in quadrant 3 and curves up into quadrant 1 and approaches y = 2. It crosses the x-axis at (negative 1, 0). A horizontal straight line is at y = negative 1.
Nοne οf the given graphs match this descriptiοn, sο nοne οf them shοw the sοlutiοn tο the equatiοn.
What is the equivalent expressiοn?Equivalent expressiοns are expressiοns that wοrk the same way despite their appearance. If twο algebraic expressiοns are equivalent, then the twο expressiοns have the same value when the variable is set tο the same value.
The equatiοn lοg Subscript 3 Baseline (x + 2) = 1 can be rewritten as 3^1 = x + 2. This simplifies tο x = 1. Therefοre, the sοlutiοn tο the equatiοn is x = 1.
On the cοοrdinate plane, this sοlutiοn is represented by a vertical line passing thrοugh x = 1.
Hence, Nοne οf the given graphs match this descriptiοn, sο nοne οf them shοw the sοlutiοn tο the equatiοn.
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Answer: A
Step-by-step explanation:
A rectangular prism measures 3 ft by 6ft by 5 ft. if the dimensions of the box were quadrupled, how would the surface area of the box change.
Answer:
The surface area would increase by a factor of 16.
Or you could also say:
Quadrupling the dimensions makes the surface area 16 times the original surface area.
Step-by-step explanation:
The surface area of a rectangular prism is calculated by adding the areas of all six faces. The formula for the surface area of a rectangular prism is 2lw + 2lh + 2wh, where l is the length, w is the width, and h is the height.
In this case, the surface area of the original rectangular prism with dimensions 3 ft by 6 ft by 5 ft would be: 2(3)(6) + 2(3)(5) + 2(6)(5) = 36 + 30 + 60 = 126 square feet.
If the dimensions of the box were quadrupled, the new dimensions would be 12 ft by 24 ft by 20 ft. The new surface area would be: 2(12)(24) + 2(12)(20) + 2(24)(20) = 576 + 480 + 960 = 2016 square feet.
So, if the dimensions of the box were quadrupled, the surface area would increase from 126 square feet to 2016 square feet. This represents an increase in surface area by a factor of 16.
Jasper had a $10 bill. He spent $5.50 with tax on plants for his fish tank. He spent some more money on a pretty rock for his tank. After he paid, he had $2.21 in change. Write an expression that shows what Jasper spent and had left. Use x to stand for the money he spent on the rock.
Answer:
$10 -$5.50 -x = $2.21
if you want to solve for x do 10-5.50-2.21=x
:D
Mixed in a drawer are 8 blue socks, 8 white socks, and 2 gray socks. You pull out two socks, one at a time, without looking. Find the probability of getting 2 socks of the same color The probability of getting 2 socks of the same color is
The probability of getting 2 socks of the same color isP(two socks of same color) = P(2 blue socks) + P(2 white socks) + P(2 gray socks)= 28/153 + 28/153 + 1/153= 57/153 = 19/51. Hence, the required probability is 19/51.
The probability of getting 2 socks of the same color is given by P(two socks of same color) = P(2 blue socks) + P(2 white socks) + P(2 gray socks).Given, There are 8 blue socks. There are 8 white socks. There are 2 gray socks. Now, we will find the probability of getting 2 blue socks: Probability of selecting one blue sock from 8 blue socks is 8/18.
Probability of selecting another blue sock from 7 blue socks is 7/17.Probability of getting 2 blue socks is P(2 blue socks) = 8/18 * 7/17 = 28/153. Now, we will find the probability of getting 2 white socks: Probability of selecting one white sock from 8 white socks is 8/18.Probability of selecting another white sock from 7 white socks is 7/17.Probability of getting 2 white socks is P(2 white socks) = 8/18 * 7/17 = 28/153.
Now, we will find the probability of getting 2 gray socks: Probability of selecting one gray sock from 2 gray socks is 2/18.Probability of selecting another gray sock from 1 gray sock is 1/17.Probability of getting 2 gray socks is P(2 gray socks) = 2/18 * 1/17 = 1/153.
Therefore,The probability of getting 2 socks of the same color isP(two socks of same color) = P(2 blue socks) + P(2 white socks) + P(2 gray socks)= 28/153 + 28/153 + 1/153= 57/153 = 19/51. Hence, the required probability is 19/51.
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Abby tosses one penny and Babby tosses two pennies. What is the probability that Babby gets the same number of heads that Abby gets?
The probability that Babby gets the same number of heads that Abby gets is 1/8 + 1/8 = 1/4. To solve this problem, we need to consider all the possible outcomes of Abby and Babby's coin tosses.
There are four possible outcomes for Abby's toss: heads or tails, and two outcomes for Babby's toss: heads or tails. Therefore, there are a total of 4 x 4 = 16 possible outcomes for the two coin tosses.
To determine the probability that Babby gets the same number of heads as Abby, we need to identify the outcomes where this happens. Abby can get either 0 or 1 heads, so we need to consider the outcomes where Babby gets 0 or 1 heads as well.
The possible outcomes where Abby gets 0 heads are:
Abby: tails, Babby: tails tails
Abby: tails, Babby: heads tails
In both of these outcomes, Babby also gets 0 heads, so the probability of this happening is 2/16 = 1/8.
The possible outcomes where Abby gets 1 head are:
Abby: heads, Babby: tails heads or heads tails
Abby: tails, Babby: heads heads
In two of these outcomes, Babby also gets 1 head, so the probability of this happening is 2/16 = 1/8. Therefore, the probability that Babby gets the same number of heads that Abby gets is 1/8 + 1/8 = 1/4.
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Which of the following lines is parallel to the line that goes through the points (5, 8) and (3, 6)? Please help me!!!!!!
Answer:
Any line with the slope 1 or y = x + b
Step-by-step explanation:
Parallel lines by definition have the same slope
Value of the y-intercept or b doesn't matter in this case
You have to find the slope of the line through (3,6) and (5,8)
Slope equation is
[tex]\frac{y_{2}-y_{1} }{x_{2}-x_{1} }[/tex]Plug in values given
[tex]\frac{8-6}{5-3}[/tex]
Evaluate
[tex]\frac{2}{2} =1[/tex]
Any line with the slope of 1 (or no co-efficient in front of x) would be parallel to the line through (3,6) and (5,8)
larry can make one batch of 3 cookies every 8 minutes. mary can make one batch of 5 cookies every 12 minutes. how long will it take them to make a combined total of 60 cookies?
The total time taken to make combined 60 cookies by Larry and Mary is equal to 75.79 minutes.
Rate at which each person can make cookies
Time to make one batch of 3 cookies made by Larry = 8 minutes
⇒Number of cookies per minute = 3/8 cookies
Time to make one batch of 5 cookies made by Mary = 12 minutes
⇒Number of cookies per minute = 5/12 cookies
Combined rate at which they make cookies,
= 3/8 + 5/12
= 9/24 + 10/24
= 19/24 cookies per minute
Together they can make 19/24 cookies per minute.
To make a total of 60 cookies,
Let 't' be the time in minutes required to make 60 cookies.
⇒ (19/24) t = 60
⇒ t = (60)/(19/24)
⇒ t = 75.79 minutes (rounded to two decimal places)
Therefore, total time taken by Larry and Mary approximately 75.79 minutes to make a combined total of 60 cookies.
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Find the Exact answer:
Answer:
-1
Step-by-step explanation:
calculator
:)
find the missing parts using trigonometry functions . round to the nearest tenth
The value of the leg x is 18. 36
What are trigonometric functions?Trigonometric functions are defined as those equalities that holds true for all the functions in a given equation.
The various types of trigonometric functions are;
sinecosinetangentcotangentsecantcosecantFor the identities, we have;
cos θ = opposite/adjacent
sin θ = opposite/hypotenuse
tan θ = opposite/adjacent
From the information given, we have;
Using the cosine identity, we get;
cos 57 = 10. 8/x
cross multiply the values
x = 10. 8/0. 5446
divide the values
x = 18. 36
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suppose that a highway is governed by a use fee charged to motorists that is based on congestion, operation and maintenance. the total traffic t is used to determine the cost of 5t2. what is the average cost per motorist?
The average cost per motorist on a highway governed by a use fee based on congestion, operation and maintenance is determined by dividing the total cost ([tex]5t^2[/tex]) by the total traffic (t). So, the average cost per motorist is 5t.
The average cost per motorist for a highway governed by a use fee based on congestion, operation and maintenance can be determined by dividing the total cost ([tex]5t^2[/tex]) by the total traffic (t).
So, the average cost per motorist is 5t.
To better understand how this works, let's look at an example.
Suppose the total traffic is 20.
In this case,
the total cost is 5 × 202 = 2000.
Therefore, the average cost per motorist is 2000/20 = 100.
The cost per motorist is determined by the total traffic because the more cars there are on the highway, the more congested the highway will be.
Consequently, the more congested the highway, the more operation and maintenance is required, and thus the higher the use fee will be.
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A number, x, rounded to the nearest 10 is 630. Another number, y, rounded to the nearest 10 is 420. What are the lower and upper bounds of x + y?
The lower and upper bounds of x + y are 1040 and 1058, respectively.
What are lower bounds and upper bounds?
Lower bounds and upper bounds are used to define the range of possible values for a given quantity or measurement.
A lower bound represents the smallest possible value that a quantity could have, based on the available information or constraints. This means that the actual value of the quantity must be greater than or equal to the lower bound. For example, if we know that a person's height is between 150cm and 170cm, then the lower bound of their height is 150cm.
An upper bound represents the largest possible value that a quantity could have, based on the available information or constraints. This means that the actual value of the quantity must be less than or equal to the upper bound. For example, if we know that a person's weight is between 50kg and 80kg, then the upper bound of their weight is 80kg.
In some cases, we may be able to determine a range of possible values for a quantity using both a lower bound and an upper bound. This range of possible values is sometimes referred to as an interval or a confidence interval.
To find the lower and upper bounds of x + y, we need to consider the possible values of x and y that would result in the maximum and minimum values of their sum when added together.
Let's start by considering the possible values of x and y that would round to 630 and 420, respectively, when rounded to the nearest 10:
x: Any number between 625 and 634 would round to 630 when rounded to the nearest 10.
y: Any number between 415 and 424 would round to 420 when rounded to the nearest 10.
To find the lower bound of x + y, we need to add the smallest possible values of x and y:
Lower bound = 625 + 415 = 1040
To find the upper bound of x + y, we need to add the largest possible values of x and y:
Upper bound = 634 + 424 = 1058
Therefore, the lower and upper bounds of x + y are 1040 and 1058, respectively.
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Pls help me with dis
Answer:
The Answers
Step-by-step explanation:
Flag = 46
Clover = 46
Hat = 27
Acorridan thing = 198
Final answer = 317
the base of a right triangular prism is a right isosceles triangle whose equal sides measure 25 cm each. the volume of the prism is 0.075 cubic meters. find the height of the prism.
The height of the right triangular prism is 84.3 cm.
To find the height of the right triangular prism, let's use the formula for the volume of a right triangular prism.
Volume of the right triangular prism = 1/2 × base × height × length
Where, base = 25 cm and height is what we need to find.
We are given that the volume of the prism is 0.075 cubic meters. We first need to convert the volume into cubic cm as the other units are given in cm. 1 cubic meter = 100 cm × 100 cm × 100 cm= 1,000,000 cubic cm
So, 0.075 cubic meters = 0.075 × 1,000,000 = 75,000 cubic cm
Substituting all the known values into the formula, we get:
75,000 = 1/2 × 25 × height × length
Hence, height = 75,000 / (1/2 × 25 × length)
Now, we need to find the length of the prism. As the base of the right triangular prism is a right isosceles triangle, its hypotenuse is the length of the prism. Using the Pythagorean theorem to find the hypotenuse, we have:
Length² = 25² + 25²
Length² = 1,250
Length = √1,250
Length ≈ 35.36 cm
Substituting this length into the equation we found earlier, we get:
height = 75,000 / (1/2 × 25 × 35.36)height ≈ 84.3 cm
So, the height of the right triangular prism is approximately 84.3 cm.
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when performing bedside spirometry on a 35-year-old woman who is 5 feet 7 inches tall, you obtain a peak flow measurement of 2.3 l/sec. the best interpretation of this test result is?
The interpretation of a peak flow measurement obtained from bedside spirometry on a 35-year-old woman who is 5 feet 7 inches tall would suggest that her lung function is lower than what is predicted for her age and height, indicating some degree of airway obstruction or restriction.
To interpret the results of the spirometry test, we need to compare the obtained peak flow measurement to the predicted values based on the individual's age, height, gender, and race. This is because the normal lung function varies depending on these factors.
For instance, the predicted peak flow measurement for a 35-year-old woman who is 5 feet 7 inches tall is approximately 4.25 l/sec.
Therefore, an interpretation of the obtained peak flow measurement of 2.3 l/sec is that it is lower than the predicted value, indicating that the woman may have some degree of airway obstruction or restriction.
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What is the positive solution to the equation y=6x^2-54?
What is the negative solution to y=½x^2+x-12?
Since we are lοοking fοr a negative sοlutiοn, the answer is x = -6.
What is Equatiοn ?In mathematics, an equatiοn is a statement that twο expressiοns are equal. An equatiοn usually cοntains οne οr mοre variables, which are placehοlders fοr unknοwn values. The variables can be represented by letters, such as x, y, z, and sο οn.
Tο find the pοsitive sοlutiοn tο the equatiοn [tex]y=6x^2-54[/tex], we can set y tο 0 and sοlve fοr x as fοllοws:
[tex]0 = 6x^2 - 54[/tex]
Adding 54 tο bοth sides:
[tex]54 = 6x^2[/tex]
Dividing bοth sides by 6:
[tex]9 = x^2[/tex]
Taking the square rοοt οf bοth sides:
x = ±3
Since we are lοοking fοr a pοsitive sοlutiοn, the answer is x = 3.
Tο find the negative sοlutiοn tο the equatiοn [tex]y =\frac{1}{2}x^2+x-12[/tex], we can set y tο 0 and sοlve fοr x as fοllοws:
[tex]0 = \frac{1}{2}x^2 + x - 12[/tex]
Multiplying bοth sides by 2 tο get rid οf the fractiοn:
[tex]0 = x^2 + 2x - 24[/tex]
Factοring the left side:
0 = (x + 6)(x - 4)
Setting each factοr equal tο zerο and sοlving fοr x, we get:
x + 6 = 0 οr x - 4 = 0
x = -6 οr x = 4
Therefοre, Since we are lοοking fοr a negative sοlutiοn, the answer is x = -6.
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