Please help!
A square hot tub will be placed in the center of an enclosed area near the pool. Each side of the hot tub measures 6 feet. It will be surrounded by x feet of deck on each side. The enclosed space is also square and has an area of 169 square feet. Find the width o the deck space around the hot tub, x.
Part 1
Write an equation for the area of the enclosed space in the form y=(side length)^2. Hint: Don't forget to add x to each side of the hot tub.
Part 2
Substitute the area of the enclosed space for y in your equation.
Part 3 Solve your equation from part 2 for x.
Part 4
What is the width of the deck around the hot tub.
Given a right prism where p is the perimeter of the base, h is the height, BA is the area of the bases, and LA is the lateral area, what is the surface area?
Check all that apply.Mulitple answers not just one answer!
A. SA=16-LA
B. SA=BA+LA
C. SA=1/2 16+LA
D. SA=BA+ph
E. SA=p+LA
Answer:
SA= BA+ph
SA= BA+LA
Step-by-step explanation:
Just did this question on APEX.
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Help please I’m stuck on this problem
What is the measure of an angle that turns through 3/4 of a complete circle
The measure of an angle that turns through 3/4 of a complete circle is 270°.
What are arithmetic Operations?
The four fundamental operations of arithmetic are addition, subtraction, multiplication, and division of two or even more items.
Included in them is the study of integers, especially the order of operations, which is important for all other areas of mathematics, notably algebra, data management, and geometry.
As per the given information in the question,
The angle of the complete circle is 360°.
Then, 3/4 of a complete circle will be,
360 × 3/4 = 270°
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What should be added to 3 to make the sum of 0?
A survey finds that 40% of students ride in a car to school. Eri would like to estimate the probability that if 3 students were randomly selected, only 1 rides in a car. To simulate this probability, she lets the numbers 0, 1, 2, and 3 represent a student who rides in a car to school and then 4, 5, 6, 7, 8, and 9 represent a student who does not ride in a car to school. She then has a computer randomly select 3 numbers. She repeats this process for 20 trials. The results of these trials are shown in the table. 468 380 120 220 553 945 935 607 473 490 074 981 692 518 408 954 943 389 594 569 Based on this simulation, what is the estimated probability that only 1 of 3 randomly selected students rides in a car to school? Enter your answer, as a decimal, in the box.
The estimated probability that only 1 of 3 randomly selected students rides in a car to school is 0.4 or 40%.
Explanation:The estimated probability that only 1 of 3 randomly selected students rides in a car to school can be calculated by dividing the number of trials where only 1 student rides in a car by the total number of trials. In this case, there were 8 trials where only 1 student rides in a car out of a total of 20 trials.
Therefore, the estimated probability is:
8 / 20 = 0.4
So, the estimated probability is 0.4 or 40%.
how to find the surface area of the cube
Malik drinks 1/2 liter of water and 1/3 liter of juice. Did Malik drink more water or juice?
Can anyone help me on this
the equation of a circle is x - y + 1 = 0 . if one end of the diameter is ( 3, p) and other end is ( a, 2 ) , find the equation of the circle.
The equation of the circle in standard form is represented by the expression x² + y² = 2.
How to analyze a geometric locus
Geometric loci are point sets that represents a figure. A circle is a case of geometric locus. In this question we must determine the coordinates of the two points contained in the circumference and derive a circle equation in standard form.
Now we proceed to solve the following system of linear equations:
p = 4 (1)
a = 1 (2)
Then, the ends of the diameter are (3, 4) and (1, 2) and the radius of the circle is found by the following Pythagorean expression:
[tex]r = \frac{1}{2}\cdot \sqrt{(1-3)^{2}+(2-4)^{2}}[/tex]
r = √2
Lastly, the equation of the circle in standard form is represented by the expression x² + y² = 2. [tex]\blacksquare[/tex]
RemarkThe statement is incomplete. Complete statement is shown below:
The equation of the diameter of a circle is x - y + 1 = 0. If one end of the diameter is (3, p) and other end is (a, 2). Find the equation of the circle.
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If 14 over 3 equals x over y to the second power than 14 over x equals
There are 36 students in the chess club , 40 students in the drama club , and 24 students in the film club. Which ratio is equivalent to 5:3
Nate tells his mom that he took a test with 60 questions and scored 85%. How many questions did he answer correctly? Show how you know.
Koji is installing a rectangular window in a office building, the window is
8
2
3
feet wide and
5
3
4
feet high. The formula for the area of a rectangle is
A=bh
.What is the area of the window?Enter your answer as a mixed number in simplest form in the box. URGENT WORTH 58 POINTS AND WILL GIVE BRAINLIEST!!
how to solve Questions 1&2?
Evaluate the expression when a=−15 and b=−5.
b2
------------ =
a + 5
Help
The value of the given mathematical expression b^2 divided by a+5 when a=-15 and b=-5 is -2.5.
Explanation:In the given expression, we're asked to evaluate b2 divided by (a + 5), where a = -15 and b = -5. First we substitute the values of a and b into the expression.
So, b2 becomes (-5)2 = 25 and a + 5 becomes -15 + 5 = -10.
Now, substituting these results back into the original expression, we get 25 divided by -10, which equals -2.5.
Therefore, the value of the given expression when a=-15 and b=-5, is -2.5.
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Jessica is saving for college. She makes a $75 deposit each week into her savings account. She also decided to use some of the money from the savings account to buy a new music player for $225. The inequality 75x−225≥975 can be used to find x, the number of weeks it will take Jessica to have at least $975 in the account for college. Which graph shows the solution of this inequality?
The Wilkes family sold both of their cars. They sold one car for $7,700 and the other for $9,050. Estimate the difference in the selling price of the two cars by rounding to the nearest thousand and then subtracting.
4/9. 11/13. 6/5. 14/21 in simplest form
In the figure, a∥e , m∥n , and m∠2 = 117°.
What is m∠5 ?
63°
90°
117°
180°
63 is the answer
what the person said
vince begin practicing up on a piano at 5:15 p.m. he stopped playing at 5:35 p.m. how many degrees did the minute hand turn during vince's
practice time explain how you found your answer.
Write each statement as a proportion using colons. 4 is to 20 as 2 is to 10.
Write the explicit formula that represents the geometric sequence -2, 8, -32, 128
The Geometric Sequence Formula:
[tex]a_n=a_1r^{n-1}[/tex]
We have:
[tex]a_1=-2,\ a_2=8,\ a_3=-32,\ a_4=128,\ ...[/tex]
[tex]d=\dfrac{a_{n+1}}{a_n}\to d=\dfrac{8}{-2}=-4[/tex]
Substitute:
[tex]a_n=-22\cdot(-4)^{n-1}=-22\cdot(-4)^n\cdot(-4)^{-1}=-22\cdot(-4)^n\cdot\left(-\dfrac{1}{4}\right)=5.5(-4)^n[/tex]
Answer:
Step-by-step explanation:
so the answer would be?????
How many 1/8s are in 3?
There are 24 number of 1/8s are in 3.
What is Division?A division is a process of splitting a specific amount into equal parts.
We need to find how many 1/8 's are in 3.
To find this we just need to divide three by 1/8.
3/1/8
Three is divided by one by eight.
The whole number is divided by the fraction.
The fractions has numerator and denominator.
When whole number is divide by the fraction the result we get by multiplying the whole number by denominator of the fraction.
3×8/1
24
Hence, there are 24 number of 1/8s are in 3.
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URGENT! ANSWER IN THE NEXT 5 MIN PLZ! BEING TIMED!!!
A trophy consists of 3 right rectangular prisms. The prisms are turned lengthwise and stacked so that the bottom face of each of the top two prisms is completely resting on the prisms below it. The lengths of the prisms from the base of the trophy to its top are 5 in 3 in and 1 in. The width of each prism are 2 in by 2 in. What is the surface area of the trophy
Surface area is _____ in2
Answer:
ITS 80!!!!
Step-by-step explanation:
Please helpppppppppppp
Is it necessary to use the formulas for special products of binomials to multiply these binomials?
Final answer:
While it's not necessary to use the binomial theorem to multiply binomials, it can greatly simplify the process. This theorem is handy for higher powers and in cases where technology tools are not available.
Explanation:
The formulas for special products, like the binomial theorem, are not always necessary for multiplying binomials, but they can simplify the process significantly, especially for higher powers. When multiplying binomials without these formulas, one would have to apply the distributive property multiple times, which can be tedious and prone to error. The binomial theorem provides a direct way to expand binomials raised to a power in a series expansion: (a + b)n = an + n*an-1*b + ... + bn. Utilizing this formula can speed up calculations and help avoid mistakes.
In understanding series expansions, working with exponents, and creating formulas based on logical sense and unit consistency, students can sometimes simplify problems without needing to memorize formulas. However, for complex problems or when working with large exponents, knowing and applying the binomial theorem can be much more efficient.
Moreover, technologies like calculators and computer software often have functions that apply these theorems or carry out the multiplications of binomials, which can make manual calculations unnecessary, provided you have access to these tools. But understanding the underlying principles is important for a strong mathematical foundation.
A cylinder has a surface area of 1850 square meters and a radius of 9 meters. Estimate the volume of the cylinder to the nearest whole number.
Describe how to draw the geometric mean in a right triangle
To draw the geometric mean in a right triangle, first draw a perpendicular from the right angle to the hypotenuse, creating two smaller triangles. Then use the properties of similar triangles or the Pythagorean theorem to find the geometric mean, which is the length of the perpendicular you drew.
Explanation:To draw the geometric mean in a right triangle, you can use the following step-by-step method:
Identify the right triangle within which you want to find the geometric mean. Assume this triangle has sides of lengths a and b, with c being the hypotenuse.Drop a perpendicular from the right angle to the hypotenuse, subdividing the original triangle into two smaller right triangles. This line segment will be the geometric mean, which we can label as x.Apply the properties of similar triangles or the Pythagorean theorem. The two smaller triangles will be similar to the original right triangle and to each other.The geometric mean x relates to the segments of the hypotenuse (which can be labeled d and e, where d + e = c), through the relationships x² = ad and x² = be.Since x is the geometric mean between a and b, the equations can also be written as x = √(ad) and x = √(be).Finally, measure the length of the perpendicular line you have drawn with a ruler to get the magnitude of the geometric mean x, or calculate it using the relationships stated.The Pythagorean theorem, a² + b² = c², can also be helpful in finding the lengths of the segments on the hypotenuse if they are not given.