HALF SOLVED PLEASE HELP
someone please help!
Find the length of a using
the Pythagorean Theorem.
8
a
6
Hint: a² + b² = c²
Round your answer to the nearest tenth.
Answer:5.3
Step-by-step explanation:
using the Pythagorean theorem 8²-6²=28 √28=5.3
5
Step-by-step explanation:
Pythagoras theorem states that
a²+b²=c²
therefore a²=b²-c²
a²=8²-6²
a=√8²-6²
=√64-36
=√28
=5.3 or approximately 5
PLSSSS HELPPPPP MEEE !!!!!
All the angles in a triangle add up to 180 degrees.
40 + x + (5x + 14) = 180
54 + 6x = 180
6x = 126
x = 21 degrees
Answer:
x=21
Step-by-step explanation:
a triangle adds up to 180 degree so to find x we will use the formula
(5x+14)+x+40=180
subtract 40 from each side so we have
(5x+14)+x=140
we have 2 terms with the same factor (x) so combine like terms
6x+14=140
subtract 14 from both sides
6x=126
divide both sides by 6
x=21
check your answer
5(21)+14
105+14=119
119+ 21+40=180
so x is equal to 21
Give the numerical coefficient of the term.
xw
The numerical coefficient is _____.
Answer:
x
Step-by-step explanation:
The numerical coefficient is x.
a 39-inch by 104-inch piece of cardboard is used to make an open-top container by removing a square from each corner of the cardboard and folding up the flaps on each side. what size square should be cut from each corner to get a container with the maximum volume? enter the area of the square and do not include any units in your answer.
According to the solving the area of the square is 68.0625.
What's a square's area?As is common knowledge, a square is a four-sided, two-dimensional figure. It is also referred to as a quadrilateral. The total quantity of unit squares forming a square is referred to as the square's area. In other words, it is described as the area that the square takes up.
According to the given data:The box formed after cutting the square from each corner will have the dimensions as,
length = 104 - 2x, width = 39 - 2x, height = x.
∴ volume of the box = length × width × height
∴ v = (104 - 2x)(39 - 2x)(x) -----(i)
∴ v = (104 - 2x) (39x - 2[tex]x^{2}[/tex])
∴ v = 104(39x - 2[tex]x^{2}[/tex]) -2x(39x - 2[tex]x^{2}[/tex])
∴ v = 4056x - 208[tex]x^{2}[/tex] - 78[tex]x^{2}[/tex] + 4[tex]x^{3}[/tex]
∴ v = 4[tex]x^{3}[/tex] - 286[tex]x^{2}[/tex] + 4056x
let f(x) = 4[tex]x^{3}[/tex] - 286[tex]x^{2}[/tex] + 4056x -----(ii)
To, find x for which f(x) is maximum,
⇒we should apply second derivative test ,
According to this test, first we should find critical points at which f'(x) = 0.
then if f''(x) < 0 for that critical point then f(x) is maximum at that critical point.
∴ let us consider, f'(x) = 0.
now, f(x) = 4[tex]x^{3}[/tex] - 286[tex]x^{2}[/tex] + 4056x
⇒ f'(x) = 12[tex]x^{2}[/tex] - 572x + 4056. -----(iii)
⇒ f'(x) = 4(3[tex]x^{2}[/tex] - 143x + 1014)
⇒ f'(x) = 0.
⇒ f'(x) = 4(3[tex]x^{2}[/tex] - 143x + 1014) = 0
⇒ x = (-b ± [tex]\sqrt{b^{2} - 4ac }[/tex])/2a ; where a = 3, b = -143, c = 1014.
∴ x = (-(-143) ± [tex]\sqrt{(-143)^{2} -4(3)(1014)}[/tex])/2×3
∴ x = (143 ± [tex]\sqrt{8281}[/tex])/6.
∴ x = [tex]\frac{143 + 91}{6}[/tex] , x = [tex]\frac{143 - 91}{6}[/tex]
⇒ x = 39, 8.25
the square of length 8.25 inch should be cut from each side to det contained with the maximum volume.
Area of the square is = [tex]x^{2}[/tex] = [tex]8.25^{2}[/tex]
∴ Area = 68.0625
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HELP
(2, -1); m = 5/4
Answer:
part b
y + 1 = 5/4(x - 2)
part c
y - 5 = 3(x - 0) or y - 5 = 3(x)
Step-by-step explanation:
Find the value of r so that the line passing through (-3, r) and (7,-6)
has a slope of 2 2/5
r =
The value of r is -10 for line with slope 2/5 .
What is slope?
A line's slope, often known as its gradient, is a numerical representation of the line's steepness and direction.
Main Body:
We know that the slope of line in two point form is
(y₂-y₁)/(x₂-x₁) = m where m = slope
given points are (-3,r) and (7,-6) m= 2/5
(-6-r)/(7+3)= 2/5
(-6-r)/10 =2/5
therefore value of r= -10
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A research association reported that 3,173,000 gas grills were shipped by various manufacturers in the U.S. in 2000.Shipment increased by 7% per year from 2000-2016.Write a function that models the number of gas grills shipped over time.
If shipments increased by 7% (which is the same as 0.07) per year, then the shipment in a year can be found by multiplying the shipments in the previous year by 1.07.
Therefore, if [tex]x[/tex] represents the number of years since 2000 and [tex]f(x)[/tex] represents the number of shipments, then [tex]f(x)=3173000(1.07)^x[/tex].
What is 12 = -4(-6x - 3)
Answer:
no solution
Step-by-step explanation:
12=-4(-6x-3)
12=24x+12
0=24x
Line K is represented by the equation y = -3/2x + 1. Line L is perpendicular to line K and passes through the point (6,2). Determine the equation is line L.
Answer:
y = (2/3)y - 2
Step-by-step explanation:
Linear equations of the form y=mx+b, describe the slope, m, and the y-intercept, b (the value of y when x=0).
Line K
y = -(3/2)x + 1 tells us that it has a slope of -(3/2) and crosses the y axis (x=0) at y = 1.
Perpendicular Lines
Perpendicular lines have a useful property in that they have a slope that is the "negative inverse" of the line they are perpendicular to. If, for example, we were ever asked what is the slope of a line perpendicular to Line L (yes, it happens), we could, with minimal effort, respond "It is the negative inverse of -(3/2)," which is a slope of (2/3).
Line L
We just accidently answered a key question when we found the negative inverse of the slope for Line K, (2/3). That will be the slope of Line L that will make it perpendicular to Line K.
Line L will have the form y = (2/3)x + b
This line will be perpendicular to Line K, no matter the value of b. But we want a perpendicular line that goes through point (6,2), so we need to find a value of b that will force it to go through that point.
The role b has in our equation is simply moving it up or down. If b were 0, the line will go through the origin (0,0). If b were 5, it would interect the y axis at 5 (0,5). We could draw a graph and get a pretty good idea what b would have to be for the line to go throgh (6,2), but most prefer the easier route: Use the (x,y) value in the above equation and solve for b. Its easy, and works great:
y = (2/3)x + b for (6,2)
2 = (2/3)(6) + b
b = 2 - (2/3)*(6)
b = 2 - 4
b = -2
The equation for Line L is thus: y = (2/3)y - 2
See the attached graph. Included are equations [marked Demo Line 1 and 2] with 2 random values of b (1 and 0), in order to:
demonstrate how b impacts the line, andsuggest try using DESMOS as a free online graphing tool.
What is 10 and 3/4 as a decimal
Answer:10.75
Step-by-step explanation:
3/4 as a decimal is 0.75. add that to the 10 gives you 10.75
Which of the following equations can be solved for x in one step by multiplying both sides of the equation by 2?
Answer:
x/2 = any number
Step-by-step explanation:
Write the linear equation in the slope intercept form.
(-6,0); slope= 2/3
Answer:
Step-by-step explanation:
y=2/3x+4
If was asked to think of a number and multiply it by 2, could
write this algebraically as 2x.
Write the following algebraically, using x as your unknown.
"I think of a number, multiply it by 5 and subtract 3 from the result."
The algebraic expression of the mentioned statement will be 5x-3.
According to the question,
An unknown number is thought of, multiplied by 5, and then subtracted by 3 from the result.
Let the unknown number be taken as x.
If we have to write the statement mathematically by taking x as a variable, the algebraic expression will be,
x* (5), which is equal to 5x, (by taking the variable x and multiplying it with 5).
For the second step, the expression will be 5x -3, (by subtracting 3 from the previous result, that is, 5x).
Hence, algebraically the final statement will be 5x -3.
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TR is the angle bisector angle ATS. The m angle RTS = (17x-5) and m angle ATS= (28x + 8). find X
Applying the definition of angle bisector, the value of x is: x = 3.
What is an Angle Bisector?An angle bisector can be defined as a ray or line that divides an angle into two parts that are congruent or equal to each other in measure.
Since TR is the angle bisector that bisects angle ATS, it implies that angle ATS is divided into equal parts.
Given the following:
Measure of angle RTS = (17x - 5)°
Measure of angle ATS = (28x + 8)°
Therefore:
Measure of angle ATS = 2(measure of angle RTS) [definition of angle bisector]
Substitute
28x + 8 = 2(17x - 5)°
28x + 8 = 34x - 10
Combine like terms
28x - 34x = -8 - 10
-6x = -18
Divide both sides by -6
-6x/-6 = -18/-6
x = 3
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cook-it rice cooker has a mean time before failure of 38 months with a standard deviation of 4 months, and the failure times are normally distributed. what should be the warranty period, in months, so that the manufacturer will not have more than 7% of the rice cookers returned? round your answer down to the nearest whole number.
In 40 months, so that the manufacturer will not have more than 7% of the rice cookers returned.
Define p- value.A p-value calculates the likelihood of getting the outcomes that were observed, presuming that the null hypothesis is correct. The statistical significance of the difference that was found increases with decreasing p-value. Statistical significance is commonly defined as a p-value of 0.05 or less. The sample data, test type, and sampling distribution of the test statistic under the null hypothesis are used to determine the p-value (lower-tailed test, upper-tailed test, or two-sided test).
Given,
Cook-it rice cooker has a mean time before failure of 38 months with a standard deviation of 4 months, and the failure times are normally distributed.
The 7th percentile, or X when Z has a p-value of 0.08, or X when Z = 0.4720, should serve as the warranty period.
Z = X - Mean/ standard deviation
0.472 = x - 38/4
0.472 (4) - x - 38
1.888 = x - 38
x = 39.88
x = 40
In 40 months, so that the manufacturer will not have more than 7% of the rice cookers returned.
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euclid, pythagoras, ptolemy, and hypatia are playing a game where they all have to think of a number, and then cube that number 20 times. hypatia doesn't want to cube large numbers, so she chooses the number $1$. euclid thinks the same thing and also chooses the number $1$. however, pythagoras and ptolemy don't think ahead and pythagoras chooses $2$ and ptolemy chooses $-2$. after they finish cubing their numbers (pythagoras and ptolemy take a while), all four players write their final numbers on a piece of paper. what is the sum of the numbers they wrote on the piece of paper?
The sum of the numbers they wrote on the piece of paper is 2,305,843,009,213,693,954
What is Pythagoras's theorem?
The Pythagorean Theorem states that the squares on the hypotenuse (the side across from the right angle) of a right triangle or in standard algebraic notation, a² + b² = c², is equal to the squares on the legs.
What is the sum of numbers?
The outcome or conclusion we arrive at when we add two or more integers is known as the sum. Addends are the numbers that are added.
Here, we calculate the sum of the given numbers
= (1³)^²⁰ + (1³)²⁰ + (2³)²⁰ + (-2³)²⁰
= 2,305,843,009,213,693,954
Hence, the sum of the numbers they wrote on the piece of paper is 2,305,843,009,213,693,954.
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if the product of five and the number is increased by seven, the result is the same as eight less than three times a number
Please helppppp
Answer:
The number is -7.5
Step-by-step explanation:
Creating an equation:
5x+7=3x-8
-> 5x = 3x-15
-> 2x=-15
-> x=-7.5
Compute and expressed the result as a mixed fraction?
1) 2+ 3/4
Answer:
2 [tex]\frac{3}{4}[/tex]
Step-by-step explanation:
2 + [tex]\frac{3}{4}[/tex]
= 2 [tex]\frac{3}{4}[/tex] ← as a mixed number
List all factors of the numerator and denominator. Use gcf method to simplify Creduce) each fraction. You must show work
The simplified form of the given fraction is, 2/3.
What is greatest common factor?
The largest gap between the two integers is considered to be the biggest common factor. Firstly, make a list of each number's prime factors to determine its largest common factor. The ages of 18 and 24 have one 2 and one 3. The GCF of 18 and 24 is obtained by multiplying them, therefore 2 * 3 = 6.
Consider, the given fraction [tex]\frac{48}{72}[/tex]
The divisors of 48 are, 1, 2, 3, 4, 6, 8, 12, 16, 24, 48.
The divisors of 72 are, 1, 2, 3, 4, 6, 8, 9, 12, 18, 24, 36, 72.
So, from above the greatest common factor of 48 and 72 is 24.
Therefore,
[tex]\frac{48}{72} = \frac{24(2)}{24(3)} = \frac{2}{3}[/tex]
Therefore, the simplified form of the given fraction is, 2/3.
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PLEASE HELP FAST!!!! ILL GIVE BRAINLIEST!!!!
Which statement correctly compares the function shown on this graph with the function y = 4x - 8?
A. The function shown on the graph has a greater rate of change but
a lower y-intercept.
B. The function shown on the graph has a smaller rate of change but
a higher y-intercept.
C. The function shown on the graph has a greater rate of change and
a higher y-intercept.
D. The function shown on the graph has a smaller rate of change and
a lower y-intercept.
Use the given vertices to graph quadrilateral TUVW and its image after a dilation centered at the origin with scale factor
k=2/3
T(9,-3), U(6,0), V(3,9), w(0,0)
Answer:We know that the dilation transformation of a figure either shrink or expand the original figure depending on the scale factor of the dilation.
As here we have scale factor=3>1.
Hence, the dilation changes the original will expand the original figure.
Hence, each of the coordinate of a figure get multiplied by 3.
Hence, the co
ordinates of the image are given as:
i.e. A(0,0) → A'(0,0)
B(2,3) → B'(6,9)
C(1,-2) → C'(3,-6)
D(-3,-3) → D'(-9,-9)
Step-by-step explanation:
Mr karki divided a sum of Rs 1,80,000 between his son and daughter in the ratio of 4:5 find the sum obtained by eachof them.
Answer:
Rs 80,0000 and Rs 100,000
Step-by-step explanation:
sum the parts of the ratio, 4 + 5 = 9 parts
divide the amount by 9 to find the value of one part.
Rs 1,80,000 ÷ 9 = Rs 20,000 , then
4 parts = 4 × Rs 20,000 = Rs 80,000 ← amount son receives
5 parts = 5 × Rs 20,000 = Rs 100,000 ← amount daughter receives
The sum obtained by the son is Rs. 80,000 and the daughter is Rs. 1,00,000.
Mr. Karki divided Rs. 1,80,000 in a ratio of 4:5 between his son and daughter.
Let the common multiple be x
∴ The son obtained Rs. 4x --------1
And daughter obtained Rs. 5x --------2
As the total sum is Rs. 1,80,000
∴ 4x + 5x = 180000
9x = 180000
x = 180000/9
∴ x = Rs. 20000
Putting the value of x in 1 and 2 we get,
The sum obtained by son = 4x = 4*20000 = Rs. 80000
And the sum obtained by daughter = 5x = 5*20000 = Rs. 100000
Thus, the son obtained Rs. 80,000 while the daughter obtained Rs. 1,00,000 which is in the ratio of 4:5.
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Use polynomial long division to find the quote and the remainder when 2x^3-4x^2-x+2 is divided by X+2
The quotient of the polynomial is 4x - 9 and the remainder is 20
What are Quotient and remainder?The resultant of the division is called the quotient while the Remainder is the number that is left after division.
In long division, the terms on top of the division symbol are called the quotient while that at the bottom is called the remainder.
When a division has no remainder it means that the polynomial is divisible by the divisor.
The body of the calculation is found in the attached file below.
In conclusion, the Quotient and remainder are 4x - 9 and 20 respectively.
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You and your friends go camping and put up a tent on camp grounds. the tent is shaped like an isosceles triangle. the sides of the tent are 5 feet each and the opening of the tent is 6 feet wide. how tall is the tent
this is my last question please help asap!!
The average rate of change of function [tex]g(x)=5(2)^{x}[/tex] from x = 3 to x = 4 is 4 times that from x = 1 to x = 2.
The correct option is (A).
What is the average rate of change of a function?
The average rate at which one quantity changes in relation to another's change is referred to as the average rate of change function.
Using function notation, we can define the Average Rate of Change of a function f from a to b as:
[tex]rate(m) = \frac{f(b)-f(a)}{b-a}[/tex]
The given function is [tex]g(x) = 5(2)^{x}[/tex],
Now calculating the average rate of change of function from x = 1 to x = 2.
[tex]m = \frac{g(b)-g(a)}{b-a}\\ m = \frac{g(2)-g(1)}{2-1}\\\\m=\frac{5(2)^{2}-5(2)^1}{2-1}\\ m=\frac{10}{1} \\m=10[/tex]
Now, calculate the average rate of change of function from x = 3 to x = 4.
[tex]m = \frac{g(b)-g(a)}{b-a}\\ m = \frac{g(4)-g(3)}{4-3}\\\\m=\frac{5(2)^{4}-5(2)^3}{4-3}\\ m=\frac{40}{1} \\m=40[/tex]
The jump from m = 10 to m = 40 is "times 4".
So option (A) is correct.
Hence, The average rate of change of function [tex]g(x)=5(2)^{x}[/tex] from x = 3 to x = 4 is 4 times that from x = 1 to x = 2.
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A) SAS
B) ASA
C) AAS
D) SSS
E) there is not enough information to guarantee congruent triangles
in a particular chi-square goodness-of-fit test, there are eight categories and 825 observations. use the 0.10 significance level. a. how many degrees of freedom are there?
By probability , 7 is degrees of freedom are there .
Describe probability using an example?
By dividing the number of preferable possibilities by the total number of potential outcomes, probability, which measures the likelihood that an event will occur, is obtained. The most basic illustration is a coin toss. There are only two outcomes that can occur when you flip a coin: either heads or tails.It is predicated on the likelihood that something will occur. The theory of probability primarily relies on the justification for probability. A coin is tossed, for instance, and the theoretical likelihood of getting a head is 1 in 2.825 Observations and 8 categories .
Degree of freedom = k - 1
df = 8 - 1
df = 7
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PLSSS I NEED HELP
Which of the following is the graph ofY= -3/5x+2
Answer:
It would be the last graph (c). It would look like the image below.
Explanation:
Since 3 is negative the answer would have a graph with a line going like this \.