Answer:
Yes
Step-by-step explanation:
18^2+24^2=900
Square root of 900 is 30
This is derived from Pythagorean Theorem
Answer:
It is a right triangle
Step-by-step explanation:
Right Triangle
A right triangle has one of its internal angles of 90°. If such triangles, Pythagora's theorem must stand.
Being a and b the shortest sides of the triangle and c the longest side (hypotenuse), then:
\(a^2+b^2=c^2\)
The shortest sides of the given triangle are 18 and 24, and the longest side is 30, thus the following condition must be met to prove it's a right triangle:
\(18^2+24^2=30^2\)
\(324+576=900\)
\(900=900\)
Since the condition is met, we can conclude it is a right triangle
The population of a town was 6,000 people last year. The population is expected to increase by 4% this year. By how many people is the population expected to increase this year?
\(\begin{array}{|c|ll} \cline{1-1} \textit{\textit{\LARGE a}\% of \textit{\LARGE b}}\\ \cline{1-1} \\ \left( \cfrac{\textit{\LARGE a}}{100} \right)\cdot \textit{\LARGE b} \\\\ \cline{1-1} \end{array}~\hspace{5em}\stackrel{\textit{4\% of 6000}}{\left( \cfrac{4}{100} \right)6000}\implies 240\)
Which inequality has -25 in its solution set?
y + 11 > -9
y - 17 Less-than-or-equal-to -46
30 Less-than-or-equal-to y + 5
y + 20 > -30
Answer:
Let's check one by one:
y + 11 > -9
-25 + 11 > -9
-14 > -9 (wrong)
y - 17 <= -46
-25 - 17 <= -46
-42 <= -46 (wrong)
30 <= y + 5
30 <= -25 + 5
30 <= -20 (wrong)
y + 20 > -30
-25 + 20 > -30
-5 > -30 (Right)
=> Last option is solution
Hope this helps!
:)
The required inequality that contains -25 in its solution is y +20 > -30.
Option D is correct.
Number of inequality is given y + 11 > -9 , y - 17≤ -46, 30 ≤ y + 5, y + 20 > -30, the inequality that contains -25 to its solution of set to be determine.
What is inequality?Inequality can be defined as the relation of an equation containing the symbol of ( ≤, ≥, <, >) instead of the equal sign in an equation.
1) y + 11 > -9
y >-20
It does not contain -25. in its solution set.
2) y - 17≤ -46
y ≤ -29
It does not contain -25. in its solution set.
3) 30 ≤ y + 5
25 ≤ y
It does not contain -25. in its solution set.
4) y + 20 > -30
y > -50
It does contain -25 in its solution.
Thus, the required inequality that contains -25 in its solution is y +20 > -30.
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What is the best approximation of the volume, in cubic units, of a cylinder of diameter 10 and height 10?
Answer:
785.4 units³ (nearest tenth)
Step-by-step explanation:
volume of a cylinder = \(\pi\)r²h
where r is the radius and h is the height
diameter of a circle = 2r
where r is the radius
Therefore, 10 = 2r ⇒ r = 5
Therefore, volume = \(\pi\) x 5² x 10 = 250\(\pi\) = 785.4 units³ (nearest tenth)
suppose you select a number at random from the sample space. Find the probability. P(the number is positive)
Answer:
Here's the picture + somewhat process? (hard to explain, please lmk if it's wrong and i'll fix it!!)
Solve for x. Round to the nearest tenth, if necessary.
Answer:
The answer is 8
Step-by-step explanation:
By using the theory of Euclid
\( {x}^{2} = 4 \times 16 = 64 \\ x = 8\)
To study the eating habits of all athletes in his school, Christopher obtains a list of the athletes, divides them into groups of varsity and junior varsity, and randomly selects a proportionate number of individuals from each group. Which type of sampling is used? Select the correct answer below: Cluster sampling Systematic sampling Convenience sampling Stratified sampling
In this case, Christopher divides the athletes into groups of varsity and junior varsity, which creates the strata. The type of sampling used in this scenario is stratified sampling.
Stratified sampling is a sampling method where the population is divided into homogeneous subgroups or strata, and individuals are randomly selected from each stratum in proportion to their representation in the population. In this case, Christopher divides the athletes into groups of varsity and junior varsity, which creates the strata.
By randomly selecting a proportionate number of individuals from each group, Christopher ensures that both varsity and junior varsity athletes are represented in the sample, maintaining the proportional representation of each group in the population. This method allows for more accurate and representative results by capturing the characteristics of both groups separately.
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(-1, 16), (-13, 6)
Write an equation in slope-intercept form.
help
Answer:
y=5/6x+101/6
Step-by-step explanation:
m=(y2-y1)/(x2-x1)
m=(6-16)/(-13-(-1))
m=-10/(-13+1)
m=-10/-12
simplify
m=5/6
y-y1=m(x-x1)
y-16=5/6(x-(-1))
y-16=5/6(x+1)
y-16=5/6x+5/6
y=5/6x+5/6+16
y=5/6x+5/6+96/6
y=5/6x+101/6
The stadium in city A seats 11500 more than the stadium in city B. The stadium in city C seats 6800 more than the stadium in city B. If the seating capacity at the stadium in city A is 75000 what is the seating capacity at the stadium in city C ?
The seating capacity of the stadium in city C is such that all given conditions satisfied will be 70300.
How to form an equation?Determine the known quantities and designate the unknown quantity as a variable while trying to set up or construct a linear equation to fit a real-world application.
Let's say the capacity in city A, city B, and city C is A, B, and C respectively.
As per the given,
A = B + 11500
C = 6800 + B
A = 75000
By substitution,
75000 = B + 11500
B = 63500
Again substitution,
C = 6800 + 63500
C = 70300
Hence "The seating capacity of the stadium in the city C such that the all given condition satisfied will be 70300".
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the area of a rectangular city park is 15/56 square miles. the width of the park is 3/7 mile. what is the length, in miles, of the park?
Answer:
5/8 is the length. Just divide 15/56 by 3/7.
Step-by-step explanation:
does anyone know how to solove for 2^-2b=8 im super confused and could you please show work(will mark brainlist if you show work) thank you
Answer:
32
since 2^-2 is equal to 0.25, you divide 8 by 0.25 which is 32
Answer b=-2
Step-by-step explanation: Simplify 2^2 to 4 so 4−2b=8 then -2b=4 b=-4/2= b-2
Hope this helped :)
rite a partial decay series for At-217 undergoing the following sequential decays: α, β, α, β.
Part A
α-decay
Express your answer as a nuclear equation.
Rite a partial decay series for At-217 undergoing the following sequential decays,
α decay:
217 At → 4 α + 213 Bi
85 2 83
In order to change into a more stable state, a radioactive atom will naturally produce radiation in the form of energy or particles. It is necessary to distinguish between radioactive material and the radiation it produces. Beta, gamma, and alpha decay are the three kinds of radioactivity.
"Alpha decay," a common form of radioactive decay, happens when a nucleus emits an alpha particle (a helium-4 nucleus). During the usual radioactive decay process known as beta decay, a nucleus generates beta particles. The child nucleus will possess a greater atomic mass than the parent nucleus.
α decay:
217 At → 4 α + 213 Bi
85 2 83
β decay:
213 Bi → 0 e + 213 Po
83 -1 84
α decay:
213 Po → 4 α + 209 Tl
84 2 82
β decay:
209 Tl → 0 e + 209 Pb
82 -1 83
Therefore,
Rite a partial decay series for At-217 undergoing the following sequential decays,
α decay:
217 At → 4 α + 213 Bi
85 2 83
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If ∆ABC ∼ ∆PQR such that AB = 1.8cm and PQ = 1.6 cm, what is the ratio of the areas of ∆ABC and ∆PQR.
Answer:
81 / 64
Step-by-step explanation:
The ratio of the areas can be obtained thus :
Area of ∆ABC / Area of ∆PQR
Area of ∆ABC / Area of ∆PQR = AB² / PQ²
AB = 1.8 ; PQ = 1.6
AB² / PQ² = 1.8² / 1.6²
= 18² / 16²
= 324 / 256
= 81 / 64
Solve the equation
4 2/5 + k = -3 2/11
K=?
In fractional form, the answer is 397/55 and in decimal form it is 7.2181.
The equation can be written as 22/5+k= -31/11
transferring 22/5 to the R.H.S., the sign will turn negative.
thus, k=-31/11-22/5
Further solving the equation by taking L.C.M. of 11 and 5 which comes to 55,
k=(155+242)/55
we get the value of k= 397/55
If we convert the given value of k into decimal, it can also be written as, 7.2181.
Thus, the value of k can b expressed in both numerical and fractional forms.
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For any two integers a and b, (a + b)2 = a2 + b?
true or false
Answer:
False.
Step-by-step explanation:
Using the property of distribution, (a + b)² will be a² + b², never a² + b.
No, for any two integers a and b, (a + b)² ≠ a² + b is a false statement.
What is termed as the distributive property of multiplication?Multiplication's distributive property allows you to simplify expressions in which you multiply a number by the a sum or difference. This property states that the product of a sum or difference of two numbers is equal to the sum as well as difference of the products. When you multiply a value by a sum, the distributive property of multiplication over addition is used.For the given two integers a and b,
The given expression
(a + b)² = a² + b (false statement)
The correct statement is-
(a + b)² = (a + b)(a + b)
(a + b)² = a² + b² + 2ab
Thus, no, for any two integers a and b, (a + b)² ≠ a² + b.
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please help lol no rush
Answer:
Step-by-step explanation:
6. ASA
7. SAS
8. ASA
9. True
10. Option 1 and 2
{(x, y)} : x3 }{ ( x, y ) : y-3} CAN ANYONE GRAPH THIS
The graph of {(x, y)} : x3 } and { ( x, y ) : y-3} is shown in image.
We have to given that;
Expression is,
⇒ {(x, y)} : x3 } and { ( x, y ) : y-3}
Now, We can find that;
Point (1.672, 4.672) is a solution of the give expression.
Hence, We get;
The graph of {(x, y)} : x3 } and { ( x, y ) : y-3} is shown in image.
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Use implicit differentiation to find an equation of the tangent line to the curve at the given point.
x^2/3 + y^2/3 = 4, (-3sqrt3, 1)
The equation of the tangent line to the curve at the point (-3sqrt3, 1) is y = (1/sqrt3)x + 4.
To find the equation of the tangent line to the curve at the given point, we will differentiate the equation implicitly with respect to x.
Differentiating both sides of the equation x^(2/3) + y^(2/3) = 4 with respect to x, we get:
(2/3)x^(-1/3) + (2/3)y^(-1/3) * (dy/dx) = 0
Now we need to find the value of dy/dx at the point (-3sqrt3, 1).
Substituting x = -3sqrt3 and y = 1 into the equation, we have:
(2/3)(-3sqrt3)^(-1/3) + (2/3)(1)^(-1/3) * (dy/dx) = 0
Simplifying, we get:
(2/3)(-1/sqrt(3)) + (2/3) * (dy/dx) = 0
Simplifying further, we have:
-2/(3sqrt3) + (2/3) * (dy/dx) = 0
Now we can solve for (dy/dx):
(dy/dx) = 2/(2sqrt3) = 1/sqrt3
So the slope of the tangent line at the point (-3sqrt3, 1) is 1/sqrt3.
Now we have the slope of the tangent line and the point (-3sqrt3, 1), we can use the point-slope form to find the equation of the tangent line. The equation is given by:
y - y1 = m(x - x1)
Substituting the values, we have:
y - 1 = (1/sqrt3)(x - (-3sqrt3))
Simplifying, we get:
y - 1 = (1/sqrt3)(x + 3sqrt3)
y - 1 = (1/sqrt3)x + 3
Finally, rearranging the equation, we have:
y = (1/sqrt3)x + 4
So the equation of the tangent line to the curve at the point (-3sqrt3, 1) is y = (1/sqrt3)x + 4.
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en una tienda de ropa, la semana pasada, 3 pantalones y 2 abrigos costaban 245€. Esta semana estos artículos tienen un descuento del 20% y 5% respectivamente. Si ahora un pantalón y un abrigo cuestan 100,75€, ¿qué costaba cada artículo antes de la rebaja?
Solving a system of equations we can see that each pair of pants costs €82.94 and each coat costs €26.37
How to find the original cost?
Let's define the variables:
x = cost of a pant
y = cost of a coat.
First, we know that:
3x + 2y = 245
And then there are discounts of 20% and 5%, and the cost of one of each is 100.75, then:
0.8x + 0.95y = 100.75
Then we have a system of equations:
3x + 2y = 245
0.8x + 0.95y = 100.75
We can isolate x on the second equation to get:
x = (100.75 - 0.96y)/0.8
x = 125.9 - 1.2y
Replace that in the other equation:
3*(125.9 - 1.2y) + 2y = 245
Solving for y:
3*125.9 - 3*1.2y + 2y = 245
y*(2 - 3*1.2) = 245 - 3*125.9
y = (245 - 3*125.9)/(2 - 3*1.2)
y = 82.94
Then the value of x is:
x = 125.9 - 1.2*82.94
x = 26.37
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(ii) Find p if 3^p =
3 square root 9/3
We must know the following exponent rules to help us solve this question:
\(a^\frac{m}{n}=\sqrt[n]{a^m}\)\(\dfrac{a^m}{a^n}=a^{m-n}\)\((a^m)^n=a^{mn}\)\(a^m=a^n, \therefore m=n\)Solving the Question
\(3^p=\dfrac{\sqrt[3]{9}}{3}\)
⇒ Rewrite \(\sqrt[3]{9}\) as \(9^\frac{1}{3}\):
\(3^p=\dfrac{(3^2)^\frac{1}{3}}{3}\)
⇒ Multiply:
\(3^p=\dfrac{3^\frac{2}{3}}{3}\)
⇒ Subtract:
\(3^p=3^{\frac{2}{3}-1}\)
\(p=\dfrac{2}{3}-1\\\\p=-\dfrac{1}{3}\)
Answer\(p=-\dfrac{1}{3}\)
first change the given pattern into a vector of zeros and ones by turning each shaded square into a 1 and each unshaded square into a 0 and then lining up each column below the column before it. then find a matrix m so that m0 but m0 for all other nonzero vectors of zeros and ones.
The pattern will be attached in the figure attached, in the matrix form.
What is the matrix?
The arrangements of numbers, variables, symbols, or phrases in a rectangular table with varying numbers of rows and columns are known as matrices, which is the plural version of the word matrix. They are rectangular arrays with defined operations for addition, multiplication, and transposition. The constituents of the matrix are its numbers or entries. Vertical entries in matrices are referred to as columns, whereas horizontal entries are known as rows. A matrix is a rectangular array of numbers, variables, symbols, or expressions that are defined for operations like subtraction, addition, and multiplication. The number of rows and columns in a matrix determines its size, sometimes referred to as its order.
We can arrange it as A = (0 0 0 0 1 1 0 0 1)
We know A*TA = 0
If A has an entry 9 then, the sum of all the diagonal elements.
So the T will be the form of the matrix attached below.
Hence the Pattern will be attached in the figure attached.
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show all the stepsParticipants in a study of a new medication received either medication A or a placebo. Find P(placebo and improvement). You may find it helpful to make a tree diagram of the problem on a separate piece of paper.Of all those who participated in the study, 80% received medication A. Of those who received medication A, 76% reported an improvement. Of those who received the placebo, 62% reported no improvement.
Tree Diagram
Of all the participants in the study, 80% received medication A (M) and 20% received the placebo (P).
The first branches of the tree diagram are:
Of those who received the placebo, 62% reported no improvement (NI), thus 38% reported improvement (I). We complete the lower branch with this information. The upper branch is not important for this question.
We want to calculate the probability of randomly selecting a participant that received a placebo and reported improvement.
We take the bottom path and determine the probability:
P = 20% × 38%
P = 0.20% × 0.38
P = 0.076
P = 7.6%
14.
a. Find the product: (5 - 2X3+ x)
#Beans "Its not a mistake, its a masterpiece"
#BEANS
If you have an actual question I'm happy to answer fren
Answer:
#Beans
Step-by-step explanation:
There Cool.
find the value of y if the line through the two given points is to have the indicated slope. (3,y) and (2,2), m=-3
The value of y for the point (3, y) on the line passing through the points (2, 2) and (3, y) with a slope of -3 is y = -1.
To find the value of y for the point (3, y) on the line passing through the points (2, 2) and (3, y) with a slope of -3, we can use the slope formula:
m = (y2 - y1) / (x2 - x1)
Substituting the given values:
-3 = (y - 2) / (3 - 2)
Next, we can cross-multiply:
-3(3 - 2) = y - 2
Simplifying:
-3 = y - 2
To isolate y, we can add 2 to both sides:
-3 + 2 = y - 2 + 2
-1 = y
Therefore, the value of y for the point (3, y) on the line passing through the points (2, 2) and (3, y) with a slope of -3 is y = -1.
So, the point (3, -1) lies on the line with a slope of -3 passing through the points (2, 2) and (3, -1).
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Two augmented matrices for two linear systems in the variables x, y, and I are given below.
The augmented matrices are in reduced row-echelon form.
For each system, choose the best description of its solution.
If applicable, give the solution.
(a)
10-1
01 1
100 0
5
100 2
0011 4
000-2
OThe system has no solution.
O The system has a unique solution.
(x,x.) - D
O The system has infinitely many solutions.
O (1.7.²) = (1.D
(1.7.2) -..D
(x,y,z) ==)
O The system has no solution.
O The system has a unique solution.
(x,y) - D
O The system has infinitely many solutions.
(x, y, z)=(xD
(2.3.²) -..D
(..)-:)
8
X
a) The system has infinitely many solutions in the following format:
(2 + z, 5 - z, z).
b) The system has no solution.
How to obtain the number of solutions of each system?To obtain the number of solutions of each system, the equations are built from the augmented matrix presented.
For item a, both sides of the matrix have one zero row, hence the system has infinitely many solutions, and the equations are given as follows:
x - z = 2.y + z = 5.Hence the solutions in terms of z are given as follows:
x = 2 + z.y = 5 - z.Thus the format of the solutions is of:
(2 + z, 5 - z, z).
For item b, the right side has three non-zero rows, while the left-side has two, meaning that it has no solutions.
This can be verified from the last line, as the equation would be of:
0z = -2.
Which has no solution.
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Find the slope of the line that passes through Point A(3, -9) and the origin using m=rise/run
Answer:
-3
Step-by-step explanation:
To find the slope (m) of the line that passes through Point A(3, -9) and the origin (0, 0), we can use the formula:m = rise/run = (change in y)/(change in x)We can calculate the change in y and change in x as follows:
Change in y = y2 - y1 = 0 - (-9) = 9
Change in x = x2 - x1 = 0 - 3 = -3
Substituting these values into the formula, we get:
m = rise/run = 9/-3 = -3
Therefore, the slope of the line that passes through Point A(3, -9) and the origin is -3.
.If x2 + kx+ 6 = (x + 2) (x + 3) for all x, then the value of k is
Answer:
k = 5
Step-by-step explanation:
\((x + 2)(x + 3) = {x}^{2} + 5x + 6\)
Now comparing left hand side & right hand side ,
\( {x}^{2} + kx + 6 = {x}^{2} + 5x + 6\)
Cancelling x^2 & 6 from both left hand side & right hand side ,
kx = 5x
=> k = 5
Which rule describes the relationship between the input and output pairs in the following table?
Input
Output
10
5
8
3
6.
1
Choose 1 answer:
Subtract 5 from the input to get the output.
Multiply the input by O. Then add 5 to the result to get the output.
Divide the input by 2. Then subtract 1 from the result to get the output.
Answer: subtract 5 from the input to get the output.
Step-by-step explanation:
HELPPP!!!!!!
Tiana and Vince are practicing their typing skills in computer science class. They both typed the same number of words, but Tiana took less time. They are participating in a typing competition next week. In the competition, they will have the same amount of time to type. Who will likely type more words during the competition?
Answer:
tiana
Step-by-step explanation:
because she took less time in the practise
Answer:
Tiana
Step-by-step explanation:
It is Tiana because she took less time while practicing.
Plzzz help! I will give brainiest and 100 points! 4x2 = 0 (the 2 is an exponent)
Answer:
x =0
Step-by-step explanation:
4x^2 =0
Divide by 4
x^2 = 0
Take the square root
sqrt(x^2) = sqrt(0)
x = 0
Answer:
x=0
Step-by-step explanation:
4x²=0
x²=0
x=√0
x=0