Answer:
1st triangle: missing angle is 100
2nd triangle: missing angles are 50
3rd triangle: missing angle is 90, this is also a right triangle. The hypotenuse on this is the side length that reaches from angle 70 to 20. the other sides are legs
Step-by-step explanation:
write the first six terms of the sequence f(n)=n^3+2
Answer:
[tex]3,10,29,66,127,218[/tex]
Step-by-step explanation:
[tex]f(n) = n^3 +2\\\\f(1) = 1^3 +2 = 1+2=3\\\\f(2) =2^3 +2 = 8+2=10\\\\f(3)=3^3 +2 = 27+2 = 29\\\\f(4) = 4^3 +2 = 64 +2 = 66\\\\f(5) = 5^3 +2 = 125+2 = 127\\\\f(6) = 6^3 +2 = 216+2 = 218[/tex]
Select the correct answer.
Simplify the expression.
1³/32r5y3
214/2ry³ 3
2x4 √4xy³
2rty 4ry³
413/21²y3
The simplification of the indices can be seen in the explanation below.
[tex]\mathbf{= \dfrac{1^3}{32r^5y^3}}[/tex]
What is the simplification of indices?The simplification of indices entails simplifying the indices to the simplest form possible by using the laws of indices.
From the information given, we have:
1.
[tex]\mathbf{= \dfrac{1^3}{32r^5y^3}}[/tex]
2.
[tex]\mathbf{= \dfrac{214}{2ry^3}}\\[/tex]
[tex]\mathbf{=\dfrac{ 107}{ry^3}}[/tex]
3.
= 2×4 √4xy³
= 8 √4xy³
= 8 × 2√xy³
= 16√xy³
4.
= 2rty 4ry³
= 2tr²y⁴
5
= 413/21²y³
= 413/441 y³
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Answer:
1.
2.
3.
= 2×4 √4xy³
= 8 √4xy³
= 8 × 2√xy³
= 16√xy³
4.
= 2rty 4ry³
= 2tr²y⁴
5
= 413/21²y³
= 413/441 y³
Step-by-step explanation:
A rectangular piece of paper with length 32 cm and width 14 cm has two semicircles cut out of it, as shown below.
Find the area of the paper that remains. Use the value 3.14 for , and do not round your answer. Be sure to include the correct unit in your answer
Answer:
Step-by-step explanation:
Find the x-intercept and y-intercept of the equation: 3x-y = -9
The x-intercept and y-intercept of the equation: 3x - y = -9 is -3 and 9 respectively.
What is a straight line?A straight line is a combination of endless points joined on both sides of the point.
The slope 'm' of any straight line is given by:
[tex]\rm m =\dfrac{y_2-y_1}{x_2-x_1}[/tex]
We have equation:
3x - y = -9
The above equation represents a linear equation;
The equation can be written as:
y = 3x + 9
To find the x-intercept plug y = 0
x = -3
To find the y-intercept plug x = 0
y = 9
Thus, the x-intercept and y-intercept of the equation: 3x - y = -9 is -3 and 9 respectively.
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A function k whose domain is the set of positive integers is defined as k(1) = 4 and k(n) =
k(n - 1) - 2
Function k was evaluated for several numbers. Which of the following are true?
Select each correct answer.
k(2)=
k(1)-24-22Option C is true
k(3)
k(2)-22-20D is true
k(4)
k(3)-2=0-2=-2k(5)
-2-2-4k(6)
-4-2-6E is not true
k(1)
k(0)-2So
k(0)-2=4k(0)=6B is false
Similarly
k(-1)-2=k(0)=6k(-1)=8-1 is not in domain even though
A is false
Only C and D are trueAnswer:
[tex]k(2) = 2[/tex]
[tex]k(3) = 0[/tex]
Step-by-step explanation:
Given:
[tex]\begin{cases}k(1)=4\\k(n)=k(n-1)-2\end{cases}[/tex]
The function [tex]k(n)[/tex] tells us that each term is 2 less than the preceding term.
Therefore:
[tex]\implies k(1)=4[/tex]
[tex]\implies k(2)=k(1)-2=4-2=2[/tex]
[tex]\implies k(3)=k(2)-2=2-2=0[/tex]
[tex]\implies k(4)=k(3)-2=0-2=-2[/tex]
[tex]\implies k(5)=k(4)-2=-2-2=-4[/tex]
[tex]\implies k(6)=k(5)-2=-4-2=-6[/tex]
Rearranging the formula to make the preceding term the subject:
[tex]\begin{aligned} k(n) & = k(n-1) - 2\\\implies k(n)+2 & = k(n-1)\\k(n-1) & =k(n)+2\end{aligned}[/tex]
Therefore:
[tex]\implies k(1)=4[/tex]
[tex]\implies k(0)=k(1)+2=4+2=6[/tex]
[tex]\implies k(-1)=k(0)+2=6+2=8[/tex]
Conclusion
Therefore, the correct answers from the answer options are:
[tex]k(2) = 2[/tex] and [tex]k(3) = 0[/tex]
Find the measures of the angles of an isosceles triangle where the ratio of the vertex angle to one of the base angles is 1:2.
Answer:
Angles of the isosceles triangle are 36°, 72° , 72°
Step-by-step explanation:
Vertex angle : Base angle = 1 : 2
Vertex angle = x
Base angle = 2x
Sum of all angles of a triangle = 180°
x + 2x + 2x = 180°
5x = 180
x = 180 ÷ 5
x = 36°
2x = 2 *36 = 72°
Angles of the isosceles triangle are 36°, 72° , 72°
which of thse numbers 516090,221640,814550 are divisible byy 4
Calculate 3.1 x 108 divided by 6.7 x 103 by using Scientific Notation and the product rule. Write your answer in Scientific Notation. Round to the nearest tenth.
After calculation the value is 4.62 * 10⁴ in Scientific Notation.
What are Scientific Notations ?It is a way of presenting very large and small number in simpler and more understandable form.
It is given that
Calculate 3.1 x 10⁸ divided by 6.7 x 10³
[tex]\rm \dfrac{3.1*10^8}{6.7*10^3}\\\\By \;the \;exponent\; theorem\\\\\dfrac{a^m}{a^n} = a ^{m-n}[/tex]
Therefore
0.462 * 10⁵
4.62 * 10⁴
Therefore the answer after calculation is 4.62 * 10⁴ .
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The ratio of ann's age to bob's age is 3:4
in 7 years time this ratio will be 4:5
0) what are their ages now?
(1) after how many years (from now)
will the ratio be 5:6?
Ann and Bob's age is 21 years and 28 years respectively and after 14 years the ratio will be 5:6.
What is Ratio ?
The comparison of one quantity to other is called a ratio and when two ratios are equal they are said to be in proportion.
It is given in the question that
The ratio of Ann's age to bob's age is 3:4
in 7 years time this ratio will be 4:5
their ages now = ?
Let the age of Ann and Bob is x and y
x:y = 3:4
x =(3/4)y
After seven years
(x+7):(y+7) = 4 :5
(x+7)/(y+7) = 4/5
((3/4)y +7)/(y+7) = 4/5
(3y +28)/(y+7) = 16/5
5*(3y+28)= 16(y+7)
15y +140 = 16y+112
y = 140-112
y =28 years
x = 21 years.
After x years suppose the ratio is 5 :6
(21+x)/(28+x) = 5:6
126 +6x = 140 + 5x
x = 14 years.
Therefore after 14 years the ratio will be 5:6.
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Adam riese developed the signs + and - as mathematical operations what is the title of the work that introduced them?
The title of the work introduced is Rechnung nach der lenge/auff den Linien und Feder.
What are mathematical operations?In mathematics, an operation is a function that takes zero or more input values to a well-defined output value.
Adam Riese developed the signs + and - as mathematical operations and the title of the work introduced is Rechnung nach der lenge/auff den Linien und Feder.
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please help please help please help please help please help please help please help please help please help please help please help please help please help please help
Suppose we take a survey and use the sample proportion to calculate a confidence interval. Which level of confidence gives the confidence interval with the largest margin of error
Answer:
See below
Step-by-step explanation:
I do not see any options, but it is important to note that the bigger the level of confidence, the larger the margin of error will be.
Simplify the square root of 5 times the cube root of 5.
Answer:
3.82362
rounded: 3.82
Step-by-step explanation:
There are eleven divers on a swim team. If the team can only send four divers to a competition, how many ways can they send four
If the team can only send four divers to a competition. Then the number of the ways will be 330.
What are permutation and combination?A permutation is an act of putting things or elements in the right sequence. Combinations are a method of picking things or pieces from a collection of objects or sets when the sequence of the objects is irrelevant.
There are eleven divers on a swim team. If the team can only send four divers to a competition.
Then the number of the ways will be
Number of ways = ¹¹C₄
Number of ways = 11! / [(11 - 4)! x 4!]
Number of ways = 330
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Find the value of y in the solution to the system of equations shown.
y = 4x - 28
y = 1.5x - 18
Answer: y = -12
Equation's:
y = 4x - 28y = 1.5x - 18Solve them simultaneously:
4x - 28 = 1.5x - 18
4x - 1.5x = -18 + 28
2.5x = 10
x = 10/2.5 = 4
Now find the value of y:
y = 4x - 28
insert x = 4
y = 4(4) - 28
y = 16 - 28 = -12
Answer:
[tex]y=-12[/tex]
Step-by-step explanation:
Given system of equations:
[tex]\begin{cases}y = 4x - 28\\y = 1.5x - 18\end{cases}[/tex]
Use the method of substitution to solve for x:
[tex]\begin{aligned}y & = y\\\implies 4x-28 & = 1.5x - 18\\4x-1.5x & = -18+28\\2.5x & = 10\\x & = 10 \div 2.5\\x & = 4\end{aligned}[/tex]
Substitute the found value of x into one of the equations and solve for y:
[tex]\begin{aligned} y & = 4x-28\\\implies y & =4(4)-28\\y & = 16-28\\y & = -12\end{aligned}[/tex]
An isosceles right triangle has an area of 8cm^2. What is the length of its hypotenuse?
Answer:
Given, an isosceles right triangle has area 8 cm². We have to find the length of its hypotenuse. We know that in an isosceles triangle two sides are of equal length. Therefore, the length of the hypotenuse is √32 cm.
The table shows points that lie on the line.
Answer:
y = 5x + 2
Step-by-step explanation:
slope intercept form is y = mx+ b
the y- intercept is 0,2 so 2 is your b.
for m you do rise over run aka y/x. for every 5 rise up the x runs one so your slope(m) = 5
so y=5x+2
Find the product or type
"impossible"
The multiplication of the matrix [tex]\left[\begin{array}{ccc}4\\9\\7\end{array}\right] \left[\begin{array}{ccc}1&-2&1\end{array}\right][/tex]will be [tex]\left[\begin{array}{ccc}4&-8&4\\9&-18&9\\7&-14&7\end{array}\right][/tex].
What is the matrix?A matrix is a representation of the rectangular arrangement of numbers into rows and columns.
Matrix multiplication refers to the product of two matrices.
The condition of matrix multiplication is that the number of columns of the 1st matrix must equal the number of rows of the 2nd one.
The given matrix are
[tex]\left[\begin{array}{ccc}4\\9\\7\end{array}\right] \left[\begin{array}{ccc}1&-2&1\end{array}\right][/tex]
The multiplication of the matrix will be
[tex]\left[\begin{array}{ccc}4&-8&4\\9&-18&9\\7&-14&7\end{array}\right][/tex]
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y varies inversely as x. If y=4 when x=15, find y when x=12
The value of y given the inverse relationship is 5.
What is the value of y?If two variables vary inversely, as one variable increases, the other decreases in value.
The equation that is used to represent inverse relationship is:
y = k/x
Where k is the constant of proportionality
k = yx
k = 4 x 15 = 60
y = 60 / 12
y = 5
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What is one solution of the following system?
StartLayout Enlarged left-brace 1st row 2 y minus 2 x = 12 2nd row x squared + y squared = 36 EndLayout
Answer:
what environmental ethics
only help if u know :D
The number of students in the school given the number of people that attended the dance is 128.
How many students are there?Percentage is the fraction of an amount that is usually expressed as a number out of hundred. The sign used to represent percentages is %.
Number of students = number of students at the dance / percentage that attended the dance
32 / 25%
32 / 0.25 = 128
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What is the recursive formula for this geometric sequence?
6, -24, 96, -384, ...
Answer: a1=6
An = An-1 - 4
Step-by-step explanation:
N represent what number in the sequence you choose. So in the equation n-1 would be the umber in the equation subtracting 1 then subtracting the difference. The factor you are multiplying by in this sequence is -4. You find the difference by taking any number in the sequence and dividing it by the previous number in the sequence.
what is the slope of 2/7x +5y=15
Answer:
-2/35
Step-by-step explanation:
Slope y-intercept form : y = mx + b
Here m is the slope and b is the y-intercept
Write the given equation in slope y-intercept form.
[tex]\sf \dfrac{2}{7}x + 5y = 15\\\\[/tex]
[tex]\sf 5y = \dfrac{-2}{7}x + 15\\\\ y =\dfrac{-2}{7*5}x + \dfrac{15}{5}\\\\ y = \dfrac{-2}{35}x + 3\\\\ \boxed{\bf Slope = \dfrac{-2}{35}}[/tex]
Need the anwser asap
Answer:
The third option.
Step-by-step explanation:
It is the third option because it is subtracting by 2 each time.
Hope this helps!
If not, I am sorry.
Answer:
388848y2
Step-by-step explanation:
yup yup
2x=-4(1/4-3/4 x)+4
solve for x
Answer:
x=-3
Step-by-step explanation:
isolate the variable by dividing each side by factors that don't contain the variable.
Answer:
Step-by-step explanation:
Multiply part of the right side by - 4
2x = -4*1/4 + 4* 3x/4 + 4 Combine
2x = - 1 + 3x + 4 Combine again
2x = 3 + 3x Subtract 3x both sides
2x - 3x = 3 Combine
-x = 3 Multiply by -1.
-1 * -x = - 1 * 3
x = - 3
Which exponential function has a growth factor of 5?
o f(x) = 2(54)
An example of a exponential function with growth rate of 5 is given as y = 2(5)^4
Exponential functionsThese are functions that increases geometrically. The standard exponential function is given as;
y = ab^x
where
a is the base valuex is the exponentb determine the growth or decayAn example of a exponential function with growth rate of 5 is given as y = 2(5)^4
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Help I want to learn how to solve this not just the answer please
Step-by-step explanation:
Cancel out the common factor 2
A plane is located at C on the diagram. There are two towers located at A and B. The distance between the towers is 7,600 feet, and the angles of elevation are given.
a. Find BC, the distance from Tower 2 to the plane, to the nearest foot.
b. Find CD, the height of the plane from the ground, to the nearest foot.
Please show work!
Answer:
part 1) BC is 17491 ft
part 2) CD is 6499 ft
Step-by-step explanation:
Using the graph, determine the coordinates of the y-intercept of the parabola.
Answer:
(0, -5)
Step-by-step explanation:
the y-intercept of the parabola is when x = 0 (crossing the y axis)
Question 4 of 10
What is the result of converting 20 ounces into pounds? Remember that 1
pound = 16 ounces.
Answer:
1 and 1/4 pounds
Step-by-step explanation: