Answer:
5
Step-by-step explanation:
[tex]\tt a_n=a_{n-1}-5\\\\ a_1=20\\a_2=a_1-5=20-5=15\\a_3=a_2-5=15-5=10\\a_4=a_3-5=10-5=5[/tex]
Given the lengths of the sides, state if the triangle is acute, obtuse, or right. 8, 15, and 17 This is a(n) blank triangle.
Answer:
This is a right triangle
Step-by-step explanation:
Pythagoras theorem is used to determine if a triangle is right, acute or obtuse
If the sum of squares of two shorter lengths is greater than the square of third side then the triangle is an acute triangle.
If the sum of squares of two shorter lengths is less than the square of third side then the triangle is an obtuse triangle.
If the sum of squares of two shorter lengths is equal the square of third side then the triangle is a right triangle.
so,
[tex](17)^2 = (15)^2+(8)^2\\289 = 225+64\\289=289[/tex]
Therefore, the given triangle is a right triangle ..
What is the explicit rule for the geometric sequence?
9.5,1.9,0.38,0.076,...
Answer:
[tex]a_n=9.5 \cdot (0.2)^{n-1}[/tex]
Step-by-step explanation:
If this is a geometric sequence, it will have a common ratio.
The common ratio can be found by dividing term by previous term.
The explicit form for a geometric sequence is [tex]a_n=a_1 \cdot r^{n-1} \text{ where } a_1 \text{ is the first term and } r \text{ is the common ratio}[/tex]
We are have the first term is [tex]a_1=9.5[/tex].
Now let's see this is indeed a geometric sequence.
Is 0.076/0.38=0.38/1.9=1.9/9.5?
Typing each fraction into calculator and see if you get the same number.
Each fraction equal 0.2 so the common ratio is 0.2.
So the explicit form for our sequence is
[tex]a_n=9.5 \cdot (0.2)^{n-1}[/tex]
Final answer:
A geometric sequence follows a specific pattern where each term is obtained by multiplying the previous term by a constant ratio. The explicit rule for a geometric sequence is defined by the first term, the term number, and the common ratio.
Explanation:
Geometric series are sequences in which each term after the first is found by multiplying the previous term by a fixed, non-zero number called the common ratio. The explicit rule for a geometric sequence is of the form an = a₁ * r⁽ⁿ⁻¹⁾, where a₁ is the first term, n is the term number, and r is the common ratio.
What else would need to be congruent to show that ABC = XYZ by ASA?
Answer:
Option B AC≅XZ
Step-by-step explanation:
we know that
ASA (angle, side, angle) means that we have two congruent triangles where we know two angles and the included side are equal
In this problem we have
∠X≅∠A
∠Z≅∠C
In the triangle ABC the included side between the angles ∠A and ∠C is the side AC
and
In the triangle XYZ the included side between the angles ∠X and ∠Z is the side XZ
therefore
AC≅XZ
[tex]x {}^{2} - x[/tex]
Factorizations by difference in two squares.
[tex]x^2-x[/tex] is nothing interesting you can just factor out x and result with [tex]x(x-1)[/tex].
However the difference of squares is defined as,
[tex]a^2-b^2=(a+b)(a-b)[/tex]
Hope this helps.
r3t40
Solve the system using substitution. y=-2x+12 3y-x+6=0. What is the solution?
Answer:
x = 6, y = 0 → (6, 0)Step-by-step explanation:
[tex]\left\{\begin{array}{ccc}y=-2x+12&(1)\\3y-x+6=0&(2)\end{array}\right\qquad\text{substitute (1) to (2):}\\\\3(-2x+12)-x+6=0\qquad\text{use the distributive property}\\(3)(-2x)+(3)(12)-x+6=0\\-6x+36-x+6=0\qquad\text{combine like terms}\\(-6x-x)+(36+6)=0\\-7x+42=0\qquad\text{subtract 42 from both sides}\\-7x=-42\qquad\text{divide both sides by (-7)}\\\boxed{x=6}\qquad\text{put it to (1)}\\\\y=-2(6)+12\\y=-12+12\\\boxed{y=0}[/tex]
Answer:
[tex]\text{\fbox{(6,~0)}}[/tex]
Step-by-step explanation:
[tex]\left \{ {{\text{y~=~-2x~+~12}} \atop {\text{3y~-~x~+~6~=~0}} \right. \\ \\ \text{We~already~have~the ~value~of ~y ~so~ substitute~ this~ value~~ of ~y ~into~ the ~second ~equation.} \\ \\ \text{3(-2x~+~12)~-~x~+~6~=~0} \\ \\ \text{Distribute~ 3 ~inside~ the~ parentheses.} \\ \\ \text{-6x~+~36~-~x~+~6~=~0} \\ \\ \text{Combine~ like~ terms. ~You ~can~ subtract~ -6x ~and ~x ~and ~add ~36 ~and ~6.} \\ \\ \text{-7x~+~42~=~0} \\ \\ \text{Subtract~ 42 ~from~ both~ sides ~of~ the ~equation.} \\ \\ \text{-7x~=~-42} \\ \\ \text{Now ~solve~ for ~x ~by ~dividing~ both~ sides ~by~ -7.} \\ \\ \text{\fbox{x~=~6}} \\ \\ \text{To~ find~ y, ~substitute~ 6 ~for~x~ into~ the~first~ equation.} \\ \\ \text{y~=~-2(6)~+~12} \\ \\ \text{Multiply ~-2~ and~ 6.} \\ \\ \text{y~=~-12~+~12} \\ \\ \text{Combine~ like ~terms~ to ~complete~ solving~ for ~y.} \\ \\ \text{\fbox {y~=~0}} \\ \\ \text{The~ solution~ to ~this ~system ~of ~equations ~is ~\fbox{(6~,~ 0)}~.}[/tex]
[tex]\text{x~=~6} \\ \text{y~=~0}[/tex]What mistake did the student make?
Answer:
A
Step-by-step explanation:
if he had multiplied the 2nd equation by 9 throughout successfully, he would have gotten :
6x - y = 16 (multiply by 9)
54x - 9y = 144
Answer:
(a) The error is in step 1.
See below.
Step-by-step explanation:
They did not multiply the 16 by 9.
This circle is centered at the origin, and the length of its radius is 6. What is
the circle's equation?
Answer:
x² + y² = 36
Step-by-step explanation:
The equation of a circle centred at the origin is
x² + y² = r² ← r is the radius
here r = 6, so
x² + y² = 6², that is
x² + y² = 36
The circle's equation is x² + y² = 36.
What is the equation for a circle?The equation of a circle provides an algebraic way to describe a circle, given the center and the length of the radius of a circle.The equation of a circle is different from the formulas that are used to calculate the area or the circumference of a circle.Given:
length of its radius is 6.
To find:
the circle's equation
The equation for a circle in center, radius form is
(x - h)² + (y - k)² = r²
The equation of a circle centered at the origin is
x² + y² = r²
Where, r is the radius of the circle
Here radius of the circle = 6
If the center is (0,0) then h = 0 and k = 0
x² + y² = 6²,
x² + y² = 36
Therefore, the circle's equation x² + y² = 36.
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Complete the three-by-three magic square (that is,the sums of the numbers in each row, in each column and in each of the diagonals are the same) using
[tex]\displaystyle\\\text{We will use numbers from 1 to 9.}\\\\1+2+3+4+5+6+7+8+9=\frac{9(9+1)}{2}=\frac{9\times10}{2}=\frac{90}{2}=\boxed{\bf45}\\\\\text{the sums of the numbers in each row, in each column are }=\frac{45}{3}=\boxed{\bf15}\\\\\text{Solution:}\\\\\boxed{\,2\,}\boxed{\,7\,}\boxed{\,6\,}\\\boxed{\,9\,}\boxed{\,5\,}\boxed{\,1\,}\\ \boxed{\,4\,}\boxed{\,3\,}\boxed{\,8\,}\\\\\text{Convenient rotation of the square gives 8 solutions.}[/tex]
what is the sum of the first four terms of a geometric series with 2 as its first term and a common ratio of 1/3
[tex]\bf \qquad \qquad \textit{sum of a finite geometric sequence} \\\\ \displaystyle S_n=\sum\limits_{i=1}^{n}\ a_1\cdot r^{i-1}\implies S_n=a_1\left( \cfrac{1-r^n}{1-r} \right)\quad \begin{cases} n=\textit{last term's}\\ \qquad position\\ a_1=\textit{first term}\\ r=\textit{common ratio}\\ \cline{1-1} n=4\\ a_1=2\\ r=\frac{1}{3} \end{cases}[/tex]
[tex]\bf S_4=2\left( \cfrac{1-\left( \frac{1}{3} \right)^4}{1-\frac{1}{3}} \right)\implies S_4 = 2\left( \cfrac{1-\frac{1}{81}}{\frac{2}{3}} \right)\implies S_4 = 2\left( \cfrac{\frac{80}{81}}{~~\frac{2}{3}~~} \right) \\\\\\ S_4=2\left( \cfrac{40}{27} \right)\implies S_4=\cfrac{80}{27}\implies S_4=2\frac{26}{27}[/tex]
Answer:
80/27.
Step-by-step explanation:
Sum of n terms = a1 * (1 - r^n) / (1 - r)
Sum of 4 terms = 2 * (1 -(1/3)^4) / ( 1 - 1/3)
= 2 * 80/81 / 2/3
= 160 / 81 * 3/2
= 480/ 162
= 80/27 (answer
A particular model of walkie-talkie can broadcast in a circular area. The radius of the broadcast area is 7,000 feet. Find the area of this circle to the nearest square foot. Use 3.14 for π.
Answer:
153938040.0259 ft2
Step-by-step explanation:
R= Square root of A/π
Answer:
153,860,000 ft^2.
Step-by-step explanation:
The area = 3.14 * r^2
= π * 7,000^2
= 153,860,000 ft^2.
A right cylinder has a radius of 2 units and a height of 5
units.
What is the volume of the cylinder? Round to the nearest
tenth.
31.4 cubic units.
62.8 cubic units
157.1 cubic units
314.2 cubic units.
Answer:
62.8
Step-by-step explanation:
The volume of the cylinder is = base * height
base=Pi*radius*radius, where
base=3.1416*2*2 , height=5
Volume=3.1416*2*2*5
Volume =62.8 cubic units.
Answer:
Option B.
Step-by-step explanation:
It is given that right cylinder has a radius of 2 units and a height of 5 units. It means
r = 2
h = 5
The volume of a right cylinder is
[tex]V=\pi r^2h[/tex]
where, r is radius and h is height of the cylinder.
Substitute r=2 and h=5 in the above formula.
[tex]V=\pi (2)^2(5)[/tex]
[tex]V=\pi (4)(5)[/tex]
[tex]V=20\pi[/tex]
On further simplification we get
[tex]V=62.831853[/tex]
[tex]V\approx 62.8[/tex]
The volume of right cylinder is 62.8 cubic units.
Therefore, the correct option is B.
Consider this equation.
7.8 + 2(0.75m + 0.4) = -6.4m + 4(0.5m - 0.8)
Mia solved the equation and determined that m = 2. Is she correct?
A. She is incorrect because when substituting 2 for m the result was a true statement.
B. She is incorrect because when substituting 2 for m the result was a false statement.
C. She is correct because when substituting 2 for m the result was a true statement.
D. She is correct because when substituting 2 for m the result was a false statement.
Answer:
B if m=2
(Just to make sure that isn't m=-2, right?)
Step-by-step explanation:
7.8 + 2(0.75m + 0.4) = -6.4m + 4(0.5m - 0.8)
Let's plug in 2 for m.
7.8+2(0.75*2+0.4) = -6.4*2+4(0.5*2-0.8)
If 2 is a solution, then both sides will be the same.
If 2 is not a solution, then both sides will be different.
If both sides are the same, it is a true equation.
If both sides are different, it is a false equation.
Let's simplify 7.8+2(0.75*2+0.4)
According to PEMDAS, we must perform the operations in the parenthesis.
We have multiplication and addition in ( ). We will do the multiplication because the MD comes before the AS.
0.75*2=1.5
So now our expression 7.8+2(0.75*2+0.4) becomes 7.8+2(1.5+0.4)
Now to do the addition in the ( ).
1.5+0.4=1.9.
So now our expression 7.8+2(0.75*2+0.4) becomes 7.8+2(1.9).
We have multiplication to be perform now because again MD becomes before AS.
7.8+2(0.75*2+0.4) becomes 7.8+3.8
Last step perform the addition (the only operation left here on the left hand side)
7.8+2(0.75*2+0.4) becomes 11.6 .
Let's focus on the right now.
-6.4*2+4(0.5*2-0.8)
-6.4*2+4(1 -0.8) I did the multiplication in the ( ) first.
-6.4*2+4(.2) I did the subtracting in the ( ).
-12.8+.8 I did the multiplication by -6.4*2 and 4*.2 simultaneously
-12
I'm going to put all of this together because I think it might be easier to read:
7.8 + 2(0.75m + 0.4) = -6.4m + 4(0.5m - 0.8)
Plug in 2 for m
7.8 + 2(0.75*2 + 0.4)=-6.4*2 + 4(0.5*2 - 0.8)
7.8 + 2(1.5 + 0.4)= -6.4*2 + 4(1 -0.8)
7.8 + 2(1.9) = -6.4*2 + 4(.2)
7.8 + 3.8 = -12.8 +.8
11.6 =-12
This is false because 11.6 is not the same as -12.
m=2 leads to a false equation
B.
The value of m for the expression 7.8 + 2(0.75m + 0.4) = -6.4m + 4(0.5m - 0.8) is -2. Hence, Mia's statement is false.
What is Simplification?Simplification in mathematical terms is a process to convert a long mathematical expression in simple and easy form.
The given equation is,
7.8 + 2(0.75m + 0.4) = -6.4m + 4(0.5m - 0.8)
Also, Mia solved the equation and determine that the value of m is 2.
To find the value of m, simplify the expression,
7.8 + 1.5m + 0.8 = -6.4m + 2m - 3.2
1.5m + 8.6 = -4.4m - 3.2
1.5m + 4.4m = -3.2 - 8.6
5.9m = -11.8
m = -2
Mia is incorrect because the value of m is -2,
Therefore the statement is false.
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What would the next figure in the geometric pattern below be?
Answer:
Hi there!
The answer to this question is: D
Step-by-step explanation:
The pattern is; up (red), down (blue), up (red)
so therefore the next pattern is down (blue) which is D
To find the next figure in the geometric pattern, analyze the given information and identify the pattern in the dot placements. Based on the description, each figure is obtained by adding dots in specific positions. The next figure can be determined by continuing this pattern.
Explanation:The next figure in the geometric pattern can be determined by analyzing the given information. Based on the description, we can infer that each figure is obtained by adding dots in a specific pattern. The third dot is located one and two-thirds perpendicular hash marks to the right of the center top perpendicular hash mark, while the fourth dot is in the same position as the Car X figure (one perpendicular hash mark above the center right perpendicular hash mark). To find the next figure, we need to continue this pattern by adding dots in the specified positions.
SOLVE 4x + 3y = –5 -2x + 2y = 6 BY USING ELIMINATION. SHOW ALL WORK!!! HELPPPP :)))) THANKS! ;)
Answer:
x= [tex]\frac{-1}{6}y+\frac{-11}{6}[/tex]
y=6x+11
Step-by-step explanation:
4x + 3y = –5 -2x + 2y = 6
- 4x - 3y –5 -2x + 2y = 6
- 4x - 3y -2x + 2y = 6+5
-4x - 3y -2x +2y =11
-6x-y= 11
Select the two values of x that are roots of this equation. x^2+2x-4=0
Answer:
[tex]\large\boxed{x=-1\pm\sqrt5}[/tex]
Step-by-step explanation:
[tex]x^2+2x-4=0\qquad\text{add 4 to both sides}\\\\x^2+2x=4\\\\x^2+2(x)(1)=4\qquad\text{add}\ 1^2=1\ \text{to both sides}\\\\\underbrace{x^2+2(x)(1)+1^2}=4+1^2\qquad\text{use}\ (a+b)^2=a^2+2ab+b^2\\\\(x+1)^2=5\to x+1=\pm\sqrt5\qquad\text{subtract 1 from both sides}\\\\x=-1\pm\sqrt5[/tex]
The two values of x for the given equation are ( -1 + √5 ) and ( - 1 - √5 ).
What is a quadratic equation?The polynomial having a degree of two or the maximum power of the variable in a polynomial will be 2 is defined as the quadratic equation and it will cut two intercepts on the graph at the x-axis.
The solution of the given equation is:-
= x² + 2x - 4
x² + 2x = 4
x² + 2x ( 1 ) + 1² = 4 + 1²
( x + 1 )² = 5
x + 1 = ± √5
x = -1 ± √5
Therefore the two values of x for the given equation are ( -1 + √5 ) and ( - 1 - √5 ).
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Martin runs 100 meters in 15 seconds. What is the equation for d, the distance in meters that Martin covers per second
Answer:
d = 6.67s
Step-by-step explanation:
This is the answer because if you take 100 and divide it by 15, then you get d as 6.6666, which rounds up to 6.67s.
If f(x)= -3x-2 ,what is f(-5)
Answer:
f(- 5) = 13
Step-by-step explanation:
To evaluate f(- 5) substitute x = - 5 into f(x)
f(- 5) = - 3 × - 5 - 2 = 15 - 2 = 13
A square pyramid has the sides of the base of 4 cm and a height of 10 cm, what is its surface area?
Answer:
A = 44.2cm²
Step-by-step explanation:
The surface area of a square pyramid that has the sides of the base of 4 cm and a height of 10 cm is 44.2cm².
Formula: A=AB(4h2+AB)+AB
A=AB(4h2+AB)+AB=4·(4·102+4)+4≈44.1995cm²
Which of the following expressions is this one equivalent to?
[tex]( {x}^{4}+ 2 {x}^{3} - x - 2) \div ( {x}^{3} - 1) [/tex]
___________________________________________
○A.
[tex] {x}^{2} + x + 1[/tex]
○B.
[tex] {x}^{2} + 3x + 2[/tex]
○C.
[tex]x + 2[/tex]
○D.
[tex]2x - 5 - \frac{3}{ {x}^{3} - 1 } [/tex]
Answer:
○C. x + 2
Step-by-step explanation:
x^4 + 2x^3 -x-2
-------------------------
x^3 -1
Factor the numerator by grouping. Take an x^3 from the first 2 terms and -1 from the last 2 terms
x^3( x + 2) -1(x+2)
-------------------------
x^3 -1
now lets factor out the x+2
( x + 2)(x^3 -1)
-------------------------
x^3 -1
Canceling out the x^3-1, we are left with
x+2
Answer:
C. x+2
Step-by-step explanation:
The given expressions are two polynomials which have to be divided in order to find the quotient. The long division method will be used to find the quotient of the two terms.
The long division is done and the picture is attached for detail.
From the picture, we can see that the correct answer is:
C. x+2 ..
Among two supplementary angles the measure of the larger angle is 44 more than
the measure of the smaller. Find their measures.
Please reply soon
The one who replies first I will answer all their questions ...............
Answer:
The smaller angle= 68°
The larger angle=112°
Step-by-step explanation:
Supplementary angles add up to 180°
Let the smaller of the angles to x then the larger angle will be x+44.
Adding the two then equating to 180°:
x+(x+44)=180
2x+44=180
2x=180-44
2x=136
x=68
The smaller angle= 68°
The larger angle=68+44=112°
Answer:
The angles are 68° , 112°
Step-by-step explanation:
Let the smaller angle be x
so the larger angle = x + 44
x , x + 44 are supplementary.
so, x + (x + 44) = 180
x + x + 44 = 180
2x = 180 - 44 = 136
x = 136/2 = 68
the larger angle = x + 44 = 68 + 44 = 112
what is the length of chord ab
Answer:
AB=20
Step-by-step explanation:
Given:
r= 14.5
AB cuts r=14.5 in two parts one parts length=4
remaining length, x = 14.5 - 4 =10.5
draw a line from center of circle to point A making right angled triangle
Now hypotenuse=r=14.5
and one side of triangle=10.5
Using pythagoras theorem to find the third side:
c^2=a^2+b^2
14.5^2=10.5^2+b^2
14.5^2-10.5^2=b^2
b^2=100
b=10
AB=2b
=2(10)
=20
Hence length of cord AB=20!
What is the equation of the oblique asymptote?
h(x)= x^2-3x-4/x+1
___________________________________________
○A. y=x+4
○B. y= x
○C. y= x^2-3
○D. y=x-4
Answer:
y=x-4
Step-by-step explanation:
What you are looking for is also known as the slant asymptote. The slant asymptote occurs when the degree of the numerator is one degree more than the denominator which is what you have.
So to find the slant asymptote we can use polynomial division.
We have a choice to use synthetic division here because the denominator is linear.
-1 goes on the outside because we are dividing by (x+1).
-1 | 1 -3 -4
| -1 4
|----------------------
1 -4 0
The asymptote is the quotient part which is y=x-4.
So answer is y=x-4.
Option D is correct, y=x-4 is the equation of the oblique asymptote h(x)= x²-3x-4/x+1
What is Equation?Two or more expressions with an Equal sign is called as Equation.
To find the equation of the oblique asymptote, we need to perform polynomial division of the numerator (x² - 3x - 4) by the denominator (x + 1):
x - 4
------------
x + 1 | x² - 3x - 4
x² + x
-------
-4x - 4
-4x - 4
-------
0
The quotient is x - 4, which represents the equation of the slant asymptote.
Hence, y=x-4 is the equation of the oblique asymptote h(x)= x²-3x-4/x+1
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Jill has quiz scores of 74, 72, 76, 80, and 73. To continue to receive her scholarship, Jill must maintain an average of 75. What is the lowest grade Jill needs to have on the next quiz to keep her scholarship?
A. 77
B. 75
C. 73
D. 71
Answer:
B
Step-by-step explanation:
(74+72+76+80+73+(AnswerB)75)÷6(total number of quizzes include the one she needed to take)=75(minimum average because she needs to get average of 75)
The overhead reach distances of adult females are normally distributed with a mean of 205 cm205 cm and a standard deviation of 8.6 cm8.6 cm.
a. Find the probability that an individual distance is greater than 215.00215.00 cm.
b. Find the probability that the mean for 2525 randomly selected distances is greater than 203.70 cm.203.70 cm.
c. Why can the normal distribution be used in part (b), even though the sample size does not exceed 30?
Answer:
a) P(z>1.16) = 0.8770
b) P(z>-0.75) = 0.2266
Step-by-step explanation:
Mean = 205 cm
Standard Deviation = 8.6 cm
a) Find the probability that an individual distance is greater than 215.00
We need to find P(X>215)
x = 215
z = x - mean /standard deviation
z = 215 - 205 / 8.6
z = 1.16
P(X>215)=P(z>1.16)
Finding value of z =1.16 from the table
P(z>1.16) = 0.8770
b) Find the probability that the mean for 25 randomly selected distances is greater than 203.70 cm
Sample size n= 25
x = 203.70
mean = x- mean / standard deviation / √sample size
mean = 203.70 - 205 / 8.6 / √25
mean = -1.3/8.6/5
mean = -0.75
Finding value from z-score table
P(mean >-0.75) = 0.2266
c) Why can the normal distribution be used in part (b), even though the sample size does not exceed 30?
If the original problem is normally distributed, then for any sample size n, the sample means are normally distributed.
the sum of two consecutive numbers is 1107. what are those numbers
PLEASE HELP !!!!!!!
[tex]\huge{\boxed{553}}\ \ \huge{\boxed{554}}[/tex]
The numbers can be represented as [tex]x[/tex] and [tex]x+1[/tex].
We know that [tex]x+x+1=1107[/tex].
Combine like terms. [tex]2x+1=1107[/tex]
Subtract 1 on both sides. [tex]2x=1106[/tex]
Divide both sides by 2. [tex]x=553[/tex]
The first number is [tex]x[/tex], which equals [tex]\boxed{553}[/tex].
The second number is [tex]x+1[/tex], which equals [tex]553+1[/tex], which is [tex]\boxed{554}[/tex].
These numbers can be presented as n and n + 1 = 1107
2n = 1106 because we combine the n terms and subtract 1 from each side.
2n ÷ 2 = n
1106 ÷ 2 = 553
We now know that n = 553.
Our second consecutive integer must be 554. This is because our second
consecutive integer represents n + 1 so 553 + 1 =554.
Therefore, are two consecutive integers are 553 and 554.
7. A photograph negative measures 15 inches by
2- inches. The printed picture is to have its
longer dimension be 4 inches. How long should
the shorter dimension be?
(A) 2
(B) 3”
(C)35"
(D) 32»
Answer:
First we need to set a proportion
Currently the negative measures 15 inches by 2 inches. And the longer dimension of the printed version is 4 inches. Therefore:
[tex]\frac{2}{y} = \frac{15}{4}[/tex]
[tex]15y = 8[/tex]
[tex]y = 0.5333[/tex]
Therefore, the dimension of the shorter dimension is 0.5333.
None of the options matches this response, so maybe you forgot to add some information?
What is the reference angle for 120°
Check the picture below.
bearing in mind that in essence, a reference angle is the angle made with the x-axis from any terminal point.
What is the sum of sqrt -2 and sqrt -18
Answer:
4i sqrt(2)
Step-by-step explanation:
sqrt(-2) + sqrt(-18)
We know sqrt(ab)= sqrt(a) sqrt(b)
sqrt(-1)sqrt(2) + sqrt(9) sqrt(-2)
sqrt(-1)sqrt(2) + sqrt(9) sqrt(2)sqrt(1)
We know the sqrt(-1) is equal to i
i sqrt(2) +3 sqrt(2) i
i sqrt(2) +3i sqrt(2)
4i sqrt(2)
Max is drawing plans for a garden, measured in feet, which is shown below on the coordinate plane. Max has two vertices
of the garden at points (-1, 2) and (-1,-2).
At which points should Max have the other two vertices in order to make the area of his garden 20 square feet?
Answer:
The other two vertices are (4 , -2) and (4 , 2) ⇒ 2nd answer
Step-by-step explanation:
* Lets explain how to solve the problem
- All the points on a vertical line have thee same x-coordinates
- In the vertical segment whose endpoints are (x , y1) and (x , y2)
its length = y2 - y1
- All the points on a horizontal line have thee same y-coordinates
- In the horizontal segment whose endpoints are (x1 , y) and (x2 , y)
its length = x2 - x1
* Lets solve the problem
- The two vertices of the garden are (-1 , 2) , (-1 , -2)
- The side joining the two vertices is vertical because the points have
the same x-coordinate
∴ The length of the height = 2 - -2 = 2 + 2 = 4
∴ The length of the height of the garden is 4 feet
∵ The garden shaped a rectangle
∵ The area of the garden is 20 feet²
- The area of the rectangle = base × height
∵ The height = 4 feet
∴ 20 = base × 4 ⇒ divide both sides by 4
∴ Base = 5 feet
∴ The length of the base of the garden is 5 feet
- The adjacent side to the height of the rectangle is horizontal line
∵ The points on the horizontal line have the same y-coordinates
∴ The adjacent vertex to vertex (-1 , 2) has the same y-coordinates 2
∵ The length of the horizontal segment is x2 - x1
∴ 5 = x - (-1)
∴ 5 = x + 1 ⇒ subtract 1 from both sides
∴ x = 4
∴ The adjacent vertex to (-1 , 2) is (4 , 2)
- Lets find the other vertex by the same way
∵ The adjacent vertex to vertex (-1 , -2) has the same y-coordinates -2
∵ x-coordinate of this vertex is the same with x- coordinate of point
(4 , 2) because these two points formed vertical side
∴ The other vertex is (4 , -2)
∴ The adjacent vertex to (-1 , -2) is (4 , -2)
* The other two vertices are (4 , -2) and (4 , 2)
Answer: Option B
(B) (4,-2) and (4,2) <======+ 100%
Step-by-step explanation:
what is the simplest form of x2+5x+-6/ x2+9x+18
Answer:
[tex]\frac{x-1}{x+3}[/tex]
Step-by-step explanation:
Let's factor the numerator and denominator first.
x^2+5x-6 is a quadratic in the form of x^2+bx+c.
If you have a quadratic in the form of x^2+bx+c, all you have to do to factor is think of two numbers that multiply to be c and add to be b.
In this case multiplies to be -6 and adds to be 5.
Those numbers are 6 and -1 since -1(6)=-6 and -1+6=5.
So the factored form of x^2+5x-6 is (x-1)(x+6).
x^2+9x+18 is a quadratic in the form of x^2+bx+c as well.
So we need to find two numbers that multiply to be 18 and add to be 9.
These numbers are 6 and 3 since 6(3)=18 and 6+3=9.
So the factored form of x^2+9x+18 is (x+3)(x+6).
So we have that:
[tex]\frac{x^2+5x+-6}{x^2+9x+18}=\frac{(x-1)(x+6)}{(x+3)(x+6)}[/tex]
We can simplify this as long as x is not -6 as
[tex]\frac{x-1}{x+3}[/tex]
I obtained the last line there by canceling out the common factor on top and bottom.
Answer:
We can simplify this as long as x is not -6 as
\frac{x-1}{x+3}
Step-by-step explanation: