[tex]x=-2.08\overline{3}\\100x=-208.\overline{3}\\1000x=-2083.\overline{3}\\1000x-100x=-2083.\overline{3}-(-208.\overline{3})\\900x=-1875\\x=-\dfrac{1875}{900}=-\dfrac{25}{12}[/tex]
What is the volume of this triangular prism?
22.4 cm
18.1 cm
28 cm
313.6 cm3
506.8 cm3
5,676.16 cm3
11,352.32 cm3
Answer:
[tex]V=5,676.16cm^3[/tex]
Step-by-step explanation:
The volume of a triangular prism is defined by the formula:
[tex]V=(area-of-base)*(length)[/tex]
In this case the base is triangular and the area of a triangle is: [tex]A=\frac{1}{2}(base)*(height)[/tex]
Then the volume is:
[tex]V=\frac{1}{2}(base*height*length)[/tex]
Now we have to replace with the given values:
[tex]V=\frac{1}{2}(22.4cm*18.1cm*28cm)\\\\V=\frac{1}{2}(11,352.32cm^3)\\\\V=5,676.16cm^3[/tex]
Then the correct answer is the third option.
[tex]V=5,676.16cm^3[/tex]
Answer:
5,676.16 is your answer 2021 Edge
I got it right
Step-by-step explanation:
In the triangle below, x=?. Round to the nearest tenth.
Please help!!
Answer:
58 deg
Step-by-step explanation:
Look at x and then look at the sides that are given... 9 is adjacent and 17 is the hypotenuse so use cosine.
cos(x)=9/17
To solve for x just use arccos( ) or cos^(-1)
Type cos^(-1)(9/17) into calc to receive answer (make sure mode is in degrees)
The answer should come to be roughly 58 deg.
Answer:
x ≈ 58.0°
Step-by-step explanation:
Since the triangle is right use the cosine ratio to solve for x
cosx° = [tex]\frac{adjacent}{hypotenuse}[/tex] = [tex]\frac{9}{17}[/tex], thus
x = [tex]cos^{-1}[/tex] ([tex]\frac{9}{17}[/tex] ) ≈ 58.0°
Indicate the equation of the given line in standard form. The line containing the longer diagonal of a quadrilateral whose vertices are A (2, 2), B(-2, -2), C(1, -1), and D(6, 4).
Answer:
3x-4y=2
Step-by-step explanation:
step 1
Plot the figure
we have
A (2, 2), B(-2, -2), C(1, -1), and D(6, 4)
using a graphing tool
The longer diagonal is BD
see the attached figure
step 2
Find the slope of the diagonal BD
we have
B(-2, -2) and D(6, 4)
m=(4+2)/(6+2)
m=3/4
step 3
Find the equation of the diagonal BD into point slope form
y-y1=m(x-x1)
we have
m=3/4
D(6,4)
substitute
y-4=(3/4)(x-6)
step 4
Convert the equation in standard form
The equation of the line in standard form is equal to
Ax+By=C
y-4=(3/4)(x-6)
y=(3/4)x-(18/4)+4
Multiply by 4 both sides
4y=3x-18+16
3x-4y=18-16
3x-4y=2 -----> equation of the diagonal in standard form
Are all of the roots of the polynomial p(x)=x^3+3x^2-11x-5 rational numbers? Why or why not?
Answer:
Step-by-step explanation:
yes. polynomials only have rational numbers
Solve the following inequality algebraically: 1<3x-2<4
A. 1
B. 0
C. 1>x>2
D. 0>x>3
Answer:
1 < x < 2
Step-by-step explanation:
Given
1 < 3x - 2 < 4 ( add 2 to each of the 3 intervals )
3 < 3x < 6 ( divide each interval by 3 )
1 < x < 2
Answer:
A
Step-by-step explanation:
Edge 2021
Choose the possible descriptions of cross sections formed by the intersection of a plane and a cylinder choose all that apply
-circle
-rectangle
-triangle
-line segment
-point
Answer:
circle and rectangle
Step-by-step explanation:
we know that
A cross section that is perpendicular to the base of cylinder is a rectangle
A cross section that is parallel to the base of cylinder is a circle
A cross section that is angled to the base of cylinder is an oval
Final answer:
A plane intersecting a cylinder can create a circle if perpendicular to the cylinder's axis, or a rectangle if cut parallel to the side of the cylinder. Ellipses are also possible when the cutting angle is oblique, and may look circular from certain perspectives. Triangles, line segments, and points are not typical cross sections for a cylinder.
Explanation:
When a plane intersects a cylinder, several different cross sections can result, depending on the angle and position of the plane relative to the cylinder. If the plane is perpendicular to the axis of the cylinder, the cross section will be a circle. If the plane intersects the cylinder at an angle to the axis, the cross section can be an ellipse, which in some cases may appear to be a circle depending on the perspective. A plane intersecting parallel to the side of the cylinder will produce a rectangle. It is not possible for a cylinder to have a triangular, line segment, or point as a cross section through normal slicing, as these do not represent the way planes intersect with the smooth curved surface of a cylinder.
What is the simplified form of the rational expression below 6x^2-54 / 5x^2+15x
Answer:
[tex]\large\boxed{\dfrac{6x^2-54}{5x^2+15x}=\dfrac{6(x-3)}{5x}=\dfrac{6x-18}{5x}}[/tex]
Step-by-step explanation:
[tex]6x^2-54\qquad\text{distributive}\\\\=6(x^2-9)=6(x^2-3^2)\qquad\text{use}\ a^2-b^2=(a-b)(a+b)\\\\=6(x-3)(x+3)\\\\5x^2+15x\qquad\text{distributive}\\\\=5x(x+3)\\-----------------\\\\\dfrac{6x^2-54}{5x^2+15x}=\dfrac{6(x-3)(x+3)}{5x(x+3)}\qquad\text{cancel}\ (x+3)\\\\=\dfrac{6(x-3)}{5x}=\dfrac{6x-18}{5x}[/tex]
8s+4(4s-3)=4(6s+4)-4
Answer:
8s + 4(4s - 3) = 4(6s + 4) - 4
8s + 16s - 12 = 24s + 16 - 4
24s - 12 = 24s + 12
This equation has no solution.
Which conic section does the equation below describe?
x^2+y^2+2x-8y-13=0
Answer: B) Circle
Step-by-step explanation:
First, complete the square:
x² + 2x + 1 + y² - 8y + 16 = 13 + 1 + 16
↓ ↑ ↓ ↑
(2/2) = (1)² (-8/2) = (-4)²
(x + 1)² + (y - 4)² = 30
The result is a circle whose center is (-1, 4) and radius is √30
conic section of the equation B .Circle.
What is conic section?A conic section (or simply conic, sometimes named a quadratic curve) exists as a curve acquired as the intersection of the surface of a cone with a plane.
The word canonical is used to indicate a particular choice from of a number of possible conventions. This convention allows a mathematical object or class of objects to be uniquely identified or standardized.
Canonical equation for circle is (x — x0)2 + (3, yo)2 = R2 ,
hence (x + 1)2 + (y — 3)2 = 4 describes a circle.
conic section of the equation B .Circle.
Standard form of a mathematical object is a standard way of presenting that object as a mathematical expression.
Often, it is one which provides the simplest representation of an object and which allows it to be identified in a unique way.
To learn more about conic section, refer
https://brainly.com/question/1941177
#SPJ2
Answer please. If you answer, you get 44 points. I don't use the points here. So answer please. I want full work.
Answer: you simplfy the two equations already there then plug them in to find factors
Step-by-step explanation:
Answer:
65
Step-by-step explanation:
These are called vertical angles. Vertical angles are equal.
145 = 2x + 15
130 = 2x
x = 65
Which graph represents an inverse variation
Answer:
The second graph.
Step-by-step explanation:
In inverse variation, an increase in one variable leads to a decrease in the other value in the relationship.
xα1/y
x=k/y
meaning
xy= constant
Such a graph slants with a negative gradient from left to right of the Cartesian plane. (the second graph).
Answer:
it's B
Step-by-step explanation:
what is 34/9 written as a decimal
Answer:
3.7
Step-by-step explanation:
To write 34/9 as a decimal you have to divide numerator by the denominator of the fraction.
We divide now 34 by 9 what we write down as 34/9 and we get 3.7777777777778
And finally we have:
34/9 as a decimal equals 3.7777777777778
Please mark brainliest and have a great day!
Answer:3.8
Step-by-step explanation:
34/9
9 into 34 is 3 remainder 7
:. 34/9
= (9 x 3 + 7)/9
=3.777778
=3.8
Which number line represents the solution set for the inequality -4(x + 3) 5-2-2x?
O
+
-7
+
-6
+
-4
-5
-3
-2
-1
0
1
2
3
4
5
6
7
-7
+
-6
+
-5
+
-4
+
-3
+
-2
+
-1
+
0
+
1
+
2
+
3
+
4
5
6
7
-7 -6 -5 -4 -3 -2 -1 0
1 2 3 4 5 6
7
+
+
+
+
+
-7
-6
-5
-4
+ +
-3 -2
+
-1
0
1
2
3
4
5
6
7
Answer:
A
Step-by-step explanation:
Consider the smaller than sign as smaller or equal to sign as I couldn,t type the sign
-4(x+3)<-2-2x
Expand the bracket
-4x-12<-2-2x
Add 2x to both sides
-2x-12<-2
Add 12 to both sides
-2x<10
add 2x to both sides
0<10+2x
minus 10 on both sides
-10<2x
SImplify
-5<x
X is larger or equal to -5 which means the option A
If A and B are dependent events, which of these conditions must be true?
Answer:
i would think A
Answer:P(B|A)is not equal P(B)
Step-by-step explanation:
Given the system of inequalities below: -3x - y < 12 2x + 3y ≥ 9 Give the coordinates of three points that are members of the solution set. () () () (-3, 7) (-3, -7) (3,-7) (-4,-0) (0,-4) (0,4) (2,3) (-2,3) (2,-3)
Answer:
The coordinates of the points that are members of the solution set
(-3,7), (0,4) and (2,3)
Step-by-step explanation:
we have
[tex]-3x-y< 12[/tex] ----> inequality A
The solution of the inequality A is the shaded area above the dashed line
[tex]2x+3y\geq 9[/tex] ----> inequality B
The solution of the inequality B is the shaded area above the solid line
The solution of the system of inequalities is the shaded area between the dashed line and the solid line
see the attached figure
Remember that,
If a ordered pair is a solution of the system of inequalities, then the ordered pair must be in the shaded area of the solution
Plot the points
(-3, 7), (-3, -7), (3,-7), (-4,-0), (0,-4), (0,4), (2,3), (-2,3), (2,-3)
therefore
The coordinates of the points that are members of the solution set
(-3,7), (0,4) and (2,3)
Answer:Answer:
The coordinates of the points that are members of the solution set
(-3,7), (0,4) and (2,3)
Step-by-step explanation:
we have
----> inequality A
The solution of the inequality A is the shaded area above the dashed line
----> inequality B
The solution of the inequality B is the shaded area above the solid line
The solution of the system of inequalities is the shaded area between the dashed line and the solid line
see the attached figure
Remember that,
If a ordered pair is a solution of the system of inequalities, then the ordered pair must be in the shaded area of the solution
Plot the points
(-3, 7), (-3, -7), (3,-7), (-4,-0), (0,-4), (0,4), (2,3), (-2,3), (2,-3)
therefore
The coordinates of the points that are members of the solution set
(-3,7), (0,4) and (2,3)
Step-by-step explanation:
SQ bisects TSR. Find the value of x.
Answer: The answer is 10
Answer:
10
Step-by-step explanation:
math
Using the triangle pictured, find the measure of side AB. Round your answer to the nearest tenth. A) 1.6 B) 2.2 C) 2.7 D) 3.3
Answer:
Option B (AB = 2.2 units).
Step-by-step explanation:
The diagram shows that there are two sides given and one angle is given. Therefore, the sine rule must be used to solve the question. The sine rule can be written as:
sin ABC / AC = sin BAC / BC.
Plugging ABC=72 degrees, AC=2.5, and BC=2.1 in the sine rule gives:
sin 72 / 2.5 = sin BAC / 2.1.
Cross multiplying gives:
sin BAC = (2.1*sin 72)/2.5.
sin BAC = 0.79888747368.
Taking sin inverse on both sides gives:
BAC = arcsin (0.79888747368) = 53.0239949 degrees.
To find AB, first, the angle ACB is required. To find that angle, use the triangular law of angles. All the three angles sum up to 180 degrees. Therefore ACB = 180 - 72 - 53.0239949 = 54.9760051 degrees.
Now applying the Sine Rule to find AB:
sin ACB / AB = sin ABC / AC.
sin (54.9760051) / AB = sin 72 / 2.5.
AB = (2.5*sin (54.9760051))/sin (72) = 2.2 (to the nearest tenth).
Therefore, AB = 2.2 units, i.e. Option B!!!
15. SHORT ANSWER Define a variable and
write an expression to represent the
following phrase.
seven years younger than Lisa
Answer:
see below
Step-by-step explanation:
Let L = lisa's age
seven years younger than Lisa
L-7
Find the common difference of the sequence shown.
1/2, 1/4 , 0, ...
Answer:
-1/4
Step-by-step explanation:
Given sequence is:
1/2, 1/4 , 0, ...
In order to find the common difference in the terms of a sequence, the preceding term is subtracted from the next term.
For example in the given sequence:
first term will be subtracted from second term and second term will be subtracted from third term
So,
[tex]\frac{1}{4}-\frac{1}{2} \\=\frac{1-2}{4}\\ =-\frac{1}{4}\\ Similarly,\\=0-\frac{1}{4} \\=-\frac{1}{4}[/tex]
The common difference is - 1/4 ..
Answer:
-1/4
Step-by-step explanation:
What is the initial value of the sequence?
The points shown on the graph represent the numbers in a
geometric sequence.
Answer:
The initial value of the given geometric sequence is 2.
Step-by-step explanation:
The given points are (1,2), (2,4) and (3,8).
It means the first term is 2, second term is 4 and third term is 8. So, the common ratio is
[tex]r=\frac{a_2}{a_1}=\frac{4}{2}=2[/tex]
A geometric sequence is defined as
[tex]f(n)=ar^{n-1}[/tex]
Where, a is first term of the sequence, r is common ratio and n is number of term. In other words f(1) is the initial value of the geometric sequence.
The given geometric sequence is
[tex]f(n)=2(2)^{n-1}[/tex]
The value of f(1) is 2.
Therefore the initial value of the given geometric sequence is 2.
Answer:Just took the test, it is 2 on edg
Step-by-step explanation:
:)
Solve the system of equations
x + 3y = −1
2x + 2y = 6
QUICK!!
The x-intercepts of a quadratic function are −3 and 5. What is the equation of its axis of symmetry?
A. x=-3
B. x=1
C. x=5
D. x=-15
Answer:
B. x=1
Step-by-step explanation:
Let us define axis of symmetry first.
The point right in between the two x-intercepts of a quadratic equation is called axis of symmetry.
We have x-intercepts of -3 and 5
In ordered to find the axis of symmetry we have to find their middle intercept
To find the axis of symmetry:
[tex]= \frac{-3+5}{2}\\=\frac{2}{2}\\ =1[/tex]
So the axis of symmetry is x = 1 ..
Answer:
B x=1
Step-by-step explanation:
edge 2020 2021
A rectangle's length is 5 inches more than twice its width. Its area is 50 square inches. Which equation can be used to find
its width, w?
Answer:
I think the answer would be 5 divided by 50 times two to find the width.
Step-by-step explanation:
I think my answer above explains it well enough.
Answer: w(2w + 5) = 50
Step-by-step explanation:
Ben climbed 15 feet up a hill,8 feet down a hill, and 11 feet up another hill. What is his overall change in elevation?
Answer:
18 feet
Step-by-step explanation:
15-8+11=18
The triangles shown below may not be congruent.
let's take a peek at the triangles.
they have a 30° angle and a 80° each, and a side that is not in between in common.
[A]ngle [A]ngle [S]ide, AAS congruence.
Answer:
Option B, False.
Step-by-step explanation:
In the given figure two triangles have been given. In these triangles two angles and corresponding side has been given as equal in measure.
Therefore, by AAS theorem for congruence, the given triangles are congruent.
The given statement that the triangle shown may not be congruent is False.
Option B is the answer.
Edna says that when (x - 2)^2 = 9, that x - 2 = 3. Use
complete sentences to explain whether Edna is correct.
Use specific details in your explanation.
Answer:
She is partially correct. There are 2 possible answers to this problem, and x - 2 = 3 is one of the answers. When applying the square root to both sides, the resulting answer could be either negative or positive. Therefore, applying the square root to both sides leads to the two following equations: x - 2 = 3 or x - 2 = -3.
What is the scale factor? ( the answer must be a fraction).
24 people go to joe's birthday party.half walk and a quarter travel by bus all the others go by taxi. How many guests walk? How many travel by bus? How many use taxis? What fraction use taxis? What fraction don't use taxis?
Answer:
How many guests walk? 12How many travel by bus? 8How many use taxis?4What fraction use taxis? [tex]\frac{1}{6}[/tex]What fraction don't use taxis?[tex]\frac{5}{6}[/tex]Step-by-step explanation:
Number of people that attended the party= 24.....let this be x
Number of people that walked= 1/2 x
[tex]=\frac{1}{2} *24 =12[/tex]
Number of people that travel by bus= 1/4 x
[tex]=\frac{1}{4} *24= 8[/tex]
Number of people that go by taxi= the rest
[tex]=24-(12+8)=24-20=4[/tex]
The fraction that used taxis= those that used tax/total number of people
Those that used taxi=4
Total number of people=24
Fraction = [tex]\frac{4}{24} =\frac{1}{6}[/tex]
Fraction that did not use taxi = whole-fraction that used taxi
[tex]\frac{6}{6} -\frac{1}{6} =\frac{5}{6}[/tex]
How will the solution of the system change if the inequality sign on both inequalities
Shown below
Step-by-step explanation:The first system of inequality is the following:
[tex]\left\{ \begin{array}{c}y>2x+\frac{2}{3}\\y<2x+\frac{1}{3}\end{array}\right.[/tex]
To find the solution here, let's take one point, say, [tex](0,0)[/tex] and let's taste this point into both inequalities, so:
FIRST CASE:First inequality:
[tex]y>2x+\frac{2}{3} \\ \\ 0>2(0)+\frac{2}{3} \\ \\ 0>\frac{2}{3} \ False![/tex]
The region is not the one where the point [tex](0,0)[/tex] lies
Second inequality:
[tex]y<2x+\frac{1}{3} \\ \\ 0<2(0)+\frac{1}{3} \\ \\ 0<\frac{1}{3} \ True![/tex]
The region is the one where the point [tex](0,0)[/tex] lies
So the solution in this first case has been plotted in the first figure. As you can see, there is no any solution there
SECOND CASE:First inequality:
[tex]y<2x+\frac{2}{3} \\ \\ 0<2(0)+\frac{2}{3} \\ \\ 0<\frac{2}{3} \ True![/tex]
The region is the one where the point [tex](0,0)[/tex] lies
Second inequality:
[tex]y>2x+\frac{1}{3} \\ \\ 0>2(0)+\frac{1}{3} \\ \\ 0>\frac{1}{3} \ True![/tex]
The region is not the one where the point [tex](0,0)[/tex] lies
So the solution in this first case has been plotted in the second figure. As you can see, there is a solution there.
CONCLUSION: Notice that when reversing the signs on both inequalities the solution in the second case is the part of the plane where the first case didn't find shaded region.
Shown below is a right angle triangle. Find the exact length of the side labeled y.
Answer:
sine 30=y/(8+10√2)
(8+10√2)sin 30=y
Check the picture below.