Answer:
y = -2x+1
Step-by-step explanation:
The slope is found by
m = (y2-y1)/(x2-x1)
= (-1-5)/(1--2)
= -6/(1+2)
= -6/3
= -2
Then we can use point slope form to make an equation
y-y1 = m(x-x1)
y-5 = -2(x--2)
y-5 = -2(x+2)
Distribute
y-5 = -2x -4
Add 5 to each side
y-5+5 = -2x-4+5
y = -2x+1
This is in point slope form
Classify the following triangle based on its angle measures.
A) Obtuse
B)Acute
C)right
D)equiangular
Answer:
A) Obtuse
Step-by-step explanation:
It is Obtuse due to the angle 115° being in the Triangle. This rules out Acute since the middle angle is not less than 90°. It is not Equiangular since all three angles are not equal. Furthermore it is not a right triangle either since there is no 90° angles. Making it Obtuse.
To classify a triangle based on angle measures, we need to know the specific angles. Triangles can be obtuse, acute, right, or equiangular, and each type has its own unique properties used in various applications across different fields.
Explanation:To classify the following triangle based on its angle measures, we must first understand the definitions of different types of triangles. A triangle can be classified as:
Obtuse: One angle is greater than 90 degrees.Acute: All angles are less than 90 degrees.Right: One angle is exactly 90 degrees.Equiangular: All angles are equal, and each measure 60 degrees since the sum of the angles in any triangle is 180 degrees.Considering these definitions, the seeking student must provide the angle measures of their specific triangle to accurately classify it.
Why Make These Distinctions?Making distinctions between different types of triangles is crucial because each classification has unique properties that are important in various fields such as mathematics, engineering, architecture, and physics. These properties assist in solving problems and understanding the world around us.
For instance, an obtuse triangle may be used in special construction scenarios, while right triangles are essential in trigonometry and geometry, appearing frequently in real-life applications like building and navigation.
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A rectangular prism has a length of 2 1/4 feet, a width of 6 feet, and a height of 3 1/2 feet.
What is the volume of the prism?
Enter your answer in the box.
ft³
For this case we have by definition, that the area of a rectangular prism is given by:
[tex]V = A_ {b} * h[/tex]
Where:
[tex]A_ {b}:[/tex] is the area of the base
h: It's the height
Before finding[tex]A_ {b}[/tex]we convert the mixed numbers to fractions:
length: [tex]2 \frac {1} {4} = \frac {4 * 2 + 1} {4} = \frac {9} {4}[/tex]
width: 6
Height:[tex]3 \frac {1} {2} = \frac {2 * 3 + 1} {2} = \frac {7} {2}[/tex]
So, we have to:[tex]A_ {b} = \frac {9} {4} * 6 = \frac {54} {4} = 13.5[/tex]
Finally, the volume is given by:
[tex]V = 13.5 * \frac {7} {2} =47.25\ ft ^ 3[/tex]
Answer:
[tex]47.25 \ ft ^ 3[/tex]
ANSWER
[tex]Volume = 47\frac{1}{4} {ft}^{3} [/tex]
EXPLANATION
The formula for calculating the volume of a rectangular prism is
[tex]Volume = l \times b \times h[/tex]
Where
[tex]l = 2 \frac{1}{4} ft[/tex]
is the length of the rectangular box,
[tex]w = 6ft[/tex]
is the width and
[tex]h = 3 \frac{1}{2} ft[/tex]
is the height of the rectangular prism.
We plug in the given dimensions into the formula to get:
[tex]Volume = 2 \frac{1}{4} \times 6 \times 3 \frac{1}{2} [/tex]
Convert the mixed numbers to improper fraction to get:
[tex]Volume = \frac{9}{4} \times 6 \times \frac{7}{2} [/tex]
Multiply out to get
[tex]Volume = \frac{189}{4} {ft}^{3} [/tex]
Or
[tex]Volume = 47\frac{1}{4} {ft}^{3} [/tex]
Write the equation of the line that has a y-value that increases by 4 for every x that increases by 1. It also crosses the y-axis at –2. A. y = 4x – 2 B. y1/4x – 2 C. y = 2x + 1/4D. y = 2x – 4
ANSWER
[tex]y = 4x - 2[/tex]
EXPLANATION
The equation of a straight line can be found using the formula
[tex]y =mx + b[/tex]
We have that,the y-value increases by 4 for every x that increases by 1.
This implies that, the slope is
[tex]m = \frac{4}{1} = 4[/tex]
The line also crosses the y-axis at –2.
Hence the y-intercept is b=-2.
Therefore the equation is
[tex]y = 4x - 2[/tex]
The correct answer is A
Two automobiles start together from the same place and travel along the same route. The first averages 40 miles
per hour and the second 55 miles per hour. How many miles further along the route is the second car at the end of
5 hours?
Make a Selection:
A. (55 x 5) - (40 x 5)
B. 55 x 5
C. 55 - 40
D. 55/5 - 40/5
NEXT >>
Answer:
A. (55 x 5) - (40 x 5)
Step-by-step explanation:
You are solving how much miles (further along) would the second car be after 5 hours.
The first car averages 40 miles per hour. 5 hours later, it will have averaged about 200 miles in 5 hours (40 x 5 = 200).
The second car averages 55 miles per hour. 5 hours later, it will have averaged about 275 miles in 5 hours (55 x 5 = 275)
Subtract: 275 - 200 = 75
The second car would have averaged 75 more miles than the first car.
~
Answer:
A. (55 x 5) - (40 x 5)
Step-by-step explanation:
The "speedier" car goes 55 mph * 5 hrs = 55*5 miles
The "slower" car goes 40mph * 5 hrs = 40*5 miles
The distance between them is
55 *5 - 40*5
how do you factor x squared minus 100
Answer:
(x - 10)(x + 10)
Step-by-step explanation:
x² - 100 ← is a difference of squares and factors in general as
a² - b² = (a - b)(a + b)
Hence
x² - 100
= x² - 10² = (x - 10)(x + 10)
find the solution set.
8x^2+7x-1=0
Answer:
x = - 1, x = [tex]\frac{1}{8}[/tex]
Step-by-step explanation:
Given
8x² + 7x - 1 = 0 ← in standard form
Consider the factors of the product of the x² term and the constant term which sum to give the coefficient of the x- term
product = 8 × - 1 = - 8 and sum = + 7
The factors are + 8 and - 1
Use these factors to split the x- term
8x² + 8x - x - 1 = 0 ( factor the first/second and third/fourth terms )
8x(x + 1) - 1(x + 1) = 0 ← factor out (x + 1) from each term
(x + 1)(8x - 1) = 0
Equate each factor to zero and solve for x
x + 1 = 0 ⇒ x = - 1
8x - 1 = 0 ⇒ 8x = 1 ⇒ x = [tex]\frac{1}{8}[/tex]
Answer:
x
=
1
8
,
−
1
x=1/8,-1 I solved using the quadratic formula
Step-by-step explanation:
ABCD is a parallelogram in which in which angle a is 110. Find the measure of each of the angles b,c,d
Answer:
m < b = 70, m < c = 110 and m < d = 70 degrees.
Step-by-step explanation:
The opposite angle a ( angle c) = a = 110 degrees (Property of a parallelogram).
The angle on the same line as a ( that is angle b) = 180 - 110 = 70 degrees.
(Property of a parallelogram).
Finally angle d which is opposite angle b = 70 degrees.
Final answer:
In parallelogram ABCD with angle A being 110 degrees, angle C is also 110 degrees as opposite angles are equal. Angles B and D are 70 degrees each since consecutive angles in a parallelogram are supplementary and add up to 180 degrees.
Explanation:
To find the measures of the angles B, C, and D in the parallelogram ABCD with angle A being 110 degrees, we can use the properties of parallelograms. Specifically, opposite angles in a parallelogram are equal, and consecutive angles are supplementary (add up to 180 degrees).
Since angle A is 110 degrees, angle C, being opposite to angle A, also measures 110 degrees. Now, to find the measures of angles B and D we know that:
Angle A and angle B are consecutive, so they add up to 180 degrees. Therefore, angle B equals 180 degrees - 110 degrees which is 70 degrees.
Similarly, angle C and angle D are consecutive, so angle D also measures 180 degrees - 110 degrees, giving us 70 degrees for angle D as well.
Thus, the measures of angles B, C, and D in parallelogram ABCD are 70 degrees, 110 degrees, and 70 degrees, respectively.
Which expressions are equivalent to 2 In a + 2 In b - In a? Refer to the picture for the option listed!
Which graph represents the linear function below? y-4= (4/3)(x-2)
Answer:
The graph in the attached figure
Step-by-step explanation:
we have
[tex]y-4=(4/3)(x-2)[/tex]
This is the equation of a line into point slope form
The point is (2.4)
The slope is m=4/3
To plot the line find the intercepts
The y-intercept is the value of y when the value of x is equal to zero
For x=0
y-4=(4/3)(0-2)
y=(-8/3)+4
y=4/3
The x-intercept is the value of x when the value of y is equal to zero
0-4=(4/3)(x-2)
-4=(4/3)x-(8/3)
Multiply by 3 both sides
-12=4x-8
4x=8-12
x=-1
we have the points
(2,4), (0,4/3),(-1,0)
Plot the line
Note With only two points it was necessary to draw the line. The third point was calculated for didactic purposes.
see the attached figure
Which variable is most important to the following problem?
Evan and Josh play on a basketball team. Evan played the whole first quarter
and the first 4 minutes of the second quarter. Josh played the rest of the
second quarter and all of the third quarter. Evan played the whole fourth
quarter. If each quarter is 10 minutes long, how long did Evan play?
A. the number of minutes Josh played in the fourth quarter
B. the number of players on the team
C. the number of minutes Evan played
D. the number of times Evan was substituted into the game
Answer:
C.
Step-by-step explanation:
Add up the number of minutes Evan played. you can ignore the number of minutes Josh played, the number of players in the team and the number of times Evan was substituted.
Answer:
The number of minutes Evan played.
Step-by-step explanation:
The most important variable is : The number of minutes Evan played.
As at the end we have to find out how long did Evan play. And to get the answer, we have to consider Evan's play time in each quarter.
By adding all those numbers, we will get the answer.
Hence, option C is correct.
Each leg of a 45°-45°-90° triangle measures 12 cm.
What is the length of the hypotenuse?
4
45°
45°
6 cm
62 cm
12 cm
12 cm
12 cm
12V3 cm
Answer:
12 sqrt(2)
Step-by-step explanation:
Givens
a = 12 cm
b = 12 cm
c = ??
The triangle is isosceles with 1 right angle and 2 45 degree angles.
Formula
c^2 = a^2 + b^2
c^2 = 12^2 + 12^2
c^2 = 144 + 144
c^2 = 288
c^2 = 144 * 2
c = sqrt(144) * sqrt(2)
c = 12 * sqrt(2)
The answer isn't there. 12*sqrt(2) is the correct answer, 12sqrt(3).
Was this just a typo of some kind.
When is g(x) = 0 for the function g(x) = 5.23x + 4?
Answer:
g(x)=4
Step-by-step explanation:
5.23(0)+4=4
Hope this helps!
Assume the two lines ab and xy intersect as in the diagram below. which of the following statements are true. Check all that Apply.
Answer:
A, B, and D are the correct statements.
4.
Find the geometric mean of 4 and 12.
24
8
The geometric mean of two numbers is the square root of their product.
sqrt{4 • 12}
sqrt{48}
sqrt{16} •sqrt{3}
4•sqrt{3}.
The geometric mean of 4 and 12 is
4•sqrt{3}.
The graphs below are both quadratic functions. The equation of the red graph is
x)= x. Which of these is the equation of the blue graph, g(x)?
Answer:
D. [tex]g(x)=\frac{1}{5}x^2[/tex]
Step-by-step explanation:
The equation of the red quadratic graph is [tex]f(x)=x^2[/tex].This is the parent quadratic function or the base of the quadratic functions.This red quadratic graph has been dilated by a certain scale factor to obtain the blue graph. Recall that, when the scale factor is a fraction, such that [tex]0\:<\:k\:<\:1[/tex] the graph is stretched horizontally.The dilated graph then becomes wider than the parent function.From the given function equations, the possible value of k can only be [tex]k=\frac{1}{5}[/tex].Therefore the blue graph has equation: [tex]g(x)=\frac{1}{5}x^2[/tex]The correct answer is D.HELP ASAP TEST IS OMOST OVER!!!!!!!!!!
John is putting a fence around his garden that is shaped like a half circle and a rectangle.
How much fencing will John need? Use 22/7 for pie
A)32 ft
B)39 ft
C)46 ft
D)57 ft
Answer: C)46 ft
Step-by-step explanation:
We know that the circumference of a circle can be calculated with this formula:
[tex]C=2\pi r[/tex]
Where "r" is the radius of the circle.
Since John is putting a fence around his garden that is shaped like a half circle and a rectangle, then we can find how much fencing he needs by making this addition:
[tex]Fencing=\frac{2\pi r}{2}+2l+w[/tex]
Where "l" is the lenght of the rectangle and "w" is the width of the rectangle.
Since we know that the radius of the circle is half its diameter, we can find "r". This is:
[tex]r=\frac{7ft}{2}=3.5ft[/tex]
Then, substituting values (and using [tex]\pi=\frac{22}{7}[/tex]), we get:
[tex]Fencing=\frac{2(\frac{22}{7})(3.5ft)}{2}+2(14ft)+7ft=46ft[/tex]
The answer is C) 46ft
Pip and Sara win some money and share it in the ratio 5:4. Pip gets £50. How much did they win in total?
Answer:
90
Step-by-step explanation:
Write the ratio this way
Pip: Sara: Total
5 : 4 : 9
We multiply each by 10 to get Pip to 50 (5*10 = 50)
5*10: 4*10: 9*10
50 : 40 : 90
Answer:
$90
Step-by-step explanation:
Given that the ratio of Pip: Sara is 5:4
This means :
Pip gets 5 parts
Sara gets 4 parts
Together they have 5 + 4 parts = 9 parts
Also given that Pip's 5 parts is equivalent to $50
Hence each 1 part is $50/5 = $10
if 1 part = $10
The total 9 parts = 9 x $10 = $90
the system of equatios is solved using the linear combination method
1/2x4y=8 -2(1/2x+4y=8) -x-8y=-16
3x+24y - 12 1/3(3x+24y= 12) x+8y=4
0=-12
what does 0 = -12 mean regarding the solution to the system?
Answer: There are no solutions to the system because the equations represent parallel lines.
The value 0 = -12 indicates an inconsistent system with no solution.
0 = -12 means that the system of equations is inconsistent, and there is no solution. In this case, the equations represent parallel lines that never intersect, hence no common solution exists.
Solve the following equation for x: 5x + 3y = 15.
A.x = negative three fifthsy − 3
B.x = negative three fifthsy + 3
C.x = three fifthsy + 3
D.x = three fifthsy − 3
Answer:
B
Step-by-step explanation:
5x + 3y = 15
5x = -3y +15
x = -3/5y +3
Answer:
The correct option is B) x = negative three fifths y + 3
Step-by-step explanation:
Consider the provided equation.
5x + 3y = 15
We need to solve the above equation for x.
Subtract both the side by 3y.
[tex]5x + 3y-3y = 15-3y[/tex]
[tex]5x= 15-3y[/tex]
To find the value of y, isolate the variable y:
Divide both the sides by 5.
[tex]\frac{5x}{5}= \frac{15}{5}-\frac{3y}{5}[/tex]
[tex]x= 3-\frac{3y}{5}[/tex]
[tex]x= -\frac{3y}{5}+3[/tex]
Hence, the correct option is B) x = negative three fifths y + 3
Solve for U
U- 4.5=6.46
Answer:
Step-by-step explanation:
U-4.5=6.46
+4.5 +4.5
U=10.96
Find the first five terms of the sequence in which a1 = –10 and an = 4an – 1 + 7, if n ≥ 2.
To determine the first five terms of the given recursive sequence, we begin with the first term, a1 = -10, and use the provided recurrence relation to calculate each subsequent term. The first five terms of the sequence are -10, -33, -125, -493, and -1965.
Explanation:The student has presented a recursive sequence with the first term stated as – 10 and a recursive formula to find any subsequent term, an, defined as an = 4an-1 + 7 for n ≥ 2.
To find the first five terms of the sequence, we'll apply the formula starting with a1 and proceed to each next term.
First term, a1: – 10
Second term, a2: 4(– 10) + 7 = – 40 + 7 = – 33
Third term, a3: 4(– 33) + 7 = – 132 + 7 = – 125
Fourth term, a4: 4(– 125) + 7 = – 500 + 7 = – 493
Fifth term, a5: 4(– 493) + 7 = – 1972 + 7 = – 1965
Therefore, the first five terms of the sequence are – 10, – 33, – 125, – 493, and – 1965.
Which is equivalent
For this case we must find an expression equivalent to:
[tex]\sqrt [5] {13 ^ 3}[/tex]
By definition of properties of powers and roots we have:
[tex]\sqrt [n] {a ^ m} = a ^ {\frac {m} {n}}[/tex]
Then, rewriting the expression:
[tex]13 ^ {\frac {3} {5}}[/tex]
Answer:
Option D
[tex]13 ^ {\frac {3} {5}}[/tex]
Which formula can be used to describe the sequence
-3, 3/5, -3/25, 3/125, -3/625
Answer:
a(n) = -3(-1/5)^(n - 1)
Step-by-step explanation:
From the first term, -3, we get the second term, 3/5, by multiplying -3 by -1/5.
Thus, the common ratio is -1/5.
The general formula in this case is a(n)=(first term)(common ratio)^(n - 1), or
a(n) = -3(-1/5)^(n - 1)
How do you convert 3.16 (6 repeating) to a fraction?
Suppose [tex]x=3.1\overline6[/tex]. Then [tex]10x=31.\overline6[/tex], and [tex]100x=316.\overline6[/tex].
Now,
[tex]100x-10x=316.\overline6-31.\overline6=316-31[/tex]
[tex]\implies90x=285[/tex]
[tex]\implies x=\dfrac{285}{90}=\boxed{\dfrac{19}6}[/tex]
The area of a triangle is 40 cm2. The height of the triangle is 4 cm. What is the measure of the base of the triangle?
A.
40 cm
B. 32 cm
C. 28 cm
D. 20 cm
Answer:
Step-by-step explanation:
Givens
Height = h = 4cm
b = ?
Area = 40 cm^2
Formula
Area = 1/2 * h * b
Solution
40 cm^2 = 1/2 * 4 * b Combine the right
40 cm^2 = 2 * b Divide by 2
40 cm^2 /2 = 2b/2 Do the division
20 cm = b
Answer D
name the property. 2(xy)=(2x)y
Answer:
associative property of multiplication
Step-by-step explanation:
If we have 3 numbers x, y and z the associative property of multiplication says that:
[tex]x (yz) = z (xy) = (xz)y[/tex]
This means that the result will be the same regardless of the order in which the multiplication takes place.
In this case we have the following equality
[tex]2(xy) = (2x)y[/tex]
Note that the property used is the associative property of multiplication
matt and brian were solving a system of equations. they both noticed that the two lines had the same slope. brian said that because each line in the system had the same slope, the two lines had to be parallel, which meant the solution to the system was "no solution" matt disagreed, and said they should also look at the y-intercepts before determining how many solutions there were. who is correct?
Answer:
Matt is correct
Step-by-step explanation:
we know that
If two lines are parallel, then their slopes are the same
In this problem we can have two cases
case 1) The two equations are equal, in this case the system has infinite solutions
case 2) The two equations have the same slope but different y-intercept, in that case the system has no solution.
therefore
Matt is correct
Matt is correct. Whether lines with the same slope are parallel or the same line depends on the y-intercepts. If y-intercepts are the same, lines are identical and have infinitely many solutions. If y-intercepts differ, lines are parallel and there's no solution.
Explanation:Matt is correct in this scenario. While it is true that lines with the same slope are either parallel or the same line, determining whether they are the same line or parallel lines requires examining the y-intercepts. If the y-intercepts are the same, then the lines are identical, and there are infinitely many solutions to the system of equations. However, if the y-intercepts are different, the lines are parallel and there is no solution to the system. So, slope, parallel lines, and y-intercept are crucial concepts in solving this problem.
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What is the missing fraction?
1/6 + ? = 11/18
A) 10/6
B) 4/9
C) 2/3
D) 10/18
Answer: B is the answer
Step-by-step explanation:
Just subtract 1/6 from 11/18 to get the answer!
the number of lattes sold daily for two coffee shops is shown in the table: Lattes 12 52 57 33 51 15 46 45 Based on the data, what is the difference between the median of the data, including the possible outlier(s) and excluding the possible outlier(s)?
A. 48.5
B. 23
C. 8.4
D. 3
Answer:
Option 4 (3)
Step-by-step explanation:
The first step involved in calculating the median it to list the observations in the ascending order. This gives:
12 15 33 45 46 51 52 57.
The second step is to identify the middle number (in case the observations are in odd numbers) or numbers (in case the observations are in even numbers) after the ascending order step has been done. It can be observed that the middle numbers in this data set are 45 and 46. Since there are two numbers, so their average will be the median of this data set. Therefore, the median is 45.5.
It can be observed that that there are 2 outliers in the data set: 12 and 15. Once removed, the data set will be:
33 45 46 51 52 57.
The middle numbers are 46 and 51 and the mean of the two middle numbers is 48.5.
Therefore, the difference between the median of the data, including the possible outliers and excluding the possible outliers is given by 48.5 - 45.5 = 3. Therefore, Option 4 is the correct answer!!!
The turning point of the curve: y=6-4x-x^2
Answer:
The turning point is (-2,10)
Step-by-step explanation:
we have
[tex]y=6-4x-x^{2}[/tex]
This is a quadratic equation (vertical parabola) open downward
we know that
The turning point of a quadratic equation is the vertex
so
Convert the quadratic equation into vertex form
[tex]y-6=-4x-x^{2}[/tex]
[tex]y-6=-(x^{2}+4x)[/tex]
[tex]y-6-4=-(x^{2}+4x+4)[/tex]
[tex]y-10=-(x^{2}+4x+4)[/tex]
[tex]y-10=-(x+2)^{2}[/tex]
[tex]y=-(x+2)^{2}+10[/tex] ----> equation in vertex form
The vertex is the point (-2,10)
therefore
The turning point is (-2,10)
The turning point of the parabola described by the equation y=6-4x-x^2 is at the point (-2, 10), which is a maximum since the parabola opens downwards.
Explanation:To find the turning point of the curve given by the equation y=6-4x-x^2, we first need to rewrite the equation in the form of the vertex of a parabola, which is given by y=a(x-h)^2+k, where (h,k) is the coordinate of the turning point or vertex. Noting that there is a mistake in the information provided since the second derivative would actually be y" = -2, and not 6x - 12, indicating that we have a concave down parabola with a maximum point, not a point of inflection. We can complete the square to rewrite the function in vertex form.
Start by completing the square: y = -x^2 - 4x + 6 can be rewritten as y = -(x^2 + 4x) + 6. Adding and subtracting 4 inside the parenthesis (which is the square of half the coefficient of x), we get y = -(x^2 + 4x + 4 - 4) + 6, which simplifies to y = -(x + 2)^2 + 10. Thus, the vertex or turning point is at (-2, 10).
This shows the turning point of the parabola is at the point (-2, 10), which is a maximum since the parabola opens downwards as reflected by the negative coefficient of the x^2 term. This can be visualized on the graph of the function as the highest point on the curve. Remember that a quadratic equation represents a parabola in a Cartesian coordinate system.