Answer:
Point-slope equation of this line:
[tex]\displaystyle y - 1 = \frac{1}{2}(x-5)[/tex].
Step-by-step explanation:
The equation for a line in a cartesian plane can take multiple forms. This question gives
a point on the line, andthe slope of the line.The point-slope form will the most appropriate.
What is the point-slope form equation of a line [tex]l[/tex]?
In general,
[tex]l:\; y - y_0 = m (x - x_0)[/tex],
where
[tex]x_0[/tex] is the x-coordinate of the given point on the line, [tex]y_0[/tex] is the y-coordinate of the given point on the line, and[tex]m[/tex] is the slope or gradient of the line.In other words, [tex](x_0,\; y_0)[/tex]the point on the line.
For this line,
The point is [tex](5,\;1)[/tex], where [tex]x_0 = 5[/tex] and [tex]y_0 = 1[/tex].Gradient of the line [tex]\displaystyle m = \frac{1}{2}[/tex].Thus the equation for this line:
[tex]\displaystyle y - 1 = \frac{1}{2} (x - 5)[/tex].
The points (0,8),(5,3),(4,2) and (-1,7) are vertices of a rectangle. Determine the coordinates of the midpoints for each side and determine if the midpoints are the vertices of a rectangle
The area of the triangle is 16.
You can find this by plotting each of the points and drawing the triangle. You can then use the distance formula to determine each side length. The rectangle will be 2 on one side and 4 on the other. When multiplied together, it will give you the above answer
The coordinates of the midpoints for each side are (2.5, 5.5) , (4.5, 2.5), (1.5, 4.5), and (- 0.5, 7.5).
And, yes, the midpoints are the vertices of a rectangle, as its opposite sides are the same in length.
Use the formula for the midpoint of two points [tex](x_1, y_1)[/tex] and [tex](x_2, y_2)[/tex] are,
[tex][\dfrac{(x_1 + x_2)}{2} , \dfrac{(y_1 + y_2)}{2} ][/tex]
Given that,
Vertices of the rectangle are (0, 8), (5, 3), (4, 2), and (- 1, 7).
Hence, the coordinates of the midpoints for each side are calculated by using the above formula,
The midpoint of two points (0, 8) and (5, 3) are,
[tex](\dfrac{(0 + 5)}{2} , \dfrac{(8 + 3)}{2} )[/tex]
[tex](2.5, 5.5)[/tex]
The midpoint of two points (5, 3) and (4, 2) are,
[tex](\dfrac{(5 + 4)}{2} , \dfrac{(3 + 2)}{2} )[/tex]
[tex](4.5, 2.5)[/tex]
The midpoint of two points (4, 2) and (-1, 7) are,
[tex](\dfrac{(4 - 1)}{2} , \dfrac{(2 + 7)}{2} )[/tex]
[tex](1.5, 4.5)[/tex]
The midpoint of two points (-1, 7) and (0, 8) are,
[tex](\dfrac{(-1 + 0)}{2} , \dfrac{(8 + 7)}{2} )[/tex]
[tex](-0.5, 7.5)[/tex]
Therefore, the coordinates of the midpoints for each side are (2.5, 5.5) , (4.5, 2.5), (1.5, 4.5), and (- 0.5, 7.5).
When the coordinates of vertices are rectangular then opposite sides are equal to each other.
So, we can check the length of each side of the coordinates of the midpoints (2.5, 5.5), (4.5, 2.5), (1.5, 4.5), and (- 0.5, 7.5).
Used the distance formula,
The distance between two points [tex](x_1, y_1)[/tex] and [tex](x_2, y_2)[/tex] is,
[tex]d = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2}[/tex]
So, The distance between the two points [tex](2.5, 5.5)[/tex] and [tex](4.5, 2.5)[/tex],
[tex]d = \sqrt{(4.5- 2.5)^2 + (2.5 - 5.5)^2}[/tex]
[tex]d = \sqrt{4 + 9}[/tex]
[tex]d = \sqrt{13}[/tex]
The distance between the two points [tex](4.5, 2.5)[/tex] and [tex](1.5, 4.5)[/tex],
[tex]d = \sqrt{(4.5- 1.5)^2 + (2.5 - 4.5)^2}[/tex]
[tex]d = \sqrt{9 + 4}[/tex]
[tex]d = \sqrt{13}[/tex]
The distance between the two points [tex](1.5, 4.5)[/tex] and [tex](-0.5, 7.5)[/tex]
[tex]d = \sqrt{(1.5+ 0.5)^2 + (7.5 - 4.5)^2}[/tex]
[tex]d = \sqrt{4 + 9}[/tex]
[tex]d = \sqrt{13}[/tex]
The distance between the two points[tex](-0.5, 7.5)[/tex] and [tex](2.5, 5.5)[/tex]
[tex]d = \sqrt{(2.5+ 0.5)^2 + (7.5 - 5.5)^2}[/tex]
[tex]d = \sqrt{9 + 4}[/tex]
[tex]d = \sqrt{13}[/tex]
Clearly, All the lengths of each side of the coordinates of the midpoints (2.5, 5.5), (4.5, 2.5), (1.5, 4.5), and (- 0.5, 7.5) are the same.
Hence, it forms a rectangle, as its opposite sides are also the same in length.
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Determine (a+h) - @) for f(x) = x2 + 5x and simplify.
To determine (f(a+h) - f(a)) for f(x) = x² + 5x, we substitute a+h and a into the function, expand, and subtract to ultimately simplify to 2ah + h² + 5h.
To determine (f(a+h) - f(a)) for f(x) = x² + 5x and simplify, we need to substitute x with a+h and a into the function separately and then find the difference. Here are the steps:
Substitute a+h into f(x) to get f(a+h) = (a+h)² + 5(a+h).
Expand the equation: f(a+h) = a² + 2ah + h² + 5a + 5h.
Substitute a into f(x) to get f(a) = a² + 5a.
Find the difference: (f(a+h) - f(a)) = (a² + 2ah + h² + 5a + 5h) - (a² + 5a).
Simplify the expression: (f(a+h) - f(a)) = 2ah + h² + 5h.
In 1983, a pair of jeans cost $66.35. If a pair of jeans costs $118.10 today, what is the CPI? a. 152 b. 156 c. 178 d. 184
Answer:
ddddddd
Step-by-step explanation:
Answer:
The correct answer is C on edge 2020
Step-by-step explanation:
Melanie is taking flute lessons. Her flute teacher charges $32.50 per hour. If Melanie has 2.5 hours of lessons each week, what is the weekly charge for her lessons?
2.5 x 32.50 = 81.25 a week
Answer:
32.50× 2 = 65
32.50 ÷ 2 = 16.25
65+16.25 = 81.25(this is the answer)
Please help me with this
Please Show a picture or either a text so that I can help you
Answer:
for x = 1 , y = 40(1) -5 ⇒ y = 35
for x = 1 , y = 40(2) -5 ⇒ y = 75
for x = 1 , y = 40(3) -5 ⇒ y = 115
for x = 1 , y = 40(4) -5 ⇒ y = 155
for x = 1 , y = 40(5) -5 ⇒ y = 195
help please with this
Answer:
None of these
Step-by-step explanation:
the answer can't have anything to do with perpendicular because you don't know if any of the angles are 90 degrees (and honestly none of them look right anyways... pun intended) and the only answer that isn't perpendicular is wrong because the lines are intersececting.
Which statement best compares the spread of the data sets?
Answer:
Choice B is correct
Step-by-step explanation:
The Interquartile Range (IQR) for Florida, 11, is greater than the IQR for Australia, 4.
The spread of a data set is a measure of the dispersion or variability of the data set. The spread can be measured by various statistical quantities depending on the nature of the data (skewed or symmetric);
The IQR
Variance
Standard Deviation
Range
A box plot is a graphical representation of the five number summary;
The minimum, first quartile, median, third quartile, and the maximum value in that order.
The IQR is defined as;
third quartile - first quartile
With this definition, the Interquartile Range (IQR) for Florida is;
28 - 17 = 11
while the Interquartile Range (IQR) for Australia is;
14 - 10 = 4
Therefore, the Interquartile Range (IQR) for Florida, 11, is greater than the IQR for Australia, 4.
If ON = OL find mOML
A. 26°
B. 48°
C. 52°
D. 64°
Please select the best answer from the choices provided
Answer:
A. 26°
Step-by-step explanation:
If ON =OL, then the two triangles are are similar.
The base angles must be equal.
[tex](9x-8)\degree=(7x+8)\degree[/tex]
We group the similar terms to obtain:
[tex]9x-7x=8+8[/tex]
[tex]2x=16[/tex]
Divide through by 2 to get:
x=8
[tex]m\angle OML=90-(7x+8)[/tex]
Substitute x=8
[tex]m\angle OML=90-(7(8)+8)[/tex]
[tex]m\angle OML=90-(56+8)[/tex]
[tex]m\angle OML=26\degree[/tex]
Answer:
The correct answer is option A. 26°
Step-by-step explanation:
From the figure we can see that,
ON = OL
OM ⊥ NL
Therefore m<N = m<L
To find the value of x
m<N = m<L
7x + 8 = 9x -8
9x - 7x = 8 + 8
2x = 16
x = 8
To find the value of m<OML
x = 8
m<L = 9x - 8
= 9*8 - 8 = 72 - 8 = 64
m<OML = 180 - (<L + <O)
= 180 - ( 64 + 90)
= 26°
Therefore the correct answer is option A. 26°
In the figure, a∥b and m∠3 = 34°.
What is the m∠7 ?
Enter your answer in the box.
Answer:
∠7 = 34°
Step-by-step explanation:
Since a and b are parallel lines then
∠3 and ∠7 are corresponding angles and congruent, so
∠7 = ∠3 = 34°
Answer:
34 degrees
Step-by-step explanation:
Please help me with this word problem!
Answer:
[tex]f(g)=25g[/tex]
Step-by-step explanation:
Let [tex]g[/tex] be the number of gallons so [tex]f(g)[/tex] is the number of miles traveled per [tex]g[/tex] gallons.
We know for our problem that Brian's car gets 25 miles per gallon. Since the gallons is represented by [tex]g[/tex], his car will travel a total distance of 25g (where g is the number of gallons.
We also know that the total distance is given by [tex]f(g)[/tex], so we can put the two expressions together to get our function:
[tex]f(g)=25g[/tex]
Let's check:
- If he uses 1 gallon (g=1), so
[tex]f(1)=25(1)[/tex]
[tex]f(1)=25[/tex] miles
He will travel 25 miles with one gallon.
- If he uses 2 gallons (g=2), so
[tex]f(2)=25(2)[/tex]
[tex]f(2)=50[/tex]
He will travel 50 miles with two gallon.
need answer will name the brainliest!!!!!!! PLZ PLZ
What question do you need answered?
Answer:
Option A.
Step-by-step explanation:
Anastasia worked for = 7 hours per day
Number of weeks she worked = 52 weeks
Number of hours she worked = 7×52
= 364 hours
Per hour earning of Anastasia = $20
Total earning of Anastasia = 364×20
= $7280
Let the monthly expenses of Anastasia = $x
Then total expenses = $12x
At the end of the year total saving = Total earning - Total expenses
= $7280 - 12x
Since she saved $2000 in a year therefore, expression that represents the savings will be
2000 = 7280 - 12x
12x = 7280 - 2000
12x = 5280
x = [tex]\frac{5280}{12}[/tex]
x = $440
Option A will be the answer.
How do you construct a regular polygon inside a circle?
You could use a ruler, think about how you want the polygon inside of the circle or how you want the circle to surround the polygon. When you use a ruler, make sure your co-ordinates inside of the circle are correct though before drawing the line.
I hope this info helps! :3
To construct a regular polygon inside a circle, divide the circle into "n" equal sectors using "n" radii, where "n" represents the number of sides in the polygon. Connect the center of the circle to each of the marked points on the circumference to create the regular polygon.
Determine the Circle: Start by drawing the given circle with a compass, and label its center as "O."
Select the Number of Sides: Decide on the number of sides for the regular polygon. Let's assume "n" as the number of sides.
Construct Diameter: Draw a diameter of the circle passing through the center "O," using a straightedge.
Construct Central Angle: To create a regular polygon with "n" sides, divide the circle into "n" equal sectors by constructing "n" radii (lines from the center to the circumference) evenly spaced around the circle. Each of these radii forms a central angle of 360°/n.
Find Vertices: On the circumference of the circle, mark "n" points (labeled A₁, A₂, A₃, ..., Aₙ) evenly spaced. These points will serve as the vertices of the regular polygon.
Connect Vertices: Use a straightedge to draw lines connecting the center "O" of the circle to each of the marked points (A₁, A₂, ..., Aₙ).
Construct Regular Polygon: The polygon with vertices A₁, A₂, ..., Aₙ, and center "O" is the regular polygon inscribed inside the circle.
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−0.7+
8
2
=
minus, 0, point, 7, plus, start fraction, 2, divided by, 8, end fraction, equals
Enter the answer as an exact decimal or simplified fraction.
[tex]-0.7+\frac{2}{8} =[/tex]
[minus, 0, point, 7, plus, 2, divided by, 8, equals]
You can make the denominators the same to combine them, so you can multiply -0.7 by [tex]\frac{8}{8}[/tex]
[tex]-0.7(\frac{8}{8})+\frac{2}{8}[/tex]
[tex]-\frac{5.6}{8}+\frac{2}{8}=-\frac{3.6}{8}= - 0.45[/tex]
Final answer:
The sum of −0.7 and ⅔ is −0.45 when the fraction is simplified to 0.25 and then added to −0.7.
Explanation:
Fractions are used extensively in mathematics, particularly in arithmetic, algebra, geometry, and calculus, as well as in everyday situations such as cooking, measurements, and financial calculations. They provide a convenient way to express quantities that are not whole numbers and to perform operations such as addition, subtraction, multiplication, and division.
The student is asking for the sum of -0.7 and the fraction 2/8. To find the answer, first simplify the fraction 2/8, which can be reduced to 1/4. Now, convert 1/4 into decimal form, which is 0.25. Next, add this decimal to -0.7 to find the sum:
-0.7 + 0.25 = -0.45.
Therefore, the exact decimal for the expression −0.7 + ⅔ is -0.45.
Choose the slope-intercept form of 3x + 2y = 5.
Answer:
[tex]y=\frac{-3}{2}x +\frac{5}{2} \\or \\y=\frac{5}{2} -\frac{3}{2} x[/tex]
Step-by-step explanation:
slope-intercept form is: [tex]y= mx+b[/tex]
3x + 2y = 5.
rearrange
[tex]2y=5-3x\\y=\frac{5}{2} -\frac{3x}{2}[/tex]
Answer:
b on ed2020
IG: user_6232003
Step-by-step explanation:
a hockey team ordered 12 wooden pedestals to mount their brass trophies on. The design pedestal is shown below. The teal is charge $0.08 per cubic inch of wood. What is the total cost of the order, rounded to the nearest dollar?
56 cause u need 12 divide by 0.08 12 times
Answer:
Total charge for wooden pedestal will be $1136
Step-by-step explanation:
Volume of the pedestal will be = volume of cube + volume of the cone
= (Side)³ + [tex]\frac{1}{3}(\pi r^{2}h)[/tex]
= 10³ + [tex]\frac{1}{3}[\pi (\frac{10}{2})^{2}(7)][/tex]
= 1000 + [tex]\frac{1}{3}[\pi 5^{2}(7)][/tex]
= 1000 + [tex]\frac{1}{3}[\pi (25)(7)][/tex]
= 1000 + [tex]\frac{1}{3}[(3.14)(25)(7)][/tex]
= 1000 + 183.17
= 1183.17 cubic inch
Total volume of 12 wooden pedestals = 12 × 1183.17 = 14198 cubic inch
Since charges of the wood is $0.08 per cubic inch
So total charges for pedestal will be = 0.08 × 14198 = $1135.84 ≈ $1136
Complete the point-slope equation of the line through (-5,4) and (1,6). Use exact numbers.
y-6=____
Answer:
as you all saw the rating of the above answer, it is incorrect. here is the correct answer with proof down in the photo below
The point-slope equation of the line passing through the points (-5,4) and (1,6) is y - 6 = 1/3(x - 1). This is derived from the standard point-slope formula y - y1 = m(x - x1) where m is the slope of the line.
Explanation:In mathematics, specifically in linear algebra, the point-slope formula is used to determine the equation of a line given a point on the line and its slope. The point-slope equation of the line through the points (-5,4) and (1,6) is found by first calculating the slope between these two points, defined as the change in y divided by the change in x. So, y2 - y1 divided by x2 - x1. In this case, (6-4) / (1 - (-5)) = 2/6 = 1/3. So, the slope of the line is 1/3. We can then use one of these coordinates (for instance, 1, 6) and the slope in the point-slope formula: y - y1 = m(x - x1). Therefore, the point-slope equation of the line through (-5,4) and (1,6) is y - 6 = 1/3(x - 1).
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Juice boxes are sold in a local store for 65 cents each. The factory has $1400 in fixed costs plus 15 cents of additional expense for each juice box made. Assuming all juice boxes manufactured can be sold, find the break-even point.
Answer:
Production of 2800 juice boxes is the break even point.
Step-by-step explanation:
Break-even point is the point where profit is zero and number of manufactured goods are all sold
Let number of juice boxes be y
charges of local store for 1 juice box= $0.65
charges of local store for y juice box=$0.65y
Factory cost of y juices boxes= $1400 + $0.15y
Assuming all juice boxes manufactured can be sold, to find the break-even point
charges of local store for y juice box= Factory cost of y juices boxes
$0.65y=$1400 + $0.15y
$0.65y-$0.15y= $1400
$0.50y=$1400
y= 1400/0.5
y=2800
hence production of 2800 juice boxes is the break even point!
find the missing term of each equivalent ratio. 90:15=_____:7
ANSWER
The missing term is 42.
EXPLANATION.
We want to find the missing term of the equivalent ratio. 90:15=_____:7
Let y be the missing term, then
90:15=y:7
We rewrite as fractions to get;
[tex] \frac{90}{15} = \frac{y}{7} [/tex]
Simplify the left ratio:
[tex] \frac{6}{1} = \frac{y}{7} [/tex]
Cross multiply:
[tex]6 \times 7 = 1 \times y[/tex]
[tex]42 = y[/tex]
Therefore the missing term is 42.
Please help me thank you
ANSWER
[tex]\theta = 0 ,\frac{7\pi}{6} ,\frac{11\pi}{6 } [/tex]
EXPLANATION
We want to solve
[tex] \sin( \theta) + 1 = \cos(2 \theta) [/tex]
on the interval
[tex]0 \leqslant \theta \: < \: 2\pi[/tex]
Use the double angle identity to obtain:
[tex] \sin( \theta) + 1 = 1 - 2\sin ^{2} \theta[/tex]
Simplify to get;
[tex] 2\sin ^{2} \theta + \sin( \theta) + 1 - 1 = 0[/tex]
[tex]2\sin ^{2} \theta + \sin( \theta) = 0[/tex]
Factorize to obtain:
[tex]\sin \theta (2\sin \theta + 1) = 0[/tex]
Either
[tex]\sin \theta = 0[/tex]
This gives us
[tex] \theta = 0[/tex]
on the given interval.
Or
[tex]2\sin \theta + 1= 0[/tex]
[tex]\sin \theta = - \frac{1}{2} [/tex]
This gives us
[tex]\theta = \frac{7\pi}{6} ,\frac{11\pi}{6 } [/tex]
Therefore the solutions within the interval are:
[tex]\theta = 0 ,\frac{7\pi}{6} ,\frac{11\pi}{6 } [/tex]
If m1=45 degrees, which other angles have a measure of 45 degrees? Select all that apply.
∠ 2
∠3
∠4
∠5
∠6
Answer:
∠4 and ∠5
Step-by-step explanation:
we know that
If a is parallel to b
then
∠5=∠1 -----> by corresponding angles
∠4=∠1 -----> by alternate interior angles
what is the value of x? enter your answer in the box.
To solve this problem, you would have to apply the Pythagorean Theorem: a^2+b^2=c^2
X is the hypotenuse; therefore:
24^2+7^2=x^2
576+49=x^2
625=x^2
To solve this you would have to figure out what the square root of 625 is.
Answer: 25
Step-by-step explanation:
Pythagoreans theory
a2 + b2 = c2
24(square) + 7(square) =c(square)
576 + 49= c square
625=c square
c=√625
c=25
which values are within the domain of the function? check all that apply
Answer:
-6 -4 -2 4
Step-by-step explanation:
A B C F
Answer:
A. B. C. F.
Step-by-step explanation:
do these numbers make a right triangle... square root of 63 then 9 then 12?
Answer:
9^2 = 81
12^2 = 144
63^= 3969
A^2 + B^2 = C^2
81 + 144 = 225
so these numbers do not make a right triangle
Final answer:
The numbers square root of 63, 9, and 12 do make a right triangle as their squares satisfy the Pythagorean theorem. The sum of the squares of 9 and square root of 63 equals the square of 12, which validates that we have a right triangle.
Explanation:
To determine if the numbers square root of 63, 9, and 12 make a right triangle, we can apply the Pythagorean theorem, which states that in a right triangle, the sum of the squares of the two shorter sides must be equal to the square of the longest side (the hypotenuse). Let's calculate the squares of each provided number:
The square root of 63 squared is 63 (because \ \ \ equals 63).9 squared is 81.12 squared is 144.Since the longest side here must be 12 (as it is the largest number), the Pythagorean theorem for these numbers would be as follows:
81 + 63 = 144?
That simplifies to:
144 = 144?
This is a true statement, which means that these numbers do indeed represent the sides of a right triangle.
A membership at a swimming pool costs a flat fee of $100, plus $50 per person. If x stands for the number of people, then the membership cost is modeled by which equation?
y=150x
y=100+50+x
y=100x+50
y=50x+100
Answer:
y=50x+100
Step-by-step explanation:
y=mx+b
100 is b because its a flat fee
The slope is 50 because it is dependent on x, the amount of people.
The correct answer is y=150x.For example, if I were to equal 300. Then that would mean two people would have bought the membership. So, X equals two.
HURRY I NEED HELP PLEASE
Answer:
The volume of the shape is 343 cm
Step-by-step explanation:
Because the formula is length x width x height
Answer:
343 cm³
Step-by-step explanation:
V = lwh
V = 7·7·7, since the sides are all 7
V = 49·7 because 7·7 = 49
V = 343 cm³
What is (x+y)(x^2-xy+y^2)
The answer is:
[tex](x+y)(x^{2}-xy+y^{2})=x^{3}+y^{3}[/tex]
Why?To find the resultant expression, we need to apply the distributive property.
It can be defined by the following way:
[tex](a+b)(c+d)=ac+ad+bc+bd[/tex]
Also, we need to remember how to add like terms: The like terms are the terms that share the same variable and exponent, for example:
[tex]x+x+x^{2}=2x+x^{2}[/tex]
We were able to add only the two first terms since they were like terms (they share the same variable and the same exponent)
So , we are given the expression:
[tex](x+y)(x^{2}-xy+y^{2})[/tex]
Then, applying the distributive property, we have:
[tex](x+y)(x^{2}-xy+y^{2})=x*x^{2}-x*xy+x*y^{2}+y*x^{2}-y*xy+y*y^{2}\\\\x*x^{2}-x*xy+x*y^{2}+y*x^{2}-y*xy+y*y^{2}=x^{3}-x^{2}y+xy^{2}+yx^{2}-xy^{2}+y^{3}\\\\x^{3}-x^{2}y+xy^{2}+yx^{2}-xy^{2}+y^{3}=x^{3}+y^{3}[/tex]
Hence, the answer is:
[tex](x+y)(x^{2}-xy+y^{2})=x^{3}+y^{3}[/tex]
Have a nice day!
What is the value expression 10p-5/5+3(p-1) when p = 2
For this case we have the following expression:
[tex]\frac {10p-5} {5 + 3 (p-1)}[/tex]
We must find the value of the expression when c[tex]p = 2[/tex].
Substituting the value of "p" we have:
[tex]\frac {10 (2) -5} {5 + 3 ((2) -1)} =\\\frac {20-5} {5 + 3 (1)} =\\\frac {20-5} {5 + 3} =\\\frac {15} {8}[/tex]
Thus, the value of the expression when [tex]p = 2, is\ \frac {15} {8}[/tex]
ANswer:
[tex]\frac {15} {8}[/tex]
Our math team had m students last year, but this year it has already n students! By what percent did the number of students grow? need percentage only 24 points
Answer:
Since is the total amount of students now and m were the students before, you subtract them both (n-m) and divide that by m. Then, since to get a percentage from a fraction you have to multiply by 100, your answer should look like this: n-m/m*100
In circle D, ∠EDH ≅ ∠EDG. What is the length of JG?
4 units
5 units
6 units
9 units
Answer:
The correct option is 2. The length of JG is 5 units.
Step-by-step explanation:
Given information: ∠EDH ≅ ∠EDG, EH=9, EJ=4.
Corresponding sides of two triangles are congruent.
[tex]EH=EG[/tex] (CPCTC)
[tex]9=EG[/tex] .... (1)
From the given figure it is clear that
[tex]EG=EJ+JG[/tex]
[tex]EG=4+JG[/tex] ... (2)
Using (1) and (2), we get
[tex]9=4+JG[/tex]
Subtract 4 from both the sides.
[tex]9-4=JG[/tex]
[tex]5=JG[/tex]
The measure of JG is 5 units, therefore the correct option is 2.
Answer:
Step-by-step explanation:
OPTION 2 OR B!!!
Factor the polynomial: -x^3-2x^2-3x
Answer:
-x(x^2+2x+3)
Step-by-step explanation:
Answer:
Step-by-step explanation:
-x is common to all three terms. Thus, -x^3-2x^2-3x = -x(x^2 + 2x + 3).
Use the quadratic formula to find the roots (and thus the factors) of
x^2 + 2x + 3: a = 1; b = 2; c = 3.
Thus, the discriminant is b^2-4ac, or 4 - 4(1)(3), or -8.
Because this discriminant is negative, x^2 + 2x + 3 has two complex, unequal roots. They are:
-2 ± i√8
x = -------------- or -1 ± i*2*√2
Thus, the three factors of the given polynomial are:
-x, (x + 1 + 2i√2), and (x + 1 - 2i√2)
2