[tex]\bf ~\hspace{7em}\textit{negative exponents} \\\\ a^{-n} \implies \cfrac{1}{a^n} ~\hspace{4.5em} a^n\implies \cfrac{1}{a^{-n}} ~\hspace{4.5em} \cfrac{a^n}{a^m}\implies a^na^{-m}\implies a^{n-m} \\\\[-0.35em] \rule{34em}{0.25pt}\\\\[/tex]
[tex]\bf \left( \cfrac{20x^5y^2}{5x^{-3}y^7} \right)^{-3}\implies \left( \cfrac{5x^{-3}y^7}{20x^5y^2} \right)^3\implies \left( \cfrac{5^3x^{-3\cdot 3}y^{7\cdot 3}}{20^3x^{5\cdot 3}y^{2\cdot 3}} \right)\implies \cfrac{5^3}{20^3}\cdot \cfrac{x^{-9}y^{21}}{x^{15}y^6} \\\\\\ \cfrac{1}{64}\cdot \cfrac{y^{21}\cdot y^{-6}}{x^{15}\cdot x^9}\implies \cfrac{1}{64}\cdot \cfrac{y^{21-6}}{x^{15+9}}\implies \cfrac{y^{15}}{64x^{24}}[/tex]
Answer:
Simplify inside the parentheses by dividing coefficients, subtracting the exponents on like bases, and raising the resulting expression to the –3 power. Then, write bases with positive exponents.
Raise the numerator and denominator to the –3 power. Then, using the power of a power property, multiply the exponents. Divide the coefficients and subtract the exponents on like bases, then write with positive exponents.
Step-by-step explanation:
{8x + 9y = −3 6x + 7y = 1 What values of x and y satisfy the system of equations
Answer:
A) 8x + 9y = −3
B) 6x + 7y = 1
We multiply A) by -(6/8)
A) -6x -6.75y = 2.25 then we add this to equation B
B) 6x + 7y = 1
.25y = 3.25
y = 13
and x = -15
Step-by-step explanation:
The value of x= -15 and the value of y= 13 for the given system of equations: 8x+9y=−3 and 6x+7y=1.
Let’s solve the system of equations:
8x+9y=−3
6x+7y=1
We can solve the system of equations using elimination.
Steps to solve:
1. Solve the second equation for y:
y= 1/7
2. Substitute this value of y into the first equation:
8x+9(1/7)=−3
8x+9/7 =−3
8x=−120
x=−15
3. Substitute x=-15 back into the second equation to solve for y:
6(−15)+7y=1
−90+7y=1
7y=91
y=13
Therefore, the value of x= -15 and the value of y= 13 for the given system of equations: 8x+9y=−3 and 6x+7y=1.
Need help with a math question
Answer:
[tex]z =3\sqrt{13}[/tex]
Step-by-step explanation:
In the figure you can identify up to 3 straight triangles.
To solve the problem, write the Pythagorean theorem for each triangle.
Triangle 1
[tex]13^2 = z^2 + x^2[/tex]
Triangle 2
[tex]z^2 = y^2 + 9^2[/tex]
Triangle 3
[tex]x^2 = y^2 + 4^2[/tex]
Now substitute equation 2 and equation 3 in equation 1 and solve for y.
[tex]13^2 = y^2 + 9^2 + y^2 + 4^2[/tex]
[tex]13^2 = 2y^2 + 9^2 + 4^2[/tex]
[tex]169 = 2y^2 + 81 + 16[/tex]
[tex]2y^2 =72[/tex]
[tex]y^2 =36[/tex]
[tex]y =6[/tex]
substitute the value of y in the second equation and solve for z
[tex]z^2 = 6^2 + 9^2[/tex]
[tex]z^2 = 36 + 81[/tex]
[tex]z^2 = 117[/tex]
[tex]z = \sqrt{117}[/tex]
[tex]z =3\sqrt{13}[/tex]
In the diagram shown, /Il m, m
1 = 3x + 25 and m_8 = 4x - 17.
Find the measure of 2.
29
49°
131°
151
Answer:
29°
Step-by-step explanation:
Angles 1 and 8 are alternate exterior angles where a transversal crosses parallel lines, so are congruent.
m∠1 = m∠8
3x+25 = 4x-17
42 = m . . . . . . . . add 17-3x
Then the measure of ∠1 is 3·42 +25 = 151 (degrees), and the measure of its supplement, ∠2 is ...
m∠2 = 180° -151° = 29°
prove algebraically that the straight line with equation x=2y+5 is a tangent to the circle with equation x^2+y^2=5
I have gotten 4/5 marks but I need to get 5/5
Thank you!
A tangent line will have a couple of characteristics:
there is exactly one point of intersection with the circlea perpendicular line through the point of tangency intersects the center of the circleSubstituting for x in the equation of the circle, we have ...
(2y+5)^2 +y^2 = 5
5y^2 +20y +20 = 0 . . . . simplify, subtract 5
5(y +2)^2 = 0 . . . . . . . . . factor
This equation has exactly one solution, at y = -2. The corresponding value of x is ...
x = 2(-2) +5 = 1
So, the line intersects the circle in exactly one point: (1, -2).
__
The center of the circle is (0, 0), so the line through the center and point of intersection is ...
y = -2x . . . . . . . . . slope is -2
The tangent line is ...
y = 1/2x -5/2 . . . . . . slope is 1/2
The product of slopes of these lines is (-2)(1/2) = -1, indicating the lines are perpendicular.
__
We have shown ...
the tangent line intersects the circle in one point: (1, -2)the tangent line is perpendicular to the radius at the point of tangency.Find the measures of two angles, one positive and one negative, that are coterminal with the given angle. 254°
Answer: 614° and -106°
Step-by-step explanation:
You have this angle in degrees:
254°
Then, in order to find the measure of a positive angle conterminal with the given angle in degrees (254°), you need to add 360 degrees. Therefore, the measure of the positive angle is:
[tex]254\°+360\°=614\°[/tex]
Now, to find the measure of a negative angle coterminal with the given angle in degrees (254°), you need to subtract 360 degrees. Therefore, this is:
[tex]254\°-360\°=-106\°[/tex]
Lisa has $150 at most to spend on clothes. She wants to buy a pair of jeans for $58 and will spend the rest on t-shirts that cost $14 each. (5 points each) 2. Create an inequality to represent the number of t-shirts that Lisa can purchase. You can create a visual model in a paint program if that helps. Make sure you explain what the variable represents in your inequality
The inequality used in this situation will be 14x + 58 < 150.
What is inequality?The word inequality means a mathematical expression in which the sides are not equal to each other.
Let the no. of T-shirts Lisa can buy be = X
Cost of each T-shirt = $14
No. of jeans she bought = 1
Cost of jeans = $58
Total money she has = $150
Hence, the inequality will be 14X + 58 < 150.
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Lisa can spend a maximum of $92 on T-shirts after buying jeans, and with each T-shirt costing $14, she can buy up to 6 T-shirts as represented by the inequality 14t <= $92, where t is the number of T-shirts.
Explanation:To create an inequality representing the number of T-shirts Lisa can purchase, let's define the variable t to represent the number of T-shirts. Lisa has $150 to spend, and she wants to buy a pair of jeans for $58, leaving $150 - $58 = $92 for T-shirts. Each T-shirt costs $14, so if Lisa buys t T-shirts, the cost for the T-shirts is 14t. The inequality to represent the maximum number of T-shirts Lisa can buy is 14t ≤ $92.
Now, to solve for t, we divide both sides of the inequality by 14: t ≤ $92 / $14, which simplifies to t ≤ 6.57. Since Lisa cannot buy a fraction of a T-shirt, the maximum number of T-shirts she can buy is 6.
Help with this question, please!
Answer:
The last choice is the one you want.
Step-by-step explanation:
Simply take the x coordinate and subtract 4, then do the same with the y coordinate since the vector movement is <-4, -4>. The first coordinate F is <4,0>. Subtract 4 from both of those coordinates and end up at <0, -4>. The second coordinate G is <1, 3>. Subtract 4 from both of those and end up at <-3, -1>. The third coordinate H is <2, 6>. Subtract 4 from both of those and end up at <-2, 2>. The last coordinate I is <4, 2>. Subtract 4 from both of those and end up at <0, -2>.
30 PTS HELP ME ASAP! PLEASE! IM TIRED AND NEED HELP!
y=7x+10 is the equation of a regression line in a scatter plot where x is the number of hours after a store opened and y is the total number of customers that have entered the store.
1. What does the slope of 6.9 mean in the correct context?
2. According to the regression equation, how many customers have entered the store after 5 hours? (Show all of your work)
Answer:
Step-by-step explanation:
Slope is an average. In this particular context, the slope of 6.9 (or 7) means that an average of 7 people entered the store every hour.
If x is the number of hours the store is open and we are told to find the number of customers that have entered the store after 5 hours, we fill in the equation as follows:
y = 7(5) + 10 and
y = 35 + 10 so
y = 45.
If you use 6.9 instead of 7:
y = 6.9(5) + 10 and
y = 34.5 + 10 so
y = 45.5
Since you can't count a half of a person, using 7 instead of 6.9 makes more sense.
15. Find the area of a triangle with a base of 10 in. and an altitude of 14 in. (The formula for the area of a triangle is A = bh ÷ 2.)
A. 280 sq in.
B. 24 sq in.
C. 70 sq in.
D. 140 sq in.
Hello There!
We know that the formula of a triangle is "Base Multiplied By Height And Then Divide It By 2"
First, let's plug in our numbers. Our base is going to be 10 inches so we have 10 multiplied by our height which is 14 inches and we get a product of 140.
Next, we divide 140 by 2 to get a quotient of 70.
Finally, our answer is 70in squared
if y is the midpoint of xz, y is located at (3,-1), and z is located at (11,-5), find the coordinates of x
[tex]\bf ~~~~~~~~~~~~\textit{middle point of 2 points } \\\\ X(\stackrel{x_1}{x}~,~\stackrel{y_1}{y})\qquad Z(\stackrel{x_2}{11}~,~\stackrel{y_2}{-5}) \qquad \left(\cfrac{ x_2 + x_1}{2}~~~ ,~~~ \cfrac{ y_2 + y_1}{2} \right) \\\\\\ \left(\cfrac{11+x}{2}~~,~~\cfrac{-5+y}{2} \right)=\stackrel{\stackrel{midpoint}{y}}{(3,-1)}\implies \begin{cases} \cfrac{11+x}{2}=3\\[1em] 11+x=6\\ \boxed{x=-5}\\ \cline{1-1} \cfrac{-5+y}{2}=-1\\[1em] -5+y=-2\\ \boxed{y=3} \end{cases}[/tex]
We define midpoint formula as
[tex]Y(x_m, y_m)=Y(\dfrac{x_2+x_1}{2}, \dfrac{y_2+y_1}{2})[/tex]
Also here are the coordinates of every point in variables so you won't get confused.
[tex]
Y(x_m, y_m) \\
X(x_1, y_1) \\
Z(x_2, y_2)
[/tex]
Which means there are two equations. One to find x of point X and one to find y of point X.
[tex]
x_m=\dfrac{x_2+x_1}{2}\Longrightarrow 3=\dfrac{11+x_1}{2} \\
6=11+x_1\Longrightarrow\underline{x_1=-5} \\ \\
y_m=\dfrac{y_2+y_1}{2}\Longrightarrow-1=\dfrac{-5+y_1}{2} \\
-2=-5+y_1\Longrightarrow\underline{y_1=3}
[/tex]
So point X has coordinates: [tex]\boxed{X(-5, 3)}[/tex]
Hope this helps.
r3t40
How does the graph of y= sec(x-2)+2 comparé to the graph of y= sec(x) ?
Answer:
The function y= sec(x-2)+2 is shifted two units to the right and 2 units upwards., compared to y=sex(x).
Step-by-step explanation:
To solve this problem we need to know the rules for translation of graphs:
Given the function y = f(x):
y=f(x-a) is the same graph shifted 'a' units to the right. If 'a' is negative, then, the graph is shifted to the left. y = f(x) - a is the same graph, but shifted 'a' units downwards. If 'a' is negative, then the graph will be shifted upwards.In this case, our main function is y=sec(x). And the function y= sec(x-2)+2 is shifted two units to the right and 2 units upwards.
Answer:
D. it is shifted two units up and two units right
Step-by-step explanation:
this is the correct answer on ed-genuity, hope this helps! :)
PLEASE HELP ASAP! SUPER URGENT!! Find each lettered angle measure without using a protractor. State the reason why you gave the measure you did using the correct vocabulary from the unit.
m∠a Reason:
m∠b Reason:
m∠c Reason:
Answer:
Step-by-step explanation:
a: 70°
Reason: a is supplementary to the angle that measures 110°, so 180° - 110° = 70°
b: 55°
Reason: b is vertical to the angle between 100° and 25° (which add up to 125°) and since all of those angles added together have to equal 180°, then the unidentified angle between 100° and 25° = 55°. b is vertical to that angle so b = 55°
c: 25°
Reason: c is vertical the angle measuring 25° so c = 25° also.
A radiator contains 10 quarts of fluid, 30% of which is antifreeze. How much fluid should be drained and replaced with pure antifreeze so that the new mixture is 40% antifreeze?
Answer:
1 3/7 quarts should be drained off and replaced with pure antifreeze.
1 3/7 ≈ 1.4286
Current amount of antifreeze in quarts is -
30/ 100 × 10 = 3
40% ---> 4 quarts
Let the amount drained of and replaced with antifreeze be x-
The amount left after draining off is 10 − x.
The amount of antifreeze is 30/ 100 (10−x).
30/100(10-x)+x=4
3-3/10x+x=4
3+x(1-3/10)=4
x=1*10/7=1 3/7 quarts
check;
10- 1 3/7 = 8 4/7
=(30/100*8 4/7)+1 3/7
=(3/10 * 60/7) + 10/7
=3*6/7 + 10/7
=28/7
=4
4 liters of pure antifreeze is mixed into 10 quarts.
Answer: A
Step-by-step explanation:
Edge
Suppose the population of a town is 127,000 in 2014. The population increases at a rate of 5.2 percent every year. What will the population of the town be in 2020? Round your answer to the nearest whole number.
Answer:
172,146
Step-by-step explanation:
you can use the exponential growth formula and get y=127000(1.052)^6. after that, you can just solve (make sure you use PEMDAS) and get 172,146.
The population in 2020 will be 177800.
What is population growth rate definition?The annual average rate of change of population size, for a given country, territory, or geographic area, during a specified period.
Population growth rate formula[tex]P = P^{'} (1+i)^{n}[/tex]
where,
P is the future population size
[tex]P^{'}[/tex] is the initial population size
[tex]i[/tex] is the growth rate
n is number of periods, such as years
According to the given question
we have
Initial population = 127000
[tex]i[/tex] = 5.2% = [tex]\frac{5.2}{100} = 0.052[/tex]
n = 6 years (2020-2014 = 6years)
therefore,
population of the town in 2020 = 127000[tex](1+0.052)^{6}[/tex]
Population of town in 2020 = 127000×[tex](1.052)^{6}[/tex]
Population of town in 2020 = 127000 ×1.4
Population of town in 2020 = 177,800
Hence, the population of town in 2020 will be 177800.
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A commercial aircraft gets the best fuel efficiency if it operates at a minimum altitude of 29,000 feet and a maximum altitude of 41,000 feet. Model the most fuel-efficient altitudes using a compound inequality.
x ≥ 29,000 and x ≤ 41,000
x ≤ 29,000 and x ≥ 41,000
x ≥ 41,000 and x ≥ 29,000
x ≤ 41,000 and x ≤ 29,000
Answer:
[tex]x\geq 29,000[/tex] and [tex]x\leq 41,000[/tex]
Step-by-step explanation:
Let
x -----> the altitude of a commercial aircraft
we know that
The expression " A minimum altitude of 29,000 feet" is equal to
[tex]x\geq 29,000[/tex]
All real numbers greater than or equal to 29,000 ft
The expression " A maximum altitude of 41,000 feet" is equal to
[tex]x\leq 41,000[/tex]
All real numbers less than or equal to 41,000 ft
therefore
The compound inequality is equal to
[tex]x\geq 29,000[/tex] and [tex]x\leq 41,000[/tex]
All real numbers greater than or equal to 29,000 ft and less than or equal to 41,000 ft
The solution is the interval ------> [29,000,41,000]
option 1 : x ≥ 29,000 and x ≤ 41,000 represents the most fuel-efficient altitudes using compound inequality.
We need to identify the correct compound inequality describing the altitude at which the aircraft operates most efficiently. The best fuel efficiency altitudes range from 29,000 ft to 41,000 ft, meaning the altitude must be at least 29,000 ft and at most 41,000 ft.
So, to represent that the altitude must be at least 29000 ft we use the mathematical expression:
[tex]x\geq 29,000[/tex]
To represent that the altitude must be 41000 ft at most we use the mathematical expression:
[tex]x\leq 41,000[/tex]
These two expression can be represented as a compound inequality as follows:
[tex]x\geq 29,000\[/tex] and [tex]x\leq 41,000[/tex]
Therefore, option 1 : x ≥ 29,000 and x ≤ 41,000 represents the most fuel-efficient altitudes using a compound inequality.
What is the length of the missing side? What is the area of the figure?
Show ALL work.
Answer:
Missing side=25 units.
Area of the figure= 470 sq units.
Step-by-step explanation:
The figure is made up of a rectangle and a triangle.
To get the base of the triangle, we find the difference between the two parallel sides, that is, 16ft and 31 ft.
31ft-16ft=15ft
The height of the triangle is 20 since it is parallel and equal to the length of the rectangle.
We therefore use pythagoras theorem to find ?
a²+b²=c²
15²+20²=c²
625=c²
c=25
ii. The figure is a trapezium therefore we use the following formula to find the area.
A= 1/2(a+b)h, where a and b are the two parallel sides. and h the distance between them.
=(1/2)(31+16)×20
=470 sq units
Given: △ABC is equilateral. The radius of each circle is r. Find: AB
Answer:
2r (1 + √3)
Step-by-step explanation:
Circle O₁ is tangent to AB. Let's call the point of intersection point D. If we draw a radius from the center O₁ to D, we know this forms a right angle.
△ABC is an equilateral triangle, so we know m∠A = 60°. If we draw a line from A to O₁, we know that bisects the angle, so m∠DAO₁ = 30°.
So △DAO₁ is a 30-60-90 triangle. We can find the length AD:
AD = r √3
Now on the other side, circle O₃ is tangent to AB. Let's call the point of intersection point E. We know it's the same triangle we found earlier, so:
EB = r √3
And finally, we can draw a rectangle connecting O₁, O₃, E, and D. The distance between O₁ and O₃ is 2r, so:
DE = 2r.
Therefore:
AB = r√3 + 2r + r√3
AB = 2r√3 + 2r
AB = 2r (1 + √3)
Here's a graph showing the steps. Hopefully this helps, let me know if you have questions!
desmos.com/calculator/hgaonfzxsm
What is the area of the sector bound by the center of the circle and arc CD in the circle below? Circle A is shown with a radius labeled 15 feet and a central angle marked 45 degrees. 9.42 ft2 19.54 ft2 34.89 ft2 88.31 ft2
Answer:
D.Area of sector=88.31 square feet.
Step-by-step explanation:
We are given that a circle A and its radius is 15 feet.
The central angle is equal to 45 degrees.
Radius of circlle=15 feet
Angle at center=[tex]\theta=45^{\circ}[/tex]
We know that the area of sector
Area of sector=[tex]\frac{\theta}{360}\times \pi r^2[/tex].
We take value of [tex]\pi=3.14[/tex]
Substituting all given values in the given formula
Area of sector=[tex]\frac{45}{360}\times 3.14\times 15\times 15[/tex]
Area of sector=[tex]\frac{31792.5}{360}[/tex]
Area of sector= 88.3125 square feet
Hence, area of sector=88.31 square feet.Therefore, option D is correct answer.
Photo question; find the length
[tex]\bf \textit{arc's length}\\\\ s=\cfrac{\pi \theta r}{180}~~ \begin{cases} r=radius\\ \theta =angle~in\\ \qquad degrees\\ \cline{1-1} \theta =135\\ r=11.4 \end{cases}\implies s=\cfrac{\pi (135)(11.4)}{180}\implies s=8.55\pi \\\\[-0.35em] \rule{34em}{0.25pt}\\\\ ~\hfill s\approx 26.86~\hfill[/tex]
Answer:
[tex]\boxed{\textbf{26.9 m}}[/tex]
Step-by-step explanation:
The formula for the arc (s) of a circle is
[tex]s = r\theta \times \dfrac{\pi }{180^{^{\circ}}}[/tex]
where θ is measured in degrees.
Data:
r = 11.4 m
θ = 135°
Calculation:
[tex]s = \text{11.4 m} \times 135^{^{\circ}}\times\dfrac{\pi}{180^{^{\circ}}} = \textbf{26.9 m}\\\\\text{The length of the arc is }\boxed{\textbf{26.9 m}}[/tex]
Please help, I'm taking the semester test.
Drag and drop an answer to each box to correctly explain the derivation of the formula for the volume of a pyramid.
Consider a prism and a pyramid with the same base and height.
The volume of the prism is blank, the volume of the pyramid.
The formula for the volume of a prism is V=Bh ,
where B is the area of the base and h is the height, so the formula for the volume of a pyramid is blank
Picture shown below
The volume of a pyramid is one-third of the volume of a prism with the same base area and height, yielding the formula V = (1/3)Bh for the volume of a pyramid.
Explanation:When comparing the volume of a prism and a pyramid with the same base and height, the volume of a pyramid is one-third of the volume of the prism. Therefore, the formula for the volume of a prism is V = Bh, where B is the base area and h is the height. Applying this to the pyramid, the pyramid's volume becomes V = (1/3)Bh. This formula tells us that the volume of a pyramid is equal to one-third of the product of the area of its base and its height.
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17. The sides of a central angle in a circle are
A. two radii.
B. a tangent and a radius.
C. two chords.
D. a diameter and a tangent.
The quoient of two rational numbers is positive. What can you conclude about signs of the dividend and the divisor?
Answer:
the two signs are the same
Step-by-step explanation:
Whenever the quotient or product of two operands is positive, the signs of the operands are both the same, both negative or both positive.
__
Comment on the general case
Whenever the product of any number of operands is positive, the number of negative signs among the factors is even.
A quotient is the product of one operand and the reciprocal of another (the denominator). A number and its reciprocal have the same sign.
Two bags contain blue and red marbles. The first bag contains 3 blue and 5 red marbles. The second bag contains
2 blue and 4 red marbles. A marble is drawn from each bag. What is the probability that both marbles are blue?
Answer: 1/8
Step-by-step explanation:
First Bag and Second Bag
[tex]\dfrac{3\ blue}{8\ total}[/tex] x [tex]\dfrac{2\ blue}{6\ total}[/tex] = [tex]\dfrac{6}{48}[/tex]
which reduces to [tex]\boxed{\dfrac{1}{8}}[/tex]
NEED HELP WITH A MATH QUESTION
For this case we have that the total of objects is given by:
Large blue objects, small blue objects, large red objects and small red objects.
In total we have: [tex]17 + 3 + 8 + 12 = 4[/tex]0 objects.
If we want to find the probality of obtaining small and blue objects we have to:
[tex]p = \frac {3} {40}[/tex]
ANswer:
[tex]p = \frac {3} {40}[/tex]
The height of a cone is two times its base diameter. What is the volume of the cone in terms of its base radius r?
A.V=[tex]\frac{2}{3}\\[/tex](pi)(r²)
B.V=[tex]\frac{4}{3}\\[/tex](pi)(r³)
C.V=[tex]\frac{1}{3}\\[/tex](pi)(r³)
D.V=[tex]\frac{1}{3}\\[/tex](pi)(r²)
Answer:
B
Step-by-step explanation:
Assume the radius is r so the diameter is 2r
Height=2*d=2(2r)=4r since the diameter is twice the radius
Volume of cone=1/3 * pi*r^2*h
= 1/3 * pi*r^2*(4r)
=4/3 *pi *r^3
So B
Answer: B
h=2d
r=d/2
so h in terms of r is;
h=4r
V=pi*r^2*h/3
V=pi*r^2*4r/3=pi*4r^3/3=4/3(pi)(r^3)
Daniel is packing his bags for his vacation. He has 5 unique socks, but only 4 fit in his bag How many different groups of 4 socks can he take
Answer:
5
Step-by-step explanation:
what is the value of x
Answer:
Correct me if I am wrong, but I believe it is B.
Step-by-step explanation:
Answer:
C. 28
Step-by-step explanation:
From the diagram diagram; [tex]\angle BAC=(x+6)\degree[/tex] and [tex]\angle ABD=2x\degree[/tex].
The opposite sides of a rhombus are parallel.The diagonals act as transversals. Therefore the co-interior angles will add up to 180 degrees.The pair of co-interior angles are [tex]\angle BAD[/tex] and [tex]\angle ABC[/tex].
Also the diagonals of a rhombus bisect corner angles.
This implies that:
[tex]\angle BAD=2(\angle BAC)\implies \angle BAD=2(x+6)\degree[/tex].
[tex]\angle ABC=2(\angle ABD)\implies \angle ABC=2(2x)\degree[/tex].
The co-interior angles are supplementary so we form the equation:
[tex]\angle BAD+\angle ABC=180\degree[/tex]
[tex]\implies 2(x+6)\degree+2(2x)\degree=180\degree[/tex]
Expand the parenthesis to get:
[tex]\implies 2x+12+4x=180\degree[/tex]
Group the similar terms:
[tex]\implies 2x+4x=180-12[/tex]
Simplify
[tex]\implies 6x=168[/tex]
Divide both sides by 6.
[tex]\implies \frac{6x}{6}=\frac{168}{6}[/tex]
[tex]\therefore x=28[/tex]
The correct answer is C.
Half of the product of two consecutive numbers is 105. To solve for n, the smaller of the two numbers, which equation can be used?
A.) n^2 + n – 210 = 0
B.) n^2 + n – 105 = 0
C.) 2n^2 + 2n + 210 = 0
D.) 2n^2 + 2n + 105 = 0
Answer:
A
Step-by-step explanation:
Consecutive nnumbers are spaced 1 units apart.
Such as 4,5,6,...
or 12,13,14,...
Thus,
if smaller number is n, then the next number (consecutive) is n+1
Since, half of the product of them is 105, we can write the equation as:
[tex]\frac{1}{2}((n)(n+1))=105[/tex]
We can do some algebra and make it in quadratic form as shown below:
[tex]\frac{1}{2}((n)(n+1))=105\\\frac{1}{2}(n^2 + n)=105\\n^2+n=2*105\\n^2+n=210\\n^2+n-210=0[/tex]
Answer choice A is right.
Answer:
A.) n^2 + n – 210 = 0
Step-by-step explanation:
just took edg 2022. hope this helps!
The bill for five glasses of apple juice and four salads is $9.50, but the total for four glasses of apple juice and five salads is $10.30. What would the be the bill for a glass of juice and a salad?
Answer:2.20
Step-by-step explanation:
In △ M N O , points R and T are the midpoints of their respective sides. MT and OR intersect at point C.
1. 14 units
2. None of the listed answers are correct
3. 15 units
4. 16.5 units
5. 12.5 units
Answer:
3. 15 units
Step-by-step explanation:
When medians intersect, the point of intersection divides the median into parts in the ratio 2:1. That is ...
OC : CR = 2 : 1 = 4 units : 2 units . . . . . . OR = (4+2) units = 6 units
MC : CT = 2 : 1 = 6 units : 3 units . . . . . . MT = (6+3) units = 9 units
The sum of lengths OR + MT is ...
6 units + 9 units = 15 units
The given question is incomplete. Without information about dimensions or additional information of the triangle or the lines, we cannot solve for lengths.
Explanation:Unfortunately, the question is incomplete, so it is impossible to answer it accurately. In the given situation, we have a triangle △MNO and points R and T are the midpoints of their respective sides. The lines MT and OR intersect at a point C. However, without explicit dimensions or additional information about the triangle or the lines, we cannot determine the length of any line segment. In geometry problems like this, it's crucial to have a complete set of given information before proceeding with the solution.
Learn more about Triangle Midpoints here:https://brainly.com/question/32842847
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