A line bisector is a straight line that divides a given line into two equal parts. Thus the following steps are required by Naomi to show that point D is equidistant from points A and C.
BD ⊥ AC (given)
BD = 3 units, and AC = 8 units.
BD is the perpendicular bisector of segment AC (given)
Thus,
<BDA ≅ <BDC (right angles formed by a perpendicular bisector)
AD ≅ DC (equal parts of a bisected line)
AD ≅ DC = 4 units
Thus joining points B to A, and B to C,
BA ≅ BC.
So that applying Pythagoras theorem to ΔABD, we have:
[tex]/hyp/^{2}[/tex] = [tex]Adj 1^{2}[/tex] + [tex]Adj 2^{2}[/tex]
[tex]AB^{2}[/tex] = [tex]3^{2}[/tex] + [tex]4^{2}[/tex]
= [tex]\sqrt{25}[/tex]
AB = 5 units
So that,
BA ≅ BC = 5 units
Therefore, it can be concluded that point D is equidistant from points A and C.
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Can someone help me please?
Answer:
1. y ax
|
A-------------------------------B
|
------------C---------------------
|
|__________________x ax
for this, your A might be (0,5), B (5,5), C (2,2).
parallel means railroad tracks: same slope, different intercepts.
line AB in this case has a slope of 0, intercept (0,5), so y₁=0x+5 or just y₁=5
the line passing through C also has slope 0, but intercept (0,2), so y₂=0x+2 or just y₂=2
2. perpendicular means that the slopes of two lines multiply out to -1. If line AB has, for example, a slope of 2/3, then the line passing through C would have slope -3/2 (negative reciprocal). To make things easier have either point A or B be on the x or y axis
khan academy has some helpful videos :)
https://www.khanacademy.org/math/geometry/hs-geo-analytic-geometry/hs-geo-parallel-perpendicular-eq/v/perpendicular-lines
Lily is 22 years old. Monica is 3 years older than Lily and 2 years younger than Christine. How old is Christine
Answer:
she would be 20 years old if lily is 22
M angle A=
M angle B=
M angle C=
Help me please Stuck on this question thanks
m<A = 28
m<B = 96
m<C = 56
can someone help me solve this problem?
Answer:
13
Step-by-step explanation:
cos17 = x/14
x = 14cos17
x= 13.38826658
to the nearest hundredth
x=13
His friends all drive more expensive cars, and Tony is now starting to desire these same expensive products. Which factor is Tony experiencing
GUYS CAN SOMEONE PLEASE HELP ASAP?
THANKS SO MUCH ULL GIVE 40POINTS AND BRAINLIEST
Answer:
1136/295 cm
Step-by-step explanation:
Corresponding lengths of similar figures are proportional.
If we let the radius of the second cylinder be x,
x/6.4 = 7.1/11.8
x = 6.4(7.1/11.8) = 1136/295 cm
Point O is the center of dilation. Triangle A B C is dilated to create triangle A prime B prime C prime. The length of O A is 3. The length of A A prime is 9.
Triangle ABC is dilated to create triangle A'B'C' using point O as the center of dilation.
What is the scale factor of the dilation?
1/3
3
4
1/4
Answer:
3
Step-by-step explanation:
9 divided by 3 is 3...
hope this helped
Answer:
its 3
Step-by-step explanation:
im doing summer school rn lol
Consider the function f(x)=1/3(6)x. What is the value of the growth factor of the function?
Answer:
F = 2
Step-by-step explanation:
Answer:6
Step-by-step explanation:i did the quiz
A farmer must add the areas of two plots of land to determine the amount of seed to plant. The area of Plot A can be represented by 3x^2 +7x - 5, and the area of Plot B can be represented by 5x^2 - 4x + 11. Write a polynomial that represents the total area of both plots of land.
Step-by-step explanation:
Combine common terms
(3x²+5x²)+(7x-4x)+(-5+11)
8x²+3x+6
The polynomial that represents the total area of both plots of land will be; 8x²+3x+6
What is a polynomial?They are mathematical expressions involving variables raised with non negative integers and coefficients(constants who are in multiplication with those variables) and constants with only operations of addition, subtraction, multiplication and non negative exponentiation of variables involved.
We are given that ;
The area of Plot A can be represented by 3x² +7x - 5, and the area of Plot B can be represented by 5x² - 4x + 11.
So the polynomial that represents the total area of both plots of land
Now Combine common terms;
(3x²+5x²)+(7x-4x)+(-5+11)
Then we get;
8x²+3x+6
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Which equation correctly describes the relationship between the measure of the inscribed angle and the measure of the intercepted arc in the figure? m∠PQR=360°−mPR⏜ m∠PQR=12mPR⏜ m∠PQR=2(mPR⏜) m∠PQR=mPR⏜ Circle with two chords. Point Q at 10 o clock, point P at 3 o clock, and point R at 6 o clock are on the circle. Segment Q R and Q P share a common end-point at point Q.
Answer:
Your answer is ∠PQR=(1/2)* m arc PR.
Step-by-step explanation:
The Angle Described is one that has its vertex in the circumference. The inscribed angle measures half of the arc it comprises.
So, in this problem, The inscribed angle=∠PQR
The arc it comprises=m arc PR too.
So therefore:
∠PQR=(1/2)* m arc PR is the answer
There are three square gardens whose lengths of the sides are 3 ft, 7ft, and 2 ft respectively. Find the total area of the three gardens in square feet.
65
60
62
64
Answer:
62
Step-by-step explanation:
1. To find the total area, we must find the area of the three individual gardens and sum them together
2. Since the gardens are square, the area is equal to the side length squared
3. Therefore, square the sides and sum:
3^2 = 9
7^2 = 49
2^2 = 4
4+9+49 = 62
if (p,4) is mapped into (q,-3) under a rotation through+90° about origin . then find the values of p and q
Answer:
p = 3
q = 4
Step-by-step explanation:
Rotation by +90° (clockwise) about the origin: (x, y) → (y, -x)
Therefore, (p, 4) rotated by +90° about the origin:
(p, 4) → (4, -p)
Therefore:
(4, -p) = (q, -3)
⇒ p = 3
⇒ q = 4
Therefore, (3, 4) is mapped into (4, -3) under a rotation by +90° about the origin.
For the following exercises, solve each inequality and write the solution in interval notation.
29. | x − 2 | > 10
Answer:
The solution to the inequality |x-2|>10 in interval notation is given by -8<x<12
Step-by-step explanation:
An absolute value inequality |x-2|>10 is given.
It is required to solve the inequality and write the solution in interval form.
To write the solution, first solve the given absolute value inequality algebraically and then write it in interval notation.
Step 1 of 2
The given absolute value inequality is $|x-2|>10$.
The inequality can be written as
x-2<10 and x-2>-10
First solve the inequality, x-2<10.
Add 2 on both sides,
x-2<10
x-2+2<10+2
x<12
Step 2 of 2
Solve the inequality x-2>-10.
Add 2 on both sides,
x-2>-10
x-2+2>-10+2
x>-8
The solution of the inequality in interval notation is given by -8<x<12.
help help help help??
Answer:
a b f would all be the correct answers
Step-by-step explanation:
Less than looks to the left
Greater than looks right
this is timed, much help is appreciated:)
The value of the angle m∠4 is 105 degrees.
How to find angles in a quadrilateral?The sum of angles in a quadrilateral is 360 degrees.
Therefore,
m∠1 + m∠2 + m∠3 + m∠4 = 360°
Hence,
x + x + 10 + x + 20 + x + 30 = 360
4x + 60 = 360
4x = 360 - 60
4x = 300
x = 360 / 4
x = 75
Therefore,
m∠4 = 75 + 30 = 105°
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what are the possible numbers of positive, negative, and complex zeros of f(x)=x^6+x^5+x^4+4x^3-12x^2+12?
The number of zeros are; Positive; 2 or 0; Negative: 4 or 2 or 0; Complex; 0, 2, 4, 6
How to find the zeros of a Polynomial?We are given the polynomial function as;
f(x) = x⁶ + x⁵ + x⁴ + 4x³ - 12x² + 12
Use Descartes Rule rule of signs allows us to determine the possible number of positive, negative, and complex roots.
For the function f(x), the number of sign changes that occur from term to term will give us the number of positive possible roots.
For the function f(-x), the number of sign changes that occur from term to term will give us the number of negative possible roots.
The numbers of complex roots is the difference between the degree of function and total number of positive and negative roots.
For f(x), the signs change 2 times. Thus, there can only be a possibility of 2 positive roots
For f(-x), we have;
x⁶ - x⁵ + x⁴ - 4x³ - 12x² + 12
Thus, the sign changes 4 times and so we have a possibility of 4 negative roots.
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Quinn wants to save $300 this year. She saves $25 after her first dog-sitting job. How much more money does Quinn need to reach her goal for the year?
Quinn needs to save another $275.
How much more money does Quinn need to reach her goal for the year?
The money that she needs will be equal to the difference between the amount that she wants to save, and the amount that she already has.
She wants to save $300.She already has $25The difference is:
D = $300 - $25 = $275
This means that, to reach her goal this year, Quinn needs to save another $275.
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One-quarter of the counters in a tub are red. The rest of the counters are green. If there are 48 green counters, how many red counters are there?
There are 16 red counters there.
Fractions and proportionsIf one-quarter of the counters in a tub are red and the rest are green, then there are three-quarter of the counter in the tub.
Let the total counter be x such that
3/4x = 48
3x = 4 * 48
x = 4 * 16
x = 64
Determine the amount of red counter
Red counter = 64 - 48
Red counter = 16
Hence there are 16 red counters there.
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PLS HELP I REALLY NEED HELP
Answer:
a) AB = 10 unitsb) Midpoint is (2, 6)===================
GivenPoints A( - 1, 10) and B(5, 2)To finda) The length of ABb) The midpoint of ABSolutiona) Use the distance formula:
[tex]d = \sqrt{(x_2-x_1)^2+(y_2-y_1)^2}[/tex]
Substitute the coordinates and calculate:
[tex]d=\sqrt{(5-(-1))^2+(2-10)^2} =\sqrt{6^2+(-8)^2} =\sqrt{36+64} =\sqrt{100} =10[/tex]
The distance is AB = 10 units
b) Use midpoint formula and find x and y- coordinates of this point:
[tex]x= \cfrac{x_1+x_2}{2}[/tex] and [tex]y= \cfrac{y_1+y_2}{2}[/tex]
Substitute coordinates and find the midpoint:
[tex]x= \cfrac{-1+5}{2} =2[/tex] and [tex]y= \cfrac{10+2}{2}=6[/tex]
The midpoint is (2, 6)
Answer:
Length of line segment AB = 10 units
Midpoint of line segment AB = (2, 6)
Step-by-step explanation:
To find length, apply the distance formula :
AB = √(5 - (-1))² + (2 - 10)²AB = √36 + 64 = √100[tex]\fbox {AB = 10 units}[/tex]To find the midpoint :
M = (-1 + 5 / 2, 10 + 2 / 2)[tex]\fbox {Midpoint = (2, 6)}[/tex]A 2012 survey of 2,254 American adults indicates that 17% of cell phone owners do their browsing on their phone rather than a computer or other device. (a) According to an online article, a report from a mobile research company indicates that 38 percent of Chinese mobile web users only access the internet through their cell phones. Conduct a hypothesis test to determine if these data provide strong evidence that the proportion of Americans who only use their cell phones to access the internet is different than the Chinese proportion of 38%. The hypotheses for this test are:
The hypothesis which can be used to show whether data provide strong evidence or not are: [tex]H_{0}:p_{1}[/tex]≠[tex]p_{2}[/tex] and [tex]H_{1}:p_{1}=p_{2}[/tex] where [tex]p_{1} and p_{2}[/tex] are the proportions of Americans and chinese people who use mobile phones to access internet.
Given proportion of Americans uses mobile phones is 17%. Proportion of chinese uses mobile phones is 38%.
Hypothesis are the statements which can be tested through its validity. There can be null hypothesis and alternate hypothesis.
The hypothesis which can be used are as under:
[tex]H_{0} :[/tex][tex]p_{1}[/tex]≠[tex]p_{2}[/tex]
[tex]H_{1}:p_{1} =p_{2}[/tex]
We have used equal to signs because we have to check whether they are different or not.
We cannot check hypothesis as we don't have standard deviation.
Hence the hypothesis for this test are: [tex]H_{0} :p_{1}[/tex]≠[tex]p_{2}[/tex] and [tex]H_{1} :p_{1} =p_{2}[/tex].
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0.65 more than -4.35
Answer:
-3.7
Step-by-step explanation:
1. More = Addition
2. 0.65 + -4.35 = -3.7
[tex]\Large\maltese\underline{\textsf{A. What is Asked}}[/tex]
0.65 more than -4.35
[tex]\Large\maltese\underline{\textsf{B. This problem has been solved!}}[/tex]
The word more means addition, thus
-4.35+0.65=
[tex]\bf{-3.7}[/tex]
[tex]\cline{1-2}[/tex]
[tex]\bf{Result:}[/tex]
[tex]\bf{=-3.7}[/tex]
[tex]\LARGE\boxed{\bf{aesthetic\not1\theta\ell}}[/tex]
HELP GEOMETRY) Fill in the blanks:
How many degrees is angle LKZ?
How many degrees is angle LMZ?
How many degrees is arc LKZ?
Answer:
Step-by-step explanation:
Which of the following represents a function
Answer:
(2,3),(4,3),(-2,-3),(-4,-3)
Step-by-step explanation:
A function is defined as a relation in which each domain element (x-value) is paired with exactly one range element (y-value).
This means that each value we input for x must have only one possible output. If the same x-value yields more than one y-value, it is not a function.
The correct answer, as shown above, meets the criteria of a function, as each x-value is shown to produce exactly one y-value. In this set of ordered pairs, if x = 2, then y = 3, and if x = -2, then x = -3.
A set of ordered pairs is not a function if there are ordered pairs with the same x-values but different y-values.
In the other sets of ordered pairs, one x-value has more than one possible y-value. Let's use the last set as an example:
(5,1),(5,2),(5,3),(5,4)
Inputting 5 as x produces four different y values; there is no one y value for the x-value. y could equal 1, 2, 3, or 4.
What is the length of BC?
From the markings on the diagram, we can tell E is the midpoint of BC and
is the midpoint of AC
We can apply the
theorem: ED = One-halfBA.
Substituting in the expressions for the lengths and solving for x, we get x =
.
Now, since BE = x, then BC =
.
Using the triangle midsegment theorem, x = 5; BC = 10 units.
What is the Triangle Midsegment Theorem?According to the triangle midsegment theorem, ED = 1/2(BA).
Given the following:
ED = x + 2
BA = 4x - 6
x + 2 = 1/2(4x - 6)
2(x + 2) = 4x - 6
2x + 4 = 4x - 6
2x - 4x = -4 - 6
-2x = -10
x = 5
BC = 2(BE)
BC = 2(x)
BC = 2(5)
BC = 10 units
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Answer:
D
Triangle Midsegment
5
10
Step-by-step explanation:
E2020 Geometry B!!:3
the number of men is five eights of the number of women working in a factory if there is 24 more women than men how many workers are all together
Answer:
104
Step-by-step explanation:
women = 8/8
men = 5/8
all workers = 8/8 + 5/8 = 13/8
extra women workers = 8/8 - 5/8 = 3/8
so...
3/8 = 24
13/8 = x
( cross multiplication method)
3/8 x = 39
x = 104
Hence, there are 104 workers
Answer:
104 workers
Step-by-step explanation:
w = women
m = men = 5/8 w
w - 5/8 w = 24
w = 64 then m = 5/8 * 64 = 40 total = 104
73. Real-World Applications
A city's population in the year 1960 was 287,500 . In 1989 the population was 275,900 . Compute the rate of growth of the population and make a statement about the population rate of change in people per year.
Answer:
The rate of growth of the population is -400, this means the growth of the population from year 1960 to 1989 has dropped by 400 per city.
Step-by-step explanation:
It is given that in a city's population in the year 1960 was 287500 , and in the year of 1989 the population was 275900 .
It is required to compute the rate of growth of population and make a statement about the population rate of 1989 with the year 1989 and the time taken to change the population.
Step 1 of 1
It is given that in a city's population in the year 1960 was 287500 , and in the year of 1989 the population was 275900 .
To find the rate of growth of population and make a statement about the population rate of change in people per year.
Now let f(x) be the number of population and x be the year and use formula of rate of change to find the change in population,
[tex]$m=\frac{f\left(x_{2}\right)-f\left(x_{1}\right)}{x_{2}-x_{1}}$[/tex]
Now substitute, 275900 for [tex]$f\left(x_{2}\right)[/tex], 287500 for then,
[tex]$$\begin{aligned}m &=\frac{275900-287500}{1989-1960} \\&=\frac{-11600}{29} \\&=-400\end{aligned}$$[/tex]
The rate of growth of population -400, so there is a drop in the population by 400 per city.
Write pqqqqrr in exponential form.
p^1
q^4
r^2
Is this what your asking for and also can you please mark me as brainlist. Thank you
Find the area of a triangle with points (-8,8) , (10,-2), and (-8,-8)
Answer:
144
Step-by-step explanation:
Base:16
Height: 18
Triangle area formula: (bxh)/2
16x18=288
288/2=144
Use the box-and-whisker plots to determine which statements are true.
The true statements are :
the average monthly temperatures of New Orleans are not as varied as that of Indianapolis.
The median of the average monthly temperatures of New Orleans is equal to the upper quartile of the average monthly temperature of Indianapolis.
What are the true options?A box plot is used to study the distribution and level of a set of scores. The box plot consists whiskers and a box. The whiskers represents the minimum and maximum scores. The difference between the minimum and maximum scores is the range.
On the box, the first line to the left represents the lower quartile. The next line on the box represents the median. The third line on the box represents the upper quartile.
Range for New Orleans = 85 - 50 = 35
Range for Indianapolis = 75 - 25 = 50
Median for New Orleans = 70
Upper quartile for Indianapolis = 70
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A rectangle is four times as long as it is wide. If its length were diminished by 6 meters and its width were increased by 6 meters, it would be a square. What are the rectangle’s dimensions?
Answer:
Length equals 16 and Width equals 4
Step-by-step explanation:
First let us create an equation. We can use L and W for length and width.
If the length is 4 times the width, then we end up with: L = 4W
It then says, " If its length were diminished by 6 meters and its width were increased by 6 meters, it would be a square."
Since a square has an equal length and width then we end up with:
L - 6 = W + 6
Knowing this we can just substitute the first equation into the second one leaving us with: 4W - 6 = W + 6
We then remove a W from both sides so that the right side is left with a 6, and add 6 to both sides to remove the -6 from the left one.
This leaves us with 3W = 12
W = 4, and if we put that into our first equation, L = 4W, then Length equals 16, and Width equals 4. We can check this by putting it into the 2nd equation. 16 - 6 = 4 + 6.