the correct option is:
"The distance from the origin to point A is equal to the radius of circle P. Therefore, point A lies on circle P."
Which of the following statements can be used to construct an algebraic proof the point A lies on circle P?
A circle is defined as the set of equidistant points to a given point which is the center of the circle.
That distance to the center is called the radius.
Here, the center is at the point (0, 0), also called the origin, so if the distance between the point A and the origin, then point A lies on top of the circle P.
From that, we conclude that the correct option is:
"The distance from the origin to point A is equal to the radius of circle P. Therefore, point A lies on circle P."
That is the only proof that we can (and should) use to prove that a point lies on a circle.
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Answer:
The distance from the origin to point A is equal to the radius of circle P. Therefore, point A lies on circle P."
Step-by-step explanation:
I did the test
Poormina spends all of her money on comic books and mandarins. in 2013, she earn $12 per hour, the price of a comic book was six dollars, and the price of a mansion was one dollar
The price of a mansion is $1.00 in 2013.
What is difference between a nominal and real variable?
Nominal variables are expressed in money or dollar terms, whereas the real variable compares the wage earned per hour to the basket of goods or services that it can purchase.
In comparing the wage earned per hour to 2 comic books, since the two would cost $12,that explains real variable, which is not required in this case.
However, comparing the the wage of $12 per hour to the price of mansion, which is $1 per one, indicates nominal variable.
In essence, the correct option in this case is that price of a mansion is $1.00 in the year 2013.
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PLEASE HELP ALOT OF POINTS
Answer: B
Step-by-step explanation:
Question
Find the point-slope form of the equation of the line satisfying the given conditions and use this to write the slope-intercept form of the equation.
x-intercept - 5 and y-intercept = 4
Answer:
y=(−2)x−-6
Step-by-step explanation:
Use the slope −2 and the point (−5,4) to find the y-intercept.
y=mx+b
⇒4=(−2×−5)+b
⇒−4=10+b
⇒b=−6
Write the equation in slope intercept form as:
y=mx+b
⇒y=(−2)x−-6
if x varies directly as y, and
X = 24 when y= 21, Find x when
Y=6
Answer:
x = 48/7
Step-by-step explanation:
There's two good ways to do this problem.
Option 1:
Translate "x varies directly as y" into the equation y=kx
Then you have to find k. After you "reset" your y=kx equation, fill in k and then solve for x. See image.
Option 2:
Translate "varies directly" into a proportion, which is two fractions equal to each other:
x/y = x/y
Fill in the three numbers given and cross multiply and solve to find the fourth number. See image.
2/120=X/80=Y/300
x=? & y=?
X=1.33
Y=4.9875;approx. 5.0
Answer:
(2/120=X/80)=Y/300
2×80=120×X
X=160/120
X=1.33
X/80=Y/300
But X=1.33
By substituting
X=1.33, We have that
1.33/80=Y/300
80×Y=1.33×300
80Y=399
Y=399/80
Y=399/80
Y=5.0 approx.
(06.04 MC)
If [tex]\int\limits^3_ {-2} \, [2f(x)+2]dx=18[/tex] and [tex]\int\limits^1_ {-2} \, f(x)dx =8[/tex], then [tex]\int\limits^3_ {1} \, f(x)dx[/tex] is equal to which of the following?
4
0
−2
−4
[tex]\huge\underline{\underline{\boxed{\mathbb {ANSWER:}}}}[/tex]
◉ [tex]\large\bm{ -4}[/tex]
[tex]\huge\underline{\underline{\boxed{\mathbb {SOLUTION:}}}}[/tex]
Before performing any calculation it's good to recall a few properties of integrals:
[tex]\small\longrightarrow \sf{\int_{a}^b(nf(x) + m)dx = n \int^b _{a}f(x)dx + \int_{a}^bmdx}[/tex]
[tex]\small\sf{\longrightarrow If \: a \angle c \angle b \Longrightarrow \int^{b} _a f(x)dx= \int^c _a f(x)dx+ \int^{b} _c f(x)dx }[/tex]
So we apply the first property in the first expression given by the question:
[tex]\small \sf{\longrightarrow\int ^3_{-2} [2f(x) +2]dx= 2 \int ^3 _{-2} f(x) dx+ \int f^3 _{2} 2dx=18}[/tex]
And we solve the second integral:
[tex]\small\sf{\longrightarrow2 \int ^3_{-2} f(x)dx + 2 \int ^3_{-2} f(x)dx = 2 \int ^3_{-2} f(x)dx + 2 \cdot(3 - ( - 2)) }[/tex]
[tex]\small \sf{\longrightarrow 2 \int ^3_{-2} f(x)dx + 2 \int ^3_{-2} 2dx = 2 \int ^3_{-2} f(x)dx + 2 \cdot5 = 2 \int^3_{-2} f(x)dx10 = }[/tex]
Then we take the last equation and we subtract 10 from both sides:
[tex]\sf{{\longrightarrow 2 \int ^3_{-2} f(x)dx} + 10 - 10 = 18 - 10}[/tex]
[tex]\small \sf{\longrightarrow 2 \int ^3_{-2} f(x)dx = 8}[/tex]
And we divide both sides by 2:
[tex]\small\longrightarrow \sf{\dfrac{2 { \int}^{3} _{2} }{2} = \dfrac{8}{2} }[/tex]
[tex]\small \sf{\longrightarrow 2 \int ^3_{-2} f(x)dx=4}[/tex]
Then we apply the second property to this integral:
[tex]\small \sf{\longrightarrow 2 \int ^3_{-2} f(x)dx + 2 \int ^3_{-2} f(x)dx + 2 \int ^3_{-2} f(x)dx = 4}[/tex]
Then we use the other equality in the question and we get:
[tex]\small\sf{\longrightarrow 2 \int ^3_{-2} f(x)dx = 2 \int ^3_{-2} f(x)dx = 8 + 2 \int ^3_{-2} f(x)dx = 4}[/tex]
[tex]\small\longrightarrow \sf{2 \int ^3_{-2} f(x)dx =4}[/tex]
We substract 8 from both sides:
[tex]\small\longrightarrow \sf{2 \int ^3_{-2} f(x)dx -8=4}[/tex]
• [tex]\small\longrightarrow \sf{2 \int ^3_{-2} f(x)dx =-4}[/tex]
what is the length of the interval of solutions to the inequality 1≤3-4x≤9?
Answer: -3 ≤ x ≤ -1
Step-by-step explanation:
1 ≤ 3 - 4x ≤ 9
1 + 3 ≤ - 4x ≤ 9 + 3; Add 3 on all sides
4 ≤ -4x ≤ 12
1 ≤ -x ≤ 3; Divide 4 on all sides
-1 ≥ x ≥ -3; Multiply -1 on all sides(FYI: When multiplying or dividing negative numbers in inequalities, make sure to reverse the signs as well)
Answer:
2
Step-by-step explanation:
1≤3-4x≤9
subtract 3
1-3≤3-4x-3≤9-3
-2≤-4x≤6
divide by 2
-1≤-2x≤3
multiply by -1
1≥2x≥-3
or
-3≤2x≤1
divide by 2
[tex]-\frac{3}{2} \leq \frac{2x}{2} \leq \frac{1}{2} \\-\frac{3}{2} \leq x\leq \frac{1}{2} \\[/tex]
length of interval
[tex]=\frac{1}{2} -(\frac{-3}{2} )\\=\frac{1}{2} +\frac{3}{2} \\=\frac{1+3}{2} \\=\frac{4}{2} \\=2[/tex]
If
f(x) = 2x2 − 7,
0 ≤ x ≤ 3,
evaluate the Riemann sum with
n = 6,
taking the sample points to be midpoints.
What does the Riemann sum represent? Illustrate with a diagram.
The Riemann sum with n = 6, taking the sample points to be midpoints is - 12.0625
What is Riemann sum?
Formula for midpoints is given as;
M = ∑0^n-1f((xk + xk + 1)/2) × Δx;
From the information given, we have the following parameters
x0 = 0 n = 6 xn = 3Let' s find the parameters
Δx = (3 - 0)/6 = 0.5
xk = x0 + kΔx = 0.5k
xk+1 = x0 + (k +1)Δx
Substitute the values
= 0 + 0.5(k +1) = 0.5k - 0.5;(xk + xk+1)/2
We then have;
= (0.5k + 0.5k + 05.)/2
= 0.5k + 0.25.
Now f(x) = 2x^2 - 7
Let's find f((xk + xk+1)/2)
Substitute the value of (xk + xk+1)/2)
= f(0.5k+ 0.25)
= 2(0.5k + 0.25)2 - 7
Put values into formula for midpoint
M = ∑05[(0.5k + 0.25)2 - 7] × 0.5.
To evaluate this sum, use command SUM(SEQ) from List menu.
M = - 12.0625
A Riemann sum represents an approximation of a region's area from addition of the areas of multiple simplified slices of the region.
Thus, the Riemann sum with n = 6, taking the sample points to be midpoints is - 12.0625
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HELP PLEASE ASAP Find the distance between A and B. (5,1) (-3,-4)
Answer:
6.32
Step-by-step explanation:
The formula we use to find the distance between two points is:
[tex]\sqrt{(x_1-x_2)+(y_1-y_2)}[/tex]
The x1 is -3, the x2 is 5, the y1 is -4, and lastly, the y2 is 1.
If we input these numbers in the equation, we end up with:
[tex]\sqrt{(-3-5)+(-4-1)}[/tex]
= [tex]\sqrt{(-8) (-5)}[/tex]
= [tex]\sqrt{40}[/tex]
= [tex]2\sqrt{10}[/tex]
= 6.32455532
Rounded to the nearest hundredth is 6.32
HOW MANY 7 DIGIT TELEPHONE NUMBERS ARE POSSIBLE IF THE FIRST DIGIT CANNOT BE ZERO AND:
A) THE TELEPHONE NUMBER MUST BE A MULTIPLE OF 100?
B) ONLY ODD DIGITS CAN BE USED?
C) THE FIRST 3 DIGITS ARE 277?
Using the Fundamental Counting Theorem, the number of possible telephone numbers is given by:
a) 900,000.
b) 78,125.
c) 10,000.
What is the Fundamental Counting Theorem?It is a theorem that states that if there are n things, each with [tex]n_1, n_2, \cdots, n_n[/tex] ways to be done, each thing independent of the other, the number of ways they can be done is:
[tex]N = n_1 \times n_2 \times \cdots \times n_n[/tex]
For item a, a multiple of 100 means that the last two digits are 00, hence the parameters are:
[tex]n_1 = 9, n_2 = n_3 = n_4 = n_5 = 10, n_6 = n_7 = 1[/tex]
Hence the number is:
N = 9 x 10^5 = 900,000.
For item b, odd digits are 1, 3, 5, 7 and 9, hence the parameters are:
[tex]n_1 = n_2 = n_3 = n_4 = n_5 = n_6 = n_7 = 5[/tex]
Hence the number is:
N = 5^7 = 78,125.
For item c, if the first 3 digits are 277, the parameters are:
[tex]n_1 = n_2 = n_3 = 1, n_4 = n_5 = n_6 = n_7 = 10[/tex]
Hence the number is:
N = 10^4 = 10,000.
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A worker uses a small table in a notebook to track the cost of materials. On the current job he has used seven sheets of plywood at $43.75 each, two boxes of screws at $4.69 each and a tube of adhesive which cost $9.89, as shown below.
The total cost of the materials calculated by the worker on the notebook is $325.52
What is an equation?
An equation is an expression that shows the relationship between two or more numbers and variables.
An independent variable is a variable that does not depend on any other variable for its value while a dependent variable is a variable that depends on other variable.
The total cost of materials = 7(43.75) + 2(4.69) + 9.89 = $325.52
The total cost of the materials calculated by the worker on the notebook is $325.52
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will give brainliest
Supervisor: "Last week, you spoke with 800 customers in 40 hours."
Employee: "That is an average of ____ customers every 30 minutes."
Answer: 10
Step-by-step explanation: 800/80 = 10
Pls answer these questions ASAP
From the given descriptions and dimensions, we have;
6. 2000 cm²
7. 81 m²
8. a. 138 m²
b. 538 m²
c. 62 cm²
9. $107.25
Which method can be used to calculate the surface areas and cost?6. Type of box = Open box with no lid
Side length of the box = 20 cm
Therefore;
Number of faces of the box, painted = 5
Area of a face of the box = 20² = 400
Area of the surface painted, A = 5 × 400 cm² = 2000 cm²7. Area of the plastic to cover one book, A, is found as follows;
A = 2 × 20 × 15 + 2 × 3 × 15 + 2 × 20 × 3
Which gives;
A = 600 + 90 + 120 = 810The area of plastic needed to cover 1000 books is therefore;
Total area = 1,000 × 810 cm² = 810,000 cm²
Conversion of cm² to m² gives;
1 m² = 10,000 cm²Therefore;
A = 810,000 cm² = 810,000 cm² × 1/10,000 m²/cm² = 81 m²
The area of plastic needed to cover 1000 books is A = 81 m²8. The surface areas are;
a. A = 2 × 3 × 6 + 5 × 6 + 7 × 6 + 2×3×(3+7)/2 = 138
The surface area is 138 m²b. A = 2 × 15 × 5 + 2×(10×5 + (6×8)/2) + 2×8×15 = 538
A = 150 + 148 + 240 = 538
The surface area is 538 m²c. From the congruent marks, we have;
A = 5 × 3 × 3 + 5×1×3 + 2×1×1 = 62
The surface area is 62 cm²9. From the congruent markings, we have;
A = 2 × (1.5 × 1.5 + (1.5 × 1.3)/2) + 5×2×1.5
A = 6.45 + 15 = 21.45
Surface area of a the canvas, A = 21.45 m²
Cost per unit area of the canvas, c = $5
Cost of the canvas for the tent, C, is therefore;
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A restaurant manager has the option of a 30-year loan of $417,000 at an annual interest rate of 3.85% or the same interest rate but on a loan for 15 years.
(a)
Calculate the monthly payment for each loan. (Round your answers to the nearest cent.)
30-year $
15-year $
(b)
Calculate the savings in interest by using the 15-year loan. (Round your answer to the nearest cent.)
$
(c)
The term of the 15-year loan is one-half the term of the 30-year loan. Is the monthly payment for the 15-year loan twice that of the 30-year loan?
Yes
No
(d)
Is the interest savings for the 15-year loan more or less than one-half of the interest paid on the 30-year loan?
more
less
a) The monthly payment for each loan is as follows:
30-year $1,954.93
15-year $3,053.25
b) The savings in interest by using the 15-year loan is $154,189,20 ($286,774.20 - $132,585).
c) No. the monthly payment for the 15-year loan is not twice that of the 30-year loan as the loan term.
d) The interest savings for the 15-year loan are more than one-half of the interest paid on the 30-year loan.
How are the calculations for periodic payments done?The calculations for the monthly payments, including interests can be carried out using an online finance calculator, as follows:
30-year Loan:N (# of periods) = 360 months (12 x 30 years)
I/Y (Interest per year) = 3.85%
PV (Present Value) = $417000
FV (Future Value) = $0
Results:
PMT = $1,954.93
Sum of all periodic payments = $703,774.80 ($1,954.93 x 360)
Total Interest = $286,774.20 ($703,774.80 - $417,000)
15-year Loan:N (# of periods) = 180 months (12 x 15 years)
I/Y (Interest per year) = 3.85%
PV (Present Value) = $417000
FV (Future Value) = $0
Results:
PMT = $3,053.25
Sum of all periodic payments = $549,585 ($3,053.25 x 180)
Total Interest = $132,585 ($549,585 - $417,000)
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Find X:
J:58
K:70
L:111
M:121
Answer:
L
Step-by-step explanation:
interior angle formula so
(number of sides - 2)*180
2*180 = 360
you can also just take an example from a square 4*90 = 360
360-121-58-70 = 111
is there anybody to solve this need step by step solution details
The circumference of the circles from biggest to smallest are; 30π, 15π and 7.5π
How to find the area of a circle?The formula for area of a circle is;
A = πr²
In geometry, the area enclosed by a circle of radius r is πr². Here the Greek letter π represents the constant ratio of the circumference of any circle to its diameter, approximately equal to 3.14159.
The area of a circle formula is useful for measuring the region occupied by a circular field or a plot. Suppose, if you have a circular table, then the area formula will help us to know how much cloth is needed to cover it completely.
The area formula will also help us to know the boundary length i.e., the circumference of the circle. Does a circle have volume? No, a circle doesn't have a volume
Area of entire circle is 706 cm².
Thus;
πr² = 706
r² = 706/π
r = √(706/π)
r ≈ 15
Circumference of biggest circle = 2πr
Circumference of biggest circle = 2π * 15
Circumference of biggest circle = 30π
Circumference of second biggest circle = 2π * (15/2)
Circumference of second biggest circle = 15π
Circumference of smallest circle = 2π * (15/4)
Circumference of smallest circle = 7.5π
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Kendra received a bonus that was 30% of her monthly earnings. If her monthly earnings were $930, how much was Kendra's bonus?
Answer:
$279
Step-by-step explanation:
100% = $930
30% = ???
(30/100) × 930
=$279
6. Find the values of x and y. 30° 17
Answer:
X = 17√3
Y = 34
Step-by-step explanation:
TO calculate the values of X and y we use SOHCAHTOA.
Calculating for Xtan 30 = opposite/adjacent
tan30 = 17/X
Cross multiply
tan30 ×X = 17
Divide bothsides by tan30
Note: tan30= 1/√3X = 17/1/√3
X=17√3
X= 29.4X = 29 ( approximately)
Calculating for y[tex]sin30 = \frac{Opposite}{Hypothenus} \\ \\ sin30 = \frac{17}{y} [/tex]
Cross multiply[tex]sin30 \times y = 17[/tex]
Divide bothsides by sin30[tex] \frac{sin30 \times y}{sin30} = \frac{17}{sin30} \\ \\ y = \frac{17}{0.5} = 34 \\ y = 34[/tex]
Is the following relation a function?
So,some please help me with this question !
=============================================================
Explanation:
Angles EBA and DBC are congruent because of the similar arc marking. Both are x each.
Those angles, along with EBD, combine to form a straight angle of 180 degrees. We consider those angles to be supplementary.
So,
(angleEBA) + (angleEBD) + (angleDBC) = 180
( x ) + (4x+12) + (x) = 180
(x+4x+x) + 12 = 180
6x+12 = 180
6x = 180-12
6x = 168
x = 168/6
x = 28
Angles EBA and DBC are 28 degrees each.
This means angle D = 3x+5 = 3*28+5 = 89
-----------
Then we have one last set of steps to finish things off.
Focus entirely on triangle DBC. The three interior angles add to 180. This is true of any triangle.
D+B+C = 180
89 + 28 + C = 180
117+C = 180
C = 180 - 117
C = 63 degrees
[tex] \qquad \qquad \bf \huge\star \: \: \large{ \underline{Answer} } \huge \: \: \star[/tex]
[tex]\qquad❖ \: \sf \: \angle C = 63 \degree[/tex]
[tex]\textsf{ \underline{\underline{Steps to solve the problem} }:}[/tex]
[tex]\qquad❖ \: \sf \:x + 4x + 12 + x=180°[/tex]
( Angle EBA= Angle DBC, and the three angles sum upto 180° due to linear pair property )
[tex]\qquad❖ \: \sf \:6x + 12 = 180[/tex]
[tex]\qquad❖ \: \sf \:6x = 180 - 12[/tex]
[tex]\qquad❖ \: \sf \:6x = 168[/tex]
[tex]\qquad❖ \: \sf \:x = 28 \degree[/tex]
Next,
[tex]\qquad❖ \: \sf \: \angle C + \angle D + x = 180°[/tex]
[tex]\qquad❖ \: \sf \: \angle C +3x + 5 + x = 180°[/tex]
[tex]\qquad❖ \: \sf \: \angle C +4x = 180 - 5[/tex]
[tex]\qquad❖ \: \sf \: \angle C +4(28) = 175[/tex]
( x = 28° )
[tex]\qquad❖ \: \sf \: \angle C +112 = 175[/tex]
[tex]\qquad❖ \: \sf \: \angle C = 175 - 112[/tex]
[tex]\qquad❖ \: \sf \: \angle C = 63 \degree[/tex]
[tex] \qquad \large \sf {Conclusion} : [/tex]
[tex]\qquad❖ \: \sf \: \angle C = 63 \degree[/tex]
THOMAS OSLER IS BUYING A TOWNHOUSE SELLING FOR $175,000. HIS BANK IS
OFFERING A 30-YEAR FIXED RATE MORTGAGE AT 5.5% WITH A MINIMUM 20% DOWN
PAYMENT. DETERMINE THE AMOUNT OF THE DOWN PAYMENT AND THE MONTHLY PAYMENT
The amount of the down payment and the fixed rate mortgage is $35000 and $9625.
According to the statement
We have given that the
Thomas osler is buying a house selling for $175,000 And we have to find the amount of the down payment and the monthly payment.
So, The down payment is :
percentage of the down payment is 20%
So,
Amount = 20/100*175000
Amount = 35,000$
And the percentage of the fixed rate mortgage with 5.5%
So,
Amount = 5.5/100*175000
Amount = $9625.
This the amount of the down payment with the given percentage and with the fixed rate mortgage.
So, The amount of the down payment and the fixed rate mortgage is $35000 and $9625.
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emily is standing 150 feet from a circular target with radius 3 inches. will she hit the target if her aim is off by 0.2 degrees?
Answer:
no
Step-by-step explanation:
The angle subtended by the radius of the target at Emily's distance can be found using the tangent relation.
Applicationtan(α) = opposite/adjacent = (1/4 ft)/(150 ft) = 1/600
The angle is found using the inverse relation:
α = arctan(1/600) ≈ 0.095°
If Emily's aim is off by 0.2°, she will miss the target by several inches.
__
Additional comment
Emily's projectile will miss her aiming point by ...
(150 ft)tan(0.2°) ≈ 0.524 ft ≈ 6.28 in
The population of a rabbit colony triples every 3 days. The population starts at 10 rabbits. Write an exponential function that will model the population of the colony after, t, days have passed.
Answer:
DO not working in you
Step-by-step explanation:
PLEASE help me in answering
Answer:
Step-by-step explanation:
The population at various days is as follows since population triples every 3 days
Day Population
0 10
3 30
6 90
9 270
.... ......
This can be modeled by the general equation
[tex]n_{t} = n_{0}(r)^{t/k}[/tex]
where
[tex]n_{t}[/tex] is the population after t days
[tex]n_{0}[/tex] is the population at start (10)
[tex]r[/tex] is the rate at which population changes ie 3
[tex]t[/tex] is the number days from start
[tex]k[/tex] is the number of days at which the population triples(here k =3 days)
We can check this by plugging in values for each of the variables
At day 0, population = 10(3)⁰ = 10. 1 = 10
Similarly populations for days 3, 6, 9 are:
[tex]\\\\10.3^{3/3} = 10. 3^1 = 10.3 = 30\\10.3^{6/3} = 10. 3^2 = 10.9 = 90\\\\10.3^{9/3} = 10. 3^3 = 10.27 = 270[/tex]
The graph shows a system of inequalities.
Graph of two inequalities. One is a dashed line increasing from left to right passing through negative 5 comma 0 and 0 comma 5, and it has shading above the line. The second is a dashed upward opening parabola with a vertex at negative 2 comma negative 9 and x-intercepts at negative 5 comma 0 and 1 comma 0. This parabola is shaded on the inside.
Which system is represented in the graph?
y > x2 + 4x – 5
y > x + 5
y < x2 + 4x – 5
y < x + 5
y ≥ x2 + 4x – 5
y ≤ x + 5
y > x2 + 4x – 5
y < x + 5
The system of inequalities having the given feasible regions and points at (-5, 0), and (0, 5), and (-2, -9), (-5, 0), and (1, 0) is the option;
y > x² + 4•x - 5
y > x + 5
How can the required system of inequalities be found?The coordinates of the given points on the linear inequality are;
(-5, 0), and (0, 5)
Slope, m, of the linear inequality is therefore;
m = (5 - 0)/(0 - (-5)) = 1
The equation of the inequality is therefore;
y - 0 > 1•(x - (-5)) = x + 5
Which gives;
y > x + 5Quadratic Inequality;
The coordinates of the points on the quadratic inequality are;
Vertex point = (-2, -9)
x-intercept = (-5, 0), and (1, 0)
Therefore, we have;
y > (x + 5)•(x - 1) = x² + 4•x - 5
y > x² + 4•x - 5The correct option is therefore;
y > x² + 4•x - 5
y > x + 5
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Answer:
y > x2 + 4x – 5
y > x + 5
Step-by-step explanation:
If you put this system into desmos you will see that it matches the photo shown in the question, and it would need to be both greater than symbols because the dotted lines indicate that it is not included in the solution.
Which of the following statements is false?
A. The parallel sides of an isosceles trapezoid are congruent.
B. Opposite sides of a parallelogram are congruent.
C. The diagonals of a rhombus are perpendicular and bisect each other.
D. The base angles of an isosceles trapezoid are congruent.
The statement which is false among the answer choices as indicated in the task content is; Choice A; The parallel sides of an isosceles trapezoid are congruent.
Which of the statements indicated in the answer choice is correct?It follows from the answer choice A that The parallel sides of an isosceles trapezoid are congruent.
However, it follows from the study of isosceles trapezoids that the base angles of such trapezoids are congruent and their measures are equal, consequently, the isosceles sides have equal length measures.
On this note, the other two sides are parallel but cannot be concluded as congruent.
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PLEASE HELP ME OUT WITH THIS QUESTION!
Answer: Choice 3
Step-by-step explanation:
Oof, this is a tough one. But anyways
Angle 19 + Angle 20 = 180
So Angle 20 = 180 - Angle 19
As l and m are parallel, Angle 20 = Angle 6 from the z rule
So Angle 6 = 180 - Angle 19
Substitute the information given at the start into the equation
2x - 4 = 180 - (5x - 8)
180 - 5x + 8 = 2x - 4
7x = 192
x = 27.42
From what we have found earlier, Angle 20 = Angle 6 so
Angle 20 = 2x - 4 = 2 * 27.42 - 4 = 50.85 rounding it to 50.9
So the answer is 50.9 or Choice 3
Solve the inequality and enter your solution as an inequality comparing the
variable to a number.
x-30 > 30
Answer:
[tex]x > 60[/tex]
Step-by-step explanation:
[tex]x-30 > 30[/tex]
[tex]x > 60[/tex] (add 30 onto both sides of the inequality)
Please help me with this question!!!!,
[tex] \qquad \qquad \bf \huge\star \: \: \large{ \underline{Answer} } \huge \: \: \star[/tex]
The contrapositive of the statement is False.
Because we already know, Cube is a 3 - dimensional shape with 6 faces, all its sides are equal and all faces are congruent.
But the contrapositive of the statement is not true, because not only cube has six faces.
There are other 3 - D shapes that have 6 faces.
[tex] \qquad \large \sf {Conclusion} : [/tex]
The contrapositive of the statement is false.
a) An adult who visited a therapist during the past year is randomly selected. What is the probability this adult used non-prescription antidepressants? Round your answer to decimal places.
(b) What is the probability that an adult visited a therapist during the past year, given that he or she used non-prescription antidepressants? Round your answer to decimal places.
The probability that this adult used non-prescription antidepressants is 0.78.
How to calculate the probability?Based on the information given, the following can be deduced:
Let A = event where adults visit therapist.
Let B = event where adults used non prescription antidepressants.
P(A) = 0.27
P(B) = 0.46
P(A n B) = 0.21
The probability that a randomly selected adult who visited the therapist used non-prescription antidepressants will be:
= 0.21/0.27
= 0.78
The probability that an adult visited a therapist during the past year, given that he or she used non-prescription antidepressants will be:
= 0.21/0.46
= 0.46
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