Step-by-step explanation:
The sum of co-interior angle = 180°
Now,
2x + 7x = 180°
9x = 180°
x = 180° ÷ 9
x = 20°
Answer:
x = 20
Step-by-step explanation:
Co-interior angles (also called same-side interior angles) are two angles that are on the same side of the transversal and on the interior of (between) the two parallel lines.
Same-side interior angles theorem: If two parallel lines are cut by a transversal, then the same side interior angles are supplementary (add up to 180º).
Therefore, if 2x and 7x are co-interior:
⇒ 2x + 7x = 180
⇒ 9x = 180
⇒ x = 20
Which ordered pair would form a proportional relationship with the point graphed below?
(–40, 20)
(–10, –20)
(15, –30)
(5, –15)
Answer:
(c) (15, -30)
Step-by-step explanation:
A proportional relationship has the equation ...
y = kx
The value of the constant of proportionality is the ratio of y to x:
k = y/x = 40/-20 = -2
__
The point that is on the line y = -2x is the point (15, -30).
If v is the circumcenter of pqr ,pr =46 ,tv=15,and vr=25 find each measure
Answer:
1. a) SR = 23
b) QV = 25
c) QT = 20
d) PQ = 40
e) VS = 4·√6
2. a) LH = 16
b) EL = 2·√185
c) JG = 30
d) EK = 22
e) KG = 30
3. a) XT = 37
b) TZ = 34
c) ZW = 17
d) XZ = 21
e) SY = 69
Step-by-step explanation:
The circumcenter ΔPQR is the center of the circle that circumscribes ΔPQR
The length of the radius of the circle ≡ VR = VP = QV = 25
a) Given that VR ≅ VP - Radius of circumcircle
VS ≅ VS Reflective property
∠VPS ≅ ∠VRS - Base angles of an isosceles triangle
Right triangle VPS ≅ Right triangle VRS -Hypotenuse and one Leg HL congruency
Therefore, SR ≅ PS -Corresponding parts of congruent triangles are congruent CPCTC
SR + PS = PR = 46
SR + PS = SR + SR = 2·SR = 46
∴ SR = 46/2 = 23
b) QV = VR = 25 = Radius of circumcircle of ΔPQR -Given V = center and Q = vertices of the triangle circumscribed by the circle referred to in the question
c) QT = √(QV² - TV²) = √(25² - 15²) = √400 = 20
d) TV ≅ TV - Reflexive property of congruency
ΔTQV ≅ ΔTVP - Hypotenuse and one Leg (HL) congruency
QT ≅ TP -Corresponding parts of congruent triangles are congruent CPCTC
PQ = QT + TP Given
∴ PQ = QT + QT since QT = TP
PQ = 2·QT = 2 × 20 = 40
e) VS = √(VR² - SR²) = √(25² - 23²) = √96 = 4·√6
2. The incenter is the center of the incircle of ΔEFG
a) LH = LK = JL = 16 -Radius of incircle of ΔEFG
b) EL = Hypotenuse of right triangle LHE = √(LH² + EH²) = √(16² + 22²) = √740 = 2·√185
c) JG = Leg length of right triangle JGL = √(LG² - JL²) = √(34² - 16²) = √900 = 30
d) EK = Leg length of right triangle LKE = √(EL² - LK²) = √(740 - 256) = 22
e) KG = Leg length of right triangle LKG = √(LG² - LK²) = √(34²- 16²) = √900 = 30
3. Point Z id the centroid of ΔRST
a) XT = XS - point X on ST bisected by median line RX
ST = XT + XS = XT + XT = 2.XT = 74
XT = 74/2 = 37
b) TZ = 2/3×TW - Length from a vertex to the centroid on a median line is equal to two third the length of the median line
TZ = 2/3×51 = 34
c) TZ + ZW = TW
∴ ZW = TW - TZ = 51 - 34 = 17
d) RZ = 42 = 2/3×RX - Length from a vertex to the centroid on a median line is equal to two third the length of the median line
∴ RX = 3/2×42 = 63
RZ + XZ = RX - Given
XZ = RX - RZ = 63 - 42 = 21
e) SZ = 2/3×SY - Length from a vertex to the centroid on a median line is equal to two third the length of the median line
SZ + ZY = SY
∴ ZY = SY - SZ = SY - 2/3×SY = 1/3×SY = 23
Which gives;
SY = 3 × 23 = 69.
The solid below is dilated by a scale factor of 3. Find the volume of the solid created
upon
dilation.
The volume of the solid created upon dilation bythe scale factor of 3 is 5832 units³.
What is the volume of the dilated solid?An image is dilated if the dimensions of the image is resized in a way that does not change the shape of the image. When an image is dilated, it is made larger.
Dimensions of the dilataed solid = 6 x 3 = 18
Volume = 18³ = 5832 units³
To learn more about dilation, please check: brainly.com/question/3457976
PLS HELP I WILL GIVE BRAINLESt TO THE PERSON WHO SOLVES ALL OF THE CORRECTLY
Answer:
m^4 - 225c^10 = (m^2 - 15c^5 )(15c^5 + m^2)
4.8xy + 36y^2 + 0.16x^2 = (6y + 0.4x)^2
1) Find the slope of the line
2) find the slope between the two points
help please, thank you
Answer:
1 = 3/2
2 = -1/14
Step-by-step explanation:
The equation for the slope of a line is [tex]\frac{y_{2}-y_{1} }{x_{2}-x_{1} }[/tex] (difference in Y divided by the difference in X) or simply just Rise/Run.
For the first one, we have to pinpoint two points on the graph. There's one point placed on the x-axis 2 units away from the origin (2,0) and one four units to the right and 3 units up from the origin (4,3). Since it's on a graph, the easiest way to calculate it is by counting the units up and then right from (2,0) to (4,3). You can count that (4,3) is 3 units up and 2 units right from (2,0). Since slope is Rise/Run, the slope is 3/2.
For the second one, you can use the equation [tex]\frac{y_{2}-y_{1} }{x_{2}-x_{1} }[/tex]. The Y of the second point is 2, and the Y of the first point is 1. The X of the second point is -17, and the X of the first point is -3.
You can plug all 4 numbers in to get (2-1)/(-17- -3)
2-1 = 1 and -17 - -3 = -14. So your slope is 1/-14 or -1/14.
Please help me with 20 through 22 please I really appreciate it! Thank you very much!
Answer:
20. 2x+y
21. 4
22. x+y
Step-by-step explanation:
20. 9x+2y - x-2y find your LCM
4 4
=(9x+2y)-(x-2y) clear bracket
4
=9x+2y-x+2y collect terms
4
=9x-x+2y+2y
4
=8x+4y factorize
4
=4(2x+y)
4
=2x+y
with this, you will understand the following
21. 4x + 8y
x+2y x+2y
=4x+8y
x+2y
=4(x+2y)
x+2y
=4
22. 2x-y + 2x+5y
4 4
=2x-y+2x+5y
4
=4x+4y
4
=4(x+y)
4
=x+y
Write the quadratic equation whose roots are 1 and −5, and whose leading coefficient is 4.
Answer:
Standard Form: y = 4(x-1)(x+5)
Step-by-step explanation:
4 is the leading coefficient, so it should go in front. When making a standard quadratic equation, you must do the opposite for each of the roots (negative to positive, positive to negative.)
if you’re asking for a general form quadratic equation, then sorry, I am unable to help you with that :(
U is the midpoint of TV and S is the midpoint of RT.
If RV=w and SU=w–30, what is RV?
Answer:
60
Step-by-step explanation:
By the triangle midsegment theorem, 2(SU)=RV.
2(w-30)=w, meaning w=60.
So, RV=60 as well
HELP PLEASE FOR NUMER 3 and 4 PLEAESE ASAP ANI WILL GIVE BRANILESS FOR THE FIRST PERSON
Wheres the ? n answers at for #3 n #4
Evaluate the triple integral. X dv, where e is bounded by the paraboloid x = 4y2 4z2 and the plane x = 4. E
The triple integral that is bounded by a paraboloid x = 4y2 4z2 given as 16.762
Parabloid, x = 4y² + 4z²
plane x = 4
x = 4y² + 4z²
x = 4
4 = 4y² + 4z²
4 = 4 (y² + z² )
1 = y² + z²
from polar coordinates
y = r cos θ
z = r sin θ
r² = y² + z²
The limits of the integral0 ≤ θ ≤ 2π
4r² ≤ x ≤ 4
0 ≤ r ≤ 1
[tex]\int\limits\int\limits\int\limits {x} \, dV = \int\limits^1_0\int\limits^a_b\int\limits^c_d {x} \, dx ( rdrdz)[/tex]
where
a = 4
b = 4r²
c = 2r
d = 0
The first integral using limits c and d gives:
[tex]2pi\int\limits^1_0\int\limits^a_b {xr} \, dx[/tex]
The second integral using limits a and b
[tex]pi\int\limits^1_0 {16 } } \, rdr - pi\int\limits^1_0 {16r^{5} \, dx[/tex]
[tex]16pi\int\limits^1_0 { } } \, rdr - 16pi\int\limits^1_0 {r^{5} \, dx[/tex]
[tex]16pi\int\limits^1_0 { } } \, [r-r^{5}]dr[/tex]
The third integral using limits 1 and 0 gives: 16.762
Read more on Triple integral here: https://brainly.com/question/27171802
The triple integral that is bounded by a paraboloid x = 4y2 4z2 given as 16.762
What is integration?Integration is defined as adding small parts to form a new significant part.
Parabloid, x = 4y² + 4z²
plane x = 4
x = 4y² + 4z²
x = 4
4 = 4y² + 4z²
4 = 4 (y² + z² )
1 = y² + z²
from polar coordinates
y = r cos θ
z = r sin θ
r² = y² + z²
The limits of the integral
0 ≤ θ ≤ 2π
4r² ≤ x ≤ 4
0 ≤ r ≤ 1
[tex]\int\int\intxdV = \int_0_1\int_b_a\int_d_cxdx(rdrdz)[/tex]
where
a = 4
b = 4r²
c = 2r
d = 0
The first integral using limits c and d gives:
[tex]2\pi\int_0^1\int_b^axydx[/tex]
The second integral using limits a and b
[tex]\pi \int_0^116rdr-\pi\int_0^116r^5dx[/tex]
[tex]16\pi \int_0^1rdr-16\pi\int_0^1 r^5dx[/tex]
[tex]16\pi\int_0^1[r-r^5]dr[/tex]
The third integral using limits 1 and 0 gives: 16.762
Read more on Triple integral here:
brainly.com/question/27171802
#SPJ4
A quantity with an initial value of 200 grows continuously at a rate of 4% per second.
What is the value of the quantity after 1.55 minutes, to the nearest hundredth?
The growth of the quantity is an illustration of an exponential function
The value of the quantity after 1.55 minutes is 76759.22
How to determine the amount of the quantity?The given parameters are:
Initial value, a = 2000
Rate, r = 4%
An exponential growth function is represented as:
y = a(1 + r)^x
Substitute the value in the equation
y = 2000(1 + 4%)^x
After 1.55 minuted, x = 1.55 * 60
So, we have:
y = 2000(1 + 4%)^(1.55 * 60)
Evaluate the expression
y = 76759.22
Hence, the value of the quantity after 1.55 minutes is 76759.22
Read more about exponential functions at:
brainly.com/question/24077767
Answer:
Step-by-step explanation:
9398.61
Are the base angles of an isosceles triangle always congruent?
Answer: Yes
Step-by-step explanation:
If you draw the altitude of an isosceles triangle from the vertex angle, then the two triangles formed are congruent, meaning the base angles are congruent by CPCTC.
Yes, the base angles of an isosceles triangle are congruent because in n isosceles triangle two of its sides are always congruent, and also angles opposite to congruent sides are congruent.
What is the isosceles triangle?An isosceles triangle is a triangle that has at least two sides of equal length.
When an altitude is drawn to the base of the isosceles triangle, it bisects the vertex angle. As it bisects the base, the two congruent triangles are created.
An isosceles triangle with only two congruent sides, the congruent sides are called legs. The third side is called the base. The angle opposite the base is called the vertex angle, and the angles opposite the legs are called base angles.Hence, Yes, the base angles of an isosceles triangle are congruent because in n isosceles triangle two of its sides are always congruent, and also angles opposite to congruent sides are congruent.
To learn more about the isosceles triangle click the link given below.
https://brainly.com/question/27177888
#SPJ4
Pamela is 6 years younger than Jiri. The sum of their ages is 78 . What is Jiri's age?
 find the equation of the line that is parallel to the line Y equals 3X -6 and passes through the points (1 -8). Write the equation in point slope form
=====================================================
Parallel lines have the same slope.
So if the given line has a slope of 3, then the line parallel to it has the same slope (3)
Now, let's write the equation of the line in Point-Slope Form.
Remember, point-slope form looks like so:-
[tex]\bigstar{\underline{\boxed{\pmb{y-y1=m(x-x1)}}}[/tex]
Where
y₁ is the y-coordinate of the point that the line passes through
m is the slope
x₁ is the x-coordinate of the point that the line passes through
In this case,
y₁ is equal to -8
m is equal to 3
x₁ is equal to 1
Plug in the values:
[tex]\longrightarrow\sf{y-(-8)=3(x-1)}[/tex]
Simplify:
[tex]\longrightarrow\sf{y+8=3(x-1)}[/tex]
and we're done!
=========================================================
note:-Hope everything is clear; if you need any more explanation/clarification, kindly let me know, and I will comment and/or edit my answer :)
What is the surface area of each figure 11 m 7 m 6 m?
Answer:
hi, I'm glad to help! 185
Step-by-step explanation:
11*7=77
11*6=66
6*7=42
77+66+42=185
3
14) There are seven million, eight hundred and fifty-four thousand,
three hundred and eight people in a country. i lleda
Round this number to the nearest ten thousand people.
Answer:
7,854,000
because the 308 people would have to be at least 500 to round up to 7,855,000
What is the volume of a sphere with a diameter of 7.5 cm, rounded to the nearest tenth of a cubic centimeter?
Answer:
V≈220.89cm³
Step-by-step explanation:
Answer: 220.9
4/3 π(3.75)^3=220.9
find the rate of interest.
Rs.8800,T=3.5years,I=Rs.2618
Answer:
Rate is 8.5%
Step-by-step explanation:
Step 1: Write the given terms
Principal (p)=Rs8800
Rate(r)=?
Time(t)=3.5 years
Interest=Rs2618
Step 2: Write the formula for calculating Simple interest
[tex]i = \frac{prt}{100} [/tex]
Step 3: Make r the subject of the equation
[tex]by \: cross \: multiplication \\ 100i = prt \\ divide \: both \: sides \: by \: pt \\ r = \frac{100i}{pt} [/tex]
Step 4: Find the value of r by substituting the values in step 1
[tex]r = \frac{100 \times 2618}{8800 \times 3.5} \\ r = \frac{261800}{30800} \\ r = 8.5[/tex]
Hence, the rate is 8.5%
need some help with these questions in the image
a. answer:_77
2_ (7 * 9) _ 16
2_ (63) _16
_61_16
_77
please help me with complement or supplement of an angles.
In the figure below, =m∠263°. Find m∠1.
Answer:
117
Step-by-step explanation:
This is an example of a supplementary angle, so in total it is 180 degrees. Subtract what we know angle 2 is, 63, and we are left with what angle 1 equals, which is 117.
Hope this helps! pls mark brainliest
Really need help, I’m trying to catch up in my math and get my marks back up before mid term..
Answer:
a) 12x + 22 b) 17[tex]x^{2}[/tex] - x
Step-by-step explanation:
Perimeter is the sum of the each side length.
The first example is a rectangle so the (4x+8) and the (2x+3) are doubled.
(4x+8) x 2 = 8x+16
(2x+3) x 2 = 4x + 6
12x+22
(6[tex]x^{2}[/tex] - 12x) + (2[tex]x^{2}[/tex] + x) + (9[tex]x^{2}[/tex] + 10x)
combine like-terms.
17[tex]x^{2}[/tex] - x
Answer:
12x + 22 for the rectangle, 17x^2 - x for the triangle
Step-by-step explanation:
The perimeter of a square/rectangle is equal to 2*width + 2*length
So for the rectangle, it would be 2*(4x + 8) + 2*(2x + 3)
This can be further simplified as 8x + 16 + 4x + 6
Which can be further simplified as 12x + 22
The perimeter of a triangle is equal to length if side one + length of side two + length of base
That would be (6x^2 - 12x) + (2x^2 + x) + (9x^2 + 10x)
Which becomes 8x^2 - 11x + (9x^2 + 10x)
17x^2 - x
Help fast please and thank you!
Answer: 1/4 .!
Step-by-step explanation: hope this helped :).
Lucy bought 4 pairs of pants for $21.79 each. She paid the cashier using as few $20 bills as necessary. How much change did she receive?
The amount of change Lucy receives if she paid with few $20 bills is $12.84
How to find amount of change to receiveCost of each pair of pants = $21.79Number of pairs of pants = 4Total cost of pants = $21.79 × 4
= $87.16
Amount paid to the cashier = few $20 billsIf the total cost of the pants exceeds $80, then she paid with 5 $20 bills
5 $20 bills = $100
Her change = $100 - $87.16
= $12.84
Learn more about cost:
https://brainly.com/question/2021001
1. Find the Area of the Sector:
2. Find the length of the missing side:
Answer:
1) 14.137 2)10
Step-by-step explanation:
area of sector is central angle / 360 times (pi)(r^2)
45/360 x pi (6^2)
1/8 x 36pi
14.137
3-4-5- right triangle. Or Pythagorean Theorem.
6^2 + 8^2 = c^2
c= 10
Marcy charges $3 to walk a small dog and $5 to walk a big dog. If Marcy walks 15 small dogs and 6 big dogs, how much money will she make?
Answer:
hee-hee!
Step-by-step explanation:
Marcy charges $3 to walk a small dog and $5 for a big dog.
She walks 15 small dogs and 6 big dogs.
We can use an expression that would show the problem:
3s + 5b
(s = small dogs & b = big dogs)
s = 15 | b = 6
3(15) + 5(6)
45 + 30 = 75
Marcy earns $75 of profit.
A principal of a large high school wants to estimate the true proportion of high school students who use the community's public library. To do so, he selects a random sample of 50 students and asks them if they use the community's public library. The 95% confidence interval for the true proportion of all students who use the community's public library is 0.25 to 0.34. If the principal had used a sample size of 200 students rather than 50 students, how would the length of the second interval compare to the original interval?
O It would be half as wide.
O It would be twice as wide.
O It would be one-fourth as wide.
O It would be four times as wide
ws
Considering the margin of error of a confidence interval, it is found that the correct option is:
It would be half as wide.
What is the margin of error of a confidence interval?It is modeled by:
[tex]M = z\frac{s}{\sqrt{n}}[/tex]
In which:
z is the critical value.s is the standard deviation.n is the sample size.From this, we get that the margin of error is inversely proportional to the square root of the sample size. Then, multiplying the sample size by 4, when it changes from 50 to 200, cuts the margin of error in half, making the interval half as wide.
More can be learned about the margin of error of a confidence interval at https://brainly.com/question/25890103
Answer: It would be half as wide
Step-by-step explanation:
If the principal had used a sample size of 200 students rather than 50 students, the length of the second interval would be half as wide compared to the original interval.
The width of a confidence interval is inversely proportional to the square root of the sample size. In this case, the sample size is multiplied by 4 (from 50 to 200), so the square root of the sample size is doubled. As a result, the width of the confidence interval is divided by 2, making it half as wide.
Therefore, the correct answer is: It would be half as wide.
In a class of 25 pupils, if 15 are females. Calculate the ratio of males : total
Answer:
2:5
Step-by-step explanation:
15 are female. 10 must be male.
Out of 25 pupils, 10 are male, so it's 10:25, or 2:5
solve pls brainliest
Answer:
[tex] 1 \frac{2}{3}\: liters [/tex]
Step-by-step explanation:
[tex]V_{soda}[/tex] in one bottle = 5/9 liters
No of bottles = 3
Total volume of soda
[tex] = \frac{5}{9} \times 3 \\ \\ = \frac{5}{3} \\ \\ = 1 \frac{2}{3} \: liters[/tex]
Please help me I will mark brainliest to whoever answers
Step-by-step explanation:
All Natural Number (1,2,3,4,5...) are integers
All Whole numbers (0,1,2,3,4...) are not natural numbers (1,2,3,4...)
All integers are rational numbers
All real numbers are not irrational numbers as real nimber contain both rational and irrational numbers hence it is false.
Hence statement 1 and statement 3 are true
Answer:
The answeris D
Step-by-step explanation:
All whole numbers are natural numbers; natural numbers are numbers we use for counting 1, 2, 3....and so on, so that makes them whole because thay have no fraction, or decimils.
please help me answer the question in the photo
Step-by-step explanation:
please mark me as brainlest
ans
[tex] \frac{3x}{x + 4} [/tex]