[tex] {\qquad\qquad\huge\underline{{\sf Answer}}} [/tex]
Let's solve ~
By using distance formula :
[tex]\qquad \sf \dashrightarrow \: \sqrt{(x_2 - x_1) {}^{2} + (y_2 - y_1) {}^{2} } [/tex]
[tex]\qquad \sf \dashrightarrow \: \sqrt{(4 - ( - 1)) {}^{2} + (4 - ( - 1)) {}^{2} } [/tex]
[tex]\qquad \sf \dashrightarrow \: \sqrt{(4 + 1) {}^{2} + (4 + 1) {}^{2} } [/tex]
[tex]\qquad \sf \dashrightarrow \: \sqrt{2(5) {}^{2} } [/tex]
[tex]\qquad \sf \dashrightarrow \: 5 \sqrt{2 }\: \: units[/tex]
The distance between two points [tex]\rm{A(x_1,y_1)} [/tex] and [tex]\rm{B(x_2,y_2)}[/tex] is given by the formula,
[tex] \rm{AB= \sqrt{(x_2-x_1)^2+(y_2-y_1)^2} }[/tex]
Proof:
[tex] \rm{Let \: X'OX \: and \: YOY' \: be \: the \: z-axis \: and \: y-axis \: respectively. Then, O \: is \: the \: origin.}[/tex]
[tex] \rm{Let \: A(x_1,y_1) \: and \: B(x_2,y_2) \: be \: the \: given \: points.}[/tex]
[tex] \rm{Draw \: AL \perp \: OX, BM \perp \: OX \: and \: AN \perp BM }[/tex]
Now,
[tex] \rm{OL=x_1,OM=x_2,AL=y_1 \: and \: BM=y_2}[/tex]
[tex]\rm\therefore{AN=LM=(OM-OL)=(x_2-x_1)}[/tex]
[tex] \: \: \: \: \rm{BN=(BM-NM)=(BM-AL)=(y_2-y_1)}[/tex]
[tex] \rm{In \: right \: angled \: \triangle ANB, by \: Pythagorean \: theorem,}[/tex]
We have,
[tex] \: \: \: \: \rm{AB^2=AN^2+BN^2}[/tex]
[tex] \rm{or,AB^2=(x_2-x_1)^2+(y_2-y_1)^2}[/tex]
[tex] \rm\therefore AB= \sqrt{(x_2-x_1)^2+(y_2-y_1)^2} [/tex]
The Given question,
Find the distance of AG if A (4,4) and G (-1,-1).
Solution,
The given points are A(4,4) and G(-1,-1).
Then,
[tex] \rm{(x_1=4,y_1=4) and (x_2=-1,y_2=-1)}[/tex]
We know that,
The distance formula,
[tex] \rm{AG= \sqrt{(x_2-x_1)^2+(y_2-y_1)^2} }[/tex]
[tex] \: \: \: \: \: \: \: \: = \sqrt{ {( - 1 - 4)}^{2} + {( - 1 - 4)}^{2} } [/tex]
[tex] \: \: \: \: \: \: \: \: = \sqrt{ {( - 5)}^{2} + {( - 5)}^{2} } [/tex]
[tex] \: \: \: \: \: \: \: \: = \sqrt{25 + 25} [/tex]
[tex] \: \: \: \: \: \: \: \: = \sqrt{50} [/tex]
[tex] \: \: \: \: \: \: \: \: = \sqrt{(2)(25)} [/tex]
[tex] \: \: \: \: \: \: \: \: = \sqrt{(2)(5)(5)} [/tex]
[tex] \: \: \: \: \: \: \: \: = \sqrt{(2)( {5}^{2}) } [/tex]
[tex] \rm \: \: \: \: \: \: \: \: = 5 \sqrt{2} \: units[/tex]
Answered by:
[tex]\frak{\red{moonlight123429}}[/tex]
A painter needs to measure the height from the ground to the base of a 2nd story window. He props his ladder against the base of the window. He finds the height from one rung of the ladder to the point on the ground below it, and the distance from that point to the base of the ladder. This is shown in the figure.
If XY = 8 inches, WY = 24 inches, and XZ = 48 inches, the height from the ground to the base of the window is inches.
The height from the ground to the base of the window is 16 inches.
What is the height from the ground to the base of the window is inches?The ladder and the wall of the window form a right angled triangle. A right angled triangle is a three-sided polygon. The square of the longest side of a right angled triangle is equal to the sum of the squares of the other two sides.
In order to determine the length from the ground to the window, the law of similar triangles would be used. The similar triangles are triangle WXY and triangle VXZ. It is expected that the length of the sides are proportional to each other.
XY / XZ = WY / VZ
(8 / 24) = WY / 48
WY = (8 X 48) / 24 = 16 inches
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Expand and simplify (2+√3)² - (2-√3)²
Answer:
8√3
I hope this helps you
A binary operation * is defined on the set of Real numbers,R by m*n=(√m +√n) (√m-√n).Find the values of P,if P*3=1
The value of P such that P*3=1 is 4
How to solve for P in the set?The set of Real numbers, R is given as
m*n=(√m +√n) (√m-√n).
The values of P, if P*3=1 is represented as:
P * 3=(√P +√3) (√P-√3).
The result of this operation is 1.
So, we have:
(√P +√3) (√P-√3) = 1
Apply the difference of two squares
P - 3 = 1
Add 3 to both sides
P = 4
Hence, the value of P such that P*3=1 is 4
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A plate of vegetables and white rice. jace is a vegetarian, eating at a local restaurant. he chooses a grilled tofu salad that includes vegetables. what change can he request to make his meal healthier? he can ask for the tomatoes to be left out. he can ask for brown rice instead of white rice. he can ask for his tofu to be fried instead of grilled. he can ask for fewer sprouts, peas, and cucumbers.
I’m stuck on this problem
The value of the f(-8) from the given f(x) is 1/53.
According to the statement
we have given that the value of f(x) and with the value of this we hav eto find the value of f(-8).
So, For this purpose,
The given value of f(x) :
The function f(x) is
f(x) = 1 / x^2 -11
Now we find the value of the f(-8) then
For this put Put x is -8 in the f(x) then the equation become
f(x) = 1 / x^2 -11
f(-8) = 1 / (-8)^2 -11
f(-8) = 1 / 64 -11
f(-8) = 1 / 53.
here the value becomes 1/53.
So, The value of the f(-8) from the given f(x) is 1/53.
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________ If an arc has measure 7π/4 radians, what is its measure in degrees?
________ What is 60° in radians?
If an arc has measure 7π/4 radians then it will be having 315 degrees and 60° in radian is π/3.
Given that arc has measure of 7π/4.
We are required to convert the measure from radian to degree measure.
Converting means chaning of units from one to another.
To convert 7π/4 into degrees we have to just put π=180 then we will get the value in degrees.
7π/4=7*180/4
=7*45
=315 degrees
Now we have to convert 60 degrees into radians.
60 degrees=60*π/180
=π/3
Hence if an arc has measure 7π/4 radians then it will be having 315 degrees and 60° in radian is π/3.
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What error did zacharias make? the –5 should be 5. the 52 should be –52. the 2 in the numerator should be –2. the 2 in the denominator should be –2.
The error made by zacharias in solving the quadratic equation 0 = -2x² + 5x - 3 using quadratic formula is; the 2 in the numerator should be –2.
Quadratic equationThere are four methods of solving quadratic equation. Namely;
Factorization methodCompleting the square methodGraphical methodFormula method0 = -2x² + 5x - 3
Using quadratic formulax = -b ± √b² - 4ac / 2a
where,
a = -2b = 5c = -3x = -b ± √b² - 4ac / 2a
x = -5 ± √5² - 4(-2)(-3) / 2(-2)
= -5 ± √25 - (24) / -2
= -5 ± √1 / -2
= -5/2 ± 1/2
= -5/2 - 1/2 or x = -5/2 + 1/2
= -5-1 / 2 or -5+1/ 2
x = -6/2 or -4/2
x = -3 or -2
Therefore, the solution to the quadratic equation is x = -3 or -2
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G
Which point is located at (-3.5.-4.5)?
Y
A
(1
-5-4-3-2-1
point A
point K
point R
4
-3-
2
10
-I ? ? + 4
2
3
2 3 4
en.
5
X
Please help
Thank you!
The given transformation is a reflection across the y-axis that changes the coordinates EFGH into E'F'G'H' as follows:
E(-4, -1) → E'(4, -1)
F(-2, -1) → F'(2, -1)
G(-1, -2) → G'(1, -2)
H(-1, -4) → H'(1, -4)
What is the transformation rule for reflection?The transformation rules for reflection are:
Reflection at y-axis: y = f(-x);
Reflection at x-axis: y = -f(x);
Calculation:The given polygon has four vertices EFGH.
Their coordinates are:
E(-4, -1), F(-2, -1), G(-1, -2), and H(-1, -4)
When the transformation rule: reflection across the y-axis is applied, the coordinates become:
y = f(-x); rule
For E(-4, -1), x-coordinate is -4. So, -(-4) = 4
⇒ E'(4, -1)
For F(-2, -1), x-coordinate is -2. So, -(-2) = 2
⇒ F'(2, -1)
For G(-1, -2), x-coordinate is -1. So, -(-1) = 1
⇒ G'(1, -2)
For H(-1, -4), x-coordinate is -1. So, -(-1) = 1
⇒ H'(1, -4)
Thus, the transformed coordinates are:
E(-4, -1) → E'(4, -1)
F(-2, -1) → F'(2, -1)
G(-1, -2) → G'(1, -2)
H(-1, -4) → H'(1, -4)
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A skateboard halfpipe is being designed for a competition. the halfpipe will be in the shape of a parabola and will be positioned above the ground such that its focus is 40 ft above the ground. using the ground as the x-axis, where should the base of the halfpipe be positioned? which equation best describes the equation of the halfpipe?
The equation of the halfpipe is Option A , (0, 20); Y equals one over eighty times x squared plus 20.
The equation of the halfpipe is Y = X²/80 +20.
What is parabola ?
A parabola is the set of points in a plane that are the same distance from a given point and a given line in that plane. The given point is called the focus, and the line is called the directrix. The midpoint of the perpendicular segment from the focus to the directrix is called the vertex of the parabola.The equation of parabola is given by
(X-h)² = 4p(Y-k)²
In this case h = 0
So we get
Y = X²/4P +k
Focus point is (h, p+k) , (p+k) = 40
Hence h, k = (0,20)
P = 40-k = 20
Equation Y = X²/80 +20
Therefore, the equation of the halfpipe is Y = X²/80 +20
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The complete question is -
A skateboard halfpipe is being designed for a competition. The halfpipe will be in the shape of a parabola and will be positioned above the ground such that its focus is 20 ft above the ground. Using the ground as the x-axis, where should the base of the halfpipe be positioned? Which equation best describes the equation of the halfpipe?
(0, 20); y equals one over eighty times x squared plus 20
(0, 20); y equals one over eighty times x squared minus 20
(0, 10); y equals one over forty times x squared plus 10
(0, 10); y equals one over forty times x squared minus 10
Suppose you invested $1000 every 3 months over a 15 year period. If money earns an annual rate of 6.5% compounded quarterly, how much would be available at the end of the time period. How much is the interest earned? Show all your calculations
Using the future value formula, it is found that $100,336.67 will be available at the end of the time period, of which $40,336.67 was of interest earned.
What is the future value formula?The future value formula is given by:
[tex]F = P\frac{(1 + i)^n - 1}{i}[/tex]
In which:
P is the periodic payment.i is the equivalent yearly interest rate.n is the number of periods.For this problem, considering the situation described, especially the quarterly compoundings, the parameters are given as follows:
P = 1000, i = 0.065/4 = 0.01625, n = 15 x 4 = 60.
Hence the amount available is given by:
[tex]F = P\frac{(1 + i)^n - 1}{i}[/tex]
[tex]F = 1000\frac{(1 + 0.01625)^{60} - 1}{0.01625}[/tex]
F = $100,336.67
The amount deposited was:
15 x 4 x $1000 = $60,000.
Hence the amount earned in interest was:
$100,336.67 - $60,000 = $40,336.67
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What is the probability distribution of X when X~B(1,1/25)?
P(X= 0) = 0.96
P(X= 1) = 0.04
P(X= 0) = 0.75
P(X= 1) = 0.25
P(X= 0) = 0.04
P(X= 1) = 0.96
P(X= 0) = 0.25
P(X= 1) = 0.75
The probability distribution of X when X~B(1,1/25) is (Option A)
P(X= 0) = 0.96P(X= 1) = 0.04See the explanation below.
What is the explanation to the above solution?Given X~B(n,p)
P(x=1) = C¹ₙ * P¹ * (1-P)ⁿ⁻¹ (n≥1)
Thus, X~B [1, 1/25]
1/25 = 0.04
hence, p(x=0)
= C⁰₁ * 0.04⁰ (1 - 0.04)¹
= 0.96
P (x=1)
= C¹₁ 0.04¹ (1-0.04)⁰
= 0.04
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A computer chip factory produces 520 chips in 13 minutes. at this rate, how many chips does it produce in 1 hour?
n January 1989, the temperature in Nome, Alaska dropped to −49° F. Would the gas in the driver's truck have remained in liquid form so he could have driven on this day? Why or why not?
Answer: The gas would not have remained liquid
Step-by-step explanation:
Since the freezing point of gasoline starts at -40°F, and the temperature that day was -49°F, we can conclude that the gasoline would not have remained liquid
A certain amount of concentrate is mixed with water to create a juice. The table shows the amount of concentrate, in ounces remaining, in the original container after x ounces of juice are made. How many ounces of concentrate were in the original container before any juice was made? PLEASE HELP ME
TheThe number of ounces of concentrate that were in the original container before any juice was made is 320 ounces and the number of juice that can be made using the whole container of concentrate is 1600 ounces.
Number of ouncesA. Let assume the two are linear relationship
Let y represent juice made
Let x represent the concentrate remaining
Hence:
Slope=600-200/200-280
Slope=400/-80
Slope=-5
y=-5x+b
Where:
x=200
y=-5(200)+b=600
y=-1000+b=600
b=1600
Thus,
y=-5x+1600
y=0. -5x+1600=0
-5x=-1600
divide both side by 5x
x=-1600/-5
x=320 ounces
B. x=0
y=1600 ounces
Therefore the number of ounces of concentrate that were in the original container before any juice was made is 320 ounces and the number of juice that can be made using the whole container of concentrate is 1600 ounces.
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help pls i will give brainleast no links
Answer: 100 square cm
Step-by-step explanation: the triangle is 33 cm and the big rectangle is 9x7 square cm. There is a small square that is 2x2 =4 cm so the total is 33 +63 + 4 which is 100 cm.
Answer: 104
Step-by-step explanation:
area of trangle =33 because 6*11/2=33
area of rectangle 9*7=63
area of rectangle 2*2=4
33+63+4=100^2
Circle X is shown. Line segments W X and Y X are radii. Tangents W Z and Y Z intersect at point Z outside of the circle. Arc W Y is 109 degrees.
What is the measure of angle WZY?
54.5°
71°
125.5°
180°
From the calculations below, it is seen that the measure of angle WZY is gotten to be 71°
How to find the angle from a circle tangent?The lines ZY and ZW are tangents to the attached circle which is centered at x.
From the properties of circles, the tangents (ZY and ZW) from an external point to the circle make an angle of 90° to the radius of the circle. i.e. XW and ZY respectively.
From the attached diagram, we see that angles ZWX and ZYX are 90° each. Since WXYZ is a quadrilateral the sum of its internal angles is 360°.
Out of the four angles of the quadrilateral, the three angles are seen as 109°, 90°, 90°. Therefore, the fourth angle is;
∠WZY = 360° - (90° + 90° + 109°)
∠WZY = 360° - 289°
∠WZY = 71°
Therefore, we can conclude from the calculations above that the measure of angle WZY is gotten to be 71°
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Answer: B. 71°
Step-by-step explanation: TRUST ME!!! Answer is correct on Edge!!! :)
I got it right!
Find the general solution of the given second-order differential equation. 12y'' − 5y' − 3y = 0
The general soultion of the given differential equation 12y'' − 5y' − 3y = 0 is
y = [tex]c_{1}e^{\frac{-1}{3}x } +c_{2}e^{\frac{3}{4} x}[/tex].
According to the given question.
We have a differential equation
[tex]12y^{"} -5y^{'} -3y = 0[/tex]
The above equation can be written as
[tex](12D^{2} -5D -3)y = 0[/tex]
The auxillary equation for the above differential equation is
[tex]12m^{2} -5m-3 = 0[/tex]
[tex]\implies 12m^{2} -9m+4m -3 = 0[/tex]
⇒ 3m(4m - 3) +1(4m - 3) = 0
⇒ (3m + 1)(4m -3) = 0
⇒ m = -1/3 or 3/4
Therefore,
[tex]C.f = c_{1}e^{\frac{-1}{3}x } +c_{2}e^{\frac{3}{4} x}[/tex]
Here, P.I = 0
As we know that the general solution of the differential equation is given by
y = PI + CF
Thereofre, the general soultion of the given differential equation 12y'' − 5y' − 3y = 0 is
y = [tex]c_{1}e^{\frac{-1}{3}x } +c_{2}e^{\frac{3}{4} x}[/tex].
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Helpppppp show your work
Answer:
-5/3
Step-by-step explanation:
Do PEMDAS
8 - 11 = -3
-3 ^ 3 = -27
-(-27) = 27
I-14I = 14
3 x 14 = 42
27 - 42 = -15
2^4 = 16
16 - 7 = 9
-15/9 = -5/3
For Exercises 11-15, sketch the locus of points in a plane that satisfy the
given conditions.
14. equidistant from both points
A and B and points C and D
B C
A
O
D
15. equidistant from the sides of
LJKL and on OC
L
A locus is a set of a given point that satisfies certain/ stated conditions. This could be in the form of a curve, circle, or line. The required construction is wherewith attached to this answer.
Construction is a topic that requires following some steps to complete or solve a given question. This majorly requires the use of materials and instruments for drawing the expected figure.
A locus is a set of a given point that satisfies some given conditions. This could be in the form of a curve, circle, or line satisfying the required condition(s).
An equidistant locus is one that is at the same distance to a reference point or a line.
In question 14, the required locus should be at the same distance to points A, B, C, and D.
In question 15, the required locus should be at the same distance to sides KJ and KL. This should pass through point C.
The required construction is herewith attached to this answer.
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What number could be added to 0.40 ml for the level of precision to be 0.01 ml? check all that apply 0.2 ml 0.154 ml 6 ml 2.02 ml 8.8331 ml
The following volumes of fluid can be added to 0.40 mL of liquid for the level of precision of 0.01 mL: a) 0.2 mL, b) 6 mL, c) 2.02 mL. The amounts 0.154 mL and 8.8331 mL are not possible due to given level of precision.
What is the amount of liquid to be added to sample according to a given precision?
If the measuring has a level of precision of 0.01 ml, this means that the measured quantities are only sensible to the smallest hundreths. Any change less than 0.01 ml and any decimal less than a hundreths are "invisible" for measuring processes.
Hence, the following volumes of fluid can be added to 0.40 mL of liquid for the level of precision of 0.01 mL: a) 0.2 mL, b) 6 mL, c) 2.02 mL. The amounts 0.154 mL and 8.8331 mL are not possible due to given level of precision.
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Answer:
B,D,E
Step-by-step explanation:
Find the indicated maximum or minimum value of f subject to the given constraint. maximum: f(x,y,z)=x2y2z2; x2 y2 z2=4
The indicated maximum or minimum value of f is subject to the given constraint maximum is 125/27.
An instance of a constraint is the fact that there are only such a lot of hours in a day to perform things. Embarrassed reserve or reticence; awkwardness. One that restricts, limits, or regulates; a take a look at.
A constraint is something that limits or controls what you can do. Their decision to abandon the trip was made due to monetary constraints. Water shortages in the location can be the primary constraint on development. Synonyms: restriction, issue, lessen, rein greater Synonyms of constraint.
Constraints are used to limit the kind of records which can move right into a desk. This guarantees the accuracy and reliability of the facts inside the table. If there's any violation between the constraint and the facts motion, the motion is aborted. Constraints can be column stage or desk level.
From &22 = x²y 2
2
Given 2²+7+2=5
= <**,4),2=>
By Logange's multijet
(2643805 = 12'aresta
Mithaling by by and
and y
x²²* = P ←
: +(1,2,2) = $
= 125
279
The maximum value is 12r
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A school counselor tests the level of depression in fourth graders in a particular class of 20 students. The counselor wants to know whether the kind of students in this class differs from that of fourth graders in general at her school. On the test, a score of 10 indicates severe depression, while a score of 0 indicates no depression. From reports, she is able to find out about past testing. Fourth graders at her school usually score 5 on the scale, but the variation is not known. Her sample of 20 fifth graders has a mean depression score of 4.4. Use the .01 level of significance.
1. The counselor calculates the unbiased estimate of the population's variance to be 15. What is the variance of the distribution of means?
A) 15/20 = 0.75
B) 15/19 = 0.79
C) 152/20 = 11.25
D) 152/19 = 11.84
2. Suppose the counselor tested the null hypothesis that fourth graders in this class were less depressed than those at the school generally. She figures her t score to be -.20. What decision should she make regarding the null hypothesis?
A) Reject it
B) Fail to reject it
C) Postpone any decisions until a more conclusive study could be conducted
D) There is not enough information given to make a decision
3. Suppose the standard deviation she figures (the square root of the unbiased estimate of the population variance) is .85. What is the effect size?
A) 5/.85 = 5.88
B) .85/5 = .17
C) (5 - 4.4)/.85 = .71
D) .85/(5 - 4.4) = 1.42
1. The variance of the distribution of means option A) 15/20 = 0.75
2. The decision that counselor should make regarding the null hypothesis is that: option "Fail to reject it"
3. The effect of the size is: option c: (5 − 4.4)/.85 = .71
What is the variance about?Note that:
Sample size = 20.
Note that for us to be able to get the answer in question one, we have to divide the unbiased estimate for the population variance by the use of 20 so that we can be able to get our unbiased estimate for the variance: And as such;
15/20 = 0.75.
The term fail to reject implies that the null hypothesis is one that has not been disproven or wrong and therefore the use of the term "failure to reject." It is one that should not be taken with acceptance.
Therefore, 1. The variance of the distribution of means option A) 15/20 = 0.75
2. The decision that counselor should make regarding the null hypothesis is that: option "Fail to reject it"
3. The effect of the size is: option c: (5 − 4.4)/.85 = .71
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Quick algebra 1 question for 10 points!
Only answer if you know the answer, quick shout-out to tariqareesha2 and MrBrainly, tysm for the help!
[tex]y = - 5x + n \\ [/tex]
( -1 , -2 ) satisfies the equation of y[tex] - 2 = - 5( - 1) + n \\ - 2 = 5 + n \\ n = - 7[/tex]
[tex]y = - 5x - 7 \\ 5x + y = - 7[/tex]
Option 2Answer:
○ [tex]5x + y = -7[/tex]
Step-by-step explanation:
The formula for forming the equation of a line given a point and a slope is:
[tex]\boxed{y- y_1 = m(x - x_1)}[/tex],
where:
m = slope (-5)
[tex]y_1[/tex] = y-coordinate of point (-2)
[tex]x_1[/tex] = x-coordinate of point (-1).
Substituting these values into the formula:
[tex]y - (-2) = -5(x - (-1))[/tex]
⇒ [tex]y + 2 = -5(x + 1)[/tex]
⇒ [tex]y + 2 = -5x -5[/tex] [expanding the brackets]
⇒ [tex]y = -5x -5 - 2[/tex] [subtracting 2 from both sides]
⇒ [tex]y = -5x - 7[/tex]
⇒ [tex]5x + y = -7[/tex] [adding [tex]5x[/tex] to both sides]
This means that the second option is correct.
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THIS IS REALLY IMPORTANT I NEED IT DONE BY TODAY PLEASE
Answer:
15. 155°
16. 115°
Step-by-step explanation:
15.
Use the big triangle.
At the top, the supplement of 60° is 120°.
The angle measuring 120° and the angle measuring 35° are the remote interior angles to exterior angle x.
120° + 35° = x
x = 155°
16.
See picture below.
x = 115°
Answer:
15) x = 155°
16) x = 115°
Step-by-step explanation:
The theorem that relates an exterior angle of a triangle to the opposite (remote) interior angles is helpful for these problems. It says the exterior angle is equal to the sum of the remote interior angles.
15)
Remove the altitude line and consider the interior angle of the triangle next to the exterior angle marked 60°. That interior angle will be ...
180° -60° = 120°
Then the angle we just found and the one marked 35° are "remote" to the exterior angle marked x. The theorem cited at the beginning tells us ...
x = 35° +120°
x = 155°
16)Extend the left side of the "parallelogram" (the side with the arrow) upward until it meets the top horizontal line. This cuts off a triangle with an exterior angle marked x, an interior angle marked 50°, and another remote interior angle at the top edge of that triangle.
The opposite angles of a parallelogram are congruent, so the external angle to the triangle at the top edge will be x, and the adjacent interior angle in the triangle will be (180° -x).
The exterior angle (x) is equal to the sum of the remote interior angles (50° and (180° -x)), so we have ...
x = 50 +(180 -x)
2x = 230 . . . . . . add x, simplify
x = 115 . . . . . . . divide by 2
The measure of the angles marked x is 115°.
Explain this diagram.
The shape that we have here is sued to show the infinite geometric progression.
What is geometric progression?This is the sequence of numbers that has all the other values in the sequence gotten by the multiplication of a certain factor
In this question or the shape we can see that the triangle is made up of smaller other triangles embedded in it.
The area of the traingle that is in the red color is seen to have been made up of 1/3 of the total triangles that we have in the shape. This can be seen to be similar as the triangles that are represented by the green and the blue color.
Putting a lot of triangles inside one big triangle gives up a pictorial diagram on how to add infinite amount of things up.
Read more on triangles here:
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2- (ITA-2007) Dentre 4 moças e 5 rapazes deve-se formar uma comissão de 5 pessoas com, pelo menos , 1 moça e 1 rapaz. De quantas formas distintas tal comissão poderá ser formada?
Answer:
Step-by-step explanation:
Solve this equation. Make sure your answer is
fully reduced.
7/8 + x = 1/4
The solution for the given equation is -5/8. By using simple algebraic operations, the equation is solved.
How a linear equation is solved?A linear equation is represented by ax + b = 0. The solution for this equation is
ax + b = 0
⇒ ax = -b
⇒ x = -b/a
Calculation:The given equation is
7/8 + x = 1/4
On simplifying,
x = 1/4 - 7/8
⇒ x = -5/8
Therefore, the solution of the given equation is -5/8.
Learn more about solving an equation here:
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42. There are eight squares on each side of a chessboard. How many squares are on a chessboard? Write an expression in exponent form then evaluate.
Answer:
Number of the squares on chessboard = 64
Exponent form = [tex]8^{2}[/tex]
Step-by-step explanation:
8 x 8 = 64
exponent form of of the chessboard
= [tex]8^{2}[/tex]
16. a) In the given figure, OB bisects ABC and OC bisects ACB, prove that BOC - BAC = ABO+ACO.
Answer:
Points ABC and points OBC form two separate triangles. Triangle ABC is made up of angles BAC, ABC, ACB, while triangle OBC is made up of angles BOC, OBC, OCB. Since interior angles of triangles add up to 180 degrees, m<BAC + m<ABC + m<ACB = 180 and m<BOC + m<OBC + m<OCB = 180. 180 is equal to 180, so m<BAC + m<ABC + m<ACB = m<BOC + m<OBC + m<OCB.
Since OB bisects <ABC and OC bisects <ACB, m<ABO = m<OBC and m<ACO = m<OCB. We can also say that m<ABC = 2m<ABO and m<ACB = 2m<ACO. Substitute and simplify the equation.
m<BAC + m<ABC + m<ACB = m<BOC + m<OBC + m<OCB
m<BAC + 2m<ABO + 2m<ACO = m<BOC + m<ABO + m<ACO
m<ABO + m<ACO = m<BOC - m<BAC