What shapes can the composite figure be decomposed into? Select two options.
A hexagon.
a rectangle and a triangle
a rectangle and two triangles
a square and two triangles
two rectangles
two trapezoids
Answer:
one of them is two trapezoids
Step-by-step explanation:
Consider the diagram and proof by contradiction.
Given: △ABC with ∠B ≅ ∠C
Prove: AB ≅ AC
Triangle A B C is shown. Angles A B C and B C A are congruent.
Which would prove that AB ≅ AC?
converse of the isosceles triangle theorem
substitution
definition of congruency
converse of the triangle parts relationship theor
The correct statement is that it is done by the converse of the triangle parts relationship theorem. The correct answer is option D.
The complete answer is given below and the figure is attached with the answer.
Consider the diagram and proof by contradiction.
Given: △ABC with ∠B ≅ ∠C
Prove: AB ≅ AC
It is given that ∠B ≅ ∠C. Assume AB and AC are not congruent. If AB > AC, then m∠C > m∠B by ________. If AC > AB, then m∠B > m∠C for the same reason. However, using the given statement and the definition of congruency, we know that m∠B = m∠C. Therefore, AB = AC and AB ≅ AC.
What is the missing reason in the proof?
the converse of the triangle parts relationship theorem
substitution
definition of congruency
the converse of the isosceles triangle theorem
What is the triangle?Triangle is a polygon that has three sides and three angles. The sum of the angle of the triangle is 180 degrees.
Isosceles triangle two sides of the triangle are equal and their opposite angles too.
Given
△ABC with ∠B ≅ ∠C
Prove that
AB ≅ AC
How to give a conclusion?
From the definition of the Isosceles triangle, it is proved that if ∠B ≅ ∠C Then AB ≅ AC. We know that if the length o the side increases then the opposite angle decreases. It is done by the converse of the triangle parts relationship theorem.
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SOMEONE PLEASE HELP ASAPP PLEASEEE
ILL GIVE BRAINLIEST AND POINTS!!!
If f(x) = 2x² + 1, what is f(x) when x = 3?
0 1
07
O 13
19
Answer:
f(x)=19
Step-by-step explanation:
2(3)²+1
2(9)+1
19
The value of function at x = 3 is,
⇒ f (3) = 19
What is mean by Function?A relation between a set of inputs having one output each is called a function. and an expression, rule, or law that defines a relationship between one variable (the independent variable) and another variable (the dependent variable).
Given that;
The function is,
⇒ f (x) = 2x² + 1
Now, Substitute x = 3 in above function,
⇒ f (x) = 2x² + 1
⇒ f (3) = 2 × 3² + 1
⇒ f (3) = 19
Thus, The value of function at x = 3 is,
⇒ f (3) = 19
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What is the equation of the parabola with focus (3,0) and directrix x= -3?
Check the picture below, so the parabola looks more or less like so, with a "p" distance of 3 and the vertex at the origin, keeping in mind the vertex is half-way between the focus point and the directrix.
[tex]\textit{horizontal parabola vertex form with focus point distance} \\\\ 4p(x- h)=(y- k)^2 \qquad \begin{cases} \stackrel{vertex}{(h,k)}\qquad \stackrel{focus~point}{(h+p,k)}\qquad \stackrel{directrix}{x=h-p}\\\\ p=\textit{distance from vertex to }\\ \qquad \textit{ focus or directrix}\\\\ \stackrel{"p"~is~negative}{op ens~\supset}\qquad \stackrel{"p"~is~positive}{op ens~\subset} \end{cases} \\\\[-0.35em] ~\dotfill[/tex]
[tex]\begin{cases} h=0\\ k=0\\ p=3 \end{cases}\implies 4(3)(x-0)~~ = ~~(y-0)^2\implies 12x=y^2\implies x=\cfrac{1}{12}y^2[/tex]
If you multiply four negative numbers, what is the sign of the product?
If you multiply five negative numbers, what is the sign of the product?
Based on the answers to these questions and the product rules, write a general rule for the sign of the product based on the number of
negative numbers in the expression.
Answer:
positive
Step-by-step explanation:
(-a) (-a) (-a) (-a) = a
(-a)(-a) = a
a (-a) = -a
-a (-a) = a --> positive sign
If you multiply four negative numbers, what is the sign of the product?
You can test this with numbers, the easiest with -1:
(-1)(-1)(-1)(-1) = (1)(-1)(-1) = (-1)(-1) = 1
General:
(-a)(-b)(-c)(-d) = abcd
The sign of the product of four negative numbers is positive.
If you multiply five negative numbers, what is the sign of the product?
Testing with -1:
(-1)(-1)(-1)(-1)(-1) = (1)(-1)(-1)(-1) = (-1)(-1)(-1) = (1)(-1) -1
General:
(-a)(-b)(-c)(-d)(-e) = -abcde
The sign of the product of five negative numbers is negative.
General rule: The product of an even number of negative numbers is positive. The product of an odd number of negative numbers is negative.
The 2 main support rods for a barbeque grill are each 7.5 cm from the centre of the
grill. the grill is 60 cm in diameter, how long is each support rod?
Answer:
58.1 cm
Step-by-step explanation:
The length of each support rod can be found using the Pythagorean theorem. The geometry can be modeled by a right triangle, such that the distance from centre is one leg and half the length of the rod is the other leg of a triangle with hypotenuse equal to the radius of the grill.
__
Pythagorean theoremThe theorem tells us that the sum of the squares of the legs of a right triangle is the square of the hypotenuse. For legs a, b and hypotenuse c, this is ...
c² = a² +b²
applicationFor the geometry of the grill, we can define a=7.5 and c=30. Then b will be half the length of the support rod.
30² = 7.5 +b²
b² = 900 -56.25 = 843.75
b = √843.75 ≈ 29.0473
The length of each support rod is twice this value, so ...
rod length = 2b = 2(29.0473) = 58.0947
Each support rod is about 58.1 cm long.
Can someone help me with this question
The probability that the selected element is a member of A n B is 2/9
How to complete the number line?The elements of the set are given as:
E = {1,2,3,4,5,6,7,8,9}
A = {1,3,4,8,9}
B = {2,4,9}
Using the above parameters, we have:
A only = {1, 3, 8}
B only = {2}
A and B = {4, 9}
None = {5,6,7}
The above dataset is the represented using the attached Venn diagram
How to determine the probability?
In (a), we have:
A and B = {4, 9}
E = {1,2,3,4,5,6,7,8,9}
The probability is then calculated as:
P(A n B) = n(A n B)/n(E)
This gives
P(A n B) = 2/9
Hence, the probability is 2/9
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By selling an article for $250, a man makes a profit of 25%. what was the cost price of the article.
Answer:
200 dollars
Step-by-step explanation:
Let's say p equals the cost price of the article. Since the man made 25% profit, that means he got 100% of what he originally paid plus another 25% of what he originally paid. In other words, he sold the article for 125% of the original price. Converting that to a decimal we get:
250=p*1.25
Some simple division gets us a cost price of 200 dollars.
HELP PLS I'LL MARK U BRAINLIST !!
Answer:
angles in a triangle add up to 180°
5:12:13 = 30
180 ÷ 30 = 6
6 × 5 = 30°
6 × 12 = 72°
6 × 13 = 78°
angles = 30°, 72°, 78°
The product of 7 and x is the same as the sum of nine and three and two. What is the value of x?
Answer:
Given:
The product of 7 & x is the same as the sum of 9 and 3 and 2.To Find:
The value of x ?Solution:
According to the question:
(1) The product of 7 & x
➝ 7x
(2) The sum of 9 and 3 and 2
➝ 9 + 3 + 2
➝ 14
From (1) and (2) , we get:
➝ 7x = 14
➝ x = 14 ÷ 7
➝ x = 2
Let's Check:Let's check whether our answer is correct or not:
• To check our answerer, let's putting the value of x :
♣ 7(2) = 14
♣ 14 = 14 ✅
Thus, our answer is correct....The value of x is 2.
Julia buys a spool with 12 yards of wire. The students in
her jewelry-making class use 4 yards 2 feet of the wire
for one project and 7 feet of the wire for another
project. How many feet of wire does Julia have left?
A plane, initially traveling 150 mi/hr due
east, suddenly enters a region where the
wind is blowing at 50 mi/hr 38° north of
east.
What is the resultant speed of the plane?
[?] mi/hr
Round to the nearest hundredth.
The resultant speed of the plane is 100 mi/hr along the northeast direction.
What is speed?Speed can be calculated as the ratio of distance traveled to the time taken
First, we need to find our coordinate axis, we will define the x-axis as the east and the y-axis as the north.
We are given that the plane travels at 150 mi/hr at 100° east of north, notice that if we measure from the positive x-axis, this is equivalent to an angle of -10°.
Then the x-component of the velocity ;
150mi/hr x cos(-10°) = 147.7 mi/hr
The y-component of the velocity;
150mi/hr x sin(-10°) = -26 mi/hr.
So, the vector is:
V = 147.7 mi/hr, -26 mi/hr
Now we know that the wind blowing at 50mi/hr at southwest, exactly southwest would be at an angle of 225°,
Thus, the components of the vector are:
x-component: 50mi/hr x cos(225°) = -35.4 mi/hr
y-component: 50mi/hr x sin(225°) = -35.4 mi/hr.
So, the vector is:
W = < -35.4 mi/hr, -35.4 mi/hr>
The sum of the vectors gives the total velocity of the plane in the wind is;
V + W = < 147.7 mi/hr -35.4 mi/hr , -26 mi/hr -35.4 mi/hr >
V + W = <112.3 mi/hr, -61.4 mi/hr>
The direction of a vector is;
θ = Atan(y/x)
Then, in this case the direction of the plane is:
θ = Atan(-61.4 mi/hr/112.3 mi/hr) = -28.7°
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The surface area of Earth is about 196.9 million square miles. The land area is about 57.5 million square miles and the rest is water. What is the probability that a meteorite will hit water?
Solve for the coordinates of the midpoint of (13, 27) and (-31, 53). Show your work to receive full credit.
Answer:
-9,40
Step-by-step explanation:
Midpoint Formula:
[tex](\frac{x^{1} +x^{2} }{2},\frac{y^{1} +y^{2} }{{2} } } )[/tex]
Answer:
Midpoint = (−9,40)
Step-by-step explanation:
Expand (x^22-3x^5 + x^-2 - 7) * (5x^4).
Can someone please explain in detail how to remove the parentheses step by step?
Let's see
[tex]\\ \rm\Rrightarrow (x^{22}-3x^5+x^{-2}-7)5x^4[/tex]
Use distributive law
a(b+c)=ab+ac[tex]\\ \rm\Rrightarrow 5x^{22+4}-15x^{5+4}+5x^{-2+4}-35x^4[/tex]
[tex]\\ \rm\Rrightarrow 5x^{26}-15x^9+5x^2-35x^4[/tex]
Answer:
[tex]5x^{26}-15x^{9}+5x^{2}-35x^4[/tex]
Step-by-explanation:
Given expression:
[tex](x^{22}-3x^5 + x^{-2} - 7) (5x^4)[/tex]
Use the Distributive Property Law (b ± c)a = ab ± ac
to remove the parentheses:
[tex]\implies 5x^4 \cdot x^{22}-5x^4 \cdot 3x^5+5x^4 \cdot x^{-2}-5x^4 \cdot 7[/tex]
Simplify by multiplying the coefficients of each term:
[tex]\implies 5x^4 \cdot x^{22}-15x^4 \cdot x^5+5x^4 \cdot x^{-2}-35x^4[/tex]
[tex]\textsf{Apply exponent rule} \quad a^b \cdot a^c=a^{b+c}[/tex]:
[tex]\implies 5x^{4+22}-15x^{4+5}+5x^{4-2}-35x^4[/tex]
[tex]\implies 5x^{26}-15x^{9}+5x^{2}-35x^4[/tex]
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From experience, an airline knows that only 70% of the passengers booked for a certain flight actually show up. If 8 passengers are randomly selected, find the probability that fewer than 7 of them show up. Carry your intermediate computations to at least four decimal places, and round your answer to two decimal places.
Using the binomial distribution, it is found that there is a 0.7447 = 74.47% probability that fewer than 7 of them show up.
What is the binomial distribution formula?The formula is:
[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]
[tex]C_{n,x} = \frac{n!}{x!(n-x)!}[/tex]
The parameters are:
x is the number of successes.n is the number of trials.p is the probability of a success on a single trial.In this problem, the values of the parameters are given as follows:
p = 0.7, n = 8.
The probability that fewer than 7 of them show up is given by:
[tec]P(X < 7) = 1 - P(X \geq 7)[/tex]
In which:
[tex]P(X \geq 7) = P(X = 7) + P(X = 8)[/tex]
Then:
[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]
[tex]P(X = 7) = C_{8,7}.(0.7)^{7}.(0.3)^{1} = 0.1977[/tex]
[tex]P(X = 8) = C_{8,8}.(0.7)^{8}.(0.3)^{0} = 0.0576[/tex]
Then:
[tex]P(X \geq 7) = P(X = 7) + P(X = 8) = 0.1977 + 0.0576 = 0.2553[/tex]
[tec]P(X < 7) = 1 - P(X \geq 7) = 1 - 0.2553 = 0.7447[/tex]
0.7447 = 74.47% probability that fewer than 7 of them show up.
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Solve for x.
40°
x + 71
75°
Answer:
x = -6.
Step-by-step explanation:
First thing to notice is that this is the third angle in a triangle, and all 3 angles have to equal 180.
Subtract 75 and 40 from 180 to get the missing angles value.
180 - 75 - 40 = 65
So now we know the missing angle has to be 65, or can be written as:
x + 71 = 65.
To solve this, just subtract 71 from both sides.
x = -6.
Please help, this is due by 2:18pm est
71 and the blank angle are a linear pair/supplementary angles, meaning that their sum is 180 degrees.
71 + y = 180
y = 109
The sum of the interior angles of a triangle is 180 degrees. Therefore, all of the angles inside of the triangle will add up to 180.
109 + 46 + x = 180
x = 25
Answer: x = 25 degrees
Hope this helps!
why the question “How many colors are there in the United States flag?” is NOT a statistical question.
Answer:
3
Step-by-step explanation:
blue, white, and red colors
On last week math tests Mr.Jones class had an average of 82 points with a standard deviation of 10 points.Mrs.Potters class had an average of 79 points with a standard deviation of 3 points.Which class was more constant and how can you tell
Mrs. Potter’s class was more consistent because their standard deviation of 3 points was lower.
What is a statistical dispersion?A statistical dispersion is also referred to as degree of dispersion and it can be defined as a measure of the extent to which a numerical value (data) is likely to vary about a mean or an average value.
In Mathematics, there are four measures of dispersion for a data set and these include the following:
RangeInterquartile rangeVarianceStandard deviationIn this scenario, we can infer and logically conclude that Mrs. Potter’s class was more consistent than Mr. Jones class because their standard deviation of 3 points was lower.
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A side of the triangle below has been extended to form an exterior angle of 131°. Find the value of x. 131⁰ to 112º
Answer:
[tex]x = 49degrees[/tex]
Step-by-step explanation:
[tex]131 + x = 180( \: < \: on \: str \: line = 180) \\ x = 180 - 131 \\ x = 49[/tex]
The required value of x for the given figure is 49°.
What is a straight line?A straight line can be defined as a locus of points satisfying the equation ax + by + c = 0 for two coordinates x and y.
The sum of the angles on a straight line is always 180°.
In the given figure the angles 131° and x° are on the same straight line.
Since, the sum of the angles on a straight line is 180°.
The following equation can be written for the given figure,
x + 131 = 180
=> x = 180 - 131
= 49
Hence, the value of x for the given figure is 49°.
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help me with this question
Answer:
a) 150
b) 2650
Step-by-step explanation:
6% of 2500 is 150
150 + 2500 = 2650
the normal yearly growth of a plant is 60 inches, the normal Grove was 10 inches more than twice the amount of last year, what was the growth of the plant last year
The growth of the plant is 25 inches last year.
Explanation:
Suppose the growth of the plant last year was y.
From the given situation, the normal growth was 10 inches more than twice the amount of last year.
So the equation will be
= 10 + 2y = 60
= 2y = 50
= y= 25 inches.
Therefore , the growth of the plant was 25 inches last year.
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3. Here is a list of questions about the students and teachers at a school. Select all the
questions that are statistical questions.
A. What is the most popular lunch choice?
B. What school do these students attend?
C. How many math teachers are in the school?
D. What is a common age for the teachers at the school?
E. About how many hours of sleep do students generally get on a school night?
F. How do students usually travel from home to school?
education Roman Catholic School one five two weeks
Cos W =0.53
Does anybody know this
Answer:
58°
Step-by-step explanation:
Apply trig inverse properties
W = arccos(0.53)
W = 2[tex]\pi[/tex] - arccos(0.53)
Carlos spent a total of $40 at the grocery store. Of this amount, he spent $14 on fruit. What percentage of the total did he spend on fruit?
What is the probability of getting tails and then tails
If f(x) = 3x²+2 and g(x)=x2-9, find (f- g)(x).
Answer:
Step-by-step explanation:
Depending on whether or not the g(x) is x^2 or 2x, I have both ways.
If g(x) is x^2 - 9...
--> (3x^2 + 2) - (x^2 - 9) = 2x^2 + 11
If g(x) is 2x...
--> (3x^2 + 2) - (2x - 9) = 3x^2 - 2x + 11
Hope this helps!
Here is an equilateral triangle. The length of each side is units. A height is drawn. In an equilateral triangle, a line drawn from one corner to the center of the opposite side represents the height. 1. Find the exact height. 2. Find the area of the equilateral triangle. 3. (Challenge) Using for the length of each side in an equilateral triangle, express its area in terms of .
1. Height of the equilateral triangle is: √3 units
2. Area of the equilateral triangle = √3 units²
3. Area = √3/4 x², when each side is x.
What is an Equilateral Triangle?A triangle that has all its three sides equal in length, is referred to as an equilateral triangle.
1. Given the each side measures 2 units, and h is the height, applying the Pythagorean theorem, we would have:
h = √(2² - 1²)
h = √(4 - 1)
h = √3
2. Area of the equilateral triangle = 1/2bh = 1/2(2)(√3)
Area of the equilateral triangle = √3 units²
3. If x is the side length of the equilateral triangle, we would have:
height (h) = √[x² - (x/2)²] = √[x² - x²/4] = √(3x²/4) = √3/2x
Area = 1/2bh = 1/2(x)(√3/2x) = √3/4 x²
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