Answer:
the answer is the first option : A
Step-by-step explanation:
Which lines can you conclude are parallel given that m14 + m2 = 180? Justify your conclusion with a theorem.
Answer:
Option 2 is correct.
Step-by-step explanation:
Given the diagram and also the condition m∠14 + m∠2 = 180°
we have to tell which lines are parallel.
By the theorem of exterior angles
Same-side exterior angles which are formed outside of the parallel lines and on same side of transversal line.
The theorem states that when parallel lines are cut by a transversal line, the sum of the same-side exterior angles is 180° i.e these are supplementary.
∴ Lines a and b are are parallel by converse of same side exterior angle theorem.
How many ways are there to place 5 basketball players on the court if you must place 2 guards, 2 forwards and a center, from a team of 12, consisting of 4 guards, 5 forwards and 3 centers?
Final answer:
There are 180 ways to place 5 basketball players on the court, selecting 2 guards, 2 forwards, and 1 center.
Explanation:
To determine the number of ways to place 5 basketball players on the court, we need to find the number of combinations of guards, forwards, and centers that can be selected from the available players. There are 4 guards, 5 forwards, and 3 centers in the team.
The number of ways to select 2 guards from 4 is C(4,2) = 6.
The number of ways to select 2 forwards from 5 is C(5,2) = 10.
The number of ways to select 1 center from 3 is C(3,1) = 3.
By the multiplication principle, the total number of ways to place the players on the court is 6 × 10 × 3 = 180.
For the following true conditional statement, write the converse. If the converse is also true, combine the statements as a biconditional. If x = 3, then x2 = 9.
Answer: The converse of the given statement is if [tex]x^2=9[/tex] ,then x=3.→ which is not true.
We cannot form a biconditional statement for the given statement because the converse is not true.
Step-by-step explanation:
Given statement: If x = 3, then [tex]x^2=9[/tex]
The converse statement of conditional statement that "if p then q" is "if q then p".
therefore, the converse of the given statement is if [tex]x^2=9[/tex] ,then x=3.
But the converse is not true since if [tex]x^2=9[/tex] then x can be 3 or -3 .
∵ [tex]3^2=9[/tex] and [tex](-3)^2=9[/tex]
A biconditional statement is true if and only if both the conditional statement and its converse are true.
Therefore, we cannot form a biconditional statement for the given statement because the converse is not true.
The converse of the conditional statement 'If x=3, then x²=9' is 'If x²=9, then x=3'. As both these statements are true, they can be combined into a biconditional statement 'x=3 if and only if x²=9'.
Explanation:
In your question, you asked how to write the converse of a given conditional statement and then combine them if the converse is also true. The original conditional statement is 'If x = 3, then x² = 9.' The converse of this statement would be 'If x² = 9, then x=3.' In this case, the converse is also true because if x² equals 9 then x does indeed equal 3. Therefore, we can combine the conditional statement and its converse into a biconditional statement: 'x = 3 if and only if x² = 9.'
Learn more about Conditional Statements here:https://brainly.com/question/19222807
#SPJ3
what is the remainder when 599 / 9
see attached picture
answer is 66 with remainder of 5
Answer: The remainder is 5
Step-by-step explanation:
599 /9
59 / 9 = 6
6 ×9 = 54
that means remainder 5
Join the 5 beside the last 9, making it 59 again
repeat the first process again, i.e 59/9 = 6
6×9 = 54
Remaining 5
Therefore 9 can go into 599, 66times with a remainder of 5
Simplify square root of (1-cos)(1+cos)/cos^2
A rectangular patio is 9 ft by 6 ft. When the length amd width are increased by the same amount, the area becomes 88 sq ft. Ginger is using the zero product property to solve the equation (6+x)(9+x)= 88. What do her solutions represent?
The solutions represent the additional length and width that need to be added to the original dimensions to achieve the desired area of 88 sq ft.
Explanation:The equation is: (6+x)(9+x) = 88. Ginger is using the zero product property to solve for x. The solutions she finds represent the value of x that, when added to both the length and width of the original patio, will result in a patio with an area of 88 sq ft.
By solving the equation, Ginger will find the possible values of x that will make the area of the new patio equal to 88 sq ft. These values represent the additional length and width that need to be added to the original dimensions to achieve the desired area.
For example, if Ginger finds that x = 2, then the new patio dimensions would be 9+2 = 11 ft by 6+2 = 8 ft, resulting in an area of 11 * 8 = 88 sq ft.
Learn more about Algebra here:https://brainly.com/question/24875240
#SPJ12
the water was pumped out of a backyard pond. what is the domain of this graph
The domain of a graph represents the set of all the possible x-values for a function. In the context of this question, the domain could represent all the possible time values it took for water to be pumped out of the pond. However, the exact domain can't be identified without specific graph or additional information.
Explanation:To determine the domain of the graph related to the water being pumped out of a backyard pond, you would need to consider the horizontal range of the graph. The domain of a graph in mathematics represents the set of all the possible x-values that the function can have. In the context of this problem, the domain could represent the time over which the water was being pumped out. The dependence of the quantity of water on the time creates a function whose domain (all possible time values during the pumping) we are looking for. However, without the specific graph or additional information, we cannot directly identify the domain.
Learn more about Domain of a Graph here:https://brainly.com/question/36431937
#SPJ11
Look at the formula for finding distance.
D=RT
Which of the following is the formula to find time (t)?
ANSWERS:
A-T=DR
B-T=R/D
C-T=D/R
D-T=D-R
Which of the following ordered pairs is represented by a point located on the x-axis?
Select one:
a. (6,-6)
b. (3,3)
c. (0,8)
d. (-5,0)
find the 5th term of the sequence in which T1=8 and Tn=3t n-1
Which of the following is the graph of y = 3/4x -3?
(Sorry the screen wouldn't fit D.)
The graph shown in option C. is the correct representation of the equation [tex]y = \dfrac{3}{4}x -3[/tex].
A graph means a visual representation of a set of entities, known as vertices or nodes, interconnected by connections, called edges.
Follow the following steps to draw the graph of the given equation:
Obtain a set of points from which the line passes, 3 or 4 points will suffice: {(0, -3), (2, -1.5), (4, 0), (8, 3)}.Locate these points on the graph.Draw a line joining these points.Thus, the line [tex]y = \dfrac{3}{4}x -3[/tex] is plotted.
Learn more about Graphs here:
https://brainly.com/question/17267403
#SPJ6
PLZ HELP I NEED THIS TODAY!!!!Write an expression for the perimeter of the triangle shown below: A triangle is shown with side lengths labeled 2.3x plus 14, 2x, and negative 0.2x plus 15.
A: 4.1x + 29
B: 4.1x - 29
C: 4.5x+ 29
D: 4.5x -29
Given the vertices of ∆ABC are A (2,5), B (4,6) and C (3,1), find the vertices following each of the
transformations FROM THE ORIGINAL vertices:
a. Rx-axis
b. Ry = 3
c. T<-2,5>
d. T<3,-6>
e. r(90◦, o)
How do you simplify this problem?
1+tan^2(x) = sec^2(x)
sec^2(x) = 1/cos^2(x)
csc(-x) / 1/cos^2(x) =
cos^2(x) csc(-x)
What is the simplified form of 20 times x to the sixth power over 15 times y to the fifth power times the fraction 5 times y squared over 6 times x to the fourth power ?
a. 9 x squared over 10 y cubed
b. 9 x cubed over 10 y squared
c. 10 x cubed over 9 y squared
d. 10 x squared over 9 y cubed
(3n)^3 without exponents
Determine if the graph is symmetric about the x-axis, the y-axis, or the origin. r = -4 + 5 cos θ
Answer:
x-axis
Step-by-step explanation:
Are right triangles always congruent
Solve log660 – log630. A. 5 B. log62 C. 2 D. log630
Answer:
Option B - [tex]\log_6 60-\log_6 30=\log_6 (2)[/tex]
Step-by-step explanation:
Given : Expression [tex]\log_6 60-\log_6 30[/tex]
To find : Solve the given expression?
Solution :
Step 1 - Write the expression
[tex]\log_6 60-\log_6 30[/tex]
Step 2 - Applying logarithmic property, [tex]\log a-\log b=\log(\frac{a}{b})[/tex]
[tex]\log_6 60-\log_6 30=\log_6 (\frac{60}{30})[/tex]
Bases are same.
Step 3 - Solve
[tex]\log_6 60-\log_6 30=\log_6 (2)[/tex]
Therefore, The solution of expression is
[tex]\log_6 60-\log_6 30=\log_6 (2)[/tex]
So, Option B is correct.
A bicyclist travels 1 mile in 5 minutes. If m represents minutes, what does the expression m over 5 represent
Graph the following piecewise function and then find the domain.
A piece of metal with a mass of 140. g is placed in a 50 mL graduated cylinder. The water level rises from 20. mL to 41 mL. What is the density of the metal?
Andre owned a 1/4 acre lot. he wanted to construct a 120’ x 80’ tennis court on the lot. what approximate percentage of the lot will be left over, if any, when he has completed the construction?
Answer:
Answer is approx 12%
Step-by-step explanation:
Total land owned by Andre = [tex]\frac{1}{4}=0.25[/tex] acres
He wants to construct a 120 feet x 80 feet tennis court on the lot.
Means the area of the court will be = [tex]120\times80=9600[/tex] square feet.
9600 square feet = 0.22 acres (divide the area value by 43560 as 1 acre has 43560 sq feet)
Area left in acres = [tex]0.25-0.22=0.03[/tex] Acres
Hence, the approximate percentage left over will be = [tex]\frac{0.03}{0.25}\times100= 12[/tex]%
What is the slope of the line that passes through the points (4, -7) and (9, 1)?
(5/8)
(8/5)
(-6/12)
(-13/6)
A hyperbola with center at (0, 0), with x-intercepts at (4, 0) and (-4, 0), with b = 1, and opening horizontally has the equation
Answer:
It´s x2/16-y2/1=1
Step-by-step explanation:
The equation of the hyperbola is x²/16 - y²/1 =1
What is a hyperbola?A symmetrical open curve formed by the intersection of a circular cone with a plane at a smaller angle with its axis than the side of the cone. A plane curve generated by a point so moving that the difference of the distances from two fixed points is a constant : a curve formed by the intersection of a double right circular cone with a plane that cuts both halves of the cone.
Given here: hyperbola with center at (0, 0), with x-intercepts at (4, 0) and (-4, 0), with b = 1 . Now we know The standard equation of the hyperbola is [(x²/a²) – (y²/b²)] = 1, where the X-axis is the transverse axis and the Y-axis is the conjugate axis.
Therefore the hyperbola opening horizontally has the equation with x-intercepts at (4, 0) and (-4, 0), with b = 1 is x²/16 - y²/1 =1
Hence, The equation of the hyperbola is x²/16 - y²/1 =1
Learn more about the hyperbola here:
https://brainly.com/question/28989785
#SPJ2
What number multiplies to -160 and adds to 27?
Δ abc is isosceles. angles b and c are congruent. the m∠a = 40°, m∠b = (3x + 1)°. find x.
a.13
b.23
c.46.3
d.70
Final answer:
In an isosceles triangle with angles B and C congruent, and with m∠A equal to 40°, the equation to find x is 40° + 2(3x + 1)° = 180°. Solving this equation yields x = 23°, which corresponds to option b.
Explanation:
Since ΔABC is an isosceles triangle and angles B and C are congruent, m∠B = m∠C. Given that m∠A = 40°, we can set up an equation to find x since the sum of all angles in a triangle equals 180°.
Equation: 40° + (3x + 1)° + (3x + 1)° = 180°
Combining like terms:
40° + 2(3x + 1)° = 180°
40° + 6x + 2° = 180°
6x + 42° = 180°
6x = 180° - 42°
6x = 138°
x = 23°
Therefore, the value of x is 23°, which corresponds to option b.
In the state of pennsylvania, each automobile license plate number consists of three letters followed by a four-digit num ber. how many distinct license plate numbers can be fonned
26 letters each place, 10 numbers each place
26 x 26 x 26 x 10 x 10 x 10 x 10 = 175,760,000 different plates can be made
The graph below represents which system of inequalities?
A y ≤ −2x + 3
y ≤ x + 3
By ≥ −2x + 3
y ≥ x + 3
C y ≤ −3x + 2
y ≤ −x + 2
D y > −2x + 3
y > x + 3
PLEASE HELP IMAGE ATTACHED!!! the area of this parallelogram is 120mm^2. Find the value of X