Name the property of equality or congruence that justifies going from the first statement to the second statement.
3x+x+7=23
4x+7=23
Answer:
Reflexive Property
There are 130 people in a
sport centre.
73 people use the
gym.
62 people use the swimming pool.
58 people use the track.
22 people use the gym and the pool.
29 people use the pool and the track.
25 people use the gym and the track.
11 people use all three facilities.
A person is selected at random.
What is the probability that this
person doesn't use any facility?
Answer:
If 11 people use all three facilities, this means:
22 − 11 or 11 are using the gym and the pool but no the track,
29 − 11 or 18 are using the pool and the track but no the gym,
25 − 11 or 14 are using the gym and the track but no the pool.
How many people use the gym only?
130 − (14 + 11 + 11) = 94
How many people use the pool only?
62 − (18 + 11 + 11) = 22
How many people use the track only?
58 − (14 + 11 + 18) = 15
How many people go in for sports?
94 + 22 + 15 + 11 + 14 + 18 + 11 = 185
How many people use exactly one of the facilities?
94 + 22 + 15 = 131
What is the probability that the person uses exactly one of the facilities?
= 131/185 ≈ 0.7081
Step-by-step explanation:
its a bit confusing
Hope It Helps !!!!
4x^{4}-x^{2} -12x-36
Answer:
(x-2)(4x³+8x²+15x+18)
What is the area of the shaded sector of the circle? 9pi units squared 27pi units squared 81pi units squared 162pi units squared
Answer:
27
Step-by-step explanation:
i promise :)
Answer:
27π units^2
Step-by-step explanation:
Hii! I need some help, would anyone mind helping me?
Find the center of this hyperbola.
[tex]\boldsymbol{x^2-25y^2-14x+100y-76=0}[/tex]
[tex]\stackrel\bigstar{\boldsymbol{\underbrace{Thankyou!!}}}[/tex]
Step-by-step explanation:
[tex] {x}^{2} - 14x - 25 {y}^{2} + 100y = 76[/tex]
Factor by grouping,
[tex]( {x}^{2} - 14x) - (25 {y}^{2} - 100y) = 76[/tex]
Complete the square, with the x variables,
[tex]( {x}^{2} - 14x + 49) - (25 {y}^{2} - 100y) = 125[/tex]
Factor out 25 for the y variables
[tex]( {x}^{2} - 14x + 49) - 25( {y}^{2} - 4y) = 125[/tex]
Complete the square
[tex]( {x}^{2} - 14x + 49) - 25( {y}^{2} - 4y + 4) = 25[/tex]
Simplify the perfect square trinomial
[tex](x - 7) {}^{2} - 25(y - 2) {}^{2} = 25[/tex]
Make the right side be 1 so divide everything by 25.
[tex] \frac{(x - 7) {}^{2} }{25} - (y - 2) {}^{2} = 1[/tex]
Here our center is (7,2).
The directrix and vertex of a parabola are shown on the graph. What is the vertex form of the equation for the associated parabola?
Considering the directrix and vertex given in the graph, the equation of the parabola is:
B. [tex]x = -\frac{1}{4}(y + 2)^2 - 2[/tex]
What is the equation of a parabola given it’s vertex?The equation of a quadratic function, of vertex (h,k), is given by:
(y - k)² = 4p(x - h).
In which the directrix is the line x = h - p.
Looking at the graph, we have that:
The vertex is (-2,-2), hence h = k = -2.The directrix is x = -1, hence -1 = -2 - p -> p = -1.Thus the equation is:
(y + 2)² = -4(x + 2).
Writing x as a function of y:
B. [tex]x = -\frac{1}{4}(y + 2)^2 - 2[/tex]
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Need to know asap thanks
Answer:
[tex]\large \boxed{\sf 16}[/tex]
Explanation:
[tex]\Rightarrow \sf \sqrt{121} + \sqrt[3]{125}[/tex]
[tex]\Rightarrow \sf{ \sqrt{11 \ x \ 11} + \sqrt[3] {\sf5 \ x \ 5 \ x \ 5}[/tex]
[tex]\Rightarrow \sf{ \sqrt{11^2} + \sqrt[\sf 3] {\sf 5^3}[/tex]
[tex]\Rightarrow \sf 11 + 5[/tex]
[tex]\Rightarrow \sf 16[/tex]
I hope this help you . the concept of sure and cube roo
Find the equation of the parabola with its focus at (6, 2) and its directrix y = 0
Answer:
y= 1/4 x-62+1
Step-by-step explanation:
A game requires players to throw a ball into a target. The table below shows values from the function that represents one path of a thrown ball, where x represents the horizontal distance the ball travels in feet and f(x) represents the height of the ball in feet.
If the ball enters the target at the highest point in its path, based on the table, what is the height of the target?
1.5 feet
4 feet
28 feet
29 feet
The height of the target is 29 feet.
The correct option is (D)
What is function?An expression, rule, or law that defines a relationship between one variable (the independent variable) and another variable (the dependent variable).
The given table path of the thrown ball,
where x represents the horizontal distance and f(x) represents the height of the ball.
Now,
when x = 1.25 feet horizontally, the height will be maximum.
also, the height of the ball at distance x = 1.25 feet is
f(1.25) = 29 feet.
Hence, height of the target is 29 feet.
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Answer:
D. 29 feet
Step-by-step explanation:
pls help me with this question
Answer:
D, C
Step-by-step explanation:
for part a, there is a negative slope with the graph shifted two units upwards
for part b, if you plug in C, you get an answer that works
The nth term of a sequence is -2n - 4. Work out the 50th term of the sequence.
Answer:
-104
Step-by-step explanation:
1) Substitute 50 into n.
-2(50) - 4
-100 - 4
-104
4 2/3 ÷ 2 1/3 ? what is the quotient?
Answer: 42/21 or 2
Step-by-step explanation:
you first convert them to improper fractions, which is 14/3 and 7/3. Then, you multiply the reciprocal and get 14/3x3/7, and get 42/21. Simplify, and you get 2.
w = -5?
w2 + 3w − 11
The value of an expression will be equal to -1.
The complete question is given below:-
If the value of w is -5 then find the value of the expression w² + 3w -11.
What is an expression?Expression in maths is defined as the collection of numbers, variables, and functions using signs like addition, subtraction, multiplication and division.
The given expression will be solved as follows:-
E = w² + 3w -11.
E = ( -5 )² + ( 3 x -5 ) -11
E = 25 - -15 - 11
E = 25 - 26
E = -1
Therefore the value of an expression will be equal to -1.
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Calculate the cost of the number of units used
Step-by-step explanation:
calculated the cost of numbers of units usex
Find cos (330°). Your answer MUST be in radical form.
Step-by-step explanation:
square root 3 divided by
2
lateral surface for a triangular prism l=8 w=4 h=6
Answer:
? i need help
Step-by-step explanation:
Which type of geometry best describes the following statement?
The boundaries of an arc are considered to be at infinity.
A. spherical geometry
B. Euclidean geometry
C. hyperbolic geometry
D. non-euclidean geometry
Answer:
B=hyperbolic geometry
Bao says: "i can prove this using the fact that opposite sides in a parallelogram are congruent, and by establishing the congruence of a single pair of triangles." which pair of triangles is bao referring to, and which criterion should he use for establishing congruence?
The pair of triangle formed are congruent using the side-side-side congruency theorem.
What are congruent triangles?Two triangles are said to be congruent if they have the same shape and their corresponding sides are congruent.
Since the opposite sides of a parallelogram are congruent, if the parallelogram is cut through the diagonal, the pair of triangle formed are congruent using the side-side-side congruency theorem.
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Which of the following is a like radical to 3√6x^2
x(3√6x)
6 (3√x²)
4 (3√6x²)
x(3√6)
Answer:
x(3√6)
Step-by-step explanation:
Radicals:
Take out a variable or number for every pair of the variable or number inside the radicals
[tex]\sf 3\sqrt{6x^2}=3*\sqrt{6*x*x}\\\\[/tex]
[tex]\sf = 3x \sqrt{6}[/tex]
Work out the value of (2^3)^2
Answer:
2⁶
Step-by-step explanation:
law of indices states multiplication of powers in and out of bracket 3×2=6
[tex]\text{Let's work out:: 2 to the power of 3 to the power of 2 }\\\text{We can start by raising 2 to the power of 3:: 2*2*2=8, then raising that}\\\text{to the power of 2:: 8*8=64}[/tex]
[tex]\rule{300}{1.7}[/tex]
[tex]\text{The value is 64}[/tex]
Based on a poll conducted by the Centers for Disease Control, 862 of 1013 randomly selected adults said that they always wear seat belts. Construct and interpret a 95% confidence interval for the proportion of adults who always wear seat belts.
The confidence interval is 0.028, 0.872
Given862 of 1013 randomly selected adults wear seat belts.
The 95% confidence interval for the proportion of adults who always wear seat belts.
What is confidence interval?A Confidence Interval is defined as a range of values we are sure our true value lies within it.
What is 95% confidence interval?A 95% confidence interval is defined as that if we take 100 different samples and compute a 95% confidence interval for each sample, then approximately 95 of the 100 confidence intervals will contain the true mean value.
= 862/1013 = 0.85
At a 95% confidence interval ,the critical value is [tex]z_{0.025} = 1.96[/tex]
The 95% confidence interval for proportion is
[tex]\widehat p +/- z0.025 * sqrt(\widehat p * (1 - \widehat p)/n)[/tex]
[tex]= 0.85 +/- 1.96 * sqrt(0.85 * (1 - 0.85)/1013)[/tex]
[tex]= 0.85 +/- 0.022[/tex]
= 0.028, 0.872
The sample should use at least 10 successes and 10 failures.
[tex]n * \widehat p = 1013 * 0.85 = 861 > 10[/tex]
[tex]n * (1 - \widehat p) = 1013 * 0.15 = 152 > 10[/tex]
As the sample size is larger, we can use an approximate formula for the standard error.
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a jacket is on sale for 30% of and its £42 after discount whats the original price
Answer:
£60
Step-by-step explanation:
70% of original price = £42
100% of original price = £42 * 10/7 = £6 * 10 = £60
simplify the equation. 3(x+2)-9x+5
Distribute
3(x + 2) - 9x + 53x + 6 - 9x + 5Add the numbers
3x + 6 - 9x + 53x + 11 - 9xCombine like terms
3x + 11 -9x-6x + 11Distribute
3(x + 2) - 9x +5
3x + 6 - 9x + 5
Add the numbers
3x + 6 - 9x + 5
3x + 11 - 9x
Combine like terms
3x + 11 - 9x
6x + 11
Point C is the center of the circle.
Options to the second answer are
A. One-half the measure of angle C
B. Not related to the measure of angle C
C. The complement of angle C
D. Equal to the measure of angle C
Answer:
D
Step-by-step explanation:
Because.............
Can you answer the question
well if its asking for an exponent then its (-5)⁴
A random sample is taken and the sample size is 25. the sample is normally distributed, the sample mean is 80, and the standard deviation is 5.5. find a 90% confidence interval for the population mean.
The 90% confidence interval for the population mean is 78.1905<x<81.8095
Confidence intervalThe formula for calculating the confidence interval is expressed as:
CI = x ± z*s/√n
Given the following parameters
mean "x" = 80
z = 1.645
s = 5.5
n = 25
Substitute
CI = 80 ± 1.645*5.5/√25
CI = 80 ± 1.8095
CI = {78.1905, 81.8095}
Hence the 90% confidence interval for the population mean is 78.1905<x<81.8095
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A rectangle has perimeter 16 m. Express the area A (in m2) of the rectangle as a function of the length, L, of one of its sides.
The area A of the rectangle as a function of the length, L of one of its sides is A = 8L - L²
What is the perimeter of a rectangle?The perimeter of a rectangle is P = 2(L + W) where
L = length of the rectangle and W = width of the rectangleGiven that P = 16 m,
P = 2(L + W)
16 = 2(L + W)
16/2 = L + W
L + W = 8
So, W = 8 - L
What is the area of the rectangle?
The area of the rectangle, A = LW where
L = length of the rectangle and W = width of the rectangleSince W = 8 - L, substituting W into the equation for A, we have
A = LW
A = L(8 - L)
A = 8L - L²
So, the area A of the rectangle as a function of the length, L of one of its sides is A = 8L - L²
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What are the solutions to the quadratic equation below in factored form?
(10x + 5)(11x - 44) = 0
= ½, x = 4
0x=
0 x = 2, x = -4
0x = 2, x = 4
○ x = − ½, x = 4
Answer:
D.) x = − ½, x = 4
Explanation:
[tex]\rightarrow \sf (10x + 5)(11x - 44) = 0[/tex]
set the factors to zero
[tex]\rightarrow \sf 10x + 5 = 0, \ 11x - 44 = 0[/tex]
exchange the sides
[tex]\rightarrow \sf 10x = -5, \ 11x = 44[/tex]
exchange the sides
[tex]\rightarrow \sf x = -\dfrac{5}{10} , \ x = \dfrac{44}{11}[/tex]
simplify the following
[tex]\rightarrow \sf x = -\dfrac{1}{2} , \ x =4[/tex]
On solving
x=-1/2 or x=4Please help me with this question!
The diameter of the sphere is 14 cm.
What is a sphere ?Sphere is a three dimensional object , it has no edges or vertices and is round in shape.
The surface area of the sphere is given by 4πr²
As radius = diameter /2
Surface area = 4π r²
196 π = 4π *(d/2)²
196/4 = d²/4
49 *4 = d²
d = 14 cm
Therefore the diameter of the sphere is 14 cm.
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Use the commutative property to simplify the expression 4/3 + 3/4 + 2/3
The simplified expression using the commutative property is : [tex]\frac{6}{3}[/tex] + [tex]\frac{3}{4}[/tex]
Meaning of commutative propertycommutative property can be defined as a mathematics attribute that is possessed by a mathematical equation, that enables the objects undergoing addition or multiplication to change position.
In conclusion, The simplified expression using the commutative property is : [tex]\frac{6}{3}[/tex] + [tex]\frac{3}{4}[/tex]
Analysis4/3 + 3/4 + 2/3 = ( [tex]\frac{4}{3}[/tex] + [tex]\frac{2}{3}[/tex] ) + [tex]\frac{3}{4}[/tex] = [tex]\frac{6}{3}[/tex] + [tex]\frac{3}{4}[/tex]
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