Therefore, the congruence theorem that may be employed to demonstrate that △WXZ and △YZX are equivalent is: AAS
Define congruence.Angles are considered congruent if the ratios of two shapes are equal. Similar to this, if the sides with one form are the same length and match the sides of yet another figure, the sides are congruent.
Here,
We are informed that ΔWXZ and ΔYZX share the same side.
The right angles ∠WXZ and ∠XZY are.
It is consistent for ∠XWZ and ∠XYZ.
Now that the parameters have been provided, we may infer that XZ is equal to itself according to the reflexive property for congruence, and as a result, we have a congruent side in each triangle.
Second, because ∠WXZ and ∠XZY were right angles, they are comparable and hence congruent to one another.
Finally, it is stated that ∠XWZ and ∠XYZ are congruent.
In conclusion, the triangles are identical according to the AAS Congruency since there are two corresponding angles one and corresponding sides that are both equal, but the comparable side wasn't with the included angles.
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use the piecewise function showing the amount of money that will be charged, c(p), for a group to go to an amusement park based on the number of people, p, in the group
By using the piecewise function that shows the amount of money that will be charged for people in the amusement park , then the value of C(25) is $1425 .
The Piecewise function is given as ⇒ [tex]\{ \begin{array}{lr} 65p \; , & 0\leq P\leq 10\\ 55+100 \; , & 10 < P\leq 20\\ 45p+300 , & 20 < p\leq 30\\ 35p+600& 30 < p \end[/tex] ;
we need to find the value of C(25) , that means we have to find the amount of money that will be charged for 25 people in the amusement park ,
From the given piecewise function , we can see that [tex]p =25[/tex] lies in the range [tex]20 < p\leq 30[/tex] ,
So , we substitute [tex]p =25[/tex] in [tex]C(p)= 45p+300[/tex] ;
we get ;
C(25) = [tex]45 \times 25 + 300[/tex]
= [tex]1125+300[/tex]
= 1425 .
Therefore , the amount that will be charged for 25 persons will be $1425 .
The given question is incomplete , the complete question is
Use the piecewise function showing the amount of money that will be charged, C(p) , for a group to go to an amusement park based on the number of people, p , n the group .
[tex]C(p)= \{ \begin{array}{lr} 65p \; , & 0\leq P\leq 10\\ 55+100 \; , & 10 < P\leq 20\\ 45p+300 , & 20 < p\leq 30\\ 35p+600& 30 < p \end[/tex]
Find C(25) ?
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if k is a positive two-digit integer, what is the tens digit of k ? (1) the sum of the tens digit of k and the units digit of k is 5. (2) the tens digit of k 6 is 3.
The tens digit of k when sum of its digits is 5 and tens digit of k + 6 is 3.
Let tens digit of k be x and units digit be y. Then
k = 10x + y
The sum of the tens digit of k and the units digit of k is 5, that is
x + y = 5
So possible combinations of (x, y) is (1, 4), (2, 3), (3, 2), (4, 1) and (5, 0).
The tens digit of k+6 is 3.
So x<=3.
14 + 6 = 20
23 + 6 = 29
32 + 6 = 38
So k is 32.
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Select all the expressions that are equivalent to 9/7x−3/4.
The expressions that are equivalent to 9/7x−3/4 are:
(9/7)x - (3/4)
(9/7)x - 3/(4*7/9)
(9/7)x - 3/28
(9/7)*x - (3/4)
(9x)/(7x) - (3/4)
(9x)/(7x) - (3/(4*x))
(9x - 3x)/(4*x)
(6x)/(4x)
(3x)/(2x)
What is the linear equation?
The definition of a linear equation is an algebraic equation in which each term has an exponent of one and the graphing of the equation results in a straight line. An example of a linear equation is y=mx + b.
All of the following expressions are equivalent to 9/7x−3/4:
(9/7)x - (3/4)
(9/7)x - 3/(4*7/9)
(9/7)x - 3/28
(9/7)*x - (3/4)
(9x)/(7x) - (3/4)
(9x)/(7x) - (3/(4*x))
(9x - 3x)/(4*x)
(6x)/(4x)
(3x)/(2x)
When you multiply or divide both the numerator and denominator of a fraction by the same non-zero number, the fraction remains equivalent.
Hence, the expressions that equivalent to 9/7x−3/4 are:
(9/7)x - (3/4)
(9/7)x - 3/(4*7/9)
(9/7)x - 3/28
(9/7)*x - (3/4)
(9x)/(7x) - (3/4)
(9x)/(7x) - (3/(4*x))
(9x - 3x)/(4*x)
(6x)/(4x)
(3x)/(2x)
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the length of a rectangle is 3 more than twice its width. the total area of the rectangle is 54 square units. what is the width and length of the rectangle?
The width and length of the rectangle is 4.5ft and 12ft.
Width of a rectangle = b = x ft.
Length of a rectangle = l = (2x+3) ft.
Area of the rectangle = l×b = 54 sq.ft.
= x (2x + 3) = 54
= 2x² + 3x = 54
(2x-9)(x+6) = 0
The size of a patch on a surface is determined by its area. Surface area refers to the area of an open surface or the boundary of a three-dimensional object, whereas the area of a plane region or plane area refers to the area of a form or planar lamina.
Area can be interpreted as the quantity of material with a specific thickness required to create a model of the shape or as the quantity of paint required to completely cover a surface in a single coat.
It is the two-dimensional equivalent of the volume of a solid or the length of a curve, both of which are one-dimensional concepts (a three-dimensional concept).
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How many vertices does this polyhedron have?
5
6
4
3
Answer:
4 I think
Step-by-step explanation:
A vertex is a point where two or more edges meet (i.e the sharp points of the figure).
A vertex (plural: vertices) is a point where two or more line segments meet. It is a Corner.
Le width of a rectangle measures (8u - 2v) centimeters, and its length measures u + 9v) centimeters. Which expression represents the perimeter, in centimeters, the rectangle?
Answer:
[tex]26u + 14v[/tex]
Step-by-step explanation:
[tex]2(8u - 2v) + 2(5u + 9v) \\ 16u - 4v + 10u + 18v \: \: \\ 26u + 14v \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: [/tex]
Describe each x-intercept as "crosses" or "touches" the x-axis
If the graph only touches the x-axis at the x-intercept, then it is said to "touch" the x-axis. This indicates that the graph does not pass through the x-axis at the x-intercept, but rather just touches it.
What is the x-intercept?The x-intercept of a graph is the point at which the graph crosses the x-axis. It is also known as the abscissa. The x-coordinate of the x-intercept is the value where the graph intersects the x-axis.
The x-intercept of a graph is the point at which the graph crosses (or, in some cases, touches) the x-axis. A graph can have one or more x-intercepts. If the graph only crosses the x-axis once, then it has only one x-intercept. If the graph crosses the x-axis twice or more, then it has multiple x-intercepts. In either case, the x-intercepts can be described as either "crosses" or "touches" the x-axis.
If the graph crosses the x-axis at the x-intercept, then it is said to "cross" the x-axis. This indicates that the graph passes through the x-axis at the x-intercept.
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a cone has a radius of 5.1 m and a slant height of 10.9 m. which would increase the cone's surface area more, doubling the radius or doubling the slant height?
A cone has a radius of 5.1 m and a slant height of 10.9 m. So the surface area of the cone is 87.3834 π m².
Determine the surface area of the coneThese are the specified parameters:
Radius (r) = 5.1 m
Cone height (h) = 10.9 m
Find the length of the cone painter's line (s)
s² = r² + h²
= 5.1² + 10.9²
= 26.01 + 118.81
= 144.82
s = √144.82
s = 12.034
Find the surface area of the cone
A = πr (r + s)
= π × 5,1 (5.1 + 12.034) m²
= 5.1 π (17.134) m²
= 87.3834 π m²
Which would increase the cone's surface area more is doubling the radius.
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Line AD is parallel to line HE, what is the value of x?
Answer: [tex]110^{\circ}[/tex]
Step-by-step explanation:
[tex]\angle ACB \cong \angle HFB[/tex] by the corresponding angles theorem.
The table below shows all of the possible outcomes for rolling two six-sided number cubes.
What is the probability of rolling an even number first and an odd number second?
The probability of getting 1st even and second odd is 9/36 = 1/4
What is Probability ?Probability refers to potential. A random event's occurrence is the subject of this area of mathematics. The range of the value is 0 to 1. Mathematics has included probability to forecast the likelihood of certain events. The degree to which something is likely to happen is basically what probability means. You will understand the potential outcomes for a random experiment using this fundamental theory of probability, which is also applied to the probability distribution. Knowing the total number of outcomes is necessary before we can calculate the likelihood that a certain event will occur.
Probability is a way to gauge how likely something is to happen. Many things are difficult to forecast with absolute confidence. Using it, we can only make predictions about the likelihood of an event happening, or how likely it is. Probability can vary from 0 to 1, with 0 being an impossibility and 1 denoting a certainty. For pupils in Class 10, probability is a crucial subject since it teaches all the fundamental ideas of the subject. One is the sum of the probabilities of all the events in a sample space.
Number of outcomes with 1st even and second odd is 9
Total number of outcomes = 36
So, the probability of getting 1st even and second odd is 9/36 = 1/4
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6.2÷(2x+1)= 7/3÷4 What is the answer?
Answer: x= 337/70 or 4 57/70
Step-by-step explanation:
A researcher made the following graph showing the number of hours per day that people spend on the computer versus the number of pounds that they overweight. predict the number of pounds overweight someone would be if they spent 8 hours per day using a computer
PLS I NEED HELP!!
Answer:
Step-by-step explanation:
Unfortunately, without more information, it is not possible to accurately predict the number of pounds someone would be overweight if they spent 8 hours per day using a computer. The graph provided does not provide enough data to make an accurate prediction. It is possible, however, to make an educated guess based on the graph. Looking at the graph, it appears that someone who spends 8 hours per day on the computer would likely be somewhere between 20 and 40 pounds overweight.
how to find the answer
x= 7; 4x + 8 ÷ 2 =
Answer: 18
unclear but appears its 18.
Step-by-step explanation:
Because x is 7; 4x+8/2 = 36.
but its not clear what is being halved: 8 or (4x+8)? so answer could be 32 as well.
How do you write a function from a table of values?
A function can be obtained from the table provided with the values of x and y in the form of a y=mx+b equation.
The above equation can be solved by plotting the graph or from table itself and after calculating its y-intercept, the value of y in the form of y= mx+ b can be obtained. Suppose the table has values of x and y as follows:
x: 0 1 2 3
y: 2 4 6 8
However, it can be seen that when x=0, y= 2, so the y-intercept i.e. the value of y obtained at x=0 is 2. And the slope can be calculated as:
m=[tex]\frac{change in y}{ change in x}[/tex]
m= [tex]\frac{4-2}{1-0}[/tex]
m=2
So the function can be written as y=2x+2
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Triangle and it’s type????
Can anyone help me with this question?
x; 2x + 1; 11 are three consecutive terms of an arithmetic sequence. Calculate: (I). x (ii)
the 30th term.
I) we can substitute x + d = 2x + 1 and x + 2d = 11 into the equation for d:
x - 1 = 2x + 1 - x = 2x - x + 1 = x + 1
x = 0
II) The 30th term of this arithmetic sequence is 29.
How to solve the given equation?To solve this problem, we can use the fact that in an arithmetic sequence, the difference between consecutive terms is constant.
(i) Let's call the common difference d. Then we can set up the equation:
x + d = 2x + 1
d = x - 1
Since we know that x; 2x + 1; 11 are three consecutive terms of an arithmetic sequence, we can substitute x + d = 2x + 1 and x + 2d = 11 into the equation for d:
x - 1 = 2x + 1 - x = 2x - x + 1 = x + 1
x = 0
(ii) To find the 30th term, we can use the formula for the nth term of an arithmetic sequence:
an = a1 + (n - 1)d
where a1 is the first term, d is the common difference, and n is the number of the term we want to find.
Substituting the known values into this formula:
a30 = x + (30 - 1)d
a30 = 0 + (29)(1)
a30 = 29
So the 30th term of this arithmetic sequence is 29.
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what is the approximate yield to maturity of a P7000 bond bearing 6% interest, bought at 90, with 15 years left to maturity?
Consequently, the yield to maturity of a P7000 bond purchased at 90 with 15 years left to maturity is approximately 6.769%.
What is yield of maturity?The rate of return an investor will receive if they hold the bond until maturity is known as the yield to maturity (YTM) of the bond. We need to know a bond's face value, coupon rate, market price, and time until maturity in order to determine its YTM.
Here,
Given :
Face value (FV) equals P7,000
Discount rate is 6%.
Market price as of today (CP) is $90.
15 years is the time to maturity (T).
To determine the YTM, we can use the bond pricing formula:
CP is equal to (FV * C) / (1 + r)T plus (FV / (1 + r)T)
Where:
(FV * Coupon Rate) / 2r = YTMT = time to maturity in years, where C is the annual coupon payment.
The result of solving the equation is 6.769% for the YTM.
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Classify each polynomial based on its degree and number of terms. Drag each description to the correct location. Each description can be used more than once. binomialtrinomialmonomial8th degreefour termsquinticcubicquarticquarticquadratic
Answer:
Step-by-step explanation:
Quadratic: binomial
Cubic: trinomial
Quartic: four terms
Quintic: five terms
8th degree: six terms
Directions: Use the Law of Sines to find each missing side or angle. Round to the nearest tenth.
Answer: 8.7
Step-by-step explanation:
The remaining interior angle is [tex]95^{\circ}[/tex].
[tex]\frac{x}{\sin 33^{\circ}}=\frac{16}{\sin 95^{\circ}}\\\\x=\frac{16 \sin 33^{\circ}}{\sin 95^{\circ}}\\\\x \approx 8.7[/tex]
need help with this question...
Answer: C - The statement is false.
Step-by-step explanation: Rhombuses also have perpendicular diagonals.
Find the volume of the given prism. Question 3 options: A) 3,568 in3 B) 1,920 in3 C) 6,336 in3 D) 1,784 in3
The area of the given prism is equal to 1,920 in³.
What is a rectangular prism?
A rectangular prism is simply a three-dimensional solid shape which with six faces that are rectangles.
We have given,
length l = 8 in.
width w = 12 in,
height h = 20 in.
The volume of a prism is defined as the total space occupied by the three-dimensional object.
The volume of a rectangular prism is given by A = l * w * h,
where 'l' is the length of the prism, 'w' is the width, and 'h' is the height.
so, A = 8 * 12 * 20 = 1,920 in³.
A = 1,920 in³.
Therefore, the area of the given prism is equal to 1,920 in³.
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What is the Inverse of 2(x-5)^2
The inverse function of y = 2(x - 5)² is [tex]y = \pm\sqrt\frac{x}{2} + 5.[/tex]
What is an inverse function?First to be an inverse function that function needs to one to one function, meaning every different preimage must correspond to a different image.
We can obtain the inverse of a function by switching the variables x and y with their respective positions and solving for y in terms of x.
Let, y = 2(x - 5)².
y/2 = (x - 5)².
Solving for 'x'.
[tex]x - 5 = \pm\sqrt\frac{y}{2}[/tex].
[tex]x = \pm\sqrt\frac{y}{2} + 5.[/tex]
Now, We have to interchange the positions of x and y.
[tex]y = \pm\sqrt\frac{x}{2} + 5.[/tex]
So, The inverse of y = 2(x - 5)² is [tex]y = \pm\sqrt\frac{x}{2} + 5.[/tex]
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taotao wants to buy a bracelet. the bracelets have different beads on them, arranged in a circle. if she can choose the colors and placement of the beads, and the beads come in orange, white, and black, how many possible bracelets can she buy?
Think of a bracelet made of five different coloured beads. Be sure to account for flipping and rotating. Check to see whether your solution is right by applying the same logic to a bracelet with four beads of four different colours.
For what is circle renowned?Properties. The form with the biggest area for a given perimeter is a circle (see Isoperimetric inequality). The circle has excellent spherical shape around the centre for all angles and every line thru the centre generates a path of reflection symmetry.
My response is: There are (n-1)!/2 potential bracelets for n different colours, as in our example. Therefore, there are 4!/2=12 various bracelets that might be made for n=5.
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Mark the givens in the diagram. Then copy the proof on paper, and fill in the blanks to complete the proof.
Given that
AR
∩
DC
= M, AD = RC and ∠A ≅ ∠R, prove that △MAD ≅ △MRC.
A
D
M
R
C
Statement1.
AD
= ____ Reason1. Given
2. ∠A ≅ ∠____ 2. Given
3. ∠AMD ≅ ∠____ 3. ________
4. △MAD≅ △____ 4. ________
The answer and prove are AD = RC, <A≅<R, <AMD≅<RMC
How to complete the table?the table shows the statement and the reasons for the proves of congruency of the angles and triangles
The table appears as follows
sn Statement Reason
1 AD = RE Given
2 <A ≅<R Given
3 <AMD ≅<RMC Vertically opposite angles
4 ΔMAD≅ΔMRC Congruent by ASA or SSA
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How many dimes and quarters equal $6.55?
Answer: 25q and 3d
Step-by-step explanation:
23 dimes and 17 quarters equal $6.55.
To find the number of dimes and quarters which equals $6.55, we can use the following method:
Let D = number of dimes
Let Q = number of quarters
40 coins ==> D + Q = 40 ==> D = 40 - Q
$6.55 total ==> 10*D + 25*Q = 655
After the value for D is substituted in the second equation,
10*(40 - Q) + 25*Q = 655
400 - 10*Q + 25*Q = 655
15*Q = 255
Q = 17
i.e., D = 40 - 17 = 23
Check: 23 dimes = $2.30
17 quarters = $4.25
Total = $6.55
Therefore, 23 dimes and 17 quarters equal $6.55.
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22. In your day-to-day routines, you use measurement to cook or do home renovations such as adding new tile floors. How do you imagine that you will use measurement in your future career?
The measurement that you can use in your future career depends on the exact career and there are many more options.
Depending on the exact career but measurements are plentiful in the healthcare business. First, you'll most likely deal with weight and height... since that's part of most healthcare consultations. Then, if you deal with medication, you'll use grams, milligrams, milliliters, and liters all the time. depending if the medication is in solid or liquid form.
Even as a nutritionist, you'll deal with grams and such for portion sizes. There are countless ways you'll use mathematics and measurements in the healthcare sector.
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Type the correct answer in each box. Spell all words correctly, and use numerals instead of words for numbers.
Leslie and Joanne are in the same class. Their school day is 6 hours long. Joanne said that she was in school for 360 minutes. Leslie said she was in school for 320 minutes. Complete the table below to see who is correct.
Answer:
.
Step-by-step explanation:
The population of a city increases by 2.2% per year. If this year's population is 137,000, what will next year's population be, to the nearest individual?
The next year's population will be 140,014. The solution has been obtained by using arithmetic operations.
What are arithmetic operations?
For all real numbers, there are four fundamental mathematical operations that are:
1. The sum of the numbers is achieved through addition ('+').
2. Subtraction with the sign "-," which yields the numbers' differences.
3. Multiplication('×') when the result is the product of the numbers.
4. Division ('÷'), which yields the numbers' quotient.
We are given that the population of a city increases by 2.2% per year and this year's population is 137,000.
Let the population of next year be 'x'
So, we get
⇒137,000 + 137,000(2.2%) = x
⇒137,000 + 3014 = x
⇒140,014 = x
Hence, the next year's population will be 140,014.
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34 1) Niko earned #60 for selling 6 sticks of barbecue. If he earned a total of $300, how many sticks of barbecue did he sell?
Answer:
$60 / 6 barbecue sticks = $x / 1 barbecue stick
Where x is the value of 1 barbecue stick.
To find the value of x, we can cross-multiply and divide by 6:
$60 = 6 barbecue sticks * $x/1
$60 = $6x
$x = $10
So, $10 will equal 1 barbecue stick, if $60 = 6 barbecue sticks.
We know that you earned $300, so we can substitute that into the proportion:
$60 / 6 barbecue sticks = $300 / n barbecue sticks
We can cross-multiply and divide by 60:
6 barbecue sticks * $300 = $60 * n barbecue sticks
n barbecue sticks = $300 * 6 / $60
n barbecue sticks = 30
Therefore, you sold 30 barbecue sticks.
Grayson is working two summer jobs, making $18 per hour lifeguarding and making $10 per hour clearing tables. In a given week, he can work a maximum of 14 total hours and must earn no less than $180. Also, he must work no more than 10 hours lifeguarding and no less than 3 hours clearing tables. If xx represents the number of hours lifeguarding and y represents the number of hours clearing tables, write and solve a system of inequalities graphically and determine one possible solution.
The system of inequalities that models this situation is given as follows:
x ≥ 0.y ≥ 3.x + y ≤ 14.18x + 10y ≥ 180.x ≤ 10.One possible solution is given as follows:
(9,4).
Meaning that he works 9 hours lifeguarding and 4 hours clearing tables.
How to model the system of inequalities?The variables for the system of inequalities in this problem are given as follows:
Variable x: number of hours lifeguarding.Variable y: number of hours clearing tables.The number of hours cannot be negative, hence the first two restrictions are given as follows:
x ≥ 0.y ≥ 0.He can work a maximum of 14 total hours, hence:
x + y ≤ 14.
He must earn no less than $180, hence, considering the rates for each job, we have that:
18x + 10y ≥ 180.
Also, he must work no more than 10 hours lifeguarding and no less than 3 hours clearing tables, hence:
x ≤ 10.y ≥ 3.The shaded region represents all possible solutions for the system of inequalities.
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