Answer:
2a+2b
Step-by-step explanation:
3a - a = 2a
4b - 2b = 2b
Answer:
2a+2b
Step-by-step explanation:
3a – a + 4b – 2b
Combine like terms
3a-a =2a
4b-2b =2b
3a – a + 4b – 2b. = 2a+2b
A, B, and C are midpoints of ∆XYZ. What is the length of yz
Answer:
Step-by-step explanation:
Comment
When you join 2 consecutive midpoints with a line between them, the length of that line is 1/2 the length of the side opposite the line you just drew.
In other words 24 is 1/2 the length of yz.
Solution
1/2 yz = AB
AB = 24
1/2 yz = 24 Multiply both sides by 2
2(1/2 yz) = 2*24
yz = 48
Answer
yz = 48
Based only on the information given in the diagram, which congruence
theorems or postulates could be given as reasons why ABC= ADEF?
Check all that apply.
AA
A. SAS
B. LL
C. LA
O. D. HA
E. HL
F. AAS
Answer:
Step-by-step explanation:
AAS and SAS
The congruence theorems or postulates could be given as reasons why ABC= ADEF are SAS, AAS the correct options are A and F.
What are congruent triangles?
Suppose it is given that two triangles ΔABC ≅ ΔDEF
Then that means ΔABC and ΔDEF are congruent. Congruent triangles are exact same triangles, but they might be placed at different positions.
The order in which the congruency is written matters.
For ΔABC ≅ ΔDEF, we have all of their corresponding elements like angle and sides congruent.
Thus, we get:
[tex]\rm m\angle A = m\angle D \: or \: \: \angle A \cong \angle D \angle B = \angle E\\\\\rm m\angle B = m\angle E \: or \: \: \angle B \cong \angle E \\\\\rm m\angle C = m\angle F \: or \: \: \angle C \cong \angle F \\\\\rm |AB| = |DE| \: \: or \: \: AB \cong DE\\\\\rm |AC| = |DF| \: \: or \: \: AC \cong DF\\\\\rm |BC| = |EF| \: \: or \: \: BC \cong EF[/tex]
(|AB| denotes length of line segment AB, and so on for others).
We are given that;
The diagram
Now,
Based on the information given in the diagram, we can use the following congruence theorems or postulates as reasons why ABC= ADEF:
SAS (Side-Angle-Side): If two sides and the included angle of one triangle are congruent to two sides and the included angle of another triangle, then the triangles are congruent.
We can use SAS to show that ABC and ADEF are congruent, since AB = AD, BC = DE, and the included angle BAC = the included angle EDF.
AAS (Angle-Angle-Side): If two angles and a non-included side of one triangle are congruent to two angles and the corresponding non-included side of another triangle, then the triangles are congruent.
We can use AAS to show that ABC and ADEF are congruent, since the included angles BAC and EDF are congruent, angle ABC is congruent to angle ADE (since they are vertical angles), and side BC is congruent to side EF.
Therefore, by congruent triangles the answer will be SAS, AAS.
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An equilateral triangle with side lengths of 8.7 centimeters is shown. An apothem has a length of a and the radius has a length of 5 centimeters. The apothem and radius form a triangle with a base length of b.
Which statements about finding the area of the equilateral triangle are true? Select three options.
The apothem can be found using the Pythagorean theorem.
The apothem can be found using the tangent ratio.
The perimeter of the equilateral triangle is 15 cm.
The length of the apothem is approximately 2.5 cm.
The area of the equilateral triangle is approximately 65 cm2.
Answer:
a,b,d
Step-by-step explanation:
A bag has 20 cubes in it. 6 of the cubes are
green.
You take one cube out of the bag at random.
Which four values below show the probability
that you take out a cube that is green?
6
14
6%
0.3
30% 0.6
3 6
5 20
6
10
60%
3
10
0.03
6
26
Answer: 0.3, [tex]\frac{6}{20}[/tex], [tex]\frac{3}{10}[/tex], 30%
Step-by-step explanation:
We will divide wanted outcomes by possible outcomes.
[tex]\displaystyle \frac{\text{wanted outcomes, green cubes}}{\text{possible outcomes, cubes in bag}} =\frac{6}{20}[/tex]
Now, we will find four values equivalent to [tex]\frac{6}{20}[/tex]. See attached.
A sports club rewards teams based on overall points earned in a season. The data for points are shown in the table, where Low represents the fewest points scored and High represents the highest points scored by a single team member.
Team Low High Range Mean Median IQR σ
Team L 4 17 13 9.4 9 9.75 4.8
Team M 6 14 8 9.7 9.5 6.25 3.2
Team N 1 20 19 13 14.5 4.75 5.6
Part A: If the club wants to award the team that has the most consistent scoring among its team members, which team should it choose and why? Justify your answer mathematically. (5 points)
Part B: If the club wants to award the team with the highest average score, which team should it choose and why? Justify your answer mathematically.
Answer:
PART A:
The range, the IQR (inter-quartile range) and the standard deviations are measures which are used to measure the spread of a data set.
A dataset is more consistent relative to another data set when the standard deviation is less than that of the other data set.
From the table, it can be seen that Team C has the least standard deviation.
Therefore, If the club wants to award the team that has the most consistent scoring among its team members, team C should be chosen.
PART B
The mean and the median is a measure of center of a data set.
The mean describes the average of a data set.
From the table, it can be seen that Team B has the highest average score.
Therefore, If the club wants to award the team with the highest average score, team B should be chosen.
Work out the rule for the nth term then work out the 100 term
th
a) 3, 5, 7, 9, 11, 13....
b) 12, 20, 28, 36, 44....
c) 19, 29, 39, 49, 59....
d) 7, 10, 13, 16, 19....
e) 14, 20, 26, 32, 38....
f) 55, 60, 65, 70, 75...
g) 8, 17, 26, 35, 44....
Find the surface area of the regular pyramid.
The surface area of the triangular pyramid shown is 94.6 in²
What is an equation?An equation is an expression that shows the relationship between two or more variables and numbers.
The surface area of the regular pyramid is given as:
Surface area = 3(0.5 * 4.3 * 13) + (0.5 * 4.3 * 5) = 94.6 in²
The surface area of the triangular pyramid shown is 94.6 in²
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A llhe intersects the points
(4, -2) and (3, 3).
m = -5
Write an equation in point-slope form
using the point (4, -2).
y- [?] =[?]
(x-[?])
Answer:
y + 2 = -5(x - 4)
Step-by-step explanation:
Point-slope form is the following: [tex]y-y_{1}=m(x-x_{1})[/tex], where m is the slope of the line and [tex](x_{1}, y_{1} )[/tex] is a point on the line. We are already given all of the information we need, so all we have to do is write it out. We are told that the slope (m) is -5, and the point the question wants us to use is (4, -2), though either of the points given would work. If we plug in the quantities, we get that y - (-2) = -5(x - 4), or y + 2 = -5(x - 4)
What is the variable of f(3) in the function below? f(x) =2^x
Hello !
We replace x by 3.
[tex]f(3) = {2}^{3} = 8[/tex]
Have a nice day ;)
[tex]\frak{Hi!}[/tex]
[tex]\orange\hspace{300pt}\above2[/tex]
We have the expression -:
[tex]\boldsymbol{\sf{f(x)=2^x}}[/tex], and we're asked to find
[tex]\boldsymbol{\sf{f(3)}}[/tex].
To do that we put in the value for x (3)-:
[tex]\boldsymbol{\sf{f(3)=2^3}}[/tex].
Evaluate-:
[tex]\boldsymbol{\sf{f(3)=2\times2\times2=8}}[/tex]
[tex]\orange\hspace{300pt}\above3[/tex]
New information obtained through research or experimentation that enables an updating or revision of the state-of-nature probabilities is known as _____. Group of answer choices joint probability sample information conditional probability expected utility
New information obtained through research or experimentation that enables an updating or revision of the state-of-nature probabilities is known as SAMPLE INFORMATION.
Hence, 2nd option is the best choice.
A statistical concept called joint probability determines the chance that two events will occur simultaneously and at the same time.
A sample is a collection of people, things, or things used in the study that is taken for analysis from a wider population. To enable us to extrapolate the study sample's findings to the entire population, the sample must be representative of the population. Sample information is the collection of the information of the sample.
The possibility of an event or outcome happening contingent on the occurrence of a prior event or outcome is known as conditional probability. The probability of the prior event is multiplied by the current likelihood of the subsequent, or conditional, occurrence to determine the conditional probability.
The expected utility of a course of action is a weighted average of the utilities of each of its potential outcomes, where the utility of a potential result indicates how much it is preferred to the alternatives.
In the question, we are asked what will be the new information obtained through research or experimentation that enables an updating or revision of the state-of-nature probabilities called.
As we are to name the information, it will be called sample information, from the above-discussed points.
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III- Hallar el módulo del vector
a (2,6)
[tex]\sqrt{2^{2}+6^{2}}=\sqrt{4+36}=\sqrt{40}=\boxed{2\sqrt{10}}[/tex]
what happens when the multiplicity of a real root is even
a. the graph crosses the y-axis
b. the graph crosses the x-axis
c. the graph is tangent to the y-axis
d. the graph is tangent to the x-axis
When the multiplicity of a real root is even, the graph of the function neither crosses nor is tangent to the x-axis. The correct answer is (c) the graph is tangent to the y-axis.
When a real root has an even multiplicity, it means that the corresponding factor appears multiple times in the factored form of the polynomial. In terms of the graph of the function, this means that the graph touches the x-axis at that root but does not cross it.
Since the graph touches the x-axis without crossing it, it remains on one side of the axis. This behavior indicates that the graph is tangent to the x-axis at the root with even multiplicity.
However, the graph can still intersect or cross the y-axis at a different point depending on other factors or terms in the polynomial. Therefore, option (a) "the graph crosses the y-axis" may or may not be true depending on the overall behavior of the function. The statement in option (b) "the graph crosses the x-axis" is incorrect for an even multiplicity root. Option (d) "the graph is tangent to the x-axis" is also incorrect for an even multiplicity root. Hence, option (c) "the graph is tangent to the y-axis" is the correct choice.
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3/8 TIMES 2/5 =
SIMPLIFIED
Answer:
3/20
decimal form: 0.15
A general formula for a parabola is y2=4px. what is the value of p in the equation y2=−4x?
The value of p is -1 in the given equation of of parabola.
What is a parabola?
A parabola is an approximately U-shaped, mirror-symmetrical planar curve. It corresponds to a number of seemingly unrelated mathematical descriptions, all of which can be shown to define the same curves. One way to describe a parabola is with a point called focus and a line called the directrix.
Equation for a Parabola
The general formula or the equation for representing a parabola is given by,
y² = 4px
Here, (h,k) being the vertex of the parabola,
y = a(x-h)² + k
x = b(y-k)² + h
The focus of this parabola is given by (p, 0).
The directrix of the parabola is the line drawn perpendicular to the y-axis and traversing the point (-p, 0). The directrix is parallel to the parabola's axis.
What is the value of p in the equation for parabola?
The given equation is,
y² = -4x
Comparing this equation with the general formula of the parabola, we get,
p = -1
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Which exponential function is represented by the table
Answer:
for x = 0 ; we have f(x) = 0,5
We can eliminate the first and the last proposal because
f(x) = 0,2(0,5ˣ) ⇒ f(0) = 0,2(0,5⁰) = 0,2 × 1 = 0,2 ≠ 0,5
f(x) = 0,2(0,2ˣ) ⇒ f(0) = 0,2(0,2⁰) = 0,2 × 1 = 0,2 ≠ 0,5
Try for x = 1, we have f(x) = 0,1
f(x) = 0,5(5ˣ) ⇒ f(1) = 0,5 × 5 = 2,5 ≠ 0,1
f(x) = 0,2(0,5ˣ) ⇒ f(1) = 0,2(0,5) = 0,1 ⇒ ok
So the answer is f(x) = 0,2(0,5ˣ)
PLS HELP
re writing expressions
The equivalent expression of [tex]\frac{2^4}{\sqrt[3]{xy}}[/tex] is [tex]\frac{\sqrt[3]{\frac{2^{12}}{xy}}}[/tex]
How to rewrite the expression?The expression is given as:
[tex]\frac{2^4}{\sqrt[3]{xy}}[/tex]
Multiply 4 by 1
[tex]\frac{2^{4 * 1}}{\sqrt[3]{xy}}[/tex]
Express 1 as 3/3
[tex]\frac{2^{4 * 3/3}}{\sqrt[3]{xy}}[/tex]
Evaluate the product
[tex]\frac{2^{12 * 1/3}}{\sqrt[3]{xy}}[/tex]
Apply the following law of indices
[tex]a^\frac 1n = \sqrt[n]{a}[/tex]
So, we have:
[tex]\frac{\sqrt[3]{2}^{12}}{\sqrt[3]{xy}}[/tex]
The numerator and the denominator have the same root
So, we have:
[tex]\frac{\sqrt[3]{\frac{2^{12}}{xy}}}[/tex]
Hence, the equivalent expression of [tex]\frac{2^4}{\sqrt[3]{xy}}[/tex] is [tex]\frac{\sqrt[3]{\frac{2^{12}}{xy}}}[/tex]
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Use the substitutions u= 1/x^2 and v= 1/y^2 to solve the system of equations. express numbers as integers or simplified fractions.
-5/x^2 + 1/y^2 =-16
13/x^2- 1/y^2 =48
Answer:
-5 u + 1 v = (-16)
12 u - 1v = 48
adding,
7 u = 32
u = 32/7V = (-16) + 5(32/7)
V = (-16) +160/7
V = -112 + 160/7
V = 48/7Triangles P and Q are similar.
Find the lengths of the sides:
Triangle P—> CA=9cm AB=4cm BC=?
Triangle Q—> XY=16cm YZ=48cm ZX=?
Answer:
if i labeled the triangle correctly BC= sqrt 97, ZX=32sqrt 2
Step-by-step explanation:
join my stream and tell me how to label the triangle
(ChildOfHermes)
Allen is horrible at managing his money. For example, he
recently invested $100,000-part of it in a company that
makes "fish-flavored" chicken and the rest in a company
that makes spray-on vitamins. Somehow he managed to earn
a 3% profit on the fish-flavored chicken investment and 1%
profit on the spray-on vitamin deal. If Allen made a profit
of $2,600 from both investments, how much did he invest in
the fish-flavored chicken company?
Answer:
$80,000
Step-by-step explanation:
Define the variables:
Let x = "fish-flavored" chicken company investment (in dollars)
Let y = spray-on vitamins company investment (in dollars)
If Allen invested a total of $100,000:
⇒ x + y = 100000
Given:
3% profit on "fish-flavored" chicken investment 1% profit on pray-on vitamins investmentTotal profit = $2,600⇒ 0.03x + 0.01y = 2600
Rewrite the first equation to make y the subject:
⇒ y = 100000 - x
Substitute into the second equation and solve for x:
⇒ 0.03x + 0.01(100000 - x) = 2600
⇒ 0.03x + 1000 - 0.01x = 2600
⇒ 0.02x + 1000 = 2600
⇒ 0.02x = 1600
⇒ x = 80000
Therefore, Allen invested $80,000 in the "fish-flavored" chicken company.
Express in exponential form.
log(10)0.001 = -3
Answer:
this gvfyftvyccg c
Step-by-step explanation:
VERBAL
2. Explain how to find the output variable in a word problem that uses a linear function.
Answer:
The dependent variables in most cases is output variable. That is a value that depends on some other input value and changes based on that input value.
Step-by-step explanation:
In the question, it is given that a problem uses an output variable.It is required to explain how to find the output variable in a word problem that uses a linear function.In order to find the output variable in a world problem, for the dependent variable. That is a value that depends on some other input value and changes based on that input value.It cannot change independently. In these types of functions, this value is mostly marked as y or f(x).Maureen says that if a system of linear equations has three equations, then there could be exactly two solutions to the system. Is
Maureen correct? Justify your reasoning.
Answer:
Yes, Maureen is correct. If a system of linear equations has three equations, then there could be exactly two solutions to the system. This is because, in general, a system of linear equations with three variables will have three equations. However, if two of the equations are the same, then there will only be two equations. In this case, there will be two solutions to the system.
Step-by-step explanation:
the function f(x) is shown below
Answer: 2
Step-by-step explanation:
A function composed with its inverse outputs the original input.
CAN SOMEONE HELP ME PLEASE:)<3
Answer: D. Cannot be determined
Step-by-step explanation: There are 3 postulates we can use for determining similar triangles.
There is Side Side Side (SSS) Postulate, which requires you have 2 sides of each triangle that are the same proportion as the other triangle. For example, in a triangle ABC, if 2 sides are 5 and 7, and in a triangle DEF, if 2 sides are 10 and 14, then the proportions 5/10 ( 1/2) and 7/14 (1/2) are equal. Thus these are similar triangles and the scale is 1/2.
There is Angle Angle (AA) postulate. If 2 angles are the same to another 2 angles in another triangle, then the two triangles are automatically similar.
The last is Side Angle Side (SAS), which requires you to have an angle that is congruent to another angle in a different triangle, and the angle is in between 2 sides that are proportionally equal to another triangle that also has the same angle in 2 sides. For example, if triangles ABC have angles A, B and C, and angle A is the same equal degrees to another angle in a triangle D, and both A and D are in between 2 sides (i.e DE and AB) that are proportionate (e.g DE and AB are proportionate.) The triangles are then similar.
None of these postulates can be applied to our given problem. Let's see why.
For Angle-Angle, we don't have 2 congruent angles. We have 2 right angles, but that's only 1 angle.
For Side Side Side, we don't have 2 sides given on each triangle, let alone proportionate ones.
For Side Angle Side, we don't even have 2 sides for each triangle given, so this cannot be used either.
explain please thanks
Answer:
26542%
Step-by-step explanation:
12,209,400/46,000 = 265.421
265.421 × 100 ≈ 26542%
. The number or expression that remains when an expression divides another expression.
Answer:
thanks for the imformation
A carnival tent is set up using a 32-foot pole as the center. The Support wires each have an angle of elevation of 38 degrees from the ground to the top of the pole. Approximately how many feet of wire is needed for one support for the tent?
Answer:
about 52 feet
Step-by-step explanation:
The figure is omitted--you may draw it to confirm my answer.
sin (38°) = 32/x
x sin (38°) = 32
x = 32 / sin (38°) = about 52 feet
Question content area top Part 1 Three friends all live on the same street that runs west to east. lives blocks from . lives from . If the street is represented by a number line and 's house is located at 0, what are the possible locations for 's house?
Based on the information, it can be inferred that Carl's house is 6 blocks from Ann's house.
How to identify where each friend's house is?To identify where each friend's house is, we must graph the information provided as shown below.
Once we have made the graph we will identify that Carl's house is 6 blocks east of Ann's house.
Note: This question is incomplete because there is some information missing. Here is the missing information:
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A silo is to be built by attaching a hemisphere roof onto a circular cylinder. The hemisphere part of the silo is constructed by a material costing $100 per square foot, and the sides are constructed with a different material costing $75 per square foot. The volume of the silo must be held to 5000 cubic feet. What radius and height, to two decimal places, will minimize the cost of the construction
The radius and height, in two decimal places are mathematically given as
r=10.60
What is the radius and height, in two decimal places?Generally, the equation for the volume is mathematically given as
[tex]V=\pi r^{2} h+\frac{2}{3} \pi r^{3}[/tex]
Therefore
[tex]5000 &=\pi 0^{2} h+\frac{2}{3} \pi r^{3}[/tex]
[tex]V(r, h) &=\pi r^{2} h+\frac{2}{3} \pi r^{3}-5000 \\\nabla V &=\left\langle 2 \pi r h+2 \pi r^{2}, \pi r^{2}\right\rangle \\[/tex]
[tex]\cos t &=100\left(2 \pi r^{2}\right)+75(2 \pi r h) \\\\\cos t &=200 \pi r^{2}+150 \pi r h \\\\\nabla C(r, h) &=\langle 400 \pi r+150 \pi h, 150 \pi r\rangle[/tex]
Using Lagrange method
[tex]$\langle 400 \pi \gamma+150 \pi \gamma h, 150 \pi \gamma\rangle=\lambda\left\langle 2 \pi \gamma h+2 \pi \gamma^{2}, \pi r^{2}\right\rangle$[/tex]
[tex]$400 \pi r+150 \pi r=\left(2 \pi r h+2 \pi r^{2}\right) \lambda$[/tex]
[tex]$400 \pi \gamma+150 \pi h=300 \pi h+300 \pi r \\\\[/tex]
[tex]$400 \pi r-300 \pi r=150 \pi h$[/tex]
[tex]$160 \pi r=150 \pi h \quad \\\\\\[/tex]
with
[tex]h=\frac{2}{3} r $[/tex]
[tex]$\pi r^{2} h+\frac{2}{3} \pi r^{3}=5000$[/tex]
[tex]\pi r}\left(\frac{2}{3} r \right)+\frac{2}{3} \pi^{3}=5000$[/tex]
[tex]$\frac{4 \pi \gamma^{3}}{3}=5000 \quad[/tex]
[tex]r^{3}=\left(\frac{5000 \times 3}{4 \pi}\right)$[/tex]
r=10.60
In conclusion, the radius and height, in two decimal places is
r=10.60
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Can someone please help me solve this question? Pls provide a step by step explanation too… Ty!
Answer:B 1/2
I can't type math symbols well in BRAINLY, so I use pictures╯﹏╰