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3.To find:
The right angle congruence theorem is used to prove that two triangles are congruent.
Solution:
In the given triangles, the corresponding hypotenuse and the corresponding angle are equal. So, the congruence used here is the Hypotenuse-Angle congruence that implies ABC is congruent to DEF.
Thus, the answer is Hypotenuse-Angle congruence.
Related Questions
answer this question please
Answers
The step function and its graph that represents the relationship between the number x of days and the total cost y of renting the chipper are present in the first option.
What is a step function?A function on the real numbers is referred to as a step function in mathematics if it can be expressed as a finite linear combination of interval indicator functions. A step function is, informally speaking, a piecewise constant function with a finite number of pieces.Given:
Charge for 1 day = $100
Charge for each additional day = $50
Let's assume
The cost of rent is y.
The number of days is x.
The total cost, y according to the data provided can be calculated by the equation,
y = 100 + 50x
Using y = mx+c, when graphing a step function that represents the relationship between the number of days and the total cost,
The gradient or slope will be always 50 for the graph.
So, when x = 0, y = 100 + 0 = 100
When x = 1, y = 100 + 50 = 150
When x = 2, y = 100 + 50 × 2 = 200
When x = 3, y = 100 + 50 × 3 = 250
Thus the step function is,
f(x) = 100 , if 0 < x ≤ 1
f(x) = 150 , if 1 < x ≤ 2
f(x) = 200 , if 2 < x ≤ 3
f(x) = 250 , if 3 < x ≤ 4
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for positive acute angles A and B, it is known that tan A = 11/60 and cos B 5/13 Find the value of cos(A - B) in simplest form
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The value of cos(A - B) in the simplest form will be 0.547.
What is geometry?It is defined as the branch of mathematics that is concerned with the size, shape, and orientation of two-dimensional figures.
It is given that,
tan A = 11/60
tan A = p/b
From Pythagoras therorm
h=√(p²+b²)
h=√(11²+60²)
h=61
Sin A = p/h = 11/60
Cos A = b/h = 60/61
If cos B = 5/13
Sin B = 12/13
cos (A - B) = cos A cos B + sin A sin B
cos (A - B) = (60/61)×(5/13) + (11/60)×(12/13)
cos (A - B) =0.547
Thus, the value of cos(A - B) in the simplest form will be 0.547.
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5. A truck rental agency charges $66 a week and $0.65 per mile to rent a truck. How many
miles can you drive in one week for $170. answer.
Answers
Answer:
I believe it's 160. Hope this helps.
Step-by-step explanation:
170 - 66 = 104
104 / 0.65 = 160
Given the following vector u and v, compute the linear combination below: Please provide a step by step solution ty :))
Answers
The linear combination of the given vector is computed to be:
[tex]-4u+v=\left[\begin{array}{ccc}23\\-28\\\end{array}\right][/tex]
How to find -4u + vgiven data
[tex]u=\left[\begin{array}{ccc}-6\\6\\\end{array}\right][/tex]
[tex]v=\left[\begin{array}{ccc}-1\\-4\\\end{array}\right][/tex]
Required to compute the linear combination in the form -4u + v
solving for -4u
[tex]-4u=\left[\begin{array}{ccc}-6*-4\\6*-4\\\end{array}\right][/tex]
[tex]-4u=\left[\begin{array}{ccc}24\\-24\\\end{array}\right][/tex]
solving for -4u + v
[tex]-4u+v=\left[\begin{array}{ccc}24+-1\\-24+-4\\\end{array}\right][/tex]
[tex]-4u+v=\left[\begin{array}{ccc}24-1\\-24-4\\\end{array}\right][/tex]
[tex]-4u+v=\left[\begin{array}{ccc}23\\-28\\\end{array}\right][/tex]
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Joe deposited $5000 into an account with a 5.2% annual interest rate, compounded quarterly. Assuming that no withdrawals are made, how long wi
the investment to grow to $6500?
Answers
Out of every 292 containers of juice bought in a grocery store, 160 are orange juice. What fraction of juice purchased is orange juice?
Answers
The fraction of juice that is orange juice is 40/73
How to determine the fraction of juice that is orange juice?From the question, we have the following parameters that can be used in our computation:
Juice containers = 292
Orange juice = 160
The fraction of juice that is orange juice is then calculated as
Fraction = Orange juice/Juice containers
Substitute the known values in the above equation
So, we have the following equation
Fraction = 160/292
Simplify the fraction
Fraction = 40/73
Hence, the fraction is 40/73
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Need help graphing some problem.
Answers
INFORMATION:
Using the graph of f(x) = x^2, we must describe transformations for the function g(x)=-8x^2
STEP BY STEP EXPLANATION:
First, we need to use the graph of f(x) = x^2 which is
Then, if analyze difference between f(x) and g(x), we can see that g(x) = -1*8*f(x)
So, to graph g(x) we have two transformations:
- Multiply f(x) by -1: When we multiply by -1 we obtain the parabola opening down
- Multiply f(x) by 8: When we multiply by 8 we obtain a more closed parabola
Finally, the final graph would be
ANSWER:
Given f(x) = 6x and g(x) = 9x² +5, find the following expressions (a) (fog)(4) (b) (gof)(2) (c) (fof)(1) (d) (gog)(0)
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The functions are solved below
What is a function?
A function from either a given Set X to a set Y allocates exactly one item of Y to each member of X. The set X is known as the function's domain, while the set Y is known as the function's codomain.
The functions are solved as follows
(a) f(4) = 6x4 = 24
(b) g(2) = 9x2² + 5 = 36 + 5 = 41
(c) f(1) = 6x1 = 6
(d) g(0) = 9x0² + 5 = 0 + 5 = 5
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What are some advantages of writing the polynomial I factored form when interpreting this situation
Answers
Answer: what
Step-by-step explanation:bye
17. Suppose 17 blackberry plants started growing in a yard. Absent constraint, the blackberry plants will spread by 90% a month. If the yard can only sustain 120 plants, use a logistic growth model to estimate the number of plants after 5 months. plants
Answers
Step 1: Write out the formula for logistic growth model
[tex]P(t)=\frac{KP_0e^{rt}}{K+P_0(e^{rt}-1)}[/tex][tex]\begin{gathered} \text{ Where} \\ K=\text{ the carrying capacity} \\ r=\text{ the growth rate (in decimal form)} \\ P_0=\text{ the initial population} \\ P(t)=\text{ the population at time t} \end{gathered}[/tex]Step 2: Write out the given values and substitute them into the formula
[tex]\begin{gathered} \text{ In this case,} \\ K=120 \\ r=\frac{90}{100}=0.9 \\ P_0=17 \\ t=5 \end{gathered}[/tex]Hence,
[tex]P(5)=\frac{120\times17\times e^{(0.9\times5)}}{120+17(e^{(0.9\times5)}-1)}[/tex][tex]P(5)=112[/tex]Hence, the number of plants after 5 months is approximately 112
A golf-course architect has 4 linden trees, 5 white birch trees, and 2 bald cypress trees to plant in a row along a fairway. In how many ways can the landscaper plant the trees in a row, assuming that the trees are evenly spaced?
Answers
The number of ways that the landscaper can plant the trees in a row, assuming that the trees are evenly spaced is 630 ways.
How to calculate the value?According to the data, the golf course architect needs to plant 2 bald cypress trees, 5 white birch trees, and 4 linden trees in a row along a fairway. It should be noted that the number of feasible arrangements will be shown as follows based on the information provided:
Based on the information given, it should be noted that n1 =4, n2 = 5 and n3 = 2.
Therefore, the number of ways that the lineup can be possible will be:
n! / (n − r)!
where n is the number of things to choose from and we choose r of them
This will be illustrated as:
= 10! /4!5!2!
= 630
There are 630 ways.
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Please answer the question in the picture, I will mark brainliest
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A two-variable linear equation is one with the formula ax + by + c = 0.
The solution of the system exists (1, 1) and (2, 4).
What is meant by linear equations?A linear equation is an algebraic equation of the form y = mx + b, where m is the slope and b is the y-intercept, and only a constant and a first-order (linear) term are included. The variables in the preceding equation are y and x, and it exists occasionally directed to as a "linear equation of two variables."A two-variable linear equation is one with the formula ax + by + c = 0, where a, b, c R, a, and b 0. An inconsistent pair of linear equations is a system of linear equations that cannot be solved.Let the system of Equations be
y = 3x - 2 and y = x²
From these Equations:
x² = 3x - 2,
simplifying the above equation, we get
⇒ x² - 3x + 2 = 0
⇒ x = 1, 2.
Therefore, the value of x exists x = 1, 2.
Therefore, the solution of the system exists (1, 1) and (2, 4).
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Given: x ∥ y
w is a transversal of x and y.
Prove: ∠4 ≅ ∠5
Parallel lines x and y are cut by transversal w. On line x where it intersects line w, 4 angles are created. Labeled clockwise, from the uppercase left: angle 2, angle 1, angle 3, angle 4. On line y where it intersects line w, 4 angles are created. Labeled clockwise, from uppercase left: angle 6, angle 5, angle 8, angle 7.
A 2-column table with 5 rows. Column 1 is labeled statements with the entries x is parallel to y, w is a transversal, angle 4 is congruent to angle 1, angle 1 is congruent to angle 5, angle 4 is congruent to angle 5. Column 2 is labeled reasons with the entries given, given, A, B, C.
Complete the two-column proof.
A
B
C
Answers
∠4 ≅ ∠5 Alternate internal angles
Applying the description we have the table is completed as follows
Statement Reasons
x is parallel to y Given
w is a transversal Given
angle 4 is congruent to angle 1 Vertical opposite angle
angle 1 is congruent to angle 5 Corresponding angle
angle 4 is congruent to angle 5 Alternate internal angles
How to find angle 4 is congruent to angle 5 ( ∠4 ≅ ∠5 )
The prove ∠4 ≅ ∠5 is done by the Alternate angle theorem
∠4 ≅ ∠ 1 vertical opposite angles
∠ 1 ≅ ∠5 Corresponding angle
then we can say that
∠ 1 ≅ ∠4 ≅ ∠5
hence: ∠4 ≅ ∠5 Alternate internal angles
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Answer:
A ✔ vertical angles
B ✔ corresponding angles theorem
C ✔ transitive property
Step-by-step explanation: i hope this helps :)
Victor found 12 sand dollars and 20 starfish at the beach cheyenne found 8 sand dollars and 16 starfish at the beach collection has a higher ratio of sand dollars to starfish
Answers
Using proportions, it is found that Victor has a higher ratio of of sand dollars to starfish.
What is a proportion?A proportion is a fraction of a total amount, and equations can be built to find the desired measures in the context of the problem using multiplications such as division or multiplication.
One example of proportions is for ratio problems, as:
The ratio between two amounts a and b is given by the division of a by b, that is, a/b.The ratio between two amounts b and a is given by the division of b by a, that is, b/a.Hence the ratios of sand dollars to starfish for Victor and Cheyenne are given as follows:
Victor: 12/20 = 0.6.Cheyenne: 8/16 = 0.5.0.6 > 0.5, hence Victor has the higher ratio.
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Please help I have no idea how to do this ❗️❗️❗️❗️❗️
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The height of the air ballon at 'm' minutes is expressed in the function and the value of h(3)=1600, h(9)=2800,h(11)=3200
We have given a function h in terms of m. Now we have to explain the contextual meaning of each and every expression it contains
1.) h = It is height at which ballon is cruising above from the ground level.
2.) m = It denotes the instance of minute at which we are talking about
3.) h(m) = The height as the function of minute, means the height of the ballon in changing with respect to the minute
4.) 1000 = It is the height at which ballon was cruising earlier and then started ascending
5.)200 = 200 feet the distance covered in a minute while ascending above
6.) 200m = distance ascended for 'm ' minutes
7.) 1000+200m = The total height that balloon covered after ascending for m minutes.
Now,
height at 3 minute = h(3) = 1000+200(3)=1000+600=1600
height at 9 minute = h(9) = 1000+200(9)=1000+1800=2800
height at x minute = h(x) = 1000+200(x)= 3200
1000 + 200x = 3200
200x = 2200
x = 11
Therefore, h(3) = 1600 , h(9)= 2800,h(11)=3200 are the different values of height 'h' at different 'm' minutes.
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Translate and solve the inequality. “Ten subtracted from the quotient of a number and seven is less than negative six.”
Answers
Given:
The objective is to translate the statement and solve the inequality.
Explanation:
Consider the unknown number as x. The quotient of a number and 7 can be written as,
[tex]Q=\frac{x}{7}\text{ . . . . .. . (1)}[/tex]By subtracting 10 from the quotient, the value is less than -6.
[tex]Q-10<-6\text{ . . . . .(2)}[/tex]On substituting the equation (2) in (1),
[tex]\frac{x}{7}-10<6\text{ . . . . . . (3)}[/tex]To find x :
On solving the equation (3), the value of x can be calculated as,
[tex]\begin{gathered} \frac{x-10(7)}{7}<-6 \\ x-70<-6(7) \\ x<-42+70 \\ x<28 \end{gathered}[/tex]Hence, the value of x is less than 28.
The functions f(x) = 2x and g(x) = 2–x + 3 are combined using division to get function h(x). Which represents the combined function?
Answers
The expression that represents the combined function of f(x) and g(x) is h(x) = 2x/(5 - x)
How to determine the equation of the function h(x)?From the question, we have the following parameters:
Function f(x) = 2x
Function g(x) = 2 - x + 3
Evaluate the like terms in the equation of the function g(x)
So, we have
g(x) = 5 - x
From the question, we understand that:
The function h(x) is a combination of the functions f(x) and g(x) by division
This can be represented as
h(x) = f(x)/g(x)
The above also implies that the function h(x) is a composite function
Substitute the known values in the above equation
So, we have the equation of the composite function h(x) to be
h(x) = 2x/(5 - x)
Hence, the equation of the composite function h(x) is h(x) = 2x/(5 - x)
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P = 12 + 4d/11
In certain deep parts of oceans, the pressure of sea water, P, in pounds per square foot, at a depth of d
feet below the surface, is given by the following equation
If a scientific team uses special equipment to measures the pressure under water and finds it to be 312
pounds per square foot, at what depth is the team making their measurements?
Answers
Depth= 45 feet
The force applied perpendicular to the surface of an object per unit area over which that force is distributed is defined as Pressure.
Pressure causes serious problems for people as you travel deeper in water because pressure increases. This is called hydrostatic pressure. Water doesn’t only push down from above. It pushes from all sides and also from below. The upward force is called buoyancy. It helps you keep afloat in water.
Given Pressure, p of under water is 312,
Given equation is:
P=12+4d/11
312=12+4d/11
312=12*11+4d
312-(12*11)= 4d
312-132= 4d
180=4d
d=180/4
=45 feet
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Evalúe the limit. Show steps
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After evaluating the limit we have came to find that the limit of [tex]\lim_{h\rightarrow 0 }\frac{(4/3 +h)^3-(4/3)^3}{h}[/tex] as h approaches 0 is Undefined
What is limit?A limit is the value that a function, sequence, or index approaches as an input or as an index approaches a particular value in mathematics. The definitions of continuity, derivatives, and integrals depend on limits, which are essential to calculus and mathematical analysis.
The concept of a limit of a sequence is further generalized to include the concept of a limit of a topological network, in addition to having a connection to the category theory concepts of limit and direct limit.
A limit of a function is typically expressed in formulas as
[tex]{\displaystyle \lim _{x\to c}f(x)=L,}[/tex]
To find the limit
⇒ [tex]\lim_{h\rightarrow 0 }\frac{(4/3 +h)^3-(4/3)^3}{h}[/tex]
Evalúe 0 as h
⇒ [tex]\frac{(4/3 +0)^3-(4/3)^3}{0}[/tex]
⇒ Undefined
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If x3 = 125, find x²
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The value of [tex]x^{2}[/tex] is 25 when we have (cube of x = 125) [tex]x^{3}[/tex] = 125.
According to the question,
We have the following expression:
[tex]x^{3} = 125[/tex]
Now, we will do the cube roots on both the sides:
[tex]\sqrt[3]{x^{3} } = \sqrt[3]{125}[/tex]
(We can find the cube roots of 125 by finding the Least Common Multiple or LCM.)
So, we will have the following expression:
x = 5
Now, to find the value of [tex]x^{2}[/tex], square on both the sides:
[tex]x^{2} = 5^{2}[/tex]
[tex]x^{2}[/tex] = 25
(More to know: when we square a number we multiply a number two times and when we find cube of a number then we multiply a number three times.)
Hence, the value of [tex]x^{2}[/tex] is 25.
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Drum Tight Containers is designing an open-top, square-based, rectangular box that will have a volume of 171.5 in.³.
What dimensions will minimize surface area?
The length of one side of the base is?
The height of the box is?
What is the minimum surface area?
Answers
The length of one side of the base is 7 inches.
The height of the box is 3.5 inches.
The minimum surface area of the box is 147 inch².
Let the length of the box be "l".Let the height of the box be "h".The volume of the box is given to be 171.5 inch³.171.5 = l²hh = 171.5/l²The surface area of the box is "A".The surface is made up of the base and the four sides of the box.A = l² + 4*h*lA = l² + 4*(171.5/l²)*lA = l² + 686/lWe need to minimize the surface area.Differentiate the equation with respect to "l".dA/dl = 2l - 686/(l²)To get the minima, put dA/dl = 0.2l - 686/(l²) = 02l = 686/(l²)l³ = 343l = 7 inchesh = 171.5/l²h = 3.5 inchesA = l² + 686/lA = 49 + (686/7)A = 147 inch²To learn more about minima, visit :
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"A line goes through the points (1, -10) and (-3, -2). Find the slope of the line and write the equation
of the line in point-slope form. Show your work algebraically for full credit."
Answers
Slope
[tex]\frac{-10-(-2)}{1-(-3)}=-2[/tex]
Equation
[tex]y+10=-2(x-1)[/tex]
1. Give the values of x for sinx=-1/2 where o' ≤ x ≤ 360°: x₁ = and x₂ =
Answers
Answer:
Sine is negative in III and IV quadrants. Now sin 30 1/2. Taking = 30, Sin (180+0) = sin (360-0): =- sin 0. So x = 210 degrees or 330 degrees
Step-by-step explanation:
Can you please solve this.
Answers
⇒I will use the laws of exponents. When you multiply powers of the same base you keep one base and add the exponents.
Below are all the steps in details
[tex]=9^{-8+(-2)} \\=9^{-8-2} \\=9^{-10} \\=\frac{1}{9^{10} } \\=\frac{1}{3486784401}[/tex]
A baking scale measures mass to the tenth of a gram, up to 650 grams. Which of the following measurements is possible using this scale?
742.5 grams
300.0 grams
85.25 grams
370 milligrams
Answers
The possible measures using this scale are 742.5 grams and 300.0 grams.
What is a scale?The link between a measurement on a model and the corresponding measurement on the real item is represented by scale.
Note that a tenth of a gram is 0.1 grams, therefore, the precision of the scale is 0.1 grams.
Note that 370 milligrams are equivalent to 0.370 grams.
Since the measures on the scale increase by 0.1 units, 0.25 and 0.370 are not possible on this scale.
Hence, the possible measures using this scale are 742.5 grams and 300.0 grams.
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question will be in picture
Answers
Step 1: Write the given expression
[tex](2y-3)^2[/tex][tex](2y-3)^2=(2y-3)(2y-3)[/tex]Step2: Expand the expression
[tex]\begin{gathered} 2y(2y-3)-3(2y-3) \\ =4y^2-6y-6y+9 \\ =4y^2-12y+9 \end{gathered}[/tex]Hence
[tex](2y-3)^2=4y^2-12y+9[/tex]hence the righ
Assume that when adults with smartphones are randomly selected, 48% use them in meetings or classes. If 15 adult smartphone users are randomly selected, find the probability that exactly 11 of
them use their smartphones in meetings or classes.
What is the probability?
Answers
The probability that exactly 11 of them use their smartphones in meetings or classes is 3.89%
What is probability ?Probability is the likelihood of something occurring. This branch of mathematics studies the nature of chance. It is expressed as a number between 0 and 1. Probability has been brought to mathematics in order to foresee the potential of events. Probability can be defined as the degree of likely that something will occur. The probability that the outcomes of a random experiment will be as expected can be calculated using this fundamental theory of probability, which is also applied to the probability distribution. To establish the probability that a particular event will occur, we must first determine the total number of choices.
x = 11
n= 15
P =48%
=0.48
P(x=11)=[tex]15C_{11} (0.48)^{11} (1-0.48)^{4}[/tex]
=1365(0.0003116403)(0.09150625)
=0.0389
=3.89%
The probability that exactly 11 of them use their smartphones in meetings or classes is 3.89%
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Please help me I was sick today and missed out on class and I don’t understand this question
Answers
I hope this is clear enough , although I did not arrive at the same answer using x in both equation .
[tex]x( {e}^{y} + 1) {}^{2} \: {e}^{ - y} dx \: + {e}^{ {x}^{2} } dy \: = 0[/tex]
Exact differential equation
Answers
The correct differential equation for [tex]x(e^{y}+1)^{2} e^{-y}dx+ e^{x^{2} }dy =0[/tex]
is [tex](e^{y}+1)^{2}e^{-y}/ -e^{x^{2}}= dy/dx\\[/tex].
to extract the differential equation we need to express it in the form of dy/dx.
[tex]x(e^{y}+1)^{2}e^{-y}dx=-e^{x^{2}}dy\\x(e^{y}+1)^{2}e^{-y} = -e^{x^{2}}dy/dx\\x(e^{y}+1)^{2}e^{-y}/ -e^{x^{2}}= dy/dx\\[/tex]
What are differential equations?
An equation involving one or more functions and their derivatives is referred to as a differential equation in mathematics. The rate of change of a function at a place is determined by the derivatives of the function. Physicists, engineers, biologists, and other professionals primarily use it in these domains.
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The area of a square garden is 81 m². How long is each side of the garden?
Each side is m long.
Answers
Answer:
each side would be 9m long
The length of each side of the square garden is 9 meters long.
What is the perimeter?The perimeter of any 2D figure is the sum of the lengths of all the sides except the circle which has a perimeter or circumference which is 2πr.
We know the area of a square is a product of any two sides of the square and all four sides of a square are of the same length.
Given a square has an area of 81m².
∴ We have to determine such a number which when multiplied by itself results in 81.
Such a unique number is 9.
So, the area of the square can be written as (9×9) m².
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