That is a change in the hypotenuse's length of -2.6 inches per second.
What in math is a rate?
A rate is a unique ratio where the two words are expressed in several units. For instance, the price is 69 for 12 ounces if a 12-ounce can of maize costs 69. This is not a proportion of two comparable units, like shirts. This ratio compares two dissimilar units: ounces and cents
h = sqr(b^2 + a^2), b=30, a=40, b'=-5, a'=-7
h' = [(1/2)/sqr(b^2+a^2)](2bb' + 2aa') = sqr(30^2+40^2)(30(5)+40(-7)
= (150-280)/sqr2500 = (-130)/50 =-- -13/5 = -2.6 inches per second
2.6 inches are lost from the hypotenuse every second.
Check the response by observing what transpires in one second.
30 to 35 on the short leg
greater leg descends from 40 to 37
From 50 to 47.4 is the hypotenuse
In one second, 50-47.4 equals a 2.6 reduction. That is a change in the hypotenuse's length of -2.6 inches per second.
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In triangle XYZ, m∠Y = 62.45° and m∠Z = 41.8°. Determine the measure of the exterior angle to ∠X.
104.25°
75.75°
37.85°
18.94°
The exterior angle to ∠X is 104.25°
What is the exterior angle theorem?The exterior angle theorem states that when a triangle's side is extended, the resultant exterior angle formed is equal to the sum of the measures of the two opposite interior angles of the triangle. The theorem can be used to find the measure of an unknown angle in a triangle.
from the above definition , if ∠Y = 62.45° and ∠Z = 41.8°
It means from exterior angle theorem that
exterior ∠X = ∠Y + ∠Z
exterior ∠X = 62.45° + 41.8°
exterior ∠X = 104.25°
In conclusion the exterior angle X is 104.25°
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How do I find all the squares from 1 to 20?
Answer:
2.4.6.8.10
Step-by-step explanation:
that's the answer
Answer:
1, 4, 9, 16, 25, 36, 49, 64, 81, 100
Step-by-step explanation:
1, 4, 9, 16, 25, 36, 49, 64, 81, 100, multiply all numbers frmo 1 to 10
Simplify each ratio. Make sure to convert the units when needed
6 hours: 4 days (Hint: There are 24 hours each day.)
Answer:
1 : 16
Step-by-step explanation:
6 hours : 4 days
6 hours : 96 hours
1 hour : 16 hours
Mary has 30 hats. She has 5 green, 7 blue, 12 red, and 6 brown. If she selects two hats at random, what is the probability that both hats are different colors?
P(Picking one Green Hat and Something Else)=
P(Picking one Blue Hat and Something Else)=
P(Picking one Red Hat and Something Else)=
p(Picking one Brown hat and something Else)=
Add the probabilities together to answer the question
The probability that both hats are different colors is; 0.7425
How to find the probability of selection?We are given;
Total number of hats = 30 hats
Number of green hats = 5 hats
Number of blue hats = 7 hats
Number of red hats = 12 hats
Number of brown hats = 6 hats
Now, if Mary selects two hats at random, then the probability that they are different colors is;
P(they are different colors) = 1 - P(both are the same color)
P(both are the same color) = (⁵/₃₀ * ⁴/₂₉) + (⁷/₃₀ * ⁶/₂₉) + (¹²/₃₀ * ¹¹/₂₉) + ( ⁶/₃₀ * ⁵/₂₉)
= (20 + 42 + 132 + 30)/(30*29)
= 224/(30*29)
= 0.2575
Thus;
P(they are different colors) = 1 - 0.2575
P(they are different colors) = 0.7425
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Last year at a certain high school, there were 60 boys on the honor roll and 100 girls on the honor roll. This year, the number of boys on the honor roll increased by 20% and the number of girls on the honor roll increased by 3%. By what percentage did the total number of students on the honor roll increase? round your answer to the nearest tenth (if necessary).
The percent increase in the total number of students on the honor roll is 9.4% .
In the question,
it is given that ,
last year , the number of boys in the honor roll is = 60 boys ,
the number of girls in the honor roll is = 100 girls ,
total number of students last year = 160
percent increase in the number of boys in the honor roll is = 20% ,
so , number of boys become = 60 + (0.20*60) = 72 boys ,
percent increase in the number of girls in the honor roll is = 3% ,
so , number of girls become = 100 + (0.03*100) = 103 girls ,
total number of students this year = 103 + 72 = 175 .
increase in number of students = 175 - 160 = 15
So , percent increase is = (15/160) × 100
= 0.09375 × 100
= 9.375 %
≈ 9.4%
Therefore , the percent increase is 9.4% .
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When solving a system of linear equations by substitution, how do you decide which variable to solve for in step 1?.
When solving a system of linear equations by substitution, normally, we want to try to solve for the easiest one to get to or we choose a variable with unit coefficient.
What you mean by a variable?A variable is a quantity that could change depending on the circumstances of an experiment or mathematical problem. Typically, a variable is denoted by a single letter. The general symbols for variables most frequently used are the letters x, y, and z.
What a coefficient means?A constant component of a word as opposed to a variable. a measurement of some property or characteristic using a number (as of a substance, device, or process)
There are many factors, it is all a matter of preference, normally, we want to try to solve for the easiest one to get to
example;
if we have
(x-3)^2+y=9
we would solve for y because it is less tricky or we choose a variable with unit coefficient.
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Literal Equations
help asap !!
Answer:
Step-by-step explanation:
y = 6x + 42
6x + 42 = y
6x = y - 42
x = (y - 42)/6
A publisher used 10 boxes to send 375 books to a local book retailer. The
small boxes hold 30 books and each large box holds 55 books. Determine
the number of small and the number of large boxes used.
Answer: Number of small boxes = 7, Number of large boxes =3
Step-by-step explanation:
Let x= Number of small boxes , y = Number of large boxes.
As per given , 30x+55y=375 (i)
x+y=10 (ii)
Multiply (ii) by 30, we get
30x+30y=300 (iii)
Eliminate (iii) from (i), we get
25y=75
⇒ y= 3 [Divide both sides by 25]
Put y=3 in (ii), we get
x+3=10 ⇒ x=7
Hence, Number of small boxes = 7, Number of large boxes =3
Hope this helps!!! :)
Given triangle ABC with m
The lengths of AN=2.5cm and MN=3.5cm
What is similar triangle?
Similar triangles are triangles that have a similar form, however their sizes might vary.
Main body:
IN ΔAMN ≈ΔABC
Since MN∣∣BC
∠AMN=∠ABC (Corresponding angles)
∠ANM=∠ACB (Corresponding angles)
∴ΔAMN∼ΔABC(By $$AA similarity criterion)
⇒AM/AB =AN/AC=MN/BC (CPCT)
since , M is the mid point of AB.
AM = 1/2 AB , OR
AM/AB = 1/2
AM/AB =AN/AC = 1/2
AN/AC = 1/2
AN/5= 1/2
AN = 2.5 cm
AM/AB =MN/BC = 1/2
[∵BC=7cm]
MN/7 = 1/2
MN= 7/2 =3.5
Hence , the lengths of AN=2.5cm and MN=3.5cm
the complete question is :
In triangle ABC, M is mid-point of AB and a straight line through M and parallel to BC cuts AC at N. Find the lenghts of AN and MN, if BC=7cm and AC=5cm.
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Describe fully the single transformation which takes shape A to shape B.
A
51
4
3
2
+
-5 -4 -3 -2 -1 0
-1
-2
-3
-4
-5
B
33/54 Maks
1 2 3 4 5
-X
D
Answer:
x=d
Step-by-step explanation:
Sheri’s house is 0.05 miles from Abdul’s house. The post office is 0.1 mile from Abdul’s house. The school is 38mile from the post office.
If Sheri stops at Abdul’s house, and the post office on her way to school, how far will Sheri walk in all?
Answer:
39.05 miles
Step-by-step explanation:
0.05+0.1+38
50 POINTS IF ANSWERED PLSS!!!!!
Mr. Hansen has three sticks that measure 5 inches, 10 inches, and 17 inches. If he connects the sticks ends, will the three sticks form a triangle?
Answer:
No
Step-by-step explanation:
5+10=15, which cannot be less than 17
8.2 end of unit assessment Triangle ABC and DEF are similar
The Assessment Triangle and the Domains and Dimensions of the Assessment Framework.
How to Find the Perimeter of Similar Triangles?If two triangles are similar to each other, and the perimeter of one is A with a side length of a, and the perimeter of the other is B with a side length of b, then, the following below is the ratio of their perimeters are intended as a reminder to professionals undertaking the assessment and to be given to parents to help them understand the areas the worker will want to explore.The PAT was originally developed in 1996 by Dr s. Ronald Dickman, Dena Brownstein and Marianne Gausche-Hill as a novel tool to standardize the initial assessment of infants and children for all levels of health care providers.Background The Paediatric Assessment Triangle (PAT) has been proven to be effective in the general impression of the health status of the child and can interlink the potential underlying pathophysiology so to alert the clinician into how critically ill/ injured the child might bePerimeter of A/perimeter of B = a/b
Given that triangles ABC and DEF are similar triangles, we have the following:
Perimeter of triangle ABC = x
One side length of triangle ABC = 4 cm
Perimeter of triangle DEF = 12 + 6 + 9 = 27 cm
One side length of triangle DEF = 6 cm
Therefore:
x/27 = 4/6
Cross multiply
6x = (27)(4)
6x = 108
6x/6 = 108/6
x = 18
Thus, the perimeter of tr8angle DEF that is similar to triangle ABC is: 18 cm.
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Jethro and $50 to hi cafeteria account that had $40 on it already each time he buy lunch $4. 50 i deducted from the account write an equation in lope intercept form relating the number of lunche purchaed X to the amount of money remaining on the cafeteria count why what i the maximum number of lunche Jethro can purchae math problem
He has a total of $90 in his cafeteria wallet, thus the most lunches he may purchase is 20.
What is division?A number is divided in division, which is a straightforward procedure. The simplest way to conceptualize it is as a set of objects being distributed among a set of individuals, as in the example given above. In mathematics, division is the process of dividing a number into equal parts and calculating the maximum number of equal parts that can be made. For instance, dividing 15 by 3 results in the division of 15 into 3 groups of 5 each.
Here,
Amount added=$50
Amount already in wallet=$40
Total amount in wallet=50+40
=$90
Cost of each lunch=$4.5
Number of lunch he can buy,
=90/4.5
=20
The maximum number of lunch he can buy is 20 lunch as he has a total of $90 in his cafeteria wallet.
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list five requirements that a person should know about their pet before owning one
The five requirements that a person should know about their pet before owning one are shown below.
What is pet?An animal that you keep as a pet in your home is for your entertainment and company.
There are 5 requirements that a person should know about their pet before owning one.
Freedom from thirst and hunger All canines and felines have to have quick access to food and clean water.
Liberation from discomfort.
Freedom from discomfort, harm, or illness.
Having the ability to act normally.
Freedom from anxiety and pain.
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Solve the system of linear equations by substitution -5x+6y=-11 6y=x+5
Answer:
Step-by-step explanation:
y = 1/6x + 5/6
-5x + 6(1/6x + 5/6) = -11
-5x + x + 5 = -11
-4x + 5 = -11
-4x = -16
x = 4
y = 2/3 + 5/6
y = 7/6 or 1 1/6
(4, 7/6)
−5 5 6 x1 1 2=? Type an integer, proper fraction, or mixed number.
Multiplying Rational Numbers Problem Solving
Answer:
-62272
Step-by-step explanation:
Multiplication on a piece of paper also a positive multiplied by a negative is negative so -556 * 112 = -66272.
What is the relationship between a 90% confidence interval around a mean and a 95% confidence interval around a mean?.
You have a 5% probability of being incorrect with a 95% confidence interval. You have a 10% probability of being incorrect with a 90% confidence interval.
What is the mean's 90% confidence interval?We can be 90% certain that the interval contains the population mean,, if the level of confidence is 90%. The associated z-scores are 1.645. We can be 95% certain that the interval contains the population mean, if the level of confidence is 95%.
What happens when two confidence intervals overlap?In other words, the difference in effect estimates between the two subgroups is deemed to be statistically unimportant if the confidence intervals overlap.
You have a 5% probability of being incorrect with a 95% confidence interval. You have a 10% probability of being incorrect with a 90% confidence interval. A 95% confidence interval is narrower than a 99% confidence interval.
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Are the lines C and D parallel? (The figure may not be drawn to scale). Giving brainliest for whoever answers correctly
1. Yes
2.no
3. Can’t be determined
The lines C and D are parallel.
What is a line?
In pure mathematics, a line is an infinitely long object with no dimension, depth, or curvature. Thus, lines ar one-dimensional objects, although they'll exist in 2, three, or higher dimension areas
Main body:
As Line LM cuts the line at C the angle made by both line is 48°
and line NP cuts the line at D , the angle made by line is 132°
we know that to make a line parallel , the sum of angle on one side of the line should be 180°
∠C +∠D = 48° +132°
= 180°
Hence , the lines C and D are parallel.
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Help solve this please:
Adam has saved £2 less than Dan.
Write and expression for the amount that Dan saved.
The graph of g(x) is a transformation of the graph of f(x) = 3^x enter the equation for g(x) in the box
Answer:
g(x)=3^x+7
Step-by-step explanation:
f(0)=3^0
that is the y-intercept
now we can take the known y-intercept of g(x) which is 8 and then we can get our b in the y=mx+b equation.
simple q help pls due tomorrow
Answer:
(1/2x+3)(1/2x+3)
OR
[tex](1/2x+3)^{2}[/tex]
Sam wants to purchase birthday gifts for his two sisters that share the same birthday. One sister likes daisies which cost $2 per stem and the other likes tulips which cost $3 per stem. 1). If he has $12 to spend, how many of each could he buy?
You must write an inequality.
2). Graph your solution
The inequality which represents is 2x + 3y ≤ 12 where x is the number of daisies and y is the number of tulips.
What is inequality?A mathematical phrase in which the sides are not equal is referred to as being unequal. In essence, a comparison of any two values reveals whether one is less than, larger than, or equal to the value on the opposite side of the equation.
Suppose the cost of one daisy is x while the cost of one tulip is y.
2x + 3y will be totally spent and it can be almost $12.
2x + 3y ≤ 12
Hence "The inequality which represents is 2x + 3y ≤ 12 where x is the number of daisies and y is the number of tulips.".
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A tate government borrow $2,000,000 at imple annual interet. Some of the money i borrowed at 6%, ome at 7. 5%, and ome at 8. 5%. Ue a ytem of linear equation to determine how much (in dollar) i borrowed at each rate given that the total annual interet i $137,000 and the amount borrowed at 7. 5% i four time the amount borrowed at 8. 5%. Solve the ytem of linear equation uing matrice
By solving the linear matrices we got the values X = 1000000 , Y = 800000 , Z = 200000
What is an equation ?According to algebra, an equation is a statement that shows the equality of two mathematical expressions. For instance, the equation 4x + 5 = 15 consists of the two equations 4x + 5 and 15, which are separated by the 'equal' sign.
According to the given information
X + Y + Z = 2000000
0.07X + 0.085Y + 0.095Z = 157000
Y = 4Z
Y = 4Z is substituted into the first and second equations as follows:
X + 5Z = 2000000
0.07X + 0.085 (4Z) + 0.095Z = 157000
X = 2000000 - 5Z
0.07X + 0.435Z = 157000
0.07 (2000000 - 5Z) + 0.435Z = 157000
140000 - 0.35Z + 0.435Z = 157000
0.085Z + 140000 = 157000
0.085Z = 17000
Z = 200000
Y = 800000
X = 1000000
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I'LL GIVE BRAINLIEST!! ANSWER THE QUESTION!!!
Part a
This represents a translation of 2 units to the right. So, the points are [tex](6, -3), (0,0), (8, -15)[/tex].
Part b
This represents a translation of 9 units up. So, the points are [tex](4,6), (-2,9), (-10,-6)[/tex].
Part c
This represents a translation of 3 units left and 1 unit down. So, the points are [tex](1, -4), (-5, -1), (-13, -16)[/tex].
HELP PLEASE
Researchers are conducting clinical trials for a new medication to treat people suffering from asthma, a respiratory disease.
They selected 100 asthma patients from a national hospitals database in these age groups: under 15 years, 15 to 60 years,
and over 60 years. In each group, half the subjects received the new medication, and the other half received a placebo. The
subjects were not informed whether they received the medication or the placebo.
Which statements about this study are true?
Answer:
1. This study uses blocking to reduce variability from known factors.
2. This study uses random sampling.
Step-by-step explanation:
Hope it helps!
I think of a number and add 3. The answer is 18
Answer: 15
Step-by-step explanation:
15+3=18
Consider the functions
Answer:
(fog)(x) = 4x^2 -12x +10
(gof)(x) = 2x^2 -1
Step-by-step explanation:
(fog)(x) = (2x-3)^2 + 1
= 4x^2 + 9 -12x +1
= 4x^2 -12x +10
(gof)(x) = 2(x^2+1)-3
= 2x^2 +2 -3
= 2x^2 -1
Help meeee how do I solve
18x2 + 9x - 20
Answer:
18x^2 + 9x - 20
18x^2 + 24x - 15x - 20
6x(3x+4) - 5(3x+4)
Therefore, (6x-5)(3x+4)
-Wilson Middle School wants to rent tables for their weeklong art festival. One rental company charges a $20 setup
fee and $12 per table for the week. Another rental company charges a $30 setup fee and $10 per table for the week.
How many tables can the school rent for the charge to be the same for both companies?
Answer:
5 tables
Step-by-step explanation:
Let x be the number of tables the school needs to rent, and c be the total cost of renting the tables.
We can use the following equation to represent the cost of renting from the first company:
c = 20 + 12x
And we can use the following equation to represent the cost of renting from the second company:
c = 30 + 10x
As c is the same constant in both equations, we can say the following:
20 + 12x = 30 + 10x
Now we can solve this equation by simplifying:
20 + 12x = 30 + 10x
20 + 2x = 30
2x = 10
x = 5
Therefore, the school will need to rent 5 tables for the cost to be the same from both renting companies.
Answer: 5 tables
Step-by-step explanation:
The first rental company will charge $32 for one table.
The second rental company will charge $40 for one table.
So if we make a table, and keep adding $12 to the first company and $10 to the second it will look like this.
First company Second company Table
$32 $40 1
$44 $50 2
$56 $60 3
$68 $70 4
$80 $80 5
Therefore, the school can rent 5 tables for the same price in both companies.