Answer:
Exercise 1: The length of the unknown leg is 4 inches.
Exercise 3: The following straws can be used to construct the triangle: b) [tex]3\,in[/tex], c) [tex]4.5\,in[/tex], d) [tex]6.5\,in[/tex], e) [tex]10\,in[/tex], f) [tex]13.5\,in[/tex]
Exercise 4: Possible options of this exercise: 1) (2, 4, 5), 2) (4, 5, 6), 3) (5, 6, 10), 4) (1, 2, 11), 5) (1, 4, 11), 6) (1, 10, 11)
Step-by-step explanation:
Exercise 1:
Let suppose that triangle represented in the figure is a right triangle, the length of the missing leg is determined by Pythagorean Theorem:
[tex]y = \sqrt{l^{2}-x^{2}}[/tex] (1)
Where:
[tex]l[/tex] - Hypotenuse, in inches.
[tex]x[/tex] - Known leg, in inches.
[tex]y[/tex] - Unknown leg, in inches.
If we know that [tex]l = 11\,in[/tex] and [tex]x = 10\,in[/tex], then the length of the unknown leg is:
[tex]y = \sqrt{21}[/tex]
Since 4 is the least whole number closest to [tex]\sqrt{21}[/tex], then we conclude that the length of the unknown leg is 4 inches.
Exercise 3:
The range of possible lengths for the missing side of the triangle is represented by the following simultaneous inequality:
[tex]x + y > l > x-y[/tex] (2)
Where:
[tex]x[/tex] - Greater side, in inches.
[tex]y[/tex] - Lesser side, in inches.
[tex]l[/tex] - Missing side, in inches.
If we know that [tex]x = 8\,in[/tex] and [tex]y = 6\,in[/tex], then we have the following range of missing sides:
[tex]14\,in > l > 2\,in[/tex]
The following straws can be used to construct the triangle: b) [tex]3\,in[/tex], c) [tex]4.5\,in[/tex], d) [tex]6.5\,in[/tex], e) [tex]10\,in[/tex], f) [tex]13.5\,in[/tex]
Exercise 4:
Let check each pair to determine possible constructions by means of the inequality used in Exercise 3:
(i) [tex]x = 4\,in, y = 2\,in[/tex]
[tex]6\,in>l>2\,in[/tex]
Possible choices: 5 inches.
(ii) [tex]x = 5\,in, y = 2\,in[/tex]
[tex]7\,in > l > 3\,in[/tex]
Possible choices: 4 inches, 6 inches.
(iii) [tex]x = 6\,in, y = 2\,in[/tex]
[tex]8\,in > l > 4\,in[/tex]
Possible choices: 5 inches, 6 inches.
(iv) [tex]x = 10\,in, y = 2\,in[/tex]
[tex]12\,in > l > 8\,in[/tex]
Possible choices: None.
(v) [tex]x = 5\,in, y = 4\,in[/tex]
[tex]9\,in > l > 1\,in[/tex]
Possible choices: 2 inches, 6 inches.
(vi) [tex]x = 6\,in, y = 4\,in[/tex]
[tex]10\,in > l > 2\,in[/tex]
Possible choices: 5 inches.
(vii) [tex]x = 10\,in, y = 4\,in[/tex]
[tex]14\,in > l > 6\,in[/tex]
Possible choices: None.
(viii) [tex]x = 6\,in, y = 5\,in[/tex]
[tex]11\,in > l > 1\,in[/tex]
Possible choices: 2 inches, 4 inches, 10 inches.
(ix) [tex]x = 10\,in, y = 5\,in[/tex]
[tex]15\,in > l > 5\,in[/tex]
Possible choices: 6 inches.
(x) [tex]x = 10\,in, y = 6\,in[/tex]
[tex]16\,in > l > 4\,in[/tex]
Possible choices: 5 inches.
Possible options of this exercise: 1) (2, 4, 5), 2) (4, 5, 6), 3) (5, 6, 10), 4) (1, 2, 11), 5) (1, 4, 11), 6) (1, 10, 11)
Answer: Give other user brainliest
Step-by-step explanation:
Identify the 31st term of an arithmetic sequence where a1 = 26 and a22 = −226.
−334
−274
−284
−346
Answer:
a31 = -334
Step-by-step explanation:
Given:
a1 = 26
a22 = -226
Find:
a31
Computation:
a22 = a + 21d
-226 = 26 + 21d
d = -12
a31 = a + 30d
a31 = 26 + 30(-12)
a31 = 26 - 360
a31 = -334
a1 = 26 and a22 = −226.
Answer:
A) −334
what is a ratio that compares quantities with unlike units of measures
Equivalent Ratios
Unit
Unit Price
Rate
Ratio
Ratio table
Terms
Barton has 4 strawberries and Ona has 8. If they want to redistribute their strawberries so they each have an equal number, how many strawberries should Ona give to Barton? There are a total of strawberries. There are a total of people. The expression to find the mean, or balance point, is . should give 2 strawberries to for the number of strawberries to be balanced.
Answer:
2 strawberries
Step-by-step explanation:
Given that:
Number of strawberries :
Ona has 8
Barton has 4
For both Ona and Barton to have the same Nunber of strawberries :
(Ona + Barton) /2 = (8 + 4) / 2 = 12 /2 = 6
That means both Ona and Barton will have 6 strawberries each
Hence,
Barton who has 4 strawberries needs 2 more while Ona who has 8 will give out 2
Hence, Ona should give two strawberries to Barton.
Answer:
total strawberries 12
total 2 people
expression to find the mean 12/2
ona should give barton 2 strawberries so the number balance's out
Step-by-step explanation:
ywww trust me
A Triangle Has A Base of X 1/2m and a height of X 3/4m. If the area of the triangle is 16m^2, what are the bade and height of the triangle
Answer:
B
Step-by-step explanation:
what's is m when u are looking for x or y intercept
Answer:
Slope.
Step-by-step explanation:
mx+b
Answer:
Slope
Step-by-step explanation:
The equation of lines are normally formatted in "slope-intercept form"
(y = mx + b)
The b in the equation would be the y-intercept of the line.
The m represents the slope.
The x and y can be replaced with any x and y value from the line (if necessary)
y
∝
√
x
If
y
=
45
when
x
=
81
find,
y
when
x
=
225
Answer:
y = 75
Step-by-step explanation:
Given that:
y [tex]\alpha[/tex] [tex]\sqrt{x}[/tex]
⇒ y = k[tex]\sqrt{x}[/tex]
where k is the constant of proportionality.
When y = 45, x = 81, then;
45 = k[tex]\sqrt{81}[/tex]
45 = 9 k
k = [tex]\frac{45}{9}[/tex]
= 5
k = 5
So that,
y = 5[tex]\sqrt{x}[/tex]
the value of y when x = 225 is;
y = 5[tex]\sqrt{x}[/tex]
= 5 x [tex]\sqrt{225}[/tex]
= 5 x 15
y = 75
Which graphs best describes the function y = 4x
Answer:
J
Step-by-step explanation:
check by multiplying each x value by 4
Answer:
D (J)
Step-by-step explanation:
y=4x is basically multiplying the x value by 4; 10*4 is 40, 20*4 is 80, and so on.
Guided Practice
Find the distance you can see to the horizon from a height of 100 feet. Use the formula d = 1.5h⎯⎯⎯⎯⎯⎯⎯√ to approximate the distance d in miles to a horizon when h is the height in feet of the viewer's eyes above the ground. Round your answer to the nearest mile.
A.
12 mi
B.
10√1.5 mi
C.
13 mi
Answer:
A. 12 mi
Step-by-step explanation:
A.
12 mi
d===≈≈1.5h⎯⎯⎯⎯⎯⎯⎯√1.5•100⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯√150⎯⎯⎯⎯⎯⎯√12.24712
The distance to the horizon is about 12 miles.
What congruence criterion shows that
A ACE A BCD
?
E
B
A
D
AAS
SAS
HL
O ASA
Answer:
SAS
Step-by-step explanation:
It shows that triangle ACE and BCD are congruent by
SAS axiom
HOPE IT HELPS :)
by sas
EC=CD[GIVEN]
AC=CB(GIVEN)
<ECA=<BCD()VERTICAL OPPOSITE ANGLE
Simplify the expression.
-2.4f + 0.3f-16 - 3
-2.4f + 0.3f-16 -3=
Answer:
-2.1f-18
Step-by-step explanation:
-2.4f+0.3f=-2.1f.
-16-3=-19
The sum of two numbers is 48.if the smaller number is subtracted from the larger the difference is 12 find the number
Answer:
18
Step-by-step explanation:
30 + 18 = 48
30 - 18 = 12
Both true, so our solution is correct.
The value of the larger number is 30 and the value of the smaller number is 18.
What is a number system?A numeral system is a writing system for expressing numbers; that is, a mathematical notation for representing numbers of a given set in a consistent manner using digits or other symbols. In different numeral systems, the same sequence of symbols can represent different numbers.
Given that the sum of two numbers is 48. if the smaller number is subtracted from the larger the difference is 12. The two numbers will be calculated as,
x + y = 48
x - y = 12
________
2x = 60
x = 30
y = 30 - 12
y = 18
Therefore, the value of the larger number is 30 and the value of the smaller number is 18.
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help me please for points
Answer:
the answer is c
Step-by-step explanation:
2/5=.4
4/8=.8
.4 is smaller than .8
Answer:
C
Step-by-step explanation:
2/5= 0.4
1/10= 0.1
4/5= 0.8
PLEASE HELP YA GIRL OUT ILL GIVE U BRAINLIST
Answer:
12.75feet (12¾)
Step-by-step explanation:
7t+1+5t+8=162feet
12t+9=162feet
12t=162-9
=153
t = 153÷9
=12.75feet (12¾feet)
HELPPPPP!
Seven more than the product of 7 and Craig's score
Answer:
14
Step-by-step explanation:
7+7
A random sample of students were asked whether they prefer milk juice or water is it results are summarized in the table.
Answer:
C
Step-by-step explanation:
The probability of students response is milk is 0.311.
What is probability?Probability deals with the occurrence of a random event. The chance that a given event will occur. It is the measure of the likelihood of an event to occur.The value is expressed from zero to one.
For the given situation,
The table shows the students preference of milk, juice or water.
Total number of students preferred milk = 14
Total number of students = 45
Thus the probability that the students response is milk is
[tex]P(e)=\frac{14}{45}[/tex]
⇒ [tex]P(e)= 0.311[/tex]
Hence we can conclude that the probability of students response is milk is 0.311.
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Which function rule for points would create the translation shown above?
(x, y) + (x+4, y+3)
(x, y) + (x-4, y-3)
(x, y) + (x+10, y+7)
(x, y) + (x-10, y-7)
Answer:
Option A
Step-by-step explanation:
Coordinates of the given points A and A',
A → (-6, -2)
A' → (-2, 1)
Rule for the translation of point A to A',
A(-6, -2) → A'(-6+h, -2+k)
Since, coordinates of A' are (-2, 1)
Therefore, -6 + h = -2
h = 6 - 2 = 4
And (-2 + k) = 1
k = 3
Therefore, rule for the translation will be,
(x, y) → (x + 4, y + 3)
Option A will be the answer.
I need help!
How do you know if an equation is exponential growth or exponential decay or not an exponential equation? For example, what is y=2(0.5)^-the exponent is x
Answer:
If a is positive and b is greater than 1 , then it is exponential growth. If a is positive and b is less than 1 but greater than 0 , then it is exponential decay
Step-by-step explanation:
small baby answer
what is 11/9 simplified
Answer:
as a mixed number 1 2/9
There are 3 feet in 1 yard. How many feet are equal to 10 yards
Answer:
30 feet
Step-by-step explanation:
There a 3 ft in a yard
If there's 10 yards
then multiply 10 x 3 to get 30 feet
Bill's favorite breakfast cereal is available in four different sizes. Which is the best buy?
15-ounce box for $4,20
B 10-ounce box for $3.10
© 22-ounce box for $5.72
18-ounce box for $4.50
Answer:
The best deal is the 18 ounce box
Answer:
the 18 ounce box is cheapest per ounce
Step-by-step explanation:
1. .28per ounce
2. .31per ounce
3. . 26per ounce
4. .25per ounce
Solve the right triangle. Round decimal answers to the nearest tenth. I can´t figure out KL and ML.
Answer:
Me to I need that Answer en m<k is 50°
Step-by-step explanation:
The measure of KL is 5.1 unit and the measure of ML is 6.1 unit.
What are trigonometric ratios?The sides and angles of a right-angled triangle are dealt with in Trigonometry. The ratios of acute angles are called trigonometric ratios of angles. The six trigonometric ratios are sine (sin), cosine (cos), tangent (tan), cotangent (cot), cosecant (cosec), and secant (sec).
Given that, MK=8 units, ∠M=40° and ∠K=50°.
We know that, sinθ=Perpendicular/Hypotenuse
Now, sin40°=KL/8
0.6427=KL/8
KL=0.6427×8
KL=5.1 units
sin50°=ML/8
0.7660=ML/8
ML=6.1 units
Therefore, the measure of KL is 5.1 unit and the measure of ML is 6.1 unit.
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Lisa is 4 years older than Thomas. Carla is twice as old as Lisa. The sum
of their ages is 56. How old is Lisa?
Answer:
Lisa is 24.
Step-by-step explanation:
56/2=28
28-4-thomas=24-lisa \
Carla is 28, Thomas is 20, and Lisa is 24. Hope this helps! :)
Solve the linear equation x - 9= 3/5x
(Please put your answer as a decimal.)
Answer:
22.5
Step-by-step explanation:
Answer:
x = 22.5
Step-by-step explanation:
x - 9= 3/5x
3/5x - x = -9
-2/5x = -9
x = 22.5
Point Q is image of (-7,-6) under the translation (x,y)=(x+12,y+8)
P varies inversely with x. If P = 7 when x = 8, find the value of P when x = 7. A. 0.125 B. 1 C. 7 D. 8
Step-by-step explanation:
P = 8
Step-by-step explanation:
Given that P varies inversely with x then the equation relating them is
P = \frac{k}{x} ← k is the constant of variation
To find k use the condition P = 7 when x = 8 , then
7 = \frac{k}{8} ( multiply both sides by 8 )
56 = k
P = \frac{56}{x} ← equation of variation
When x = 7 , then
P = \frac{56}{7} = 8
Identify the excluded values of this product. Then rewrite the product in simplest form.
Answer:
2y+10/y
Step-by-step explanation:
Plato
Answer:
2(y+5)/y
Step-by-step explanation:
edmentum
Plz help me I need this stuff plz
sorry i want get points
Help please
I need the correct answer to this pic
I will mark you brainliest for this correct answer
Answer:
the answer is B hope this helps you out
Tell which term you would add or subtract on both sides side of the equation so that the variable is only on one side.
7X – 1 = 2x + 5
Answer:
x=6/5
Step-by-step explanation:
Solve for w.
44=2w
Simplify your answer as much as possible.
Answer:
The answer is 22.
Step-by-step explanation:
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