The longest and shortest possible lengths of the third side of the triangle are 4.9 cm and 11.1 cm.
What does the Angle Bisector Theorem state?It states that the opposite side of a triangle is divided into segments by each angle bisector that are proportional in length to the adjacent sides.
Given:
An angle bisector divides the opposite side of the triangle into segments 6 cm and 4 cm long.
Second side of the triangle is 7.4 cm.
We have to calculate the longest and shortest possible lengths of the third side of the triangle.
By Angle Bisector Theorem we can solve this problem,
In the triangle ABC, AD is the angle that bisects angle A, placing D on side BC.
Now, BD / DC = AB / AC
BC = 6 + 4 = 10 cm
Angle bisector divides BC into 2 segments,
BD = 6 cm
CD = 4 cm
If AB = 7.4 cm,
6/4 = 7.4 / AC
AC = 7.4(4) / 6
AC = 29.6 / 6
AC = 4.94 cm (shortest possible length of the third side of the triangle)
If AC = 7.4 cm
6/4 = AB/7.4
AB = 6(7.4)/4
AB = 44.4/4
AB = 11.1 cm (longest possible length of the third side of the triangle)
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When you sold your shares, your account showed $4680.00 ($72.00 × 65 shares), for a total gain of $357.50 ($4680.00 – $4322.50). What percentage gain did you experience?
The percentage that 7.64% gain experienced you if sold your shares, your account showed $4680 for a total gain of $357.50.
What is the percentage?The percentage is defined as a ratio expressed as a fraction of 100.
For example, If Saima obtained a score of 57% on her exam, that corresponds to 67 out of 100. It is expressed as 57/100 in fractional form and as 57:100 in ratio form.
Given that when you sold your shares, your account showed $4680.00 ($72.00 × 65 shares)
For a total gain of $357.50 ($4680.00 – $4322.50).
Let the percentage gain you experienced be x %
As per the given data, the solution would be as:
⇒ x% of 357.50 = 4680.00
x% is expressed as x/100 in fractional form
⇒ (x/100)(357.50) = 4680.00
⇒ x = 357.50/4680.00 × 100
⇒ x = 7.64%
Therefore, the percentage that 7.64% gain experienced you.
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Graph the linear function p(x) = 4x
The graph is attached below.
We are given a linear function.The function p(x) equals 4x.We have to graph the function.In mathematics, a function is an expression, rule, or law that establishes the relationship between an independent variable and a dependent variable. In mathematics, functions exist everywhere, and they are crucial for constructing physical links in the sciences.Let "y" denote p(x).y = 4xNow, we can get several pairs of coordinates that satisfy the above linear function.We plot the points on the graph and join them.We can see that the given function is an equation of a straight line that passes through the origin and has a positive slope of magnitude 4.To learn more about functions, visit :
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a₁ = 4; a = (a)²-3 (n ≥2) list the first five terms
The first five terms of the given sequence are 4, 1, 6, 13, 22
We can solve this problem by following a few steps.
The formula to find the next four terms is, a = (n)²- 3, (n ≥2) as per the question.
Where n is the sequence of the number ( n = 2, 3, 4, 5, 6, etc. )
So, for the 2nd term A₂ = 2² - 3 = 4 - 3 = 1 [As n = 2 for the second term ]
Similarly, for the 3rd term A₃ = 3² - 3 = 9 - 3 = 6 [ As n = 3 for the third term ] ,
for the 4th term A₄ = 4² - 3 = 16 - 3 = 13 [ As n = 4 for the second term ] ,
for the 5th term A₂ = 5² - 3 = 25 - 3 = 22 [As n = 5 for the second term ]
Now, we can conclude that the first five terms of the given sequence are 4, 1, 6, 13, 22
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The correct question is :
a₁ = 4; a = (n)²-3 (n ≥2) list the first five terms
The height of a wave in California varies directlywith the seconds that pass by. At 4 seconds,the wave is 6 feet high. Find the constant ofvariation.Weight varies directly with arit
The constant variation of hight(y) to seconds(x) is 3y/2x.
What is the constant variation?The quantity that connects two variables that are directly or inversely proportional to one another is known as the constant of variation. By dividing the y-coordinate by the x-coordinate, we can find k when given any point because it is constant (the same for every point). For instance, the constant of variation is k = = 3 if y varies directly as x and y = 6 when x = 2.So, let the second be 'x' and the height is 'y'.
At 4 seconds the wavelength is 6 ft high.
Constant variation:
y/x = 6/4 = 3/23y/2xSo,
x = 4, x = 8, x = 12y = 6, y = 12, x = 18Therefore, the constant variation of hight(y) to seconds(x) is 3y/2x.
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3. a) Jack needs to purchase a painting for his room. Jack measured the painting as 5 ft. The actual
was 4.1 ft. What is John's percent decrease on his measurement?
measurement
Jack's percentage decrease on his measurement of painting by 18%.
What is meant by percentage change?
Measures of percent change include percent increase and percent decease, which indicate how much an element of a variable changes in terms of intensity, size, extent, or value.
Given that,
Jack's measurement for his room = 5 ft (taking this as old value)
Actual measurement for Jack's room = 4.1 ft (taking this as new value)
Using formula for Percent change = [tex]\frac{new - old}{old}[/tex] × 100% = [tex]\frac{4.1 - 5}{5}[/tex] × 100%
= [tex]\frac{-0.9}{5}[/tex] × 100% = -0.18 × 100%
= -18%
Here, minus sign represents the decrease in percentage.
Hence, Jack's percentage decrease on his measurement of painting by 18%.
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Correct question will be :
Jack needs to purchase a painting for his room. Jack measured the painting as 5 ft. But the actual measured painting is 4.1 ft. What is Jack's percent decrease on his measurement of the painting?
As long as you follow through with a plan to save $2000 a year, at the end of each year, in your account that earns 4% interest how much would you have after 25 years future value?
We have to use the simple interest formula.
[tex]A=P(1+rt)[/tex]Where P = 2,000, r = 0.04, t = 25. Let's solve for A
[tex]\begin{gathered} A=2,000(1+0.04\cdot25)=2\cdot2,000 \\ A=4,000 \end{gathered}[/tex]Therefore, you will have $4,000 in 25 years.Under a rotation about the origin, the point A ( 5 , − 1 ) is mapped to the point A ' ( 1 , 5 ) . What is the image of the point B ( − 4 , 6 ) under this rotation? Explain.
The image of the point B ( − 4 , 6 ) under 270° clockwise rotation is point (-6 , -4).
A transformation that revolves a figure around a point is called a rotation. The rotational center is where we refer to it. The shape and dimensions of a figure remain the same while facing in a different direction. You can rotate a figure either clockwise or counterclockwise.
Under a rotation about the origin, the point A ( 5 , − 1 ) is mapped to the point A ' ( 1 , 5 ) is a -
270° clockwise rotation: (x,y) becomes (-y,x)
The image of the point B ( − 4 , 6 ) under this rotation is
(x , y) = (-y , x)
i.e. (-6 , -4)
Assuming that the rotation's center is at (0, 0). Here are the guidelines for rotation:
90° clockwise rotation: (x,y) becomes (y,-x)90° counterclockwise rotation: (x,y) becomes (-y,x)180° clockwise and counterclockwise rotation: (x, y) becomes (-x,-y)270° clockwise rotation: (x,y) becomes (-y,x)270° counterclockwise rotation: (x,y) becomes (y,-x)Therefore , The image of the point B ( 4, 6) when rotated 270 degrees clockwise is point (-6 , -4).
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what is an equation
We have to write the equation of the line that pass through (4,-5) and (2,0).
We can calculate the slope as:
[tex]m=\frac{y_2-y_1}{x_2-x_1}=\frac{0-(-5)}{2-4}=\frac{5}{-2}=-2.5[/tex]We can then write the slope-point form of the equation as:
[tex]\begin{gathered} y-y_0=m(x-x_0) \\ y-0=-2.5(x-2) \\ y=-2.5x+5 \end{gathered}[/tex]Answer: y=-2.5x+5
Please help, Pre-Algebra super easy math question
Answer:
-16
Step-by-step explanation:
b) -x²; x = -4
-(-4)²
-(16)
-16
I hope this helps!
Answer: -16
Step-by-step explanation:
(x^3y^5)^3 × -x^6y^5
To simplify the expression you can first use this property of exponents
[tex](a\cdot b)^m=a^mb^m[/tex]Then you have
[tex]\begin{gathered} (x^3y^5)^3=(x^3)^3(y^5)^3 \\ (x^3y^5)^3=x^{3\cdot3}y^{5\cdot3} \\ (x^3y^5)^3=x^9y^{15} \end{gathered}[/tex]Now apply this property of exponents
[tex]a^b\cdot a^c=a^{b+c}[/tex]Therefore, you have
[tex]\begin{gathered} (x^3y^5)^3\cdot-x^6y^5=x^9y^{15}\cdot-x^6y^5 \\ (x^3y^5)^3\cdot-x^6y^5=x^9\cdot-x^6\cdot y^{15}\cdot y^5 \\ (x^3y^5)^3\cdot-x^6y^5=-x^{9+6}\cdot y^{15+5} \\ (x^3y^5)^3\cdot-x^6y^5=-x^{15}\cdot y^{20} \\ (x^3y^5)^3\cdot-x^6y^5=-x^{15}y^{20} \end{gathered}[/tex]The vertices of triangle FGH are F(-5,1,) G(-2,4), and H(-1,2) the vertices of triangle F’G’H are F’(-5,-1) G(-2,-4) H (-1-2)Identify the transformation of triangle FGH to triangle F’G’H A. A translation across the x-axis B. A reflection across the x-axis C. A dilation D. A rotation
The transformation of △FGH to △F’G’H is (B) the reflection across the x-axis.
What do we mean by reflection across the x-axis?The x-coordinate remains constant when a point is reflected across the x-axis, but the y-coordinate is assumed to be the additive inverse. Point (x, y) is reflected across the x-axis as (x, -y).A graph will appear to be inverted or on the other side of an axis, such as the x-axis, when it is reflected along that axis.If you look closer, you'll notice that it's symmetrical, meaning that each point is equally spaced from the axis of reflection and the axis of its reflection.As a result, if you reflect a point (x, y) along the x-axis, its x abscissa will remain the same but its y ordinates will negate. So (x,y) becomes (x, -y)
So, the difference between the vertices of triangle FGH and F’G’H is the y-coordinates of the F’G’H triangle are inverse of the y-coordinates of the FGH triangle.
And as we know that in reflection across x-axis the x-coordinate remains constant when a point is reflected across the x-axis, but the y-coordinate is assumed to be the additive inverse.Therefore, the transformation of △FGH to △F’G’H is (B) the reflection across the x-axis.
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How would I solve this?
Write an equation of the line containing the given point and parallel to the given line.
(8, -3); 2x - 56 = 3
Type an equation using slope-intercept form or using the given point in point-slope form.
An equation of the line containing the given point and parallel to the given line is y = 2x - 19.
The condition for two parallel lines.
In Mathematics, two (2) lines are considered to be parallel if their slopes are the same (equal) and they've different y-intercepts. This ultimately implies that, two (2) lines are parallel under the following conditions:
m₁ = m₂
Note: m is the slope.
Mathematically, the point-slope form of a line is given by this equation:
y - y₁ = m(x - x₁)
Where:
x and y are the points.m represents the slope.Given the following equation:
2x - 56 = 3 ⇒ m₁ = 2
Therefore, m₁ = m₂ = 2.
At point (8, -3), we have:
y - y₁ = m(x - x₁)
y - (-3) = 2(x - 8)
y + 3 = 2(x - 8)
y + 3 = 2x - 16
y = 2x - 16 - 3
y = 2x - 19
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Find the value of x
.............................
Assume that when you take a bath, you fill a tub to the haltway point. The tub measures 5 feet by 2 feet by 2.7 feet. When you take a shower, you
use a shower head with
flow rate of 2.03 gallons per minute, and you typically spend 9 minutes in the shower. There are 7.5 gallons in one cubic
foot. Complete parts (a) through (c) below.
a. Do you use more water taking a shower or taking a bath? Select the correct choice below
and fill in the answer box to complete your choice.
(Round to one decimal place as needed.)
O A. Shower; you use
more cubic feet of water than taking a bath.
• B. Bath; you use
more cubic feet of water than you do taking a shower.
The person is therefore using more water for bathing than for showering, according to the conclusion.
Half of the tub's total water is consumed while taking a bath.
Water used divided by volume equals
[tex]\frac{volume}{2}[/tex]
= [tex]\frac{(5)(3)(2.8)}{2}[/tex]
=[tex]\frac{42}{2}[/tex]
=21 cubic feet.
The following will provide the total amount of water utilized while having a shower:
Total water Equals rate ×time
= 1.52 × 12
= 18.24 gallons.
So, if there are 7.5 gallons in a cubic foot, the amount of water in cubic feet will be amount
=[tex]\frac{18.24}{7.5}[/tex]
=2.432 cubic feet.
The person is therefore using more water for bathing than for showering, according to the conclusion.
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Determine the number of large cups that would contain the same amount as 10 1/2 small cups if a large cup holds 1 3/4 times the quantity of liquid that's in a small cup.
The number of large cups that would contain the same amount as 10 1/2 small cups is 6.
How to illustrate the information?From the information, it was stated that we should find the number of large cups that would contain the same amount as 10 1/2 small cups if a large cup holds 1 3/4 times the quantity of liquid that's in a small cup.
This simply means that we have to divide the values that are given. This will be illustrated as:
= 10 1/2 ÷ 1 3/4
= 10.5 / 1.75
= 6
There'll be 6 large cups.
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10. An express train is travelling at 80 km/h. How far does it go in:
(a) 1 minute (b) 1 second?
The coldest recorded temperature in the United States is
–
80°F, in Alaska. The warmest recorded temperature in the United States is 134°F, in California.
How much higher is the warmest recorded temperature than the coldest recorded temperature?
The warmest recorded temperature is 214°F higher than the coldest temperature.
Since the sign of the two numbers are same, their final values will be added and the result will have the same signs as the two numbers (or the one with the greater absolute value). This is called the multiplicative property.
Expression for difference between the two temperatures is,
= 134−(−80)
By applying the multiplicative property of negative sign, we get
=134+80
= 214°F
Therefore, we conclude that the warmest recorded temperature is 214°F higher than the coldest temperature.
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Answer to exercise 1 please
Using an exponential function and a differential equation, the constant k for the situation is given by:
k = 0.03.
What is an exponential function?An increasing exponential function is modeled according to the following rule:
[tex]A(t) = A(0)e^{kt}[/tex]
In which:
A(0) is the initial amount of the function.k is the exponential growth rate of the function, as a decimal.This exponential function is the solution to the following differential equation:
A'(t) = kA(t)
One example of application of these functions is for continuous compounding, in which the value of an investment of P(0) after t years is given by:
[tex]P(t) = P(0)e^{kt}[/tex]
For the continuous compounding situation in this problem, the interest rate is of 3%, hence k = 0.03, which is the desired parameter.
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1/16x+1/320y-29=0 rewrite the equation as a function of x
The equation as a function of x is y = 9280 -20x
What is equation ?Equations are logical assertions in mathematics that have two algebraic expressions on either side of an equals (=) sign. The expression on the left and the expression on the right are shown to be equal in reference to one another. LHS = RHS (left hand side = right hand side) appears in all mathematical equations. You can solve equations to determine an unknown variable's value, which corresponds to an unknown quantity. It is not an equation if there is no "equal to" sign in the statement. It shall be taken into account as an expression.
The equation is =[tex]\frac{1}{16}x + \frac{1}{320}y - 29= 0[/tex]
Now rearranging the function we write
[tex]\frac{y}{320}= 29 -\frac{x}{16}[/tex]
y = 9280 -20x
The equation as a function of x is y = 9280 -20x
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The Life time in hours of a certain aircraft has the normal distribution with mean 80, Standard devation 16. What is the probability that the aircraft Will last 100 hours
1.25 is the probability that the aircraft Will last 100 hours.
What is probability?The area of mathematics described as probability concerns with numerical representations of the likelihood that an event will occur or that an assertion is correct. An event's probability is a number between 0 and 1, where, roughly speaking, 0 indicates the event's impossibility and 1 represents certainty.
Given Data
Mean = 80
Standard deviation = 16
P( x < 100)
P( x < 100) = P( Z< [tex]\frac{x- mean}{standard deviation}[/tex])
P(x<100 ) = P( Z < [tex]\frac{100-80}{16}[/tex])
P(x< 100) = P(Z< [tex]\frac{20}{16}[/tex])
P(x < 100) = 1.25
1.25 is the probability that the aircraft Will last 100 hours.
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simplify (-2)(-3)(6) 20 points plus brainliest if right
Answer:
36
Step-by-step explanation:
-2(-3)(6)
6(6)
36
Answer:
-8/2 / 6/-3 -8/2 x -3/6 24/12= 2
Step-by-step explanation:
Ventana High School has found that some offerings on the lunch menu aremuch more popular than others. The following table displays students'favorite lunch choices:1875923PizzaTacosSubSandwichesChineseComboPlate98What is the estimated population proportion of students who prefer tacos?A. 0.12B. 0.32C. 0.16D. 0.06
Answer:
C. 0.16
Explanation:
In the table there are 59 students that prefer tacos and there are 367 students in total because
187 + 59 + 23 + 98 = 367
Then, the estimated population proportion of students that prefer tacos is calculated as
P = 59/367 = 0.16
Therefore, the answer is
C. 0.16
A high school band raises $6, 764 to buy instruments
and uniforms for its members. Half the money is spent
on new instruments. They buy 38 new uniforms with
the remaining money.
Answer:
$89 dollars per uniform
Step-by-step explanation:
Total amount of money raised= $6,764.
Money spent on new instruments= $6,764÷1/2 = $3382
The number of new uniforms bought with the remaining money= 38.
How much was spent on one= $3,382÷38 = $89
What is the equation of the line that passes through (-3,-1) and has a slope of 2/5? Put your answer in slope intercept form 1. Y=2/5x+1/52. Y=2/5x-1/53. Y= -2/5x-1/5
We are asked to determine the equation of a line that passes through the point (-3, -1) and has a slope 2/5. To do that we will use the point-slope form of a line equation:
[tex]y-y_0=m(x-x_0)[/tex]Where:
[tex]\begin{gathered} (x_0,y_0)=\text{ point on the line} \\ m=\text{ slope} \end{gathered}[/tex]Now, we plug in the values:
[tex]y-(-1)=\frac{2}{5}(x-(-3))[/tex]Simplifying we get:
[tex]y+1=\frac{2}{5}(x+3)[/tex]Now, we apply the distributive law:
[tex]y+1=\frac{2}{5}x+\frac{6}{5}[/tex]Now, we subtract 1 from both sides:
[tex]\begin{gathered} y=\frac{2}{5}x+\frac{6}{5}-1 \\ \\ y=\frac{2}{5}x+\frac{1}{5} \end{gathered}[/tex]and thus we get the equation of the line.
Pls help i need this ASAP!
The solution for the given inequalities are as follows
(17)k≥1 ,(18)c > 14 ,(20)y ≥ 2 ,(21)z < 9 ,(23)x < 1 ,(24)v ≤ -1 .
In the question ,
it is given that
(17) the inequality
3(k-5)+9k≥-3
3k-15+9k ≥ -3
12k -15 ≥ -3
12k ≥ 15-3
12k ≥ 12
k≥1
(18) the inequality
-(7c-18)-2c > 0
-7c+126-2c>0
-9c+126>0
-9c > -126
c > 126/9
c > 14
(20)given the inequality
-4 ≤ 4(6y-12)-2y
-4 ≤ 24y - 48 -2y
-4 ≤ 22y - 48
48-4 ≤ 22y
44/22 ≤ y
y ≥ 2
(21) given the inequality
30 > -(5z+15)+10z
30 > -5z -15 +10z
30 > 5z-15
45 > 5z
45/5 > z
z < 9
(23) given the inequality
4x+3 < 3x+6
4x-3x < 6-3
3x < 3
x < 1
(24) given the inequality
4v+8 ≥ 6v+10
-10+8 ≥ 6v-4v
-2 ≥ 2v
-2/2 ≥ v
-1 ≥ v
v ≤ -1
Therefore , the solution for the given inequalities are (17)k≥1 ,(18)c > 14 ,(20)y ≥ 2 ,(21)z < 9 ,(23)x < 1 ,(24)v ≤ -1 .
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Solve the following question show your work
Solution:
iven :
[tex]7\frac{1}{5}\times4\frac{5}{6}[/tex]To solve,
step 1: Convert the mixed fractions into improper fractions.
[tex]\begin{gathered} Given\text{ an improper fraction of the form: a}\frac{b}{c},\text{ to convert to an } \\ improper\text{ fraction, we have} \\ \frac{(c\times a)+b}{c} \\ \end{gathered}[/tex]Thus,
[tex]\begin{gathered} 7\frac{1}{5}=\frac{(7\times5)+1}{5}=\frac{35+1}{5}=\frac{36}{5} \\ 4\frac{5}{6}=\frac{(4\times6)+5}{6}=\frac{24+5}{6}=\frac{29}{6} \end{gathered}[/tex]step 2: Perform the operation of multiplication between both fractions.
Thus,
[tex]\begin{gathered} \frac{36}{5}\times\frac{29}{6}=\frac{36\times29}{5\times6} \\ cancel\text{ out common factor,} \\ =\frac{6\times29}{5} \\ =\frac{174}{5} \end{gathered}[/tex]step 3: Convert the resulting improper fraction into a mixed fraction.
Thus,
[tex]\frac{174}{5}=34+\frac{4}{5}[/tex]Hence, the solution is
[tex]34\frac{4}{5}[/tex]a 20$ bill, two $10 three $5 and four $1 are placed in a bag, if a bill is chosen at random what is the expected value for the amount choses
The expected value for the amount chosen from the bag is $5.90
How to get the expected value?
We have
one $20 bill.two $10 bills.three $5 billsfour $1 bills.So in total, we have 1 + 2 + 3 +4 = 10 bills.
The expected value will be then given by the sum of the products between the value of each bill and the number of bills of that type, divided by the total number of bills.
EV = (1*$20 + 2*$10 + 3*$5 + 4*$1)/10 = $5.9
The expected value is $5.9
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dses 12.4. lete the following: Find the intercepts and domain and perform the symmetry test on each parabola with equations. (n) = 8 (d) x - 4y the vertex, focus, and endnoin
Find the intercepts and domains
1. Intercepts
x-intercept (when y = 0)
x = 0
y-intercept (when x = 0)
y = 0
Domain
y = All real numbers
Symmetry
Yes it is symmetry
You purchase 5 tickets to a football game from TicketMaster. In addition to the cost per ticket, the agency charges a convenience charge of $2.50 per ticket. You also choose to pay for rush delivery, which costs $15. The total cost of your order is $352.50. What is the price per ticket before the convenience charge?
The price per ticket, excluding the convenience charge, is $65.
How to solve for the privce per ticketthe rush delivery is given as $15.
The total cost of the tickets is said to be put at $352.50
Then the value that we would have for the the 5 tickets wpould be 352.50 - 15 = $337.50.
There is the convenience charge of $2.50 per ticket. This charge is excluded from the convenience charge that is to be paid.
Hence you would have to make the payment of
337.50 - 5*2.50
= 325.
Next we are to solve for the price of the ticket whioch is independent of the convenience charge
= 325 / 5
= $65
Hence the price per ticket is given as 65 dollars
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Show how you can make a ten to find the sum of 6+5
By rewritting the 6 as 5 + 1 we will get:
1 + 5 + 5 = 1 + (5 + 5) = 11
How to make a ten to simplify the sum?
One trick we do a lot when we do additions os making tens (or hundreds, thousands, etc... depending on the case).
This means that we play with the numbers in such a way that we can make tens, in this case we have the sum:
6 + 5
We can rewrite this as:
6 + 5 = 1 + 5 + 5
Using the associative property we rewrite:
1 + 5 + 5 = 1 + (5 + 5)
1 + (5 + 5) = 1 + 10 = 11
The sum is equal to 11.
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