The speed of the boat in still water is 18 mph.
What is a numerical expression?A numerical expression is a mathematical statement written in the form of numbers and unknown variables. We can form numerical expressions from statements.
We know distance = speed×time.
Therefore, time = distance/speed.
Let, The speed of the boat at still water be 'x'.
Therefore, From the information,
94/(x + 6) = 47/(x - 6).
94(x - 6) = 47(x + 6).
94x - 564 = 47x 282.
47x = 846.
x = 18.
So, The speed of the boat is 18 mph in still water.
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The area of a rectangle is 20 square meters. The length of the rectangle is (x-3) meters and the
width of the rectangle is (x - 2) meters. Find the length and the width of the rectangle.
With steps and explanation please.
Answer:
length = 4 cm
Width = 5 cm
Step-by-step explanation:
Area of rectangle:Area of rectangle = length * width
length = (x - 3) meters
Width = (x - 2) meter
Area = 20 square meters
(x - 3)*(x - 2) = 20
Use FOIL method.
x*x + (x)(-2) + (-3)*x + (-3)*(-2) = 20
x² -2x - 3x + 6 =20
Combine like terms
x² - 5x + 6 = 20
Now subtract 20 from both side
x² - 5x + 6 - 20 = 0
x² - 5x - 14 = 0
Factorize the equation and find the roots
Sum = -5
Product = -14
Factors = (-7) , 2
When we add (-7) + 2 = -5 and when we multiply (-7)*2 = -14
x² + 2x - 7x - 14 = 0
x(x + 2) -7(x + 2) = 0
(x + 2)(x - 7) = 0
x - 7 = 0 {Ignore (x + 2 = 0) as measurements wont't be in negative}
x = 7
length = x - 3
= 7 - 3
[tex]\sf \boxed{\bf length = 4 \ cm}[/tex]
width = x - 2
= 7 - 2
[tex]\sf \boxed{\bf width = 5 \ cm }[/tex]
The height in feet, h, of a model rocket t seconds after launch is given by the equation h (t) = 3 + 70 t minus 16 t squared. The average rate of change in h(t) between t = 1 second and t = 3 second is 6. What does the average rate of change tell you about the rocket?
The rocket is traveling six times as fast when t = 3 than it is when t = 1.
The rocket is at a greater height when t = 3 than it is when t = 1.
The rocket is 6 feet higher above the ground when t = 3 than it is when t = 1.
The rocket is traveling at a constant rate of 6 feet per second between t = 1 and t = 3.
The average rate of change in h(t) is 6.
What is Average Rate of change?It is a measure of how much the function changed per unit, on average, over that interval.
h(t) = 3 + 70t - 16t²
Average rate of change
At t = 1 second
h(1) = 3 + 70(1) - 16(1)^2
h(1) = 57
At t = 3 second
h(3) = 3 + 70(3) - 16(3)^2
h(3) = 69
Average rate of change = Δh / Δt
=[h(3) - h(1)] / (3 - 1)
= (69 - 57) / 2
= 12 / 2
= 6.
Hence, the rate of change is 6.
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A researcher finds that the more hours students party per week, the lower their gpas (grade point averages). she questions whether there may be other issues affecting the students' gpas that weren't taken into account, such as the number of hours spent studying, class attendance, or the number of hours worked at campus jobs. what are these additional factors called
Answer:
I believe "uncontrolled variables."
Step-by-step explanation:
Since there was no measure, nor control, of these other variables, the data may be questionable.
Please help i dont get this at all so please i will highly appreciate it .Thank youuu!!!
Answer:
D
Step-by-step explanation:
definitely
Solve the equation 2x + 10 = 30.
Answer:
X=10
Step-by-step explanation:
1. Subtract 10 from both sides
2. Simplify
3. Divide both sides by the same factor
4. Simplify
I need this due by tonight what is 45+x=75
Answer:30
Step-by-step explanation: jus subtract total number by 45 to c what u missin
Given: [tex]\textsf{45 + x = 75}[/tex]
Need: [tex]\textsf{The value of the unknown x}[/tex]
Solution: In order to solve for the unknown we must subtract 45 from both sides which would isolate x and given us the value.
Subtract 45 from both sides
[tex]\textsf{45 - 45 + x = 75 - 45}[/tex][tex]\textsf{x = 75 - 45}[/tex][tex]\textsf{x = 30}[/tex]After simplifying the expression we were able to determine that x is equal to 30.
The triangle inequality theorem states the sum of the lengths of any two sides of a triangle is _____ the length of the third side.
Answer:
see explanation
Step-by-step explanation:
the sum of the lengths of any two sides of a triangle is greater than the length of the third side.
if the sides are a, b, c , then the following must be true
a + b > c
a + c < b
b + c > a
for the 3 sides to form a triangle
Describe a real-world example in which hidden variables may be an issue, taking care to identify each variable and its relationship to the others.
A real-life example of a hidden variable would be age in research that checks the correlation between shirt sizes in grade school and reading ability.
What is a real-world example of hidden variables?In a research that checks whether student shirt sizes (independent variable) have an impact on reading ability, it is found that students with high shirt sizes are better at reading.
A hidden variable here is age. Students who are older will more likely have a higher shirt size and better reading comprehension.
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Consider the following graph.
Which statement best describes Cheryl's commute?
A. Cheryl accelerated to 65 mph, made a stop for 5.5 minutes, and then decelerated to 45 mph.
B. Cheryl accelerated to 65 mph, drove at a constant speed for 5.5 minutes, and the decelerated to 45 mph.
C. Cheryl drove at a speed of 65 mph for 1 minute, drove at a constant speed for 5.5 minutes, and then drove at a speed of 45 mph for 2.5 minutes.
D. Cheryl drove at a speed of 65 mph for 1 minute, made a stop for 5.5 minutes, and then drove at a speed of 45 mph for 2.5 minutes
Cheryl drove at a speed of 65 mph for 1 minute, drove at a constant speed for 5.5 minutes, and then drove at a speed of 45 mph for 2.5 minutes.Option C is correct.
What is a graph?A diagram depicting the relationship between two or more variables, each measured along with one of a pair of axes at right angles.
Cheryl traveled at a steady pace for 5.5 minutes, then 45 mph for 2.5 minutes after traveling at 65 mph for a minute.
Statement C best describes Cheryl's commute.
Hence option C is correct.
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culture started with 2,000 bacteria. After 3
ours, it grew to 2,600 bacteria. Predict how
any bacteria will be present after 9 hours.
ound your answer to the nearest whole
umber.
P = Aekt
Step-by-step explanation:
2600 = 2000•e^3k
e^3k = 2600/2000
e^3k = 13/10
3k = ln(13/10)
k ≈ 0.087
P = 2000•e^0.087•9
P = 4376
Please help!!!! ASAP!!!!!!!!!!
Answer:
[tex]\sqrt[]{4+\frac{1}{25}y }[/tex]
Step-by-step explanation:
Transform - y-25^2=-100
divide
simplify
x plus-minus [tex]\sqrt[]{4+\frac{1}{25}y }[/tex]
whenx=2y=50 and whenx=4y=100 Which direct variation equation can be used to model this function?
The equation which is used to model this function is y = 25x.
What is equation?An equation is a mathematical expression that contains an equals symbol. Equations often contain algebra.
Given:
x=2 , y=50
x=4, y=100
As, corresponding to x =2 , y =50
For x=1 , y=25
Hence, the equation which is used to model this function is y = 25x.
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find the range of the given function y= 8x +1, where x>2
Answer:
infinite or if where using whole numbers
y≥25
Hope This Helps!!!
Vincent and Aidan buy the same number of pens. Vincent buys packs of 6 pens, and Aidan buys boxes of 20 pens. What is the least number of pens each boy can have brought?
The least number of pens each boy can have brought is 60
How to determine the least number of pen?We have:
Vincent = 6 packs
Aidan = 20 boxes
Factorize 6 and 20
6 = 1 * 2 * 3
20 = 1 * 2 * 2 * 5
Multiply all factors
LCM = 1 * 2 * 2 * 3 * 5
Evaluate the product
LCM = 60
Hence, the least number of pens each boy can have brought is 60
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11 potters can make 143 pots in 8 days. How many potters will be required to make 169 pots in 4 days?
26 potters will be required to make 169 pots in 4 days.
Given: 11 potters can make 143 pots in 8 days.
Step 1:
1 potter makes 143 pots in 8 × 11 days.
1 potter can make 1 pot in
(8 × 11)/143 days.
Step 2:
Let the number of potters required be x, then
x potters can make 1 pot in (8 × 11)/( 143 × x) days
x potters can make 169 pots in (8 × 11 × 169)/(143 × x ) days
Step 3:
The number of days given is 4. Hence equating the above equation to 4.
(8 × 11 × 169)/(143 × x ) = 4
Step 4:
Solve for x
14872/(143x) = 4
572x = 14872
x = 14872/572
x = 26
Thus, 26 potters will be required to make 169 pots in 4 days.
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Which expression is equivalent to
( 4^(1/3) × 4^(2/6) ) ^(3/4)
( ---------÷------------ )
( 4^(5/6) )
*All the numbers in the division problem are in parenthesis with the ^(3/4) on the outside.*
A: (1/4)^(3/66)
B: (1/4)^(-3/66)
C:(1/4)^(-1/11)
D: (1/4)^(1/11)
The simplified form of the expression is [tex]4^{-1/3}[/tex]
Indices and exponentsGiven the indices expression as shown;
[tex]\frac{(4^{1/3}\times 4^{2/6} )^{3/4}}{4^{5/6}}[/tex]
Applying the product and quotient law of indices
[tex]\frac{(4^{1/3+1/3})^{3/4}}{4^{5/6}}\\\frac{(4^{2/3})^{3/4}}{4^{5/6}}\\\frac{4^{1/2}}{4^{5/6}}\\[/tex]
Take the difference in the power to have:
4^(1/2 - 5/6)
4^(-2/6)
[tex]4^{-1/3}[/tex]
Hence the simplified form of the expression is [tex]4^{-1/3}[/tex]
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What is the value of x in the following equation?
11-2x+6x+5=32
Answer:
The value of x is 4
Step-by-step explanation:
Step 1: Simplify both sides of the equation.
11−2x+6x+5=32
11+−2x+6x+5=32
(−2x+6x)+(11+5)=32
4x+16=32
4x+16=32
Step 2: Subtract 16 from both sides.
4x+16−16=32−16
4x=16
Step 3: Divide both sides by 4.
((4x)/4) = (16/4)
x = 4
Answer:
11-2x+6x=32-5
-2x+6x=27-11
-2x+6x=16
4x÷4=16÷4
x=4
Solve for [x]. The polygons in each
2x-20
16
16
8
[tex]\quad \huge \quad \quad \boxed{ \tt \:Answer }[/tex]
[tex]\qquad \tt \rightarrow \:x = 16 [/tex]
____________________________________
[tex] \large \tt Solution \: : [/tex]
If two polygons are similar, their corresponding sides ratios will be equal to each other.
[tex]\qquad \tt \rightarrow \: \cfrac{8}{16} = \cfrac{2x - 20}{24} [/tex]
[tex]\qquad \tt \rightarrow \: \cfrac{1}{2} = \cfrac{2x - 20}{24} [/tex]
[tex]\qquad \tt \rightarrow \: 2x - 20 = \cfrac{24}{2} [/tex]
[tex]\qquad \tt \rightarrow \: 2x = 12 + 20[/tex]
[tex]\qquad \tt \rightarrow \: 2x = 32[/tex]
[tex]\qquad \tt \rightarrow \: x = 16[/tex]
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two consecutive odd integers such that 4 times the larger is 29 more than 3 times the smaller
Answer:
21
Step-by-step explanation:
a,a+2,..
4(a+2)=29+3a
4a+8=29+3a
4a-3a=29-8
a=21
Another one. Which term best describes the slope of the line below?
Here is an equation: 5x - 2y = 10
Create 3 equations that result in…
1. 1 solution
2. No Solutions
3. Infinitely many solutions
You should provide three different answers and an explanation why your equations work.
Answer:
one solution from the amount of numbers
a. What type of triangle is Triangle ABC?
b. Give reasons for your answer
Since two of the angles are equal, hence the triangle ABC is isosceles triangle
What is a triangle?A triangle is a 2D shape that has 3 sides and angles
From the given triangle
<CAB = 50 (alternate angle) and;
<ACB = 180 - (50 + 80)
<ACB = 180 -130
<ACB = 50 degrees
Since two of the angles are equal, hence the triangle ABC is isosceles triangle
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URGENT: Which equation correctly uses the value of b to solve for a?
Triangle ABC is a right triangle and cos(22.6°) = [tex]\frac{b}{13}[/tex]. Solve for b and round to the nearest whole number.
OPTIONS:
1 ) tan(22.6°) = [tex]\frac{a}{13}[/tex]
2 ) tan(22.6°) = [tex]\frac{13}{a}[/tex]
3 ) tan(22.6°) = [tex]\frac{a}{12}[/tex]
4 ) tan(22.6°) = [tex]\frac{12}{a}[/tex]
Answer:
Option 1
Step-by-step explanation:
See attached image
x=y²-1
2x - y = 4
Which of the following equations could be the result of using substitution to solve the system?
2y²-y-5=0
2y2-y-6=0
2y2-2y-5=0
Answer:
B) 2y² - y - 6 = 0
Given following:
x = y² - 1 ___equation 12x - y = 4 ___equation 2Insert equation 1 into 2:
2(y² - 1) - y = 42y² - 2 - y = 42y² - y - 2 - 4 = 02y² - y - 6 = 0Put in second
2x-y=42(y²-1)-y=42y²-2-y=42y²-y-6=0Help question is in the pic
Which of the following is not a good conductor of heat?
Joe kept track of how much TV she watched each day for two weeks how many hours did she spend watching TV
The total hours joe spent watching TV each day for two weeks is 12 1/2 hours
Total hours spent watching TVTotal hours spent watching TV for two weeks = Number of hours × days
= (0 × 1) + (1/4 × 1) + (1/2 × 1) + (3/4 × 3) + (1 × 3) + (1 1/4 × 4) + (1 1/2 × 1)
= 0 + 1/4 + 1/2 + 9/4 + 3 + 5 + 3/2
= 8 + (1+2+9+6) / 4
= 8 + 18/4
= 8 + 4 2/4
= 8 + 4 1/2
= 12 1/2 hours
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What is the value of x?
(See attached image for details.)
Enter your answer in the box.
x =
Answer:
x = 8°
y = 6°
Step-by-step explanation:
Hello!
All 3 sides of the triangle are equal, indicating that it is an equilateral triangle. The rules of this particular triangle say that all angles are equal to 60°.
We can solve for x by setting the equation 7x+4 to 60.
Solve for x7x + 4° = 60°7x° = 56°x = 8°The value of x is 8°.
We can go ahead and solve for y by setting that equation to 60°.
Solve for y8y + 12° = 60°8y = 48°y = 6°The value of y is 6°.
(X-3)2 -0
Ajuda, alguém ajuda?
Answer:
(X- 3)² - 0
(X - 3 )( X - 3 )
x² + 9 - 6x
x² - 6x + 9
a = 1
b = -6
c = 9
Which statement explains how you could use coordinate geometry to prove that quadrilateral ABCD is a square?
Shape ABCD is shown. Point A is at negative 3, 5. Point B is at 1, 7. Point C is at 3, 3. Point D is at negative 1, 1.
