[tex]b \geqslant x \leqslant a[/tex]
38. Evaluate the expression
52 - (3²+4)
Find the tangent of the angle indicated by each of the following right angle triangles.
Answer:
56.31 degrees
Step-by-step explanation:
6 = opposite and 4 = adjacent
Tan = opposite over adjacent
Tan(theta)=6/4
=56.30993247
A bottle contains 3.6 liters of water, water drips out of the bottom of the bottle at a rate of 20 millilitres per minute, work out how long it takes for the bottle to empty, give your answer in hours.
Answer: 3 hours
Step-by-step explanation:
Bottle = 3.6 liters / 3600 milliliters
Rate = 20 ml a minute
3600 / 20 = 180 minutes
60 minutes = 1 hour
180 / 60 = 3 hours
A training field is formed by joining a rectangle and two semicircles, as shown below. The rectangle is 86m long and 64m wide. Find the area of the training field. Use the value 3.14 for π, and do not round your answer. Be sure to include the correct unit in your answer.
The area of the training field to the nearest whole number is 8719 msq. meter
Area of composite solidThe given field is made up of a rectangle and 2 semi circles. The formula for calculating the area of the field is:
Area of the field = area of circle + area of rectangle
Area of field = 3.14(32)² + (86)(64)
Area of field = 3215.36 + 5504
Area of the field = 8719 msq. meter
Hence the area of the training field to the nearest whole number is 8719 msq. meter
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Simplify the expression below as much as possible.
(7-i) + (5 + 3i) - (-3 + 2i)
A. 15
OB. 9
O C. 15-4i
OD. 9-4i
answer: 15
steps:
i means √-1
but in this problem treat
i like x
(7-i) + (5 + 3i) - (-3 + 2i) =
(7-i) + (5 + 3i) +3 - 2i
7-i + 5 + 3i +3 - 2i =
7-i + 5 + 3i +3 - 2i
7+5+3-i+3i-2i
7+5+3+2i-2i
7+5+3 =
15
State the center coordinate and radius length of the circle: x^2 + y^2 - 8x + 12y + 40 = 0
Answer:
Below in bold.
Step-by-step explanation:
x^2 + y^2 - 8x + 12y + 40 = 0
x^2 - 8x + y^2 + 12y = -40
Complete the square on the x and y terms:-
(x - 4)^2 - 16 + ( y + 6)^2 - 36 = -40
(x - 4)^2 + (y + 6)^2 = -40 + 16 + 36
(x - 4)^2 + (y + 6)^2 = 12
So the centre is at (4, -6) and the radius is √12.
Answer:
The circle is centered at (4,-6) and has a radius of √12.
Step-by-step explanation:
The standard form for the circle equation is:
[tex](x-a)^2+(y-b)^2=r^2[/tex]
You have:
[tex]x^2+y^2-8x+12y+40=0[/tex]
First complete the square for the 'x' terms:
[tex](x^2-8x+40)+y^2+12y=0[/tex]
[tex](x^2-8x+16-16+40)+y^2+12y=0[/tex]
[tex](x^2-8x+16)+y^2+12y+24=0[/tex]
[tex](x-4)^2+y^2+12y+24=0[/tex]
The 'x' terms are now in standard form. Work on the 'y' terms by completing the square once again:
[tex](x-4)^2+(y^2+12y+36-36+24)=0[/tex]
[tex](x-4)^2+(y^2+12y+36)-12=0[/tex]
[tex](x-4)^2+(y+6)^2-12=0[/tex]
Add the 12 to the other side:
[tex](x-4)^2+(y+6)^2=12[/tex]
The circle is centered at x = 4, y = -6, and has a radius of √12.
Write the expressions for (f x g) (x) and evaluate (f-g) (4)
The product and the sum of the functions will be 3x² - 6x - 24 and 4x + 2. The value of the function (f - g) at x = 4 is negative 18.
What is a function?In mathematics, functions are everywhere and are necessary for constructing physical connections. A function is a statement, rule, or law that establishes the connection between two variables.
The functions are given below.
f(x) = x - 4
g(x) = 3x + 6
Then the product of the functions will be
(f × g)(x) = (x - 4)(3x + 6)
(f × g)(x) = 3x² -12x + 6x - 24
(f × g)(x) = 3x² - 6x - 24
Then the sum of the functions will be
(f + g)(x) = x - 4 + 3x + 6
(f + g)(x) = 4x + 2
Then the difference in the functions at x = 4 will be
(f - g)(4) = (x - 4) - (3x + 6)
(f - g)(4) = x - 4 - 3x - 6
(f - g)(4) = -2x - 10
(f - g)(4) = -2 (4) - 10
(f - g)(4) = -8 -10
(f - g)(4) = -18
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Choose the function that correctly identifies the transformation of f(x) = x2 shifted four units right and seven units down.
Answer:
Ok hello my name is Christopher and I have already done this and the answer is (6,-7)
Step-by-step explanation:
A student would like to estimate the mean length of words in a book report he just finished writing. He selects a random sample of 20 words and determines the mean length to be 4 characters. Later, he discovers how to use a built-in function of his word-processing program that reveals that the mean length of all words in his book report is 4.3 characters. Which of the following describes the number, 4.3?
sample
statistic
population
parameter
Answer:
Parameter
Step-by-step explanation:
A statistic is a piece of data we derive from analyzing the data from a sample, a subset of a larger population. A parameter is derived from analyzing that population. Here, we would call the mean of the sample - 4 - a statistic, and the mean of the population - 4.3 - a parameter.
A textbook has `428` numbered pages, starting with 1.
You are equally likely to stop on any of the pages if you flip through the book randomly.
If you repeat this experiment `50` times, about how many times do you expect to turn to an even-numbered page?
There are 7 red marbles and 8 blue marbles in a bag. (a) What is the ratio of blue marbles to all marbles in the bag? (b) What is the ratio of blue marbles to red marbles?
Answer: (a) 8 : 15 (b) 8 : 7
Step-by-step explanation: all marbles is 8+7 = 15
ratio of blue marbles to ALL marbles
8 : 15
ratio of blue marbles to red
8 : 7
Graph the equations to find the solution(s) to the system. y=x+3y=13(x+5)(x−1) Use the Line tool to graph the line. Use the Parabola tool to graph the parabola. Choose maximum or minimum point first and then a point on the parabola.
The solutions to the equations are (1.702,4.7) and (-4.7,-1.7).
What is an equation?It is defined as the relation between two variables, if we plot the graph of the linear equation we will get a straight line.
The two given equations ( x + 3 ) and ( 13 ( x+5)(x-1) intersects at the ponits (1.702,4.7) and (-4.7,-1.7).
The graph of the above equations is attached with an answer.
Therefore the solutions to the equations are (1.702,4.7) and (-4.7,-1.7).
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Reduce the following fractions to lowest terms: 36/39
Answer:
12/13
Step-by-step explanation:
36/39
Divide by 3
12/13
please help will mark Brainliest!!
Answer:
Because -4 is 4 units away from 0.
Step-by-step explanation:
Answer:
A
Step-by-step explanation:
Help solve 100 points!!!!!
Answer:
4 weeks
Step-by-step explanation:
Given information:
Starting account balance = $85Weekly deposit = $8 + $10 = $18Given equation:
[tex]\sf b = 85 + w(10 + 8)[/tex]
(where b is the balance and w is the number of weeks)
To find the number of it will take to have a balance of $150, substitute b = $150 into the given equation and solve for w:
[tex]\implies \sf 85+w(10+8)=150[/tex]
[tex]\implies \sf 85+18w=150[/tex]
[tex]\implies \sf 85+18w-85=150-85[/tex]
[tex]\implies \sf 18w=65[/tex]
[tex]\implies \sf \dfrac{18w}{18}=\dfrac{65}{8}[/tex]
[tex]\implies \sf w=3.6111...[/tex]
[tex]\implies \sf w=4\:weeks[/tex]
Therefore, there will be $150 in the bank account 4 weeks from now.
Solve the system of equations below by graphing both equations with a pencil and paper. What is the solution?
y = -x - 1
y = x + 3
A. (-2, 1)
B. (-1, 2)
C. (0, 3)
D. (0, -1)
Answer:
Step-by-step explanation:
x + 3 = -x - 1
2x + 3 = -1
2x = -4
x = -2
y = -2 + 3
y = 1
(-2, 1)
answer is A
ANSWER THIS CORRECTLY FOR BRAINLIEST!!!!
This is 8th grade
algebra btw
Answer:
V = 2143.57
Step-by-step explanation:
To find the volume of a sphere you need to use this formula:
[tex]V = \frac{4}{3}\pi r^{3}[/tex]
r = radius
Solve:
You need the radius from the diameter. Divide 16/2 which is
8.
[tex]V = \frac{4}{3}(3.14) 8^{3}[/tex]
V = 2143.57
Two polygonal regions are similar with scale factor 7. The area of the smaller region is 490 cm2. What is the area of the larger region? Explain your reasoning.
Two polygonal regions are similar with scale factor 7, if the area of the smaller region is 490 cm² then the area of the larger region would be 3430 cm²
What is an equation?An equation is an expression that shows the relationship between two or more numbers and variables.
Dilation is the increase or decrease in the size of a figure by a scale factor.
Two polygonal regions are similar with scale factor 7. The area of the smaller region is 490 cm², hence:
Area of larger region = 7 * 490 cm² = 3430 cm²
Two polygonal regions are similar with scale factor 7, if the area of the smaller region is 490 cm² then the area of the larger region would be 3430 cm²
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4u(y+6) + a(y+6) in factored form
Answer:
( 4u + a ) + ( y + 6 )
Step-by-step explanation:
4u(y+6) + a(y+6) ...
The answer is ( 4u + a ) + ( y + 6 )
Look at the street map. What street intersects with Polk Street?
A. Union Street
B. Church Street
C. Geary Street
D. Fulton Blvd.
Answer:
Geary street :D
they intersect here
click on the photo. it's not a link it's a screenshot of where they intersect
Please help asap! Thanks
[tex]y=f(x)= \dfrac x 3 \\\\\text{Replace x with y and then solve for y,}\\\\~~~~x = \dfrac y 3\\\\\implies y = 3x \\\\\implies f^{-1}(x) =3x[/tex]
Tickets are $10 for adults, a, and $5 for students, s, and they expect that twice as many students as adults will attend Their goal is to earn $1,500 from ticket sales. Write a system of equations to model the ticket sales, assuming the student councll> meets their goal. Use the model to determine the number of adult tickets and student tickets they expect to sell. Show work.
Using a system of equations, it is found that they expect to sell 175 adult tickets and 350 student tickets.
What is a system of equations?A system of equations is when two or more variables are related, and equations are built to find the values of each variable.
In this problem, the variables are:
Variable a: Number of adults that attend.Variable s: Number of students that attend.They expect that twice as many students as adults will attend, hence:
s = 2a.
Their goal is to earn $1,500 from ticket sales, hence:
10a + 5s = 1500.
10a + 5(2a) = 1500.
20a = 1500.
a = 1500/20.
a = 175.
s = 2a = 2 x 175 = 350.
They expect to sell 175 adult tickets and 350 student tickets.
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What is 3/4 of two gallons
Answer:
1.5 gallons
Step-by-step explanation:
(3/4) × (2 gallons) = 1.5 gallons
HOPE THIS HELPS AND HAVE A NICE DAY <3
need help with this math
Answer :
It will take 5 hours for Rachel to catch up with Nick.Explaination :
Here we are given with two equations,
f = 7h + 20 (Equation No 1)f = 10h + 5 Equation No 2)So in order to calculate the number of hours (h). We would simply substitute the value of f in first equation. (i.e., keeping them equal)
>> 7h + 20 = 10h + 5
>> 10h - 7h = 20 - 5
>> 3h = 15
>> h = 15 / 3
>> h = 5
Solve the radical equation.
X+4=√x+10
What is the extraneous solution to the radical equation?
O The solution -1 is an extraneous solution.
O Both -1 and -6 are true solutions.
O The solution -6 is an extraneous solution.
O Neither -1 nor -6 is a true solution to the equation.
The answer is c
Step-by-step explanation:
that kind of wording is always misleading.
please give my regards and comments to your teacher.
a square root has ALWAYS 2 solutions : a positive AND a negative one.
in that sense the negative solution to a square root is NOT an extraneous solution.
only any value of x < -10 (to make the argument of the square root negative) as solution would be extraneous.
so, if your teacher wants to say that only the positive solutions of a square root are allowed, it has to be said as an extra definition or by applying the "+" sign to the square root.
so,
x + 4 = sqrt(x + 10)
since the 2 solutions are already given to us, we only need to use them in the equation and see what happens.
x = -1
-1 + 4 = sqrt(-1 + 10)
3 = sqrt(9) = 3 (actually, it is ±3)
so, x = -1 is a real solution.
x = -6
-6 + 4 = sqrt(-6 + 10)
-2 = sqrt(4) = 2 (actually, it is ±2)
so, based on your teacher's expectation of only positive results of the square root (even though it was not stated),
x = -6 is an extraneous solution.
therefore, the third answer (c) is the "correct" answer.
but actually, formally, the second answer (b) is the truly correct answer.
“Solve the following system of equations using the method of substitution.” Please help!!!
Answer: -17/4
Step-by-step explanation:
The diameter of the circle above is 26 in. What is the circumference of the circle? Use = 3.14.
Circumference = 275
A.40.82 in
В.530.66 in
C.81.64 in
D. 1,061.32 in
Answer:
C
Step-by-step explanation:
the circumference (C) of a circle is calculated as
C = 2πr = πd ( d is the diameter and d = 2r ) , then
C = πd = 3.14 × 26 = 81.64 in
Find the equation of the line passing through the points (−4,−7) and (−4,−6).
Your answer should take the form x=a or y=a, whichever is appropriate.
Answer:
y=x-7
Step-by-step explanation:
Rise over run
-6-(-7)
---------- = 0
-4-(-4)
Point Slope form
y+7=0(x+4)
Y=MX + B
y=x-7
The equation of the line passing through the points (−4,−7) and (−4,−6) in the form of a will be a + 4 = 0.
What is the equation of a line passing through two points?Let the equation of the line pass through (x₁, y₁) and (x₂, y₂).
Then the equation of the line is given as,
[tex]\rm (y - y_2) = \left (\dfrac{y_2 - y_1}{x_2 - x_1} \right ) (x - x_2)[/tex]
The equation of the line passing through the points (−4,−7) and (−4,−6) will be
y + 6 = [(−6 + 7) / (−4 + 4)] (x + 4)
y + 6 = (1/0)(x + 4)
x + 4 = 0
Put x = a, then the equation will be
x + 4 = 0
a + 4 = 0
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Easy 30 points ……………
Answer:
D.
Step-by-step explanation:
it should be the sales tax because you pay a little bit more.
Solve for x. Round to the nearest tenth.
Answer:
x = 4.55
Step-by-step explanation:
Tan(75) = 17/x
3.73 = 17/x
x3.73 =17
x = 4.55