You have the following algebraic expression:
-6у - 9х - 1 - 3х - у
in order to simplify the previous expression, order like terms first:
-6у - 9х - 1 - 3х - у =
-6y - y - 9x - 3x - 1
next, simplify like terms:
-6y - y - 9x - 3x - 1 =
-7y - 12x - 1
Hence, the simplified expression is -7y - 12x - 1
please help this is for my study guide thanks! (round the awnser to the nearest hundredth)
Given that the radius and the height of the cylinder are:
[tex]\begin{gathered} r=10\operatorname{mm} \\ h=10\operatorname{mm} \end{gathered}[/tex]You can use the formula for calculating the volume of a cylinder:
[tex]V=\pi r^2h[/tex]Where "r" is the radius and "h" is the height.
Then, using:
[tex]\pi\approx3.14[/tex]You can substitute values into the formula and evaluate:
[tex]V=(3.14)(10\operatorname{mm})^2(10\operatorname{mm})[/tex][tex]V=(3.14)(100\operatorname{mm}^2)(10\operatorname{mm})[/tex][tex]V\approx3140\operatorname{mm}^3[/tex]Therefore, the answer is:
[tex]V\approx3140\operatorname{mm}^3[/tex]The tower shown is supported by parallel guy wires such that m<1 = (2x +20)° and m<2 = (4x-6)° Government regulations stale the angle the wire forms with the ground cannot exceed 45°. Does the angle of the guy wire fall within government regulation
The wires are parallel lines. If you consider the floor to be a perpedicular line that crosses both parallel lines. Then angles m∠1 and m∠2 are corresponding angles (the lines form an F shaped line), this means, that they are equal, so:
m∠1=m∠2
If you replace ir with the given expressions you will determine a one unknown equation:
[tex]2x+20=4x-6[/tex]Solve for x
[tex]\begin{gathered} 2x-4x=-6-20 \\ -2x=-26 \\ x=13 \end{gathered}[/tex]Using the value of x replace in the formulas to determine the measure of the angles
m∠1=2x+20=2*13+20=46º
m∠2=4x-6=4*13-6=46º
The angle og the guy wires are off the goverment regulations by one degree.
Mario made a 75 on his last test. If he scores 20% higher on this test, what will be his higher test score?
We can answer this by the rule of three.
[tex]\begin{gathered} 75\rightarrow100 \\ x\rightarrow120 \end{gathered}[/tex]Then:
[tex]x=\frac{120\cdot75}{100}=\frac{9000}{100}=90[/tex]Therefore his score will be 90 points.
If you have a sample size of 4 and a population standard deviation of 12, what is your standard error of the mean?ANDIf you have a population standard deviation of 2 ad a sample size of 9, what is your standard error of the mean?
The standard error is given by the formula:
[tex]SE=\frac{\sigma}{\sqrt[]{n}}[/tex]Where: σ is the standard deviation and (n) is the number of samples
Given: a sample size of 4 and a population standard deviation of 12
So, n = 4 and σ = 12
So, the standard error =
[tex]SE=\frac{12}{\sqrt[]{4}}=\frac{12}{2}=6[/tex]And, If you have a population standard deviation of 2 and a sample size of 9
The standard error will be =
[tex]SE=\frac{2}{\sqrt[]{9}}=\frac{2}{3}[/tex]Select all intervals where f is decreasing A: -2 < x < -1.5B : -1 < x < 0C: 0 < x < 1d: mone of the above
the functiion of graph at the fourth quadrant is a decreasing.
The options that are given dosent match the decrasing graph.
Hence the answer is option d. none of the above.
Which of the following are fifth degree polynomial functions? Select all that apply.2 answers
The greatest power of the polynomial function is its degree
Since we need the 5th degree, then the greatest power of x must be 5
From the given figure, we can see that the function in answer A is
[tex]f(x)=x-x^5[/tex]The function has the greatest power of x = 5, then
This function in answer A is in the 5th degree
The function in answer D is
[tex]f(x)=(x^2-1)(x^3+x-3)[/tex]When we multiply the 2 brackets we will find the greatest power of x will be 5
[tex]\begin{gathered} f(x)=x^2(x^3)+x^2(x)+x^2(-3)-1(x^3)-1(x)-1(-3) \\ f(x)=x^5+x^3-3x^2-x^3-x+3 \end{gathered}[/tex]Since the greatest power of x is 5, then
The function in answer D is in the 5th degree
The answers are A and D
Paul has 5 books to place on a shelf. How many possible arrangements of all 5 books are there?
Explanation
In the question, we are told that paul has 5 books to place on a shelf. This is a case of arrangement which requires also using permutation to solve the question.
We will apply the formula below;
[tex]n!=n(n-1)(n-2)(n-3)\ldots\ldots\ldots\text{.}[/tex]Thereofore,
[tex]n!=5\times4\times3\times2\times1=120\text{ways}[/tex]Answer:
if you have a system of the two equations with two unknowns, and the graphs of the two equations intersect, the system must have ___. A. more than one solution b. exactly one solution c. at least one solution d. no solution
Given: A system of the two equations with two unknowns, and the graphs of the two equations intersect.
Required: Number of solutions
Explanation:
Since the graphs are intersecting, therefore, the system of equations is consistent.
It means they have a sloution.
Number of solutions depend upon the number of times the graphs are intersecting.
So. the system of equations have at least one solution for sure.
Final Answer: Option c is correct.
Answer:
More than 1 solution.
Step-by-step explanation:
Convert the angle in degrees to radians. Round to two decimal places.170°
Determine the domain and range of the function f(x) = Sqrt x – 4. Enter your answersin interval notation. Please see picture
The domain is the values that the input can take
[tex]\sqrt[]{x-4}\ge0[/tex]Solving this equation
x must be greater than or equal to 4
In interval notation
[4,∞)
The range is the value that the output can take
We know that the output must be greater than or equal to zero
y ≥ 0
In interval notation
[0,∞)
The price of veronicas meal before tax and tip was $11.92,Veronica paid 8% tax, then added a 15% tip to the total. To the nearest cent, how much money did Veronica pay for her meal?
The price of the meal before tax and tips = $11.92
8% tax will be
[tex]\frac{8}{100}\times11.92=\frac{95.36}{100}=0.9536[/tex]15% tips to the total will be
[tex]\frac{15}{100}\times12.8736=\frac{193.104}{100}=1.93104[/tex]Amount she paid for the meal is
[tex]11.92+0.9536+1.93104=\text{ \$}14.80464\approx\text{ \$14.80}[/tex]Which system of equations has an infinite solution?y=2x-72x + y = 510x+8y=-16-5x - 4y+28x= 3y + 1512 y = 4x-60y = 8x = 8
In order to determine which of the given equation has infinite solutions, you consider that infinite solutions mean that any value of the implied variable is valid for the
Which of the following expressions is a common factor when the expressions x2 -9 and 32 – 50 + 6 are factored? A. : +3 в. x — 3 C. 2 - 2 D. x2
Here, we want to get the common factor when the two given expressions are factorised
We can factorize the first expression by the use of differeence of two squares
We have this as;
[tex]x^2-9\text{ = (x+3)(x-3)}[/tex]For the second expression, we have the factorization as follows;
[tex]x^2-5x+6=x^2-3x-2x+6\text{ = (x-3)-2(x-3) = (x-2)(x-3)}[/tex]What this mean is that we have the common factor of the two expressions as (x-3)
-8 cm6 cm3 cmMove numbers to the lines to show how to find the area of the figure.+6 x 36+38 x38 + 38 x 68 + 6
To be able to find the area of the g
how fast is the angle of depression of the telescope changing when the boat is 260 meters from shore
Given:
The boat moves at a rate = 15 meters per second
The telescope is 40 meters above the water level
Let the distance between the boat and tower of the telescope = x
so,
[tex]\begin{gathered} \tan \theta=\frac{x}{40} \\ \\ x=40\tan \theta \end{gathered}[/tex]Differentiate both sides with respect to the time (t)
[tex]\frac{dx}{dt}=40\cdot\sec ^2\theta\cdot\frac{d\theta}{dt}[/tex]Where: (dx/dt) is the speed of the boat
(dθ/dt) is the change of the angle of the telescope
Substitute with (dx/dt = 15) and
When the boat is 260 meters from shore
[tex]\begin{gathered} \tan \theta=\frac{260}{40}=6.5 \\ \theta=\tan ^{-1}6.5\approx81.254\degree \end{gathered}[/tex]so,
[tex]\begin{gathered} 15=40\cdot(\sec 81.254)^2\cdot\frac{d\theta}{dt} \\ \\ \frac{d\theta}{dt}=\frac{15}{40\cdot(\sec 81.254)^2} \end{gathered}[/tex]Using the calculator:
[tex]\frac{d\theta}{dt}=0.0087[/tex]so, the answer will be 0.0087 degrees per seconds
Convert from to radians per second
So,
[tex]0.0087\cdot(\frac{\pi}{180})=0.0002\text{ rad/s}[/tex]Lin runs 2 3/4 miles in 2/5 of an hour. Tlyer runs 8 2/3 miles in 4/3 of an hour. How long does it take for each of them to run 10 mileshow long does it take Tyler to run 10 miles at that rate?
Answer
Lin will cover 10 miles in 1.45 hours.
Tyler will cover 10 miles in 1.54 hours.
Explanation
We need to note that speed is given as
Speed = (Distance)/(Time)
For Lin,
Distance = 2 3/4 miles = 2.75 miles
Time = (2/5) hour = 0.40 hour
Speed = (Distance)/(Time)
= (2.75/0.40)
= 6.875 miles per hour
For Tyler
Distance = 8 2/3 miles = 8.67 miles
Time = (4/3) hour = 1.33 hour
Speed = (Distance)/(Time)
= (8.67/1.33)
= 6.5 miles per hour
We can then calculate how long it will take each of them to cover 10 miles
Speed = (Distance)/(Time)
For Lin
Speed = 6.875 miles per hour
Distance = 10 miles
Time = ?
Speed = (Distance)/(Time)
6.875 = (10/Time)
Cross multiply
Time = (10/6.875)
Time = 1.45 hours
For Tyler
Speed = 6.5 miles per hour
Distance = 10 miles
Time = ?
Speed = (Distance)/(Time)
6.5 = (10/Time)
Cross multiply
Time = (10/6.5)
Time = 1.54 hours
Hope this Helps!!!
what is the value of B ( area of the base) for the following triangular prism? Remember there are 10 millimeters in a centimeter.3 cm^230 cm^215 cm^21.5 cm^2
Firstly, the base is a rectangle (specifically, an oblong). There is a general formula for its area (B):
[tex]B=\text{ (width)}\cdot(length)[/tex]The trick behind the question is the units of the width (cm) and the length (mm). Due to the options, we have to convert 12mm to its corresponding value in cm. Let's remember that 1cm is 10mm; thus, 12mm is 1.2cm. Let's apply the formula.
[tex]B=4\cdot1.2=4.8\operatorname{cm}[/tex]4) Two angles form a linear pair. If the angles are (4x - 20º and (x)', then whatIs the measure of those angles?
When 2 angles form a linear pair, they form a straight line, that has a measure of 180°.
So, the sum of both angles is equal to 180°:
4x-20 +x =180
Solving for x:
4x+x-20=180
5x-20=180
5x=180+20
5x=200
x=200/5
x= 40
Now, replace the value of x in each angle:
4x-20 = 4(40)-20 = 160-20= 140°
x=40°
So:
Angle 1 = 140°
Angle 2 = 40°
What is the area of a right triangle with vertices of (-2, 4), (2, 4), and (2,5)?O 6 unitsO 18 unitsO 36 units?O 97 units
In order to determine the are of the given triangle, you first calculate the distance between vertex of the triangle. You use the following formula for the distance betwen two points of coordinates (x1,y1) and (x2,y2):
d = √((x2 - x1)² + (y2 - y1)²)
distance between (-2,-4) and (2,-4):
d1 = √((2 - (-2))²+(-4-(-4))) = √16 = 4
distance betwee (2,-4) and (2,5):
d2 = √((2-2)+(5-(-4))) = √1 = 3
each of the prvious distances represent a side of the right triangle. The area is calculated by using the following formula:
A = d1 x d2)/2
What is the steps of this equation? (the answer is $908.51). I don't need to know the information. Just how to do the equation and the answer. Thank you!
Answer:
Explanation:
Given:
Final Amount = $1000
Time in years = 3
interest rate = 3.25% = 0.0325
To find the principal amount for the given investment, we use the formula:
[tex]P=\frac{A}{(1+\frac{r}{n})^{nt}}[/tex]Where:
P= Principal Amount
A=Final Amount
r= interest rate in decimal
t=time in years
n= the number of times interest is compounded per unit t
It is mentioned that it is compounded annually, so the value of n=1.
P=1000(1.0325) -³ is from the formula:
We plug in what we know:
[tex]\begin{gathered} P=\frac{A}{(1+\frac{r}{n})^{nt}} \\ =\frac{1000}{(1+\frac{0.0325}{1})^{(1)(3)}} \\ \text{Simplify} \\ =\frac{1000}{(1+0.0325)^3} \\ P=\frac{1000}{(1.0325)^3}=908.51 \\ or \\ P=1000(1.0325)^{-3} \\ \text{Calculate} \\ P=908.51 \end{gathered}[/tex]Therefore, Kyle should invest $908.51
WXYZ is a parallelogram. After solving, b =So m
It is given that the quadrilateral WXYZ is a parallelogram.
By property of parallelogram the adjacent angles are supplementary so it follows:
[tex]\begin{gathered} \angle W+\angle Z=180 \\ 18b-11+9b+2=180_{} \\ 27b=189 \\ b=7 \end{gathered}[/tex]Since the value of b is 7, the angle Z is given by:
[tex]\angle Z=9b+2=9(7)+2=65^{\circ}[/tex]Hence b=7 and angle Z is 65 degrees.
this is a practice sheet and i am unsure how to so this question
Slope m= 3, for Line I
Line k is parallel to Line I
Then also
m'= 3
and equation of Line k is
y= 3x + b
Then , rest to find b in this equation
with point (3,10)= (x,y)
b = y - 3x = 10 - 3•3= 10-9=1
b= 1
THEN
Equation for Line k
ANSWER IS
y= 3x + 1.
OPTION D)
A business sells $23,000 worth of merchandise, and its cost of inventory was $13000. what is the gross profit listed on the income statement?A.$13,000B.$ 36,000C.$23,000D.$10,000
ANSWER
[tex]D.\text{ }\$10,000[/tex]EXPLANATION
To find the gross profit, find the difference between the cost of goods and the revenue obtained.
Therefore, the gross profit is:
[tex]\begin{gathered} P=\$23,000-\$13,000 \\ \\ P=\$10,000 \end{gathered}[/tex]That is the answer (option D).
Pedro spent 2 1/5 hours on his math homework and half as long on his science homework one weekend if his English and social studies homework took 7/8 as long how much time did he spend on homework that weekend
He spend [tex]6\frac{3}{16}[/tex] hours on homework in that weekend
Number of hours Pedro spent for his math homework = [tex]2\frac{1}{5}[/tex] hours
Convert the mixed fraction to simple fraction
[tex]2\frac{1}{5}[/tex] hours = 11/5 hours
He spent half as long on his science homework
(11/5) × 1/2 = 11/10 hours
Total time taken = 11/5 + 11/10
= 33/10 hours
He spend 7/8 as long for English and social studies homework
33/10 × 7/8 = 231/80
Total time taken = 33/10 + 231/80
= 99/16 hours
Convert the simple fraction to mixed fraction
99/16 hours = [tex]6\frac{3}{16}[/tex] hours
Hence, then he spend [tex]6\frac{3}{16}[/tex] hours on homework in that weekend
Learn more about mixed fraction here
brainly.com/question/2753661
#SPJ1
apply properties of logarithms to solve exponential and logarithmic equations
Given:
Given the equation
[tex]\log_3(4-a)=\log_3(-2a+2)[/tex]Required: Value of a
Explanation:
The given equation can be written as
[tex]\log_3(4-a)-\log_3(-2a+2)=0[/tex]Use the property
[tex]\log_bp-\log_bq=\log_b\frac{p}{q}[/tex]Thus,
[tex]\log_3(\frac{4-a}{-2a+2})=0[/tex]Take antilogarithm on both sides.
[tex]\begin{gathered} \frac{4-a}{-2a+2}=3^0 \\ 4-a=-2a+2 \\ -a+2a=2-4 \\ a=-2 \end{gathered}[/tex]Final Answer: The value of a is -2.
How high must a 800-gallon rectangular tank be if the base is a square 4ft 6in. on a side? (1 cu ft ≈7.48 gallons)(Type an integer or decimal rounded to the nearest tenth as needed.)
Given:
Volume of the rectangular tank is 800 gallon.
Side of the square is 4 ft 6 in.
[tex]\begin{gathered} 12\text{ foo}t=1\text{ inch} \\ 6\text{ inch=}\frac{6}{12}\text{ feet} \\ =\frac{1}{2}\text{feet} \\ =0.5\text{feet} \end{gathered}[/tex]So, 4 ft 6 inch is 4.5 feet.
Let h be the height of the rectangular tank.
The volume is given as,
[tex]\begin{gathered} V=l\times b\times h \\ 800\times\frac{1ft^3}{7.48\text{ gallons}}=4.5\times4.5\times h \\ h=\frac{800}{7.48\times20.25} \\ h=5.28 \end{gathered}[/tex]So, the height of tank is 5.3 ft
Write an equation in slope intercept form that has a slope of negative 3 and they y-intercept of 5
We will investigate the formulation of an equation of a straight line.
All equation of a straight line are mostly expressed in the general slope-intercept form as follows:
[tex]y\text{ = m}\cdot x\text{ + c}[/tex]Where,
[tex]\begin{gathered} m\text{ : Slope/gradient} \\ c\colon\text{ y-intercept} \end{gathered}[/tex]The above two parameters ( m and c ) distinguish amoung different equation of a straight line.
We are given the values of the two parameters as follows:
[tex]\begin{gathered} m\text{ = -3} \\ c\text{ = 5} \end{gathered}[/tex]We will go ahead and plug in the respective values of the two parameters in the generalized formulation of an equation of a straight line:
[tex]y\text{ = -3x + 5}[/tex]Therefore, the equation of the straight line is:
[tex]y\text{ = -3x + 5 }\ldots\text{ Answer}[/tex]Find the perimeter of the triangle whose vertices are the following specified points in the plane.
Let A = (1,-5), B = (2,9) and C = (-6,-8). Solve first for AB, BC, and CA.
[tex]\begin{gathered} \text{Solve for }\overline{AB} \\ \overline{AB}=\sqrt[]{(1-2)^2+(-5-9)^2} \\ \overline{AB}=\sqrt[]{(-1)^2+(-14)^2} \\ \overline{AB}=\sqrt[]{1+196} \\ \overline{AB}=\sqrt[]{197} \\ \overline{AB}\approx14.04\text{ units} \end{gathered}[/tex][tex]\begin{gathered} \text{Solve for }\overline{BC} \\ \text{ }\overline{BC}=\sqrt[]{(2-(-6))^2+(9-(-8))^2} \\ \text{ }\overline{BC}=\sqrt[]{(8)^2+(17)^2} \\ \text{ }\overline{BC}=\sqrt[]{(64)^{}+(289)^{}} \\ \text{ }\overline{BC}=\sqrt[]{353^{}} \\ \overline{BC}\approx18.79\text{ units} \end{gathered}[/tex][tex]\begin{gathered} \text{Solve for }\overline{CA} \\ \text{ }\overline{CA}=\sqrt[]{(-6-1)^2+(-8-(-5))^2} \\ \text{ }\overline{CA}=\sqrt[]{(-7)^2+(-3)^2} \\ \text{ }\overline{CA}=\sqrt[]{49+9} \\ \text{ }\overline{CA}=\sqrt[]{58} \\ \text{ }\overline{CA}\approx7.62\text{ units} \end{gathered}[/tex]Now solve for Perimeter
[tex]\begin{gathered} P=\overline{AB}+\overline{BC}+\overline{CA} \\ P=14.04+18.79+7.62 \\ P=40.45\text{ units} \end{gathered}[/tex]Therefore, the perimeter of the triangle whose points in the plane are (1,-5), (2,9) and (-6,-8) is 40.45 units.
What is the radius of a sphere with a volume of 996 cm", to thenearest tenth of a centimeter?
The volume of a sphere is:
Since we know V = 996 cm^3, then we need to find r
[tex]\begin{gathered} V=\frac{4}{3}\pi r^3 \\ r^3=\frac{3}{4}\cdot\frac{V}{\pi} \\ r=\sqrt[3]{\frac{3}{4}\cdot\frac{V}{\pi}} \\ r=\sqrt[3]{\frac{3}{4}\cdot\frac{996}{\pi}} \end{gathered}[/tex]The value of r is 6.195, but approaching to the nearst tenth, r = 6.2
Find the measurement of each deferment. assume that each figure is not drawn to scale
From the present figure, we can conclude that the distance from W to Y must be equal the sum of the distance from W to X with the disctance from X to Y, because it is a straight line. From this, we can write a math relation as follows:
[tex]WY=WX+XY[/tex]We know the distance from X to Y (XY) and from W to Y (WY). Substituting these values into the relation we have, we cansolve it as follows:
[tex]\begin{gathered} 100\operatorname{cm}=WX+89.6\operatorname{cm} \\ WY=100\operatorname{cm}-89,6\operatorname{cm} \\ \\ WY=10.4\operatorname{cm} \end{gathered}[/tex]From the above solution, we conclude that the correct answer is the second option: 10.4 cm