Let's use the variable x to represent the shortest side of the triangle.
If one side is 4 times longer than the shortest side, it measures "4x".
If the third side is 3 cm less than twice the length of the shortest side, it measures "2x - 3".
So, if the perimeter is 46 cm, we have:
[tex]\begin{gathered} x+4x+2x-3=46 \\ 7x-3=46 \\ 7x=49 \\ x=\frac{49}{7}=7 \end{gathered}[/tex]So the shortest side measures 7 cm.
You are starting your first job as a salesperson at a clothing store. You receive a base salary of $10.00 per hour with time-and-a half for hours in excess of 40 hours per week. If you are paid biweekly (every two weeks), what will one gross base paycheck be? Assume 40 hours a week, no overtime. a760 b840 c400 d800
1) Given that you are paid every two weeks, consider that the base salary is $10 per hour. And 1.5 times for hours in excess.
2) But notice that the pay will not include overtime.
3) Thus, we can write out the following:
[tex]\begin{gathered} 40\:hours\:\times2=80\:hours \\ \\ 80\:\times10=800 \end{gathered}[/tex]Note that this is the gross paycheck (no taxes).
For his phone service, Bob pays a monthly fee of $29, and he pays an additional $0.06 per minute of use. The least he has been charged in a month is $90.44. What are the possible numbers of minutes he has used his phone in a month? Use for the number of minutes and solve your inequality for?
The number of minutes Bob has used his phone in a month is 1024 minutes.
What is meant by the term inequality?In mathematics, an inequality is a link between two expressions as well as values that aren't equal to each other.For the given question;
Monthly phone service paid by Bob = $29.
Additional charges = $0.06 per minute of use.
Total last month charge = $90.44.
Let number of minutes he used be 'm'.
The, the inequality forms is-
90.44 ≤ 29 + 0.06m
Simplifying,
0.06m ≥ 61.44
m ≥ 1024
Thus, the number of minutes Bob has used his phone in a month is 1024 minutes.
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, Assuming that the relationship between the miles driven and the amount of gasneeded is DIRECT VARITION, and that your car uses 1.6 gallons to go to Salt Lake from yourhome in Clinton (32 miles). Find the amount of gallons of gas that your car needs to go to LasVegas from your house, knowing that Salt Lake is 420 away from Vegas.Then, using the right numbers,distanceFirst, find the constant of variation,gasolinesolve the equationMy car needsgallons
Given:
Car uses 1.6 gallons to go 32 miles
Let's find the amount of gallons of gas the car needs to travel 420 miles.
Here, the relationship between the miles driven and the amount of gas needed is direct variation.
Since it is a direct variation, we have the variation equation when y varies directly with x:
y = kx
Where k is the constant of variation.
Hence, we have:
32 = 1.6k
Let's solve for k.
Divide both sides by 1.6:
[tex]\begin{gathered} \frac{32}{1.6}=\frac{1.6k}{1.6} \\ \\ 20=k \\ \\ k=20 \end{gathered}[/tex]The constant of variation is 20.
The equation that represents this situation is:
y = 20x
Therefore, to find the amount of gallons of gas needed if the car travels 420 miles, substitute 420 for y and solve for x.
420 = 20x
Divide both sides by 20:
[tex]\begin{gathered} \frac{420}{20}=\frac{20x}{20} \\ \\ 21=x \\ \\ x=21 \end{gathered}[/tex]Therefore, the car needs 21 gallons of gas
In the unit circle, if the arc length is 1/20 of the circumference, find the area of the sector.
Given:
The length of the arc is (1/12) x circumference of unit circle.
The objective is to find the area of the sector.
Since it is given as a unit cirle, the radius of the circle will be 1 unit.
The circumference of the circle will be,
[tex]\begin{gathered} C=2\cdot\pi\cdot r \\ =2\pi\text{ units.} \end{gathered}[/tex]Then, the length of the arc will be,
[tex]\begin{gathered} l=\frac{1}{12}\times2\pi \\ =\frac{\pi}{6}\text{ units} \end{gathered}[/tex]Now, the formula to find the area of the sector is,
[tex]\begin{gathered} A=\frac{1}{2}r^2\cdot\theta \\ =\frac{1}{2}r^2\cdot\frac{l}{r} \\ =\frac{l\cdot r}{2} \end{gathered}[/tex]On plugging the values in the above relation,
[tex]\begin{gathered} A=\frac{\pi}{6}\times\frac{1}{2} \\ =\frac{\pi}{12} \\ =0.262\text{ sq. units} \end{gathered}[/tex]Hence, the area of the sector is 0.262 square units.
255 is 88% of what? Round to the nearest tenth.
Answer:
289.8.
Explanation:
Let the number = x
Then, it implies that:
[tex]88\%\text{ of }x=255[/tex]Next, solve for x:
[tex]\begin{gathered} \frac{88}{100}\times x=255 \\ 88x=25500 \\ x=\frac{25500}{88} \\ x=289.8 \end{gathered}[/tex]The number is 289.8 to the nearest tenth.
Sketch and label a graph of both an increasing and a decreasing exponential function.
An exponential function is one in which the independent variable x appears in the exponent and has a constant a as its base. Its expression is:
[tex]f(x)=a^x[/tex]With a being a positive real, a > 0, and different from 1, a ≠ 1.
When 0 < a < 1, then the exponential function is a decreasing function and when a > 1, it is an increasing function.
For example: the function
[tex]f(x)=2^x[/tex]Since a = 2 > 1, the function is increasing. We have the graph below:
And the function
[tex]f(x)=0.5^x[/tex]Since a = 0.5 < 1, the function is decreasing. Then, the graph is:
What number should be in the box to make the equation below true
So,
We want to find the value in the box such that:
[tex]\frac{(\frac{2+x}{6}+1)}{4}=\frac{3}{8}[/tex]I wrote x instead the box.
To solve this equation, the first thing we need to do is to let the "x term" alone.
For this, we could start by multiplying both sides of the equation by 4:
[tex]\frac{2+x}{6}+1=\frac{12}{8}[/tex]Now, we could substract 1 to both sides:
[tex]\begin{gathered} \frac{2+x}{6}=\frac{12}{8}-1 \\ \\ \frac{2+x}{6}=\frac{4}{8} \end{gathered}[/tex]And then multiply by 6:
[tex]2+x=\frac{24}{8}[/tex]Now, substract 2:
[tex]\begin{gathered} x=\frac{24}{8}-2 \\ \\ x=3-2 \\ x=1 \end{gathered}[/tex]Therefore, the value in the box should be 1.
The point Q(3,-4) is translated 1 unit right and 1 unit down. What are the coordinates of the
resulting point, Q?
Answer:Q(2,-3)
Step-by-step explanation:
Can you help me find the cube root of .216
Given
0.216
Find
Cube root of the given number
Explanation
Cube root is the value which when multiplying by itself thrice or three times produces the original number
0.216 can be written as the product of
[tex]\begin{gathered} 0.216=\frac{216}{1000} \\ \end{gathered}[/tex]prime factorization of 216 and 1000
prime factorization of 216 =
[tex]\begin{gathered} 2\times2\times2\times3\times3\times3 \\ \end{gathered}[/tex]1000 -
[tex]\begin{gathered} 10\times10\times10 \\ 10 \end{gathered}[/tex]we have to find the cube root so , we make pair of three
so
[tex]\begin{gathered} (2\times2\times2)\times(3\times3\times3) \\ 2\times3 \\ 6 \end{gathered}[/tex]hence
[tex]\begin{gathered} \frac{6}{10} \\ 0.6 \end{gathered}[/tex]so , the cube root of 0.216 is 0.6
Final Answer
Therefore , The cube root of 0.216 is 0.6
Directions - Graph the following slope intercept equation:y=2/3x-2
Answer
Explanation
The best way to plot graphs, especially straight line graphs, is to use the intercepts. The intercepts are the point(s) that the graph of the function crosses or touches the x and y axis.
The equation is
y = (2/3)x - 2
when x = 0,
y = (2/3)x - 2
y = (2/3)(0) - 2
y = 0 - 2
y = -2
The first point on the graph is (0, -2)
when y = 0,
y = (2/3)x - 2
0 = (2/3)x - 2
(2x/3) = 2
Cross multiply
2x = (2) (3)
2x = 6
Divide both sides by 2
(2x/2) = (6/2)
x = 3
The second point on this graph is (3, 0)
So, the two points are (0, -2) and (3, 0)
We can then easily plot this graph by marking out those two points on the graph and connect the two points for the equation of that line.
What number is 345% of 8.6?
Answer:
29.7
Step-by-step explanation:
To calculate this we need to convert the percentage to a decimal and then multiply. 345% is 3.45, so our math problem is 8.6 x 3.45. If you put that into a calculator you will get 29.67, but since the least precise number is to one decimal place (8.6), I put my answer to one decimal place as well - I rounded 29.67 to the nearest tenth.
Find three consecutive odd integers such that the sum of the first and second is 27 less than three times the third
The consecutive integers that are odd numbers are 17, 19 and 21.
How to determine the value of three consecutive integers
In this problem we need to find the values of three consecutive integers that odd integers such that the following equation is satisfied:
x₁ + x₂ = 3 · x₃ - 27
Please notice that two odd numbers are consecutive when their difference is 2.
x₁ + (x₁ + 2) = 3 · (x₁ + 4) - 27
2 · x₁ + 2 = 3 · x₁ + 12 - 27
2 · x₁ + 2 = 3 · x₁ - 15
17 = x₁
x₁ = 17
Thus, the three odd integers that are consecutive are 17, 19 and 21, respectively.
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Hi, I was absent today in class and I really need help with question 6I will be much appreciated if you show work and the step so I can be more understanding thank you!
Recall that:
[tex]\log _ba=\frac{\ln a}{\ln b}\text{.}[/tex]Therefore:
[tex]\begin{gathered} x=\log _7513=\frac{\ln (513)}{\ln (7)} \\ x\approx\frac{6.24027584}{1.94591014}, \\ x\approx3.207. \end{gathered}[/tex]Answer:
[tex]x\approx3.207.[/tex]65% of the people at the party were females. The rest were males. How many
were males were there at the school party? There are 1,600 people
Answer:
560
Step-by-step explanation:
If 65% were females, 35% were males.
1600(35%) = 1600(0.35) = 560
Imagine that you are a scientist studying the effects of a new medication on the treatment of patients who get headaches. You separate all the patients into three groups. Group A is given 1 pill with a dose of 20 milligrams of medication once per day. Group B is given 1 pill with a dose of 40 milligrams of the medication once per day. Group C is given 1 pill that looks like the others but is really a sugar pill that contains no medication. The results: 20 percent of the people in Group A claimed that they got fewer headaches, while 80 percent of the people in Group B daimed that they had fewer headaches. Only 1 percent of people in Group C noticed a decrease in their headaches. What might you be able to conclude from this experiment? Explain by identifying the control, the dependent variable, and the independent variable in the experiment.
The control group is the group C, since they take sugar pills.
The dependent variable is the percentage of people that got fewer headaches.
The independent variables is the type of pills they gave to each of the groups.
The equation of a line is given below.Find the x-intercept and the y-intercept.Then use them to graph the line.SHOW POINTS WHEN GRAPHING
Given
2x + 6y = -18
Find
x intercept and y intercept. Then use them to graph the line.
Explanation
to find the y intercept , put x = 0
2(0) + 6y = -18
6y = -18
y = -3
now , put y = 0 to find the x intercept
2x + 6(0) = -18
2x = -18
x = -9
we have two points ; (0 , -3) and (-9 , 0)
plot these points on graph to make a line
Final Answer
Hence , the x intercept is -9 and y intercept is -3. The required graph is shown above.
can you please help me
In this problem we can see that the intercept with the y axis is positive one, so we know that the answer is A) or D), now we can see that the slope is positie so the term with the x has to be positive so the correct function is:
[tex]y=x+1[/tex]P(x)=(x+5)(x-5) and q(x)=(x+3)(x-3) where do the graphs of the two intersects
For the equation P(x)=(x+5)(x-5) and q(x)=(x+3)(x-3) the graph of the two equation never intersect each other.
What is a conic section?It is defined as the curve which is the intersection of cone and plane. There are three major conic sections; parabola, hyperbola, and ellipse (a circle is a special type of ellipse).
The given equations are,
P(x)=(x+5)(x-5)
q(x)=(x+3)(x-3)
Parabola is defined as the graph of a quadratic function that has something bowl-shaped.
(x - h)² = 4a(y - k)
(h, k) is the vertex of the parabola:
a = √[(c-h)² + (d-k²]
(c, d) is the focus of the parabola:
The given equation represents a parabola as the equation is graphed we see that the graph of the two never intersects each other.
Thus,for the equation P(x)=(x+5)(x-5) and q(x)=(x+3)(x-3) the graph of the two equation never intersect each other.
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Stacey's text messaging plan costs $7 for the first 550 messages and 30¢ for each additional text message. If she owes$39.40 for text messaging in the month of May, how many text messages did she send that month?
658 text messages
Explanation:
. Since you already know that for 7$ she gets 550 text messages, we can remove the 7$ from the 39.40$ she spent for the month, which leaves 39.40 - 7 = 32.40$
. Now since we know that for each extra 30 cents she gets to send one addition text,
=> we need to figure out first how many cents there is in the amount of money left she had to pay 32.40 * 100 = 3240 cents { since 1 $ = 100 cents }
=> then we need to figure out how many text does 3,240 cents represent, since 1 text is equivalent to 30 cent it means that in 3,240 / 30 = 108 texts messages is the amount of text she got to send with 32.40$
So in total she sent 550 + 108 = 658 texts messages for 39.40$
let E b the event where the sun of two rolled dice is greater than or equal to 3. lost the outcomes in E^c
We have the event E defined as:
E: The sum of two rolled dice is greater than or equal to 3
The event E^c is the negation of the event E. Then:
E^c: The sum of two rolled dice is smaller than 3
For two dice, the minimum sum is 2, so this is equal to the event "the sum of two rolled dice is 2". There is only one outcome:
Dice 1: 1
Dice 2: 1
Sum: 2
Then, the only possible outcome for E^c is {1, 1}
A line passes through the point (6, -6) and has a slope of 3/2.
Write an equation in point-slope form for this line.
Answer:
y+6=(3/2)(x-6)
Step-by-step explanation:
Point slope form is: y-y1=m(x-x1)
We know:
x1= 6
y1= -6
m=3/2
help me pleaseeeeeeeeeeeeeeeeeeeeeeeeeeee
thank you
The domain and range for the relation is [-∞, ∞] and [0,-3], and both of them can be described by interval notation .
Since the graph given to us present a relation or a function, The domain and range of a function are the set of all the inputs and yield a function that can grant separately. The domain and range are vital viewpoints of a function. The domain takes all the conceivable input values from the set of real numbers and the range takes all the yield values of the function. In simple words, the domain is the set of all "x" values and the range is the set of all "y" values in a set of ordered sets and the requested sets are composed as in the form (x, y) or [x,y]
For the given the points are : (0,-3),(1,-3),(2,-3),(3,-3),(4,-3),(5,-3),(-1,-3)(-2,-3),(-3,-3),(-4,-3),(-5,-3)
so the domain set is ={-5,-4,-3,-2,-1,0,1,2,3,4,5}
and the range set is ={0,-3,-4,-5,-6,-7,-8}
so the domain and range is [-∞, ∞] and [0,-3]
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What is the answer please
The measure of angle m∠CGE is 83°
Given,
∠AGF = 62°
∠DGB = 35°
Since, ∠DGB is vertically opposite angle of ∠CGA
Then, ∠CGA = 35°
And also,
∠AGF is vertically opposite angle of ∠EGB
Then, ∠EGB = 62°
Now, we know that CD is straight line
Using angle - sum property,
Then,
∠CGE + ∠EGB + ∠CGA = 180°
Putting the values we get
∠CGE + 62° + 35° = 180°
∠CGE + 97° = 180°
∠CGE = 180° - 97°
∠CGE = 83°
Hence, ∠CGE = 83°
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Write a multiplication expression with a product of x^20
Answer:
x¹¹ • x⁹
Step-by-step explanation:
so hope it help
have a nice day
A paper airplane is thrown off a 64-foot bridge into the water below. It’s height, in feet, is represented by f(x)= -16(x^2 - 3x - 4), where x is the number of seconds since the airplane was thrown. The height of the airplane is 0 feet when it hits the water. C. What do the zeros mean in terms of the situation?D. Do both zeros have a real world meaning? E. How long does it take the airplane to hit the water?
According to the problem, the function f(x) represents the height of the airplane, and x is the time in seconds since the airplane was thrown.
C.The graph shows the zeros x = -1 and x = 4, however, the positive zero is the only one that makes sense to the problem because time can't be negative. So, the zero x = 4 means that the paper airplane will reach the water level after 4 seconds.
D.As we said, just the positive zero has meaning to this situation because, in real life, time is not negative.
Therefore, just one zero (x=4) has real-world meaning.
E.According to the zero x = 4, the paper airplane will hit the water after 4 seconds.
The points (−7,−4) and (3,8) are the endpoints of the diameter of a circle. Find the length of the radius of the circle.
The length of the radius of the circle is √61.
Here there are two endpoints of the circle (-7,-4) and (3,8)
To find the length between the two points we have a formula:
length = [tex]\sqrt{(x_{2} - x_{1})^{2} + (y_{2} - y_{1} )^{2} }[/tex]
So here we have
([tex]x_{1} , y_{1}[/tex]) = (-7, -4)
([tex]x_{2} , y_{2}[/tex]) = ( 3,8)
Putting the value we have,
[tex]\sqrt{(3 -(-7)^{2} + ( 8-(-4)^{2} }[/tex]
=[tex]\sqrt{10^{2} + 12^{2} }[/tex]
=[tex]\sqrt{100+ 144}[/tex]
=√244
=2√61
The diameter is 2√61
radius = diameter/2
= 2√61/2
= √61
Therefore the length of the radius of a circle is √61.
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3. John rode is bike 20 kilometers on Monday. How many feet did John ride?
John rode his bike 65616.8 feet on Monday which is determined by converting 20 kilometers into feet.
What are Arithmetic operations?Arithmetic operations can also be specified by adding, subtracting, dividing, and multiplying built-in functions.
John rode his bike 20 kilometers on Monday which is given in the question.
To determine the number of feet John rides.
We have to convert 20 kilometers into feets
We know that
one kilometer = 3280.84 feet
Here 20 kilometers into feet will be:
⇒ 20 × 3280.84
Apply the multiplication operation, and we get
⇒ 65616.8 feet
Therefore, John rode his bike 65616.8 feet on Monday
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Solve for t: -3 = -t/15t=??[tex] - 3 = - \frac{t}{15} \\ \\ \\ t = [/tex]
Explanation:
[tex]-3=-\frac{t}{15}[/tex]First we can see that there's a minus sign in both sides of the equation, so we can take it out:
[tex]3=\frac{t}{15}[/tex]Now we have to multiply both sides by 15:
[tex]\begin{gathered} 3\cdot15=\frac{t}{15}\cdot15 \\ 45=t \end{gathered}[/tex]Answer:
t = 45
I need help with this I have only questions1. Where is y when x is 02. find f(-4)3. what is x when y is 4?4. What is X when f(X)=0? There are two answers put the smaller number in the first answer blank ____ and ____
1) y = 1 2) y =3 3) x = -3 4) y= -7 and y = 1
We are to answer the questions stated using the graph:
1) From the graph, when x = 0:
To understand this, check the point on the line that only lies on y
y = 1
2) f(-4) is the same as what is the value of y when x = -4
This is because f(x) = y
From the graph, when x = -4
y = 3
3) From the graph, when y =4
Trace the value of y=4 on the line to get corresponding x value:
x= -3
4) When f(x) = 0
This means what is the value of x when y = 0. This is because f(x) = y.
From the graph, we have two values of x when y = 0
y = -7
y = 1
To fill the blank spaces starting with the smaller number:
-7 and 1
1/8 x 240 please???? Hurry
Answer:
30
Step-by-step explanation:
