[tex]x^{2} + 2x _5=0[/tex]
Step-by-step explanation:
Substitute the values
a
=
1
,
b
=
−
2
, and
c
=
−
5
into the quadratic formula and solve for
x
.
2
±
√
(
−
2
)
2
−
4
⋅
(
1
⋅
−
5
)
2
⋅
1
Simplify.
x
=
1
±
√
6
Simplify the expression to solve for the
+
portion of the
±
.
x
=
1
+
√
6
Simplify the expression to solve for the
−
portion of the
±
.
Determine if the table shows a proportional relationship. x 42.5 29.2 69.4 y 21.25 14.6 34.7 Yes, it is proportional because the ratios for y over x are all equivalent to one half. Yes, it is proportional because the ratios for y over x are all equivalent to one third. No, it is not proportional because 21.25 over 42.5 is not equal to 29.2 over 14.6. No, it is not proportional because 42.5 over 21.25 is not equal to 34.7 over 69.4.
Yes, it is proportional because the graph of these coordinates is a straight line and the ratios for [y] over [x] are all equivalent to one half.
What is proportional relationship?Proportional relationships are relationships between two variables where their ratios are equivalent. A straight line represents a proportional relationship. Mathematically -
y = kx + c
(y - c)/x = k [k is constant]
or
y = kx
k = y/x [k is constant]
Given is the following data -
[x] 42.5 29.2 69.4
[y] 21.25 14.6 34.7
In order to find if the given coordinates represent proportional relationship, plot these coordinates on graph. If the by joining the coordinate points, we get a straight line, then it represents a proportional relationship. Graph is attached with the answer. It can be seen that its graph is a straight line and hence represents a proportional relationship.
Now, the ratio of [y] by [x] -
m = (21.25 - 14.6)/(42.5 - 29.2) = 6.65/13.3 - 0.5 = 1/2
Therefore, we can say that, Yes, it is proportional because the graph of these coordinates is a straight line and the ratios for [y] over [x] are all equivalent to one half.
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Answer: Yes, it is proportional because the ratios for y over x are all equivalent to one half.
Step-by-step explanation:
I did the test. :)
Which inequality represebts the graph shown below
Answer:
x > -2
Step-by-step explanation:
The table shows a proportional relationship.
x 12 8 24
y 3 2 6
Describe what the graph of the proportional relationship would look like.
A line passes through the point (0, 0) and continues through the point (3, 12).
A line passes through the point (0, 0) and continues through the point (2, 8).
A line passes through the point (0, 0) and continues through the point (6, 24).
A line passes through the point (0, 0) and continues through the point (12, 3).
A graph which best describes what the proportional relationship would be D. A line that passes through the point (0, 0) and continues through the point (12, 3).
What is a graph?In Mathematics, a graph is used to graphically represent data points on both the horizontal and vertical lines of a cartesian coordinate, which are the x-axis and y-axis respectively.
Additionally, a graph which shows a proportional relationship between two variables would always have a straight line with its data points passing through the origin (0, 0).
Since the graph represents a proportional relationship we will get;
Constant of proportionality, we get;
k = 12/3 = 8/2 = 24/6
k = 4
Ratio,
24:6
= 12:3.
Therefore, A line that passes through the point (0, 0) and continues through the point (12, 3).
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Explain the meaning of the expression tan 32°= 0.624
The meaning of the expression tan 32°=0.624 is the adjacent side of ratio is 0.624m.
What is ratio?
the ratio is the number that can be used to express one is quantity as a fraction of the other ones. The two of numbers in a ratio can only be compared when they have the same unit. We are make use of ratios o compare two things.
Sol- let's take an example first
In a triangle abc
C is 32°
tan 32° = AB/BC =0.624m
By applying the theorem we know that
In a right triangle , tan 32° is the ratio of the constant to the adjacent side the ratio is
0.624 m.
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Please answer the following questions. What is the slope of the line? How much does the distance increase for each hour since Alan crossed the bridge?
SOLUTION
The slope of the line can be gotten using the formula
[tex]\begin{gathered} \text{Slope =}\frac{change\text{ in distance}}{\text{change in time }}\text{ = }\frac{d2-d1}{t2-t1} \\ \text{Taking two points on along the line we have } \\ \text{Slope = }\frac{350-100}{7-2} \\ \\ \text{Slope =}\frac{250}{50} \\ \\ \text{Slope = 50} \end{gathered}[/tex]The slope is 50. This means the distance increased by 50 miles for every hour.
the scale of topographical of map is 1:50000.what is the area of a dam which is represented on the map by an area of 3.5 centimeter square
The scale of a topographical map is 1:50000. This means that 1 cm on the map is 50 000 cm on reality.
[tex]1\operatorname{cm}\rightarrow50000\operatorname{cm}[/tex]Now, we can take the
Jenna bought a new car for $29,000. She paid a 10% down payment and financed
the remaining balance for 48 months with an APR of 4.5%. Determine the monthly
payment that Jenna pays.
The monthly payment that Jenna pays for the new car is $1279.411 .
What is compound interest and how is it calculated?
The interest that is calculated using both the principal and the interest that has accrued during the previous period is called compound interest. It differs from simple interest in that the principal is not taken into account when determining the interest for the subsequent period with simple interest.
Mathematically, A = P (1 + (R/n))^t
Given, total cost of the car = $29,000
Percentage of amount paid while in down payment = 10%
Therefore, amount paid as down payment = (10/100)*29000 = $2900
Now, amount put on loan by Jenna = A = 29000 - 2900 = $26,100
Also, number of years for which amount is loaned = n = 4 years
Annual Percentage Rate of the loan allowed = R = 4.5
Following the formula established in the literature above, we have:
26100 = P (1 + (4.5/4))⁴ ⇒ P = 26100/(1 + (4.5/4))⁴ ⇒ P = 26100/20.4
= 1279.411
The monthly payment that Jenna pays for the new car is $1279.411
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Point F is located at (-6, -2) on the coordinate plane. Point Fis reflected over the
y-axis to create point F'. What ordered pair describes the location of F'?l
The ordered pair describes the location of F' is (6, -2) reflected over the
y-axis.
What is meant by the term reflection?A reflection is the shape's mirror image. The line of reflection is formed when an image reflects through a line. A figure is said to reflect another figure when every point in one figure has been equidistant from every point in another figure. The reflected image should be the same shape and size as the original, but it should face in the opposite direction. Translation can also occur as a result of changes in position.The Y-coordinates of a point remain constant when it is reflected across the Y-axis. However, the X-coordinates are transformed into their inverse signs.
As a result, the Y-axis reflection of a point (x, y) is (-x, y).
For the given question;
Point F (-6, -2) is reflected along the y-axis to form a point F'.
The coordinates of F' becomes (6, -2), negative x axis will becomes positive.
Thus, the ordered pair describes the location of F' is (6, -2) reflected over the
y-axis.
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Evaluate the following quotient. Leave your answer in scientific notation(5.44 x 10-18) + (6.8 x 10-))Answer
Given:
[tex](5.44\times10^{-18})\div(6.8\times10^{-9})[/tex]It can be written as follows.
[tex](5.44\times10^{-18})\div(6.8\times10^{-9})=\frac{5.44\times10^{-18}}{6.8\times10^{-9}}[/tex][tex]\text{Use }\frac{1}{10^{-9}}=10^9.[/tex][tex]=\frac{5.44\times10^{-18}\times10^9}{6.8^{}}[/tex][tex]=\frac{5.44\times10^{-18+9}^{}}{6.8^{}}[/tex][tex]=\frac{5.44\times10^{-9}}{6.8^{}}[/tex]Dividing 5.44 by 6.8, we get
[tex]=0.8\times10^{-9}^{}[/tex][tex](5.44\times10^{-18})\div(6.8\times10^{-9})=0.8\times10^{-9}[/tex]
Hence the quotient is
[tex]0.8\times10^{-9}[/tex]Which IRS form is provided at the end of the year by employers, so employees can use it to file taxes?
The IRS form is provided at the end of the year by employers, so employees can use it to file taxes is Form W-2.
What is Form W-2?Form W-2 can be described as the form that is been offered from the Internal Revenue Service which can be considered as the (IRS) tax form .
It should be noted that this form is been used in the United States so that the wages that is been paid to employees as well as their taxes can be reported. withheld from them
It should be noted that the form is been provided when the year is coming to an end by employers.
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A triangle with sides 10, 24, and 25 is a right triangle True/ False
Answer:
False
Step-by-step explanation:
Check using Pythagorean theorem (proof for right triangles)
[tex]10^2+24^2=25^2[/tex]
[tex]100+576=625[/tex]
[tex]676\neq 625[/tex]
False
I Need Help Quick!! A recycling machine crushes 175 pounds of cans in 5 minutes.
How many pounds of cans will the machine crush in 16 minutes?
A. 560 pounds
B. 955 pounds
C. 1,925 pounds
D. 2,805 pounds
Answer:
560 pounds
Step-by-step explanation:
175 pounds divided by 5 minutes.
= 35 pounds per minute
35 pounds per minute multiplied by 16 minutes
= 560 pounds
63 ÷ 5 = 12 R3 solve the problem
Answer:
12r^3
Step-by-step explanation:
10) Find DF if LF = 2X - 8 and LD = X - 3
Answer:
DF = 4
Step-by-step explanation:
You want DF when L is the midpoint, LD = x-3 and LF = 2x-8.
Congruent segmentsSegments DL and LF are marked the same, so are congruent. Using the given expressions, we have ...
LF = LD
2x -8 = x -3
x = 5 . . . . . . . . add 8-x to both sides
Then the measures of the segments are ...
LF = 2(5) -8 = 2
LD = 5 -3 = 2
DF = DL +LF = 2 +2 = 4
The length of DF is 4 units.
Please finish the question provided with a screen shot.
Answer:
Angle VSR + Angle SRU = 180° (corresponding angles, sum of angles on a straight line = 180°)
(5x + 4) + (44 + x) = 180
6x + 48 = 180
6x = 132
x = 22
2x-3=4+2x solve for x
Answer:
no solution
Step-by-step explanation:
After you level up solving equations, sometimes there is NO solution (and sometimes there is infinite solutions) instead of always getting a number answer.
How do you know when?
Solve as usual:
2x - 3 = 4 + 2x
Subtract 2x from both sides.
-3 = 4
When all your variables "fall out" of the equation and you end up with a false statement, then you have NO Solution.
arrange the numbers in increasing order a. 8.08 8.081 8.09 8.008b. 14.204. 14.200. 14.240 14.210
Given:
a)
[tex]8.08,8.081,8.09,8.008[/tex]b)
[tex]14.204,14.200,14.240,14.210[/tex]Required:
To arrange in the increasing order.
Explanation:
a)
Here, the first two places' numbers are the same.
Let us check the hundredth decimal place.
The lowest number is 8.008.
The second lowest number is 8.08.
The third lowest number is 8.081
The fourth lowest number is 8.09.
So, the numbers are in ascending order is,
[tex]8.008,8.08,8.081,8.09[/tex]b) Here, the first t places' numbers are the same.
Let us check the hundredth decimal place.
The lowest number is 14.200.
The second lowest number is 14.204.
The third lowest number is 14.210.
The fourth lowest number is 14.240.
So, the numbers ar
What is the average rate of change of the function x increases from -3 to 5
The average rate of change when x increases from -3 to 5 is given as follows:
r = (f(5) - f(-3))/8.
What is the average rate of change of a function?The average rate of change of a function is given by the change in the output divided by the change in the input. Hence, over an interval [a,b], the average rate of change is given by the fraction presented as follows:
[tex]r = \frac{f(b) - f(a)}{b - a}[/tex]
In the context of this problem, the input x increases by -3 to 5, hence the change in the input is given as follows:
b - a = 5 - (-3) = 5 + 3 = 8.
The change in the output is given as follows:
f(b) - f(a).
(the problem is incomplete hence the answer is given in general terms).
Then the average rate of change of the function when x increases from -3 to 5 is given as follows:
r = (f(5) - f(-3))/8.
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Greg is at his house he gets in his car drives north 8. 9 miles and stops at a store then he turns around and drives south 7. 7 miles to his friends house how far is the friends house from Greg’s houses?
His friend's house is 1.2 miles away from his house.
How do you know his friend's house is 1.2 miles away from his house?Well, the solution to this math problem is very simple. We just need to remove a number away from another. In other words, we only need to do some subtraction.
Subtraction is one of four main arithmetic operations in which we use to take away a number or an amount from another number or amount. Remember that the commutative law doesn't apply to subtraction, so we really need to be careful to pick what number is subtracted by the other number.
The distance from Greg's house to the store is 8.9 miles away. That's the number that is going to be subtracted. His friend's house is 7.7 miles away from the store. This is the number that we're going to subtract from the previous number. Mathematically, we can express this as:
8.9 - 7.7 = 1.2
We're left with 1.2, which is the distance in miles from Greg's house to his friend's house.
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Part A Write the multiplication expression shown by the model. Do not solve the problem.
Explain the expression written in Part B. Include the final product and how it is shown with the model.
The multiplication model represented by the image is given as follows:
12(4 x 10) + (3 x 10) + (6 x 10) + 18.
What is a multiplication operation?A multiplication operation is equivalent to consecutive additions.
For the green squares, the following addition is obtained:
10 + 10 + 10 + 10 + 6.
(which is the number of squares painted green).
Considering a multiplication with consecutive additions, it is written as follows:
4 x 10 + 6.
For the red squares, the expression is:
4 + 4 x 10 + 2 = 4 x 10 + 6.
For the blue squares, the expression is:
8 + 3 x 10 + 8
3 x 10 + 16
For the white squares, the expression is:
2 + 6 x 10
Hence the total model is calculated as follows:
4 x 10 + 6 + 4 x 10 + 6 + 3 x 10 + 16 + 2 + 6 x 10
(4 x 10)(6 + 6) + (3 x 10) + (6 x 10) + 18.
12(4 x 10) + (3 x 10) + (6 x 10) + 18.
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what is the radius of the circle?
Answer:
7 units
Step-by-step explanation:
Hello!
The radius of a circle is the distance from the center of the circle to it's outer edge.
The radius of this circle is 7 units, as the distance from the center to the outer edge is 7.
Answer:
7 units
Step-by-step explanation:
count from the center to the circle to one of the sides which is 7 units
If you vertically compress the absolute value parent function, f(x) = Ixl, by afactor of 4, what is the equation of the new function?A. g(x)=xB. g(x) = 4xC. g(x) = 14x1D. g(x) = |x-41
Solution:
Given the absolute value parent function below
[tex]f(x)=|x|[/tex]If the function is vertically compressed by a factor of 4, the function becomes
[tex]g(x)=\frac{1}{4}f(x)[/tex]Where
[tex]\begin{gathered} f(x)=|x| \\ g(x)=\frac{1}{4}|x| \end{gathered}[/tex]Hence, the answer is
[tex]g(x)=\frac{1}{4}\lvert x\rvert[/tex]Option A
Rewrite the fraction in the sentence below as a percentage. From 125 yards away, a marksman hit 13/20 of the targets last year.
The fraction, 13 / 20 when converted to percentage is 65%.
What is the percentage?A fraction is a non-whole number that has a numerator and a denominator. An example of a fraction is 13 / 20. 13 is the numerator and 20 is the denominator.
A percentage is when a fraction is converted to a number out of 100. In order to convert a fraction to a percentage, multiply the fraction by 100. The sign that represents percentage is %. Percentage is used to measure the frequency of a dataset.
In order to rewrite the fraction as a percentage, multiply the fraction by 100.
Percentage of times he hit the target = ( number of times he hit the target / number of hits) x 100
(13 / 20) x 100 = 65%
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Find the first five terms of the sequence defined below, where n represents the position of a term in the sequence. Start with n = 1.an = 4n − 5
Okay, here we have this:
Considering the provided sequence, we are going to find the requested first five terms of the sequence, so we obtain the following:
So what we will do is replace n from 1 to 5, we have:
n=1:
an=4n-5
a1=4(1)-5
a1=4-5
a1=-1
n=2:
an=4n-5
a2=4(2)-5
a2=8-5
a2=3
n=3:
an=4n-5
a3=4(3)-5
a3=12-5
a3=7
n=4:
an=4n-5
a4=4(4)-5
a4=16-5
a4=11
n=5:
an=4n-5
a5=4(5)-5
a5=20-5
a5=15
Finally we obtain that the first five terms are: -1, 3, 7, 11, 15
I need the answer soon!
A museum charges $10 for general admission and $2 for each special exhibit you attend.
What does f(0) = 10 represent in the context of this problem?
In linear equation, If the person doesn't attend any events, n = 0, and the price stays at 10, therefore f(n) = 10 + 2n.
What in mathematics is a linear equation?
An x-y linear relationship, or two variables in which the value of one of them (often y) relies on the value of the other one, is what is known as a linear equation in two variables (usually x).The dependent variable in this scenario is y since it depends on the independent variable, x.To describe the cost of attending n events, create an equation using function notation.
A 10 dollar entrance fee is required each time, and a further 2 dollars must be paid for each unique exhibit that a visitor chooses to visit.
The function, which would depend on n events, is
If the person doesn't attend any events, n = 0, and the price stays at 10, therefore f(n) = 10 + 2n.
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Two cylinders have the same volume. The first has a radius of 5cm and a height of 10 cm. The second has a radius of 10cm. The surface area of the first cylinder is and the surface area of the second i s
ANSWER
[tex]\begin{gathered} 1)150\pi \\ 2)250\pi \end{gathered}[/tex]EXPLANATION
For the first cylinder;
[tex]\begin{gathered} r=5 \\ h=10 \end{gathered}[/tex]Recall, the formula for calculating the surface area of a cylinder is;
[tex]A=2\pi rh+2\pi r^2[/tex]Now, substitute the values for the first cylinder;
[tex]\begin{gathered} A=2\pi rh+2\pi r^{2} \\ =2\times\pi\times5\times10+2\times\pi\times5^2 \\ =100\pi+50\pi \\ =150\pi \end{gathered}[/tex]The volume of the first cylinder is calculated using the formula;
[tex]\begin{gathered} V=\pi \cdot \:r^2\cdot \:h \\ \end{gathered}[/tex]Substitute the values of r and h for the first cylinder;
[tex]\begin{gathered} V=\pi \cdot \:r^2\cdot \:h \\ =\pi\times5^2\times10 \\ =\pi\times25\times10 \\ =250\pi \end{gathered}[/tex]To get the surface area of the second cylinder, we need to calculate the height (h).
To get the height, we use the volume of the first cylinder to get the height of the second (since they have the same volume).
Hence;
[tex]\begin{gathered} V=250\pi \\ r=10 \\ V=\pi r^{2}h \\ 250\pi=\pi\times10^2\times h \\ h=\frac{V}{\pi \cdot \:r^2} \\ h=\frac{250\pi }{\pi 10^2} \\ =2.5 \end{gathered}[/tex]Substitute the height to calculate the surface area is calculated thus;
[tex]\begin{gathered} A=2\pi rh+2\pi r^{2} \\ =2\times\pi\times10\times2.5+2\times\pi\times10^2 \\ =50\pi+200\pi \\ =250\pi \end{gathered}[/tex]
The amount of money an engineer receives from a bank if he invests $50,000 for 7 years at 11.5% per annum compound interest.
Answer:
$107125.80
working out:
50000x1.115^7=107125.8 (rounded)
2. Mr V bought 2 pajama sets for christmas for $25. He realized that he needed 2 more pajama sets. So now he bought 4 pajama sets for $50. Part A: Is this relationship proportional? Explain. *
We will have that the relationship is proportional because each time he bought more sets they had the same cost, and the total cost added to the sum of the independent cost. And we have the following relationship for the 2 sets and 4 sets:
2 sets:
[tex]\frac{25}{2}=12.5[/tex]So, each individual set is $12.5.
4 sets:
[tex]\frac{50}{4}=12.5[/tex]So, each individual set is $12.5.
So, each individual set for each relationship has the same cost, therefore the relationship is proportional.
Your bill at TGI Friday's was $90.00. If you leave a 20% tip, what will your total Bill be ? TIP = Total bill = ---- + ---- =
Its a bill question , and percentages
20% of $90.00 .
then 10% of $90 is 9 dollars
so then 2x10% = 20% of $90 is 2x9= 18 dollars
Now add then original pay to tip Pay ,
then
Pay original + Tip = $90 + 18 = $108 dollars
