y=the amount of money in the checking account
x=number of months
y=200-20x
700 – 35w = 450 + 15w
Answer:
5
Step-by-step explanation:
700-35w=450+15w
Subtract 15 from -35
700-50w=450
Subtract 700 from 450
-50w=-250
divide -250 by -50w
answer is 5
[tex]700-35w=450+15w\qquad\text{subtract 700 from both sides}\\\\-35w=-250+15w\qquad\text{subtract 15w from both sides}\\\\-50w=-250\qquad\text{divide both sides by (-50)}\\\\\boxed{w=5}[/tex]
Can you help me with numbers 14 and 15. Thank you!!!!
Answer:
14th answer is [tex]x=\sqrt{288} \\ x= -\sqrt{288}[/tex]
15th answer is [tex]xy^{2} \sqrt{5}[/tex]
Step-by-step explanation:
14)
triangle is a right triangle, the legs will have the same measure
let the legs be x
x^2 + x^2 = 24^2
2x^2 = 576
x^2 = 288
[tex]x=\sqrt{288} \\ x= -\sqrt{288}[/tex]
15)
[tex]area of the circle[/tex][tex]=\pi r^{2}[/tex]
[tex]5x^{2} y^{4} \pi =\pi r^{2} \\ r^{2} =5x^{2} y^{4} \\ r\sqrt{5x^{2} y^{4} } \\ r=\sqrt{5} xy^{2}[/tex]
If (x)=x^2+2x-5. What is f(a+1)
Answer:
a^2+4a-2
Step-by-step explanation:
f(x)= x^2+2x-5
f(a+1) = (a+1)^2 + 2(a+1) -5
= a^2 + 2a + 1 + 2a +2 -5
=a^2+4a -2
Which of the following functions is graphed below?
Answer:
y = abs (x-5) -4
Step-by-step explanation:
We are shifting the absolute value function
f(x) = |x| to
g(x) = | x +h| + k
where h is a shift left if h > 0
right if h < 0
and k is a shift up if k> 0
down if k< 0
Since the graph is shifted down and to the right
k is <0 and h < 0
where k = -4 and h=-5
What is the sum of (8y+2) + (7y+6) ?
Answer:
combine like terms
15y+ 8
Of fabric costs $5.00 per yard, how much will 7/8 yards cost?
Answer: It would be $4.38
Step-by-step explanation: If you divide the $5 by .8 it will give you what 1/8 of it would be then you multiply it by 7 to get the 7/8 of it.
Explain how you can use a table of values, an equation, and a graph to determine whether a function represents a proportional relationship.
Answer:
From the table: you have to have the same increment for the x values and the same increment for the y values. Doesn't have to be the same increment for both x and y values.
From an equation: the exponent of the x and y should be 1. The equation should be a line equation.
From a graph: the graph should be a continuous straight line.
Step-by-step explanation:
The function f(x)=5^(x-1) is shown on the coordinate plane. Select from the drop down menus to correctly describe the end behavior of f(x)
Answer: The end behavior of the given function is,
[tex]f(x)\rightarrow 0[/tex] as [tex]x\rightarrow -\infty[/tex]
And, [tex]f(x)\rightarrow \infty[/tex] as [tex]x\rightarrow \infty[/tex]
Step-by-step explanation:
Since, by the property of the graph of the exponential function,
If an exponential function is, [tex]f(x) = ab^x[/tex]
If b >1 ( increasing function ) then its end behavior is,
[tex]f(x)\rightarrow 0[/tex] as [tex]x\rightarrow -\infty[/tex]
And, [tex]f(x)\rightarrow \infty[/tex] as [tex]x\rightarrow \infty[/tex]
While b < 1 ( decreasing function, then its end behavior is,
[tex]f(x)\rightarrow \infty[/tex] as [tex]x\rightarrow -\infty[/tex]
And, [tex]f(x)\rightarrow 0[/tex] as [tex]x\rightarrow \infty[/tex]
Here, given function is, [tex]f(x)=5^{x-1}[/tex]
Since 5 > 1
Therefore, the end behavior of the given function is,
[tex]f(x)\rightarrow 0[/tex] as [tex]x\rightarrow -\infty[/tex]
And, [tex]f(x)\rightarrow \infty[/tex] as [tex]x\rightarrow \infty[/tex]
The equation of a circle is given below. x ^2 +(y-2.25)^2 =196/169. What is the center? What is the radius?
Answer:
center : (0, 2.25)
radius: 14/13
Step-by-step explanation:
x^2+(y-2.25)^2=196/169
Rewrite x^2+(y-2.25)^2=196/169
(x-0)^2+(y-2.25)^2=(14/13)^2
c=(0,2.25),r= (14/13)
hope this helps<3
Final answer:
The center of the circle described by the equation is at (0, 2.25), and its radius is 14/13 units.
Explanation:
The equation given is x^2 + (y-2.25)^2 = 196/169. This equation is of the form (x-h)^2 + (y-k)^2 = r^2, where (h, k) is the center of the circle, and r is the radius. To find the center and radius, we compare the given equation to the standard form.
Center: By comparison, h=0 and k=2.25, so the center is at (0, 2.25).
Radius: The radius is the square root of 196/169, which is 14/13. Therefore, the radius is 14/13 units.
Help with this question!
Answer:
see below
Step-by-step explanation:
In a right triangle, sin = opposite /hypotenuse
but m is adjacent to the angle, so we need to use cosine
cos = adjacent /hypotenuse
cos 73 = m/9
Multiply each side by 9
9 cos 73 = m
2.631345343 =m
4m4 - 8m3 - 7m) + (4m4 - 7m2 - 5m
Answer:
8m^4 -8m^3 -7m^2 -12 m
Step-by-step explanation:
(4m^4 - 8m^3 - 7m) + (4m^4 - 7m^2 - 5m)
I like to line them up vertically. I put 0 in the spots to keep them lined up
4m^4 - 8m^3 +0m^2 -7m
+4m^4 +0m^3 - 7m^2 - 5m
--------------------------------------------
8m^4 -8m^3 -7m^2 -12 m
[tex](4m^4-8m^3-7m)+(4m^4-7m^2-5m)\\\\=4m^4-8m^3-7m+4m^4-7m^2-5m\qquad\text{combine like terms}\\\\=(4m^4+4m^4)-8m^3-7m^2+(-7m-5m)\\\\=\boxed{8m^4-8m^3-7m^2-12m}[/tex]
Sin theta+costheta/sintheta -costheta+sintheta-costheta/sintheta+costheta=2sec2/tan2 theta -1
[tex]\dfrac{sin\theta + cos\theta}{sin\theta-cos\theta}+\dfrac{sin\theta-cos\theta}{sin\theta+cos\theta}=\dfrac{2sec^2\theta}{tan^2\theta-1}[/tex]
From Left side:
[tex]\dfrac{sin\theta + cos\theta}{sin\theta-cos\theta}\bigg(\dfrac{sin\theta+cos\theta}{sin\theta+cos\theta}\bigg)+\dfrac{sin\theta-cos\theta}{sin\theta+cos\theta}\bigg(\dfrac{sin\theta-cos\theta}{sin\theta-cos\theta}\bigg)[/tex]
[tex]\dfrac{sin^2\theta+2cos\thetasin\theta+cos^2\theta}{sin^2\theta-cos^2\theta}+\dfrac{sin^2\theta-2cos\thetasin\theta+cos^2\theta}{sin^2\theta-cos^2\theta}[/tex]
NOTE: sin²θ + cos²θ = 1
[tex]\dfrac{1 + 2cos\theta sin\theta}{sin^2\theta-cos^2\theta}+\dfrac{1-2cos\theta sin\theta}{sin^2\theta-cos^2\theta}[/tex]
[tex]\dfrac{1 + 2cos\theta sin\theta+1-2cos\theta sin\theta}{sin^2\theta-cos^2\theta}[/tex]
[tex]\dfrac{2}{sin^2\theta-cos^2\theta}[/tex]
[tex]\dfrac{2}{\bigg(sin^2\theta-cos^2\theta\bigg)\bigg(\dfrac{cos^2\theta}{cos^2\theta}\bigg)}[/tex]
[tex]\dfrac{2sec^2\theta}{\dfrac{sin^2\theta}{cos^2\theta}-\dfrac{cos^2\theta}{cos^2\theta}}[/tex]
[tex]\dfrac{2sec^2\theta}{tan^2\theta-1}[/tex]
Left side = Right side so proof is complete
Answer:
\dfrac{sin\theta + cos\theta}{sin\theta-cos\theta}+\dfrac{sin\theta-cos\theta}{sin\theta+cos\theta}=\dfrac{2sec^2\theta}{tan^2\theta-1}
From Left side:
\dfrac{sin\theta + cos\theta}{sin\theta-cos\theta}\bigg(\dfrac{sin\theta+cos\theta}{sin\theta+cos\theta}\bigg)+\dfrac{sin\theta-cos\theta}{sin\theta+cos\theta}\bigg(\dfrac{sin\theta-cos\theta}{sin\theta-cos\theta}\bigg)
\dfrac{sin^2\theta+2cos\thetasin\theta+cos^2\theta}{sin^2\theta-cos^2\theta}+\dfrac{sin^2\theta-2cos\thetasin\theta+cos^2\theta}{sin^2\theta-cos^2\theta}
NOTE: sin²θ + cos²θ = 1
\dfrac{1 + 2cos\theta sin\theta}{sin^2\theta-cos^2\theta}+\dfrac{1-2cos\theta sin\theta}{sin^2\theta-cos^2\theta}
\dfrac{1 + 2cos\theta sin\theta+1-2cos\theta sin\theta}{sin^2\theta-cos^2\theta}
\dfrac{2}{sin^2\theta-cos^2\theta}
\dfrac{2}{\bigg(sin^2\theta-cos^2\theta\bigg)\bigg(\dfrac{cos^2\theta}{cos^2\theta}\bigg)}
\dfrac{2sec^2\theta}{\dfrac{sin^2\theta}{cos^2\theta}-\dfrac{cos^2\theta}{cos^2\theta}}
\dfrac{2sec^2\theta}{tan^2\theta-1}
Left side = Right side so proof is complete
Step-by-step explanation:
Find the common ratio of the sequence. 3, 9, 27, 81, . . . 6 –6 3
Answer:
The common ratio is 3
Step-by-step explanation:
To determine the common ratio, we take the second term and divide by the first term
9/3 =3
To verify this we take the third term and divide by the second term
27/9 = 3
How do you say the number .0088?
I think it's Ten thousandths, zero eighty-eight.
I'm not too sure on this, but hopefully i helped you.
The students in the fourth and fifth grades are going to a concert. There are 178 students. Each row has 8 seats. The fifth grade students fill 12 rows. How many rows are needed for the fourth graders?
Final answer:
Fifth graders take up 96 seats, leaving 82 fourth graders. Dividing 82 by 8 seats per row yields 10.25, which we round up to 11 rows needed for the fourth graders.
Explanation:
To calculate the number of rows needed for the fourth graders, we need to first determine the total number of seats taken by the fifth graders. Since each row has 8 seats and the fifth graders fill 12 rows, the total number of seats taken by the fifth graders is 12 rows × 8 seats/row = 96 seats.
Now, we subtract the number of seats taken by the fifth graders from the total number of students attending to find out how many fourth graders there are: 178 students - 96 seats taken by fifth graders = 82 fourth graders.
The number of rows needed for the fourth graders can be calculated by dividing the total number of fourth graders by the number of seats per row: 82 fourth graders ÷ 8 seats/row = 10.25 rows. Since we can't have a fraction of a row, we round up to the next whole number. Therefore, the fourth graders will need 11 rows.
[tex]4(2x + 7) = 12 - 2(10 - 2x)[/tex]
Given the functions f(x)=3x^2 g(x)=x^2-4x+5 and h(x)=-2x^2+4x+1 rank them from least to greatest based on their axis of symmetry
ok, ranked by axis of symmetry
basically x=something is the axis of symmetry
the way to find the axis of symmetry is to convert to vertex form and find h and that's the axis of symmetry
but there's an easier way
for f(x)=ax^2+bx+c
the axis of symmetry is x=-b/2a
nice hack my teacher taught me
so
f(x)=3x^2+0x+0
axis of symmetry is -0/(3*2), so x=0 is the axis of symmetry for f(x)
g(x)=1x^2-4x+5,
axis of symmetry is -(-4)/(2*1)=4/2=2, x=2 is axis of symmetry for g(x)
h(x)=-2x^2+4x+1
axis of symmetry is -4/(2*-2)=-4/-4=1, x=1 is the axis of symmetry for h(x)
0<1<2
axisies
f(x)<h(x)<g(x)
order based on their axises of symmetry is f(x), h(x), g(x)
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Answer:
To find the axis of symmetry.
A quadratic equation is in the form of :
[tex]ax^2+bx+c =0[/tex] where a, b and c are coefficients and x is the variable
Axis of symmetry is given by :
[tex]x = -\frac{b}{2a}[/tex]
First identify a, b and c in the equation
[tex]f(x) = 3x^2[/tex]
⇒ a= 3 , b= 0 and c =0
[tex]g(x) = x^2-4x+5[/tex]
⇒ a = 1 , b = -4 and c =5
and
[tex]h(x) = -2x^2+4x+1[/tex]
⇒ a = -2 , b =4 and c =1
Using above formula of the axis of symmetry:
[tex]x = -\frac{b}{2a}[/tex]
then;
In f(x)
Axis of symmetry: [tex]x = -\frac{0}{2 \cdot 3} = 0[/tex]
Similarly;
In g(x)
Axis of symmetry : [tex]x = -\frac{-4}{2 \cdot 1} = \frac{4}{2} =2[/tex]
In h(x)
Axis of symmetry : [tex]x = -\frac{4}{2 \cdot -2} = \frac{4}{4} =1[/tex]
Rank from least to greater on basis of axis of symmetry: 0 , 1 , 2
⇒ f(x); h(x) ; g(x)
Try to determine how much money you would have if for a month you were given a nickel on day one, two nickels on day two, three nickel on day three and so on. what type of process would you use?
Answer:
In a 28 day month 20 dollars and 30 cents
Step-by-step explanation:
1+2+3+4+5+6+7......
Answer*5=Cents
If cents equal to or greater than 100 than = dollar
$30 money you would have if for a month you were given a nickel on day one, two nickels on day two, three nickels on day three, and so on.
What is arithmetic series?The arithmetic series is a series in which the numbers are in the order of some common difference. The difference between any two consecutive numbers is constant.
[tex]a_n = a_1 + (n -1)d[/tex]
you would be using a be using the [tex]a_n = a_1 + (n -1)d[/tex] meaning that it's the previous entry plus the different process.
[tex]a_n = a_1 + (n -1)d[/tex]
[tex]a_{30} = .05 + (30-1).05[/tex]
[tex]a_{30}[/tex] = $29.10
Thus, $30 money you would have if for a month you were given a nickel on day one, two nickels on day two, three nickels on day three, and so on.
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If a job pays $45,000 per year, you live in a state where our total tax burden is 22% and you recieve a weekly paycheck, what is your take-home pay from a paycheck?
Final answer:
The weekly take-home pay from a $45,000 annual salary with a 22% total tax burden is approximately $675.00 after taxes.
Explanation:
To calculate the take-home pay from a paycheck when you know the annual salary and the total tax rate, you must first determine the amount of money deducted for taxes and then subtract that from the gross (before-tax) pay. If a job pays $45,000 per year and the total tax burden is 22%, we can find the annual take-home salary and then divide by the number of pay periods per year to get the weekly take-home pay.
First, calculate the total annual taxes: $45,000 * 0.22 = $9,900.
Next, subtract the annual taxes from the annual salary to get the annual take-home salary: $45,000 - $9,900 = $35,100.
Since there are 52 weeks in a year, divide the annual take-home salary by 52 to find the weekly take-home pay: $35,100 / 52 \\approx $675.00.
Therefore, the weekly take-home pay would be approximately $675.00.
How do I order rational and irrational numbers from least to greatest
Answer: Rational numbers are any numbers that can be expressed by a fraction with integers in both the numerator and the denominator. The amount of time and paper it takes to put them into an increasing line depends on how many numbers there are and how big of a range they have.
1.Rewrite improper fractions
An improper fraction is a fraction with a bigger numerator than denominator. These numbers can be difficult to compare. For example, numbers such as 26/7, 31/9, 12/5, 8/3 and 22/13 do not have an obvious highest or lowest term. Rewrite improper fractions as mixed numbers or as numbers with decimals. To turn an improper fraction into a decimal, divide the numerator by the denominator. If the denominator is large or a prime number greater than five, use a calculator. For example, divide the numbers 26/7, 31/9, 12/5, 8/3 and 22/13 to create 3.71, 3.44, 2.4, 2.67 and 1.69.
2.Find the highest and lowest terms
Figure out where your number line starts and ends. Put the lowest term on the far left and the highest term on the far right. Remember, negative numbers are lower than positive numbers, and the greater a negative number's distance from zero, the lower it is.
3.Mark benchmark terms
Draw a line extending through your lowest and highest points. Figure out some major points between these values and mark them on your line. For example, if your lowest number is negative 25 and your highest number is 50, find where zero and 25 would be. Mark these as benchmarks or guides.
4.Fill in the remaining numbers
Using your guides, fill in the rest of the numbers. Start with the lowest values on the left and work your way up.
Rational and irrational numbers can be ordered from least to greatest by converting them into decimal forms. Once in decimal form, they can be compared and ordered just like regular real numbers.
Explanation:To order rational and irrational numbers from least to greatest, first you need to understand what these numbers are. Rational numbers are numbers that can be expressed as a ratio of two integers, while irrational numbers cannot be expressed as such ratio and their decimal expansions are non-repeating and non-terminating.
If you are given both rational and irrational numbers, you can start by converting all of the numbers to decimal form if they are not already. Then, you can simply order them from least to greatest, just like how you order regular real numbers.
For example, if you are given the numbers 3/2, √2, and 1. You would convert 3/2 to 1.5 and approximate √2 as 1.414. Then you would order them as 1 (1.0), √2 (1.414), and 3/2 (1.5).
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Help please need this answer
Answer:
The answer is option A.
True
Hope this helps you
CMON PLEASE NEED CORRECT ANSWER PLEASE NEED HELP!!!!!!!!!!!!!):
How far are 27 and -54 apart on the number line?
Answer: 71 numbers apart
Step-by-step explanation: 27 and -54 are 71 numbers apart. In order for 27 to each -54 it must first reach 0. You basically add them while ignoring any negatives. Hope this helped :)
Three trigonometric functions for a given angle are shown below. sin theta = -77/85, cos theta=36/85 tan theta=77/36 What are the coordinates of point (x, y) on the terminal ray of angle theta assuming that the values above were not simplified?
A) (-77,-36)
B)(-77,36)
C) (-36,77)
D) (36, -77)
Answer:
The correct option is D.
Step-by-step explanation:
It is given that
[tex]\sin \theta =\frac{-77}{85}[/tex]
[tex]\cos \theta =\frac{36}{85}[/tex]
The angle of terminal ray is θ, it means the angle between x-axis and terminal ray is θ.
[tex]\sin \theta =\frac{perpendicular}{hypotenuse}[/tex]
[tex]\cos \theta =\frac{base}{hypotenuse}[/tex]
Therefore the length of perpendicular is 77 and the base of the triangle is 36.
Since sinθ is negative and cosθ is positive, it means point must be lies on fourth quadrant because in fourth quadrant cosine in positive but sine is negative.
The point of terminal ray is (base, perpendicular) and the sign are used according to the quadrant.
Therefore the point of terminal ray is (36,-77) because in fourth quadrant x is positive but y is negative. Option D is correct.
The coordinates of the point (x, y) on the terminal ray of angle theta are (36, -77).
Given
Three trigonometric functions for a given angle are shown below.
sin theta = -77/85, cos theta=36/85, tan theta=77/36.
What is a terminal ray of angle?A ray is defined as the initial side of the angle.
The second ray which is called the terminal side of the angle.
The value of the sin and cos theta then, the co-ordinate lies in the fourth quadrant.
Therefore, the coordinates of the point (x, y) on the terminal ray of angle theta are (36, -77).
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Find the coordinates of the midpoint of the segment whose endpoints are H(6,4) and K(2,8).
Answer:
The midpoint is (4,6)
Step-by-step explanation:
When we have 2 points, we can find the midpoint by using the formula
midpoint = (x1+x2)/2, (y1+y2)/2
= (6+2)/2, (4+8)/2
= (8/2), 12/2
= 4,6
Below is a double bar graph indicating the number of left handed students and right handed students in Mr. Jude's class. The bar graph shows the results in terms of boys versus girls. Use the graph to determine the difference between the number of right handed and left handed students in Mr. Jude's class. Type a numerical answer
Answer:
13 more right handed students PLEASE GIVE BRAINLIEST
Step-by-step explanation:
left handed
3 boys + 4 girls = 7 left handed students
right handed
9 boys + 11 girls = 20 right handed students
20 - 7 = 13 more right handed students
Answer: 13 more right handed girls and boys.
Hope this helped and also please give brainlist really need it need 2 more if you do me as one only need one more and I need them before the end of toaday.
what is 12 1/4 simplifying
Answer:
12.25 or 49/4
Step-by-step explanation:
12.25 is the decimal version because 1/4 is equal to 0.25 as a decimal and then add the 12 on.
13/4 is the improper fraction. To get an improper fraction, you multiply the main number (12) by the denominator (4) this gives you 48. Then, you have to add your numerator (1), leaving you with 49 over 4.
The value of the mixed fraction number 12 ¹/₄ will be 12.25.
What is the value of the expression?When the relevant components and basic processes of a numerical method are given values, the expression's result is the result of the computation it depicts.
The definition of simplicity is making something simpler to achieve or grasp while also making it a little less difficult.
The mixed fraction number is given below.
⇒ 12 ¹/₄
Convert the mixed fraction number into a decimal number. Then we have
⇒ 12 ¹/₄
⇒ 12 + ¹/₄
⇒ 12 + 0.25
⇒ 12.25
The value of the mixed fraction number 12 ¹/₄ will be 12.25.
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ursula drew a polygon in which all the triangles were obtuse. what kind of polygon could she have drawn?
A. Trapezoid
B. Parallelogram
C. Triangle
D. Pentagon
Ursula could have drawn a pentagon because all angles of a pentagon are obtuse angles.
What is an obtuse angle?An angle greater than 90° is called an obtuse angle.
Trapezoid: A quadrilateral with at least one pair of parallel sides is called
a trapezoid.
In a trapezoid, all the angles are not greater than 90° i.e. all the angles are not obtuse angles.
Similarly, In triangles and parallelograms, all the angles are not obtuse angles.
Pentagon: In a pentagon, all angles are greater than 90° i.e. obtuse angles.
Hence, Ursula could have drawn a pentagon because all angles of a pentagon are obtuse angles.
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PLS I NEED HELP!!!!!
Amy’s room is 12 feet long X 10 feet wide. She plans to purchase carpet for the entire room. The carpet costs $25 per square meter. What will be the total cost of the new carpet to the nearest cent?
Calculate total area:
12 x 10 = 120 square feet
Convert square feet to square meters:
1 square foot = 0.0929 square meters
120 x 0.0929 = 11.1484 square meters
Total cost = 11.1484 x 25 = $278.71
complete the solution of the equation find the value of y when x equals -7. -7x-5y=54
Answer:
Y= -1
Step-by-step explanation:
Final answer:
To find the value of y when x equals -7 in the equation -7x - 5y = 54, substitute -7 for x, simplify the equation, and solve for y. The value of y is -1.
Explanation:
To complete the solution of the equation and find the value of y when x equals -7, we will plug -7 in for x in the equation -7x - 5y = 54.
Here is the step-by-step process:
Substitute x with -7: -7(-7) - 5y = 54.Multiply -7 by -7: 49 - 5y = 54.Subtract 49 from both sides: -5y = 54 - 49.Simplify the equation: -5y = 5.Divide both sides by -5: y = 5 / (-5).Calculate the value of y: y = -1.So, the value of y when x equals -7 is -1.
help me hurry can someone these equations
f(x) + n - move the graph n units up
f(x) - n - move the graph n units down
n · f(x) - stretch by n in the y-direction
1/n · f(x) - compress by n in the y-direction
-------------------------------------------------------------------------
First:
[tex]A)\ y=x^2\\\\B)\ y=x^2-4\\\\C)\ y=x^2-2\\\\D)\ y=x^2+2\\\\E)\ y=x^2+4[/tex]
Second:
[tex]A)\ y=x^2\\\\K)\ y=4x^2\\\\L)\ y=2x^2\\\\M)\ y=\dfrac{1}{2}x^2\\\\N)\ y=\dfrac{1}{4}x^2[/tex]