Answer:
-19000
Step-by-step explanation:
1000-20000=-19000
Answer:
C -19000
Step-by-step explanation:
1,000
- 20,000
----------------------=
-19000
What is the area of the parallelogram?
Answer:
140 inches
Step-by-step explanation:
You do the base(14) times the hieght(10)
14x10=140
In which set of ordered pairs ,(x,y) Is y NOT a function of x?
Answer:
B. I belive ^_^
Step-by-step explanation:
Answer:
The third answer choice.
Step-by-step explanation:
If a function has more than one ordered pairs with the same x value (in this case it is x= 4), then it cannot be a function :)
Please help!!!!
Solve the following inequality -1/2 p < -16
Answer:
option A is correct...
Step-by-step explanation:
just got done with that question and am now on my 10th, wish me luck!
To solve the inequality -1/2 p < -16, multiply all parts of the inequality by '-2' and reverse the inequality sign, yielding 'p' > 32. Therefore, any real number greater than 32 will satisfy the original inequality.
Explanation:For solving the inequality -1/2 p < -16, you want to find the value of 'p' where the inequality holds true. To do that, you should remove the fraction from the inequality. You can do this by multiplying every part of the inequality by '-2', however, remember that when you multiply or divide by negative numbers in an inequality, the direction of the inequality sign changes.
So, (-1/2 p) * -2 becomes 'p' and -16 * -2 becomes 32, reversing the inequality sign results in 'p' > 32.
In terms of a solution set, this implies that any real number greater than 32 will satisfy the original inequality -1/2 p < -16.
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(25 POINTS!!)What is the equation of the line that passes through the points (15,9) and (-2,9)?
I need this answered with in the next 20 minutes so someone please help :,D
The answer is gonna be a equation like y=
Let's use the point-slope formula...
y-y1=m(x-x1)
m is the slope.
y--9=7(x--2)
Subtracting a negative number is the same as adding a positive number...
y+9=7(x+2)
y+9=7x+14
Let's subtract 9 from both sides...
-9+y+9=7x+14-9
y=7x+5
The formula is now in the format of...
y=mx+b
This is known as slope-intercept.
m is the slope.
b is the y-intercept, the value of y when x=0.
Standard formula is...
Ax+By=C
Neither A nor B equal zero.
A is greater than zero.
y=7x+5
Let's move 7x to the left side of the equation. It becomes negative.
-7x+y=5
Let's multiply both sides by -1 to render A greater than zero.
-1(-7x+y)=(5)(-1)
7x-y=-5
This is the equation in standard form.
[tex]
\text{d stands for distance between two points} \\
d(A, B)=\sqrt{(\Delta{x})^2+(\Delta{y})^2} \\
\text{or simply} \\
d(A, B)=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2} \\
\text{now put in the data} \\
d(A, B)=\sqrt{(-2-15)^2+(9-9)^2} \\
d(A, B)=\sqrt{(-17)^2} \\
d(A, B)=\boxed{17} \\
[/tex]
7. Nick's new home had a purchase price of $145,500.
He got a 30-year fixed mortgage for 75% of the
purchase price. The interest rate on the loan is
3.15%. What is his monthly payment?
$3,437.44
$1,145.81
$467.72
$109.13
$145.50
To calculate Nick's monthly mortgage payment, determine the loan amount, convert the interest rate to a monthly rate, and use the formula for fixed mortgage payments. The monthly payment for Nick's mortgage is $467.72.
The monthly payment can be calculated using the loan amount, interest rate, and loan term.
Calculate the loan amount: $145,500 × 75% = $109,125.
Convert the annual interest rate to a monthly rate: 3.15% ÷ 12 = 0.2625%.
Plug the values into the formula for fixed mortgage payments: [tex]$109,125*\frac{0.002625*(1+0.002625)^{30*12}}{(1+0.002625)^{30*12}-1}[/tex]
The monthly payment for Nick's mortgage is $467.72.
The correct answer is option C. The monthly payment for Nick's mortgage is $467.72.
First, we calculate the mortgage amount, which is 75% of the purchase price:
[tex]\[ \text{Mortgage amount} = \frac{75}{100} \times \$145,500 = \$109,125. \][/tex]
Next, we convert the annual interest rate to a monthly interest rate:
[tex]\[ \text{Monthly interest rate} = \frac{3.15\%}{12} = \frac{0.0315}{12} \approx 0.002625. \][/tex]
Now, we use the formula for the monthly payment (M) on a fixed-rate mortgage, which is given by:
[tex]\[ M = P \times \frac{r(1 + r)^n}{(1 + r)^n - 1}, \][/tex]
where P is the principal loan amount, r is the monthly interest rate, and n is the number of payments (30 years times 12 months per year).
So, we have:
[tex]\[ P = \$109,125, \][/tex]
[tex]\[ r = 0.002625, \][/tex]
[tex]\[ n = 30 \times 12 = 360. \][/tex]
Plugging these values into the formula gives us:
[tex]\[ M = \$109,125 \times \frac{0.002625(1 + 0.002625)^{360}}{(1 + 0.002625)^{360} - 1}. \][/tex]
Calculating this expression yields:
[tex]\[ M \approx \$467.72. \][/tex]
The complete question is:
Nick's new home had a purchase price of $145,500. He got a 30-year fixed mortgage for 75% of the purchase price. The interest rate on the loan is 3.15%. What is his monthly payment?
A. $3,437.44
B. $1,145.81
C. $467.72
D. $109.13
E. $145.50
The equation of a graph is 4x - 3y = 5. What is the x-intercept?
Answer:(5/4,0)
Step-by-step explanation:
What is the answer for #9?
I think that it’s n>7
i think it’s 7 bc u gotta distribute the 5 w the n and 8 and then it equals to 5n+40>75 then just subtract 40 from each side and then ur left w 5n>35, divide each side by 5 and u get n>7
What number line represents the solution to the inequality below
HELP ITS DUE TOMORROW !!!!!!!!!
Answer:
B
Step-by-step explanation:
Step 1: Add 2 to both sides.
x−2+2>3+2
x>5
Write the expression in terms of cosine.please help.
Answer:
cos13°
Step-by-step explanation:
Using the cofunction identity
sinx° = cos(90 - x)°
sin77° = cos(90 - 77)° = cos13°
Help me please!!!!! Thank you
Answer:
15/2 in³
Step-by-step explanation:
The formula for the vol. of a pyramid
is
V = (1/3)(area of base)(height of pyramid)
Here, the volume is:
V = (1/3)( [1/2][5 in][9 in] )·(10 in)
= (9/3)(5/2)(10) in³
= 450/6 in³ = 150/2 in³ = 75 in³ Volume of the pyramid
Answer:
75 in³Step-by-step explanation:
The formula of a volume of a pyramid:
[tex]V=\dfrac{1}{3}BH[/tex]
B - area of a base
H - height
In a base we have the right triangle with legs 9in and 5in.
The formula of an area of a right triangle:
[tex]A=\dfrac{ab}{2}[/tex]
ab - legs
Substitute:
[tex]B=\dfrac{(5)(9)}{2}=\dfrac{45}{2}\ in^2[/tex]
The height H = 10 in.
Calculate the volume:
[tex]V=\dfrac{1}{3\!\!\!\!\diagup_1}\left(\dfrac{45\!\!\!\!\!\diagup^{15}}{2\!\!\!\!\diagup_1}\right)(10\!\!\!\!\!\diagup^5)=(1)(15)(5)=75\ in^3[/tex]
Solve the following system by substitution. m+n=5 and 5m+5n=25. Solve.
Answer:
Infinitely many solutions (x ∈ R)Step-by-step explanation:
[tex]\left\{\begin{array}{ccc}m+n=5&\text{subtract}\ n\ \text{from both sides}\\5m+5n=25\end{array}\right\\\\\left\{\begin{array}{ccc}m=5-n&(1)\\5m+5n=25&(2)\end{array}\right\qquad\text{put (1) to (2):}\\\\5(5-n)+5n=25\qquad\text{use the distributive property}\\\\(5)(5)+(5)(-n)+5n=25\\\\25-5n+5n=25\qquad\text{cancel}\ 5n\\\\25=25\qquad\bold{TRUE}[/tex]
Select all of the terms that apply to the shape.
pentagon
hexagon
heptagon
octagon
nonagon
decagon
regular polygon
irregular polygon
concave
convex
Answer:
Hexagon
Regular polygon
Convex
Step-by-step explanation:
Hexagon is the name of the shape.
A regular polygon is a polygon with equal sides.
Convex means "A shape with no indentations."
895 472 nearest 100000
The process of rounding 895,472 to the nearest 100,000 involves examining the ten thousands place of the number. Given it's 9, the number is rounded up to 900,000.
Explanation:The question is asking to round the number 895,472 to the nearest 100,000. To do this, you should look at the ten thousands place of the number, which is 9. If this digit is 5 or greater, round the hundreds of thousands place up. If it is less than 5, round down. In this case, since the ten thousands place is 9, we round 800,000 up to 900,000. Therefore, 895,472 rounded to the nearest 100,000 is 900,000.
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Mr Turner bought stock for $15,000. If the value of the stock decreases 4% each year when will it be worth 80% of original price?
Answer:
[tex]5.5\ years[/tex]
Step-by-step explanation:
we know that
In this problem we have a exponential function of the form
[tex]f(x)=a(b^{x})[/tex]
where
x is the time in years
f(x) is the value of the stock
a is the initial value
b is the base
r is the rate
b=(1-r)
we have
[tex]a=\$15,000[/tex]
[tex]r=4\%=4/100=0.04[/tex]
[tex]b=(1-0.04)=0.96[/tex]
substitute
[tex]f(x)=15,000(0.96^{x})[/tex]
80% of original price is equal to
[tex]f(x)=0.80(15,000)=12,000[/tex]
so
For f(x)=12,000 ------> Find the value of x
[tex]12,000=15,000(0.96^{x})[/tex]
[tex](12/15)=(0.96^{x})[/tex]
Apply log both sides
[tex]log(12/15)=log(0.96^{x})[/tex]
[tex]log(12/15)=(x)log(0.96)[/tex]
[tex]x=log(12/15)/log(0.96)[/tex]
[tex]x=5.5\ years[/tex]
Need Help Assappp 10 points
5(2x − 3) = 5
How many solutions does this equation have?
What are the solutions to this equation
Please show your work
Answer:
Step-by-step explanation:
The only solution is x=2
5(2x-3)=5
Divide each term by 5 and simplify
2x−3=12x-3=1
Move all terms not containing x
to the right side of the equation.
2x=42x=4
Divide each term by 2
x=2
Answer:
The given solution has only one solution which is x=2
Step-by-step explanation:
Given the equation
[tex]5(2x-3)=5[/tex]
we have to find the solution of above equation.
Equation is
[tex]5(2x-3)=5[/tex]
Divide by 5 throughout the equation
[tex]2x-3=\frac{5}{5}=1[/tex]
[tex]2x-3=1[/tex]
Adding 3 on both sides
[tex]2x=4[/tex]
Dividing throughout by 2, we get
[tex]x=\frac{4}{2}=2[/tex]
Hence, the given solution has only one solution which is x=2
Which expression is equivalent to? Please help! Screenshots attached.
Answer:
[tex]\frac{\sqrt{5} }{x^{2} y}[/tex]
Step-by-step explanation:
That's a complex expression, let's simplify it, step by step, off the start, we'll simplify the 55/11:
[tex]\sqrt{ \frac{55 x^{7} y^{6} }{11 x^{11} y^{8} } } = \sqrt{ \frac{5 x^{7} y^{6} }{x^{11} y^{8} } }[/tex]
Then we'll simplify the x's and y's:
[tex]\sqrt{ \frac{5 x^{7} y^{6} }{x^{11} y^{8} } } = \sqrt{ \frac{5}{x^{4} y^{2} } }[/tex]
Let's split the square root in two and solve the bottom part:
[tex]\sqrt{ \frac{5}{x^{4} y^{2} } } = \frac{\sqrt{5} }{\sqrt{x^{4} y^{2}} } = \frac{\sqrt{5} }{x^{2} y}[/tex]
The solution is then:
[tex]\frac{\sqrt{5} }{x^{2} y}[/tex]
The expression which is equivalent to the given expression is:
[tex]\dfrac{\sqrt{5}}{x^2y}[/tex]
Step-by-step explanation:We are given a expression as:
[tex]\sqrt{\dfrac{55x^7y^6}{11x^{11}y^8}}[/tex]
Now we know that:
[tex]55=11\times 5[/tex]
Hence, we get:
[tex]\sqrt{\dfrac{55x^7y^6}{11x^{11}y^8}}=\sqrt{\dfrac{11\times 5x^7y^6}{11x^{11}y^8}[/tex]
which is written as:
[tex]\sqrt{\dfrac{5x^7y^6}{x^{11}y^8}}[/tex]
Also, we know that if n>m
Then
[tex]\dfrac{a^m}{a^n}=\dfrac{1}{a^{n-m}}[/tex]
Hence, we have the expression as:
[tex]=\sqrt{\dfrac{5}{x^{11-7}y^{8-6}}}\\\\\\=\sqrt{\dfrac{5}{x^4y^2}[/tex]
This could be given as:
[tex]=\dfrac{\sqrt{5}}{\sqrt{x^4}\sqrt{y^2}}[/tex]
Now, we know that:
[tex]\sqrt{x^4}=\sqrt{(x^2)^2}=x^2\\\\and\\\\\sqrt{y^2}=y[/tex]
Hence, we get that:
[tex]\sqrt{\dfrac{55x^7y^6}{11x^{11}y^8}}=\dfrac{\sqrt{5}}{x^2y}[/tex]
multiply each set of numbers and match it with it’s product
Answer:
1. [tex]1. (\frac{5}{16}) (-2) (-4) (\frac{-4}{5})= -2 \\2. (2\dfrac{3}{5}) (\frac{7}{9})=(\frac{91}{45})\\3. (\frac{2}{3})(-4)(9)= -24\\4. (\frac{-3}{4}) (\frac{7}{8})=(\frac{-21}{32})[/tex]
Step-by-step explanation:
These are simple multiplication questions of fractions. We multiply numerator with numerators and denominators with denominators. If numerator and denominator is both divisible by same number we can divide them for simplification.
1. [tex](\frac{5}{16}) (-2) (-4) (\frac{-4}{5})[/tex]
[tex]=(\frac{-10}{16}) (-4) (\frac{-4}{5})\\=(\frac{40}{16}) (\frac{-4}{5})\\=(\frac{-160}{80}) \\dividing\,\, numerator\,\, and\,\, denominator\,\, by\,\, 80\,\,\\= -2[/tex]
2. [tex](2\dfrac{3}{5}) (\frac{7}{9})[/tex]
Converting mixed form into fraction form,
[tex]=(\frac{13}{5})(\frac{7}{9})[/tex]
Multiplying numerators with each other and denominators with each other
[tex]=(\frac{13*7}{5*9})\\=(\frac{91}{45})[/tex]
3. [tex](\frac{2}{3})(-4)(9)[/tex]
Multiplying these terms with each other:
[tex]=(\frac{2*-4}{3})(9)\\=(\frac{-8}{3})(9)\\=(\frac{-8*9}{3})\\=(\frac{-72}{3})\\[/tex]
Dividing numerator and denominator with 3
[tex]=-24[/tex]
[tex]4. (\frac{-3}{4}) (\frac{7}{8})\\=(\frac{-3}{4}) (\frac{7}{8})\\=(\frac{-3*7}{4*8})\\=(\frac{-21}{32})[/tex]
A square has a perimeter of 36 units.
One vertex of the square is located at (3, 5) on the coordinate grid.
What could be the x- and y- coordinates of another vertex of the square?
(12,5) (3, -9) (3,14) (-6,5)
The radius of a circle is 10. Using π, which equation expresses the ratio of the circumference of the circle to the circle's diameter?
Answer:
Step-by-step explanation:
Help please about this math work
There is a 46% chance of a female patient having type-O blood
Answer:
19.6
Step-by-step explanation:
The question is slightly ambiguous. The data tells us that the number of females with O blood is 140.
I think you take this out of the entire population which is 714
The % is (140 / 714) * 100 = 19.61%
I wouldn't bet on these numbers being accurate.
What is the value of t?
7 × 2 × 11 = t × 11
a.154
b.22
c.15
d.14
Answer:
The answer is going to be D) . 14
Step-by-step explanation:
Hello!
Answer:
D
Step-by-step explanation:
7.2.11 = 11.t
14.11 = 11.t
154 = 11.t
14 = t
How many cubes are inside the rectangular prism?
A) 21 cubes
B) 28 cubes
C) 36 cubes
D) 42 cubes
Answer:
D.) 42 cubes
Step-by-step explanation:
Instead of counting each cube, you can find the volume.
The formula to find volume is ( Volume = Length x Width x Height)
( V= 2 x 7 x 3)
2 x 7 x 3 = 42 cubes
I hope this helped you ; )
Answer:
21
Step-by-step explanation:
If each term of a sequence changes by a common difference,d, what would a general rule for this type of sequence
A.) a(n)=(d)n-1
B.) an=an-1+d
C.) an=an-1+an-2
D.) an=n-1+an-2+d
===================================================
Explanation:
The idea is that for any term, we add on the common difference d to get the next term. For example, the sequence {3, 7, 11, 15, 19, 23, ...} has us add on 4 each time so d = 4 in this case.
3+4 = 7
7+4 = 11
11+4 = 15
and so on. The nth term is represented by the notation[tex]a_n[/tex] while the term just before the nth term is written as [tex]a_{n-1}[/tex]
So adding d onto the term just before the nth term gets us the nth term which is how we end up with [tex]a_n = a_{n-1}+d[/tex]
This is the recursive form of the arithmetic sequence. The closed form is written as [tex]a_n = a_1 + d(n-1)[/tex]
please hepppp due tomarrow means a lot
Answer:
1.4
Step-by-step explanation:
PLEASE ANSWER RIGHT AWAY
Answer:
[tex]y=2\sin (x-\pi)[/tex]
Step-by-step explanation:
The sine graph has an amplitude of 2.
The period of this function is [tex]2\pi[/tex]
The graph is obtained by shift the graph of [tex]y=\sin x[/tex] [tex]\pi[/tex] units to the right.
Among the given equations, the only function which has these properties is
[tex]y=2\sin (x-\pi)[/tex]
The correct answer is option A
ab=6cm Ac=12 calculate the lenght of cd
This problem involves the uses of the Pythagorean Theorem as well as the use of Sine.
To start we need to identify what we know and what we don't know. We know that there are two triangles. We are given 2 sides lengths and an angle in one and only an angle in the other. They share one side meaning when we are given 2 sides in one triangle it will be easy to get the third side. What we don't know is the side length of CB DB or CD. We need to find CB in order to find CD.
Pythagorean Theorem for side length CB:
12^2-6^2=√108
√108=10.4 (average)
So CB is equal to 10.4
Sine Calculation for side length CD:
Since we have angle 56* we will use the length we found which will be the opposite side from the angle and then input x for our hypotenuse CD in order to solve.
sin 56* = 10.4/x
sin 56* × x = 10.4/x × x
sin 56*x = 10.4
/sin 56* /sin 56*
x = 12.544....
or 12.6 (average)
So, to conclude, our answer for CD is 12.6cm.
Hope I helped!
Answer:
12.7 cm
Step-by-step explanation:
Given information: AB=6cm AC=12cm.
Pythagoras theorem: In a right angle triangle
[tex]hypotenuse^2=base^2+perpendicular^2[/tex]
Using Pythagoras in triangle ABC we get
[tex](AC)^2=(AB)^2+(BC)^2[/tex]
[tex](12)^2=(6)^2+(BC)^2[/tex]
[tex]144-36=(BC)^2[/tex]
[tex]108=(BC)^2[/tex]
Taking square root on both sides.
[tex]\sqrt{108}=BC[/tex]
Law of sine:
[tex]\dfrac{a}{\sin A}=\dfrac{b}{\sin B}=\dfrac{c}{\sin C}[/tex]
Using law of sin we get
[tex]\dfrac{CD}{\sin (90)}=\dfrac{\sqrt{108}}{\sin (55)}[/tex]
[tex]\dfrac{CD}{1}=\dfrac{\sqrt{108}}{\sin (55)}[/tex] [tex][\because \sin 90^{\circ}=1][/tex]
[tex]CD=12.6866616739[/tex]
Approx the data to three significant figures.
[tex]CD\approx 12.7[/tex]
Therefore, the length of CD is 12.7 cm.
How do I simplify the operation?
Hi, hope this helps you out. I understand how this can be confusing. Have a great day! :)
Answer:
[tex]\frac{10y - 11}{(y - 1)(y - 2)( y + 1)}[/tex]
Step-by-step explanation:
1. Factor [tex]y^2 - 3y + 2[/tex]:
How-to:
After breaking the expression into groups, you're left with [tex](y^2 - y) + (-2y + 2)[/tex]. Factor out y from [tex]y^2 - y[/tex][tex]: y(y - 1)[/tex]. Factor out [tex]-2[/tex] from [tex]-2y + 2: -2(y - 1)[/tex] = [tex]y( y - 1) - 2(y - 1)[/tex]. Finally, factor out common terms (in your case, y -1 ) and you're left with: [tex](y - 1)(y - 2)[/tex] Now you have [tex]\frac{3}{(y - 1)(y - 2)} + \frac{7}{y^2 - 1}[/tex]
2. Find the least common multiple of [tex]( y - 1)(y - 2), (y + 1)(y - 1)[/tex].
How-to:
Find an expression comprised of factors that appear in [tex]( y - 1)(y - 2), (y + 1)(y - 1)[/tex]. You'll find [tex](y - 1)(y - 2)(y + 1)[/tex]. Adjust your fractions based on the LCM and you'll get [tex]\frac{3(y + 1)}{(y - 1)(y - 2)(y + 1)} + \frac{7 (y - 2)}{(y + 1)(y - 1)(y - 2)}[/tex]
3. Since the denominators are equal, combine the fractions above. You'll get [tex]\frac{3(y + 1) + 7(y - 2)}{(y - 1)(y - 2)(y + 1)}[/tex]
4. Expand [tex]\frac{3(y + 1) + 7(y - 2)[/tex] and you'll get [tex]10y - 11[/tex]. This is your new numerator.
Finally, your simplified operation is: [tex]\frac{10y - 11}{(y - 1)(y - 2)( y + 1)}[/tex]
To simplify an operation in mathematics, follow these steps: combine like terms, perform arithmetic operations, simplify fractions, and express the result in a simplified form.
Explanation:When simplifying an operation in mathematics, you want to reduce the expression or equation to its simplest form. This may involve combining like terms, performing any necessary arithmetic operations, or simplifying fractions. Here are the steps to simplify an operation:
Combine like terms.Perform any necessary arithmetic operations such as addition, subtraction, multiplication, or division.Simplify fractions by finding the greatest common factor and dividing.Reduce any radical expressions to simplest form.If possible, express the result in a more simplified or concise form.By following these steps, you can simplify any mathematical operation.
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How do businesses help a country’s economy?
A. By investing in goods and services
B. By increasing the unemployment rate
C. By making profits
Answer:
A
Step-by-step explanation:
Answer:
Option A, By investing in goods and services
, is the right answer.
Step-by-step explanation:
Option A, investing in goods and services is the correct answer because the investment on goods and services will generate employment in the country and person will be able to earn more and consequently the expenditure will also increase. Moreover, if there will be more production of goods and services then the country’s GDP and economy will boost.
A certain shampoo is available in two sizes. A 14.2- ounce bottle costs $4.98. A 23.7- ounce bottle costs $6.97. Find the unit price for each size. Then state which size is the better buy based on the unit price. Round your answers to the nearest cent
Answer:
the 23.7 ounce bottle is the better price because the 14.2 ounce bottle is $0.35 and the 23.7 ounce bottle is $0.29.
Step-by-step explanation:
you simply divide the cost by the ounces and get the unit price
To find the unit price for each size, divide the cost of the shampoo by the number of ounces. The 23.7-ounce bottle is the better buy based on the lower unit price.
Explanation:To find the unit price for each size, divide the cost of the shampoo by the number of ounces in each bottle. For the 14.2-ounce bottle, the unit price is $0.35 per ounce ($4.98 / 14.2). For the 23.7-ounce bottle, the unit price is $0.29 per ounce ($6.97 / 23.7).
To determine which size is the better buy based on the unit price, compare the unit prices. Since the 23.7-ounce bottle has a lower unit price ($0.29 per ounce) compared to the 14.2-ounce bottle ($0.35 per ounce), the larger size is the better buy.
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Solve the system y = -x + 7 and y = 0.5(x - 3)2
explain the answer
Answer:
x=5, x=-1
Step-by-step explanation:
Since both equations are equal to y, we can set them equal to each other
y = -x + 7 and y = 0.5(x - 3)2
-x + 7 = 0.5(x - 3)^2
Distribute the right hand side by Foiling
-x+7 =.5 ( x^2 -3x-3x+9)
Combine like terms
-x+7 = .5( x^2 -6x+9)
Distribute the .5
-x+7 = .5x^2 -3x+4.5
Add x to each side
-x+x+7 = .5x^2 -3x+x+4.5
7 = .5x^2 -2x+4.5
Subtract 7 from each side
7 -7= .5x^2 -2x+4.5-7
0 = .5x^2 -2x-2.5
Multiply by 2 to clear the decimals
0 = x^2 -4x -5
Factor
0 = (x-5) (x+1)
Using the zero product property
x-5=0 x+1 =0
x=5, x=-1