The solutions to the quadratic equation 2x^2 - 8x + 7 = 0 are x = 2 + √2 / 2 and x = 2 - √2 / 2 using the quadratic formula.
To solve the equation 2x2 - 8x + 7 = 0, we will use the quadratic formula, where 'x' equals minus 'b', plus-or-minus the square root of 'b' squared minus four 'a' 'c', all over two 'a'. The coefficients in this case are a = 2, b = -8, and c = 7.
First, we calculate the discriminant, which is b2 - 4ac. Substituting our values we get:
(-8)2 - 4(2)(7) = 64 - 56 = 8.
The square root of 8 can be simplified to 2√2, because 8 = 4 × 2 and √4 = 2.
Finally, we substitute the values into the quadratic formula:
x = (-(-8) ± √8) / (2 × 2)
x = (8 ± 2√2) / 4
Dividing each term by 4 gives us:
x = 2 ± √2 / 2
Therefore, the solutions to the equation are:
x = 2 + √2 / 2 and x = 2 - √2 / 2
Maddy made $22.50 for babysitting for 5 hours for her aunt. Maddy was paid $21.00 for 3.5 hours of babysitting for her neighbor. How much more per hour does Maddy’s neighbor pay than her aunt?
Answer:Her Aunt paid her 4.50 and hour and her neighbor 6 an hour. The difference is 1.5
Step-by-step explanation:
Sidneys made $38 more than 3 times Casey’s weekly salary. If x represents Casey’s weekly salary , write an expression for sidneys weekly salary
y=3x+38 is the expression for Sidney's weekly salary.
Step-by-step explanation:
Given,
Casey's weekly salary = x
Let,
y be the weekly salary of Sidney's.
According to given statement;
Sidney makes $38 more than 3 times Casey's weekly salary.
Sidney's weekly salary = 3 times Casey's weekly salary + $38
[tex]y=3x+38[/tex]
y=3x+38 is the expression for Sidney's weekly salary.
Keywords: variable, addition
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Determine if the following system of equations has no solutions, infinitely many
solutions or exactly one solution.
5x + 3y = 9
-10x – 6y = -18
Answer:
The system has infinitely many solutions
Step-by-step explanation:
we have
[tex]5x+3y=9[/tex] ----> equation A
[tex]-10x-6y=-18[/tex] ----> equation B
Multiply by -2 both sides equation A
[tex]-2(5x+3y)=-2(9)[/tex]
[tex]-10x-6y=-18[/tex] ----> equation C
Compare equation B and equation C
The equations are identical (is the same line)
therefore
The system has infinitely many solutions
Is a consistent dependent system
How many times can 27 go into 224
Answer:
27 can go into 224 8 times by dividing 224 by 27 .
1. What is the solution to the equation -5(s - 30) = -10?
Answer:
s = 32
Step-by-step explanation:
-5(s - 30) = -10
-5s + 150 = -10
-5s = -10 - 150
-5s = -160
s = -160/-5
s = 32
What is the equation of a line through the points (0, 9) and (3, 0)?
because m = StartFraction 9 minus 0 Over 0 minus 3 EndFraction; y = –3x + 9 because m = StartFraction 9 minus 0 Over 0 minus 3 EndFraction; y = –3x + 3 because m = StartFraction 3 minus 0 Over 0 minus 9 EndFraction; y = negative one-third x + 9
because m = StartFraction 3 minus 0 Over 0 minus 9 EndFraction; y = negative one-third x + 3 Mark
Answer:
m = StartFraction 9 minus 0 Over 0 minus 3 EndFraction; y = –3x + 9
Step-by-step explanation:
The given points are the y-intercept and the x-intercept, so they can be used directly in the intercept form of the equation of a line.
x/(x-intercept) +y/(y-intercept) = 1
x/3 +y/9 = 1
Multiplying by 9 gives ...
3x +y = 9
This can be rearranged to the slope-intercept form ...
y = -3x +9
_____
The answer selection shown above is the only one that matches the slope and y-intercept of the line through the given points.
Answer:
because m = StartFraction 9 minus 0 Over 0 minus 3 EndFraction; y = –3x + 9
Step-by-step explanation:
Mofor’s school is selling tickets to the annual talent show. On the first day of ticket sales the school sold 4 senior citizen tickets and 6 student tickets for a total of $96. The school took in $202 on the second day by selling 8 senior citizen tickets and 13 student tickets. Find the price of a senior citizen ticket and the price of a student ticket.
Answer:
Senior citizen tickets = 9
Student tickets = 10
Step-by-step explanation:
We begin by converting the question into simultaneous linear equations;
Senior citizen tickets = a
Student tickets = b
4a + 6b = 96
8a + 13b = 202
to find a,
if 4a +6b = 96
a = 96/4 - 6b/4
a = 24 - 1.5b
We now substitute this into the second equation
8(24 - 1.5b) + 13b = 202
192 - 12b + 13b = 202
b = 202 - 192
b = 10
We now put the value of b in either equation
4a + 6b = 96
4a + 6(10) = 96
4a + 60 = 96
4a = 96 - 60
4a = 36
a = 9
160 dogs,there are 17 trucks each truck can hold 9 dogs.how much trucks you will need to hold 9 dogs in each truck?
Answer:
160-153=7 dogs
you will need 1 more truck to hold 160 dogs
Step-by-step explanation:
1 truck=9 dogs
9x17=153 dogs
160-153=7 dogs
you will need 1 more truck to hold 160 dogs
Does the bowling ball have more potential energy or kinetic energy as it sit on top of the building? Why?
Answer:
The bowling ball has only potential energy as it sits on top of a building.
The potential energy "stored" in the bowling ball will convert to kinetic energy as the ball is pushed from the top of the building and starts to fall.
The energy spent in raising the ball against gravity to the top of the building is equal to the amount of potential energy "stored" in the bowling ball.
Therefore the bowling ball will have more potential energy as it sits on top of the building.
Step-by-step explanation:
The bowling ball has only potential energy as it sits on top of a building.
The potential energy "stored" in the bowling ball will convert to kinetic energy as the ball is pushed from the top of the building and starts to fall.
The energy spent in raising the ball against gravity to the top of the building is equal to the amount of potential energy "stored" in the bowling ball.
Therefore the bowling ball will have more potential energy as it sits on top of the building.
Answer:
Before the ball hits the ground it has more potential energy but when is going down it looses potential energy and creates kinetic energy so when the ball hits the floor it would have more kinetic energy.
Step-by-step explanation:
The area of a right triangle is 315 square meters. The height of the right triangle is 15 meters. What is the length of the hypotenuse of the right triangle rounded to the nearest meter? No points given without showing your work.
Answer:
45 metres
Step-by-step explanation:
You have to get the base to answer the question.
Do this by dividing 315 by 15 then timesing by 2
You get 42.
Do 42^2 = 1764
Do 15 ^2 = 225
Because you want the hypotenuse you add them
1764 + 225 =1989
Do the square root of 1989 which is 45 to the nearest metre
Answer:
25.80
Step-by-step explanation:
Area = 315 [tex]m^{2}[/tex]
Area = l*b
315 = 15 *b
b= 315/15
b = 21
From Right angled Triangle ,
Hypotenuse square = side square + side square
[tex]x^{2}[/tex] = [tex]21^{2}[/tex] + [tex]15^{2}[/tex]
[tex]x^{2}[/tex] = 441 + 225
[tex]x^{2}[/tex] = 666
apply sq root on both sides, the we get
[tex]\sqrt{x^{2}} = \sqrt{666}[/tex]
x= 25.80
What is the degree of the polynomial below?
2х^2 + 3x +1
Answer:
the degree for the polynomial is 2
does anyone know the answer ?
Answer:
15.7cm
Step-by-step explanation:
2 + 1.4 + 1.3 + 1.2 + 4.1 + 1.3 + 1.4 + 3
If the circumference of each tire on a vehicle is approximately 88 in., how many miles will the vehicle travel when the tires make
23
23,000 revolutions?
Answer:
31.94 miles
Step-by-step explanation:
we know that
The circumference of a tire represents the distance traveled by the vehicle in one revolution
so
by proportion
Find out the distance traveled by the vehicle in 23,000 revolutions
[tex]\frac{88}{1}\ \frac{in}{rev}=\frac{x}{23,000}\ \frac{in}{rev}\\\\x=88(23,000)\\\\x=2,024,000\ in[/tex]
Convert inches to miles
Remember that
[tex]1\ mile=63,360\ inches[/tex]
To convert inches to miles divided by 63,360
therefore
[tex]2,024,000\ in=2,024,000/63,360=31.94\ miles[/tex]
The stock of Company A gained 4% today to $47.84. What was the opening price of the stock in the beginning of the day?
Answer:
46
Step-by-step explanation:
47.84 / 1.04, which is 46
The opening price of Company A's stock before the 4% increase to the closing price of $47.84 was $46.00.
To calculate the opening price of Company A's stock at the beginning of the day, before the 4% gain, we need to work backwards from the closing price. Since the stock closed at $47.84 after gaining 4%, we can represent the closing price as 104% of the opening price. Thus, the equation to find the opening price (OP) is:
OP x1.04 = $47.84
Now we solve for OP:
OP = $47.84 / 1.04
OP = $46.00
The opening price of Company A's stock at the beginning of the day was $46.00.
a recycling plant processes an average of 1/3 ton of glass each minute.At approximately what rate does the recycling plant process glass,in tons per day?
Answer:
480 tons
Step-by-step explanation: You have to figure out how many minutes are in 24 hours. (1440 min) Then, you multiply 1440 x 1/3.
Answer:
the answer is 480
Step-by-step explanation:
it is common sense but in your case it is uncommon sense
How do you divide a decimal by a whole fraction
Answer
wherever the decimal is, put it directly on top of the dividing line thing. Now that the decimal looks like a regular whole number you can divide like you usually would. Whenever you do regular long division, your answer is always going to be on the top of the line. Your answer should have a decimal in it ... and that should be your answer.
2. What can you conclude about two triangles when you know that two pairs of
corresponding sides and the corresponding included angles are congruent?
We can conclude that, if two pairs of corresponding sides and the corresponding included angles are congruent, the two triangles will be congruent.
Given that, two pairs of corresponding sides and the corresponding included angles are congruent.
What is the congruence theorem?Triangle congruence theorem or triangle congruence criteria help in proving if a triangle is congruent or not. The word congruent means exactly equal in shape and size no matter if we turn it, flip it or rotate it.
If two pairs of corresponding sides are equal and corresponding included angles are equal.
By SAS congruence theorem, two triangles are congruent.
Therefore, we can conclude that, if two pairs of corresponding sides and the corresponding included angles are congruent, the two triangles will be congruent.
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Jeannie needs 2 cups of milk to make her homemade brownies. How many fluid ounces does Jeannie need?
Answer:
16 fluid ounces=2 cups
Hope this helps!
Step-by-step explanation:
Answer:
16 fluid ounces
Step-by-step explanation:
1 cup is equal to 8 fluid ounces, so 2 cups is 16 fluid ounces.
If the number of professors in a college is P and the number of students is S, and there are 19 times as many students as professors,write an algebraic equation that shows the
Answer:
[tex]S =19P\\S-19P = 0[/tex]
Step-by-step explanation:
We are given the following in the question:
Let P be the number of professor and S be the student in a college.
According to the question:
There are 19 times as many students as professors.
We have to write an equation to show the given relationship between professors and students.
[tex]S =19P\\S-19P = 0[/tex]
The above situation is the situation that represents the given relationship.
Joe's annual income has been increasing in the same dollar amount. The first year his income was $15,200, and the 4th year his income was $17,900. In which year was his income $19,700?
Answer:
Therefore 6th year his income was $19,700.
Step-by-step explanation:
Given, Joe's annual income has been increasing in some dollar amount . The first year his income was $15,200 and 4th year his income was $17,900.
A=$17900, P= $15,200 and n = 3 year
[tex]A= P(1+\frac{r}{100} )^n[/tex]
[tex]\Leftrightarrow 17900=15200(1+\frac{r}{100})^3[/tex]
[tex]\Leftrightarrow (1+\frac{r}{100})^3=\frac{17900}{15200}[/tex]
[tex]\Leftrightarrow (1+\frac{r}{100})=(\frac{17900}{15200})^{\frac{1}{3} }[/tex]
[tex]\Leftrightarrow \frac{r}{100}=(\frac{17900}{15200})^{\frac{1}{3} }-1[/tex]
[tex]\Leftrightarrow r=5.60[/tex]
Let [tex]t^{th}[/tex] year Joe's income was $19,700.
[tex]\therefore 19700=15,200(1+\frac{5.60}{100} )^{t-1}[/tex]
[tex]\Leftrightarrow 1.296= (1+0.056)^{t-1}[/tex]
[tex]\Leftrightarrow 1.296= (1.056)^{t-1}[/tex]
[tex]\Leftrightarrow log(1.296)= (t-1)log(1.056)[/tex]
[tex]\Leftrightarrow \frac{log(1.296)}{log(1.056)}= (t-1)[/tex]
[tex]\Leftrightarrow t-1= 4.75[/tex]
[tex]\Leftrightarrow t= 4.75+1[/tex]
[tex]\Leftrightarrow t = 5.75[/tex] ≈6
Therefore 6th year his income was $19,700.
Due to a slump in the economy a mutual fund has dropped by 30% from last year to this year. If the fund is now worth $13,902, how much was the fund last year?
Answer: The Fund last year was 19,860
Step-by-step explanation:
Just set up a ratio using 70 over 13902 and set it equal to 100 over x and cross multiply to get x = 19,860
8 1/9-6 7/9
Show how you got the answer
Answer:
7 10/9 - 6 7/9
1 4/9
Step-by-step explanation:
the denominator stays the same
Change the FIRST fraction to an improper mixed fraction
then keep the denominators the same and subtract the numerators
subtract the whole numbers
Expand to write an equivalent expression: -1/4(8x+12y)
Answer:
-2x-3y
Step-by-step explanation:
-1/4(8x+12y)
-8/4x-12/4y
-2x-3y
Final answer:
The expression -1/4(8x+12y) is expanded by distributing -1/4 to both 8x and 12y, resulting in the equivalent expression -2x - 3y.
Explanation:
To expand the expression -1/4(8x+12y), you need to distribute the term outside the parenthesis (-1/4) to each term inside the parenthesis. This process is known as the distributive property of multiplication over addition. Here's the step-by-step process:
Multiply -1/4 by 8x to get -2x.Multiply -1/4 by 12y to get -3y.Combine these two products to get the expanded expression: -2x - 3y.In conclusion, the equivalent expression after expanding -1/4(8x+12y) is -2x - 3y.
How to divide 704 by 3 using long division
Answer:
Step 1: D for Divide. How many times will 5 go into 65? ...
Step 2: M for Multiply. You multiply your answer from step 1 and your divisor: 1 x 5 = 5. ...
Step 3: S for Subtract. Next you subtract. ...
Step 4: B for Bring down. ...
Step 1: D for Divide. ...
Step 2: M for Multiply. ...
Step 3: S for Subtract.
Step-by-step explanation:
A figure is dilated by a factor of 3. which statement about the mesurements of the image is true
A Dilation factor of 3 means that all dimensions of the figure are three times larger than those of the original figure. This applies to every dimension of the figure including height, width, and depth (if applicable). An example is a rectangle with original measurements 2 cm by 4 cm becoming 6 cm by 12 cm after dilation.
When a figure undergoes a dilation, all its dimensions are altered by the dilation factor.
In this case, the dilation factor is 3, which means that each dimension of the figure is three times larger than before.
It is important to note that this applies to all dimensions: height, width, and depth (if applicable).
For instance, suppose you have a rectangle with a height of 2 cm and width of 4 cm.
If the rectangle is dilated by a factor of 3, the new dimensions would be 6 cm (2 cm * 3) for height and 12 cm (4 cm * 3) for width.
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The question probable may be:
Explain the concept of dilation and provide an example illustrating how the dimensions of a figure change when subjected to a dilation factor. In particular, discuss the scenario where a rectangle with a height of 2 cm and width of 4 cm undergoes a dilation by a factor of 3. What are the new dimensions, and how does this align with the general principle of dilation?
Find the area of the figure.
triangle with base 27.5 m and height 4.8 m
Answer:66
Step-by-step explanation:
27.5x4.8/2
Answer:
66 meters squared
Step-by-step explanation:
You multiply 27.5 and 4.8. Which gets you 132. And because your finding the area of a triangle you have to divide 132 by 2 which gets you 66.
Nara multiplied two whole numbers together to equal a product of 90.
Then she accidentally spilled ketchup on her work.
Select the three responses below that could be one of the numbers Nara multiplied.
Answer:
30×3=90 10×9=90 45×2=90 . .
Answer: 5, 10, 18
Step-by-step explanation:
Each of the four sides of a swimming pool measures 12 meters the pool is 6 meters deep how much water will be needed to fill it completely
It will need 864 meters³ of water to fill it completely
Step-by-step explanation:
The formula of the volume of a prism is V = B h, where
B is the area of its baseh is the length of its heightThe swimming pool is shaped a prism
∵ The length of each side of the four sides is 12 meters
- That means its base is shaped a square with side length 12 meters
∵ Area of a square = (side)²
∴ The area of the base of the swimming pool = (12)² = 144 meters²
∴ B = 144
∵ The pool is 6 meters deep
- That means its height is 6 meters
∴ h = 6
The volume of the water in the swimming pool is equal to the volume of the swimming pool because it will be needed to fill completely
∴ The volume of the water = B h
∴ The volume of the water = 144(6)
∴ The volume of the water = 864 meters³
It will need 864 meters³ of water to fill it completely
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PLEASE HELP ME THIS IS DUE TODAY! TYSM IF YOU CAN. a.) Lines AD and BE intersect at point C, as shown. Create an expression that represents the measure of angle DCE in terms of X. b.) Using your expression, solve for the missing value of X if DCE was 120 degrees.
Answer:
1) ∠DCE = (180 - x)°
2) x = 60°
Step-by-step explanation:
Here, given : Lines AD and BE intersect at point C
(a) Now, as we know, c BE is a straight line.
⇒∠BCD + ∠DCE = 180 ° (LINEAR PAIR)
⇒x ° + ∠DCE = 180 °
or, ∠DCE = (180 - x)° ....... (1)
(b) ∠DCE = 120°
Putting the value in the equation (1), we get:
120° = (180 - x)°
or, x = 180 - 120° = 60°
or, x = 60°
What is the value of y if formula is 4/5
Step-by-step explanation:
The complete question:
What is the value of y in the formula shown when x = [tex]\dfrac{4}{5}[/tex] ?
[tex]y=\dfrac{4}{x}+\sqrt{x+0.2}-5x[/tex]
We have,
[tex]\dfrac{4}{x}+\sqrt{x+0.2}-5x[/tex] ...... (1)
To find, the value of y = ?
Put x = [tex]\dfrac{4}{5}[/tex] in equation (1), we get
[tex]y=\dfrac{4}{\dfrac{4}{5}}+\sqrt{\dfrac{4}{5}+0.2}-5(\dfrac{4}{5})[/tex]
[tex]=5+\sqrt{0.8+0.2}-4[/tex]
[tex]=1+\sqrt{1}[/tex]
= 1 + 1
= 2
Thus, the value of y is equal to 2.