Answer:
Perpendicular lines are lines that cross one another at a 90° angle. They have slopes that are opposite reciprocals of one another. Unlike parallel lines that never touch, perpendicular lines must intersect.
Therefore, the shape with 2 lines that don't intersect/touch each other, is the shape that does not have perpendicular lines.
The function f is defined by f(x) = x2 - 6x +21.
What are the solutions of f(x) = 0?
Show your work on the scratchpad.
The solutions are:
[tex]x =3+2\sqrt{3}i\\\\\:x=3-2\sqrt{3}i[/tex]
Solution:
[tex]f(x) = x^2 - 6x + 21[/tex]
We have to find solutions when f(x) = 0
[tex]x^2 - 6x + 21 = 0[/tex]
Solve by quadratic formula
[tex]\mathrm{For\:a\:quadratic\:equation\:of\:the\:form\:}ax^2+bx+c=0\mathrm{\:the\:solutions\:are\:}\\\\x=\frac{-b\pm \sqrt{b^2-4ac}}{2a}\\\\\mathrm{For\:}\quad a=1,\:b=-6,\:c=21\\\\x=\frac{-\left(-6\right)\pm \sqrt{\left(-6\right)^2-4\cdot \:1\cdot \:21}}{2\cdot \:1}[/tex]
[tex]x = \frac{6 \pm \sqrt{\left(-6\right)^2-4\cdot \:1\cdot \:21}}{2\cdot \:1}\\\\Simplify\\\\x = \frac{6 \pm \sqrt{36 - 84}}{2}\\\\x = \frac{6 \pm \sqrt{-48}}{2}\\\\x = \frac{6 \pm i \sqrt{48}}{2}\\\\simplify\\\\x = \frac{6 \pm 4\sqrt{3}i}{2}\\[/tex]
[tex]x = 3 \pm 2 \sqrt{3} i[/tex]
We have two solutions:
[tex]x = 3 + 2 \sqrt{3} i\\\\x = 3 - 2 \sqrt{3} i[/tex]
Thus the solutions are:
[tex]x =3+2\sqrt{3}i\\\\\:x=3-2\sqrt{3}i[/tex]
Easy question! Please help! And please tell me which line to use! (open circle or closed circle)
Answer:
See below
Step-by-step explanation:
The inequality is d<-80 since the problem states you go deeper than -80 feet.
As for graphing the inequality, you use a open circle with the arrow pointing left.
<= means closed
>= means closed
< means open
> means open
Answer:
Question: You need to figure out the inequality. Here is the full question: On their first dive, scientists explore a part of the ocean floor that is 80 feet below sea level. This depth can be represented by the integer -80. On their second dive, they explore a deeper depth. Write an inequality that represents the possible depth, d, of the scientist's second dive. After you figure that out you can answer the question above.
d < -80
Open ended at -80 pointing toward -200
the ratio of mystery books to fiction books is 2 to 3. if there are 12 mystery books, how many fiction books are there
Answer:
18
Step-by-step explanation:
First you would have the divide 2 and 12 which is 6 then you would muplty 6 by 3 because you need to find how many fictional book which is 18
p. ls I am 99% sure this explanation is right
The number of fiction books is 18.
What is a ratio?Ratio expresses the relationship between two values. It is the number of times that one value is contained within other value(s).
How many books are there?Number of books = (number of mystery books x sum of ratios) / ratio of mystery books
(12 x 5) / 2 = 30 books
What is the number of fiction books?number of fiction books = (ratio of fiction books / sum of ratios) x total number of books
3/5 x 30 = 18 books
To learn more about ratios, please check: https://brainly.com/question/25927869
The bill at a restaurant is $32 before tax. The tax on the bill is 5%.
How much is the final bill including tax?
32 + 5% = 1.6
The tax is $1.60
The final bill is $33.60
Answer: the answer is $33.60
Last week the office used 7 and 1/12 boxes of paper. This week, they used 3 and 5/12 boxes of paper. How many more boxes did they use last week then this week?
Answer:
3 and 8/12
Step-by-step explanation:
You subtract 3 5/12 from 7 1/12 to get 3 8/12
Answer:
1 and 8/12 or 1 and 2/3
Step-by-step explanation:
7 1/12-3 5/12
2 1/12- 5/12
1 8/12
Find the area of this figure
28 cm
23.7 cm
8 cm
5.7 cm
Solve this quadratic equation using the quadratic formula.
2x^2 - 10x + 7 = 02x2 - 10x + 7 = 0
Answer:
I'm assuming the equation is:
2x^2 -10x +7 = 0
x = (-b +- sqr root (b^2 - 4ac)) / 2a
x = (--10 +-sqr root (100 -4*2*7)) / 4
x = (10 +- sqr root (44)) / 4
x1 = (10 + 6.6332495807 ) /4
x1 = 16.6332495807 / 4
x1 = 4.1583123952
x2 =(10 - 6.6332495807 ) /4
x2 = 3.3667504193 / 4
x2 = 0.8416876048
Step-by-step explanation:
y = x² + 4x + 8
Sketch the graph of each function be sure to show your table of values
Answer:
see attachment
Step-by-step explanation:
We want to sketch the graph of
[tex]y = {x}^{2} + 4x + 8[/tex]
We want to use tables so we choose some few points and plot.
When x=-6,
y=(-6)²+4(-6)+8=20
When x=-4,
y=(-4)²+4(-4)+8=8
When x=0,
y=(-2)²+4(-2)+8=4
When x=0,
y=(0)²+4(0)+8=8
When x=2,
y=(2)²+4(2)+8=20
The table and graph are shown in attachment.
at current prices, roberta can drive her car 8.2 miles per dollar of gasoline that she buys. Roberta and three of her friends decide to go on a road trip to a neighboring university that is 105 miles away and agree to split the cost evenly . to the nearest cent, how much money will each have to contribute to get to the university and back?
Answer:
I think it's $12.80 but I might be wrong.
Each person will have to contribute $6.40.
Explanation:To find out how much money each person will have to contribute to get to the university and back, we can first find the total cost of the trip. The distance to the university and back is 2 times the distance to the university, which is 105 miles. So the total distance is 2 * 105 = 210 miles. Roberta's car can travel 8.2 miles per dollar of gasoline, so the total cost of the trip is 210 / 8.2 = 25.61 dollars. Since Roberta and three friends are splitting the cost evenly, each person will have to contribute 25.61 / 4 = 6.4025 dollars. Rounding to the nearest cent, each person will have to contribute $6.40.
3(2+5)-5(3)+8 help me
Answer:
3(7) -15+8
21-15+8
6+8= 14
solve for x
x/4 ≥ -8
a) x≤-2
b)x≥-32
c)x≥-2
d)x≤-32
Answer:
B
Just multiply by 4 to isolate x; because 4 isn't negative, u keep the sign the same.
Are 3/4 and 7/8 equivalent
Answer:
No.
Step-by-step explanation:
3/4 cannot be simplified. Neither can 7/8. Also, 3/4 as a decimal is 0.75, and 7/8 as a decimal is 0.875.
Answer:
No
Step-by-step explanation:
Is 3/4 less than 7/8? Is 3/4 smaller than 7/8? These are the same questions with one answer.
To get the answer, we first convert each fraction into decimal numbers. We do this by dividing the numerator by the denominator for each fraction as illustrated below:
3/4 = 0.75
7/8 = 0.875
Then, we compare the two decimal numbers to get the answer.
0.75 is less than 0.875.
Therefore, 3/4 is less than 7/8 and the answer to the question "Is 3/4 less than 7/8?" is yes.
An orange has 20 fewer calories
than a banana. If 7 bananas have
the same number of calories as 9
oranges, how many calones are in a
banana?
Answer:
90 calories in total
Step-by-step explanation:
We can solve this equation through the following steps:
Step One: Since we are told that a banana is 20 less calories than an orange, we can create the Let Statements:
Let x= the calories in a banana
Let x-20=the calories in an orange
Step Two: Create an equation
Since we are told "7 bananas have the same calories as 9 oranges" we translate"
7x=9(x-20) Distribute
7x=9x-180 Subtract 9x from both sides of the equation
7x-9x=-180 Simplify
-2x=180 Divide both sides by -2
x=90
∴There are 90 calories in a banana.
On a fishing trip, Mariko caught 24 fish. She caught some rockfish averaging 2.5lbs and some bluefish averaging 8lb. The total weight of the fish was 137lbs how may of each fish did she catch.
Mariko caught 10 rockfish and 14 bluefish on her fishing trip.
Explanation:Let's define the number of rockfish caught as x and the number of bluefish caught as y.
According to the given information, the average weight of each rockfish is 2.5lbs and the average weight of each bluefish is 8lbs.
We can form two equations based on the total weight of all the fish and the total number of fish caught:
Equation 1: x + y = 24 (since Mariko caught a total of 24 fish)Equation 2: 2.5x + 8y = 137 (since the total weight of the fish was 137lbs)We can solve this system of equations to find the values of x and y by either substitution or elimination method. Using the elimination method:
Multiplying Equation 1 by 2.5, we get 2.5x + 2.5y = 60
Subtracting this equation from Equation 2, we get 8y - 2.5y = 137 - 60
Simplifying, we have 5.5y = 77
Dividing both sides by 5.5, we get y = 14
Substituting this value back into Equation 1, we have x + 14 = 24
Simplifying, we get x = 10
Therefore, Mariko caught 10 rockfish and 14 bluefish.
Directions: Consider a 2-kg bowling ball sits on top of a building that is 40 meters tall. It falls to the ground. Think about the amounts of potential and kinetic energy the bowling ball has:
What is the kinetic energy of the ball as it is half way through the fall?
Answer:
it cant be kinetic unless its pushed and gains height, as its falling it is simply potential energy and gets speed in different stages of the fall.
Step-by-step explanation:
show all work to multiply (6+√-64)(3-√-16)
Step-by-step explanation:
6 ( 3 - √-16) + √-64 ( 3- √-16)
18 - 6(-4)^2*1/2 + 3 × (-8)^2*1/2 - √1024
18 - 6 (-4) + 3× (-8) - 32
18 + 24 - 24 - 32
18 - 32
-14
Please help me I'm confused how to do it
Answer:
59 sq ft
Step-by-step explanation:
Area of the entire shape is 13x5=65
but then you have to subtract for the missing portion
the area of that piece is 3x2=6
65-6=59
Select the number line that represents the solution of the inequality
7- x 24.
Answer:
The correct answer is A.
There are two buses. Bus A can travel 125 miles in 3 hours,
and Bus B can travel 85 more miles than bus A within the
same time. What is the speed of Bus B?
mph.
The speed is the distance covered by an object at a particular time. The speed of bus B is 70 miles per hour.
What is speed?The speed is the distance covered by an object at a particular time. Therefore, it is the ratio of distance and time.
[tex]\rm{Speed = \dfrac{Distance}{Time}[/tex]
Given that Bus A can travel 125 miles in 3 hours. While Bus B can travel 85 more miles than bus A within the same time. Therefore, we can write,
Distance traveled by Bus B = 125 miles + 85 miles = 210 miles
Time is taken by Bus B = 3 hours
Now, the speed of the bus B can be written as,
Speed of Bus B = Distance Covered / Time taken
= 210 miles / 3 hours
= 70 miles per hour
Hence, the speed of bus B is 70 miles per hour.
Learn more about Speed here:
https://brainly.com/question/15100898
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pens cost x pence and pencils cost y pence. Write a formula for the total cost (T) of 7 pens and 11 pencils
PLEASEEEE HELPPP
3. Triangle ABC has angle measures as shown.
(a) What is the value of x? Show your work.
The value of x is 13°.
Solution:
In triangle, sum of all the interior angles = 180°
m∠A + m∠B + m∠C = 180°
(3x)° + (4x – 1)° + 90° = 180°
3x° + 4x° – 1° + 90° = 180°
7x° + 89° = 180°
Subtract 89° from both sides of the equation, we get
7x° = 91°
Divide by 7 from both sides of the equation, we get
x° = 13°
The value of x is 13°.
look at the picture below
Answer:
1.8
Step-by-step explanation:
12/4 - 1.2
3 - 1.2 = 1.8
Ellen bought a new computer tablet for $460. She paid $100 at the time of purchase and will make monthly payments of $45 to finish paying for the tablet. She used the equation to determine the number of months (m) she needs to make payments. For how many months will she make payments?
Please help this is urgent!
Answer:
The answer is 8 months
Step-by-step explanation:
The new computer tablet is $460. She paid $100 at the time so I subtracted $100 from $460, which equals to $360. The monthly payments are $45 a month, so I divided $360 by $45, which equals 8. It takes 8 more months to finish the payment.
MARK AS BRAINLIEST
Answer:
8 payments
Step-by-step explanation:
460-100=360
45 x 8 = 360
If y = 7x - 5, which of the following sets represents possible inputs and outputs of the function, represented as ordered pairs?
{(-5, 0), (9, 2), (-26, -3)}
{(2,7), (1,6), (3, 13)}
{(0, -5), (2,9), (-3, -26)}
{(1, 3), (6, 18), (8, 15)}
option c {(0, -5), (2,9), (-3, -26)} is correct . All others doesn't satisfy the equation .
Step-by-step explanation:
We have , If y = 7x - 5, following set of ordered pairs {(0, -5), (2,9), (-3, -26)} . Let's check for this
(0, -5):
⇒ [tex]y = 7x-5[/tex]
⇒ [tex]y = 7(0)-5[/tex]
⇒ [tex]y =-5[/tex]
So , it's correct ordered pair .
(2,9):
⇒ [tex]y = 7x-5[/tex]
⇒ [tex]y = 7(2)-5[/tex]
⇒ [tex]y =9[/tex]
So , it's correct ordered pair .
(-3,-26):
⇒ [tex]y = 7x-5[/tex]
⇒ [tex]y = 7(-3)-5[/tex]
⇒ [tex]y =-26[/tex]
So , it's correct ordered pair .
Therefore, option c {(0, -5), (2,9), (-3, -26)} is correct . All others doesn't satisfy the equation .
128/148 simplest form
Reduce the expression by cancelling the common factors.
= 32/37
In decimal;
0.864
(4x+40)=3x what is x
Answer: x=40
Step-by-step explanation:
(4x+40)=3x
Step 1: open the bracket
4x + 40 = 3x
Step 2: Combine like terms
4x - 3x = 40
x = 40
I hope this helps.
the number. Find the nume.
Eight times a number plus 3 times
the number is the same as 9 more
than 12 times the number. Find the
number.
Answer: 8x+3x=12x+9
The number is -9.
Step-by-step explanation: Combine like terms.
11x=12x+9
Subtract 12x from the other side. 11x-12x= -1x
-1x+9
Divide by -1 to isolate x.
-1/-1 cancels out.
9/-1= -9
x=-9
Plug in -9 to check your answer if you want to double check.
I NEED HELP ASAP Please
go to negative to and move left once and that'll give you 2 and 1 6ths then go to 1 and move right once cause 7 over 6 is 1 and 1 over 6
[tex]0 = \frac{i}{8} [/tex]
what is i?
Answer:
0
Step-by-step explanation:
i/8=0
i=0*8
i=0
can someone help me ?
Answer:
y = -3/4x + 5
Step-by-step explanation:
Slope intercept form is y=mx + b
First, find the slope of the line. the points are (0,5) and (4,2), as marked. To find the slope, you do (y2-y1)/(x2-x1). Fill in the numbers and you get
(2-5)/(4-0). Simplify and you get -3/4 is the slope. Then, to find b, you have to fill in one coordinate pair and the slope into y=mx+b. So, I used (0,5).
5=(-3/4)(0) + b
Then you get 5=b by solving, and you fill in the slope and the y intercept in the slope intercept form equation. y = -3/4x +5. This is how you find the answer.