Answer: 256
Step-by-step explanation:
x² + 6x - 55 = 0
The values under the radical are: b² - 4ac
(6)² - (4)(1)(-55)
= 36 - (-220)
= 36 + 220
= 256
find the surface area of the figure
Answer:
The answer is 165 in.
Step-by-step explanation:
The first shape (On the right) has a length of 3in. If you look at the top. and the height is 9in. Now you can find the width by looking at the other shape on the left and its width is 3in. Good thing the width on that shape matches the width on the right shape. so now you multiply 3, 3, and 9 and you get 81.
Now you look at the shape on the left. We already know the width which is 3in. and the height is 4in. to find the length don't look at the 10in. the 10 is the 1st and 2nd shape put together. look at the top of the shape on the left and there is a 7. That 7 is your length. now you multiply 7, 3, and 4 and you should get 84. Now you add 84 and 81 and you are left with the answer of 165in squared.
The total surface area of the two cubical figures is A = 224 inches²
What is the surface area of cuboid?A cuboid is defined as a three-dimensional shape, that has six rectangular faces, eight vertices and twelve edges
The total surface area of the cuboid is given by the formula
Surface Area = 2 ( LH + LW + HW )
where ,
Length of the cuboid = L
Width of the cuboid = W
Height of the cuboid = H
Given data ,
Let the surface area of the figure be represented as A
Now , let the surface area of the first cuboid be A₁
And , let the surface area of the second cuboid be A₂
On simplifying the equation , we get
The surface area of the cuboid A₁ = ( 3 x 4 ) + 2 ( 7 x 3 ) + 2 ( 7 x 4 )
The surface area of the cuboid A₁ = 12 + 42 + 56
The surface area of the cuboid A₁ = 110 inches²
And ,
The surface area of the cuboid A₂ = 2 ( 3 x 3 ) + 3 ( 9 x 3 ) + ( 5 x 3 )
The surface area of the cuboid A₂ = 18 + 81 + 15
The surface area of the cuboid A₂ = 114 inches²
So , the total surface area of the figure A = surface area of the cuboid A₁ + surface area of the cuboid A₂
The total surface area of the figure A = 110 inches² + 114 inches²
The total surface area of the figure A = 224 inches²
Hence , the total surface area of the figure A = 224 inches²
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Which is bigger -2/3 -2/8
Answer:
-2/8
Step-by-step explanation:
Since both numbers are negative we want to find which ever is closer to 0. -2/8 is -1/4 which is closer to 0 then -2/3 so -2/8 is larger
Somebody please help me idk what to do ♂️♂️
Answer:
21
Step-by-step explanation:
Note that n! = n(n - 1)(n - 2) ..... × 3 × 2 × 1, thus
7! = 7 × 6 × 5 × 4 × 3 × 2 × 1
5! = 5 × 4 × 3 × 2 × 1
2! = 2 × 1
Hence
cancel 5 × 4 × 3 × 2 × 1 on numerator/ denominator, leaving
[tex]\frac{7(6)}{2(1)}[/tex] = [tex]\frac{42}{2}[/tex] = 21
Technician A says that the piston's most important function is to transfer the force produced by the burning air-and-fuel mixture into usable power. Technician B says that the piston size is used to help form a seal between the piston and the cylinder walls. Who is right?
A. Technician B only
B. Technician A only
C. Both Technicians A and B
Answer:
Option B.
Technician A only
Step-by-step explanation:
Since we are talking about the most important function of a piston, the technician A is correct.
A piston is used to transfer force from expanding gas in the cylinder to the crankshaft , in an engine.
In a pump, its purpose is compressing or ejecting the fluid in the cylinder.
Technician B is not correct, because piston rings are used for creating a seal between piston and cylinder walls.
Answer:
B. Technician A only
Step-by-step explanation:
PENN
please help me question 1-4
The midsegment is half the length of the base.
1) 32 ÷ 2 = 16
So, 16 is the midsegment
2) 11 ÷ 2 = 5.5
So, 5.5 is the midsegment
3) 32 ÷ 2 = 16
So, 16 is the midsegment
4) 14 ÷ 2 = 7
So, 7 is the midsegment
(08.06)
Jamie is 5 years older than Ella. Jamie's age is 11 years less than three times Ella's age. The system below models the relationship between Jamie's age (j) and Ella's age (e):
j = e + 5
j = 3e − 11
Which of the following methods is correct to find Jamie's and Ella's age?
Solve j + 5 = 3j − 11 to find the value of j.
Write the points where the graphs of the equations intersect the x-axis.
Write the points where the graphs of the equations intersect the y-axis.
Solve e + 5 = 3e − 11 to find the value of e.
Answer:
Solve e + 5 = 3e − 11 to find the value of e
Step-by-step explanation:
Let
j------> Jamie's age
e----> Ella's age
we know that
[tex]j=e+5[/tex] -----> equation A
[tex]j=3e-11[/tex] -----> equation B
equate equation A and equation B and solve for e
[tex]e+5=3e-11[/tex]
[tex]3e-e=5+11[/tex]
[tex]2e=16[/tex]
[tex]e=8[/tex]
Find the value of j
[tex]j=8+5=13[/tex]
Jamie's age is 13 years old
Ella's age is 8 years old
pierre bounce a ball for 1/3 of his recess time he threw the ball in the air and caught it 3/6 of the time he carrie it the rest of the time what fraction of his recess time did he carrie the ball
Answer: [tex]\frac{5}{6}[/tex]
Step-by-step explanation:
Let's call the time he carried the ball: t
You know that he bounced the ball for 1/3 of his recess.
You also know that he threw the ball in the air and caught it 3/6 of the time.
Therefore, to solve the exercise you only need to add both fractions, as you can see below. Therefore, the result is:
[tex]t=[/tex][tex]\frac{1}{3}[/tex]+[tex]\frac{3}{6}[/tex]
[tex]t=[/tex][tex]\frac{5}{6}[/tex]
How many students watch less than 3 hours of tv a day
7 students watch less than 3 hours of tv a day.
Hope this helps.
You should just count the x's in slots 0, 1, and 2, so the answer should be 7 (or however many those 7 x's represents)
What number is 100% of 113. Help me please
100% is always the full number so 113 is your answer
Hope this helps and have a blessed day
Answer:
88.5
Step-by-step explanation:
100:113*100 =
(100*100):113 =
10000:113 = 88.5
factor completely:
4x²-8
4(xsquared -2) thats the answer
So, this is technically (4x×4x)-8. Therefore, the answer is 16x-8.
Carmen sold 600 liters of soda at a baseball game. How much is this in milliliters? Be sure to include the correct unit in your answer.
Answer:
600,000 mL
Step-by-step explanation:
Since there is 1,000 mL in 1 L, 600 L = 600,000 mL.
If Carmen sold 600 liters of soda, then he would have sold 600000 milliliters of soda. 1 liter= 1000 milliliters
stan needs 90 points to get a passing grade in class. He already has6 points. If each book report is worth 7 points, what is the fewest number of book reports Stan can do and still pass the class?
Answer:
12
Step-by-step explanation:
6 + 7n = 90
n = number of book reports
6 + 7n = 90
7n = 84
n = 12
12 book reports
stan needs to report at least 12 books to get passing marks.
What is inequality?In mathematics, inequalities specify the connection between two non-equal numbers. Equal does not imply inequality. Typically, we use the "not equal sign ()" to indicate that two values are not equal. But several inequalities are utilized to compare the numbers, whether it is less than or higher than.
Given, stan needs 90 points to get a passing grade in the class. He already has6 points.
Let "x " be the number of books he Reports.
Since each book report is worth 7 points.
Thus, if he reports x books he will get = 7 * x points
Since he already has 6 points
So, the total points stan has for reporting x books = 7x + 6
Thus inequality,
7x + 6 ≥ 90
=> 7x + 6 ≥ 90
=> 7x ≥ 84
=> x ≥ 12
therefore, stan needs to report at least 12 books to get passing marks.
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two adjacent angles form a right angle. What type of angle pair do they form?
Answer:
complementary angles
Step-by-step explanation:
Adjacent angles form a right angle.
A right angle is 90 degrees.
Two angles that add to 90 degrees are complementary.
The adjacent angles are complementary
Which is the simplified form of
Answer: [tex]\frac{1}{r^{7} } +\frac{1}{s^{12} }[/tex]
Step-by-step explanation:
With negative powers, [tex]r^{-7} = \frac{1}{r^{7} }[/tex]
do the same for s too
For this case we have that by definition of power properties:
[tex]a ^ {- 1} = \frac {1} {a ^ 1} = \frac {1} {a}[/tex]
We have the following expression:
[tex]r^{-7} + s ^{-12}[/tex]
We can rewrite it as:
[tex]\frac {1} {r ^ 7} + \frac {1} {s ^{ 12}}[/tex]
Finally:
[tex]r ^ {- 7} + s ^ {- 12} = \frac {1} {r ^ 7} + \frac {1} {s ^ {12}}[/tex]
Answer:
Option D
A is directly proportional to B when A =12 and B =3
A.)find a formula for A in terms of B
B.)find the value of A when B =5
C.)find the value of B when A =36
A) To find A in terms of B, we need to find A = xB. One given is A = 12 and B = 3. We substitute, which gives us 12 = x4. Divide both sides by 4, which gives us x = 3. This means that A = 3B.
B) For this, we can just plug in 5 as B in our equation. A = 3*5 -> A = 15.
C) We can plug in A as 36. 36 = 3B -> B = 12.
A.) The formula for A in terms of B is A = 4B. B.) When B = 5, A = 20. C.) When A = 36, B = 9.
Explanation:A.) To find the formula for A in terms of B, we can set up a proportion using the given values. Since A is directly proportional to B, we can write the proportion as A/B = k, where k is the constant of proportionality. Substituting the values A = 12 and B = 3, we have 12/3 = k. Solving for k, we find k = 4. Therefore, the formula for A in terms of B is A = 4B.
B.) To find the value of A when B = 5, we can substitute B = 5 into the formula A = 4B. A = 4(5) = 20.
C.) To find the value of B when A = 36, we can rearrange the formula A = 4B to solve for B. Dividing both sides by 4, we get B = A/4. Substituting A = 36, we have B = 36/4 = 9.
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Veronica is filling a bag with marbles. She fills the bag with 8 green marbles for every 6 red marbles. The table below shows the numbers of green and red marbles she used.
Green Marbles 8 12 16 20
Red Marbles 6 9 12 15
Using the information from the table, choose the correct statement.
A.
The ratio of the number of red marbles to the total number of marbles is 7:3.
B.
There are 4 green marbles, for every 3 red marbles.
C.
For each red marble, there are 2 green marbles.
D.
The ratio of the number of green marbles to the total number of marbles is 4:3.
Answer: Off the top of my head, I can see that B is a correct statement.
Step-by-step explanation: 4 x 2 = 8
3 x 2 = 6
this multiplication shows that statement B is true.
What are the zeros of the function f(x)=x2+12x+38
Answer:
The zero would be -2.714 (x-intercept)
Cheryl went on a 3-hour train ride the train traveled at an average speed of 75 miles per hour what was the total distance in miles that Cheryl traveled
A: 225
B: 215
C: 25
D: 72
The answer is A: 225
the following represent the favorite color reported by young children at a birthday party. blue green red blue blue yellow red blue blue green blue. which of the following would be best to describe a typical value in th data set? the mean the median the mode
The mode would be best because it describes the color used most often.
Answer:
Mode because its the number shown most.
Step-by-step explanation:
PERFORM MULITIPLICATION FFAAAASSSSTTTTT!
(b–2)(b+2)(b^2+4)
Does the graph of the function y–x^2=9 intersect the following. If the answer is ‘yes’, determine the coordinates of the points of intersection the y axis
Answer:
The function intersects the y-axis at point (0.9) (vertex)
Step-by-step explanation:
we know that
The equation of a vertical parabola into vertex form is equal to
[tex]y=a(x-h)^{2}+k[/tex]
where
(h,k) is the vertex of the parabola
if a>0 then the parabola open upward (vertex is a minimum)
In this problem we have
[tex]y-x^2=9[/tex] -----> [tex]y=x^2+9[/tex]
This is a vertical parabola open upward
The vertex is the point (0,9)
The vertex is a minimum
see the attached figure to better understand the problem
The graph does not intersect the x-axis (the function has no real roots)
The function intersects the y-axis at point (0.9) (vertex)
A peach has 85 calories. It has w calories more than an orange. Write an expression for the number of calories in an orange. "MUST show work"
Answer:
Step-by-step explanation:
Let p represent the number of calories in a peach and g the number of calories in an orange.
Then p = g + w.
From this we get g = p - w.
In words: "The number of calories we get from an orange is equal to p, the number of calories from a peach, less w calories."
A line is parallel to the y-axis on a coordinate plane. Which best describes the slope of the line
Answer:
well if it is parallel it would but 2 lines going in the same direction. it will never touch
Step-by-step explanation:
Answer:
The slope of this line is undefined.
Explanation:
The slope of a line is rise over run, where the rise is the change in y value and the run is the change in x. Since there is no change in x when a line is parallel to the y-axis, any slope would mean you would divide by 0.
[tex]m=\frac{rise}{run}\\m = \frac{rise}{0} \\m= \frac{anything}{0}\\[/tex]
Since you cannot divide by 0 the answer will always be undefined no matter what the numerator is. The slope of any vertical line will be undefined.
Use technology to approximate the solution(s) to the system of equations to the nearest tenth of a unit. f(x)=x^2+4/4x+3 g(x)=|x+4|
Answer:
Solution 1
(x,y) = (-1,3)
Solution 2
(x,y) = (1,5)
Step-by-step explanation:
To easily solve this question, we use a graphing tool, or a calculator to plot each graph.
The solution of the system of equations corresponds to the intersection between both graphs
f(x)=x^2 + 4/4x + 3
g(x)=|x+4|
Please see image below
Solution 1
(x,y) = (-1,3)
Solution 2
(x,y) = (1,5)
Graphical methods or numerical methods such as Newton's method are used to approximate the solution(s) to the system of equations represented by f(x) and g(x) to the nearest tenth of a unit.
Explanation:To approximate the solution(s) to the given system of equations f(x) = x^2 + 4 / (4x + 3) and g(x) = |x + 4| using technology, one can employ a graphing calculator or graphing software. By plotting both functions on the same set of axes, the point(s) of intersection represent the solution(s) to the system. To find the approximate solution to the nearest tenth, it may be necessary to use the graph's zoom and trace features to accurately determine the x-values where the two graphs intersect.
If this graphical method is insufficient, numerical methods such as Newton's method can provide a more precise approximation.
Use the distributive property to simplify the expression 8(5x-9)
Answer:
[tex]40x-72[/tex]
Step-by-step explanation:
we have
[tex]8(5x-9)[/tex]
Applying the distributive property
taking the outer term and multiplying it by each term inside the parenthesis
so
[tex]8(5x-9)=8*5x-8*9[/tex]
[tex]40x-72[/tex]
Answer:
[tex]8(5x - 9) = 40 x - 72[/tex]
Step-by-step explanation:
Let a, b, and c be any real number. Then
[tex]a(b + c) = ab + bc[/tex]
This is called the distributive property.
The given expression is
[tex]8(5x - 9)[/tex]
Or
[tex]8(5x + - 9)[/tex]
Let a=8, b=5x and c=-9
We apply the distributive property to obtain:
[tex]8(5x - 9) = 8 \times 5 x + 8 \times - 9[/tex]
We simplify to get:
[tex]8(5x - 9) = 40 x - 72[/tex]
Marco left his house and went to the sporting goods store to buy a basketball. He then went to jays house. Together the boys headed to the park along the route shown. How far did Marco travel in all?
The map tells you 1 inch = 0.5 miles.
Multiply each dimension on the map by 0.5 to get the miles, then add them together:
House to Sports store = 2 x 0.5 = 1 mile.
Sports store to Jay's house = 3.75 x 0.5 = 1.875 miles.
Jay's house to park = 1.5 + 0.5 = 2 inches x 0.5 = 1 mile.
Total distance = 1 + 1.875 + 1 = 3.875 miles.
The total distance covered in miles is; 3.875 miles
What is the total distance travelled?From the map, we see that;
1 inch = 0.5 miles.
Now, total distance in inches is;
D = 2 + 3.75 + 1.5 + 0.5
D = 7.75 inches
Using the given conversion rate to miles, we have;
D = 7.75 * 0.5
D = 3.875 miles.
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A motorboat traveling downstream covers the distance between port M and port N in 6 hours. Once, the motorboat stopped 40 km before reaching N, turned around, and returned to M. This took the motorboat 9 hours. Find the speed of the motorboat in still water if the speed of the current is 2 km/hour.
Answer:
18 km/h
Step-by-step explanation:
Let S km be the distance between ports M and N, x km/h be the speed of the motorboat in still water. Then x-2 km/h is the speed of the motorboat upstream and x+2 km/h is the speed of the motor boat downstream.
1. The motorboat traveling downstream covers the distance between port M and port N in 6 hours, then
[tex]\dfrac{S}{x+2}=6[/tex]
2. Once, the motorboat stopped 40 km before reaching N, turned around, and returned to M. This took the motorboat 9 hours. Then
[tex]\dfrac{S-40}{x+2}+\dfrac{S-40}{x-2}=9[/tex]
From the first equation [tex]S=6(x+2)=6x+12.[/tex] Substitute it into the second equation:
[tex]\dfrac{6x+12-40}{x+2}+\dfrac{6x+12-40}{x-2}=9,\\ \\\dfrac{6x-28}{x+2}+\dfrac{6x-28}{x-2}=9.[/tex]
Now
[tex]\dfrac{(6x-28)(x-2)+(6x-28)(x+2)}{(x-2)(x+2)}=9,\\ \\(6x-28)(x-2+x+2)=9(x^2-4),\\ \\(6x-28)\cdot 2x=9x^2-36,\\ \\12x^2-56x-9x^2+36=0,\\ \\3x^2-56x+36=0,\\ \\D=(-56)^2-4\cdot 3\cdot 36=2704,\\ \\x_{1,2}=\dfrac{56+\sqrt{2704}}{2\cdot 3}=\dfrac{56\pm52}{6}=\dfrac{2}{3},\ 18.[/tex]
The speed of the motorboat cannot be less than the speed of the current, thus, x=18 km/h.
The speed of the motorboat in still water if the speed of the current is 2 km/hour is 18 km/hour.
Suppose the distance between port M and N =d
Suppose the speed of the motorboat in still water =x
The speed of the current =2 km/h (given)
So, the downstream speed of the boat = (x+2)
Upstream speed of the boat = (x-2)
What is speed?Speed is the distance covered in unit time.
According to the question, a motorboat travelling downstream covers the distance between port M and port N in 6 hours.
This means, [tex]\frac{d}{x+2} =6[/tex]
So, [tex]d=6(x+2)[/tex]
Distance covered by the motorboat when the motorboat stopped 40 km before reaching N = d-40
=[tex]6(x+2)-40[/tex]
=[tex]6x-28[/tex]
So, [tex]\frac{6x-28}{x+2} + \frac{6x-28}{x-2} =9[/tex]
So, [tex]x=18[/tex]
[tex]x=\frac{2}{3}[/tex](not possible)
Therefore, the speed of the motorboat in still water if the speed of the current is 2 km/hour is 18 km/hour.
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You are looking for your first credit card...?
Answer:
You are looking for your first credit card. You plan to use this credit card only for emergencies and to pay the credit card balance in full each month. Which credit card feature is most important?
a. No annual feeb. Low APR
c. Generous rewards program
d. No balance transfer fee
Solve the following system of equations.
-3x + 5y =85
x + 4y =34
A. x = 2, y = 18.2
B. x = 11, y = -10
C. x = -10, y = 11
D. x = 8, y = 6.5
Answer: option C
[tex]x=-10\\y=11[/tex]
Step-by-step explanation:
You can apply the elimination method:
- Multiply the second equation by 3.
- Add both equations to cancel out the variable x.
- Solve for y:
[tex]\left \{ {{-3x+5y=85} \atop {(3)(x+4y)=34(3)}} \right.\\\\\left \{ {{-3x+5y=85} \atop {3x+12y=102}} \right.\\-------\\17y=187\\y=11[/tex]
- Substitute y=11 into any of the original equations ans solve for x. Then:
[tex]x+4(11)=34\\x=34-44\\x=-10[/tex]
The answers are:
[tex]x=-10\\y=11[/tex]
Why?We can solve system of equations using several methods, but the simplest way to solve it, is isolating variables in terms of another variables.
So, isolating "x" from the second equation we have:
[tex]x + 4y =34\\x=34-4y[/tex]
Then, substituting "x" into the first equation, we have:
[tex]-3(34-4y) +5y =85\\-102+12y+5y=85\\17y=85+102\\17y=187\\y=\frac{187}{17}=11\\[/tex]
Now, substituting "y" into the second equation to calculate "x", we have:
[tex]x + 4(11) =34\\x=34-44\\x=-10[/tex]
So, the solutions for the system of equations are:
[tex]x=-10\\y=11[/tex]
Have a nice day!
Find the length of AC. Express your answer in terms of pi.
Answer options: 5, 30, 45, 15.
Answer:
The correct answer is 3πcm
Step-by-step explanation:
The length of an arc is calculated using the formula P=∅/360×2πr
where ∅is the angle the arc subtends at the center of the circle, and r is the radius of the circle of which the arc is part.
2r gives the diameter which from the diagram corresponds to AB=36 cm
therefore P=30/360×π×36
=3πcm
5pi is the answer
..............................