[tex]~~x^2+16\\ \\=x^2-(-16)\\\\=x^2-(4i)^2\\\\=(x+4i)(x-4i)[/tex]
Answer:
(x + 4)(x + 4)Step-by-step explanation:
Given expression:
x² + 16Clearly, 16 is a perfect square as 4 x 4 is 16.
Thus, this expression can be written as:
⇒ x² + 16⇒ x² + 4²Using the formula "a² + b² = (a + b)(a + b)"
⇒ x² + 4² ⇒ (x + 4)(x + 4)How many solutions does the equation
below contain?
-4-3t+ 1) - 7+ = 51 - 4
A.
no solution
B.
one solution
C. two solutions
D. infinitely many solutions
Answer:
A.no solution
Step-by-step explanation:
[tex]12t- 4 - 7t = 5t - 4[/tex]
[tex]12t - 7t = 5t - 4[/tex]
[tex]5t = 5t - 4[/tex]
[tex]5t - 5t = - 4[/tex]
[tex]0 = - 4[/tex]
it takes 1 1/2 hours to fill 1/2 of a tank how long will it take to fill 2 tanks completely
Answer:
15
Step-by-step explanation:
hope this helps
please help I will give brainiest pls
Looking for good answer on this
[tex]\dfrac{6x-24}{16-x^2}\\\\=\dfrac{6(x-4)}{4^2 -x^2}\\\\=\dfrac{6(x-4)}{(4+x)(4-x)}\\\\=-\dfrac{6(x-4)}{(x+4)(x-4)}\\\\=-\dfrac{6}{x+4}[/tex]
Please answer .....
there are 5 blue, 4 red, 1 yellow and 2 green bead in a bag.
A) Find the probability that a bead chosen at random from the bag is blue?
B) Find the probability that a bead chosen at random from the bag is red or yellow?
C) Find the probability that a bead chosen at random from the bag is white?
D) Find the probability that a bead chosen at random from the bag is NOT yellow?
Q4) A fruit bowl contains 4 apples, 3 oranges, and 8 bananas, find the probability of
a) Randomly selected orange
b) Randomly selected apples
c) Randomly selected apple or banana
d) Randomly selected orange ,replace it then select banana
Q5) a number cube labeled by the numbers (3,3,3,3,5,5),what is the probability of
a) The number cube shows a 5
b) The number cube shows a 3
c) Having 5 and then 5 when the number cube rolled twice
d) Having 5 and then 3 when the number cube rolled twice
Answer:
A) 5/12
B) 5/12
C) 0/12
D) 11/12
-------------
Q4.
A) 3/15
B) 4/15
C) 12/15
D) 8/15
-----------------
Q5.
A) 2/6 or 1/3
B) 4/6 or 2/3
C)
D)
Step-by-step explanation:
Write the equation of the line that is parallel to the line y=3x+7 and passes through the
point (-4,-14).
Answer:
Step-by-step explanation:
hello :
note :
Use the point-slope formula.
y - y_1 = m(x - x_1) when : x_1= -4 y_1= -14
m= 3 (parallel means same slope)
an equation in the point-slope form is : y +14 =3(x+4)
please help me find Find AB
Answer:
AB=4
Step-by-step explanation:
[tex]\frac{10+x}{2}[/tex][tex]=7[/tex]
Multiply both sides by 2.
10+x=14
x=14-10
x=4
Barry's income can be calculated as $17 times the number of hours worked (h) added to his commission of $200. If he subtracts $300 to pay a bill, his income totals $580. Which expression represents Barry's income?
Simplify the following expression.
6.64 ÷ 8
A.
1.245
B.
0.664
C.
0.83
D.
0.93
Answer:
[tex]0.83[/tex]
Step-by-step explanation:
[tex]6.64 \div 8[/tex]
[tex]0.83[/tex]
Answer:
The answer should be C.)0.83, hope this helps.
the function f(x)=2^x and g(x)=f(x)+k if k=2 what can be concluded about the graph of g(x)?
i need help please !!
Answer:
22x + 155
Step-by-step explanation:
9(x-3)+ 13(x+14) use distributive law
9x - 27 + 13x + `182 gather 'like' terms
(9x+13x) + ( -27+ 182) simplify
22x + 155
An air traffic controller is tracking two planes. To start, Plane A is at an altitude of 4057 feet and Plane B is at an altitude of 5000 feet. Plane A is gaining altitude at 60.75 feet per second and Plane B is gaining altitude at 40.25 feet per second.
How many seconds will pass before the planes are at the same altitude?
What will their altitude be when there’re at the same altitude?
Answer:
46 seconds6851.5 feetStep-by-step explanation:
The altitude of each plane can be expressed by an equation that adds the initial altitude and the product of time and its rate of climb.
plane A: y = 4057 +60.75t
plane B: y = 5000 +40.25t
__
We want to find the time when their altitudes are the same:
4057 +60.75t = 5000 +40.25t . . . . equate the expressions for y
20.50t = 943 . . . . . . . . . subtract (40.24t +4057)
t = 46 . . . . . . . . . . . . divide by the coefficient of t
At t=46, the altitude of the planes will be ...
y = 5000 +40.25(46) = 5000 +1851.5 = 6851.5
The planes are at the same altitude after 46 seconds.
Both planes will be at an altitude of 6851.5 feet.
The area of circles
Answer:
Formula for the area of a circle;
A = π[tex]r^{2}[/tex]Where 'π' represents pi(3.14 or 22/7), and 'r' represents the radius which is being squared.
Plug in the radius into this formula:-
A = π[tex]r^{2}[/tex]
Note: I will be using 3.14 as pi(π).A = 3.14(4^2)
A = 3.14(16)
A = 50.24 centimetres is the area for this circle.
Heather invested $11,600 in an account that pays 5% simple interest. If she invests the money for 6 years, how much will she have?
The total amount in the account after 6 years is $______?
Answer
$15080
Step-by-step explanation:
ok so i havent done these in a while but basically.
First, we need to find out what the 6% is.
[tex]\frac{5}{100} \times \frac{11600}{1}[/tex]
5/100 because it's PERCENT, and well we need to put the 11600 out of 1.
Wich gives us
$580. THen, we multiply that by 6, (6 years). Which gives us
$3480. Now, we add that to the $11600. WHich gives us
$15,080.
Hope this helps!
Please I need a lot of help
Answer:
that's a computer I'm sorry di ko po Alam
Step-by-step explanation:
ty sa points
A cylinder has a diameter of 6 cm and a height of 3 cm. What is the surface area of the cylinder? Enter your answer, in exact form, in the box.
If the diameter and height of the cylinder are 6 cm and 3 cm. Then the surface area of the cylinder is 56.55 square cm.
What is a cylinder?A cylinder is a closed solid that has two parallel circular bases connected by a curved surface.
A cylinder has a diameter of 6 cm and a height of 3 cm.
Then the surface area of the cylinder will be
[tex]\rm SA = \pi d h[/tex]
We have
d = 6 cm
h = 3 cm
Then the surface area will be
[tex]\rm SA = \pi \times 6 \times 3 \\\\SA = 56.55[/tex]
More about the cylinder link is given below.
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please help
Find the volume of each prism. Round to the nearest tenth if nessary
Write a Pseudo code for average speed
Answer:
SEQUENCE represents linear tasks sequentially performed one after the other.
WHILE a loop with a condition at its beginning.
REPEAT-UNTIL a loop with a condition at the bottom.
FOR another way of looping.
IF-THEN-ELSE a conditional statement changing the flow of the algorithm.
CASE the generalization form of IF-THEN-ELSE
Step-by-step explanation:
Always capitalize the initial word (often one of the main 6 constructs).
Have only one statement per line.
Indent to show hierarchy, improve readability, and show nested constructs.
Always end multiline sections using any of the END keywords (ENDIF, ENDWHILE, etc.).
Keep your statements programming language independent.
Use the naming domain of the problem, not that of the implementation. E.g., “Append the last name to the first name” instead of “name = first+ last.”
Keep it simple, concise, and readable.
Which of the following steps would you perform to the system of equations
below so that the equations have opposite y-coefficients?
4x+2y - 4
12x - y - 26
O A. Divide both sides of the top equation by 3
O B. Multiply both sides of the top equation by 2
O C. Multiply both sides of the bottom equation by 2
O D. Divide both sides of the bottom equation by 3
Step-by-step explanation:
please mark as brainliest please
.......................................................
What is the scale factor of the enlargement of shape A to shape B?
Answer:
scale factor = 6
Step-by-step explanation:
the scale factor is the ratio of corresponding sides, shape B to shape A
base of shape A = 1 , base of shape B = 6 , then
scale factor = [tex]\frac{6}{1}[/tex] = 6
After finding the ratio of their corresponding sides of triangles the scale factor we get is 6.
The difference in scale between an original item's scale and a new object that is its representation but is larger or smaller is known as a scale factor.
From figure
For small triangle:
base = 1 units
For large triangle:
base = 6 units
Now the scale factor = ratio of adjacent sides
Scale factor = (Base of large triangle)/(Base of small triangle)
Scale factor = 6/1
Scale factor = 6
Hence,
The scale factor is 6.
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Leila wanted to order her IFTAR meal from La Gondola, Al Khobar. The menu stated that their pasta is a blend of wheat and corn. La Gondola does not disclose the percentage of each ingredient in the blend but we know that the wheat in the blend contains 5% protein, and the corn in the blend contains 10% protein. Overall, each 57 gram serving of pasta contains 4 grams of protein.
Leila told her sister that there was more wheat than corn in the pasta. Use multiple representations to justify if this is a true statement. (You may use DESMOS for graphing. You must also put in the algebraic solution and a table.)
Step-by-step explanation:
Let the amount of wheat is x and amount of corn is y.
The total amount of pasta is
x + y = 57Amount of protein in same pasta is
5% of x + 10% of y = 4or
0.05x + 0.1y = 4The graphical solution is attached
x = 34, y = 23It is easy to solve the system by substitution
y = 57 - x0.05x + 0.1(57 - x) = 40.05x + 5.7 - 0.1x = 40.1x - 0.05x = 5.7 - 40.05x = 1.7x = 1.7/0.05x = 34Then the value of y is
y = 57 - 34 = 23As we see x > y, so Leila is right
The above problem is solved using Multiple Representations. Multiple representations are used to achieve a deeper comprehension of concepts related to the same operation.
How do we evaluate the veracity of Leila's assertion?We can arrive at whether the statement is true or false by solving for the value of Y using the graphical method. Where Y is the amount of wheat and X is the amount of corn.
Our function is given as follows:
X + Y= 57. ..........1
Recall that the total amount of pasta is 57 grams
Recall as well that the total amount of protein in the pasta is given as:
0.05x + 0.1y= 4grams.......2
By inputting equations 1 and 2 into the Desmos Graph, we have x to be equal to = 34, and y = 23. (please see the attached image).
Recall that Leila's assertion was that there is more corn in the Pasta. Since x is the amount of corn, then Leila's assertion is True that: x>y.
The algebraic solution is arrived at using substitution.
Rewriting equation (1), we have
y = 57 - x .......................(3)
Let us substitute y into equation (2) above. That gives us:
0.05x + 0.1(57 - x) = 4.........................(4)
Expanding the brackets, we obtain
0.05x + 5.7 - 0.1x = 4
Collecting like terms, we can rewrite the quation as:
0.1x - 0.05x = 5.7 - 4
0.05x = 1.7
Rewriting the equation such that it is subject to x, we have
x = 1.7/0.05
x = 34
If from the above, x = 34, inputting that into equation (3) above, we have
y = 57 - 34; Therefore,
y = 23
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You would use a back-to-back stem-and-leaf plot when you want to analyze the heights of the boys on the basketball team.
False
True
Answer:
true because there are going to be many heights already
Step-by-step explanation:
i it's true
this is because already there will be
so many heights
what number equals 2/9?
The number of jelly beans placed in jars by a class of kindergarteners is normally distributed with an unknown population
mean and standard deviation. A random sample of 20 jars is taken and results in a sample mean of 43 jelly beans and
sample standard deviation of 6 jelly beans.
Using the t-distribution, the 80% confidence interval for the mean number of jelly beans is (41.22, 44.78).
What is a t-distribution confidence interval?The confidence interval is:
[tex]\overline{x} \pm t\frac{s}{\sqrt{n}}[/tex]
In which:
[tex]\overline{x}[/tex] is the sample mean.t is the critical value.n is the sample size.s is the standard deviation for the sample.The critical value, using a t-distribution calculator, for a two-tailed 80% confidence interval, with 20 - 1 = 19 df, is t = 1.3277.
The other parameters are given as follows.
[tex]\overline{x} = 43, s = 6, n = 20[/tex].
Hence, the bounds of the interval are given by:
[tex]\overline{x} - t\frac{s}{\sqrt{n}} = 43 - 1.3277\frac{6}{\sqrt{20}} = 41.22[/tex]
[tex]\overline{x} - t\frac{s}{\sqrt{n}} = 43 + 1.3277\frac{6}{\sqrt{20}} = 44.78[/tex]
The 80% confidence interval for the mean number of jelly beans is (41.22, 44.78).
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The sum of the interior angle of a polygon is 1260 degrees. How many sides does the polygon have?
Answer: 9 sides
Step-by-step explanation:
If this is a perfect polygon then the answer is 9 sides. A perfect polygon is a polygon where all the sides and angles are congruent to each other.
180°(n-2) = 1,260°
n - 2 = 7
n = 9
A game requires rolling a six-sided die numbered 1 to 6 and flipping a coin. What is the
probability rolling an even number and flipping a head
Answer:
1/4
Step-by-step explanation:
on flipping a coin, we either get a heads or a tails and both the events are equally likely. So the probablity of getting a tails is 1/2.
Now
On rolling a die, we can get 6 possible outcomes(1,2,3,4,5,6)
But the favourable outcomes (an even number) are only 3. So the probablity of getting an even number is 3/6=1/2
In case. we have 2 events that need to occur together, we simply need to multiply their individual probablities to get the probablity of getting both the events together
So our required answer is
p(even number)× p(tails)= 1/2 × 1/2 = 1/4
A swimming pool is in the shape of a cylinder 7 feet deep and 9 feet in radius. Find the exact volume of the pool.
Answer:
16
Step-by-step explanation:
Hope this helps
find the value of x and y in the figure below
Step-by-step explanation:
First find out the value of X and second find the value of Y and where is figure
Height of a Toy Rocket A toy rocket (not internally powered) is launched straight up from the top of a building 50 ft tall at an initial velocity of 200 ft per sec. a. Give the function that describes the height of the rocket in terms of timet b. Determine the time at which the rocket reaches its maximum height and the maximum height in feet. c. For what time interval will the rocket be more than 300 ft above ground level? d. After how many seconds will it hit the ground?
The height of the toy is an illustration of the height function
The function of the toy velocityThe given parameters are:
Initial velocity, Vo = 200 ft per secInitial height, H = 50 ftThe function of the height is calculated as:
h(t) = -16t² + Vot + H
This gives
h(t) = -16t² + 200t + 50
Hence, the velocity function is h(t) = -16t² + 200t + 50
The time of maximum heightIn (a), we have:
h(t) = -16t² + 200t + 50
Differentiate
h'(t) = -32t + 200
Set to 0
-32t + 200 = 0
Subtract 200 from both sides
-32t = -200
Divide both sides by -32
t = 6.25
Substitute 6.25 for t in h(t)
h(6.25) = -16 *6.25² + 200 * 6.25 + 50
h(6.25) = 675
Hence, the time to reach the maximum height is 6.25 seconds and the maximum height is 675 feet
When the rocket will be at a height more than 300This is represented as
h(t) >300
So, we have:
-16t² + 200t + 50 > 300
Subtract 300 from both sides
-16t² + 200t - 250 > 0
Using a graphical calculator, we have:
t = 11.09s and t = 1.41 s
Hence, the rocket will be at a height more than 300 at 11.09s and 1.41 s
When it will hit the ground?This means that
h(t) = 0
So, we have:
-16t² + 200t + 50 = 0
Using a graphical calculator, we have:
t = 12.75
Hence, the rocket will hit the ground at 12.75s
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