Answer:
The domain of the function in interval notation is -∞ < x < -2, -2 < x < 4, x > 4
Step-by-step explanation:
The given function is presented as follows;
[tex]G(x) = \dfrac{x^2 + 8 \cdot x + 12}{x^2 - 2 \cdot x - 8}[/tex]
The function given in rational format will not be defined when the value of the denominator = 0
Therefore, for the function to be undefined, we have;
x² - 2·x - 8 = 0
(x - 4)·(x + 2) = 0
Which gives;
x = 4, or x = -2
Therefore, the function is undefined for x = 4 and x = -2
The domain of the function in interval notation = -∞ < x < -2, -2 < x < 4, x > 4
10-3x=16 solving two-step equations
Answer:
x = -2
Step-by-step explanation:
10 - 3x = 16
-3x = 16 - 10
-3x = 6
x = 6/-3
x = -2
Will mark Brianliest !!!!!!!!!!!!!! Answer correctly please !!!!
Answer:
54 degrees
Step-by-step explanation:
Since we know that the angles are supplementary, we can set them to be equal to 180 degrees when combined.
(7x+14) + (5x-26)=180
Drop the parentheses.
7x+14+5x-26=180
Combine like terms.
12x-12=180
Add 12 to both sides.
12x=192
Divide both sides by 12.
x=16
Since the question asks for the measure of angle B, we need to plug x back into that expression to find its measure.
5(16)-26
80-26
54
Angle B has a measure of 54 degrees.
HTH :)
Rounding Decimals 5.5252; ones
Answer:
6
Step-by-step explanation:
Identify the ones place and check the number to the right.
5.5252
Since we round up if the number to the right is greater than or equal to 5, and the number is a 5, we round up.
Therefore,
5.5252 ≈ 6
Hope this helps.
What is the equation, in slope-intercept form, of the line that passes through the points (−24, 5) and (16, −20)?
A. Y = -8/5x + 10
B. Y = -8/5x - 10
C. Y = -5/8x - 10
D. Y = -5/8x + 10
Answer:
C (Y = -5/8x - 10)
Step-by-step explanation:
first find the slope (y₂ - y₁) ÷ (x₂ - x₁)
(5 - (-20)) ÷ (-24 - 16)
-5/8 = slope (m)
now that we know the slope is -5/8 we can rule out A and B
now to find the y intercept just substitute a point in for x and y
5 = (-5/8)(-24) + b
multiply
5 = 15 + b
subtract 15 from both sides tp isolate b
-10 = b
I need help on this one
Answer:
d
Step-by-step explanation:
please give brainliest
write 0.00000029 in scientific notation.
Answer:
2.9 x 10∧-7
Step-by-step explanation:
Answer:
2.9 × 10^-7
Hope this helps
Please help!!!!!!!!!!
The function n(t) = 825(1.12)t models the number of bacteria, n(t), after t weeks. What does 825 represent?
Answer: it represents “n” which is the number of bacteria
Step-by-step explanation:
Triangles P Q R and S T U are shown. Angles P R Q and T S U are right angles. The length of P Q is 20, the length of Q R is 16, and the length of P R is 12. The length of S T is 30, the length of T U is 34, and the length of S U is 16. Using the side lengths of △PQR and △STU, which angle has a sine ratio of Four-fifths?
Answer:
<p
Step-by-step explanation:
Answer: <p
Step-by-step explanation: I did the quiz
The equation of a line perpendicular to the line represented by the equation y=-1/2-5x and passing through (6,-4) is
Answer:
line represented by the equation y=−12x−5 and passes through (6,−4) ... y−6=2(x+4) ... First find the slope m for the new line, rule for a perpendicular slope is: your equation is in slope intercept form y=mx+b : ... m=−12 so your new slope m'=−1−12=2 ... graph{y=-1/2x - 5 [-18.92, 21.08, -14.56, 5.44]}.
Plz mark brainliest
Steve has 8 biscuits in a tin. There are 5 digestive and 3 chocolate biscuits. Steve takes two biscuits at random from the tin. Work out the probability that he chooses two different types of biscuits.
Probability that he chooses two different types of biscuits is 53.65 %.
What is probability?Probability is a measure of the likelihood of an event to occur. Many events cannot be predicted with total certainty. We can predict only the chance of an event to occur i.e. how likely they are to happen, using it.
Given
Total biscuits, n = 8
Digestive biscuits = 5
Chocolate biscuits = 3
There are two patterns to chose two different biscuits; a digestive then a chocolate or a chocolate and then a digestive.
∴ The probability of choosing a digestive then a chocolate
= [tex]\frac{5}{8}\times\frac{3}{7}[/tex]
= [tex]\frac{15}{56}[/tex]
= 0.267
The probability of choosing chocolate and then a digestive.
= [tex]\frac{3}{8} \times\frac{5}{7}[/tex]
= [tex]\frac{15}{56}[/tex]
= 0.267
Hence, The combined probability
= [tex]\frac{15}{56}+ \frac{15}{56}[/tex]
= [tex]0.536[/tex]
= 53.6 5 %
Probability that he chooses two different types of biscuits is 53.65 %.
Find out more information about probability here
https://brainly.com/question/11234923
#SPJ2
Line A has a slope of -4/3 and line B has a slope of -3/4. Are both lines perpendicular?
Answer:
no they are not
Step-by-step explanation:
Answer:
Yes, they are perpendicular to each other.
Step-by-step explanation:
If lines are corresponding in any way, they are automatically perpendicular. These lines are corresponding to each other when switching the x and y values.
Feel free to give brainliest.
Have an excellent day!
help! which one is it?
Answer:
quadratics and absolute value
Step-by-step explanation:
they both go up but Quadratic is U and absolute value is V
what is the common difference of 4,-3,-10,17 ?
Answer:
13 and -13
Step-by-step explanation:
because 17 - 4= 13 and -10 - -3 = 7 because two neg equals pas
16. (03.06 LC)
What is the value of 1-251? (1 point)
Choose the word that correctly completes the statement. Triangle A B C is shown. Angle A C B is 45 degrees, angle C B A is 75 degrees, and angle B A C is 60 degrees. Since angle B is the largest angle, Line segment A C is the ________ side. adjacent included longest shortest
Answer:
longest
Step-by-step explanation:
was Answer Expert Verified on a different question :)
Answer:
Longest
Step-by-step explanation:
Edgen 2021
A person has $28,000 invested in stock A and stock B. Stock A currently sells for $50 a share and stock B sells for $60 a share. If stock B triples in value and stock A goes up 50%, his stock will be worth $69,000. How many shares of each stock does he own?
Answer:
Number of stock A = 200
Number of stock B = 300
Step-by-step explanation:
Let :
Number of stock A shares = a
Number of stock B shares = b
Worth of stock A = 50 * a = 50a
Worth of stock B = 60 * b = 60b
50a + 60b = 28000 - - - (1)
Triple the value of stock B:
3 * 60 = 180
Value of stock A goes up by 50%
(100 + 50)% * 50 = 1.5 * 50 = 75
75a + 180b = 69000 - - - (2)
50a + 60b = 28000
75a + 180b = 69000
Multiply equation 1 by 3 and subtract
150a + 180b = 84000
75a + 180b = 69000
75a = 15000
a = 15000/75
a = 200
75(200) + 180b = 69000
15000 + 180b = 69000
180b = 69000 - 15000
180b = 54000
b = 300
How much pure alcohol must a nurse add to 10 cubic centimeters of a 60% alcohol solution to strengthen it to a 90% solution? Plsss help ASAP
10 cubic centimeters of a 60% alcohol solution, would mean 10 x 60% = 6 cc is alcohol the other 4 cc is water.
To make a 90% solution, the water would be 10% of the solution.
If 4 cc is 10%, the total is 40 cc.
40 - 10 = 30 cc
30 cubic centimeters needs to be added.
Hey i need help finding the orthocenter for the following points, please show the steps you used. thanks
(-3, 0.5)
(3,3)
(2,-1)
9514 1404 393
Answer:
(81/43, -31/43) ≈ (1.884, -0.7209)
Step-by-step explanation:
The orthocenter is the intersection point of the altitudes of the triangle. Since this is not a right triangle, you need to find the equations of the altitude lines, then find where those intersect.
If we call the points A, B, C in the order given, the attached figure shows the altitude lines from B perpendicular to AC, and from C perpendicular to AB.
We can find the equation of the perpendicular line using the form ...
∆x·x +∆y·y = c
where ∆x and ∆y are the differences in coordinates between the points on the "side" and the value of constant 'c' is determined by evaluating the expression using x and y as the coordinates of the opposite vertex.
__
For line AC, we have ...
(∆x, ∆y) = C - A = (2, -1) -(-3, 0.5) = (2+3, -1-0.5) = (5, -1.5)
Then the equation of the first altitude line is ...
5x -1.5y = 6(3) -1.5(3) = 10.5
Multiplying by 2 puts this in standard form:
10x -3y = 21
__
For line AB, we have ...
(∆x, ∆y) = B - A = (3, 3) -(-3, 0.5) = (3+3, 3-0.5) = (6, 2.5)
Then the equation of the second altitude line is ...
6x +2.5y = 6(2) +2.5(-1) = 9.5
Multiplying by 2 puts this in standard form:
12x +5y = 19
__
Then the orthocenter is the solution to the system of equations ...
10x -3y -21 = 0
12x +5y -19 = 0
This set of equations can be solved a number of ways. One is the "cross-multiplication" method.
1/(10·5 -12·(-3)) = x/(-3·(-19) -5·(-21)) = y/(-21(12) -(-19)(10))
x = 162/86 = 81/43
y = -62/86 = -31/43
The orthocenter is (81/43, -31/43) ≈ (1.884, -0.7209).
_____
Additional comment
The "cross multiply method" is based on cross products when the equations are written in standard form:
ax +by +c = 0
dx +ey +g = 0
Usually, the coefficients are written in two rows of four, with the first column repeated at the end:
a b c a
d e g d
Then cross products are formed, where diagonal down is positive and diagonal up is subtracted from that:
p1 = (ae -db), p2 = (bg -ec), p3 = (cd -ga)
These give the solution to the equations when put in the form ...
1/p1 = x/p2 = y/p3 ⇒ x = p2/p1 and y = p3/p1
If you look at videos of this "cross multiply method," they will put the 1/p1 at the end of the string of equalities, and they will use the coefficients in the order starting with b instead of a. I find the arrangement here easier to remember, so less likely to get confused.
Further comment
You can, of course, find the slopes of the lines, and their opposite reciprocals, then use a point-slope form or some other method for writing the equations of the altitude lines. The solution to the equations can proceed by substitution or elimination. No doubt these methods are somewhat familiar. The method used here tries to get to the answer much more quickly with a lot less writing. (Unfortunately, it takes a bit of writing to explain it all.)
1. In order to increase sales the price of a Concorde airliner is reduced from
$30,000,000 to 28,400,000, what percentage reduction is this?
Answer:
5.33%
Step-by-step explanation:
(28,400,000÷30,000,000 ) × 100%
= 94.67%
the reduced amount = 100 - 94.67
= 5.33%
Answer:
5.333333333333334%
Step-by-step explanation:
5.333333333333334% of 30,000,000 = 1,600,000
Tip: Don't get scared by numbers, percentage don't change by how many zeros, i found this just by figuring out by: 1.6 is what percentage of 30?
You could find it on a "Percentage calculator"
Hope this helps!
Ace Carlos
I have a two digit number the sum of the digits is 12 the first digit is 4 Less Than 3 times the second what is my number
Answer:
84
Step-by-step explanation:
Let the first digit = x
Let the second digit =y
x + y = 12
x + 4 = 3*y
===========
From the second equation, we learn that x = 3y - 4
Put that into the first equation.
3y - 4 + y = 12 Combine the left side
4y - 4 = 12 Add 4 to both sides
4y = 16 Divide by 4
4y/4 = 16/4
y = 4
=================
x + 4 = 12
x + 4 - 4 = 12-4
x = 8
So the number is 84
An item is originally priced 68.89 dollars. It was on sale for 42 percent of the original price. Which is an estimate of the sale price? A. 2.00 dollars B.3.50 dollars C. 20 dollars or D. 28 dollars.
Answer:
D. 28 dollars
Step-by-step explanation:
42% = .42
"of" means to multiply
68.89 × .42= 28.9
28 is the closest answer.
Answer:
The answer would be D.28 dollars
Step-by-step explanation:
Its 28 dollars because,
Discount = Original Price x Discount %/100
Discount = 68.99 × 42/100
Discount = 68.99 x 0.42
You save = $28.98
Final Price = Original Price - Discount
Final Price = 68.99 - 28.9758
Final Price = $40.01
5, 18, 6, 18, 13 WHATS THE INTERQUARTILE RANGE??
Answer: 12.5
Step-by-step explanation:
25th Percentile: 5.5
50th Percentile: 13
75th Percentile: 18
Interquartile Range: 12.5
four times a number is greater then 48. what are the possible values for the number?
Any number that is 13 to Infinity
Any number greater then 12
Assume;
Given number = a
So,
Four times a number;
4 × a
4a
Greater then 48
So,
4a > 48
By solving inequality
a > 12
So,
Any number greater then 12 is the possible value
Learn more:
https://brainly.com/question/1301963?referrer=searchResults
10=7-m two step equations
Step-by-step explanation:
10=7-m
10-7=-m
3=-m
m=-3
Answer and Step-by-step explanation:
For this two step equation, to solve for m, we need to subtract 7 from both sides, then divide by -1 to get m.
10 = 7 - m
3 = -m
-3 = m
#teamtrees #WAP (Water And Plant)
can i get some help on this im confused!!!
Step-by-step explanation:
a) ST = 7m
b) SU = 8m
c) angle R = 46deg
d) angle Q = 75deg
e) angle S = 59deg
Solve for x. Round your answer to the nearest tenth if necessary.
Answer: 13.56
Step-by-step explanation:
Pythagorean theorem says base^2 + perpendicular ^2 = hypotenuse^2
So base^2 + 21^2 = 25^2
Or 25^2 - 21^2 = base^2 = 184
Base = root 184 or 13.56
PLease answer the slope
!!!!!!!!!!!!!!!!!!!
what the slope of (15,9) (-10,3)
♥️♥️♥️♥️♥️♥️♥️♥️♥️♥️♥️♥️♥️♥️
[tex]slope = \frac{3 - 9}{ - 10 - 15} \\ [/tex]
[tex]slope = \frac{ - 6}{ - 25} \\ [/tex]
[tex]slope = \frac{6}{25} \\ [/tex]
♥️♥️♥️♥️♥️♥️♥️♥️♥️♥️♥️♥️♥️♥️
Answer:
The slope is [tex]\frac{6}{25}[/tex] or [tex]0.24[/tex].
Step-by-step explanation:
This is the formula to calculate the slope from two given points: [tex]slope=\frac{y_2-y_1}{x_2-x_1}[/tex] . Now, substitute (x1, y1) and (x2, y2) for (15,9) and (-10,3). [tex]slope=\frac{3-9}{-10-15}[/tex] . That equation becomes [tex]slope=\frac{-6}{-25}[/tex] . You have to change [tex]\frac{-6}{-25}[/tex] to [tex]\frac{6}{25}[/tex] . The slope is 6/25 or in decimal form, 0.24.
Write the word sentence as an equation. Then solve. The sum of a number y and −3 is −8.
need asap
Answer:
y + (-3) = -8
Step-by-step explanation:
i just know
pls mark branliest