Answer:
When a number and its pair are added, the sum is greater
11. Find the solutions of x^2-x-30 = 0.
Please give a walkthrough/step by step I am trying to learn how to do it!
To find the solutions of quadratic equation, there are two ways to do which are:
FactorizeQuadratic FormulaStep 1
- Factor the expression.
To factor the expression, refer below:
[tex] \displaystyle \large{ (x - a)(x - b) = {x}^{2} - bx - ax + ab}[/tex]
For bx and ax, both can be common-factored. Therefore
[tex] \displaystyle \large{ (x - a)(x - b) = {x}^{2} - (b + a)x + ab}[/tex]
From the above, we conclude that:
The middle term is b+aThe last term is a×bThus, we have to find two numbers that satisfy a+b and a×bFrom the expression, 30 comes from 5×6 and when 5-6 = -1. Therefore, a can be 5 and b can be 6.
[tex] \displaystyle \large{{x}^{2} - x - 30 = (x + 5)(x - 6)}[/tex]
Because in the middle term, it is -x which is negative, we have to let the highest number become negative.
From the factored expression:
The middle term = 5x + (-6x) = -xThe last term = 5 × (-6) = -30Then we replace the standard equation with factored form.
[tex] \displaystyle \large{ (x + 5)(x - 6) = 0}[/tex]
For this part, we solve like a linear equation where we isolate x. Just think you are solving two linear equations!
Hence
[tex] \displaystyle \large{ x = - 5, 6}[/tex]
Therefore, the solutions are x = -5, 6.
The temperature in a town is 33.6°F during the day and - 17.3°F at night. Find the difference in the temperatures.
The difference in temperature is
F.
Answer:
the difference between the temperatures is -50.9. f=-50.9
Step-by-step explanation:
33.6°F+17.3°F=50.9
33.6°F+F= -17.3°F
33.6°F+(-50.9°F= -17.3°F
so, F=-50.9°F
Step-by-step explanation:
d=T2-T1=(-17.3-33.6)=-50.9°F
Please help me with these questions if you have time
Answer:
Use the following formulas for the tables
Step-by-step explanation:
For the tables given bellow use these formulas for part 7 a and b
y2-y1 over x1-x1
that would give us the slope then plug that into y=mx+b
Answer:
7. a. y=5x+29
b. y=9x+4
l have answer question number 7a and 7b
Help finding the sketch of a graph pls i’ll rate brainliest
Answer:
A
Step-by-step explanation:
X^3+1
Y int = 1
X int = -1
We can clearly see that the x int(when y = 0) for c = -3 so C is incorrect.
b is wrong because it's a quadratic(ax^2+bx+c) and d wrong because it linear(y=mx+c).
Knowing all this we can safely say that A is the correct answer choice.
Answer:
we firstly need to find x intercept and y intercept
If a = b, then a^2 = b^2
What is the proof of this statement?
Step-by-step explanation:
a²=b²
since a=b, therefore we can write a in place of b or b in place of a,
a²=a² or b²=b²
Hence, it is proved.
I hope it helped U
I hope it helped Ustay safe stay happy
What is the least common multiple of 8, 17, and 14?
Answer:
952
Step-by-step explanation:
LCM(8,14) = (8 × 14) = (8 × 14) / 2 = 112 / 2 = 56
LCM(56,17) = (56 × 17)
= (56 × 17) / 1
= 952 / 1
= 952
Therefore,
LCM (Lowest common multiple) (8, 14, 17) = 952
if 5-3(2a+1)=-4a+10, what is the value of a+2
Answer:
-2
BRAINLIEST, PLEASE!
Step-by-step explanation:
5 - 3(2a + 1) = -4a + 10
5 - 6a - 3 = -4a + 10
2 - 6a = -4a + 10
-2a = 8
a = -4
-4 + 2 = -2
Answer:
a+2 = -4+2 = -2
Step-by-step explanation:
5-3(2a+1)=-4a+10
Distribute
5 - 6a -3 = -4a +10
Combine like terms
-6a +2 = -4a +10
Add 6a to each side
-6a+2 +6a = -4a+6a +10
2 = 2a+10
Subtract 10 from each side
2-10 =2a+10-10
-8 = 2a
Divide by 2
-8/2 =2a/2
-4=a
Milan sold an article for Rs 450 with a loss of 10%. Find his CP. At what price it should be sold so as to gain 5 %.
Pls-- help request!!
Evaluate using the order of operations. Show your work.
2. (30.6 +5.03) - 7
[tex]\huge\text{Hey there!}[/tex]
[tex]\huge\boxed{\mathsf{{2 (30.6 + 5.03) - 7}}}\\\huge\boxed{\mathsf{\rightarrow 2(\bold{35.63)}} - 7}\\\huge\boxed{\rightarrow\mathsf{\bold{71.26}} - 7}\\\huge\boxed{\rightarrow\mathsf{\bf = 64.26}}\\\huge\boxed{\huge\text{Therefore, your answer is: \bf 64.24}}[/tex]
[tex]\huge\text{\text{Good luck on your assignment \& enjoy your day!}}[/tex]
~[tex]\frak{Amphitrite1040:)}[/tex]
Answer:
0.5
Step-by-step explanation:
2.30 divided by 4.5 = 0.5
please enjoy your day <3
Find the differential of the function w=x^(4)sin(y^(4)z^3)
Step-by-step explanation:
[tex]w = x^4\sin(y^4z^3)[/tex]
The differential [tex]dw[/tex] is
[tex]dw = 4x^3\sin(y^4z^3)dx [/tex]
[tex]\:\:\:\:\:\:\:\:\:\:\:+ x^4\cos(y^4z^3)(4y^3z^3)dy [/tex]
[tex]\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:+ x^4\cos(y^4z^3)(3y^4z^2)dz[/tex]
which equation shows the valur of -2/5- (-9/15)
Answer:
3/15
Step-by-step explanation:
-2/5=-6/15
(-6-(-9))/15=(-6+9)/15=3/15
Really need to someone to break this down so I can understand it
(a) Find the slope of the curve y= x^2 - 2x - 3 at the point P(2, -3) by finding the limit of the secant slopes through point P.
(b) Find an equation of the tangent line to the curve at P(2, -3)
Answer:
Part A)
The slope is two.
Part B)
[tex]\displaystyle y = 2x - 7[/tex]
Step-by-step explanation:
Part A)
We want to find the slope of the curve:
[tex]\displaystyle y = x^2 - 2x - 3[/tex]
At the point P(2, -3) by using the limit of the secant slopes through point P.
To find the limit of the secant slopes, we can use the difference quotient. Recall that:
[tex]\displaystyle f'(x) = \lim_{h \to 0} \frac{f(x+h) - f(x)}{h}[/tex]
Since we want to find the slope of the curve at P(2, -3), x = 2.
Substitute:
[tex]\displaystyle f'(2) = \lim_{h \to 0} \frac{f(2 + h) - f(2)}{h}[/tex]
Simplify. Note that f(2) = -3. Hence:
[tex]\displaystyle \begin{aligned} f'(2) &= \lim_{h\to 0} \frac{\left[(2+h)^2 - 2(2+h) - 3\right] - \left[-3\right]}{h} \\ \\ &=\lim_{h \to 0}\frac{(4 + 4h + h^2)+(-4-2h)+(0)}{h} \\ \\ &= \lim_{h\to 0} \frac{h^2+2h}{h}\\ \\&=\lim_{h\to 0} h + 2 \\ \\ &= (0) + 2 \\ &= 2\end{aligned}[/tex]
(Note: I evaluated the limit using direct substitution.)
Hence, the slope of the curve at the point P(2, -3) is two.
Part B)
Since the slope of the curve at point P is two, the slope of the tangent line is also two.
And since we know it passes through the point (2, -3), we can consider using the point-slope form:
[tex]\displaystyle y - y_1 = m(x-x_1)[/tex]
Substitute. m = 2. Therefore, our equation is:
[tex]\displaystyle y + 3 = 2(x-2)[/tex]
We can rewrite this into slope-intercept if desired:
[tex]\displaystyle y = 2x - 7[/tex]
We can verify this by graphing. This is shown below:
helpppp!!!!!!!!!!!!!!!!!!!!!
Answer:
Below
Step-by-step explanation:
DO=15
OB=3x+7
DB=9x-2
O is between D and B
So,
OB+DO=DB
or, 9x-2+3x+7=15
or, 12x=15-5
or, x=10/12
Thus, x=5/6
Evaluate the expression 3(x^2-y) +4 if x=3 and y=2
f.) 16
g.) 25
h.) 29
j.) 33
Step-by-step explanat
(g) 3[(3)²-2]+4=3(9-2)=3×7=21+4=25
Sorry for my bad handwriting
Answer:
No it is good
Step-by-step explanation:
I like it. good luck
Answer:
Rs 18.30
Step-by-step explanation:
100-(25.75+20.50+35.45)=100-81.70=Rs18.30
what is 0.4 repeating written as a fraction
Answer:
0.4 as a fraction would be 2/5
Answer: 4/9
Step-by-step explanation:
Find and simplify the expression if f(x)=x^2-1.
f(x-3)
Answer:
Step-by-step explanation:
f(x)=x²-1
f(x-3)=(x-3)²-1
=x²-6x+9-1
=x²-6x+8
Doanh thu công ty ABC năm hiện tại 6.500 triệu USD, doanh lợi tiêu thụ (ROS) 8%. Dự kiến trích 8% lợi nhuận sau thuế chia cổ tức cho các cổ đông. Xác định lợi nhuận để lại của công ty ABC?
Answer:
ill answer if u can make it english
Step-by-step explanation:
define complementary angle
Answer:
Complementary angles are 2 angles whose sum is 90 (ex 35° and 55°)
Step-by-step explanation:
complenentary angles are the pair angles with the sum of 90°
Question 9 of 10 Which of the following is most likely the next step in the series? OA. O B. O C. O D.
Answer: B
Step-by-step explanation:
The most likely the next pattern in the series is 2 lines with red color. Therefore, option B is the correct answer.
What is pattern?A recurring arrangement of numbers, forms, colours, and other elements constitutes a pattern in mathematics. The Pattern can be connected to any kind of occasion or thing. When a group of numbers are arranged in a particular way, the arrangement is referred to as a pattern. Patterns can also occasionally be referred to as a series.
From the given patterns
Figure 1 has 5 lines and it is blue in color.
Figure 2 has 4 lines and it is red in color.
Figure 3 has 3 lines and it is blue in color.
So, Figure 4 must has 2 lines and red in color.
Therefore, option B is the correct answer.
Learn more about the pattern here:
https://brainly.com/question/23136125.
#SPJ7
(Urgent please!!) Given the lines AB and CD, determine the slope of line CD. Type a numerical answer in the space provided. If necessary. Use the /key to represent a fraction bar. Do not put spaces in your answer
Answer:
-5/4
Step-by-step explanation:
C is at the point (2,3) and D is at the point (6,-2)
-2-3 = -5 which would be the top part and 6-2=4 and that's the bottom part.
Do the following graphs represent a mathematical function? If not, explain why.
Answer:
1 = Yes
2 = NO
Step-by-step explanation:
Answer:
Step-by-step explanation:
Yes for both.
Each value of x has only one image (an y value)
What is the largest multiple of 4 that is less than 30 ?
Answer:
The multiples of 4 that are less than 30 are 4, 8, 12, 16, 20, 24, 28
of the 420 students enrolled in basic math only 41% are first-year students. How many
are first-year students? How many are not?
Answer:
Step-by-step explanation:
There are 420 students.
41% are first year students.
41% = 41/100
420 * 41/100 = 172.4
What do you do about the 0.4? I would just round to the nearest whole number which is 172.
There are 420 - 172 = 248 who are not first year students.
5.4 - (9.5 - 8) - 2.5
(pls help and explain pls)
Answer:1.4
Step-by-step explanation:
3. Solve and plot your answer on the number line below:
9.28 + 2x = 18.14
Step by step
Determine the range of the following graph:
y
12
11
10
9
8
7
2
1
-12-11-10-9-8-7-6-5-4-3-2-11
1 2 3 4 5 6 7 8 9 10 11 12
- 2
-3
-4
-8
-9
-10
-11
-12
Answer:
r = (-4,9]
Step-by-step explanation:
hope this will help
Answer:
-4<y≤2
Step-by-step explanation:
The range of a graph is the range of the y values.
what are the exponent and coefficient of the expression 4b^-3
Answer:
exponent is -3 and coefficient is 4
Why are fractions difficult to teach and learn? Give 5 reasons.
Answer:
It is not hard
Step-by-step explanation:
•Once you get familiar with the lesson you understand it in a much easier way by doing problems pretty often
•If you want get more comfortable with it just search for a few questions in internet specifically educational platforms in schools like teachers
•But if your still confused you can always study it for free by byjus or vedantu and the best option in my opinion is ask your teacher to explain it once more
•It is very hard to solve questions if you are not freindly with the chapter
• Do not hesitate to ask questions if your doubting or anything you might face problems in higher grades with the topic
Sam hits a golf ball from a elevated tee
First take a derivative,
[tex]\frac{d}{dx}-5t^2+10t+30=-10t+10=-10(t-1)[/tex]
Now compute the critical point where the slope is 0,
[tex]-10(t-1)=0\implies t-1=0\implies t=1[/tex]
And done.
The maximum height is at [tex]t=1[/tex] of [tex]h(1)=-5+10+30=35[/tex].
Hope this helps :)