Answer:
Points lie on the same line if and only if the points are collinear
Step-by-step explanation:
(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:
Step-by-step explanation:
P=(2,-3)
Q=(a,a²-2a-3)
[tex]\Delta y=a^2-2a-3-(-3)=a^2-2a\\\Delta x=a-2\\\\\displaystyle \lim_{a \to 2} \dfrac{a^2-2a-3-(-3)}{a-2} \\\\=\lim_{a \to 2} \dfrac{a^2-2a}{a-2} \\\\=\lim_{a \to 2} \dfrac{a(a-2)}{a-2} \\\\=\lim_{a \to 2} \dfrac{a}{1} \\\\=\lim_{a \to 2} a \\\\=2\\[/tex]
Proof:
y'=(x²-2x-3)'=2x-2
y'(2)=2*2-2=2
Write the following phrase as a variable expression. Use x to represent "a number" the sum of a number and seventeen
translation is:
Answer:
[tex]x+17[/tex]
Step-by-step explanation:
Hi there!
Let [tex]x[/tex] represent "the number".
The sum of a number and seventeen
⇒ [tex]x+17[/tex]
I hope this helps!
Are Quadrilaterals A and C congruent??
Answer:
It turns out that knowing all four sides of two quadrilaterals are congruent is not enough to conclude that the quadrilaterals are congruent. Unlike with triangles, some information about angles is needed in order to conclude that two quadrilaterals are congruent. I will give you the video that might be helpful. I dont own the video but i hope it helps you . <3
Step-by-step explanation:
https://www.khanacademy.org/math/cc-fifth-grade-math/properties-of-shapes/imp-quadrilaterals-2/v/quadrilateral-types-exercise
What angles would have to be congruent to prove the triangles are congruent by SAS?
A. AEB = CED
B. AEB = DEC
C. ECD = EAB
D. CDE = ABE
Simplify.
Rewrite the expression in the form 4".
49
45
Answer:
[tex]4^{9-5}[/tex] = [tex]4^{4}[/tex]
Step-by-step explanation:
PLEASE HELP
To find the area of a triangle, use the formula on, where bis the base
and h is the height. What is the area in square inches of a triangle with
a height of 6 inches and base of 8 inches.
Answer:
A=24
Step-by-step explanation:
Triangle Area formula: h*b
h: 6
b: 8
6*8=24
One third of a bamboo is buried in mud, one sixth of it is in water and the part above the water is greater than or equal to 3 meters. Find the length of the shortest pole.
Answer:
6m
Step-by-step explanation:
Buried in mud: 3
In and above the water: 6
Total buried in the mud and in/above the water: 3 + 6 = 3 ÷ 6 = 2m
The length of the shortest pole?
Based to the question,
2m + 3m = ...?
= 2m x 3m
= 6 m
The length of the shortest pole is 6m.
Find the solution to the system of equations below
y=-5x+3
2x-3y=8
Answer: (1, -2)
Concept:
There are three general ways to solve the system of equations:
Elimination SubstitutionGraphingHere, we are going to use the elimination method to solve.
Solve:
Given
[tex]\left \{ {{y=-5x+3} \atop {2x-3y=8}} \right.[/tex]
Convert the first equation's arrangement to correlate with the second equation
[tex]\left \{ {{5x + y=3} \atop {2x-3y=8}} \right.[/tex]
Multiply 3 on both sides in the first equation
[tex]\left \{ {{15x + 3y=9} \atop {2x-3y=8}} \right.[/tex]
Eliminate [y] by adding the two equations
[tex]17x = 17[/tex]
Divide both sides by 17
[tex]17x / 17=17/17[/tex]
[tex]x=1[/tex]
[tex]y=-5x+3=-5(1)+3=-5+3=-2[/tex]
[tex](1, -2)[/tex]
Hope this helps!! :)
Please let me know if you have any questions
Factor over the Reals
Answer:
(x - 2y)³(1 - x+ 2y)(1 + x - 2y)
Step-by-step explanation:
Given
(x - 2y)³ - [tex](x-2y)^{5}[/tex] ← factor out (x - 2y)³ from both terms
= (x - 2y)³(1 - (x - 2y)²) ← difference of squares which factors in general as
a² - b² = (a - b)(a + b) , then
1 - (x - 2y)²
= 1² - (x - 2y)²
= (1 - (x - 2y) )(1 + (x - 2y) )
= (1 - x + 2y)(1 + x - 2y)
Then
(x - 2y)³ - [tex](x-2y)^{5}[/tex]
= (x - 2y)³(1 - x + 2y)(1 + x - 2y) ← in factored form
solve for X
1/2(10x+4)=12
Answer:
x = 2
Step-by-step explanation:
Distribute the 1/2 on the left side to each term
1/2 * 10x + 1/2 * 4 = 12
Now multiplication first before addition on the left side.
5x + 2 = 12
Subtract 2 on both sides
5x = 10
Divide by 5 on both sides
x = 2
Check work
1/2(10(2) + 4) = 12
1/2(20 + 4) = 12
1/2 * 24 = 12
24/2 = 12 = 12
The distance from Tallahassee, Florida, to London, England, is 4.368 x 103 miles. The distance from
London, England, to Tokyo, Japan, is 6.424 x 103 miles. If you were to fly from Tallahassee to London
and then to Tokyo, how many miles would you have traveled?
A. 2.056 x 103
B. 28.06 x 103
C. 1.0792 x 104
D. 10.792 x 106
Gabriel's family is investing $5,000 into two different bonds for college. One bond gave
an interest of 5% per year, and the other 3%. If the combined interest for the year was
$220, how much money was invested in each bond?
The amount invested in the bond that yields 5% is $3500 and the amount invested in the bond that yields 3% is $1500
This question would be solved using simultaneous equation
Two equations can be derived from this question
a + b = 5000 equation 1
0.05a + 0.03b = 220 equation 2
where a = amount invested in the bond that bears 5% per month
b = amount invested in the bond that bears 3% per month
Multiply equation 1 by 0.05
0.05a + 0.05b = 250 equation 3
Subtract equation 2 from 3
0.02b = 30
Divide both sides of the equation by 0.02
b = 1500
Substitute for b in equation 1
a + 1500 = 5000
subtract 1500 from both sides of the equation
a = 5000 - 1500 = 3500
Amount invested in the bond that yields 5% is $3500
Amount invested in the bond that yields 3% is $1500
To learn more about simultaneous equation, please check : https://brainly.com/question/15165519?referrer=searchResults
Find the distance between X(-3, 8) and Z(-1,5) *
what is it :’)
Find the height of the triangle by applying formulas for the area of a triangle and
your knowledge about triangles.
A. 5.8 mm
B. 2.0 mm
OC. 4.4 mm
D. 6.2 mm
Answer:
Step-by-step explanation:
a= 12 mm ; b = 16 mm ; c = 18 mm
s = (a + b+c)/2
[tex]=\dfrac{12 + 16 + 8}{2}\\\\= \dfrac{36}{2}\\\\= 18\\\\[/tex]
s -a = 18 - 12 = 6 mm
s -b = 18 - 16 = 2 mm
s -c = 18 - 8 = 10 mm
[tex]area = \sqrt{s(s -a)(s-b)(s-c)}[/tex]
[tex]= \sqrt{18*6*2*10}\\\\= \sqrt{2160 }\\\\=46.47\\\\=46 \ mm^{2}\\[/tex]
[tex]\dfrac{1}{2}* \ base * \ height = 46\\\\\dfrac{1}{2}*16* \ height = 46\\\\height = \dfrac{46*2}{16}\\\\[/tex]
= 5.75
Height = 5.8 mm
Answer:
A. 5.8mm
Step-by-step explanation:
[tex]area \: of \: triangle = \sqrt{s(s - a) \times (s - b) \times (s - c)} \\ s = \frac{a + b + c}{2} \\ s = \frac{12 + 8 + 16}{2} \\ s = 18 \\ area \: of \: triangle \: = \sqrt{18(18 - 12) \times (18 - 8) \times (18 - 16)} \\ = \sqrt{2160} \\ = 46.47 {m}^{2} \\ area \: of \: triangle \: = \frac{1}{2} \times base \times height \\ 46.47 = \frac{1}{2} \times 16 \times h \\ h = \frac{46.47}{8} \\ h = 5.8mm[/tex]
CAN SOMEONE TAKE A QUICK LOOK AT THIS AND HELP ME OUT
Answer:
9/79/169%, 523.2, 458 (to 3sf)
Step-by-step explanation:
Example 1:
16/169×100%=9/79/169% of the students
Example 2:
87.2%×600=523.2 students
Example 3:
27.3%=125 students
100%=458 students (to 3sf)
A 2-pound bag of potatoes costs $0.96. What is the price per ounce?
Answer:
.03
Step-by-step explanation:
1 pound = 16 ounces 2 pounds is 32
and 96/32 is 3
Answer:
$.03 per ounce
Step-by-step explanation:
1 pound = 16 ounces
2 pounds = 32 ounces
Take the price and divide by the number of ounces
.96 / 32 ounces
.03 per ounce
What is the midpoint of line segment EF?
O (2,2)
O (-3,-2)
O (-2,1)
• (-4,2)
answers in the grid on
Око
28) f(x) = ax? + bx+c is a quadratic function where a, b and c are constant,
the value of x of the point of intersection of this quadratic function and linear
function g(x) = 2x - 1 is 3. The vertex of f(x) is at (-3,-1). What is the
product of a, b and c?
Answer:
a= 1/6
b=1
c=1/2
a*b*c = [tex]\frac{1}{12}[/tex]
Step-by-step explanation:
Y = Ax2 Bx C
Enter coefficients here >>> 1/6x^2+ 1x+ 0.5
4) Write the following rational number in Pq form 1.) 2.514
Answer:
3 or 2.5
both are correct answers
Can somebody please help? I been struggling to answer this!
Answer:
the first option is the answer. I am sure of this
Answer:
the first option is the answer
An angle measures 46° more than the measure of its complementary angle. What is the
measure of each angle?
Answer:
Angle + the Complementary angle = 90 degrees. Let x be the measure of the angle under the question. Then the measure of the Complementary angle is (x+46) degrees, and you have this equation x + (x+46) = 90, or 2x+ 46 = 90, or 2x = 90 - 46 = 44. Then x =  = 22. The given angle has the measure of 22 degrees. The complementary angle is 90-22 = 68 degrees. Check. 68 - 22 = 44 degrees. Correct !!
Find the perimeter of a square with sides 2 5/8 .
Answer:
10.5
Step-by-step explanation:
2⅝×4=10.5
..............
Lynn regularly works a 40-hour week and earns $14 per hour. She receives time-and-a-half pay for each hour of overtime she works. Last week she worked 43 hours.
a) What was her regular pay for the week?
b) | What is her hourly overtime rate?
c) What was her overtime pay for the week?
d) What was her total gross pay for the week?
e) What was her approximate NET pay for the week?
Answer:560
Step-by-step explanation:
62.9042 to the nearest hundredth
Answer:
62.9
Step-by-step explanation:
Slope-Intercept
Functions
Acellus
Find the equation to the line below.
1
Answer:
y=4x+1
Step-by-step explanation:
First the slope of the line is 4. The equation of the line is y-1=4x, y=4x+1
What is the first step to solving the division problem below?
6288 divided by 8
Answer:
devide it by 2 three times
Step-by-step explanation:
6288/2=3144
3144/2=1572
1572/2=786
i think that's the easiest way to do it
Find the difference. 87,000,000,976 – 6,998,765,824
Answer:
80001235152
Step-by-step explanation:
hope this helped!
Please help with geometry
Answer:
x
Step-by-step explanation:
4 (y + z); use y = 5 and z = 4
Answer:
It is 9
Step-by-step explanation:
[tex]4(y + z)[/tex]
when y is 5, z is 4
substitute:
[tex] = 4(5 + 4) \\ = 36[/tex]
Answer:
y=5 z = 4 - substitution
4 (5 + 4) = 4 (9) = 36
The length of a rectangle is 2m-1 and the width is m+3. Simplify an expression for the perimeter of the rectangle.
Answer:
6m+ 4
Step-by-step explanation:
2(2m-1) + 2(m+3)
4m - 2 + 2m + 6
6m + 4