#1
k=3Lets verify
kx²+5x+23x²+5x+23x²+3x+2x+23x(x+1)+2(x+1)(3x+2)(x+1)Yes verified
#2
k=4Lets verify
9x²+kx-59x²+4x-59x²+9x-5x-59x(x+1)-5(x+1)(9x-5)(x+1)Yes verified
Rule to be noted:-
If ax²+bx+c be a function
Then
b=a+cFind the amount of work W done by a force F = 115i +350j
in moving an object in a straight line given by the displacement vector D = -13i+15j.
The work is equal to the dot product of the force and displacement vectors:
W = (115 i + 350 j) • (-13 i + 15 j)
W = 115 × (-13) + 350 × 15
W = 3755
This equation shows the relationship between the amount of water (w), in liters, filled in Tank A and the number of minutes (m) it took to fill it.
w = 100 + 80.5m
This table shows the relationship between the amount of water, in liters, filled in Tank B and the number of minutes it took to fill the tank
Amount of water filled in Tank B:
Minutes: Amount of water: (liters)
0 154
2 384
6 844
What is the difference, in liters, between the total amount of water filled in Tank A and Tank B after 4 minutes?
Answer:
192 liters
Step-by-step explanation:
Tank A
w = 100 + 80.5m
where:
w = water in litersm = time in minutesTherefore, when m = 4:
⇒ w = 100 + 80.5(4) = 422 liters
Tank B
Given ordered pairs: (0, 154) (2, 384) (6, 844)
[tex]\sf slope\:(m)=\dfrac{change\:in\:y}{change\:in\:x}=\dfrac{384-154}{2-0}=115[/tex]
Point-slope form of linear equation: [tex]\sf y-y_1=m(x-x_1)[/tex]
(where m is the slope and (x₁, y₁) is a point on the line)
[tex]\sf \implies y-154=115(x-0)[/tex]
[tex]\sf \implies y=115x+154[/tex]
Therefore, the equation for Tank B is:
w = 115m + 154
Therefore, when m = 4:
⇒ w = 115(4) + 154 = 614 liters
Difference
614 - 422 = 192 liters
Find equation for tank B
(0,154)(2,384)Slope:-
m=384-154/2=230/2=115Equation in point slope form
w-154=115(m)w=115m+154For tank B
w=100+80.5mPut 4on both
Tank A:-
w=100+80.5(4)w=100+322w=422LTankB
w=115(4)+154w=460+154w=614LDifference:-
614-422192LIn each circle, find the value of x. Please help
In a circle, angles subtended by the same arc at the circumference are equal. This means that angles in the same segment are equal.
Using this equation, we can create the following equation:
[tex]4x=3x+10[/tex]
For which we can solve to get:
[tex]x=10[/tex]
Hope this helps!
If you spin the spinner 9 times, what is the best prediction possible for the number of times it will land on yellow?
Answer:
0? There's no yellow.
Step-by-step explanation:
please help!! very important!!
Answer:
d
Step-by-step explanation:
Hardware store:
4 bulbs = $20
1 bulb = $20 / 4 = $5
Grocery store:
6 bulbs = $24
1 bulb = $24 / 6 = $4
The difference in price = $5 - $4 = $1
The grocery store sells at the lesser price.
So, the grocery store charges $1 less per light bulb than the hardware store.
3. The number 84 can be expressed as the
sum of 54 + 30. Which shows how to use
the distributive property to rewrite that
sum as a multiple of a sum whose addends
have no common factors greater than 1?
A. 2(27 + 15)
B. 3(18 + 10)
C. 5(11 + 0)
D. 6(9 + 5)
Answer:
D. 6(9 + 5)
Step-by-step explanation:
What is the measure, in degrees, of
Answer:
Hi good job
Step-by-step explanation:
Please help me as soon as posable!! In hurry!!(24 points)
In a geometric sequence, a_ 2 = 2, a_ 3 = 20, and a_4 = 200.
Which equation can be used to find the nth term of the sequence, a_n?
A) a_n =2^n-1
B) a_n =2 · 18^n-1
C) a_n =10 · 2^n-1
D) a_n =1/5 · 10^n-1
The sequence is geometric, so
[tex]a_n = r a_{n-1}[/tex]
for some constant r. From this rule, it follows that
[tex]a_3 = r a_2 \implies 20 = 2r \implies r = 10[/tex]
and we can determine the first term to be
[tex]a_2 = r a_1 \implies 2 = 10 a_1 \implies a_1 = \dfrac15[/tex]
Now, by substitution we have
[tex]a_n = r a_{n-1} = r^2 a_{n-2} = r^3 a_{n-3} = \cdots[/tex]
and so on down to (D)
[tex]a_n = r^{n-1} a_1 = 10^{n-1} \cdot \dfrac15[/tex]
(notice how the exponent on r and the subscript on a add up to n)
Use the quadratic formula to find the solutions to the quadratic equation below. x^2 - 6x - 5 = 0
Step-by-step explanation:
We know the quadratic formula, which is :
[tex] \\ {\longrightarrow \qquad{ \sf{x = \frac{ - b \pm \sqrt{ {b}^{2} - 4ac } }{2a} }}} \\ \\ [/tex]
Here,
a = 1b = -6c = -5So,
[tex] \\ {\longrightarrow \qquad{ \sf{x = \frac{ - ( - 6) \pm \sqrt{ {( - 6)}^{2} - 4(1)( - 5) } }{2(1)} }}} \\ \\ [/tex]
[tex] {\longrightarrow \qquad{ \sf{x = \frac{ 6 \pm \sqrt{ 36 - 4( - 5) } }{2} }}} \\ \\ [/tex]
[tex]{\longrightarrow \qquad{ \sf{x = \frac{ 6 \pm \sqrt{ 36 + 20 } }{2} }}} \\ \\ [/tex]
[tex]{\longrightarrow \qquad{ \sf{x = \frac{ 6 \pm \sqrt{ 56 } }{2} }}} \\ \\ [/tex]
[tex]{\longrightarrow \qquad{ \sf{x = \frac{ 6 \pm \sqrt{ 2(28) } }{2} }}} \\ \\ [/tex]
[tex]{\longrightarrow \qquad{ \sf{x = \frac{ 6 \pm \sqrt{ 2(2)(14) } }{2} }}} \\ \\ [/tex]
[tex]{\longrightarrow \qquad{ \sf{x = \frac{ 6 \pm \sqrt{ 2(2)(2)(7) } }{2} }}} \\ \\ [/tex]
[tex]{\longrightarrow \qquad{ \sf{x = \frac{ 6 \pm \sqrt{ 2} . \sqrt{2} . \sqrt{2 . 7} }{2} }}} \\ \\ [/tex]
[tex]{\longrightarrow \qquad{ \sf{x = \frac{ 6 \pm 2 \sqrt{14} }{2} }}} \\ \\ [/tex]
Now, Separating the solutions :
[tex] \\ {\longrightarrow \qquad{ \sf{x = \frac{ 6 + 2 \sqrt{14} }{2} }}} \\ \\ [/tex]
[tex] {\longrightarrow \qquad{ \sf{x = 3 + \sqrt{14}}}}\\ \\ [/tex]
[tex]\\ {\longrightarrow \qquad{ \sf{x = \frac{ 6 - 2 \sqrt{14} }{2} }}} \\ \\ [/tex]
[tex] {\longrightarrow \qquad{ \sf{x = 3 - \sqrt{14}}}}\\ \\ [/tex]
Help help help help math math
Answer:
[tex]x = \geqslant 34[/tex]
Step-by-step explanation:
x is greater than or equal to 34, because the illustration shows, that it can go beyond 34. The filled in dot also means that x can also be equal to 34. (i hope i explained it in a good way)
Find the volume of the triangular prism to the right.
5 ft
10 ft
The volume of the prism is ? ft^3
Answer:
rectangular is 114ft and triangular is 112ft
Step-by-step explanation:
Let the volume of a rectangular prism be VR and that of right triangular prism be VT. If The volume of the rectangular prism is 32 cubic feet more than the volume of the right triangular prism, then VR = 32 + VT
Since VR = length * width and height
VR = 6*x*3
VR = 18x ft³
Also VT = Length *width * Height/2
VT = (7 * x * 4)/2
VT = 28x/2
VT = 14xft³
Since VR = 32 + VT
18x = 32+(14x)
collect like terms
18x-14x = 32
4x = 32
divide both sides by 4
4x/4 = 32/4
x = 8
Volume of the rectangular prism = 18x
Volume of the rectangular prism = 18*8
Volume of the rectangular prism = 144ft³
Volume of the right triangular prism = 14x
Volume of the rectangular prism = 14*8
Volume of the rectangular prism = 112ft³
Answer correctly for brainliest I dont want to rush you but i need this in like 1-2 minutes
Answer:
the correct answers are A, C, and D
Step-by-step explanation:
Those are the only ones that make sense enough!
What is the average height of 6th grade students?
And
What was the low temperature...?
Those responses will be given as numerical values
E.G. 162cm or 2 degrees Celsius (2*C)
(Edit: the first & third options are the correct ones)
Hope this helps!
The temperature in Denver, Colorado this
morning was -7°. In the afternoon, the
temperature rose to 16º.
What does this mean?
A. The temperature is 16° below zero
B. The temperature is 16° above zero
PLEASE HELP!!
Mr. Chau is planting a circular flower garden in his backyard. If the diameter of his garden is 12 feet, what is the area of the garden?
Answer:
A = 113.04 ft² or 36π ft²
Step-by-step explanation:
Area of a circle: πr²
radius: d/2 (12/2 = 6 ft)
π (pi) = 3.14
Solve:
A = πr²
A = 3.14(6)²
A = 3.14(36)
A = 113.04 ft² or 36π ft²
Hope this helps!
Pls help me
Pls show your answer pls and thank you
Answer:
Step 1
According to given details
Number of delivered pizzas at the weekly meeting=5
Number of slices in one pizza =8
(a)
Now evaluate total number of slices
Number of slices in one pizza =8
Total slices =8x5
=40 slice
(b)
Yes, we can find more than one way
= 5 ÷ 1/8
= 5x8/1
=40/1
a circular wall clock with a circumference of 94.2 cm is mounted on a wall. How much area of the wall did it occupy
please i reallly need help right now 25 points
Answer:
D) all real numbers except x = 6
Step-by-step explanation:
If there is a solid line or dot at an x value, then it is included in the domain. Since there are open dots at x = 6, that means it is not included in the domain. With that being said, the domain can be written as:
(-∞, 6)∪(6, ∞)
Hope this helps!
Hector was thinking of a two-digit counting number, and he asked Simon to guess the number. Describe how you can find the probability that Simon will guess correctly on the first try.
Answer:
1/89
Step-by-step explanation:
Two digit numbers include all numbers from 10 to 99. 99-10 = 89. Therefore the probability that Simon guesses the number correctly on the first try is 1 out of 89 which can be written as 1/89.
Can Some1 Please Help Me!!!
The ratio of men to women working for a company is 4 to 3. If there are 161 employees total, how many men work for the company?
Answer:
i dont know
Step-by-step explanation:
hope you find you answer
Need this asap first gets brainliest
Answer:
Step-by-step explanation:
5a)→Solution,
[tex]\hookrightarrow 46+90=x[Sum\: of\: interior \:angle\: is\: equal\: to \:exterior\:angles]\\\\\hookrightarrow x=136[/tex]
5b)→Solution,
77+x=180
x=180-77
x=103
During its grand opening sale, a local electronics store gave customers a chance to win a new flat screen TV. Customers only had to fill out a card with their name, address, and telephone number and drop it into a box. One winner would be chosen at random. This is an example of a
Using sampling concepts, it is found that this is an example of a random sample.
How are samples classified?Samples may be classified as:
Convenient: Drawn from a conveniently available pool.Random: All the options into a hat and drawn some of them.Systematic: Every kth element is taken. Cluster: Divides population into groups, called clusters, and each element in the cluster is surveyed.Stratified: Also divides the population into groups. Then, a equal proportion of each group is surveyed.In this problem, one winner is chosen at random from all the participants, hence random sampling is used.
More can be learned about sampling concepts at https://brainly.com/question/25122507
Two vertices of a rectangle are located at (6, 1) and (8, 1). The rectangle has an area of 18 units2 and is entirely in the first quadrant. What are the other two vertices?
The two other two vertices will be (6, 10) and (8, 10)
How to calculate the area of a rectangle?A rectangle is a 2-dimensional shape with equal opposite sides. The formula for calculating the area is given as:
Area = length * width
Given;
Area = 18 square units
Length = x2 -x1 = 8 -6
length = 2 units
Determine the width
Width = A/l
Width = 18/2
Width = 9 units
Hence the two other two vertices will be (6, 10) and (8, 10)
Learn more on area of rectangle here: https://brainly.com/question/2607596
What is 180-90-37 as a degree?
Answer:
53 degrees
Step-by-step explanation:
since 180 is a straight line and 90 is half of that, all you need to do is take 37 away from 90 and you get 53
The equivalent degree of the of the expression is 53 degrees .
Given,
180° - 90° - 37°
Now,
The equivalent value of the expression :
180° - 90° - 37°
Firstly compute the like terms,
-90° - 37°
= -127°
Now,
180° - 127°
= 53°
Know more about degrees,
https://brainly.com/question/364572
#SPJ6
the three sides of a triangle are 11/3 cm , 15/4 cm and 26/9 cm . find it's perimeter .
[tex] \sf\longmapsto \: \frac{371}{36} [/tex]
☘︎ Solution :- Given : Three sides are 11/3 cm , 15/4 cm and 26/9 cm To find : perimeter of the trianglePerimeter of a triangle = Sum of the length of the three sides
perimeter of the given triangle = 11/3 + 15/4 + 26/9
Make the denominator same by taking the LCM of the denominators .( LCM of 3 , 4 and 9 is 36 )
[tex]\sf\longmapsto \: \frac{132 \: + \: 135 \: + \: 104}{36} \: \: \: [/tex]
[tex]\sf\longmapsto \: \frac{371}{36} \: cm \: [/tex]
♧ Therefore, the perimeter of a triangle is 371/36 cm
PLEASE HELP
What can you say about the y-values of the two functions f(x) = 3x2 -3 and
g(x) = 2* -3?
A. f(x) and g(x) have equivalent minimum y-values.
B. f(x) has the smallest possible y-value.
C. The minimum y-value of g(x) approaches -3.
D. g(x) has the smallest possible y-value.
Answer:
g(x) has the smallest possible y-value of -3
Step-by-step explanation:
f(x) = 3ˣ - 3 This is an exponential graph shifted down three units. So, it has an asymptote at y = -3, which means it approaches -3 but does not touch it.Range: y > 3 (-3, ∞) g(x) = 7x² - 3 ⇒ g(x) = 7(x - 0)² - 3 This is a parabola with vertex at (0, -3) Range: y ≥ 3 [-3, ∞)
arrange in ascending order. : 5/8, 3/4, 7/12, 1/2
Answer:
1/2, 7/12, 5/8, 3/4.
Step-by-step explanation:
I did that in ascending order.
write an expression for the cost of t books at 13 cents each
Answer:
13n+20 is the correct answer to ypur question
Step-by-step explanation:
Identify the elements for each problem
find circumference of the circle whose parameter is 14 cm
Find the circumference of a circle with diameter 14 cm
Please HELP NEED ASAP>
Tyrone conducted an experiment with a spinner. He spun the arrow on the spinner 20 times and recorded the results in the table shown. Which statement below is a true statement based on the statement above. Please no links.
Answer:
A)
Step-by-step explanation:
The experimental probability on 'A' is higher than the theoretical probability of landing on 'A'.
Kevin is an auto mechanic. He spends 3 hours when he replaces the shocks on a car and 2 hours when he replaces the brakes. He works no more than 36 hours a week. He routinely completes at least 2 shocks replacements and 3 brake replacements a week. If he charges $400 for labor replacing shocks and $200 in labor for replacing brakes, how many jobs of each type should he complete a week to maximize his income?
Answer:
See below ....question is a bit unclear
Step-by-step explanation:
He makes 133.33 per hour with shocks and only 100 per hour with brakes.
he should only do 36/3 = 12 shock jobs per week and no brakes.
if he HAS to do at LEAST 3 brake jobs
then he should do 3 brakes and 10 shocks