The value of k is -3, if x-1 is a factor of 4x³+3x² −4x + k
Quadratic Equation:
A quadratic equation is a second-order algebraic equation in x. The quadratic equation in standard form is ax2 + bx + c = 0. where a and b are the coefficients, x is the variable, and c is the constant term. The first condition of the quadratic equation is that the coefficients of x² are non-zero terms (a ≠ 0). To write a quadratic equation in standard form, first write the x² term, then the x term, and finally the constant term. The numbers for a, b, and c are generally written as whole numbers, not as fractions or decimals.
According to the Question:
Let P(x) = 4x³+3x² −4x + k
Given, (x−1) is a factor of P(x)
x−1 = 0
x= 1
∴ p(1) = 4×(1)³+3×(1)² −4×(1)+k = 0
⇒ 4+3−4+k = 0
⇒ k+3=0
⇒ k=−3
Hence, the value of k is −3.
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1. The midsegment of a trapezoid is half the sum of the bases.
true or false ?
Answer:
TRUE
Step-by-step explanation:
TRUE
Therefore, the given statement "The midsegment of a trapezoid is half the sum of the bases" is True.
What is a trapezium?A trapezium is a quadrilateral with two parallel sides. It has two non-parallel sides that are called the legs of the trapezium, and the other two sides are called the bases.
The midsegment of a trapezoid is a line segment that connects the midpoints of the two non-parallel sides of the trapezoid. Since the midsegment connects the midpoints of the two non-parallel sides, it will always have the same length as half the sum of the two bases.
Therefore, the given statement is True.
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Find the measure of the side indicated (x). Round to the nearest tenth. Show your work to support your answer.
Answer:
x = 13.77
Step-by-step explanation:
cos 37° = 11/x
0.7986 = 11/x
0.7986x = 11
x = 11/0.7986
x = 13.77
The value of the hypotenuse x will be 14.37.
What will be the value of the hypotenuse?Here in the triangle, it is given that
The angle between base and hypotenuse = [tex]37^0[/tex]
The base =11
So from the property
[tex]COS\theta=\dfrac{Base}{Hypotenuse}[/tex]
[tex]Cos37=\dfrac{11}{x}[/tex]
[tex]x=\dfrac{11}{0.7654}[/tex]
[tex]x=14.37[/tex]
Thus the value of the hypotenuse x will be 14.37.
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What is the image point of (-5,0) after a translation left 2 units and down 1 unit?
Answer:
The image point of (-5, 0) after a translation left 2 units and down 1 unit would be the point (-7, -1).
Step-by-step explanation:
The original point is located at (-5, 0), a translation of two units to the left would be an increase of -2 in the x-axis, and a translation of down 1 unit would be an increase of -1 in the y-axis. Using the translation, you can infer that the new coordinate would be (-5 - 2, 0 - 1) or (-7, -1).
A scientist selected a random sample of seven varieties of peach ice cream to investigate the relationship between the density, in pounds per cubic inch, of the varieties of ice cream and the percent concentration of peaches in the ice cream. Assuming all conditions for inference are met, which of the following significance tests should be used to investigate whether there is convincing evidence at the 0.05 level of significance that a greater percent of peaches in the ice cream is associated with an increase in the density of the ice cream?
A. A two-sample t-test for a difference between means
B. A chi-square test of independence
C. A linear regression t-test for slope
D. A two-sample z-test for a difference between proportions
E. A matched pairs t-test for a mean difference
Answer:
The significance test that would be used to investigate whether there is convincing evidence at 0.05 level of significance that a greater percent of peaches in the ice cream is associated with an increase in the density of the ice cream is option C;
C. A linear regression t-test for slope
Step-by-step explanation:
The linear regression t-test for slope is a test for determining the existence of a statistically significant linear relationship between two variables, a independent variable, X and an dependent variable Y in the following form;
Y = B₀ + B₁·X
The test is used to test the regression line slope where we have;
B₀ = The constant
B₁ = The slope also known as the regression coefficient
The given information tested in the question is if an increase in the peaches in the ice cream is associated with an increase in the density of the ice cream, therefore, the test to investigate the relationship between the rate of both variables is the linear regression t-test for slope.
Therefore, we have
Y = B₀ + B₁·X
Where;
X = The percentage of peaches in the ice cream
Y = The density of the ice cream
Help please I would appreciate it
Answer:
A
Step-by-step explanation:
see attached .
hope it's helps .
Keiko’s class collected money to donate to charity. When Keiko counted the money, there were 140 five-dollar bills, and 255 one-dollar bills. What expression could he use to find out how much money was collected?
Whoever answers first gets brainlest! :)
Answer:
(140 × $5) + (255 × $1)
Therefore, the money was collected is $ [tex]955[/tex].
What is an expression?
An expression or mathematical expression is a finite combination of symbols that is well-formed according to rules that depend on the context.
Here given that,
Keiko’s class collected money to donate to charity. When Keiko counted the money, there were [tex]140[/tex] five-dollar bills, and [tex]255vvv[/tex] one-dollar bills.
So, it is of the form:-
[tex](140[/tex] ×[tex]5)+(255[/tex] ×[tex]1)[/tex]
[tex]=700+255\\\\[/tex]
[tex]=955[/tex]$
Hence, the money was collected is $ [tex]955[/tex].
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help now please no links
Answer:
60 cm^2
Step-by-step explanation:
I did it hope it helps
Answer: 60 cm²
Step-by-step explanation:
OUTLINE:
1. Find the area of triangles
2. Find the area of rectangles
SOLVE:
#1 Area of Triangles
Formula: a=(1/2)bh
a=area
b=base
h=height
b=6 cm
h=4 cm
a=(1/2)bh
a=(1/2)(6)(4)
a=12 cm²
There are 2 triangles ⇒ 12×2=24 cm²
#2 Area of Rectangles
Formula: a=bh
b=base
h=height
b=6 cm
h=2 cm
a=bh=6×2=12 cm²
There are 3 rectangles ⇒ 12×3=36 cm²
Find the total surface area: 36+24=60 cm²
Hope this helps!! :)
Please let me know if you have any questions
.............................
Answer:
the last one
Step-by-step explanation:
The height of 44 students (in centimeter) are presented in the frequency distribution below. Complete the table, and then find the median.
Height
182 - 188
175 - 181
168 - 174
161 - 167
154 - 160
147 - 153
140 - 146
Frequency
1
3
6
15
12
4
3
L
Given:
The height of 44 students (in centimeter) are presented in the given frequency distribution.
To find:
The median of the given data.
Solution:
The given intervals are inclusive first make the intervals exclusive by adding 0.5 in upper limit and by subtracting 0.5 from the lower limit.
The complete frequency distribution table is shown below:
Height Frequency L <cf
182 - 188 1 181.5 - 188.5 44
175 - 181 3 174.5 - 181.5 43
168 - 174 6 167.5 - 174.5 40
161 - 167 15 160.5 - 167.5 34 Median class
154 - 160 12 153.5 - 160.5 19
147 - 153 4 146.5 - 153.5 7
140 - 146 3 139.5 - 146.5 3
We have, [tex]n=44[/tex].
[tex]\dfrac{n}{2}=\dfrac{44}{2}[/tex]
[tex]\dfrac{n}{2}=22[/tex]
The 22th term is include in the class 160.5 - 167.5 because is cf is greater than 22 but the cf of o preceding class is less than 22. So, it is the median class is 160.5 - 167.5.
Formula for median:
[tex]Median=l+\dfrac{\dfrac{n}{2}-cf}{f}\times h[/tex]
Where, l is the lower limit of median class, cf is the cumulative frequency of preceding class, f is the frequency of median class and h is the size of the class.
Now, [tex]l=160.5,f=15,cf=19,h=7[/tex].
[tex]Median=160.5+\dfrac{22-19}{15}\times 7[/tex]
[tex]Median=160.5+\dfrac{3}{15}\times 7[/tex]
[tex]Median=160.5+1.4[/tex]
[tex]Median=161.9[/tex]
Therefore, the median of the given data table is 161.9.
The school has 978 pencils. They want to divide them equally among the 84 students. How many pencils will each student get?
Answer:
each student gets 11 pencils
Step-by-step explanation: I searched it up
Find the missing lengths of this triangle.
Can someone help me???
HELP PLEASE HELP PLEASE NO EXPLANATION
Sunlight hits the Earth at an angle. As a result of the tilt of the Earth, some areas of the Earth receive more direct sunlight than others, which means they receive more solar energy. Which statement correctly describes how solar energy changes as latitude changes?
A.
Oceans and lakes receive more solar energy than land masses.
B.
Lower latitudes receive more solar energy than higher latitudes.
C.
The poles receive the most solar energy of all places on the Earth.
D.
The equator receives the least solar energy compared to any other latitude.
Answer:
B. Lower latitudes receive more solar energy than higher latitudes.
i know i was late srry
If AC = 9 cm and tan ABC = 0.75, what is the length of BC?
Answer:
12 cm confirm ...................
From the concept of trigonometric ratios, we determine the length of the side BC is 6.75 cm.
What are trigonometric ratios in terms of a right-angle triangle?We know a right-angled triangle has three sides they are -: Hypotenuse,
Opposite and Adjacent.
We can remember SOH CAH TOA which is,
sin = opposite/hypotenuse, cos = adjecen/hypotenuse and
tan = opposite/adjacent.
Given, The length of the side AC = 9cm.
The measure of tan∠ABC = 0.75.
We know tan = opposite/adjacent.
Here, the opposite is AC and adjacent is BC.
Therefore, 0.75 = 9/BC.
BC = 9×0.75.
BC = 6.75.
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BRAINLIEST
a. 45
b. 34
c. 29
d. 56
Answer:
(d). 56°
Step-by-step explanation:
cos x° = [tex]\frac{5}{9}[/tex]
x° = [tex]cos^{-1}[/tex] [tex]\frac{5}{9}[/tex]
x° ≈ 56.25° ≈ 56°
Help please it’s timed
Answer: a
Step-by-step explanation:
Whats the volume of the cone?
use the fórmula V=1/3πr^2h.
D is correct. you’re welcome.
PLSSS HELPPPP I WILLL GIVE YOU BRAINLIEST!!!!!! PLSSS HELPPPP I WILLL GIVE YOU BRAINLIEST!!!!!! PLSSS HELPPPP I WILLL GIVE YOU BRAINLIEST!!!!!! PLSSS HELPPPP I WILLL GIVE YOU BRAINLIEST!!!!!!PLSSS HELPPPP I WILLL GIVE YOU BRAINLIEST!!!!!! PLSSS HELPPPP I WILLL GIVE YOU BRAINLIEST!!!!!! PLSSS HELPPPP I WILLL GIVE YOU BRAINLIEST!!!!!!
Answer:
a) Line M
b)Line M
c)y=1/2x+2
Step-by-step explanation:
a) Line M has a greater y-intercept since its y-intercept is at (0,2) while Line N's y-intercept is at (0,1)
b) Line M has a greater slope since its line is steeper
c) Use the formula y=mx+b
Use the points ( 0,1) and (-4,-1)
m(slope)= y2-y1/x2-x1
m= (-1-1)/(-4-0)
m=-2/-4
m=1/2
substitute
(0)=1/2(-4)+b
2=b(y-intercept)
y=1/2x+2
Answer:
Red line has higher intercept and slope.
The equation for the line: y= 0.5x
Step-by-step explanation:
Brainliest can only be awarded when two people have answered the question.
The population of a colony of mosquitoes obeys the law of uninhibited growth. If there are 1000 mosquitoes initially and there are 1900 after 1 day, what is the size of the colony after 4 days? How long is it until there are 40,000 mosquitoes? What is the size of the colony after 4 days?
Answer:
5832 mosquitoes
Step-by-step explanation:
As we know
[tex]A = A_0 * e^{kt}\\[/tex]
Where A is the population after t days
A0 is the initial population
k is rate constant and
t is the time in days
Substituting the given values we get
[tex]1900 = 1000 * e^{1 * k}\\1.9 = e^{1 * k}\\k = 0.587[/tex]
Size of colony after 4 days
[tex]A = 1000 * e^ {(0.587*4)}\\A = 5832[/tex]mosquitoes
Write the point-slope form of an equation of the line through the points (-2, -3) and (-7, 4).
A. y+2=−75(x+3)
B. y−4=−75(x−7)
C. y+3=−75(x+2)
D. y+7=−75(x−4)
Answer:
458435464546484845kdnh
Answer:
C. y+3=−7/5(x+2)
Step-by-step explanation:
Line is passing through the points (-2, -3) and (-7, 4).
Slope of line = (-3 - 4)/[-2-(-7)]= (-7)/(-2+7) = - 7/5
Equation of line in the point-slope form is given as with point (-2, -3).
y - (-3) = - 7/5[x - (-2)]
y + 3 = - 7/5(x +2)
identify the vertex of the graph
Answer:
(-1,-3)
Step-by-step explanation:
Answer:
y = a(x – h)2 + k,
Step-by-step explanation:
Parabolas always have a lowest point (or a highest point, if the parabola is upside-down). This point, where the parabola changes direction, is called the "vertex". If the quadratic is written in the form y = a(x – h)2 + k, then the vertex is the point (h, k). This makes sense, if you think about it.
In ADEF, what is sin D, in simplified form?
Answer:
In simplified form, sin D is;
4/5
Step-by-step explanation:
The given figure and dimension parameters in the question are;
Triangle ΔDEF is a right triangle
The length of leg [tex]\overline{EF}[/tex] which is opposite side to the reference angle = 20
The length of segment [tex]\overline{ED}[/tex] which is the hypotenuse side of the right triangle ΔDEF = 25
The length of segment [tex]\overline{DF}[/tex] which is adjacent side to the reference angle = 15
By trigonometric ratios, we have;
[tex]sin\angle X = \dfrac{Opposite \ leg \ length}{Hypotenuse \ length}[/tex]
Therefore, we have;
[tex]sin\angle D = \dfrac{Opposite \ leg \ length}{Hypotenuse \ length} = \dfrac{20}{25} = \dfrac{4}{5}[/tex]
∴ In simplified form, sin(D) = 4/5.
What’s 6 x 5 * divide* 10? I need answers plz
Answer:
It is 3
Step-by-step explanation:
6*5= 30
30/10= 3
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26 + 58 rounded to the nearest ten
Answer:
80
Step-by-step explanation:
Answer:
80
Step-by-step explanation:
26+58=84
Rounded=80
a) 12, 10, 7,3,
Rule:
b) 1,3,9, 27,
Rule:
I
c) 4, 19, 34, 49
Rule:
PLEASE HELP ME ASAP
Answer: -2
Step-by-step explanation: add all of the answers together to get -18. Then, divide by the total amount of numbers, 9 numbers in total. -18/9=-2
Answer:
2.111...
Step-by-step explanation: add the numbers altogether and divide by how many number you added
Determine the measure of angle b using the photo.
Answer:
m<b = 41
Step-by-step explanation:
<b = 41 because of vertical angle thm
Justin buys a shirt that costs 24 dollars and a jacket that costs 54 dollars. If sales tax is 7%, what is the total purchase price including tax?
Answer:
$83.46
Step-by-step explanation:
24 + 54 =78
78 × 7% = 5.46
78 + 5.46 = $83.46
4.
Do the data in the table represent a direct variation or an inverse variation? Write an equation to model the data in the table.
A. inverse variation; xy = 20
B. direct variation; y = 20x
C. direct variation; [tex]y=\frac{20}{x}[/tex]
D. inverse variation; [tex]\frac{y}{x} =20[/tex]
Answer: A. inverse variation; xy = 20
ANSWER
Step-by-step explanation: Brainly
B) xy=20
Inverse because it is of the form y=k/x, intuitively you can see that as x increases y decreases, hence "inverse variation".
...............................................................................................................................................
Answer:
Option B is correct
Inverse variation , xy = 20
Step-by-step explanation:
Inverse variation states:
If
then the equation is in the form of:
or
xy = k ....[1]
As per the statement:
Given the data:
x : 2 4 8 12
y : 10 5 5/2 5/3
Let any value of x and y to find k:
x = 4 and y = 5
Substitute in [1] we have;
⇒20 = k
or
k = 20
then we get;
xy = 20
Check:
Substitute x = 12 and y = 5/3
⇒ true.
Therefore, the the data in the table represent a inverse variation and an equation to model the data in the table is, xy = 20
In a survey of 232 students, about 5.5% have attended more than one play. Which is closest to the number of students in the survey who have attended more than play? 5 7 13 16
Answer:
13
Step-by-step explanation:
Number of students that attended more than play = percentage of students that attended more than play x total number of students
5.5% x 232
0.055 x 232 = 12.76 students
to round off to the nearest whole number, look at the first number after the decimal, if it is less than 5, add zero to the units term, If it is equal or greater than 5, add 1 to the units term.
Since the first term is 7 which is greater than 5, 1 would be added to it.
This gives 13
Johnny's father made a deal with him. He would pay him 30 cents to work for him the first day and double the amount every day.
Answer:
wow Johnny is going to be a million-are by the end of the year :) lol
Step-by-step explanation:
Have a nice night mate
:)
mark brainliest please :)
Answer:
I.d.k wut the question is asking but...
Step-by-step explanation:
30 cents a day then for every day he adds on so day 1 = 30 cents
Day 2 will be 60 cents day 3 would be 90 cents and so on just keep adding 30 cents per day Hope this helps if i didnt answer wut you were asking comment wut you were looking for and i will gladly help :D