Answer:
Option (3)
Step-by-step explanation:
We have to divide polynomial given as (x³ - 21x² + 147x - 343) by (x - 7) by synthetic division.
7 | 1 -21 147 -343
↓ 7 -98 343
1 -14 49 0
Therefore, quotient is (x² - 14x + 49) and the remainder will be 0.
Option (3) will be the answer.
What is the y-coordinate of point D after a translation of
(x, y) - (x + 6,7 - 4)?
Hey There!!
Your answer will be 1.
Step-by-step explanation:
If the coordinates of the point D' are (x, y), then, after translation, it will be
D(x + 6, y - 4).
that is 6 units right and 4 units down
It is given that the point before translation is D'(3, 5).
So, x + 6 = 3 + 6 = 9 and
y - 4 = 5 - 4 = 1
So, the y coordinate of point D after translation is 1.
Hope This Helps!!!
By ♡Itsbrazts♡
A man walks east for 4 miles Then south for 3 miles Then west for 2 miles Then north for 1 mile Then west for 2 miles In which direction and for how far should he walk to return to his starting point?
Answer:
Walk north 2 miles
Step-by-step explanation:
The man needs to walk two miles in the north to reach the starting point.
What are the directions?The direction is the four cardinal directions, these four direction points in four different directions, therefore, in east, west, north, and south.
The man will be 2 miles away from the starting point and will be the south of the starting point. Hence, the man needs to walk two miles in the north to reach the starting point.
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Q3. Ishah spins a fair 5-sided spinner. She then throws a fair coin.
(i) List all the possible outcomes she could get. The first one has been done for you.
(1, H)
(ii) Ishah spins the spinner and tosses the coin.
Work out the probability that she will get a 2 and a head.
Answer:
see below
Step-by-step explanation:
1.
1, H - 2, H - 3, H - 4, H - 5, H
1, T - 2, T - 3, T - 4, T - 5, T
2.
2,H is one out of 10 possible outcomes, so the probability is 1/10
the bible predicted many things about: answers: man's sin, God the Father, Christ.
Answer:
of what's right and wrong
Step-by-step explanation:
if you don't follow the Bible, when your a Christian, some say you go to the underworld
Instructions: Find the measurement of the angle indicated in the following parallelogram.
You are remodeling your kitchen. You've contacted two tiling companies who
gladly told you how long it took their workers to tile a floor of a similar size.
Jim completed half the floor in 12 hours. Pete completed the other half of the
floor in 10 hours. If Pete can lay 25 more tiles per hour than Jim, what
equation would you use to find the rate that Jim can lay tiles? Let x represent
Jim's rate.
Answer:
12x=10(25+x)
Step-by-step explanation:
Jim's rate=x
Pete's rate=y
Jim and Pete lays the same number of tiles.
So we have,
12x=10y
Pete's can lay 25 more tiles than Jim per hour
We have
y=25+x
Substitute y=25+x into 12x=10y
12x=10y
12x=10(25+x)
12x=250+10x
12x-10x=250
2x=250
x=250/2
=125
x=125
12x=10(25+x) is the equation used to find the rate that Jim can lay tiles
Translate the sentence into an inequality. Twice the difference of a number and 8 is greater than −21. Use the variable b for the unknown number.
Answer:
b > - 5/1Step-by-step explanation:
The statement
Twice the difference of a number and 8 is written as
2( b - 8)
The expression is greater than - 21 so we represent it by the > sign
So we have
2( b - 8) > - 21
Expand
2b - 16 > - 21
2b > - 21 + 16
2b > - 5
Divide both sides by 2
b > - 5/2Hope this helps you
Orion is working with a data set that compares the outside temperature, in degrees Celsius, to the number of gallons of ice cream sold per day at a local grocery store.
The data has a line of best fit modeled by the function f(x) = 3x + 4 . Orion determines that when the temperature is 25∘C, the store should sell about 79 gallons of ice cream. The correlation coefficient of the data is 0.39.
Explain how accurate Orion expects the prediction to be.
Answer: kindly check Explanation.
Step-by-step explanation:
The function f(x) = 3x + 4 is a linear regression model. Orion's prediction was obtained by Substituting 25 for x to obtain the predicted variable
f(25) = 3(25) + 4 = 75 + 4 = 79.
However, with a correlation Coefficient of 0.39, which is a numerical value of range - 1 to +1 and is used to measure the statistical relationship between the dependent variable (number of gallons of ice-cream sold per day) and the independent variable (temperature).
The closer the correlation Coefficient (r) value is to +1 or - 1, the stronger the degree of correlation. Positive r values depicts positive relationship while negative r values depicts negative relationship. The closer the r value is to 0. The weaker the relationship and a r value of means there is no Relationship exists between the two variables.
With a correlation Coefficient of 0.39, we can Infer that that only a moderate positive relationship exists between temperature and gallons of ice cream sold per day.
1. A game is played by spinning a wheel that contains the words Win and Lose. The wheel has 10 slots, with Win written four times and Lose written six times. If the wheel lands on win, you win
$5; on lose, you win nothing. It costs $2 to play. What is the expected value?
Answer:
i think its -$2
Step-by-step explanation:
The expected value of profit or loss is ZERO
What is spinning wheel game?Picker Wheel is a wheel spinner for a random picker. Various functions & customization. Enter choices or names, spin the wheel to decide a random result.
We have
If the wheel lands on win, you win $5;
on lose, you win nothing.
It costs $2 to play.
According to the question
Win written four times and Lose written six times.
P (W) = 4/10 = 0.4
P (L) = 6/10 = 0.6
x net p(x) xP(x)
Win 5 - 2 = 3 0.4 1.2
Loose 0 - 2 = -2 0.6 -1.2
∑xP(x) = 1.2 - 1.2 = 0
Hence , expected value of profit or loss is ZERO
or
You can say expected value is 2 $ against 2$ cost
5(0.4) + 0(0.6) = 2 against 2 $ ticket.
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34.5% of _____ = 333.27
Answer:
966.
Step-by-step explanation:
Think of the word "of" as a sign that you have to multiply.
Thus, you can divide 333.27 by 34.5%.
You derive 966.
- Hope this helped.
THIS IS A WHOLE PAGE ITS FOR 40 points MIDDLE SCHOOL PLEASE HELP
Answer:
the leanth of the track is 1/2 miles long.
Step-by-step explanation:
Im sorry that i couldn't complete all the questions, I had a family thing to go to so sorry.
How many ways are possible to choose 3 days out of February? NOTE: Use 28 days for the number of days in February. A) 3276 B) 378 C) 20475 D) 2925
Answer:
A) 3,276 ways.
Step-by-step explanation:
In this case, choosing February 1, February 12, and February 20 would be the same thing as choosing February 12, February 1, and February 20. So, since order does not matter, we will use a combination to solve the question.
The formula for combinations is...
n! / [r!(n - r)!], where n = the number of days in February (28) and r = the number of days you are choosing (3).
28! / [3! * (28 - 3)!]
= 28! / (6 * 25!)
= (28 * 27 * 26) / 6
= (14 * 9 * 26) / 1
= 14 * 9 * 26
= 126 * 26
= A) 3,276.
Hope this helps!
The area of a rectangular garden is given by the quadratic function:A(x)=-6x^2+105x-294A . Knowing that the area, length, and width all must be a positive value puts restrictions on the value of x. What is the domain for the function? Explain how you determined the domain. For what value of x, produces the maximum area? What is the maximum area of the garden? What is the Range of the function? Explain how you determined the range? What value(s) of x produces an area of 100 square units?
Answer and Step-by-step explanation:
The domain of a function is the values the invariable can assume to result in a real value for the variable. In other words, it is all the values x can be.
Since it's related to area, the values of x has to be positive. The domain must be, then:
[tex]-6x^{2} + 105x - 294 = 0[/tex]
Solving the second degree equation:
[tex]\frac{-105+\sqrt{105^{2} - 4(-2)(-294)} }{2(-6)}[/tex]
x = 3.5 or x = 14
The domain of this function is 3.5 ≤ x ≤ 14
The maximum area is calculated by taking the first derivative of the function:
[tex]\frac{dA}{dx} = -6x^{2} + 105x - 294[/tex]
A'(x) = -12x + 105
-12x + 105 = 0
-12x = -105
x = 8.75
A(8.75) = [tex]-6.8.75^{2} + 105.8.75 - 294[/tex]
A(8.75) = 165.375
The maximum area of the garden is 165.375 square units.
The Range of a function is all the value the dependent variable can assume. So, the range of this function is: 0 ≤ y ≤ 165.375, since this value is the maximum it will reach.
A(x) = 100
[tex]100 = -6x^{2} + 105x-294[/tex]
[tex]-6x^{2} + 105x - 394 = 0[/tex]
Solving:
[tex]\frac{-105+\sqrt{105^{2}-4(-6)()-394} }{2(-6)}[/tex]
x = 5.45 or x = 12.05
The values of x that produces an area of 100 square units are 5.45 and 12.05
Q2.
If ε={1, 2, 3, 4,………….., 10} and
A = Set of even numbers between 1 and 10.
B = Set of odd numbers between 1 and 10
C = Set of prime numbers between 1 and 10
(i)
List down the elements of sets A, B and C.
(ii)
List down the number of elements in sets A, B and C.
(iii)
Find AUC.
(iv)
Find BC.
(v)
Find AC
Answer:
hope its helpful to uh....
What are the roots of the function y = 4x2 + 2x - 30?
To find the roots of the function, set y = 0. The equation is 0 = 4x2 + 2x - 30.
Factor out the GCF of
Next, factor the trinomial completely. The equation becomes
Use the zero product property and set each factor equal to zero and solve.
The roots of the function are
Answer:
-3, 5/2
Step-by-step explanation:
What are the roots of the function y = 4x2 + 2x – 30?
To find the roots of the function, set y = 0. The equation is 0 = 4x2 + 2x – 30.
Factor out the GCF of : 2, so the equation becomes 0 = 2(2x2+x-15)
Next, factor the trinomial completely. The equation becomes: 0=2(x+3)(2x-5)
Use the zero product property and set each factor equal to zero and solve.
x+3=0 2x-5 = 0
x = -3, 5/2
The roots of the function are -3, 5/2.
Hope this helped!
The roots of the function y = 4x² + 2x - 30 are -3, 5/2 after using the zero product property.
What is a function?It is defined as a special type of relationship, and they have a predefined domain and range according to the function every value in the domain is related to exactly one value in the range.
We have:
y = 4x² + 2x - 30
To find the roots of the quadratic equation plug y = 0
4x² + 2x - 30 = 0
4x² + 12x - 10x - 30 = 0
4x(x + 3) - 10(x + 3) = 0
(x + 3)(4x -10) = 0
x + 3 = 0 or 4x - 10 = 0
x = -3 or x = 10/4 = 5/2
Thus, the roots of the function y = 4x² + 2x - 30 are -3, 5/2 after using the zero product property.
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I am being timed pls asap
Answer:
Writing it in matrix form
- 2 - 4 - 5 - 155
1 1 6 101
2 2 - 3 37
I hope this helps you
PLEASE HELP ASAP !!!!!! In the diagram, ∠J ≅ ∠M and JL ≅ MR. What additional information is needed to show ΔJKL ≅ △MNR by SAS? KL ≅ NR ∠L ≅ ∠R ∠K ≅ ∠N JK ≅ MN
Answer:
D. JK ≅ MN
Step-by-step explanation:
i tookthe test
A fruit company delivers its fruit in two types of boxes: large and small. A delivery of 3 large boxes and 8 small boxes has a total weight of 106 kilograms. A delivery of 5 large boxes and 2 small boxes has a total weight of 103 kilograms. How much does each type of box weigh? Weightofeachlargebox:kilogram(s) Weightofeachsmallbox:kilogram(s)
Answer:
The Large Box Weighs 18 kg, and the small box weighs 6.5 kg
Step-by-step explanation:
Let a= the weight in kg of a large box
Let b= the weight in kg of a small box
Multiply both sides of (1) by 4 and subtract (2) from (1)
1. 20a+8b=412
2. -3a-8b= -106
17a=306
a=18
and
5*8+2b=103
90+2b=103
2b=13
b=6.5
2(4 – 16) – (–30) 2(–12) – (–30) 24 – (–30) 54
Step-by-step explanation:
2(4 – 16) – (–30) 2(–12) – (–30) 24 – (–30) 54= 2×4-2×16 -×-30×2×-12-×-30×24-×-30= 8-32+30-24+30×24+30: 732
Answer:
2(4 - 16) - (-30) 2(-12) - (-30) 24 - (-30) 54
Solve the ones in the bracket first
Thus
2(-12) - 720 + 720 + 1620
= -24 + 1620
= 1596
Hope this helps
In ΔABC, if AB = 10 and BC = 6, AC can NOT be equal to
A. 4
B. 6
C. 8
D. 10
Answer:
A
Step-by-step explanation:
The answer is A because in the triangle, the two smaller sides added up have to be more than the bigger side, or equal, if it is a right triangle. so 4 is the smallest 4+6=10, so it does not work, but lets see if it is a right triangle
4^2+6^2=16+36=52. it would have to equal 100 to be a right triangle. Use Pythagorean thereon.
For a triangle, the any two sides must be greater than the third side.The measure of AC cannot be equal to 4
What is a triangle?A triangle has three sides and angle. For a triangle, the any two sides must be greater than the third side.
Given the following parameters
AB = 10 and
BC = 6
The measure of AC must be 8 for the theorem above to be true
6 +8 > 10
6 +10 > 8
10 + 8 > 6
Hence the measure of AC cannot be equal to 4
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help i need to submits this quickly
============================================================
Explanation:
Pick two points on this diagonal line where (x,y) has whole number coordinates. Two such points that fit the description are (-3,2) and (1,-1)
Use the slope formula to find the slope through these points
m = (y2-y1)/(x2-x1)
m = (-1-2)/(1-(-3))
m = (-1-2)/(1+3)
m = -3/4 is the slope
-------------------------
Extra info:
It doesn't matter which two points you pick as you'll always get the same slope value. Of course, the points must be on the diagonal line.
The negative slope indicates the line goes downhill as you move from left to right.
slope = rise/run = -3/4
rise = -3, a negative rise means we go down 3 units
run = 4, we go to the right 4 units
so we go down 3 and over to the right 4. This will move us from (-3,2) to (1,-1)
Maureen spent sh 207 to buy 7 exercise books and 4 pens while Sharon spent sh 165 to buy 5 exercise books and 5 pens of same type.Find the cost of each item
Answer:
book 25; pen 8
Step-by-step explanation:
If we let b and p represent the cost of a book and a pen, respectively, then the two purchases can be written as ...
7b +4p = 207
5b +5p = 165
Multiply the second equation by 4/5 and subtract the result from the first equation:
(7b +4p) -4/5(5b +5p) = (207) -4/5(165)
3b = 75 . . . . simplify
b = 25 . . . . . divide by 3
Dividing the second equation by 5 gives ...
b + p = 33
Solving for p, we have ...
p = 33 -b = 33 -25 = 8
The cost of an exercise book is 25; the cost of a pen is 8.
Write an equation in slope-intercept form of the line that passes through (-3,3) and (1,2)
Answer:
y = -1/4x + 9/4
Step-by-step explanation:
Slope-intercept form: y = mx + b
m = slope
b = y-intercept
Slope = [tex]\frac{y_2-y_1}{x_2-x_1}[/tex]
3-2/-3-1
Slope = [tex]-\frac{1}{4}[/tex]
In this problem, to find the y-intercept [tex]y-y_1 = m (x-x_1)\\[/tex].
y-3 = -1/4 (x+3)
y= -1/4x + 9/4
Answer:
yoo
Step-by-step explanation:
The sum of the digits of a two-digit number is 5. If nine is subtracted from the number, the digits will be reversed. Find the number. Also, If the tens digit is x, then the equation is: ___?
PLEASE HELP IMMEDIATELY
Find x when[tex] - \frac{1}{2} + x = - \frac{21}{4} [/tex]
[tex] - \frac{23}{4} [/tex]
[tex] - \frac{19}{4} [/tex]
[tex] \frac{19}{4} [/tex]
[tex] \frac{23}{4} [/tex]
Answer:
[tex]x = - \frac{19}{4} [/tex]Option B is the correct option.
Step-by-step explanation:
[tex] - \frac{1}{2} + x = - \frac{21}{4} [/tex]
Move constant to R.H.S and change its sign:
[tex]x = - \frac{21}{4} + \frac{1}{2} [/tex]
Take the L.C.M
[tex]x = \frac{ - 21 + 1 \times 2}{4} [/tex]
[tex]x = \frac{ - 21 + 2}{4} [/tex]
Calculate
[tex]x = - \frac{19}{4} [/tex]
Hope this helps...
Good luck on your assignment..
Step-by-step explanation:
-19/4 is the correct answer for your question
Anya graphed the line (y−2)=3(x−1) on the coordinate grid. A coordinate plane with a line passing through the points, (negative 2, negative 7), (0, negative 1), and (1, 2). What is the slope of Anya’s line? −3 −1 1 3
Answer:
Slope of Anya's line is m = 3
Step-by-step explanation:
Explanation:-
Given Anya graphed the line
(y−2)=3(x−1)
we know that slope intercept form is
y = mx +c
now given Anya line
y−2=3(x−1)
⇒ y - 2 = 3x - 3
⇒ y = 3x - 3 + 2
⇒ y = 3 x - 1
Comparing slope -intercept form
y = mx +c
slope of Anya's line is m = 3 and y-intercept C = -1
Answer:
M=3
Step-by-step explanation:
Hope this helps!
The volume of a right circular cone with both
2507
diameter and height equal to his What is the
3
value of h?
A) 5
B) 10
C) 20
D) 40
Question:
The volume of a right circular cone with both diameter and height equal to h is 250/7 cm³.
What is the value of h?
Answer:
A. 5
Step-by-step explanation:
Given
Solid Shape: Cone
Volume = 250/7
Diameter = Height
Required
Find the height of the cone
Provided that the diameter (D) and the height (h) are equal; This implies that
D = h ------ (1)
Also, Diameter (D) = 2 * Radius (r)
D = 2r
Substitute 2r for D in (1)
2r = h
Multiply both sides by ½
½ * 2r = ½ * h
r = ½h
Volume of a cone is calculated by;
Volume = ⅓πr²h
⅓πr²h = 250/7
Substitute ½h for r
[tex]\frac{1}{3} * \pi * (\frac{1}{2}h)^2 * h = \frac{250}{7}[/tex]
Take π as 22/7, the expression becomes
[tex]\frac{1}{3} * \frac{22}{7} * (\frac{1}{2}h)^2 * h = \frac{250}{7}[/tex]
Open the bracket
[tex]\frac{1}{3} * \frac{22}{7} * \frac{1}{4}h^2 * h = \frac{250}{7}[/tex]
Multiply both sides by 7
[tex]7 * \frac{1}{3} * \frac{22}{7} * \frac{1}{4}h^2 * h = \frac{250}{7} * 7[/tex]
[tex]\frac{1}{3} * 22 * \frac{1}{4}h^2 * h = 250[/tex]
Multiply both sides by 3
[tex]3 * \frac{1}{3} * 22 * \frac{1}{4}h^2 * h = 250 * 3[/tex]
[tex]22 * \frac{1}{4}h^2 * h = 750[/tex]
Multiply both sides by 4
[tex]4 * 22 * \frac{1}{4}h^2 * h = 750 * 4[/tex]
[tex]22 * h^2 * h = 3000[/tex]
[tex]22 * h^3 = 3000[/tex]
Divide both sides by 22
[tex]h^3 = \frac{3000}{22}[/tex]
[tex]h^3 = 136.36[/tex]
Take cube root of both sides
[tex]h = \sqrt[3]{136.36}[/tex]
[tex]h = 5.15[/tex]
[tex]h = 5[/tex] (Approximated)
If f(x) = 3x - 5 and g(x) = 7x + 2, what is f(x) x g(x)
Answer:
21x + 1
Step-by-step explanation:
f[g(x)]
= f(7x + 2)
= 3(7x + 2) - 5
= 21x + 6 - 5
= 21x + 1
Need help quick!
What is the product?
(-1 2 4) (3 6 1 2 4 0 0 6 2)
Answer:
[1 26 7]
Step-by-step explanation:
[1 26 7]
one row three column
==========================================================
Explanation:
We have a 1x3 matrix multiplied with a 3x3 matrix. This is a valid operation since the number of columns in the first matrix matches with the number of rows in the second matrix.
The resulting answer matrix will be 1x3 as it takes the number of rows of matrix A and the number of columns from matrix B, helping forming the answer matrix C.
The answer matrix looks like
[tex]C = \begin{bmatrix}x & y & z\end{bmatrix}[/tex]
where x, y and z are placeholders for actual numbers.
To get the value of x, we apply the dot product of the left matrix with the first column of the right matrix
x = (-1)(3)+(2)(2)+4(0) = -3+4+0 = 1
We'll do a similar set of steps to find y
Apply the dot product on the second column this time
y = (-1)(6)+2(4)+4(6) = -6+8+24 = 26
and the third column as well
z = (-1)(1)+2(0)+4(2) = -1+0+8 = 7
Since x = 1, y = 26 and z = 7, we can say
[tex]C = \begin{bmatrix}x & y & z\end{bmatrix}[/tex]
becomes
[tex]C = \begin{bmatrix}1 & 26 & 7\end{bmatrix}[/tex]
solve for n. 6n+14=25
Answer: n=1.8
Step-by-step explanation:
6n+14=25
-14 on both sides
25-14=11
6n=11
divide 6 on both sides
n=1.83333..
Answer:
n=[tex]\frac{11}{6}[/tex] of 1.8333...
Step-by-step explanation:
6n+14=25
-14 -14
6n=11
÷6 ÷6
n=[tex]\frac{11}{6}[/tex]
DOUBLE CHECK
6([tex]\frac{11}{6}[/tex])+14=25
11+14=25