Answer:X-3 is a factor of x³+ax²–2x+3
Step-by-step explanation:X-3 is a factor of x³+ax²–2x+3
p(x)=x
3
−ax
2
+2x+a−1
⇒ p(a)=(a)
3
−a(a)
2
+2(a)+a−1
⇒ 0=a
+2a+a−1=0
⇒ 3a−1=0
⇒ 3a=1 a=
3
1
Question
Solve 2y−18x=−26 for y.
Answer:
-26
Step-by-step explanation:
NAME
DATE
PERIC
Lesson 3: More about Constant of Proportionality
Cool Down: Fish Tank
Mai is filling her fish tank. Water flows into the tank at a constant rate. Complete the table
as you answer the questions.
1.
How many gallons of water will be in the fish tank after 3 minutes? Explain your
reasoning.
2.
How long will it take to fill the tank with 40 gallons of water? Explain your reasoning
3. What is the constant of proportionality?
The ratio of one variable quantity to another that is always constant and to which it is proportional is known as the constant of proportionality then the constant of proportionality exists r = 1.6.
What is meant by constant of proportionality?The ratio of one variable quantity to another that is always constant and to which it is proportional is known as the constant of proportionality.
Given
x y
0.5. 0.8
1. 1.6
3. 4.8
25. 40
To estimate the constant of proportionality uses the following formula:
y = r x
Where r is the constant of proportionality;
Simplify the value of r, we get
r = y/x
Substitute the values of x = 0.5 and y = 0.8, in the above equation then
r = 0.8/0.5
r = 1.6
When x = 1 ; y = 1.6
r = 1.6/1
r = 1.6
When x = 3; y = 4.8
r = 4.8/3
r = 1.6
When x = 25 ; y = 40
r = 40/25
r = 1.6
The value of r exists constant.
Therefore, the constant of proportionality exists r = 1.6.
The complete question is:
Mai is filling her fish tank. Water flows into the tank at a constant rate. Complete the table and answer the question below.
time (minutes) water (gallons)
0.5 0.8
1
3
40
What is the constant of proportionality?
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please help need this asap!!!!! PLEASE SOMEONE ANSWER I WILL GIVE EXTRA POINTS!!!
The area of the circles are as follows:
254.34 km²1962.5 mm²379.94 m² 907.46 cm²How to find area of a circle?The area of a circle can be found as follows;
area of a circle = πr²
where
r = radiusTherefore,
a.
area of the circle = πr²
diameter = 18km
r = 18 / 2
r = 9 km
Hence,
area of the circle = πr²
area of the circle = 3.14 × 9²
area of the circle = 254.34 km²
b.
area of the circle = 3.14 × 25²
area of the circle = 3.14 × 625
area of the circle = 1962.5 mm²
c.
area of the circle = 3.14 × 11²
area of the circle = 3.14 × 121
area of the circle = 379.94 m²
d.
area of the circle = 3.14 × 17²
area of the circle = 3.14 × 289
area of the circle = 907.46 cm²
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What is the equation of the line that passes through the point (−3,1) and has a slope of −3?
Of 85 entries in the parade, 19 were
marching bands. How many entries were
not marching bands?
If x is a positive integer, this expression is equivalent to what?
Given:
[tex]\text{ Th expression is }4x^{\frac{1}{2}},\text{ x is a positive integer.}[/tex]Required:
Which option is equivalent?
Explanation:
The equivalent for is
[tex]\begin{gathered} =4x^{\frac{1}{2}} \\ =4\sqrt{x} \end{gathered}[/tex]Answer:
Option B is correct answer.
please help me solve this
It is to be noted that:
The current total bid for Empire design is $3,060,000The current total bid for Build-EM-UP-CO is $ 3,120,000.What is a bid?Bidding is an individual or business's offer to establish a price for a product or service or a demand that something be done. Bidding is a method of determining the price or worth of something. Bidding may be done by a person who is influenced by a product or service in a given setting.
The calculations are given as follows:
Given:
Proposal of Empire design:
$30000 x b
$ 60000/ I beam
Proposal of Build-EM-UP-CO.
$32000 x b
$ 40000/ I beam
Empire Design
Since b = 9ft; and number of I beams = 6, Hence
Total bid = (300,000 * 9) + (60,000 * 6)
= $3,060,000
Build-EM-UP-CO.
Recall that b = 9ft; and number of I beams = 6, Hence
Total Bid = (320,000 * 9) + (40,000 * 6)
Therefore,
Total bid = $3,120,000.
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Full Question:
For full details of the question, see the attached image
In the figure ZX = 2x + 1 YW = 3x - 1 and YX = 1, find perimeter of VYZ
The perimeter of triangle VYZ is 12 units.
How to find the perimeter of a triangle?The perimeter of a triangle is the sum of the whole sides of the triangle.
In other words, the perimeter of a triangle is the total distance covered by its boundaries or the sides.
Therefore,
perimeter of ΔVYZ = VY + ZY + ZV
Therefore,
VY = ZY = ZV = XW
Hence,
YW = YX + XW
Therefore,
XW = YW - YX
YW = 3x - 1
YX = 1
Hence,
XW = 3x - 1 - 1
XW = 3x - 2
Therefore,
perimeter of ΔVYZ = 3x - 2 + 3x - 2 + 3x - 2
perimeter of ΔVYZ = 9x - 6
ZX = YW
2x + 1 = 3x - 1
2x - 3x = - 1 - 1
-x = -2
x = 2
Therefore,
perimeter of ΔVYZ = 9(2) - 6
perimeter of ΔVYZ = 18 - 6
perimeter of ΔVYZ = 12 units
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Express each phrase as a rate and unit rate.
(Round your answer to the nearest hundredth.)
1) 7 calculators cost $120.00
Answer:
$100.00
Step-by-step explanation:
5 and above ex: 150 =200 140=100 under 5 keep the first letter then turn the other numbers into 0's 5 and above make the first number go up one then turn the rest of the numbers in to 0's
3 movie tickets cost $36. At this rate, what is the cost per ticket?
Answer:
12
Step-by-step explanation:
36 divided by 3 is 12
What is the solution set of the following equation?
-8x + x + 15 = -7x + 12
a. Ø
b. {all reals}
c. {1/7}
Answer:
A
Step-by-step explanation:
(-8x + x) + 15 = -7x +12
-7x +15 = -7x + 12
15 = 12 There are no solutions
What is the answer to f(2)=
the answer is 2f
Re-order terms so constants are on the left
f×2=2f
(Can anyone answer this please? I need it ASAP!!) A2B3C4 (in hexadecimal) - 3F2E1D (in hexadecimal) = ______________
The hexadecimal value from the operation is 6385A7
Hexadecimal NumbersTo solve this problem, we have to subtract the hexadecimal numbers from one another.
In doing so, we would subtract 3F2E1D from A2B3C4.
This would give us,
[tex]A2B3C4 - 3F2E1D = 6385A7[/tex]
The value of the expression is 6385A7.
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Which is larger, 52 or 33?
Answer:
52
Step-by-step explanation:
52 is a bigger number than 33?
A =
h(a + b)/2 solve for b
Answer: b = (−ah+2a)/h
Step-by-step explanation:
Step 1: Flip the equation.
Step 2: Add (-1)/2ah to both sides.
Step 3: Divide both sides by h/2.
Question 5Which of the following is equivalent to (2 – 2) (x - 1)
A 100ml tub of ice cream costs £1.50. Work out how much 500ml tub of ice cream would cost.
Answer:
Answer: 7.5 or 7 1/2.
Which numbers I have to put in the boxes
0.8-2x=-1.4
Solve for x
Answer:
x= -0.3
Step-by-step explanation:
0.8-2x=1.4 Set up equation
-2x=1.4-0.8 Put Like terms together
-2x=0.6 Subtract like terms
x=0.6/-2 Divide
x=-0.3 Answer
Please help me find out what 758x92 is
Answer:69736
Step-by-step explanation:
Which system is responsible for carrying this oxygen to the muscles?
Answer:
The circulatory system
Step-by-step explanation:
Is this math? lol
:]
You invested $101 and received $106.05 after one year. What was the interest rate?
The rate of interest was 5%.
The rate of interest and simple interest can be related through the formula -
S.I. = PRT/100, where S.I. stands for simple interest, P stands for principal, R stands for rate of interest and T stands for time.
Amount = Principal + Interest
Interest = 106.05 - 101
Performing subtraction on Right Hand Side of the equation
Interest = $5.05
Rate of interest = (5.05×100)/(101×1)
Performing multiplication in numerator and denominator
Rate of interest = 505/101
Performing division
Rate of interest = 5
Therefore, to earn $106.05 from $101 in one year, the rate of interest should be 5%.
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Using Pythagoras' Theorem please solve it.
[tex] \huge\underline\mathcal{Answer \: - }[/tex]
Pythagoras theorem states that the square of hypotenuse equals the sum of square of other two sides.
therefore ,
[tex](25) {}^{2} = (x + 3) {}^{2} + 4 { }^{2} (x + 2) {}^{2} \\ \\ \longrightarrow \: 625 = x {}^{2} + 9 + 6x + 16(x {}^{2} + 4 + 4x) \\ \\ \longrightarrow \: 625 = x {}^{2} + 9 + 6x + 16x {}^{2} + 64x + 64 \\ \\ \longrightarrow \: 625 = 17x {}^{2} + 70x + 73 \\ \\ \longrightarrow \: 17x {}^{2} + 70x + 73 - 625 = 0 \\ \\ \longrightarrow \: 17x {}^{2} + 70x - 552 = 0[/tex]
now using quadratic formula ,
[tex]x = \frac{ - b \: \pm \: \sqrt{b {}^{2} - 4ac} }{2a} \\ [/tex]
here , a = 17 , b = 70 , c = -552
substituting the values in the equation above ,
[tex]x = \frac{70 \: \pm \: \sqrt{70 {}^{2} - 4(17)( - 552)} }{2 \times 17} \\ [/tex]
after simplifying we get ,
[tex]\boxed{x = 4} \: \: or \:\boxed{ x = \frac{ - 138}{7} } \\ [/tex]
since length can't be negative , therefore the other value will be neglected and hence ,
[tex]\boxed{value \: of \: x \: = \: 4 \: cm}[/tex]
hope helpful ;-;
======================================================
Work Shown:
As you mentioned, we'll use Pythagoras' Theorem aka Pythagorean Theorem.
[tex]a^2+b^2 = c^2\\\\(x+3)^2+(4(x+2))^2 = 25^2\\\\(x+3)^2+16(x+2)^2 = 625\\\\(x^2+6x+9)+16(x^2+4x+4) = 625\\\\x^2+6x+9+16x^2+64x+64 = 625\\\\17x^2+70x+73 = 625\\\\17x^2+70x+73-625 = 0\\\\17x^2+70x-552 = 0\\\\[/tex]
Next, we'll use the quadratic formula with a = 17, b = 70, c = -552.
[tex]x = \frac{-b\pm\sqrt{b^2-4ac}}{2a}\\\\x = \frac{-70\pm\sqrt{(70)^2-4(17)(-552)}}{2(17)}\\\\x = \frac{-70\pm\sqrt{42436}}{34}\\\\x = \frac{-70\pm206}{34}\\\\x = \frac{-70+206}{34} \ \text{ or } \ x = \frac{-70-206}{34}\\\\x = \frac{136}{34} \ \text{ or } \ x = \frac{-276}{34}\\\\x = 4 \ \text{ or } \ x \approx -8.1176\\\\[/tex]
Ignore the negative x value solution. The sides (x+3) and 4(x+2) will be negative values if we plugged in x = -8.1176, but negative side lengths do not make sense.
This makes x = 4 the only possible solution.
----------------
If x = 4, then,
vertical leg = x+3 = 4+3 = 7horizontal leg = 4(x+2) = 4*(4+2) = 4*6 = 24This is a 7-24-25 right triangle.
We can confirm this using the pythagorean theorem
[tex]a^2+b^2 = c^2\\\\7^2+24^2 = 25^2\\\\49+576 = 625\\\\625 = 625 \ \ \ \checkmark[/tex]
"-2+8" > "-2" heeeeelpp
Answer: Yes this equation means 6 is greater than -2, making this a true statement if that was what you're asking for.
find the area. please explain how to get it
Answer:
Step-by-step explanation:
(the small double lines like = means that the length of those sides are all same)
So, if one length is considered as x
the other two will also be x
we see that the length of one side is given which is 27
to find x
x + x + x = 27
3x = 27
so, x = 27/3
x = 9m
(the small vertical single line means that those sides are equal)
so if one side is y, the other two are also y
so , y + y+ y = 30
3y = 30
y = 10m
If we imagine the stairs to be made of small rectangles of length 10m and base 9m , finding area will be easier.
we will see that there are 9 rectangles in total
area of rectangle = length x base
so, area of 1 rectangle = 9x10
= 90[tex]m^{2}[/tex]
so area of 9 identical rectangles = 9 x 90
= 810 [tex]m^{2}[/tex]
what is 0.4111111… as a fraction
Find the equation of the line that contains the point (-1,-6) and is parallel to the line 4x + 7y=11. Write the equation in slope-intercept form, if possible.
answer box to complete your choice.
Answer:
y = -4/7x - 46/7
Step-by-step explanation:
4x+7y=11
7y=11-4x
y=-4/7x + 11/7
Slope or parallel line: -4/7
Point=(-1,-6)
y+6 = -4/7(x+1)
y = -4/7x - 46/7
:]
please show work out
find the dimension of A34×b41 matrix]
A34 should represent either a square matrix with number of columns=number of rows =34 or the 4th element in the 3rd row in the matrix A [which is not possible in the given matrix since each row has only 3 elements]
The dimension of a matrix is given as (the number of rows it has, say a) x (the number of columns it has, say b) [read as a by b].. The given matrix has 4 rows and 3 columns, so its dimension is 4x3.
For a matrix A of dimension axb to be multiplied with a matrix B of dimension cxd, the number of columns of matrix A should be equal to the number of rows of matrix B, that is b = c should be satisfied. In this case both matrices are of the same dimension 2x3 but 3 (number of columns in first matrix) is not equal to 2 (number of rows in second matirx). So these matrices cannot be multiplied as their dimensions do not match.
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A retired couple invested $8000 in bonds. At the end of one year, they received an interest payment of $456. What was the simple interest rate of the bonds?
5.7%
Explanaton:let amount invested = Principal = $8000
time = 1 year
rate = ?
Interest = $456
To get the rate, we'll apply simple interest formula:
[tex]\begin{gathered} I\text{ = PRT} \\ I\text{ = interest, P = principal, R = rate, T = time} \end{gathered}[/tex][tex]\begin{gathered} 456\text{ = 8000}\times R\times1 \\ 456\text{ = 8000R} \\ \text{divide both sides by 8000:} \\ \frac{456}{8000}\text{ =}\frac{8000R}{8000} \\ \\ R\text{ = 0.057} \\ In\text{ percent, rate = 0.057}\times100 \\ \text{Rate = 5.7\%} \end{gathered}[/tex]Hence, the simple rate of the bonds is 5.7%
Choose the statements that are true about a cube with side length 1 unit.
It has a volume of 6 cubic units.
It has a volume of 1 cubic unit.
It has a volume of 3 cubic units.
It is called a "one block."
It can be used to measure volume.
It is called a "unit cube."
The answer to the mentioned statement are :
first statement is WRONG
the second statement is RIGHT
The third statement is also WRONG
the fourth statement is RIGHT
fifth statement is RIGHT
sixth statement is WRONG
The side of the given cube is 1 unit.
This means that the Length= Breadth = Height = 1 unit because it is cube
This means that the volume can be described as
( side ) ³
that is 1 × 1 × 1 = 1 cubic unit
thus the first statement is WRONG
However the second statement is RIGHT
The third statement is also WRONG
since it is a cube whose volume is 1 cubic unit
thus we can say that it is one block
Thus the fourth statement is RIGHT
fifth statement is RIGHT
sixth statement is WRONG
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