Answer:
x = - [tex]\frac{3}{2}[/tex], x = 3
Step-by-step explanation:
To find the zeros let p(x) = 0 , that is
2x² - 3x - 9 = 0
Consider the factors of the product of the x² term and the constant term which sum to give the coefficient of the x- term.
product = 2 × - 9 = - 18 and sum = - 3
The factors are - 6 and + 3
Use these factors to split the x- term
2x² - 6x + 3x - 9 = 0 ( factor the first/second and third/fourth terms)
2x(x - 3) + 3(x - 3) = 0 ← factor out (x - 3) from each term
(x - 3)(2x + 3) = 0
Equate each factor to zero and solve for x
2x + 3 = 0 ⇒ 2x = - 3 ⇒ x = - [tex]\frac{3}{2}[/tex]
x - 3 = 0 ⇒ x = 3
Write an equation of the line that passes through the point (4,5) and has a slope of -2.
Answer:
y = - 2x + 13
Step-by-step explanation:
The equation of a line in slope- intercept form is
y = mx + c ( m is the slope and c the y- intercept )
Here m = - 2 , then
y = - 2x + c ← is the partial equation
To find c substitute (4, 5) into the partial equation
5 = - 8 + c ⇒ c = 5 + 8 = 13
y = - 2x + 13 ← equation of line
Answer:
Step-by-step explanation:
slope=-2
now using slope intercet formof equation of straight line,we get
y=mx+b
or, y=-2x + b
y + 2x =b
2x + y=b ...................... eq(i)
since the line passes through the point (4,5) it satisfies the equation (i)
y=5 and x=4 so,
equation is 2x +y =b
2*4 + 5=b
8+5=b
13=b
substituting the value of b in eq(i)
2x + y=b
2x + y=13
2x + y-13=0 is the required equation of the line.
How many three digit numbers greater than 540 can be formed using the digits
0,2,4,5,6,8 ?
Answer:
Step-by-step explanation:
Use the Substitution method to solve the system of equations
3x+4y=10
y=x-1
Answer: 2
Step-by-step explanation:
3x+4y=10
3x+4(x-1)=10
3x+4x-4=10
7x-4=10
Add 4 to both sides
7x=14
x=2
Answer:(2,1)
Step-by-step explanation:ap3x beans
Solve for r.
Enter the solutions from least to greatest.
-2x2 – 9 = -107
lesser I =
greater x =
Step-by-step explanation:
[tex] - 2 {x}^{2} - 9 = - 107 \\ - {2x}^{2} = - 98 \\ {x}^{2} = 49 \\ x = \sqrt{49} \\ x = 7 \\ { \boxed{lesser : \: - 7}} \\ { \boxed{greater : \: + 7}}[/tex]
I need help with number 1 and 2
Answer:
1. 452.39
2. 615.75
Step-by-step explanation:
area of a circle = A=πr2
A 5 kg stone falls from height of 100m and penetrate 2m in a layer of sand. The force applied by ground is
Answer:
49N
Step-by-step explanation:
Below is the calculation for the force applied:
It is given that the mass of stone is 5 kg and it falls from the height of 100 meters. Therefore, a force can be determined by multiplying the mass will a constant value of "a".
Force = Mass x a
Force = 5 x 9.8
Force = 49 N
Since the action-reaction are equal and opposite so the each will apply the same force.
The area of a rectangular wall of a barn is 135 square feet. It's length is 6 feet longer than a width. Find the length and width of the wall of the barn
Answer: [tex]15\ ft,6\ ft[/tex]
Step-by-step explanation:
Given
The area of a rectangular wall of a barn is [tex]135\ ft^2[/tex]
Suppose the width of the wall is [tex]x[/tex]
So, the length of the wall is [tex]6+x[/tex]
Area can be written as the product of length and width
[tex]\Rightarrow (6+x)x=135\\\Rightarrow 6x+x^2=135\\\Rightarrow x^2+6x-135=0\\\Rightarrow x=\dfrac{-6\pm \sqrt{6^2-4(1)(-135)}}{2(1)}\\\\\Rightarrow x=\dfrac{-6\pm 24}{2}\\\\\Rightarrow x=-15,9[/tex]
neglecting the negative value, width of the wall is [tex]9\ ft[/tex]
So, the length of the wall is [tex]9+6=15\ ft[/tex]
PLEASE HELPP
64, 16, 4, 1 converging or diverging
Answer:
The series 64, 16, 4, 1 is convergent.
Step-by-step explanation:
Let be [tex]\{x_{1}, x_{2},...,x_{n}\}[/tex] the set of values of the series. A series is convergent if and only if:
[tex]\frac{x_{i + 1}}{x_{i}} < 1, \, \forall\,i\in \mathbb{N}[/tex] (1)
If we know that [tex]x_{1} = 64[/tex], [tex]x_{2} = 16[/tex], [tex]x_{3} = 4[/tex] and [tex]x_{4} = 1[/tex], then the convergence ratio of each pair of consecutive values are, respectively:
[tex]\frac{x_{2}}{x_{1}} = \frac{1}{4}[/tex], [tex]\frac{x_{3}}{x_{2}} = \frac{1}{4}[/tex], [tex]\frac{x_{4}}{x_{3}} = \frac{1}{4}[/tex]
Hence, the series 64, 16, 4, 1 is convergent.
determine the equation of the circle graphed below.
( please help me )
Answer:
(x - 3)² + (y + 5)² = 10
Step-by-step explanation:
The equation of a circle in standard form is
(x - h)² + (y - k)² = r²
where (h, k) are the coordinates of the centre and r is the radius
Here (h, k) = (3, - 5 ) , then
(x - 3)² + (y - (- 5) )² = r² , that is
(x - 3)² + (y + 5)² = r²
r is the distance from the centre to a point on the line
Calculate r using the distance formula
r = [tex]\sqrt{(x_{2}-x_{1})^2+(y_{2}-y_{1})^2 }[/tex]
with (x₁, y₁ ) = (3, - 5) and (x₂, y₂ ) = (6, - 4)
r = [tex]\sqrt{(6-3)^2+(-4+5)^2}[/tex]
= [tex]\sqrt{3^2+1^2}[/tex]
= [tex]\sqrt{9+1}[/tex]
= [tex]\sqrt{10}[/tex] ⇒ r² = ([tex]\sqrt{10}[/tex] )² = 10
(x - 3)² + (y + 5)² = 10 ← equation of circle
Evaluate the exponential expression.
3•42
Answer:
48
Step-by-step explanation:
Trust me
Henry sees a train with 8 cars. Each car has 5 windows on the side that henry sees. Which number sentence can be used to find how many windows henry sees
Answer:
8 x 5 x 2
Step-by-step explanation:
total number of windows seen = total number of cars x total number of windows a car has
total number of windows a car has = number of windows a car has x total number of sides = 5 x 2
total number of windows seen = 8 x 5 x 2
Tell whether the triangle with the given side lengths is a right triangle.
60, 63, 88
The answer is
yes or
no
Answer:
no
Step-by-step explanation:
so in order for it to be a right triangle this would have to be true:
a^2 + b^2 = c^2
since c represents the hypoteneuse, it will be the longest side. so:
60^2 + 63^2 = 88^2
3600 + 3969 = 7744
7569 = 7744
since that statement is not true, the answer is no.
it is not a right triangle
the square root of 7569 is 87, so the triple would have to be : {60,63,87}
Avery invested $8,100 in an account paying an interest rate of 6 1 4 6 4 1 % compounded continuously. Khloe invested $8,100 in an account paying an interest rate of 5 5 8 5 8 5 % compounded monthly. To the nearest hundredth of a year, how much longer would it take for Khloe's money to double than for Avery's money to double
Answer:
1.26 years
Step-by-step explanation:
Help? Luis has saved $15. He doubles the amount he saves each week. Does this represent an exponential function? Choose the correct word in each drop-down menu.
This___ represent an exponential function, because his savings increase by a constant___
1st blank (does not, does)
2nd blank (ratio, difference)
Answer:
1). Does Not
2). Ratio
Step-by-step explanation:
According to the Question,
Given that, Luis has saved $15. He doubles the amount he saves each week.
This DOES NOT represent an exponential function, because his savings increase by a constant RATIO.a circular tabletop has a diameter of 2.1 m. what is its area
HI I NEED HELP ASAP I GIVE BRAINLEST IF YOU GET IT RIGHT
у X -7 -5 -5 -4 -3 -2 ברן 4 LO- To 2 -3 -6 -7 In this graph, the v-intercept of the line is 1. The equation of the line is v=
Answer:
The y intercepts is -2
y = 1x-2
Step-by-step explanation:
The y intercept is where it crosses the y axis
The y intercepts is -2
We need to determine the slope, by using to points on the line
(0,-2) and (2,0)
m = (y2-y1)/(x2-x1)
= (0 --2)/(2-0)
= (0+2)/(2-0)
= 2/2
= 1
The equation for the line is
y = mx+b where m is the slope and b is the y intercept
y = 1x-2
Which is equal to 6-45?
Answer:
-39
Step-by-step explanation:
Please give me brainliest.
Answer:
-39
Step-by-step explanation:
6-45
A buyer owes a seller $45 and has gone to pay $6. The remaining dollars which the buyer must give the seller is $39.
jalil asked for two triple-dip ice-cream cones.if each single -dip cone costs $1.69 and each extra scoop of ice cream is 00. 85 how much will he have to pay
Which of the following rational functions is graphed below?
Answer:
"C" has to be the answer...
there is a vertical asymptote at -5
thus you need a denominator that is zero at -5
plug in -5 into the equations only "C" ends up with a zero in the denominator at that point
Step-by-step explanation:
Sides are added to a convex polygon so that the sum of its interior angle measures is increased by 540°. How many sides are added to the polygon. Explain your reasoning.
The figure below is a square. Find the length of side x in simplest radical form with a
rational denominator.
VT
Answer:
x = [tex]\sqrt{14}[/tex]
Step-by-step explanation:
[tex]\sqrt{7}[/tex] / sin(45) = x / sin(90) (Cause its a square, the edges are 90 degrees)
[tex]\sqrt{14}[/tex] = x / 1
x = [tex]\sqrt{14}[/tex]
Rina added 5/6 of a bag of soil to her garden,Her neigboir Jessa Added 1 1/8 bags of soil to her garden,How much more soil did jessa add than rina?
(b) Simplify 4q2 – 3q2
Hellllllppppppppppp
Plsssss
Answer:
q^2
Step-by-step explanation:
Answer:
q^2
Step-by-step explanation:
4q^2 – 3q^2
Factor out the q^2
q^2 ( 4-3)
q^2(1)
1q^2
q^2
PLEASE HELP! NO SPAMMING! SHOW WORK!
The ratio of the dimensions of the model to the dimensions of the Great Pyramid is about 1 to 38. The surface area of the real pyramid is about how many times the surface area of the model.
Dimensions: a pyramid with a square base.
base sides: 6m
height: 4m
========================================================
Explanation:
Consider a square on paper that is 3 inches by 3 inches. It's area would be 3*3 = 9 square inches.
The ratio 1 to 38 means that 1 inch on paper corresponds to 38 inches in real life (assuming the "1 to 38" doesn't have any verbal units attached to it; if so, then refer to the note below). So a 3 by 3 square corresponds to a 114 by 114 square because 3*38 = 114.
The area of the second larger square is 114*114 = 12,996 square inches.
Now divide the two areas: (12,996)/(9) = 1444
It's probably not entirely obvious, but through a bit of playing around with various numbers, you should find that 38^2 = 1444. It's not a coincidence that this happens. The linear scale factor is 38 which means the area scale factor is 38^2 = 1444.
In short, the larger square in real life has area that is 1444 times that of its scaled down counterpart.
Or put another way:
large area = 1444*(small area)
------------------
Side note: This all assumes that the numbers in "1 to 38" are both the same unit. If we had a mixed ratio of units like "1 inch to 38 feet", then the answer would be different. You would need to convert from feet to inches, and then follow the steps above to get a different answer.
Can someone please help me with this question
Answer:
If x is the one vertically opposite to 40, then x will be 40, due to vertically opposite angles.
HELP PLEASE HELP MEEEE PLEASEEE
Answer: a. x=4 b. x=17.5
Step-by-step explanation:
a. 5x/2+1=11
subtract 1 from both sides : 5x/2=10
multiply both sides by 2 : 5x=20
divide both sides by 4 : x=4
b. 2x/7-3=2
add 3 to both sides : 2x/7=5
multiply both sides by 7 : 2x=35
divide both sides by 2 : x=17.5
(47.5+45.5+48.5+46.5+47+45+48+46+49)/9
:)
Answer:
47 and now I'm just typing so it lets me answer
Step-by-step explanation:
calculator
Can someone please help me?
create your own scale, it could be 2cm=40mm, so 3cm=60mm and 2.5cm=50mm.
then draw your trapezium in the given space using your scale
helpppppppppp plzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzz
Step-by-step explanation:
The left side represent the tens place of the number, and the right side represent the one sides of the number. So the numbers are
12,12,13,14,18,19,19, 20,23,26,27,31,31,31,32,34,41,44,45,48.
a. There are 20 terms so this equation 20/2=10 means the 10th term will be the median. make sure to also include the number 11th term becuase the number of terms is even. The 10th and 11th term are 26,27 so the median is the midpoint.
[tex] \frac{26 + 27}{2} = 26.5[/tex]
The median is 26.5
b. The range is maximum value minus minimum value.
[tex]48 - 12 = 36[/tex]
c. The mode is the number that appear the most
That number is 31.
d. 20 students took apart of this survey.