The Fundamental Theorem of Algebra asserts that this 2 n d degree polynomial must have precisely two roots.
What is algebra?According to the Fundamental Theorem of Algebra, this 2 n d degree polynomial must have precisely two roots. Algebra is the branch of mathematics that aids in the representation of problems or situations using mathematical expressions. In algebra, we utilize integers with definite or fixed values such as 2, 7, 0.068, and so on. In algebra, we employ variables such as x, y, and z in addition to integers. Elementary algebra, advanced algebra, abstract algebra, linear algebra, and commutative algebra are all sub-branches of algebra. In algebra, an algebraic expression is composed of integer constants, variables, and the basic arithmetic operations of addition(+), subtraction(-), multiplication(), and division(/). 5x + 6 is an example of an algebraic expression.
Here,
According to the Fundamental Theorem of Algebra, this 2 n d degree polynomial must have precisely two roots.
To know more about algebra,
https://brainly.com/question/24875240
#SPJ4
an anchor line for a tower needs to be replaced the tower is 96ft tall. the anchor line is 105ft long. how far from the tower can it be placed, to the from the nearest tenth
a). 142.3ft
b). 42.5ft
c). 9ft
d). 60 ft
Answer: 42.5ft
Step-by-step explanation: The wording in your question is a little unclear. I assume that you are looking for how far the anchor line is from the base of the tower.
If so, you can use the Pythagorean Theorem.
a^2 + b^ = c^2
96^ + b^2 = 105^2
Solve for b, gives you about 42.53ft round up and it is 42.5 ft :)
Happy to help
10 is 70% of what number? If necessary, round to the nearest tenth.
Answer:
The required answer is 7.
Step-by-step explanation:
=10*70/100
=7
A 15 foot ladder leans against a house with the base of the ladder 4 feet from the house. How high, to the nearest foot, up the wall will the ladder reach?
Answer:
height of house to ladder reach is 14 ft
Explanation:
Given data
ladder = 15 ft
base = 4 ft
to find out
height of house
solution
we know this is triangle shape so we apply here
so we consider here x is ladder and y is base and z is height
so
by pythagoras theorem
z² + y² = x²
so here
z² = x² - y²
put value
z² = 15² - 4²
z² = 209
z = 14.45 = 14
so height of house to ladder reach is 14 ft
Step-by-step explanation:
The ladder and the ground form a right triangle. Use the Pythagorean Theorem to find the other leg of the triangle.
a^2 + b^2 = c^2
a^2 + 4^2 = 15^2
a^2 + 16 = 225
a^2 = 209
a = 14.5 feet
solve for x for the first and second question.
Answer:
Step-by-step explanation:
I assume the figures are parallelograms, then
1). KL = MJ and
12x - 22 = 7x - 2
12x - 7x = 22 - 2
5x = 20
x = 4
2). m∠RQT + m∠QTS = 180°
(The picture is not clear and I might be wrong about coefficients by x for ∠RQT and ∠QTS)
(3x + 5)° + (9x - 17)° = 180°
12x - 12 = 180
12x = 192
x = 16
Felix said quadrilateral ABCD is a parallelogram because
BE = DE. What was his error?
Answer:
There is no angle E in the quadilateral presented in the question. Also, the angles he used are not on opposite side.
Step-by-step explanation:
To classify a quadrilateral is a parallelogram, a quadrilateral with both pairs of opposite sides must be parallel or congruent, that is in a quadrilateral ABCD, angle AB must equal CD and angle AD must equal BC.
Hence, when Felix said quadrilateral ABCD is a parallelogram because of BE = DE. His error was that "there is no angle E in the quadrilateral presented in the question and the angle he used are not on opposite side"
y = -[tex]\frac{4}{5}[/tex]x - 2
Which equation best describes the graph?
A. y = -[tex]\frac{4}{5}[/tex]x + 2
B. y = [tex]\frac{4}{5}[/tex]x + 2
C. y = [tex]\frac{5}{4}[/tex]x - 2
D. y = -[tex]\frac{5}{4}[/tex]x + 2
HELP PLEASE!! I WILL GIVE BRAINLIEST
Kevin went to the nursery and bought a 5 ft tall tree. After planting the tree, Kevin made a table to record the
height, h, of the tree, t years after it was planted. Verbally describe the relationship between h and t. (make an equation to illustrate the relationship between the height of the tree
and the number of years since it was planted. How tall will the tree be in 8 years?)
PLEASE HELP RN
If cot theta = 8/7, which equation represents cotangent theta? cotangent theta = StartFraction StartRoot 15 EndRoot Over 8 EndFraction cotangent theta = StartFraction StartRoot 15 EndRoot Over 7 EndFraction cotangent theta = StartFraction 7 StartRoot 15 EndRoot Over 15 EndFraction cotangent theta = StartFraction 8 StartRoot 15 EndRoot Over 15 EndFraction
Answer:
The second option, [tex]\frac{\sqrt{15}}{7}[/tex]
Step-by-step explanation:
Edge '21
The equation for cot θ is √15/7. Therefore, option B is the correct answer.
Given that, cosec θ=8/7.
We need to find the ratio of cot θ.
What is the ratio of cot θ?The ratio of cot θ is cot θ=Adjacent/Opposite.
As we know, cosec θ=Hypotenuse/Opposite.
So, 7²+x²=8²
⇒x=√15
Now, cot θ=√15/7.
The value of cot θ is √15/7. Therefore, option B is the correct answer.
To learn more about trigonometric ratios visit:
https://brainly.com/question/1201366.
#SPJ5
Dana is buying Grandparents Day gifts at the mall. She spends $13.75 on a teacup for her grandmother. She spends
4
5
of that on a coffee mug for her grandfather. How much money does Dana spend in all?
Answer:
$24.75
Step-by-step explanation:
4/5 of 13.75 = 11
11+13.75= 24.75
Dana spends $24.75 in all.
What is an Equation ?An equation is a mathematical statement that equates two algebraic expression by an equal sign.
The data given in the question is
Dana spends $13.75 on a teacup for her grandmother
She spends 4/5 of that on a coffee mug for her grandfather.
The total amount she spends is given by $x
The equation becomes
x = 13.75 + (4/5) * 13.75
x = $24.75
Therefore she spends $24.75 in all.
To know more about Equation
https://brainly.com/question/10413253
#SPJ2
Eight minus a number divided by three is greater than or equal to eleven
Answer:
Step-by-step explanation:
8-x/3>=11 is the equation, and the answer is:
x<= -9, so any number less than -9 is correct.
The solution is x ≤ -9
What are Inequality Equations?
Inequalities are the mathematical expressions in which both sides are not equal. In inequality, unlike in equations, we compare two values. The equal sign in between is replaced by less than (or less than or equal to), greater than (or greater than or equal to), or not equal to sign.
In an inequality, the two expressions are not necessarily equal which is indicated by the symbols: >, <, ≤ or ≥.
Given data ,
Let the number be x
8 - x/3 ≥ 11
Subtracting 8 on both sides , we get
-x/3 ≥ 3
Multiplying by 3 on both sides , we get
-x ≥ 9
Interchanging the sign on both sides , we get
x ≤ -9
Hence , the solution is x ≤ -9
To learn more about inequality equations click :
https://brainly.com/question/84497
#SPJ2
A country trying to decide whether to join the United Nations must determine whether it is willing to: O A. give up its own national laws in favor of international laws set by the UN. O B. occasionally go against its own interests in favor of international priorities. O C. supply a large number of military forces to the UN standing army. O D. leave any regional intergovernmental organizations it has already joined.
Answer:
to guarantee equality for all
Step-by-step explanation:
The league of nations was created to prevent another global war
Divide. Express your answer in simplest form.
11/12 ÷ 3/4=
Answer:
11/9
hope this helped :)
Step-by-step explanation:
Answer:
Step-by-step explanation:
11 / 12 = 0,91 and a periodic 6
3 / 4 = 0,75
11 / 12 = 3 / 4 = 0,916 ÷ 0,75
(-3, -14) and (0, -9)
Answer: -26
Step-by-step explanation: hope this helps :)
find the vertex of the quadratic function f(x) = (x-4) (x+2)
Answer:
vertex = (1, - 9 )
Step-by-step explanation:
The x- coordinate of the vertex is at the midpoint of the zeros.
Given
f(x) = (x - 4)(x + 2)
Find the zeros by letting f(x) = 0 , that is
(x - 4)(x + 2) = 0
Equate each factor to zero and solve for x
x + 2 = 0 ⇒ x = - 2
x - 4 = 0 ⇒ x = 4
Then
[tex]x_{vertex}[/tex] = [tex]\frac{-2+4}{2}[/tex] = [tex]\frac{2}{2}[/tex] = 1
Substitute x = 1 into f(x) for corresponding y- coordinate
f(1) = (1 - 4)(1 + 2) = (- 3)(3) = - 9
Vertex = (1, - 9 )
The cost of 9 scarves is $56.25. What is the unit price?
Answer:
6.25
Step-by-step explanation:
plz solve it and help me for it
Given:
Base angle of an isosceles triangle is 15 degrees more than its vertical angle.
To find:
The measure of each angle of the triangle.
Solution:
Let x be the vertical angle. Then,
One base angle = x+15 degrees
We know that base angles of an isosceles triangle are equal.
Another base angle = x+15 degrees
Now, the sum of all angles of a triangle is 180 degrees by the angle sum property.
[tex]x^\circ+(x+15)^\circ+(x+15)^\circ=180^\circ[/tex] (Angle sum property)
[tex](3x+30)^\circ=180^\circ[/tex]
[tex]3x+30=180[/tex]
[tex]3x=180-30[/tex]
[tex]3x=150[/tex]
Divide both sides by 3.
[tex]x=\dfrac{150}{3}[/tex]
[tex]x=50[/tex]
The measure of base angles is
[tex](x+15)^\circ=(50+15)^\circ[/tex]
[tex](x+15)^\circ=65^\circ[/tex]
Therefore, the measure of angles are 50°, 65° and 65°.
> Find the area of a circle with diameter 12 yd. Use the value 3.14 and do not round your answer. Be sure to include the correct unit in your answer. 12 yd
[tex]area = \pi {r}^{2} [/tex]
[tex]area = (3.14) {(6)}^{2} [/tex]
[tex]area = (3.14)(36)[/tex]
[tex]area = 113.04 \: yd[/tex]
The terrace of a house is rectangular in shape with a length of 10m and a width of 5m. Find the volume of
rainfall collected on the terrace if its height is 1m, Express in liter.
Answer:
Step-by-step explanation:
Volume = Area of the base times the height
V = length * width * height
V = 10 * 5 * 1
V = 50 m^3
Now change it to liters
50 * 1000 = 50000 liters^3
A dairy facility has a bulk milk tank that is shaped like a right circular cylinder. The
tank has a height of 12 feet and a diameter of 216 inches.
Answer:336
Step-by-step explanation:
12
216 = 336
En la tabla 1.8 se presentan los puntos de ebullición aproximados de algunos elementos de la tabla periodica flúor -180 hidrogeno -253 argón -186 helio -269 nitrógeno -196 neón -246 ¿Cuál es el elemento químico con el mayor punto de ebullición?¿ y con el menor?
Answer:
Lowest boiling point = helium.
Highest boiling point = fluorine
Step-by-step explanation:
Given :
fluorine -180
hydrogen -253
argon -186
helium -269
nitrogen -196
neon -246
Arranging the boxing points of each chemical element on a number line, the least which will be located to the leftmost part is Helium with a boiling point of - 269 ; while the highest will be fluorine which is - 186°C
solve the inequality -3x + 6 > -2
Answer:
x<8/3
Step-by-step explanation:
Your answer is x is less than 8 over 3
Answer:
Answer is d
Step-by-step explanation:
x<8/
Whats 4x+2=2(x+6) ?
Just want to see your answers
Answer:
x = 5
Step-by-step explanation:
4x + 2 = 2(x + 6)
4x + 2 = 2x + 12 (after you distribute the 2)
add and subtract like terms
4x - 2x = 12 - 2
2x = 10
x = 5
you can double check by substituting the x with 5 in the equation
4 (5) + 2 = 2(5 + 6)
20 + 2 = 2(11)
22 = 22
A rectangle has a length of 2x+7 and a width of 3x+8. Write and simplify an expression for the perimeter of that rectangle.
A perimeter is a sum of lengths of sides of a lateral.
[tex]2x+7+3x+8=5x+15[/tex].
4.
The area of the figure formed by joining the mid-points of the adjacent sides of a rhombus
with diagonals 16cm and 12cm is
Answer:
48 cm²
Step-by-step explanation:
The diagonals are in a proportion of 4:3, thus sides of a Pythagorean Triple; they cross at a right angle. The figure formed by joining the midpoints of adjacent sides is a rectangle with sides half the lengths of the original diagonals. 8×6=48
Otis is packing two gift boxes in a shipping carton. The rest of the space in the carton will be filled with packing pellets. What is the volume of the space that needs to be filled with packing pellets?
Answer:
[tex]V_3 = 1916in^3[/tex]
Step-by-step explanation:
Given
See attachment for gift items and the shipping carton
Required
Determine the volume of the empty space
First, we calculate the volume of the carton.
[tex]V = LWH[/tex]
From the attachment
L = 16; W =11 and H =13
So:
[tex]V = 16*11*13[/tex]
[tex]V = 2288[/tex]
Next, calculate the volume of the blue wrap
[tex]V = lwh[/tex]
From the attachment
l = 9; w =9 and h =2
So:
[tex]V_1 = 9 * 9 * 2[/tex]
[tex]V_1 = 162[/tex]
Next, calculate the volume of the pink wrap
[tex]V = lwh[/tex]
From the attachment
l = 6; w =5 and h =7
So:
[tex]V_2 = 6*5*7[/tex]
[tex]V_2 = 210[/tex]
The volume of the rest space (V3) is then calculated as:
[tex]V_3 = V - V_1 -V_2[/tex]
[tex]V_3 = 2288 - 162 -210[/tex]
[tex]V_3 = 1916[/tex]
Hence, the rest volume is 1916in^3\
hhhheeeepppp pleas e e e e e e e e e e e e e e branlist
Answer:
27
Step-by-step explanation:
a+b/2 times h
thats teh formula for the area of a trapezoid so a and b are the top and bottom sides of the trapezoid
so 6 on the bottom and 3 on the top
add those and it equals 9 then divide by 2 gives us 9/2
then the height would be 6
so we multiply 9/2 by 6 giving us 54/2
simplified equals 27 so ur answer would be 27 units squared
Answer:27
Step-by-step explanation:
melitón se comió 3 rebanadas de una pizza pequeña de seis rebanadas Cómo se representa una fracción
[tex] \frac{3}{6} [/tex]
Explicación:El numerador es lo que melitón se comió...
Y el denominador son las porciones (rebanadas) en que esta dividida la pizza.
A line is represented by the equation y = 3x – 7. Which statement about the line is TRUE?
A.
The y-intercept is 7.
B.
The line has a positive slope.
C.
The point (1, 4) lies on the line.
D.
This line is parallel to the line whose equation is y = 2x – 7.
Answer:
B
Step-by-step explanation:
because the slopes is 3.
Mark scored 138 points in 6 games. How many points did he score per game?
Answer:
23 Points
Explanation:
The answer you are looking for is 23 points per game.
To find this answer, you simply divide 138 by 6.
I hope this helps!
pls pls help me! Trousers bought 1400 dollars with 20% discount. How much is the original price?
Answer:1120 dollars. Δ
Step-by-step explanation:You will pay $1120 for a item with original price of $1400 when discounted 20%. In this example, if you buy an item at $1400 with 20% discount, you will pay 1400 - 280 = 1120 dollars.
#I hope this helps!!!
~Regards~
44014137