Answers
9514 1404 393
Answer:
(c) The solution -6 is an extraneous solution
Step-by-step explanation:
If you solve the equation graphically, you can avoid extraneous solutions. The true solution is x = -1.
You can tell from the equation that the domain will be restricted to values of x that make the radical non-negative:
x+4 ≥ 0 ⇒ x ≥ -4
Then x=-6 must be an extraneous solution. It arises when the negative square root is used.
__
The conventional solution method has you square both sides and solve the resulting quadratic.
(x +4)² = x +10
x² +7x +6 = 0
(x +6)(x +1) = 0 ⇒ x = -6 or -1
The solution x=-6 is not in the domain, so is extraneous.
__
Additional comment
Graphical solution is often easier if the equation is in the form f(x) = 0. That form can be had by subtracting one side of the equation from both sides. In the attached, we subtracted √(x+10) from both sides. (We added the negative branch of the square root function to show where the extraneous root comes from.)
Related Questions
Please help I’ll give brainliest
Answers
if f(x)=3^x+10x and g(x)=5x-3, find (f-g)(x)
Answers
Answer:
[tex]3^x+5x+3[/tex]
Step-by-step explanation:
Given that,
[tex]f(x)=3^x+10x[/tex]
and
[tex]g(x)=5x-3[/tex]
We need to find (f-g)(x).
We know that,
(f-g)(x) = f(x)-g(x)
[tex]=3^x+10x-(5x-3)\\\\=3^x+10x-5x+3\\\\=3^x+5x+3[/tex]
So, the value of (f-g)(x) is [tex]3^x+5x+3[/tex].
1850=12
2918=20
5044 = ?
7573=56
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Answer:
1623 jajaggkcgaiahvs Kah kaye kaha
A larger number is double the sum of 3 and a smaller number. The larger number is 2 less than 3 times the smaller number. If y represents the larger number and x represents the smaller number, which equations model the situation? Check all that apply.
y=3x-2
3x-y=2
3x-y=-2
y=2-3x
y=2(x+3)
Answers
Answer:
1,2, and 5
Step-by-step explanation:
y=2*(3+x)
y=3x-2
3x-y=2
Which expression is equivalent to 96?
Answers
Answer:
[tex]4\sqrt{6}[/tex]
Step-by-step explanation:
[tex]\sqrt{96}[/tex]
[tex]\sqrt{2*2*2*2*2*3}[/tex]
[tex]2*2\sqrt{2*3}[/tex]
[tex]4\sqrt{6}[/tex]
In one area, the lowest angle of elevation of the sun in winter is 20 degrees. Find the distance x that a plant needing full sun can be placed from a fence that is 10.5 feet high. Round your answer to the tenths place when necessary.
Answers
Answer:
11.1 feet
Step-by-step explanation:
From the solution triangle attached, the required distance is represented as x ; the value of x can be obtained using trigonometry ;
Cosθ = opposite / Adjacent
Cos 20 = 10.5 / x
x * Cos 20 = 10.5
x = 10.5 / cos 20
x = 11.174 feets
Solve the system of equations by graphing on a separate sheet of paper. Write your solutions as ordered pairs from least to greatest with respect to the x-coordinate.
y=x2+6x+4
y=x
Answers
Answer:
x= -2
y= -2
Step-by-step explanation:
y = 8x + 14
y = x
Now by subtraction of these two equation,
So 0 = 7x + 14
x = -2
y = -2
Can y’all please help me which equation has an infinite number
Answers
Answer:
B
Step-by-step explanation
: )
which functions have a range of.. SELECT MORE THAN 1
Answers
Answer:
The 3rd and the 5th
Step-by-step explanation:
The graphs of the 3rd and the 5th functions are straight lines
The 1st and 2nd are parabolas
The 4th is an exponential
You must look at the graph: it shall include all the real values for the y coordinate
Which ordered pair is the best estimate for the solution of the system of equations?
y=32x+6
y=14x−2
(−7, −3.5)
(−7, −4)
(−6.5, −3.5)
(−6, −3)
Answers
Answer:
x=-4/9, y=-74/9.
Step-by-step explanation:
y=32x+6
y=14x-2
-----------
32x+6=14x-2
32x-14x+6=-2
18x+6=-2
18x=-2-6
18x=-8
x=-8/18
simplify
x=-4/9
y=14(-4/9)-2=-56/9-2=-74/9
Divisibility rules for 2, 5, and 10
Which numbers are divisible by 10?
A)222
B)185
C)847
or none of these
Answers
Answer:
none of these
Step-by-step explanation:
A number is divisible by 10 if the last digit of the number is 0. The numbers 20, 40, 50, 170, and 990 are all divisible by 10 because their last digit is zero, 0.
In the diagram AB is parallel to CD. Calculate the value of A ?
Answers
The image of the diagram is missing, so i have attached it.
Answer:
a = 30°
Step-by-step explanation:
From the diagram attached, we can see that the 2 angles a and 5a are interior supplementary angles.
The sum of interior supplementary angles is 180°
Thus;
5a + a = 180
6a = 180
a = 180/6
a = 30°
I need help does the table represent a function
Answers
Answer:
b. no, because one x-value corrseponds to two different y-values
Step-by-step explanation:
for a set/table to be a function, the each x-value must correspond to exactly one value, not more, therefore the set of points in this table do not represent a function as the x-value 6 corresponds to more than one number.
How do you solve x^2+5x-14=0
Answers
Answer:
x = -7 , x = 2
Step-by-step explanation:
[tex]x^2 + 5x -1 4= 0\\\\x^2 + 7x -2x - 14 = 0\\\\x(x + 7) -2(x + 7) = 0\\\\(x+7)(x-2) = 0\\\\x+ 7 = 0 , \ x - 2 = 0 \\\\x = - 7 , \ x = 2[/tex]
Answer:
x = - 7, x = 2
Step-by-step explanation:
Solve by factoring , that is
x² + 5x - 14 = 0
Consider the factors of the constant term (- 14) which sum to give the coefficient of the x- term (+ 5)
The factors are + 7 and - 2 , since
7 × - 2 = - 14 and 7 - 2 = + 5 , then
(x + 7)(x - 2) = 0 ← in factored form
Equate each factor to zero and solve for x
x + 7 = 0 ⇒ x = - 7
x - 2 = 0 ⇒ x = 2
A group of 5 friends shares 35 pieces of candy equally. How many pieces of candy does each friend receive?
Answers
Divide total pieces of candy by total people:
35 / 5 = 7
Each person receives 7 pieces of candy
Answer:
7
Step-by-step explanation:
35 divided by 5 equals 7
Please help! Will give brainliest! Lucy is going to spin the spinner 85 times. the spinner is divided into equal sections
Answers
We can say 85 because we will spin it 85 times and it can happen we will not C
Not sure at all ....
PERFORMANCE TASK : “TRANSVERSAL CITY MAP”
This project will help you to demonstrate your knowledge of parallel lines, transversals and the angles that are created by them. You will be designing a city map using the guidelines listed below. Your map must be drawn on construction paper or poster board. Use a ruler to make your streets straight! Have a title for your map, and make it neat and organized! You will be graded on accuracy, creativity and neatness.
Guidelines:
1) There must be a title for your map.
2) Your city must have three streets that are parallel to each other and one street that intersects all three of the parallel streets. You must name all of these streets.
3) Your city has a hospital that is alternate exterior to the school that is in your city. Draw and name the hospital and the school.
4) The school and the drugstore are at corresponding locations. Draw and name the drugstore.
5) The drugstore and the pet shop are at vertical locations. Draw and name the pet shop.
6) The pet shop and the gas station are at alternate interior locations. Draw and name the gas station.
7) The hospital and the park are at same side exterior locations. Draw and name the park.
8) The gas station and the grocery store are at same side interior locations. Draw and name the grocery store.
9) The grocery store and the nail salon are at vertical locations. Draw and name the salon.
10) The nail salon and bank are at corresponding locations. Draw Target.
11) The bank and a fast food restaurant are at same side interior locations. Draw and name the fast food restaurant.
12) Your city has a mall that is in a corresponding location to the bookstore that is in your city. Draw and name the mall and the bookstore. (If you did all of the others correctly, then the bookstore and the mall only have one place to be located)
Answers
In constructing a transversal city map by applying the knowledge of transversal and parallel lines, a map named California City Map has been drawn as shown in the image attached below.
(See attachment).
Recall:
Parallel lines are straight lines that do not meet each other.Transversal line is a that run through two or more straight lines that are parallel.Special angles are formed when transversal intersects parallel lines, which are: corresponding angles, same-side interior angles, same-side exterior angles, alternate exterior and alternate interior angles, and vertical angles.Using the knowledge of all these, an map named, "California City Map" has been drawn as shown in the image attached below.
The details are as follows:
1. Title for the map is:
California City Map.2. The three streets that are parallel are:
Adams BoulevardBeverly DriveCarroll AvenueThe street (transversal) that intersects the three is:
Darlin Way3. St. Michael Hospital is alternate exterior to Baptist Model School
4. Baptist Model School and Living Well Drug Store are in corresponding locations to each other.
5. Living Well Drug Store and Vik Pet Store are at vertical locations.
6. Vik Pet Store and Elite Gas-station are at alternate interior locations.
7. St. Michael Hospital and Livingstone Park are at same-side exterior locations.
8. Elite Gas-station and Richie Grocery Store are at same-side interior locations.
9. Richie Grocery Store and Beautyjay Nail salon are at vertical locations.
10. Beautyjay Nail salon and Retro Bank Plc are at corresponding locations.
11. Retro Bank Plc and Tessy's Fast Food Restaurant are at same-side interior locations.
12. California City Mall and Remis Bookstore are at corresponding locations.
In summary, in constructing a transversal city map by applying the knowledge of transversal and parallel lines, a map named California City Map has been drawn as shown in the image attached below.
(See attachment).
Learn more here:
https://brainly.com/question/13207832
Are the two triangles similar? How do you know? Explain your reasoning thoroughly.
Answers
Answer:
Yes, the triangles are similar ([tex]\triangle HMG \sim \triangle KMJ[/tex]).
Step-by-step explanation:
We're given that the two triangles share at least one angle, angles H and K. The two angles in the triangles at point M, [tex]\angle HMG[/tex] and [tex]\angle KMJ[/tex] are vertical angles, meaning they are on opposite sides of a point of intersection between two lines. Since vertical angles are always equal, these two angles are also equal.
If two triangles share two angles, they must share all three, because all triangles have a total sum of interior angles of 180 degrees. Therefore, the triangles share all 3 angles. AAA (Angle-Angle-Angle) is a proof of similarity, where two triangles share all three of their angles. Thus, the two triangles are similar.
Similarity statement (vertices should correspond):
[tex]\triangle HMG \sim \triangle KMJ[/tex]
Need help! I will give brainless to person who helps
Answers
Answer:
1. X-intercept
Step-by-step explanation:
Answer:
quadranttwo
linear
Step-by-step explanation:
1 across
quadranttwo
14 across
linear
A side of the triangle below has been extended to form an exterior angle of 62°. Find the value of x
Answers
Answer:
16 degrees
Step-by-step explanation:
62= 46+x
16=x
What's the area of the entire shape?
Answers
Answer:
30
Step-by-step explanation:
you need to multiply its length by its with
Y=(x+2)(x-4)
Expanded form:
Y-intercept
Answers
The answer would be y=-8
help help helpppppppppp
Answers
Answer:
28 answer write ✍️ now ok
If f(x) = x -5, what is f(2)
Answers
f(2) = -3
Step-by-step explanation:
f(x) = x - 5
f(2)) = (2) - 5 = -3
Math help please show work thanks
Answers
Answer:
The curve surface area(CSA) of a cylinder is 2πrh.
Since diameter=1.5 in.
radius=diameter/2
=1.5/2 in.
=0.75 in.
And, the height of the bottle is 5 in.
Now,
CSA=2πrh
=2π*0.75*5 in^2
=15π/2 or 23.56 in^2
The size of the label needed to cover the entire bottle is 15π/2 or 23.56 in^2.
"which of the numbers below can be classified as an integer" and the options are . 10÷2 , -0.3 ,√20 ,. 0.4
Answers
Answer:
The number 10/2 = 5 is an integer.
Step-by-step explanation:
An integer is a whole number which cannot be expressed in fractions. For example, 1, 2, 3...
Integer can be positive, negative of zero.
[tex]\frac{10}{2}=5[/tex]
It is a whole number so it is an integer.
- 0.3
It is not an integer as it has a fractional part.
[tex]\sqrt20[/tex]
It also has a fractional part, so it is not an integer.
0.4
It also has a fractional part, so it is not an integer.
Solve the right triangle. Round decimal answers to the nearest tenth.
Answers
Answer:
c=√a²+b²
Step-by-step explanation:
You can use this equation to solve it.
En una panadería se dispone diariamente de 80 kg de masa y de 24 kg de frutas (secas y confitadas) para preparar dos tipos de panetones: especial y Premium, según estos requerimientos: Panetón especial: 1kg de masa y 200 g de frutas Panetón Premium: 1kg de masa y 400 g de frutas Si el panetón especial se vende a $3 y el Premium a $4, ¿Cuántos panetones especiales y Premium deben hacerse para obtener el máximo ingreso?
Answers
Answer:
x₁ = 40 x₂ = 40 z (max) = 280
Step-by-step explanation:
El presente es un problema de programación lineal, este problema se resuelve por el procedimiento o Método Simplex, con programas de resolución en línea. Como en este caso se trata de que se venden unidades enteras ( es decir las variables son enteros reales) entonces hay que imponer esa condición a nivel de la solución
Para preparar:
Masa Kg Frutas Kg Precio de venta $
Panetón tipo esp. x₁ 1 0.2 3
Panetón tipo Prem x₂ 1 0.4 4
Disponibilidad 80 24
Función Objetiva
z = 3*x₁ + 4*x₂ a maximizar
Sujeto a:
Restricciones o condicionantes:
1.- Cantidad de masa 80 Kgs
1*x₁ + 1*x₂ ≤ 80
2.- Cantidad de frutas 24 kgs.
0.2*x₁ + 0.4*x₂ ≤ 24
x₁ ≥ 0 x₂ ≥0 deben ser enteros
El modelo es:
z = 3*x₁ + 4*x₂ a maximizar
Sujeto a:
1*x₁ + 1*x₂ ≤ 80
0.2*x₁ + 0.4*x₂ ≤ 24
x₁ ≥ 0 x₂ ≥0 deben ser enteros
Usando Atomzmath on-line, después de 6 iteracciones, la solución óptima es:
x₁ = 40 x₂ = 40 z (max) = 280
Divisibility rules for 2, 5, and 10
Which numbers are divisible by 5?
A)222
B)185
C)847
or none of these
Answers
Answer:
185 is divisible by 5.
Step-by-step explanation:
Anything that ends in a 0 or 5 can be divisible by 5.
Answer:
Hello There!!
Step-by-step explanation:
The answer is B)185 because a number divisible by 5 ends in 0 or 5.
hope this helps,have a great day!!
~Pinky~
A 12 pack of lemonade costs $5.40.how much do each lemonade costs?
