Answer:
A. 30
Step-by-step explanation:
30*.08=24
how many triangles are there that satisfy the conditions a=13, b=6, a= 6°
Answer:
1 triangle is possible
Step-by-step explanation:
If there are two sides and a non included angle is given then there could be 0,1 or 2 triangles depend on the measure of the given angle and the lengths of the given sides.
We will discuss some conditions which will clarify that how many triangles are there in the given condition.
CASE 1: If A is obtuse and a>b then there is 1 triangle.
CASE 2: If A is obtuse and a<b then there is 0 triangle.
CASE 3: If A is acute and a>b then there is 1 triangle.
CASE 4: If A is acute and h<a<b then there are 2 triangles possible.
CASE 5: If A is acute and a=h then there is 1 right angle triangle.
CASE 6: If A is acute and a<h then there are 0 triangles possible.
Therefore according to the given condition A= 6° which is acute and a>b, So this condition matches the CASE 3:
According to this there is 1 triangle possible....
Choose the correct translation for the following statement.
It is at most ten.
x < 10
x ≤ 10
x > 10
x ≥ 10
Answer:
[tex]x\leq10[/tex]
Step-by-step explanation:
we know that
The algebraic expression of the phrase "It is at most ten" is equal to
[tex]x\leq10[/tex]
All real numbers less than or equal to 10 (the number 10 is included)
The solution of this inequality is the interval -----> (-∞,10]
Answer:
B
Step-by-step explanation:
A wooden pole is 20 m high. A steel wire is tied to the top of the pole and fixed to the ground. If the angle made by the
wire with the ground is 60°, find the length of the steel wire.
Answer:
23.09 meters.
Step-by-step explanation:
Sin(60) = opposite / hypotenuse = pole / steel wire
pole = 20 m
angle = 60 degrees.
sin(60) = 20/ hypotenuse multiply both sides by the hypotenuse
hypotenuse * sin(60) = 20 divide by sin(60)
hypotenuse = 20 / 0.866 do the division
hypotenuse = 23.09
The steel wire = 23.09 meters.
The domain of a function is
A. The set of all points on the function
B. The set of all first elements of the function
C. The set of all second elements of the function
Answer:
B.the set of all first elements of the function
Step-by-step explanation:
the domain is all the x variables in a function
Answer:
B. The set of all first elements of the function.
Step-by-step explanation:
We have been given a incomplete sentence. We are asked to complete our given sentence.
We know that the domain of a function is all real values of independent variable for which a function is defined and gives exactly one output.
We know that independent variable is x, which is first element of a point, therefore, the domain of a function is the set of all first elements of the function.
The price of a concert ticket was $85.00 two decades ago. A report says that a concert ticket is now 250% of what it was 20 years ago, how much would it cost today? Express answer rounded to the nearest cent.
Answer: $212.5
Step-by-step explanation:
250% = 2.5
So we multiply 85.00 by 2.5
85*2.5=212.5
So it is $212.5
Answer:
your answer is $212.5
Step-by-step explanation:
Solve the system of equations below by graphing both equations with a
pencil and paper. What is the solution?
y=x+5
y=-2x-1
A cleaner recommends mixing 1 1/2 cup of cleaner for every 12 cups of water. What is the ratio of cleaner to water.
Answer: [tex]\frac{1}{8}[/tex] or [tex]1:8[/tex]
Step-by-step explanation:
First, you can convert the mixed number [tex]1\ \frac{1}{2}[/tex] into a decimal number. To do this, you need to divide the numerator (which is 1) by the denominator (which is 2) of the fraction:
[tex]\frac{1}{2}=0.5[/tex]
Now you must add 0.5 to the whole number part. Then:
[tex]1+0.5=1.5[/tex]
In order to find the ratio of cleaner to water, you must divide 1.5 cups of cleaner by 12 cups of water.
Therefore, the ratio is:
[tex]ratio=\frac{1.5}{12}=\frac{1}{8}[/tex] or [tex]1:8[/tex]
Richard wants to buy a LCD flat panel monitor measuring 14 inches by 16 inches. What is the measure of the diagonal of the monitor?
(JUSTIFY)
Answer:
21.26 inches to the nearest hundredth.
Step-by-step explanation:
By the Pythagoras theorem
d^2 = 14^2 + 16^2 (where d = the length of the diagonal).
d^2 = 452
d = 21.26 inches.
Answer:
21.26 inches.
Step-by-step explanation:
It can be inferred that the shape of the monitor is a rectangle, in which the length of the monitor is 16 inches and the height of the monitor is 14 inches. The diagonals of the rectangle cut it into two congruent right-angled triangles. Therefore, to find the length of the diagonal of the monitor, use the Pythagoras Theorem. Since the base (b) is 16 inches and the perpendicular (p) is 14 inches, the distance of the hypotenuse (i.e. the diagonal, denoted by h) can be found by the following formula:
[tex]h^2 = b^2 + p^2 [/tex]
Plugging in the values:
[tex]h^2 = 16^2 + 14^2[/tex]
Simplifying gives:
[tex]h^2 = 452[/tex]
Taking square root on both sides gives:
h = 21.26 inches (to the nearest 2 decimal places)
Therefore, the measure of the diagonal is 21.26 inches!!!
Let v=-3sqrt2i-4sqrt2j, find a unit vector that points in the opposite direction
Answer:
[tex]\^v=-\frac{3}{5}i+\frac{4}{5}j[/tex]
Step-by-step explanation:
We have the following vector
[tex]v=3\sqrt{2}i-4\sqrt{2}j[/tex]
First we calculate its magnitude
The magnitude of the vector v will be
[tex]|v|=\sqrt{(3\sqrt{2})^2 + (4\sqrt{2})^2}\\\\|v|=\sqrt{9*2+16*2}\\\\|v|=\sqrt{18+32}\\\\|v|=5\sqrt{2}[/tex]
Now to create a unitary vector in the opposite direction to v, we divide the vector v between the negative of its magnitude
we call this new vector "[tex]\^v[/tex]"
[tex]\^v=\frac{3\sqrt{2}}{-5\sqrt{2}}i-\frac{4\sqrt{2}}{-5\sqrt{2}}j[/tex]
[tex]\^v=-\frac{3}{5}i+\frac{4}{5}j[/tex]
Two boats depart from a port located at (–8, 1) in a coordinate system measured in kilometers and travel in a positive x-direction. The first boat follows a path that can be modeled by a quadratic function with a vertex at (1, 10), whereas the second boat follows a path that can be modeled by a quadratic function with a vertex at (0, –7). Which system of equations can be used to determine whether the paths of the boats cross?
Answer:
[tex]\left\{\begin{array}{l}y=-\dfrac{1}{9}x^2 +\dfrac{2}{9}x+\dfrac{89}{9}\\ \\y=\dfrac{1}{8}x^2 -7\end{array}\right.[/tex]
Step-by-step explanation:
1st boat:
Parabola equation:
[tex]y=ax^2 +bx+c[/tex]
The x-coordinate of the vertex:
[tex]x_v=-\dfrac{b}{2a}\Rightarrow -\dfrac{b}{2a}=1\\ \\b=-2a[/tex]
Equation:
[tex]y=ax^2 -2ax+c[/tex]
The y-coordinate of the vertex:
[tex]y_v=a\cdot 1^2-2a\cdot 1+c\Rightarrow a-2a+c=10\\ \\c-a=10[/tex]
Parabola passes through the point (-8,1), so
[tex]1=a\cdot (-8)^2-2a\cdot (-8)+c\\ \\80a+c=1[/tex]
Solve:
[tex]c=10+a\\ \\80a+10+a=1\\ \\81a=-9\\ \\a=-\dfrac{1}{9}\\ \\b=-2a=\dfrac{2}{9}\\ \\c=10-\dfrac{1}{9}=\dfrac{89}{9}[/tex]
Parabola equation:
[tex]y=-\dfrac{1}{9}x^2 +\dfrac{2}{9}x+\dfrac{89}{9}[/tex]
2nd boat:
Parabola equation:
[tex]y=ax^2 +bx+c[/tex]
The x-coordinate of the vertex:
[tex]x_v=-\dfrac{b}{2a}\Rightarrow -\dfrac{b}{2a}=0\\ \\b=0[/tex]
Equation:
[tex]y=ax^2+c[/tex]
The y-coordinate of the vertex:
[tex]y_v=a\cdot 0^2+c\Rightarrow c=-7[/tex]
Parabola passes through the point (-8,1), so
[tex]1=a\cdot (-8)^2-7\\ \\64a-7=1[/tex]
Solve:
[tex]a=-\dfrac{1}{8}\\ \\b=0\\ \\c=-7[/tex]
Parabola equation:
[tex]y=\dfrac{1}{8}x^2 -7[/tex]
System of two equations:
[tex]\left\{\begin{array}{l}y=-\dfrac{1}{9}x^2 +\dfrac{2}{9}x+\dfrac{89}{9}\\ \\y=\dfrac{1}{8}x^2 -7\end{array}\right.[/tex]
What is the y-intercept of the line perpendicular to the line y = -x + 1 that includes the point (4, 1)?
Answer:
-3
Step-by-step explanation:
If a line is perpendicular to another the product of their slope should equal -1. The slope of the first equation is -1 and -1*1=-1 so the slope of the second equation is 1. That means that the equation looks like y=x+b. We know that when x is 4 y is 1. So plugging in those values you get 1=4+b, subtracting 4 you get -3=b. So the y-intercept is -3
Find the height of the triangle by applying formulas for the area of a triangle and your knowledge about triangles.
This is a triangle. side a has a length of 9mm. side b has a length of 6 mm. side c has a length of 12 mm. The altitude to side c has a length of X mm.
The height of the triangle is approximately [tex]4.35\text{ mm}[/tex]
Step-by-step explanation:
The area of a triangle can be calculated by using the Heron's formula.
Heron's formula:
Suppose a triangle has sides [tex]a'[/tex], [tex]b'[/tex] and [tex]c'[/tex], then the semi-perimeter [tex]S[/tex] of the triangle is represented by the expression,
[tex]S=\frac{a'+b'+c'}{2}[/tex]
The area [tex]A[/tex] of the traingle is formulated below.
[tex]\fbox {\begin\\A=\sqrt{s(s-a')(s-b')(s-c')}\end{minispace}}[/tex]
To calculate the area of the triangle with sides [tex]9 \text{ mm}[/tex] , [tex]6 \text{ mm}[/tex] and [tex]12 \text{ mm}[/tex], first find the semi-perimeter.
[tex]S=\frac{9+6+12}{2}\\S=\frac{27}{2}\\S=13.5 \text{ mm}[/tex]
Now, the area of the triangle is calculated below.
[tex]A=\sqrt{s(s-a)(s-b)(s-c)}\\A=\sqrt{13.5(13.5-9)(13.5-6)(13.5-12)}\\A=\sqrt{13.5 \times 4.5 \times 7.5 \times 1.5}\\A=\sqrt{\frac{135}{10}\times\frac{45}{10}\times\frac{75}{10}\times\frac{15}{10}} \\A=\sqrt{\frac{(15\times3\times3) \times (15\times3) \times (15\times5) \times15}{100\times100}}\\A=\frac{15\times15\times3\sqrt{15 } }{100} \\A=2.25\times3\times3.87\\A=26.122[/tex]
Area A of a triangle with a altitude P and one side as base B on which the altitude P is drawn, can be calculated as,
[tex]\fbox{\begin\\A= \left[\frac{1}{2}(B)(P)\right]\\\end{minispace}}[/tex]
Now, the area of the same triangle can also be calculated as,
[tex]A=\frac{1}{2}(12)(x)\\A=6x[/tex]
In the above calculations, area of the triangle is calculated in two ways.
Therefore, both the areas can be equated to obtain the altitude [tex]x[/tex].
[tex]6x=26.122\\x=\frac{26.122}{6}\\x=4.35[/tex]
Thus, the height of the triangle is evaluated as [tex]\fbox{4.35 \text{ mm}}[/tex].
Learn more:
1. Prove that AB2+BC2=AC2https://brainly.com/question/1591768
2. Which undefined term is needed to define an angle? https://brainly.com/question/3717797
3. Look at the figure, which trigonometric ratio should you use to find x? https://brainly.com/question/9880052
Answer Details
Grade: Junior High School
Subject: Mathematics
Chapter: Area of triangle
Keywords: area of triangle, heron's formula, base multiplied by height, base multiplied by perpendicular, base multiplied by altitude, right triangle, altitude corresponding to base, area of right triangle
Answer:
4.3 mm
Step-by-step explanation:
I got it correct on founders edtell
Consider this algebraic expression: 5 + 3x – 1 + 4x
What is the simplified expression?
Answer:
3x+8 I think
Step-by-step explanation:
add 5, -1 and 4
Answer:
The CORRECT answer is C, 7x+4
Step-by-step explanation:
Which represents the measures of all angles that are coterminal with a 500° angle? (40 + 360n)° (140 + 360n)° (220 + 360n)° (320 + 360n)°
Check the picture below.
so a full circle is 360°, then if we just go 140° more, we'll be landing at 500°.
If we go from the 140° location and add say 360°, well end up 500, if we add another 360°, we'll be at 860° or the same location of 140° and 500°, and if we add again 360° we'll be landing on the same spot again and again.
(140 + 360n)°. where "n" is an integer.
The expression that represents the measures of all angles that are co-terminal with a 500° angle is 140 + 360n
What are co-terminal angles?Co-terminal angles are angles in a standard position
The angle is given as:
Angle = 500
Add 0 to 500
Angle = 500 + 0
Express 0 as -360 + 360
Angle = 500 - 360 + 360
Evaluate the difference
Angle = 140 + 360
Express as a function
f(1) = 140 + 360 * 1
Substitute 1 for n
f(n) = 140 + 360 * n
This gives
f(n) = 140 + 360n
Hence, the expression that represents the measures of all angles that are co-terminal with a 500° angle is 140 + 360n
Read more about co-terminal angles at:
https://brainly.com/question/19891743
The problem refers to triangle ABC. Find the area of the triangle. Round to three significant digits. B = 9° 20', C = 80° 40', b = 2.92 ft
Answer:
Area of the triangle is 25.9 feet²
Step-by-step explanation:
* Lets explain how to solve the problem
- In Δ ABC
∵ m∠ B = 9° 20' = 9 + 20/60 = (28/3)°
∵ b = 2.92 feet
- b is the side opposite to angle B
∵ m∠ C = 80° 40' = 80 + 40/60 = (242/3)°
- Lets find c the side opposite to angle C by sing the sine rule
∵ [tex]\frac{b}{sinB}=\frac{c}{sinC}[/tex]
∴ [tex]\frac{2.92}{sin(28/3)}=\frac{c}{sin(242/3)}[/tex]
- By using cross multiplication
∴ [tex]c=\frac{2.92(sin(242/3)}{sin(28/3)}=17.77[/tex]
- The area of the triangle = 1/2 (b)(c)sin∠A
∵ The sum of the interior angles of a triangle is 180°
∴ m∠ A + m∠ B + m∠ C = 180°
∵ m∠ B = (28/3)°
∵ m∠ C = (242/3)°
∴ m∠ A + 28/3 + 242/3 = 180
∴ m∠ A + 90° = 180° ⇒ subtract 90 from both sides
∴ m∠ A = 90°
∴ Area of the triangle = 1/2 (2.92)(17.77) sin(90)
∵ sin(90) = 1
∴ Area of the triangle = 1/2 (2.92)(17.77) = 25.9 feet²
* Area of the triangle is 25.9 feet²
What is the solution to the equation 6x+2=9x-1
Answer:
1
Step-by-step explanation:
To solve, combine like terms.
Subtract 6x from both sides.
[tex]2=3x-1[/tex]
Add 1 to both sides.
[tex]3=3x[/tex]
Divide both sides by 3.
[tex]1=x[/tex]
Use the substitution method to solve the system of equations. Choose the
correct ordered pair.
y = 7x + 8
y = x+ 20
Answer:
(2, 22 )
Step-by-step explanation:
Given the 2 equations
y = 7x + 8 → (1)
y = x + 20 → (2)
Substitute y = 7x + 8 into (2)
7x + 8 = x + 20 ( subtract x from both sides )
6x + 8 = 20 ( subtract 8 from both sides )
6x = 12 ( divide both sides by 6 )
x = 2
Substitute x = 2 in (2) for corresponding value of y
y = x + 20 = 2 + 20 = 22
Solution is (2, 22 )
Answer:
(2,22)
Step-by-step explanation:
A-P-E-X :)
6. what percent the comes clonefro modelories e
A serving of ice cream contains 5000 calories. 200 calories come from
fat. What percent of the total calories come from fat?
Step-by-step explanation:
200 calories come from fat, out of 5000 calories total. We can find the percentage with a proportion:
200 / 5000 = x / 100
x = 4
4% of the total calories come from fat.
A sink is shaped like a half sphere,as shown in the diagram. Find it’s approximate volume,ignoring the space occupied by the drain
Answer:
Option C. 2508 cubic inches is the correct answer
Step-by-step explanation:
From the figure we can see that, a sink
Points to remember
Volume of hemisphere = (2/3)πr³
Where 'r' is the radius
To find the volume of large hemisphere
Here radius = 13 in
Volume V₁ = (2/3)πr³
= (2/3) * 3.14 * 13³
= 4599.33 cubic inches
To find the volume of small hemisphere
Here radius = 13 - 3 = 10 in
Volume V₂ = (2/3)πr³
= (2/3) * 3.14 * 10³
=2093.33 cubic inches
To find the volume of sink
Volume = V₂ - V₁
= 4599.05 - 2093.33
=2505.72 ≈ 2508 cubic inches
Option C. 2508 cubic inches is the correct answer
Lola tossed a coin twice. She made a tree diagram to show the possible outcomes. Which tree diagram shows the sample
Answer:
Its C. XD sorry i just answered this.
Step-by-step explanation:
Hope this helped again! :3
Answer:
Each path in the diagram is a possible outcome with a probability of 1/4. The sum of all paths should equal 1.
The answer is C.
Let f(x) = -4x + 7 and g(x) = 2x - 6. Find (gof) (1)
Answer:
(gof) (1) = 0
Step-by-step explanation:
f(x) = -4x + 7
g(x) = 2x - 6
(gof) (1)
First find f(1)
f(1) = -4(1) + 7
f(1) = -4+7=3
Then put 3 in for x in g(x)
g(f(1) = 2(f(1))-6
= 2 (3) -6
= 6 -6
= 0
[tex](g\circ f)(x)=2(-4x+7)-6=-8x+14-6=-8x+8\\\\(g\circ f)(1)=-8\cdot1+8=0[/tex]
Which expression is equivalent to (x^6y^8)^3\x^2y^2
Answer:
[tex]\large\boxed{\dfrac{(x^6y^8)^3}{x^2y^2}=x^{16}y^{22}}[/tex]
Step-by-step explanation:
[tex]\dfrac{(x^6y^8)^3}{x^2y^2}\qquad\text{use}\ (ab)^n=a^nb^n\ \text{and}\ (a^n)^m=a^{nm}\\\\=\dfrac{(x^6)^3(y^8)^3}{x^2y^2}=\dfrac{x^{(6)(3)}y^{(8)(3)}}{x^2y^2}=\dfrac{x^{18}y^{24}}{x^2y^2}\qquad\text{use}\ \dfrac{a^m}{a^n}=a^{m-n}\\\\=x^{18-2}y^{24-2}=x^{16}y^{22}[/tex]
Answer: [tex]x^{16}\ y^{22}[/tex]
Step-by-step explanation:
The given expression : [tex]\dfrac{(x^6y^8)^3}{x^2y^2}[/tex]
Using identity , [tex](a^m)^n=a^{mn}[/tex] , we have
[tex]{(x^6y^8)^3=x^{6\times3}\ y^{8\times3}\\\\=x^{18}\ y^{24}[/tex]
Now, [tex]\dfrac{(x^6y^8)^3}{x^2y^2}=\dfrac{x^{18}\ y^{24}}{x^2\ y^2}[/tex]
( its also an equivalent expression to given expression.)
Using identity , [tex]\dfrac{a^n}{a^m}=a^{n-m}[/tex] , we have
[tex]\dfrac{x^{18}\ y^{24}}{x^2\ y^2}=x^{18-2}\ y^{24-2}\\\\=x^{16}\ y^{22}[/tex]
Hence, the expression is equivalent to given expression :
[tex]x^{16}\ y^{22}[/tex]
If you have a system of two equations with two unknowns, and the graphs of
the two equations are the same, the system must have.
A. 1 solution
B. No Solution
C.At Least 1 Solution
D. More Than 1 Solution
Answer:
D. More Than 1 Solution
Step-by-step explanation:
Let the system of equations be:
[tex]a_1x+b_1y=c_1...(1)[/tex]
[tex]a_2x+b_2y=c_2...(2)[/tex]
If the graph of equation (1) and (2) are the same, then the two graphs coincide with each other.
What that means is that; the two graphs intersects at infinitely many points.
Therefore the system must have infinitely many solutions.
In other words the system has more than one solution.
NB: At least one solution means exactly one solution and/or more than one solution. But lines that coincide cannot have exactly one solution.
what is the 7th term in the sequence
a(1 )=12
a(n)=a(n)-1+4
I need help finding the recursive formula.
Answer:
Explicit form: [tex]a_n=8+4n[/tex]
Seventh term: [tex]a_7=36[/tex]
You gave the recursive form:
[tex]a_n=a_{n-1}+4 \text{ with } a_1=12[/tex]
Step-by-step explanation:
You already have the recursive formula which is:
[tex]a_n=a_{n-1}+4[/tex] where [tex]a_1=12[/tex].
Maybe you looking for the explicit form and also the 7th term?
You were just looking for the 7th term. Sometimes you can read the recursive formula pretty easily and understand the pattern that is happening.
[tex]a_{n-1}[/tex] is the term right before [tex]a(n)[/tex]. Just like [tex]a_5[/tex] would be the term right before [tex]a_6[/tex].
Anyways becak to our recursive for a sequence that was given:
[tex]a_{n}=a_{n-1}+4[/tex] says term=previous term+4.
So you adding 4 over and over to generate the terms of a sequence. This is arithmetic sequence because it is going up by same number (or could go down by same number). The common difference is 4.
[tex]a_1=12[/tex]
[tex]a_2=12+4=16[/tex]
[tex]a_3=16+4=20[/tex]
[tex]a_4=20+4=24[/tex]
[tex]a_5=24+4=28[/tex]
[tex]a_6=28+4=32[/tex]
[tex]a_7=32+4=36[/tex]
Now if you don't like that. You could just blindly without trying to understand the meaning of it just plug numbers in:
[tex]a_1=12[/tex]
For if we wanted to know the 2nd term; we would plug in 2 for n:
[tex]a_2=a_{2-1}+4[/tex]
[tex]a_2=a_1+4[/tex]
[tex]a_2=12+4[/tex]
[tex]a_2=16[/tex]
Plug in 3 for the 3rd term:
[tex]a_3=a_{3-1}+4[/tex]
[tex]a_3=a_2+4[/tex]
[tex]a_3=16+4[/tex]
[tex]a_3=20[/tex]
Plug in 4 for the 4th term:
[tex]a_4=a_{4-1}+4[/tex]
[tex]a_4=a_3+4[/tex]
[tex]a_4=20+4[/tex]
[tex]a_4=24[/tex]
Plug in 5 for the 5th term:
[tex]a_5=a_{5-1}+4[/tex]
[tex]a_5=a_4+4[/tex]
[tex]a_5=24+4[/tex]
[tex]a_5=28[/tex]
Plug in 6 for the 6th term:
[tex]a_6=a_{6-1}+4[/tex]
[tex]a_6=a_5+4[/tex]
[tex]a_6=28+4[/tex]
[tex]a_6=32[/tex]
Plug in 7 for the 7th term:
[tex]a_7=a_{6-1}+4[/tex]
[tex]a_7=a_5+4[/tex]
[tex]a_7=32+4[/tex]
[tex]a_7=36[/tex]
Now if you look at the points we just got (I will just go up to 4 terms):
n (treat as x) | 1 2 3 4
a(n) (treat as y| 12 16 20 24
The explicit form in not in terms of other terms of the sequence. You are looking here for an equation that relates n (x) to a(n) (y).
I'm just going to use x and y until the end where I will replace them back in terms of n and a(n).
This is a line because the's rise/run (the slope) is the same per choosing of points.
That is the following is true:
[tex]\frac{16-12}{2-1}=\frac{20-16}{3-2}=\frac{24-20}{4-3}[/tex] son on....
These all the the value 4, the same number that the arithmetic sequence is going up by.
So in an arithmetic sequence, the common difference is the slope of the line.
I'm going to use point-slope formula which is [tex]y-y_1=m(x-x_1)[/tex] where [tex](x_1,y_1)[/tex] is a point on the line and [tex]m[/tex] is the slope.
So we have m=4 and [tex](x_1,y_1)[/tex] could be any of the 7 we found, but I will choose (1,12) for it:
[tex]y-12=4(x-1)[/tex]
Add 12 on both sides:
[tex]y=12+4(x-1)[/tex]
[tex]a_n=12+4(n-1)[/tex].
This is actually in the form of most books formulas for an explicit form which is [tex]a_n=a_1+d(n-1)[/tex] where [tex]a_1[/tex] is the first term and d is the common difference.
So another way to do the problem:
You would have to know the following are equivalent:
[tex]a_n=a_{n-1}+d[/tex] with [tex]a_1 \text{ is given}[/tex]
and
[tex]a_n=a_1+d(n-1)[/tex].
If you know these are equivalent then you could compare [tex]a_n=a_{n-1}+d[/tex] to [tex]a_n=a_{n-1}+4[/tex] and determine d is 4.
You could also see that [tex]a_1[/tex] is give as 12.
Then you just plug into:
[tex]a_n=a_1+d(n-1)[/tex]
[tex]a_n=12+4(n-1)[/tex].
You could also simplify this equation just a bit.
You could distribute and then combine a pair of like terms.
Like so,
[tex]a_n=12+4(n-1)[/tex]
[tex]a_n=12+4n-4[/tex]
[tex]a_n=8+4n[/tex]
Write as an equation: Patrick age increased by 8 years is 18 years
Let P = Patrick's age
P + 8 = 18
The equation is P + 8 = 18
Let P = Patrick's age
What's an equation example?An equation is a mathematical statement this is made up of expressions related with the aid of the same signal. for instance, 3x – five = 16 is an equation. Solving this equation, we get the price of the variable x as x = 7.
A one-step equation is an algebraic equation you may resolve in the most effective one step. You've got solved the equation when you get the variable through itself, and not using numbers in the front of it, on one side of the same signal.
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Express each ratio as a fraction in lowest terms.
1) 3 goals in 6 attempts:
2) 5 quarters out of 15 coins:
Express each rate as a unit rate.
If the answer is in dollars and cents, it must begin with a dollar sign ($).
3) $197 for 4 theater tickets:
(Price per ticket in dollars and cents)
mph (Answer rounded to nearest tenth of a
4) 111.7 miles in 8.4 hours:
mile per hour.)
Roopesh has $24 dollars to spend on a birthday gift. The store where he is shopping has a sale offering $5 off the regular price, r, of any item. Write an inequality that can be used to determine the regular price of an item in the store that Roopesh can afford. (Assume there is no tax.)
What is the unknown?
Which expression can represent the sale price?
Which comparison could be used?
Which inequality represents the situation?
Roopesh has $24 dollars to spend on a birthday gift. The store where he is shopping has a sale offering $5 off the regular price, r, of any item. Write an inequality that can be used to determine the regular price of an item in the store that Roopesh can afford. (Assume there is no tax.)
What is the unknown?
Which expression can represent the sale price?
Which comparison could be used?
Which inequality represents the situation?
vRoopesh has $24 dollars to spend on a birthday gift. The store where he is shopping has a sale offering $5 off the regular price, r, of any item. Write an inequality that can be used to determine the regular price of an item in the store that Roopesh can afford. (Assume there is no tax.)
What is the unknown?
Which expression can represent the sale price?
Which comparison could be used?
Which inequality represents the situation?
Roopesh has $24 dollars to spend on a birthday gift. The store where he is shopping has a sale offering $5 off the regular price, r, of any item. Write an inequality that can be used to determine the regular price of an item in the store that Roopesh can afford. (Assume there is no tax.)
What is the unknown?
Which expression can represent the sale price?
Which comparison could be used?
Which inequality represents the situation?
Roopesh has $24 dollars to spend on a birthday gift. The store where he is shopping has a sale offering $5 off the regular price, r, of any item. Write an inequality that can be used to determine the regular price of an item in the store that Roopesh can afford. (Assume there is no tax.)
What is the unknown?
Which expression can represent the sale price?
Which comparison could be used?
Which inequality represents the situation?
Roopesh has $24 dollars to spend on a birthday gift. The store where he is shopping has a sale offering $5 off the regular price, r, of any item. Write an inequality that can be used to determine the regular price of an item in the store that Roopesh can afford. (Assume there is no tax.)
What is the unknown?
Which expression can represent the sale price?
Which comparison could be used?
Which inequality represents the situation?
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Roopesh has $24 dollars to spend on a birthday gift. The store where he is shopping has a sale offering $5 off the regular price, r, of any item. Write an inequality that can be used to determine the regular price of an item in the store that Roopesh can afford. (Assume there is no tax.)
What is the unknown?
Which expression can represent the sale price?
Which comparison could be used?
Which inequality represents the situation?
Answer:
r ≤ 29, r-5
The sale price can be compared with the regular price, r-5 ≤ 24
Step-by-step explanation:
Amount to spend = $24
Regular price = r
Sale = $5
Sale Price = r-5
The regular price will be $5, at the max, more than the amount Roopesh has to spend.
The sale price will be $24 or less than that for Roopesh to afford.
Inequality for regular price:
r-5 ≤ 24
r ≤ 29
So, the product Roopesh can afford is $29 or less than that.
What is the unknown? r ≤ 29
Following expression can represent the sale price:
Sale price = r-5
The sale price can be compared with the regular price with the following:
Inequality representing the situation: r-5 ≤ 24
Answer:
Step-by-step explanation:
What is unknown?
We are missing the regular price of an item
Which expression can represent the sale price?
$24 - x = the sales price
and the x equals the original price since we don't know the actual price.
Which comparison could be used?
$24 spend on a birthday gift to a the shopping sale offering $5 off the regular price.
And the rest I don't know son or girl
x+6y=27
7x-3y=9 por metodo de igualacion
Answer:
(3,4)
Step-by-step explanation:
The system of equations is:
x+6y=27
7x-3y=9.
I looked up "metodo de igualacion". It is basically American for doing substitution.
However, the only difference is you are asked to solve both equations for a variable.
The first equation looks easy to solve for x. So I'm going to solve both equations for x.
x+6y=27
Subtract 6y on both sides:
x =-6y+27
7x-3y=9
Add 3y on both sides:
7x =3y+9
Divide both sides by 7:
x =3/7 y +9/7
So both equations are solved for x. You want to find when the x's are the same because you are looking for a common amongst the lines given.
So we have
-6y+27=3/7 y +9/7
I hate the fractions honestly so I'm going to multiply both sides by 7 so they will no longer be for now:
-42y+189=3y + 9
Now add 42y on both sides:
189=45y+9
Subtract 9 on both sides:
180=45y
Divide both sides by 45:
4=y
If 4=y, then y=4.
So now once we have obtain 4 for y, we will use one of the equations given along with it to find x. Just choose one. Choose the easier looking one to you.
I like the x=-6y+27 with y=4.
So replace y with giving you:
x=-6(4)+27
x=-24+27
x=3
So the solution is (x,y)=(3,4).
x=3 and y=4.
By using the method of substitution, we isolate one variable, substitute it in the other equation, and solve for the remaining variable. Applying these steps to the provided system of equations gives us the solution x=3, y=4.
Explanation:The provided system of equations can be solved using the method of substitution. For this method, we first need to isolate one variable in one of the two equations. In this case, let's isolate 'x' from the first equation, which gives us:
x = 27 - 6y.
Now, we substitute this 'x' value into the second equation to get:
7(27 - 6y) - 3y = 9.
This simplifies to:
189 - 42y - 3y = 9
Combining like terms gives us:
-45y = -180
We can solve for 'y' by dividing each side by -45:
y = 4.
Substituting this value of 'y' back into the first equation gives us:
x = 27 - 6(4) = 3.
Therefore, the solutions for the system are x=3 and y=4.
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Rhombus EFHS is shown. What is the measure of HGJ? Help me ASAP
Answer:
Id say 35
Sorry of im wrong :{
How to do solve this?
4x^2(5x^4 / 2x^2)
Answer:
4x^2(5x^4 / 2x^2)= 10 x^4
Step-by-step explanation:
We want factorize the expression 4x^2(5x^4 / 2x^2)
And to do this, we need to remember key properties of exponents.
Those are:
[tex]x^{m} / x^{n} = x^{m-n}[/tex]
[tex]x^{m} * x^{n} = x^{m+n}[/tex]
So
4x^2(5x^4 / 2x^2)= 4x^2(5/2 x^2)=10 x^4