This situation can be expressed by the equation [tex]x-\frac{x}{2} +8=18[/tex], her weekly allowance is $20.
What is an equation?
The description of an equation in algebra is a mathematical proposition that demonstrates the equality of two mathematical expressions.For instance, the equation 3x + 5 = 14 consists of the two equations 3x + 5 and 14, which are separated by the 'equal' sign. Mathematical algebraic equations typically have one or more variables.Let the weekly allowance of anna be = X
Allowance spent on movies= X/2
The extra money from the car wash = 8
Allowance retained with anna = 18
This situation can be expressed by the equation,
[tex]x-\frac{x}{2} +8=18[/tex]
Solving the above equation, we get,
[tex]\frac{x+16}{2} =18[/tex]
x+16=36
x=20
Therefore, her weekly allowance is $20.
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14/3 = 7y solve for y and simplify your answer as much as possible
Answer:
2/3 = y
Step-by-step explanation:
to solve you got to cancel out the 7
so 7y/7.
whatever you do to one side, you do to the other.
14/3 ÷ 7 = 7y/7
14/3 ÷ 7 = 0.6666... = 2/3 = y
x²y6/xy²
What is the value of the expression above
if x = -2 and y = 2?
answer
11
Step-by-step explanation:
4x+1/3y^24(2)+1/3(3)^28+1/3(9)8+3
Simplify the expression. 1-31
1. 5/6(-2y+3)=
2. 6(3s-2.5-5s)=
3. 3/10(4m-8)+9m=
4. 2.25-2(7.5-4h)=
5. 3(a-7)=
6.-6(2+x)=
7. -5(3m-4)=
8. -9(-5-4c)=
9. 4.5(3s+6)=
10. -1.4(-5+7g)=
11. 2/5(6-5p)=
12. -4/3(3q-10)=
13. 2(3+4y+5)=
Factor the expression using the GCF.=
14. The expression 8x + 2 factored using the GCF is=
15. The expression 3y-24 factored using the GCF is =
16. The expression 14p-28 factored using the GCF is=
17. The expression 6+16k factored using the GCF is=
Factor out the coefficient of the variable term.=
18. The expression 1/7a + 1/7 factored is=
19. The expression 1/3b - 1/3 factored is=
20. The expression 3/8d + 3/4 factored is=
21. The expression 2.2x+ 4.4factored is=
22. The expression 0.15c - 0.072 factored is=
23. The expression 3/8z + 1 factored is=
24. The expression 6s - 3/4 factored is=
25. The expression 5/2k - 2 factored is=
26. Factor -4 out of 8d + 20 The factored expression is=
27. Factor -6 out of 18z - 15 The factored expression is=
28. Factor -0.25 out of 7g + 3.5 The factored expression is=
29. Factor -1/2 out of -1/2x+ 6 The factored expression is=
30. Factor -1.75 out of -14m - 5.25n The factored expression is=
31. Factor -1/4 out of -1/2x - 5/4y The factored expression is=
The answers are given below.
First of all, we will know about GCF and expressions.
GCF (GREATEST COMMON FACTOR) - The largest number, which is the factor of two or more number is called the Greatest Common Factor (GCF). It is the largest number (factor) that divide them resulting in a Natural number. Once all the factors of the number are found, there are few factors which are common in both.
Expression are mathematical statements that have a minimum of two terms containing numbers or variables, or both, connected by an operator in between.
1). 5/6(-2y+3) (simply multiply 5/6 with both terms using expansion)
=-2(5/6)+3(5/6)
=-5/3+5/2
2). 6(3s-2.5-5s)= 18s-15-30s = -12s-15
3). 3/10(4m-8)+9m = 12/10m-24/10+9m
= 6/5m-12/5+9m
=6/5m+9m-12/5
=51/m-12/5
4). 2.25-2(7.5-4h)= 2.25-15+8h
= 8h-12.75
5). 3(a-7)= 3a-21
6). -6(2+x)= -12-6x
7). -5(3m-4)= -15m+20
8). -9(-5-4c)= 45+36c
9). 4.5(3s+6)= 13.5s+27
10). -1.4(-5+7g)= 7-9.8g
11). 2/5(6-5p)= 12/5-2p
12). -4/3(3q-10)= -4q+40/3
13). 2(3+4y+5)= 6+8y+10 = 8y+10
14. The expression 8x + 2 factored using the GCF is= 2(4x+1)
15. The expression 3y-24 factored using the GCF is = 3(y-8)
16. The expression 14p-28 factored using the GCF is= 14(p-2)
17. The expression 6+16k factored using the GCF is= 2(3+8k)
The coefficient of the variable terms of following are given below
18. The expression 1/7a + 1/7 factored is= 1/7
19. The expression 1/3b - 1/3 factored is= 1/3
20. The expression 3/8d + 3/4 factored is= 3/8
21. The expression 2.2x+ 4.4factored is= 2.2
22. The expression 0.15c - 0.072 factored is= 0.15
23. The expression 3/8z + 1 factored is=3/8
24. The expression 6s - 3/4 factored is=6
25. The expression 5/2k - 2 factored is=5/2
26. Factor -4 out of 8d + 20 The factored expression is= -4(-2d-5)
27. Factor -6 out of 18z - 15 The factored expression is=-6(-3z+5/2)
28. Factor -0.25 out of 7g + 3.5 The factored expression is=-0.25(-28g-14)
29. Factor -1/2 out of -1/2x+ 6 The factored expression is=-1/2(x-12)
30. Factor -1.75 out of -14m - 5.25n The factored expression is=-1.75(8m+3n)
31. Factor -1/4 out of -1/2x - 5/4y The factored expression is=-1/4(2x+5y)
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Give a polynomial of degree 3 that has zeros of 18, 10i, and −10i, and has a value of −3434 when x=1. Write the polynomial in standard form axn+bxn−1+….
The polynomial in standard form is 2x³+200x-36x²-3600
A polynomial is a mathematical formula that involves only the operations subtraction, addition, multiplication, and powers of positive integers of the variables and is composed of coefficients and indeterminates.
It is common to refer to the x of a polynomial as a variable or an indeterminate. The symbol x is fixed and has no significance when the polynomial is viewed as an expression (its value is "indeterminate"). The argument of the function is represented by x, which is referred to as a "variable" when considering the function that the polynomial defines.We know the roots of the polynomial as 18, 10i, and −10i.
therefore the polynomial is of the form.
a(x-18)(x-10i)(x+10i)
= a (x-18)(x²-100i²)
= a (x-18)(x²+100)
= a (x³+100x-18x²-1800)
Now at x =1 The value of the polynomial is -3434
Therefore
-3434 = a(1+100-18-1800)
or, a = 2
Therefore the polynomial is of the form: (2x³+200x-36x²-3600)
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2. Find the slope and y-intercept of the line.
O slope=3 y-intercept=2
O slope 2 y-intercept=3
O slope 3/2 y-intercept=2
O slope 2/3 y-intercept=2
the cost to rent a moving van is $51 plus an additional $7 per hour. If a moving van is rented for 2 hours, what is the cost?
We know that
The cost to rent a moving van is $51 plus an additional $7 per hour.Based on the given information, we define the following
[tex]51+7(2)=51+14=65[/tex]Therefore, the cost is $65.The cost to rent a moving van is $51 plus an additional $7 per hour.
Based on the given information,
Can someone help me with this please?
Step-by-step explanation:
in general, a linear function is always of the structure
y = ax + b
"a" is the slope of the line and is the ratio (y coordinate difference / x coordinate difference) when going from one point on the line to another.
"b" is the y-intercept (the y-value when x = 0).
so, if we don't see the solution right away with experience, we have to use the data points (usually starting with the first 2) to solve them 2 equations with 2 variables a, b :
2 = a×1 + b = a + b
1 = a×2 + b = 2a + b
now we can simply subtract the first equation from the second and get
1 = 2a + b
- 2 = a + b
------------------
-1 = a + 0
a = -1
1 = 2×-1 + b = -2 + b
b = 3
and the equation is
y = -x + 3
therefore, when the input is n (that means f(n))
y = output = -n + 3
A. Solve each absolute value equation. /2.5pts
1)| 3x| = 9
Answer:
x = 3
or
x = -3
(explanation in the picture above)
Answer: x = 3 or x = -3
Step-by-step explanation:
Absolute values make the answer always positive, as they cancel out the negative sign. So to solve an absolute value equation, we must solve for both the positive and negative of the answer.
3x = 9
3x = -9
x = 3 or x = -3
Carmen is about to complete a jigsaw puzzle the puzzle and one remaining piece are shown below what transformation can shark Carmen apply to the final piece to fit into the puzzle
We can see that the holes of the piece are already oriented in a way the piece will fit in the missing hole of the puzzle, so it doesn't need a rotation or reflection.
Then, in order to fit the piece in the hole, we need to move the piece 3 positions to the left and 1 position down.
Therefore the transformation needed is: a translation of 3 units to the left and 1 unit down.
please someone help me there are only 3 questions
If the corresponding elements of two sequences of numbers, frequently experimental data, have a constant ratio, known as the coefficient of proportionality or proportionality constant, then the two sequences of numbers are proportional or directly proportional.
Definition of the proportionality constant?
The ratio connecting two given numbers in what is known as a proportional relationship is the constant of proportionality. Constant ratio, constant rate, unit rate, constant of variation, and even rate of change are other names for the constant of proportionality.
K = y/x is the equation for the proportionality constant. The equation for the slope of a line through the origin, m = y/x, is the same as this. One can determine the value by using the equation for the line's slope.
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At the beginning of spring, Anand planted a small sunflower in his
backyard. The sunflower's height in inches, h, after w weeks, is given by the equation h = 3.75w+18. What
could the number 3.75 represent in the equation?
Hint: this equation is in slope-intercept form: y=mx+b
The rate of change in the sunflower's height
The sunflower's height after one week
The sunflower's height when it is planted
Answer:
3.75 represents how much the flower grows every week.
Step-by-step explanation:
Find the equation of a line perpendicular to y=x-1 and passes through the point (-1,-5)
A. y+5= -(x+1)
B. y-5=x-1
C. y+5=x+1
D. y-5= -(x-1)
Step-by-step explanation:
d
since you add them up you will have a certain answer that will match up
Please help
Name the reciprocals of each equation
Equations in picture
1. (3/4)x = 9. Multiply both sides by the reciprocal of 3/4: (4/3)(3/4)x = (4/3)(9)
x = 12.
2 . -4=4/7*x
4x/7=-4
x=-7
3. -1/5*x=6
-x/5=6
Multiply all terms by the same value to eliminate fraction denominators
Cancel multiplied terms that are in the denominator
x=-30
With an example, what is a reciprocal equation?
An inverse of a number or value is referred to as reciprocal. If x is any real number, then 1/x will be the reciprocal of that number. For instance, 1/8 is the reciprocal of 8, which is 1 divided by 8. 1/8's reciprocal is equal to 8.
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What is the length of cd ?
Answer:
7
Step-by-step explanation:
since 3x-6 and x+8 are congruent x had to make both the equations equal eachother. 7 is the only number that does that
Tanya sells cars. Her yearly salary is $35,000 plus 8% of her sales. Type and solve an inequality to determine her necessary sales to earn over $50,000.
Tanya yearly salary is
$35000 + 8% of her sales
Let her sales be x
Since, her sales is x
35000 + 0.08x > salary
To determine her necessary sales to earn over $50, 000
Let $50, 000 be her benchmark salary
35,000 + 0.08 * x > 50000
35000 + 0.08x > 50000
0.08x > 50000 - 350000
0.08x > 15000
Divide both sides by 0.08
0.08x/0.08 > 15000/0.08
x > 15000 / 0.08
x > 187,500
Therefore, she will need a sales of 188,000 and above to earn above $50,000
Given a normal distribution with mean M = 8 and σ = 3,
What is the x value corresponding to z = 0.4?
123
[tex]123 > x = 10 > 6[/tex]
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A triangle has height 4ft and area 32 ft². What is the length of its base?
Step-by-step explanation:
1st
[tex]area = \frac{1}{2} base \times hight[/tex]
2nd
[tex]32 = \frac{1}{2} base \times 4[/tex]
3rd
[tex]32 \div 4 = \frac{1}{2} base[/tex]
4th
[tex]8 \times 2 = base[/tex]
answer
[tex]base = 16ft[/tex]
When going out for dinner, Sally left an 18% tip. The tip was 9.50. How much was the dinner bill before the tip?
The dinner bill of Sally before the tip is $53.
Given that, Sally left an 18% tip. The tip was 9.50.
What is an equation?In mathematics, an equation is a formula that expresses the equality of two expressions, by connecting them with the equals sign =.
Let the dinner bill of Sally be x.
Now, 18% of x = 9.50
⇒ 18/100 × x = 9.50
⇒ 0.18x = 9.50
⇒ x = 9.50/0.18
⇒ x = 52.77
≈ 53
Therefore, the dinner bill of Sally before the tip is $53.
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Consider the line y =
9
7
x-9.
Find the equation of the line that is parallel to this line and passes through the point (-7, 4).
Find the equation of the line that is perpendicular to this line and passes through the point (-7, 4).
Answer:
Axis interception points [tex]97x-9[/tex] x intercepts: [tex](\frac{9}{97} ,0),[/tex]Y intercepts:[tex](0,-9)[/tex]
Step-by-step explanation:
Slope of 97x-9 : m=97
Domain: 97 x - 9
Range: 97 x - 9
A sea turtle is 3 feet below the surface of the sea. If its position can be recorded as −3 feet, what would the position 0 represent in this situation? (4 points)
Group of answer choices
A.) the height of the turtle
B.) the distance above the surface of the sea
C.) the distance below the surface of the sea
D.) the surface of the sea
Answer:
D
Step-by-step explanation:
-3 ft means that it is three feet below zero. That means 0 means the sea level.
What percentage of the number 1 to 20 contain the digit 2????
The amount as a percentage is 15% which represents the number 1 to 20 containing the digit 2.
What is the percentage?The percentage is defined as a ratio expressed as a fraction of 100.
We know that the numbers 1 to 20 that contain the digit 2 are 2,12, and 20.
So, the quantity of the numbers is 3
It’s out of 20 numbers, this means 3/20
Calculating percentages indicated above can be readily computed using the formula below:
Percentage = (Value/Total Value) × 100
The amount as a percent = (Value/Total Value) × 100
The amount as a percent = (3/20) × 100
The amount as a percent = 15%
Thus, the amount as a percentage is 15% which represents the number 1 to 20 containing the digit 2.
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Identify the factors of x2 − 5x − 24. (1 point) (x + 8)(x − 3) (x − 8)(x + 3) (x + 4)(x − 6) (x − 4)(x + 6)
Answer:
(x+3)(x–8)
Step-by-step explanation:
Normally you will always write factors in this form: (variable + smallest number)(variable – largest number)
Correct form: (x+2)(x–8)
Incorrect form: (x–2)(x+8)
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-7 -6 -5 -4 -3 -2 ONO MN ++ HA -6-5-4-3-2-1 + 11 2 3 4 5 6 7 8 9 -2 -3 F-4 -5 -6 -7 -A + jo voo Alcon ixth If this is the graph of f(-x) = a +k, then : A. 0 < a < 1 B. a < 0 O c. a> 1 O D. K> 1
The function is
[tex]f(x)=a^{(x+h)}+k[/tex]The limit when x->+/- infinite are (analitically)
[tex]\begin{gathered} \lim _{x\to\infty}f(x)=a^{(\infty+h)}+k=a^{\infty}+k \\ \text{and} \\ \lim _{x\to-\infty}f(x)=a^{(-\infty+h)}+k=\frac{1}{a^{\infty}}+k \\ \end{gathered}[/tex]And, from the figure,
[tex]\begin{gathered} \lim _{x\to\infty}f(x)=\infty \\ \text{and} \\ \lim _{x\to-\infty}f(x)=-4 \end{gathered}[/tex]Therefore,
[tex]\begin{gathered} \Rightarrow a^{\infty}+k=\infty \\ \Rightarrow a>1 \\ \text{and} \\ \Rightarrow-4=\frac{1}{a^{\infty}}+k,a>1 \\ \Rightarrow-4=k \end{gathered}[/tex]Therefore, the answer is option C, a>1.
4x + 10 =-26 solve for x
Answer:
x=-9Step-by-step explanation:
To solve for x, isolate this equation from left to right.
4x+10=-26
First, subtract by 10 from both sides.
4x+10-10=-26-10
Solve.
-26-10=-36
4x=-36
Then, you divide by 4 from both sides.
4x/4=-36/4
Solve.
-36/4=-9
[tex]\Rightarrow \boxed{\sf{x=-9}}[/tex]
As a result, the solution is x=-9, which is the correct answer.
I hope this helps, let me know if you have any questions.
Answer:
-9
Step-by-step explanation:
First you subtract 10 from each side
4x + 10 = -26
-10 -10
then you divide by your x
4x = -36
4 4
the 4s cancel out leaving you with x only
x = -36/4
x = -9
42
X
40
Find the unknown side length, x. Write your answer in simplest radical form.
A. 241
B. 4 29
C. 48
D. 58
The unknown side length of the right triangle is 58 units.
What is pythagoras theorem for a right triangle?
In essence, the Pythagorean theorem is used to determine a triangle's angle and length of an unknown side. In a right-angled triangle, the square of the hypotenuse side is equal to the sum of the squares of the other two sides, according to Pythagoras's Theorem. These triangle's three sides are known as the Perpendicular, Base, and Hypotenuse. Due to its position opposite the 90° angle, the hypotenuse in this case is the longest side. When the positive integer sides of a right triangle (let's say sides a, b, and c) are squared, the result is an equation known as a Pythagorean triple.
Mathematically, Hypotenuse² = Base² + Perpendicular²
Given, the length of the perpendicular of the right triangle = 42 units
Also, the length of the base of the right triangle = 40 units
Let the length of the hypotenuse of the right triangle = 'x' units
Following the statement of the pythagoras theorem as established in literature, we have: Hypotenuse² = Base² + Perpendicular²
Substituting the values from the question given, we get:
x² = 42² + 40² = 3364 ⇒ x = √3364 ⇒ x = √58² ⇒ x = 58
Therefore, the unknown side length of the right triangle is 58 units.
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PLEASE HELP
Classify the equation 6x + 4x-1= 2(5x + 4) as having one solution, infinitely many solutions, or no solution by
solving the problem. Solve the equation for x then classify the solution.
Answer: NO SOLUTION
Step-by-step explanation:
6x + 4x - 1 = 2(5x + 4)
10x - 1 = 2(5x+4)
10x - 1 = 10x + 8
-1 = 8
NO SOLUTION
!!!Need Help ASAP
R=42−0.7t
Quinn returned home one summer's day to find it extremely hot. He turned the air conditioner on, and the room's temperature began decreasing at a constant rate. The equation shown above gives the room's temperature, R, in degrees Celsius, t minutes after Quinn turned on the air conditioner. What was the room's temperature, in degrees Celsius, when Quinn returned home?
The room's temperature when Quinn returned home is the y-intercept of the equation, which is: 40 degrees Celsius.
What is the Y-intercept or Initial Value of a Linear Equation?The equation of a linear relationship between two variables, x and y, can be expressed in slope-intercept form as y = mx + b, where we have the initial value or the y-intercept as "b", and the rate of change or unit rate as "m".
Alternatively, it can be rewritten as y = b + mx.
R = 42 - 0.7t represents the equation for the Quinn's room's temperature, R, in degrees Celsius, and t in minutes after Quinn turned on the air conditioner.
Interpreting the equation, we can deduce the following:
The initial value or the y-intercept (b) was the room's temperature when Quinn returned home.
The unit rate or rate of change (m) = -0.7 degrees per minute.
Thus, Quinn's room's temperature when she returned was 40 degrees Celsius.
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Learn with an example
or Watch a video D
Two cars leave the same parking lot, with one heading north and the other heading east.
After several minutes, the northbound car has traveled 3 kilometers, and the eastbound car
has traveled 4 kilometers. Measured in a straight line, how far apart are the two cars?
kilometers.
The two cars are 5 kilometers far apart from each other.
What is Pythagoras theorem?
The Pythagoras theorem states that in a right triangle, the square of the hypotenuse is equal to the sum of the square of the other two sides.
Given that;
Two cars leave the same parking lot, with one heading north and the other heading east.
After several minutes, the northbound car has traveled 3 kilometers, and the eastbound car has traveled 4 kilometers.
Now,
The straight path is find by using the Pythagoras theorem as;
Straight path = √3² + 4²
= √9 + 16
= √25
= 5 km
Therefore,
The two cars are 5 kilometers far apart from each other.
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A company is constructing an open-top, square-based, rectangular metal tank that will have a volume of 48.5 (ft) with superscript (3). What dimensions yield the minimum surface area? Round to the nearest tenth, if necessary.
The dimensions that yield the minimum surface area of the open-top square-based, rectangular metal tank that will have a volume of 48.5 ft³ are:
Length = 3.65 ftWidth = 3.65 ft.What are the dimensions of an area?The dimensions of an area, which is a two-dimensional object, refer to the length and the width.
On the other hand, the dimensions of the volume refer to the length, width, and height.
The volume of the square-based rectangular tank = 48.5ft³.
The length of each side of the surface area = 3.6468 ft (∛48.5ft)
Check:
Volume = height x length x width
= 3.6468 x 3.6468 x 3.6468
= 48.499 ft³
= 48.5 ft³
Thus, the dimensions of the surface area include the length and the width without the height.
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