Answer:
exact form: 43/2
decimal form: 21.5
mixed number form: 21 1/2
Step-by-step explanation:
i have no idea ahahahahhahahahha
Answer: " s = 21. 5 " ; or, write as: " s = \(21\frac{1}{2}\) "
____________________________
Step-by-step explanation:
____________________________
Given:
63 – 4 = 8 (2+1/4s) ; Solve for: "s" ;
Note: Rewrite the equation:
↔ 8 (2+1/4s) = 63 - 4 ; (commutative property);
Start with the "right-hand side" of the equation:
" 63 − 4 " ; which equals: " 59. "
___________________________
Rewrite the equation:
___________________________
→ 8 (2 + 1/4s) = 59 ;
Now, let us examine the "left-hand side" of the equation:
" 8 (2 + 1/4s) " ;
Note the "distributive property" of multiplication:
a(b + c) = ab + ac ;
As such:
" 8 (2 + 1/4s) " ;
= (8×2) + (8× 1/4s) ;
= 16 + 8/4s ;
= 16 + 2s ;
Now, rewrite the equation:
16 + 2s = 59 ; Subtract "16" from each side of the equation:
16 + 2s − 16 = 59 − 16 ;
to get: 2s = 43 ;
Now, divide each side of the equation by "2" ;
to isolate "s" on one side of the equation; & to solve for "s" ;
2s / 2 = 43 / 2 ;
to get:
s = 21. 5 ;
or; write as " \(21 \frac{1}{2}\) " .
___________________________
Hope this answer—and explanation—helps you!
Best of luck to you!
___________________________
A pitcher contains 17.5 cups of iced tea. You drink 2.25 cups of the tea each morning and 1.25 cups of the tea each evening. When will you run out of iced tea?
Answer:
5 days
Step-by-step explanation:
A person is watching a boat from the top of a lighthouse. The boat is approaching the lighthouse directly. When first noticed, the angle of depression to the boat is 19° 14'. When the boat stops, the angle of depression is 54° 12'. The lighthouse is 200 feet tall. How far did the boat travel from when it was first noticed until it stopped? Round to the nearest foot.
A. 474ft
B. 414 ft
C.452 ft
D.429 ft
Answer:
answer in link
Step-by-step explanation
alekscgi/x/Isl.exe
Determine the turning points and distinguish between them when necessary y=x³ - 3x - 9x + 4
The turning points of the function y = x³ - 3x² - 9x + 4 are (3, -23) and (-1, 9).
To determine the turning points of the given function y = x³ - 3x² - 9x + 4, we need to find the critical points where the derivative of the function is equal to zero.
1. Find the derivative of the function:
y' = 3x² - 6x - 9
2. Set the derivative equal to zero and solve for x:
3x² - 6x - 9 = 0
3. Factorize the quadratic equation:
3(x² - 2x - 3) = 0
4. Solve the quadratic equation by factoring or using the quadratic formula:
(x - 3)(x + 1) = 0
This gives us two possible values for x: x = 3 and x = -1.
5. Substitute these critical points back into the original function to find the corresponding y-values:
For x = 3:
y = (3)³ - 3(3)² - 9(3) + 4
= 27 - 27 - 27 + 4
= -23
For x = -1:
y = (-1)³ - 3(-1)² - 9(-1) + 4
= -1 - 3 + 9 + 4
= 9
6. Therefore, the turning points are (3, -23) and (-1, 9).
Note: It appears that there was a typo in the original equation, where the term "-9x" should have been "-3x²". The above solution assumes the corrected equation.
For more such questions on points, click on:
https://brainly.com/question/26865
#SPJ8
I need help with math problem: 5(2x+6)
Hey there!
5(2x + 6)
= 5(2x) + 5(6)
= 10x + 30
Answer: 10x + 30 ☑️
Good luck on your assignment and enjoy your day!
~Amphitrite1040:)
Answer:
10x + 30
Step-by-step explanation:
When there is a number before parenthesis it means we have to multiply, so we will apply the distribution property.
5(2x) + 5(6)
Then we just multiply
10x + 30
Because we do not know the value of "x" we will leave it like this.
Hope it was helpful ;)
Given f(x) = x2 – 7x + 10 and g(x) = x2 – x – 20, find the y-intercept of open parentheses g over f close parentheses of x
0
–2
2 over 3
negative one half
If f(x) is x²-7x+10 and g(x) is x²-x-20, then the y-intercept of (g/f)(x) is 2
Given the functions
f(x) = x²– 7x + 10g(x) = x² – x – 20First, we need to get the composite function g/f((x)
(g/f)(x) = \(\frac{x^2-x-20}{x^2-7x+10}\)
The y - intercept of the function occurs at when x = 0
Substitute x = 0 into the resulting expression:
\((g/f)(0)=\frac{x^2-x-20}{x^2-7x-10}\\ (g/f)(0)=\frac{0^2-0-20}{0^2-7(0)-10}\\(g/f)(0)=\frac{-20}{-10}\\(g/f)(0) = 2\)
Hence the y-intercept of (g/f)(x) is 2
Learn more here; https://brainly.com/question/1744326
Find the equation of the parabola with the following properties. Express your answer in standard form.
Symmetric with respect to the line y = 2
Directrix is the line x = 11
P = -3
The equation of the parabola with the following properties y = (-1/4)(x+3)^2 -1
What is the equation of the parabola?To find the equation of a parabola, we can use the formula f(x) = ax^2 + bx + c, where a, b and c are congruent vertices.
Alternatively, we can use PF = PM to find the equation of the parabola.
vertex is half way between the focus and directrix
It's a downward opening parabola, general form
y= a(x-h)^2 + k
where (h,k) = vertex= (-3,-1)
plug in another point on the parabola to solve for a which gives
am answer with either x coefficient = -1'/4 or =4 Check the math.
one or the other is right another point is the y intercept = 9a-1
Another point is directly to the right of the focus (-1, -2) It's 2 down from the directrix and 2 to the right of the focus, equidistant. plug that point into y= a(x+3)^2 -1 and solve for "a"
-2 = a((-1+3)^2 -1
-2 = 4a -1
4a = -
a = -1/4
The parabola is y = (-1/4)(x+3)^2 -1
Learn more about the equation of the parabola on https://brainly.com/question/4074088
#SPJ1
Judy’s Cake Shop makes fresh cakes to customer orders. After receiving the order by Judy’s assistant, which takes 2 minutes, Judy then takes 8 minutes to mix the ingredients for the cake and loads a cake pan for baking. Then the cake is put into the oven for 30 minutes. The oven can hold three cakes at one time. When the cake is taken out of the oven, it is cooled for 1 hour. The assistant then takes 2 minutes to pack the cake for pickup and bills the customer, which takes 3 minutes. a. What is the capacity of the process, and what is the bottleneck? b. What is the throughput time for a typical cake? c. If on average five orders are taken per hour, how many cakes are there in the process (on average)?
Answer:
Kindly check explanation
Step-by-step explanation:
Given that :
Time taken to receive order = 2 minutes
Ingredient mixing and cake loading = 8 minutes
Baking time = 30 minutes
Number of cakes oven can hold at a time = 3
Cooling time = 1 hour = 60 minutes
Cake packing = 2 minutes
Billing customer = 3 minutes
a. What is the capacity of the process, and what is the bottleneck?
The capacity of the process:
Within an hour : two bakings can be done =(30 minutes * 2) = 60 minutes
Also oven can hold 3 cakes, so, 3 cakes can be baked at a time.
Hence, 3 cakes in 30 minutes ;
6 cakes in an hour;
Hence, capacity of the process is 6cakes per hour.
The bottleneck is the oven, because if the number of ovens were to be increased, the process capacity will increase, similarly, if one of the oven gets faulty, then the process capacity reduces further.
b. What is the throughput time for a typical cake?
The throughput time, is the summation of all the time taken to fully complete an order :
Receipt of order + mixing + baking + cooling + packing + billing
2 + 8 + 30 + 60 + 2 + 3 = 105 minutes
c. If on average five orders are taken per hour, how many cakes are there in the process (on average)?
(Throughput time / 60) * average number of order
(105/60) * 5
= 1.75 * 5
= 8.75
How many terms of the sequence 10,12,14 will add up to 190
Answer:
required value is n = 10
Step-by-step explanation:
by ingnoring the negative value n = -14
How to tell if a graph is a function in algebra
Answer:
Inspect the graph to see if any vertical line drawn would intersect the curve more than once.
Step-by-step explanation:
If there is any such line, the graph does not represent a function. If no vertical line can intersect the curve more than once, the graph does represent a function.
Brittany is taller than 5 feet (Brittany's height = n). = The inequality that describes this situation is
Answer:
n>5 feet
Step-by-step explanation:
1) we know that brittany is taller than 5 feet, meaning that she can't be five feet tall exactly
2) n>5 feet (we do not include the line underneath the greater than symbol because she cannot be exactly 5 feet)
Graph:
-------------->
<-------------------|-----------------------|---------------------------------o------------>
-5 0 5
Tyler is 6 feet tall and Blake measures his shadow to be 10 ½ feet long. Maddie measures the shadow of the tree to be 21 feet long. How tall is the tree to the nearest tenth of a foot.
20 Points
The tree is approximately 12 feet tall to the nearest tenth of a foot.
We have,
To find the height of the tree, we can set up a proportion using the measurements of the shadow.
Since we know that Tyler is 6 feet tall and his shadow is 10 ½ feet long, we can set up the following expression:
Tyler's height / Tyler's shadow length = Tree's height / Tree's shadow length
6 feet / 10.5 feet = Tree's height / 21 feet
To find the tree's height, we can cross-multiply and solve for it:
6 feet x 21 feet = 10.5 feet x Tree's height
126 feet = 10.5 feet x Tree's height
Dividing both sides of the expression by 10.5 feet:
126 feet / 10.5 feet = Tree's height
12 feet = Tree's height
Therefore,
The tree is approximately 12 feet tall to the nearest tenth of a foot.
Learn more about expressions here:
https://brainly.com/question/3118662
#SPJ1
What is the correct sum of 2.34 and 128.8
Answer:
131.14
Step-by-step explanation:
Hope this helps!! Good luck!!
Answer:
131.14
Step-by-step explanation:
2.34 + 128.8 = 131.14
in what time will a sum of rs2000 amounts to rs2240 at 4% pa simple interest
Answer: The time it takes for a sum of money to amount to a certain amount at a certain interest rate can be calculated using the following formula:
Time = (100 x (Amount - Principal)) / (Principal x Rate)
In this case, the principal is Rs. 2000, the amount is Rs. 2240, and the rate is 4%. Therefore, the time is:
Time = (100 x (2240 - 2000)) / (2000 x 4) = 3 years
Therefore, it will take 3 years for Rs. 2000 to amount to Rs. 2240 at 4% simple interest.
Step-by-step explanation:
Use the quadratic formula to find the exact solutions of 3x2 − 6x + 2 = 0.
a. negative 1 plus or minus the square root of 3 divided by 3
b. 1 plus or minus the square root of 3 divided by 3
c. negative 1 plus or minus the square root of 15 divided by 3
d. 1 plus or minus the square root of 15 divided by 3
The exact solutions of the qudratic equation 3x^2 - 6x + 2 = 0 are:
a. negative 1 plus or minus the square root of 3 divided by
3 (x = (-1 ± √3) / 3) .So, option a is the correct answer.
To find the solutions of the quadratic equation 3x^2 - 6x + 2 = 0, we can use the quadratic formula, which states that for an equation of the form ax^2 + bx + c = 0, the solutions are given by:
x = (-b ± √(b^2 - 4ac)) / (2a)
In this case, a = 3, b = -6, and c = 2. Substituting these values into the formula, we have:
x = (-(-6) ± √((-6)^2 - 4(3)(2))) / (2(3))
x = (6 ± √(36 - 24)) / 6
x = (6 ± √12) / 6
x = (6 ± 2√3) / 6
x = (3 ± √3) / 3
Therefore, the exact solutions of the equation 3x^2 - 6x + 2 = 0 are:
a. negative 1 plus or minus the square root of 3 divided by 3 (x = (-1 ± √3) / 3)
So, option a is the correct answer.
To learn more about : quadratic
https://brainly.com/question/1214333
#SPJ11
1. Which model represents 3/5 of 10?
As you need to identify 3/5 of 10:
Divide 10 into 5 equal groups (each group represents 1/5 of 10)
Then, you shadow 3 of those grups to represent 3/5 of 10:
\(\frac{1}{5}+\frac{1}{5}+\frac{1}{5}=\frac{3}{5}\)9) The 50 cars used by a firm were inspected. 10 had faulty brakes and 15 had faulty tyres. There were 2 cars with faulty brakes but good tyres. How many cars had good brakes and good tyres? The answer is 33
Based on the information, there are 25 cars with good brakes and good tires.
How to calculate the valueTotal cars = 50
Cars with faulty brakes = 10
Cars with faulty tires = 15
Cars with faulty brakes and good tires = 2
Let's calculate the number of cars with good brakes and good tires:
Cars with faulty brakes or faulty tires = Cars with faulty brakes + Cars with faulty tires - Cars with faulty brakes and good tires
= 10 + 15 - 2
= 25
Cars with good brakes and good tires = Total cars - Cars with faulty brakes or faulty tires
= 50 - 25
= 25
Therefore, there are 25 cars with good brakes and good tires.
Learn more about numbers on
https://brainly.com/question/25734188
#SPJ1
Find the tangent of the larger acute angle in a right triangle with side lengths 3, 4, and 5.
Write your answer as a fraction.
The tangent of the larger acute angle is ______?______
The tangent should be in fraction is 4/3
Calculation of the tangent:
Since in a right triangle with side lengths 3, 4, and 5
Here there is the larger acute angle in the 3, 4 and 5 so it should be lies between 3 and 5
So, it should be like
= opposite side ÷ adjacent side
= 4/3
Hence, The tangent should be in fraction is 4/3
Learn more about fraction here: brainly.com/question/19107557
Solve for x 4x^2+72x+320=0
Answer:
i hope this helps
Step-by-step explanation:
if you had 341 milliliters of milk, how many liters is this equal to?
Which property is illustrated by the following ?
if 2(x+y)= z, then 2x + 3y= z
A football team scored fewer than 16 points in Saturday’s game. Than wants to write an inequality for the number of points. He uses the variable s in his inequality. What does s represent? A - the number of fans of the team
B - the number of games played by the team
C - the number of points scored by the team
D - the number of players on the team
Find the larger solution of the exponential
equation
2^x^2= 4^3x
Answer:The larger solution is 6
Step-by-step explanation:
Can anyone help me solve this or atleast give me the answers
The measure of the angles formed between parallel lines and their transversals indicates;
(c)(e)(a)(d)(b)(f)(e)(a)m∠MNP = 56°m∠WXZ = 130°9. m∠3 = 97°, m∠5 = 97°, m∠10 = 97°, m∠7 = 83°
What are parallel lines?Parallel lines are lines that maintain the are equidistant from each other and have the same slope on the coordinate plane.
The angles formed between the parallel lines and their transversal are;
1. Alternate exterior angles; (c) ∠9 and ∠16
2. Supplementary angles (e); ∠15 & ∠11
3. Alternate interior angles (a); ∠10 & ∠15
4. Vertical angles (d); ∠12 & ∠15
5. Corresponding angles (b); ∠9 & ∠11
6. None (f); ∠9 & ∠15
7. Supplementary angles (e); ∠13 & ∠14
8. Alternate interior angles; ∠14 & ∠11
9. The alternate interior angles theorem indicates that we get;
(a + 28) = 2·a
Therefore; 2·a - a = 28
2·a - a = a, therefore;
a = 28
∠MNP = (a + 28)° = (28 + 28)° = 56°
10. The alternate interior angles theorem indicates that we get;
5·y° = (2·y + 78)°
Therefore;
5·y - 2·y = 78
3·y = 78
y = 78/3 = 26
The measure of the angle WXZ, m∠WXZ = 5·y°
Therefore; m∠WXZ = 5 × 26 = 130
m∠WXZ = 130°
9. ∠2 ≅ ∠3 (Vertical angles theorem)
m∠2 = m∠3
Therefore; m∠3 = m∠2 = 97°
m∠5 + m∠6 = 180° (Linear pair angles theorem)
m∠5 + 83° = 180°
m∠5 = 180° - 83° = 97°
∠10 and ∠2 are corresponding angles, therefore;
m∠10 = m∠2 = 97°
∠7 and ∠6 are vertical angles, therefore;
m∠7 = m∠6 = 83°
∠9 and ∠3 are same side interior angles, therefore;
m∠9 + m∠3 = 180°
m∠9 = 180° - m∠3
m∠9 = 180° - 97° = 83°
∠8 and ∠6 are linear pair angles, therefore; m∠8 = 180° - 83° = 97°
∠16 and ∠6 are same side exterior angles, therefore;
m∠16 + m∠6 = 180°
m∠16 = 180° - 83° = 97°
Learn more on angles formed between parallel lines and their transversals here: https://brainly.com/question/10253728
#SPJ1
grade 11 2022 June common test mathematics memorandum?
Note that the roots of the equation Unequal and rational (Option D)
How is this so ?The roots of the equation (x - 3)² = 4 can be found by taking the square root of both sidesof the equation.
x - 3 = ±√4
⇒ x - 3 = ±2
Solve for x
For the positive square root.
x - 3 = 2
x = 2 + 3
x = 5
For the negative square root.
x - 3 = -2
x = -2 + 3
x = 1
Since the equation has two roots, x = 5 and x = 1. These roots are unequal and rational. (Option D)
Learn more about roots of equation at:
https://brainly.com/question/30090611
#SPJ1
Full Question:
Although part of your question is missing, you might be referring to this full question:
The roots of the equation (x - 3)² = 4 are
A.Unequal and irrational.
B.Equal and rational.
C. Equal and irrational.
D. Unequal and rational.
The vector ⇀
= ⟨2, 3⟩ is multiplied by the scalar –4. Which statements about the components, magnitude, and direction of the scalar product –4⇀
are true? Select all that apply.
A. The component form of −4⇀
is ⟨–8, –12⟩.
B. The magnitude of −4⇀
is 4 times the magnitude of ⇀
.
C. The direction of −4⇀
is the same as the direction of ⇀
.
D. The vector −4⇀
is in the fourth quadrant.
E. The direction of −4⇀
is 180° greater than the inverse tangent of its components.
Answer:
Therefore, the correct statements are A, B, and E.
Explanation:
Based on my knowledge, a vector is a quantity that has both magnitude and direction. A scalar is a quantity that has only magnitude. When a vector is multiplied by a scalar, the magnitude of the vector is multiplied by the absolute value of the scalar, and the direction of the vector is either preserved or reversed depending on the sign of the scalar.
To answer your question, we need to find the component form, magnitude, and direction of the scalar product –4⇀
.
- The component form of −4⇀
is obtained by multiplying each component of ⇀
by –4. Therefore, −4⇀
= ⟨–8, –12⟩. This means that statement A is true.
- The magnitude of −4⇀
is obtained by multiplying the magnitude of ⇀
by 4. The magnitude of ⇀
is √(2^2 + 3^2) = √13. Therefore, the magnitude of −4⇀
is 4√13. This means that statement B is true.
- The direction of −4⇀
is opposite to the direction of ⇀
because the scalar –4 is negative. This means that statement C is false.
- The vector −4⇀
is in the third quadrant because its components are both negative. This means that statement D is false.
- The direction of −4⇀
is 180° greater than the inverse tangent of its components because it is opposite to ⇀
. The inverse tangent of its components is tan^(-1)(–12/–8) = tan^(-1)(3/2). Therefore, the direction of −4⇀
is 180° + tan^(-1)(3/2). This means that statement E is true.
Therefore, the correct statements are A, B, and E.
2x+3y=-12
2x+t=-16
X=. Y=
Help plz
To make this problem solvable, I have replaced the 't' in the second equation for a 'y'.
Answer:
x = -9
y = 2
Step-by-step explanation:
Solve the system:
2x + 3y = -12 [1]
2x + y = -16 [2]
Subtracting [1] and [2]:
3y - y = -12 + 16
2y = 4
y = 4/2 = 2
From [1]:
2x + 3(2) = -12
2x + 6 = -12
2x = -18
x = -18/2 = -9
Solution:
x = -9
y = 2
x + 121 = 4x - 20 what is x
Answer:
x = 47
Step-by-step explanation:
x + 121 = 4x - 20
-3x + 121 = - 20
-3x = -141
x = 47
So, the answer is x = 47
Four sparking plugs and a fan belt cost $10.50 if the fen belt costs $1.75 more than sparking plugs. Find the cost of each material
Answer: x = $1.75
Step-by-step explanation:
Let's assume that the cost of each sparking plug is x dollars. Then, the cost of the fan belt is x + $1.75 since it costs $1.75 more than each sparking plug.
According to the problem, the total cost of four sparking plugs and a fan belt is $10.50. We can express this as an equation:
4x + (x + $1.75) = $10.50
Simplifying and solving for x, we get:
5x + $1.75 = $10.50
5x = $8.75
x = $1.75
Therefore, each sparking plug costs $1.75 and the fan belt costs $3.50 ($1.75 + $1.75).
please help. ill give points
Sophie invested some of her $20,000 in bonds that made an 8% profit and the rest in bonds that made a 7% profit. If the profit on the 8% bonds was 700$ more than the profit on the 7% bonds, how much did she invest in the 7% bonds?
The amount of investment in 8% and 7% of the profit will be $14,000 and $6,000, respectively.
What is the solution to the equation?The allocation of weights to the important variables that produce the calculation's optimum is referred to as a direct consequence.
Sophie put a portion of her $20,000 in bonds that created an 8% gain and the rest in bonds that created a 7% gain. In the event that the benefit on the 8% bonds was 700$ more than the benefit on the 7% bonds.
Let 'x' be the amount of investment in 8% profit. Then the amount of investment in 7% profit is ($20,000 - x). Then the equation is given as,
0.08x - 0.07(20,000 - x) = 700
0.08x + 0.07x - 1,400 = 700
0.15x = 2,100
x = $14,000
Then the amount of investment in 7% profit will be given as,
($20,000 - x) = $20,000 - $14,000
($20,000 - x) = $6,000
The amount of money in 8% and 7% of the benefit will be $14,000 and $6,000, separately.
More about the solution of the equation link is given below.
https://brainly.com/question/545403
#SPJ1
Note: If p(a) = 0 then (x - a) is a factor of p(x)
given that f(-1), f(-2) are zeros of f(x) find the missing values of these coefficients p, q
f(x) = x³ + px² - qx - 4
After finding the values of the coefficients factor and find the solutions of x1, x2 and x3.
Answer:
Since f(-1) = 0 and f(-2) = 0, we can set up two equations:
(-1)³ + p(-1)² - q(-1) - 4 = 0
(-2)³ + p(-2)² - q(-2) - 4 = 0
Simplifying each equation, we get:
-1 + p - q - 4 = 0
-8 + 4p - 2q - 4 = 0
Simplifying further, we get:
p - q = 5
2p - q = 6
Solving for p and q, we can add the two equations together to eliminate q:
p - q + 2p - q = 5 + 6
3p - 2q = 11
Then, we can substitute the value of q from the first equation into this equation to solve for p:
3p - 2(q + 5) = 11
3p - 2q - 10 = 11
3p - 2q = 21
3p - 2(5 + p) = 21
p - 10 = 7
p = 17
Substituting this value of p into either equation for q, we get:
q = p - 5 = 12
Therefore, the coefficients are p = 17 and q = 12. To factor the expression, we can use synthetic division or long division. Using synthetic division, we get:
-1 | 1 17 -12 -4
|__ -1 -16 28
1 1 12
This gives us the factorization:
f(x) = (x + 1)(x² + x + 12)
To find the solutions, we can use the quadratic formula on the quadratic factor:
x = (-1 ± sqrt(1 - 4(1)(12))) / 2(1)
x = (-1 ± sqrt(1 - 48)) / 2
x = (-1 ± sqrt(-47)) / 2
x1 = (-1 + i(sqrt(47))) / 2
x2 = (-1 - i(sqrt(47))) / 2
Therefore, the solutions are x1 = (-1 + i(sqrt(47))) / 2, x2 = (-1 - i(sqrt(47))) / 2, and x3 = -1.
Step-by-step explanation:
give me thanks for more! your welcome bud!