Answer: -2
Step-by-step explanation: The answer is -2 because -1 x 8 = -8, and -8 x 4 = -32. Because multiplying two negatives cancels out and becomes positive, we can apply this same principle and figure out that -32 x -2 would give us positive 64. Hope this helps!
A leak in a pool causes the height of the water to decrease by 0.25 foot over 2 hours. After the leak is fixed, the height of the water is 4.75 feet. The equation 4.75 = x + (negative 0.25) can be used to find x, the original height of the water in a pool.
What was the original height of the water in the pool in feet?
4.5
5.0
6.5
7.0
The original height of the water in a pool is 5 ft , Option B is the correct answer.
What is an Equation ?An equation can be defined as a mathematical statement when two algebraic expressions are equated using an equal sign.
It is given in the question that
A leak in a pool causes the height of the water to decrease by 0.25 foot over 2 hours.
the height of the water is 4.75 feet.
The equation
4.75 = x + (negative 0.25)
can be used to find x, the original height of the water in a pool.
4.75 = x - 0.25
x = 5
Therefore the original height of the water in a pool is 5 ft , Option B is the correct answer.
To know more about Equation
https://brainly.com/question/10413253
#SPJ1
Answer:
B
Step-by-step explanation:
Which function is shown in the graph below?
O y = logo 4x
O y = log₁x
O y = log3x
O y = log10x
The correct function shown in the graph is,
⇒ log₁₀ (ax) = 1
What is mean by Function?A relation between a set of inputs having one output each is called a function. and an expression, rule, or law that defines a relationship between one variable (the independent variable) and another variable (the dependent variable).
It has been given that the point (3,1) is on the graph. For the point (3,1) to be on the graph, the following must hold true:
⇒ log₁₀ (ax) = 1
or , ax = 10¹ = 10
Thus, x = 10/a
So, in order for the point (3,1) to lie on the graph, of all the given options the closest we can get is when we have Option D, that is, when a = 3. That will make x = 3.33 and thus, .
⇒ log (3 × 3.33) = 0.99 ≈ 1
Thus, out of the given options only Option D seems to be the most probable answer.
Learn more about the function visit:
https://brainly.com/question/11624077
#SPJ5
A rectangular deck has a length of 12 feet and a perimeter of 36 feet. What is the deck's width and area?
Answer:
Deck's width is 6 feet.The area is 72 sq. ft.Step-by-step explanation:
First, label it out:
Length: 12 ft.Width: ?Area: ?Perimeter: 36 ft.Then, we add up 12 twice (Since the length is on 2 sides):
12 + 12 = 2436 - 24 = 1212 - ? = ?Now, we write down a 6 in the ?:
12 - 6 = 6.Width = 6.
We are not done!
Now, we have to solve for area.
12 * 6= 72Answers are:Area = 72 sq. ft.Width = 6 ft.What is P(greater than 8)?
Answer:
Yes
Step-by-step explanation:
The sum must be greater than 8 it can't be 7 anyway. Sums can be 9, 10 or 12. P = (4+3+1)/36 = 3/36
ZA=C
Round your answer to the nearest hundredth.
C
B
6
8
A
?
Answer:
? = 41.41°
Step-by-step explanation:
The known side length is adjacent to the angle we need to find hence we will use cosine
cosx = adjacent /hypotenuse
cos(?) = 6 / 8
simplify fraction, cos(?) = 3 / 4
? = arccos(3 / 4)
The average Wealth of a person in Richville is $150,000 and the average wealth of a
person in Poorville 15 $20,000. Suppose Richville and Poorville combine to form Mediumville.
Which of the following rules is the composition of a dilation of scale factor 2, then a translation of three units to the right? a) (2x+3,y) b) (2x+6, 2y) c) (2x +3, 2y) d) (2x+6, y)
Answer:
The answer is C: (2x +3, 2y)
Step-by-step explanation:
When applying the dilation of a scale factor of 2, you have to apply it to both the x and y coordinate, which means you are multiplying the coordinates by 2.
Let's assume the coordinates you start with are (x, y). Apply the dilation of 2.
(x, y) -----> (2x, 2y)
Now you are moving the figure right. When moving right, this only effects the x coordinate since the x axis moves left and right. Moving right indicates you will add the number of units translated to the x coordinate.
Translation 2 units right:
(2x, 2y) -----> (2x +3, 2y)
Forming quadratic expression.Two consecutive odd numbers are such that their product is 35.find the numbers
Answer:
Numbers are 5 , 7
Step-by-step explanation:
Forming quadratic equation and solving:Let the two consecutive odd numbers be (2x + 1) and (2x + 3)
Their product = 35
(2x + 1)(2x + 3) = 35
Use FOIL method.
2x*2x + 2x*3 + 1*2x + 1*3 = 35
4x² + 6x + 2x + 3 = 35
Combine like terms
4x² + 8x + 3 = 35
4x² + 8x + 3 - 35 = 0
4x² + 8x - 32 = 0
Quadratic equation: 4x² + 8x - 32 = 0Solving:
4x² + 8x - 32 = 0
Divide the entire equation by 2
[tex]\sf \dfrac{4}{2}x^2 +\dfrac{8}{2}x - \dfrac{32}{2}=0[/tex]
2x² + 4x - 16 = 0
Sum = 4
Product = -32
Factors = 8 , (-4)
When we multiply 8*(-4) = -32 and when we add 8 + (-4) = 4.
Rewrite the middle term
2x² + 8x - 4x - 16 = 0
2x(x + 4) - 4(x + 4) = 0
(x + 4) (2x - 4) = 0
2x - 4 = 0 {Ignore x +4 = 0 as it gives negative number}
2x = 4
x = 4/2
x= 2
2x + 1 = 2*2 + 1 = 5
2x + 3 = 2*2 +3 = 7
The numbers are 5 , 7
(A+1)/a = y make a the subject of this equation
The shorter leg of a right triangle is 5 inches shorter than the longer leg. The hypotenuse is 5 inches longer than the longer leg. Find the side lengths of the triangle.
Answer:
longer leg: 20 in
shorter leg: 15 in
hypotenuse: 25 in
Formulas:
Pythagorean Theorem
[tex]c^2 = a^2 + b^2[/tex]
c ... hypotenuse
a ... one leg
b ... another leg
Pythagorean theorem is used in right triangles (triangles in which one angle is 90°).
Step-by-step explanation:
longer leg: x
shorter leg: x - 5
hypotenuse: x + 5
To find x (longer leg), let's use Pythagorean theorem.
[tex]c^2 = a^2 + b^2\\(x+5)^2 = x^2 + (x-5)^2\\x^2 + 10x + 25= x^2 + x^2 -10x + 25\\x^2 + 10x = 2x^2 - 10x\\0 = x^2 - 20x[/tex]
Now let's factorize to get solutions for x.
[tex]0 = x(x-20)[/tex]
First solution:
[tex]x = 0[/tex]
Second solution:
[tex]x - 20 = 0\\x = 20[/tex]
Since a side of a triangle has to be a positive number, x is equal to 20.
Now let's just substitute x back to get side lengths. From the question the lengths are in inches.
longer leg: x = 20 in
shorter leg: x - 5 = 20 - 5 = 15 in
hypotenuse: x + 5 = 20 + 5 = 25 in
Solve for p: -3p + 2 > 5
To solve these types of problems:
⇒ just solve like a regular algebraic equation
⇒ with an inequality sign in the middle
Let's solve:
[tex]-3p + 2 > 5\\-3p > 3[/tex]
whenever there is any division/multiplication⇒ must change the inequality sign to face the other direction
[tex]-3p > 3\\p < -1[/tex]
Answer: p < -1
Hope that helps!
Answer:
p < -1
Step-by-step explanation:
-3p + 2 > 5
subtract 2 from both sides
-3p + 2 - 2 > 5 - 2
-3p > 3
divided both sides by -3 to get p alone
-3p / -3 > 3 / -3 reverse the inequality
p > -1
Find the solution set for |2x-3|=9
Answer:
x = 6, -3
Step-by-step explanation:
. . . . . . . . . . . . . . . . .
What is the value of
(1/8)^-1/3
PLEASE I NEED THE AWNSER QUICK PLEASE AND TY
Answer:
2.66666666667
Step-by-step explanation:
(1/8)^-1/3 means 1/8 to the -1/3 power, which equals 2.66666666667. So the answer is 2.66666666667.
Consider the function.
Which conclusions can be drawn about f–1(x)? Select two options.
f–1(x) has a slope of .
f–1(x) has a restricted domain.
f–1(x) has a y-intercept of (0, –36).
f–1(x) has an x-intercept of (–36, 0).
f–1(x) has a range of all real numbers.
The statement f⁻¹(x) has a y-intercept of (0, –36) and f⁻¹(x) has a range of all real numbers options third and fifth are correct.
What is a function?
It is defined as a special type of relationship, and they have a predefined domain and range according to the function every value in the domain is related to exactly one value in the range.
The question is incomplete.
The question is: Consider the function f(x) = (-2/3)x - 24 Which conclusions can be drawn about f⁻¹(x) Select two options:
f⁻¹(x) has a slope of -2/3
f⁻¹(x) has a restricted domain.
f⁻¹(x) has a y-intercept of (0, –36).
f⁻¹(x) has an x-intercept of (–36, 0).
f⁻¹(x) has a range of all real numbers.
f(x) = (-2/3)x - 24
To find the inverse of a function:
interchange the x and y
x = (-2/3)y - 24
y = (-3/2)(x + 24)
y = (-3/2)x - 36
The slope of a function f⁻¹(x) is -3/2
From the graph, we can see the y-intercept is (0, -36) and the range will be all real numbers.
Thus, the statement f⁻¹(x) has a y-intercept of (0, –36) and f⁻¹(x) has a range of all real numbers options third and fifth are correct.
Learn more about the function here:
brainly.com/question/5245372
#SPJ1
Answer:
D and E
Step-by-step explanation:
did the test
93/100
Natalie needs 3 1/2 cups of flour to make 4 dozen cookies. How many.cups will she
need to make 2 dozen cookies?
7 cups
1 cup
13/4 cups
11/2 cups
Answer:
3/4 cups
Step-by-step explanation:
3 1/2 divided by 2
The grade 10 class is going to bake muffins. The recipe that they are going to use requires the following ingredients: RECIPE ✓2 Egga ✔125ml Cooking oll ✓375ml brown sugar (300g) ✓800ml Milk ✓300g Whole wheat flour ✓ 375ml cake flour (210g) ✓5ml Salt ✓ 5ml Vanilla Essence ✓ 10ml Bicarbonate of soda ✓ 250ml Raisins (150g) 2.1 The volume of 150g of Whole wheat is 250ml. Calculate the volume of the Whole wheat flour in the recipe 2.2 When they are all mixed together, all the above ingredients make up 2 litres of mixture (because some parts dissolve into other parts). 2.2.1 Convert 2 litres into ml 2.2.2 How many muffins can the above recipe make if 60ml is required for each muffin? 2.2.3 Using your answer to question 2.2.2, how many eggs will the girls need to buy to make 500 muffins? 2.3 The students need to make 500 muffins, using muffin trays that hold 6 muffins par tray. They plan to put 4 trays at a time into the ovens. Each oven takes 30 minutes to bake. How long will they take to make 500 muffins if they will be using 4 ovens?
The conversion of 2 liters into millimeters from the information regarding the muffins is 2000ml.
How to convert?From the information, we are told to convert 2 litres into ml. This will be:
= 1000 × 2
= 2000ml
The number of eggs that will be bought to make 500 muffins will be:
= 500 × 2
= 1000 eggs.
Learn more about conversion on:
brainly.com/question/97386
#SPJ1
If Rita receives $63.90 Interest for a deposit earning 6% simple interest for 150 days, what is the amountof her deposit to the
nearest dollar (zero decimal place). Use a 360-day year
The amount of Rita deposit is $2556.
What is Simple Interest ?The interest calculated on the principal amount or the initial investment.
It is given in the question
If Rita receives $63.90 Interest for a deposit earning 6% simple interest for 150 days.
P = ?
S.I. = $63.90
Interest = 6%
T = 150days
S.I. = (P *R*T)/100
63.90 = P * 6 * 150*100 /360
63.90 * 360*100 /( 150 *6) = P
P = $2556
Therefore the amount of Rita deposit is $2556.
To know more about Simple Interest
https://brainly.com/question/22621039
#SPJ1
Which pair of angles is an example of supplementary angles?
Answer:
Angle1 and Angle2 are supplementary.
Step-by-step explanation:
There are at least 8 pairs and I want to say up to maybe 16 pairs if angles that are supplementary.
Supplementary angles add up to 180°. So any pair that is lying together on a straight line (that's 180°) are supplementary:
1&2
2&4
3&4
1&3
5&6
6&8
7&8
5&7
Since angles don't have to touch in order to be supplementary there are many more pairs.
When -3v = -18 is solved, the result is:
Answer:
When -3v = -18 is solved, the result is:
21v
The result of this mathematical sentence is v=6
First degree equationFirst degree equation is a mathematical sentence - having at least one unknown. Its representation is given by ax + b = 0. To calculate an equation, as it is in the expression in the statement, simply: isolate x and divide the second to the first member.
*Note: Equal signs, the result will be equated as positive.
-3v = -18
v = -18/-3
v = 6
Therefore, the correct value of this equation is v = 6.
The data below represent a demand schedule.
Product Price: $30, $25, $20, $15, $10
Quantity Demanded: 5, 15, 25, 35, 45
Using the midpoint approach, determine the price elasticity of demand between each of the following prices:
A. Between P1 = $30 & P2 = $25, Ed=?
B. Between P1 = $25 & P2 = $20, Ed=?
C. Between P1 = $20 & P2 = $15, Ed=?
D. Between P1 = $15 & P2 = $10, Ed=?
Round your answers to two decimal places. Enter your answers as a positive value (absolute value).
By using the midpoint approach, the price elasticity of demand between each of the given prices are:
5.502.251.170.63What is the price elasticity of demand?The price elasticity of demand measures the responsiveness of the quantity demanded by a consumer with respect to a specific change in price of the product, all things being equal (ceteris paribus).
By using the midpoint approach, the price elasticity of demand between each of the given prices is given by:
Price elasticity of demand = (Q₂ - Q₁)/[(Q₂ + Q₁)/2]/(P₂ - P₁)/[(P₂ + P₁)/2]
Price elasticity of demand = (15 - 5)/[(15 + 5)/2]/(25 - 30)/[(25 + 30)/2]
Price elasticity of demand = 1/-0.1818
Price elasticity of demand = 5.50.
Part B.Price elasticity of demand = (Q₂ - Q₁)/[(Q₂ + Q₁)/2]/(P₂ - P₁)/[(P₂ + P₁)/2]
Price elasticity of demand = (25 - 15)/[(25 + 15)/2]/(20 - 25)/[(20 + 25)/2]
Price elasticity of demand = 0.5/-0.2222
Price elasticity of demand = 2.25.
Part C.Price elasticity of demand = (Q₂ - Q₁)/[(Q₂ + Q₁)/2]/(P₂ - P₁)/[(P₂ + P₁)/2]
Price elasticity of demand = (35 - 25)/[(35 + 25)/2]/(15 - 20)/[(15 + 20)/2]
Price elasticity of demand = 0.33/-0.2857
Price elasticity of demand = 1.17.
Part D.Price elasticity of demand = (Q₂ - Q₁)/[(Q₂ + Q₁)/2]/(P₂ - P₁)/[(P₂ + P₁)/2]
Price elasticity of demand = (45 - 35)/[(45 + 35)/2]/(10 - 15)/[(10 + 15)/2]
Price elasticity of demand = 0.25/-0.4
Price elasticity of demand = 0.63.
Read more on price elasticity here: https://brainly.com/question/24384825
#SPJ1
The function f(x) = x + 21 is one-to-one.
a. Find an equation for f1(x), the inverse function.
b. Verify that your equation is correct by showing that f(f(x)) = x and f¯¹ (f(x)) = x.
Answer:
a. D. f⁻¹(x) = x - 21, for all x
b. f(f ⁻¹(x)) = f(x - 21) = x and f ⁻¹(f(x)) = f ⁻¹(x + 21) = x
Step-by-step explanation:
See attached picture.
The required answers are:
a. The inverse of the function is f1(x) = x - 21
b. Verified by showing that f(f(x)) ≠ x and f¯¹(f(x)) = x.
a. To find the inverse function of f(x) = x + 21, we can interchange x and y and solve for y:
x = y + 21
Now, let's solve for y:
y = x - 21
Therefore, the equation for f1(x), the inverse function, is f1(x) = x - 21.
b. To verify that the equation is correct, we need to show that f(f(x)) = x and f¯¹ (f(x)) = x.
First, let's calculate f(f(x)):
f(f(x)) = f(x + 21) = (x + 21) + 21 = x + 42
Since f(f(x)) = x + 42, we can see that f(f(x)) is not equal to x. Therefore, f(f(x)) ≠ x.
Now, let's calculate f¯¹(f(x)):
f¯¹(f(x)) = f¯¹(x + 21) = (x + 21) - 21 = x
Since f¯¹(f(x)) = x, we can see that f¯¹(f(x)) is equal to x.
Thus, we have verified that the equation for the inverse function, f1(x) = x - 21, is correct by showing that f(f(x)) ≠ x and f¯¹(f(x)) = x.
Therefore, the required answers are:
a. The inverse of the function is f1(x) = x - 21
b. Verified by showing that f(f(x)) ≠ x and f¯¹(f(x)) = x.
Learn more about inverse functions here:
https://brainly.com/question/29141206
#SPJ2
Which of the following is an arithmetic sequence with common difference –5?
The arithmetic sequence that has a common difference of -5 from the options given is: A. 8, 3, -2, -7...
What is the Common Difference of an Arithmetic Sequence?The common difference of an arithmetic sequence is determined as: a term - previous term.
For the sequence, 8, 3, -2, -7,.. the common difference is:
-7 - 2 = -2 - 3 = 3 - 8 = -5.
Therefore, the arithmetic sequence with a common difference of -5 is: A. 8, 3, -2, -7...
Learn more about common difference on:
https://brainly.com/question/503167
#SPJ1
Une fonction polynomiale du second degré possède les caractéristiques
suivantes :
• La fonction est croissante sur l'intervalle [0, 8].
• La fonction est décroissante sur l'intervalle ]-10, 0].
• La courbe passe par le point (-8, 4).
PSST
↓
Voici les symboles dont tu pourrais avoir besoin dans ta réponse. N'hésite pas à
les copier-coller à partir d'ici si tu ne les trouves pas sur ton clavier.
[]%
SAVOIR-FAIRE
INDICE
Représente graphiquement la fonction, puis détermine son codomaine. Utilise la
notation décimale au besoin.
Le codomaine est.
Je n’arrive pas à trouver le co domaine si quelqu’un peut m’aider svp?
A second-degree polynomial takes the form
[tex]f(x) = ax^2 + bx + c[/tex]
for some constants a, b, and c. Such a function is continuous and differentiable everywhere in its domain.
Differentiating f(x) with respect to x gives
[tex]\dfrac{df}{dx} = 2ax + b[/tex]
We're told that
• f(x) is increasing on [0, 8]
• f(x) is decreasing on ]-10, 0]
and since df/dx is continuous, this tells us that df/dx = 0 when x = 0. It follows that b = 0, and we can write
[tex]f(x) = ax^2 + c[/tex]
We're also given that the curve passes through the point (-8, 4), which gives rise to the constraint
[tex]f(-8) = 64a - 8b + c = 4 \implies 64a + c = 4[/tex]
Since f(x) is decreasing on ]-10, 0], we have df/dx < 0 when x = -8, so
[tex]2ax+b < 0 \implies -16a < 0 \implies a > 0[/tex]
This means f(x) is minimized when x = 0, with min{f(x)} = c, so the co-domain of f(x) is the set {f(x) ∈ ℝ : f(x) ≥ c}.
Without another condition, that's all we can say about the co-domain. There are infinitely many choices for the constants a and c that satisfy the given conditions. For example,
a = 1, c = -60 ⇒ f(x) = x² - 60 ⇒ f(-8) = 4
⇒ co-domain = {f(x) ∈ ℝ : f(x) ≥ -60}
a = 2, c = -124 ⇒ f(x) = 2x² - 124 ⇒ f(-8) = 4
⇒ co-domain = {f(x) ∈ ℝ : f(x) ≥ -124}
etc.
Help!!!!! Meeee!! Asappppp
Reason:
Refer to the diagram below. The tiny square angle markers tell us we have a 90 degree angle, meaning those lines are perpendicular.
You can think of the parallel lines being the metal part of train tracks, while the perpendicular line connecting the metal rails is the wooden part of the train tracks.
y=-3³ +4
step by step of the rules and formula of this equation
1) Which is the first INCORRECT step in the
solution of the inequality shown below?
2(x+1)-(3-x) ≤ -4:
Step 1: 2x + 2-3+x≤-4;
Step 2: 3x - 1≤-4;
Step 3: 3x
-3;
Step 4: x>-1
(a) Step 1
(b) Step 2
(c) Step 3
(d) Step 4
Step-by-step explanation:
we are missing the inequality sign in step 3.
step 1 and step 2 are correct.
step 4 is wrong.
the correct step 3 looks like
3x <= -3
if your original step 3 says the same, then the first wrong step is step 4.
if your original step 3 does not say the same, then the first wrong step is step 3.
Katherine wants to use a sheet of fiberboard 18 inches long to create a skateboard ramp with a 17
∘
∘
angle of elevation from the ground. How high will the ramp rise from the ground at its highest end? Round your answer to the nearest tenth of an inch if necessary.
The rise from the ground by the skateboard is 5.5 inches
How to determine the height above the ground?The length of the skateboard is given as:
Length (l) = 18 inches
The angle of elevation (x) is
x = 17∘
Represent the height with h.
The value of h is calculated using the following tangent ratio:
tan(x) = h/l
Make h the subject
h = l * tan(x)
Substitute known values
h = 18 * tan(17)
Evaluate
h = 5.5
Hence, the rise from the ground by the skateboard is 5.5 inches
Read more about elevation at:
https://brainly.com/question/19594654
#SPJ1
Answer: 5.3
Step-by-step explanation:
SOH-CAH-TOAsin 17=oppositehypotenuse=x18sin 17=hypotenuseopposite=18xsin 17=sin 17= x1818xsin 171=1sin 17= x1818x18 sin 17=18 sin 17= xxx=5.262690...≈5.3x=5.262690...≈5.3
the lenghts of five boxes are shown in the table which line plot shows the data from the table
Answer:
The bottom right line plot.
Step-by-step explanation:
In the table, 9 1/4 shows up twice. This can be represented in the line plot by putting 2 x's over the 9 1/4 point.
7) $72.45 -28.98 Rounded estimate
Answer:
$43
Step-by-step explanation:
$72.45 can be rounded down to $72.00
$28.98 can be rounded up to $29.00
$72-$29= $43
Estimate the product.
14×212