A number is divided in the ratio of 5:9. If the first part is 35, the number will be 7.
What is the unitary method?The unitary method is a method for solving a problem by the first value of a single unit and then finding the value by multiplying the single value.
A number is divided in the ratio of 5:9. If the first part is 35, then we need to find the number.
By unitary method
5x = 35
x = 7
Then the other number will be
9x = 9(7)
= 63
Thus, A number is divided in the ratio of 5:9. If the first part is 35, the number will be 7.
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The area of Louisiana is approximately 4 x
104 square miles. The area of the United
States is approximately 225 times greater
than the area of Louisiana. What is the
approximate area of the United States?
Answer:
93,600
Step-by-step explanation:
4x104= 416
416x225 = 93,600
find the perimeter of a triangular field whose length of edges are 14 m, 12m 10 m Also find the length of required to fence 4 times around it?
Answer: 36 m, 144 m
Step-by-Step Explanation:
a = 14 m
b = 12 m
c = 10 m
Perimeter = a + b + c
Therefore,
= a + b + c
= 14 + 12 + 10
= 26 + 10
=> 36
Perimeter = 36 m
Length of Fence required for Fencing 4 times = Perimeter * 4
Therefore,
= Perimeter * 4
= 36 * 4
= 144
Length of Fence required for Fencing 4 times = 144 m
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.
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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
Sin 0 = -8/17 and cos 0 = 15/17 find tan0
Answer:
Step-by-step explanation:
Givens
sin(theta) = - 8/17
cos(theta)= 15/17
Tan(theta) = ?
Comment
Without using the Pythagorean Theorem, you could simply use tan(theta) = Sin(theta) / cos(theta)
Tan(theta) = sin(theta) / cos(theta)
Tan(theta) =[tex]\dfrac{\dfrac{-8}{17} }{\dfrac{15}{17} }[/tex]
Now turn the bottom fraction upside down and multiply.
Tan(theta) = [tex]\dfrac{-8}{17}*\dfrac{17}{15} = \dfrac{-8}{15}[/tex]
Answer Tan(theta) = -8/15
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.
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.
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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...
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Seven increased by the product of six and the number is 19
The number is that was multiplied by 6 is 2.
What is the number?The equation that can be derived from the question is :
7 + (6a) = 19
Where a is the unknown number that 6 was multiplied with
Given the above equation, in order to determine the value of a, take the following steps:
Combine similar terms: 6a = 19 - 7
Subtract similar terms: 6a = 12
Divide both sides by 6: a = 12 / 6
a = 2
Here is the complete question:
Seven increased by the product of six and the number is 19. What is the number?
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X =
(19) Find the values for X and Y, and then solve for the side lengths.
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.
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
( brain + 95 points ) A triangular prism has a height of 10 cm and the triangle has a base of 4 cm and a height of 6 cm. Find the volume of the triangular prism.
Area of base
1/2BH1/2(4)(6)2(6)12cm²Volume
Area of base× height12(10)120cm³7) $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
please help asap 100 points
Answers:
Problem #1: Option C, 166 yards cubed
Problem #2: Option A, 10
Step-by-step solution:
The first problem may seem a lot more confusing that it really is and this actually happened to me when I looked at it. Just because the cylinder is slanted that actually doesn't change any of the volume that we would have if it was straight up with the same diameter and height.
Using what we know about cylinders, let us plug all the information inside of the formula to determine the volume of the cylinder. However, before doing that we need to determine the radius of the circle from the diameter that was given.
Divide the diameter by two to get the radius
[tex]Radius = \frac{Diameter}{2}[/tex][tex]Radius = \frac{5.2\ yd}{2}[/tex][tex]Radius = 2.6\ yd[/tex]Plug in the values
[tex]V_{cylinder} = (\pi * radius^2)*height[/tex][tex]V_{cylinder} = (\pi * (2.6\ yd)^2)*7.8\ yd[/tex]Simplify the exponent
[tex]V_{cylinder} = (\pi * (2.6)^2 *(yd)^2)*7.8\ yd[/tex][tex]V_{cylinder} = (\pi * 6.76\ yd^2)*7.8\ yd[/tex]Simplify the expression
[tex]V_{cylinder} = (21.237\ yd^2)*7.8\ yd[/tex][tex]V_{cylinder} = 165.65\ yd^3[/tex]Therefore, after simplifying the expression using the cylinder volume formula and the given information we were able to determine that the option that best fits the description of our answer is option C, 166 cube yards.
Now that we completed the first question, we can move onto the second question. In this question we are given a figure along with 3 numbers and one unknown, x, which we need to find the value of. We need to use the Secant-Secant Power Theorem to help determine our solution.
Make an expression to represent the scenario
[tex]32(x + 32) = 28(20 + 28)[/tex]We know have an expression which we can now simplify and get the value of the unknown easily. The first step would be to distribute the 32 and 28.
Distribute both sides
[tex]32(x + 32) = 28(20 + 28)[/tex][tex](32 * x) + (32 * 32) = (28 * 20) + (28 * 28)[/tex][tex]32x + 1024 = 560 + 784[/tex]Simplify the expression
[tex]32x + 1024 = 1344[/tex]We now have a simple expression where we can now subtract both sides by 1024 to help isolate x with its coefficient.
Subtract 1024 from both sides
[tex]32x + 1024 - 1024 = 1344 - 1024[/tex][tex]32x = 1344 - 1024[/tex][tex]32x = 320[/tex]The final step that we have to help fully isolate x by itself is to divide both sides by 32 which would remove the coefficient from x.
Divide both sides by 32
[tex]\frac{32x}{32} = \frac{320}{32}[/tex][tex]x = \frac{320}{32}[/tex][tex]x = 10[/tex]After simplifying the expression completely, we are able to see that the best option that fits our description is option A, 10.
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
Find the solution set for |2x-3|=9
Answer:
x = 6, -3
Step-by-step explanation:
. . . . . . . . . . . . . . . . .
Which of the following is an even function?
Of(x) = (x - 1)²
Of(x) = 8x
Of(x)=x²-x
Of(x) = 7
COFFE
Sinte echinat
SUMPARNI
Answer:
Step-by-step explanation:
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.
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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.
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)
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.
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
A class of 30 students plans to collect at least $500 in donations for a rehabilitation camp. They have collected $270. How much more should each student collect?
can you help me with this question
y=-3³ +4
step by step of the rules and formula 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
If £2000 is placed into a bank account that pays 3% compound interest per year
how much will be in the account after 2 years?
Answer:
£ 2121.8
Step-by-step explanation:
The formula to find the compound interest is :
[tex]A=P(1+\frac{R}{100} )^n[/tex]
Here,
A = Amount ⇒ ?
P ⇒ Principal ⇒ £2000
R ⇒ Interest rate ⇒ 3%
n ⇒ Time ⇒ 2 years
Let us find now.
[tex]A=P(1+\frac{R}{100} )^n[/tex]
[tex]A=2000(1+\frac{3}{100} )^2[/tex]
[tex]A=2000(1+0.03 )^2[/tex]
[tex]A=2000(1.03 )^2[/tex]
[tex]A=2000*1.0609[/tex]
[tex]A=2121.8[/tex]
Therefore, there will be £ 2121.8 in the bank account after 2 years.
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.
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Which shows one way to determine the factors of Which shows one way to determine the factors of x3 + 4x2 + 5x + 20 by grouping? by grouping?
The factored expression of the expression x^3 + 4x^2 +5x + 20 is (x^2 + 5)(x + 4)
How to determine the factors?The expression is given as:
x^3 + 4x^2 +5x + 20
Group the expression into two
(x^3 + 4x^2) + (5x + 20)
Factorize each group
x^2(x + 4) + 5(x + 4)
Factor out x + 4
(x^2 + 5)(x + 4)
Hence, the factored expression of the expression x^3 + 4x^2 +5x + 20 is (x^2 + 5)(x + 4)
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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.