Mike can determine the width of his scale model car by setting up and solving a proportion. Using the ratio of the actual car's dimensions, calculate an equivalent ratio for the model. The width of the model car should be 6 inches.
Explanation:To solve this problem, you can set up a proportion based on the known dimensions of the actual car and Mike's model. Given the actual car's length and width are 8 feet and 4 feet, and Mike's model length is 12 inches, we can set up the proportion like this:
8 feet : 4 feet = 12 inches : X
First, we need to convert all measurements to the same unit. Let's use inches since Mike's model is in inches (remember that 1 foot equals to 12 inches). So, the car's length is 96 inches and its width is 48 inches. Now, the proportion would be:
96 inches : 48 inches = 12 inches : X
To find the value of X (the width of the model), we can cross-multiply:
(96 * X) = (48 * 12)
Solve for X by dividing each side by 96, we get:
X = 6 inches
So, Mike's model car should be 6 inches wide to maintain the same ratio as the actual car.
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Find the greatest possible error for each measurement.
10 1/8 oz
Answer:
0.0005 oz
Step-by-step explanation:
Usually, the greatest number that is allowed for approximation, assuming that the number itself is obtained by approximation, is the greatest possible error of it.
It is normally half the place value of the last digit in a number.
Like here we have [tex]10\frac{1}{8}[/tex] oz which is equal to [tex]10.125[/tex] oz. The last digit is 5 which is at the thousandth place (0.001) so the greatest possible error for this would be its half.
[tex]\frac{0.001}{2}[/tex] = 0.0005 oz
PLEASE HELP! 30 POINTS! Drag the tiles to the correct boxes to complete the pairs. Not all tiles will be used.
Match each statement with the equation that represents it.
In the given scenarios: 1. Car speed (x) determines distance covered (y) in 30 minutes (y = 30x). 2. Tina's age (y) is 5 years more than Tim's age (x) (y = x + 5). 3. Chair cost (x) relates to table cost (y) as y = 2x. 4. Baking time for chocolate muffins (y) is 2 minutes longer than for vanilla muffins (x) (y = x + 2). These equations establish connections between variables in different real-world situations.
In these scenarios, we encounter different situations where certain variables and their relationships are described. Let's elaborate on each scenario and express it in a more detailed manner:
1. **Car Speed and Distance:** The speed of a car is represented by the variable 'x' in miles per hour. The total distance covered by the car in 30 minutes, denoted as 'y,' can be expressed using the formula: y = 30x. This equation relates the speed 'x' to the distance 'y' covered in a specific time period.
2. **Sibling Ages:** Tim's age, represented by 'x,' and Tina's age, represented by 'y,' are related. Tina's age is 5 years more than Tim's age, which can be expressed as y = x + 5. This equation defines the age difference between the siblings.
3. **Cost of Furniture:** In this scenario, the cost to produce a chair is 'x,' and the cost to produce a table is 'y.' The relationship is that the cost of producing a table is two times the cost of producing a chair, which can be expressed as y = 2x. This equation shows the cost relationship between chairs and tables.
4. **Muffin Baking Times:** The time required to bake a vanilla muffin is 'x,' and the time required to bake a chocolate muffin is 'y.' The relationship is that the time to bake a chocolate muffin is 2 minutes more than the time to bake a vanilla muffin, which can be expressed as y = x + 2. This equation establishes the time difference between baking these two types of muffins.
In summary, these scenarios involve different relationships and equations that connect variables and quantities in various real-world contexts, such as car speed and distance, sibling ages, furniture production costs, and muffin baking times. These equations help describe and quantify these relationships, making them useful for solving practical problems.
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If the ratio of the areas of two similar polygons is 25:49, what is the ratio of the corresponding side length
Answer:
5:7
Step-by-step explanation:
Ratio of the areas of similar shapes is equal to the square of the scale:
A₂ / A₁ = r²
Ratio of the side lengths of similar shapes is equal to the scale:
s₂ / s₁ = r
Therefore:
A₂ / A₁ = (s₂ / s₁)²
25/49 = (s₂ / s₁)²
s₂ / s₁ = 5/7
The ratio of the side lengths is 5:7.
Answer:
5 : 7
Step-by-step explanation:
Given 2 similar figures then
ratio of sides = a : b
ratio of areas = a² : b²
Here the ratio of areas = 25 : 49, hence
ratio of sides = [tex]\sqrt{25}[/tex] : [tex]\sqrt{49}[/tex] = 5 : 7
The probability of flipping a coin and getting a head is 0.5 if the coins is flipped two times, the probility of getting a hard two miles is 0.25
Answer:
0.75 so FALSE
Step-by-step explanation:
It is the only number that could be left after 0.5 and 0.25
identify an equation in point - slope form for the line parllel to y = 1/2 x - 7 that passes through (-3,-2)
A. y-2=1/2(x-3)
B.y+2=1/2(x+3)
C.y+3=-1/2(x+2)
D.y+2=2(x+3)
Answer:
B. y + 2 = ½(x + 3)
Step-by-step explanation:
Insert the coordinates into the formula with their CORRECT signs. Remember, in the Point-Slope Formula, y - y₁ = m(x - x₁), all the negative symbols give the OPPOSITE term of what they really are.
what is the product PLEASE HELP
Answer:
C
Step-by-step explanation:
Each term in the second factor is multiplied by each term in the first factor, that is
- 2x(- 4x - 3) - 9y²(- 4x - 3) ← distribute both parenthesis
= 8x² + 6x + 36xy² + 27y² → C
Your school needs 9 buses for this field trip.
Additionally, you must include a $100 tip. If your school
spends $1829.82. how much does each bus?
Answer: 203.31
Step-by-step explanation:
Each bus have 214.42.
What is Unitary method?The unitary method is a technique for solving a problem by first finding the value of a single unit, and then finding the necessary value by multiplying the single unit value
Give:
Total buses=9
Charges for tip= $ 100
Total money spends = $ 1829.82
Amount with tip = $ 1829.82+$ 100 = $ 1929.82
So, each bus have = 1929.82/9
= 214.42
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Find 3 numbers in a geometrical sequence if:
a1+a2+a3=21
a1xa2xa3=64 (That x is multiplying)
a1+a2+a3=21
(a1=1,a2=3,a3=7)
a1xa2xa3=64
(a1=2,a2=4,a3=8)
What is the value of (5.3x 10^4
(4.2x10^3) in scientific notation?
1) 2.226 x 10^6
2) 22 26x 10^7
3) 2226x 10^8
4) 22.26 x 10^12
The value of (5.3x 10^4) (4.2x10^3) in scientific notation Option C 2.226 times 10^8
5.3×10^4 × 4.2 × 10^3
We multiply the numbers out front
5.3× 4.2 = 22.26
We add the exponents
10^(4+3) = 10^7
22.26×10^7
But we are not done yet because The number out front has to be between 1 and less than 10
Move the decimal 1 place to the left and add 1 to the exponent
2.226 × 10 ^(7+1)
=2.226×10^8.
What is Scientific notation?Scientific notation is a way of writing very large or very small numbers. A number is written in scientific notation when a number between 1 and 10 is multiplied by a power of 10. For example, 650,000,000 can be written in scientific notation as 6.5 ✕ 10^8.
What is scientific notation mean in math?Scientific Notation is the expression of a number n in the form a∗10b. where a is an integer such that 1≤|a|<10. and b is an integer too. Multiplication: To multiply numbers in scientific notation, multiply the decimal numbers.
How do you write a scientific notation?The proper format for scientific notation is a x 10^b where a is a number or decimal number such that the absolute value of a is greater than or equal to one and less than ten or, 1 ≤ |a| < 10. b is the power of 10 required so that the scientific notation is mathematically equivalent to the original number.
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to create an all purpose cleaning product, 1.5 ounces of cleaner must be added to one gallon of water. How many ounces of cleaner will be added to 8.5 gallons of water?
Answer:
12.75 oz
Step-by-step explanation:
1 gallon is equivalent to 64 oz.
Writing and solving an equation of ratios, we get:
1.5 oz 1 gal
----------- = ------------
x 8.5 gal
Here we must cross-multiply to solve for x.
x(1 gal) = (1.5 oz)(8.5 gal) = 12.75 oz
Thus, x = 12.75 oz of cleaning product must be added to 8.5 gal of water to create the desired solution.
To make an all-purpose cleaner, you need 12.75 ounces of cleaner for 8.5 gallons of water.
This is determined by multiplying the ratio of 1.5 ounces per gallon by 8.5 gallons.
follow these steps:
First, determine the ratio of cleaner to water. The ratio is 1.5 ounces of cleaner per gallon of water.Next, multiply this ratio by the number of gallons to find the total amount of cleaner needed for 8.5 gallons of water.Calculate: 1.5 ounces/gallon * 8.5 gallons = 12.75 ounces.Therefore, 12.75 ounces of cleaner will be added to 8.5 gallons of water.
Find the coordinates of the reflected image.
A triangle with vertices F(–1, 9), G(–2, 1), and H(–7, 4) is reflected over the x-axis.
Answer:
see explanation
Step-by-step explanation:
Under a reflection in the x- axis
a point (x, y ) → (x, - y ), hence
F(- 1, 9) → F'(- 1, - 9)
G(- 2, 1) → G'(- 2, - 1)
H(- 7, 4) → H'(- 7, - 4)
James fenced in his backyard. The perimeter of his fence is 20 feet, and the width of his yard is 2 feet wide. Use the perimeter formula to find the length of his rectangular yard in inches: P = 2L + 2W.
A.8 in.
B.18 in.
C.72 in.
D.96 in.
Answer:
D. 96 inches
Step-by-step explanation:
Perimeter (P) = 2L + 2W , Where L is the length and W is the width.
20 ft = 2L + 2(2 ft)
2L = 20 ft - 4 ft = 16 ft
L = [tex]\frac{16}{2}[/tex] ft = 8 ft
1 ft = 12 inches
8 ft = ?
Cross-multiplying this gives; [tex]\frac{8}{1}[/tex] × 12 = 96 inches
Answer: D) 96 inches.
Step-by-step explanation: To calculate the lenght of James' rectangular yard, we need to isolate L from the given formula:
P=2L+2W
P-2W=2L
[tex]L=\frac{P-2W}{2}[/tex]
Now we replace the given values of P and W in the equation:
[tex]L=\frac{20feet-2*2feet}{2}[/tex]
[tex]L=\frac{20feet-4feet}{2}[/tex]
[tex]L=\frac{16feet}{2}[/tex]
[tex]L=8feet[/tex]
1feet=12inches so:
L=8feet*12inches/1feet
L=96 inches.
The product of a fraction and the sum of 5 1/3 and 6 1/3 is 3. What is the fraction?
Answer:
The fraction = 9/35
To find the fraction, calculate the sum of 5 1/3 and 6 1/3, which is 35/3, then divide the final product, 3, by this sum. The fraction that when multiplied by the sum equals 3 is 9/35.
The question asks us to find the fraction when the product of the fraction and the sum of 5 1/3 and 6 1/3 is 3.
First, let's calculate the sum of 5 1/3 and 6 1/3:
5 1/3 can be written as (5*3 + 1)/3 = 16/3.
6 1/3 can be written as (6*3 + 1)/3 = 19/3.
Adding these fractions, we get (16/3) + (19/3) = (35/3).
So, we have the equation:
Fraction imes (35/3) = 3
To find the unknown fraction, we divide both sides by 35/3:
Fraction = 3 / (35/3) = 3 imes (3/35) = 9/35
Therefore, the fraction we are looking for is 9/35.
Factor completely 3x3 + 12x2 + 18x.
Step-by-step explanation:
solved in the picture....
Answer:
The factored form of the given expression is [tex]3x(x^2+4x+6)[/tex].
Step-by-step explanation:
The given expression is
[tex]3x^3+12x^2+18x[/tex]
we need to find the factored form of the given expression.
Taking GCF common, we get
[tex]3x(x^2+4x+6)[/tex]
If a quadratic expression is defined as [tex]ax^2+bx+c[/tex] and
[tex]b^2-4ac<0[/tex], then the expression can not be factored further.
In the above parentheses the quadratic expression is [tex]x^2+4x+6[/tex],
[tex]b^2-4ac=(4)^2-4(1)(6)=-8<0[/tex]
It means the quadratic expression is [tex]x^2+4x+6[/tex] can not be factored further.
Therefore the factored form of the given expression is [tex]3x(x^2+4x+6)[/tex].
The cone in the diagram has the same height and base area as the prism. What is the ratio of the volume of the cone to the volume of the prism?
h hl
base area-B
base area =B
volume of cone_1
volume of prism 2
volume of cone 1
volume of prism 3
volume of cone 2
volume of prism 3
OC.
OD.
volume of cone
volume of prism
E.
volume of cone
volume of prism
3
2
Answer:
[tex]\large\boxed{\dfrac{V_{cone}}{V_{prism}}=\dfrac{1}{3}}[/tex]
Step-by-step explanation:
[tex]\text{The formula of a volume of a cone:}\ V_{cone}=\dfrac{1}{3}B_cH_c\\\\B_c-base\ area\ of\ a\ cone\\H_c-height\ of\ a\ cone\\\\\text{The formula of a volume of a prism:}\ V_{prism}=B_pH_p\\\\B_p-base\ area\ of\ a\ prism\\H_p-height\ of\ a\ prism\\\\\text{The cone and the prism have the same base area and height.}\\\text{Therefore}\\\\V_{cone}=\dfrac{1}{3}BH\ \text{and}\ V_{prism}=BH\\\\\text{The ratio of the volume of the cone to the volume of the prism:}[/tex]
[tex]\dfrac{V_{cone}}{V_{prism}}=\dfrac{\frac{1}{3}BH}{BH}=\dfrac{1}{3}[/tex]
Answer:
See the image attached for answer
Step-by-step explanation:
The sum of the page numbers on the facing pages of a book is 73. What are the page numbers?
Answer:
The page numbers are 36 and 37.
Step-by-step explanation:
n + (n + 1) = 73
2n + 1 = 73
n = (73 - 1)/2
= 72/2 = 36
Follow below steps:
The sum of the page numbers on the facing pages of a book is 73. To solve this, we need to establish that facing pages in a book are always one number apart. If we call one page number x, then the other page number is x+1 because page numbers are consecutive.
Now, we can create the equation x + (x+1) = 73 to find the value of x. Solving this equation, we get:
2x + 1 = 73
2x = 73 - 1
2x = 72
x = 72 / 2
x = 36
Since x is the lower of the two page numbers, then the pages are 36 and 37.
What is the perimeter of an isosceles triangle with each leg measuring 2x+3 and the base measuring 6x-2?
Answer:
10x + 4
Step-by-step explanation:
The Total perimeter is 2 * leg measurement + base
P = 2(2x + 3) + 6x - 2 Remove the brackets.
P = 4x + 6 + 6x - 2 Add like terms
P = 10x + 4 Answer
Answer:
10x + 4
Step-by-step explanation:
An isosceles triangle has two sides equal
Perimeter is the sum of all sides
2(2x + 3) + 6x - 2
4x + 6 + 6x - 2
10x + 4
Solve the following addition problem. Remember to carry as necessary. 6cu yd9cu ft134cu in+1cu yd12cu ft200cu in
Answer:
150.6 ft^9
Step-by-step explanation:
The easisest way to solve this problem is to convert everything to the same unit
1 cu yd = (27 cu ft)
1 cu in = (0,000578704 cu ft)
The expression is
6cu yd* 9cu ft * 134cu in + 1cu yd* 12cu ft* 200cu in
= 6(27 cu ft) * 9cu ft * 134(0,000578704 cu ft) + 1(27 cu ft)* 12cu ft* 200(0,000578704 cu ft)
Please see attached image below
The answer is
150.6 ft^9
What is the point-slope form of the
equation for the line with a slope of
-2 that passes through (1, 4)?
A y + 1 = -2(x + 4)
B y-1=-2(x-4)
C y + 4 = -2(x + 1)
D y - 4 = -2(x - 1)
Answer:
87n+6*55n
Step-by-step explanation:
classify the system of equations x=-5-y 4+y=-x+3
Answer: Inconsistent.
Step-by-step explanation:
The equation of the line in Slope-Intercept form is:
[tex]y=mx+b[/tex]
Where "m" is the slope and "b" is the y-intercept.
Solve for "y" in each equation:
Equation 1
[tex] x=-5-y\\\\y=-x-5[/tex]
Equation 2
[tex]4+y=-x+3\\\\y=-x+3-4\\\\y=-x-1[/tex]
You can notice that the slope of the Equation 1 is:
[tex]m_1=-1[/tex]
And the slope of the Equation 2 is:
[tex]m_2=-1[/tex]
Observe that [tex]m_1=m_2[/tex], then you can conclude that the lines are parallel and the System of equations has No solution.
When there is no solution the classification of the system of equations is: "Inconsistent".
raise each side of the equation as the power of the base of the log, 0.98 = log x
Answer:
see explanation
Step-by-step explanation:
Given
[tex]log_{10}[/tex] x = 0.98, then
x = [tex]10^{0.98}[/tex]
Find the missing measure for a right circular cone TA is 12 pi and LA is 8 pi
Answer:
The radius of the base of the cone is 2 units
The slant height of the cone is 4 units
The height of the cone is 2√3 units
The volume of the cone is [tex]\frac{8\sqrt{3}\pi}{3}[/tex]units³
Step-by-step explanation:
* Lets revise the total surface area and the lateral area of a cone
- The lateral area of cone = π r l , where r is the radius of the base
and l is the slant height of the cone
- The surface area of the cone = π r l + π r², where π r l is the lateral
area and π r² is the base area
- The cone has three dimensions radius (r) , height (h) , slant height (l)
- r , h , l formed right triangle, r , h are its legs and l is its hypotenuse,
then l² = r² + h²
- The volume of the con = [tex]\frac{1}{3}[/tex] (π r² h)
* Now lets solve the problem
- We will use the total area to find the radius of the base
∵ TA = 12π
∵ TA = LA + πr²
∵ LA = 8π
- Substitute the value of the lateral area in the total area
∴ 12π = 8π + π r² ⇒ subtract 8π from both sides
∴ 12π - 8π = π r²
∴ 4π = π r² ⇒ divide both sides by π
∴ r² = 4 ⇒ take square root for both sides
∴ r = 2
* The radius of the base of the cone is 2 units
- We will use the lateral area to find the slant height
∵ LA = π r l
∵ LA = 8π
∵ r = 2
∴ π (2) l = 8π ⇒ divide both sides by π
∴ 2 l = 8 ⇒ divide both sides by 2
∴ l = 4
* The slant height of the cone is 4 units
- Use the rule l² = r² + h² to find the height of the cone
∵ r = 2 and l = 4
∵ l² = r² + h²
∴ (4)² = (2)² + h²
∴ 16 = 4 + h² ⇒ subtract 4 from both sides
∴ 12 = h² ⇒ take square root for both sides
∴ h = √12 = 2√3
* The height of the cone is 2√3 units
∵ The volume of the con = [tex]\frac{1}{3}[/tex] (π r² h)
∵ r = 2 and h = 2√3
∴ V = [tex]\frac{1}{3}[/tex] (π × 2² × 2√3) = [tex]\frac{1}{3}[/tex] (π × 4 × 2√3) = [tex]\frac{1}{3}[/tex] (π × 8√3)
∴ V = [tex]\frac{8\sqrt{3}\pi}{3}[/tex]
* The volume of the cone is [tex]\frac{8\sqrt{3}\pi}{3}[/tex]units³
it cost Andrea $50 per day to rent a moving truck and an additional $3 for every mile that she drove it. It Andrea spent a total of $104 after renting the truck for 1 day, which equation shows how many miles Andre drove?
Evaluate
a/b for a = -6 and b = -2.
-12
The expression a/b is evaluated by dividing -6 by -2. Since both numbers are negative, the result is a positive 3.
Explanation:The problem asks you to evaluate a/b with a=-6 and b=-2. The expression a/b means 'a divided by b'. Thus, to evaluate this expression, you simply divide -6 by -2. Remember that when you divide a negative number by another negative number, the result is positive. So, -6 divided by -2 equals 3.
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We substitute -6 for a, and -2 for b in the expression a/b, obtaining -6/-2, which equals 3 because division of two negative numbers yields a positive number.
Explanation:To evaluate the expression a/b for a = -6 and b = -2, we can substitute the given values into the expression. This gives us -6 / -2. Dividing a negative number by another negative number gives a positive result. Therefore, -6 / -2 equals 3. The notion that dividing a negative number by another negative number results in a positive number is a fundamental rule in mathematics.
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What is the equation of the line that passes through the points (2, –1) and (6, 1)? A.y=1/2x -2 B.y=2x-5 C.y=-1/2x-1 D. y=-2x-3
Answer:
option A.
y = (1/2)x - 2
Step-by-step explanation:
It is given that, line that passes through the points (2, –1) and (6, 1)
Slope m = (y₂ - y₁)/(x₂ - x₁)
= (1 - -1)/(6 - 2)
= (1 + 1)/4 = 2/4
= 1/2
To find the equation of the line
Equation of a line passing through the points (x₁, y₁) and slope m is given by,
(y - y₁)/(x - x) = m
Here (x₁, y₁) = (2, -1) and m = 1/2
(y - -1)/(x - 2) = 1/2
(y + 1) = (x - 2)/2
y = -1 + x/2 - 2/2
= -1 + x/2 - 1
= x/2 - 2
The equation of the line is,
y = (1/2)x - 2
The correct answer is option A.
y = (1/2)x - 2
What is the value of n?
Answer:
The correct answer is option D. 85°
Step-by-step explanation:
Here we consider two angles be <1, <2 and < 3, where <1 is the linear pair of angle measures 133° and <2 be the linear pair of angle measures 142°
To find the value of m<1
m<1 = 180 - 133 = 47°
To find the value of m<2
m<2 = 180 - 142 = 38°
To find the value of m<3
By using angle sum property,
m<1 + m<2 + m< 3 = 180
m<3 =180 - (m<1 + m<2)
= 180 - (47 + 38))
= 180 - 85
= 95°
To find the value of n
Here n and <3 are linear pair,
n + m<3 = 180
n = 180 - m<3
= 180 - 95 = 85°
Therefore the value of n = 85°
The correct answer is option D. 85°
can someone answer this plz (-2z^2-14)-(-12z^2)
Answer:
[tex]\large\boxed{(-2z^2-14)-(-12z^2)=10z^2-14}[/tex]
Step-by-step explanation:
[tex](-2z^2-14)-(-12z^2)=-2z^2-14+12z^2\qquad\text{combine like terms}\\\\=(-2z^2+12z^2)-14=10z^2-14[/tex]
ndicate in standard form the equation of the line through the given points. P(0, -4), Q(5, 1)
Answer:
y=x-4
Step-by-step explanation:
Standard form is y=mx+b
the coordinates (0, -4) tell you that the y intercept is at -4 which means b will be -4. To find slope you have to find the change in y over the change is x. 1--4=5 and 5-0=5. 5/5 is 1 so the slope, or m, is 1. x stays the same since it's the variable. it'll become y=1x-4 and since you don't have to place a coordinate of one in front of a variable, you can just write it as y=x-4
Help asap
Which of the following constants can be added to x^2 - 3x to form a perfect square trinomial?
A. 1 1/2
B. 2 1/4
C. 4 1/2
Answer:
B.2 1/41
Step-by-step explanation:
In a perfect square trinomial of the form ax+bx+c where a, b and c are constants, the value of (b/2)²=ac
In the provided equation the value of a=1, b=-3 c=?
Therefore, (-3/2)²=c since a-the coefficient of x²=1 and 1×c=c
c=2.25= 2 1/4
Thus the trinomial x² - 3x + 2 1/4 is a perfect square.
The area of a triangle is 24sq inches. If the base of the triangle is 6 inches, what is the height?
Answer:
8 inches
Step-by-step explanation:
To find the area of a triangle, we use the formula
A = 1/2 bh where b is the length of the base and h is the height
A = 24 and b = 6
24 = 1/2 (6) * h
24 =3h
Divide each side by 3
24/3 = 3h/3
8 =h
The height is 8 inches
The answer is:
The height of the triangle is equal to 8 inches.
[tex]height=8in[/tex]
Why?To find the height of the triangle, we need to use the formula to calculate the area of a triangle, it's given by the following expression:
[tex]Area=\frac{base*height}{2}[/tex]
So, since we already know the area and the base, we need to isolate the height from the formula, so, isolating we have:
[tex]Area=\frac{base*height}{2}\\\\\frac{Area*2}{base}=height[/tex]
We know that:
[tex]Area=24in^{2} \\base=6in[/tex]
Now, substituting we have:
[tex]height=\frac{Area*2}{base}[/tex]
[tex]height=\frac{24in^{2} *2}{6in}=8in[/tex]
Hence, we have that the height of the triangle is equal to 8 inches.
[tex]height=8in[/tex]
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