Answer:
-5/4
Step-by-step explanation:
Step 1: Convert to algebraic equation.
4x +7 = 2
Step 1: Subtract 7 from both sides.
4x +7 −7 = 2 −7
Step 2: Divide both sides by 4.
(4x /4) = (-5 /4)
Step 3: Get your answer!
x = -5/4
Answer:
x = -1.25
Step-by-step explanation:
A number = x
7 + 4x = 2
Subtract 7 on both sides
4x = -5
Divide both sides by 4
x = -1.25 OR -5/4
What is the leading coefficient of the following polynomial function have?
ƒ (x) = 5x² + 3x³ + 2x^5 + 3x
Answer:
Step-by-step explanation:
2
Answer:
The leading coefficient is 2.
Step-by-step explanation:
Leading coefficients are the numbers with the highest degree or exponent.
What’s equivalent to 11:1 answer
Answer:
11
Step-by-step explanation:
11:1 = [tex]\frac{11}{1}[/tex] = 11
Answer: 11, 22:2, 33:3, etc.
Step-by-step explanation:
A ratio is dividing.
11/1 = 11.
This means that numerous ratios can be used, to the point where the answers are infinite.
A light bulb consumes 8400 watt-hours in 3 days and 12 hours. How many watt-hours does it consume per day?
Answer:
2400Watt Hours isn't it A Right Answer?
Is it possible for a number to be a product of 2, a product of 5,
and a product of 10? Explain.
Yes, it is possible for a number to be a product of 2, 5, and 10.
All multiples of 10 such as 10, 20, 30, 40, 50, 60, ,,,, are a product of 2, 5, and 10.
What is an expression?An expression is a way of writing a statement with more than two variables or numbers with operations such as addition, subtraction, multiplication, and division.
Example: 2 + 3x + 4y = 7 is an expression.
We have,
A number that is a product of 2, 5, and 10.
Example:
10 = 2 x 5
10 = 5 x 2
10 = 10 x 1
20
20 = 2 x 10
20 = 5 x 4
20 = 10 x 2
100
100 = 2 x 50
100 = 5 x 20
100 = 10 x 10
We see that all multiples of 10 are a product of 2, 5, and 10.
Thus,
All multiples of 10 are a product of 2,5, and 10.
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Identify the domain and range of each graph
NO LINKS!! Please help me with this graph
=========================================================
Explanation:
The three points are at these locations:
A = (10, 6)B = (1,-3)C = (-5, 3)The notation "d(A,C)" means "the distance from A to C". It's equivalent to saying "the length of segment AC".
Then writing [tex]\left[d(A,C)]^2[/tex] means we'll square that distance.
Use the distance formula to get...
[tex]A = (x_1,y_1) = (10,6) \text{ and } C = (x_2, y_2) = (-5,3)\\\\d = \sqrt{(x_1 - x_2)^2 + (y_1 - y_2)^2}\\\\d = \sqrt{(10-(-5))^2 + (6-3)^2}\\\\d = \sqrt{(10+5)^2 + (6-3)^2}\\\\d = \sqrt{(15)^2 + (3)^2}\\\\d = \sqrt{225 + 9}\\\\d = \sqrt{234}\\\\[/tex]
This is the exact length of segment AC. That value squares to 234.
[tex]d = \sqrt{234} \ \to \ d^2 = (\sqrt{234})^2 = 234\\\\[/tex]
The square root and squaring operation cancel each other out. Think of it like fire vs water.
So we really only care about what's under the square root; rather than the entire square root expression itself. Which is nice because we don't have to worry about pesky things like decimal values.
This is why 234 is typed into the first box.
---------------------
Next, use the distance formula to find how far it is from A to B. Square the result to get what you see below.
[tex]A = (x_1,y_1) = (10,6) \text{ and } B = (x_2, y_2) = (1,-3)\\\\d = \sqrt{(x_1 - x_2)^2 + (y_1 - y_2)^2}\\\\d = \sqrt{(10-1)^2 + (6-(-3))^2}\\\\d = \sqrt{(10-1)^2 + (6+3)^2}\\\\d = \sqrt{(9)^2 + (9)^2}\\\\d = \sqrt{81 + 81}\\\\d = \sqrt{162}\\\\d^2 = (\sqrt{162})^2\\\\d^2 = 162\\\\[/tex]
This is the value of [tex]\left[d(A,B)\right]^2[/tex]
Now find the distance from B to C, and square the result.
[tex]B = (x_1,y_1) = (1,-3) \text{ and } C = (x_2, y_2) = (-5,3)\\\\d = \sqrt{(x_1 - x_2)^2 + (y_1 - y_2)^2}\\\\d = \sqrt{(1-(-5))^2 + (-3-3)^2}\\\\d = \sqrt{(1+5)^2 + (-3-3)^2}\\\\d = \sqrt{(6)^2 + (-6)^2}\\\\d = \sqrt{36 + 36}\\\\d = \sqrt{72}\\\\d^2 = \left(\sqrt{72}\right)^2\\\\d^2 = 72\\\\[/tex]
Add this to the previous squared value and we get 162+72 = 234, which matches exactly with the 234 found up toward the top.
We'll write 234 in the 2nd box as well.
This shows that [tex]\left[d(A,C)\right]^2 = \left[d(A,B)\right]^2+\left[d(B,C)\right]^2[/tex] is a true statement. By the converse of the Pythagorean theorem, we have confirmed this is a right triangle.
In other words, we've shown that [tex]a^2+b^2 = c^2[/tex] is a true statement (a,b,c are the sides of the right triangle such that c is the hypotenuse).
---------------------
Recall that we found these segment lengths:
[tex]AB = \sqrt{162} = \text{leg1}\\\\BC = \sqrt{72} = \text{leg2}\\\\AC = \sqrt{234} = \text{hypotenuse}\\\\[/tex]
The legs of a right triangle represent the base and height, in either order. This is because the legs are perpendicular to one another. They form a right (aka 90 degree) angle.
[tex]\text{area} = \frac{1}{2}*\text{base}*\text{height}\\\\\text{area} = \frac{1}{2}*\text{AB}*\text{BC}\\\\\text{area} = \frac{1}{2}*\sqrt{162}*\sqrt{72}\\\\\text{area} = \frac{1}{2}*\sqrt{162*72}\\\\\text{area} = \frac{1}{2}*\sqrt{11664}\\\\\text{area} = \frac{1}{2}*108\\\\\text{area} = 54\\\\[/tex]
Here are some alternative methods you can follow to find the area of this triangle.
Pick's TheoremShoelace TheoremCreate a bounding box around the triangle. Make the box as small as possible. Find the area of the whole box, and subtract off the smaller pieces outside the triangle.Heron's FormulaAs for verifying the answers, you can use a tool like GeoGebra.
Answer:
[tex][d(A,C)]^2=\boxed{234}[/tex]
[tex][d(A,B)]^2+[d(B,C)]^2=\boxed{234}[/tex]
[tex]\sf Area=\boxed{54}\; units^2[/tex]
Step-by-step explanation:
From inspection of the given diagram:
A = (10, 6)B = (1, -3)C = (-5, 3)If ΔABC is a right triangle, the sum of the squares of the two shorter sides will equal the square of the longest side. This is the definition of Pythagoras Theorem.
Use the distance formula to find the length of each side of the triangle.
[tex]\boxed{\begin{minipage}{7.4 cm}\underline{Distance between two points}\\\\$d=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}$\\\\\\where $(x_1,y_1)$ and $(x_2,y_2)$ are the two points.\\\end{minipage}}[/tex]
[tex]\begin{aligned}d[(A,C)]&=\sqrt{(x_C-x_A)^2+(y_C-y_A)^2}\\&=\sqrt{(-5-10)^2+(3-6)^2}\\&=\sqrt{(-15)^2+(-3)^2}\\&=\sqrt{225+9}\\&=\sqrt{234}\end{aligned}[/tex]
[tex]\begin{aligned}d[(A,B)]&=\sqrt{(x_B-x_A)^2+(y_B-y_A)^2}\\&=\sqrt{(1-10)^2+(-3-6)^2}\\&=\sqrt{(9)^2+(-9)^2}\\&=\sqrt{81+81}\\&=\sqrt{162}\end{aligned}[/tex]
[tex]\begin{aligned}d[(B,C)]&=\sqrt{(x_C-x_B)^2+(y_C-y_B)^2}\\&=\sqrt{(-5-1)^2+(3-(-3))^2}\\&=\sqrt{(-6)^2+(6)^2}\\&=\sqrt{36+36}\\&=\sqrt{72}\end{aligned}[/tex]
Therefore:
The longest side of the triangle is line segment AC.The two shorter sides of the triangle are line segments AB and BC.[tex]\boxed{\begin{minipage}{9 cm}\underline{Pythagoras Theorem} \\\\$a^2+b^2=c^2$\\\\where:\\ \phantom{ww}$\bullet$ $a$ and $b$ are the legs of the right triangle. \\ \phantom{ww}$\bullet$ $c$ is the hypotenuse (longest side) of the right triangle.\\\end{minipage}}[/tex]
Therefore, the triangle is a right triangle if:
[tex][d(A,B)]^2+[d(B,C)]^2=[d(A,C)]^2[/tex]
Substitute the found side lengths into the formula:
[tex]\implies [\sqrt{162}]^2+[\sqrt{72}]^2=[\sqrt{234}]^2[/tex]
[tex]\implies162+72=234[/tex]
[tex]\implies 234=234[/tex]
Hence proving that ΔABC is a right triangle.
To find the area of a right triangle, half the product of the two shorter sides:
[tex]\begin{aligned}\implies \sf Area &= \dfrac{1}{2}bh\\&=\dfrac{1}{2} \cdot [d(A,B)] \cdot [d(B,C)]\\&=\dfrac{1}{2} \cdot \sqrt{162} \cdot \sqrt{72}\\&=\dfrac{1}{2} \cdot \sqrt{162 \cdot 72}\\&=\dfrac{1}{2} \cdot \sqrt{11664}\\&=\dfrac{1}{2} \cdot \sqrt{108^2}\\&=\dfrac{1}{2} \cdot 108\\&=54 \sf \; units^2\end{aligned}[/tex]
A trucking company has 5 trucks and 4 drivers available when requests for 3 trucks are received. How many different ways are there of selecting the trucks and the drivers to meet these requests?
The different ways that are there of selecting the trucks and the drivers to meet these requests is 240 ways.
How to calculate the number of ways?Combinations are also referred to as selections. Combinations imply the selection of things from a given set of things. In this case, we intend to select the objects.
Combination formula
ⁿCr = n! / ((n – r)! r!)
n = the number of items.
r = how many items are taken at a time.
The number of ways to select 3 trucks will be:
= ⁵C₃ = 10
The number of ways to select 3 drivers will be:
= ⁴C₃ = 4
Number of ways to arrange them = 3! = 3 × 2 = 6
Therefore the total number of ways will be:
= 10 × 4 × 6
= 240 ways
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The graph shows the percentage of citizens in a certain country who trust in their government. Complete parts a through c below.
Could someone please explain how to do part B. and C. in depth, thanks.
If the given equation is y-25=-0.92(x-4). The equation in the slope-intercept form is y=-0.92x+28.68.
What is a linear equation?It is defined as the relation between two variables, if we plot the graph of the linear equation we will get a straight line.
If in the linear equation, one variable is present, then the equation is known as the linear equation in one variable.
The given equation is,y-25=-0.92(x-4)
The slope-intercept form of the equation is,
y=mx+c
m is the slope and c is the intercept.
Thus if the given equation is y-25=-0.92(x-4). The equation in the slope-intercept form is y=-0.92x+28.68.
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A rectangle is drawn so the width is 4 inches longer than the height. If the rectangle's diagonal
measurement is 28 inches, find the height.
The height is 17.69 inches.
From the question, we have
Let height= h
width = h+4
diagonal = 28 inches
Using Pythagoras Theorem
28² = h² + (h+4)²
784 = h² +h² +16+8h
784 = 2h² +16+8h
2h²+8h-768 = 0
Solving this, we get
h=−2+2*√97
h=17.69 inches
Multiplication:
Finding the product of two or more numbers in mathematics is done by multiplying the numbers. It is one of the fundamental operations in mathematics that we perform on a daily basis. Multiplication tables are the main use that is obvious. In mathematics, the repeated addition of one number in relation to another is represented by the multiplication of two numbers. These figures can be fractions, integers, whole numbers, natural numbers, etc. When m is multiplied by n, either m is added to itself 'n' times or the other way around.
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Divide:
3⁄5 ÷ 1⁄5 =
. .
Answer: 3/1
Step-by-step explanation:3 ÷ 1 =1÷3 =3
5 5 = 5÷5=1
therefore, 3 by five divided by 1 by five is equal to 3 by 1 ,
A light bulb consumes 2100 watt-hours in 3 days and 12 hours. How many watt-hours does it consume per day?
Answer:
below
Step-by-step explanation:
12 hours is .5 day so a total of 3.5 days
2100 w-h / 3.5 d = 600 w-h per day
Housing value are appreciating at a rate of 11.3% a year how much will your 810,000 house be worth in 5 years if this rate of appreciation continues
[tex]\qquad \textit{Amount for Exponential Growth} \\\\ A=P(1 + r)^t\qquad \begin{cases} A=\textit{accumulated amount}\\ P=\textit{initial amount}\dotfill &810000\\ r=rate\to 11.3\%\to \frac{11.3}{100}\dotfill &0.113\\ t=\textit{years}\dotfill &5\\ \end{cases} \\\\\\ A=810000(1 + 0.113)^{5} \implies A=810000(1.113)^5\implies A \approx 1383441.63[/tex]
What equation is graphed in this figure?
Responses
y−4=−13(x+2)
y minus 4 equals negative fraction 1 over 3 end fraction open parenthesis x plus 2 close parenthesis
y−3=13(x+1)
y minus 3 equals fraction 1 over 3 end fraction open parenthesis x plus 1 close parenthesis
y+2=−3(x−1)
y plus 2 equals negative 3 left parenthesis x minus 1 right parenthesis
y−5=3(x−1)
y minus 5 equals 3 left parenthesis x minus 1 right parenthesis
Number graph ranging from negative four to four on the x and y axes. A line is drawn on the graph that passes through begin ordered pair negative one comma four end ordered pair and begin ordered pair one comma negative two end ordered pair
The linear equation shown in the graph is the one in the third option.
y + 2 = -3*(x - 1)
What is the equation graphed?Here we have a graph, and there we can see a linear equation, on that graph, we can see that:
The y-intercept is y = 1.
For each horizontal unit, the line goes 3 units down, then the slope is -3.
Then the linear equation is:
y = -3*x + 1
If now we add 2 in both sides, we get:
y + 2 = -3x +1 + 2
y + 2 = -3x + 3
y + 2 = -3*(x - 1)
So the correct option is the third one.
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Quiero el resultado de la ecuación 5 x + 2 y = 90
Answer:
x=18-2/5y
y=-5/2x+45
Step-by-step explanation:
5x+2y=90
Nosotros queremos resolver para x o y
5x=90-2y
x=18-2/5y
o
2y=90-5x
y=-5/2x+45
Answer:
x=18-2y/5
Step-by-step explanation:
Please help! What is the equation of the line?
y=-3x
y=3x
y=3x+1
y=4x
Answer: y=3x
Step-by-step explanation:
The equation can be found by finding the slope of the given line. Visually, this can be found by counting the distance between two points. From (1,3) and (2,6), the line "rises" 3 units and "runs" 1 unit to the right. Since slope is calculated as rise over run, this gives us 3/1, or just 3 for slope. In slope-intercept form, this becomes y=3x.
Just to note, we know it is not negative because of the direction of the slope. Visually, if the slope "moves" in the direction of upwards and to the left, it will be positive. This can be calculated more accurately using the slope formula (y2-y1/x2-x1)
Antoinette solves the linear equation 3 (x minus 3) + 2 x + 9 = 2 x + 2 (x minus 1) using the steps shown below.
Step 1: 3 x minus 3 + 2 x + 9 = 2 x + 2 (x minus 1)
Step 2: 5 x + 6 = 4 x minus 1
Step 3: 5 x minus 4 x = negative 1 minus 6
Step 4: x = negative 7
She checks her solution by substituting –7 for x in the original equation. She determines that her answer is incorrect. Which best describes Antoinette’s error?
She distributed incorrectly.
She incorrectly combined like terms.
She incorrectly applied the addition and subtraction properties of equality.
She incorrectly applied the multiplication and division properties of equality.
Answer:
She distributed incorrectly.
Step-by-step explanation:
In the first step, [tex]3(x-3)=3x-9[/tex], not [tex]3x-3[/tex].
1. Find the equation of the line that has a slope of 7 and passes through the point (-8,3).
The equation of the line has a slope of 7 and passes through the point (-8,3) is y = 7x + 59.
What is a linear function?A straight line on the coordinate plane is represented by a linear function.
A linear function always has the same and constant slope.
The formula for a linear function is f(x) = ax + b, where a and b are real values
The general form of a linear equation is the slope(m) and y-intercept (c) is given as
y = mx + c
Slope m =7
y = 7x + c
Substitute, (-8,3)
3 = 7(-8) + c
c = 59
Thus, y = 7x + 59 will be the equation.
Hence "The equation of the line has a slope of 7 and passes through the point (-8,3) is y = 7x + 59".
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Oliver saves %10 of their weekly earnings for living expenses. oliver usually makes $520 each week. This week oliver made %10 more. incorrectly oliver claims that has $520 left for spending money this week. Calculate the amount of spending money left for this week. What error did olive likely make?
Oliver is left with $514.8
A percentage is a number or ratio expressed as a fraction of one hundred. If we need to calculate a percentage of a number, divide it by the whole and multiply by 100. As a result, the percentage represents one part in a hundred. The term % stands for one hundred percent.
His usual salary = $520 per week
This week he earned = Usual salary + 10% of usual salary
10% of usual salary =520 x (10/100)
Thus, this week's earnings = $520 + $52 = $572
Amount spent = 10% of this week =572 x (10/100)
= 57.2
Thus, the left amount is calculated by:
Left amount = this week's salary - the amount spent
Amount left = $572 - $57.2 = $514.8
Thus, Oliver is left with $514.8
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A rare coin increases in value according to the function f(x)=100(1.07)x
f(x)=100(1.07)x where x represents the amount of years that the coin is owned and value is measured in US dollars. What is the value of the coin after 5 years?
The value of the coin after five years is 535 when the value increases with the function f(x) = 100(1.07)x
The value of a rare coin rises in accordance with the function f(x)
f(x) = 100(1.07)x
where x represents the number of years that the coin is owned and value is measured in US dollars
Now, Simplifying the given function, we have :
f(x) = 100(1.07)x
f(x) = 107x
Now, we need to find the value of the coin after five years, then
Putting x = 5 in the function,
f(x) = 107 * 5 = 535
Hence, the value of the coin after five years is 535 when the value increases with the function f(x) = 100(1.07)x
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Can anybody help me with this question?
Answer:
x=3
Step-by-step explanation:
any horizontal line is equal to x
the y is equal to 0
a horizontal line is undefined
All families in a given nation with four children were asked to report the sexes of the children.
What percent of families would be expected to have children who are all boys? Write your answer as an exact percentage.
The percent of families would be expected to have children who are all boys is 6.25%
How to calculate percentage?The following can be illustrated:
all 4 boys BBBB 1 1/16
3 boys 1 girl BBBG,GBBB,BGBB,BBGB 4 4/16
2 boys 2 girl BBGG,BGBG,GBGB,BGGB,GBBG, GGBB 6 6/16
1 boy 3 grisl BGGG,GBGG,GGBG,GGGB 4 4/16
all 4 girls GGGG 1 1/16
Therefore, the percent of families would be expected to have children who are all boys will be:
= All boys × 100
= (1/16)*100
= 6.25%
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0/1
3. At the carnival, there is a game with 600 ducks. If 25% of the ducks have stars on the
bottom, how many ducks have stars? Make sure to label your answer in ducks
8
011 (part 1 of 2) 10.0 points
Young David, who slew Goliath, experi- mented with slings before tackling the gi- ant. He found that with a sling of length 0.566 m, he could revolve the sling at the rate of 10.7 rev/s. If he increased the length to 0.87 m, he could revolve the sling only 7.7 rev/s.
a) What is the larger of the two linear speeds?Answer in units of m/s.
part 2
b) Using the sling length 0.87 m, what is the centripetal acceleration at 7.7 rev/s?
Answer in units of m/s2.
this is physics
The 0.566 meter, 0.87 meter, 10.7 rev/s and 7.7 rev/s radii and respective rotational speeds of young David's slings indicates.
a) The larger linear speed is 42.09 m/s
b) The centripetal acceleration of the sling at 7.7 rev/s is approximately 2,036.39 m/s²
What is a linear speed?A linear speed is a measure of the rate at which the distance traveled by an object in rotary motion changes with time.
When the length of the sling = 0.566 m, The rate of revolving of the sling = 10.7 rev/s
When the length of sling = 0.87 m, the rate of revolving the sling = 7.7 rev/s
Linear speed = Angular speed ×Radius length
The angular speed when the length of the is 0.566 m, ω₁, is found as follows;
One complete 360° rotation = 2·π radians
ω₁ = 10.7 rev/s × 2·π ≈ 67.23 rad/s
The linear speed is; v₁ ≈ 67.23 rad/s × 0.566 m ≈ 38.05 m/s
The angular speed when the length is increased to 0.87 meters is therefore;
ω₂ = 7.7 rev/s × 2 × π ≈ 43.38 rad/sec
The linear speed is; v₂ ≈ 43.38 rad/s × 0.87 m ≈ 42.09 m/sThe larger of the two linear speed is approximately 42.09 m/s
Part 2: The centripetal acceleration, [tex]a_c[/tex], is found using the following formula;
[tex]a_c = \dfrac{v^2}{r}[/tex]
When the radius is r = 0.87 meters, the linear speed v₂ ≈ 42.09 m/s, which indicates;
[tex]a_c=\dfrac{42.09^2}{0.87} \approx 2,036.39[/tex]
The centripetal acceleration is approximately [tex]a_c[/tex] ≈ 2,036.39 m/s²
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Which set of side lengths will NOT create a triangle? Responses 3, 4, 5 3,, , 4,, , 5, EndFragment, 10, 13, 14 10, 13, 14, EndFragment, 10, 20, 30 10, 20, 30, 16, 20, 30
The set of side lengths that would not create a triangle is; 10, 20, 30.
Which set of side lengths will not create a triangle?It follows from the task content that the set of side lengths which will not create a triangle are to be determined from the given task content.
Since the triangle inequality theorem states that; the sum of two side lengths of a triangle is always greater than the third side length and also, the difference of two side lengths of a triangle is less than the third side length.
On this note, for a triangle with side-lengths a, b and c; the inequalities which hold are;
a + b > c and a - b < c.
Therefore, the set of side-lengths which will not create a triangle is; 10, 20, 30.
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Which question can be represented by the equation ? × 1/8 = 3
A) how many 3s are in 1/8?
B) what is 3 groups of 1/8?
C) how many 1/8s are in 3?
D) what is 1/8 of 3?
The question that can be represented by the equation ? × 1/8 = 3 is C. how many 1/8s are in 3?
What is an equation?An equation is the statement that illustrates that the variables given. In this case, two or more components are taken into consideration to describe the scenario.
In this case, the question is how many 1/8s are in 3. This will be:
= 3 ÷ 1/8
= 3 × 8
= 24
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Identify the function shown in this graph.
A. y= 3x - 3
B. y= -3x + 3
C. y= -3 x- 3
D. y= -1/3x + 3
The length of a rectangle is 10, the width 3, and the height x. The surface area and the volume are equal. What is the value of x?
Answer:
x = 15
Step-by-step explanation:
Please refer photo
A falcon flies 800,000 meters in 4 hours. Use the formula d = rt, where d represents distance, r represents rate, and t represents time, to answer the following questions. Show your work.
Part A: Rearrange the distance formula, d = rt, to solve for rate.
Part B: Find the falcon's rate in meters per hour.
Part C: Find the falcon's rate in kilometers per hour.
Part D: Which unit, meters, or kilometers, makes more sense to use in this scenario, and why?
PLEASE HELP FAST I RLLY NEED THIS
The information about the Falcon fly is represented below
Part A: 800 000 = 4r
part B: 200 000 meters per hour
Part C: 200 kilometer per hour
Part D: Kilometers makes more sense because it makes the number easier to write and remember
How to find the falcon's rate in meters per hourThe rate as used refers to speed which is distance / time
using the representation 800 000 = 4r
rate, r = 800 000 / 4
r = 200 000 meters per hour
converting meter to kilometer is achieved by dividing by 1000
r = 200 000 meters per hour / 1000
r = 200 kilometers per hour
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I’m really stuck on how to answer this question I need help
Angelo constructed 8 playing card houses in 4 minutes. How long would it take for him to construct 20
houses?
Answer:
10 minutes.
Step-by-step explanation:
8 houses are done in 4 minutes
The ratio is 2:1
20 houses are done in 10 minutes
20:10 = 2:1
Answer:
It would take Angelo 10 minutes to construct 20 playing card houses.
first way to solve it (recommended):
Step one: See how much it takes to build one house
4 / 8 = 0.5
0.5 minutes to build one house
Step two: multiply by amount of houses (20)
0.5 x 20
Step three: get your answer!
It would take Angelo 10 minutes to make 20 houses.
second way to solve it (ratios):
Step one: see the ratio of minutes to houses
minutes : houses
4 : 8
Step two: simplify the ratio
4 : 8
1 : 2 (divide both sides by four)
Step three: multiply
x minutes : 20 houses
1 minutes : 2 houses
multiply both sides by 10
10 minutes : 20 houses
Step four: get your answer!
It would take Angelo 10 minutes to make 20 houses.
I hope my answer helped you!