Answer:
y = -3x - 27
Step-by-step explanation:
0 = -3[-9] + b
-27 = b
y = -3x - 27
* Perpendicular Lines have OPPOSITE MULTIPLICATIVE INVERSE RATE OF CHANGES [SLOPES]:
⅓ → -3
I am joyous to assist you anytime.
Find the slope of the line joining each pair of points. Then draw the line in a coordinate plane:
I(5, 2), J(5, −4)
I know this should be infinity or no solutions, but my homework site is marking both answers as wrong. I don't know what else it can be.
Answer:
Step-by-step explanation:
Here slope = (y2-y1)/(x2-x1)
Which comes out to be: (-4-2)/5-5 = -6/0 !!!
But we cannot divide by 0. So the slope is undefined. This is basically a vertical line. The "slope" of a vertical line. A vertical line has undefined slope because all points on the line have the same x-coordinate.
If your hw website is not accepting undefined as answer then what are the options that it provides?
The diameter of a circle is 5 kilometers. What is the area?
Answer:
[tex]\large\boxed{A=6.25\pi\ km^2\approx19.625\ km^2}[/tex]
Step-by-step explanation:
The formula of an area of a circle:
[tex]A=\pi r^2[/tex]
r - radius
We have the length of a diameter d = 5 km
We know: d = 2r. Therefor r = 5km : 2 = 2.5 km.
Substitute:
[tex]A=\pi(2.5)^2=6.25\pi\ km^2[/tex]
If you want an approximation, then
[tex]\pi\approx3.14\to A\approx(6.25)(3.14)=19.625\ km^2[/tex]
Hey!
-----------------------------
Formula: A = πr²
Diameter: d / 2 = r
-----------------------------
Solution:
A = (3.14)(2.5)²
A = (3.14)(6.25)
A = 19.625km.
-----------------------------
Answer:
The area of the circle is 19.625km. or 6.25π km.
-----------------------------
Hope This Helped! Good Luck!
6 hundreds divided by 10=
2 thousands divided by 10=
Answer:
1. 60 2. 200
Step-by-step explanation:
600÷10= 60
2000÷10=200
Answer:
60 and 200
Step-by-step explanation:
When divideing by 10 you can cancel the zeros from both the numertor and denominator
What’s the value of the 3 in 783.97
A box contains 6 red balls, 7 yellow balls, and 2 green balls. All the balls are the same except for their color, Jaime picks a ball from the
box, records the color, then returns the ball to the box. He does this 3 times
What is the probability that all three balls that Jaime picked were red?
Answer:
The answer is 8/27
The probability that all three balls that Jaime picked were red is '0.064'
Now the box contains 6 red balls, 7 yellow balls, and 2 green balls
Thus the total number of balls in the box can be find by summing up all the balls in the box
Thus we get,
Total number of balls = 6 + 7 + 2 = 15 balls
Thus there are total of 15 balls in the box
Now Jamie picks a ball from the box, records the color, then returns the ball to the box.
Thus in the first try, the probability that the ball picked up is red:
Probability that the first ball picked is red = [tex]\frac{6}{15}[/tex]
where, '6' is the number of red balls
and '15' is the number of total balls in the box
Similarly as the ball picked up is again returned to the box the number of red balls and total number of balls won't change
Similarly probability that the second ball picked is red = [tex]\frac{6}{15}[/tex]
Similarly probability that the third ball picked is red = [tex]\frac{6}{15}[/tex]
Thus to find the combined probability we need to multiply all three probabilities
Thus probability that all three balls that Jaime picked were red is,
[tex]\frac{6}{15} *\frac{6}{15} *\frac{6}{15} = \frac{36}{225}* \frac{6}{15}\\ \frac{6}{15} *\frac{6}{15} *\frac{6}{15} =\frac{216}{3375}\\ \frac{6}{15} *\frac{6}{15} *\frac{6}{15} =0.064[/tex]
Thus '0.064' is our required answer
Describe a way to calculate 304-81 mentally by using reasoning other that the common subtraction algorithm. Then write a coherent sequence of equations that correspond to your reasoning
Answer:
The required way is shown above.
Step-by-step explanation:
Consider the provided calculation.
304 – 81 is very close to 304 – 100,
Now subtract 100 from 304 mentally, it will gives us 204
Now add 19 as we round 81 to 100.
204 + 19 = 223
So, the answer is 223.
Now write a coherent sequence of equations that correspond to your reasoning.
304 – 81 = 304 – (100 – 19)
= (304 – 100) + 19
= 204 + 19 = 223
Hence, the required way is shown above.
To subtract 81 from 304 mentally, round 81 to 80, subtract from 304 to get 224, and then add 1 to compensate for the rounding, giving a final answer of 225.
Explanation:To calculate 304-81 mentally, we can use the strategy of rounding and compensating. First, we can round 81 up to a number that is easier to subtract from 304, such as 80 or 100, and then we adjust the final result to account for the rounding. Here's how to think through it:
The coherent sequence of equations that correspond to this reasoning would be:
This mental math strategy involves rounding and compensation, which allows us to handle subtraction problems quickly without having to use the standard subtraction algorithm. Checking that the answer makes sense in the context of the original problem is a good practice to ensure accuracy.
f(x) = 10x – 4
What is the inverse for this?
Answer:
Step-by-step explanation:
f(x) = 10x – 4
10x = f(x)+4
x = f(x)/10 + 2/5
the inverse is y = x/10 + 2/5
Using the properties of shapes, explain why all parallelograms are trapezoids.
Answer:
All parallelograms are trapezoids.
Step-by-step explanation:
A parallelogram has two pairs of parallel sides. A trapezoid has at least one pair of parallel sides. So if all parallelograms have two pairs, they are in the same category of the trapezoids.
Final answer:
A parallelogram is considered a trapezoid because it has at least one pair of parallel sides, which fits the basic definition of a trapezoid. Parallelograms have additional properties like equal opposite sides and angles, but these do not contradict the broader trapezoid classification.
Explanation:
Why All Parallelograms Are Trapezoids
A trapezoid is defined as a quadrilateral with at least one pair of parallel sides. A parallelogram, by definition, has two pairs of parallel sides. Therefore, since a parallelogram inherently possesses at least one pair of parallel sides, it meets the minimum criterion to be considered a trapezoid. This logical inclusion is based on the definition of shapes within geometry, and thus all parallelograms can be classified as trapezoids.
Properties of Parallelograms and Trapezoids
Parallelograms have some additional properties that trapezoids don't necessarily share, such as opposite sides being equal in length and opposite angles being equal. This does not, however, preclude them from the broader categorization of trapezoids because those extra properties do not contradict the definition of a trapezoid.
Applying similar triangles and their properties, although useful for understanding relationships between different shapes, is not directly necessary for explaining why parallelograms are trapezoids. Instead, it's the fundamental definitions of these shapes that establish the relationship between parallelograms and trapezoids. The Theorem 26 states that any triangle is always of equal area to a certain parallelogram having an equal base and half the altitude. While this theorem relates parallelograms to triangles, it does not affect the classification of parallelograms as trapezoids.
whats the answer too -8(x + 4) -6x
Answer:
Step-by-step explanation:
-8(x + 4) -6x = -8 * x + (-8) * 4 - 6x
= -8x - 32 -6x
= -14x -32
What is the degree of the polynomial 5a^6bc^2+8d^5+7e^6f^2-10g^4h^7
Final answer:
The degree of the polynomial 5a⁶bc²+8d⁵+7e⁶f²-10g⁴h⁷ is 11, determined by the highest sum of exponents in any term of the polynomial, which is found in the term -10g⁴h⁷.
Explanation:
The degree of a polynomial is the highest exponent of its variables when it is expressed in standard form. To find the degree of the given polynomial 5a⁶bc²+8d⁵+7e⁶f²-10g⁴h⁷, we look at each term individually and sum the exponents of the variables within that term. The terms of the polynomial are:
5a⁶bc² with a degree of 6 + 1 + 2 = 9
8d⁵ with a degree of 5
7e⁶f² with a degree of 6 + 2 = 8
-10g⁴h⁷ with a degree of 4 + 7 = 11
Comparing the sums of the exponents, we see that the term -10g⁴h⁷ has the highest sum which is 11. Therefore, the degree of the given polynomial is 11.
For the function f(x) = 6x - 8, identify the values of f(o), f(1/2), and f(-2).
O 8; -5; 4
O -8; -11; -20
O 8; -11; 4
© -8; 15; -20
Answer:
-8, -5, -20.
Step-by-step explanation:
f(0) = 6(0) - 8 = -8
f(1/2) = 6(1/2) - 8 = -5
f(-2) = 6(-2) - 8 = -20.
[tex]\text{Hello there!}\\\\\text{You're plugging in the values 0, 0.5, and -2 to x}\\\\\text{Plug them into the equation:}\,\,f(x) = 6x - 8\\\\\text{Solve:}\\\\f(x) = 6(0) - 8\\\\\boxed{f(x)=-8}\\\\f(x) = 6(0.5) - 8\\\\f(x) = 3 - 8\\\\\boxed{f(x)=-5}\\\\f(x) = 6(-2) - 8\\\\f(x)=-12-8\\\\\boxed{f(x)=-20}\\\\\text{Those three solutions will be your answer}\\\\\large\boxed{\text{Answer:}\,\,-8;-5;-20}[/tex]
Starting from the same place, Karina walks due west and Lucas walks due east. On the number line, 0 represents their starting point, negative values represent the distance traveled west and positive values represent the distance traveled east. All values are given in feet. How many feet apart are Karina and Lucas on the number line? Enter your answer in the box.
Answer:
The answer is 480
Step-by-step explanation:
2. Nine more than the opposite of a number is three less than twice the number. What is
the number?
Answer:
The number is 4
Step-by-step explanation:
* Lets revise some words in mathematics and how change them to
mathematical symbols
- More than ⇒ add (+)
- Less than ⇒ subtract (-)
- Twice ⇒ Multiplied by 2 (× 2)
- Opposite of a number ⇒ change its sign (additive inverse of it)
* Now lets solve the problem
- Nine more than the opposite of a number is three less than twice
the number
- Assume that the number is x
∴ 9 more than the opposite of x
- That means find the opposite of x and add it by 9
∵ The opposite of x is -x
∴ Nine more than the opposite of a number = -x + 9
- Three less than twice the number means 3 less than twice x
∵ The number is x
∴ Twice the number = 2 × x = 2x
∵ Three less than twice x = 2x - 3
∴ Three less than twice the number = 2x - 3
- The meaning of "is" between the two the statements is "="
∴ Nine more than the opposite of a number is three less than twice
the number is ⇒ -x + 9 = 2x - 3
* Lets solve the equation to find x
∵ -x + 9 = 2x - 3
- add x in both sides
∴ 9 = 3x - 3
- Add 3 to both sides
∴ 12 = 3x
- Divide both sides by 3
∴ x = 4
∵ x represents the number
∴ The number is 4
* Lets check the answer
9 more than opposite 4 is 3 less than twice 4
9 + (-4) = 2 × 4 - 3
9 - 4 = 8 - 3
5 = 5
The answer is right
Evaluate −5(12)^3x for x = 1.
Answer:
x=3
Step-by-step explanation:
Answer: The answer is -8640.
Step-by-step explanation:You would first off by multiplying what's in the parenthesis by its exponent: (12)^3(1)= 1720. Then multiply 1728 by 5 so get your overall correct answer of -8640. Hope I helped you a lot and my answer is correct.!!
simplify the given expression
expression:1
9(2+ 7f)
expression:2
6•7-3^2•9+4^3
show your work
Answer:
Expression: 1 ⇒ 18 + 63 f
Expression: 2 ⇒ 25
Step-by-step explanation:
* Lets revise at first the order of operations
- The order of these operations is:
# Parenthesis
# Exponents
# Multiplication and Division which comes first from left to right
# Addition and Subtraction which comes first from left to right
- There is a word made from the first letter of each operation
PEMDAS to remember the order of operations
* Lets solve the problem
# Expression: 1
∵ 9(2 + 7 f)
- To simplify this expression multiply the bracket by 9
∵ 9(2 + 7 f) = 9 × 2 + 7 f × 9
∵ 9 × 2 = 18
∵ 7 f × 9 = 63 f
∴ 9(2 + 7 f) = 18 + 63 f
* Expression: 1 ⇒ 18 + 63 f
# Expression: 2
∵ 6 × 7 - 3² × 9 + 4³
- At first simplify exponent
∵ 3² = 9 and 4³ = 64
∴ 6 × 7 - 3² × 9 + 4³ = 6 × 7 - 9 × 9 + 64
- Solve the multiplication first
∵ 6 × 7 = 42
∵ 9 × 9 = 81
∴ 6 × 7 - 3² × 9 + 4³ = 42 - 81 + 64
- Solve 42 - 81 first because it comes first from left to right
∵ 42 - 81 = - 39
∴ 6 × 7 - 3² × 9 + 4³ = - 39 + 64
- Add them
∵ - 39 + 64 = 25
∴ 6 × 7 - 3² × 9 + 4³ = 25
* Expression: 2 ⇒ 25
3. Noah is helping to collect the entry fees at his school's sports game. Student entry
costs $2.75 each and adult entry costs $5.25 each. At the end of the game, Diego
collected $281.25.
Select all equations that could represent the relationship between the number of
students, s, the number of adults, a, and the dollar amount received at the game.
A. 281.25 – 5.25a = 2.75s
B. a = 53.57 - 13:25
C. 281.25 -5.25s = a
D. 281.25 +2.75a = s
E. 281.25 +5.25s = a
281.25-5.25a=2.75
step by step:
so you divide the total amount by two and you get 140.62
then you divide that by 5.25 and you get 26.78
plug that into a and you get 140.62
then you take the remainder which is 140.62 and you divide that by 2.75
which is 51.13 and that will be your number for s
and at the end you should get the remainder of 140.62
then you multiply 140.62 by 2 and you get were you started and thats how you check your answer
Select all equations that could represent the relationship between the number of
number ofstudents, s, the number of adults, a, and the dollar amount received at the game.
The equations that could represent the relationship between the number of students, s, the number of adults, a, and the dollar amount received at the game is 281.25 – 5.25a = 2.75s
let
student fee = $2.75
Adult fee = $5.25
Total income = $281.25
Number of students = s
Number of adults = a
The equation:
Total income = (student fee × Number of students) + (Adult fee × Number of adults)
281.25 = (2.75 × s) + (5.25 × a)281.25 = 2.75s + 5.25a281.25 - 5.25a = 2.75sA. 281.25 – 5.25a = 2.75s
True
B. a = 53.57 - 13:25
Not true
C. 281.25 -5.25s = a
Not true
D. 281.25 +2.75a = s
Not true
E. 281.25 +5.25s = a
Not true
Therefore, the equations that could represent the relationship between the number of students, s, the number of adults, a, and the dollar amount received at the game is 281.25 – 5.25a = 2.75s
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28 - 6(2x + 4) = 124
Answer: x = -12 is the correct answer
Step-by-step explanation: the moderator that deleted this if is so wrong then just tell me why is wrong if you are so smart.
PLEASE HELP ME(picture is shown) Set up the equation and find the length of BC
Step-by-step explanation:
From the diagram,
AC = AB + BC
BC = AC - AB
BC = 54 - 25 = 29
the sum of two numbers is 84. The first is 9 more than 4 times the second. Find the numbers.
Answer:
69 and 15
Step-by-step explanation:
Second number=x
First number 4x+9
4x+9 +x = 84
5x+9=84
5x=75
x=15
15*4=60
60+9=69
69+15=84
If you're driving at 25 miles per hour through a school zone and a child runs out in front of you, how much distance will
your car cover before stopping?
Answer:
depending on the car type
probs about 5-10 feet
Step-by-step explanation:
Which two numbers are 4 units away from -1
The two numbers are 3 and -5. Let's start with 3. To get three, add 4 to -1. That means, going 4 to the right on a number line. When you do so, you will end up with 3. Since adding always go up.
Let's move onto -5 now. For this, go 4 to the left. Subtracting from negative numbers will be negative numbers. Since subtracting is going down, you go down on the number line.
Therefore, 3 and -5 is the answer!
Explaining channel:
Type HWsolver-Brainly. It should pop up at the bottom with a person thumbs up.
The two numbers that are 4 units away from -1 are -5 and 3.
What is a number line?In math, a number line can be defined as a straight line with numbers placed at equal intervals or segments along its length.
Now the given integer is, -1.
To find the numbers that are 4 units away we need to subtract and add 4 to get the required number.
So, 4 units forward from -1 is,
-1 + 4 = 3
And 4 units backward from -1 is,
-1 - 4 = -5
So the two numbers we get are 3 and -5.
Thus, the two numbers that are 4 units away from -1 are -5 and 3.
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Between 10 pm and 7:45 am the water level in a swimming pool decreased by 13/16 inch. Assuming the constant rate how much did it drop each hour
Answer:
[tex]\frac{1}{12} [/tex] inches per hour .
Step-by-step explanation:
Between 10 pm and 7:45 am there are 9 hours and 45 minutes i.e. [tex]9+\frac{45}{60} =\frac{39}{4}[/tex] hours
The water level in a swimming pool decreased by amount in [tex]\frac{39}{4}[/tex] hours = [tex]\frac{13}{16}[/tex] inches
The water level in a swimming pool decreased by amount in 1 hour:
= [tex]\frac{\frac{13}{16}}{\frac{39}{4}}[/tex] inches
= [tex]\frac{13}{16} \times \frac{4}{39}[/tex] inches
= [tex]\frac{1}{4} \times \frac{1}{3}[/tex] inches
= [tex]\frac{1}{12} [/tex] inches
Hence it drop by [tex]\frac{1}{12} [/tex] inches each hour .
How much did it drop each hour is 0.08333 inches/hour
First step is to calculate the Decrease
Decrease = 13/16 inches
Decrease=0.8125 inches
Second step is to calculate the time interval
From 10 pm to 7:45 hours will be 9.45 hours
Time interval= (9 + 45/60) hours
Time interval=9.75 hours
Now let determine How much did it drop each hour
0.8125/9.75 inches/hour
=0.08333 inches/hour
Inconclusion How much did it drop each hour is 0.08333 inches/hour
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The function f(x) = 5One-fifth is reflected over the y-axis. Which equations represent the reflected function? Select two options.
f(x) = One-fifth
f(x) = One-fifthOne-fifthOne-fifth
f(x) = 5One-fifth
f(x) = 5(5)x
f(x) = 5(5)–x
Answer:
The equations that represent the reflected function are
[tex]f(x)=5(\frac{1}{5})^{-x}[/tex]
[tex]f(x)=5(5)^{x}[/tex]
Step-by-step explanation:
The correct question in the attached figure
we have the function
[tex]f(x)=5(\frac{1}{5})^{x}[/tex]
we know that
A reflection across the y-axis interchanges positive x-values with negative x-values, swapping x and −x.
therefore
[tex]f(−x) = f(x).[/tex]
The reflection of the given function across the y-axis will be equal to
(Remember interchanges positive x-values with negative x-values)
[tex]f(x)=5(\frac{1}{5})^{-x}[/tex]
An equivalent form will be
[tex]f(x)=5(\frac{1}{5})^{(-1)(x)}=5[(\frac{1}{5})^{-1})]^{x}=5(5)^{x}[/tex]
therefore
The equations that represent the reflected function are
[tex]f(x)=5(\frac{1}{5})^{-x}[/tex]
[tex]f(x)=5(5)^{x}[/tex]
Answer:
c,d
Step-by-step explanation:
Yara multiplies and divides a certain number by the same
power of 10. The product she gets is 40,000 and the
quotient she gets is 0.000004. Find Yara's number and
the power of 10 she used. Explain your reasoning.
For this case we have to:
x: Represents the unknown number
y: Represents the exponent of base 10
So, considering a system of equations we have:
[tex]x * 10 ^ y = 40,000\\\frac {x} {10 ^ y} = 0.000004[/tex]
From the first equation we have:
[tex]10 ^ y = \frac {40,000} {x}[/tex]
Substituting in the second equation:
[tex]\frac {x} {\frac {40,000} {x}} = 0.000004\\\frac {x ^ 2} {40,000} = 0.000004\\x ^ 2 = 40,000 * 0.000004\\x ^ 2 = 0.16\\x = \pm \sqrt {0.16}[/tex]
We choose the positive value:
[tex]x = 0.4[/tex]
So, the number is 0.4.
So:
[tex]10 ^ y = \frac {40,000} {0.4}\\10 ^ y = 100,000\\y = 5[/tex]
Thus, the exponent is 5.
Answer:
Yara use 0.4 and[tex]10 ^ 5[/tex]
Answer:
0.4 and 10.5
Step-by-step explanation:
inverse of y= x-6/x+5
as you would already know, we start off to gettting any inverse of any expression by doing a quick switcheroo on the variables and then we solve for "y".
[tex]\bf y = \cfrac{x-6}{x+5}\implies \stackrel{\textit{quick switcheroo}}{x = \cfrac{y-6}{y+5}}\implies x(y+5)=y-6\implies xy+5x=y-6 \\\\\\ xy+5x+6=y\implies 5x+6=y-xy\implies 5x+6=\stackrel{\textit{common factor}}{y(1-x)} \\\\[-0.35em] \rule{34em}{0.25pt}\\\\ ~\hfill \cfrac{5x+6}{1-x}=\stackrel{f^{-1}(x)}{y}~\hfill[/tex]
The cost of renting a car is $25 per day plus a one-time fee
of $75.50 for insurance. How many days can the car be
rented if the total cost is to be no more than $525? Write
and solve an inequality to find the solution, and graph the
solution on a number line.
For $525 we can rent the car for 17 complete days.
What are inequalities and their types?Inequality is a relation that compares two numbers or other mathematical expressions in an unequal way.
The symbol a < b indicates that a is smaller than b.
When a > b is used, it indicates that a is bigger than b.
a is less than or equal to b when a notation like a ≤ b.
a is bigger or equal value of an is indicated by the notation a ≥ b.
Given, The cost of renting a car is $25 per day plus a one-time fee
of $75.50 for insurance.
Assuming the no. of days we can rent the car for $525 is x.
∴ 25x + 75.50 ≤ 525.
25x ≤ 449.5
x ≤ 449.5/25.
x ≤ 17.98 Or 17 complete days.
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Laura is looking for a way to save money this year on her medical expenses. Insurance is starting to get expensive, and her budget is tight. She figures that she has a 75% chance of needing to visit the doctor and get medication once in the winter, for a total of about $400. She also figures there should be some room in the budget for emergencies, so she estimates a 5% chance she will need to spend $300 at an emergency room.
Is it reasonable for Laura to set her medical budget at $300 for the year?
Answer: A
Step-by-step explanation: The expected value is over $300, so Laura will likely need more money to cover her expenses.
its not that hard
It's not reasonable for Laura to set her medical budget at $300 for the year. Considering her predicted medical expenses, her expected annual cost is $315, making her budget slightly understated.
Explanation:The answer to whether Laura's medical budget of $300 for the year is reasonable or not involves a concept in probability known as expected costs. Let's consider both events: there is a 75% chance of spending $400 and a 5% chance of spending $300.
We calculate the expected cost for both scenarios:
The expected cost for the doctor visit and medication is 0.75 * $400 = $300The expected cost for emergency spending is 0.05 * $300 = $15
Adding these costs, we find that her expected annual medical costs are $315, not $300. Therefore, Laura might need to reconsider her budget, possibly increasing it slightly.
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10 POINTS BOIII
What is the slope of the line on the graph? P.S it's supposed to be a number.
Answer:
1/2
Step-by-step explanation:
HURRY PLZZZZ!!!!!!!!!!
The width of a rectangle is 4 more than half the length. If the perimeter of the rectangle is 74, what is the width? Perimeter of rectangle: P = 2l + 2w
i'll give brainliest
Answer:Width = 15 units .
Step-by-step explanation:
Given : The width of a rectangle is 4 more than half the length. If the perimeter of the rectangle is 74,
To find : what is the width.
Solution : We have given perimeter of the rectangle is 74,
Let the Length = x .
According to question :
The width of a rectangle is 4 more than half the length.
Width = 4 + [tex]\frac{x}{2}[/tex].
Perimeter = 2 length + 2 width .
Plugging the values,
74 = 2 ( x ) + 2 (4+[tex]\frac{x}{2}[/tex]).
74 = 2x + 8 + x .
Combine like terms
74 = 2x +x + 8.
74 = 3x +8.
On subtracting both sides by 8.
74 -8= 3x .
66 = 3x
On dividing both sides by 3
x = 22.
Width = Width = 4 + [tex]\frac{22}{2}[/tex].
Width = 4 +11.
Width = 15 units .
Therefore, Width = 15 units .
Henry is 4 years younger than Linda. Linda is 20 years old.
After correctly carrying out the Solve step of the five-step problem-solving plan, which solution should you arrive at to find Henry’s age?
28
24
16
12
Answer:
16
Step-by-step explanation:
20-4=16
pls give brainliest