Answer:
Length= 12 ft
Width= 25 ft
Step-by-step explanation:
We will use the area of the rectangle formula to solve this question. The formula is: [tex]Area= length* width[/tex]
Let, the width of the rectangle is x, so the length is one foot more than twice it’s width, and is written as:
width= 2x+1
Now the area of the rectangle is given as:
300 [tex]ft^2[/tex]
So using the formula of the area of a rectangle, we get:
[tex]Area= length* width\\\Rightarrow 300= x(2x+1)\\\Rightarrow 2x^2+x-300=0\\\Rightarrow x=\frac{-1 \pm \sqrt{1^2-4 \cdot \:2\left(-300\right)}}{2\cdot \:2}\\\Rightarrow x=12,\:x=-\frac{25}{2}\\[/tex]
But we will take only positive value of x, as length can't be negative.
So the dimensions of the rectangle are:
Length= 12 ft
Width= 25 ft
To solve for the dimensions of the rectangle with an area of 300 square feet and a length one foot more than twice its width, you begin with the formula for the area of a rectangle. After setting up the quadratic equation, solving it yields a width of 10 feet and a length of 21 feet, making the dimensions 10 feet by 21 feet.
Explanation:To find the dimensions of a rectangle where the length is one foot more than twice its width, and the area is 300 square feet, you set up two equations based on the given information.
Let the width be w feet. Then, the length l would be 2w + 1 feet. The area A of a rectangle is given by the formula A = w × l. Substituting the known area and the expression for l, we have 300 = w × (2w + 1).
To solve for w, we should solve the quadratic equation w^2 + w - 150 = 0. Factoring the quadratic, we get (w - 10)(w + 15) = 0. This gives us two possible solutions for the width: w = 10 or w = -15. Since a negative width doesn't make sense in this context, we use w = 10 feet. The length is thus 2 × 10 + 1 = 21 feet.
Therefore, the dimensions of the rectangle are 10 feet by 21 feet.
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At a malt shop 8/10 of the malts sold were chocolate. What percent of malts sold were chocolate?
Answer: 80 %
Step-by-step explanation: take it and multiply by ten to get 80/100 then turn to percent to get 80%
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Answer:
80%
Step-by-step explanation:
8 divided by 10 is .8
.8 is equal to 80%
Mr. Duncan mixed 0.00055 pounds of sulfur and 0.00104 pounds of iron powder in a test tube before heating it. What is the total weight of the mixture in the test tube?
Answer:
1.59 × 10-3 pounds
Step-by-step explanation:
Add the weights of the sulfur and iron powder to find the total weight of the mixture.
First, write both numbers in scientific notation.
Now that both numbers are written in scientific notation, compare the exponents. Since both exponents are not the same, rewrite 5.5 × 10-4 as 0.55 × 10-3. Now the numbers multiplied by the powers of 10 can be added while keeping the power of 10 the same.
So, the total weight of the mixture in the test tube is 1.59 × 10-3 pounds.
–2(g − 13) + 15 = 1
how do you do this
Answer:g=20
Step-by-step explanation:
-2g+26+15=1
-2g+41=1
-2g=1-41
-2g=-40
-40/-2= 20
Answer:
20=g
Step-by-step explanation:
-2g--26+15=1
-2g+26+15=1
-15 -15
-2g+26= -14
-26 -26
-2g= -40
-40/-2
g=20
The following examples illustrate the commutative property of multiplication.
5 · 2 · 9 = 2 · 5 · 9
Study the examples, then choose the statement that best describes the property.
a · b = a ÷ b
a · (b · c) = (a · b) · c
a · b = b · a
a · b = a · c
The statement that best describes the property is a · b = b · a.
What is commutative property?The commutative property of multiplication states that if there are three numbers x, y, and z, then x × y × z = z × y × x = y × z × x or another possible arrangement can be made.
If you observe the given equation, you will find that the commutative property can be applied. If x = 131, and y = 56 and z = 72, then we know that 131 x 56 x 72 = 72 x 131 x 56.
Given statement:
5 · 2 · 9 = 2 · 5 · 9
So, we can see that only the place has been changed
So, it is commutative property
Hence, the correct statement is a · b = b · a
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2.13 x 10^24 molecules of water is how many moles of water?
Answer:
1 mole of anything = 6.023 * 10^23
2.13 * 10^24 divided by 6.023 * 10^23 =
3.54 moles
Step-by-step explanation:
What are the zeros of f(x) = x2 + 2x - 80?
-20 and 4
®
-4 and 20
-10 and 8
-8 and 10
Answer:
The zeros are 8 and -10, all u have to do is substitute x for those values, factor it, or graph it.
The zeros of f(x) = x2 + 2x - 80 are -10, 8
What is Mathematical function ?
Function is defined as the expression or relation between any given two variables such as x and y and there must be an independent variable and dependent variable.
In other words the function represents the graph between x and y that is for each value of x there exist one value of y but here there is no restriction in values of y that is y can have infinity values.
zero's are nothing but the roots of the equation which by putting in the equation gives zero value.
Given equation is f(x) = x^2 + 2x - 80 solving it to find the zero's by factorization :
f(x) = x^2 + 2x - 80
f(x) = x^2 + 10x-8x - 80
f(x) = x(x+10)-8 (x + 10)
f(x) = (x+10)(x-8)
Now equating it to zero we get
x= -10, 8
Therefore, the zeros of f(x) = x2 + 2x - 80 are -10, 8
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If an elevator traveled 70 meters in 1/2 minutes how many km/h was it going?
Answer:
8400 km/hr
Step-by-step explanation:
70+70= 140 which is for one minute. Multiple 140 by 60 (60 min in a hour) to get 8400
Answer:
7.14 km/h
Step-by-step explanation:
find out how many meters per minute it is going.
70×2 =140
140 meters per minute
THere are 1000 meters in one kilometer so you would do 1000÷140.
THe answer for 1000÷140 is 7.142, your final answer.
a tugboat traveled 1.5 miles in 0.3 hours what is its velocity
Answer:
5 mph
Step-by-step explanation:
1.5miles/.3 hours =
5 miles/hour =
5 mph
The is its velocity 5 mph
What are velocity and example?In simple phrases, speed is the velocity at which something actions in a selected path. For example, the velocity of an automobile journeying north on a motorway, or the rate a rocket travels after launching.
The rapidity of movement or operation; swiftness; speed: a high wind velocity. Mechanics, the time fee of exchange of function of a body in a unique route. The rate of pace with which something occurs; rapidity of action or reaction.
1.5miles/.3 hours
=5 miles/hour
=5 mph
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What is the solution to the system of equations below?
y = three-fourths x minus 12 and y = negative 4 x minus 31
(–4, –15)
(–4, –12)
(4, –9)
(4, –47)
Answer:
A
Step-by-step explanation:
did the test
The required solution for the equations is (-4,-15).
y = 3/4x-12 and y = -4x-31 Solution for both the equation to be determine.
Solutions of equation hat points where both the equation terminate to zero or the I've same value.
y = 3/4x-12 ------(1)
y = -4x-31 ------(2)
Put y from 2 in equation 1
-4x-31= 3/4x-12
19/4x=19
x = -4
Now put this x in equation 2
y = 16-31
y = -15
Thus, the required solution for the equation is (-4,-15).
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Vlad tried to solve an equation step by step.
\qquad\begin{aligned} -8p+14&=42\\\\ \\ -8p&=28&\green{\text{Step } 1}\\\\ \\ p&=-3.5&\blue{\text{Step } 2}\\\\ \end{aligned}
−8p+14
−8p
p
=42
=28
=−3.5
Step 1
Step 2
Answer:
Vlad did not make a mistake
Step-by-step explanation:
Simplify.
3+ (-2) • 6
Step-by-step explanation:
[tex]3 + ( - 2) \ast6 \\ = 3 + ( - 2 \times 6) \\ = 3 + ( - 12) \\ = 3 - 12 = - 9[/tex]
A satellite is 6,000 miles from the horizon of Earth. Earth’s radius is about 4,000 miles. Find the approximate distance the satellite is from the point directly below it on Earth’s surface. The diagram is not to scale.
Answer:
3211 miles
Step-by-step explanation:
A right triangle can be used to model the geometry of the problem. One leg of it is the radius of the Earth. The leg at right angles to that is the satellite-to-horizon distance of 6000 miles. The hypotenuse of the triangle is the distance from the satellite to the center of the Earth, so the question will be answered by subtracting the Earth radius from that.
The Pythagorean theorem relates the various distances. Refer to the attachment.
AB² = AD² +BD²
(BC +4000)² = 4000² +6000² . . . . . . . . . . . . use given values
BC +4000 = 1000√(4² +6²) = 2000√13 . . . . take the square root
BC = 2000(√13 -2) . . . . . subtract 4000
BC ≈ 3211.1
The satellite is about 3211 miles from the point directly below it.
-53 + n = -28 solve for n
Answer:
n will be equal 25
Step-by-step explanation:
-53 + n = -28
collect like terms, and we will have
n = -28 + 53
n = 25
Answer: n = -25
Since, -23 + -25 = -53
Given: f(x)=-2x+2 and g(x)=4x+8 which table set up is correct to solve the equation f(x)=g(x)
The solution to f(x) = g(x) is x = -1.
To find the value of x that satisfies the equation f(x) = g(x), we set the two
functions equal to each other and solve for x.
This gives us the equation -2x + 2 = 4x + 8.
Combining like terms, we get 6x = -6.
Dividing both sides by 6, we find that x = -1.
Therefore, the solution to f(x) = g(x) is x = -1.
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Calculate mean, median, and mode for each set of data. IQ’s: 78, 79, 87, 88, 101, 120, 132
Answer:The median is 88,The mode is none because they all repeat the same. The mean is 97.9
Step-by-step explanation:
Answer
The median is 88. The mode is none because they all repeat the same. The mean is 97.9
Step-by-step explanation:
multiply 13 x 7/9 answer this question as a simplified mixed number
Answer:
13 x 7/9 = Its about 10.11
Step-by-step explanation:
Answer:
10 1/9
13 x 7/9 = 91/9 or 10 1/9 in simplest form
The x-intercept of a function y = f(x) are the real solutions of the
equation f(x) = 0.
The given statement "The x-intercept of a function y = f(x) are the real solutions of the equation f(x) = 0." is True because the x-intercepts of a function y = f(x) are points on graph where function crosses x-axis.
At these points, the value of y (f(x)) is equal to 0. In other words, the x-intercepts are the real solutions of the equation f(x) = 0.
To find the x-intercepts of a function, we set f(x) equal to 0 and solve for x. The solutions to this equation will be the x-coordinates of the x-intercepts.
For example, given the function y = 2x - 6, to find the x-intercept, we set y (f(x)) equal to 0:
0 = 2x - 6
Now, solve for x:
2x = 6
x = 6 / 2
x = 3
The x-intercept is (3, 0) since at x = 3, the value of y (f(x)) is 0.
In conclusion, the statement is true. The x-intercepts of a function y = f(x) are the real solutions of the equation f(x) = 0.
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Find the slop for each ordered pair
Answer: Slope between two points equation is y2-y1/x2-x1
Step-by-step explanation:
A circular hedge surrounds a sculpture on a square base. The radius of the hedge is 6x. The side length of the square sculpture base is 4x. What Is the area of the hedge? Write your answer in factored form.
Answer:14
Step-by-step explanation:
luna wants to know what proportion of 7th graders at her school are interested in taking art classes.which Is the best group to survey to find this information?
Answer: Ask every 12th person who leaves school one afternoon.
Roll dice to determine which person to ask first.
Answer: Ask every 12th person who leaves school one afternoon.
Roll dice to determine which person to ask first.
Step-by-step explanation:
What is the slope of the line represented by y = 1 - 8x?
Answer:
It’s -8
Step-by-step explanation:
Just the number multiplied by x if we have the form y=ax+b or y=b+ax
The slope of a line is represented by the coefficient of the x term in the equation. In the equation y=1−8x, the coefficient of the x term is −8. Therefore, the slope of the line is −8.
Another way to think about the slope of a line is to imagine that the line is a hill. The slope of the hill tells you how steep it is. A positive slope means that the hill is going up, while a negative slope means that the hill is going down. A steeper slope means that the hill is rising or falling more quickly.
In the case of the line y=1−8x, the slope is −8, which means that the line is going down very steeply. For every 1 unit that you move to the right on the x -axis, you move 8 units down on the y -axis.
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what is 6 and 2 thirds minus 2 and 4 fifths?
Answer:
58/15
Step-by-step explanation:
Step 1: Convert words into an expression
6 and 2 thirds minus 2 and 4 fifths
6 2/3 - 2 4/5
Step 2: Make common denominator aka 15
6 2/3 = 6*3/3 + 2/3 = 18/3 + 2/3 = 20/3
20*5 / 3*5 = 100/15
2 4/5 = 2*5/5 + 4/5 = 10/5 + 4/5 = 14/5
14*3 / 5*3 = 42/15
Step 3: Subtract
100/15 - 42/15
58/15
Answer: 58/15
The third term of an arithmetic sequence is -8, and the fourth term is -20. What is the second term?
Answer:
the answer is 6
Step-by-step explanation:
In mathematics, an arithmetic progression or arithmetic sequence is a sequence of numbers such that the difference between the consecutive terms is constant. so -20 + 14 is -8 so you just have to add 14 again to -8 to get 6
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Is –9 + –97 positive or negative?
A) Positive
B) Negative
Answer:
B) Negative
Step-by-step explanation:
–9 + –97
= –9 + (–97)
= –9 - 97
= -106 (negative number)
A soccer goal is 24 feet wide. Point A is 40 feet in front of the center of the goal. Point B is 40
feet in front of the right goal post.
a) find the measure of ∠A and ∠B
b) which angle is larger, ∠A or ∠B?
c) from which point would you have a better chance of kicking the ball into the goal? Why?
Answer:
a) Angles A and B are 90 degree.
b) The 2 angles are equal
c) From point A having a better chance to kicking the ball in to goal
Step-by-step explanation:
a, b) 2 points are in front of the center and right post of goal. Because there is no detail, we can assume that point A, point B, center of goal, right goal post make up a rectangle. Therefore, the 2 angles are measured equally as 90 degree.
c) Because it's a rectangle, the distance between point A and center of goal is shorter than that between point B and center of goal.
To determine the measures of ∠A and ∠B and identify which is larger, trigonometry is used based on the geometry of the soccer goal and the distances given. ∠A is associated with a larger shooting angle and a better chance of scoring compared to ∠B.
Explanation:The situation presents a geometry problem involving a soccer goal and positions A and B. To find the measure of ∠A and ∠B, we can visualize the scenario as two triangles with a common side, the 24-foot width of the goal. The distance from the center of the goal to both points A and B is 40 feet. We can use trigonometry to solve for the angles.
For ∠A, we have a right triangle where the width of the goal forms one leg (half is 12 feet, as it is from the center), and 40 feet is the hypotenuse. Applying the cosine function:
cos(∠A) = adjacent / hypotenusecos(∠A) = 12 / 40
Calculating this gives ∠A.
For ∠B, the full width of the goal (24 feet) is the adjacent side of the right triangle, and 40 feet again is the hypotenuse. Therefore:
cos(∠B) = adjacent / hypotenusecos(∠B) = 24 / 40
Calculating this gives ∠B.
Comparing the cosine values will indicate which angle is larger, since a smaller cosine correlates with a larger angle.
From which point would you have a better chance of scoring a goal? Since ∠A is larger, it represents a wider view of the goal, suggesting that kicking the ball from Point A provides a better chance of scoring because you see more of the goal, giving you a larger target area to aim at. This is an application of the concept of shooting angles in soccer.
A large bench is 7 feet long. It is 17 inches longer than a shorter bench. How many inches long is the shorter bench?
Answer:
67 in
Step-by-step explanation:
Convert 7bft to inches by multiplying by 12
Then subtract 17.
Russel wants to buy three ties and a belt and must spend no more that $80. The belt costs $28.50. If three ties are the same price, then how much can he pay for each tie?
Answer:
About $17.16
Step-by-step explanation:
$80-$28.50= 51.5
Then you divide that by 3 (for the 3 ties)
Russel can spend a maximum of $17.17 on each tie after accounting for the cost of the belt.
To determine how much Russel can spend on each tie, we first need to account for the cost of the belt. The belt costs $28.50 and Russel's total budget is $80. Therefore, the remaining amount for the ties is $80 - $28.50 = $51.50.
Since Russel wants to buy three ties, we need to find the maximum price he can pay for each tie. We can do this by dividing the remaining budget by the number of ties:
$51.50 / 3 = $17.17
Therefore, Russel can spend a maximum of $17.17 on each tie.
A cube has a length, width and height of 6 feet. What is the volume in cubic INCHES?
Answer:
Step-by-step explanation:
Answer: (6)(6)(6) 216
Step-by-step explanation:
the base is 6 and a cube has all equal sides so you multiply 6, 3 times because the equation for volume is base x height x width. which equals=216
Percy is plotting points on a graph. The ratio of y value to x value is 2 to 3 for each point what will be the x value of a point with y value of 18
Answer: point X would be 27.
I think this because if you ratio is 2:3, y:x the 2x9 is 18, y, and 3x9 is 27, X.
This gives a final ratio of 18:27 which, when reduced by nine is 2:3.
Answer:
Step-by-step explanation:
x = 27
A rectangular box has a width of x meters, length of x + 3 meters, and a height of x – 2 meters. Write an expression for its volume. Remember an expression does NOT have an equal sign
Answer:
x(x+3)(x-2)
Step-by-step explanation:
you can't multiply any of them so the expression is that. x cannot be multiplied with x+3 because x+3 are together.