Answer:
Length = x + 3 ft
Width = x - 3 ft
Area of new patio = x² - 9 sq ft
If original side length = 8, new area = 55 sq ft
Step-by-step explanation:
The original patio has side length of x
If one side is reduced by 3 we get (x - 3) as the new side
If the side is increased by 3' we get (x + 3) as the new side
Area of new Patio = (x - 3)(x+3) = x² - 9
Original patio is 8 x 8
New patio width = 8 - 3 = 5
New patio length = 8 + 3 = 11
Area = 5 x 11 =55 sq ft
The equation, x + 0.06x - 1.50 = 3.80 can be solved using the steps below.
Step 1: (1 + 0.06)x - 1.50 = 3.80
Step 2: 1.06x - 1.50 = 3.80
Step 3: 1.06x = 5.30
Step 4: x = 5.00
Match each step with the correct property used.
Associative property
Substation property
addition property of equality
division property of equality
distributive property
commutative property
The properties in each step is:
Step 1 and 2: distributive property
Step 3: addition property of equality
Step 4: division property of equality
How to Apply the Property of Equality?Given the equation, x + 0.06x - 1.50 = 3.80, we can solve for x using the steps with the following appropriate properties shown below:
Step 1:
(1 + 0.06)x - 1.50 = 3.80 (distributive property)
Step 2:
1.06x - 1.50 = 3.80 (distributive property)
Step 3: Add 1.50 to both sides of the equation
1.06x = 5.30 (addition property of equality)
Step 4: Divide both sides by 1.06
x = 5.00 (division property of equality)
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What is the slope of the line passing through the points
(2,5) and (4, 1)?
Answer:
-2
Step-by-step explanation:
Slope = rise/run
[tex]\mathrm{Slope} = \frac{y_2-y_1}{x_2-x_1}\\m=\frac{1-5}{4-2}\\1 - 5 = -4\\4 - 2 = 2\\=\frac{-4}{2}\\ =-2[/tex]
A handyman company serves customers from two cities 60 miles apart, Jonesville and Bellevue. The company would like to position a new office between the two cities using weighted averages based on the typical number of calls received from each city. If Jonesville has a weight of 3 and Bellevue has a weight of 5, how far from Bellevue should the office be located?
_____ miles.
It should be noted that the distance of
Bellevue from the office be located will be 13.85 miles.
How to illustrate the information?It should be noted that based on the information, the handyman company serves customers from two cities 60 miles apart, Jonesville and Bellevue and the vompany would like to position a new office between the two cities using weighted averages based on the typical number of calls received from each city.
From the information, Jonesville has a weight of 3 and Bellevue has a weight of 5, the distance of
Bellevue from the office be located will be:
= (0 × 5 + 60 × 4) / (5 × 8)
= 180 / 13
= 13.85
The office should be 13.85 miles from Bellevue.
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40 points!!!
Simplify 5 - 2 · 3 + 4.
-5
21
13
3
Answer:
3
Step-by-step explanation:
Parenthesis
Exponents
Multiplication
Division
Addition
Subtraction
5-2*3+4 First multiply.
5-6+4 Now do addition or subtraction what comes first, from left to right.
-1+4 =
3
Determine whether each set of numbers can be the measures of the sides of a triangle. If so, classify the triangle as acute, obtuse, or right. Justify your answer.
16,18,26
Yes, the given set of numbers can be the measures of the sides of a triangle. The triangle is acute.
By the triangle inequality theorem, the sum of the lengths of any two sides should be greater than the length of the third side.
16 + 18 > 26
18 + 26 > 16
26 + 16 > 18
Hence, these set of numbers can be the measures of the sides of a triangle.
According to the Pythagorean Inequality Theorem, a triangle whose sides measure a, b, and c where c is the largest, the triangle can be characterized as:
acute if [tex]a^{2} + b^{2} < c^{2}[/tex]
obtuse if [tex]a^{2} + b^{2} > c^{2}[/tex]
right if [tex]a^{2} + b^{2} = c^{2}[/tex]
∴The longest side is 26.
Hence, a = 16, b = 18 and c = 26;
Consider [tex]a^{2} + b^{2[/tex] :
= [tex]16^{2} + 18^{2}[/tex]
= 580.
Now consider [tex]c^{2}[/tex] :
= [tex]26^{2}[/tex]
= 676.
Thus, [tex]a^{2} + b^{2} < c^{2}[/tex].
Hence, the triangle is acute.
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If f(x) = -3x - 5 and g(x) = 4x - 2, find (f+ g)(x). PLEASE HELP!!!
Option D) is correct option that is the function , (f + g)(x) = x – 7
Note that if we have been given two functions which are f(x) and g(x) then their addition will be given as
(f + g)(x) = f(x) + g(x) (1)
We have been given the equation as
f(x) = -3x - 5 and g(x) = 4x – 2
putting the required value in equation (1) we get
(f + g)(x) = (-3x-5) + (4x-2)
(f + g)(x) = -3x – 5 + 4x – 2
(f + g)(x) = x – 7
Thus option D) is the correct option that is the function, (f + g)(x) = x – 7
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Which ordered pairs are solutions to the inequality y−3x<10?
(0,-4) , (0,-1) , (4,-1) are the ordered pairs are solutions to the inequality
y − 3x < 10 which is option (A) , (D) and (E) .
An inequality compares two values and indicates whether one is less than, greater than, or equal to another. a ≠ b indicates that a is not equal to b a < b indicates that a is less than b a > b indicates that a is greater than b (These two are known as strict inequalities) a ≤ b means that a is less than or equal to b a ≥ b means that a is greater than or equal to b.
We have to check whether the given options are the solutions to the inequality y− 3x < 10 . ...(1)
(A) If (0,-4) is the solution of given inequality y− 3x < 10 then it must satisfy the equation .
Putting x = 0 and y = -4 in equation (1) , we get
[tex]-4-3(0) < 10\\-4 < 10[/tex]
As the above condition is true so (0,-4) is the solution of given inequality
(B) If (-6,0) is the solution of given inequality y− 3x < 10 then it must satisfy the equation .
Putting x = -6 and y = 0 in equation (1) , we get
[tex]0-3(-6) < 10\\18 < 10[/tex]
As the above condition is not true so (-6,0) is not the solution of given inequality .
(C) If (-1,7) is the solution of given inequality y− 3x < 10 then it must satisfy the equation .
Putting x = -1 and y = 7 in equation (1) , we get
[tex]7-3(-1) < 10\\7+3 < 10\\10 < 10[/tex]
As the above condition is not true so (-1,7) is the not the solution of given inequality .
(D) If (0,-1) is the solution of given inequality y− 3x < 10 then it must satisfy the equation .
Putting x = 0 and y = -1 in equation (1) , we get
[tex]-1-3(0) < 10\\-1 < 10[/tex]
As the above condition is true so (0,-1) is the solution of given inequality.
(E) If (4,-1) is the solution of given inequality y− 3x < 10 then it must satisfy the equation .
Putting x = 4 and y = -1 in equation (1) , we get
[tex]-1-3(4) < 10\\-1-12 < 10\\-13 < 10[/tex]
As the above condition is true so (4,-1) is the solution of given inequality.
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Which number line best shows how to solve −4 − (−6)?
Answer:
D
Step-by-step explanation:
You want to find the number line that shows the solution to -4 -(-6).
Number line operationsThe first number in the "sum" is -4, so the first arrow on the number line should go from 0 to -4. (All choices show that.)
The second number is -6. Addition of -6 would create an arrow from -4 going 6 units to the left. Subtraction works in the opposite direction, so the subtraction of -6 will show as an arrow from -4 extending 6 units to the right. Only answer choice D shows this.
__
Additional comment
You know the solution is -4 -(-6) = -4 +6 = +2, so the graph showing the solution will have an arrow ending at +2. This eliminates all answer choices except the correct one.
<95141404393>
Solve for y.
A. 12
B. 13.5
C. 9
D. 10.5
Answer: C
Step-by-step explanation:
180° = 96° + 8y + 12
180° = angles on a straight line
180 - 96 - 12 = 8y
8y = 180 - 96 - 12
8y = 72
y = 72 / 8
y = 9
A not allowed
The students in a class were asked whether they preferred basketball,
netball or floorball. The ratio of students who preferred basketball to netball
to floorball was 10:9: 6. What percentage of students preferred netball?
Watch video
Answer>
Based on the given conditions, formulate: 9÷(6+10+9)
Calculate the sum or difference: 9/16+9
Calculate the sum or difference:9/25
Multiply a number to both the numerator and the denominator:9 x 4/25 x 4
Calculate the product or quotient: 36/100
Rewrite a fraction with denominator equals 100 to a percentage is 36%
therefore the percentage of the students preferred netball is 36%.
In mathematics, a percentage is a number or ratio that can be expressed as a fraction of 100. If we have to calculate percent of a number, divide the number by the whole and multiply by 100. Hence, the percentage means, a part per hundred. The word per cent means per 100.One percent is one hundredth of a whole. It can therefore be written as both a decimal and a fraction. To write a percentage as a decimal, simply divide it by 100. For example, 50% becomes 0.5, 20% becomes 0.2, 1% becomes 0.01 and so on.Percentages are used widely and in many different areas. For example, discounts in shops, bank interest rates, rates of inflation and many statistics in the media are expressed as percentages. Percentages are important for understanding the financial aspects of everyday life.to know more about percentage ;
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plsss helppp meeee i have more questions toooo
Answer:
you should use subtraction to solve this problem
Antonio spent 1/2 hours longer at soccer practice then baseball practice
Step-by-step explanation:
9/10-2/5
9/10-4/10
=
5/10 or 1/2
-1.4 + (-1.2) thanks
Answer:
-2.6
Step-by-step explanation:
Refer to ®N . Identify each.
b. a diameter
The diameter is the length of the line passing through the center and touching two points on the circle's edge.
What is the diameter?In geometry, a circle's diameter is any straight line segment that passes through the center of the circle and has endpoints on the circle. It is also referred to as the circle's longest chord. Both definitions apply to a sphere's diameter.
The diameter is defined as the length of a line passing through the center and touching two points on the circle's rim.
A circle's diameter extends from one side to the other, with its midpoint in the center. Divide the radius of the circle by two to get the diameter.
A circle's diameter divides the shape in half. The radius of a circle is half the length of its diameter (or, conversely, the diameter of a circle is twice the length of its radius).
The complete question is:
Identify each
b. a diameter
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What is the image of the point (3,4)(3,4) after a rotation of 90^{\circ}90 ∘ counterclockwise about the origin?
The image of the point (3,4)(3,4) after a rotation of 90^{\circ}90 ∘ counterclockwise about the origin is (-3,4).
What is meant by the image of the points?A point's reflection
The mirror's "reflection" of the specified point P causes it to appear at an equal distance away on the other side of the line. To view this, move the point P. According to tradition, the "image" of point P is the reflection of point P across the line, which is designated by the term P' (pronounced "P prime").
As the rotation is counterclockwise around the origin,
the coordinates of the image will be - (-3,4)
The graph is attached at the end of the solution.
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Answer:
-4, 3
Step-by-step explanation:
Find the sum.
2
3
+
1
5
Answer:
23+15 or 2/3+1/5
Step-by-step explanation:
23+15=48
2/3+1/5= 13/15
Add all numerators above the least common denominator then add the numbers
Shaquana has a points card for a movie theater.
She receives 40 rewards points just for signing up.
• She earns 13.5 points for each visit to the movie theater.
• She needs 175 points for a free movie ticket.
How many visits must Shaquana make to earn a free movie ticket?
What is the conclusion of the given conditional
statement.
If it is a Thanksgiving, then we are not in
school.
Answer:
we are not in school
Step-by-step explanation:
Conditional: If it is a Thanksgiving, then we are not in school.
Hypothesis: If it is a Thanksgiving, then we are not in school.
Conclusion: If it is a Thanksgiving, then we are not in school.
Answer: we are not in school
i’m doing my geometry homework with the equation 1/2h(b1+b2) but i can’t figure this one out. please help
Answer:
Step-by-step explanation:
to find the bottom base you add the two numbers that make it
5+18=23
now put everything in the formula
[tex]\frac{1}{2}*12(12+23)\\[/tex]
parathesis first
12+23=35
[tex]\frac{1}{2} *12*35[/tex]
multiply in order
6*35
210
Step-by-step explanation:
i’m doing my geometry homework with the equation 1/2h(b1+b2) but i can’t figure this one out. please help
1/2h (b1 + b2) is the formula for finding the area of the figure (trapezoid)
1/2 * 12 (18 + 5 + 12)=
6 * 35=
210 units²
−
7
4
p+(−
7
2
p)+
7
1
1
Answer: god please help the world
Step-by-step explanation: we are struggling
Answer: -6/7p+1/7
Step-by-step explanation: thank god I'm smart lol... I'm a big brain!!!
i don’t know how to do this
The perimeter of a square is 4 times as
great as the length of any of its sides.
Determine if the perimeter of a square is proportional to its side length. Explain.
Answer:
Perimeter of a square is proportional to side length
Step-by-step explanation:
We have the relation p = 4a, p = perimeter, a = side length
This is the equation for a proportionate relationship of the form y = k.x where y ∝ x , y directly proportional to x => y varies as x varies and always by the same constant
k is known as constant of proportionality
Here k = 4
Let's say the side of square is 1. Then perimeter = 4
If side is increased to 2, then perimeter = 4 x 2 = 8
If side is increased to 3, then perimeter is 4 x 3 = 12
So perimeter increases by a factor of 4 for every unit increase in side length
5/9 (d - 12) = 10 A linear equation is shown above. Which of the following values of d is a solution to the equation?
For the given equation, the value of d = 30
How to solve an equation?To solve linear equations, utilize the steps that are provided below. Remove parenthesis from either side of the equation and combine similar phrases to make it simpler. To separate the variable term on one side of the equation, use addition or subtraction. To find the variable, use division or multiplication.
Divide both sides of the equation by the coefficient of variable: d-12 = 10÷ 5/9
Divide a fraction by multiplying its reciprocal: d 9 -12=10 x 9/5
Write as a single fraction: d-12 = (10 x 9) / 5
Calculate the product or quotient: d-12= 90 / 5
Reduce fraction to the lowest term by canceling the greatest common factor: d-12 = 18
Rearrange unknown terms to the left side of the equation: d=18+12
Calculate the sum or difference: d=30
Answer: d=30
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(k^2-5k-2)(k^2+2) polynomial in standard form
Answer:
[tex]K^{4} -5k^{3} -10k-4[/tex]
Step-by-step explanation:
How do I find angle x?
The value of x is 280
How to determine the angleFrom the information given, we have that;
Angle at the circumference = xAngle at the center = 140It is important to note that, the angle subtended by an arc at the center is twice the angle subtended at the circumference.
Example;
If AOB is the angle at the circumference and ACB is the angle at the center
Then, we have that;
Angle AOB = 2 × Angle ACB
2(140) = x
expand the bracket
x = 280
Thus, the value of x is 280
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30 POINTS!!!!
A linear function is shown on the graph.
a linear function beginning with closed circle at 2 comma 0 and ending with a closed circle at 9 comma 7
What is the domain of the function?
{x | 2 < x < 9}
{x | 2 ≤ x ≤ 9}
{y | 0 < y < 7}
{y | 0 ≤ y ≤ 7}
The domain of the function is {x | 2 ≤ x ≤ 9}
What is the domain of a function?The domain of the function is the set of input values of the graph
How to determine the domain of the function?The given parameters are
A linear function begins with closed circle at (2,0) and ends with a closed circle at (9,7)
This is represented as
(x, y) = Closed (2, 0)
(x, y) = Closed (9, 7)
Remove the y values to determine the domain
x = Closed 2
x = Closed 9
The closed statement represents the inequality ≤
So, we have
2 ≤ x ≤ 9
Hence, the domain of the function is {x | 2 ≤ x ≤ 9}
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Answer:
B. {x | 2 ≤ x ≤ 9}
Step-by-step explanation:
Which of the following situations could be represented by a graph with a y-intercept of -8?
A. Hal bought $8 worth of supplies, then sold x buttons for $3 each. His profit is y dollars.
B. Mr. May has 3 sticks left, and each student needs 8 sticks to make their craft project. There are x students, and they need y sticks in all.
C. Kim ran 3 laps clockwise and 8 laps counterclockwise, for a total of 5 miles of the track. The track is x miles long and she ran a total of y laps.
D. Jian bought 8 packs of paper and sold 3 origami swans. His current profit is -$5. A pack of paper costs x dollars and he sells the swans for y dollars.
The situation given that can be represented by a graph with a y-intercept of -8 is A. Hal bought $8 worth of supplies, then sold x buttons for $3 each. His profit is y dollars.
How to use the y-intercept?The y-intercept is a figure in the linear equation that shows the original number of units before the value of x either started to increase or to decrease and therefore cause a change in x.
The situation where Hal bought $8 worth of supplies would be represented by the y-intercept of -8 because the $8 that Hal bought represents his total profit before he sells anything. That total profit is -8 because Hal has spent -$8 but has not sold anything.
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Roxy and Randy are selling pancake breakfast plates to raise money for a class trip.
Roxy is selling plates for $5.00 and has already raised $175. Randy is selling plates for $3.50 and has already raised $250.
Which equation can be used to nd p, the number of plates that Roxy and Randy must sell so that the total amount raised is the same for both Roxy and Randy?
The total amount raised is the same for both Roxy and Randy if they sell 50 Plates.
Let the number of plate = 'p'
Roxy :
Selling price of plates = $5.00
Raised = $175
Total plates sold = 5.00p
Total amount raised = 5.00p + 175 ...eq.(1)
Randy :
Selling price of plates = $3.50
Raised = $250
Total plates sold = 3.50p
Total amount raised = 3.50p + 250 ...eq.(2)
Now we will equate the eq.(1) and eq.(2) to find the same amount raised by both Roxy and Randy ,
5.00p + 175 = 3.50p + 250
5.00p - 3.50p =250 - 175
1.5p = 75
p = 75/1.5
p = 50
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Simplify the expression.
6-5 / 4-2
The simplified expression for (6-5 / 4-2) is 1/2 .
The given expression is,
6-5 / 4-2
First we need to solve the numerator which is (6-5) and on simplifying the numerator we can write,
Numerator = ( 6 - 5 ) = 1 equation 1
Similarly, now we can proceed to solve the denominator which is (4 - 2) and on simplifying the denominator we write,
Denominator = (4 - 2) =2 equation 2
Now we can substitute the value of numerator and the denominator from equation 1 and equation 2 in the given expression (6-5 / 4-2) as,
(Numerator / Denominator) = (6-5 / 4-2) = 1/2
The simplified expression for (6-5 / 4-2) is 1/2 .
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In this problem, you will investigate the relationships among three points of concurrency in a triangle.
a. Draw an acute triangle and find the circumcenter, centroid, and orthocenter.
Construct an acute triangle and find the centroid (medians), circumcenter (perpendicular bisectors), and orthocenter (altitudes). Take note of how these three centers interact with one another from the figure.
What are acute triangles?
An acute angle triangle (also known as an acute-angled triangle) is a triangle with all of its interior angles being acute angles. Remember that an acute angle is one that is less than 90°.
A triangle with three acute angles is known as an acute triangle. An obtuse triangle has one obtuse angle and two acute angles. Because the angles of a triangle in Euclidean geometry must sum to 180°, no Euclidean triangle can have more than one obtuse angle.
Construct an acute triangle and find the centroid (medians), circumcenter (perpendicular bisectors), and orthocenter (altitudes). Take note of how these three centers interact with one another from the figure.
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Translate each sentence into an equation.
1. The sum of three times a and four is the same as five times a.
2. One fourth of m minus six is equal to two times the sum of m and 9.
3. The product of five and w is the same as w to the third power.
Translate each sentence into an equation. which are as follows the value of a is 2, the value of m is 13.71 and the value of w is the root of 5.
1. The sum of three times a and four is the same as five times a.
3a+4 = 5a
3a = 5a -4
4 = 5a-3a
4= 2a
2 =a
2. One-fourth of m minus six is equal to two times the sum of m and 9.
1/4m - 6 = 2 (m+9)
1/4m = 2m +18+6
1/4m = 2m + 24
2m -1/4 m = -24
7/4 m = -24
m = -24*4/7 = 13.71
The value of m is 13.71
3. The product of five and w is the same as w to the third power.
5*w = w.w.w
5 = w.w.w/w
5 = w.w
root of 5 = w
The value of w is the root of 5
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