An expression can be used in algebra to represent a value, and that value may rely on the values given to the variables that appear in the expression.
If the expression be (-3)(-9) then the value of (-3)(-9) is 27.
What is an expression?A mathematical expression is a finite combination of symbols that is well-formed in accordance with context-specific norms.In order to help establish the order of operations and other elements of logical syntax, mathematical symbols can be used to represent numbers (constants), variables, operations, functions, brackets, punctuation, and grouping.An expression can be used in algebra to represent a value, and that value may rely on the values given to the variables that appear in the expression.Let (-3)(-9) be the given expression
We know the rule , (-) × (-) = (+)
(-3) × (-9) = +27
Therefore, the value of (-3)(-9) is 27.
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Evaluate a + b for a = 2 and b = 3.
06
5
<
01
C
Answer:
5
Hope this helps :)
Step-by-step explanation:
1. Solve by adding since a = 2 and b = 3.
2 + 3 = 5
Check:
5 - 3 = 2 ✓
(1/2a+2d)^2 = bao nhieu
Hi ~
﹌﹌﹌﹌﹌﹌﹌﹌﹌﹌﹌﹌﹌﹌﹌﹌﹌﹌﹌
* ˚ ✦ E x p l a n a t i o n : - * ˚ ✦
Combine multiplied terms into a single fraction.
[tex]\bold{(\frac{1}{2} \: a \: + \: 2d)^2}[/tex]
[tex]\bold{(\frac{1a}{2} \: + \: 2d)^2}[/tex]
﹌﹌﹌﹌﹌﹌﹌﹌﹌﹌﹌﹌﹌﹌﹌﹌﹌﹌﹌﹌﹌﹌﹌
Multiply by 1.
[tex]\bold{(\frac{1a}{2} \: + \: 2d)^2}[/tex]
[tex]\bold{(\frac{a}{2} \: + \: 2d)^2}[/tex]
﹌﹌﹌﹌﹌﹌﹌﹌﹌﹌﹌﹌﹌﹌﹌﹌﹌﹌﹌﹌﹌﹌﹌
Find common denominator.
[tex]\bold{(\frac{a}{2} \: + \: 2d)^2}[/tex]
[tex]\bold{(\frac{a}{2} \: + \: \frac{2 \: ^. \: 2d}{y})^2}[/tex]
﹌﹌﹌﹌﹌﹌﹌﹌﹌﹌﹌﹌﹌﹌﹌﹌﹌﹌﹌﹌﹌﹌﹌
Combine fractions with common denominator.
[tex]\bold{(\frac{a}{2} \: + \: \frac{2 \: ^. \: 2d}{y})^2}[/tex]
[tex]\bold{(\frac{a \: + \: 4}{2})^2}[/tex]
﹌﹌﹌﹌﹌﹌﹌﹌﹌﹌﹌﹌﹌﹌﹌﹌﹌﹌﹌﹌﹌﹌﹌
Multiply the numbers.
[tex]\bold{(\frac{a \: + \: 2 \: ^. \: 2d}{2})^2}[/tex]
[tex]\bold{\frac{(a \: + \: 4d \: ^. \: 2d)}{2^2}^2}[/tex]
﹌﹌﹌﹌﹌﹌﹌﹌﹌﹌﹌﹌﹌﹌﹌﹌﹌﹌﹌﹌﹌﹌﹌
Distribute exponent.
[tex]\bold{(\frac{a \: + \: 4d}{2}^2)}}[/tex]
[tex]\bold{\frac{(a \: + \: 4d)}{2}^2}[/tex]
﹌﹌﹌﹌﹌﹌﹌﹌﹌﹌﹌﹌﹌﹌﹌﹌﹌﹌﹌﹌﹌﹌﹌
Evaluate the exponent.
[tex]\bold{\frac{(a \: + \: 4d)}{2^2}^2}}[/tex]
[tex]\bold{\frac{(a \: + \: 4d)}{4}^2}}[/tex]
Your answer would be is:
[tex]{\huge{\boxed{\bold{{\rightarrow{\frac{(a \: + \: 4d)}{4}^2}}}}[/tex]
Hope It Helps...
[tex]\textsc{Answer:}[/tex]
TheAestheticGirl
Determine whether the quadrilateral can always, sometimes, or never be inscribed in a circle. Explain your reasoning.
rhombus
Not all rhombus can be inscribed in a circle until the rhombus has four 90º angles which is a square.
A rhombus can only be can be inscribed in a circle. basically the opposite angles there in the rhombus are congruent. if the opposite angles are not supplementary, that rhombus cannot be encircled, while that rhombus had four 90º angles, which means if it is a square, as in general a rhombus has two diagonals that are not equal except square so the endpoints of the shorter diagonal would not be points on the circle.
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explain how to use addition properties to find the value of 6+8+4
Round decimals
What is 8.749 rounded to the nearest tenth?
Answer:
8.7
Hope this helps <3
Have a great day!
Manisha's age is 6 times Rahul's age. After 4 years, Manisha's age will be four times of Rahul's age. Find their present ages.
Answer:
Manisha is 36 and Rahul is 6.
Step-by-step explanation:
Let m = Manisha's current age
Let r - Rahul's current age.
Today:
m = 6r
In for years:
m+ 4 = 4(r + 4) Distribute the 4
m + 4 = 4r + 16 Substitute in 6r for me
6r + 4 = 4r + 16 Subtraction 4r from both sides
2r + 4 = 16 Subtract 4 from both sides
2r = 12 Divide both sides by 2
r = 6 Rahul is 6 Plug 6 for r into either of the two original equations to find Manisha's age.
m = 6r
m = 6(6)
m = 36
Rahul's present age is 6 years, and Manisha's present age is 36 years.
Let's use the letters "M" for Manisha's current age and "R" for Rahul's.
Given information:
1. Manisha's age is 6 times Rahul's age: M = 6R
2. After 4 years, Manisha's age will be four times Rahul's age: M + 4 = 4(R + 4)
We have a system of two equations with two variables. We can use these equations to solve for their present ages.
Equation 1: M = 6R
Equation 2: M + 4 = 4(R + 4)
Substitute the value of M from Equation 1 into Equation 2:
6R + 4 = 4(R + 4)
Distribute the 4 on the right side:
6R + 4 = 4R + 16
Subtract 4R from both sides:
2R + 4 = 16
Subtract 4 from both sides:
2R = 12
Divide by 2:
R = 6
Now that we know Rahul's age (R = 6), we can find Manisha's age using Equation 1:
M = 6R = 6 × 6 = 36
So, Manisha is 36 years old and Rahul is 6 years old at the moment.
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Two suitcases are similar rectangular prisms. The smaller suitcase is 68 centimeters long, 47 centimeters wide, and 27 centimeters deep. The larger suitcase is 85 centimeters long.
b. What is the volume of the larger suitcase? Round to the nearest tenth.
The volume of the larger suitcase, a rectangular prism 85 centimeters long, is 168,539.1 cubic cm.
Solids of the same type that have proportional corresponding linear
measures are similar solids. In the case of similar rectangular prisms:
length of A / length of B = width of A / width of B = height of A / height of B
Using this scale, if the larger suitcase is 85 centimeters long, and the smaller suitcase is 68 centimeters long, 47 centimeters wide, and 27 centimeters deep, then:
length of larger suitcase / length of smaller suitcase = 85 cm / 68 cm = 5/4
width of larger suitcase / width of smaller suitcase = 5/4
width of larger suitcase = 5/4 (47 cm)
width of larger suitcase = 58.75 cm
depth of larger suitcase / depth of smaller suitcase = 5/4
depth of larger suitcase = 5/4 (27 cm)
depth of larger suitcase = 33.75 cm
Solving for the volume of the larger suitcase using the formula for the volume of rectangular prism:
V = lwh
V = 85 cm (58.75 cm) (33.75 cm)
V = 168,539.0625 cubic cm
Rounding off to the nearest tenth.
V = 168,539.1 cubic cm
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Last year, there were 156 pies baked for the bake sale. This year, there were d pies baked. Using d, write an expression for the total number of pies baked in the two years.
The expression for the total number of pies baked in the two years is 156 + d
What are algebraic expressions?Algebraic expressions can be defined as expressions composed of variables, terms, factors, coefficients and constants.
They are also made up of mathematical operations such as division, addition, subtraction, multiplication, etc
From the information given, we have;
156 pies baked for the bake sale for the previous yearThere were d pies baked this yearThe expression is written as;
Total number of baked pies = 156 + d
Thus, the expression for the total number of pies baked in the two years is 156 + d
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The area of the triangular
Answer:
24 [tex]cm^{2}[/tex]
Step-by-step explanation:
a = [tex]\frac{bh}{2}[/tex]
We have the base, we need the height. Use the Pythagorean Theorem
[tex]a^{2}[/tex] + [tex]b^{2}[/tex] = [tex]c^{2}[/tex]
[tex]6^{2}[/tex] + [tex]b^{2}[/tex] = [tex]10^{2}[/tex]
36 + [tex]b^{2}[/tex] = 100 Subtract 36 from both sides
[tex]b^{2}[/tex] = 64
[tex]\sqrt{b^{2} }[/tex] = [tex]\sqrt{64}[/tex]
b = 8
a = [tex]\frac{bh}{2}[/tex]
a =[tex]\frac{6x8}{2}[/tex] =[tex]\frac{48}{2}[/tex] = 24
Please help asap!!!!!
Find the sum. Enter your answer in the box below as a fraction, using the
slash mark (/) for the fraction bar.
37+23/7-2
17 17
Answer:
[tex]6/17[/tex]
Step-by-step explanation:
I assume you want the question in the picture solved as your written question is different but appears to be copied and pasted from the text.
1. When adding fractions the denominator (number on the bottom) must be the same between the two fractions, i.e. having a common denominator. In this case they are already the same, that is, 17 and 17. Just add the top numbers (numerators) together, and leave the denominator the same. So,
[tex]\frac{3}{17} +\frac{3}{17} =\frac{6}{17}[/tex]
fill in the table using function rule.
y=3x-1
Answer:
2; 11; 17; 23
Step-by-step explanation:
when you have an x you plug it in for the y
so
for the first one
you do
y = 3(1) - 1
y = 3 - 1
y = 2
that is the first one
you do this for the next 3 too
y = 3(4) - 1
y = 12 - 1
y = 11
y = 3(6) - 1
y = 18 - 1
y = 17
y = 3(8) - 1
y = 24 - 1
y = 23
those are your answer
For each system, choose the method of solving that seems easier to use. Explain why you made each choice. Solve each system.
3x - y = 5 , y = 4x + 2
By substitution, the solution of the system of equations, 3x - y = 5 and y = 4x + 2, is (-7 , -26).
A system of linear equations is a set of two or more equations which includes common variables. To solve system of equations, we must find the value of the unknown variables used in the equations that must satisfy both equations.
There are three methods that can be used to solve system of linear equations.
1. Elimination
2. Substitution
3. Graphing
Given two linear equations in x and y,
3x - y = 5 (equation 1)
y = 4x + 2 (equation 2)
Use substitution method since the second equation is already expressed in y in terms of x. Substitute the value of y to the first equation.
3x - y = 5 (equation 1)
3x - (4x + 2) = 5
3x - 4x - 2 = 5
Combining all terms containing the variable x on one side and the constants on the other side of the equality, and solve for x.
3x - 4x - 2 = 5
3x - 4x = 5 + 2
-x = 7
x = -7
Substitute the value of x in the second equation and solve for y.
y = 4x + 2 (equation 2)
y = 4(-7) + 2
y = -28 + 2
y = -26
Hence, the solution of the given system of equations is (-7 , -26).
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31. Solve for x.
(4x + 7)°
[2x +5)°
For the equation (4 x + 7)° = (2 x + 5)°, we get the value of x as - 1.
We are given an equation as:
(4 x + 7)° = (2 x + 5)°
We need to solve this equation to find the value of the variable x.
We first will subtract 7 from both the sides:
4 x + 7 - 7 = 2 x + 5 - 7
4 x = 2 x - 2
Now Subtract 2 x from both the sides:
4 x - 2 x = 2 x - 2 - 2 x
2 x = - 2
Divide both sides by 2
2 x / 2 = - 2 / 2
x = - 1
Therefore, for the equation (4 x + 7)° = (2 x + 5)°, we get the value of x as - 1.
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The diagram at right is the floor plan of Randy's apartment. The living room is 15 feet long, and
one of the walls of the bedroom is 10 feet. Homework Help
a. What are the dimensions of the bathroom?
b. Randy's friends are coming to visit him soon. He will not need to clean his bedroom since
he plans to keep his friends out of his bedroom. But he will have to clean the rest of the
house. How much area will he have to clean?
have
Answer:
Step-by-step explanation:
4 and 1 over 7 divided by 2 over 3
(Ignore messy writing I rush myself)
Answer:
6 3/14
Step-by-step explanation:
[tex]4\:1/7 \div 2/3 = 29/7 \div 2/3\\= 29/7 \div 2/3\\= \frac{29*3}{7*2}\\= 87/14\\= 6\:3/14[/tex]
Please Help! Due in 20 minutes
Answers
1.1) So, we're given that 6cm is 15 ft to scale. That means that every 2cm = 5ft. So, the dimensions of her room are 5ft x 10ft.
1.2) In square feet that makes 15 (length*width)
1.3) We want a 3-foot wide couch (1/5 of 15) which means it will be 1/5 of 6cm, which equals 1.2 cm wide.
What is the reciprocal of 1 7/11
Point D is located on line MV. The coordinates of D are (0,−3/4). What ratio relates MD to DV?
If you do solve this can you show your work so I know how to solve problems like this, too?
Point M coordinates: (-6, 3)
Point V coordinates: (2, -2)
If point D is located on the line MV, then the ratio that relates MD to DV is 3 : 1
How to determine the ratio that relates MD to DV?The given parameters are
Point M coordinates: (-6, 3)Point V coordinates: (2, -2)Point D coordinates: (0, -3/4)Calculate the distance between point D and point M using
d = √(x2 - x1)^2 + (y2 - y1)^2
So, we have
MD = √(-6 - 0)^2 + (3 + 3/4)^2
Calculate the distance between point D and point V using
d = √(x2 - x1)^2 + (y2 - y1)^2
So, we have
DV = √(2 - 0)^2 + (-2 + 3/4)^2
The ratio that relates MD to DV is represented as
Ratio = MD : DV
So, we have
MD : DV = √(-6 - 0)^2 + (3 + 3/4)^2 : √(2 - 0)^2 + (-2 + 3/4)^2
This gives
MD : DV = √(-6)^2 + (3 3/4)^2 : √(2)^2 + (-1 1/4)^2
Evaluate the exponents
MD : DV = √[36 + 225/16] : √[4 + 25/16]
Evaluate the sum
MD : DV = √[801/16] : √[89/16]
Divide ratios by √[89/16]
MD : DV = √9 : √1
Evaluate the exponent
MD : DV = 3 : 1
Hence, the ratio that relates MD to DV is 3 : 1
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Dalton Alexander's gross weekly pay is $576. His earnings to date for the year total $13,824. What amount is
deducted from his pay per week for Medicare, which is taxed at 1.45 percent?
According to the given statement;
Amount is deducted from his pay per week for Medicare, which is taxed at 1.45 percent is $8.35
What is gross pay?Gross pay is the sum of a person's earnings during a specific time period before any deductions are made. The calculation of gross pay does not take into account deductions for employer-provided health insurance, retirement plans, or compulsory taxes and Medicare contributions. Since it does not reflect a person's take-home pay, the gross pay definition is different from the one for net pay.
According to the given value;
Dalton's gross pay = 576
his medicare tax rate = 1.45% = 0.0145
the tax on his medicare = 0.0145 x 576 = $8.35
Hence,Amount is deducted from his pay per week for Medicare, which is taxed at 1.45 percent is $8.35
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Solve for y 2x - 5y= - 12
Answer: y= 2/5x+12/5
Step-by-step explanation:
when you subtract 2x from both sides you get
-5y=-12-2x
and then you divide by -5 to get
y=-12-2x/-5
and you see that all the terms have negatives so you can just change them all to positives to get
y=12+2x/5
and then making the equation into y=mx+b format (which is prettier)
you get y=2/5x+12/5
yw
Step-by-step explanation:
2x - 5y= - 12
-2× -2x
0 -5y = -12 - 2x
÷-5y ÷-5y ÷-5y
y = 12/5 + 2x/5 or y = 2x/5 + 12/5
(its recommended to but the variable number in front)
Evaluate.
5/4 ÷ 3/5
help pls!!!!!
Answer: 25/12
Step-by-step explanation:
at school 350 students joined a club for math,english,science, music or historythe breakdown of the club is given in the pie chart
Answer:
Step-by-step explanation:
350 * 40% = 140 (MATH)
350 * 10% = 35 (ENGLISH)
350 * 25% = 87.5 so about 88 (SCIENCE)
350 * 10% = 35 (MUSIC)
350 * 15% = 52.5 also about 53 (HISTORY)
Solve each equation. Check each solution. 2/y + 1/2 = 5/2y
The solution of the equation 2/y + 1/2 = 5/2y is y = 1
In this question, we have been given an equation.
2/y + 1/2 = 5/2y
We need to find the solution of given equation.
⇒ 2/y + 1/2 = 5/2y
⇒ (4 + y)/2y = 5/2y
⇒ 4 + y = 5
⇒ y = 5 - 4
⇒ y = 1
We need to check above solution.
So, substitute y = 1 in given equation.
⇒ 2/y + 1/2 = 5/2y
⇒ 2/(1) + 1/2 = 5/2(1)
⇒ 2 + 1/2 = 5/2
⇒ 5/2 = 5/2
⇒ LHS = RHS
Therefore, the solution of the equation 2/y + 1/2 = 5/2y is y = 1
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A googol is the number 1 followed by 100 zeros. Earth's mass is 5. 972 × 10^24 kilograms. How many Earths
are needed to have a total mass of 1 googol kilograms? Write your answer in scientific notation with the coefficient
rounded to 2 decimal places.
The number of Earths needed have a total mass of 1 googol kilograms is 1.67 x [tex]10^{75}[/tex].
How many Earths is needed?Scientific notation is used to compress large numbers in smaller numbers. In order to write a number in scientific notation, the number is written as a decimal number, between 1 and 10 and multiplied by a power of 10.For example: 1 x 10² is equivalent to 100
A googol in scientific notation is 1 x [tex]10^{100}[/tex]
The number of Earths needed have a total mass of 1 googol kilograms =
(1 x [tex]10^{100}[/tex]) ÷ (5.972 ×[tex]10^{24}[/tex])
(1 ÷ 5.972) x ([tex]10^{100 - 24}[/tex])
0.16745 x [tex]10^{76}[/tex]
= 1.67 x [tex]10^{75}[/tex]
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Part 1 of 3
Use the number line below, where RS= 8y + 2, ST = 4y + 5, and RT = 79.
a. What is the value of y?
b. Find RS and ST.
R
a. What is the value of y?
Please help me
Using the segment addition postulate, the values are:
a. y = 6
b. RS = 50
ST = 29
How to Apply the Segment Addition Postulate?Based on the segment addition postulate, the following equation is true which we can use in finding the missing measures:
RS + ST = RT.
Given:
RS = 8y + 2,
ST = 4y + 5,
RT = 79.
a. Plug in the given values into RS + ST = RT:
8y + 2 + 4y + 5 = 79
12y + 7 = 79
12y = 79 - 7
12y = 72
y = 6
b. RS = 8y + 2 = 8(6) + 2
RS = 50
ST = 4y + 5 = 4(6) + 5
ST = 29
Thus, using the segment addition postulate, the values are:
a. y = 6
b. RS = 50
ST = 29
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What are the solutions of the equation cscxtanx=2sqrt3/3 on the interval [0,2pi)?
im having trouble understanding this, can someone help?
The solutions of the trigonometric equation are x₁ = π / 6 and x₂ = 5π / 3.
How to solve a trigonometric equation on a given interval
In this problem we find a trigonometric equation which has to be simplified and solved for x to find the family of solutions within the given interval:
csc x · tan x = 2√3 / 3
(1 / sin x) · (sin x / cos x) = 2√3 / 3
1 / cos x = 2√3 / 3
cos x = 3 / 2√3
cos x = √3 / 2
Then, by inverse trigonometric functions:
x₁ = π / 6, x₂ = 5π / 3
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y varies directly with x .If y = (1/2) when x=4 , find y when x=5 .
The required value of y is 5/8.
What is the constant of proportion?
A constant of proportion is illustrated as the ratio which relates two given quantities with each other in the relationship of proportion. Constant of proportion is also called constant variation, rate of change, and constant ratio.
Solving for the value of y
let k be the constant of proportion
When a quantity varies directly with others, then we have a relation, y = kx —-- 1
Now, find k for given x = 4 and y = ½, we need to put these values in equation 1, i.e.
½ = k(4)
k = ⅛
Further calculate y for given x = 5 and constant of proportion, k = 1/8 i.e.
y = (⅛)(5)
y = 5/8
Hence, the required value of y is 5/8.
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Which graph represents the solution set to the following system of linear inequalities?
First graph y-intercepts. second, use slope. third, determine if solid/dashed line.
y_>2x+7
y>-1/3x-2
The answer is B but can someone explain with the step by step notes mentioned?
Answer:
B
Step-by-step explanation:
Let's start by evaluating each of the equations:
[tex]y\geq 2x+7[/tex]
To begin to understand this equation, first, graph line by replacing the inequality symbol with an equal sign:
The graph of this line is the first attached image at the bottom of this answer.
The inequality reads, y is greater than or equal to 2x + 7.
The "equal to" is very important. This means that the line [tex]y= 2x+7[/tex] is a solution to this problem, so the line is drawn as a SOLID line.
Because the inequality is GREATER than, that means that all values greater than the function are solutions! Thus the area ABOVE the line is shaded. The second image attached below shows the shaded graph.
Now, let's look at the second equation:
[tex]y > -\frac{1}{3} x-2[/tex]
Start by replacing the inequality symbol with an equal sign and graphing the line. See the third image below for that line.
Now, THIS inequality is just GREATER than, not equal to. This means that the line that we just graphed, [tex]y = -\frac{1}{3} x-2[/tex] is NOT a solution to the equation! Therefore, the line is drawn as a dashed line. This means it is NOT included in the solution.
Again, since it is greater than, the area ABOVE the line is shaded. See the fourth image attached below to see the graph.
Now, let's combine these graphs! In the fifth image below, the blue represents [tex]y\geq 2x+7[/tex], and the red represents [tex]y > -\frac{1}{3} x-2[/tex].
The area where the red and blue overlap is the area to keep for the solution of this problem, since these equations represent a system of linear inequalities. I hope this helped!
A flowerbed is shaped like a rectangle. The length of the flowerbed is represented by
the expression 4x -2, and the width of the flowerbed is represented by the expression
x² + 2. What is the expression, in standard form, that represents the area of the
flowerbed. Please explain your answer!!
Answer:
18x+66=6(3x+11) square feet
Step-by-step explanation:
