A property of equality that you should apply to keep the equation 22 . a = 242 in balance when solving include the following: A. The division property of equality.
What is the subtraction property of equality?In Mathematics and Geometry, the subtraction property of equality states that the two (2) sides of an algebraic expression or equation would still remain equal even when the same number has been subtracted from both sides of an equality.
Based on the information provided above, we can logically deduce the following equation:
22 . a = 242
22 × a = 242
By applying the division property of equality, we have the following:
a = 242/22
a = 11.
Read more on subtraction property of equality here: brainly.com/question/16993368
#SPJ1
what is(7x10^-6) (5x10^-6) in scientific notation?
Answer:
Step-by-step explanation:
Move the decimal so there is one non-zero digit to the left of the decimal point. The number of decimal places you move will be the exponent on the 10. If the decimal is being moved to the right, the exponent will be negative. If the decimal is being moved to the left, the exponent will be positive. So 3.5 times 10 to the power of -11
Calculate the value of a in the triangle below.
15 cm
12 cm
a cm
Answer:
a = 11cm
Step-by-step explanation:
We can use the Pythagorean theorem to find the value of a.
Let us solve it now.
[tex] \sf {a}^{2} + {12}^{2} = {15}^{2} [/tex]
Now solve for a and and find the length of the side.
[tex] \sf {a}^{2} + 144 = 225 \\ \sf {a}^{2} = 225 - 144 \\ \sf{a}^{2} = 121 \\ \sf \: a = \sqrt{121} \\ \sf \: a = 11[/tex]
The amount of paint needed to cover the walls of a room varies jointly as the perimeter of the room and the
height of the wall.
Veronica needed 11.2 quarts of paint to paint a room with perimeter 40 feet and wall height 14 feet.
How much paint will she need to cover the walls of a room with perimeter 50 feet and wall height 15 feet?
Round your answer to one decimal place.
quarts
She need 15 quarts to cover the walls of a room with perimeter 50 feet and wall height 15 feet.
Define area.The region that an object's shape defines as its area. The area of a figure or any other two-dimensional geometric shape in a plane is how much space it occupies.
Given Data
Veronica needed 11.2 quarts of paint to paint a room with perimeter 40 feet and wall height 14 feet.
Area of room = 40(14)
Area of room = 560
She need to cover the walls of a room with perimeter 50 feet and wall height 15 feet
Area = 50(15)
Area = 750
Let q be the number quarts of paints
[tex]\frac{560}{750}[/tex] = [tex]\frac{11.2}q{}[/tex]
Cross multiplying,
560q = 11.2(750)
q = [tex]\frac{11.2(750)}{560}[/tex]
q = 15
She need 15 quarts to cover the walls of a room with perimeter 50 feet and wall height 15 feet.
To learn more about area, visit:
https://brainly.com/question/27683633
#SPJ13
A print shop a $10 flat fee for each print and then $0.25 for each page printed. Which of the following tables shows relationship between the number of pages and cost of order?
The equation to represent the number of pages is: 0.25x = 10.
What is equation?
In mathematics, the statement based problems can be solved by forming the equation. And it consists of dependent variable as well as independent variable.
According to the question, the given parameters to form the equation are as follows:
The cost of each print is: $10
The cost of each page printed: $0.25
Now, let us assume number of printed pages are: 'x'
Therefore, the equation which shows the relationship between the number of pages and the cost of order is: 0.25x = 10
Hence, the equation to represent the number of pages is: 0.25x = 10
To learn more about the equation from the given link:
https://brainly.com/question/1214333
#SPJ9
Suppose that 19 inches of wire costs 76 cents.
At the same rate, how many inches of wire can be bought for 64 cents?
Answer: 16 inches
Step-by-step explanation: well, if you do 76/19, it gives you four, so the ratio is 1-inch costs 4 cents.
Then you just have to do 64/4, which gives you 16. You can buy 16 inches of wire with 64 cents
Thank you to who ever helps
Applying the transitive property of congruency and other postulates, lines l and m are proven to be parallel as explained below.
What is the Transitive Property of Congruency?The transitive property of congruency states that when two angles are sides are congruent to another third angle or side, then the three sides or angles are all congruent to each other.
For example, if <A = <C, and <B = <C, then <A = <B.
The proof that shows that lines l and m are congruent is explained below:
Statement Reason
1. r║s, <5 is congruent to <6 1. Given
2. <5 is supplementary to <4 2. Same-side interior angles theorem
3. <4 is supplementary to <6 3. Transitive property of congruency
4. l║m 4. Converse of same-side interior <s theorem
Learn more about transitive property of congruency on:
https://brainly.com/question/2437149
#SPJ1
Solve the inequality r divided by negative 3.2 is greater than or equal to 7.6 for r.
r ≥ −24.32
r ≤ −24.32
r ≥ 2.375
r ≤ −2.375
Answer:
r ≤ -24.32
Step-by-step explanation:
r/-3.2 > 7.6
r /-3.2 × 3.2 > 7.6 × -3.2
r ≤ -24.32
Answer: r ≤ −24.32
Step-by-step explanation:
The inequality you provided is:
r/-3.2 >= 7.6
To solve for r, we can multiply both sides of the inequality by -3.2 to get:
r <= -24.32
Therefore, r is less than or equal to -24.32.
I hope this helps! Let me know if you have any other questions.
The scale of a map is 1 in.: 100 mi. Is the actual distance between two towns 100 times the map distance between the two towns? Explain.
The given statement is not true because the actual distance between two towns is greater than 100 times the map distance since 100 miles is more than 100 times as great as 1 inch.
What is the scale of the map?
We are given the scale of the map as;
1 inch : 100 miles
What this means is that 1 inch on the map represents an actual distance of 100 miles.
Now, from conversion values, we know that;
1 mile = 63360 inches
Now, the question is trying to suggest that the actual distance between two towns 100 times the map distance between the two towns
The given statement is not true because as seen from the conversion above, the actual distance between two towns is greater than 100 times the map distance since 100 miles is more than 100 times as great as 1 inch.
Read more about Scale of map at; https://brainly.com/question/105644
#SPJ1
In a scale diagram, 0.15 inch represents 150 feet. How many inches represent 2.5 feet?
Answer:
.0025 inches
Step-by-step explanation:
[tex] \frac{.15}{150} = \frac{x}{2.5} [/tex]
[tex]150x = 3.75[/tex]
[tex]x = .0025[/tex]
IIIO GEOMETRYVolume of a sphereThe radius, R, of a sphere is 6.2 m. Calculate the sphere's volume, V.Use the value 3.14 for n, and round your answer to the nearest tenth. (Do not round any intermediate computations.)
The formula for calculating the volume of a sphere is expressed as
Volume = 4/3 x pi x radius^3
From the information given,
pi = 3.14
radius = 6.2
By substituting these values into the formula, we have
Volume = 4/3 x 3.14 x 6.2^3
Volume = 997.7999
Rounding to the nearest tenth,
Volume = 997.8 m^3
What is the equation of the linear model shown? (Hint: Pick two points closest to
the line and complete it by hand. No need to use the calculator.)
Y= 0.8x +4
Y= 1.25x -0.5
Y=0.8x + 0.4
Y=-0.8x+20
find five soultion linear eqation x+y=3
The definition of an equation in algebra is a mathematical statement that proves two mathematical expressions are equivalent.
What are Equations?Equations are logical formulations of the connection between two values. A mathematical equation can be defined in a variety of ways. The given equation is x + y = 3Let the value of x = 0,then,0 + y = 3⇒ y = 3One of the solutions for x + y =3, is (0,3)Similarly, If x = 1,then,1 + y =3⇒ y = 3 - 1 = 2One of the solutions for x + y =3, is (1,2)If x = 2,then,2 + y = 3⇒ y = 3 - 2 = 1One of the solutions for x + y =3, is (2,1)If x = 3, then,3 + y = 3⇒ y = 3 - 3 = 0One of the solutions for x + y =3, is (3,0)If x = 4,then, 4 + y = 3⇒ y = 3 - 4 = -1One of the solutions for x + y =3, is (4, -1)Hence, five solutions of the equation x + y = 3, are:(0,3), (1,2), (2,1), (3,0) and (4, -1).Mathematical variables are used in even the most fundamental and straightforward algebraic equations. There could be multiple variables in a linear equation. A linear equation is one in which the variable's maximum power is consistently 1.A one-degree equation is another name for it. At least one variable should be raised to exponent 2 in quadratic equations.To learn more about Equations, refer to:
https://brainly.com/question/10413253
#SPJ10
The five solution of the linear equation x+y=3 is = (0,3), (1,2), (2,1), (3,0) and (4, -1).
What are Equations?Equations are logical formulations of the connection between two values. A mathematical equation can be defined in a variety of ways. Mathematical variables are used in even the most fundamental and straightforward algebraic equations.
There could be multiple variables in a linear equation. A linear equation is one in which the variable's maximum power is consistently 1.
A one-degree equation is another name for it. At least one variable should be raised to exponent 2 in quadratic equations.
What is the linear equation's general form?Ax+By=C is the usual form for two-variable linear equations. For example, 2x+3y=5 is a linear equation in standard form.
Let the value of
x = 0,
then,
0 + y = 3
⇒
y = 3
One of the solutions
for x + y =3, is =(0,3)
Similarly, If x = 1,
then,
1 + y =3 ⇒ y = 3 - 1 = 2
One of the solutions for x + y =3, is
(1,2)
If x = 2,
then,
2 + y = 3
⇒ y = 3 - 2 = 1
One of the solutions for x + y =3, is
(2,1)
If x = 3, then,
3 + y = 3
⇒ y = 3 - 3 = 0
One of the solutions for x + y =3, is
(3,0)
If x = 4,
then,
4 + y = 3
⇒ y = 3 - 4 = -1
One of the solutions for x + y =3, is
(4, -1)
Hence,
five
solutions of the equation x + y = 3, are:
(0,3), (1,2), (2,1), (3,0) and (4, -1).
To learn more about Linear Equation here-
https://brainly.com/question/11897796
#SPJ10
A grocery store sells a bag of 5 oranges for $2.85. If Rashaad spent $3.42 on oranges, how many did he buy?
Answer:
6 oranges
Step-by-step explanation:
1) I know that 5 oranges equals to $2.85
2)I need to find the cost of 1 orange
3)Divide the 3.42 to the cost of 1 orange
MY WORK:
2.85 / 5= $0.57 ( the cost per orange )
3.42 / 0.57= 6 oranges
Hope this helps!
The table contains data on the number of people visiting a historical landmark over a period of one week.
From the data provided, we can consider the following function as a good approximation:
[tex]y=2.57+49.29x-3.86x^2[/tex]Therefore:
The answer is:
a quadratic function with a negative value of a
The diagram shows a triangle. 35° 2w 3w What is the value of w?
Applying the triangle sum theorem, the value of w in the triangle is calculated as: w = 29.
What is the Triangle Sum Theorem?The triangle sum theorem states that if we add up all the three interior angles of any given triangle, we will have a sum of 180 degrees.
This means that, irrespective of whatever triangle that is given, the sum of all the interior angles of such triangle will be equal to 180 degrees.
The diagram attached below shows the following interior angle measures of a triangle: 35°, 2w, and 3w.
To find the value of w in the triangle given, we have to create an equation using the triangle sum theorem that will enable us solve for the value of w.
Thus:
35 + 2w + 3w = 180° [according to the triangle sum theorem]
Combine like terms
35 + 5w = 180
Subtract both sides by 35
35 + 5w - 35 = 180 - 35 [subtraction property of equality]
5w = 145
Divide both sides by 5
5w/5 = 145/5 [division property of equality]
w = 29
Learn more about the triangle sum theorem on:
https://brainly.com/question/7696843
#SPJ1
A ribbon is 3 4/5 feet long. Each hair tie needs
2/5 feet. How many hair ties can you make?
A ribbon is 3 4/5 feet long. Each hair tie needs 2/5 feet. Number of hair ties is 6
What is meant by fraction?A fraction represents a part of a whole or, more generally, any number of equal parts.Dividing two fractions is the same as multiplying the first fraction by the reciprocal of the second fraction.The first step to dividing fractions is to find the reciprocal (reverse the numerator and denominator) of the second fraction, Next, multiply the two numerators. Then, multiply the two denominators.
No of hair ties = 6
How to find number of hair ties :
Length of the ribbon = 3 4/5 feet
Length of each hair tie needed = 2/5 feet
To find how many ties , divide the total length of ribbon by 2/5
That is = [tex]\frac{3 (4/5)}{2/5}[/tex]
= 6 You can make 6 no. of hair tie from 3 4/5 feet ribbon.
T0 learn more about fraction refer :
https://brainly.com/question/17220365
#SPJ13
13. pls help will mark brainliest to anyone
The equation of the line in slope intercept form is found as y = x/5 + 24/5, where slope is (-1/5) and y-intercept is 24/5.
What is named as the slope-intercept form?The slope intercept type of composing a straight line equation is y = mx + b. In the equation 'y = mx + b,' 'b' represents the point in which the line intersects the 'y axis,' and'm' represents the slope of the line. A line's slope or gradient describes how steep it is. It may have a positive or negative value.For the given question;
Two points are given as;
(x1, y1) = (-6, 6)
(x2, y2) = (9, 1)
The slope of the line is found as;
slope = m = (y2 - y1)/(x2 - x1)
m = (1 - 6)/(9 + 6)
m = -5/15
m = -1/5
The equation of the line in slope-intercept form is found as;
y - y1 = m(x - x1)
y - 6 = (-1/5)(x + 6)
5y - 30 = -x - 6
5y = -x + 24
y = -x/5 + 24/5
Thus, the equation of the line is found as y = x/5 + 24/5, where slope is (-1/5) and y-intercept is 24/5.
To know more about slope-intercept form, here
https://brainly.com/question/1884491
#SPJ13
when a number is added to 18 the answer is the same as 59 mins 20. what is the number?
Type the correct answer in each box.If , then a = , b = , c = , and d =
Consider the following matrix equation:
Applying the additive property, this is equation is equivalent to:
[tex]\begin{bmatrix}{a-2} & {b+5} & {} & {} \\ {c\text{ -10}} & {d\text{ +6}} & {} & {} \\ {} & {} & {} & {} \\ {} & {} & {} & {}\end{bmatrix}=\text{ }\begin{bmatrix}{4} & {8} & {} & {} \\ \text{ -}{1} & {0} & {} & {} \\ {} & {} & {} & {} \\ {} & {} & {} & {}\end{bmatrix}[/tex]This is equivalent to the following linear system of equations:
Equation 1:
[tex]a\text{ - 2 = 4}[/tex]Equation 2:
[tex]b+5=8[/tex]Equation 3:
[tex]c\text{ -10= -1}[/tex]Equation 4:
[tex]d\text{ +6=0}[/tex]From equation 1, we get:
[tex]a\text{ = 4+2=6}[/tex]From equation 2, we get:
[tex]b=8\text{ - 5 = 3}[/tex]From equation 3, we get:
[tex]c\text{ = -1+10 = 9}[/tex]From equation 4, we get:
[tex]d\text{ = -6}[/tex]we can conclude that the correct answer is:
Answer:[tex]a\text{ = 6}[/tex][tex]b=\text{ 3}[/tex][tex]c\text{ = 9}[/tex]and
[tex]d\text{ = -6}[/tex]Calculate the rise and run to find the slope of each line! Please help me!!!
Answer:
Slope = 2
Step-by-step explanation:
See attached graph/worksheet.
What does it multiply too
0.88
X 1.2
Answer:
1.056
Step-by-step explanation:
radium-221 has a half-life of 30 sec. how long will it take for 86% of a sample to decay? (round your answer to the nearest whole number.)
If radium-221 has half life of 30 seconds. To decay 86% of the the sample, it will take 85.09 seconds
The half life of the radium-221 = 30 seconds
To decay 86% of the sample
The equation of the half life N = [tex]N_0(\frac{1}{2} )^\frac{t}{t_1}[/tex]
Where N is the quantity of substance remaining
[tex]N_0[/tex] is the initial quantity of substance
t is the time elapsed
[tex]t_1[/tex] is the half life of the substance
Substitute the values in the equation
0.14[tex]N_0[/tex] = [tex]N_0(\frac{1}{2} )^\frac{t}{30}[/tex]
Cancel the [tex]N_0[/tex] from each side
0.14 = [tex](\frac{t}{30} )^\frac{t}{30}[/tex]
[tex]2^\frac{t}{30}=\frac{1}{0.14}\\ \frac{t}{30}=log_2\frac{1}{0.14}\\ t = 30log_2\frac{1}{0.14}[/tex]
t = 85.09 seconds
Hence, if radium-221 has half life of 30 seconds. To decay 86% of the the sample, it will take 85.09 seconds
Learn more about half life here
brainly.com/question/24710827
#SPJ1
The location between the park and Ray's
home is indicated in the graph.
Each unit represents a mile.
What is the distance, in miles, from the
park to Ray's home, rounded to the
nearest tenth?
A 16.6
B 15.6
C 14.1
D 143
E 11.0
The answer to the question is A-
16.6
Answer:
A. 16.6
Step-by-step explanation:
d = sqrt{(x2 - x1)^2 + (y2-y1)^2}
so this is our distance formula
now we need the two points
(-6, -6) and (3, 8)
lets plug these into our formula
d = sqrt{(3 - (-6))^2 + (8 - (-6))^2}
lets simplify
d = sqrt{(9)^2 + (14) ^2}
d = sqrt{277}
d = 16.64 or 16.6
Which situation can be represented by the expression 2.5 X
Given the expression:
2.5x
Let's determine the situation which best represents the expression.
Let's start from the first statement:
• A. The total amount of change received to pay for an item that cost $2.50:
The best representation for this is: C = A - 2.50
Where A is the amount paid, C is the amount of change.
• B. The area of a rectangle with side lengths 2.5 and x:
The best representation for this situation is:
2.5x
• C. The total cost of an item that is 2.50 more than x dollars:
T = 2.50 + x
• D. The total square footage of a yard when 2.50 yards is divided into equal parts:
This expression cannot be represented by 2.5x
Therefore, the situation which can be represented by the expression 2.5 is:
The area of a rectangle with side lengths 2.5 and x
ANSWER:
B. The area of a rectangle with side lengths 2.5 and x
Find the slope of the line graphed below.
Answer:
3/4
Step-by-step explanation:
up 3 right 4
2 +4
5
3
Please help me
We convert 2 into 6/3.
Now, we add the fraction part of the mixed number with 6/3
-> 5/3 + 6/3 = 11/3
So, it is equal to 4(11/3)
Now, we convert 11/3 into 3(2/3)
-> 4(11/3) = 4+3(2/3) = 7(2/3).
Answer:
based on the bodmass 4×5÷3=6.7+2=8.7
Given: AABC, mzC = 90°
m2A = 30°, BC = 16
Find: AB and AC
Help fast
The most appropriate choice for trigonometry will be given by -
AB = 32
AC = [tex]16\sqrt{3}[/tex]
What is Trigonometry?
Trigonometry shows the relationship between sides and angles of a right angled triangle.
There are six trigonometrical functions. They are
[tex]sin\theta,[/tex] [tex]cos\theta[/tex], [tex]tan\theta[/tex], [tex]cot\theta[/tex], [tex]sec\theta[/tex], [tex]cosec\theta[/tex]
[tex]sin\theta=\frac{perpendicular}{hypotenuse}\\\\cos\theta=\frac{base}{hypotenuse}\\\\tan\theta=\frac{perpendicular}{base}\\\\cot\theta=\frac{base}{perpendicular}\\\\sec\theta=\frac{hypotenuse}{base}\\\\cosec\theta=\frac{hypotenuse}{perpendicular}[/tex]
Trigonometry is a very important tool in mathematics.
Here,
The figure has been attached here.
Since this is a right angled triangle, trigonometry can be applied here,
Since ∠C = 90°, AB is the hypotenuse of [tex]\DeltaABC[/tex][tex]\Delta ABC[/tex] as the side opposite to 90° angle is the hypotenuse.
Let BC be the base of [tex]\DeltaABC[/tex][tex]\Delta ABC[/tex]
BC = 16
m∠B = 180 - (90 + 30)
= 180 - 120
= 60°
cos 60 = [tex]\frac{BC}{AB}[/tex]
[tex]\frac{1}{2} = \frac{16}{AB}\\AB = 16\times 2\\AB = 32[/tex]
sin 60 = [tex]\frac{AC}{AB}[/tex]
[tex]\frac{\sqrt{3}}{2} = \frac{AC}{32}\\\\AC = 32 \times \frac{\sqrt{3}}{2}\\\\AC = 16\sqrt{3}[/tex]
To learn more about trigonometry, refer to the link
https://brainly.com/question/24349828
#SPJ9
it is 76 at the 6000 foot level of a mountain and 49 at the 12000 foot level of the mountain. write a linear equation to find the temperature T at an elevation X on the mountain, where x is in thousands of feet
The most appropriate choice for Linear equation will be given by-
[tex]2000T = -9X+206000[/tex]
This is the required equation to find the temperature T at an elevation X on the mountain.
What is linear equation?
Equation shows the equality between two expressions by connecting the expressions with an equal to sign.
A one degree equation is called linear equation.
Here,
Let X denotes the elevation of the mountain and T is the temperature
Let the equation be T = pX + c
It is 76 at the 6000 foot level of a mountain
Putting T = 76 and X = 6000
6000p + c = 76 .........(1)
It is 49 at the 12000 foot level of the mountain
Putting T = 49 and X = 12000
12000p + c = 49..........(2)
Subtracting (2) from (1),
6000 p = -27
[tex]p = \frac{-27}{6000}\\\\p = \frac{-9}{2000}[/tex]
Putting the value of p in (1),
[tex]6000 \times \frac{-9}{2000} + c = 76\\-27 + c = 76\\c = 27 + 76\\c = 103[/tex]
Equation
[tex]T = \frac{-9}{2000}X+103[/tex]
[tex]2000T = -9X+206000[/tex]
This is the required equation to find the temperature T at an elevation X on the mountain.
To learn more about linear equation, refer to the link:
https://brainly.com/question/2030026
#SPJ9
A baseball is thrown from a height of 5 feet. The height, h, of the ball at time t seconds is modeled by the equation h(t)=−16t2+100t+5. How long will it take the ball to reach the ground?
Select one:
a. 5.8 seconds.
b. 6.3 seconds.
c. 7.2 seconds.
d. 7.6 seconds.
please help:)
The ball takes 6.3 seconds to reach the ground when thrown upwards.
The height of the baseball thrown is 5 feet.
The function or equation for the height of the ball at a certain time t is given as:
h( t ) = - 16t² + 100t + 5
When the ball will reach the ground the height of the ball will be h = 0.
Therefore,
- 16t² + 100t + 5 = 0
Comparing the equation with general quadratic equation ax² + bx + c =0
We have, a = - 16, b = 100, and c = 5
Using the quadratic formula,
[tex]t=\frac{-b\pm \sqrt{b^{2} - 4ac } }{2a}[/tex]
[tex]t = \frac{-100\pm \sqrt{(100)^{2} - 4(-16)(5) } }{2(-16)}[/tex]
[tex]t=\frac{-100 \pm \sqrt{10000+320} }{-32}[/tex]
[tex]t = \frac{-100\pm \sqrt{10320} }{32} \\[/tex]
t = [ 25 ± √(645) ] / 8
When,
t = [ 25 + √(645) ] / 8 = 6.299 = 6.3 seconds
t = [ 25 - √(645) ] / 8 is false as the time cannot be negative.
The correct option is (b) 6.3 seconds.
Learn more about equation here:
brainly.com/question/2972832
#SPJ1
2x - 8 + 3x - 10 = 10x - 43
The value of variable x in the equation is 5.
How to solve for x in an equation?An equation is a mathematical statement that is made up of two expressions connected by an equal sign.
Therefore, let's solve for variable x in the equation below.
2x - 8 + 3x - 10 = 10x - 43
A variable is number represented with a letter in an equation.
Hence,
2x - 8 + 3x - 10 = 10x - 43
2x + 3x - 8 - 10 = 10x - 43
5x - 18 = 10x - 43
5x - 10x = - 43 + 18
-5x = - 25
divide both sides of the equation by -5
-5x / - 5= - 25 / -5
Therefore,
x = 5
learn more on equation here: https://brainly.com/question/11720294
#SPJ1
