Answer: y=[tex]-\frac{1}{10} x-7[/tex]
Step-by-step explanation: The slope of a perpendicular line is always negative and the reciprocal (opposite fraction) of the regular slope so the slope would be [tex]-\frac{1}{10}[/tex]. If the line passes through (-10,-6) then the y intercept would be (0,-7) because every time x goes 10 right y goes down 1 because of the slope.
If the ratio of A to B is 3 : 4, and the ratio of B to C is 2 : 3, what is the value of A when C is 5?
If the ratio of A to B is [tex]3 : 4[/tex], and the ratio of B to C is [tex]2 : 3[/tex], then the value of A when C is [tex]5[/tex] is [tex]2.5[/tex].
In the given question,
The ratio of A to B is [tex]3 : 4[/tex].
The ratio of B to C is [tex]2:3[/tex].
We have to find the value of A.
It is given that the value of C is [tex]5[/tex].
The given ratios are,
A : B [tex]=3 : 4[/tex]
B : C [tex]=2:3[/tex]
As we can see that the ratio of B is not same in both ratio so we first equal the ratio of B.
We can equal the ratio of B by multiplying [tex]2[/tex] on both side in the ratio of
B : C.
B : C [tex]=2\times2:3\times2[/tex]
After multiplying we get
B : C [tex]=4:6[/tex]
As given in the question that C [tex]=5[/tex].
They given in the ratio which means there have any number in the multiple of ratio. That which we can get real value from the ratio.
So we used [tex]x[/tex] as a multiple of ratio.
And the ratio of C is [tex]6x[/tex].
So we get that
[tex]6x=5[/tex]
Hence the value of [tex]x=\frac{5}{6}[/tex].
Now finding the value of A.
The ratio of A is [tex]3x[/tex].
And the value of [tex]x=\frac{5}{6}[/tex].
Now putting the value
A [tex]=3\times\frac{5}{6}[/tex]
A [tex]=\frac{5}{2}[/tex]
A =[tex]2.5[/tex].
The value of A is [tex]2.5[/tex].
Hence, if the ratio of A to B is [tex]3 : 4[/tex], and the ratio of B to C is [tex]2 : 3[/tex], then the value of A when C is [tex]5[/tex] is [tex]2.5[/tex].
To learn more about ratio link is here
brainly.com/question/13419413
#SPJ1
find the sime interest owed for the loan $5,100 at 10% for 1 year
Step 1: write out the formula
The simple interest on the loan can be calculated using the formula:
[tex]\text{simple int}erest\text{ =}\frac{p\text{ x r x t}}{100}[/tex]where p is the principal, in our case, it is the loan = $51000
r is the rate = 10%
t is the time = 1 year
Step2: substitute the values into the equation.
Our next step is to put the values of p, r, and t into the equation so that
[tex]\text{simple interest =}\frac{51000\text{ x 10 x 1}}{100}=5100\text{ }[/tex]Therefore, the simple interest on the loan is $5, 100
If c is a number with no exponent, what is the value of c in the equation below?[tex]\frac{ {4}^{7} }{ {4}^{3} } = {a}^{b} = c[/tex]
Answer:
c = 256
Explanation:
Given the equation:
[tex]\frac{ {4}^{7} }{ {4}^{3} }={a}^b=c[/tex]We apply the division law of indices to obtain:
[tex]\frac{ {4}^{7} }{ {4}^{3} }={4^{7-3}=4^4=256}[/tex]The value of c is 256.
Solve for x:
4(4/4x) + 5 = 32
The value of x when he equation given is solved is x = 4/27.
How to Solve for x in an Equation?To solve for x in an equation, we have to apply all necessary properties of equality to will enable us isolate x to one side of the equation. The value of x is the solution to the equation that will make the equation a true statement.
Given the equation:
4(4/4x) + 5 = 32
Subtract 5 from both sides
4(4/4x) + 5 - 5 = 32 - 5 [subtraction property of equality]
4(4/4x) = 27
4/x = 27
Cross multiply
4 = 27(x)
4 = 27x
Divide both sides by 27 [division property of equality]
4/27 = 27x/27
4/27 = x
x = 4/27
Learn more about equations on:
https://brainly.com/question/25678139
#SPJ1
Answer:
6.75
Step-by-step explanation:
I've had this question before. You solve like this:
4/4 = 1 so x.
so 4 times x is 4x. You then subtract 5 from each side.
4x+5-5=32-5
4x=27 Divide both sides by 4 to get
x=27/4 which as a decimal is 6.75.
given < 1 and 3 prove < 6 and <4
It is given that ∠1 ≅ ∠3 and ∠1 = ∠4 and ∠3 = ∠6 as of vertically opposite angles, therefore ∠6 ≅ ∠4 too.
What is vertically opposite angles?Vertical angles, also known as vertically opposite angles, are formed when two lines cross each other at an angle that is opposite to it. Angles that are vertically opposite to one another are always equal to one another.
A vertical angle and the angle to which it is adjacent are also supplementary angles; that is, they add up to 180 degrees. As an illustration, if two lines intersect to form an angle, say X=45°, then the opposite angle is also 45°. And angle X's neighbor will have a measure of 180 minus 45, or 135 degrees.
Two lines are said to intersect when they come together at a single point in a plane. They are referred to as parallel lines when they do not intersect anywhere in a plane.
We have given that ∠1 ≅ ∠3
We can see that ∠1 = ∠4 as they are vertically opposite angles.
Also ∠3 = ∠6 as they are vertically opposite angles.
Thus, It is given that ∠1 ≅ ∠3 and ∠1 = ∠4 and ∠3 = ∠6 as of vertically opposite angles, therefore ∠6 ≅ ∠4 too.
Learn more about vertically opposite angles
https://brainly.com/question/68367
#SPJ9
help asap! this is due in 30 minutes!
Answer:
0.5Step-by-step explanation:
By determining the value of y when x=1, we'll find the constant of proportionality.
[tex]\sf y=0.5[/tex]
when, x = 1
The constant of proportionality:-
[tex]\sf \cfrac{y}{x},\:is\:\cfrac{0.5}{1}\: or \: 0.5[/tex]
Therefore, your answer is 0.5 .
________________________
Hope this helps!
Have a great day!
Of the 175 dogs that were groomed 3/25 had a red collar. How many of the dogs had a red collar
Answer:
21
Step-by-step explanation:
175 x 3 = 525. Divide that by 25 and you get 21.
What is 32% of 495. I have to type more because its not in the 20 charter lenth.
Answer:
158.4
Step-by-step explanation:
32% multiple 495
=158.4
the 1st question can someone help a bro out
Answer:
3/19
Step-by-step explanation:
No. of people who ordered the small lemon yogurt divided by total no. of people
= 9/57
= 3/19
a new community wellness complex is being built in hadleyville. the perimeter of the rectangular playing field is 290 yards. the length of the field is 5 yards less than double the width. what are the dimensions of the playing field
The rectangular playing field's perimeter is 290 yards. The field's length is 5 yards less than its width. The playing field's measurements length and width will be 70 and 75.
Given that,
In Hadleyville, a brand-new community wellness complex is being constructed. The rectangular playing field's perimeter is 290 yards. The field's length is 5 yards less than its width.
We have to find what are the playing field's measurements.
Take the width as x.
Length is x-5.
Perimeter of the rectangle is 2l+2w
290=2l+2w
290=2(x-5)+2x
290=2x-10+2x
290=4x-10
4x=290+10
4x=300
x=300/4
x=75
The length will be x-5=75-5=70
The width will be x=75
Therefore, the playing field's measurements length and width will be 70 and 75.
To learn more about perimeter visit: https://brainly.com/question/6465134
#SPJ10
Gavin is working two summer jobs, making $14 per hour tutoring and $13 per
hour landscaping. Last week Gavin worked a total of 10 hours and earned a
total of $137. Determine the number of hours Gavin worked tutoring last
week and the number of hours he worked landscaping last week.
Gavin worked 7 hours on his tutoring job and 3 hours on his landscaping job
System of EquationsA system of equations is a group of two or more equations with the same variables. A solution to a system of equations is the values of the variables that make all of the equations in the system true. A solution to a system is also an intersection point of the graphs of the equations in the system.
Let;
Tutoring hours = xLandscaping hours = yWe need to write system of equations to solve this problem.
14x + 13y = 137 ...eq(i)
x + y = 10 ...eq(ii)
Solving equation (i) and (ii),
x = 7 and y = 3
He worked 7 hours tutoring and 3 hours landscaping
Learn more on system of equations here;
https://brainly.com/question/13729904
#SPJ1
simply (4x-6)-(5x+1)
Through the given equation the simplification of (4x-6)-(5x+1) is = -x -7.
What is an example of distributive property?An illustration of distributive property:
When you multiply a value by a sum, the distributive property of multiplication over addition is used. Say you wish to multiply 5 by the product of 10 plus 3. When two terms are similar, we often sum the two amounts before multiplying by 5. However, the property states that you should first multiply each addend by 5.
The expression provided is:
(4x-6)-(5x+1)
Using the distributive property, expand the brackets to get:
4x-6- 5x-1
Organize the terms to get,
4x- 5x -1 -6
combine similar phrases to simplify to obtain;
-x -7
To learn more about Simplification here-
https://brainly.com/question/23509407
#SPJ10
camille finds a pieace of wood that is 15.65 centimeters long and thier freind finds one that is 16.24 centimeter what is the total lenght if camille attched them together
The total length of the wood attached together is 31.89 centimetres
Size of the wood found by Camille = 15.65 centimetres
Size of the wood found by her friend = 16.24 centimetres
The act of determining an object's length in some standard or non-standard units is known as a length measurement. In our daily lives, the ability to measure length is crucial.
Let's say Mathew is shopping with a friend when he notices a lovely picture frame that can be displayed in his parent's bedroom. But how would he go about telling them how long the frame was? If he knows the length of a particular unit, such as 3 feet, he can do that.
The total length of the wood = 15.65 + 16.24 = 31.89 centimeter
Learn more about length:
https://brainly.com/question/8552546
#SPJ1
carlos tiene 120 dolares, roxana tiene 200 dolares, claudina 180 dolares ; para viajar a ambato el pasaje cuesta 18 dolares ¿cuántos viaje de vueltas hay para viajar en el mundo? ayudenme plis unu es para mañana
The number of trips that can be taken based on the money than they have is 27 trips.
How to calculate the value?The amount that each person has is illustrated below:
Carlos = $120
Roxana = $200
Claudia = $180..
In order to travel around Ambato, $18 is needed. Therefore, the trips that can be taken will be:
= Total amount / Value for each trip
= ($120 + $200 + $180) / 18
= 500 / 18
= 27
There'll be 27 trips.
Learn more about money on:
brainly.com/question/24373500
#SPJ1
I need help with this.
Answer: A 550g box for $10.89
Step-by-step explanation:
Represent each option as grams per dollar
225g / $5.77 = 38.99g / $1.00
550g / $10.89 = 50.51g / $1.00
725g / $16.89 = 42.92g / $1.00
The second option gives the most grams per dollar
Elijah bought earrings to give to his mother for her birthday. The earrings are in a case shaped like a rectangular prism that is 2 inches long, 1 1/2 inches wide, and 1 1/2 inches tall. He doesn't want his mother to guess what the gift is, so he put the case in a larger, cube-shaped gift box. The gift box is 4 inches along each edge.
What is the volume of the extra space left in the gift box?
A student claims that 3.8¯ is an irrational number because it is a non-terminating decimal. Is the student correct? Justify your answer. If the student is incorrect, write 3.8¯ as a fraction. If the student is correct, use mathematics to explain how you know you cannot write the number as a fraction. Enter your answer and your work or explanation in the space provided.
If a student claims that 3.8¯ is an irrational number because it is a non-terminating decimal, then, he/she is incorrect as 3.8¯ can be represented as a fraction which is (35/9).
As per the question statement, a student claims that 3.8¯ is an irrational number because it is a non-terminating decimal.
We are required to determine if the claim is correct or incorrect, and if the claim is correct, then we will have to justify our answer, while if it is incorrect, we will have to determine the fraction that is equal to 3.8¯.
To solve this question, let us first try to convert our concerned decimal 3.8¯ into its equivalent fraction.
Now, 3.8¯ = 3.888...
Let us assume a random variable "x" such that, 3.8¯ = x = 3.888...
Then, 10x = (10 * 3.888...) = 38.888...
Now, [(10x - x) = {(38.888...) - (3.888...)}]
Or, (9x = 35)
Or, x = (35/9)
That is, the non-terminating decimal 3.8¯ can be converted to a fraction which is equal to (35/9).
Hence, the student's claim that that 3.8¯ is an irrational number because it is a non-terminating decimal is incorrect.
To learn more about Irrational Numbers and Non-Terminating Decimals, click on the link below.
https://brainly.com/question/6782325
#SPJ1
Find the least common denominator. Then express each fraction using the least common denominator.
3/10 and 2/15
The least common denominator (LCD) of the fractions 3/10 and 2/15 is 30.
Given fractions:
3/10 and 2/15
First the least common multiple for denominators (10,15) is 30.
Calculations to rewrite the original inputs to equivalent fractions with LCD:
3/10 = 3/10 * 3/3 = 9/30
2/15 = 2/15 * 2/2 = 4/30
Therefore the least common denominator (LCD) of the fractions 3/10 and 2/15 is 30.
Learn more about the least common denominator and fractions here:
https://brainly.com/question/8393834
#SPJ1
How do you write 3.2 x 10° in standard form? i cant seem to figure this out could somebody pls help me out?
Answer:
3.2
Step-by-step explanation:
Any number raised to the zero power is one. 3.2 x 1 = 3.2
Help pls asap thx alot lol
The expression that is equivalent to [tex]\frac{5^{-10}}{5^{4}5^{0}}[/tex] is 1/5¹⁴
Expression:
An expression is a mathematical statement that does not contain an equal sign. It cannot be solved for unless the value of the variable is given.
Given,
Here we have the expression [tex]\frac{5^{-10}}{5^{4}5^{0}}[/tex]
Now we need to find the equivalent expression for this one.
In order to find the equivalent expression first we have to simplify the given expression.
For that we have to use the exponent rule,
1) Product of powers rule
When we multiplying two bases of the same value, keep the bases the same and then add the exponents together to get the solution.
2) Quotient of powers rule
When we dividing two bases with same value, keep the base the same, and then subtract the exponent values.
3) Negative exponent rule.
While we have the negative exponent then we have to convert them into fraction.
Based on the rule 1, we have simplify the denominator as,
[tex]\frac{5^{-10}}{5^{4}5^{0}}=\frac{5^{-10}}{5^{4+0}}\\\\= > \frac{5^{-10}}{5^{4}}[/tex]
Now we have to apply the rule (2), then we get,
=> 5⁻¹⁰⁻⁴
=> 5⁻¹⁴
Finally, we have to apply the thirds rule,
=> 1/5¹⁴
Therefore, the equivalent expression is 1/5¹⁴.
To know more about Expression here.
https://brainly.com/question/14083225
#SPJ1
Mr. Apple noticed that an error had been made on his account. The "loss of $800" should have been a "gain of $800." Locate and label both points that represent "a loss of $800" and "a gain of $800" on the number line below. Describe the relationship of these two numbers when zero represents no change (gain or loss). HHHHHHHHH O
A loss is represented as a negative number (a number less than 0) and a gain is represented by a possitive number (a number grather than 0)
For the given data you get the next graph:
The relationship as 0 is not change is: The loss is a change of $800 being a decrease of the amount in the account. The gain is a change of $800 being a increase of the amount in the account.
Both are changes of $800 but represent different types of changes (increase and decrease)
y = 2x+1 how do I solve this?
Solving an inequality, it is found that the interval over which the function y = 2x + 1 is positive is given by:
(-1/2, ∞).
When a function is positive and when it is negative?To verify if the function is positive or negative, we have to look at the graph of the function relative to the x-axis, as follows:
A function is positive when it is above the x-axis, that is, if y > 0, as the x-axis represents y = 0.A function is negative when it is below the x-axis, that is, if if y < 0.In the context of this problem, the function is given by:
y = 2x + 1.
We want to find when the function is positive, hence we have to solve this following inequality:
y > 0
2x + 1 > 0
2x > -1
x > -1/2.
Hence the interval is:
(-1/2, ∞).
What is the missing information?The problem asks for the interval in which the function is positive.
More can be learned about the signal of a function at https://brainly.com/question/1527366
#SPJ1
Jasmine ran for 98.4 minutes. Throughout her run, she ran at a pace of 8.2 minutes per mile.How many miles did Jasmine run? Jasmine ran___ miles.
In this case, we'll have to carry out several steps to find the solution.
Step 01:
time = 98.4 minutes
rate = 8.2 minutes per mile = 8.2 minutes / mile
distance = ?
Step 02:
[tex]\begin{gathered} \text{distance = time / rate } \\ \text{distance = }\frac{98.4\text{ minutes}}{8.2\text{ minutes /mile}} \end{gathered}[/tex]distance = 12 miles
The answer is:
Jasmine ran 12 miles.
How many times greater is 3.08\times 10^{8}3.08×10
8
than 4.4\times 10^{6}4.4×10
6
? Express your answer using either standard notation or scientific notation.
The number of times that 3.08 × 10^8 is greater than 4.4 ×× 10^6 as a scientific notation is 0.7 × 10^2.
What is scientific notation?Scientific notation simply means the way of expressing numbers that are too big or too small.
In this case, the numbers that are given are 3.08 × 10^8 and 4.4 ×× 10^6
Then we have to divide them to know the number of times that it's greater. This will be:
= (3.08 × 10^8) / (4.4 × 10^6)
= 0.7 × 10^2
This illustrates scientific notation.
Learn more about scientific notation on:
brainly.com/question/1767229
#SPJ1
4 x + 2 + x = blank x – 19
The result of the equation 4 x + 2 + x = x – 19 is - 5.25.
The definition of an equation in algebra is a mathematical statement that demonstrates the equality of two mathematical expressions. For instance, the equation 3x + 5 = 14 consists of the two equations 3x + 5 and 14, which are separated by the 'equal' sign.
There are two kinds of equations: identities and conditional equations. An identity is true for all values of the variables.
Given equation -
4 x + 2 + x = x – 19
Simplify the equation
5x + 2 = x - 19
5x - x = -19 - 2
4x = -21
x = -21 / 4
x = -5.25
Hence, -5.25 is the answer to the equation 4 x + 2 + x = x - 19.
To learn more about Equation
https://brainly.com/question/25896797
#SPJ1
Shannon read that the latest model of a car made in Europe travels to speeds up to 120 kilometers per hour. Approximately how many per miles is 120 kilometers per hour? Show your work.
74.5645 miles is 120 kilometers per hour.
Both kilometers and miles represent units used to measure distance, and their magnitudes are comparable. The only distinction left is in the length units because both speed units have a time dimension that is measured in hours. A kilometer is a unit first from the metric system, whereas the mile is a part of something like the imperial unit system, which is used in many nations like the United States as well as the United Kingdom.Although it is a more recent measurement, the mile does have a lengthy history, going at least as far back as the Romans.The Roman mile was approximately 5,000 feet long, as well as additional miles with differing lengths in various locales and eras, such as the English, Irish, and Italian miles.Divide the speed of the vehicle by 1.609 to get an approximation.
Therefore, 120 kilometers per hour = 120/1.609
=74.5645 miles per hour
74.5645 miles is 120 kilometers per hour.
Learn more about speed here:
https://brainly.com/question/13943409
#SPJ1
can you help me please
lilkyky67, this is the solution:
Let's recall that the angles in the image are consecutive interior angles and they add up to 180 degrees.
Therefore,
12x - 29 + 4x + 1 = 180
16x - 28 = 180
Adding 28 at both sides:
16x - 28 + 28 = 180 + 28
16x = 208
Dividing by 16 at both sides:
16x/16 = 208/16
x = 13
Now, we can find out the measures of the two angles, as follows:
First angle:
12x - 29 = 12 * 13 - 29
156 - 29 = 127
Second angle:
what is 7.13X6=????????????????????
7.13 x 6 = 42.78
7 x 6 = 42
0.1 x 6 = 0.6
0.03 x 6 = 0.18
12 + 0.6 + 0.18 = 42.78
what is the fraction in decimal form ?19/25choose : 0.76, 1.31, 2.06, 7.6
We want to write in decimals the following fraction
[tex]\frac{19}{25}[/tex]To write this as a decimal number, first we need to convert the denominator to a power of 10. We can do that by multiplying both the numerator and denominator by 4.
[tex]\frac{19}{25}=\frac{19}{25}\cdot\frac{4}{4}=\frac{19\cdot4}{25\cdot4}=\frac{76}{100}[/tex]Now, we just effectuate the division
[tex]\frac{76}{100}=0.76[/tex]0.76 is our answer.
find the equivalent function for f(x)=6(2)3xthe 3x is supposed to be an exponent pls help
Answer:
An equivalent function to the given function is;
[tex]f(x)=6(8)^x[/tex]Explanation:
Given the function;
[tex]f(x)=6(2)^{3x}[/tex]we want to find an equivalent function to the given function;
Applying the rules of exponent;
[tex]\begin{gathered} f(x)=6(2)^{3x}=6(2^3)^x \\ =6(2\times2\times2)^x \\ =6(8)^x \end{gathered}[/tex]Therefore, An equivalent function to the given function is;
[tex]f(x)=6(8)^x[/tex]