[tex]-6x+12y=24\\\\x-intercept\ for\ y=0:\\\\-6x+12(0)=24\\-6x=24\qquad\text{divide both sides by (-6)}\\\boxed{x=-4}\to(-4,\ 0)\\\\y-intercept\ for\ x=0:\\\\-6(0)+12y=24\\12y=24\qquad\text{divide both sides by 12}\\\boxed{y=2}\to(0;\ 2)[/tex]
Chris works at Higgins’ Automart and is selling a new Shelby Mustang for $59,000. If he earns a commission of 3%, how much money does he earn? Write a proportion and show all steps of your work.
The answer I came up with is 177.
Answer:
$1770
Step-by-step explanation:
Remember that percent means "out of 100". 3% as a ratio is 3:100 or 3/100.
59,000 is the total amount, the whole, so it corresponds to 100%.
The problem is asking:
59,000 is to 100 as what is to 3?
59,000/100 = x/3
Cross multiply:
100x = 59,000 * 3
100x = 177,000
x = 1770
The commission is $1770.
An artist is creating a large butterfly sculpture outside a museum. There is a circular dot on each wing made out of metal ring. The distance around each dot is 24π inches. The artist plans to fill the inside of each dot with blue colored glasses. What is the area of the blue glass will be needed to fill each butterfly dot?
The area of the blue glass needed to fill each dot is 144π square inches.
Explanation:To find the area of the blue glass needed to fill each dot, we need to first determine the radius of the dot. The distance around each dot is given as 24π inches, which means the circumference of the dot is 24π inches.
Using the formula for circumference, 2πr = 24π, we can solve for the radius r, which is 12 inches. The area of the blue glass needed to fill each dot is then the area of a circle with radius 12 inches, which is given by the formula A = πr^2.
Substituting the value for r, we get A = π(12)^2 = 144π square inches.
Use an equation to find the value of k so that the line that passes through (-4, k)(−4, k) and (6, −7) has a slope of m= -1/5.
Answer:
The value of k is -5.
Step-by-step explanation:
To find the value of k, start by using the known information we have in the equation for slope. The equation is below.
m(slope) = (y2 - y1)/(x2 - x1)
In this equation, the first ordered pair would be (x1, y1) and the second would be (x2 , y2). So we put the values in for these variables and we get.
-1/5 = (-7 - k)/(6 + 4)
-1/5 = (-7 - k)/10
Now we can use cross multiplication to solve for k.
-1/5 = (-7 - k)/10
-1*10 = 5(-7 - k)
-10 = -35 - 5k
25 = -5k
-5 = k
Answer:
k=-5
Step-by-step explanation:
To find the value of k, start by using the known information we have in the equation for slope. The equation is below.
m(slope) = (y2 - y1)/(x2 - x1)
In this equation, the first ordered pair would be (x1, y1) and the second would be (x2 , y2). So we put the values in for these variables and we get.
-1/5 = (-7 - k)/(6 + 4)
-1/5 = (-7 - k)/10
-1/5 = (-7 - k)/10
-1*10 = 5(-7 - k)
-10 = -35 - 5k
25 = -5k
-5 = k
42 is 60% of what number
Question
42 is 60% of what number
Answer:
70Step-by-step explanation:
42 : 60 * 100 =
70
--------------------
check
70 * 60% =
42
the answer is good
Are these fractions proportional? 1/3 = 6/20
Answer:
They are not proportional.
Step-by-step explanation:
To check if the fractions are proportional, we can use cross products.
1 6
----- = --------------
3 20
1 * 20 = 3 * 6
20 = 18
This is not true, so they are not proportional.
Answer,
No
Explanation,
To find out if a pair of fractions are proportional you can use cross multiplication. Only fractions that are equivalent to eachother are proportional.
1/3 = 6/20
1 * 20 = 20
3 * 6 = 18
As we can see they are not equivalent, therefore it is not proportional.
Hope This Helps :-)
solve for 7 + y = -2 -3x
Answer:
y = -3x-9
Step-by-step explanation:
7 + y = -2 -3x
To solve for y, subtract 7 from each side
7 -7+ y = -2 -3x-7
y = -3x-9
(1.02 x 10^8) + (9.4 x 10^7) + (6.8 x 10^7)
I NEED HELP!!!!
Answer:
2.64 × 10⁸
Step-by-step explanation:
When you add numbers in scientific notation, you must convert them to have the same exponents.
One way is to divide the pre-exponential term by some power of 10 and multiply the exponential term by the same number.
1.02 × 10⁸ = 1.02 × 10⁸
+ (9.4/10¹) × (10⁷×10¹) = 0.94 × 10⁸
+ (6.8/10¹) × (10⁷×10¹) = 0.68 × 10⁸
TOTAL = 2.64 × 10⁸
The equation below describes a circle. What are the coordinates of the center of the circle? (X-4)^2+ (y+12)^2=17^2
Answer:
(4,-12)
Step-by-step explanation:
The equation of a circle has the following form:
[tex](x-h)^2+(y-k)^2=r^2[/tex] where (h,k) is the center of a circle with radius r.
Our equation is:
[tex](x-4)^2+(y+12)^2=17^2[/tex]
The center is (4,-12).
Answer:
(4,-12)
Step-by-step explanation:
Using the GCF, what is the factored form of 24v – 84?
Answer:
12(2V -7)
Step-by-step explanation:
Using the Greatest Common Factor, we need to find factor out the greatest common factor of the two numbers ; 24 and 84. That is; the greatest number that can divide 24 and 84
The easiest way to find the greatest common factors is;
1. To first find the factors of each number
2. Find the common factors of the two numbers
3. Find the greatest number among those factors
Factors are number that can divide a number without a remainder.
Factors of 24 are; 1, 2, 3, 6, 8, 12 and 24
Factors of 84 are; 1, 2, 3, 6, 7, 12, 14, 42 and 84
common factors are the factors that are common between the two numbers. That is; factors we can find in 24 and as well as 84
common factors are; 1, 2, 3, 6, and 12
Greatest Common Factor : This is also known as the highest common factor, it is the highest among the common factors.
Greatest Common Factor is 12.
Now after we've gotten our Greatest Common Factor(GCF), The next is to factor out this Greatest Common Factor(GCF);
24v - 84 = 12(2v - 7)
Therefore, the factored form of 24v - 84 is 12(2v -7)
The factored form of the given expression is 12(2v-7)
Equations are expressions separated by an equal sign
Greatest common factor is the highest value that can go in a particular expressions
Given the expression 24v - 84
Find that factors of both terms
24v = 12 × 2v
84 = 12 × 7
Since 12 is common to both terms, hence the GCF form of the expression will be written as;
24v - 84 = 12(2v - 7)
Hence the factored form of the given expression is 12(2v-7)
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Simplify: -|-10| + 3-39/4
|-10| = 10
39/4 = 9 3/4
-|-10| + 3 - 39/4 = -10 + 3 - 9 3/4 = -7 - 9 3/4 = -16 3/4
A part of your bike has broken. You decide to send it back for a full refund. It has cracked along every line of symmetry.
How many lines of symmetry does the shape have?
Answer:
1
Step-by-step explanation:
line is going along the whole bike
if lines m and n are parallel, and < 1 measures 125°, which is the measure of < 2?
a. 25°
b. 40°
c. 55°
d. 150°
Answer: 55°
Step-by-step explanation:
Line n is irrelevant.
Angle 1 plus angle 2 is 180° because line m is a straight line
180 - 125 is 55
Jeff uses 116Rubber bands to make a rubber band ball. He estimates that he has used 448 rubber bands to make 12 rubber band bottles of the same size. Use estimation to check and explain whether his answer is reasonable or not.
Answer:
His answer is not reasonable.
Step-by-step explanation:
448 rubber bands to make 12 rubber band bottles of the same size.
450 divided by 10 is about 45 rubber band per rubber band bottle.
This is nowhere near the the 116 rubber bands to make a rubber band ball.
If the are about the same size, we should use about the same number of rubber bands.
If he used about 100 rubber bands per rubber band bottle * 12 bottles, that would be about 1200 rubber bands.
The actual length of side y is 22 cm. Use the scale drawing to find the actual length of side x
Answer:
the answer is 28.3 cm
Step-by-step explanation:
Answer:
The answer is 28.3cm
Step-by-step explanation:
You take the "new" side length, 22 cm, over the "old" side length, 1.4 cm and write the proportion 22/1.4= x/1.8 cm using x as the unknown, and 1.8 cm as the other "old" side length. Then solve. Multiply 22 x's 1.8. Then divide by 1.4. Giving us the solution x= 28.3 cm.
Hope this helps!
Help me on number problem 7 please
Answer:
D: (-infinity, infinity) R: (-infinity, infinity)
Step-by-step explanation:
The absolute value of x - 3 is x+ 3.
y = x + 3 + 1
y = x + 4
Your y intercept is your c value. Your c value is 4.
4 is your y intercept.
Place a point on 4. This is your starting point. Rise over run is 1/1
To find the positive points, go up one from the y intercept and over one, repeating the process until you reach the edge of the graph.
To find the negative points, do the opposite. Go down one and to the left, but still repeat the process until you reach the end of the graph.
Linear equations are always ended with arrows on both sides, meaning that the line continues forever, or infinitely.
To find domain, look at the x values.
Because the lines go on infinitely, you know that your domain is (-infinity, infinity).
To find your range, look at your y values.
Because the lines go on infinitely, you know that your range is also (-infinity, infinity).
Make sure to use the symbol for infinity instead of the words. In case you do not know what the infinity symbol is, it simply looks like an 8 that is rotated 90 degrees.
What is e-1/2f when e=15 and f=2
Answer:
14
Step-by-step explanation:
Replace with the values
15-1/2(2) = 15-1 = 14
Answer:
14
Step-by-step explanation:
e-1/2f
Let e =15 and f =2
We can substitute these values into the expression
15 - 1/2 (2)
15 - 1
14
if you have 5 apples and gave me 4 how many apples do you have
Answer:
I would have 1 apple
Step-by-step explanation:
5 apples
Gave 4 away
5 - 4 = 1
So you would have 1 apple
Gas costs $2.09 and you figure you will use 30 gallons on your trip with your two friends. You will stay 4 nights at a hotel (one room) for $98 a night, and spend $25 each per day on food for 5 days. What is the total cost of your trip?
Final answer:
The total trip cost, including gas, hotel, and food for three people, is $829.70, calculated by multiplying the quantities by their respective unit prices and summing up all costs.
Explanation:
Calculating the Total Trip Cost
To calculate the total cost of the trip, we need to consider the cost of gas, hotel, and food. For gas, the cost is $2.09 per gallon, and the consumption is 30 gallons. The hotel cost is $98 per night for 4 nights. Each person's food cost is $25 per day for 5 days.
Here is the detailed calculation:
Therefore, the total cost of the trip is $829.70.
The total cost of the trip is $705.70.the total cost of the trip amounts to $705.70. This includes various expenses such as gas for the trip calculated at $62.70, hotel expenses totaling $392 for the four-night stay, and food expenses adding up to $375 for three people over five days.
Explanation:To calculate the total cost, start with the gas cost: 30 gallons * $2.09/gallon = $62.70. Next, calculate the hotel expenses: 4 nights * $98/night = $392. Then, calculate the food expenses: 3 people * $25/day * 5 days = $375. Add all these expenses together: $62.70 (gas) + $392 (hotel) + $375 (food) = $829.70.
However, to account for the cost shared among friends, divide the total by 3: $829.70 / 3 = $276.57 per person. Finally, multiply the individual cost by 3 people to find the total cost: $276.57/person * 3 people = $829.70. The final total cost of the trip, considering shared expenses, is $705.70. This includes gas, hotel accommodation, and food for three individuals across the entire trip duration.
In summary, the total cost of the trip amounts to $705.70. This includes various expenses such as gas for the trip calculated at $62.70, hotel expenses totaling $392 for the four-night stay, and food expenses adding up to $375 for three people over five days.
The calculation incorporates sharing costs among the three friends, dividing the overall expenses equally. Each individual's share amounts to $276.57, resulting in a final total cost of $705.70 for the entire trip. This comprehensive calculation considers all major expenses incurred during the trip and divides the shared costs among the friends, arriving at the total trip expenditure.
Insert parentheses in the expression 6 + 10 x 2 so that the expression equals 32
Final answer:
By inserting parentheses to create the expression (6 + 10) x 2, we change the order of operations and get the desired result, which is 32.
Explanation:
The question involves inserting parentheses in the expression 6 + 10 x 2 so that the result of the expression equals 32. According to the order of operations, we typically perform multiplication before addition, so if we compute the expression as it stands, we would get 6 + (10 x 2) = 6 + 20 = 26, which is not the result we want. To achieve the desired result, we need to adjust this order. By adding parentheses, we can change the order in which the operations are performed. Thus, the correct placement of parentheses would be (6 + 10) x 2, which gives us (16) x 2 = 32.
25 Points!! Need help ASAP!!! Plzz help!!!
<1 and <5 are _____ angles.
A. alternate exterior
B. alternate interior
C. supplementary
D. right
<5 and <7 are _____ angles.
A. alternate exterior
B. alternate interior
C. supplementary
D. right
E. corresponding
Answer:
C and E
Step-by-step explanation:
Supplementary angles add up to 180
Corresponding angles are the same angle in a different location
Answer:
1 and 5 are supplementary angles
5 and 7 are corresponding angles
Step-by-step explanation:
John creates a regression line for his data and then plots the residuals. The residual plot looks like a quadratic function. What does this mean?
A) A pattern in the residuals has no meaning.
B) That the original data forms a quadratic pattern.
C) That his regression equation is a quadratic function.
D) That the regression equation is not a good fit for the data.
Based on the information given regarding the regression line, the correct option is D. That the regression equation is not a good fit for the data.
What is a regression line?A regression line simply means a single line that best fits the data. It should be noted that the formula for the regression line is y = mx + b.
Based on the question asked, since the residual plot looks like a quadratic function, it means that the regression equation is not a good fit for the data.
If the regression line is a good fit for the model, there'll be no pattern in the residual. In this case, since there is a residual, it means that the regression equation is not a good fit for the data.
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A residual plot showing a quadratic pattern suggests the current linear regression model is inappropriate and a non-linear model might be required. Answer D is correct: the residual plot indicates the regression equation is not a good fit for the data.
When a residual plot exhibits a pattern, such as a quadratic function, this indicates that the regression equation used to fit the data may not be appropriate; specifically, it suggests that a linear model does not properly capture the relationship between the variables. Instead, the underlying relationship may be better modeled with a non-linear equation, such as a quadratic function.
The correct answer to the student's question is D) That the regression equation is not a good fit for the data.
A good residual plot will have residuals scattered randomly around the horizontal axis, which means that the regression model adequately captures the pattern in the data.
What is the value of f(–1)?
Answer:
The answer is: 1
Step-by-step explanation: f(1) = -1, so f(-1) must be 1.
The value of the function by using a given table would be, f (- 1) = 0
Hence, option 3 is true.
Given that,
The function to find the value, f (- 1)
Used the concept of function which stated that, A relation between a set of inputs having one output each is called a function.
Now from the given table,
At x = - 5;
f (- 5) = 4
Similarly,
At x = - 1;
f (- 1) = 0
Therefore, the value of function f (- 1) would be 0.
So, Option 3 is true.
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The complete question is shown in the attached image.
Lucia has 48 markers and 64 stickers that she wants to give as favors for a party. She wants to put an equal number of markers and an equal number of stickers into each favor bag. She uses all the markers and stickers
Answer:
8
Step-by-step explanation:
1) find the least common denominator
48/8=6
64/8=8
2) check
8 times 6 is 49
8 times 8 is 64
what is the inequality of p-1>3
Answer:
p > 4 if thats what ur asking.
Step-by-step explanation:
p-1>3
Add 1 to each side, it cancels out the -1
p > 4
Answer:
p>4
Step-by-step explanation:
p-1>3 given
p>4 addition property of equality
what substitution should he used to rewrite x^8-3x^4+2
Answer:
The correct
answer between all the choices given is the second choice or letter B. I am
hoping that this answer has satisfied your query and it will be able to help
you in your endeavor, and if you would like, feel free to ask another question.
evaluate ( 25/36)^ 1/2.
Answer:
The correct option is C.
Step-by-step explanation:
The given expression is
[tex](\frac{25}{36})^{\frac{1}{2}[/tex]
It can be written as
[tex]\sqrt{\frac{25}{36}}[/tex] [tex][\because x^{\frac{1}{2}=\sqrt{x}][/tex]
Using the property of radical expression, we get
[tex]\frac{\sqrt{25}}{\sqrt{36}}[/tex] [tex][\because \sqrt{\frac{a}{b}}=\frac{\sqrt{a}}{\sqrt{b}}][/tex]
[tex]\frac{5}{6}[/tex]
The value of given expression is 5/6. Therefore the correct option is C.
two runners start 30kilometer apart and run toward each other. they meet after 3hours. One Runner runs 2 kilometers per hour faster than the other runner. What rate do they run
Let the slower runners speed be X kilometers per hour.
Then the faster runners speed would be X+2 kilometers per hour.
The formula for distance is Speed times time.
The distance is given as 30 kilometers and time is given as 3 hours.
Since there are two runners you need to add the both of them together.
The equation becomes 30 = 3x + 3(x+2)
Now solve for x:
30 = 3x + 3(x+2)
Simplify:
30 = 3x + 3x +6
30 = 6x + 6
Subtract 6 from each side:
24 = 6x
Divide both sides by 6:
x = 24/6
x = 4
The slower runner ran at 4 kilometers per hour.
The faster runner ran at 4+2 = 6 kilometers per hour.
At the animal shelter, there are 8 cats and 20 dogs. What is the ratio of cats to dogs?
Answer:
2:5
Step-by-step explanation:
cats: dogs
8:20
We can divide each by 4
8/4: 20/4
2:5
f(x) = x + 5 If you know that the range is {0, 10}, then... The domain must be ??
Answer:
domain {- 5, 5 }
Step-by-step explanation:
given values in the range, that is values of y then to find the domain equate f(x) to the given values in the range, that is
x + 5 = 0 ⇒ x = - 5
x + 5 = 10 ⇒ x = 10 - 5 = 5
domain is x ∈ { - 5, 5 }
Lily is saving for her first car. She has $2,500 in a savings account that pays 4.25% annual interest.