Answer:
x = 2, y = 3 → (2, 3)Step-by-step explanation:
[tex]\left\{\begin{array}{ccc}4x = -3y + 17&\text{add}\ 3y\ \text{to both sides}\\3x - 4y = -6\end{array}\right\\\\\left\{\begin{array}{ccc}4x+3y=17&\text{multiply both sides by 4}\\3x - 4y = -6&\text{multiply both sides by 3}\end{array}\right\\\\\underline{+\left\{\begin{array}{ccc}16x+12y=68\\9x -12y = -18\end{array}\right}\qquad\text{add both sides of the equations}\\.\qquad25x=50\qquad\text{divide both sides by 25}\\.\qquad x=2\\\\\text{Put the values of }\ x\ \text{to the second equation}[/tex]
[tex]3(2)-4y=-6\\6-4y=-6\qquad\text{subtract 6 from both sides}\\-4y=-12\qquad\text{divide both sides by (-4)}\\y=3[/tex]
Emily has $3.15 worth of dimes and quarters. She has twice as many dimes as quarters. Determine the number of dimes and the number of quarters that Emily has.
Answer:
The number of dimes is 14 and the number of quarters is 7.
Step-by-step explanation:
Given:
Emily has $3.15 worth of dimes and quarters.
She has twice as many dimes as quarters.
Now, to determine the number of dimes and the number of quarters.
Let the number of quarters be [tex]x.[/tex]
And the number of dimes be [tex]2x.[/tex]
So, the total worth of dimes and quarters = $3.15.
Now, to get the number of dimes and quarters:
According to question:
[tex]0.10(2x)+0.25x=3.15[/tex]
[tex]0.20x+0.25x=3.15[/tex]
[tex]0.45x=3.15[/tex]
Dividing both sides by 0.45 we get:
[tex]x=7.[/tex]
Thus, the number of quarters = 7.
So, the number of dimes = [tex]2x=2\times 7=14.[/tex]
Therefore, the number of dimes is 14 and the number of quarters is 7.
Rudolph ate 30 pounds of reindeer food in 3 hours. How many pounds did he eat each hour?
Answer:
Step-by-step explanation:
30 lbs in 3 hrs....
30/3 = 10 lbs per hr <==
Answer:
10 pounds
Step-by-step explanation:
if you divide 30 by 3 you will get 10 and becuase there are three hours you will have the answer as 10
30÷3=10
10×3=30
A waiter received a $15.25 tip. If the check totaled $25, what percentage was received?
Answer:
61%
Step-by-step explanation:
15.25/25
=0.61
Multiply it by 100 and you will get the answer
Whole row form: 15.25/25*100
61 percentage was received.
Hope that helps! :)
Answer: He received 61%
Step-by-step explanation:
Hi, to answer this question we have to analyze the information given:
Tip (t) : $15.25 Total amount (T): $25To, find the percentage (p):
p = t/T x 100
Replacing with the values given:
p = (15.25/25)x100
p= 0.61 x 100=61%
He received 61%
Feel free to ask for more if needed or if you did not understand something.
Vivi is a drummer for a band. She burns 756756756 calories while drumming for 333 hours. She burns the same number of calories each hour.
How many calories does Vivi burn per hour?
burned: 756 calories
hours: 3
same number of calories each hour
-> to find this, we must split the number of calories evenly among the hours
steps
756/3
= 252 calories per hour
Answer:
252
Step-by-step explanation: 756/3
The scatterplot represents the total fee
for miles traveled on a toll road.
The line of best fit for the data is
y = 0.043x + 0.324.
Use the line of best fit to predict the toll
when 100 miles are driven.
Answer:
[tex]4.624[/tex]
Step-by-step explanation:
[tex]y=0.043x+0.324\\given \ miles \ x=100\\y= 0.043\times100+0.324\\=4.3+0.324\\=4.624[/tex]
There were 9 beluga whales, 3 bowhead whsles, and 2 narwhales. Each whale travels 6 miles. How many miles did the whale trvael?
84 miles I would think
Explanation:
14 whales in all, each travelled 6 miles.
14x6=84
Hope I helped :)
The axis of symmetry for a quadratic equation can be found using the formula x =
where a and b are coefficients in the
quadratic equation and x represents the values along a vertical line on the coordinate plane.
What is the equation when solved for a?
Answer:
The denominator of the fraction is 2x and the answer is a= -[tex]\frac{b}{2x}[/tex]
Step-by-step explanation:
Suppose we have a quadratic equation of the form:
ax²+bx+c
The axis of symmetry of the parabola is given by:
[tex]x= \frac{-b}{2a}[/tex]
From here, we must clear the value of a.
For this, we follow the following steps:
1) Pass 2a multiplying to the other side of the equation:
2ax=-b
2) Clear the value of a by passing 2x to divide:
[tex]a= \frac{-b}{2x}[/tex]
Answer:
B.
a= -b/2x
Step-by-step explanation:
What is a rational number equivalent to ——
3.12
Answer:
[tex]\frac{78}{25}[/tex]
Step-by-step explanation:
A rational number has the form
[tex]\frac{a}{b}[/tex] ← where a and b are integers
3.12 = [tex]\frac{312}{100}[/tex] ← divide numerator/denominator by 4, thus
3.12 = [tex]\frac{78}{25}[/tex] ← in simplest form
Solve for x
Y= 0.39(8x+30)
Answer:
[tex]\large\boxed{x=\dfrac{50y-585}{156}}[/tex]
Step-by-step explanation:
[tex]y=0.39(8x+30)\qquad\text{use the distributive propety}\\\\y=(0.39)(8x)+(0.39)(30)\\\\y=3.12x+11.7\qquad\text{multiply both sides by 100}\\\\100y=312x+1170\qquad\text{subtract 1170 from both sides}\\\\100y-1170=312x\qquad\text{divide both sides by 312}\\\\\dfrac{100y-1170}{312}=x\\\\x=\dfrac{100y:2-1170:2}{312:2}\\\\x=\dfrac{50y-585}{156}[/tex]
Thomas is starting a new company. He has two quotes from a computer company for the cost of computers and printers. If he buys three computers and one printer, the cost is $825. if he buys 4 computers and 2 printers, the cost is $1200. How much does each computer and printer cost?
Each computer costs $225 and each printer costs $150
Step-by-step explanation:
Thomas is starting a new company. He has two quotes from a computer company for the cost of computers and printers
If he buys three computers and one printer, the cost is $825If he buys 4 computers and 2 printers, the cost is $1200We need to find how much each computer and printer costs
Assume that the cost of each computer is $x and the cost of each printer is $y
∵ The cost of each computer is $x
∵ The cost of each printer is $y
∵ The cost of 3 computers and one printer is $825
- Multiply x by 3 and add the product to y, equate the sum by 825
∴ 3x + y = 825 ⇒ (1)
∵ The cost of 4 computers and 2 printers is $1200
- Add the product of 4, x and the product of 2 , y and equate the
sum by 1200
∴ 4x + 2y = 1200 ⇒ (2)
Now we have a system of equations to solve it
Multiply equation (1) by -2 to eliminate y
∵ -6x - 2y = -1650 ⇒ (3)
- Add equations (2) and (3)
∴ -2x = -450
- Divide both sides by -2
∴ x = 225
Substitute the value of x in equation (1) to find y
∵ 3(225) + y = 825
∴ 675 + y = 825
- Subtract 675 from both sides
∴ y = 150
Each computer costs $225 and each printer costs $150
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You can learn more about the system of equations in brainly.com/question/2115716
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By setting up a system of equations from the scenarios provided, we can determine that each computer costs $225 and each printer costs $150.
To determine the cost of each computer and printer, we can set up a system of equations based on the information provided. Let C represent the cost of one computer and P represent the cost of one printer. Using the first scenario where three computers and one printer cost $825, we can write the first equation as:
3C + P = $825 ... (1)
For the second scenario where four computers and two printers cost $1200, we can write the second equation as:
4C + 2P = $1200 ... (2)
Next, we'll solve this system of equations using either substitution or elimination method. To use elimination, we can multiply equation (1) by 2 to eliminate the printers:
6C + 2P = $1650 ... (3)
Now, we subtract equation (2) from equation (3) to find C:
6C + 2P - (4C + 2P) = $1650 - $1200
2C = $450
C = $225
We now know each computer costs $225. To find the cost of a printer, we can replace C in either equation (1) or (2). Let's use equation (1):
3(225) + P = $825
675 + P = $825
P = $825 - 675
P = $150
Thus, each computer costs $225 and each printer costs $150.
What is the y-intercept of the function f(x) = -3x
Ο
Ο
on who wire on
Ο
Ο
Answer:
see the explanation
Step-by-step explanation:
we know that
The y-intercept is the value of the function when the value of x is equal to zero. Also is called the initial value of the function
I will analyze two cases
Part 1) we have
[tex]f(x)=-3x[/tex]
so
For x=0
substitute
[tex]f(0)=-3(0)=0[/tex]
therefore
The y-intercept is the point (0,0)
Part 2) we have
[tex]f(x)=-3^x[/tex]
so
For x=0
substitute
[tex]f(0)=-3^0=-1[/tex]
therefore
The y-intercept is the point (0,-1)
please help me I need it.
Deon needs 50g of shugger to make 15 biscuits.
she also needs three times as much flour as sugar
two times as much butter as sugar
Deon is going to make 60 biscuits
work out the amount of flour she needs.
Answer:
200g of sugar, 600g of flour, 400g of butter
Step-by-step explanation:
50g sugar = 15 biscuits
3 x 50g = flour --) 150g = flour
2 x 50g = butter --) 100g = butter
60/15 = 4; 4 times as much
4 x 50g = 200g of sugar
4 x 150g = 600g of flour
4 x 100g = 400g of butter
The amount of flour she needed is 600g.
Given that,
Deon needs 50g of shugger to make 15 biscuits. she also needs three times as much flour as sugar two times as much butter as sugar. Deon is going to make 60 biscuits.Based on the above information, the calculation is as follows:
50g sugar = 15 biscuits
[tex]= 3 \times 50g\\\\ = 150g\ flour[/tex]
And.
[tex]= 2 \times 50g \\\\= 100g \ butter[/tex]
Now
[tex]= 60\div15[/tex]
= 4 times
Therefore, the amount of floor should be
[tex]= 150 \times 4[/tex]
= 600 grams.
Learn more: brainly.com/question/6201432
Worst Buy, a local electronics store, advertises a sale price of 25% off all televisions 42" or bigger. Model the sale price (original price minus discount) of those televisions, y, as a function of the regular price of the TV, x.
25% off means it would be selling for 75% of the original price ( 100% - 25% = 75%).
To find the sale price you would multiply the regular price by 75%:
The equation would be y = 0.75x
PLEASE help me I really need this done by today
will mark Brainliest!!
What is the domain for the piece of the function represented by f(x) = x + 1? x < –1 –1 ≤ x ≤ 1 1 ≤ x < 2 x > 1
Note: As you missed to mention the graph for f(x) = x + 1 from where we had to check which option defines the accurate graph. But, after a little research, I was able to get the graph of this question, and hence attaching the graph. So, I am answering based on that graph which, anyways, would clear your concept about determining the domain of the function that shows in a graph.
Answer:
x > 1 is the domain of the f(x) = x + 1.
Step-by-step explanation:
A domain is the set of all x values that a function passes through. It means a domain is set of all input values where the function is defined, meaning whatever you input the x value, for every x-value there is only one y-value that corresponds to it.
So, now lets talk about the given function f(x) = x + 1 and its graph as shown in attached figure. Carefully observe the top right part of the graph of f(x) = x + 1. It is validating the condition of x > 1.
For example,
Just input some x values, greater than 1 i.e. x > 1, in f(x) = x + 1 to determine the output values.
For example, for x > 1
For x = 2, f(x) = 3. So, the graph must pass through of P(2, 3)For x = 3, f(x) = 4. So, the graph must pass through of P(3, 4)For x = 4, f(x) = 5. So, the graph must pass through of P(4, 5)and so on.
So, the top right part of the graph of f(x) = x + 1 is validating the condition of x > 1 as it is passing through P(2, 3), P(3, 4) and P(4, 5) etc. and so on.
So, x > 1 is the domain of the f(x) = x + 1.
Keywords: domain, function
Learn more about domain of the function from brainly.com/question/5401106
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Answer:
"D" X > 1
Step-by-step explanation:
HOPE THIS HELPS!!!
mike scored a 125 at a semi final diving competition season. He scored a 95 at this final season. what is the percent decrease?
Answer:
24%
Step-by-step explanation:
Formula:
x new price - old price
--------- = ---------------------------------
100% old price
Round 8923 to the thousands
Answer:
9000
Step-by-step explanation:
When you are rounding to the thousands, if the hundreds place is 500 or greater you have to round up in the thousands place.
That would mean 8923 rounded to the thousands place would equal 9000
Hope This Helps!
Answer:
9000
Step-by-step explanation:
To round a number to the nearest thousand, you look at the number in the hundreds place.
If the number in the hundreds place is
greater than 5, you add 1 to the number in the thousands place less than 5, you keep the number in the thousands place exactly 5 with only zeros following it, you round the number in the thousands place to the nearest even numberHere's how to round 8923 to the nearest thousand.
The digit in the thousands place is the 8. The number in the hundreds place (8) is greater than 5. Add 1 to the digit in the thousands place.The rounded number is 9000.
What’s equivalent to 25x + 35y
Answer:5x+7y
Step-by-step explanation:
Your welcome
Six more than five times a number is the same as nine less than twice the number. Find the number.
Answer:
x = -5
Step-by-step explanation:
let the number be x
"five times a number" : 5x
"Six more than five times a number" : 5x + 6
"twice the number" = 2x
"Six more than five times a number = 2x - 9
"Six more than five times a number" = "Six more than five times a number
5x + 6 = 2x - 9
5x - 2x = -9 -6
3x = -15
x = -15 / 3
x = -5
y-5, y=2x^2-16x+29, use substitution to solve the system of equations
Answer:
2x^2-16x+34
Step-by-step explanation:
Since Y is equal to -5
And you substitute -5 in the equation.
You now have -5=2x^2-16x+29
Add 5 to both sides
5-5=2x^-16x+29+5
The solution of the system of equations will be given as x = 4 ± i.
What is the solution of the equation?The solution of the equation means the value of the unknown or variable.
The equations are given below.
y = – 5 ....1
y = 2x² – 16x + 29 ....2
From equation 1 and 2, we have
2x² – 16x + 29 = –5
2x² – 16x + 34 = 0
x² – 8x + 17 = 0
Then the value of x will be
[tex]\rm x = \dfrac{-(-8) \pm \sqrt{(-8)^2 - 4 * 1 * 17}}{2*1}\\\\x = \dfrac{8\pm \sqrt{-4}}{2}\\\\x = \dfrac{8 \pm 2\iota}{2}\\\\x = 4 \pm \iota[/tex]
More about the solution of the equation link is given below.
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Nati randomly selected 10 girls and 10 boys from her 7th grade class and recorded their heights in inches. The results are shown. Girls: 61, 58, 63, 57, 58, 59, 62, 60, 64, 56 Boys: 58, 55, 63, 60, 58, 65, 60, 57, 63, 62 A. Find the mean and median of the girls’ heights. Show your work.
Answer:
Mean= 59.8 and median = 59.5
Step-by-step explanation:
Mean = Summation of values/ No. of Values
Mean of Girls' height= 61+58+63+57+58+59+62+64+60+56/10
Mean= 598/10= 59.8
Arranged Data = { 56, 57,58,58,59, 60, 61,62,63,64}
As the number of observations is even so the 5th and 6th value will be added and divided by 2
59+60/2= 59.5
Median = 59.5
A little towns population is growing at an annual rate of 7.5%, annually. What is it’s growth rate per 3 years? Per 5 years? Round to the nearest tenth of a percent.
Answer:
A) The increase population of town after 3 years is 1.2 times initial population
B) The increase population of town after 5 years is 1.4 times initial population .
Step-by-step explanation:
Given as :
The rate of growth of population of a town = r = 7.5%
Let The initial population of town = p
A ) Let The increase population of town after 3 years = P
The time period = n = 3 years
Now, According to question
The increase population of town after n years = initial population of town × [tex](1+\dfrac{\textrm rate}{100})^{\textrm time}[/tex]
Or, The increase population of town after n years = initial population of town × [tex](1+\dfrac{\textrm r}{100})^{\textrm n}[/tex]
Or, The increase population of town after 3 years = p × [tex](1+\dfrac{\textrm 7.5}{100})^{\textrm 3}[/tex]
Or, P = p × [tex](1.075)^{3}[/tex]
Or, P = p × 1.242
So, The increase population of town after 3 years = P = 1.2 times initial population
Hence,The increase population of town after 3 years is 1.2 times initial population . Answer
B ) Let The increase population of town after 5 years = P'
The time period = n = 5 years
Now, According to question
The increase population of town after n years = initial population of town × [tex](1+\dfrac{\textrm rate}{100})^{\textrm time}[/tex]
Or, The increase population of town after n years = initial population of town × [tex](1+\dfrac{\textrm r}{100})^{\textrm n}[/tex]
Or, The increase population of town after 5 years = p × [tex](1+\dfrac{\textrm 7.5}{100})^{\textrm 5}[/tex]
Or, P' = p × [tex](1.075)^{5}[/tex]
Or, P' = p × 1.4356
So, The increase population of town after 5 years = P' = 1.4 times initial population
Hence,The increase population of town after 5 years is 1.4 times initial population . Answer
5/6 ÷2/7 divide the fraction
Answer:
35/ 12
Step-by-step explanation:
5/6 divided by 2/7
= 5/6 x 7/2
= 35/ 12
The buyer for a chain of stores purchased lawn ornaments in bulk, paying $23 each. The stores will sell each lawn ornament for $37.08. What is the mark-up percentage?
Answer:
The markup percentage is 61.2
Step-by-step explanation:
Given as :
The cost price of each ornaments = $23
The sell price of each ornament = $37.08
Let The markup percentage = x
Now, According to question
Markup percentage = [tex]\dfrac{s.p - c.p}{c.p}[/tex] × 100
Or, x% = [tex]\dfrac{37.08 - 23}{23}[/tex]
Or, x% = [tex]\dfrac{14.08}{23}[/tex]
Or, x% = 0.612
∴ x = 0.612 × 100
I.e x = 61.2
So, The The markup percentage = x = 61.2
Hence, The markup percentage is 61.2 Answer
please help I need to get this done today
Answer:
18) If ∠1 = 124° , then ∠4 = 56°.
19) if ∠2 = 48°, then ∠3 = 132°.
20) if ∠4 = 55°, then ∠2 = 55°.
21) if ∠6 = 120° , then ∠8= 120°.
22) if ∠7 = 50.5 , then ∠6= 50.5°.
23) if ∠3 = 118.7°, then ∠2= 61.3°
Step-by-step explanation:
Given two parallel lines a and b.
And other line, which is called transversal line cuts these two parallel lines to make 8 angles.
Now,
18) Given, ∠1 = 124°
Now, sum of consecutive interior angles made by transversal line with parallel lines = 180° .
⇒∠1 + ∠4 = 180°
⇒∠a = 180° - 124° = 56°.
19) ∠2 = 48°.
as sum of consecutive interior angles made by transversal line with parallel lines = 180° .
∠2 + ∠3 = 180°.
⇒ ∠3 = 180° - 48° = 132°.
20) ∠4 = 55°
Alternate angles made by transversal line with parallel lines are equal .
⇒∠2 = ∠4 = 55°.
21) ∠6 = 120°
As corresponding angles made by transversal line with parallel lines are equal. ∠6 = ∠3 = 120°.
now, also opposite angles are equal
⇒ ∠3 = ∠8 = 120°.
22) ∠7 = 50.5
As corresponding angles made by transversal line with parallel lines are equal. ∠7 = ∠2 = 50.5°.
now, also opposite angles are equal
⇒ ∠2 = ∠6 = 50.5°.
23) ∠3 = 118.7°
as sum of consecutive interior angles made by transversal line with parallel lines = 180° .
∠3 + ∠2 = 180°.
⇒ ∠2 = 180° - 118.7° = 61.3°
NEED NEED HELP! !!!!
the midpoint is AB is M(3,-2). One endpoint is A(7,-9). Find the coordinates of the other endpoint B.
To find the coordinates of the other endpoint B given the midpoint M and one endpoint A. Apply the midpoint formula and solve the equations to find the coordinates of B(-1, 5).
Explanation:The midpoint coordinates are given as M(3, -2) and one endpoint is given as A(7, -9). To find the coordinates of the other endpoint, we can use the midpoint formula which states that the coordinates of the midpoint are the average of the coordinates of the two endpoints.
Let the coordinates of the other endpoint be B(x, y). Using the midpoint formula, we have:
[(x + 7) / 2, (y + -9) / 2] = (3, -2)
Simplifying the equation, we get:
(x + 7) / 2 = 3
(y - 9) / 2 = -2
Multiplying both sides by 2, we have:
x + 7 = 6
y - 9 = -4
Subtracting 7 from both sides, we get:
x = -1
Subtracting -9 from both sides, we get:
y = 5
Therefore, the coordinates of the other endpoint are B(-1, 5).
X/28=2/10 I need help solving for X
Answer:
x = 28/5
Step-by-step explanation:
Step 1: Cross-multiply
x / 28 = 2/10
x*(10)=(2)*(28)
10x=56
Step 2: Divide both sides by 10.
10x / 10 = 56/10
x = 28/5
The given ratios can be solved to obtain x as 5.6.
What is the application ratio and proportion?A ratio is the relation between two numbers as a / b. A proportion is the equality of two ratios as a / b = c / d.
Ratio and proportion can be applied to solve Mathematical problems dealing with unit values of the quantities.
The given expression is x/28 = 2/10.
In order to find the equality of two ratios, the cross products of their numerators and denominators are equal which is given as,
10x = 2 × 28
⇒ x = 56/10
⇒ x = 5.6
Hence, the value of x is given as 5.6.
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Find the X COORDINATE OF THE intersection of 9x - 6y = 12 and 3x + 2y =8
Answer: [tex]x=2[/tex]
Step-by-step explanation:
Given a System of linear equations, the solution of the system is the point [tex](x,y)[/tex] in which the lines intersect, where "x" is the x-coordinate and "y" is the y-coordinate.
Having the following System of equations:
[tex]\left \{ {{9x - 6y = 12} \atop {3x + 2y =8}} \right.[/tex]
You can use the Elimination method to find the value of "x":
-Multiply the second equation by 3.
- Add the equations.
- Solve for "x".
Then, you get:
[tex]\left \{ {{9x - 6y = 12} \atop {9x +6y =24}} \right.\\.......................\\18x=36\\\\x=\frac{36}{18}\\\\x=2[/tex]
Solve for X
12.8 = 8x