Madelyn and her friend Beth are each baking apple pies and tarts for a bake sale, using the same recipes. Madelyn baked 1 apple pie and 3 apple tarts, using a total of 19 apples. Beth made 10 apple pies and 10 apple tarts, which used 110 apples. How many apples does each dessert require?
An apple pie uses ____ apples and an apple tart requires____apples.
Answer:
An apple pie uses 7 apples and an apple tart requires 4 applesStep-by-step explanation:
Apple pie - p, apple tart - t
Set the system as follows:
p + 3t = 1910p + 10t = 110Solve by substitution, p = 19 - 3t:
10(19 - 3t) + 10t = 110190 - 30t + 10t = 11020t = 190 - 11020t = 80t = 4Find the value of p:
p = 19 - 3*4 = 19 - 12 = 7The equations are
x+3y=19--(1)10x+10y=110=>x+y=11---(2)Subtracting both equations
[tex]\\ \sf\longmapsto 2y=8[/tex]
[tex]\\ \sf\longmapsto y=4[/tex]
Put in equation (2)
[tex]\\ \sf\longmapsto x+4=11[/tex]
[tex]\\ \sf\longmapsto x=7[/tex]
Solve the inequality 2(4x – 3) ≤ 5x – 27
Answer:
( -7, ∞)
Step-by-step explanation:
2(4x - 3) ≥ 5x - 27
8x - 6 ≥ 5x - 27
3x - 6 ≥ -27
3x ≥ -27 +6
3x ≥ -21
x ≥ -7
All numbers great than -7
At the local deli, David bought two ginger ales and two bagels for $6.60. Sumaiya bought four ginger ales and three bagels for $11.70.
Find the exact cost of one bagel and one ginger ale.
PLS HELP
Step-by-step explanation:
let the ginger ales be $x and the bagels $y.
Case 1, 2x+2y=6.60 x+y=3.30 ......1
Case 2, 4x+3y=11.70. .....2
1, x+y=3.30...×4
2, 4x+3y=11.70...×1
1, 4x+4y=13.20
2, 4x+3y=11.70
(-) (-) (-)
____________
y=1.50
____________
now, placing the value of y in equation 1,
x+y=3.30
x+1.50=3.30
x=1.80
therefore, the exact cost of one bagel and one ginger ale is $1.50 and $1.80 respectively.
hope this helps you.
Nicole is running for school president. Her best friend designed her campaign poster, which measured 3 feet by 2 feet. Nicole liked her poster so much, she reproduced the artwork on rectangular buttons that measured 2 inches by 1 1/3 inches. What is the scale factor?
Answer:
1 feet = 12 inches3 feet = 36 inchesLarger of buttons dimension is 2 inches
Step-by-step explanation:
Boris buys a car for $23,000. The value of this car reduces by 8% each year. Find the number of complete years it takes for the value of the car to fall below $11,500.
Answer:
2 years
Step-by-step explanation:
casue if you multilpy 2 x 11,500 you get 23,000
6973x63 pls explain how u did it!
Answer:
4,39299
Step-by-step explanation:
I multiplied 3 x all the numbers in 6,973, then 6 x all the numbers (I added a 0 before I multiplied, then added both the products and got my answer.
pls answer 4th and 5th question . i do not understand
Step-by-step explanation:
4) total length of the journey is
1st hr = 74km 224m = 74224m
2nd hr = 74km 224m = 74224m
3rd hr = 58km 56m = 58056m
4th hr = 62km 8m = 62008 m
total distance (adding all) = 268512m = 268km 512m .
5) total weight = 22kg 200g = 22200g
mangoes weight = 14kg 750g = 14750g
apples weight = 5kg 80g = 5080g
total weight - fruits weight
(22200-14750-5080)g
= 2370g
= 2kg 370g.
hope this helps you.
What is the first time after midnight that all the digits on the display of a digital clock are prime numbers?
Which component is missing from the researcher’s process?
A.
B.
C.
D.
Answer:
It is B I believe, if not it's you're fault for not putting the choices...
Which of the following equations represents a quadratic relation?
Question 1 options:
2x+y=3
y=2x2+1
y=3x+1
y=2x3
Answer:
y=2x^2+1
Step-by-step explanation:
a quadratic equation has a x^2 term
if motorist drove a distance of 90km at constant speed for the first 40km and then drove 30 km/hr faster for the rest of the journey if the journey took him one hour, his average speed for the first 40 km is
Answer:
Step-by-step explanation:
The motorist drove at a distance of 90km at a constant speed for the first 40km, and then 20 km/hr faster for the rest of the journey.
The whole journey took him 1hr.
Let S denotes the average speed (in km/hr) for the first 40 km.
Hence we get the following relation,
40/S + (90 - 40)/(S + 20) = 1
or 50/(S + 20) = 1 - 40/S = (S - 40)/S
or (S + 20)(S - 40) = 50S or S^2 - 70S - 800 = 0 or (S - 80)(S + 10) = 0
or S = 80 (km/hr) [Ans]
[S cannot be negative value]
PLEASE HELP!
Use a compass and straightedge to complete the following construction Leave all construction marks. Having a sharpened pencil will allow for more precise arcs. Make sure that your construction marks are dark enough to see.
Construct a perpendicular line to the given line through the point on the line.
link to the plot: https://www.mathopenref.com/constperplinepoint.html
Answer:
draw a line straight down through p
how do i solve -3x--3+8x-24=6x+7-5x
Answer:
[tex]x=7[/tex]
Step-by-step explanation:
[tex]-3x--3+8x-24=6x+7-5x[/tex]
Two negative signs equate to a positive sign, so we can write [tex]--3[/tex] as just [tex]3[/tex]:
[tex]-3x+3+8x-24=6x+7-5x[/tex]
Add up similar terms:
[tex]5x-21=x+7[/tex]
Add 21 to both sides:
[tex]5x-21+21=x+7+21[/tex]
[tex]5x=x+28[/tex]
Subtract x from both sides:
[tex]5x-x=x+28-x[/tex]
[tex]4x=28[/tex]
Divide both sides by 4:
[tex]\frac{4x}{x} =\frac{28}{4}[/tex]
[tex]x=7[/tex]
(0, 6) and (2, 96) in exponential function
Answer:
If one of the data points has the form \displaystyle \left(0,a\right)(0,a), then a is the initial value. Using a, substitute the second point into the equation \displaystyle f\left(x\right)=a{\left(b\right)}^{x}f(x)=a(b)
x
, and solve for b.
If neither of the data points have the form \displaystyle \left(0,a\right)(0,a), substitute both points into two equations with the form \displaystyle f\left(x\right)=a{\left(b\right)}^{x}f(x)=a(b)
x
. Solve the resulting system of two equations in two unknowns to find a and b.
Using the a and b found in the steps above, write the exponential function in the form \displaystyle f\left(x\right)=a{\left(b\right)}^{x}f(x)=a(b)
x
.
Step-by-step explanation:
simplify 6(x+3-2) (4-x)
Write the equation of the line from the graph.
Answer: y = 4x + 2
Step-by-step explanation:
A linear equation is usually in y= mx + b form, where m is the slope and b is the y-intercept.
In order to calculate the slope, we choose two-point from the graph. (-1 ,-2) and (0, 2).
slope = [tex]\frac{y_{2}- y_{1} }{x_{2} -x_{1} }[/tex]
= (2 - (-2)) / (0 - (-1))
= (2 + 2) / (0 + 1)
= 4 / 1
= 4
y-intercept means the y value when x is 0, according to the graph, the y value when x at 0 was 2. So the y-intercept is 2.
Plug both slope and y-intercept in, we get the equation:
y = 4x + 2
Answer: y = 4x + 2
Step-by-step explanation:
Find the value of x in the triangle shown below.
102
48
Answer:
The sum of the angles of a triangle is always 180, so the answer is
180-102-48=30
Step-by-step explanation:
The formula to find the volume of a sphere is = 4 3, where is the radius of the 3
sphere. What is the formula in terms of ?
Answer:
d.
took the test
Step-by-step explanation:
The local sporting goods store is having a 40% off sale on hockey gear that normally costs $100. You will have to pay a 7% sales tax, based on the discounted price, on any purchase you make. Which statements are true about the problem? Check all that apply.
A.You can simplify the problem by calculating 33% of $100.
B.You should find the discounted price of the gear first.
C.The tax should be calculated on the original $100 price.
D.The discount should be calculated on the original $100 price.
Answer:
a, d
Step-by-step explanation:
Hope this helps
let me know weather it is right or wrong
Which one is not a function? And why not ?
Answer:
the selected answer/2
Step-by-step explanation:
not a function because the same y has 2 different x values
Solve for the variable in the following proportion.
1/4 is to 1 1/4 as 2 is to b
B =
Can someone give an explanation?
Answer: b = 10
Step-by-step explanation:
We want a ratio of b/2 that is equal to the ratio of 1/4 to 1 1/4 (or 5/4).
Ratio of (1/4)/(5/4):
(1/4)/(5/4) = (1/4)*(4/5) = 4/20 = 1/5 or 0.2
We want 2/b = 1/5 or 0.20
2/b = 0.20
b = 2/0.20
b = 10
--
Check: Does 10/2 = (1/4)/(5/4)?
Yes
b is 10
NEED HELP NOW thanks
Answer:
13 uvugugugugycycycycycycy
Step-by-step explanation:
cycle yvy
Step-by-step explanation:
it's somehow confusing because there's no coordinates for line k
Find a point-slope form for the line with slope
and passing through the point (-4,-7).
Answer:
[tex]\displaystyle y + 7 = \frac{1}{5}(x + 4)[/tex]
General Formulas and Concepts:
Algebra I
Point-Slope Form: y - y₁ = m(x - x₁)
x₁ - x coordinate y₁ - y coordinate m - slopeStep-by-step explanation:
Step 1: Define
Identify variables.
Point (-4, -7)
Slope m = [tex]\displaystyle \frac{1}{5}[/tex]
Step 2: Find Equation
Substitute in variables [Point-Slope Form]: [tex]\displaystyle y - -7 = \frac{1}{5}(x - -4)[/tex]Simplify: [tex]\displaystyle y + 7 = \frac{1}{5}(x + 4)[/tex]dose anyone know the answers?
Answer:
Number 1 is 3.5, Number 2 is 4.29(because their are 30 days in april), Number 3 is 11, Number 4 is 90.5 miles per hour(MPH) i think
Step-by-step explanation:
a hockey team earns 2 points for a win,1 point for a tie, and 0 points for a loss. the number of points earned can be calculated using this formula
P = 2x + y where P = number of points
x = number of wins
y = number of ties
How many points would a team earn if they played 52 games, won 24 and lost 19?
Answer: 57
Step-by-step explanation: First add the won and lost games then subtract the sum from the total games played to determine how many games were tied. Then take the won games and multiply them by 2, take the tied games, and add them together to get your answer: 57.
The prices of items in a shop were reduced by 10% during reduction sales. if a costumer buys an electric fan at $810.00. What was the original price?
Answer:
See below:
Step-by-step explanation:
Hello! I hope you are having a nice day.
We can solve the problem in 2 steps, one being Solving, and the second being Comprehending. I'll start with comprehending.
Comprehending
We can start by analyzing the problem and creating an equation to then begin solving.
So, we know that a number, which we will call [tex]x[/tex] has a discount of 10% to get the current price of $810. We know that when there is a discount, we need to find what the 10 percent is then add it to the current price;$810.
We can create a formula and steps by doing the following:
[tex]x*0.9=810[/tex]
We have 0.9 as there is a 10% discount (0.1) and we subtract 1.00 by 0.1 to get 0.9. (Which is 90%).
This states that 90% of a number is equal to 810.
Now that we have an equation, we can begin solving.
Solving
We can solve the problem by using basic algebra.
[tex]x*0.9=810\\x*\frac{9}{10}=810\\x=(810*10)\div 9\\x=8100 \div 9\\x=900[/tex]
On step 1, we convert the decimal to a fraction for easy simplification/solving.
On step 2, we split the fraction into two and since we're dividing, we can flip the fraction and multiply by 10 and divide by 9.
On step 3, we use basic algebra and after step 4 we get our answer.
We can double check out answer by doing the following:
[tex]900-(900*0.10)=810?\\900-90=810?\\810=810[/tex]
We have checked our answer and gotten our answer of $900.
Cheers!
There are 495 pages in the mathematic book, from this 330 pages are included for the first term. Find the proportion of total pages to allotted pages in simplest form.
Answer:
330/495 = 2/3
the answer is 2/3
Answer:
3 : 2
Step-by-step explanation:
Total pages : allotted pages = 495 : 330
Find the HCF of 495 and 330
495 = 5 * 3*3*11
330 = 5 * 3 * 2 * 11
HCF = 5 * 3 * 11 = 165
Divide 495 and 330 by 165
495 : 330 = 3 : 2
Can somebody help me with this. Thank you.
Answer:
There wasn’t any question posted
Step-by-step explanation:
The question was not posted, therefore there is no logical way to help you with the question.
What is 0.375 as a whole percent?
Answer:
0.375 is 37.5 % of 1
Step-by-step explanation:
HELP PLEASE!!!
Identify a point and two x intercepts to write the x-intercept form equation of each parabola.
x intercepts are 5 and 7
The third point I used was (6,-2); however, you can use any other point you want as long as it's not one of the x intercepts mentioned.
==========================================================
Explanation:
The x intercepts are 5 and 7, where the parabola crosses the x axis. Because of these roots, the two factors are x-5 and x-7.
We can think of the root x = 5 turning into x-5 = 0 after subtracting 5 from both sides. The same goes for x = 7 turning into x-7 = 0.
Put together, the two factors lead to (x-5)(x-7) and we get the equation y = (x-5)(x-7). Plugging either x = 5 or x = 7 into this equation produces y = 0.
-------------------
Notice that plugging in x = 6 leads to...
y = (x-5)(x-7)
y = (6-5)(6-7)
y = (1)(-1)
y = -1
However, the graph shows that x = 6 should lead to y = -2 instead. To fix this, we can stick a 2 out front like so
y = 2(x-5)(x-7)
y = 2(6-5)(6-7)
y = 2(1)(-1)
y = -2
The error has been fixed. As you can see, we need this third point to help nail down the parabolic equation. You can pick any other x value you want as long as it's not 5 or 7.
-------------------
Let's try another x value. Let's say we pick x = 8
y = 2(x-5)(x-7)
y = 2(8-5)(8-7)
y = 2(3)(1)
y = 6
We see that x = 8 leads to y = 6. This matches what the graph shows that (8,6) is a point on the parabola. I'll let you try other x values.
-------------------
In short, we used the roots 5 and 7 to generate the partial factorization (x-5)(x-7). Then we used a third point (6,-2) to help determine the coefficient out front which was 2.
So after using that point, we go from y = (x-5)(x-7) to y = 2(x-5)(x-7) which is the final answer. This is considered x-intercept form because we can quickly read off the x intercepts from this equation.