Answer:
hamburger = h = $0.22
Fries = f = $0.96
Cola = c = $0.82
Step-by-step explanation:
Let
last year's price for each item be hamburger = h
Fries = f
Cola = c
h + f + c = 2.00 (1)
The price of a hamburger has increased by 10%
New price of hamburger = 1.10h
The price of fries has increased by 30%
New price of fries = 1.30f
The price of cola has increased by 40%
New price of cola = 1.40c
The same meal now costs $2.58.
1.1h + 1.3f + 1.4c = 2.58 (2)
If the price of a cola is now 9 cents more than that of a hamburger
1.4c = 1.1h + .09
1.4c - 1.1h = .09
Multiply (1) by 1.4
h + f + c = 2.00 × 1.4
1.4h + 1.4f + 1.4c = 2.8 (3)
1.1h + 1.3f + 1.4c = 2.58 (2)
subtract the new equation:
0.3h + 0.1f = 0.22
Multiply by 10
3h + f = 2.2
Recall,
1.4c - 1.1h = .09
1.4h + 1.4f + 1.4c = 2.8 (3)
- 1.1h + 0.0f + 1.4c = .09
Subtract
2.5h + 1.4f = 2.71
multiply by 10
25h + 14f = 27.1
Recall
3h + f = 2.2
Multiply by 14
42h + 14f = 30.8
25h + 14f = 27.1
Subtract to eliminate f
17h = 3.7
Divide both sides by 17
h = 3.7 / 17
= 0.22
h = 0.22
Substitute h into
1.4c - 1.1h = .09
1.4c - 1.1(0.22) = .09
1.4c - 0.242 = .09
1.4c = .09 + 0.242
1.4c = 1.142
Divide both sides by 1.4
c = 1.142 / 1.4
= 0.82
c = 0.82
Substitute values of c and h into
h + f + c = 2.00
0.22 + f + 0.82 = 2.00
1.04 + f = 2.00
f = 2.00 - 1.04
f = 0.96
Therefore, the price of each item last year was
hamburger = h = $0.22
Fries = f = $0.96
Cola = c = $0.82
find the length of the third side. if necessary, write in simplest radical form.
Answer:
10
Step-by-step explanation:
Let x represent the third side
This is a right triangle
In right triangle the sum of square value of both legs is equal to square value of hypotenuse(the third side in this case)
Let x represent the third side
5^2 + 5[tex]\sqrt{3}[/tex]^2 = x^2
25 + 75 = x^2
100 = x^2 find the root for both sides
10 = x
Find the measure of angle m
4. The measure of angle m is 110°
- since the two angles are vertical, they are congruent.
:)
Help Math, Need someone to help with vertical angles
DOWN BELOW
Answer:
x = 25°
Step-by-step explanation:
The angles are equal and opposite. This means that if the top angle is 150°, then the angle at the bottom must be 150° too. However, it is currently 2x° + 100°, which turns it into an equation. So far we have 100° as a known angle, so we subtract that from 150° to get the value of 2x.
2x° = 50
Now we divide 50 by 2, and that gives us 25°.
x = 25°
- Educationist
the quotient of a and 5
Answer:
Step-by-step explanation:
For exact divisions such as 10 ÷ 5 = 2, we have an integer as a quotient, and for divisions such as 12 ÷ 5 = 2.4, the quotient is a decimal.
2x + 2y = 0 and y = 2x – 3
I
I need help asap
Answer:
x=1 and y=−1
Step-by-step explanation:
Use substitution in order to solve this.
Paper clips are sold in boxes of 1000.
Each box costs £15.40
The table below shows the discount offered for large orders.
Total order Discount
£40 - £54.99 5%
£55 - £79.99 6.5%
£80
8%
above
Ethan orders 5 boxes of paper clips.
Work out the amount of discount Ethan gets.
Please solve both. I’ll give brainliest
Answer:
Part a: A square and a rhombus both have sides of equal length.
Let's calculate the length of each side.
[tex]\overline{PL}: \sqrt{(0-5)^2+(3-3)^2}=\sqrt{25+0}=5\\\overline{LA}\sqrt{(5-2)^2+(3-(-1))^2}=\sqrt{3^2+4^2}=5\\\overline{AN}:\sqrt{(2-(-3))^2+(-1-(-1))^2}=\sqrt{25+0}=5\\\overline{NP}:\sqrt{(-3-0)^2+(-1-3)^2}=\sqrt{3^2+4^2}=5[/tex]
All sides measure 5. So it's at least a rhombus (think of a square as a rhombus with extra restrictions).
Part b: A square has extra restriction, more important all angles being 90° and diagonals having the same length. If you discussed about slopes it's easy to see that two sides are horizontal but the other two are NOT vertical. Which might be proof enough.
But the exercise looks about lengths on the plane, so let's measure diagonals.
[tex]\overline{PA}=\sqrt{(0-2)^2+(3-(-1))^2}= \sqrt{2^2+4^2}=\sqrt{20}\\\overline{LN}=\sqrt{(5-(-3))^2+(3-(-1))^2}= \sqrt{8^2+4^2}=\sqrt{80}[/tex]
The two diagonals have different lengths, so the figure cannot be a square.
Look at balance scale. If one
balance the scale?
is equivalent to two
what should be added to sides
1)
Side x
Side y
A) One can
B) One ball and one can
C) One ball
D) Two cans and one ball
Answer:
C-One ball
Step-by-step explanation:
Side x- 4
Side Y- 6
Ball equals 2
4+2=6
6=6
In a recent year, 33..9% of all registered doctors were female. If there were 53,100 female registered doctors that year, what was the total number of registered doctors?
Round your answer to the nearest whole number.
Answer:
88145 doctors
Step-by-step explanation:
Percentage of male doctors=64/100×53100=
35046%.
Therefore 53100+35046=
88145 doctors
Simplify the following expression [tex]\sqrt(75)+\sqrt(108)=a\sqrt(b)[/tex] If the expression is simplified completely, what does a equal and what does b equal
Answer:
the answer I got is:
a= 11√3b/b
b= 363/a^2
The following triangles are similar. True or False.
Answer:
It would be true
AngleFBC and AngleCBG are supplements, AngleDBG and AngleDBF are supplements, and AngleCBG Is-congruent-to AngleDBF.
4 lines are shown. A horizontal line with points F, B, G intersects a vertical line with points A, B, E at point B and forms a right angle. Another diagonal line with points D, B, C intersects the other 2 lines at point B between angle F B E and angle A B G. A fourth line intersects 3 lines at points A, C, G.
By the congruent supplements theorem, what can you conclude?
AngleCBG Is-congruent-to AngleDBG
AngleFBC Is-congruent-to AngleDBG
AngleCBG is supplementary to AngleDBF.
AngleFBC is supplementary to AngleDBG.
Answer:
FBC=DBG
Step-by-step explanation:
Edge 2020
Based on the congruent supplements theorem which says that two angles are that are supplements of the same angle are congruent, therefore: ∠FBC ≅ ∠DBG.
What is the Congruent Supplements Theorem?The congruent supplements theorem states that when two angles are congruent or supplements of the same angle, therefore, the two angles can be proven to be congruent angles.
Therefore, from the information given, we can conclude based on the congruent supplements theorem that: ∠FBC ≅ ∠DBG.
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Solve the inequality.
3y <-9
Answer:
y < -3
Step-by-step explanation:
Answer: y<-3
Step-by-step explanation:
1) 3y<-9 divide both sides of the inequality by 3
2) 3y÷3< -9÷3
3)any expression divided by itself equals 1
y<-9÷3
4) calculate the quotient y<-3
Give two examples of each type of number: real, natural, integers, rational and irrational.Explain step-by-step how to simplify -5(2x – 3y + 6z – 10)
9514 1404 393
Answer:
real, natural, integers, rational: 2, 3irrational: √2, √3use the distributive propertyStep-by-step explanation:
A) Any positive integer is all of real, natural, integer, and rational. A couple of examples of positive integers are 2, and 3.
Any non-complex number is real: -98.6, +29.7π.
Natural numbers are positive integers: 89, 10103.
Integers are any positive or negative number that has no fractional part. Zero is also an integer. A couple are -3, 0.
A rational number is one that can be expressed as the ratio of two integers. Any finite decimal number and any repeating decimal number are rational numbers. A couple of these are 22/7 and -0.0037285.
An irrational number is a number that cannot be expressed as the ratio of two integers. A cube root of a number that is not a perfect cube will be irrational, for example, The same is true of other roots. √2, ∛-5 are irrational. Pi (π) is a famous irrational number, along with 'e', the base of natural logarithms.
__
B) The terms inside parentheses are unlike, so cannot be combined. The only way this expression can be simplified is by removing the parentheses using the distributive property.
-5(2x -3y +6z -10) = (-5)(2x) +(-5)(-3y) +(-5)(6z) +(-5)(-10)
= -10x +15y -30z +50
HELPPPPPPP PLEASE ITS TIMED
If necessary, round your answer to the nearest tenth,
Check the picture below.
How many solutions does the equation 4x 8 = −2 − 2 5x have? two one none infinitely many
The equation 4x+8 = -2-2+5x has only one solution x=12.
Given equation is:
4x+8 = -2-2+5x
What is an equation?An equation is an operator (denoted by =) that equates the two expressions.
On bringing variables to the left side and constants on the right side
4x-5x = -2-2-8
-x = -12
x =12
Therefore, the equation 4x+8 = -2-2+5x has only one solution x=12.
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Find the slope of the line through each pair of points.
1) (19,8),(-2, 11)
Answer:
The slope of the line is [tex]-\frac{1}{7}[/tex]
Step-by-step explanation:
The rule of the slope of a line which passes through points
(x1, y1) and (x2, y2) is
[tex]m=\frac{y2-y1}{x2-x1}[/tex]∵ The line passes through points (19, 8) and (-2, 11)
∴ x1 = 19 and x2 = -2
∴ y1 = 8 and y2 = 11
→ Use the rule above to find the slope of the line
∵ [tex]m=\frac{11-8}{-2-19}=\frac{3}{-21}[/tex]
→ Simplify the fraction by divide up and down by 3
∴ [tex]m=-\frac{1}{7}[/tex]
∴ The slope of the line is [tex]-\frac{1}{7}[/tex]
You pick a card at random from an ordinary deck of 52 cards. if the card is a diamond, you get some points; if not, you lose 2 points. what value for the diamonds would make the game fair? 12 6 24 3
The value for the diamonds which would make the game of pick a diamond from a deck of 52 cards fair is 6.
What is probability?Probability of an event is the ratio of number of favorable outcome to the total number of outcome of that event.
From a card at random from an ordinary deck of 52 cards is picked.If the card is a diamond, you get some points. There are total 13 diamonds in a deck of cards.
Thus, the probability of picking a diamond from 52 cards is,
[tex]P=\dfrac{13}{52}\\P=\dfrac{1}{4}[/tex]
The probability of not picking a diamond from 52 cards is,
[tex]P'=1-\dfrac{1}{4}\\P'=\dfrac{3}{4}[/tex]
If the picked card is not a diamond, then the 2 points are lost. Let X is the score in the game. If the game is fair then the expected value for this should be 0. Thus,
[tex]0=x\times \dfrac{1}{4}+2\times\dfrac{(-3)}{4}\\x=6[/tex]
Hence, the value for the diamonds which would make the game of pick a diamond from a deck of 52 cards fair is 6.
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Answer:
6
Step-by-step explanation:
The answer above is correct.
what is the area of 3ft and 12ft?
Answer:
36 ft
Step-by-step explanation:
3 × 12 = 36 ftI hope this helps!
I need help solving this problem.
Answer:
Step-by-step explanation:
area of parking lot=(100-x)(100+x)=100²-x²=(10000-x²)ft²
original area=100²=10000 ft²
x²>0
so new area is decreased.
How do I do this? I’m very confused
I need help on this
Answer:
A. 75.6 in³
Step-by-step explanation:
The volume of a rectangular prism is V = Bh, where B = area of the base and h = height. We're given the dimensions of the base as 4.2 and 3, and the height as 6.
4.2 × 3 = 12.612.6 × 6 = 75.6 cubic inchesHave a lovely rest of your day/night, and good luck with your assignments! ♡
Answer:
A. 75.6 in³
Step-by-step explanation:
Given :-
Base area = 4.2 in x 3 in
Height = 6 in
To find :-
Volume
Formula required :-
Volume = length x breadth x height
Volume = base area x height
Solving :-
V = 4.2 x 3 x 6
V = 12.6 x 6
V = 75.6 in³
Solution :-
A. 75.6 in³
At the end of the night, mrs johnson works with the student council to determine their profit on the fundraiser the least popular item was chips in which they sold on 21 bags. the chips cost a total of 48.10
Answer:
21+48.10=69.10
Step-by-step explanation:
21
+
48.10
=
69.10
In calculating the monthly payment for a loan with an 8.5% interest rate compounded monthly, what value should be used for i, the interest rate per period, as it appears in the following formula? p = p v times startfraction i over 1 minus (1 i) superscript negative n endfraction a. 8.5 b. 0.71 c. 0.085 d. 0.0071
The value of i, the interest rate per period(monthly here) that should be used in the considered formula is given by: Option B: 0.71
How to find the monthly payment?If we're given that:
[tex]P_v[/tex] = present value[tex]P[/tex] = monthly payment to be paidi = interest rate per monthn = number of periods.Then, we get:
[tex]P = P_v\left(\dfrac{i}{1-(1+i)^{-n}}\right)[/tex]
For this case, we're provided that:
i = interest rate per period
And we have:
Interest rate compounding monthly = 8.5%
The interest rates are usually given for annual basis. Since i represents the rate per period, which is monthly here, thus, we will convert the rate 8.5% from annually to monthly.
Since 1 year = 12 months,
so 8.5% per year compounding monthly = (8.5/12)% per month compounding monthly
Thus, i = interest per period = interest per month = 8.5/12≈ 0.71 (in percentage)
Thus, the value of i, the interest rate per period(monthly here) that should be used in the considered formula is given by: Option B: 0.71
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Answer:
Its D :)
Step-by-step explanation:
MATH HW URGENT!!!
Whoever solves one question at least will be brainliest!!!!
Answer: Equation of the line from D to C is y=2x+6?
Step-by-step explanation: Lines A to B and D to C looks parallel meaning they have the same slope but different Y intercept?
Remington needs at least $3,000 to buy a used car. He already has $1,800. If he saves $50 per week. Which inequality best matches the situation?
Answer:
24 weeks
Step-by-step explanation:
I'm not sure exactly what you're asking but if he's making $50 a week it would take him 24 weeks to have enough money for the car. Here is an inequality for the amount he needs: 50x+1800≥3000
Which equation represents a line parallel to 2x+y=-2?
A. y=-2x+3
B. x+y=5
C. y-x=-1
D. y-2x=3
Answer:
Option A
Step-by-step explanation:
To find the answer we need to graph the following equations to see which equation is parallel to the given equation 2x + y = -2x. Your answer is option A or "y = -2x + 3." One of the biggest rules when trying to find out if the two lines are parallel to each other is seeing if the two lines intercept. In this case if you graph all the following options, the only line that does not intercept the first line 2x + y = -2 is the option A, which means it's your answer.
Hope this helps.
giving brainlist for correct answer. :))
Answer:
Here is the steps. 67.5 cm^3
Step-by-step explanation:
4.5 * 6 = 27
27 * 2.5 = 67.5
Answer:
67.5 cm
Step-by-step explanation:
[tex]4\frac{1}{2}[/tex] × [tex]6[/tex] ×[tex]2\frac{1}{2}[/tex] = [tex]67\frac{1}{2}[/tex] or [tex]67.5[/tex]
Find the approximate unknown angle o using inverse trigonometric ratios (sin-1,cos-1, or tan-1)
Answer:
[tex]\displaystyle 0,1922986515...\pi = \theta \\ 35° \approx \theta[/tex]
Step-by-step explanation:
[tex]\displaystyle sec^{-1}\:1\frac{177}{823} = \theta; 0,1922986515...\pi\:[or\:34,613757274...°] \\ \\ \boxed{0,1922986515...\pi = \theta\:[35° \approx \theta]}[/tex]
OR
[tex]\displaystyle cos^{-1}\:\frac{823}{1000} = \theta; 0,1922986515...\pi\:[or\:34,613757274...°] \\ \\ \boxed{0,1922986515...\pi = \theta\:[35° \approx \theta]}[/tex]
I am joyous to assist you at any time.