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Gina sells 216 cakes in the ratio small :medium:large 5:7:12. The profit for one medium cake is twice the profit for one small cake. The profit for one large cake is three times the profit for one small cake. Her total profit id £648.45. Work out the profit for one small cake.
Answers
Answer:
£1.31
Step-by-step explanation:
5+7+12=24
216÷24=9
Small=9x5=45
Medium=9x7=63
Large=9x12=108
2x= Medium, Large= 3x, Small=x
Small=45x, Medium= 63x2=126x, Large=108x3=324x
45x+126x+324x=495x
£648.45=495x
£648.45÷495=x
£1.31=x
The profit for one small cake will be £ 1.31. The profit of the one small cake is the amount of benifit obtained to sell one cake.
What is profit?When money generated from a commercial activity exceeds the expenses, costs, and taxes involved in maintaining the activity in question, profit is earned.
The ratio of the small :medium: large cake is 5:7:12.
Let the cake is considered to be x;
The sum of alll the cakes is;
5x+7x+12x=24 x
The total no of cake is 216
Each no of cake is found as;
[tex]\rm 24 x = 216 \\\\ x = 9[/tex]
The number of the small cake;
N(s) = 9 ×5 =45
N(m)=9×7=63
N(l)=9×12=108
Let the small cake is x
The profit for one medium cake is twice the profit for one small cake;
P(m)=2x
P(l)=3x
P(s)=x
The small medium and the large cake according to the new condition will be 45 x,126x,324x respectively.
The sum of all the cakes according to the new condition is found as;
[tex]4s x +126 x+324 c \\\\ 495 x=648.45 \\\\ x=\£ \ 1.31[/tex]
Hence the profit for one small cake will be £ 1.31.
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Jason is buying hamburgers and hot dogs for a barbecue. One package of hamburgers costs $10. One package of hotdogs costs $5. He has $60 to spend, and must buy AT LEAST 3 packages of hot dogs.
What 2 inequalities can be used?
Answers
he needs AT LEAST 3 packages of hotdogs
so
[tex]d \geqslant 3[/tex]
each packet costs $5 so he must spend $15 in total on hotdogs
so he can spend NO MORE than $45 on hamburgers so can buy no more than 4 packs of hamburgers
so
[tex]b \leqslant 4[/tex]
Answer:
10x + 5y ≤ 60 & y ≥ 3Step-by-step explanation:
Let x = the number of hamburgers
Let y = the number of hotdogs
Let us first represent the amount of food:
10x + 5y ≤ 60
This means x packages of $10 hamburgers plus y packages of $5 hotdogs is greater than or equal to $60.
However, we have also been given another important piece of information and that is that he must buy at least three packages of hotdogs.
y ≥ 3
this means that the packages of hotdogs must be no less than 3.
Hence or two inequalities are 10x + 5y ≤ 60 & y ≥ 3.
This also means that the least he can spend on hotdogs is $15. The most he can spend on hamburgers is $45, meaning the most packages of hamburgers he can get is 4
PLEASE MARK BRAINLIEST
PLEASE HELP NOW I ONLY NEED TO KNOW NUMBER 5. 25 POINTS!!!
Points C and D are equidistant from point A. Complete the following table to prove that AEC ≅ AED.
Answers
AC = AD (S) (Points C and D are equidistant from point A)
AE = AE (S) (The two triangle shared the same side)
∠CAE = ∠EAD (A) (This angle is between the two sides that we just proved to be equal)
By SAS,
ΔEAD ≡ ΔEAC
Would be glad if you answer my question!
Answers
and it's not that you just have to divide the 'a' from both sides giving the answer as p = (px+c) ÷ a, but you have to write in terms of ' a,x and c'.
so ap = px+c
1)collect all the likes to one side (ap - px = c)
2) Take the common out [ p(a-x) = c ]
3) Divide by '(a-x)' to put equation in terms of "p="
4) therfore, p = c ÷ (a-x)
Hope this answered your question
Maria sets a goal of jogging 17.5miles this week. She plans on running 2.75 miles each day for 7 days . If she follows her plan which is true
Answers
19.25 miles.
She completes her goal of jogging 17.5 miles that week.
This net folds into a cube. Which two letters appear on opposite faces?
-D and A
-A and E
-C and D
-B and E
Answers
Answer:
- B and EStep-by-step explanation:
If this net folds into a cube, then, when we form the cube, side B and side E becomes opposite sides, because side D and side F would be placed next to side B, having side E as opposite.
Therefore, the right answer is the last choice. Sides B and E appear on opposite sides.
Help please asap, thanks
can someone explain how you factor 6x^3 + 8x^2 + 2x
Answers
6x3+8x2+2x
=2x(3x+1)(x+1)
Answer:
2x(3x+1)(x+1)
The first thing you should do in this case is to take out the common factor of all the terms of the expression.
We have then:
Step 1:
2 * (3x ^ 3 + 4x ^ 2 + x)
Step 2:
2x * (3x ^ 2 + 4x + 1)
Step 3:
2x * 3((x + 1) * (x + 1/3))
2 x * ( x + 1 ) ( 3x + 1 )
Answer:
The factored expression is:
2 x * ( x + 1 ) ( 3x + 1 )
Determine the number of possible triangles, ABC that can be formed given angle A=30 degrees, a=4 and b=6
Answers
Answer:
One possible triangle
Step-by-step explanation:
Given that in a triangleABC given one angle A =30 , two sides a and b
We can use sine angle formula for triangles
[tex]\frac{a}{sinA} =\frac{b}{sinB} =\frac{c}{sinC}[/tex]
Substitute to get
[tex]\frac{4}{sin30} =\frac{6}{sin B} =\frac{c}{sinC}[/tex]
[tex]sin B = 0.75\\B=48.6[/tex]
C=[tex]180-30-48.6\\= 101.4[/tex]
[tex]c=8sin 101.4\\c=7.842[/tex]
There can be only one triangle
The line segment is dilated by a factor of 1/2 with respect to the origin. What is the length of the dilated line segment?
A. 1 unit
B. 2 units
C. 3 units
D. 4 units
Answers
The length of the dilated line segment is 2 units. ( option B)
A scale factor is a ratio that describes the proportional change in size between two similar geometric figures.
Scale factor = Dimension of new length /dimension of original length
The dimension of the original length is 4 units
scale factor = 1/2
let the new length be x
Therefore;
1/2 = x/4
2x = 4
x = 4/2 = 2units
Therefore, the length of the dilated segment is 2units
Which expression gives the distance between the points (4, 6) and (7, -3)?
Answers
[tex]\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}[/tex]. In the ordered pair (4, 6), 4 is the x-coordinate and 6 is the y-coordinate. In the ordered pair (7, -3), 7 is the x-coordinate and -3 is the y-coordinate. Substituting those values in gives us
[tex]\sqrt{(4-7)^2+(6--3)^2}[/tex]. Since subtracting a negative is the same as adding a positive, we now have
Answer:
The expression gives the distance between the points (4, 6) and (7, -3) is Option (C) .
i.e
[tex]Distance\ formula = \sqrt{(7 - 4)^{2} + (6 +3)^{2}}[/tex]
Step-by-step explanation:
Formula
[tex]Distance\ formula = \sqrt{(x_{2} - x_{1})^{2} + (y_{2} - y_{1})^{2}}[/tex]
As the point are (4, 6) and (7, -3) .
Put points in the formula
[tex]Distance\ formula = \sqrt{(4 -7)^{2} + (6- (-3))^{2}}[/tex]
[tex]Distance\ formula = \sqrt{(7 - 4)^{2} + (6 +3)^{2}}[/tex]
[tex]Distance\ formula = \sqrt{(3)^{2} + (9)^{2}}[/tex]
[tex]Distance\ formula = \sqrt{9 + 81}[/tex]
[tex]Distance\ formula = \sqrt{90}[/tex]
[tex]\sqrt{90} = 9.5\ units\ (Approx)[/tex]
Distance formula = 9.5 Units (Approx)
Therefore Option (C) is correct.
Solve the system of equations using the linear combination method.
{5p−3q=−39
{−2p−3q=3
Enter your answers in the boxes.
Answers
- (-2p - 3q = 3)
==> 7p = -42 ==> p = -6
==> p = -6
-2(-6) - 3q = 3 ==> 12 - 3q = 3
==>p = -6
-3q = 3 - 12 ==> -3q = -9
==> p = -6
q = 3
By solving the equations through linear combination method we are going to get the values of p and q are -6 and three.
What is linear combination method?It is a bit like elimination method of solving equations within which one variable is eliminated so we'll get the worth of another variable.
How to solve an equation?We are having two equations:
5p-3q=-39-------------1
-2p-3q=3---------------2
equation1 * 2 and equation 2 *5
10p-6q=-78
-10p-15q=15
Now add both equations
10p-6q-10p-15q=-78+15
-21q=-63
q=3
Put the worth of q in 1
5p-3(-3)=-39
5p+9=-39
5p=-30
p=-6
Hence the system of equations have the worth of p=-6 and q=3.
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Which phrase describes an unknown or changeable quantity? A. 60 seconds multiplied by 5 B. 2 times the number of pages in the book C. 15 years of schooling D. 3 dollars and 76 cents
Answers
The correct answer for APEX is B (2 times the number of pages in the book)
What is the sum of 4.9 × 102 and 6.8 × 103?
( one answer )
Answers
= 10^2(4.9 + 68)
= 72.9 x 10^2
= 7.29 x 10^3
answer
7.29 x 10^3
Answer:the answer is 7290
Step-by-step explanation:
From the given expression
4.9*10^2 =4.9*100=490
and
6.8*10^3=6.8*1000=6800
490+6800=7290
in quadrilateral abcd , angle A=57 degrees , angle B=65 degrees and angle c=118 degrees What is the measure of an exterior angle at D
Answers
you are given 57, 65, 118
That is 240
to solve for the last angle
360-240
120
The exterior angle of a D would be the number that you add that will make it 180 degrees.
meaning 180-120 is
The exterior angle of angle D is 60 degrees.
Hope this helps
The following is an incomplete paragraph proving that the opposite angles of parallelogram ABCD are congruent: According to the given information, and . Using a straightedge, extend segment AB and place point P above point B. By the same reasoning, extend segment AD and place point T to the left of point A. Angles BCD and PBC are congruent by the Alternate Interior Angles Theorem. Angles PBC and BAD are congruent by the ____________. By the Transitive Property of Equality, angles BCD and BAD are congruent. Angles ABC and BAT are congruent by the _____________. Angles BAT and CDA are congruent by the Corresponding Angles Theorem. By the Transitive Property of Equality, ∠ABC is congruent to ∠CDA. Consequently, opposite angles of parallelogram ABCD are congruent. What theorems accurately complete the proof?
Answers
Given a parallelogram ABCD, refer to the attached image.
To prove: Opposite angles are congruent.
Proof:
According to the given information,
Step 1: Using a straightedge, extend segment AB and place point P above point B.
Step 2: By the same reasoning, extend segment AD and place point T to the left of point A.
Step 3: Angles BCD and PBC are congruent by the Alternate Interior Angles Theorem.
Step 4: Angles PBC and BAD are congruent by the Corresponding Angles Theorem. ( If two parallel lines are cut by a transversal, then the pairs of corresponding angles are congruent. Corresponding angles are the angles which occupy the same relative position at each intersection where a straight line crosses two others.)
Step 5: By the Transitive Property of Equality, angles BCD and BAD are congruent.
Step 6: Angles ABC and BAT are congruent by the Alternate Interior Theorem.(The Alternate Interior Angles theorem states, if two parallel lines are cut by a transversal, then the pairs of alternate interior angles are congruent. Alternate Interior angles are a pair of angles on the inner side of each of those two lines but on opposite sides of the transversal.)
Step 7: Angles BAT and CDA are congruent by the Corresponding Angles Theorem.
Step 8: By the Transitive Property of Equality, ∠ABC is congruent to ∠CDA. Consequently, opposite angles of parallelogram ABCD are congruent.
The proof requires the use of specific theorems such as the Vertical Angles Theorem and Corresponding Angles Theorem to establish the congruence of angles in a parallelogram.
Theorems that accurately complete the proof:
Angles PBC and BAD are congruent by the Vertical Angles Theorem.
Angles ABC and BAT are congruent by the Corresponding Angles Theorem.
Theorem 12 states that if two angles are congruent, their supplementary angles are also congruent.
Which of the following is a logarithmic function? A. Y=0.25X B. Y=x^0.25 c.y=log25^x d.y=(0.25)^x
Answers
Answer:
The correct option is C .
Step-by-step explanation:
A logarithm function is written in the form of [tex]y=log_ax[/tex],
Since, y = 0.25x is the type of function y = mx + c,
Which is the general form of a linear function,
⇒ y = 0.25x is not a logarithm function,
[tex]y=x^{0.25}[/tex] is the type of function [tex]y=kx^a[/tex], where k and a are any real number,
Which is the general form of a power function,
⇒ [tex]y=x^{0.25}[/tex] is not a logarithmic function.
[tex]y=(0.25)^x[/tex] is the type of function [tex]y=ab^x[/tex]
Which is the general form of exponential function,
⇒ [tex]y=(0.25)^x[/tex] is not a logarithmic function,
Hence, only the function in option C has written in the form of [tex]y=log_ax[/tex].
Option C is correct.
help with these two please....
Answers
Answer: fourth choice 6, - 3+3√3 i, and -3 - 3√3 i
Solution:
1) Factor x^3 - 216 as a difference of cubes:
(x)^3 - (6)^3 = (x - 6) (x^2 + 6x + 6^2) = (x - 6) (x^2 + 6x + 36) = 0
3) first factor = 0 => x - 6 = 0 => x = 6
4) second factor = 0 => x^2 + 6x + 36 = 0
Using the quadratic formula:
x = [ - 6 +/- √(6^2 - 4*1*36) ] / (2)
=> x = [ - 6 +/- √ (-108) ] / 2 = -3 +/- 3√3 i
=> x = - 3 + 3√3 and x = - 3 - 3√3 i
Answer: 3, - 3+3√3 i, and -3 - 3√3 i
2) Which is equivalent to (2p^2 + 5pq - q^2) + (p^2 + 3pq - 2q^2) ?
Answer: first option 3p^2 + 8pq - 3q^2
Solution:
1) eliminate parenthesis:
2p^2 + 5pq - q^2 + p^2 + 3pq - 2q^2
2) combine like terms:
2p^2 + p^2 = 3p^2
5pq + 3pq = 8pq
-q^2 - 2q^2 = - 3q^2
3) The result is 3p^2 + 8pq - 3q^2, which is the first option.
Y varies inversley with x y= 0.5 x= 3 what is the value of k the constant of inverse variations
Answers
y = k/x
when y = 0.5, x = 3
0.5 = k/3
k = 0.5 x 3 = 1.5
k = 1.5
y = 1.5/x or y = 3/2x
Of all the houses on kermit lane, 20 have front porches, 20 have front yards, and 40 have back yards. how many houses are on kermit lane?
Answers
reflect point A(5, 7, 2) across the xz-plane. where will the new point be located?
(-5, -7, 2)
(-5, -7, -2)
(-5, 7, -2)
(5, -7, 2)
Answers
In this case, the point A (5,7,2) is reflected along xz plane. So x and z coordinates will be opposite in signs after reflection and y coordinate will not be changed.
So after reflection along xz plane, the new point will be (-5, 7, -2). Thus 3rd option is the correct answer
Mr Daniels is organizing a class field trip on a budget of $900.The bus rental costs $600. Mr.daniels will also buy tickets that will cost $9.50 per student. Write an inequality to represent the number students,y, that he can bring on the trip.
Answers
600 fixed amount
9.5 is the variable changing amount and differs among number of students taken
Answer:
y ≤ 31 students
Step-by-step explanation:
The rental cost is a fixed cost that will be incurred irrespective of the number of students embarking on the class field trip. This cost added to the total ticket cost must be less than or equal to the budget.
the total ticket cost for y number of students
= 9.5y
Hence the total cost = 9.5y + 600 ( measured in $)
In inequality form,
9.5y + 600 ≤ 900 (all in $)
9.5y ≤ 900 - 600
9.5y ≤ 300
y ≤ 300/9.5
y ≤ 31 students
Gina earns $19,750 annually and has 20% of her gross earnings
withheld. What is the net amount of her paycheck each pay period if
she is paid biweekly?
a. $607.69
b. $658.33
c. $14,000
d. $134.62
ANSWER ASAP AND GET BRAINEST
Answers
15800 / 26 = 607.69
Answer is A
Which of the following statements is not true about reflections?
The image faces the same direction as the pre-image.
The image is the same shape as the pre-image.
The image is the same size as the pre-image.
Points on the pre-image are the same distance from the line of reflection as the corresponding points on the image.
Answers
Hope this helps ^_^
Answer: The image faces the same direction as the pre-image.
Step-by-step explanation:
Reflection is a transformation in which a geometric shape (pre- image) is reflected across a line called as axis of reflection, producing a mirror image.
It is a rigid transformation because the image is the same size and shape as the pre-image.
Since it produces the mirror image of the original image therefore, the points on the pre-image are the same distance from the line of reflection as the corresponding points on the image.
So the only statement is not true about reflection is "The image faces the same direction as the pre-image. ".
A Rectangle launch tray has a length of X centimeters and a width of 15 cm the trays length is at least 20% greater than it's width. right an inequality to represent this situation. suppose X is a whole number find the least possible permitted and the least possible area of the lunch tray
Answers
x-------------> length rectangle launch tray
w------------< width rectangle launch tray------> 15 cm
length is at least 20% greater than it's width
x>=1.2w---------> x>=1.2*15
the answer part a) is
x>=18 ---------------> ( inequality to represent this situation)
part b) suppose X is a whole number find the least possible permitted and the least possible area of the lunch tray
the least possible permitted length is 18 cm
the least possible area of the lunch tray is 18*15=270 cm²
You are looking for your first credit card. You plan to use this credit card only for emergencies and to pay the credit card balance in full each month. Which credit card feature is most important?
a.
No annual fee
b.
Low APR
c.
Generous rewards program
d.
No balance transfer fee
Answers
Answer:
A
Step-by-step explanation:
EDU
The credit card feature of "No annual fee" represents the correct alternative of the given ones.
What is credit card?A credit card is a payment card issued to users to enable the cardholder to pay a merchant for goods and services based on the cardholder's accrued debt.
Given is that you are looking for your first credit card. You plan to use this credit card only for emergencies and to pay the credit card balance in full each month.
The credit card feature of "No annual fee" is suitable for emergencies.
Therefore, the credit card feature of "No annual fee" represents the correct alternative of the given ones.
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A square has sides of length s. A rectangle is 6 inches shorter and 1 inch longer than the square. Which of the following polynomials represents the area of the rectangle? Select all that apply.
Answers
The width of the rectagle is b=s-6
Area of the rectangle is A = a * b = (s+1) (s-6) = s^2 - 5s - 6
You didn't submit any polynomials.........
Michelle draws a card from a standard deck of 52 cards. She replaces the card and draws a second card. What is the probability that she draws a red card and then a black card
A) 1/16
B)1/26
C)1/4
D)1/52
Answers
Multiply the probabilities.
1/2 * 1/2 = 1/4
The answer is C. 1/4
If y is directly proportional to x and y is 12 when x = 10, what is the constant of variation?
Answers
constant of variation = 1.2
Explanation:
y varies directly with x means that as x increases, y increases and vice versa.
This can be translated into the following equation:
y = kx
where k is the constant of pvariation.
We are given that:
y = 12 when x = 10.
Therefore, we will substitute with these values in the above equation and solve for k as follows:
y = kx
12 = k * 10
k = 12 / 10
k = 1.2
This means that the equation relating x and y is:
y = 1.2x
where 1.2 is the constant of variation.
Hope this helps :)
Answer:constant of variation = 1.2
Step-by-step explanation:
helppppppppppppppppppppppppp[
Answers
We have:
g [h (x)]
We have then:
g [h (x)] = ((4-x) +1) / ((4-x) -2)
We rewrite:
g [h (x)] = (5-x) / (2-x)
then:
g [h (-3)] = (5 - (- 3)) / (2 - (- 3))
g [h (-3)] = 8/5
Answer:
8/5
The sum of two consecutive integers is 37. Write an equation that models this situation and find the values of the two integers.
Answers
n+n + 1 = 37
2n + 1 = 37
2n = 36
n = 18
n+1 = 19
18 and 19
Hope this helps ^_^