Grace has $105 to buy a cake and pizza for her cousin’s birthday party. She knows she needs to set aside $25 for the cake, and the rest of the money she can spend on pizzas. Each pizza costs $9.25. How many pizzas can Grace afford to buy?
a.write and solve an inequality to answer the question
b. each pizza serves 4 people. if 22 people reply that they will attend the party, how many pizzas should grace buy? explain your reasoning.
im sorry its alot but this will help me lots
Answer:
A. She can buy 8 pizzas; B. At least 6 pizzas.
Step-by-step explanation:
Since Grace has $105, we can set our inequality to be less than or equal to that amount of money. We also know she needs to spend $25 on the cake no matter what. Assuming x is the amount of pizzas she can buy and each pizza costs $9.25, our inequality looks like this:
9.25x + 25 ≤ 105
To solve this inequality, we first subtract 25 from both sides, which gives us:
9.25x ≤ 80
Then we divide by 9.25 on both sides, giving us:
x ≤ 8.6486
Since Grace is only able to buy whole pizzas, the most she can buy is 8 pizzas.
If each pizza serves 4 people and there are 22 people attending, we need to be able to feed 22 or more people. We can use this inequality, where x is still the number of pizzas.
4x ≥ 22
Dividing both sides by 4, we get:
x ≥ 5.5
Again, assuming we can only buy whole pizzas, we would need at least 6 pizzas to feed the entire party.
52x+3 =
3x+2+4x-3-5x-1=
x-5x+4=
Answer:
x= -3/52
x= 2
x= -1
Step-by-step explanation:
number 1
52x+3=0
52x=-3
x=-3/52
number 2
2x+2+4x-3-5x-1=0
x-2=0
x=2
number 3
x-5x+4=0
4x+4=0
4x=-4
x=-1
Use the following function rule to find f(0).
f(x)= 12(9)^x
f(0) =
Answer:
12
Step-by-step explanation:
f(0)=12(9)^0
(9)^0=1
f(0)=12(1)=12
[tex]f(x) = 12 \cdot 9^x\\\\f(0) = 12 \cdot 9^0 = 12 \cdot 1 =12[/tex]
28. Overhead Projectors Your teacher draws a circle on an overhead projector.
The projector then displays an enlargement of the circle on the wall. The circle
drawn has a radius of 3 inches. The circle on the wall has a diameter of 4 feet.
What is the scale factor of the enlargement?
a
A scale factor is a factor that can be used to either increase or decrease the size of a given figure. Therefore, the scale factor of the enlargement is [tex]\frac{1}{8}[/tex].
Scale drawing is a type of drawing that requires the use of a factor to either enlarge or reduce the size of a given figure. The factor required is called a scale factor. It can be expressed as:
scale factor = [tex]\frac{length of side of image}{length of side of object}[/tex]
In the given question, the radius of the circle drawn is 3 inches, while that on the wall has a diameter of 4 feet.
Thus;
diameter of circle = 2 * 3
= 6 inches
But;
1 feet = 12 inches
So that;
x = 6 inches
⇒ x = [tex]\frac{6}{12}[/tex]
= [tex]\frac{1}{2}[/tex]
x = 0.5 feet
Thus, the diameter of the circle is 0.5 feet.
So that;
scale factor = [tex]\frac{0.5 feet}{4 feet}[/tex]
= 0.125
scale factor = [tex]\frac{1}{8}[/tex]
The scale factor of the enlargement is [tex]\frac{1}{8}[/tex].
For more on scale factor, visit: https://brainly.com/question/10253650
Steel is a mixture of iron, carbon, and other elements. The table shows the number of parts each element in two different-sized samples of steel.
A table with the composition of two samples is shown. Sample one is ninety parts iron, three parts carbon, and seven parts other elements. Sample two is forty-five parts iron, one and a half parts carbon, and three and a half parts other elements.
Question 1
Part A
What is the unit rate of parts iron to parts carbon?
Enter the correct answer in the box.
parts iron per part carbo
Answer:
Step-by-step explanation:
Sample One, Parts and % Sample Two, Parts and %
Fe 90 (90%) 45 (90%)
C 3 (3%) 1.5 (3%)
Other 7 (7%) 3.5 (7%)
100 parts 50 parts
Parts Fe/Parts Carbon = 90/3 or 30/1 in both cases [45/1.5 = 30/1]
What is 6 percent of 435000
Answer:
26,100
Step-by-step explanation:
[Given] 6 percent of 435000
[6% as a decimal] 0.06 of 435000
[Multiply] 26,100
Have a nice day!
I hope this is what you are looking for, but if not - comment! I will edit and update my answer accordingly. (ノ^∇^)
- Heather
PLEASE HELP!! PLEASE AND THANK YOU!
Answer:
50.05 feet
Step-by-step explanation:
The tower have 32.57 feet, and you can find it using the same method than I used in your other question
Now you find the length of the guy wire using the Pythagorean theorem:
38²+32.57² = guy wire²
2504.8 = guy wire²
guy wire = √2504.8
guy wire = 50.05 feet
a What is the slope of a line that passes through the points (1, 2) & (4, 12
Answer:
10/3 or 3.33333
Step-by-step explanation:
Images Below
Hope this Helps
Work out m and c for the line: 2 y + 6 x = 4
Answer:
m = -3
c = 2
Step-by-step explanation:
if m = slope and c = y-intercept:
Convert to slope - intercept form : y = mx + b, or y = mx + c
2y + 6x = 4
2y = -6x + 4
y = -3x + 2
(m)Slope = -3
(c)y - intercept = 2
-Chetan K
Josef and Mai divided some stamps between themselves. Josef got 60% of the stamps. If Josef received 500 more stamps than Mai, how many stamps did Josef receive?
The number of stamps Josef received out of the total stamps of 2,500 is 1,500 stamps
let
x = total number of stamps
Josef share = 60% of x
= 0.60 × x
= 0.60x
Mai = 40% of x
= 0.40x
Josef = 0.40x + 500
Total = Josef + Mai
x = (0.40 + 500) + 0.40x
x = 0.40x + 500 + 0.40x
x = 0.80x + 500
x - 0.80x = 500
0.20x = 500
x = 500/0.20
x = 2,500
Josef share = 60% of x
= 60/100 × 2,500
= 0.60 × 2,500
= 1,500 stamps
Therefore, the total number of stamps shared between Josef and Mai is 2,500
Read more:
https://brainly.com/question/16450098
how to convert m to mm
there are 15 pieces of fruit in a bowl and 6 of them are oranges.what is the percenage of fruits are in oranges
Hi there!
We can find the percentage by expressing the amount of oranges to total fruits as a fraction:
[tex]\text{ oranges to total fruit} = \frac{\text{x Oranges}}{\text{ y total pieces of fruit}}[/tex]
Plug in the given values:
[tex]\text{ oranges : total fruit} = \frac{\text{6}}{\text{15}} = 0.4[/tex]
Convert to a percentage by multiplying by 100:
0.4 × 100 = 40%.
[tex]\boxed{\text{40\% of total pieces of fruit are oranges}}[/tex]
(2/3)³×(-3/4)²×(-1)²⁰⁰³
(2/5)²×(-5/12)³
Answer:
Step-by-step explanation:
[tex](-1)^{n} = -1 , if \ n \ is \ a \ odd \ integer\\\\\\\\(-1)^{2003} =-1 \\\\(\dfrac{-3}{4)}^{2}=\dfrac{3}{4}, \ as \ 2 \ is \ even \ number.\\\\(\dfrac{2}{3})^{3}*(\dfrac{-3}{4})^{2}*(-1)^{2003}=\dfrac{2^{3}}{3^{3}}*\dfrac{3^{2}}{4^{2}}*(-1)\\\\\\=\dfrac{2^{3}}{3^{3}}*\dfrac{3^{2}}{2^{4}}*(-1)\\\\\\=\dfrac{-1}{3^{3-2}*2^{4-3}}\\\\\\=\dfrac{-1}{3^{1}*2^{1}}\\\\=\dfrac{-1}{6}[/tex]
[tex](\dfrac{2}{5})^{2}*(\dfrac{-5}{12})^{3}=\dfrac{2^{2}}{5^{2}}*\dfrac{(-5)^{3}}{(2^{2}*3)^{3}}\\\\\\=\dfrac{2^{2}}{5^{2}}*\dfrac{- 5^{3}}{2^{6}*3^{3}}\\\\\\= -\dfrac{5^{3-2}}{2^{6-2}*3^{3}}\\\\\\= -\dfrac{5}{2^{4}3^{3}}\\\\= -\dfrac{5}{16*3}\\\\\\= \dfrac{-5}{48}[/tex][tex]HINT: \dfrac{a^{m}}{a^{n}}=a^{m-n}, m >n\\\\\\\dfrac{a^{m}}{a^{n}}=\dfrac{1}{a^{n-m}}, n >m\\\\\\(a^{m})^{n}=a^{m*n}[/tex]
when identifying the rate lf change using a graph check ___ over __
Answer: rise over run
======================================================
Explanation:
The rate of change is the same as slope. Slope is often defined as the ratio of rise over run.
In other words, slope = rise/run.
For instance, a slope of 2/3 means we go up 2 and to the right 3 units.
Another example: slope = -1/5 means we go down 1 and to the right 5.
The term "rise" indicates a change in y. The run is the change in x. If the rise is positive, then you go up. Negative rise values mean that you go down. The run always moves to the right.
How to convert minutes and seconds into grades.
Answer:
Step-by-step explanation:
To convert time to time, kernel time with 24 (number of time in a day).
To convert time to minutes, kernel with time with 1440 (number of minutes in a day = 24 * 60).
To convert s to seconds, multiply the time by 86400 (number of s in a day = 24 * 60 * 60).
Which system of inequalities is shown?
a.y > x
y > 2
b. y > x
y < 2
c. y < x
y < 2
d. y < x
y > 2
y < x
y < 2
==================================================
Explanation:
The horizontal line is y = 2 since all points on this line have a y coordinate of 2. Eg: (0,2) and (5,2)
Since we shade everything below this line, we're describing the inequality y < 2. All points in the shaded region for this describe anything with a y coordinate smaller than 2. Eg: (7,1)
-------------
At the same time, we're also shading below the line y = x to form the inequality y < x.
So that's how we end up with this system
[tex]\begin{cases}y < x\\y < 2\\\end{cases}[/tex]
which describes the set of all points below the lines y = 2 and y = x. The dashed lines indicate that points on the boundary do not count as solution points. For example, (5,2) is not a solution because it rests on the upper horizontal boundary.
what is the slope of (16,1) and (17,7)
Help pls it’s a bit tricky
[tex]2x-5y=10\\\\\implies 5y = 2x-10\\\\\implies y =\dfrac{2x-10}5 = \dfrac{2}5 (x-5) = \dfrac{2x}5 - 2[/tex]
Answer:
(D) [tex]y = - \frac{2x}{5} - 2[/tex]
Step-by-step explanation:
The problem consist in isolate the [tex]y[/tex] variable
The steps are below:
[tex]2x -5y = 10\\-5y = 10 - 2x\\y = \frac{10 - 2x}{5}[/tex]
Know the trick is in separate the fraction in two others as this example:
[tex]\frac{a+b}{c} = \frac{a}{c} + \frac{b}{c}[/tex]
So in our case we have:
[tex]y = -\frac{10}{5} - \frac{2x}{5}\\y = -2 -\frac{2x}{5}[/tex]
That correspond to D
PLZZZZZ HELP ITS TIMED
Answer:
2. a.
3. g.
4. e.
1. 24x - 18
-
A. 6(4x-3) B. 6
-
C. 4(6x - 4) D. 12x - 9
It’s a select all that apply question
[tex] \: [/tex]
the right answer is
A. 6(4x-3)Step-by-step explanation:
[tex]24x - 18[/tex]
Factor out 6 from the expression[tex] = 6(4x - 3)[/tex]
so we got the answerhope it helps[tex] \: [/tex]
In which diagram are angles 1 and 2 vertical angles?
Answer:
Step-by-step explanation:
can you upload diagram?
What is the answer? I have looked and there is no question that is close to mine.
Answer:
Since there is a right angle, this is a right-angled triangle and we can solve for x using Pythagoras Theorem that goes [tex]a^2+b^2=c^2[/tex], where c is the hypotenuse (longest side of the triangle).
In this case, x would be the c.
Substitute in values of a and b:
[tex]10^2+10^2=c^2[/tex]
[tex]c^2=200[/tex]
[tex]c=\sqrt{200}[/tex]
[tex]c=10\sqrt{2}[/tex] (Option A)
simplify the expression.
20a^4 × (1/2 a^3 )^2
Answer:
5a^10
Step-by-step explanation:
Value of x.
2x
120
140
100
110
130
150
846
Step-by-step explanation:
Evaluate the formula χ2=
(n−1)s2
σ2 when σ=1.61, n=39, and s=3.79.
Work Shown:
[tex]\chi^2 = \frac{(n-1)s^2}{\sigma^2}\\\\\chi^2 = \frac{(39-1)(3.79)^2}{(1.61)^2}\\\\\chi^2 = \frac{38*14.3641}{2.5921}\\\\\chi^2 = \frac{545.8358}{2.5921}\\\\\chi^2 \approx 210.57667528259\\\\\chi^2 \approx 210.577\\\\[/tex]
Can you give me the answer?
Answer:
39
Step-by-step explanation:
The inside of a triangle adds up to 180:
90 because that square box is 90 degrees
90+50=141
180-141=39
Simplify the monomial (final answers should contain
positive exponents only.):
The side length of a cube can be represented by the
expression 2x. If the side length is doubled, write an
expression to represent the new volume of the cube.
[Hint: V=lwh, all sides are equal in a cube]
==========================================
Work Shown:
old side length = 2x
new side length = 2*(old side length) = 2*2x = 4x
For any cube, the length, width and height are all the same. So L = W = H.
volume = L*W*H
volume = L*L*L
volume = L^3
volume = (4x)^3
volume = 4^3*x^3
volume = 64x^3
-2x + 2y = 10
Y = x + 5
A. The graphs of the equation are lines that intersect at one point because the equations have the same slope and same y-intercept. Therefore, the system has exactly one solution.
B. The graphs of the equations are the same line because the equations have the same slope and same y-intercept. Therefore, the system has infinitely many solutions.
C. The graphs of the equations are lines that intersect at one point because the equations have the same slope but different y-intercepts. Therefore, the system has exactly one solution.
D. The graphs of the equations are parallel lines because they have the same slope but different y-intercepts. Therefore, the system has no solution.
PLS HELP ASAP !!
A boy has climbed 210m up a 350m vertical cliff, and is trapped there.
A rescue helicopter is hovering 65m above the top of the cliff.
Calculate how far a rescue must be lowered to reach the boy.
You may draw a sketch to help you.
(i'll mark as brainliest if u answer:))
Answer:
205
Step-by-step explanation:
helicopter=65m
tap of the cliff=
the boy=350m
210=
that makes the answer 205
Answer:
205 meters
Step-by-step explanation:
The cliff is 350m, and the rescue helicopter is 65m above the top of the cliff.
This means that the helicopter is 415 meters above the bottom of the cliff.
The boy is 210m above the bottom of the cliff.
So, you have to subtract 210 from 415 to get 205.
Therefore, you have to lower the rescue 205m to reach the boy.
[tex]\frac{4x}{5}+\frac{5x}{6}[/tex]
To solve this issue, first we have to match the denominators, for this we have to take the LCM from the denominators 5.6, Then just solve the fraction normally, See:
[tex]\sf \dfrac{4x}{5}+\dfrac{5x}{6}\to LMC~(5,6)=30\\\\\\\sf =\dfrac{24x}{30}+\dfrac{25x}{30}\\\\\\\sf =\dfrac{24x+25x}{30}\\\\\\\boxed{\sf \frac{49x}{30}}[/tex]
Okay?!