Kimo went into a bakery where they sell cookies for $0.75 each and brownies for $1.25 each. Kimo has $15 to spend and must buy no less than 12 cookies and brownies altogether.
a. Define the variables. (4 pts)
b. Write the system of inequalities that could be used to solve the situation. DO NOT SOLVE. (4 pts)
a) The variables are:
x = number of cookies bought.y = number of brownies bought.b)
x + y ≥ 12
x*$0.75 + y*$1.25 ≤ $15
How to write the system of inequalities?a) First we need to define the variables, in this case we have:
x = number of cookies bought.y = number of brownies bought.b) Now we want to write the system, we know that he must buy at least 12 items, then:
x + y ≥ 12
And he can spend, at most, $15, then:
x*$0.75 + y*$1.25 ≤ $15
These two inequalities conform the system of inequalities:
x + y ≥ 12
x*$0.75 + y*$1.25 ≤ $15
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What is the volume, measured in cubic centimeters, of the box below? Do not
include units in your answer.
5 cm
4 cm
3 cm
Answer:
v =L× b×h
=5× 4×3
=60 cubic centimeter
The triangles are similar. Find the value of the variable.
Answer:
y = 27
Step-by-step explanation:
The given are two similar triangles.
We can use the following equation to find the variables:
[tex]\frac{y-3}{32} = \frac{18}{24}[/tex]
Cross multiply fractions
32*18 = 24(y-3)
576 = 24y - 72
add 72 to both sides
648 = 24y
divide both sides by 24
27 = y
find the smallest number by which 29160 should be divided so that the quotient becomes a perfect cube
The smallest number by which 29160 should be divided so that the quotient becomes a perfect cube is 5
Perfect cube quotient of a division
The given number is 29160
Note that:
29160 can be factored into 5832
That is, 29160 = 5832 x 5
Take the cube of 5832:
[tex]\sqrt[3]{5832}=18[/tex]
Since it has been confirmed that 5832 is a perfect cube, the smallest number by which 29160 should be divided so that the quotient becomes a perfect cube is 5
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A freezer is shaped like a rectangular prism. It has a length of 8 feet and a height of 3 feet. The volume is 54 cubic feet. Find the width of the freezer.
show your work
The width of the freezer is 2.25ft
Volume of a rectangular prismThe formula for calculating the volume of rectangular prism is expressed as:
V = lwh
Given the following
length l = 8feet
w is the width
height h = 3feet
Substitute
54 = 8*3w
54 = 24w
w = 54/24
w = 2.25ft
Hence the width of the freezer is 2.25ft
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help what’s the answer? confused
Answer:
D. continuous
7/11 = x/9
Round your answer to the nearest tenth.
The solution to the given fraction 7/11 = x/9 to the nearest tenth is 5.7
Fraction7/11 = x/9
cross product7 × 9 = 11 × x
63 = 11x
divide both sides by 11x = 63/11
x = 5.72727272727272
Approximately,
x = 5.7
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PLEASE ANYONE: The tennis club has 5 new members each member buys a racet and a tube of balls. If 6 racket cost $186.00 and 6 tubes of balls cost $27.00 how much do the 5 people pay for rackets and balls?
Answer:
Total cost is $177.50.
Step-by-step explanation:
Rackets:
Divide the cost for racket by 6 to find the cost per racket.
186÷6=31
Multiply 31 by 5 to find the cost for 5 rackets.
31×5=155
$155
Tubes of balls:
Divide 27 by 6 to find the cost per a tube of balls.
27÷6=4.50
Multiply 4.50 by 5 to find the cost for 5 tubes of balls.
4.50×5=22.50
$22.50
Add the amounts for rackets and tubes of balls to find the total cost.
155+22.50=177.50
The total cost is $177.50.
Hope this helps!
A 2-column table with 3 rows. Column 1 is labeled x with entries 2, 4, 5. Column 2 is labeled y with entries 5, 10, 12.5.
Use the information in the table to find the constant of proportionality and write the equation.
The constant of proportionality is
.
The equation that represents this proportional relationship is
.
The constant of proportionality is 2.5.
First, There is a proportional relationship
Two values x and y are said to be in a proportional relationship if y=kx, where x and y are variables and k is a constant.
y = kx
The constant k is the constant of proportionality
As shown that ,
A 2-column table with 3 rows.
Column 1 is labeled x with entries 2, 4, and 5.
Column 2 is labeled y with entries 5, 10, and 12.5.
According to the Above statement, the calculation is as follows:
5/2 = 2.5 , here we get is 2.5
10/ 4 = 2.5 so Here we get 2.5 and so on
Hence, The constant of proportionality is 2.5.
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the current value of a new car is 18,000. the car will depreciate 15% per year over the next 5 year. which exponential equation models this situation
The exponential equation that models this situation is:
[tex]V(t) = 18000(0.85)^t, 0 \leq t \leq 5[/tex].
What is an exponential function?A decaying exponential function is modeled by:
[tex]A(t) = A(0)(1 - r)^t[/tex]
In which:
A(0) is the initial value.r is the decay rate, as a decimal.For this problem, the parameters are:
A(0) = 18000, r = 0.15.
Hence the equation for the value of the car over the next 5 years is:
[tex]A(t) = A(0)(1 - r)^t[/tex]
[tex]A(t) = 18000(1 - 0.15)^t[/tex]
[tex]V(t) = 18000(0.85)^t, 0 \leq t \leq 5[/tex].
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Select the correct answer from each drop-down menu.
The general form of the equation of a circle is 7x2 + 7y2 − 28x + 42y − 35 = 0.
The equation of this circle in standard form is. The center of the circle is at the point, and its radius is units
Step-by-step explanation:
the equation in the standard form is :
( x - 2 ) 2+ ( Y + 3 ) 2 = 18
the center is at the point ( 2, - 3 ).
its radious is : /18 = 3/ 2 units
Describe the steps you would take to solve the given literal equation for m as shown.
For finding the given literal equation is necessary to apply the power 2 on both sides of the given equation and after that you should rewrite the equation as a function of the variable m .
Power RulesThere are different power rules, see some them:
1. Multiplication with the same base: you should repeat the base and add the exponents.
2. Division with the same base: you should repeat the base and subctract the exponents.
3.Power. For this rule, you should repeat the base and multiply the exponents.
4. Zero Exponent. When you have an exponent equals to zero, the result must be 1.
The question gives: [tex]t=2\pi *\sqrt{\frac{m}{k}}[/tex] and from the previous equation, you should find [tex]m=\frac{kt^2}{4\pi ^2}[/tex].
STEP 1 - Applying the power 2 on both sides of the equation [tex]t=2\pi *\sqrt{\frac{m}{k}}[/tex].
[tex]t=2\pi *\sqrt{\frac{m}{k}}\\ \\ t^2=(2\pi *\sqrt{\frac{m}{k}})^2\\ \\ t^2=4\pi ^2*\frac{m}{k}[/tex]
STEP 2 - Rewriting the equation [tex]t^2=4\pi ^2*\frac{m}{k}[/tex] as a function of the variable m .
[tex]t^2=4\pi ^2*\frac{m}{k}\\ \\ t^2k=4\pi ^2m\\ \\ m=\frac{kt^2}{4\pi ^2}[/tex]
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Answer:
1. divide both sides of the equation by 2pi
2. square both sides of the equation
3. use the rule to simplify a fraction to a power
4. multiply both sides of the equation by k
Step-by-step explanation:
edg '22
WILL MAKE BRAINLIEST!!
Find the measure of the angle indicated.
53°
44°
127°
52°
Answer:
53 degrees
Step-by-step explanation:
If the two lines intersected by a transversal are parallel then the same side interior angle should add up to 180 degrees.
180-127 = 53 degrees
Determine the length of side QR in the following triangle
The length of the side QR in the task content can be determined as; 12.22cm.
What is the length of the third side QR?It follows from the task content that 2 lengths and one included angle are given in the task content. It therefore follows that the length of side QR can be evaluated by the cosine rule as follows;
QR² = 13² + 4² - (2×4×13×cos70)
QR = √149.4
QR = 12.22cm
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Find the surface area of the composite figure. Round to the nearest tenth if necessary.
By definition of surface area, the composite figure reports an area of 233.6 square centimeters.
How to calculate the surface area of a composite figure
In this question we need to determine the surface area of a composite figure, which is the sum of all the areas of the faces, which are combinations of triangles and quadrilaterals. Now we proceed to calculate the surface area:
A = 2 · (6 cm) · (3 cm) + 2 · (8 cm) · (6 cm) + 2 · (8 cm) · (3.6 cm) + 2 · (8 cm) · (2 cm) + 4 · (1/2) · (3 cm) · (2 cm)
A = 233.6 cm²
By definition of surface area, the composite figure reports an area of 233.6 square centimeters.
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A group of birds are flying, they meet another group of birds. They ask 'hello hundred.' They replied we are not 100. we need half of us plus you to be hundred. How many birds are needed?
Answer:
Step-by-step explanation:
You answer
give: ∠BDE ≅ ∠CDE and BD ≅ CD.
Prove ∠ABD ≅ ∠ACD
3) [tex]\angle ADB[/tex] and [tex]\angle BDE[/tex] are supplementary (if two angles form a linear pair, they are supplementary)
4) [tex]\angle ADC[/tex] and [tex]\angle CDE[/tex] are supplementary (if two angles form a linear pair, they are supplementary)
5) [tex]\angle ADB \cong \angle ADC[/tex] (supplements of congruent angles are congruent)
6) [tex]\triangle ADB \cong \triangle ADC[/tex] (SAS)
7) [tex]\angle ABD \cong \angle ACD[/tex] (CPCTC)
The vertices of a quadrilateral on the coordinate plane are (2, 4), (-4, -2), (-2, 4), and (4, -2). What type of quadrilateral has these vertices
Answer: Isosceles Trapezoid
Step-by-step explanation:
See the graph of the quadrilateral.
(-4, 8) and (6, 2). Slope
Answer:
In order to go from the first point to the second, we need to rise from 4 to 7, i.e. by 3. We also need to run from -4 to -2, i.e. by 2. Therefore the slope is 32 .
Step-by-step explanation:
URGENT! WILL GIVE BRAINLIEST!
Answer:
150 [tex]m^{2}[/tex]
Step-by-step explanation:
Consider the figure as an isosceles triangle and a rectangle combined.
ISOSCELES TRIANGLE
[tex]A = \frac{1}{2} bh[/tex]
[tex]A = \frac{1}{2} *15*12[/tex]
A = 90
RECTANGLE
[tex]A=lw[/tex]
[tex]A = 5*12[/tex]
[tex]A = 60[/tex]
60 + 90 = 150
Answer:
150m
Step-by-step explanation:
break up the polygon into a triangle and a rectangle.
Triangle:
to find the height of the triangle, subtract 5 from 20
height = 15m base = 12m
[tex]area=\frac{1}{2}bh\\ A=\frac{1}{2} (12)(15)\\A=6(15)\\A=90m[/tex]
rectangle:
[tex]A=bh\\A=12(5)\\A=60m[/tex]
Add both areas together:
[tex]90+60=150m[/tex]
Which expression is equivalent to (2 Superscript one-half Baseline times 2 Superscript three-fourths Baseline) squared?
RootIndex 4 StartRoot 2 cubed EndRoot
StartRoot 2 Superscript 5 EndRoot
RootIndex 4 StartRoot 4 cubed EndRoot
StartRoot 4 Superscript 5 EndRoot
Answer:
D
Step-by-step explanation:
Quick algebra 1 question for 50 points!
Only answer if you know the answer, quick shout-out to Yeony2022, tysm for the help!
Answer:
b
Step-by-step explanation:
b shows direct variation because we can clearly tell that the slope of the graph is 1/2. The graph is also linear, and it crosses the origin (0,0).
a: This graph can be represented as y=2, and that is not a direct variation.
b: Above explanation. This graph is a direct variation.
c: This graph can be represented as x=-8, and that is not a direct variation.
d: This graph has the slope, but it does not cross the origin, so it is not a direct variation.
Answer:
Graph b
Step-by-step explanation:
Direct variation means "y varies directly as x”:
Direct variation equation:
[tex]y=kx[/tex]
where k is the (non-zero) constant of variation.
Note, therefore, that a direct variation equation passes through the origin, as when x = 0:
[tex]\implies y=k(0) \implies y=0[/tex]
Graph a
y does not change as x varies.
Therefore this graph does not model a direct variation.
Graph b
As x gets bigger, so does y. As x gets smaller, so does y.
The line passes through the origin (0, 0).
Therefore this graph models a direct variation.
Graph c
x does not change as y varies.
Therefore this graph does not model a direct variation.
Graph d
As x gets bigger, so does y. As x gets smaller, so does y.
However, the line does not pass through the origin (0, 0).
Therefore this graph does not model a direct variation.
Select the correct answer.
Choose the system of inequalities that best matches the graph below.
Considering the linear functions on the graph, the inequality that matches the situation is:
B.
[tex]y \geq \frac{1}{2}x + 2[/tex][tex]y \leq 2x + 1[/tex]What is a linear function?A linear function is modeled by:
y = mx + b
In which:
m is the slope, which is the rate of change, that is, by how much y changes when x changes by 1.b is the y-intercept, which is the value of y when x = 0, and can also be interpreted as the initial value of the function.The lower bound of the interval is a linear function with y-intercept of b = 2, that also passes through (2,3), hence the slope is:
m = (3 - 2)/(2 - 0) = 1/2.
Hence the inequality is:
[tex]y \geq \frac{1}{2}x + 2[/tex]
The upper bound of the interval is a linear function with y-intercept of b = 1, that also passes through (2,5), hence the slope is:
m = (5 - 1)/(2 - 0) = 2.
Hence the inequality is:
[tex]y \leq 2x + 1[/tex]
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The length of the rectangle is 10.4cm. the perimeter of the rectangle is 28cm. calculate the area of the rectangle.
Answer:
37.44 cm²
Step-by-step explanation:
To find the width, follow these steps.
10.4*2=20.8
28-20.8=7.2
7.2/2=3.6
The width is 3.6.
To find the area, multiply the width and the length together.
10.4*3.6=37.44
The area of the rectangle is 37.44 cm²
Hope this helps!
Help! asap!
As shown in the figure below, a || b and c is the transversal, m∠1= 40°, m∠2= 70°.
Question: m∠3= ?
The measure of angle 3 from the figure is 110 degrees
Lines and anglesAn angle is the intersection between two lines. From the given figure, we have the following parameters
m∠1= 40°,
m∠2= 70°.
Required
Measure of angle 3
The sum of the interior angles of the triangle is equal to the exterior
Sum of interior = <1 + <2
Sum of interior = 40 + 70
Sum of interior =110 degrees
Hence the measure of angle 3 from the figure is 110 degrees
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Determine the perimeter of the figure.
Answer:
[tex]\huge\boxed{\sf 7x + 10\ cm}[/tex]
Step-by-step explanation:
Perimeter:Sum of all sides of a figure is the perimeter of the figure.Perimeter of the figure:= 5 + 2x + 2x + 5 + 3x
Combine like terms
= 2x + 2x + 3x + 5 + 5
= 7x + 10 cm
[tex]\rule[225]{225}{2}[/tex]
Answer:
7x + 10
Step-by-step explanation:
Perimeter is the sum of all the sides together, the distance around a shape.
3x + 5 + 2x + 2x + 5
Organize so the variables are on one side
3x + 2x + 2x + 5 + 5
Combine like terms:
7x + 10
Your answer would be: 7x + 10
I hope it helps! Have a great day!
bren~
Consider trapezoid LMNO.
Trapezoid L M N O is shown. Sides L M and O N are parallel.
What information would verify that LMNO is an isosceles trapezoid? Check all that apply.
LN ≅ MO
LM ≅ ON
LO ≅ MN
∠L ≅ ∠N
∠L ≅ ∠M
The side LO is congruent to the side MN, the diagonal LN is congruent to the diagonal MO, and the angle L is congruent to the angle M in an isosceles trapezoid, denoted by the symbols LMNO.
What are the conditions for an Isosceles Trapezoid?
The conditions listed below demonstrate that any trapezoid is an isosceles trapezoid:
The length of both legs is the same.2nd condition: The base angles are of equal proportion.The length of the diagonals is the same.When these conditions are met by the given trapezoid LMNO, it will be referred to as an isosceles trapezoid. Hence, the following conditions of trapezoid LMNO need to be fulfilled,
LN ≅ MO
LO ≅ MN
∠L ≅ ∠M
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✔ (A.) LN ≅ MO
✔ (C.) LO ≅ MN
✔ (E.) ∠L ≅ ∠M
Solve for the unknown measure of this equation in degrees.
< X in 15^(2) = 13^(2) + 10^(2) -2(13)(10) cos X
Also a question down below.
Answer:
12
Step-by-step explanation:
Well they are similar I assume so 5 / 3.5 = roughly 1.43 and 8.4 x this number gives you 12 so I would say 12
On a number line, point D is at -6, and point E is at 8. Point F lies between points D and E. If DF: FEis 3: 1, where does point F lie on the
number line?
F is located on the number 4.5 on the number line.
Where does point F lie on the number line?We know that point D is at -6
Point E is at 8.
Point F is between D and E, such that the ratio:
DF:FE is 3:1
So if we divide the distance between D and E in 4 parts, 3 of these parts are DF, and one of these parts is FE.
First, the distance between E and D is:
distance = 8 - (-6) = 14 units.
Now, if we divide that by 4, we get:
14/4 = 3.5
Then we have:
DF = 3*(3.5) = 10.5
This means that F is at 10.5 units to the right of D, then:
F = D + 10.5 = -6 + 10.5 = 4.5
F is located on the number 4.5 on the number line.
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Answer:
4.5 is the answer :D
Step-by-step explanation:
If point (4, 5) is on the graph of a function, which equation must be true?
f(5)=4
f(5,4)=9
f(4)=5
f(5,4)=1
Answer:
f(4) = 5
Step-by-step explanation:
Think about it this way
a point with an x value of 4,
this x value is put into the function,
then the function outputted a y value (or value) of 5.
So, we can name this function f(x)
Then, we let x = 4,
then the output for f(4) = 5
Answer: f(4) = 5
Step-by-step explanation:
If the point (4, 5) is on the graph of a function, this means that when you input 4 you get an output of 5.
Inputs are usually shown with the x-coordinate, and outputs are usually shown with the y-coordinate.
This means that (4, 5) is an input of 4 for an output of 5.