Kayla gave 13 of a pan of brownies to Ella and 16 of the pan to Eli. Which choice is the MOST reasonable for the part of the pan of brownies Kayla gave away?
The reasonable fraction for the part of the pan of brownies Kayla gave away is 1/2.
How to illustrate the information?Kayla gave 1/3 of a pan of brownies to Ella and 1/6 of the pan to Eli.
Therefore, the part given away will be the addition of the fractions. This will be:
= 1/3 + 1/6
= 2/6 + 1/6
= 3/6
= 1/2
Therefore, 1/2 of the brownies were given away.
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NEED HELP PLEASE!!!!!
Answer: [tex]x=-\frac{1}{2}, y=\frac{9}{2}[/tex]
Step-by-step explanation:
[tex]5x+7=7x+8\\\\2x=-1\\\\x=-\frac{1}{2}\\\\\implies y=5\left(-\frac{1}{2} \right)+7=\frac{9}{2}[/tex]
The side lengths of a rectangle have a ratio of 7 to 5. If the perimeter is 300 meters, find the length and width of the rectangle.
The length is 25 cm and width is 35 cm. A rectangle is a closed two-dimensional shape with four sides, four corners, and four right angles (90°). A rectangle's opposite sides are equal and parallel.
What is perimeter?A perimeter is a closed path that encompasses, surrounds, or outlines a two-dimensional shape or length. The circumference of a circle or an ellipse is its perimeter. There stood several practical applications for calculating the perimeter. Perimeter is the length of the shape's boundary. It is given by the sum of the shape's sides. It has one dimension and is measured in linear units. Area, on the other hand, quantifies the amount of space occupied by the shape. It has two dimensions and is measured in square units. The perimeter of an object is the distance around it.Therefore,
The sides of the rectangle are in the ratio of 7: 5
Let the length 1=5x
and the breadth b=7 x
Now, perimeter =2(1+b)=300cm
2(5 x+7 x)=300
2(35 x)=300
70 x=300
x=4.28
Therefore, Length 1=5x =25 cm
and the breadth b=7x= 35 cm
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Determine whether the two triangles are similar. If they
are similar, write the
similarity statement.
Answer:
not similar
Step-by-step explanation:
You want to know if two isosceles triangles are similar, given that one has a base angle of 78°, and the other has an a.pex angle of 16°.
Base angleThe base angles of the triangle with a.pex angle 16° will be ...
(180° -16°)/2 = 82° . . . . . . not 78°
SimilarityTwo isosceles triangles will be similar if they have congruent base angles. These triangles do not, so they are not similar.
How many positive factors of 96 are also multiples of 12?
The number of positive factors of 96 which are also multiples of 12 are 4 which are 12,24,48, and 96.
Positive factors of 96 = 1,2,3,4,6,8,12,16,24,32,48 and, 96
Multiples of 12 upto 96 = 12,24,36,48,60,72, 84 and 96
Common numbers between the two are 12,24,48 and 96.
Hence, there are only 4 positive factors of 96 which are also the multiples of 12
Factors
Factors are the numbers that can divide a number exactly. Hence, after division, there is no remainder left.
Multiples
A multiple is a result obtained by multiplying a number by an integer(it shouldn’t be a fraction). The multiples of the whole number are obtained by taking out the product of the counting numbers and that of whole numbers.
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Ms.walker bought a computer for 15% off from the list price of p dollars. if the sales tax was 8%, how much did she pay for the computer including sales tax?
Ms. Walker paid $0.918*p for the computer including sales tax .
In the question ,
it is given that
discount on list price for the computer is 15%
sales tax = 8%
let the list price for the computer be $p .
So, sales price is = p - 0.15*p = 0.85*p
tax on sale price is = 8% of 0.85*p = 0.08*0.85*p = 0.068*p
Total Price = sale price + tax on sale price
Substituting the values of tax and sale price ,
we get
total price = 0.85*p + 0.068*p
= 0.918*p
Therefore , she paid $0.918*p for the computer including the sales tax .
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Sandi randomly selects a single bill from an envelope containing 8 ones, 5 fives, 4 tens, and 3 twenties. Whatis the expected value of the money she selects?expected value =
the formula to get the expected value is
[tex]E(x)=\sum ^n_{i\mathop=1}x_if(x_i)[/tex]So, first we calculate teh probabilities. We have 20 bills in total. so we divide the quantity of bills of each value by the total:
we have 8 ones: 8/20= 2/5
5 fives: 5/20=1/4
4 tens: 4/20= 1/5
3 twenties = 3/20
now, we multiply each value with te probabilitiy of picking it and add all
[tex]E=\text{ 1}\cdot\frac{2}{5}+5\cdot\frac{1}{4}+10\cdot\frac{1}{5}+3\cdot\frac{3}{20}=\text{ 4.1}[/tex]the expected value is 4.1
Are null and alternative hypotheses statements about samples, about populations, or does it depend on the situation? explain.
The null and alternative are always claims about the population. That's because the goal of hypothesis testing is to make inferences about a population based on a sample.
Null hypothesis testing is a formal approach to deciding whether a statistical relationship in a sample reflects a real relationship in the population or is just due to chance.
A segment MN has endpoints M(-7.-6) and N(7,7). Find the coordinates of partition point P that divides the segment into a 5:2 ratio.
A segment MN has endpoints M(-7.-6) and N(7,7). Find the coordinates of partition point P that divides the segment into a 5:2 ratio.
___________________________
Find the coordinates of partition point P that divides the segment into a 5:2 ratio.
5:2 means that it is divided into 7, and we do not move two positions from (7,7)
X axis
7- (-7) = 14
14/7 = 2
7-2*2 = 3
Y axis
7-(-6)= 13
13/7 =
7 - 2* (13/7) = 49/7 - 26/ 7 = 23/7 = 3 2/7
______________________________
Answer
(3, 3 2/7)
For a particular rectangle, twice the width is 4 meters shorter than the length. The area of the rectangle is 126 square meters. What is the perimeter of the rectangle? ? meters
Let l be the length of the rectangle and w its width.
Then its area is given by:
a = l*w
Its perimeter is given by:
p = 2l + 2w
We also know that, for this specific triangle, we have:
2w = l - 4
l = 2w + 4
a = 126 m²
Applying this result in the area formula, we have:
w*l = 126
w(2w + 4) = 126
2w² +4w = 126
2w + 4w - 126 = 0
Therefore, w = 7 m and l = 2*7 + 4 = 10 m
Then, the perimeter is given by:
p = 2*18 + 2*7 = 36 + 14 = 50 m
In 2022, a company made a profit of $1.38 million. That amount is $2.54 million more than the profit from 2021.
What is the profit from 2021? Write & solve an Algebraic Equation.
help please do in few mins
The length of the red line segment on this number line is: C. 2 1/2.
What is a number line?A number line simply means a type of graph with a graduated straight line which comprises both positive and negative numbers that are placed at equal intervals along its length.
This ultimately implies that, a number line can be used to compare or determine the difference (distance) between two numbers plotted on it. Additionally, a number line primarily increases in numerical value towards the right and decreases in numerical value towards the left.
Note: Each interval on this number line represents 1/4 and the total intervals between the red dots is 10.
From the number line shown above, we have:
Distance = 10 × (1/4)
Distance = 10/4
Distance = 5/2
Distance = 2 1/2.
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David will rent a car foe a day. The rental company offers two pricing options: Option A and Option B. For each pricing option, cost (in dollars) depends on miles driven, as shown below.
Let
y ----> total cost in dollars
x -----> number of miles
we have that
Option B
y=50
Option A
Find out the slope
take two points from the graph
(0,20) and (150,50)
m=(50-20)/(150-0)
m=30/150
m=1/5=$0.20 per mile
therefore
y=0.20x+20
Part A
For x=75 miles
Option A -----> y=0.20(75)+20=$35
Option B ------> y=$50
therefore
Option A costs less
Find out the difference
$50-$35=$15
Cost $15 less than the other option
Part B
Looking at the graph
For x=150 miles
Both options cost the same
If David drives more than this amount option B costs less
Kara is building a fence. The drawing above shows two sections of the fence. Help Kara figure out the
materials and cost for her project. Show all work. Use a calculator and round answers to the nearest
hundredth.
(a) The vertical fence posts are 5 feet tall. The diagonal pieces are 9 feet. How far apart should the fence posts be placed
(b) Kara's fence needs to reach at least 93 feet. How many fence posts will she need?
(c) How many diagonal pieces will she need?
(d) The fence posts cost $17 and the diagonal pieces cost $3.50. Calculate Kara’s total cost.
The materials and cost of Kara's project obtained using Pythagorean theorem, are;
(a) Distance between fence posts is 2•√(14) feet
(b) Kara needs about 12 fence posts
(c) Kara will need 22 diagonal pieces
(d) Kara's total cost is $281
What is the Pythagorean theorem?Pythagoras theorem can be stated as, the square of the length of the hypotenuse side of a right triangle is equal to the sum of the squares of the other two sides.
The drawing obtained from a similar question consists of two diagonals between consecutive posts.
(a) The given parameters are;
Height of the fence post = 5 feet
Length of the diagonal pieces = 9 feet
The distance, d, between the fence posts using Pythagorean theorem gives;
d² = 9² - 5² = 56
d = 2•√(14)
The distances between the fence posts should therefore be 2•√(14) feet
(b) The number of fence posts, n, is given by the equation;
2•√(14) × n = 93
Which gives;
[tex] \displaystyle {n = \frac{93 }{2 \cdot \sqrt{14}} \approx 12.43}[/tex]
Given that after the 12th post, the 1st post comes next and the distance remaining is less than d, the number of posts, n is 12
(c) The number of diagonal pieces, m, needed, given that there are two diagonal pieces between two posts and there is only 11 in between spaces, gives;
m = 2 × 11 = 22
There are 22 diagonal pieces
(d) Cost of a fence post = $17
Cost of a diagonal piece = $3.5
Total cost, C, is therefore;
C = 12 × 17 + 22 × 3.5 = 281
Kara's total cost is $281
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2. How do you determine the equation of the asymptote of an exponential function?
The general form of exponential function is given below:
[tex]\begin{gathered} y=a.b^x+c \\ \text{When a.b}^x=0,\text{ the asymptote of the function becomes } \\ y\text{ = c , which is, y-intercept} \\ \text{But where c=0, the asymptote is the line y = 0} \end{gathered}[/tex]
Consider the line whose equation is y=-1/2x+3
any line that is perpendicular to this line is
Answer:
positive
Step-by-step explanation:
for a line to be perpendicular to another line, the slope must be reciprocaled and if its positive it becomes negative (vice versa)
y = -1/2x+3 = Line A
y = 2x+3 = PERPENDICULAR to Line A
Which number is greatest?
-1
-4
-6
Answer:
Step-by-step explanation:
-1>-4>-6
-1 is the greatest number.
A fish tank sprung a leak and loses 45% of its water.
There is now 363 litres of water in the fish tank.
How much water was in the fish tank before the leak?
Answer:
689.7
Step-by-step explanation:
Math
Simplify each expression. show your solution
To simplify a phrase, create an equivalent expression without any terms that are identical.The expression will then be rewritten using the fewest terms feasible.
What is an equation to simplify?
A mathematical expression is simplified when it is replaced with a simpler, typically shorter, equivalent statement.The fundamental guidelines and procedures to simplify any algebraic statement are as follows:By multiplying factors, remove any grouping symbols like brackets and parenthesis.If the words contain exponents, use the exponent rule to eliminate grouping.Add or subtract like terms to combine them.Add the constants together. Add numbers
2+1
= 3
2³ = 8
first one 8
2. x²× x°
= x ²+°
3.a6_a4
= a2
4. x×x×y×y
=x²y²
5 x²×x×y×y²
= x³y³
6.(mn)5
= m5N5
7 (abc)²
= a²b²c²
8.(p²q)³
p6q3
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Solve the proportion 4/x = 7/26 X=
given the proportion :
[tex]\frac{4}{x}=\frac{7}{56}[/tex]we will find x as follows:
[tex]\begin{gathered} \frac{7}{56}=\frac{7\cdot1}{7\cdot8}=\frac{1}{8} \\ \\ \frac{4}{x}=\frac{1}{8} \\ \\ x=4\cdot8=32 \end{gathered}[/tex]So, the answer is: x = 32
I need some explanation on how to do piece wise functions? Where do I even start with this equation, can you explain this step by step? Including breaking down the graphing of absolute functions?
A piecewise function is basically a function that behaves differently at different domain intervals.
The given piecewise function is
[tex]\begin{cases}2x\quad \quad \quad \quad \quad \quad x\le3 \\ \frac{1}{3}x^2-2x+9\quad x>3\end{cases}[/tex]As you can see, the function has a different expression for the interval x is less than or equal to 3 and a different expression for the interval x is greater than 3.
The easiest way to determine which graph corresponds to the given piecewise function is to evaluate the piecewise function at different values of x and graph it.
Evaluate the piecewise function for the interval x is less than or equal to 3.
[tex]\begin{gathered} 2x \\ x=1\rightarrow2(1)=2 \\ x=2\rightarrow2(2)=4 \\ x=3\rightarrow2(3)=6 \end{gathered}[/tex]Evaluate the piecewise function for the interval x is greater than 3.
[tex]\begin{gathered} \frac{1}{3}x^2-2x+9 \\ x=4\rightarrow\frac{1}{3}(4)^2-2(4)+9=6.33 \\ x=6\rightarrow\frac{1}{3}(6)^2-2(6)+9=9 \\ x=8\rightarrow\frac{1}{3}(8)^2-2(8)+9=14.33 \end{gathered}[/tex]Now, let us graph these points
As you can see from the graph, it matches with the graph of the 2nd option.
Therefore, the correct graph of the given piecewise function is the 2nd graph.
A circle passes through the points (3, 2) and (7, 2) and has radius 2√2. Find the two possible equations for this circle.
Answer:
(x-5)²+y² = 8(x-5)²+(y-4)² = 8Step-by-step explanation:
radius, r = 2√2
let the center be A(a, b):
The distance from the center to any of the 2 points is r.
So for (7, 2):
it satisfies the equation:
(x-a)²+(y-b)² = r²
Substituting x and y:
(7-a)²+(2-b)² = (2√2)²
squaring both sides:
(7-a)² + (2-b)² = 8
a² +b² - 14a -4b + 49+ 4= 8
a² +b² - 14a -4b + 45= 0 (Eqn 1)
For (3, 2):
it also satisfies the equation:
(x-a)²+(y-b)² = r²
Substituting x and y:
(3-a)²+(2-b)² = (2√2)²
squaring both sides:
(3-a)² + (2-b)² = 8
a² +b² - 6a -4b + 9+ 4= 8
a² +b² - 6a -4b + 5= 0 (Eqn 2)
We can now proceed by elimination:
(Eqn 2) - (Eqn 1):
(a² +b² - 6a -4b + 5) - (a² +b² - 14a -4b + 45) = 0
- 6a - -14a+ 5 - 45 = 0
8a - 40 = 0
8a = 40
a = 40/8
a = 5Putting a back into (Eqn 2):
a² +b² - 6a -4b + 5= 0
5² +b² - 6(5) -4b + 5= 0
25 +b² - 30 -4b + 5= 0
b² -4b = 0
b(b -4) = 0
Values of b:
b = 0 and b = 4POSSIBLE EQUATIONS OF CIRCLE:
Since we have 2 values of b, we have 2 possible centers:
(5, 0) and (5, 4)
Putting the centers into the standard equation of the circle above, we obtain:
(x-5)²+y² = 8 and(x-5)²+(y-4)² = 8PLEASE VOTE AS BRAINLIEST.
BLAISE M.
HELP NEEDED FOR GEOMETRY PROOFS!!! I will give brainliest
The method used to prove the specified geometric relationship between the angles and sides of the triangles are as follows:
24. ΔDAE ≅ ΔBAC by SAS postulate, therefore
∠B ≅ ∠E CPCTC25. ΔACD ≅ ΔBCD by ASA postulate
∡A ≅ ∡B CPCTC26 ΔACD ≅ ΔBCD LH postulate.
∡A ≅ ∡B CPCTCWhat are the congruency postulates?The congruency postulates include, SSS, Side-Side-Side, AAS, Angle-Angle Side, SAS, Side-Angle-Side, HL, Hypotenuse Leg.
24. The two column proofs are presented as follows;
Statements Reasons
1. [tex]\overline{CD}[/tex] bisects [tex]\overline{BE}[/tex] 1. Given
2. [tex]\overline{BA}[/tex] = [tex]\overline{AE}[/tex] 2. Definition of bisected line
3. . [tex]\overline{BA}[/tex] ≅ [tex]\overline{AE}[/tex] 3.. Definition of congruency
4. [tex]\overline{CA}[/tex] = [tex]\overline{AD}[/tex] 4. Definition of bisection of line [tex]\overline{CD}[/tex]
5. [tex]\overline{CA}[/tex] ≅ [tex]\overline{AD}[/tex] 5. The definition of congruency
6. ∠DAE ≅ ∠BAC 6. Vertical angles theorem
7. ΔDAE ≅ ΔBAC 7. SAS congruency postulate
8. ∠B ≅ ∠E 8. CPCTC
The acronym, CPCTC represents Corresponding Parts of Congruent Triangles are Congruent
25. Statement Reasons
1. [tex]\overline{CD}[/tex] ⊥ [tex]\overline{AB}[/tex] 1. Given
2. [tex]\overline{CD}[/tex] bisects ∠ACB 2. Given
3. ∠3 = ∠4 = 90° 3. Definition of bisected lines
4. ∠1 ≅ ∠2 4. Definition of bisected angle ∡ACB
5. ΔACD ≅ ΔBCD 5. ASA congruency postulate
6. ∡A ≅ ∡B 6. CPCTC
26. Statement Reason
1. m∠1 = m∠2 = 90° 1. Given
2. ΔACD and ΔBCD are right triangles 2. Definition
3. [tex]\overline{AC}[/tex] ≅ [tex]\overline{BC}[/tex] 3. Given
4. [tex]\overline{CD}[/tex] ≅ [tex]\overline{CD}[/tex] 4. Reflexive property
5. ΔACD ≅ ΔBCD 5. LH Congruency postulate
6 ∡A ≅ ∡B 6. CPCTC
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Reuben drove 243 miles using 12 gallons of gas. At this rate, how many miles would he drive using 16 gallons of gas?
Answer:
324 miles
Step-by-step explanation:
Set up a proportion
243
12
=
x
16
Cross multiply
12
x
=
3888
x=324 miles
Theorems and Proofs problemIll send a picture of the question
According to the given information, the reason for the second statement is definition of supplementary angles, this is because the definition of supplementary angles says that the sum of two supplements is 180°.
It means that the answer is B. Definition of supplementary angles.
Can someone please answer this!
Answer: see the attachment
Step-by-step explanation:
h = # of hours worked
{10h and {15(h-40)+400 are both functions i.e. simplified equations
simply fit the # of hours worked in each equation to get the values. you can also double check your work or to understand better
to do so, take (h) # of hours worked and multiply by the pay rate. This gives the total pay over the work week. then take the extra hours beyond the 40. ie 7. if $10 is the pay rate per hour and OT is 1.5xnormal pay then 10x1.5=15. Multiply 15x7 and you get 105 then add to 400 and you get $505. 400 comes from 10(40).
part b and c is just setting the functions.
so instead of 40 hrs per week your full-time rate is now 38 and anything beyond would be counted as overtime. so a normal work week of 38 hrs x the $10/hr would equate to $380 for the week.
part c, if the hours per week were kept normal at 40hrs/week but the pay rate is increased this then changes 10 = h to 12 = h. if 12=h and you work 40hrs/week, then 12(40)=$480 for the normal work week. also this changes your OT pay from 10(1.5)=15 to 12(1.5)=$18
12. Find the value of x.
+f
(7x+4) +(10x-11)=180 mid segment
The value of x is 11.
What is an equation?
Equations are mathematical statements which contains two algebraic expressions on both sides of an equal to '=' sign. it represents the relationship of equality among the expressions.
We are given an equation (7x+4)+(10x-11)=180
We open brackets and simplify the equation by adding similar values we get
17x-7=180
17x=187
on dividing both sides by 17 we get
x=11
Hence the value of x is 11
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Practice Problems
1. Mai and Priya were on scooters. Mai traveled 15 meters in 6 seconds. Priya travels
22 meters in 10 seconds. Who was moving faster? Explain your reasoning
2. Here are the prices for cans of juice that are the same brand and the same size at
different stores. Which store offers the best deal? Explain your reasoning
Store X: 4 cans for $2.48
per can
Store Y: 5 cans for $3.00
Store Z: 59 cents
Topic B
3. Costs of homes can be very different in different parts of the United States.
1. A450-square-foot apartment in New York City costs $540,000. What is the
price per square foot? Explain or show your reasoning
2. A 2,100-square-foot home in Cheyenne, Wyoming, costs $110 per square
foot. How much does this home cost? Explain or show your reasoning
4. There are 33.8 fuld ounces in a liter. There are 128 fuid ounces in a galon. About
how many liters are in a gation?
A 2
B. 3
C. 4
D. 5
Is your estimate larger or smaller than the actual number of liters in a gallon? Explain
how you know.
-
Answer:
1. Mai was moving faster as she covered a greater distance in the same amount of time.
Speed = Distance
-----------
Time
2. The best deal is Store Z. We must divide to determine the price each business is charging for a single can in order to particularly choose the greatest deal.
For Store X, each can is $0.62
For Store Y, each can is $0.60
Store Z is the best deal due to how cheap each can of juice costs.
3 (Part 1) It costs $1,200 for each square foot. The cost of the apartment is $540,000 & the area of the apartment is 450 feet. You can divide 540,000 by 450 and you should get 1,200.
3 (Part 2) The home costs $231,000. You can use the two numbers in the question "2,100" and "110". You should get $231,000 after adding those two numbers.
4. Approximately 3.8 liters are in a gallon. 3.8 is closest to 4 so you can round it up to 4 liters.
Step-by-step explanation:
3,4,16/3 find the 10 term
The 10th term of the Geometric Sequence {3,4,16/3....} is 262144/6561.
The [tex]n^{th}[/tex] term of the Geometric Sequence is
given by the formula
aₙ = a*rⁿ⁻¹
where , a is the first term , r is the common ratio .
in the question ,
the sequence is given as {3,4,16/3....}
here we need to find the common ratio(r) ,
we know , r = a₂/a₁
So , r= 4/3 .
Since we need to find the 10th term , so n=10 .
Substituting the values in the nth term formula , we get
a₁₀ = (3)*(4/3)¹⁰⁻¹
= 3* (4/3)⁹
= 4⁹/3⁸
= 262144/6561
The 10th term is 262144/6561.
Therefore , the 10th term of the Geometric Sequence {3,4,16/3....} is 262144/6561.
The given question is incomplete , the complete question is
Find the 10th term of the Sequence {3,4,16/3....} ?
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awnser for this question
The equation of the line that is parallel to k and passes through (-1, 3) is
- x + 2y = 7
How to find the equation of a line?The equation of a line can be represented in different form such as point slope form, slope intercept form and standard form.
Therefore, the equation of the line is parallel to k.
Parallel line shave the same slope.
Therefore, let's find the slope of k to find the slope of the equation of the line.
Hence, using (7, 2)(1, -1)
m = -1 - 2 / 1 - 7
m = - 3 / -6
m = 1/ 2
Therefore, the slope of the line is 1 / 2. Let's find the y-intercept using the point (-1, 3)
3 = 1 / 2(-1) + b
3 = - 1 / 2 + b
b = 3 + 1 / 2
b = 7 / 2
Hence, the equation is as follows;
y = 1 /2x + 7 / 2
2y = x + 7
2y - x = 7
- x + 2y = 7
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