Answer:
Option 4 is correct.
The equation [tex]4x^2 -24x + 4y^2 + 72y = 76[/tex] is equivalent to [tex]4(x-3)^2 + 4(y+9)^2 =436[/tex]
Step-by-step explanation:'
Given equation: [tex]4x^2 -24x + 4y^2 + 72y = 76[/tex]
First group the terms with x and those with y;
[tex](4x^2-24x)+(4y^2+72y) = 76[/tex]
Next, we complete the squares.
We can do this by adding a third term such that the x terms and the y terms are perfect squares.
For this we must either add the same value on the other side of the equation or subtract the same value on the same side so that the equality is maintained.
⇒[tex]4(x^2-6x) +4(y+18y) = 76[/tex]
or
[tex]4(x^2 -6x +3^2 -3^2) + 4(y^2 +18y +9^2 -9^2) = 76[/tex]
[tex]4(x^2-6x + 3^2) - 36 + 4(y^2+18y +9^2) - 324 = 76[/tex]
[tex]4(x-3)^2 + 4(y+9)^2 - 360 =76[/tex]
Add 360 on both sides we get;
[tex]4(x-3)^2 + 4(y+9)^2 =360 +76[/tex]
Simplify:
[tex]4(x-3)^2 + 4(y+9)^2 =436[/tex]
Therefore, the given equation is equivalent to [tex]4(x-3)^2 + 4(y+9)^2 =436[/tex]
During The Month Of October, Sophie Raised $25 for a charity. During November, she raised 5 times as much money for charity. How much money did sophie raise in November
Shiloh opens a savings account in which interest is compounded annually. The balance in the account is given by the following exponential expression, where t represents the time in years. Which statement correctly interprets the given expression? 125(1.025)t
A. Shiloh initially invested $125, which grows annually at a rate of 2.5%.
B. Shiloh initially invested $125, which grows annually at a rate of 1.025%.
C. Shiloh initially invested $1,025, which grows annually at a rate of 12.5%.
D. Shiloh initially invested $1,025, which grows annually at a rate of 1.25%.
Help asp
Answer:
Shiloh initially invested $125, which grows annually at a rate of 2.5%.
Step-by-step explanation:
The balance in the account is given by the following exponential expression,
[tex]125(1.025)^t[/tex]
Exponential growth formula is
[tex]A= P(1+r)^t[/tex]
Where P is the initial amount invested
r is the rate of interest
When we compare the formula with given expression , we can see that we have 125 in the place of P
So initial amount invested is $125
Now we find out 'r'
1+ r = 1.025
Subtract 1 on both sides
r= 0.025
To get percentage we multiply by 100
0.025 * 100 = 2.5%
Shiloh initially invested $125, which grows annually at a rate of 2.5%.
Mrs. Johnson is 3 times as old as her son. Ten years ago she was 5 times as old as her son was then. Find each of their ages
Answer:
her son is 20, Mrs. Johnson is 60
Step-by-step explanation:
if her son is x, Mrs. Johnson is 3x,
Ten years ago,
her son is x-10, Mrs. Johnson is 3x-10,
so:
3x-10=5(x-10)
x=20
The price of a cantaloupe at a fruit stand goes up 4 cents each month. The first month the stand was open, a cantaloupe cost $1.25.
What will the cost of a cantaloupe be in the 40th month?
A. $157.25
B. $16.85
C. $3.35
D. $2.81
Answer:
D. $2.81
Step-by-step explanation:
The statement says that the price of a cantaloupe goes up 4 cents each month and that the cost of the cantaloupe was $1.25 on the first month. Tto determine the cost in the 40th month, you have to multiply 4 cents for 39 months as the price for the first month was given and then you have to add this with the price for the first month:
0,04*39= 1.56
1.56+1.25= $2.81
The price in the 40th month is $2.81.
2. Use a graph to find the solution.
You want to set up an aquarium and need to determine what size tank to buy...
Answer:
The correct option is 3. Capacity of smallest tank is 15-gallons.
Step-by-step explanation:
The graph shows the relationship between capacity of tank and combined length of fish it can hold.
The line passing through (0,1) and (1,2).
Slope of the line is
[tex]m=\frac{y_2-y_1}{x_2-x_1}=\frac{2-1}{1-0}=1[/tex]
Slope intercept form of a line is
[tex]y=mx+b[/tex]
Where, m is slope and b is y-intercept.
The slope of the line is 1 and the y-intercept is 1, therefore the equation of line is
[tex]y=x+1[/tex] ..... (1)
If we want four 2-inch platys, three 1-inch guppies and a 3-inch loach, then the combined length of fish is
[tex]4\times 2+3\times 1+1\times 3=8+3+3=14[/tex]
Therefore the combined length of fish is 14.
Put x=14 in equation 1.
[tex]y=14+1=15[/tex]
Therefore, the capacity of smallest tank is 15-gallons and option 3 is correct.
Answer: got answer from someone, 12 and 14 were wrong.
Step-by-step explanation:
connexus unit 8 lesson 1 PRACTICE!
1) B
2) C
3) A
4) C
5) B
6) A
7) D
8) A
9) D
10) A
11) A
12) not C
13) D
14) not C
15) B
Delany can run 1 1/2 of a mile at a rate 16 minutes and 30 seconds. At this rate how many minutes will it take him to run one mile?
Answer:
11 minutes
Step-by-step explanation:
Do 16 mins. 30 secs. divided by 1.5, since that is what you divide the miles by to get the base amount. The answer is 11 minutes.
A student multiplied –8 × 334 as shown. One step is missing. Which is the missing step? –8 × 334 = ? = –8 × 3 + (–8) × 34 = –24 + −8 × 324 = –24 + −244 = –24 + (–6) = –30
Answer:
–24 + −8 × 324
Step-by-step explanation:
Well, if you go through the answer choices, there is only one that gives you the correct answer. The product is -2672, and the only answer choice that this satisfies is the second one.
Answer:
It's C
Step-by-step explanation:
Item 9 A group of tourists spends $156 to rent snorkels and fins. A total of 15 snorkels and 18 pairs of fins are rented. Renting a snorkel costs four times as much as renting a pair of fins. How much does it cost to rent a snorkel?
Answer:
$8
Step-by-step explanation:
A group of tourists spends $156 to rent snorkels and fins.
They rented 15 snorkels and 18 pairs of fins.
Renting a snorkel costs four times as much as renting a pair of fins.
Let us assume that the rental cost of a pair of fins is x, so the rental cost of snorkel will be 4x.
Then total cost of 15 snorkels and 18 pairs of fins will be,
[tex]=15(4x)+18x[/tex]
[tex]=60x+18x[/tex]
[tex]=78x[/tex]
But it is given as $156, so
[tex]\Rightarrow 78x=156[/tex]
[tex]\Rightarrow x=2[/tex]
Therefore, the rental cost of a pair of fins is $2 and cost of snorkel is [tex]2\times 4=\$8[/tex]
Line segment AB has a length of 15 and angle a=35degrees . A segment with a length of 12 will form the third side of the triangle. What are the possible measures of the angle opposite side AB? Please explain the process.
Answer:
C = 45.8 or C = 117.69
Step-by-step explanation:
Remark
Only SSA gives the possibility of 2 answers. This one does not give that opportunity. There is one unique answer. We'll discuss 2 and zero after finding 1 answer. On looking at it again, the question might be ambiguous. We'll check that out as well.
Given
AB = 15
<A = 35
point C opposite line AB such that CB = 12 These givens give a unique answer.
Solution
Sin(35) / 12 = Sin(C) / 15 Multiply both sides by 15
15*Sin(35) / 12 = Sin(C) Find 15/12
1.25*sin(35) = Sin(C) Write Sin(35)
1.25*0.5736 = Sin(C) Multiply the left
0.71697 = Sin(C) Take the inverse Sin
C = 45.805 degrees This is the angle opposite AB
Angle B = 180 - 35 - 45.805 = 99.2
Ambiguous Case
If AC = 12 we have another answer entirely. This is SAS which will give just 1 set of answers for the triangle. The reason the case is ambiguous is because we don't exactly know where that 12 unit line is. It could be AC or BC.
I will set up the Sin law for you, and let you solve it
Sin(B) / 12 = Sin(35)/15
When you solve for Sin(B) as done above you, get 0.45886 from which B = 27.31 degrees
C = 180 - 35 - 27.31 = 117.69
So that's two values that C could have. I think that's all given these conditions.
Two Cases or None
<A = 35 degrees
AC = 15
CB = 12
This should give you two possible cases or none. You can check which by finding the height of the triangle from C down to AB (which has no distinct length. The h is 15 * Sin35 = 8.6. If CB < 8.6, there are no solutions. If CB < AC then if CB > that 8.6, there are 2 solutions.
What is 2.45 x 10^4
A: 2450
B: 24,500
C: 245
D: 245,000
Answer:
I got B. 24,500 as my answer.
Step-by-step explanation:
2.45 x (10^4) = 24,500
Which expression is equal to (In picture)
[tex]3x^2+12x-15=3(x^2+4x-5)=3(x^2+5x-x-5)\\\\=3[x(x+5)-1(x+5)]=3(x+5)(x-1)\\----------------------\\4x^2+4x-8=4(x^2+x-2)=4(x^2+2x-x-2)\\\\=4[x(x+2)-1(x+2)]=4(x+2)(x-1)\\----------------------\\2x^2-8=2(x^2-4)=2(x^2-2^2)=2(x-2)(x+2)\\----------------------\\x^2-5x=x(x-5)\\----------------------\\\\\dfrac{3x^2+12x-15}{4x^2+4x-8}\cdot\dfrac{2x^2-8}{x^2-5x}\\\\=\dfrac{3(x+5)(x-1)}{4\!\!\!\!\diagup_2(x+2)(x-1)}\cdot\dfrac{2\!\!\!\!\diagup^1(x-2)(x+2)}{x(x-5)}\\\\\text{Canceled:}\ (x-1)\ \text{and}\ (x+2)[/tex]
[tex]=\boxed{\dfrac{3(x-2)(x+5)}{2x(x-5)}}[/tex]
Wally purchased a desk that was on sale do 2/3 of the original price. If the original price was $450, what was the price that Wally Paid?
Answer:
2/3 of 450 is 300 :)
RESPOND QUICK
Solve the first proportion for x. Use that value to solve the second proportion for
y. ,
x/24 = 9/72,
x/9 = y/12
A. x = 3, y = 4
B. x = 4, y = 3
C. x = 27, y = 36
D. x = 3, y = 6
Answer:
A
Step-by-step explanation:
3/24=9/72 3*3=9 24*3=72 x=3
3/9=y/12 9/3=3 12/3=4 y=4
X=3 y=4
Camp Oakes gets 32 juice boxes of orange juice and 56 boxes of apple juice each shelf in the cup board can hold eight boxes of juice what is the least number of cells needed for all the juice box
Which best describes this triangle?
A.
All sides are the same length; each angle measures 90°.
B.
Two sides are the same length; one angle measures 90°.
C.
Two sides are the same length; one angle is obtuse.
D.
All sides are the same length; each angle is acute.
Which angles are corresponding angles
Answer:
Step-by-step explanation:
corresponding angles are congruent to eachother for example 1&3, 5&7, 2&4, 8&6
Answer:
Option B, C, D are the correct options
Step-by-step explanation:
When two parallel lines are intersected by a transverse then two angle which are relatively at the the same position are called as corresponding angles.
As given in the picture attached, ∠1 and ∠2 are corresponding angles.
Similarly, ∠3 and ∠4 re corresponding angles.
Now we come to our question. In this question corresponding angles are
1) 2 and 4
2) 6 and 8
3) 1 and 3
4) 5 and 7
Therefore, Options. B, C and D are the correct options.
he data set represents the number of miles Mary jogged each day for the past nine days.
6, 7, 5, 0, 6, 12, 8, 6, 9
The outlier of the data set is
Answer:
zero is your answer.
Step-by-step explanation:
Your answer for this question is 0
A horseback riding trail is 1 mi 40.8 ft long. How long is the trail in yards, feet, and inches?
Answer: 1773.6 yards 5320.8 feet 64324.8 inches
Step-by-step explanation:
1 mile in yards = 1760 40.8 feet in yards = 13.6 1760 + 13.6 = 1773.6 yards
1 mile in feet = 5280 + 40.8 = 5320.8 feet
1 mile in inches = 63360
40.8 feet in inches = 964.8
63360 + 964.8 = 64324.8 inches
hope this helps :)
The length of a rectangular storage room is 3 feet longer than its width. if the area of the room is 40 square feet, find the width.
Answer:
Width of rectangular storage room= 5 feet.
Step-by-step explanation:
Let x be the width of storage room.
We have been given that the length of a rectangular storage room is 3 feet longer than its width. So the length of storage room will be x+3.
We are also given that the area of the room is 40 square feet.
Since the area of a rectangle is length times width.
[tex]\text{Area of rectangle}=\text{Length* Width}[/tex]
Let us substitute our given values in area formula.
[tex]40=x*(x+3)[/tex]
Upon distributing x we will get,
[tex]40=x^2+3x[/tex]
[tex]x^2+3x-40=0[/tex]
Now let us factor out our quadratic equation using splitting the middle term.
[tex]x^2+8x-5x-40=0[/tex]
[tex]x(x+8)-5(x+8)=0[/tex]
[tex](x+8)(x-5)=0[/tex]
[tex]x+8=0[/tex] or [tex]x-5=0[/tex]
[tex]x=-8[/tex] or [tex]x=5[/tex]
Since width can not be negative, therefore, the width of rectangle will be 5 feet.
Let us verify our answer.
Length of rectangular storage room is 3 feet longer than its width. So length will be 5+3=8.
Given: Area=40 square feet.
5*8=40.
Hence, width of rectangular storage room is 5 feet.
What is the midpoint of a segment whose endpoints are (9, −9) and (−3, 7)?
Answer:
The midpoint is (3,-1)
Step-by-step explanation:
The midpoint of a segment is found by adding the ends together and dividing by 2
midpoint = (x1+x2)/2 , (y1+y2)/2
=(9+-3)/2 , (-9+7)/2
= 6/2, -2/2
=3,-1
Find the domain of the following graph:
−7 < x ≤9
−7 < y ≤ 9
−7 < x ≤5
−7 < y ≤ 5
Answer:
[tex]-7<x\leq 9[/tex]
Step-by-step explanation:
The domain is the set of all x-values. We can find the domain by finding the left boundary of the graph (the furthest left x-value) and then the right boundary (the furthest right x value).
The furthest left x-value is -7. Notice it has a large open circle here that is not filled in. This means the function does not include -7 but includes numbers very close to it like-6.999999..... We sue use an inequality sign without an equal to to write -7. x >-7.
The furthest right x value is 9. It has a closed circle or "filled in" circle so we write with an equal to sign. [tex]x\leq 9[/tex].
We combine the two into [tex]-7<x\leq 9[/tex].
How many 3 over 8 pound bags of trail mix can be made from 6 and 3 over 8 pounds of trail mix ? Write a division expression
Answer:
[tex]\frac{\frac{51}{8}} {\frac{3}{8}}[/tex]
17 bags.
Step-by-step explanation:
We are asked to find the number of bags with weight 3/8 pound can be made from [tex]6\frac{3}{8}[/tex].
To find the number of
[tex]\text{Number of bags that can be made from available mix trail}=6\frac{3}{8}\div \frac{3}{8}[/tex]
Convert mixed fraction into improper fraction.
[tex]\text{Number of bags that can be made from available mix trail}=\frac{51}{8}\div \frac{3}{8}[/tex]
Since we know that dividing a fraction with another fraction is same as multiplying the 1st fraction with the reciprocal of 2nd fraction.
[tex]\text{Number of bags that can be made from available mix trail}=\frac{51}{8}\times \frac{8}{3}[/tex]
After cancelling out 8 from numerator and denominator we will get,
[tex]\text{Number of bags that can be made from available mix trail}=\frac{51}{3}[/tex]
[tex]\text{Number of bags that can be made from available mix trail}=17[/tex]
Therefore, 17 bags each of weight 3/8 pounds can be made from [tex]6\frac{3}{8}[/tex] pounds of mix trail.
Simplify the expression
Answer:
729
Step-by-step explanation:
[(-1)^3]^2 /[(-3)^-3]^2
= 1 * [(-3)^3]^2
= 1 * 729
= 729
Answer:
729
To solve this, we need to start on the inside and work out; solving one part at a time.
[{(-1)^3 / (-3)^-3}]^2
1. (-1)^3 = -1
2. (-3)^-3 = - 1/27
3. (-1) / (- 1/27) = 27
4. 27^2 = 729
Carmen sells electronics. She made a 10% commission on every dollar sale that she makes. One month Carmen got a commission check for $2500. What were her sales in dollars that month.
Answer: 25000
Step-by-step explanation:
.1=10%
So, 2500/.1=25000
25000*.1=2500
Please answer this question!! 20 points and brainliest!
Answer:
A
Step-by-step explanation:
We can find the surface area of the object by adding the surface areas of each part. We have many rectangle faces to count and two triangular faces. Each has a formula for the area. We will find the area of each and then add them all together.
Triangle - 0.5 *b*h
Rectangle - b*h
Triangles
There are two triangles on either side. The height is 1.5. The base is 1.8.
0.5(1.5)(1.8)=1.35 meters squared
Since there are two, we will add 1.35+1.35 in our final calculation.
Rectangles
We will start by calculating the largest rectangle on the side. It has height of 4 and a base of 2.5 (shown above left).
4(2.5)=10
Since there are two (one we can see and one we can't), we will add 10+10 in our final calculation.
Next we calculate the top and bottom. The height is 3 and the base is 2.5 on top. But the bottom sticks out more and adds 1.8 to its base.
Top - 3(2.5)=7.5
Bottom-3(2.5+1.8)=12.9
Finally, we will calculate the front side and back(not visible) as well as the slant up front. The back side has height 4 and base 3. The front side has base 3 and height 4-1.5=2.5. The slant has base 2.3 and height 3.
Back - 4(3)=12
Front- 3(2.5)=7.5
Slant - 3(2.3)=6.9
We add all together for the total surface area: 1.35+1.35+10+10+7.5+12.9+12+7.5+6.9=69.5 meters squared.
Please help Mrs.Johnson spend $611 buying lunch for 78 students. If all lunches cost the same, about how much did she spend on each lunch
Answer:
She spend 7.33 on each lunch.
Step-by-step explanation:
We have been given that Mrs. Johnson spend $611 buying for 78 students
If each lunch cots the same we have to find how much did she spend on each lunch:
We can calculate the price of each lunch by dividing the total cost she spend upon the lunch she bought.
let the cost of each lunch be x
Hence, [tex]x=\frac{611}{78}=7.33[/tex]
HELP ASAP 98 points and brainliest
Look at the parallelogram ABCD shown below: The table below shows the steps to prove that if the quadrilateral ABCD is a parallelogram, then its opposite sides are congruent:
Statement Reasons 1 AB is parallel to DC and AD is parallel to BC Definition of parallelogram 2
angle 1 = angle 2, angle 3 = angle 4 If two parallel lines are cut by a transversal then the _______________ are congruent 3
BD = BD Reflexive Property 4
triangles ADB and CBD are congruent If two angles and the included side of a triangle are congruent to the corresponding angles and side of another triangle then the triangles are congruent by ASA postulate 5
AB = DC, AD = BC Corresponding parts of congruent triangles are congruent
Which choice completes the missing information for reason 2 in the chart?
alternate interior angles
corresponding angles
same-side interior angles
vertical angles
Answer:
The correct option is 1.
Step-by-step explanation:
Statement 1: AB is parallel to DC and AD is parallel to BC.
Reason: Definition of parallelogram
Statement 2: ∠1 = ∠2, ∠3 = ∠ 4.
Reason: If two parallel lines are cut by a transversal then the alternate interior angles are congruent.
Statement 3: BD = BD.
Reason: Reflexive Property.
Statement 4: ΔADB≅ΔCBD.
Reason: If two angles and the included side of a triangle are congruent to the corresponding angles and side of another triangle then the triangles are congruent by ASA postulate.
Statement 5: AB = DC, AD = BC.
Reason: Corresponding parts of congruent triangles are congruent.
The missing information for reason 2 in the chart is alternate interior angles .
Therefore the correct option is 1.
In the pully system shown in this figure, MQ = 10 in, NP = 3in and QP=24in. Find MN
a. 25
b. 26
c. 27
d. 28
Answer:
The correct option is a. The length of MN is 25.
Step-by-step explanation:
Given information: MQ = 10 in, NP = 3 in and QP=24 in.
If the centers of two circles of radius r₁ and r₂ are d units apart, then the length of the direct common tangent between them is
[tex]l=\sqrt{d^2-(r_1-r_2)^2}[/tex]
[tex]24=\sqrt{d^2-(10-3)^2}[/tex]
Square both sides.
[tex]576=d^2-49[/tex]
[tex]625=d^2[/tex]
Take square root both sides.
[tex]25=d[/tex]
Therefore length of MN is 25 and option a is correct.
To find MN in the given pulley system, we can use the concept of similar triangles.
Explanation:In the pulley system shown in the figure, we can use the concept of similar triangles to find MN. The triangle MQP is similar to the triangle MNP. This means that the ratios of their corresponding sides are equal.
So we have:
MQ/MP = NP/MN
Substituting the given values:
10/24 = 3/MN
Cross multiplying:
10 * MN = 24 * 3
MN = (24 * 3) / 10
MN = 72/10
MN = 7.2 inches
Therefore, the length MN is approximately 7.2 inches.
A 25-foot ladder is leaning against the side of a house. The top of the ladder is 20 feet above the ground. To the nearest degree, find the angle of elevation between the ground and the ladder.
To find the angle of elevation between the ground and the ladder, we can use the tangent function and the given measurements. The angle is approximately 39.8 degrees.
Explanation:To find the angle of elevation between the ground and the ladder, we can use trigonometry. Since the top of the ladder is 20 feet above the ground and the ladder is 25 feet long, we can use the opposite and adjacent sides of a right triangle. The trigonometric function that relates these sides is the tangent function:
tan(angle) = opposite/adjacent
Plugging in the known values, we get: tan(angle) = 20/25
Using a calculator to find the inverse tangent (arctan) of both sides, we get the angle to be approximately 39.8 degrees to the nearest degree.
Jonas is conducting an experiment using a 10-sided die. He determines that the theoretical probability of rolling a 3 is 1/10. He rolls the die 20 times. Four of those rolls result in a 3. Which adjustment can Jonas make to his experiment so the theoretical and experimental probabilities are likely to be closer?
A.) He can decrease the sample space.
B.) He can increase the sample space.
C.) He can decrease the number of trials.
D.) He can increase the number of trials.
Answer:
D. He can increase the number of trials.
Step-by-step explanation:
Jonas is conducting an experiment using a 10-sided die. So the theoretical probability of rolling a 3 in a single trial is, [tex]\dfrac{1}{10}[/tex]
So the theoretical expected outcome of 3 in 20 roll would be,
[tex]=\dfrac{1}{10}\times 20=2[/tex]
But when he rolled the die 20 times, where four of those rolls resulted 3.
Which is 2 times more than the theoretical expectation.
Increasing the number of trials from 20, the expected outcome will increase.
As the number of trials is multiplied with [tex]\dfrac{1}{10}[/tex], so bigger the number is from 20, bigger the value.
As we know,
[tex]E(x)=n\cdot P(x)[/tex]
If we want to increase the expected value, we have to increase the number of trials.
Answer with explanation:
Number of faces of this unique Die = 10
Theoretical probability of rolling a 3 [tex]=\frac{1}{10}[/tex]
Now, the die is rolled 20, times.
Number of times, the rolls results in 3= 4
Probability of rolling '3' [tex]=\frac{4}{20}=\frac{1}{5}[/tex]
but, if you roll the die twenty times, Probability of rolling '3' should be [tex]=\frac{2}{20}=\frac{1}{10}[/tex]
When we want, theoretical probability and experimental probability,match each other, the number of trials should be large enough to get closer and better results.
The adjustment can Jonas make to his experiment so the theoretical and experimental probabilities are likely to be closer:
D: He can increase the number of trials.