6. Tell whether the sequence is arithmetic. If it is, what is the common difference?
-19, -11, -3, 5,...
Oyes; 5
Oyes; 6
Oyes; 8
O no
The sequence -19, -11, -3, 5,... is arithmetic with a common difference of 8.
An arithmetic sequence is a sequence of numbers in which each term is obtained by adding a constant value, called the common difference (d), to the preceding term. To determine if the given sequence is arithmetic, we can find the differences between consecutive terms.
The difference between the second and first terms is 11 - (-19) = 30, and the difference between the third and second terms is -3 - (-11) = 8. The difference between the fourth and third terms is 5 - (-3) = 8. Since the differences between consecutive terms are the same, the sequence is arithmetic.
The common difference can be found by subtracting any term from the term that follows it. For example, the common difference can be obtained by subtracting the second term (-11) from the third term (-3), or by subtracting the third term (-3) from the fourth term (5).
In both cases, we get a common difference of 8. Therefore, the common difference of the given sequence is 8.
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100 Points! Algebra question. Graph the function. Describe the key characteristics. Only looking for an answer to A. Photo attached. Thank you!
The graph of function is shown in image.
We have to given that;
The Function is,
f (x) = ∛ (x + 1)
Now, We can find the domain and range as;
Since, We know that the set of all inputs of the function is called Domain of set.
Hence, Domain of function is,
D = (- ∞,∞)
And, Range is,
R = (- ∞,∞)
Here, In the function there is no inflection point in present.
And The end behavior of the function y =∛ (x + 1) is as x approaches negative infinity, y approaches negative infinity, and as x approaches positive infinity, y approaches positive infinity.
Thus, The graph of function is shown in image.
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Determine the equation of the parabola that opens down, has vertex (-8,5) and a focal diameter of 28
The equation of the parabola that opens down, has vertex (-8,5) and a focal diameter of 28.
To determine the equation of the parabola that opens down, has vertex (-8,5) and a focal diameter of 28, we need to use the standard form of the equation of a parabola:
(x - h)^2 = -4p(y - k)
where (h,k) is the vertex and p is the distance from the vertex to the focus (which is half the focal diameter in this case).
Using the given information, we can plug in the values for h, k, and p:
(h,k) = (-8,5)
p = 28/2 = 14
(x + 8)^2 = -4(14)(y - 5)
Simplifying this equation, we get:
(x + 8)^2 = -56(y - 5)
And that is the equation of the parabola that opens down, has vertex (-8,5) and a focal diameter of 28.
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Solve the System. Give your answer as (x, y, z).
-3x + 2y - 4z = 1
-6x-2y - 5z = 8
12x - 2y-z = -10
(x, y, z) =
=
=
=
Answer:
(x, y, z) = (-1, -1, 0)
Step-by-step explanation:
You want the solution to the system of equations ...
-3x +2y -4z = 1-6x -2y -5z = 812x -2y -z = -10SolutionThe calculator solution is shown in the attachment.
(x, y, z) = (-1, -1, 0)
Ad hocThe coefficient of the y-variable is 2 or -2, which means we can eliminate y terms by adding pairs of equations. Adding the first equation to each of the other two reduces the system to ...
-9x -9z = 99x -5z = -9Adding these two equations together gives ...
-14z = 0 ⇒ z = 0
Substituting this into the second of the reduced equations gives ...
9x = -9 ⇒ x = -1
And substituting for x and z in the first of the original equations gives ...
-3(-1) +2y = 1
2y = -2 . . . . . . . . subtract 3
y = -1
The solution is (x, y, z) = (-1, -1, 0).
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Nam asked his mother's permission to go buy toys to give to Tuan's friend on the occasion of his birthday. Men buy two toys with list prices of VND 45,000 and VND 25,000 respectively and receive a 10% discount. how much does the male have to pay to buy those two toys?
Nam needs to pay VND 63,000 for the two toys after receiving the 10% discount.
Nam asked his mother for permission to buy toys as a gift for Tuan's friend on his birthday.
He chose two toys with list prices of VND 45,000 and VND 25,000, respectively.
However, the good news is that he was able to receive a 10% discount on the total cost of both toys.
To calculate the amount that Nam has to pay for both toys, we first need to calculate the total cost of the two toys.
The cost of the first toy is VND 45,000 and the cost of the second toy is VND 25,000, so the total cost of both toys is:
Total cost = VND 45,000 + VND 25,000 = VND 70,000
Now that we have calculated the total cost of both toys, we can calculate the amount of discount that Nam will receive. The discount is equal to 10% of the total cost, which is:
Discount = 10% x VND 70,000 = VND 7,000
Therefore, the amount that Nam has to pay for both toys after the discount is:
Amount to pay = Total cost - Discount
= VND 70,000 - VND 7,000
= VND 63,000
In conclusion, Nam has to pay VND 63,000 to buy both toys after receiving a 10% discount.
It's a great deal, and Tuan's friend will surely love the toys as his birthday gift.
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Sara purchased school supplies at the school store. She spent $20.50. She
purchased some pens, pencils, and erasers. She purchased four more pencils
than pens and two fewer erasers than pens.
Part A: If you represent pens with x write an equation to model this scenario
Part B: Solve for the number of pens that Sara purchased.
Needddddddd helpppppp with thiss
The matrix after the operation is:
[tex]\left[\begin{array}{ccc}1&8/3&67/3\\-5&-13&-109\end{array}\right][/tex]
We have,
Matrix
[tex]\left[\begin{array}{ccc}3&8&67\\-5&-13&-109\end{array}\right][/tex]
To get a 1 in row 1.
We apply the operation:
Row 1 ÷ 3
So,
[tex]\left[\begin{array}{ccc}1&8/3&67/3\\-5&-13&-109\end{array}\right][/tex]
Thus,
The matrix after the operation is:
[tex]\left[\begin{array}{ccc}1&8/3&67/3\\-5&-13&-109\end{array}\right][/tex]
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Concentrated Liquid Plant Food. Bottle contains 1500ml plant food. Instructions to feed each plant - mix 15ml plant food with 1 litre of water Juba uses 15ml of plant food with 1 litre of water to feed 1 plant. She has 9 plants growing in the greenhouse that need feeding with food once a week. She has 11 plants in the vegetable plot that need feeding with food twice a week. How many bottles of plant food does Juba use in 12 weeks??
She will need to use 4 bottles of plant food in 12 weeks.
To solve this problemTo feed one plant, Juba mixes 15ml of plant food with 1 liter of water. She will therefore require the following to feed nine plants in the greenhouse once a week:
9 plants × 15 ml plant food every week = 135 ml plant food.
To feed 11 plants in the vegetable plot twice a week, she will need:
11 plants x 15 ml plant food x 2 times = 330 ml plant food per week
Juba will therefore require a total of 135 ml + 330 ml = 465 ml of plant food per week.
She will require: 465 ml x 12 weeks = 5580 ml.
Plant food comes in bottles of 1500 ml each. Juba will therefore require:5580 ml ÷ 1500 ml/bottle = 3.72
Therefore, She will need to use 4 bottles of plant food in 12 weeks.
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4. What is the acceleration of the car in each section?
b
с
d
a
The acceleration for each section is shown below.
We know the formula
Acceleration = change in haste/ time taken
1. For a
= (12-0)/4
= 12/4
= 3
For b:
= (12-12)/ 5
=0
For c:
= (6-12)/ (2)
= -3
For d:
= (10-6) / 4
= 4/4
= 1
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Peter has money in two savings accounts. one rate is 12% and the other 13%. if he $150 dollars more in the 13% account and the total interest is $54, how much is invested in each savings account?
Peter invested $138 in the 12% account and $288 in the 13% account.
Let x be the amount invested in the 12% account and y be the amount invested in the 13% account.
We know that the total amount invested is the sum of the two accounts, so: x + y = total amount invested
We also know that Peter has $150 more in the 13% account, so:
y = x + 150
The total interest earned is $54, which can be expressed as:
0.12x + 0.13y = 54
Substituting y with x + 150, we get:
0.12x + 0.13(x + 150) = 54
Simplifying and solving for x, we get:
0.12x + 0.13x + 19.5 = 54
0.25x = 34.5
x = 138
Therefore, Peter invested $138 in the 12% account and $288 in the 13% account.
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Write a system of equations to describe the situation below, solve using any method, and fill in the blanks.
Jada and Mackenzie are hosting events that are catered by the same company. Jada plans to have 78 adults and 78 children attend, so the total projected cost of her meals is $3,354. Mackenzie has 58 adults and 76 children on her guest list, so she will pay the caterer $2,800. How much does the caterer charge for each meal?
Every adult's meal costs $____, and every child's meal costs $____.
Every adult's meal costs $26, and every child's meal costs $17.
How to write system of equation?Let
cost of adults = x
Cost of child = y
78x + 78y = $3,354
58x + 76y = $2,800
From (1)
Divide through by 78
x + y = 43
x = 43 - y
Substitute into (2)
58x + 76y = $2,800
58(43 - y) + 76y = 2800
2494 - 58y + 76y = 2800
- 58y + 76y = 2800 - 2494
18y = 306
y = 306/18
y = 17
Substitute the value of y into
x = 43 - y
x = 43 - 17
x = 26
Therefore, the cost of adults meal is $26 and child's meal is $17
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A rectangular field is 125 meters long and 85 meters wide.
Give the length and width of another rectangular field that has the same perimeter but a larger area.
Answer: Length 105 Width 105
There are other possible answers
Step-by-step explanation:
Perimeter of the field is = (2)*(125) + (2)*(85) = 420
Area of the field is = (85)*(125) = 10,625
You need to find two other numbers that when doubled add up to 420, and when multiplied together are greater than 10,625. Guess and check can work, however making a square will yield the highest results, you can find the dimensions of said square by dividing 420 by 4 to get 105.
(2)*(105) + (2)*(105) = 420
(105)(105) = 11,025
420 = 420
11,025 > 10,625
root((sqrt(7 ^ 4)) ^ 6, 3) * sqrt((root(7 ^ 8, 6)) ^ 3)
Review the following diagram. Calculate the area tot he nearest square foot.
The area for the figure in this problem is given as follows:
A = 1216 ft².
How to calculate the area of a circle?The area of a circle of radius r is given by the multiplication of π and the radius squared, as follows:
A = πr²
The figure in this problem is composed as follows:
Rectangle of dimensions 55.75 ft (as each ft has 12 inches, hence 9 inches = 0.75 ft) and 17.5 ft.Circle (composition of two half circles) of radius 17.5/2 = 8.75 ft.Hence the area of the figure is calculated as follows:
A = 55.75 x 17.5 + π x 8.75²
A = 1216 ft².
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What is the previous term for: -6, 1, 8, 15...
Answer:
- 13---------------------
Given sequence:
-6, 1, 8, 15...This is a AP since the difference is common:
1 - (-6) = 7,8 - 1 = 7,15 - 8 = 7.The previous term is going to be 7 less than the subsequent term:
- 6 - 7 = - 13In a shooting contest in which 50 people participated, the following frequency table was obtained.
a.Calculate the mean score, correct to the nearest whole number.
The mean score to the nearest whole number is equal to 5.0
How to calculate the mean for the set of data?In Mathematics and Geometry, the mean for this set of data can be calculated by using the following formula:
Mean = [F(x)]/n
For the total number of data based on the frequency, we have;
Total score, F(x) = 1(3) + 2(1) + 3(4) + 4(10) + 5(15) + 6(9) + 7(3) + 8(5)
Total score, F(x) = 3 + 2 + 12 + 40 + 75 + 54 + 21 + 40
Total score, F(x) = 247
Now, we can calculate the mean score as follows;
Mean = 247/50
Mean = 4.94 ≈ 5.0.
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please help with this
Answer:
Step-by-step explanation:
To avoid dividing by zero, denominator cannot equal 0:
[tex]x^2-9\neq 0[/tex]
[tex](x+3)(x-3)\neq0[/tex]
[tex]x\neq-3 \text{ and }x\neq3[/tex]
Solution: We cannot use [tex]x=-3 \text{ and }x=3[/tex].
the area of the base of a rectangular prism is 15m2 and the height measures 5m. what is the volume of the pyramid with the same dimensions as the rectangular prism?
Answer:
V = 25 cm³
Step-by-step explanation:
the volume (V) of a rectangular prism is calculated as
V = Ah ( A is the area of the base and h the height )
V = 15 × 5 = 75 cm³
the volume of the pyramid is one third the volume of the prism , then
V = 75 × [tex]\frac{1}{3}[/tex] = 25 cm³
Enter the number that belongs in the green box please help
Answer:
14.0
Step-by-step explanation:
Using sine rule
sin A/a = sin B/b
sin 70/15 = sin 61/b
b sin 70 = 15 sin 61
b = (15 sin 61) / sin 70
b = 13.96126278
b = 14.0
In the circle below, UV is a diameter and UX is tangent at U. Suppose m UVW=202 degrees. Find the following.
Find the length of CD. The length of BE is 22cm
Applying the Triangle Midsegment Theorem, the length of CD in the triangle is: 44 cm.
How to Apply the Midsegment of a Triangle Theorem?Based on the Triangle Midsegment Theorem, the line segment that joins the midpoints of two sides of a triangle is parallel to the third side of the triangle and is also half of the length of the third side.
Thus, BE is the midsegment of the triangle with length of 22 cm. Since CD is the third side of the triangle, therefore we have:
Length of BE = 1/2(length of CD)
Plug in the values:
22 = 1/2(CD)
2 * 22 = CD
44 = CD
Length of CD = 44 cm.
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I cannot solve this question no matter how hard I try , I tried many different answers & kept getting 8.04 but it said it was wrong
hmm well, let's firstly convert all the mixed fractions to improper fractions, then we'll get the dot product.
[tex]\left < 3\frac{1}{2}~~,~~4\frac{2}{3} \right > \hspace{5em}\left < 7\frac{1}{4}~~,~-8\frac{1}{2} \right > \\\\[-0.35em] ~\dotfill[/tex]
[tex]\stackrel{mixed}{3\frac{1}{2}}\implies \cfrac{3\cdot 2+1}{2}\implies \stackrel{improper}{\cfrac{7}{2}}~\hfill \stackrel{mixed}{4\frac{2}{3}} \implies \cfrac{4\cdot 3+2}{3} \implies \stackrel{improper}{\cfrac{14}{3}} \\\\\\ \stackrel{mixed}{7\frac{1}{4}}\implies \cfrac{7\cdot 4+1}{4}\implies \stackrel{improper}{\cfrac{29}{4}}~\hfill \stackrel{mixed}{8\frac{1}{2}} \implies \cfrac{8\cdot 2+1}{2} \implies \stackrel{improper}{\cfrac{17}{2}} \\\\[-0.35em] ~\dotfill[/tex]
[tex]\left < 3\frac{1}{2}~~,~~4\frac{2}{3} \right > ~~\cdot~~\left < 7\frac{1}{4}~~,~-8\frac{1}{2} \right > \\\\[-0.35em] ~\dotfill\\\\ \left( \cfrac{29}{4} \right)\left( \cfrac{7}{2} \right)~~ + ~~\left( -\cfrac{17}{2} \right)\left( \cfrac{14}{3} \right)\implies \cfrac{203}{8}-\cfrac{119}{3}\implies \cfrac{-343}{24} ~~ \approx ~~ \stackrel{ \textit{dot product} }{-14.29}[/tex]
Figure A is a scale image of figure A. Enter the scale factor applied to figure A to produce figure B
The scale factor here is 2.1.
To calculate the scale factor, you need two corresponding measurements from two similar objects or figures. The scale factor is the ratio of the corresponding lengths or dimensions between the two objects.
Now, the scale factor is
= 12.5 / 5
= 125/50
= 21/10
= 2.1 : 1
Thus, the scale factor here is 2.1.
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According to the general equation for conditional probability if P(A B)=2/9 and P(B)=1/3, what is P(A B)
Answer:
P(A | B) = 2/3----------------------
The general equation for conditional probability is:
P(A | B) = P(A B) / P(B)Using this equation and the given values, we can calculate P(A | B) as follows:
P(A B) = 2/9 and P(B) = 1/3 P(A | B) = P(A B) / P(B) P(A | B) = (2/9) / (1/3) = (2/9) * (3/1) = 6/9 = 2/3Therefore, P(A | B) = 2/3.
R
S
57°
15
T
find sidelength of RS and RT
The side lengths of RS and RT are 4 and 5 units
Finding the side lengths of RS and RTFrom the question, we have the following parameters that can be used in our computation:
The right triangles (See attachment)
The side lengths of RS and RT are calculated using
RT = KS = 4
Then we apply the pythagoras theorem for RS as follows
RS² = RK² + KS²
substitute the known values in the above equation, so, we have the following representation
RS² = 3² + 4²
So, we have
RS = 5
Hence, the side lengths of RS and RT are 4 and 5 units
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The elderly people use a 300 ml jug, as seen in the picture below to fill up their 3-litre kettl The kettle boil the water at 360°F for few minutes. 275 226 175 125 75 METRIC 300ml 250 200 150 100 Use the information above to answer the questions that follow. 1.2.1. Write down the volume of a jug. 1.2.2. Convert the 3 litres to millilitres. 1.2.3. Write the ratio of the jug to the kettle in a simplified form. 1.2.4. Convert 360°F to °C, rounded off to the nearest 10 °C. You may use the formula: °F (C x 1.8) +32 T
The jug used by older adults has a volume of 300 ml. To convert 3 liters to milliliters.
We multiply three by 1000, giving us 3000 ml. The ratio of the jug to the kettle can be simplified to 1:10.
To convert 360°F to °C, we use the formula (360-32) ÷ 1.8, which gives us 182°C rounded off to the nearest 10°C.
Urgent!!!!!
Help please I have to answer these questions using the graph.
a.) The concentration of the drug after 8 hours in the blood would be = 24 mg/L.
b.) The concentration increases over the interval of 0-2 hours.
c.) The maximum concentration of the drug is at 2 hours after intake which is 64 mg/L.
d.) After the drug reaches its maximum concentration, it will take 8 hours to decrease to 16mg/L.
e.) The concentration of the drug in the blood after one week will be zero.
f.) In summary, the concentration of the drug in the blood stream after the first 20 hours will be done below.
What is the drug blood concentration?Drug blood concentration is defined as the amount of drug that is absorbed into the blood stream that contains a particular quantity per liter of blood.
The graph above represents the relationship between the concentration of a drug in the blood and the time it was taken.
For a ) The concentration of the drug after 8 hours in the blood would be = 24 mg/L.
For b.) The concentration increases over the interval of 0-2 hours.
For c.) The maximum concentration of the drug is at 2 hours after intake which is 64 mg/L.
For d.) After the drug reaches its maximum concentration, it will take 8 hours to decrease to 16mg/L.
For e.) The concentration of the drug in the blood after one week will be zero.
For f.) In summary, the concentration of the drug in the blood stream after the first 20 hours is not the same as observed in the graph above. There is a spike increase after the first two hours of intake after which a decrease in concentration was observed through our the remaining hours.
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Natalie borrowed money from her parents to pay for a trip.
Natalie will pay her parents in equal amounts every week until she pays back the entire amount she borrowed.
The table below shows the amount of money Natalie still owes her parents at the end of every two weeks for the first eight weeks.
Natalie owes $18 at the end of every two weeks.
To find the weekly payment amount, we can use the given data to write a system of equations. Let's assume that Natalie borrowed x amount from her parents.
From the given table, we can write the following equations:
At the end of 2 weeks, Natalie still owes:
x - 2d = 180 ...(1)
At the end of 4 weeks, Natalie still owes:
x - 4d = 144 ...(2)
Solving equations (1) and (2), we get:
2d = 36
d = 18
Therefore, Natalie owes $18 at the end of every two weeks.
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Find the distance around each figure. Use 3.14 as an approximation for π
30. The figure is made up of a rectangle and two identical semicircles.
Answer: 1507.84ft^2
Step-by-step explanation:
Semicircle r = 16ft
Rectangle width = 22ft (because the radius of the semicircle is 16 and there are two of them, 2 x 16 = 32, 54 - 32 = 22)
Rectangle height = 32ft
Area of rectangle:
22 x 32 = 704ft^2
Area of circles:
16^2 x 3.14 = 803.84ft^2
No need to half the area for a semicircle because there are 2 of them
Therefore:
803.84 + 704 = 1507.84ft^2
4x3 = -5x - 21 solve for x
To solve for x in the equation 4x3 = -5x - 21, we can follow these steps:
1. Move all the terms containing x to one side of the equation, and move the constant term to the other side. We can do this by adding 5x to both sides and then adding 21 to both sides:
4x3 + 5x = -21
2. Factor out x from the left-hand side of the equation:
x(4x2 + 5) = -21
3. Divide both sides by (4x2 + 5):
x = -21 / (4x2 + 5)
So the solution for x is x = -21 / (4x2 + 5). Note that this is a rational function, which means that the value of x depends on the value of the variable x. This equation has no real solutions because the denominator is always positive, and the numerator is negative.
