Given:
An arithmetic series a₁ = -10 and S6 = -285
We will find the common difference (d) using the formula of the sum.
[tex]S=\frac{n}{2}(2a+(n-1)d)[/tex]Substitute S= -285, a = -10, n = 6
[tex]\frac{6}{2}(2(-10)+(6-1)d)=-285[/tex]Solve the equation to find (d):
[tex]\begin{gathered} 3(-20+5d)=-285 \\ -20+5d=-\frac{285}{3} \\ \\ -20+5d=-95 \\ 5d=-95+20 \\ 5d=-75 \\ \\ d=-\frac{75}{5}=-15 \end{gathered}[/tex]So, the answer will be option C) -15
evaluate the expression and enter your answer below. 3x10+15-6^2
3*10 + 15 - 6^2
3*10 + 15 -36 (Raising 6 to the power of 2, because of the order of operations)
30 + 15 - 36 (Multiplying, because of the order of operations)
45 - 36 (Adding)
9 (Subtracting)
The answer is equal to: 9
Ms. Wheeler asks her students to look at their desks. What do the desks represent inEuclidean geometry?
To determine the what desk represents in Euclidean geometry?
Euclidean geometry, sometimes called parabolic geometry, is a geometry that follows a set of propositions that are based on Euclid's five postulates
The most basic terms of geometry are a point, a line, and a plane. A point has no dimension (length or width), but it does have a location
In its rough outline, Euclidean geometry is the plane and solid geometry commonly taught in secondary schools
“A point is that which has no part” and “a line is a length without breadth.” Proceeding from these terms, he defined further ideas such as angles, circles, triangles, and various other polygons and figures.
For example, an angle was defined as the inclination of two straight lines, and a circle was a plane figure consisting of all points that have a fixed distance (radius) from a given centre.
Hence in Euclidean geometry the desk represent the plane
The vertices of a y rectangle are 8 A(1,7), B (3,7). C(3, 1.5), and 6 D (1, 1.5). Find the perimeter and the area of 3 the rectangle.
Let us first find the measures of the sides.
Width
We can find the width calculating the distance between points A and B. Doing so, we have:
The distance on the y-axis is 0 as they have the same coordinate
The distance on the x-axis is 2 ( x2 - x1= 3 - 1 = 2)
So, the width of the rectangle is 2.
Length
We can find the length calculating the distance between points B and C. Doing so, we have:
The distance on the x-axis is 0 as they have the same coordinate
The distance on the y-axis is 5.5 ( y2 - y1= 7 - 1.5 = 5.5)
So, the length of the rectangle is 5.5.
Using the formula for the perimeter, we have:
P= 2L + 2W (P:perimeter, l: length, w:width)
P= 2*(5.5) + 2*(2) (Replacing)
P= 11 + 4 (Multiplying)
P=15 (Adding)
The perimeter is 15
Using the formula for the area, we have:
A=l*w (A:area, l: length, w:width)
A=(2)*(5.5) (Replacing)
A= 11 (Multiplying)
The area is 11
The concession stand sells 3 hot dogs forevery 4 hamburgers they prepare. Howmany hot dogs do they make if theyprepare 24 hamburgers?
3 Hotdogs are prepared for 4 hamburgers
N Hotdogs. For. 24. Hamburgers
Then make cross multiplication
3 x 24 = N x 4
Now find N
N = (3x24)/4 = 72/4 = 18 HOtdogs
Given the following piecewise function, determine h(x)h(x) = { -x, if x greater than or equal to -2{ 2, if x > -2h(-6) =h(-2) =h(6) =
Part 1) h(-6)
h(x)=-x
x=-6
so
h(-6)=6
Part 2) h(-2)
h(x)=-x
For x=-2
h(-2)=2
Part 3) h(6)
h(x)=2
x=6
so
h(6)=2
Factor out the GCF in the polynomial.32x - 24 =
The Solution:
The given expression is
[tex]32x-24[/tex]To factor out the Greatest Common Factor of the above expression, we have
[tex]8(4x-3)[/tex]So, the Greatest Common Factor is 8.
Mia was baking cupcakes for a party. She makes four drops of red food coloring for every six drops of yellow food coloring to dye her icing Orange. What is the ratio that would create the same orange color .
To find the ratio that would create the same orange color, we need to find the value from the division of the number of drops of each color of the food coloring.
From the present question, we know that Mia uses 4 drops of red for every 6 drops of yellow. It means that, for every 10 drops, 4 is red and 6 is yellow.
The ratio is:
( I will be finishing once I understand the best way to give you the final answer"
How do I find the minimum and maximum in a factored quadratic equation
Supposed you have a quadratic equation
x^
What is the equation of the following graph?A. f(x) = 3(2³)OB. f(x) = 5()*Oc. f(x) = ()*D.) = 2(3³)
From the graph,
when x = 0, y = 2
when x = 1, y = 6
Considering option D,
f(0) = 2(3^0) = 2 * 1 = 2
f(1) = 2(3^1) = 2 * 3 = 6
Thus, the correct option is
D
Simplify. (Assume all variables represent positive numbers.)✓32a5b15Need Help?Watch ItAdditional MaterialseBook
We have the next expression
[tex]\sqrt[]{32a^5b^{15}}[/tex]In order to simplify we will factorize the expression in a next way
[tex]\sqrt[]{4\cdot4\cdot2\cdot a^4\cdot b^{14}\cdot b}[/tex][tex]\sqrt[]{4}\cdot\sqrt[]{4}\cdot\sqrt[]{2}\cdot\sqrt[]{a^4}\cdot\sqrt[]{b^{14}}\cdot\sqrt[]{ab}[/tex]Then we simplify the results
[tex]2\cdot2\cdot a^2\cdot b^7\cdot\sqrt[]{2ab}[/tex][tex]4a^2b^7\sqrt[]{2ab}[/tex]the simplification is
[tex]4a^2b^7\sqrt[]{2ab}[/tex]trapon 3 5 Which to 2 and 3 I and 2 32- integers does V5 go batwsen? 00 7 and 8 -80 S pues Simplify -3(2x+h 6.5.10 Simplify 8.42x104 45x10 08:00 18.28x02 EUDE 6 (L-6) 57 irrational Surve 4x - y=10 -2x + y=-8 (63)
The angles shown in the picture are over the same horizontal line and share a vertex and one side. These angles are a line pair, which means that they are supplementary, you can write the following expression:
[tex](32º+x)+48º=180º[/tex]From this expression, you can determine the value of x.
-First erase the parentheses, order the like terms together and simplify them:
[tex]\begin{gathered} 32º+48º+x=180º \\ 80º+x=180º \end{gathered}[/tex]-Subtract 80º from both sides of the equation
[tex]\begin{gathered} 80º-80º+x=180º-80º \\ x=100º \end{gathered}[/tex]The population, P, of a species of fish is decreasing at a rate that is proportional to the population itself. If P=200000 when t=3 and P=150000 when t=4, what is the population when t=10?Round your answer to the nearest integer. Tries 0/99
The Solution:
Given:
[tex]\begin{gathered} P=200,000\text{ when }t=3 \\ \\ P=150,000\text{ when }t=4 \end{gathered}[/tex]Required:
Find P when t = 10.
Clearly, the proportion is an inverse proportion.
[tex]\begin{gathered} P=\frac{k}{t} \\ \\ Where\text{ k}=constant\text{ of proportionality.} \end{gathered}[/tex]Applying the given values:
[tex]\begin{gathered} 200000=\frac{k}{3} \\ \\ k=3\times200,000=600,000 \end{gathered}[/tex]This gives the formula:
[tex]P=\frac{600,000}{t}[/tex]Substitute t=10, and find P.
[tex]P=\frac{600,000}{10}=60,000[/tex]Answer:
The population is 60,000 when t = 10.
Convert this decimal into its fractionalform, simplified completely.0.300
The given decimal is 0.300
In order to convert it to decimal, we would start by making 1 the denominator. it becomes
0.3/1
We would multiply the numerator and denominator by 10. It becomes 3/10
Therefore, the answer in fractional form is 3/10
Josh took 300 minutes to get to work. How many hours is this?
Problem Statement
The question tells us that it
Find the area under the Standard Normal Curve in-between z = -2.39 and z = 1.03Use the Normal table and give answer using 4 decimal places.
Recall that the area under the standard normal curve in-between z₁ and z₂ is:
[tex]P(z_1We know that:[tex]P(z_1Therefore the area under the Standard Normal Curve in-between z = -2.39 and z = 1.03 is:[tex]P(z<1.03)-P(z<-2.39).[/tex]From normal tables we get:
[tex]\begin{gathered} P(z<1.03)=0.84849, \\ P(z<-2.39)=0.0084242. \end{gathered}[/tex]Therefore the area under the Standard Normal Curve in-between z = -2.39 and z = 1.03 is:
[tex]0.84849-0.0084242=0.8400658\approx0.8401.[/tex]Answer: 0.8401.
Use properties to rewrite the given equation. Which equations have the same solution as 2.3p – 10.1 = 6.5p – 4 – 0.01p? Select two options. 2.3p – 10.1 = 6.4p – 4 2.3p – 10.1 = 6.49p – 4 230p – 1010 = 650p – 400 – p 23p – 101 = 65p – 40 – p 2.3p – 14.1 = 6.4p – 4
The equations that have the same solution as 2.3p – 10.1 = 6.5p – 4 – 0.01p are (b) 2.3p – 10.1 = 6.49p – 4 and (c) 230p – 1010 = 650p – 400 – p
How to determine the equations with the same solution?The equation is given as
2.3p – 10.1 = 6.5p – 4 – 0.01p
Evaluate the like terms on the right-hand side
So, we have the following representation
2.3p – 10.1 = 6.49p – 4
The above equation is indicated in option (b)
Multiply through the equation by 100
So, we have:
100(2.3p – 10.1 = 6.5p – 4 – 0.01p)
Evaluate
230p – 1010 = 650p – 400 – p
The above equation is indicated in option (c)
Hence, the equations with the same solution are (b) and (c)
Read more about equivalent equations at
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subtract 3x^2 - 2x - 4 and 2x^2 - 4x - 6
3x^2 - 2x - 4 - (2x^2 - 4x - 6)
1.- Remove the parentheses
3x^2 - 2x - 4 - 2x^2 + 4x + 6
2.- Simplify like terms
x^2 + 2x + 2
3.- Result
x^2 + 2x + 2
I need help with this question its on arithmetic growthanddecay , been stuck on it for many days and i need help! pleasep
We are given the following information about the arithmetic sequence
First two rows = 27 chairs
Last two rows = 114 chairs
Common difference = 3 chairs
Recall that the general formula for an arithmetic sequence is given by
[tex]a_n=a_1+(n-1)d[/tex](a) Let us substitute the given values into the above formula and solve for n
[tex]\begin{gathered} a_n=a_1+(n-1)d \\ 114=27_{}+(n-1)\cdot3 \\ 114-27=_{}(n-1)\cdot3 \\ 87=_{}(n-1)\cdot3 \\ \frac{87}{3}=_{}n-1 \\ 29=_{}n-1 \\ 29+1_{}=_{}n \\ 30=n \end{gathered}[/tex]There are 30 rows of chairs.
(b) Let us find the number of chairs in the 13th and 30th row.
i) 13th row:
Substitute n = 13
[tex]\begin{gathered} a_{13}=27_{}+(13-1)\cdot3 \\ a_{13}=27_{}+12\cdot3 \\ a_{13}=27_{}+36 \\ a_{13}=63 \end{gathered}[/tex]There are 63 chairs in the 13th row.
ii) 30th row:
Substitute n = 30
[tex]\begin{gathered} a_{30}=27_{}+(30-1)\cdot3 \\ a_{30}=27_{}+29\cdot3 \\ a_{30}=27_{}+87 \\ a_{30}=114 \end{gathered}[/tex]There are 114 chairs in the 30th row.
URGENT!! ILL GIVE
BRAINLIEST!!!! AND 100 POINTS!!!!!
The value of angle is ∠P is 140° and ∠Q is 110°.
What do you mean by the exterior and interior angles of a triangle?
The angle between any two of a triangle's three sides is referred to as the interior angle. Any angle that is created when one of a polygon's sides intersects with a line that extends from another side is considered its external angle.
∠P and ∠Q is the exterior angle of the triangle.
we know that the sum of the exterior angle is the sum of the opposite interior angle.
9is the sum of the opposite interior angles that is (110°+30°) = 140°
∠Q is the sum of the opposite interior angles that are (30°+80°)= 110°
Hence,
∠P is 140° and ∠Q is 110°.
to learn more about the exterior and interior angles of a triangle from the given link,
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original price of pants is 2995 the discount is 10%
Ok,
Since we have that the price of the pants is $2995 and that represents the 100%.
In order to determine the total value since we get a 10% discount, we do as follows:
[tex]2995\to100\text{ \& x}\to10[/tex]We determine the 10%, multiplying the percentage we want to know (10%) times the total ammount of money the pants cost ($2995) and then divide by the total percentage (100%):
[tex]x=\frac{2995\cdot10}{100}\Rightarrow x=299.5[/tex]x represents our 10% and so we extract x from the total:
[tex]T=2995-299.5\Rightarrow T=2695.5[/tex]Therefore the total price to pay is $2695.5
what is the factor of 2 and 10
The factor of 2 and 10 is equal to adding up 10, 2 times:
[tex]2\cdot10=10+10=20[/tex]This way, the factor is 20
What is the second term of the sequence generated by the fo02O 3O 5O 6
1) Since no other information has been given, we need to assume that the numbers used in this Sequence are whole numbers.
2) Therefore, we can write this:
[tex]undefined[/tex]how do you draw a model to explain 3/4 x 24
3 / 4 x 24 = 3 x 6 = 18
A fair coin is tossed 3 times in succession. The set of equally likely outcomes is (HHH, HHT, HTH, THH, HTT, THT, TTH, TTT). Find the probability of getting a tailon the second toss
A fiar coin is tossed 3 times in succession.
The results for each experiment is displayed as follows;
[tex]\begin{gathered} \text{HHH} \\ \text{HHT} \\ \text{HTH} \\ \text{THH} \\ \text{HTT} \\ \text{THT} \\ \text{TTH} \\ \text{TTT} \end{gathered}[/tex]On each toss from the above results, the probability of getting a tail would include all results that has a tail come up. That would be;
[tex]P\lbrack\text{Event\rbrack}=\frac{\text{Number of required outcomes}}{Number\text{ of all possible outcomes}}[/tex][tex]P\lbrack\text{tail\rbrack}=\frac{4}{8}[/tex]Note that to get a tail on the "second toss" would mean to get a result with a tail as the second out of three. We have 7 outcomes with tails. However 4 of these has a tail as a second outcome, hence we have the required outcome as 4 out of a total of 8.
ANSWER:
Probability of getting a tail on the second toss is
[tex]P\mleft\lbrace\text{tail}\mright\rbrace=\frac{1}{2}[/tex]A cylinder has a radius of 10' and a height of 11.4' what is the approximate volume of the cylinder used 3.14 for pi.
A cylinder has a radius of 10' and a height of 11.4' what is the approximate volume of the cylinder used 3.14 for pi.
So, the formula for the volume of the cylinder is:
V= Pir²*h, in which:
Pi= 3.14
r is the radius of the circumference in the base, which is 10'
h is the height of the cilynder, which is 11.4'. So:
V= 3.14*10²*11.4
V= 3,579.6
Ethan and Michael played tablebasketball using wadded up bitsof paper and plastic cups. Eachbasket was worth 2 points.Ethan scored 18 points andMichael scored 24 points. Howmany goals did the boys scorealtogether?
Given:
Total score of Ethan, E=18 points.
Total score of Michael, M=24 points.
The score for each basket, N=2.
The total points scored by both boys is,
[tex]\begin{gathered} T=E+M \\ T=18+24 \\ T=42 \end{gathered}[/tex]Now, the number of goals scored by both boys is,
[tex]\begin{gathered} n=\frac{T}{N} \\ =\frac{42}{2} \\ =21 \end{gathered}[/tex]Therefore, the number of goals scored altogether by the boys is 21.
5 is 100 times? I am not sure.Solve question 1
Answer:
0.005
0.05
50
Explanation:
For the first question;
Let the number be x.
So let's go ahead and solve for x as shown below;
[tex]\begin{gathered} 10\times x=0.05 \\ x=\frac{0.05}{10} \\ x=0.005 \end{gathered}[/tex]For the 2nd question;
Let the missing number be y.
We can solve for y as seen below;
[tex]\begin{gathered} 100\times y=5 \\ 100y=5 \\ y=\frac{5}{100} \\ y=0.05 \end{gathered}[/tex]For the 3rd question;
Let the missing number be z.
We can solve for z as shown below;
[tex]\begin{gathered} \frac{1}{100}\times z=0.5 \\ \frac{z}{100}=0.5 \\ z=100\times0.5 \\ z=50 \end{gathered}[/tex]Graphing with end behavior
SOLUTION
End behaviour
This describe the behaviour of the graph of a function at the end of the x-axis.
The end behavior of a function describes the trend of the graph if we look to the right end of the x-axis (as xxx approaches +∞, infinity) and to the left end of the x-axis (as x approaches -∞, negative infinity).
Does the set of ordered pairs {(-5, 0), (0, 1}, (5, 2), (10, 3), (15, 4)} represent a function? Why or why not?
Answer:
YES, it represents a function
Explanation:
For a relation to be a function, each member of the domain (input) must be matched to only one element in the range (output).
According to ordered pairs, we can see that the domain values are all unique as shown;
As you can see from the diagram, each input only has a unique corresponding co-domain (range). This shows that the ordered pairs represents a FUNCTION.
I tried solving this and I got the 2nd option. Is it correct?
Explanation
We are required to determine the double angle for sin 120°.
We know that the double angle identity states thus:
So. we have:
[tex]\begin{gathered} \sin2\theta=2\sin\theta\cos\theta \\ \sin120\degree=\sin2(60\degree)=2\sin60\degree\cos60\degree \\ \Rightarrow2(\frac{\sqrt{3}}{2})(\frac{1}{2})=\frac{\sqrt{3}}{2} \end{gathered}[/tex]Hence, the answer is:
[tex]\frac{\sqrt{3}}{2}[/tex]The second option is correct.