Work Shown:
m = (y2-y1)/(x2-x1)
m = (7-2)/(11-3)
m = 5/8
m = 0.625
m = 0.6
7 th term and 14 th term of an Arithmetic sequence are 36 and 64 respectively , find the common difference and ,25th term
Answer:
(a) The common difference is 4
(b) The 25th term is 108
Step-by-step explanation:
Given
[tex]T_7 = 36[/tex]
[tex]T_{14} = 64[/tex]
Solving (a): The common difference
The nth term of an AP is:
[tex]T_n = a + (n -1)d[/tex]
For the 7th term, we have:
[tex]36 = a + (7 -1)d[/tex]
[tex]36 = a + 6d[/tex]
For the 14th term, we have:
[tex]64 =a + (14 -1)d[/tex]
[tex]64 =a + 13d[/tex]
Subtract both equations
[tex]64 - 36 = a - a +13d-6d[/tex]
[tex]28 = 7d[/tex]
Divide by 7
[tex]d = 4[/tex]
Solving (b): The 25th term
First, we calculate the first term (a)
The 7th term of the progression is:
[tex]36 = a + 6d[/tex]
Substitute [tex]d = 4[/tex]
[tex]36 = a + 6 * 4[/tex]
[tex]36 = a + 24[/tex]
Subtract 24
[tex]a = 36 -24[/tex]
[tex]a = 12[/tex]
The 25th term is:
[tex]T_{25} = a + (25 - 1)d[/tex]
[tex]T_{25} = 12 + (25 - 1)*4[/tex]
[tex]T_{25} = 12 + 24*4[/tex]
[tex]T_{25} = 108[/tex]
f(x)=x2. What is g(x)?
Answer:
(2x)^2 the answer is option a
Select the correct answer.
The elimination method is ideal for solving this system of equations. By which number must you multiply the second equation to eliminate the
y variable, and what is the solution for this system?
x+3y= 42
2x - y = 14
OA. Multiply the second equation by-3. The solution is x= 12, y=9.
OB. Multiply the second equation by -2. The solution is x = 12, y=10.
OC. Multiply the second equation by 2. The solution is x = 15, y = 9.
OD. Multiply the second equation by 3. The solution is x = 12, y = 10.
Answer:
Multiply the second equation by 3. The solution is x = 12, y = 10.
Step-by-step explanation:
The given equations are :
x+3y= 42 ....(1)
2x - y = 14 ...(2)
For elimination method,
Multiply the second equation by 3.
6x-3y=42 .....(3)
Adding equations (1) and (3).
x+3y+6x-3y=42+42
7x = 84
x = 12
Put the value of x in equation (1).
12+3y= 42
3y = 30
y = 10
So, x = 12 and y = 10. Hence, the correct option is (d).
Combine like terms to create an equivalent expression.
3.26d+9.75d-2.653.26d+9.75d−2.653, point, 26, d, plus, 9, point, 75, d, minus, 2, point, 65
Answer:
3.26d+9.75d-2.653.26d+9.75d−2.653, point, 26, d, plus, 9, point, 75, d, minus, 2, point, 65
Step-by-step explanation:
Answer:
13.01d-2.65
Step-by-step explanation:
I got it right on Khan Academy just combine like terms and you have your answer.
What is the value of x in the equation -3/4 = x/24
[tex]\implies {\blue {\boxed {\boxed {\purple {\sf { \: x = - 18}}}}}}[/tex]
[tex]\large\mathfrak{{\pmb{\underline{\red{Step-by-step\:explanation}}{\red{:}}}}}[/tex]
[tex] \frac{ - 3}{4} = \frac{x}{24} [/tex]
➼ [tex] \: x = \frac{ - 3 \times 24}{4} [/tex]
➼ [tex] \: x = \frac{ - 72}{4} [/tex]
➼ [tex] \: x = - 18[/tex]
Therefore the value of [tex]x[/tex] is -18.
[tex]\large\mathfrak{{\pmb{\underline{\blue{To\:verify}}{\blue{:}}}}}[/tex]
[tex] \frac{ - 3}{4} = \frac{ - 18}{24} [/tex]
➼ [tex] \: \frac{ - 3}{4} = \frac{ - 3}{4} [/tex]
➼ L. H. S. = R. H. S.
Hence verified.
[tex]\bold{ \green{ \star{ \orange{Mystique35♨}}}}⋆[/tex]
Find the value of x in the triangle shown below
Answer:
x = 48°
Step-by-step explanation:
Two sides of the triangle are equal, both 7, Then the 2 base angles are congruent, both 66°
The sum of the 3 angles in the triangle sum to 180° , so
x = 180° - (66 + 66) = 180° - 132° = 48°
Answer:
[tex]{ \tt{x + 66 + 66 = 180}} \\ x = 48 \degree \\ \\ { \boxed{ \bf{or : }}} \\ { \bf{ from \:lamis \: theorem : }} \\ { \tt{ \frac{5.7}{ \sin(x) } = \frac{7}{ \sin(66 \degree) } }} \\ \\ { \tt{x = { \sin }^{ - 1}( \frac{5.7 \times \sin(66 \degree) }{7} ) }} \\ x = 48 \degree[/tex]
Find the slope of the line. Describe how one variable changes in relation to the other. How did you find this?
A, 2/3; the amount of water decreases by 2 gallons every 3 minutes.
B, - 2/3; the amount of water decreases by 2 gallons every 3 minutes.
C, - 3/2; the amount of water decreases by 3 gallons every 2 minutes.
D, -1; the amount of water decreases by 1 gallon per minute.
According to the given information, the slope of the line is -1.
What is slope ?In mathematics, slope is a measure of how steep a line is, or how much y (vertical) changes for a given x (horizontal) change. It is represented by the letter "m" and is calculated as the change in y divided by the change in x, or rise over run. The slope can be positive, negative, zero, or undefined.
According to given information :The answer is D, -1; the amount of water decreases by 1 gallon per minute.
To find the slope of the line, we need to use the slope formula:
slope = (change in y)/(change in x)
In this case, the change in y represents the change in the amount of water, and the change in x represents the change in time.
Option A says that the slope is 2/3, which means that for every 3 minutes, the amount of water decreases by 2 gallons. This is incorrect because as time increases, the amount of water should decrease, so the slope should be negative.
Option B says that the slope is -2/3, which means that for every 3 minutes, the amount of water decreases by 2 gallons. This is the same as option A but with a negative slope, which is correct because the amount of water decreases over time.
Option C says that the slope is -3/2, which means that for every 2 minutes, the amount of water decreases by 3 gallons. This is incorrect because the amount of water should decrease by the same amount every minute.
Option D says that the slope is -1, which means that for every minute, the amount of water decreases by 1 gallon. This is the correct answer because it describes a constant rate of change in the amount of water over time.
Therefore, according to the given information, the slope of the line is -1.
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A square coffee shop has a perimeter of 20 meters. How long is each side of the coffee shop?
Answer:
5 Meters
Step-by-step explanation:
Perimiter of a square would be P/4
So we take 20 and divide it by four.
We would get 5 as a result so each side is 5 meters.
Hope this helps.
A parabola can be represented by the equation x2 = –20y.
What are the coordinates of the focus of the parabola?
(–5,0)
(5,0)
(0,5)
(0,–5)
Answer:
[tex] {x}^{2} = - 20y \\ y = - \frac{1}{20} {x}^{2} \\ { \tt{y = 4a {x}^{2} }} \\ a = - \frac{1}{5} \\ \\ { \tt{focus = (0, \: - 5)}}[/tex]
The requried coordinates of the focus of the parabola x² = -20y are (0, -2.5), which corresponds to the option (0, -5).
What is a parabola?A parabola is a cross-section cut out of the cone and represented by an equation y = 4ax².
The standard form of the equation of a parabola is (y - k) = (1 / 4p)(x - h)², where (h, k) is the vertex and p is the distance from the vertex to the focus. We can convert the given equation x² = -20y into this standard form by completing the square:
x² = -20y
x² / (-20) = y
x² / (-20) + 0 = y + 0
(x - 0)² = -20(y - 0)
Comparing this equation to the standard form, we can see that the vertex is at (h, k) = (0, 0), and that 4p = -20, so p = -5/2.
Since the focus is a distance of p below the vertex, the focus is at (h, k - p) = (0, -5/2), which is the same as (0, -2.5).
Therefore, the coordinates of the focus of the parabola x² = -20y are (0, -2.5), which corresponds to the option (0, -5).
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The probability that Andrew has heart disease The two events are independent, so you need to find
the product of their probabilities: 0.9 x 0.75 = 0.675. Enter the
correct answer The probability that Andrew has heart disease
Answer:
correct bayan HAHAHAHAHAHA
What the car monthly payment?? Show work plz
Answer:
$656.25
p=35000
t=5
r=2.5
interest=ptr/100
=35000x5x2.5/100
=4375
amount=p+i
=35000+4375
=39375
now,
5 yr= 5x12months = 60 months
$39375/60=$656.25
i think so...
$12.80 nearest cent
Answer:
13
Step-by-step explanation:
it just 13$ so yeah your welcome
Answer:
12.8
Step-by-step explanation:
Look at the zero in the end (hundreths place). Since it is zero keep everything the same!
If it is higher than 5, round up
If it is 5 or below round down.
0 is special because you can just keep everything the same.
Hope this helps!
A=9 b=12 c=15 sin b cos b tan b
Answer:
according to right , we use Phythgorous
tanb= 9/12
cosb=12/15
and sinb=9/15
Consider the following simple regression model: y = 0 + 1 x 1 + u. In order to obtain consistent estimators of 0 and 1, when x and u are correlated, a new variable z is introduced into the model which satisfies the following two conditions: Cov( z, x) 0 and Cov ( z, u) = 0. The variable z is called a(n) _____ variable. 答案选项组 dummy instrumental lagged dependent random
Answer:
Instrumental variable
Step-by-step explanation:
cov(z,u) shows that the instrumental variable is exogenous. An instrumental variable can also be regarded as a third variable, It is included in the model if you have an issue of endogeneity in your regression model. An endogeneity problem arises if there are other variables are being influenced by other independent variable in the same regression model. we use z to account for these behaviours in the model. this variable controls for measurement errors as well as confounding errors.
In the triangles, GK PN and HG 2MP.
Which statement correctly compares the angles?
H
M
Angle G is congruent to angle P.
O Angle G is smaller than angle P.
O Angle G is larger than angle P.
O Angle G is congruent to angle N.
32 cm
40 cm
G
K
P
N
Answer:
G is smaller than P. Visually comparing G to P you are doing a rough comparison to a 90° (or right) angle. Angle G is a little bit tilted to the right making it just under 90°
The statement which correctly compares the angles is Angle G is smaller than angle P.
What is Congruence of Triangles?Two or more triangles are said to be congruent if and only if sides and angles of one triangle is equal to the corresponding sides and angles of another triangle.
Given are two triangles.
Given that,
GK is congruent to PN.
HG is congruent to MP.
Also, given that,
HK = 32 cm and MN = 40 cm
Angle G is opposite to the side HK.
Angle P is opposite to the side MN.
Angles opposite to the greater side will be greater.
So angle P is greater than angle G
Or, angle G is smaller than angle P.
Hence, Angle G is smaller than angle P.
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Which points are solutions to the system of inequalities shown below?
Check all that apply.
у< x
y< 5
X<4
A. (3,0)
B. (1,7)
C. (6,2)
D. (0,-1)
E. (2, 1)
F. (3, 4)
Answer:
A. (3,0)
D. (0,-1)
E. (2, 1)
Step-by-step explanation:
A. (3,0)
B. (1,7)
C. (6,2)
D. (0,-1)
E. (2, 1)
F. (3, 4)
у< x #############################
A. (3,0)
C. (6,2)
D. (0,-1)
E. (2, 1)
y< 5 ####################
A. (3,0)
C. (6,2)
D. (0,-1)
E. (2, 1)
X<4 ###################
A. (3,0)
D. (0,-1)
E. (2, 1)
What is the value of x in the equation of 7x-8=13
PLEASE HELP MEEE
Answer:
x = 3
Step-by-step explanation:
7x-8=13
Add 8 to each side
7x-8+8=13+8
7x = 21
Divide each side by 7
7x/7 = 21/7
x = 3
Please help I’ll give brainliest
Answer:
1000 cubic metre
Step-by-step explanation:
hopes it help
Answer:
solution,
length=10 cm
volume=?
now,
volume of cube=l×l×l
=10×10×10
therefore,the answer is 1000 cubic centimeter
The rule g = b + 3 expresses the relationship between the
number of girls g and the number of boys b in a classroom.
Rewrite this rule another way.
Answer:
g = 3 + b
b + 3 = g
3 + b = g
Step-by-step explanation:
Answer:
[see below]
Step-by-step explanation:
Rewriting the rule so 'b' would be the subject:
[tex]g = b + 3\\\\g - 3 = b + 3-3\\\\g-3=b\\\\\boxed{b=g-3}[/tex]
Hope this helps.
The container of orange juice held 53 cups of juice. If a serving of orange juice is ã of a cup of orange juice, to the
nearest whole serving, how many servings were in the container?
05 servings
O 6 servings
15 servings
19 servings
Mark this and return
Save and Exit
Next
Submit
Answer:
5 servings = 265 cups of orange juices
5 servings = 318 cups of orange juices
5 servings = 795 cups of orange juices
5 servings = 1,007 cups of orange juices
Step-by-step explanation:
Given:
1 serving contain = 53 cups of orange juices
Find:
Serving in;
5 servings
6 servings
15 servings
19 servings
Computation:
5 servings = 53 x 5
5 servings = 265 cups of orange juices
5 servings = 53 x 6
5 servings = 318 cups of orange juices
5 servings = 53 x 15
5 servings = 795 cups of orange juices
5 servings = 53 x 19
5 servings = 1,007 cups of orange juices
Help me plsssssssss
[tex]y \: \alpha \: x[/tex]
Let c be the constant
[tex]y = cx \\ 16 = c4 \\ c = \frac{16}{4} \\ c = 4[/tex]
SO:-[tex]y = cx \\ y = 4 \times ( - 2) \\ y = ( - 8)[/tex]
Answer:
y = 4x
Step-by-step explanation:
Given y varies directly with x then the equation relating them is
y = kx ← k is the constant of variation
To find k use the condition y = 16 when x = 4 , then
16 = 4k ( divide both sides by 4 )
4 = k
y = 4x ← equation of variation
When x = - 2 , then
y = 4 × - 2 = - 8
When 4 is added to three times of a number, the answer is the same as subtracting 2 from the number. What is the number ?
Answer:
- 3
Step-by-step explanation:
let n be the number , then
3n + 4 = n - 2 ( subtract n from both sides )
2n + 4 = - 2 ( subtract 4 from both sides )
2n = - 6 ( divide both sides by 2 )
n = - 3
The number is - 3
The number is - 3.
To find the number.
What is integer?
An integer is a whole number (not a fractional number) that can be positive, negative, or zero. All the whole numbers are also integers, because integers include all the positive and negative numbers.
Given that:
let n be the number , then
3n + 4 = n - 2 ( subtract n from both sides )
2n + 4 = - 2 ( subtract 4 from both sides )
2n = - 6 ( divide both sides by 2 )
n = - 3
So, the number is - 3.
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Take the square of every integer between $-20$ and $20$ (including $-20$ and $20$), and write them down on a list. The first few numbers in the list should be $(-20)^2 = 400$, $(-19)^2 = 361$, and $(-18)^2 = 324$. How many different numbers are there on the list
Answer:
There are 21 distinct numbers on the list
Step-by-step explanation:
Square of integers between - 20 and 20
-20² = 400
-19² = 361
-18² = 324
-17² = 289
-16² = 256
-15² = 225
-14² = 196
-13² = 169
-12² = 144
-11² = 121
-10² = 100
-9² = 81
-8² = 64
-7² = 49
-6² = 36
-5² = 25
-4² = 16
-3² = 9
-2² = 4
-1² = 1
0² = 0
1² = 1
2² = 4
3² = 9
4² = 16
5² = 25
6² = 36
7² = 49
8² = 64
9² = 81
10² = 100
11² = 121
12² = 144
13² = 169
14² = 196
15² = 225
16² = 256
17² = 289
18² = 324
19² = 361
20² = 400
these marbles are placed in a bag and two of them are randomly drawn. what is the probability of drawing two blue marbles if the first marble is placed back in the bag before the second draw
In other words, the number 4 goes in the green box.
============================================================
Explanation:
2 yellow + 3 pink + 5 blue = 10 total marbles
We have 5 blue out of 10 total, so 5/10 = 1/2 represents the probability of picking a blue marble.
Picking two marbles in a row is represented by the probability (1/2)*(1/2) = 1/4
The fraction 1/2 stays the same for both selections because we put the first marble back.
203 cm
196 cm
Question 1:
The formula to calculate the perimeter of the banner is
(a) 2 (1+ b)
(b) 2xrh + 2A
(c) a + (21 + b)
(d) 2 (1 + b) + ar
Answer:
πr + (2l + b)
Step-by-step explanation:
The figure is a composite figure, consisting of a semicircle and a rectangle :
The perimeter of a rectangle is the sum of the sides ;
Perimeter of semicircle is the 2πr/2 (Circumference / 2)
For the triangle, we take the sum of 3 sides ;
Length + length + breadth = 2l + b
Hence, the perimeter is :
2πr/2 + 2l + b
πr + (2l + b)
10 points!!!!!
1-16 please finish quickly
the question is blurry for me take a picture of that again
what is the order of the numbers from least to greatest
Answer:
-3.7, -1.9, -1/2, 1 1/3, 1.6, 2 1/3
Step-by-step explanation:
I believe this is correct, if not feel free to let me know and I will fix it. I'm sorry in advance if this answer is wrong.
Answer:
-3.7, -1.9, -1/2, 1 1/3, 1.6, 2 1/3
Step-by-step explanation:
hope this helps! have a great day!
2 extra large chocolate shakes contain 85 ounces of ice cream. How many ounces of ice cream are there in 12 extra large chocolate shakes?
plz show work
Answer:
It will be 1020
Step-by-step explanation:
2 extra large = 85 ounces
multiply by 6 to get to 12 cups
85*12=1020
Put these numbers in order from greatest to least.
0.24,0.73,1/4, and 3/4
Answer:
3/4, 0.73, 1/4, 0.24
Step-by-step explanation:
1/4=25/100=0.25
3/4=75/100=0.75
Select a figure from the options which will replace the(?) as established by the problem figure
Answer:
a) is the correct answer.
