The first term of an arithmetic progression of 4 terms and ratio equal to 4 whose sum is 100 is 19.
How to calculate arithmetic progression?The first term of an arithmetic progression can be calculated using the following expression:
Sn = n/2 [2a + (n − 1)d]
Where;
a = first termUn = sumn = no of termsd = common ratio100 = 2 [2a + (4 - 1)4]
100 = 4a + 24
4a = 100 - 24
a = 76/4
a = 19
Therefore, the first term of an arithmetic progression of 4 terms and ratio equal to 4 whose sum is 100 is 19.
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Simplify the expression.
3.2a + 3.5b – 2.1a
Answer:
1.1a+3.5b
Step-by-step explanation:
Which statement is true about the polynomial
5s6t2 + 6st9 – 8s6t2 – 6t7 after it has been fully simplified?
It has 3 terms and a degree of 9.
It has 3 terms and a degree of 10.
It has 4 terms and a degree of 9.
It has 4 terms and a degree of 10.
The polynomial 6st⁹ – 3s⁶t² – 6t⁷ has 3 terms and the degree of the polynomial is 10. Then the correct option is B.
What is polynomial?A polynomial expression is an algebraic expression with variables and coefficients.
The polynomial is given below.
5s⁶t² + 6st⁹ – 8s⁶t² – 6t⁷
Then polynomial can be arranged as
⇒ 6st⁹ + 5s⁶t² – 8s⁶t² – 6t⁷
⇒ 6st⁹ – 3s⁶t² – 6t⁷
The polynomial 6st⁹ – 3s⁶t² – 6t⁷ has 3 terms and the degree of the polynomial is 10.
Then the correct option is B.
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A. 10
B. 11
C. 12
D. 13
Answer:
D. 13
Step-by-step explanation:
13 is the answer I guess I hope it will be the right answer
Determine whether each triangle with sides of given length is a right triangle. justify your answer
7 yd, 5 yd, 9 yd
10 ft, 24ft, 26 ft
The triangles with the side lengths 10 ft, 24ft, 26 ft, is a right triangle while a triangle with side lengths of 7 yd, 5 yd, 9 yd is NOT based on the Pythagorean theorem.
What is a Right Triangle?A triangle is said to be a triangle based on the Pythagorean theorem, if the square of the longest side equals the sum of the squares of the other smaller sides of the triangle.
9² = 7² + 5²
81 = 74 (NOT TRUE), therefore, the triangle with the side lengths 7 yd, 5 yd, 9 yd, is not a right triangle.
26² = 10² + 24²
676 = 676 (TRUE), therefore, the triangle with the side lengths 10 ft, 24ft, 26 ft, is a right triangle.
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what is the area of triangle ABC
Answer:
enter traverse Does the middle traverse indeed bisect the triangle?
Angles In the triangle ABC, the ratio of angles is: a:b = 4: 5. ...
Triangle P2 Can a triangle have two right angles?
Diagonal Can be a diagonal of diamond twice longer than it side?
Similarity coefficient The triangles ABC and A "B" C "are similar to the similarity coefficient 2. ...
That how u find the area
It wont always be easy, but always try to do what ' s right!
In a world of worriers, be the warrior!
When nothing goes right, go left.
Answer;
The area of a triangle is the region enclosed between the sides of the triangle. Area of ΔABC = 1/2 × Base × Height. Let us know the basics of the area of a triangle. If ABC is an equilateral triangle, Area of ΔABC = (√3/4)a2 where a is the length of a side of the equilateral triangle.
A winery has a vat with two pipes leading to it. The inlet pipe can fill the vat in 3 hours, while the outlet pipe can empty it in 10 hours. How long will it take to fill the vat if both pipes are left open?
The time it will take to fill the vat if both pipes are left open is = 4.3 hours
Calculation of time taken to fill vatThe number of pipes a vat has = 2
The time it takes the inlet pipe to fill the vat = 3hrs
The time it takes the outlet pipe to empty the vat= 10hrs
Therefore, the time it will take to fill the vat if both pipes are left open is;
1/t = 1/3-1/10
1/t = 7/30
Make t the subject of formula,
t = 30/7
t= 4.3 hours
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Find the value of x.
[tex]3(x+4)=90\\x+4=30\\x=26[/tex]
how to solve 52 divided by 4!
Identify the fractions labeled with the letters a and b on the scale below
In the given fraction, we have the value of 1 divided in four portions and we just have to identify which portion does A and B fall into
FractionThis can be defined as a part of portion of a complete value.
In the first part, the portion A is representing 1 out of 5 parts. So, the fraction of A is
[tex]A = \frac{1}{5}[/tex]
In the second fraction B, we can say that B is representing 3 out of 5 parts.
[tex]B = \frac{3}{5}[/tex]
From the above, the value of A and B are
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Write the standard equation of the circle with center (-4,-4) and radius 6.8
Answer: [tex](x+4)^{2}+(y+4)^{2}=46.24[/tex]
Step-by-step explanation:
[tex](x+4)^{2}+(y+4)^{2}=6.8^{2} \\(x+4)^{2}+(y+4)^{2}=46.24[/tex]
Scan the n the questions
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165464775250023655713488
63
Answer:
what man we can barley see
Step-by-step explanation:
Simplify the quotient 3-¹ ÷34
Answer:
[tex]\frac{1}{102}[/tex]
Step-by-step explanation:
1) Negative Power Rule: [tex]x}^{-a}=\frac{1}{{x}^{a}}[/tex].
[tex]\frac{1}{3}\div 34[/tex]
2) Use this rule: [tex]a\div \frac{b}{c}=a\times \frac{c}{b}[/tex].
[tex]\frac{1}{3}\times \frac{1}{34}[/tex]
3) Use this rule: [tex]\frac{a}{b} \times \frac{c}{d}=\frac{ac}{bd}[/tex].
[tex]\frac{1\times 1}{3\times 34}[/tex]
4) Simplify [tex]1\times 1[/tex] to [tex]1[/tex].
[tex]\frac{1}{3\times 34}[/tex]
5) Simplify [tex]3\times 34[/tex] to [tex]102[/tex] .
[tex]\frac{1}{102}[/tex]
Mr. Apollo’s art class is designing tiles for a mosaic.
The class worked in groups, and each group selected a color and a set of shapes to use.
Match the shape names of all of the shapes in each group by dragging them to the correct color in the table.
Names may be used once, more than once, or not at all.
Set 1 has 4 blue rectangles, Set 2 has 4 red triangles, Set 3 has 4 green kites and Set 4 has 3 yellow trapezoids.
Rectangle returned to the choices list. Parallelogram
Rhombus
Square
Trapezoid
Rectangle
Triangle
Right Triangle
Isosceles Trapezoid
Obtuse Triangle
Blue
Red
Green
Yellow
To complete this task classify the shapes by considering both the color and the features of the shape.
How to classify a shape?Identify the shape. For example, a triangle has 3 sides and if one of the sides has a 90° angle, the triangle is a right triangle.Assign the name to the shape.Identify the color.Match the shape to set 1, 2 or 3. For example if the right triangle is red, this will belong to set 2.Note: This question is incomplete because the shapes are not given; due to this, the answer is based on general knowledge.
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What is c value in the equation
Log 57.9/c=0.293
If a log has no base written, you should generally (in algebra classes) assume that the base is 10
we raise 10 to the power log 57.9/c = 57.9/c
and 10 to the power 0.293 = 1.9633602768
so 57.9/c = 1.96
c = 57.9 /1.96 = 29.5
Could someone Help it’s a new topic
Answer:
So to do this you need a protactor and measure it with it, then add the total
Step-by-step explanation:
PLEASE 100 POINTS AMD BRAINLIEST IF YOU ANSWER ALL
Deion has 62 m of fencing to build a four-sided fence around a rectangular plot of
land. The area of the land is 228 square meters. Solve for the dimensions (length and
width) of the field?
The dimensions of the the plot of land is a length of 19 meters and width of 12 meters.
What is an equation?An equation is an expression that shows the relationship between two or more numbers and variables.
Let x represent the length of the field and y represent the width of the field, hence:
Deion has 62 m of fencing:
2(x + y) = 62
x + y = 31
y = 31 - x (1)
The area of the land is 228 square meters. hence:
xy = 228
x(31 - x) = 228
x² - 31x + 228 = 0
x = 12 or x = 19
when x = 12; y = 31 - 12 = 19
when x = 19; y = 31 - 19 = 12
The dimensions of the the plot of land is a length of 19 meters and width of 12 meters.
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A rocket is launched from the ground at an initial velocity of 39.2 meters per second. Which equation can be used to model the height of the rocket after t seconds?
s(t) = –4.9t2 + 39.2
s(t) = –4.9t2 + 39.2t
s(t) = –4.9t2 + 39.2t + 39.2
s(t) = –4.9t2 + 39.2t – 39.2
The quadratic equation that models the height of the rocket after t seconds is:
s(t) = -4.9t² + 39.2t.
What is the quadratic function for a projectile's height?Considering the height in meters, the equation is given by:
s(t) = -4.9t² + v(0)t + h(0)
In which:
v(0) is the initial velocity, in m/s.h(0) is the initial height, in m.In this problem, we have that v(0) = 39.2, h(0) = 0, hence the equation is:
s(t) = -4.9t² + 39.2t.
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Answer: B
Step-by-step explanation: on Edge (*^*)
What does negative 3 over 5 > −2 indicate about the position of negative 3 over 5 and −2 on the number line?
A. negative 3 over 5 is located on the right of −2
B.negative 3 over 5 is located on the left of −2
C.negative 3 over 5 is located on the right of 0 and −2 is located on the left of 0 D.negative 3 over 5 is located on the left of 0 and −2 is located on the right of 0
Will mark Brainliest!
Answer: A. negative 3 over 5 is located on the right of −2
Step-by-step explanation:
On a number line, the greater numbers are to the right and the smaller numbers are to the left.
Suppose that the function f is defined, for all real numbers, as follows.
-x-1 if x #-2
f(x)=
3
if x = -2
Find f(-4), f(-2), and ƒ(0).
S(-4)= 0
X
ƒ(-2) - D
ƒ(o) - D
S
?
The solutions of the function are:
When f(x) = -4, the solution is -4When f(x) = -2, the solution is -5/2When f(x) = 0, the solution is -1How to solve for the equationThe equation is given as
[tex]\frac{3}{4} x-1\\\\[/tex]
When x = -4
3/4 * -4 -1
= -12/4 - 1
= -4
When x = -2
3/4*(-4) - 1
= -6/4 - 1/1
Take the lcm
-10/4
= -5/2
When x = 0
3/4(0) - 1
= -1
When f(x) = -4, the solution is -4
When f(x) = -2, the solution is -5/2
When f(x) = 0, the solution is -1
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(-2p+7) (4p - 3) please help
Answer:
Step-by-step explanation:
-8p^2 + 6p + 28p - 21
-8p^2 + 34p - 21
Answer:
-8p² + 34p - 21
Step-by-step explanation:
(-2p + 7)(4p-3)
= -2p*4p -2p*-3 + 7*4p + 7*-3
= -8p² + 6p + 28p - 21
= -8p² + 34p - 21
What does the expression n + 3 represent?
Answer:
Step-by-step explanation:
BASICALLY ANYTHING WITH 3
Draw and simplify the karnaugh maps of x,y,Z for (a)m0 +m1+ m5+m7. (b)F(1,3,5,4,7). (c)m0+m2+m4+m6. (d)F(0,2,4,6)
The simplified Karnaugh maps are F(A, B, C) = A’B’ + AC , F(A, B, C) = C + AB’, F(A, B, C) = C’.
What are Karnaugh Maps ?A Karnaugh map can be compared to a more advanced version of a truth table
In a K-map there are all the possible input variables and outcomes stored in cells.
It is a method to simplify and optimize Boolean expressions.
(a) m0 +m1+ m5+m7
Mapping the given function in a Karnaugh map,
The image is attached with the answer.
we can see two pairs
Pair-1 is m0 + m1
and Pair-2 is m5 + m7
= A’B’C’ + A’B’C + AB’C + ABC
= A’B’(C’ + C) + AC(B’ + B)
= A’B’ + AC
Therefore the simplified Boolean expression for the given data is
F(A, B, C) = A’B’ + AC.
(b) F(1,3,5,4,7)
On Mapping the given function in a Karnaugh map, we will see
1 Pair and 1 Quad
Pair is m4 + m5
Quad is m1 + m3 + m5 + m7
= A’B’C + A’BC + AB’C + ABC + AB’C’ + AB’C
= A’C(B’ + B) + AC(B’ + B) + AB’(C’ + C)
(B +B' ) = 1 , (C’ + C) = 1
= A’C + AC + AB’
= C(A’ + A) + AB’
= C + AB’
Therefore the simplified Boolean expression for the given data is
F(A, B, C) = C + AB’.
(c) m0+m2+m4+m6.
On Mapping the given function in a Karnaugh map, we will see
2 Pairs
Pair-1 is m0 + m4
Pair-2 is m2 + m6
= A’B’C’ + AB’C’ + A’BC’ + ABC’ = B’C’(A’ + A) + BC’(A’ + A)
= B’C’ + BC’
= C’(B’ + B)
= C’
Therefore the simplified Boolean expression for the given data is
F(A, B, C) = C’.
(d) (0,2,4,6)
It will have the same expression as that of Option (c)
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Nick walked 5 miles to reach his aunt's house. From there he traveled 8 miles to the shopping mall on a bicycle. He traveled 80% faster on the bicycle than on foot. Let r represent his rate of walking in miles per hour. Identify the expression that represents the number of hours Nick took to reach the shopping mall in terms of r. Then find the time taken by Nick to reach the shopping mall if he walked at an average speed of 3 miles per hour
The number of hours Nick took to reach the shopping mall in terms of r is ; 3.14 hours.
What is rate?Rate is a measure of a quantity using another quantity as the basis.
Analysis:
speed travelling on foot = r
distance travelled on foot = 5 miles
time taken = 5/r
speed travelling on bicycle 80 percent faster than on foot is 1.8r
distance travelled on bicycle = 8 miles
time taken = 8/1.8r = 40/9r
total time taken to get to the mall = 5/r + 40/9r = 85/9r
speed while walking = 3 miles per hour = r
time taken = 85/9 x 3 = 3.14 hours
In conclusion, number of hours Nick took to reach the shopping mall in terms of r is 85/9r is 3.14 hours.
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Answer:
3 hours 9 minutes
Use the spinner shown to answer the question. Assume that it is equally probable that the pointer will land on any one of the colored regions. If the pointer lands on a borderline, spin again
If the spinner is spun once, find the probability that the pointer lands in a region that is red or blue.
D
The probability that the pointer lands in a region that is red or blue is
(Type an integer or a simplified fraction.)
The probability that the pointer lands in a region that is red or blue is 1/2
How to determine the probability?The spinner that completes the question is added as an attachment
From the attached spinner, we have:
Total section = 8Red or blue = 4The probability is then calcuated as:
P =Red or blue/Total section
This gives
P =4/8
Evaluate
P= 1/2
Hence, the probability that the pointer lands in a region that is red or blue is 1/2
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Pls help. Answer the question in the picture. I will give 5 stars, a thanks, and brainliest!
*20 points*
Answer:
1/5x + 2
Step-by-step explanation:
hope this helps
7. A man leaves ⅓of his property to his son, two fifths to his wife and the remainder to his daughter. If the daughter received sh. 24,000, what was the total amount left?
Answer:
sh 90,000
Step-by-step explanation:
let x be the total amount left , then
x = [tex]\frac{1}{3}[/tex] x + [tex]\frac{2}{5}[/tex] x + 24,000
multiply through by 15 ( the LCM of 3 and 5 ) to clear the fractions
15x = 5x + 6x + 360,000
15x = 11x + 360,000 ( subtract 11x from both sides )
4x = 360,000 ( divide both sides by 4 )
x = 90,000
the total amount left was sh 90,000
he graph of the function f(x) = –(x + 3)(x – 1) is shown below. On a coordinate plane, a parabola opens down. It goes through (negative 3, 0), has a vertex at (negative 1, 4), and goes through (1, 0). What is true about the domain and range of the function? The domain is all real numbers less than or equal to 4, and the range is all real numbers such that –3 ≤ x ≤ 1. The domain is all real numbers such that –3 ≤ x ≤ 1, and the range is all real numbers less than or equal to 4. The domain is all real numbers, and the range is all real numbers less than or equal to 4. The domain is all real numbers less than or equal to 4, and the range is all real numbers.+
What is true about the domain and range of the function is; The domain is all real numbers, and the range is all real numbers less than or equal to 4.
How to find the domain of a graph function?Let us first find the roots of the function f(x):
0 = (x - 3)(x + 1)
(x - 3) = 0
x = 3
and (x + 1) = 0
x = -1
Therefore, the roots of the function are x = 3 and x = -1.
Now, the vertex is between the roots (x = 1) and has a negative value of y (y = -4), therefore, we can say that the concavity of the parabola is upwards.
This means that the graph is decreasing until it reaches the vertex, then the graph is increasing.
Therefore, we can conclude that the graph is positive and decreasing for all real values of x where x < -1.
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Answer:
The domain is all real numbers, and the range is all real numbers less than or equal to 4.
Step-by-step explanation:
Minh is packing books into
boxes. The mass of one of the boxes is 20 kilograms. If the box
holds 10 books that each have the same mass, what is the mass of
each book in grams?
The mass of each book in grams if each box weighs 20 kilograms is 2000 grams
Mass of each box = 20 kilogramsTotal books in the box = 10 booksConverting kilograms to grams1 kilograms = 1000 grams
20 kilograms = 20,000 grams
Mass of each book in grams = 20,000 grams / 10
= 2000 grams
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Solve, using the substitution method.
x = 10
y = 2x – 6
(10, 14)
(10, 4)
(10, –4)
(10, –1)
Answer:
10/14
Step-by-step explanation:
substitute x in equation 2
y= 2(10) -6
y= 20 - 6
y= 14
substitute y in equation 2
14 = 2x - 6
-2x= -6-14
-2x= -20
divide both sides by -2
-20/-2
x= 10
y= 14, x= 10