Answer:
1
Key:
[tex]a^0=1,\:\quad \:a\ne \:0[/tex]Step-by-step explanation:
[tex]2^0=1[/tex]
A triangular prism. The rectangular sides are 3 feet by 2 feet, 3 feet by 2.5 feet, and 3 feet by 1.5 feet. The 2 triangular sides have a base of 2 feet and height of 1.5 feet.
Trenton is building a skateboarding ramp in the shape of a triangular prism. According to his plan, the ramp would have a base of 2 feet, a height of 1.5 feet, and a length of 3 feet. The riding surface would measure 2.5 feet.
If Trenton wants to cover all faces of the ramp with plywood, how much plywood will he need to buy?
Trenton will need
square feet of plywood.
The amount of plywood that he needs to buy will be 21 square feet.
What is the surface area of the triangular prism?Let the prism with a length of L of the rectangular surface.
And the dimension of the triangle is A, B, and C. Then we have
SA = 2(area of triangle) + 3(area of rectangle surface)
A triangular prism.
The rectangular sides are 3 feet by 2 feet, 3 feet by 2.5 feet, and 3 feet by 1.5 feet.
The 2 triangular sides have a base of 2 feet and a height of 1.5 feet.
Then the area of the triangle will be
⇒ 1/2 x 2 x 1.5
⇒ 1.5 square feet
The area of the rectangles will be
⇒ 3 x 2 + 3 x 2.5 + 3 x 1.5
⇒ 18 square feet
Then the surface area of the triangular prism will be
Surface area = 2 x 1.5 + 18
Surface arae = 3 + 18
Surface area = 21 square feet
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The box-and-whisker plot represents a data set. Which statements are never true for this data set?
The statement that can never be true is the data set contains a value of 3.
What is box plot?A box plot is used to study the distribution of a dataset. The box plot consists of two lines and a box. The two lines are known as whiskers. The end of the first line represents the minimum number and the end of the second line represents the maximum number.
minimum number = 8
maximum number = 22
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A certain population of bacteria has an initial population of 225. the bacteria triples every hour. determine the multiplier that would allow you to predict the population of bacteria after 2 hours.
Using an exponential function, it is found that the multiplier that would allow you to predict the population of bacteria after 2 hours is of 9.
What is an exponential function?An exponential function is modeled by:
[tex]y = ab^x[/tex]
In which:
a is the initial value.b is the growth rate.In this problem, the bacteria triples every hour, hence the rate of change is b = 3, and the equation is:
[tex]y = a(3)^x[/tex]
Hence, after 2 hours:
[tex]y = a(3)^2 = 9a[/tex]
Which means that the multiplier is of 9.
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Monique goes out for coffee once per week. she has already spent $40.86 this year on her coffees and each one is $4.54.
what is the first term of the sequence?
to get to the next term, you would_____
this is a _____ sequence
there are 27 weeks left in this school year for monique. if she continues getting coffee at this rate how much money will she have spent on coffee by the end of the year?
If Monique continues getting coffee at this rate then the money that she will have spent on coffee by the end of the year is $163.44.
What is an arithmetic sequence?An arithmetic sequence is a sequence of integers with its adjacent terms differing with one common difference.
If the initial term of a sequence is 'a' and the common difference is of 'd', then we have the arithmetic sequence as:
a, a + d, a + 2d, ... , a + (n+1)d, ...
Its nth term is
Tₙ = a + (n-1)d
(for all positive integer values of n)
Given Monique goes out for coffee once per week. she has already spent $40.86 this year on her coffees and each one is $4.54. Therefore, the sequence can be written as,
4.54, 9.08, 13.62, 18.16, 22.7, 27.24, .........
Therefore,
The first term of the sequence is 4.54, To get the next term you need to add 4.54. This is an arithmetic sequence.Since 9 weeks (40.86/4.54 = 9) are already over, and there are 27 more weeks, therefore, the spending till 36 weeks will be,
a₃₆ = 4.54 + (36-1)4.54
a₃₆ = 163.44
Hence, if Monique continues getting coffee at this rate then the money that she will have spent on coffee by the end of the year is $163.44.
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1. Solve the equation using square roots.
x² +10=9
Answer:
x=±√−1 (NO REAL SOLUTION)Step-by-step explanation:
x² + 1 = 0
1× x²+1=0
x=±√(−1×1)
x=±√−1 (NO REAL SOLUTION)
Based on the information in the table what is the probability of being a girl and choosing lemonade?
Select one:
a.
21%
b.
.20
c.
20%
d.
38%
e.
.38
Using it's concept, it is found that the probability of being a girl and choosing lemonade is given by:
b. 0.2.
What is a probability?A probability is given by the number of desired outcomes divided by the number of total outcomes.
In this problem, out of 130 people, 26 are girls who choose lemonade, hence the probability is given by:
p = 26/130 = 0.2, which means that option b is correct.
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Given that 2x³-5x² - 4x+8 = (Ax - 1)(x-B)(x + 1) + C for all values of x, find the
values of A, B and C.
Answer:
A=2, B=3, C=5
Step-by-step explanation:
Two polynomials are equal for all values of the variable if the corresponding coefficients are the same. The way to solve the problem is to multiply the RHS, rewrite it in a more orderly way
[tex](Ax-1)(x-B)(x+1)+C = \\Ax^3+(A-AB-1)x^2+(B-AB-1)x +B+C[/tex]
Now, for the two polynomials to be the same we need to have, at the same time
[tex]x^3: A=2\\x^2: A-AB-1= -5\\x:B-AB-1=-4\\1: B+C=8[/tex]
You might notice that we have more conditions than variables, but you can consider one of the two in the middle as a "check" option.
Now, grabbing the value from the first condition into the second we get B=3. Replacing both value in the third we see that the equality still holds, and replacing into the fourth we get C =5.
PLEASE HELP simplify (-2)(-3)^2-2(2-5)
Answer: -12
Step-by-step explanation: When solving this problem, PEMDAS is a key component. What is PEMDAS?
PEMDAS stands for the following:
P- Parentheses
E- Exponents
M-Multiplication
D- Division
A-Addition
S-Subtraction
This is also known as order of operations. Following this order, we can easily simplify the problem.
P-Parentheses
(-2)(-3)^2-2(2-5)
Our parentheses is (2-5). We can simply this to -3. Our problem now is
(-2)(-3)^2-2(-3)
E-Exponents
We have one set of exponents in this. It is -3^2. This simplifies to 9. Our problem now is
(-2)(9)-2(-3)
M- Multiplication
We can simply to.
-18+6
These simplifies into
-12
Answer:
-12
Step-by-step explanation:
-2*9-2(2-5) : Raise -3 to the power of 2
-18-2(2-5) : Multiply -2 by 9
-18-2*-3 : Subtract 5 from 2
-18+6 : Multiply -2 by -3
-12 : Add -18 and 6
There is a pair of parallel sides in the following shape 6,4,8 what is the area of the shape?
How many different sequences of 3 playing cards (from a single 52-card deck) exist?
22,100
140,608
132,600
24,804
There 1,32,600 possibilities to withdrawn 3 different sequence of playing cards from 52 cards.
What is Permutations?A permutation of a set is, loosely speaking, an arrangement of its members into a sequence or linear order, or if the set is already ordered, a rearrangement of its elements.
Here, total number of cards = 52
Number of Withdrawn cards = 3
Possibilities of different sequences of 3 playing cards = 52 X 51 X 50
= 132600
Thus, there 1,32,600 possibilities to withdrawn 3 different sequence of playing cards from 52 cards.
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Answer:
132,600
Step-by-step explanation:
To determine the number of different sequences of 3 playing cards from a 52-card deck, we can use the formula for permutations, which is given by:
P(n, k) = n! / (n-k)!
Where n is the total number of items (in this case, the number of cards in the deck) and k is the number of items chosen (in this case, 3 cards).
Plugging in the values:
n = 52 (total number of cards in the deck)
k = 3 (number of cards chosen)
P(52, 3) = 52! / (52-3)!
Calculating the factorial terms:
52! = 52 x 51 x 50 x ... x 3 x 2 x 1
(52-3)! = 49! = 49 x 48 x ... x 3 x 2 x 1
Simplifying the equation:
P(52, 3) = 52 x 51 x 50
P(52, 3) = 132,600
Therefore, there are 132,600 different sequences of 3 playing cards that can be formed from a single 52-card deck.
Given the circle below secant kjI and tangent hi find the length of hi round to the nearest tenth if necessary.
The length of the segment HI in the figure is 32.9
How to determine the length HI?To do this, we make use of the following secant-tangent equation:
HI² = KI * JI
From the figure, we have:
KI = 21 + 24 = 45
JI = 24
So, we have:
HI² = 45 * 24
Evaluate the product
HI² = 1080
Take the square root of both sides
HI = 32.9
Hence, the length of the segment HI is 32.9
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Please answer this question
Answer:
A: Isosceles B: EquilateralC: ScaleneD: Isosceles E: Isosceles F: ScaleneStep-by-step explanation:
We can classify triangles by their sides into three types:
Equilateral: It is when the triangle has all the equal sides.Isosceles: It is when the triangle has only two equal sides.Scalene: It is when none of the sides of a triangle are equal. MissSpanishFor the quadrilateral on the grid, the slope of WX is 0, the slope of XY is , the slope of YZ is 0, and the slope of ZW is .
Which statement verifies that quadrilateral WXYZ is a parallelogram?
The difference of the slope of adjacent sides is .
The slopes of adjacent sides are opposite reciprocals.
The opposite sides have the same slope.
XY and YZ have the same slope.
The statement that verifies that quadrilateral WXYZ is a parallelogram is C)The opposite sides have the same slope.
What is a Parallelogram?This refers to a four-sided figure that is used in geometry and has parallel opposite sides.
Hence:
Remember that the opposite sides of a parallelogram are parallel.
We would solve:
Slope WX = 0
Slope XY= 5/2
Slope XZ= 0
Slope ZW= 5/2
The next step would be:
Slope WX= Slope YZ
Slope XY = Slope ZW
Based on the fact that the opposite sides have the same slopes, we can conclude that quadrilateral WXYZ is a parallelogram
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Line segment pr is a directed line segment beginning at p(-10,7) and ending at r(8,-5). find point q on the line segment pr that partitions it into the segments pq and qr in the ratio 4:5.
[tex]\textit{internal division of a line segment using ratios} \\\\\\ P(-10,7)\qquad R(8,-5)\qquad \qquad \stackrel{\textit{ratio from P to R}}{4:5} \\\\\\ \cfrac{P\underline{Q}}{\underline{Q} R} = \cfrac{4}{5}\implies \cfrac{P}{R} = \cfrac{4}{5}\implies 5P=4R\implies 5(-10,7)=4(8,-5)[/tex]
[tex](\stackrel{x}{-50}~~,~~ \stackrel{y}{35})=(\stackrel{x}{32}~~,~~ \stackrel{y}{-20})\implies Q=\underset{\textit{sum of the ratios}}{\left( \cfrac{\stackrel{\textit{sum of x's}}{-50 +32}}{4+5}~~,~~\cfrac{\stackrel{\textit{sum of y's}}{35 -20}}{4+5} \right)} \\\\\\ Q=\left( \cfrac{-18}{9}~~,~~\cfrac{15}{9} \right)\implies Q=\left( -2~~,~~\cfrac{5}{3} \right)[/tex]
Solve for x. Round your answer to the nearest tenth if necessary.
Answer: 8.8
Step-by-step explanation:
Because [tex]\angle S \cong \angle S[/tex] by the reflexive property, we know that [tex]\triangle STU \sim \triangle SQR[/tex] by AA.
So, by the triangle proportionality theorem,
[tex]\frac{x}{5.3}=\frac{11.1}{6.7}\\x=(11.1/6.7)(5.3) \approx \boxed{8.8}[/tex]
Consider the graph of the linear function h(x) = -x + 5. Which could you change to move the graph down 3 units?
O the value of b to -3
the value of m to -3
the value of b to 2
O the value of m to 2
Intro
Done
Answer:
the value of b to 2
The value of b changes to 2.
The correct option is C.
What is Linear Equation?A linear equation is an algebraic equation of the form y=mx+b, where m is the slope and b is the y-intercept, and only a constant and a first-order (linear) term are included.
We have,
Equation: h(x) = -x + 5
Now, using the slope intercept form
y = mx + b
From which we get
m = -1 and b=5
Now, we need to move the graph 3 units down then we need to subtract given function by 3, we get
y = -x+5 -3
y = -x +2.
Here y-intercept is 2.
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-33 + 8x = -3 (3x+6) + 2
Answer:
x = 1
Step-by-step explanation:
-33 + 8x = -9x - 18 + 2
8x+ 9x = -18 + 2 + 33
17x = -16 + 33
17x = 17
x = 1
give me brainliest please!
hope this helps :)
Solve the equation for x
z=m+x-y a)x=-z+m+y b)x=z-m+y c)x=z+m-y d)x=z+y+m
Answer:
x = z - m + y
Step-by-step explanation:
Given:
[tex]\displaystyle \large{z = m+x-y}[/tex]
To solve for x-term, we have to isolate it. We can do by subtracting m-term both sides and add y-term both sides.
[tex]\displaystyle \large{z-m+y=m+x-y-m+y}\\\\\displaystyle \large{z-m+y=x}\\\\\displaystyle \large{x=z-m+y}[/tex]
Therefore, the answer to this question is x = z - m + y
Please let me know if you have any questions regarding my answer or explanation!
what is the answer to −1.4+(−1.2)
Answer:
-2.6
Step-by-step explanation:
-1.4+(-1.2)
-1.4-1.2=-2.6
Hope this helps!
If not, I am sorry.
What is the diameter of a circle that has a circumference of 120 pi
Answer:
38.1971
Step-by-step explanation:
The formula for diameter is circumference/ pi. So 120/3.14... is 38.1971
2. Ozzie Foster deposits $2,000 at the end of each year (ordinary annuity) into an Individual Retirement
Account at Bishop Bank. The account pays 7% compounded annually. a) How much will be in the account
in 25 years? b) If Ozzie haddeposited the $2,000 at the beginning of each year (annuity due), how much
would be in the account in 25 years?
Answer:
250.000$
Step-by-step explanation:
so you multiple 2.000 by 25
What is the value of y?
log^464 = y
OA. 16
OB. 8
OC. 3
OD. 4
The value of y in the given logarithmic equation is 3. The correct option is C. 3
Evaluating Logarithmic equationFrom the question, we are to determine the value of y in the given logarithmic equation
The given equation is
[tex]log_{4}64=y[/tex]
By applying one of the laws of logarithm, we get
[tex]64 = 4^{y}[/tex]
Now, express 64 in index form,
[tex]4^{3} = 4^{y}[/tex]
Since the bases are equal, we can equal the powers to get
3 = y
∴ y = 3
Hence, the value of y in the given logarithmic equation is 3. The correct option is C. 3
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In circle P, diameter QS measures 20 centimeters.
Circle P is shown. Line segment Q S is a diameter. Line segment R P is a radius. Angle R P S is 123 degrees.
What is the approximate length of arc QR? Round to the nearest tenth of a centimeter.
9.9 centimeters
19.9 centimeters
21.5 centimeters
43.0 centimeter
The approximate length of arc QR to nearest tenth is 9.9cm
Length of an arcThe formula for calculating the length of an arc is expressed as:
L = r theta
where
r is the radius of an arc = 20cm/2 = 10cm
theta = 180 - 123 = 57 degrees
Determine the length of an arc
L = 10(57π/180)
L = 57π/18
L = 9.94cm
Hence the approximate length of arc QR to nearest tenth is 9.9cm
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Answer:
9.9
Step-by-step explanation:
The sum of the volume of two rectangular prisms, box a and box b are 14.325cm cubed. Box a has a volume of 5.61cm.
The equation that could be used to determine the volume of Box B is (B = 14.325cm³ - 5.61cm³) and the volume of Box B is 8.715cm³.
This question is incomplete, the complete question is:
The sum of the volume of two rectangular prisms, box a and box b are 14.325cm cubed. Box a has a volume of 5.61cm.
a. Let B represent the volume of Box B in cubic centimeters. Write an equation that could be used to determine the volume of Box B.
b. Solve the equation to determine the volume of Box B
What is volume?Volume is simply the amount of space that is enclosed within a container.
Given that;
Sum of the volume of two rectangular prisms A&B = 14.325cm³Volume of Box A = 5.61cm³a)
Let B represent the volume of Box B in cubic centimeters. The equation that could be used to determine the volume of Box B will be;
Sum of the volume of two rectangular prisms A&B = Volume of Box A + Volume of Box B
14.325cm³ = 5.61cm³ + B
B = 14.325cm³ - 5.61cm³
Hence, The equation that could be used to determine the volume of Box B is B = 14.325cm³ - 5.61cm³
b)
To determine the volume of Box B, we solve the equation.
B = 14.325cm³ - 5.61cm³
B = 8.715cm³
Hence, the volume of Box B is 8.715cm³.
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help please and I'll mark you brainiest.
The probability will include:
P(A and 1) = 1/24P(C and 2) = 1/12.P(B and 3) = 1/12.P(A and 4) = 1/12How to calculate the probability?The probability of P(A and 1) will be:
= 1/4 × 1/6
= 1/24
The probability of P(C and 2) will be:
= 1/4 × 2/6
= 1/12
The probability of P(B and 3) will be:
= 2/4 × 1/6
= 1/12
The probability of P(A and 4) will be:
= 1/4 × 2/6
= 1/12
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find the height of a a cuboid if it's length is 10m , breadth is 5m and LSA is 180m² .
NONSENSE = REPORT
[tex]\huge\sf\underline{Answer}[/tex]
Let's find out ~
Given :-
Length ( l ) = 10m Breadth ( b ) = 5m LSA = 180m²Solution :-
[tex]\sf\rightarrow \:LSA \: of \: cuboid \: = 2h \: ( \: l + b \: )[/tex]
[tex]\sf\rightarrow \: 180 = 2h \: (10 + 5)[/tex]
[tex]\sf\rightarrow180 = 2h \: \times 15[/tex]
[tex]\sf\rightarrow 180 = 30h \: [/tex]
[tex]\sf\rightarrow \: 30h \: = 180[/tex]
[tex]\sf\rightarrow \: h = \frac{180}{30} [/tex]
[tex]\sf\rightarrow \: 6[/tex]
Thus , the height of cuboid is 6m
what is the value of the digit 5in the number 734.95?
Answer:
0.05
explanation
value means total value
so it's 5*0.01
=0.05
Cut-1 Cut-2 Number of rope cutting 1 2 3 Resulting pieces 3 5 7 1.2.1 The number of pieces of ropes for FIVE cuts. 4 S
The answer to the all parts given below.
What is sequence?A sequence is an ordered list of numbers (or other elements like geometric objects), that often follow a specific pattern or function.
For 5 cuts number of pieces will be 11 pieces.
General formula:
Tn= 2n+1
For 153 rope pieces number of rope cutting
2n+1=153
2n= 152
n= 76
For 11 cuttings rope pieces will be
2(11)+1
= 23
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please help... The triangle represents a cross section from a 3D prism. Draw or describe the 3D prism that produced this cross section.
The 3D prism that produced the cross-section of a triangle is a triangular prism.
How to describe the 3D prism?From the given figure, we can see that the cross-section is a triangle
One of the faces of a triangular prism is a triangle.
This means that when the triangular prism is cut vertically, a triangle face is created
Hence, the 3D prism that produced the cross-section of a triangle is a triangular prism.
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pick one of the following sums and investigate these
What happens?
what is the general rule for each sums?
how does the rule work?
3.7+7.3=
6.4+4.6=
9.1+1.9=
5.5+5.5=
The general rule for each sum is that when you add the tenth term together we will get ten which will make the value an integer. The whole sum is equals to eleven.
How to find the general rule for a sum?Let's sum the decimal numbers to know the general rule,
Therefore,
3.7 + 7.3 = 11.0
6.4 + 4.6 = 11.0
9.1 + 1.9 = 11.0
5.5 + 5.5 = 11.0
Therefore, the values added are the reverse of the decimals. example is 3.7 and 7.3 or 6.4 and 4.6.
When you add the tenth term together we will get ten which will make the value an integer
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