Let a represent a positive number and let b represent a negative number. Tell whether each statement is True or False. True False a. The difference (a - b) could be negative. True False b. The difference (b − a) cannot be positive. True False C. The sum (a + b) could be positive. True False d. The sum (b + a) must be negative.
a. False; if b is negative, then -b is positive, so
a - b = a + (-b)
is the sum of two positive numbers, which must be positive.
b. True; the sum of two negative numbers is again negative.
c. True; a + b will be positive as long as a > |b|. (For example, if a = 2 and b = -1, then of course 2 > |-1| = 1, and a + b = 2 + (-1) = 1 > 0.)
d. False; this would contradict the result of part (c). b + a is only negative if a ≤ |b|. (For example, if a = 1 and b = -2, then b + a = -2 + 1 = -1 < 0.)
please answer these 3 question
Answer:
i think 5 prisms are cool
Step-by-step explanation:
Use the bar graph below to answer the following question.
Which girl is the shortest?
Answer:
ling
Step-by-step explanation:
you just have to compair the girls
and from the bar gragh ling is he sortest.
110 4t + 90 t=?
Please help!
Answer:
because of some theorm or postulate i forget the name of, angles on opposite sides are equal
110 = 4t + 90
20 = 4t
5 = t
t is equal to 5 degrees
Proving circles are similar: Choose any of the transformations that would be a step in proving that Circle A is similar to Circle C. Select ALL that apply.
A.
Reflect A over the line y=x
B.
Translate C (x+5,y-4)
C.
Dilate A by 3/2
D.
Dilate C by 3/2
E.
Translate A by (x-5, y+4)
The transformations that would prove that circles A and C are similar are:
A. Reflect A over the line y=xC. Dilate A by 3/2How to prove that circle A and circle C are similar?The circles are given as:
Circle A and B
Assume the following parameters:
The center of circle A is (2,3) with a radius of 2The center of circle B is (3,2) with a radius of 3To start with;
The circle A must be reflected across the line y = x with the following transformation rule:
(x,y) -> (y,x)
So, we have:
(2,3) -> (3,2)
Next, the radius of A must be dilated by 3/2 as follows:
New Radius = 3/2 * 2 = 3
After the transformations, we have the following parameters:
The center of circle A is (3,2) with a radius of 3The center of circle B is (3,2) with a radius of 3Notice that both circles now have the same center and radius.
Hence, both circles are similar
Read more about similar circles at:
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a _______has one endpoint line or ray
Answer:
Ray.
Step-by-step explanation:
Lines have no endpoints, while rays have 1 endpoint (:
he roof of a castle tower is shaped like a cone. The base of the cone is 24 m across and the height is 16 m. The slant height of the roof, which is unknown, is the hypotenuse of the right triangle formed with the radius and the height of the cone.
What is the slant height of the roof?
==========================================================
Explanation:
The base of the cone is 24 m across. This is the diameter of the circle. Divide it in half to get 24/2 = 12 m as the radius.
We can form a right triangle inside the cone such that the horizontal piece is the radius 12 m and the vertical piece is the height 16 m. The hypotenuse of this right triangle is the slant height. This is all mentioned in the instructions of course.
We'll use the pythagorean theorem to find the hypotenuse.
[tex]a^2 + b^2 = c^2\\\\c = \sqrt{ a^2 + b^2 }\\\\c = \sqrt{ 12^2 + 16^2 }\\\\c = \sqrt{ 144 + 256 }\\\\c = \sqrt{ 400 }\\\\c = 20 \text{ meters is the slant height}\\\\[/tex]
It is the distance from the circular base to the peak of the cone, when traveling along the outside of the cone. This is a straight line distance.
Surface Area:Question 6
What is the total surface area of the figure shown?
Select one:
96 square feet
60 square feet
0 72 square feet
36 square feet
[tex]\qquad\huge\underline{{\sf Answer}} ♨[/tex]
Total surface area :
[tex]\qquad \sf \dashrightarrow \:2(lw + wh + lh)[/tex]
[ l = Length, w = width, h = height ]
[tex]\qquad \sf \dashrightarrow \:2 \{(6 \times 2) + (2 \times 3) + (6 \times 3) \}[/tex]
[tex]\qquad \sf \dashrightarrow \:2 \{12 + 6+ 18\}[/tex]
[tex]\qquad \sf \dashrightarrow \:2 (36)[/tex]
[tex]\qquad \sf \dashrightarrow \:72 \: ft {}^{2} [/tex]
what is 20 - 10
what is 20+ 10
Answer:
20-10=20
20+10=30
Step-by-step explanation:
For 20-10 let's assume John has 20 apples. He gives 10 to Carol.
Understand that subtraction can mean taking away or finding a difference. For example, 13 – 8 can mean, “How many are left when you take 8 away from 13?” Or, 13 – 8 can be interpreted as, “How much more is 13 than 8?” Understand that subtraction is the opposite of addition. Know the addition facts up to 9 + 9.
If john has 20 apples and gives 10 to carol, he will have 10 left.
For 20+10, we do the opposite operation, which is addition.
Addition is finding the total value of two or more numbers. Addition is shown using the + symbol in maths sums.
If john has 20 apples and buys 10 more, he will have 30 apples.
How many members did not vote there is 75% and 60 people?
Answer:
15
Step-by-step explanation:
if 75% voted that is 45 people meaning 15 did not vote.
-8/7 / 5/4 as a fraction
Answer:
- 32/35
Step-by-step explanation:
-8/7 / 5/4 = -32/35
Please help The diagram below shows a square prism. The plane ABC is inside the
prism, and M is the midpoint of the base diagonal BC. MD. = square root 18
b Hence find, correct to the nearest degree, the angle that the plane ABC
makes with the base of the prism. Diagram is attached below.
Answer:
43°
Step-by-step explanation:
Triangle ADM is a right triangle with legs AD=4 cm and DM=√18 cm. The angle at M is the angle of interest. It can be found using the inverse tangent function.
Tan = Opposite/Adjacent
tan(∠AMD) = AD/MD = 4/√18
∠AMD = arctan(4/√18) ≈ 43.31°
The angle the plane makes is about 43°.
Answer:
the measure of the angle that the plane ABC makes with the base of the prism = 43 degree (to the nearest degree)
Step-by-step explanation:
We notice that the plane ABC and the base of the prism intersect along the line BC
And as the plane (ADM) is perpendicular to the line BC
then the angle between the plane ABC and the base of the prism is the angle AMD
Let θ be the measure of the angle AMD
[tex]\begin{aligned}\tan (\theta) &=\frac{A D}{M D} \\&=\frac{4}{\sqrt{18}}\end{aligned}[/tex]
[tex]\begin{aligned}\Rightarrow \theta &=\tan ^{-1}\left(\frac{4}{\sqrt{18}}\right) \\&=43,31385 \ldots\end{aligned}[/tex]
Triangle XYZ is translated by the rule (x + 1, y − 1) and then dilated by a scale factor of 4 centered at the origin. Which statement describes the properties of triangles XYZ and X''Y''Z'' after the transformations?
A. Y and ∠Y'' are congruent after the translation, but not after the dilation.
B. ∠Y and ∠Y'' are congruent after the dilation, but not after the translation.
C. segment YZ and segment Y double prime Z double prime are proportional after the translation, but not after the dilation.
D. segment YZ and segment Y double prime Z double prime are proportional after the dilation and congruent after the translation.
The statement that described the triangle properties is that the segment YZ and segment Y"Z" should be proportional when the dilation is done and it should be congruent when the translation should be done.
Given that,
There is the rule i.e. (x +1, y - 1) and it should be dilated by a scale factor of 4 centered at the origin.Based on the above information,
The figure should be proportional as the angle and the points should be the same. And, when the translation is done the image should be congruent to the pre-imageTherefore we can conclude that option d is correct.
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For what values of "x" is the inequality 3(x+2)-x<8 true?
x > 1
x < 1
x < 7
x > 7
We can't determine right off the bat what values of x make this inequality true, so we should solve it first.
First, use the distributive property and distribute 3 :
3(x+2)-x<8
3x+6-x<8
Now subtract 6 on both sides :
3x-x<8-6
3x-x<2
now , subtract the x's :
2x<2
Divide by 2 on both sides :
x<1
So the values of x less than 1 make this inequality true.Let's try -1 (-1 is less than 1)
Plug it in ↓
3(-1+2)-(-1)<8
3(1)+1<8
3+1<8
4<8
4 is less than 8.
Therefore, the values of x that make this inequality true are indeed less than 1.hope helpful ~
Answer:
x < 1
Step-by-step explanation:
Expand the brackets: 3 * x = 3x and 3 * 2 = 6
Current inequality: 3x + 6 - x < 8
Collect like x terms: 3x - x = 2x
Current inequality: 2x + 6 < 8
Collect like integer terms: subract 6 from both sides
Current inequality: 2x < 2
Convert 2x to x: divide both sides by 2
Final answer = x < 1
Hope this helps :)
Yo I need to bring up my grade bad so
3x=3y-6
(please show it graphed already :D)
Answer:
Step-by-step explanation:
find the volume
6ft
4ft
3ft
(i know it’s not 72)
Answer:
[tex] \fbox{Volume \: of \: pyramid \: = 24 ft³}[/tex]
Step-by-step explanation:
Given:
shape of object = Pyramidal
length of base l= 4ft
width of base w = 3ft
height of pyramid h = 6 ft
To find:
volume of pyramid = ?
Solution:
[tex]Volume \: of \: pyramid= \frac{l \times w \times h}{3} \\ Volume \: of \: pyramid= \frac{6 \times 4 \times 3}{3} \\ Volume \: of \: pyramid= \frac{24 \times \not3}{ \not3} \\ Volume \: of \: pyramid= 24 \: {ft}^{3} [/tex]
[tex] \fbox{Volume \: of \: pyramid \: = 24 ft³}[/tex]
Thanks for joining brainly community!What is the MEAN of the following data set?
31, 27, 19, 18, 22, 21, 25, 29, 34, 30
Step-by-step explanation:
31+27+19+18+22+21+25+29+34+30 divided by 10
Find the sum of -50 + (-44) + (-38) + ... + 2038 + 2044.
Answer:
3950
Step-by-step explanation:
-50 + (-44) + (-38) + 2038 + 2044
-94 + (-38) + 2038 + 2044
-132 + 2038 + 2044
1906 + 2044
3950
Hope this helps :)
Solution:
348950
Explanation:
first lets confirm, which series this is from,( first term + third term )/2 = second term
(-50 + (-38) )/2 = -44-44 = -44Thus it is arithmetic series.
[tex]\sf S_n = \dfrac{n}{2} (2a+(n-1)d)[/tex]
Solving step-wise:
a₁ = -50aₙ = 2044n = ? = 350d = + 6=================
aₙ = a₁ + d(n-1)2044 = -50 + 6(n-1)6(n) - 6 = 20946(n) = 2100n = 350Here,
[tex]\sf S_n = \dfrac{n}{2} (2a+(n-1)d)[/tex]
[tex]\sf S_n = \dfrac{350}{2} (2(-50)+(350-1)(6))[/tex]
[tex]\sf S_n =348950[/tex]
Find the volume of the sphere. Round your answer to the nearest tenth.
Use 3.14 for a.
A sphere has a radius of 3.5 feet.
The volume of the sphere is about
ft?
Answer:
179.50
Step-by-step explanation:
The formula for calculating pi is as followed: 4/3·π·r³
The question is either asking to calculate using 3.14 for π or add π at the end of your answer instead of completing it. I will substitute π for 3.14.
∴V=4/3·3.14·3.5³
V=179.503333333
Round your answer to the nearest hundredth:
179.503333333 rounded to the nearest hundredth becomes 179.50
∴V=179.50
-------------------------------------------------------------------------------------------------------------
Another way to answer this question is to use the same formula; but not substitute 3.14 into the answer.
V=π.4/3·r³
V=π·57.1666666667
Round 57.1666666667: 57.17
V=57.17π
Either one would work. Hope this works.
1. Find the lateral area and surface area of the given prism. Round your
answer to the nearest whole number
Answer:
LA = 720 , SA = 780
Step-by-step explanation:
find the missing length of the triangle using Pythagoras then use this value (8) to find the surface area of the sides and the triangle.Add up the values.
Answer:
Step-by-step explanation:
To find the lateral surface area of triangular prism, first we need to know the three sides of the triangle. Here, one side is missing and we have to find that using Pythagorean theorem. Let the unknow side of the triangle be 'c'
Pythagorean theorem,
15² + c² = 17²
225 + c² = 289
c² = 289 - 225
c² = 64 = 8*8
c = 8 in
a = 17 in & b = 15 in & h = 18 in
[tex]\boxed { \text{Lateral surface area = (a + b + c)*h }}[/tex]
= ( 17 + 15 + 8 ) * 18
= 40 * 18
= 720 in²
[tex]\boxed { \text{total surface area = LSA + 2* area of base triangles}}[/tex]
[tex]\text{ area of base triangles = 2* $ \dfrac{1}{2}*base*height $}[/tex]
= base * height
= 8 * 15
= 120 in²
Total surface area = 720 + 120
= 840 in²
5x²+y+10 what is the cofficient of x²
On a piece of paper, graph f(x) = (3x if x< 3) (f(x) = 2x if x > 3) Then determine which answer
choice matches the graph you drew.
[tex]if\ \alpha < 3[/tex]
[tex]f(\alpha )=3\alpha[/tex]
[tex]if\ x\ \geqslant 3[/tex]
[tex]f(x)=2x[/tex]
[tex]Sin\ you\ get\ the[/tex]
[tex]yoiclure\ on\ the[/tex]
[tex]right.[/tex]
I hope this helps you
:)
The choice that matches the graph of the function as is defined to us is: Graph A.
What is a function?A function in math is a rule or expression that defines a relationship between one variable (the input or independent variable) and another variable (the output or dependent variable).
We are given a function f(x) as:
f(x)= 2x if x < 3 and 4 if x ≥ 3
This means that in the region (-∞,3) the graph of a function is a straight line that passes through the origin and has a open circle at x=3. and in the region [3,∞) the graph is a straight horizontal line i.e. y=4.
Hence, the graph of this function is: Graph A.
Learn more about functions, click;
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The angle turns through 1/5 of the circle.What is the measure of the angle?
Classify each of the following angles as acute, obtuse,right,straight, or reflex
Answer:
The first one is obtuse because it is larger than 90 degrees.
The second one is reflex shown below:
Step-by-step explanation:
Write an equation using x when the sum of a number and 8 is multiplied by 3and the answer is 6
Answer:
3(x + 8) = 6
Step-by-step explanation:
let the number be x then the sum of x and 8 is x + 8 and multiplied by 3 is
3(x + 8) = 6 ( divide both sides by 3 )
x + 8 = 2 ( subtract 8 from both sides )
x = - 6
the number x is - 6
What is the value of n when 2/3 of n equals 42?
what value of x makes the equation true?
Answer:
[B] - 1/3
Step-by-step explanation:
Given:
-8x-5(1-x)=6x-2
Solve:
Expand : -8x - 5(1-x) : -3x -5
-3x - 5 = 6x -2
Add 5 to both sides (Balance)
-3x-5+5=6x-2+5
Simplify
-3x = 6x + 3
subtract 6x to both sides (Balance)
-3x - 6x = 6x +3 -6x
Simplify
-9x = 3
Divide both sides by -9 (Balance)
-9x/-9=3/-9
Simplify
x = -1/3
[RevyBreeze]
Help!!!
Find the sum of the mean, median, and mode for this data 86,72,16,42,16,55,16,12,91,55
Answer:
mean=86+72+16+42+16+55+16+12+91+55/2
mean=230.5
mode=16-unimodal
median the middle value but in the first arrange in ascending order.
12,16,42,55,72,86 and 91
median=55
hope it helps!
Layla makes necklaces to sell online. she spends $46 on supplies at the first store and then $30 at the second store. she press to make a necklaces and sell each necklace at a markup of 75%. how much will she charge for each necklace?
Please answer. I need it to be right.
Answer:
75
- _____________
10x^4−27
Step-by-step explanation:
Answer:
Step-by-step explanation:
First we do all brcakets becuase we are following the law of BODMAS.
2×-5×3 = -10×3= -30
Now we do all powers and indices:
-5²= 25
10²= 100
3³ = 27
Now we do the top of the fraction:
25+100 = 125
Now we do the bottom bit of the fraction:
-30+27 = -3
Now we divide 125 by -3:
-41 2/3
-41.666.....
