Answer:
what number must be added to sum of two angles that the sum of three angles become 180.
Since sum of two angles is 100 , 80 must be added to 100 to make it equal to 180.
Step-by-step explanation:
Given
sum of measure of angle of triangle = 180°
given two angles 40°and 60°
Let the third angle be x°
thus
40°+ 60°+x° = 180°
100°+x° = 180°
x° = 180°- 100° = 80°
Thus, third angle measure 80°
She must have sum the first two known angles.
as given sum of three angles are 180
she must have assumed other angle to be x
then sum of all three angles must be 180
now to find third angle she subtracted sum of two known angles to find third angle.
other way can what number must be added to sum of two angles that the sum of three angles become 180.
Since sum of two angles is 100 , 80 must be added to 100 to make it equal to 180.
Isabelle bought some stationery. 1/3 of them were pencils. 5/8 of the remainder were erasers and the rest were rulers. The cost of the stationery is - a Pencil: $1.20, an eraser: $1 and a ruler: $0.50. She spent a total of 169.50 on all stationery. How much more did she spend on erasers than rulers.
Answer:
Isabelle spent $52.50 more on Erasers than rulers.
Step-by-step explanation:
Step 1
Find the quantity of each stationery bought in fraction
Let us represent the total fraction of what Isabelle bought as: x
1/3x = quantity of pencils bought
5/8 of the remainder = quantity of erasers bought
The remainder = x - 1/3x = 2/3x
5/8 of 2/3x = 5/8 × 2/3x = 5/12x
Hence, 5/12x = quantity of erasers bought
The rest is rulers
1 - (1/3 + 5/12)
1 - (4 + 5/12)
1 - 9/12
1 - 3/4
= 1/4x
Hence, 1/4 = quantity of rulers bought.
Step 2
We find the number of stationeries that Isabelle bought.
The cost of the stationery is
a Pencil: $1.20
an eraser: $1
a ruler: $0.50.
Total amount spent on stationery = 169.50
We have this equation
1.20 × 1/3x + 1 × 5/12x + 0.50 × 1/4x = 169.50
0.4x + 0.4166666667x + 0.125x =
169.50
0.9416666667x = 169.50
x = 169.50 /0.9416666667
x = 179.99999999
Approximately , the number of stationeries that Isabelle bought = x = 180
Step 3
Find the number and the amount spent on each stationery that Isabelle bought
a) i) Quantity of pencils bought = 1/3 x
x = 180
= 1/3 × 180
= 60 pencils
ii) Amount spent on pencils
If 1 pencil = $1.20
60 pencils =
60 × 1.20 = $72
b) i) Quantity of Erasers bought = 5/12x
x = 180
= 5/12 × 180
= 75 pencils
ii) Amount spent on Eraser
If 1 pencil = $1
75 pencils =
75 × 1 = $75
c) i) Quantity of rulers bought = 1/4 x
x = 180
= 1/4 × 180
= 45 pencils
ii) Amount spent on pencils
If 1 pencil = $0.50
45 pencils =
45 × 0.50 = $22.50
Step 4
We were asked to calculate how much more did she spend on erasers than rulers.
In step 3, the amount spent on Erasers = $75
the amount spent on ruler = $22.5
The difference in the amount spent = $75 - $22.5
= $52.5
Therefore, Isabelle spent $52.50 more on Erasers than rulers.
 Which correlation best describes the data below.
no correlation
weak positive
strong positive
strong negative
Answer:
strong positive
Step-by-step explanation:
both variables are moving in the same direction and is nearly a line
As x increases, y increases. This has a strong positive correlation
Solve each of the following exponential equations using common bases:
1.) 4^(3x+5)=8^(4x-3)
2.) 9^(2x+3)=〖(1/27)〗^(3x+1)
3.) 4^(x+6)∙8^(x-9)=64
Answer:
x=19/6, x=-9/13, x=33/4
Step-by-step explanation:
1) 2^(6x+10)=2^(12x-9), 6x+10=12x-9, x=19/6
2) 3^(4x+6)=3^(-9x-3), 4x+6=-9x-3, x=-9/13
3) 2^(x+6)*2^(3x-27)=2^(6), 4x-27=6, x=33/4
Given the lengths of two sides of a triangle, find the range for the length of the third side. (Range means find between which two numbers the length of the third side must fall.) Write an inequality. 13.2 and 6.7
Answer:
6.5<3rd side <19.9
Step-by-step explanation:
Extremely easy. All you have to do to get the first answer is minus 13.2-6.7 which is 6.5. Then add 13.2+6.7 to get 19.9 for the other answer. So the two answers would be 6.5 and 19.9.
Your welcome
Round to the nearest penny.
$11,579.9998
Answer:
Step-by-step explanation:
So basically, we would need to divide to the nearest 0.01 or hundredths place. All you would need to do is round from each place which would soon get you to 11,580.00. Simple right!!
I hope this helps!! Have a good rest of your day! :)
math now..!! Help..?
Answer:
2p + 12
2 (p = +6) + 12 = 20
Answer:
I think its 6
Step-by-step explanation:
because you have to add 9 and 3 together then you get 12 and you have to divide 2p with 12 and you'll get 6
3 X 5 power or 2
answers:
1. 30
2. 225
3. 45
4. 75
answer quickly .
a piece of paper is 5.5 x 10^-4 inches thick. If jennifer has 35 such pieces,how thick is the whole stack? Write your answer in standard form.
Answer:
T = 0.01925 m
Step-by-step explanation:
It is given that,
Thickness of a piece of a paper is [tex]5.5\times 10^{-4}\ m[/tex]
Total number of pieces are 35
We need to find the thickness of the whole stack. It is simply a case of unitary method.
For 35 pieces, thickness is :
[tex]T=35\times 5.5\times 10^{-4}\\\\T=0.01925\ m[/tex]
So, the thickness of the whole stack is 0.01925 metres.
factorise the quadratic equation x square + 2 x + 36
Answer:
Click on the link below to view the answer with the explanation in futher detail
Explanation:
Click the attached link to view the answer
CAN ANYBODY HELP ME OUT
Answer:
Correct option is
b. If two sides and one included angle are equal in triangles PQS and PRS, then their corresponding sides are also equal.
Step-by-step explanation:
Here, we are given the line RQ, which is divided in two equal parts by a line PS which is perpendicular to RQ.
The foot S of PS is on the line RQ.
First of all, let us do a construction here.
Join the point R with P and P with Q.
Please refer to the attached image.
Now, let us consider the triangles PQS and PRS:
Side QS = RS (as given)[tex]\angle PSR = \angle PSQ = 90^\circ[/tex]Side PS = PS (Common side in both the triangles)Now, Two sides and the angle included between the two triangles are equal.
So by SAS congruence we can say that [tex]\triangle PRS \cong \triangle PQS[/tex]
Therefore, the corresponding sides will also be equal.
RP = QP
RP is the distance between R and P.
QP is the distance between Q and P.
Hence, to prove that P is equidistant from R and Q, we have proved that:
b. If two sides and one included angle are equal in triangles PQS and PRS, then their corresponding sides are also equal.
35. What is the point-slope form of the
equation for the line with a slope of
-2 that passes through (1,4)?
A. y + 1 = -2(x + 4)
B. y - 1 = -2(x - 4)
C. y + 4 = -2(x + 1)
D. y - 4 = -2(x - 1)
Answer:
D) y - 4 = -2 ( x - 1 )
Step-by-step explanation:
Point-slope form is y - y₁ = m ( x - x₁ )
so you just plug in your points, hope this helped
2^4=(a-b) rewrite as a logarithmic equation
Answer:
log 2 (a−b)=4Step-by-step explanation:
Factorise : a^2+4a-60 Step by Step
Answer:
Step-by-step explanation:
Sum = 4
Product = -60
Factors = 10 , -6
a² + 4a - 60 = a² + 10a - 6a + (-6) * 10
=a(a + 10) - 6(a +10)
= (a +10) (a -6 )
Sentense 2: what is the answer?
which one represents translation
Answer:
The third one
Step-by-step explanation:
Translation is when it moves
–14=–(-2x+2)8)51=7(-1+2v)+2
Answer:
x = -6; v = 4.
Step-by-step explanation:
–14 = –(-2x + 2)
-14 = 2x - 2
2x - 2 = -14
2x = -12
x = -6.
51 = 7(-1 + 2v) + 2
51 = -7 + 14v + 2
51 = 14v - 5
14v = 56
v = 4.
Hope this helps!
30 times the square of a nonzero number is equal to eight times the number what is the number
Answer: 4/15
Step-by-step explanation:
Answer:
[tex]\frac{4}{15}[/tex]
Step-by-step explanation:
Number sentence: [tex]30x^{2}[/tex] = [tex]8x[/tex]
You can start by applying algebra to the left side of the equation by dividing each side by x. This should be how it looks now: 30x = 8
Now divide each side by 30 to keep reducing it: [tex]x = \frac{8}{30}[/tex]
Now that we have [tex]\frac{8}{30}[/tex], we can reduce that by dividing the top and bottom by 2:
[tex]\frac{8}{30} = \frac{4}{15}[/tex].
Therefore, the number is [tex]\frac{4}{15}[/tex].
Line A is represented by the following equation: X + y = 2
What is most likely the equation for line B so the set of equations has no solution?
Answer:
x+y=3
Step-by-step explanation:
For an equation to have no solution, their slope needs to be same and y intercept needs to be different,
so in this case where x+y=2
doing simply, x+y=3 makes a set of equation which has no solution, you can take any real value which is not 2
Which of the following functions has a vertical asymptote at x = 2, a horizontal
asymptote at f(x) = 1, and a root at x = -1?
A.f(x) = 2 + 1
B.f(x) = x 2 + 1
c.f(x) = x 2 - 1
D.f(x) == +1
Answer:
First, an asymptote means that the function "tends to go" to a value, bt actually never reaches it.
The functions here are:
A.f(x) = 2 + 1
B.f(x) = x^2 + 1
c.f(x) = x^2 - 1
D.f(x) == +1
The functions are really poorly written, but i will try to answer this.
first:
"a root at x = -1"
Means that f(-1) = 0,
The only function that is zero when x = -1, is the option c.
f(-1) = (-1)^2 - 1 = 1 - 1 = 0.
Now, if we want to have a vertical asymptote at x = 2, then we should have a function like:
[tex]f(x) = \frac{something}{x - 2}[/tex]
So we want to have a quotient, where the denominator is equal to zero when x = 2, this will lead to a vertical asymptote.
I can not see this in the options provided, so i guess that the functions are just not well written.
For a horizontal asymptote, we have something like:
[tex]f(x) = \frac{something}{x} + 1[/tex]
So as x starts to grow, the first term in the function will start to decrease, until it becomes really close to zero (but is never equal to zero) so in that case we have an horizontal asymptote to f(x) = 1.
Solve for X. Geometry
Answer: " x = 10 " .
Step-by-step explanation:
Note the top "line segment" ; and the bottom "line"; have equal measurements:
The length of the top line segment is:
" (2x − 8) + 5 ."
The length of the bottom line is: " (x + 7) " ;
__________
To solve for "x" ;
___________
(2x − 8) + 5 = (x + 7) ;
Rewrite as:
2x − 8 + 5 = x + 7 ;
Note: −8 + 5 = -3 ;
_______________
Rewrite the equation as:
2x − 3 = x + 7 ;
We can subtract "x" from each side of the equation;
and add "3" to each side of the equation:
2x − 3 − x + 3 = x + 7 − x + 3 ;
_______________
to get:
_______________
x = 10 .
_______________
Let us check our answer
(2x − 8) + 5 =? (x + 7) ;
________
(2*10 − 8) + 5 =? (10 + 7) ? ;
(20 − 8) + 5 =? 17 ?
12 + 5 =? 17 ? Yes!
_______________
Best wishes in your academic pursuits!
_______________
What is the value of x?
Answer:
The triangles are similar, therefore the ratio of 2:1 is constant for all sides as shown in 20:10.
Therefore, x is 14.
Evaluate 10 + 8 ÷ 2 − 4
Step-by-step explanation:
we will solve this question according to BODMAS rule...
B for bracket
O for of
D for division
M for multiplication
A for addition
S for Subtraction
10+4-4
14-4
10 Answer..
Answer:
10
Step-by-step explanation:
Using order of operations as stated in PEMDAS , that is
division is performed before addition/ subtraction , then
10 + 8 ÷ 2 - 4
= 10 + 4 - 4
= 14 - 4
= 10
Revolve into factor : 2x square + 5xy + 2y square
Answer:
(2x + y) ( x + 2y)
Step-by-step explanation:
A man has two sons, one twice as old as the other. The man is four times as old as the older boy. In three years he will be five times as old as the younger boy. Find their present ages.
Answer:
Man's present age: 32 years
Older son's present age: 8 years
Younger sons present age: 4 years
Step-by-step explanation:
Let their present ages be represented by:
Man = a
Older boy = b
Younger boy = c
A man has two sons, one twice as old as the other:
b = 2 × c
b = 2c......... Equation 1
The man is four times as old as the older boy:
a = 4 × b
a = 4b.......Equation 2
In three years he will be five times as old as the younger boy:
a + 3 = 5 (c + 3)
a + 3 = 5c + 15........Equation 3
Since b = 2c and a = 4b
Subtitute 2c for b in Equation 2
a = 4b
a = 4 × 2c
a = 8c
Subtitute 8c for a in Equation 3
a + 3 = 5c........Equation 3
8c + 3 = 5c + 15
Collect like terms
8c - 5c = 15 - 3
3c = 12
c = 4
Therefore since c, represents the present age of the younger son, the younger son is 4 years old
b = 2c
b = 2 × 4
b = 8
Since b is the present age of the older son, the older son is 8 years old
a = 4b
b = 8
a = 4 × 8
a = 32
Since a is the present age of the man, the man is 32 years old
Therefore,
Man's present age: 32 years
Older son's present age: 8 years
Younger sons present age: 4 years
Please Help!!! What is 2x = 40?
Answer:
Friend your answer is 20
Step-by-step explanation:
You divide 40 by the co-efficient of 2=20
[tex]\boxed{x = 20}[/tex]
There is only one step to this equation. We use inverse operations to isolate the x by dividing 2 on both sides; because 2 is being multiplied by x, and the inverse operation for multiplication is division.
2x/2 = x
40/2 = 20
The equation now looks like:
x = 20
This is your answer.
Help please and explain
Answer:
30 ft
Step-by-step explanation:
We can use ratios
3 6
------ = ------------
15 x
Using cross products
3x = 6*15
Divide each side by 3
3x/3 = 6*15/3
x = 30
Answer:
30 ft
Step-by-step explanation:
6/3 = x/15
2 = x/15
2×15 = x
30 = x
2.6767.......
How do I write 2.67 w/ repeating 67 as a simplified fraction,...
Please show work (or provide explination)
Answer:
[tex]\displaystyle \frac{265}{99}[/tex]
Step-by-step explanation:
Hi there!
Let [tex]x[/tex] be equal to the fraction form of the decimal.
[tex]x=2.\overline{67}[/tex]
Multiply both sides by 100:
[tex]100x=267.\overline{67}[/tex]
The reason we multiply both sides by 100 is that 2.6767... has two repeating decimals, 6 and 7, and 100 has two zeros.
Now, we have these two equations:
[tex]100x=267.\overline{67}[/tex]
[tex]x=2.\overline{67}[/tex]
Subtract [tex]x=2.\overline{67}[/tex] from [tex]100x=267.\overline{67}[/tex]:
[tex]100x=267.\overline{67}\\- x=2.\overline{67}\\\rule{70}{0.5}\\99x=265[/tex]
Isolate [tex]x[/tex] by dividing both sides by 99:
[tex]\displaystyle x=\frac{265}{99}[/tex]
I hope this helps!
Please help explanation if possible
Answer:
17.6
Step-by-step explanation:
Answer:
80 pennies ; 160 nickels
Step-by-step explanation:
Given the 2 equations
0.01p + 0.05n = 8.80 → (1)
n = 2p → (2)
Substitute n = 2p into (1)
0.01p + 0.05(2p) = 8.80
0.01p + 0.1p = 8.80
0.11p = 8.80 ( divide both sides by 0.11 )
p = 80
Substitute p = 80 into (2)
n = 2 × 80 = 160
There are 80 pennies ; 160 nickels
On a plane trip, baggage over 40 pounds is charged at the rate per pound of 1% of the one-way fare. The charge for a bag weighing 52 pounds on a trip where the one-way fare is $98 is:
Answer:
$11.76 is the charge for bag.
Step-by-step explanation:
Given:
One way fare = $98
Weight of bag = 52 pounds
Rate per pound Charges on baggage over 40 pounds = 1% of the one-way fare
To find:
Charge for bag = ?
Solution:
Pounds more than 40 pounds = Weight of baggage - 40 pounds
[tex]\Rightarrow 52-40 = 12\ pounds[/tex]
Charges on extra baggage = 1% of one-way fare multiplied by pounds more than 40.
Here one way fare is $98.
So, charges on extra baggage will be:
[tex]1\%\ of\ 98 \times (52-40) \\\Rightarrow 1\%\ of\ 98\times (12)\\\Rightarrow \dfrac{1}{100}\ of\ (98 \times 12)\\\Rightarrow \dfrac{1}{100}\times (98 \times 12)\\\Rightarrow \bold{\$11.76}[/tex]
So, the charge for the baggage is $11.76.
Sunita bought a 10 kg box of grapes from the market. She gave 3 1/2 kg of her grapes to her friend Reena and 2 1/4 kg to Anita. How many kilograms of grapes were left with her?
Answer:
17/4 kg
Step-by-step explanation:
Sunita has = 10kg of grapes
Quantity given out :
To Reena =3 1/2
7/2 kg
To Anita =2 1/4
9/4 kg
Total quantity of grape given out
7/2+9/4
(14+9)/4
23/4
Quantity left after giving out = Total quantity of grape before giving out minus quantity of grape given out
10/1 - 23/4
40-23)/4
= 17/4 or 4 1/4
Hence, she has 17/4 kg of grape left with her