Answer:
Caleb's actual height is 48 inches
Step-by-step explanation:
Alison's height in the photograph= 4 cm
Caleb's height in the photograph= 3.2 cm
Alison's actual height= 60 in
Caleb's actual height=x in
60 in= 152.4 cm
Alison's height in photograph : Her actual height = Caleb's height in photograph : his actual height
4cm : 152.4cm = 3.2cm : xcm
4 / 152.4 = 3.2 / x
Cross product
4 * x = 152.4 * 3.2
4x = 487.68
Divide both sides by 4
x= 121.92 cm
121.92 cm = 48 in
Caleb's actual height is 48 in
I cant find whats wrong
What point would you have when (-7, 3) is reflected over the line y=x?
A. (3,-7)
B. (-3,7)
C. (7,-3)
D. (-7,3)
The point would you have when (-7, 3) is reflected over the line y=x is (7, -3).
The line y=x looks like an even, the diagonal line going through (0, 0) on a graph.
If you have (-7,3), you are in the first quadrant (in the upper left square of the graph).
What is the reflection?Reflection is the change in direction of a wavefront at an interface between two different media so that the wavefront returns to the medium from which it originated.
If you reflect it diagonally, the digits themselves would remain that same, but the value would flip (if it’s positive, it’ll become negative, if it’s negative, it’ll become positive).
So if we do that with (-7, 3), it becomes (7, -3).
The point would you have when (-7, 3) is reflected over the line y=x is (7, -3).
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What is 50 percent of 62? 0.31 3.1 31 310
Answer:
[tex]\Huge \boxed{\mathrm{31}}[/tex]
Step-by-step explanation:
50 percent of 62 is also one half of 62.
62 × [tex]\frac{1}{2}[/tex] = 31
Answer:
50 is 31% of 62.
Step-by-step explanation:
To solve this, we need to set up our problem like this, since percentages are written with %, and add up to 100%.
[tex]\frac{62}{x} =\frac{100}{50}[/tex]
Next, we flip the denominators with the numerators so that the x ends up on the top.
[tex]\frac{x}{62}=\frac{50}{100}[/tex]
Finally, we can see that 50/100 is 1/2, so to solve x/62, we have to divide 62 by 2 to get our answer.
62 ÷ 2 = 31
Our answer is 31%.
Dena bought 4 stuffed animals and 7 toy trains for $75. At the same prices, Nico bought 6 stuffed animals and 5 toy trains for $74. What is the price of a stuffed animal?
Answer:
$6.50
Step-by-step explanation:
Create a system of equations, where s represents the price of a stuffed animal and t represents the price of a toy train:
4s + 7t = 75
6s + 5t = 74
Solve by elimination by multiplying the top equation by 3 and the bottom equation by -2:
12s + 21t = 225
-12s - 10t = -148
11t = 77
t = 7
Plug 7 in as t to find s:
4s + 7t = 75
4s + 7(7) = 75
4s + 49 = 75
4s = 26
s = 6.5
= $6.50 for a stuffed animal
An amount of #550,000.00 was realised when a principal,x was saved 2% simple interest for 5 years. Find the value of x
Answer:
£500,000.00
Step-by-step explanation:
Principal = x
Saving rate = 2% PA simple
Time = 5 years
Final amount = £550,000
x*(1+ 2*5/100) = 550,000x*(1 + 0.1) = 550.0001.1x = 550,000x= 550,000/1.1x= 500,000Principal amount is £500,000
Answer:
[tex]\huge \boxed{{x=500,000}}[/tex]
Step-by-step explanation:
[tex]A=P(1+rt)[/tex]
[tex]A[/tex] = amount ⇒ 550000
[tex]P[/tex] = principal amount ⇒ x
[tex]r[/tex] = rate ⇒ 2%
[tex]t[/tex] = time ⇒ 5
[tex]\displaystyle 550000=x(1+\frac{2}{100} (5))[/tex]
Solve for the brackets.
[tex]\displaystyle 550000=\frac{11}{10}x[/tex]
Multiply both sides of the equation by [tex]\frac{10}{11}[/tex].
[tex]500000=x[/tex]
The value of x (principal amount) is 500,000.
what is a theory in science
A scientific theory is a validated explanation of some aspect of the natural world, based on multiple facts that have been frequently verified through research and experimentation. Fact theories are not "guesses" but reliable accounts of the real world.
The regular price for a T-shirt is $25 and the regular price for a pair of jeans is $75. If the T-shirt is sold at a 30% discount and the jeans are sold at a 10% discount, then
the total discount is
Answer:
$7.50
Step-by-step explanation:
Discount for t-shirt:
30/100 × $25 = 30/4 × 1
= 30/4
= $7.50
Discount for a pair of jeans:
10/100 × $75 = 10/4 × 3
= 30/4
= $7.50
Total discount:
= $7.50 + $7.50
= $15
Answer:
$7.50
Step-by-step explanation:
Discount for t-shirt:
30/100 × $25 = 30/4 × 1
= 30/4
= $7.50
Discount for a pair of jeans:
10/100 × $75 = 10/4 × 3
= 30/4
= $7.50
Total discount:
= $7.50 + $7.50
= $15
Twelve relatives always give gifts to one another. They have been doing it for eight years. How many exchanges have happened so far?
Answer:
1,056 gifts
Step-by-step explanation:
If twelve relatives give gifts to one another
This means each of the twelve relatives gets gifts from the other 11 relatives
=12 relatives * 11 gifts
= 132 gifts per year
They have been doing it for 8 years
Total gifts exchanged for 8 years= 132 gifts × 8 years
=1,056 gifts
Therefore, number of gifts exchanged for 8 years among 12 relatives is 1,056 gifts
Which image shows a reflection?
Answer:
A
Step-by-step explanation:
We can see that:
- Shape B has just been translated down (moving down a couple of squares)
- Shape C has been rotated 90° clockwise
1. Name the vertex of the angle
2. Name the sides of the angle.
3. Give three ways to name the angle.
4. Classify the angle.
Answer:
see explanation
Step-by-step explanation:
1. The angle is RST
2. The sides of the angle are SR and ST
3. The angle can be named as ∠ RST, ∠ TSR, ∠ S
Note in the 3 letter angle name the vertex of the angle is in the middle
4 The square at S indicates the angle is right, that is 90°
2.5=25% is it true or false
Answer:
[tex]\huge \boxed{\mathrm{false}}[/tex]
Step-by-step explanation:
25% is 25 out of 100.
[tex]\displaystyle \frac{25}{100} = 0.25[/tex]
[tex]2.5\neq 0.25[/tex]
The statement is false.
Which equations have one solution
Answer: C and F
Step-by-step explanation:
Remember that for two equations to have the same solutions they need to have the different slopes and different y intercepts or they could have the same y-intercepts but different slopes.
First we will simply each of the equations
A. [tex]\frac{1}{3} x + 3 = 26 + \frac{6}{18}x - 23[/tex] reduces to .[tex]\frac{1}{3}x + 3 = \frac{1}{3} x + 3[/tex] Since this have the same slopes and same y-intercept they have infinitely many solutions
B. x +3 + 3x = -3 +4x +6 reduces to 4x + 3 = 4x +3 This also have the same slopes and same y-intercepts which means it also have infinitely many solutions.
C. 2(1/5 + 1/4x) -2x = x -1 reduces to -3/2x +2/5 = x -1 This have different slopes and different y intercepts so they have One solution.
D . 4.3x + 2.5 -2.2x + 2.2 -2.1x = 0 reduces to 4.7 = 0 which means that this equation have no solution because 4.7 does not equal 0.
E. 2(4x +3) + 2x= 5(2x + 3) reduces to 10x + 6 = 10x + 15 which means this also have No solution because they have the same slopes but different y-intercepts.
F. 2/5x + 10 + 3/5x = 2x + 5 reduces to 1x + 10 = 2x + 5 This also have 1 solution because they have different slopes and different y intercepts.
Domain And Range. Need Help
Answer:
The first option.
Step-by-step explanation:
Domain is anything less than or equal to 2, but anything greater than or equal to -4
Range is anything greater than or equal to -4, but also less than or equal to 4
Find the component form of the vector that translates P(−3, 6)
to P′(−4, 8).
Answer:
Component form of the vector will be (-1, 2).
Step-by-step explanation:
When [tex]P(x_1, y_1)[/tex] translates to [tex]P'(x_2,y_2)[/tex] vector V formed after the translation will be,
V = [tex]<(x_2-x_1), (y_2-y_1)>[/tex]
If we draw this vector on a graph,
Vector will start from origin and the terminal point will be at [tex][(x_2-x_1), (y_2-y_1)][/tex]
Therefore, component form of the vector that translates from P(-3, 6) and P'(-4, 8) will be,
V = [tex]<(-4+3),(8-6)>[/tex]
V = [tex]<(-1,2)>[/tex]
Translation involves changing the position of a point
The vector that translates P to P' is [tex]\mathbf{ <-1,2>}[/tex]
The points are given as:
[tex]\mathbf{P = (-3,6)}[/tex]
[tex]\mathbf{P' = (-4,8)}[/tex]
The translation rule is calculated as:
[tex]\mathbf{(x,y) = P' - P}[/tex]
So, we have:
[tex]\mathbf{(x,y) = (-4,8) - (-3,6)}[/tex]
Combine
[tex]\mathbf{(x,y) = (-4+3,8-6)}[/tex]
[tex]\mathbf{(x,y) = (-1,2)}[/tex]
Express as vectors
[tex]\mathbf{<x,y> = <-1,2>}[/tex]
Hence, the vector that translates P to P' is [tex]\mathbf{ <-1,2>}[/tex]
Read more about translations at:
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What is the fractional equivalent of the repeating decimal 0.6 ?
Answer:
2/3
Step-by-step explanation:
We know that 0.6 is part of the 1/3 family.
1/3 would be equal to 0.333...
2/3 would be equal to 0.666...
3/3 would equal to 1
Alternatively, we know that anything out of 9 or 99 would be a repeating decimal. Simply take 6 and divide it by 9:
6/9 = 0.666
We can then simplify the fraction by dividing both top-bottom by 3:
6/9 = 2/3
ax+ by = c
solve for y
Answer:
[tex]\boxed{y=\frac{c}{b}-\frac{ax}{b}}[/tex]
Step-by-step explanation:
[tex]ax+by=c\\\\ax-ax+by=c-ax\\\\by=c-ax\\\\\frac{by=c-ax}{b}\\\\\boxed{y=\frac{c}{b}-\frac{ax}{b}}[/tex]
Hope this helps.
In Buffalo, New York, the temperature was -14°F in the morning. If the temperature dropped 7°F, what is the temperature now?
Answer:
-21 F
Step-by-step explanation:
it already was -14
then dropped 7
so it becomes
-14 - 7 = -12 f
write the sets of all possible factors and the sets of common factors of the pairs of numbers, then find their H.C.F. could you show step by step.
a. 8,12
b. 12,18
c. 16,24
d. 20,30
e. 24, 36
Answer:
a= 1,2,4 b= 1,2,3,6 c=1,2,4 d=1,2,5,10 e=1,2,3,4,6,12 H.C.F of all the pairs= 2
Step-by-step explanation:
Factors of:
a. 8=1,2,4,8
12=1,2,3,4,6,12.
common factor=1,2,4
b. 12=1,2,3,4,6,12
18=1,2,3,6,9,18
common factor=1,2,3,6
c. 16=1,2,4,16
24=1,2,3,4,6,8,12,24
common factor=1,2,4
d. 20=1,2,4,5,10,20
30=1,2,3,5,6,10,15,30
common factor=1,2,5,10
e. 24=1,2,3,4,6,8,12,24
36=1,2,3,4,6,9,12,18,36
common factor=1,2,3,4,6,12
HIGHEST COMMON FACTOR (H.C.F)=
The factor common to the whole pairs
which is 1 and 2
therefore 1 multiplied by 2 which is equal to 2
(and in Mathematics means multiplication)
Rain began failling at 2:18 . It rained for 1 hour and 36 minutes
Answer:
It stopped raining at 3:54
Step-by-step explanation:
The area of a square field is 841m.A rectangular field whose length is twice it's breath has its perimeter equal to square field.Find the area of square field
Given: The area of a square field is 841 sq.m
Since side of square = √Area
So, side of square field = [tex]\sqrt{841} =29[/tex]
Thus , side of square field = 29 m
Perimeter of square = 4( side) = 4(29) = 116 m
Let x be the breadth of rectangle then 2x be the length
Perimeter of rectangle = 2 (length+breadth) = 2(2x+x)= 2(3x)=6x
As per question, perimeter of rectangle= Perimeter of square
[tex]\Rightarrow\ 6x=116\\\\\Rightarrow\ x=\dfrac{116}{6}=\dfrac{58}{3}\ m[/tex]
Length : [tex]2x =2\dfrac{58}{3}=\dfrac{116}{3}\ m[/tex]
Area of rectangle = length x breadth
[tex]=\dfrac{116}{3}\times\dfrac{58}{3}=\dfrac{6728}{9}\\\\=747\dfrac{5}{9}\ m^2[/tex]
Area of rectangle = [tex]747\dfrac{5}{9}\ m^2[/tex]
Victoria searched her house for quarters. She started with 17 quarters and found 6 more quarters. She then goes to the arcade. If a game costs 2 quarters to play, how many games can she play and how many quarters are left over? Victoria can play times and there will be quarters left over.
Answer:
11 games
Step-by-step explanation:
17+6=23
23/2=11.5
Victoria can play 11 games. You'd usually round up, but in this case you can't play half a game so she'll play 11 games and have one quarter leftover.
Answer:
Victoria can play 11 games and have 1 quarter left over.
Step-by-step explanation:
17 given quarters +6 found quarters = 23 total quarters.
Since 23 is an odd number and we want to divide by 2, we have to go down to the last even number: 22. (This gives us the left over quarter)
22 quarters/2quarters per game = 11 games
There is a quadrilateral MNPQ in which side MN is congruent to side PQ and side NP is parallel to side MQ. The diagonal MP and the diagonal NQ intersect each other at point R. If MP = 6x − 5, QR = 3x + 1, and RN = 6, what is QN?
Answer: QN = 12
Step-by-step explanation: This quadrilateral is a paralelogram because its 2 opposite sides (NP and MQ) are parallel and the other 2 (MN and PQ) are congruent.
In paralelogram, diagonals bisect each other, which means QR = RN.
If QR = RN:
QR = 6
Then,
QN = QR + RN
QN = 6 + 6
QN = 12
The diagonal QN of quadrilateral MNPQ is QN = 12.
A shirt regularly priced at $36.00 was on sale for 25% off.
What was the sale price?
A. $9.00
B. $24.00
C. $27.00
D. $48.00
E. None correct
In the figure below,m /_ 1=58º. Find m/_2
Answer:
32°
Step-by-step explanation:
What we have to notice here is that m∠1 and m∠2 are complementary angles. This means that their angles add up to 90°.
Since we know the measure of m∠1, we can easily find the measure of m∠2 since both add up to 90.
m∠1 is 58, so:
[tex]58 + x = 90[/tex]
[tex]x = 90-58\\\\x=32[/tex]
Hope this helped!
function f(x) = 4x - 6 with a domain of (-3,5), identify the range
Answer:
(-18,5)
Step-by-step explanation:
Integrated math ll
I need help ASAP
Answer:
x = 12; m<ABC = 76
Step-by-step explanation:
The two angles whose measures are given form a linear pair. Therefore, they are supplementary angles, and their measures add up to 180 degrees.
8x - 20 + 116 - x = 180
7x + 96 = 180
7x = 84
x = 12
The angle with measure 8x - 20 and angle ABC are vertical angles. That means that their measures are equal.
m<ABC = 8x - 20 = 8(12) - 20 = 96 - 20 = 76
Answer: x = 12; m<ABC = 76
the SI unit of work is
Answer:
[tex] \boxed{ \bold{ \blue{ Joule}}}[/tex]Step-by-step explanation:
The SI unit of work is Joule.
Further more explanation:
▪️[tex] \blue{ \mathsf{ {What \: is \: Work \: ?}}}[/tex]
⇒Work done by a force acting on a body is defined as the product of force and displacement of the body in the direction of the force.
▪️[tex] \blue{ \bold{ \sf{What \: is \: SI \: unit \: ?}}}[/tex]
⇒The system of units which is agreed by the international convention of scientists held in France in 1960 is called SI unit.
▪️[tex] \blue{ \bold{ \sf{What \: do \: you \: mean \: by \: \: one \: joule \: work \: \: ?}}}[/tex]
⇒One joule is the amount of work done when one Newton force displaces a body through one metre in its own direction.
Hope I helped!
Best regards!
Follow the steps to solve for the variable in this two-step equation: 5x – 10 = 0
Which angle measures are correct? Select three options,
OmZX= 55°
OmZW = 125°
OmZW = 55°
mZZ = 125°
mZZ = 55°
PLEASE ANSWER FAST TIMED TEST
Answer:
m∠W = 125°
m∠X = 55°
m∠Z = 55°
Step-by-step explanation:
The explanation of angle measures is shown below:-
The shape which is parallelogram WXYZ. m∠Y = 125
A parallelogram represents the shape of quadrilateral in which both opposite sides and opposite angles are similar to each other. One parallelogram diagonals bisect each other. Consecutive angles are also supplementary to a parallelogram.
In WXYZ parallelogram is there
m∠Z + m∠Y = 180° is an angle of Consecutive in a parallelogram is supplementary
m ∠ Z + 125 = 180
m ∠ Z = 180 - 125
m ∠ Z = 55°
m ∠ W which equals to m∠Y where equal angles are Opposite
m∠W = 125°
m ∠ W + m ∠ X = 180°
which is the angle of Consecutive in a parallelogram called supplementary)
m ∠ X + 125 = 180
m ∠ X = 180 - 125
After solving the above equation we will get
m ∠ X = 55°
Find the area of the triangle.
16 in.
25 in.
Answer:
The area of the triangle with the given measurements is 200 in²
Step-by-step explanation:
For this problem, we will need to know the formula for finding the area of a triangle.
A = 1/2(bh)
Now, let's plug in these numbers so we can find the area.
A = 1/2(bh)
A = 1/2(16*25)
A = 1/2(400)
A = 200 in.²