Answer:
The correct option is;
C. Transformation
Step-by-step explanation:
In mathematics, transformation refers to the relocation of an object called the pre-image from initial position to another new location at which point the object will be known as the image whereby there is a one to one mapping from each point on the pre-image to the image
The types of transformation includes reflection, rotation, and translation which involve changes in position and dilation, which involves changes in the size of the pre-image.
Roberto is x years older than his only sister but 10 years ago he was twice her age. What are the current ages of the siblings?
Answer:
S = x + 10
R = 2x + 10
Step-by-step explanation:
If R is Roberto's age, and S is his sister's age, then:
R = S + x
R − 10 = 2 (S − 10)
Solve with substitution.
S + x − 10 = 2 (S − 10)
S + x − 10 = 2S − 20
S = x + 10
R = 2x + 10
P(x) =2x3 -11x2 -4x +1 g(x) =2x +1
Answer:
see explanation
Step-by-step explanation:
If (2x + 1) is a factor then x = - [tex]\frac{1}{2}[/tex] is a root and P(- [tex]\frac{1}{2}[/tex] ) = 0 ← Factor theorem
P(- [tex]\frac{1}{2}[/tex] )
= 2(- [tex]\frac{1}{2}[/tex] )³ - 11(- [tex]\frac{1}{2}[/tex] )² - 4(- [tex]\frac{1}{2}[/tex] ) + 1
= - [tex]\frac{1}{4}[/tex] - [tex]\frac{11}{4}[/tex] + 2 + 1
= - [tex]\frac{12}{4}[/tex] + 3
= - 3 + 3
= 0
Since P(- [tex]\frac{1}{2}[/tex] ) = 0 then g(x) is a factor of P(x)
At what rate per annum will N250 amount to N330 in 4 years.
Answer:
[tex] \boxed{ \bold{ \huge{ \boxed{ \sf{8 \: \% \: }}}}}[/tex]Step-by-step explanation:
Given,
Principal ( P ) = N 250
Time ( T ) = 4 years
Amount ( A ) =N 330
Rate ( R ) = ?
First, finding the Interest :
According to definition of Amount ,
Amount = Principal + Interest
plug the values
⇒[tex] \sf{330 = 250 + I}[/tex]
Move i to left hand side and change it's sign
⇒[tex] \sf{ - I = 250 - 330}[/tex]
Calculate
⇒[tex] \sf{ - I = - 80}[/tex]
Change the signs of the both equation
⇒[tex] \sf{I = 80 }[/tex]
Interest = 80
Finding the rate :
Simple Interest = [tex] \sf{ \frac{PTR}{100} }[/tex]
plug the values
⇒[tex] \sf{80 = \frac{250 \times 4 \times R}{100} }[/tex]
Multiply the numbers
⇒[tex] \sf{80 = \: \frac{1000 \: R}{100} }[/tex]
Apply cross product property
⇒[tex] \sf{1000R = 100 \times 80}[/tex]
Multiply the numbers
⇒[tex] \sf{1000R = 8000}[/tex]
Divide both sides of the equation by 1000
⇒[tex] \sf{ \frac{1000R}{1000} = \frac{8000}{1000} }[/tex]
Calculate
⇒[tex] \sf{R = 8 \: \% \: }[/tex]
Thus, Rate = 8 %
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Let's learn about Principal , Interest , Time , Rate and Amount :
Principal = The money which is borrowed or deposited is called principal.Interest = The additional amount of money which is paid by borrower to the lender is called interest.Time = The duration of time for which principal us deposited or borrowed is termed as time period.Rate = The condition under which the insterest is charged is called rate.Amount = The sum of principal and Interest is called an amount.Hope I helped!
Best regards!!
What is the answer to (6/7)/(12/21) = 4/x Algebra plz help
Answer:
(6/7)/(12/21) = 4/x
the first part of the expression :
when divide fraction: turn the sign from ÷ to × and flip the second fraction
(6/7)×(21/12)=4/x
126/84=4/x ( simplify the fraction 126/84)
GCF of 126 and 84 is 42 ( 126/48=3 and 84/42=2)
3/2=4/x ( cross multiplication ( butterfly)
1.5=4/x
1.5x=4
x=4/1.5=2.6666.......
What is the answer!!
Answer:
∠ G = 121°
Step-by-step explanation:
The sum of the 3 angles in a triangle = 180°
Sum the 3 given angles and equate to 180
x + 3x + 25 + x - 5 = 180 , that is
5x + 20 = 180 ( subtract 20 from both sides )
5x = 160 ( divide both sides by 5 )
x = 32
Thus
∠ G = 3x + 25 = 3(32) + 25 = 96 + 25 = 121°
Answer:
121
Step-by-step explanation:
Make the biggest possible number using the digits below only once 0 , 3 , 4
Answer:
12,157,665,459,057,000,000
Step-by-step explanation:
It seems like it would have to involve exponents. 3 to the 40th power would be 12,157,665,459,057,000,000.
Simplify
2x + 5x^3 + 3x - 4x^3
Answer:
x³ + 5x
Step-by-step explanation:
2x+5x3+3x−4x3
=2x+5x3+3x+−4x3
Combine Like Terms:
=2x+5x3+3x+−4x3
=(5x3+−4x3)+(2x+3x)
=x3+5x
Answer:
[tex]\large \boxed{x^3+5x}[/tex]
Step-by-step explanation:
[tex]2x + 5x^3 + 3x - 4x^3[/tex]
[tex]\sf Group \ like \ terms.[/tex]
[tex]5x^3 - 4x^3+2x+3x[/tex]
[tex]\sf Combine \ like \ terms.[/tex]
[tex]x^3+5x[/tex]
this is urgent...please help!
the brown family is ordering pizza. they are trying to decide whether to order a large pizza or a monster pizza. a monster pizza (m) has six fewer slices than twice the number of slices on a large pizza (l). the difference between the number of slices on a monster pizza and the number of slices on a large pizza is five slices. which system of equations below can be used to determine the number of slices on a large pizza and a monster pizza?
a) m - 2 l = 5
m - l = 6
b) 2m - l = 6
m - l = 5
c) 2m - l = -6
m - l = 5
d) m - 2 l = - 6
m - l = 5
Answer:
d) m - 2 l = - 6; m - l = 5
Step-by-step explanation:
Twice the number of slices on a large pizza is 2l. 6 fewer than that is 2l-6. This is the number on a monster pizza, so we have ...
m = 2l -6
Subtracting 2l from both sides gives the equation ...
m -2l = -6 . . . . . matches choice D
Given: D is the midpoint of AB; E is the midpoint of AC.
Prove: DE BC
y
Complete the missing parts of the paragraph proof.
Proof:
To prove that DE and BC are parallel, we need to show
that they have the same slope.
slope of DE = 12-11=_C-C
X2 - x1 a + b - b
A(2b, 2c)
D(b, c)
Ela + bc)
slope of BC =
B(0,0)
C(2a, 0)
Therefore, because
DE 1 BC.
Answer:
The lines DE and BC have the same slope, therefore the two lines, DE and BC, are parallel
Step-by-step explanation:
To prove that DE is parallel to BC, we have;
The slope, m of the lines DE and BC are found from the following equation;
[tex]Slope, \, m =\dfrac{y_{2}-y_{1}}{x_{2}-x_{1}}[/tex]
Where;
(x₁, y₁) and (x₂, y₂) = (b, c) and (a + b + c) for DE, we have;
[tex]Slope, \, m =\dfrac{c - c}{a + b-b} = 0[/tex]
Where we have (x₁, y₁) and (x₂, y₂) = (0, 0) and (2a, 0) for BC, we have;
[tex]Slope, \, m =\dfrac{0 - 0}{2a-0} = 0[/tex]
Therefore, because the lines DE and BC have the same slope, the two lines DE and BC are parallel.
Answer:
slope of DE = 0
slope Bc = 0
slopes are =
Step-by-step explanation:
19 x97 find the product using suitable properties
Answer:
19 x 97 = 1843
3/4a-1/6=2/3a+1/4? Please i need help!!!!
Answer: a=5
Step-by-step explanation:
1/12a=10/24
24a=120
a= 5
How would you write Twice the difference of 9 and a number.
Answer:
Hey there!
You would write that as 2(9-n), where n is the number.
Hope this helps :)
A line that contains the points (5, −3) and (7, 3) has a slope, m, that equals
Answer:
m = 3
Step-by-step explanation:
Calculate the slope m using the slope formula
m = [tex]\frac{y_{2}-y_{1} }{x_{2}-x_{1} }[/tex]
with (x₁, y₁ ) = (5, - 3) and (x₂, y₂ ) = (7, 3)
m = [tex]\frac{3+3}{7-5}[/tex] = [tex]\frac{6}{2}[/tex] = 3
can someone explain this please?
Answer:
Hey there!
Our equation can be: 2y+3=4y+2
Hope this helps :)
Answer:
2y+3=4y+2
I hope you got it..
5/14, 7/10, 5/6, 11/15, 19/2
Answer:
5/14 = 0.36
7/10 = 0.7
5/6 = 0.83
11/15 = 0.73
19/21 = 0.9
(round to the tenth)
so the answer is;
5/14, 7/10, 11/15, 5/6, 19/21
Step-by-step explanation:
Hope it helps!
A grocery store bought some mangoes at a rate of 5 for a dollar. They were separated into two stacks, one of which was sold at a rate of 3 for a dollar and the other at a rate of 6 for a dollar. What was the ratio of the number of mangoes in the two stacks if the store broke even after having sold all of its mangoes?
Answer:
The ratio of the number of mangoes in the $3 stack to those in the $6 stack is 1 : 2
Step-by-step explanation:
Let the number of mangoes bought by the grocery store be n. Also let the number of mango sold for $3 in one stack be x and the number of mango sold for $6 in the second stack be y.
Therefore:
x + y = z (1)
Also, the mangoes was sold at break even price, that is the cost of the mango and the price it was sold for was the same. Therefore:
Cost of buying = Price it was sold for
The cost of the mango = 5z and the price it was sold for = 3x + 6y
3x + 6y = 5z (2)
Substituting z = x + y in equation 1
3x + 6y = 5(x + y)
3x + 6y = 5x + 5y
6y - 5y = 5x - 3x
y = 2x
x / y = 1/ 2 = 1 : 2
The ratio of the number of mangoes in the $3 stack to those in the $6 stack is 1 : 2
what is the value of 600.79-40.0032+5.01 to the nearest Hundredths
Answer:
565.80
Step-by-step explanation:
600.79-40.0032+5.01 = 565.7968
565.7968 to the nearest Hundredths =
565.80
Answer:
565.80
Step-by-step explanation:
600.79 - 40.0032 + 5.01
600.79 - 40.0032 = 560.7868
560.7868 + 5.01 = 565.7968
565.7968 to the nearest hundredth = 565.80
Please answer this question now
Answer:
320 sq in
Step-by-step explanation:
4(1/2*8*16) + (8*8)
= 4(64) + (64)
= 5(64)
= 320
Find the degree of the monomial.
s8t
The degree is
Answer:
Step-by-step explanation:
the degree of 8^8t
16777216t : the degree of the mnonmial is 1, because the degree of the variable is 1
) Martha went to the store with $75.00. She bought 3 pairs of socks for $4.00 each, she bought 2 shirts for $20.00 each, and she bought a skirt for $21.00. How much money did she have left?
Answer:
She had $2.00 left.
Step-by-step explanation:
PEMDAS
$75 - [(3 x $4) + (2 x $20) + $21 ]
$75 - [ $12 + $40 + $21]
$75 - [ $52 + $21]
$75 - $73
$2
Find all the solutions to \[\frac{x+4}{x+5} = \frac{x-5}{2x}.\][tex]Find all the solutions to\[\frac{x+4}{x+5} = \frac{x-5}{2x}.\][/tex]
Answer:
x = -4 + 3 i or x = -4 - 3 i
Step-by-step explanation:
Solve for x:
(x + 4)/(x + 5) = (x - 5)/(2 x)
Hint: | Multiply both sides by a polynomial to clear fractions.
Cross multiply:
2 x (x + 4) = (x - 5) (x + 5)
Hint: | Write the quadratic polynomial on the left hand side in standard form.
Expand out terms of the left hand side:
2 x^2 + 8 x = (x - 5) (x + 5)
Hint: | Write the quadratic polynomial on the right hand side in standard form.
Expand out terms of the right hand side:
2 x^2 + 8 x = x^2 - 25
Hint: | Move everything to the left hand side.
Subtract x^2 - 25 from both sides:
x^2 + 8 x + 25 = 0
Hint: | Using the quadratic formula, solve for x.
x = (-8 ± sqrt(8^2 - 4×25))/2 = (-8 ± sqrt(64 - 100))/2 = (-8 ± sqrt(-36))/2:
x = (-8 + sqrt(-36))/2 or x = (-8 - sqrt(-36))/2
Hint: | Express sqrt(-36) in terms of i.
sqrt(-36) = sqrt(-1) sqrt(36) = i sqrt(36):
x = (-8 + i sqrt(36))/2 or x = (-8 - i sqrt(36))/2
Hint: | Simplify radicals.
sqrt(36) = sqrt(4×9) = sqrt(2^2×3^2) = 2×3 = 6:
x = (-8 + i×6)/2 or x = (-8 - i×6)/2
Hint: | Factor the greatest common divisor (gcd) of -8, 6 i and 2 from -8 + 6 i.
Factor 2 from -8 + 6 i giving -8 + 6 i:
x = 1/2-8 + 6 i or x = (-8 - 6 i)/2
Hint: | Cancel common terms in the numerator and denominator.
(-8 + 6 i)/2 = -4 + 3 i:
x = -4 + 3 i or x = (-8 - 6 i)/2
Hint: | Factor the greatest common divisor (gcd) of -8, -6 i and 2 from -8 - 6 i.
Factor 2 from -8 - 6 i giving -8 - 6 i:
x = -4 + 3 i or x = 1/2-8 - 6 i
Hint: | Cancel common terms in the numerator and denominator.
(-8 - 6 i)/2 = -4 - 3 i:
Answer: x = -4 + 3 i or x = -4 - 3 i
What are the answers to the following.
Answer:
Step-by-step explanation:
[tex]8-11 =-3\\\\b. -8+10 = 2\\\\c. 13+(-6) = 13-6 \\= 7\\\\d. 7-(-3)\\= 7+3\\=10\\\\e.-5-(-2)\\=-5+2\\=-3\\\\f. -15-(-25)\\=-15+25\\=10\\\\g. -3+(-6)-(-9)\\= -3-6+9\\=-9+0\\=0\\\\h.-20-(-9)-(-8)\\=-20+9+8\\-20+17\\=-3\\\\[/tex]
[tex]-2+3-(-4)+(-5)\\-2+3+4-5\\= 1-1\\=0\\\\\\b. 18-(-10)+(-19)-8\\=18+10-19-8\\28-27\\=1\\\\c. 65+(-72)-(-45)\\= 65-72+45\\=-7+45\\=38[/tex]
consider the polynomial 8x^3+2x^2-20x-5 factor
Answer:
(4x + 1)(2x² - 5)
Step-by-step explanation:
Given
8x³ + 2x² - 20x - 5 ( factor the first/second and third/fourth terms )
= 2x²(4x + 1) - 5(4x + 1) ← factor out (4x + 1) from each term
= (4x + 1)(2x² - 5)
Answer:
blank 1 is -20-5
blank 2 is 4x+1
blank 3 is -5
blank 4 is 2x^2-5
Step-by-step explanation:
how 45 degree angles does it take to make a full turn?
PLSSSSSSSSSSSSSSS HELP
Answer:
8 turns
Step-by-step explanation:
If we want to take a full turn, we'd turn around 360° since we'd be in the same position.
If we turn in intervals of 45°, we need to find how many times 45 goes into 360. To do this, we can divide.
[tex]360\div45=8[/tex]
Hope this helped!
Answer:
It will take 8 45 degree angles to make a full turn
Step-by-step explanation:
360 degrees is a full turn
360/45 =8
It will take 8 45 degree angles to make a full turn
Show by shading , the region in a Venn diagram represented by the set notations I)(AUB) NC ii) AU ( BNC)
See the diagram, and tell me if it's clear
The straight line PQ with a gradient -2 passing through point (-3, 10). Find the y-intercept of the straight line PQ . Please help me and explain it . Thank you so much
Answer:
y- intercept = 4
Step-by-step explanation:
The equation of a line in slope- intercept form is
y = mx + c ( m is the slope( gradient ) and c the y- intercept )
Here m = - 2 , thus
y = - 2x + c ← is the partial equation
To find c substitute (- 3, 10) into the partial equation
10 = 6 + c ⇒ c = 10 - 6 = 4
Thus y- intercept c = 4
The grades on the last art exam had a mean of 75%. Assume the population of grades on art exams is known to be distributed normally, with a standard deviation of 7%. Using the empirical rule, approximately what percent of students earn a score between 75% and 82%? 68% 16% 32% 34%
Find the z-score for both 75% and 82% then subtract them.
Z-score for 75%:
75 -75 /7 = 0-7 = 0
Using empirical rule, This translates to a percentile if 50%
Z-score for 82%
82-75 /7 = 7/7 = 1
Using empirical rule, this translates to 84.13%
Answer = 84.13-50 = 34.13% round to 34%
Answer:
34%
Step-by-step explanation:
Well 75+7=82 and one hop on the graph is 34%.
How do I even start this? And how to i order the equation to solve
[tex]f(g(h(x)))=f(g(\sqrt x))=f(\sqrt x-1)=\boxed{(\sqrt x-1)^4+4}[/tex]
This is because
[tex]h(x)=\sqrt x[/tex]
[tex]g(x)=x-1[/tex]
[tex]\implies g(h(x))=\sqrt x-1[/tex]
(that is, replace any instance of x in the definition of g with √x )
and
[tex]f(x)=x^4+4[/tex]
[tex]\implies f(\sqrt x-1)=(\sqrt x-1)^4+4[/tex]
(replace any x in f with √x - 1)
Also acceptable:
[tex](\sqrt x-1)^4+4=((\sqrt x)^4-4(\sqrt x)^3+6(\sqrt x)^2-4\sqrt x+1)+4[/tex]
[tex]=\boxed{x^2-4x\sqrt x+6x-4\sqrt x+5}[/tex]
(assuming x is not negative)
-\dfrac{1}{6} \times \left(-\dfrac{9}{7}\right)− 6 1 ×(− 7 9 )minus, start fraction, 1, divided by, 6, end fraction, times, left parenthesis, minus, start fraction, 9, divided by, 7, end fraction, right parenthesis
Answer:
[tex]\dfrac{3}{14}[/tex]
Step-by-step explanation:
The even number of minus signs means the product will be positive. A factor of 3 can be removed to simplify the product. As usual, the numerator of the product is the product of numerators, and the denominator of the product is the product of denominators.
[tex]-\dfrac{1}{6} \times \left(-\dfrac{9}{7}\right)=\dfrac{1\cdot 9}{6\cdot 7}=\dfrac{3\cdot 3}{3\cdot 14}=\boxed{\dfrac{3}{14}}[/tex]
Answer:
→ 3/4 ←
-1/6 × (-9/7)= 1·9/6·7 3·3/3·14 = 3/4
The line plot below displays the fraction of incoming calls answered before the second ring by a group of employees. What fraction of employees answered less than of their incoming calls before the second ring?
Answer:
1/6
Step-by-step explanation:
People who answered less than 1/2 were: 2 + 1 + 3 = 6 people.
There are a total of 36 people.
People who answered their calls before the second ring were only 6/36.
When we simplify the fraction, we get 1/6.
So, the answer is 1/6
