The distributive property of multiplication over addition for rational numbers is (a) -3/4 × {2/3 + (-5/6)} = [-3/4 × 2/3] + [-3/4 × (-5/6)]
Complete questionWhich of the following is an example of distributive property of multiplication over addition for rational numbers
(a) -3/4 × {2/3 + (-5/6)} = [-3/4 × 2/3] + [-3/4 × (-5/6)]
(b) -3/4 × {2/3 + (-5/6)} = [3/4 × 2/3] - (-5/6)
(c) -3/4 × {2/3 + (-5/6)} = 2/3 + (-3/4) × -5/6
(d) -3/4 × {2/3 + (-5/6)} = {2/3 + (-5/6)} - 3/4
How to determine the correct distributive property?The distributive property of multiplication states that:
a * (b + c) = (a * b) + (a * c)
From the given question, we have:
-3/4 × {2/3 + (-5/6)}
This means that:
a = -3/4
b = 2/3
c = -5/6
Recall that a * (b + c) = (a * b) + (a * c)
So, we have:
-3/4 × {2/3 + (-5/6)} = [-3/4 × 2/3] + [-3/4 × (-5/6)]
Hence, the distributive property of multiplication over addition for rational numbers is (a) -3/4 × {2/3 + (-5/6)} = [-3/4 × 2/3] + [-3/4 × (-5/6)]
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Julie invests money in an account that pays compound intrestof 5% per annum after 3 years julie has 2778.30 how much did julie initially invest
Answer:
[tex]\huge\boxed{2400}[/tex]
Useful Information:
The formula for compound interest is: [tex]initial.amount*interest.rate^{no.years}[/tex]
Step-by-step explanation:
To work this out, you would first have to convert the percentage into a decimal. You can do this by dividing the percentage of 5% by 100, which gives you 0.05. This is because percentages are out of 100.
The next step is to add 1 to 0.05, this gives you 1.05. This is because you are working out the percentage increase.
The next step is to substitute the values into the formula. This gives you[tex]initial.amount*1.05^{3}=2778.30[/tex]
To work out the initial value, you would divide the final amount of 2778.30 by [tex]1.05^3[/tex], which gives you 2400. This is because you are rearranging the formula to find the initial investment.
1) Divide 5 by 100.
[tex]\frac{5}{100}=0.05[/tex]
2) Add 1 to 0.05.
[tex]1+0.05=1.05[/tex]
3) Substitute the values into the formula.
[tex]initial.amount*1.05^{3}=2778.30[/tex]
4) Divide 2778.30 by [tex]1.05^3[/tex].
[tex]\frac{2778.30}{1.05^3}=2400[/tex]
A shoe making company makes 256 pairs of boots in a day how many pairs of boots do they make in 260 days
Answer:
66560 pairs
Step-by-step explanation:
let the number of pairs of boots the company makes in 260 days = X
1day -----------------256pairs
260days-------------X
cross multiplying
1×X = 260×256
X= 66560
therefore, in 260days, he makes 66560 pairs
I need this answer . I would be happy if I got it .
Answer:
15cm
Step-by-step explanation:
PC = 15
BR = 15
.
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HELP ASAP/NOW....NO JOKES OR LINKS!!!!!!
what is the vale of the expression -2x^2-4x+10 when x= -3
A. -20
B. 16
C. 40
D. 4
Answer:
D. 4
Step-by-step explanation:
Given expression:
[tex]-2x^2-4x+10[/tex]
To find the value of the expression when x = -3, substitute x = -3 into the expression:
[tex]\implies -2(-3)^2-(-3)x+10[/tex]
Apply exponent rule [tex](-a)^2=a^2[/tex]:
[tex]\implies -2(3^2)-4(-3)+10[/tex]
[tex]\implies -2(9)-4(-3)+10[/tex]
[tex]\implies -18-4(-3)+10[/tex]
Apply rule [tex]-(-a)=a[/tex] :
[tex]\implies -18+(4)(3)+10[/tex]
[tex]\implies -18+12+10[/tex]
Add/subtract from left to right:
[tex]\implies -6+10[/tex]
[tex]\implies 4[/tex]
Let's find
-2x²-4x+10-2(-3)²-4(-3)+10-2(9)+12+10-18+224Paolo and Monika are both travelling by train.
Paolo's train travels 70 km in 35 minutes.
Monika's train travels 684 km.
It leaves at 16:15 and arrives at 20:45.
Work out the difference, in km/h, between the average speed of their trains.
Answer:
32 km/hr
Step-by-step explanation:
Firstly, you need to find the speed of both trains in km/hr.
Paolo's train= (70km x 60hr)/35= 120 km/hr
Monika's train= 684km/4.5hr= 152 km/hr
Then find the difference in speed:
152-120=32 km/hr
Identify the equation with an x-intercept of 3 and a y-intercept of -2.
The equation of line is 2x - 3y = 6.
What is intercept?The x-intercept is the point where a line crosses the x-axis, and the y-intercept is the point where a line crosses the y-axis.
The x-intercept is 3 and the y-intercept is -2.
So, the line passes through the points (3, 0) and (0, -2)
Now, slope of line is
m= -2-0/ 0-3 = 2/3
Equation of line is
y = 2/3 x - 2
y = 2x-6 /3
3y= 2x -6
2x - 3y = 6
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What percent of patients with type-B blood are male? Round your answer to the nearest tenth of a percent.
Answer:
54%
Step-by-step explanation:
To find the probability for a male patient to have B blood, find the number of male patients who do have B blood and divide it by the number of patients with type B.
The number of male and B blood is 99.
The number of patients with B blood is 183.
The probability is 99/183 = 0.54.
The percent is found by multiplying by 100.
0.54*100 = 54%
simplify
5cat + 3act - 6tac
Answer:
the correct answer is 2 act
Step-by-step explanation:
there is same base (act)
then 5+3=8
and 8-6 = 2act
If t = 0 in 1980, find the value for t in 1990
The value of t is 6.65
What is exponential function?An exponential function is a mathematical function of the following form: f ( x ) = a^x. where x is a variable, and a is a constant called the base of the function.
Given:
A= 210 million
P= A e^(kt)
225 = 210 * e ^ (0.0069t)
225/210= e ^ (0.0069t)
1.07 = e ^ (0.0069t)
Taking log on both side
log 1.047 = 0.0069 t log e
[tex]\frac{0.0069t\ln \left(e\right)}{0.0069\ln \left(e\right)}=\frac{\ln \left(1.047\right)}{0.0069\ln \left(e\right)}[/tex]
t= log ( 1.047) / 0.0069
t= 6.65
Hence, value of t is 6.65.
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Answer:
Step-by-step explanation:
The dimensions of a rectangles are 8cm and 12cm. What is the ratio of its length to its perimeter?
Answer:
Dimensions = 8 CM and 12 CM
length = 12 CM
width = 8 cm
perimeter = 2 ( length + width)
= 2( 12 + 8)
= 2 ( 20)
= 40 CM
ratio = 12/40
= 6/20
= 3/10
= 3 : 10Someone help me with 4 pleaseeeeee
Answer:
C
Step-by-step explanation:
Use the equation [tex]a^2 + b^2 = c^2[/tex]
Input the numbers----> [tex](2865)^2 +(4550)^2=c^2[/tex]
Simplify ----> [tex]28910725=c^2[/tex]
Find the square root------->[tex]5376.9=c[/tex]
good afternoon can someone please helppp :))))
Triangle XYZ is dilated by a scale factor of 1/4 to form triangle X'Y'Z'. Side YZ measures 18. What is the measure of side Y'Z'?
(Round your answer to the nearest tenth)
If with 150 grams of ground meat a tortilla is prepared to make a hamburger. How many tortillas can I make with one and a half kilograms of ground meat?
Answer:
You can make 10 tortillas with one and a half kilograms of ground meat
Step-by-step explanation:
one and a half kilograms to grams
1.5kg x 1000 = 1500g
150 grams prepared to make 1 hamburger
than, 150 x h = 1500
h = 1500 / 150
h = 10
Answer:
10 tortillas
Step-by-step explanation:
First convert kilograms to grams:
1 kg = 1000 g
⇒ 1.5 kg = 1500 g
Let x = number of tortillas made with 1500 g of meat
Set up a ratio of tortillas and meat and solve for x:
⇒ 1 tortilla : x tortillas = 150 g meat : 1500 g meat
[tex]\sf \implies \dfrac{1}{x}=\dfrac{150}{1500}[/tex]
[tex]\sf \implies 1 \cdot 1500= 150 \cdot x[/tex]
[tex]\sf \implies 1500=150x[/tex]
[tex]\implies \sf x=\dfrac{1500}{150}[/tex]
[tex]\implies \sf x=10[/tex]
Therefore, 10 tortillas can be made with 1.5 kg of ground meat.
-19+[27-(14+(5-2)×4÷2))]
simplify
Answer:
-12
Step-by-step explanation:
One of the solutions to x² - 2x - 15 = 0 is x = -3. What is the other solution?
O x=-5
O x=-1
O x = 1
O x = 5
Answer:
x= 5
Step-by-step explanation:
factorised the equation is (x-5) (x+3)
x=5 x=-3
Aneesha travels at a rate of 50 miles per hour. Morris is traveling 3 feet per second less than Aneesha. Which is the best estimate of the speed Morris is traveling?
1 mile = 5,280 feet
45 miles per hour
46 miles per hour
47 miles per hour
48 miles per hour
Answer:
48 miles per hour I hope I helped you have a nice day
Solve using a proportion.
A carpet store charges $150 to install 12 square yards of carpet. How much should it cost to
install 24 square yards?
A. $250
B. $300
C. $3,600
D. $192
A square garden has a side length of 5 ft. What is the area of the garden?
O 5ft²
O 10ft²
O 20ft²
O 25 ft²
formula is lsquare so answer is 25ft
find the average rate of change
Answer:
[tex]\dfrac{26}{3}[/tex]
Step-by-step explanation:
The average rate of change of function f(x) over the interval a ≤ x ≤ b is given by:
[tex]\dfrac{f(b)-f(a)}{b-a}[/tex]
Given function: [tex]f(x)=3^{x-1}+2[/tex]
Given interval: 1 ≤ x ≤ 4
Therefore, a = 1 and b = 4
Therefore, find the value of the given function when x = 1 and x = 4:
[tex]\begin{aligned}\implies f(1) & =3^{1-1}+2\\ & = 3^0+2\\ & = 1+2\\ & = 3 \end{aligned}[/tex]
[tex]\begin{aligned} \implies f(4) & = 3^{4-1}+2 \\ & = 3^3+2\\ & = 27+2\\ & = 29 \end{aligned}[/tex]
Substitute the found values into the formula:
[tex]\begin{aligned}\implies \dfrac{f(b)-f(a)}{b-a} & =\dfrac{f(4)-f(1)}{4-1}\\\\ & =\dfrac{29-3}{4-1}\\\\ & = \dfrac{26}{3} \end{aligned}[/tex]
. All the students in SS3 of a named school take either Mathematics (M), or Physics (P) or Chemistry (C). 40 take Mathematics, 42 take physics, 38 take Chemistry, 20 take Mathematics and Physics, 28 take Physics and Chemistry while 25 take mathematics and chemistry.
How many take
(a) All the three subject:
(b) Mathematics, but neither Physics nor Chemistry
(c) Physics, but neither Mathematics nor Chemistry
Answer:
(a) = 13
(b) = 8
(c) = 5
Step-by-step explanation:
Addition theorems on sets are
Theorem 1 :
n(AuB) = n(A) + n(B) - n(AnB)
Theorem 2 :
n(AuBuC) : = n(A) + n(B) + n(C) - n(AnB) - n(BnC) - n(AnC) + n(AnBnC)
Total number of students in the school is not given
so let there are 60 students in the school
using theorem 2
n(AuBuC) : = n(A) + n(B) + n(C) - n(AnB) - n(BnC) - n(AnC) + n(AnBnC)
let n(A) = Mathematics, n(B) =Physics and n(C) = Chemistry
so putting values,
60 = 40 + 42 + 38 - 20 - 28 - 25 + n(AnBnC)
60 +73 -120 = n(AnBnC)
13 = n(AnBnC)
therefore, there are total 13 students who take all three subjects
Number of students who had taken only Mathematics =
n(A) - n(AnB) - n(AnC) + n(AnBnC)
40 - 20 - 25 + 13
53 - 45 = 8 students
Number of students who had taken only Physics =
n(B) - n(BnA) - n(BnC) + n(AnBnC)
42 - 20 - 28 + 13
53 - 48 = 5 students
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Analyze the diagram below and complete the instructions that follow.
/
Find the value of x.
A.
4
B.
5
C.
6
D.
9
Please select the best answer from the choices provided
A
B
C
D
The value of x will be 4 , Option A is the answer.
What is a Right Angled Triangle ?A triangle that has one angle as 90 degree is called a Right angled Triangle.
In a right angled triangle
the length of the sides can be determined using Pythagoras Theorem
The length of the side is given in the image attached as
x-2 , x , √20
Hypotenuse ² = Perpendicular² + Base²
(√20)² = x² + (x-2)²
20 = x² + x² +4 -4x
2x²-4x -16 = 0
x² -2x -8 = 0
x² - 4x +2x -8 = 0
x (x-4) +2(x-4) = 0
(x+2)(x-4) = 0
x = -2 , 4
The value of x will be 4 .
Therefore Option A is the answer.
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How many sulotions does this system have? 6x-y=-1 6x+y=-1
Answer:
6/6
Step-by-step explanation:
6/6 not equal -1/1 so these lines intersect each other at only one point hence these have only one solution.
Answer:
I can give you the answer if you can answer a question
Step-by-step explanation:
Find the highest common factor [HCF] of 10 and 17
Answer
Step by step explanation
7. Ms. Vickory assigned the problem: 8/9-4/6. Three of her students' responses are below. Who completed the problem correctly? What common mistakes did the other two students make?
The three students
Sue- 8/9-4/6=4/3 or 1 1/3
Jim- 8/6 - 4/6 = 48/54 - 36/54= 12/54 or 2/9
Bob- 8/9- 4/6 = 8/54-4/54= 4/54 = 2/27
Answer:
Jim: 2/9
Step-by-step explanation:
8/9-4/6
48/54-36/54 [Convert each fraction to a common denominator: 54
Multiply (8/9)*(6/6)=48/54; Multiply (4/6)*(9/9) = 36/54]
48/54-36/54 = 12/54
12/54 can be reduced to 2/9
Jim also has 2/9
Sue- 8/9-4/6=4/3 or 1 1/3: Sue subtracted both the numerator and denominator. This is not correct.
Jim- 8/6 - 4/6 = 48/54 - 36/54= 12/54 or 2/9: Good Job Jim
Bob- 8/9- 4/6 = 8/54-4/54= 4/54 = 2/27: Bob converted both denominators to 54, but did not multiply the numerators by the same numbers. Bad Bob.
Could use help asap please
Observe the diagram below with indexes on the shapes.
The transformations are:
Shape I is given a 90° clockwise rotation about the origin and then a reflection across the x-axis.Kyle claimed that the given quadrilaterals are similar because the ratio of their corresponding sides is equal. Is Kyle's claim Incorrect or correct? In two or more complete sentences, Justify your answer.
In square, all angles are of 90°, but in rhombus, opposite angles are equal, but adjacent angles are not equal. Kyle's claim is Incorrect.
What is a quadrilateral?It is a polygon with four sides. The total interior angle is 360 degrees.
Kyle claimed that the given quadrilaterals are similar because the ratio of their corresponding sides is equal.
Kyle's claim is Incorrect. Because the shapes are square and rhombus.
In square, all angles are of 90°, but in rhombus, opposite angles are equal, but adjacent angles are not equal.
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Use the discriminant to describe the roots of each equation. Then select the best description.
3x^2 - 2 + 7x =0
Answer options:
•double root
•imaginary root
•real and irrational root
•real and rational root
The quadratic equation 3 · x² + 7 · x - 2 = 0 has a positive discriminant. Thus, the expression has two distinct real roots (real and irrational roots).
How to determine the characteristics of the roots of a quadratic equation by discriminant
Herein we have a quadratic equation of the form a · x² + b · x + c = 0, whose discriminant is:
d = b² - 4 · a · c (1)
There are three possibilities:
d < 0 - conjugated complex roots.d = 0 - equal real roots (real and rational root).d > 0 - different real roots (real and irrational root).If we know that a = 3, b = 7 and c = - 2, then the discriminant is:
d = 7² - 4 · (3) · (- 2)
d = 49 + 24
d = 73
The quadratic equation 3 · x² + 7 · x - 2 = 0 has a positive discriminant. Thus, the expression has two distinct real roots (real and irrational roots).
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Parallelogram EASY is drawn with diagonal ES. The measure of Angle AES is 40 degrees and the measure of Angle Y is 110
degrees.
Find the measure of Angle A, Angle YEA, Angle ESA, and Angle ESY.
Answer:
Step-by-step explanation:
Givens
Parallelogram EASY with diagonal ES
<AES = 40
<Y = 110
Solution
<AES = 40 GIVEN
<ESY = 40 Z THEOREM OF A PRALLELOGRAM
<A = <Y PROPERTY OF A PARALLELOGRAM
<A = <110 <A = 110 BECAUSE <Y = 110
<YES = 180 - <Y -<ESY EVERY TRIANGLE HAS 180o
<YES = 180 - 110 - 40 SIMPLIFY
<YES = 30
<YEA = <YES + <AES WE KNOW BOTH ANGLES ON THE RIGHT.
<YEA = 30 + 40 COMBINE
<YEA = 70
You could do <YEA by noting that consecutive angles of a Parallelogram equal 180
(6+9)2+6(600-9)+600 divide 30
Step-by-step explanation:
GIVEN
HERE
= 6+9+2+6+600÷30 { firstly add numbers }
= 623 ÷ 30
= 20
I think you understand
How do I answer this question pls help me
Answer:
14.7 quarts
Step-by-step explanation:
Use the given equivalence figures to write a proportion. Solve the proportion for the unknown value.
__
quarts/liters = x/14 = 1/0.95 . . . . . the conversion is given as 1 qt = 0.95 L
Multiply by 14 to find x.
x = 14(1/0.95) ≈ 14.7
There are about 14.7 quarts in 14 liters.
_____
Additional comment
You are given a value in liters (14 liters) and asked for the equivalent in quarts. That means you want to change the units from liters to quarts. To do that, you can multiply the given value (14 liters) by a conversion factor that has quarts in the numerator and liters in the denominator. That is what the fraction 1/0.95 is in the above. You will note that units of liters cancel in this equation.
[tex](14\text{ liters})\times\dfrac{1\text{ quart}}{0.95\text{ liter}}=\dfrac{14}{0.95}\text{ quarts}\approx14.7\text{ quarts}[/tex]
This rule, "use a conversion factor that divides by the units you don't want and multiplies by the units you do want" applies to any units conversion problem. The conversion factor you use should always have equal quantities in the numerator and denominator. (Here, the equal quantities are 1 quart and 0.95 liters.)
You will notice that we treat units just like any variable. They can be multiplied, divided, cancelled, raised to a power. Only terms with like units can be added or subtracted.
