Solve the system:
p-3q=-1
-5p+16q=5
a. (2,1)
b.(3,3)
c. (-1,0)
d.(5,2)
Answer: The correct option is
(c) (-1, 0).
Step-by-step explanation: We are given to solve the following system of equations :
[tex]p-3q=-1~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~(i)\\\\-5p+16q=5~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~(ii)[/tex]
From equation (i), we have
[tex]p-3q=-1\\\\\Rightarrow p=3q-1~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~(iii)[/tex]
Substituting the value of p from equation (iii) in equation (ii), we get
[tex]-5(3q-1)+16q=5\\\\\Rightarrow -15q+5+16q=5\\\\\Rightarrow q=5-5\\\\\Rightarrow q=0.[/tex]
From equation (i), we get
[tex]p=3\times0-1=-1.[/tex]
Thus, the required solution is (p, q) = (-1, 0).
Option (c) is CORRECT.
HELP PLEASE!!!!!
Find the radius of a circle if a central angle of 3π/2 intercepts an arc of 26.4 centimeters.
0.19 cm
3.14 cm
5.6 cm
Find the measure of a central angle that intercepts an arc of 81.5 cm in a circle whose radius is 16.3 cm.
5 rad16 rad65 radFind the arc length intercepted by a central angle of 3π/4 radians in a circle whose radius is 18.4 inches.
13.8π15.2π24.5πAnswer:
Find the radius of a circle if a central angle of 3π/2 intercepts an arc of 26.4 centimeters.
Ans: 5.6 cm
Find the measure of a central angle that intercepts an arc of 81.5 cm in a circle whose radius is 16.3 cm.
Ans: 5 rad
Find the arc length intercepted by a central angle of 3π/4 radians in a circle whose radius is 18.4 inches.
Ans: 13.8π
What number appears 7 times in the multiplication table?
In a multiplication table, each number from 1 to 12 would appear 12 times corresponding to each multiplier. In a table specific for a single number, that number would repeat 12 times.
Explanation:The question is asking about a number that appears 7 times in a multiplication table. In a multiplication table, numbers 1 through 12 are repeated 12 times, once for each multiplier. However, in a multiplication table between 1 and 10, the number 1 appears multiple times as it is a factor for every other number. As an exception, if we have a multiplication table that is specific to a certain number, for example, the number 7, then number 7 would appear 12 times as it is the constant multiplier for each number in the table.
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What number gives you the same result when multiplied by 6 as it does when 6 is added to it?
Ou can draw a quadrilateral with two sets of parallel lines and no right angles.
a. True
b. False
If Michelle walked 5 meters how many inches did she walk
HELP ME PLS!!
The function graphed shows the total cost for a taxi cab ride for x miles.
Select from the drop-down menus to correctly identify the taxi cab ride information provided by the graph.
The slope is
5, 3, 2.5, 0.2
The slope represents
1)the total cost of the taxi ride
2)the total number of miles traveled
3)the cost per miles traveled
4)the initial cost of the ride
The slope of the line between cost of taxi and distance is 2.5 and it represents the cost of taxi per mile of distance travelled.
What is slope of line ?
Slope of line is the angle made by the line from positive x-axis in anticlockwise direction, it also denoted the steepness of the line.
The function graphed shows the total cost for a taxi cab ride for x miles the cost in taxi is shown in y axis and the distance covered by taxi in x axis. Now, to find put the slope we must two coordinates which can be found out from the graph easy by observation as (0,3) and (2,8).
How using slope formula to find the slope of line :
[tex]\begin{aligned}\frac{y_{2}-y_{1}}{x_{2}-x_{1}}&=\frac{8-3}{2-0}\\&=\frac{5}{2}\\&=2.5\end{aligned}[/tex]
It represents the cost of taxi per mile of distance travelled.
Therefore, the slope of the line between cost of taxi and distance is 2.5 and it represents the cost of taxi per mile of distance travelled.
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Solve the system by substitution, show all steps.
-x-y-z=-8
-4+4y+5z=7
2x+2z=4
Answer:
In Point Form: (x,y,z)= (3,6,-1)
In Equation Form: x=3, y=6, z=-1
Step-by-step explanation:
1) Solve for x
2x+2z=4 (Subtract 2z from both sides)
-2z -2z
2x= 4-2z (Divide 2 from both sides)
/2 /2
x=2-z
2) Substitute 2-z for x in
-x-y-z=-8
-(2-z)-y-z=-8
-2+z-y-z=-8 (Combine Like Terms)
-2-y=-8 (Add 2 to both sides)
+2 +2
-y=-6 (Divide -1 from both sides)
/-1 /-1
y=6
3) Substitute 2-z for x & 6 for y in
-4x+4y+5z+=7
-4(2-z)+4(6)+5z=7 (Get rid of parentheses)
-8+4z+24+5z=7 (Combine Like Terms)
9z+16=7 (Subtract 16 from both sides)
-16 -16
9z+=-9 (Divide 9 from both sides)
/9 /9
z=-1
4) Now find x by substituting -1 for z in
x=2-z
x=2-(-1)
x=2+1
x=3
Therefore the answer is:
In Point Form: (x,y,z)= (3,6,-1)
In Equation Form: x=3, y=6, z=-1
Is the point (−7,1) a solution to the inequality
y < 0.5x + 9 ?
Question 1 options:
True
False
The given point (−7,1) is a solution to the inequality.
What is inequality?Inequality is defined as mathematical statements that have a minimum of two terms containing variables or numbers that are not equal.
We must determine if the inequality holds for a certain set of ordered pairs in order to determine which ordered pairs constitute the answer to the inequality.
We have been given inequality is:
⇒ y < 0.5x + 9
To determine the point (−7,1) a solution to the inequality
Substitute x = -7 and y = 1 in the inequality, we get
⇒ y < 0.5x + 9
⇒ 1 < 0.5(-7) + 9
⇒ 1 < -3.5 + 9
Apply the subtraction operation in the above inequality, we get
⇒ 1 < 5.5
This is true.
Hence, the given point (−7,1) is a solution to the inequality.
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Select the postulate that is illustrated for the real numbers.
6 + 0 = 6
The commutative postulate for multiplication
Multiplication by one
The addition inverse postulate
Commutative postulate for addition
The distributive postulate
The additive identity postulate
The multiplication inverse
Answer:
The additive identity postulate
Step-by-step explanation:
6 + 0 = 6
Any number added with zero, we get the same number.
That is, a + 0 = a, where "a" is any real number.
Let's take a = 9, we get
9 + 0 = 9
Let's check out a few more examples:
-9 + 0 = -9
2/3 + 0 = 2/3
22 + 0 = 22
You can see any number added with 0, we get the same number.
Here 0 is additive identity, this is called additive identity postulate.
We are given 6 + 0 = 6 which illustrated by "The additive identity postulate."
Therefore, answer is "The additive identity postulate"
An aluminum recycling center pays0.08 per pound for cans how much will make receive for 21.5 pounds of cans
The noise rating of an air conditioner is 50 decibels, and the noise rating of a washing machine is 65 decibels. Determine how many time greater the washing machine's intensity of sound is.
Use the formula , β = 10log I/I 0 where β is the sound level in decibels, I is the intensity of sound you are measuring, and Io is the smallest sound intensity that can be heard by the human ear (roughly equal to 1 x 10^-12 watts/m2).
The washing machine's intensity of sound is (blank) times greater than that of the air conditioner.
Answer:
the answer is 31.6 on PLATO
Find the side length of a square with the same perimeter as a equilateral triangle with side 7 cm.
Final answer:
The side length of a square with the same perimeter as an equilateral triangle with side 7 cm is 5.25 cm.
Explanation:
To find the side length of a square with the same perimeter as an equilateral triangle with sides of 7 cm, first calculate the perimeter of the triangle, which is 7 cm x 3 = 21 cm. Since a square has four equal sides, divide the perimeter by 4 to get the side length of the square. Thus, the side length would be 21 cm ÷ 4 = 5.25 cm.
Which of the following is a function equivalent to f(x) = 5(1.9)3x?
f(x) = 34.29x
f(x) = 5(6.86x)
f(x) = 5(6.86)x
f(x) = 328.51x
The function equivalent to f(x) = 5(1.9)3x is f(x) = 5(6.86)x.
Explanation:The function equivalent to f(x) = 5(1.9)3x is f(x) = 5(6.86)x.
A student’s construction of the perpendicular bisector of is shown below. What is the student’s error?
The test that gives a list of the possible rational zeros of a polynomial function is called the test.
Answer:
rational zero
Step-by-step explanation:
Kevin earns $15 per hour for working 8 hours then he earns $18 per hour for working overtime for 4 hours a day what is the average time he works
Find an equation for a line that passes through the point (0, –3) and parallel to another line whose slope is 1.2.
Final answer:
The equation of the line that passes through the point (0, -3) and is parallel to another line with a slope of 1.2 is y = 1.2x - 3.
Explanation:
To find an equation for a line that passes through the point (0, –3) and is parallel to another line with a slope of 1.2, we use the fact that parallel lines have the same slope. Since a line's equation can be written in the form y = mx + b, where m is the slope and b is the y-intercept, and we already know the slope (m = 1.2) and the y-intercept (b = -3, since the line passes through (0, -3)), our equation becomes:
y = 1.2x - 3
This means that any line parallel to one with a slope of 1.2 and passing through (0, -3) will also have a slope of 1.2, but the y-intercept will be unique to the point it passes through.
Each exterior angle of an equilateral triangle has which measure?
Answer:
60 degreesStep-by-step explanation:
You purchased a shirt on sale for $17.55. The discount on the shirt was $5.85. What was the original price of the shirt?
Which equation best models the scenario above?
x + 5.85 = 17.55
x - 5.85 = 17.55
x + 17.55 = 5.85
x - 17.55 = 5.85
The original price of the shirt is simply the sum of the purchased price and the discount price, that is:
original price = $17.55 + $5.85
original price = $23.40
The equation that best model this scenario is:
x - 5.85 = 17.55
where x is the original price
What transformation takes
f(x)=15x+3 to g(x)=5x+3 ?
Question 1 options:
a horizontal compression by a factor 1/3
a translation 6 units right
a horizontal stretch by a factor of 3
a translation 6 units down
30 POINTS PLEASE HELP! An investment in a savings account grows to three times the initial value after t years.
If the rate of interest is 5%, compounded continuously, t = (blank) years.
∠1 is a complement of ∠4, and m∠1=33∘m. Find m∠4.
a jar of coins contains dimes pennies and quarters there are 88 pennies in a jar. There are 5 dimes for every 4 pennies and there are 7 quarters for every 11 dimes how many coins are in the jar? A 180 B 258 C 268 D 350
Answer:
c 268
Step-by-step explanation:
i did the test on the home school time for learning
Which system is represented by the graph?
a. y > 2x
x + 2y ≤ –8
b. y ≥ 2x
x + 2y < –8
c. y < 2x
x + 2y ≥ –8
d. y ≤ 2x
x + 2y > –8
To determine the system of two inequalities which is represented by the graph, you have to do such steps:
1 step. The dashed blue line represents sign > or <. The line has the equation y=2x, then the inequality should be y>2x or y<2x. Since point (-1,1) belongs to the blue shaded region, then the inequallity y>2x is true.
2 step. The solid red line represents sign ≤ or ≥. The line has the equation x+2y=-8, then the inequality should be x+2y≤-8 or x+2y≥-8. Since the origin (0,0) doesn't belong to the red shaded region, then the inequallity x+2y≤-8 is true.
Thus, the system is
[tex]\left\{\begin{array}{l}y>2x\\x+2y\le-8.\end{array}\right.[/tex]
Answer: correct choice is A.
A scuba diver used the expression below to describe his position in relation to sea level.
2 + (–20) + 8
Which statement could describe the diver’s movements?
Starting on a platform 2 feet above sea level, dive down to a location that is 18 feet below sea level, and then rise 8 feet.
Starting on a platform 2 feet above sea level, dive down to a location that is 20 feet below sea level, and then rise 8 feet.
Starting 2 feet below sea level, dive down 20 more feet, and then rise to a location that is 8 feet below sea level.
Starting 2 feet below sea level, dive down 18 more feet, and then rise to a location that is 8 feet below sea level.
Answer:
Starting on a platform 2 feet above sea level, dive down to a location that is 20 feet below sea level, and then rise 8 feet.
Step-by-step explanation:
A scuba diver used the expression below to describe his position in relation to sea level.
2 + (–20) + 8
positive number is the feet above the sea level
negative number is the feet below the sea level (deep)
starting at 2 , 2 feet above sea level then down the sea 20 feet down,
finally rise 8 feet above the sea level
So, Starting on a platform 2 feet above sea level, dive down to a location that is 20 feet below sea level, and then rise 8 feet.
How do you write this number in standard form
15,000+7000+400+9
9+7r>r–3≥7r+3
Gonna' have to spam this and make it more points, PLEASEEE!, ALSO GONNA' TALK IN ALL CAPS FOR BETTER UNDERSTANDING!
Write a polynomial function in factored form with zeros at −2, 0, and 3.
How do I solve this??