Answer:
values of x,y and z are x = -2, y= -9 and z=5
Step-by-step explanation:
2x+4y+1z=−35 eq(1)
3x+7y+7z=−34 eq(2)
2x+10y+6z=−64 eq(3)
We can solve using elimination method
Subtracting eq (1) from eq(3)
2x + 10y +6z = -64
2x +4y +1z = -35
______________
6y + 5z = -29 eq(3)
Multiplying eq(2) with 2 and eq(3) with 3 and subtracting
6x + 14y +14z = -68
6x + 30y +18z = -192
- - - +
_________________
-16y -4z = 124 eq(4)
Multiply eq(3) with 4 and eq(4) with 5 and add both equations
24y + 20z = -116
-80y - 20z = 620
______________
-56y = 504
y = -504/56
y= -9
Putting value of y in equation(3)
6y + 5z = -29
6(-9) + 5z = -29
-54 + 5z = -29
5z = -29+54
5z = 25
z = 25/5
z =5
Now, putting value of y and z in eq(1)
2x + 4y +1z = -35
2x + 4(-9) +1(5) = -35
2x -36+5 = -35
2x -31 = -35
2x = -35+31
2x = -4
x= -4/2
x=-2
So, values of x,y and z are x = -2, y= -9 and z=5
you read 4 1/2 pages in 12 minutes. at the same rate, how many pages could you read in an hour?
Answer:
22.5 pages
Step-by-step explanation:
First divide the page number by the minutes it takes to read them to find pages per minute-
4.5 / 12 = .375
Then take that number and multiply it by the minutes in an hour-
(.375) (60) = 22.5
22.5 pages in one hour.
Answer:
22 1/2 pages
Step-by-step explanation:
60/12 = 5
5(4.5) = 22 1/2
Does this graph show a function? explain how you know
Answer:
C
Step-by-step explanation:
The vertical line test is basically just drawing a vertical line and seeing if the line intersects the graph more than once. If it does, then it is not a function, if it doesn't than it is a function.
Answer:
C
Step-by-step explanation:
which statement best describes a line in a slope-intercept form when the coeficient of the x-term is negative?
@ line slants down
b- line slants up
c-line is horizontal
d- line is vertical
Answer:
Option a: Line slants down.
Step-by-step explanation:
It is important to remember that the equation of the line in Slope-Intercept form is the following:
[tex]y=mx+b[/tex]
Where "m" is the slope of the line and "b" is the y-intercept.
The slope of a line can be positive (The line slopes upwards to the right), negative (The line slopes downwards to the right), zero (Horizontal line), or undefined (Vertical line).
Therefore, the statement that best describes a line in a slope-intercept form when the coeficient of the x-term (The slope) is negative is: "Line slants down".
Knowing that sin 30° = 1/2 , what is a?
Answer:
14! Hope you ace your test!!
Step-by-step explanation:
The value of the side 'a' will be 14 units.
What is trigonometry?The branch of mathematics sets up a relationship between the sides and the angles of the right-angle triangle is termed trigonometry.
The value of a is calculated as:-
Sin 30 = P / H
Sin 30 = 7 / a
1 / 2 = 7 / a
a = 7 x 2
a = 14 units
Therefore the value of the side 'a' will be 14 units.
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The diameter of circle A is EF.
True
False
That is true.
The diameter is a line that passes through the center of a circle.
Answer: True is the answer
How many 5-digit numbers can be formed using the digits 0,1,2,3,4,5,6, if repetition of digits is not allowed?
A. 119
B. 16,807
C. 2,520
D. 120
To find the number of 5-digit numbers that can be formed using the digits 0-6 without repetition, we use permutations. The answer is 5,040.
Explanation:To find the number of 5-digit numbers that can be formed using the digits 0, 1, 2, 3, 4, 5, 6 (without repetition), we need to use the concept of permutations.
Since repetition is not allowed, for the first digit, we have 7 choices (0 cannot be the first digit). For the second digit, we have 6 choices (since one digit has been used). For the third digit, we have 5 choices (since two digits have been used), and so on.
Therefore, the number of 5-digit numbers that can be formed is 7 x 6 x 5 x 4 x 3 = 5,040.
Will needs 8 hours of sleep every night, Brad needs 9 hours, and Nick needs 10. One Saturday, they all have to get up at 6 a.m. to go fishing. On Friday evening, who will be the first to bed?
Answer: Nick
Step-by-step explanation:
Nick is the one who will go to bed first because he needs the most sleep. Nick needs 10 hours of sleep, then it would be Brad who needs 9 , then Will who needs 8
Nick will be the first to bed on Friday evening out of Will, Brad, and Nick.
On Friday evening, Nick would be the first to bed among Will, Brad, and Nick. Nick needs 10 hours of sleep every night, so to wake up at 6 a.m. on Saturday, he would have to go to bed earlier than Will and Brad who need 8 and 9 hours of sleep, respectively.
Given the function f(x)=0.5|x-4| -3, for what values of x is f(x)=7
Answer:
x = -16 or x = 24Step-by-step explanation:
[tex]f(x)=0.5|x-4|-3\\\\f(x)=7\Rightarrow0.5|x-4|-3=7\qquad\text{add 3 to both sides}\\\\0.5|x-4|=10\qquad\text{multiply both sides by 2}\\\\|x-4|=20\iff x-4=\pm20\\\\x-4=-20\qquad\text{add 4 to both sides}\\x=-16\\\\x-4=20\qquad\text{add 4 to both sides}\\x=24[/tex]
A sphere with a radius of 5 cm is enlarged by a scale factor of 2. What is the approximate volume of the new sphere in cubic inches?
To find the volume of the new sphere, calculate the volume of the original sphere and then multiply it by the scale factor cubed. Convert the volume from cubic centimeters to cubic inches using the conversion factor: 1 cm³ = 0.0610237 in³. The approximate volume of the new sphere in cubic inches is 255.3 in³.
To find the volume of the new sphere, we need to first find the volume of the original sphere and then multiply it by the scale factor cubed. The formula for the volume of a sphere is V = (4/3)πr³, where r is the radius.
Given that the radius of the original sphere is 5 cm, we can calculate its volume using the formula:
V1 = (4/3)π(5 cm)³ ≈ 523.6 cm³.
Next, we can calculate the volume of the new sphere by multiplying the volume of the original sphere by the scale factor cubed:
V2 = V1 × (2)³ = 523.6 cm³ × 8 ≈ 4188.8 cm³.
Finally, to convert the volume from cubic centimeters to cubic inches, we need to use the conversion factor: 1 cm³ = 0.0610237 in³. Therefore, the approximate volume of the new sphere in cubic inches is:
V2 ≈ 4188.8 cm³ × 0.0610237 in³/cm³ ≈ 255.3 in³.
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The table shows a pattern of exponents.
What is the pattern as the exponents decrease?
Answer:
Option C is correct.
Step-by-step explanation:
We need to find the pattern as the exponent decreases.
the first value in the table is 125.
if we divide 125 by 5 i.e 125/5 we get 25
the next value in the table is 25
if we divide 25 by 5 i.e 25/5 we get 5
the next value in the table is 5
if we divide 5 by 5 i.e 5/5 we get 1
the next value in the table is 1
if we divide 1 by 5 i.e 1/5 we get 1/5
the next value in the table is 1/5
if we divide 1/5 by 5 i.e 1/5*5 we get 1/25
the next value in the table is 1/25
So, the pattern is if we divide the previous value by 5 we get the next value in the table.
So, Option C is correct.
Answer:
The answer is C
Step-by-step explanation:
I just took the test
The value of the square root of 13 is between
Answer:
the square root of thirteen is 3.6
Step-by-step explanation:
if you put the 13 with the square root box and press the = button you will get the square root of 13 is 3.6
Suppose that the height of the slide is 2 feet,
when x = 20. What is the average rate of change
over the entire slide?
The average rate of change over the entire slide is [tex]\( \frac{1}{10} \)[/tex] feet per foot.
To find the average rate of change over the entire slide, we need to calculate the change in height divided by the change in distance over the entire slide.
Let's denote:
- [tex]\( h_1 \)[/tex] as the initial height (when x = 0),
- [tex]\( h_2 \)[/tex] as the final height (when x = 20).
Given that the height of the slide is 2 feet when ( x = 20 ), we have:
[tex]\[ h_2 = 2 \, \text{feet} \][/tex]
We also know that the height of the slide is 0 feet when ( x = 0 ), so:
[tex]\[ h_1 = 0 \, \text{feet} \][/tex]
Now, the change in height ([tex]\( \Delta h \)[/tex]) over the entire slide is:
[tex]\[ \Delta h = h_2 - h_1 = 2 \, \text{feet} - 0 \, \text{feet} = 2 \, \text{feet} \][/tex]
The change in distance ([tex]\( \Delta x \)[/tex]) over the entire slide is simply the distance traveled, which is:
[tex]\[ \Delta x = 20 \, \text{feet} \][/tex]
The average rate of change over the entire slide ([tex]\( \text{Avg ROC} \)[/tex]) is then:
[tex]\[ \text{Avg ROC} = \frac{\Delta h}{\Delta x} \][/tex]
[tex]\[ \text{Avg ROC} = \frac{2 \, \text{feet}}{20 \, \text{feet}} \][/tex]
[tex]\[ \text{Avg ROC} = \frac{1}{10} \][/tex]
The average rate of change of the slide height is calculated as 0.1 feet per foot, indicating that the height increases by 0.1 feet for every foot along the slide.
Step by step calculation:
The average rate of change of a function over an interval is calculated using the formula:
Average Rate of Change = (Change in Height) / (Change in Distance)In this problem, we know the height ( extit{y}) of the slide at x = 20 feet is 2 feet. Let's assume the starting height at x = 0 is 0 feet.Using the points (0, 0) and (20, 2), we apply the formula:Average Rate of Change = (2 - 0) / (20 - 0) = 2 / 20 = 0.1 feet per foot
This means the height increases by 0.1 feet for every foot traveled along the length of the slide.
The latitude value of Liverpool is 53.41 degrees, and the longitude value is -2.99 degrees. The latitude value of Melbourne is -37.81 degrees, and the longitude value is 144.96 degrees. The two cities are degrees apart in latitude. The two cities are degrees apart in longitude. Reset Next
Answer:
degrees apart in latitude: 91.22
degrees apart in longitude: 147.95
Step-by-step explanation:
Liverpool and Melbourne are two cities that are located very far away from each other. Liverpool is located in the northwestern part of England, while Melbourne is located in the southeastern part of Australia, so understandably their latitudes and longitudes are very different. In order to get to the distance in degrees between these two cities in latitude and longitude, we just simply need to sum the degrees of both of them and we will get to the result. The reason why simple summing will do the job is because they are on separate hemispheres, with Liverpool being on the Northern and Western Hemisphere, while Melbourne being on the Southern and Western Hemisphere.
Latitude distance:
53.41 + 37.81 = 91.22
Longitude distance:
2.99 + 144.96 = 147.95
Answer:
degrees apart in latitude: 91.22
degrees apart in longitude: 147.95
Which of the following theorems verified that angle xyz is congruent too angle uwv?
Answer:
Option B. AA
Step-by-step explanation:
we know that
Angle-Angle (AA) Similarity Postulate, states that If two angles of one triangle are congruent to two angles of another, then the triangles must be similar
In this problem
In the triangle XYZ
∠X=70°
∠Y=90°
∠Z=90°-70°=20° (remember that angle X and angle Z are complementary)
In the triangle UWV
∠V=20°
∠W=90°
∠U=90°-20°=70° (remember that angle V and angle U are complementary)
therefore
Traingles XYZ and UWV are similar by AA Similarity Postulate
A quality control manager at a factory selects 7 lightbulbs at random for inspection out of every 400 lightbulbs produced. At this rate how many lightbulbs will be inspected if the factory produces 20000 lightbulbs?
Answer:
350 lightbulbs
Step-by-step explanation:
First, we need to find the rate of lightbulbs that are inspected. This can be calculated as the division between the number of lightbulbs selected for inspection and the number of light bulbs produced. This is:
Rate = 7/400 =0.0175
That means that for every lightbulb produced, 0.0175 are inspected. Then if the factory produces 20000 light bulbs, the number of light bulbs inspected is:
20000*0.0175 = 350 lightbulbs
By solving for the unknown, the number of lightbulbs inspected can be determined as 350.
The quality control manager selects 7 lightbulbs out of 400 for inspection.
To find the number of lightbulbs inspected, we set up a proportion:
7 lightbulbs / 400 lightbulbs = x lightbulbs / 20000 lightbulbs
Solving for x gives:
x = (7/400) * 20000 = 350 lightbulbs inspected.
The graph represents this system of equations:
2x + y = 3
2x - 5y = 15
What is the solution to the system of equations
represented by the graph?
(0, -3)
(1,1)
(1.5,0)
(2.5, -2)
Answer:
(2.5, - 2)
Step-by-step explanation:
The solution to a system of equations given graphically is at the point of intersection of the 2 lines, that is
(2.5, - 2 ) ← point of intersection
Answer:
Option D is the correct answer.
Step-by-step explanation:
Refer the given figure showing the graph.
We can see the point of intersection is (2.5, -2).
Option D is the correct answer.
Alternatively:
2x + y = 3 ---------------------eqn 1
2x - 5y = 15 ---------------------eqn 2
eqn1 - eqn 2 gives
2x + y - ( 2x - 5y) = 3 - 15
6y = -12
y = -2
Substituting in eqn 1
2x - 2 = 3
x = 2.5
Point of intersection is (2.5, -2).
Option D is the correct answer.
Select the solution(s) of the original equation. x=sqrt 2 x=1 x=i x = - sqrt 2 x=-i
Answer:
A. x = √2
B. x = 1
D. x = -1
E. x = -√2
Step-by-step explanation:
Correct 100%
Without the complete equation, we cannot provide a definitive solution. However, it seems like you are dealing with a quadratic equation where possible solutions can be found using the quadratic formula, '-b ± √ (b² - 4ac) / 2a'. Please provide the full equation for a more precise answer.
Explanation:The original equation mentioned in your question is missing, but I'll assume you are referring to solutions of the equation x² = √ ( 2x² - 1 ). This equation can be solved by first simplifying the condition as 2(x² - 1)² ≤ 1. Following the standard method for solving quadratic equations, we can use the quadratic formula -b ± √ (b² - 4ac) / 2a. Unfortunately, without a full equation, we cannot provide a comprehensive answer. Please, provide the complete equation for a more accurate solution.
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Which expression has a value of 1?
A; 4/8 x 8/16
B; 2/3 x 3/2
C; 8/4 x 4/4
D; 2/3 x 3/3
Helpppppppp meeeeee pleaseeeee
Answer:
C
Step-by-step explanation:
(f - g)(x) = f(x) - g(x)
f(x) - g(x) = [tex]4^{x}[/tex] - 8 - (5x + 6)
= [tex]4^{x}[/tex] - 8 - 5x - 6 ← collect like terms
= [tex]4^{x}[/tex] - 5x - 14 → C
A baker makes a cake shaped like a hexagonal prism of it takes 32 ounces of batter to make a cake with height of 5 inches which Of These is the area of hexagonal base use 1 ounce ~3.125
A) 25 square
B)20 Square
C) 15.625 square
D) 100 square
Answer:
c
Step-by-step explanation:
Follow below steps:
The area of the hexagonal base of the cake:
Calculate the volume of the cake: 32 ounces * 3.125 = 100 cubic inches.
The volume of a hexagonal prism: Volume = area of base * height. Since height is 5 inches, the area of the base is 100 / 5 = 20 square inches.
The function f(x)=603(1.3)^x represents the number of students enrolled at a university x years after it was founded. Each year, the number is students is______ the number the year before.
Answer: 0.3 times
Step-by-step explanation:
Answer:
1.3 times
Step-by-step explanation:
The function [tex]f(x)=603(1.3)^{x}[/tex] represents the number of students enrolled at a university, x years after it was founded.
So the sequence will be formed to represent the number of students will be
f(1) = 603(1.3)
f(2) = 603(1.3)²
f(3) = 603(1.3)³
and so on.
Now the common ratio between second and first term will be
= [tex]\frac{(603)(1.3)^{2}}{603(1.3)}=1.3[/tex]
Therefore, second term of the sequence will be 1.3 times of the first term.
Answer will be - "Each year, the number of students will be 1.3 times the number the year before".
For 2 cups of flour for every 3 cups of milk. If u use 6 cups of flour, how many cups of milk do you need?
Answer:
9 cups of milk
Step-by-step explanation:
2 cups of flour - 3 cups of milk
4- cups of flower - 6 cups of milk
6 cups of flower - 9 cups of milk
Please mark brainliest and have a great day!
Answer:
9 cups of milk
Step-by-step explanation:
2 cups of flour need 3 cups of milk
1 cup of milk needs 3/2 cups of milk
:. 6 cups of milk will need
(6 x 3/2) = 18/2
= 9 cups of milk
Solve for x
6(x-1) =9(x+2)
Answer:
ive got you fam <3 your answer is x= -8
Step-by-step explanation:
isolate the variable by dividing each side by factors that dont contsin the variable
An angle is formed by
Answer:
2 lines meet at a shared point.
Step-by-step explanation:
Hope my answer has helped you!
Combine like terms to create an equivalent expression
-2.5(4x-3)
Hello!
Answer:
[tex]\boxed{-10x+7.5}[/tex]
Step-by-step explanation:
Distributive property: a(b+c)=ab+ac
[tex]-2.5*4x-(-2.5)*3[/tex]
[tex]-4*2.5x+3*2.5[/tex]
Simplify.
[tex]4*2.5=10[/tex]
[tex]3*2.5=7.5[/tex]
[tex]=-10x+7.5[/tex]
[tex]\boxed{-10x+7.5}[/tex], which is our final answer.
I hope this helps you!
Have a nice day! :)
Thanks!
Answer:
The answer is -10x+7.5
Step-by-step explanation:
Please help me solve this problem
Answer:
Option B , D and E are correct.
Step-by-step explanation:
We set the denominator equal to zero to find the number to put in division box
So, if 3 is in the division box then the denominator will be
x-3 = 0 => x=3 is the root.
So, Option E is correct
2x^2-2x-12 ÷ x-3 = 2x+4 is correct.
because after division the result given is 2x+4 which is correct.
So, Option B is correct
x-3 is a factor of 2x^2-2x-12 because because when the term is divided we get the remainder 0.
So, Option D is correct
So, Option B,D and E are correct.
In which step did Rena make the first error?
Answer: Step 4
Step-by-step explanation:
Rena made the first mistake in step 4 because she left the terms [tex]2^{3} and (-1)^{21}[/tex] in the denominator, when in the previous step they were also in the denominator but raised to -1, which means that they should be in the numerator.
The right step 4 would be:
[tex]\frac{2^{3} (-1)^{21} }{2^{6} } =\frac{-1}{2^{3} } =\frac{-1}{8}[/tex]
Answer: step 4
!!
Step-by-step explanation:
What is the value of x?
Answer:
x = 2
Step-by-step explanation:
Given 2 secants intersecting a circle from an external point, then
The product of the external part and the entire part of one secant is equal to the product of the external part and the entire part of the other secant, that is
(x + 1)(x + 1 + 11) = (x + 4)(x + 4 + 1)
(x + 1)(x + 12) = (x + 4)(x + 5) ← expand both sides
x² + 13x + 12 = x² + 9x + 20
Subtract x² + 9x from both sides
4x + 12 = 20 ( subtract 12 from both sides )
4x = 8 ( divide both sides by 4 )
x = 2
What is the distance between the points (-4, 1) and (6, 8)?
Round your answer to the nearest hundredth.
Answer:
12.21
Step-by-step explanation:
Step 1: You got to find the distance between your x's
Step 2: You got to find the distance between your y's
Step 3: Apply Pythagorean Theorem: That is do:
[tex]\sqrt{ (\text{ distance of x})^2+( \text{ distance of y})^2}\\[/tex]
So x distance is 10 (I just did 6-(-4))
So y distance is 7 (I just did 8-1 )
As per the formula, I'm going to square both... Then add those squared results together like so 100+49=149
Last step is the square root...
[tex]\sqrt{149} \approx 12.21 [/tex]
Answer:
12.21
Step-by-step explanation:
hope it helps
(HELP PLEASE!) Which expression is equivalent to? Assume.
Answer:
Option 1
Step-by-step explanation:
Given expression is:
[tex]\frac{(2mn)^{4}}{6m^{-3}n^{-2}} \\=\frac{2^{4}m^{4}n^{4}}{6m^{-3}n^{-2}}\\=\frac{16m^{4}n^{4}}{6m^{-3}n^{-2}}\\=\frac{8*2*m^{4}*n^{4}}{2*3*m^{-3}*n^{-2}} \\=\frac{8*m^{4+3}n^{4+2}}{3}\\=\frac{8m^{7}n^{6}}{3}[/tex]
So option 1 is the correct answer ..