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[tex]\diamond\large\blue\textsf{\textbf{\underline{\underline{Given question:-}}}}[/tex]
11z-6=16, what is z?
[tex]\diamond\large\blue\textsf{\textbf{\underline{\underline{Answer and how to solve:-}}}}[/tex]
We need to make sure that all variables are on the left-hand side and the numbers are on the right-hand side.
Since we have a number on the left-hand side, we need to move it to the right-hand side with the opposite operation:-
11z=16+6
[tex]\it{11z=22}[/tex]
Divide by 11 on both sides:-
[tex]\it{z=2}[/tex]
We can check our solution by replacing z with 2 and seeing whether or not we end up with a true statement:-
[tex]\it{11(2)-6=16}[/tex]
[tex]\it{22-6=16}[/tex]
[tex]\it{16=16}[/tex]
So we conclude that our solution, z=2, is correct.
Good luck with your studies.- - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
Answer:
z=2
Step-by-step explanation:
11(2)-6=16
22-6=16
Find three consecutive even integers such that the sum of 5 and the second is multiplied by -7, the result is 11 greater than 5 times the opposite of the third
Answer:
-20, -18, -16
Step-by-step explanation:
For consecutive integer problems, it often works well to let a variable represent the middle one (or their average value).
__
Here, we can let x represent the second integer. Then the first is (x-2), and the third is (x+2). The given relation can be written as ...
(5 +x)(-7) = 11 +5(-(x+2))
-35 -7x = 11 -5x -10 . . . . . . eliminate parentheses
-36 = 2x . . . . . . . . . add 7x -1
-18 = x . . . . . . . . divide by 2
The three integers are -20, -18, -16.
Lacey had $603 in her checking account. Then, she spent $252 from the account. How much money is left in Lacey's checking account?
Answer:
In this problem we are given the initial amount of money that Lacey has in her account and we are also given the amount of money that she has spent using that account. We are told to check how much money is left in her account and we can do this with a simple subtraction.
[tex]Initial\ Amount - Money\ Spent[/tex]
[tex]\$603-\$252[/tex]
[tex]\$351[/tex]
Therefore, our final answer is that Lacey has $351 left in her account.
Hope this helps! Let me know if you have any questions
Mick recently had new carpet installed. the cost of the carpet including installation was $8.14 per square foot before any discounts. the rectangular room he had carpeted measured 24 feet long and 18 feet wide. if mick actually paid $3,235.16, what discount percentage did he receive? assume there are no taxes.
Answer:
8%
Step-by-step explanation:
Let’s first determine the cost before any discount.
To do so, we first need to determine the area to be carpeted:
Area of Rectangle = Length × Width = 24 ft × 18 ft = 432 square feet.
To find the cost before discount we need to multiply the area by the cost per square foot:
Cost Before Discount = Area × Cost per square foot
Cost Before Discount = 432 square feet × $8.14 per square foot
Cost Before Discount = $3,516.48
We can now determine the discount percentage he received:
Cost After Discount = Cost Before Discount − (Discount % × Cost Before Disc.)
$3,235.16 = $3,516.48 – (Discount % × $3,516.48)
To solve, it is easiest to plug in each answer to see which discount percentage is the correct solution (i.e. “work backwards” from the given answers) or use the equation solver on our calculator.
We find that a discount of 8% is the correct solution.
If you instead prefer to use algebra to solve for the discount percentage, here are the steps.
We will rewrite the equation, using x to represent “Discount %”.
$3,235.16 = $3,516.48 − (x × $3,516.48)
$3,235.16 = $3,516.48 − $3,516.48x
Factoring out $3,516.48 we have:
$3,235.16 = $3,516.48(1 − x)
Note: Once you get comfortable with this type of problem you should skip straight to the step above.
Dividing both sides by $3,516.48 we have:
$3,235.16$3,516.48=1−x
0.92 = 1 − x
x = 0.08 = 8%
5) For the geometric sequence with the following terms, a8= 32 and a11= 256, find the ratio and then find a13
Using geometric sequence concepts, it is found that:
The common ratio is of 2.The 13th term is of 1024.What is a geometric sequence?A geometric sequence is a sequence in which the result of the division of consecutive terms is always the same, called common ratio q.
The nth term of a geometric sequence is given by:
[tex]a_n = a_1q^{n-1}[/tex]
In which [tex]a_1[/tex] is the first term.
As a function of the mth term, the nth term is given by:
[tex]a_n = a_mq^{n - m}[/tex]
Hence, considering the 8th and the 11th term, the common ratio is found as follows:
[tex]a_{11} = a_8q^3[/tex]
[tex]32q^3 = 256[/tex]
[tex]q^3 = 8[/tex]
q = 2.
Then, considering the 11th term and the common ratio, the 13th term is given as follows:
[tex]a_{13} = a_{11}q^2 = 256 \times 2^2 = 1024[/tex]
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Which is the length of the hypotenuse of the triangle? Triangle A B C. Side A C is 12 feet and side C B is 35 feet. StartRoot 94 EndRoot ft
Answer:37
Step-by-step explanation:
just took the test
Solve the system using linear combination. Show all work.
{9x + 4y = 28
{2x + 4y = 0
Answer:
(4,-2)
Step-by-step explanation:
What is linear combination?
Linear combination is the process of adding two equations to eliminate a variable so that we are able to solve for the other variable.
Here we are given the two equations 9x + 4y = 28 and 2x + 4y = 0. We can use linear combination to cancel out the two 4y terms leaving us with only x variables in which we can solve for.
Adding the two equations. (subtracting the second equation from the first) we really are subtracting the second equation from the first because if we were to add we would get 4y + 4y which wouldn't cancel out the terms therefore we would have to subtract the two equations to get 4y - 4y which cancels out the terms.
9x + 4y = 28
- (2x + 4y = 0)
==> remove parenthesis and apply negative sign
9x + 4y = 28
-2x - 4y = -0
----------------------
7x = 28
==> divide both sides by 7
x = 4
Finding the y value:
The solution is written as (x,y) meaning we also need the value of y. To find it we can plug in the value of x into one of the equations and then we can solve for y.
2x + 4y = 0
==> plug in x = 4
2(4) + 4y =0
==> multiply 2 and 4
8 + 4y = 0
==> subtract 8 from both sides
4y = -8
==> divide both sides by 4
y = -2
so we have x = 4 and y = -2
the solution of the equation would be (4,-2)
Checking our work
If our answer is correct we can plug in the values of x and y into both equations and the outcome will be valid ( or correct )
Equation 1 : 9x + 4y = 28
==> plug in x = 4 and y = -2
9(4) + 4(-2) = 28
==> multiply 9 and 4
36 + 4(-2) = 28
==> multiply 4 and -2
36 - 8 = 28
==> subtract 8 from 36
28 = 28
Equation 2 : 2x + 4y = 0
==> plug in x = 4 and y = -2
2(4) + 4(-2) = 0
==> multiply 2 and 4
8 + 4(-2) = 0
==> multiply 4 and -2
8 - 8 = 0
==. Subtract 8 from 8
0 = 0
Both are correct so our solution is correct!
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GIVING BRAINLIEST!!!!!
A cylindrical pipe is 28m long.its internal radius is 3.5 and external radius is 5 cm calculate:
The volume in cm,of the metal used in making the pipe
The volume of water in litres that the pipe can hold when full,correct to one decimal place
The volume in cm 112098 cm³.
The volume of water in liters 112 liter.
What is volume of cylinder?The volume of a cylinder is equal to the product of the area of the circular base and the height of the cylinder.
Given: height= 28m= 2800cm, internal radius= 3.5 cm, external radius = 5 cm.
Volume of cylinder
= πr²h
= 3.14(5²-3.5²)2800
=3.14*12.75*2800
=112098 cm³
Volume of water in liter is 112.098 or 112 liter.
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what’s the circumference, to this problem ?
Answer:
= 20.7345115137
or
≈ 21
Step-by-step explanation:
Circumference = 2 x π x radius
Circumference = 2 x π x 3.3
hope this helps
have a good day
Answer:
The formula to get the circumference of a circle is [tex]C=2*\pi * r[/tex]. We can then input the value and we get that [tex]C=2*\pi*3.3[/tex] and as we solve it more the final answer that we get is [tex]C=20.735[/tex].
Hope this helps! Let me know if you have any questions
RIGHT ANSWER GETS BRAINLIST WORTH 30+ POINTS
Two number cubes are rolled.
What is the probability that the first lands on 6 and the second lands on an even number?
Select your answer, as a fraction in simplified form.
Question 5 options:
1/6
2/6
1/12
1/3
Answer:
Hi. Here is your answer:
1/6
Step-by-step explanation:
this is because 1/6 is equal to 5/30 of your answer.
here is proof.
which school do you go to?
Hope this helps
Brainliest please
Have a great day
Please fully rate!
The probability that the first lands on [tex]6[/tex] and the second lands on an odd number is [tex]\frac{1}{12}[/tex]
Calculation of the probabilities:Since The probability of rolling a [tex]6[/tex] should be [tex]\frac{1}{6}[/tex] because there are [tex]6[/tex] total numbers.
Now The probability of rolling an odd number is [tex]\frac{1}{2}[/tex], since there are an equal number of odd and even numbers on a die.
Now the final probability should be
[tex]=\frac{1}{6}*\frac{1}{2}[/tex]
[tex]=\frac{1}{12}[/tex]
Therefore, The probability that the first lands on [tex]6[/tex] and the second lands on an odd number is [tex]\frac{1}{12}[/tex]
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The length of a race is 26 miles and 385 yards. what is the length of the marathon in yards
Answer:
46,145 yards
Step-by-step explanation:
convert miles to yards then add
Drag the tiles to the correct boxes to complete the pairs. Not all tiles will be used.
Match each description with the correct inequality.
(5x)2 ≤ 46,
(5x)2 ≥ 46,
x2 + 5x ≥ 46,
5x2 > 46,
x2 + 5x ≤ 46,
5x2 < 46,
The square of the product
of 5 and a number is
no less than 46.
arrowBoth
The product of 5 and the
square of a number is
greater than 46.
arrowBoth
The sum of the square of a
number and five times that
number is no more than 46.
Answer:
(5x)² ≥ 46
x² + 5x ≤ 46
5x² > 46
Step-by-step explanation:
Suppose number is x
1)The square of the product of 5 and a number is not less than 46.
Step 1
Product of 5
5x
Step 2
Square of the product of 5
(5x)²
Step 3
A number is not less than 46
(5x)² ≥ 46
2)The sum of square of a number and five times that number is no more than 46
Step 1
Square of a number
x²
Step 2
Five times that number
5x
Step 3
The sum
x² + 5x
Step 4
Is no more than 46
x² + 5x ≤ 46
3)The product of 5 and the square of a number is greater than 46
Step 1
The square of a number
x²
Step 2
The product of 5
5x²
Step 3
Is greater than 46
5x² > 46
Given 184% what is the equivalent fraction and decimal in simplest form?
Step-by-step explanation:
184% = 46/25 = 1 21/25 as a fraction
Simpifly : -5/6-7/-8+11/12–1/6+0- -7/16
Answer:
the chosen topic is not meant for use with this typ of problem try the examples below
Step-by-step explanation:
Please answer the following for 50 points, if you get it right you can get brainly, Please hurry!
Answer:
3.2 and 3.92
Step-by-step explanation:
pls help and thank you
Answer:
cost price of the bat: $3130.43
Step-by-step explanation:
3600/1.15 = 3130.43
Hope this helps
A listing for a home for sale is shown as follows: "4/3/2 house for sale. Price
$140,000." What does "4/3/2" mean?
This figure shows three identical spherical billiard balls of diameter 6 cm inside an equilateral triangular frame.
Work out the perimeter of the frame, leaving your answer
in surd form.
Answer:
Perimeter = 18(1 + √3 ) cm
Step-by-step explanation:
The radius of each ball = 1/2 * 6 = 3 cm.
Lines drawn from the 2 points of contact for one billiard ball to the center of the ball are at right angles to the sides of the triangle ( Tangent/radius theorem).
If we now draw a line from the vertex of the big triangle to the center of the ball we get 2 right triangles, and they are 30-60-90 triangles.
If the adjacent side of a triangle ( which is part of the side of the big triangle) = x:
tan 30 = 3 / x
x = 3 / tan 30
= 3 / 1/√3
= 3√3 cm.
There are 6 of these sides in the big triangle so their total length =
18√3 cm.
The three 'middle' sides joining 2 billiard balls each have a length of 2 radii = 6 cms ( as they form a rectangle with the radii of 2 billiard balls).
So the perimeter of the triangle = 18√3 + 3(6)
= 18(1 + √3 ) cm
I would have liked to transfer a diagram but I can't get to copy it to this site.
How would logx (49) = x look like in exponential form
I'm assuming the given log equation is [tex]\log_{\text{x}}(49) = \text{x}[/tex]
If so, then the exponential form is [tex]\text{x}^{\text{x}} = 49[/tex]
This is because the general form [tex]\log_{\text{b}}(\text{x}) = \text{y}[/tex] transforms into [tex]\text{y} = \text{b}^{\text{x}}[/tex]
For both equations, the 'b' is the base.
are all natural numbers also a rational number? (yes/no)
Answer:
Yes
Step-by-step explanation:
But not all rational numbers are natural numbers, so be careful of that.
Nick's science class is learning about animal classification, and they listed as many animals as they could in a minute. They came up with 32 mammals, 16 birds, 8 amphibians, 8 reptiles, 12 fish, and 4 invertebrates.
Select all of the statements that describe the data.
They listened to an equal of amphibians and reptiles.
There are more mammals on the list than birds and fish combined.
The modes of the data are amphibians and reptiles.
A quarter of the animals they listened are either amphibians or fish.
Answer:
The second one is the correct answer
Step-by-step explanation:
There are more mammals on the list than birds and fish combined.
i have a slight feeling the answer ain’t 21
Answer:
I think it is
Step-by-step explanation:
4,8,5,15,6,12,7,6
8,5,15,6,12,7
5,15,6,12
15,6
15+6=21
C. A store window has a perimeter of 18 feet. The width
is 6 feet. Find the length and the area.
211 +18).
A cylindrical tank has diameter 3.2 m and length
12.7 m.
What is the surface area of the tank, to 1 decimal
place?
Answer:
143.8 m²
Explanation:
Surface Area of cylinder = 2πr(r + h)
Here given,
diameter: 3.2 mradius: d/2 = 3.2/2 = 1.6 mlength: 12.7mSurface Area of cylinder:
⇒ 2π(1.6)(1.6+ 12.7)
⇒ 174.2955 m²
⇒ 143.8 m² (rounded to nearest 1 decimal place)
Question 3 :
Find the value of 3x3 - 4x2 + x - 5 when x = -3
(A) -54 (B) -71 (C) -32
3x∧2±6x±x±20 sole by factorization
Answer:
just look at the algebra formula and simplify to get your answer. Remember to use your powers well
Grace bought a new sweater on sale for 20% off the original price and an additional 15% off the discounted price. If the sweater originally cost $60, what was the final cost that Grace paid for the discounted sweater?
Answer:
$40.80.
Step-by-step explanation:
60 - 0.20*60
= 60 - 12
= $48
48 - 48*0.15
= 48 - 7.20
= $40.80.
On a number line, the directed line segment from q to s has endpoints q at –14 and s at 2. point r partitions the directed line segment from q to s in a 3:5 ratio. which expression correctly uses the formula (startfraction m over m n endfraction) (x 2 minus x 1) x 1 to find the location of point r? (startfraction 3 over 3 5 endfraction) (2 minus (negative 14)) (negative 14) (startfraction 3 over 3 5 endfraction) (negative 14 minus 2) 2 (startfraction 3 over 3 5 endfraction) (2 minus 14) 14 startfraction 3 over 3 5 endfraction (negative 14 minus 2) minus 2
The mathematical expression correctly uses the formula (startfraction m over m n endfraction) (x 2 minus x 1) x 1 to find the location of point r is:
" (startfraction 3 over 3 5 endfraction) (2 minus (negative 14)) (negative 14)" (Option A)
What is a mathematical expression?A mathematical expression is a statement that contains numbers, variables, functions, etc that are related to one another in a very logical way.
It can also be defined as a mathematical phrase that comprises:
NumbersVariables or both.Learn more about mathematical expression at:
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Answer:
A
Step-by-step explanation:
Find the Volume of a triangular pyramid! ~
Answer:
20
Step-by-step explanation:
using the given formula:
V = 1/3(Base Area)(height)
V = 1/3 (5)(12)
V = 1/3 (60)
V = 20
Answer:
20
Step-by-step explanation:
V = 1/3Bh
V = 1/3 x 5 x 12
V = 4 x 5
V = 20 cubic feet
Write the system of equations and construct the corresponding matrix model for the following exercise.Suppose that one of three different alleles is present in each individual in a population. In each generation the following happens: 8% of individuals carrying allele X mutate to carry allele Y, 6% mutate to allele Z; and the rest remain unchanged; 0.1% of individuals carrying allele Y mutate to carry allele Z and the rest remain unchanged; 90% of individuals carrying allele Z mutate to carry allele X and the rest remain unchanged.
The system of equations and the corresponding matrix model for the following above is given and explained below.
What is a system of equations?A system of Equations refers to a set of equations that one must solve or interact with all at once.
What is the system of equation for the exercise above?Let's call the person who carries alleles X, Y, and Z - Xt, Yt, and Zt, respectively.
Also, lets assume that 5 percent of X alleles mutate from X to Y and 3 percent mutate from X to Z in each generation, thus the percent of X alleles remains constant at:
100 - (5 percent + 3 percent) = 92 percent.
Also, because only 0.1 percent of Y alleles evolve from Y to Z, the percentage of Y alleles remains constant at 99.9%.
We must also consider that 90 percent of Z alleles do not change from Z to X, implying that 10% of Z alleles are indifferent.
Hence, the various equations describing the system will be given as:
Xt+1 = 0.92Xt + 0.92Zt
Yt+1 = 0.05Xt + 0.999Yt
Zt+1 = 0.03Xt + 0.01Yt + 0.1Zt
or
Xt+1 = 0.92Xt + 0.000Yt + 0.9Zt
Yt+1 = 0.05Xt + 0.999Yt + 0.0Zt
Zt+1 = 0.03Xt + 0.01Yt + 0.1Zt.
The Matrix Model is given as follows:
[tex]\begin{bmatrix}X_{t+1} \\Y_{t+1} \\Z_{t+1} \end{bmatrix}[/tex] = [tex]\left[\begin{array}{ccc}0.92&0&0.9\\0.05&0.999&0\\0.03&0.001&0.1\end{array}\right][/tex] = [tex]\begin{bmatrix}X_{t} \\Y_{t} \\Z_{t} \end{bmatrix}[/tex]
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