Answer:
x = 3
Step-by-step explanation:
2x - 3y - z = 7 (equation 1)
3x + 5y - 3z = -2 (equation 2)
4x – y + 2z = 17 (equation 3)
(1) * 3 : 6x - 9y - 3z = 21 (1)'
(1)' - (2) : 3x - 14 y = 23 (equation 4)
(1) * 2 : 4x - 6y - 2z = 14 (1)"
(1)" + (3) : 8x - 7y = 31 (equation 5)
(5)*2 : 16x - 14y = 62 (5)'
(5)' - (4) : 13x = 39
x = 3
So thus, x = 3 in this system of equations, you can plug x back into equation 4 or 5 to find y and then plug x and y back into equations 1, 2, or 3 to find z
A researcher is comparing the effectiveness of three devices designed to help people who snore. There are 210 people who snore participating in the experiment. Using a table of random digits starting from the first row and column, the researcher will randomly place the participants into three equally sized treatment groups suitable for comparison.
Which number range would be needed to label the subjects correctly?
0–2
1–3
000–210
001–210
The range would be needed to label the subjects correctly is 000-210.
What is Statistics?Statistics is the discipline that concerns the collection, organization, analysis, interpretation, and presentation of data.
Given that a researcher is comparing the effectiveness of three devices.
There are 210 people who snore participating in the experiment
The researcher will randomly place the participants into three equally sized treatment groups suitable for comparison.
We need to find the range which would be needed to label the subjects correctly.
210 people are participating in experiment
We need to label subjects from 001 to 210
Since there is no value in using 000 to indicate someone.
Hence, 000–210 is the range would be needed to label the subjects correctly.
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Triangle JKL is similar to triangle MNO. Find the measure of side MN. Round your answer to the nearest tenth if necessary.
Answer:
I believe the answer is 47. Forgive me if I'm wrong
Please Help Me!
Solve for x. Round to the nearest tenth if necessary.
what does 1/4 divided by 1/10 equal
Answer: 2/5
Step-by-step explanation: hope it helps
76 is 0.4% of what number? Use pencil and paper. Would you expect the answer to be a lot less than 76. Slightly less than 76, slight greater than 76, or a lot greater than 76? Explain.
Answer:
Step-by-step explanation:
It's a lot greater. If you take 0.4% of some number and the answer is 76, you better be starting with something that is very large. The formula will make the solution automatic.
Formula
Let the number be x
0.4% x = 76
0.4% = 0.4/100
0.4 / 100 * x = 76 Multiply both sides of the equation by 100
0.4x = 76*100 Combine the right.
0.4x = 7600 Divide by 0.4
x = 7600/0.4
x = 19000 Which is quite a bit larger than 76
Answer:
greater than 76
Step-by-step explanation:
hope it will help goodbye
what is 5 over 4 in math
Answer:
An improper fraction
Step-by-step explanation:
In improper fraction is when the numerator (top number) is greater than or equal to the denominator (bottom number)
Solve by using the quadratic formula. (If there is no solution, enter NO SOLUTION.)
1/7x^2+1=3/7x
smaller value of x =
larger value of x=
[tex]\dfrac 17 x^2 + 1 = \dfrac 37 x\\\\\implies x^2 +7 =3x~~~;[\text{Multiply both sides by 7}]\\\\\implies x^2 -3x +7 =0\\\\\text{Apply quadratic formula}~ x = \dfrac{-b \pm \sqrt{b^2 -4ac}}{2a}.\\\\\text{In this case ,}~ a =1, b= -3 , c =7\\\\x = \dfrac{-(-3) \pm \sqrt{(-3)^2 - 4(1)(7}}{2(1)}\\\\\implies x= \dfrac{3 \pm \sqrt{-19}}{2}\\\\\implies x =\dfrac{ 3 \pm i\sqrt{19}}2\\\\\\\text{Smaller value of x } =\dfrac{ 3 -i\sqrt{19}}2\\\\\text{Larger value of x } =\dfrac{ 3 +i\sqrt{19}}2[/tex]
log 95 The expression Tog2 is the result of applying the change of base formula to a logarithmic expression. Which could be the original expression? log, 2 3 log, 3 2 O log حاد 3 1 1093 2
Answer:
third option: log_2 1/3
Step-by-step explanation:
change of base formula:
log_b a= (log_x a)/(log_x b)
(log 1/3)/(log 2)
apply reverse change of base formula
2 from log 2 becomes new base, and 1/3 becomes the other number
=log_2 1/3
The original logarithmic expression which when undergoes the change of base formula gives the expression ㏒ (1/3) / ㏒ (2) is third option ㏒₂ (1/3).
Given a logarithmic expression,
㏒ (1/3) / ㏒ (2)
This expression is the result of a logarithmic expression when undergoes change of base formula.
The change of base formula is as given below.
㏒ₐ (x) = ㏒ₙ (x) / ㏒ₙ (a)
Using the same formula here,
We have the expression ㏒ (1/3) / ㏒ (2).
Here x = 1/3 and a = 2
So, the required expression is,
㏒ₐ (x) = ㏒₂ (1/3)
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Let f be a differentiable function. If h (x) = (2+ f (sin x))", which of the following gives a correct process for finding h' (x) ?
Answer:
[tex]\displaystyle h'(x) = \cos (x) f'(\sin x)[2 + f(\sin x)]'''[/tex]
General Formulas and Concepts:
Calculus
Differentiation
DerivativesDerivative NotationDerivative Property [Addition/Subtraction]: [tex]\displaystyle \frac{d}{dx}[f(x) + g(x)] = \frac{d}{dx}[f(x)] + \frac{d}{dx}[g(x)][/tex]
Derivative Rule [Basic Power Rule]:
f(x) = cxⁿf’(x) = c·nxⁿ⁻¹Derivative Rule [Chain Rule]: [tex]\displaystyle \frac{d}{dx}[f(g(x))] =f'(g(x)) \cdot g'(x)[/tex]
Step-by-step explanation:
Step 1: Define
Identify.
[tex]\displaystyle h(x) = [2 + f(\sin x)]''[/tex]
Step 2: Differentiate
Derivative Rule [Chain Rule]: [tex]\displaystyle h'(x) = [2 + f(\sin x)]''' [2 + f(\sin x)]'[/tex]Rewrite [Derivative Property - Addition/Subtraction]: [tex]\displaystyle h'(x) = [2 + f(\sin x)]''' \bigg[(2)' + [f(\sin x)]' \bigg][/tex]Derivative Rule [Basic Power Rule]: [tex]\displaystyle h'(x) = [2 + f(\sin x)]''' [f(\sin x)]'[/tex]Derivative Rule [Chain Rule]: [tex]\displaystyle h'(x) = [2 + f(\sin x)]''' f'(\sin x)(\sin x)'[/tex]Trigonometric Differentiation: [tex]\displaystyle h'(x) = \cos (x) f'(\sin x)[2 + f(\sin x)]'''[/tex]From here, if you would like, you can take the 3rd derivative of the last piece.
Topic: AP Calculus AB/BC (Calculus I/I + II)
Unit: Differentiation
Find all the numbers for each shape
Answer:
1 = pentagon2 = diamond3 = square5 = circle6 = rectangle7 = oval8 = triangle9 = hexagon10 = trapezoidStep-by-step explanation:
Each half of a hanger divides the total weight in half. The right-most vertical has a total weight of 80/16 = 5. It consists of a square and a diamond, and we know the square is 1 more than the diamond. That means 2 diamonds weigh 5 -1 = 4. A diamond weighs 2, and a square weighs 3. The other half of that balance is a circle, which weighs 5.
The total of a square and oval is 10, so the oval is 10 -3 = 7. The two trapezoids weigh 20, so each is 10.
The second vertical from the left is a circle and diamond which will weigh 5+2 = 7. That makes the sum of a pentagon and rectangle also be 7. The 7+7 = 14 below the square on the left branch makes the total of that branch be 14+3 = 17, which is also the sum of the triangle and hexagon.
The weight below the rectangle at top left is 17+17 = 34, and the weight of that entire branch is 40. Thus the rectangle is 40-34 = 6, which makes the pentagon 7-6 = 1.
We require the sum of the triangle and hexagon be 17, with the triangle being the smaller value, and both being 9 or less (the trapezoid is the only figure weighing more than 9). Hence the triangle is 8 and the hexagon is 9.
The weights are summarized in the answer section, above.
will give brainlyist
What is the quotient of 1 and 7 over 8 ÷ 3 over 8?
Answer:
5
Step-by-step explanation:
[tex]1\frac{7}{8}\div\frac{3}{8}[/tex]
[tex]=\frac{15}{8}\div \frac{3}{8}[/tex]
[tex]=\frac{15\times \:8}{8\times \:3}[/tex]
[tex]=\frac{15}{3}[/tex]
[tex]=5[/tex]
The quotient is 5.
[tex]\large\underline{\sf{Solution-}}[/tex]
[tex]\textsf{Given that:}\\[/tex]
[tex] \sf1 \dfrac{7}{8} \div \dfrac{3}{8} \\ [/tex]
[tex] \sf \longmapsto \: \dfrac{7 \times 8}{8} \div \frac{3}{8} \\ [/tex]
[tex] \sf \longmapsto \: \dfrac{15}{8} \div \dfrac{3}{8} \\ [/tex]
[tex] \sf \longmapsto \: \dfrac{ \dfrac{15}{8} }{ \dfrac{3}{8} } \\ [/tex]
[tex] \sf \longmapsto \: \dfrac{ \dfrac{15}{8} \times \frac{8}{3} }{ \dfrac{ \cancel \green3}{ \cancel \red8} \times \frac{ \cancel \red8}{ \cancel \green3} } \\ [/tex]
[tex]\sf \longmapsto \dfrac{ \dfrac{15}{8} \times \frac{8}{3} }{1} \\ [/tex]
[tex]\sf \longmapsto \: \dfrac{15}{ \cancel \red8} \times \dfrac{ \cancel \red8}{3} \\ [/tex]
[tex]\sf \longmapsto \: \dfrac{15}{3} \\ [/tex]
[tex]\sf\longmapsto \:\dfrac{15÷3}{3÷3}\\[/tex]
[tex]\sf\longmapsto \:\dfrac{5}{1}\\[/tex]
[tex]\sf\longmapsto \:\boxed{5} \: Answer.\\[/tex]
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please help 31 pts and brainlist if you give me a step by step explanation on how to do this
Answer: Hence, by ASA ( Angle side Angle) Rule of congruency two triangles;
Angle ADE = CDF Hence proved.
Step-by-step explanation:Diagram of two triangles are given such that side ED = FD and <AED = < CFD = 90
To Find: TO prove <ADE = <CDF
Solution; In figure ; we can see that <EDA and <FDC are vertically opposite angles and hence are equal.
=> <EDA = <FDC |Vertically opposite angles
<DEA = <CFD = 90 |Given
Also, ED = FD |Given
Hence, by ASA (Angle Side Angle)
Rule of congruency two triangles; <ADE = <CDF
Hence Proved.
Find the value of x, y and z in the rhombus below
Answer:
... ................................
9x-5y=2
3x-4y=10
can anyone please explain how the answer of this question is:
x=-4
y=-2
Answer:
9x-5y=2======>9x-5y=2===>(+)7y=-28=>y=-4=>(1)3x-4(-4)=10=>x+16=20=>x=4
3x-4y=10(1)=>(×-3)-9x+12y=-30=>(+)
What is the Area of semicircle?
Step-by-step explanation:
Area of Semi Circle
The area of a semicircle is half of the area of the circle. As the area of a circle is πr2. So, the area of a semicircle is 1/2(πr2 ), where r is the radius.
Here is the equation of a circle: x2 + y2 + 12x + 2y + 12 = 0
Find the center and radius of the circle.
Answer:
centre = (- 6, - 1 ) , radius = 5
Step-by-step explanation:
The equation of a circle in standard form is
(x - h)² + (y - k)² = r²
where (h, k ) are the coordinates of the centre and r is the radius
Given
x² + y² + 12x + 2y + 12= 0
Collect the x- terms and the y- terms together and subtract 12 from both sides
x² + 12x + y² + 2y = - 12
Using the method of completing the square
add ( half the coefficient of the x / y coefficients )² to both sides
x² + 2(6)x + 36 + y² + 2(1)y + 1 = - 12 + 36 + 1
(x + 6)² + (y + 1)² = 25 ← in standard form
with (h, k ) = - 6, - 1 ) as centre and r = [tex]\sqrt{25}[/tex] = 5
please help brainliest
Solve. −7/8=−1/6−3/10x Enter your answer as a mixed number in simplest form in the box. x =
Answer:
X=[tex]\frac{36}{85}[/tex]
Step-by-step explanation:
-[tex]-\frac{7}{8}=-\frac{1}{6}-\frac{3}{10x}[/tex]
move the contants to the right hand side
[tex]-\frac{3}{10x}=-\frac{1}{6}+\frac{7}{8}[/tex]
Add the to terms on the right
[tex]-\frac{3}{10x}=\frac{17}{24}[/tex]
Cross multiply
72=170x
Swap sides of the equation
170x=72
Divide by 170 to both sides
x=[tex]\frac{36}{85}[/tex]
This is the simplest form.
The solution of the linear equation −7/8 = −1/6 − (3/10)x in the form of a mixed fraction number will be 2 ¹³/₃₆.
What is the solution to the equation?The allocation of weights to the important variables that produce the calculation's optimum is referred to as a direct consequence.
The definition of simplicity is making something simpler to achieve or grasp while also making it a little less difficult.
The linear equation is given below.
−7/8 = −1/6 − (3/10)x
Simplify the equation, then we have
−7/8 = −1/6 − (3/10)x
(3/10)x = −1/6 + 7/8
(3/10)x = 17/24
x = 85/36
x = 2 ¹³/₃₆
The arrangement of the direct condition −7/8 = −1/6 − (3/10)x as a blended part number will be 2 ¹³/₃₆.
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6m+7n+5m−3n simpified
Answer:
11m + 4n
Step-by-step explanation:
when two numbers with the same variable are added together or subtracted the result is just the numbers added or subtracted. So you can add 6m and 5m to get 11m. and you can subtract 3n from 7n to get 4n
11m + 4n
In a bag there are pink buttons, yellow buttons and blue buttons.
There are five times as many pink buttons as yellow buttons.
number of yellow buttons : number of blue buttons = 4 : 7
One button is selected at random.
Work out the probability that the button is either pink or blue.
Give your answer as a fraction in its simplest form.
Answer:
27/31
Step-by-step explanation:
5pink : 1yellow
4yellow : 7blue
times the first ratio by 4 so that the yellows are equal (if that makes sense)
20pink : 4yellow : 7blue = 31 buttons
so the total is 31 buttons alltogether
and the pink and blue buttons together = 27 buttons
so 27/31 is the probability the button is pink or blue
4. Find the solution for each equation:
x + 4 = 16
Answer:
[tex]x=12[/tex]
Step-by-step explanation:
when solving and equation with a variable, you must work backwards and do the opposite of the equation
sooo… you must subtract 4 (opposite of +4 is -4)
[tex]16-4=2[/tex]
x=12
Answer:
12 easy
Step-by-step explanation:
4 +12 =16 it's easy
help me solve this please
Answer:
[tex] \sqrt{8} [/tex]
Step-by-step explanation:
an
irrational number can only be written in the form with never ending,non-repeatinng digits after the decimal comma
Have students write the answer to the Essential Question and draw examples to explain their answer
Qui est grand 0 ou -2,5
Answer:
0
Step-by-step explanation:
positive numbers are always bigger than negative numbers
a) 9 b) 10 c) 12 d) 15
will give brainliest plz help
[tex]y = \frac{x}{2} [/tex]
[tex]2x + 2y = \sqrt{180} \\ = > 2x + 2( \frac{x}{2} ) = \sqrt{180} \\ = > 2x + x = \sqrt{2 \times 2 \times 3 \times 3 \times 5} \\ = > 3x = 2 \times 3\sqrt{5} \\ = > 3x = 6 \sqrt{5} \\ = > x = \frac{6 \sqrt{5} }{3} \\ = > x = 2 \sqrt{5} [/tex]
[tex]x.y \\ = x \times \frac{x}{2} \\ = \frac{ {x}^{2} }{2} \\ = \frac{ {(2 \sqrt{5} )}^{2} }{2} \\ = \frac{4 \times 5}{2} \\ = \frac{20}{2} \\ = 10[/tex]
Answer:
10
Hope you could get an idea from here.
Doubt clarification - use comment section.
Answer:
b
Step-by-step explanation:
Given
2x + 2y = [tex]\sqrt{180}[/tex] = [tex]\sqrt{36(5)}[/tex] = 6[tex]\sqrt{5}[/tex]
and y = [tex]\frac{x}{2}[/tex] , then
2x + (2 × [tex]\frac{x}{2}[/tex] ) = 6[tex]\sqrt{5}[/tex]
2x + x = 6[tex]\sqrt{5}[/tex]
3x = 6[tex]\sqrt{5}[/tex] ( divide both sides by 3 )
x = 2[tex]\sqrt{5}[/tex]
and y = [tex]\frac{2\sqrt{5} }{2}[/tex] = [tex]\sqrt{5}[/tex]
Then
xy = 2[tex]\sqrt{5}[/tex] × [tex]\sqrt{5}[/tex] = 2 × 5 = 10 → b
answer for this question plz
Step-by-step explanation:
in that case we can imagine a diagonal line DB that splits the quadrilateral into 2 right-angled triangles: ADB and CDB.
the area of the quadrilateral is then the sum of the areas of the 2 triangles.
the area of a right-angled triangle is
leg1 × leg2 / 2
with the legs being the sides that enclose the 90 degree angle.
so, for ADB we get
AD × AB / 2 = 3 × 11 / 2 = 33/2 = 16.5
for CDB we get
BC × CD / 2 = 7 × 9 / 2 = 63/2 = 31.5
so, in total for the area of the quadrilateral we get
16.5 + 31.5 = 48
someone help pleaseee
Answer:
(x+1)x(x+7)x(3x-4)
Step-by-step explanation:
Please help me with the following question:
Answer:
the answer to this problem is D: 180 + w-z
Marlee had a certain amount of money (x) in her bank
account. She deposited $60.00 from her grandmother
for her birthday. She then spent of the money in her account on rent that totaled $550. Which equation represents this situation?
Answer:
x-490=t
Step-by-step explanation:
Marlee has x money
She deposited $60 meaning adding $60 to the bank
So x+60
THen Marlee need to withdraw $550 from her bank to rent
So the equation is now
x+60-550
60-550 is -490
Thus:
x-490
(I will represent (t) as the money she has left for the equation)
Thus the equation is
x-490=t
Hope this helps!
Martin measure the length of his window he measures 26 inches the actual of the window was 25 inches what percent of this an era is this
Answer:
4% maybe
Step-by-step explanation:
if ab =8 and a square + bsquare =35 then (a-b) cube
[tex]\text{Given that,}\\\\ab = 8 ~ \text{and}~ a^2 +b^2 = 35\\\\\text{Now,}\\\\(a-b)^2 = a^2 +b^2 -2ab\\\\\implies (a-b)^2 =35 - 2 (8) \\\\\implies (a-b)^2 = 19\\\\\implies a-b = \pm\sqrt{19}\\\\\text{Case 1:}\\\\(a-b)^3 = (a-b)^2(a-b)\\\\\implies (a-b)^3 = 19 \left(\sqrt{19}\right)\\\\\text{Case 2:}\\\\(a-b)^3 = (a-b)^2(a-b)\\\\\implies (a-b)^3 = -19 \left(\sqrt{19}\right)[/tex]