Step-by-step explanation:
Given:
log_(a) abc = x+1,
log_(b) abc = y+1,
log_(c) abc =z+1
Asked: x + y + z + 2 = ?
Solution:
Let
log_(a) abc = x+1 ⇛log_(abc) a = {1/(x+1)} →→→Eqn(1)
log_(b) abc = y+1 ⇛log_(abc) b = {1/(y+1)} →→→Eqn(2)
log_(c) abc = z+1 ⇛log_(abc) c = {1/(z+1)} →→→Eqn(3)
On adding equation (1),(2) and (3) then
log_(abc) a + log_(abc) b + log_(abc) c = {1/(x+1) + {1/(y+1)} + {1/(z+1)}
⇛log_(abc) abc = {{(y+1)(z+1) + (z+1)(x+1) + (x+1)(y+1)}/{(x+1)(y+1)(z+1)}]
⇛1 = {{(y+1)(z+1) + (z+1)(x+1) + (x+1)(y+1)}/{(x+1)(y+1)(z+1)}]
⇛{(x+1)(y+1)}(z+1) = (y+1)(z+1) + (z+1)(x+1) + (x+1)(y+1)
⇛{x(y+1)+1(y+1)}(z+1) = (y+1)(z+1) + (z+1)(x+1) + (x+1)(y+1)
⇛{xy + x + 1 + y}(z+1) = (y+1)(z+1) + (z+1)(x+1) + (x+1)(y+1)
⇛{xy + x + y + 1}(z+1) = (y+1)(z+1) + (z+1)(x+1) + (x+1)(y+1)
⇛z(xy + x + y + 1) + 1(xy + x + y + 1) = (y+1)(z+1) + (z+1)(x+1) + (x+1)(y+1)
⇛xyz + xz + yz + z + xy + x + y + 1 = (y+1)(z+1) + (z+1)(x+1) + (x+1)(y+1)
⇛xyz + xz + yz + z + xy + x + y + 1 = y(z+1)+1(z+1) + z(x+1)+1(x+1) + x(y+1)+1(y+1)
⇛xyz + xz + yz + z + xy + x + y + 1 = yz + y + z + 1 + xz + z + x + 1 + xy + x + y + 1
⇛x+y+z = y + z + 1 + x + 1
⇛x+y+z = x + y + z + 2
Therefore, x + y + z + 2 = x + y + z
Answer: Hence, the value of x + y + z + 2 = x + y + z.
also read similar questions: Let p= 5/((1/log2x)+(1/log3x)+(1/log4x)+(1/log5x)) and (120)^p=3 2,then
the
value
of
x?
https://brainly.com/question/26624014?referrer
7. 65 out of 105
Simplify
Answer:
13/21
Step-by-step explanation:
65/105 = 13/21
A welder needs a piece of half inch pipe 14 3/8 inch long. She has a peace that is 25 1/16 inch long how much must she cut off from the longer piece?
well, the longer piece is clearly the latter, so let's firstly convert the mixed fractions to improper fractions and then subtract.
[tex]\stackrel{mixed}{14\frac{3}{8}}\implies \cfrac{14\cdot 8+3}{8}\implies \stackrel{improper}{\cfrac{115}{8}} ~\hfill \stackrel{mixed}{25\frac{1}{16}}\implies \cfrac{25\cdot 16+1}{16}\implies \stackrel{improper}{\cfrac{401}{16}} \\\\[-0.35em] ~\dotfill\\\\ \cfrac{401}{16}~~ - ~~\cfrac{115}{8}\implies \implies \cfrac{(1)401~~ - ~~(2)115}{\underset{\textit{using this LCD}}{16}}\implies \cfrac{171}{16}\implies 10\frac{11}{16}[/tex]
After four days, Trudy's average exercise time was 45 minutes per day. If she exercises 60 minutes on the fifth day, what will be her average time in
Answer:
240
Step-by-step explanation:
because adding the 45's 4 times then adding 60.
sorry if im wrong btw.
2 2/5 divided by 2 1/10
firstly let's convert the mixed fractions to improper fractions and then divide.
[tex]\stackrel{mixed}{2\frac{2}{5}}\implies \cfrac{2\cdot 5+2}{5}\implies \stackrel{improper}{\cfrac{12}{5}} ~\hfill \stackrel{mixed}{2\frac{1}{10}}\implies \cfrac{2\cdot 10+1}{10}\implies \stackrel{improper}{\cfrac{21}{10}} \\\\[-0.35em] ~\dotfill\\\\ \cfrac{12}{5}\div \cfrac{21}{10}\implies \cfrac{12}{5}\cdot \cfrac{10}{21}\implies \cfrac{120}{105}\implies \cfrac{8}{7}\implies 1\frac{1}{7}[/tex]
Answer:
first make them improper fractions
2 2/5 = 12/5
2 1/10 = 21/10
now set them up
12/5 divided by 21/10
make 21/10 a reciprocal(flip the fraction upside down) and multiply across
12/5 x 10/21 = 1.14 or 1 1/7
8.If 20 is 50% of a number, what is the number
Percentage
100:50 x 20 = 40
Math help 3 help me please!
#1
Answers are
Perpendicular bisector of KLOnly this rest are not possible
#2
No perpendicular bisectorAngle bisectorMedian Altitude#3
Perpendicular bisectorAngle bisectorMedianAltitudethere are 3 piles papers on a desk each pile has 21 papers how many papers are there total
Answer:
63 papers total.
Step-by-step explanation:
3 piles, 21 papers a pile, 3*21 =63.
Answer:
63
Step-by-step explanation:
because 3x21 is 63
Use the model below to calculate
2
3
×
3
4
.
A rectangle is shown divided into 3 rows and 4 columns. 3 of the 4 columns are shaded blue.
A.
3
12
or
1
4
B.
12
12
or
1
C.
4
12
or
1
3
D.
6
12
or
1
2
Answer:
D
Step-by-step explanation:
i already did the test
Answer:
d
Step-by-step explanation:
GIVING BRAINIEST IF CORRECT!!!
Farmer Taja needs a field for her horses to graze. She found a field that has a width of x+4. The length of the field is more than twice the width. What is the area of the field Taja found?
Given :
w = x + 4L = 3+ 2(w) = 3 + 2 (x + 4)Solution:
Area = L × WArea = [3 + 2 (x + 4) ]× x + 4Area = [3 + 2x + 8] × x + 4Area = [2x + 11] × x + 4Area = 2x² + 11x + 8x + 44Area = 2x² + 19x + 44hope it helped!
What is the exact value of 5 5/6 - (1 1/4 + 3 7/8)?
A. 17/24
B. 1 1/6
C. 8 11/24
D. 10 23/24
A standard pair of six-sided dice is rolled. What is the probability of rolling a sum less than or equal to 8? Express your answer as a fraction or a decimal
rounded to four decimal places.
Answer:
2/3
Step-by-step explanation:
Which of the following is the inverse of p → ~q?
Answer:
K/q = p if you're taking about the inverse proportions
Answer is linked below.
Answer:
- 7x² + 12x - 9Step-by-step explanation:
Given:
A = 3x² - 7x + 8B = x² + 8x - 3C = - 5x² - 3x + 2Find B + C - A:
B + C - A = x² + 8x - 3 + (- 5x² - 3x + 2) - (3x² - 7x + 8) = x² + 8x - 3 - 5x² - 3x + 2 - 3x² + 7x - 8 =(1 - 5 - 3)x² + (8 - 3 + 7)x + (-3 + 2 - 8) = - 7x² + 12x - 9A = [tex]3x² - 7x + 8[/tex]
B = [tex]x² + 8x - 3[/tex]
C = [tex]-5x²-3x + 2[/tex]
Lets find B + C - A :
→ [tex]B + C - A[/tex]
→ [tex]x² + 8x - 3+ (- 5x²-3x + 2)-(3x² - 7x + 8)[/tex]
→ [tex]x² + 8x - 3-5x² - 3x + 2-3x² + 7x - 8[/tex]
→[tex] (1-5-3)x² + (8 -3 + 7)x+ (-3 + 2 - 8)[/tex]
→ [tex]- 7x² + 12x - 9[/tex]
[tex]5+2x^{2} +x+3x^{2} +7+6x[/tex]
Answer:
Don't know the answer but good luck?
Step-by-step explanation:
The width, W , of a rectangle is 4 less than 6 times the length, which would find the area.
Group of answer choices
Solution:
Note that:
W = 6L - 4Area = LWSubstitute the value of W into the formula (Area = LW).
Area of rectangle = LWArea of rectangle = L x WArea of rectangle = L x (6L - 4)Area of rectangle = L(6L - 4)Option C is correct.
The price of a technology stock has risen to $9.77 today. Yesterday's price was $9.68. Find the percentage Increase. Round your answer to the nearest tenth of a percent.
PLEASE HELP ME PLEASE
Answer:
0.75 lb potato salad = $2.22
Step-by-step explanation:
If 1 pound of potato salad = $2.96
Then 0.75 pounds of potato salad = 0.75 x 2.96 = 2.22
What is the length of the altitude drawn to the hypotenuse? The figure is not drawn to scale. * 12 3 X W3 x 12 Z Y Your answer
Answer:
What is the length of the altitude drawn to the hypotenuse?, Corollary: The length of the altitude to the hypotenuse of a right triangle is the geometric mean of the lengths of the two segments of the hypotenuse.
Furthermore, When an altitude is drawn to the hypotenuse of a given right triangle the new figure comprises two similar right triangles?, Theorem 62: The altitude drawn to the hypotenuse of a right triangle creates two similar right triangles, each similar to the original right triangle and similar to each other. Figure 2 shows the three right triangles created in Figure . They have been drawn in such a way that corresponding parts are easily recognized.
Finally, When the altitude is drawn to the hypotenuse of a right triangle three similar triangles are formed?, The Inscribed Similar Triangles Theorem states that if an altitude is drawn from the right angle of any right triangle, then the two triangles formed are similar to the original triangle and all three triangles are similar to each other. Perpendicular lines are lines that intersect at a 90^{circ} angle.
Step-by-step explanation:
Anyone know answers to these? I don’t understand these at all
Answer:
[tex]\red{ m\angle B= 121\degree}\\\\\purple{AD=23\: units}[/tex]
Step-by-step explanation:
Quadrilateral ABCD is a parallelogram.
opposite angles of a parallelogram are equal in measure.
[tex]\implies (10x-19)\degree=(9x-5)\degree[/tex]
[tex]\implies 10x-19=9x-5[/tex]
[tex]\implies 10x-9x=19-5[/tex]
[tex]\implies x=14[/tex]
[tex]m\angle B= (9x-5)\degree[/tex]
[tex]\implies m\angle B= (9*14-5)\degree[/tex]
[tex]\implies m\angle B= (126-5)\degree[/tex]
[tex]\huge\implies m\angle B= 121\degree[/tex]
Opposite sides of a parallelogram are equal.
3y - 1 = y + 15
3y - y = 15 + 1
2y = 16
y = 16/2
y = 8
AD = 3y - 1 = 3*8 - 1 = 24 - 1
AD = 23
The prime number in the following list is....
A. 19
B. 21
C. 38
D. 39
Answer:
19
Step-by-step explanation:
Answer:
19
because it has only two factors and prime has only two factors
You have been sent to grocery shop. They gave you $25.00 and the list of what
you need to buy, would you need more money or would you have enough money?
Here is the grocery list:
2 pounds of ham: $4.59/pound
3 bags of chips: $3.00/bag
2 loaves of bread: $1.99/loaf
Please calculate the above and write down how much it equals and what you will
have left after you buy it.
Answer:
you would have $2.98 left
Step-by-step explanation:
$4.59 x 2=9.18
3.00 x 3=9.00
$1.99 x 2=3.98
$9.18+$9.00+$3.98=22.16
$25.00-$22.16 = $2.89
Ms. Jacobi writes the equation x+y=z. If x = 5, y = 3, and z = 53,
is the equation true? Explain your reasoning.
Answer:
no
Step-by-step explanation:
Because if we substitute the value of x,y and z we get
x+y=z
5+3=53(FALSE)
Answer and Step-by-step explanation:
No, this equation is not true. But in order to show this, we need to write out the equation. So if x = 5, and y = 3, then the equation for this equation would look like this:
5 + 3 = 8.
That is incorrect because 5 + 3 does not equal 53. This is a trick question that is trying to trick you. Now if that 5 was a 50, then this equation would be true.
So, 5 + 3 ≠ 53.
I hope that this helps.
what does a(b-c) = to?
Solution:
The expression "a(b-c)" is an example of distributive property. To simplify it, simply multiply a by the terms inside the bracket.
Simplifying the distributive property.
=> a(b - c)=> (a x b) + (a x -c)=> ab - acHence, the simplified expression is ab - ac.
We can use the distributive law to simplify it or factor it but more
[tex]\\ \tt\hookrightarrow a(b-c)[/tex]
[tex]\\ \tt\hookrightarrow a(b)-a(c)[/tex]
[tex]\\ \tt\hookrightarrow ab-ac[/tex]
Substitute this simultaneous linear equation
[tex]x - 4y = - 6 \\ 2x + 3y = 10[/tex]
Answer:
[tex]x - 4y = - 6 \: ......(1) \\ \\ 2x + 3y = 10 \: .......(2)[/tex]
from equation (1)
[tex]x - 4y = - 6 \\ \\ 4y = x + 6 \\ \\ y = \frac{x + 6}{4} [/tex]
Substitute " y " in equation (2)
[tex]2x + 3y = 10 \\ \\ 2x + 3( \frac{x + 6}{4} ) = 10 \\ \\ 2x +( \frac{3x + 18}{4} ) = 10 \\ \\ \\ \frac{8x + 3x + 18}{4} = 10 \\ \\ \\ 8x + 3x + 18 = 10 \times 4 \\ \\ 11x + 18 = 40 \\ \\ 11x = 40 - 18 \\ 11x = 22 \\ \\ x = \frac{22}{11} \\ \\ x = 2[/tex]
[tex]y = \frac{x + 6}{4} \\ \\ y = \frac{2 + 6}{4} \\ \\ y = \frac{8}{4} \\ \\ y = 2[/tex]
Give answer as positive exponent
[tex]\huge\textbf{Hey there!}[/tex]
[tex]\mathsf{x^4\ \bullet \ x^{-7}}\\\\\mathsf{\rightarrow x\bullet x\bullet x\bullet x (\dfrac{1}{x\bullet x \bullet x \bullet x\bullet x \bullet x \bullet x})}\\\\\mathsf{\star \heartsuit \ - 7 = \bf -3 \ \star \heartsuit}\\\\\mathsf{\rightarrow \dfrac{1}{x\bullet x \bullet x}}\\\\\mathsf{\approx \dfrac{1}{x^3}}\\\\\\\huge\textbf{Therefore, your answer is: \boxed{\mathsf{\dfrac{1}{x^3}}}}\huge\checkmark[/tex]
[tex]\huge\textbf{Good luck on your assignment \& enjoy}\\\huge\textbf{your day!}[/tex]
~[tex]\frak{Amphitrite1040:)}[/tex]
Suppose that 12 inches of wire costs 48 cents.
At the same rate, how much (in cents) will 31 inches of wire cost?
Answer:
It will cost 124 cents to buy 31 inches of wire.
Step-by-step explanation:
12 inches costs 48 cents
1 inches will cost her [tex]\frac{48}{12}[/tex] → 4 cents
Then 31 inches will cost: 31 * 4 → 124 cents
Answer:
124 centsStep-by-step explanation:
Solve using ratios since this is a proportional relationship:
12/48 = 31/x1/4 = 31/xx = 31*4x = 124 centsNEED HELP ASAP
Which statement correctly explains the association in the scatter plot?
Answer:
Negative relationship
Step-by-step explanation:
It is going in a negative direction.
Pls mark brainliest :)
what's the slope
(1, 1)
(3, 4)
Answer:
y= 3/2x-1/2
Step-by-step explanation:
Answer:
3/2 or 1.5
Step-by-step explanation:
gradient = ∆y/∆x
∆y = 4 - 1 =3
∆x = 3 - 1 = 2
∆y/∆x = 3/2
There are 21 students in class. The median age of the students is 23. The oldest student is 29
Please explain
Answer:
At least one student is 23: Must be true
Some students are younger than 15: Could be true
Step-by-step explanation:
Statement 1: A median is a number in the middle for ex. 1, 2, 3, 4, 5 in this example 3 is the median. Another ex could be 1, 2, 3, 4, 5, 6. This time you would have to add (3 + 4), divide by 2, which equals 3.5.
Since there are 21 students in class making it an odd number 23 must be true.
Statement 2: Based on the information I am given, I would say could be true because the difference between the oldest and the median is 29 - 23 = 6 so it could be true.
Answer:
1) At least one (the 11th) student is 23 (years old), Must be true
2) Some students are younger than 15 Could be true
Step by step explanation:
1) The given parameters are;
The number of student in the class = 21
The median age of the student = 23
The age of the oldest student = 29
Therefore, given that the median age = The age of the (n + 1)/2 the student
Where;
n = The number of student in the class = 21
The median age = The age of the (21 + 1)/2 th = 11 th student, when the age of the students are arranged in increasing order, therefore, we have;
At least one (the 11th) student is 23 (years old), Must be true
2) Given that there are 10 students with ages equal to or lower than the median age, and the difference between the median age and the age of the oldest student = 29 - 23 = 6 years, we have;
Some students are younger than 15 Could be true
Express each fraction as a percent. Round your answer to the nearest whole number. 76/125
Answer:
61%
Step-by-step explanation:
Multiply the fraction by 100%.
76/125 × 100% = (7600/125)% = 60.8% ≈ 61%