x = 2y + 7 (*)
x = y + 4 (**)
Substitute (*) to (**):
2y + 7 = y + 4 subtract 7 from both sides
2y = y - 3 subtract y from both sides
y = -3Put the value of y to the second equation:
x = -3 + 4
x = 1use the law of sines to find the length of side c
Look at the picture.
The law os sine:
[tex]\dfrac{a}{\sin A}=\dfrac{b}{\sin B}=\dfrac{c}{\sin C}[/tex]
We have
[tex]m\angle A=46.7^o\\\\m\angle C=48^o\\\\a=44\\\\c=?[/tex]
Substitute:
[tex]\dfrac{c}{\sin48^o}=\dfrac{44}{\sin46.7^o}\\\\\boxed{c=44.93}\to\boxed{A.}[/tex]
Answer:
A!
Step-by-step explanation:
Michelle multiple 3.4×52. she incorrectly wrote 1,768 as her product.
Answer:
Wrong Answer 176.8
Step-by-step explanation:
Multiply 3.4 * 52 = 176.8
please help me Find the legth of x
Answer: 6
=====================================
Explanation:
The triangles are similar triangles (we can use the AA similarity theorem to prove this). So the vertical sides pair up, and the horizontal sides pair up, to form the proportion below
x/4.5 = 8/6
Note the order of the terms. I'm dividing the upper triangle's sides by the corresponding lower triangle's sides. Cross multiply and solve for x
x/4.5 = 8/6
6x = 4.5*8
6x = 36
x = 36/6
x = 6
Help!
If I were to Buy a bright bomer from the item shop and buy the glider. The Bright bomer is Rare and so is the glider. How much?
Answer: 2000 v-bucks
Step-by-step explanation: The bright bomber costs 1,200 and the glider costs 800
How many permutations are possible for 11 objects taken 7 at a time? 330 5,040 237,600 1,663,200
The number of permutations possible for 11 objects taken 7 at a time is 1663200
Using the permutation formula :
nPr = n!/(n - r)!Here ,
n = 11 ; r = 7Inputting our values:
11P7 = 11!/(11 - 7)!
Evaluate:
11P7 = 1663200
Express 1.05 as a percent
1. 05 × 100
105%
(You move the decimal over twice)
Answer: 105%
Step-by-step explanation:
A ramp 31ft long raises to a platform. the bottom of the platform is 16ft from the foot of the ramp. find x, the angle of elevation of the ramp. round your answer to the nearest tenth of a degree.
The angle of elevation of the ramp (x) is approximately 58.9 degrees.
How to find the angle of elevation
To find the angle of elevation (x) of the ramp using the cosine function,
cos(x) = adjacent / hypotenuse
Given:
Adjacent side = 16 ft
Hypotenuse = 31 ft
Plug in these values into the formula
cos(x) = 16 / 31
To find x, take the inverse cosine (arccos) of both sides:
x = arccos(16 / 31)
Using a calculator, arccos(16 / 31) is approximately 58.9 degrees.
Therefore, rounding to the nearest tenth of a degree, the angle of elevation of the ramp (x) is approximately 58.9 degrees.
Which value is the same as 2 tenths?
Answer:
0.2
Step-by-step explanation:
2/10=0.2
using the random digits table from the lesson, start with the number in the tenth column, eighth row. list that number and next 4 numbers in the column.
First number
54, 50, 98, 82, 71, 19, 99, 09, 10
second number
09, 54, 98, 10, 19, 99, 71, 50, 82
third number
54, 99, 19, 98, 71, 50, 09, 10, 82
fourth number
99, 10, 98, 19, 54, 50, 09, 71, 82
fifth number
10, 99, 82, 19, 50, 54, 71, 09, 98
Answer:
19, 82, 54, 09 and 99
Step-by-step explanation:
From the random table, row numbers are given on the left side of the table and the column numbers are given on the top of the table.
On seeing them, the number on the tenth column and eighth row is 19.
The next 4 numbers on the same column are the elements in the 9th, 10th, 11th and 12 rows and on the same tenth column.
They are:
82, 54, 09 and 99.
Answer:
19, 82, 54, 09 and 99
Step-by-step explanation:
From the random table, row numbers are given on the left side of the table and the column numbers are given on the top of the table.
On seeing them, the number on the tenth column and eighth row is 19.
The next 4 numbers on the same column are the elements in the 9th, 10th, 11th and 12 rows and on the same tenth column.
They are:
82, 54, 09 and 99.
Step-by-step explanation:
The length of a rectangle is three centimeters more than twice the width. The perimeter is 78 centimeters. Define a variable and write and solve an equation to find out how long and wide the rectangle is?
I need to find the length? how?
Nicole drove
355 miles using 17 gallons of gas. At this rate, how many gallons of gas would she need to drive 284 miles?
Answer:
13.6 i believe, but that could, should be right tho.
Step-by-step explanation:
355/17=20.88235294 then 284/20.88235294=13.6
For this case, you want to know how many gallons of gasoline Nicole needs to drive 284 miles, knowing that with 17 she drove 355 miles. For this, we make a rule of three:
[tex]355 \ miles -----------> 17 \ gallons\\284 \ miles -----------> x[/tex]
Where "x" represents the number of gallons consumed in 284 miles.
[tex]x = \frac {284 * 17} {355}\\x = 13.6 \ gallons[/tex]
So, Nicole will need 13.6 gallons of gas to drive 284 miles
Answer:
13.6 gallons
What is the graph of the inequality?
x > -3
Help!
Two factory plants are making TV panels. Yesterday, Plant A produced 6000 panels. Seven percent of the panels from Plant A and 2 % of the panels from Plant B were defective. How many panels did Plant B produce, if the overall percentage of defective panels from the two plants was 4 % ?
Answer:
1% of 4000 + 4% of B = 2% of (4000 + B)
40 + 0.04*B = 0.02( 4000 + B)
40 + 0.04* B = 80 + 0.02*B
40 + 0.04*B - 80 - 0.02B = 0
0.02*B - 40 = 0
0.02*B = 40
2B = 4000
B = 2000
Step-by-step explanation:
Plant B produced 1000 panels.
The total number of defective panels from Plant A is 7% of 6000,
= (7/100) x 6000
= 420 panels.
and, total number of defective panels from Plant B is 2% of x,
= (2/100) x
= (1/50) x.
The overall number of defective panels from both plants is 4% of the total number of panels
= (4/100)(6000 + x)
= (1/25) (6000 + x).
Now, set up the equation:
420 + (1/50) x = (1/25) (6000 + x)
To solve for x, we can multiply both sides of the equation by 50 * 25 to eliminate the fractions:
50 . 25 . 420 + 50 x = 25 (6000 + x)
125000 + 50x = 150000 + 25x
50x - 25x = 150000 - 125000
25x = 25000
x = 25000 / 25
x = 1000
Therefore, Plant B produced 1000 panels.
Learn more about Equation here:
https://brainly.com/question/29657983
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Which expression is equivalent to -9( -2x - 3)
Answer:
-18x+ 27
Step-by-step explanation:
I need to know where did kellys collection go the most?
Answer:
What options are there
Step-by-step explanation:
Answer:
Step-by-step explanation:
Between the third and fourth months, the size of K's collection grew by 3. This is the steepest slope / greatest rate of change.
Divide. 413÷129 Enter your answer, as a mixed number in simplest form, in the box.
For this case we must divide the following expression:
[tex]\frac {413} {129}[/tex]
The expression can not be simplified. When dividing we have that its decimal form is given by:
3,201550
If we convert to a mixed number we have:
[tex]3 \frac {26} {129}[/tex]
Verifying:
[tex]3 \frac {26} {129} = \frac {129 * 3 + 26} {129} = \frac {413} {129}[/tex]
Answer:
[tex]3 \frac {26} {129}[/tex]
Can you solve this for me please in a good way
Answer:
x = -2
Step-by-step explanation:
If you factor out 1/9 you get rid of the fractions and that makes the equation a whole lot easier.
[tex](5x+10)^2 - x(25x+27) + 46 = 0[/tex]
Next, eliminate the brackets:
[tex]25x^2 +100x + 100 - 25x^2 - 27x + 46 = 0[/tex]
Combine the terms:
[tex]x = \frac{- 146}{73} = -2[/tex]
Answer:
x = - 2
Step-by-step explanation:
The 9 does absolutely nothing. Multiply the whole equation by. 9. Remember that each term must show the 9 is missing
(5x + 10)^2 - x(25x + 27) + 46 = 0
Next expand the first and second binomial so that the brackets can be removed.
(25x^2 + 100x + 100) - (25x^2 + 27x) + 46 = 0
Now remove the brackets
25x^2 + 100x + 100 - 25x^2 - 27x + 46 = 0
Collect the like terms
25x^2 - 25x^2 + 100x - 27x + 100 +46 = 0
73x + 146 = 0
Subtract 146 from both sides
73x = - 146
Divide by 73
x = - 146/73
x = - 2 <<<< Answer
Find the constant of variation for the relationship described in the table.
x f(x)
–2 –60
1 30
4 120
5 150
90
30
f(x)
x
Answer:
i believe the answer is 30
Step-by-step explanation:
Three distributions, labeled (a), (b), and (c), are represented below by their histograms. Each distribution is symmetrical and is made of
measurements. Without performing any calculations, order their respective standard deviations
,
, and
.
Answer:
order is
αb<αc<αa
Step-by-step explanation:
in a )
number 4 and number 12 are showing 3 bullets while number 7 and 9 showing 2 bullets hence
standard deviation for a=3-2=1
in b)
number 4 ,7,9 and number 12 are showing 2 bullets while number 3 and 13 showing 1 bullet hence
standard deviation for a=2-1=1
in c)
number 4 ,7,9 and number 12 are showing 2 bullets while number 5 and 11 showing 1 bullet hence
standard deviation for a=2-1=1
order isαb<αc<αa
Which logarithmic equation is equivalent to the exponential below? e^a= 35
Answer:
[tex]log_{e}[/tex] 35 = a
Step-by-step explanation:
using the law of logarithms
• [tex]log_{b}[/tex] x = n ⇔ x = [tex]b^{n}[/tex]
[tex]e^{a}[/tex] = 35 ⇒ [tex]log_{e}[/tex] 35 = a
what is 6.5 as a fraction
Answer:
13/2 is 6.5 as a fraction
The graph shows calories compared to grams of protein.
What information can you draw from the point (3, 12) on the graph?
There are 3 calories in 1 gram of protein.
There are 3 calories in 12 grams of protein.
There are 12 calories in 3 grams of protein.
There is 1 calorie in 4 grams of protein.
Hello :3
Your answer would be C. (or "There are 12 calories in 3 grams of protein).
Hope This Helps (Hope i am not to late sorry if i am)
Cupkake~
F(x)=5x-3 what does f(5)=
f(5) means that x=5
Now, we solve 5x-3 because we know what x is.
5(5)-3
25-3
22
F(5)=22
Answer:
F (5)= 22
Step-by-step explanation:
Explain when you know you need to rename a mixed number to subtract
When subtracting mixed numbers, rename the mixed number if the subtrahend is larger than the minuend by converting them into improper fractions and then subtracting the numerator while keeping the denominator the same.
Explanation:When subtracting mixed numbers, you may need to rename the mixed number if the subtrahend is larger than the minuend.
This means that the whole number part of the subtrahend is greater than the whole number part of the minuend, or the fractions have different denominators.
To rename the mixed number, you convert it into an improper fraction.
Once both mixed numbers are in the same form, you can subtract them by subtracting the numerator and keeping the denominator the same. Finally, simplify the answer if needed.
What is the exact value of arcsin(−2√2)
Answer:
π4;3π4
Step-by-step explanation: Trig table gives:
sinx=√22 --> arc x=π4
Unit circle gives another arc x that has the same sin value:
x=π−π4=3π4
The exact value of [tex]\(\arcsin(-2\sqrt{2})\)[/tex] is not defined within the real numbers because the sine function has a range of [tex]\([-1, 1]\)[/tex], and the argument [tex]\(-2\sqrt{2}\)[/tex] lies outside this interval. The arcsine function, [tex]\(\arcsin(x)\)[/tex], is only defined for [tex]\(x\)[/tex] in the interval [tex]\([-1, 1]\)[/tex] .
To illustrate, the sine function reaches its maximum value of [tex]\(1\)[/tex] at [tex]\(\frac{\pi}{2}\)[/tex] and its minimum value of [tex]\(-1\)[/tex] at [tex]\(-\frac{\pi}{2}\)[/tex]. Any value outside the interval [tex]\([-1, 1]\)[/tex] is not within the domain of the inverse sine function. Therefore,[tex]\(\arcsin(-2\sqrt{2})\) does not have a real value.[/tex]
However, if we were to consider complex numbers, we could use Euler's formula and the definition of the complex logarithm to find a complex value for [tex]\(\arcsin(-2\sqrt{2})\)[/tex]. The general formula for the arcsine of a complex number [tex]\(z\)[/tex] is given by:
[tex]\[ \arcsin(z) = -i \ln\left(iz + \sqrt{1 - z^2}\right) \][/tex]
For [tex]\(z = -2\sqrt{2}\)[/tex], we would have:
[tex]\[ \arcsin(-2\sqrt{2}) = -i \ln\left(-2i\sqrt{2} + \sqrt{1 - (-2\sqrt{2})^2}\right) \][/tex]
Simplifying the expression under the square root:
[tex]\[ \sqrt{1 - (-2\sqrt{2})^2} = \sqrt{1 - 8} = \sqrt{-7} \][/tex]
Since [tex]\(\sqrt{-7} = i\sqrt{7}\)[/tex], we can continue the calculation:
[tex]\[ \arcsin(-2\sqrt{2}) = -i \ln\left(-2i\sqrt{2} + i\sqrt{7}\right) \][/tex]
This expression involves the complex logarithm, which is multi-valued due to the periodicity of the complex exponential function. Therefore, the value of [tex]\(\arcsin(-2\sqrt{2})\)[/tex] in the complex plane is not unique and requires careful handling of the branch cuts of the logarithm function. However, as stated earlier, within the realm of real numbers, [tex]\(\arcsin(-2\sqrt{2})\)[/tex] is undefined.
I need help with 9 & 10 please!
Profit P(x) can be calculated as revenue minus cost. R(x) = 55x - 2x2 C(x) = 21x + 97 P(x) = - 2x2 + 34x - 97 Calculate the x-value that maximizes profit.
8.5
Step-by-step explanation:The vertex of a quadratic ax²+bx+c is located at x = -b/(2a). When the x² coefficient is negative, the vertex represents a maximum.
For P(x), the x-value of the maximum profit is ...
... x = -34/(2(-2))
... x = 8.5
Marie plants flowers in a planter that is 1 1/2 feet long and 1 2/3 feet wide. She plans to cover the entire area with fertilizer. How much area will she need to spread with fertilizer
Answer:
2 3/6
Step-by-step explanation:
You must turn 1 2/3 and 1 1/2 into improper fractions. You then multiply them and get an answer of 15/6, but since 6 can go into 15 twice (6x2=12+3=15), you get a whole of 2 and 3/6.
Final answer:
Marie will need to cover an area of 2 1/2 square feet with fertilizer for her planter that is 1 1/2 feet long and 1 2/3 feet wide.
Explanation:
The question asks to calculate the area that needs to be covered with fertilizer for a planter with given dimensions.
Step-by-Step Solution:
Convert the dimensions of the planter into improper fractions for easier multiplication. The length is already given as an improper fraction (1 1/2 feet which is 3/2 feet). The width is 1 2/3 feet, which is 5/3 feet when converted.
Multiply the length by the width to find the area in square feet: (3/2) × (5/3) = 15/6 square feet.
Simplify the calculated area if necessary. The area 15/6 can be simplified to 2 1/2 square feet.
Therefore, Marie will need to spread fertilizer over an area of 2 1/2 square feet.
evaluate the expression 2m +n for m=13 and n=3
Answer:
This is equal to 29
Step-by-step explanation:
2(13)+3=29
1. without graphing, where do the graphs of y = x^2 and y = 25 intersect? Explain.
2. Without graphing, where do the graphs of y = x^2 and y = 121 intersect? Explain.
"The graphs of [tex]\( y = x^2 \)[/tex] and [tex]\( y = 25 \)[/tex] intersect at the points where the value of [tex]\( x^2 \)[/tex] is equal to 25. To find these points, we set the equations equal to each other and solve for x :
[tex]\[ x^2 = 25 \][/tex]
Taking the square root of both sides gives us two solutions:
[tex]\[ x = \pm 5 \][/tex]
Therefore, the graphs intersect at [tex]\( (-5, 25) \) and \( (5, 25) \)[/tex].
Similarly, the graphs of [tex]\( y = x^2 \)[/tex] and [tex]\( y = 121 \)[/tex] intersect at the points where the value of [tex]\( x^2 \)[/tex] is equal to 121. We set the equations equal to each other and solve for [tex]\( x \)[/tex]:
[tex]\[ x^2 = 121 \][/tex]
Taking the square root of both sides gives us two solutions:
[tex]\[ x = \pm 11 \][/tex]
Thus, the graphs intersect at[tex]\( (-11, 121) \) and \( (11, 121) \)[/tex].
In both cases, the intersection points are determined by finding the values of [tex]\( x \)[/tex] that satisfy the equation [tex]\( x^2 = k \)[/tex], where[tex]\( k \)[/tex]is the constant on the right side of the equation[tex]\( y = k \)[/tex].
The solutions are the positive and negative square roots of [tex]\( k \)[/tex], since [tex]\( x^2 \)[/tex] is equal to [tex]\( k \)[/tex] at these points."