Answers
[tex]\text{It is an equilateral triangle, so all angles are equal to}~ 60^{\circ}\\\\~~~~~~m\angle 2 = x+72\\\\\implies 60 = x+72\\\\\implies x = 60-72\\\\\implies x = -12[/tex]
Related Questions
x/13 - 1 = 5x/2 + 1/2
please answer the question pls pls pls pls
Answers
[tex]\huge\underline{\red{A}\blue{n}\pink{s}\purple{w}\orange{e}\green{r} -}[/tex]
the given expression can be solved as follows ~
[tex] \frac{x}{13} - 1 = \frac{5x}{2} + \frac{1}{2} \\ [/tex]
taking LCM both the sides ,
[tex] \frac{x - 13}{13} = \frac{5x + 1}{2} \\ [/tex]
on cross multiplying ,
[tex](x - 13)2 = (5x + 1)13 \\ \\ \implies \: 2x - 26 = 65x + 13[/tex]
let's now gather the like terms at either sides of the equation ~
[tex]65x - 2x = - 26 - 13 \\ \\ \implies \: 63x = - 39 \\ \\ \implies \: x = \frac{\cancel{ - 39}}{\cancel{63}} [/tex]
on simplifying the equation ,
[tex] \implies \frac{-13}{21}\\[/tex]
hope helpful ~
Which of these scenarios illustrate independent events?
Answer:
A. Only ll
B. only ll
C. Both l and ll
D. Neither l nor ll
Answers
Answer:
The answer would be C, Both I and II.
Step-by-step explanation:
You can find an attached file which shows the scenarios incase your confused.
what is the weight of a rectangular prism with the length of 1.75 width of 3.5 and a height of 7
Answers
Answer:
13.125
Step-by-step explanation:
I need the answer soon please help. 20 points
Divide. −3 6/8 Enter your answer as a mixed number, in simplified form, in the box.
Answers
Answer:
The solution is in the image
1. Emilio earns $150 per week plus 38% commission. He sells $2 000.00 in one week. What are his gross weekly earnings?
Answers
Answer:
more than what i have
Step-by-step explanation:
Last week a pizza restaurant sold 36 cheese pizzas, 64 pepperoni pizzas, and 20 veggie pizzas. based on this data, which number is closest to the probability that
the next customer will buy a cheese pizza?
a) 0.84
b) 0.64
c 0.36
d 0.30
Answers
36+ 64 + 20 = 120
For cheese: 36/120 = 0.3
What is the answer of 11 6/9 - 4 4/9
Answers
Answer:
[tex]7 \frac{2}{9} [/tex]
Step-by-step explanation:
here is your answer
Calculation steps:
[tex]11 \frac{6}{9} - 4 \frac{4}{9} [/tex]
[tex] = (14 - 4) + ( \frac{6}{9} - \frac{4}{9} )[/tex]
[tex] = 7 + \frac{6 - 4}{9} [/tex]
[tex] = 7 + \frac{2}{9} [/tex]
[tex]7 \frac{2}{9} [/tex]
[tex]11 \frac{6}{9} - 4 \frac{4}{9} [/tex]
solution:[tex]11 \frac{6}{9} - 4 \frac{4}{9} [/tex]
[tex] = \frac{35}{3} - \frac{40}{9} [/tex]
[tex] = \frac{(35 \times 9) - (40 \times 30)}{3 \times 9} [/tex]
[tex] = \frac{315 - 120}{27} [/tex]
[tex] = \frac{195}{27} [/tex]
[tex] = 7 \frac{2}{9} [/tex]
11 x_
= 121 what is the missing number?
Answers
Answer:
11
Step-by-step explanation:
11x=121
11x/11 = 121/11
x = 11
So, 11*11 = 121
A store is giving out cards labelled 1 through 10 when customers enter the store. If the card is an even number, you get a 10% discount on your purchase that day. If the card is an odd number greater than 6, you get a 40% discount. Otherwise, you get a 20% discount. The table shows the results of 400 customers. What is the relative frequency for each discount? Use pencil and paper. If the manager of the store wants to approximately half of the customers to receive the 20% discount, does this seem like an appropriate method? Explain.
Answers
Answer:
Relative frequency for each discount :
10% - 0.4925, 20% - 0.3325, 40% - 0.175
Since only 33.25% of customers got 20% discount, it is not an appropriate method.
Step-by-step explanation:
relative frequency = number of frequency/total number of frequency
you can find out relative frequency for each number and add them up to get relative frequencies of discounts.
What is the equation of the line shown in the graph?
Answers
Answer:
y = -x – 2
Step-by-step explanation:
Slope is ΔY/ΔX = -1
plug this into the equation:
1=-(-3) +b
= -2=b
so we get; y = -x – 2
Answer: y = -x - 2
Step-by-step explanation:
I will be writing this equation in slope-intercept form.
First, we will find our m value, also known as the slope.
[tex]\displaystyle \frac{\text{change in y}}{\text{change in x}} =\frac{1--4}{-3-2} =\frac{5}{-5}=-1[/tex]
Now, we will find our b value, or the y-intercept.
-> The line intercepts the y-axis at (0, -2), so our y-intercept is -2.
Lastly, we will write our equation.
y = mx + b
y = -x - 2
Read more about writing slope-intercept equations here:
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i could use some help with this question pleaseeeee, i'll give brainliest and an explanation for future reference would be appreciated^^
if L,M are the two roots of the equation : 8x² - 40x + 11 = 0 , then L+M = ...........
a) 40
b) -40
c) 5
d) -5
Answers
Answer:
c) 5
Step-by-step explanation:
we know that,
alpha + beta = -b/a
here, we are given that alpha is L and beta is M (roots of the quadratic equation)
therefore,
L+M = -b/a
L+M = -(-40)/8
L+M = 40/8
L+M = 5
HOPE IT HELPS!!
PLEASE MARK BRAINLIEST... ♡
Answer:
L + M are 5.122 and -0.122 so I am assuming the answer you want is 5 or c.
Step-by-step explanation:
SOME OF THIS I NEEDED TO RESEARCH BECAUSE I FEEL LIKE THIS IS OUT OF MY DEPTH BUT I GUESS HERE YOU GO
STEP
1
:
Equation at the end of step 1
(23x2 - 40x) - 5 = 0
STEP
2
:
Trying to factor by splitting the middle term
2.1 Factoring 8x2-40x-5
The first term is, 8x2 its coefficient is 8 .
The middle term is, -40x its coefficient is -40 .
The last term, "the constant", is -5
Step-1 : Multiply the coefficient of the first term by the constant 8 • -5 = -40
Step-2 : Find two factors of -40 whose sum equals the coefficient of the middle term, which is -40 .
-40 + 1 = -39
-20 + 2 = -18
-10 + 4 = -6
-8 + 5 = -3
-5 + 8 = 3
-4 + 10 = 6
-2 + 20 = 18
-1 + 40 = 39
Observation : No two such factors can be found !!
Conclusion : Trinomial can not be factored
Equation at the end of step
2
:
8x2 - 40x - 5 = 0
STEP
3
:
Parabola, Finding the Vertex:
3.1 Find the Vertex of y = 8x2-40x-5
Parabolas have a highest or a lowest point called the Vertex . Our parabola opens up and accordingly has a lowest point (AKA absolute minimum) . We know this even before plotting "y" because the coefficient of the first term, 8 , is positive (greater than zero).
Each parabola has a vertical line of symmetry that passes through its vertex. Because of this symmetry, the line of symmetry would, for example, pass through the midpoint of the two x -intercepts (roots or solutions) of the parabola. That is, if the parabola has indeed two real solutions.
Parabolas can model many real life situations, such as the height above ground, of an object thrown upward, after some period of time. The vertex of the parabola can provide us with information, such as the maximum height that object, thrown upwards, can reach. For this reason we want to be able to find the coordinates of the vertex.
For any parabola,Ax2+Bx+C ,the x -coordinate of the vertex is given by -B/(2A) . In our case the x coordinate is 2.5000
Plugging into the parabola formula 2.5000 for x we can calculate the y -coordinate :
y = 8.0 * 2.50 * 2.50 - 40.0 * 2.50 - 5.0
or y = -55.000
Parabola, Graphing Vertex and X-Intercepts :
Root plot for : y = 8x2-40x-5
Axis of Symmetry (dashed) {x}={ 2.50}
Vertex at {x,y} = { 2.50,-55.00}
x -Intercepts (Roots) :
Root 1 at {x,y} = {-0.12, 0.00}
Root 2 at {x,y} = { 5.12, 0.00}
Solve Quadratic Equation by Completing The Square
3.2 Solving 8x2-40x-5 = 0 by Completing The Square .
Divide both sides of the equation by 8 to have 1 as the coefficient of the first term :
x2-5x-(5/8) = 0
Add 5/8 to both side of the equation :
x2-5x = 5/8
Now the clever bit: Take the coefficient of x , which is 5 , divide by two, giving 5/2 , and finally square it giving 25/4
Add 25/4 to both sides of the equation :
On the right hand side we have :
5/8 + 25/4 The common denominator of the two fractions is 8 Adding (5/8)+(50/8) gives 55/8
So adding to both sides we finally get :
x2-5x+(25/4) = 55/8
Adding 25/4 has completed the left hand side into a perfect square :
x2-5x+(25/4) =
(x-(5/2)) • (x-(5/2)) =
(x-(5/2))2
Things which are equal to the same thing are also equal to one another. Since
x2-5x+(25/4) = 55/8 and
x2-5x+(25/4) = (x-(5/2))2
then, according to the law of transitivity,
(x-(5/2))2 = 55/8
We'll refer to this Equation as Eq. #3.2.1
The Square Root Principle says that When two things are equal, their square roots are equal.
Note that the square root of
(x-(5/2))2 is
(x-(5/2))2/2 =
(x-(5/2))1 =
x-(5/2)
Now, applying the Square Root Principle to Eq. #3.2.1 we get:
x-(5/2) = √ 55/8
Add 5/2 to both sides to obtain:
x = 5/2 + √ 55/8
Since a square root has two values, one positive and the other negative
x2 - 5x - (5/8) = 0
has two solutions:
x = 5/2 + √ 55/8
or
x = 5/2 - √ 55/8
Note that √ 55/8 can be written as
√ 55 / √ 8
Solve Quadratic Equation using the Quadratic Formula
3.3 Solving 8x2-40x-5 = 0 by the Quadratic Formula .
According to the Quadratic Formula, x , the solution for Ax2+Bx+C = 0 , where A, B and C are numbers, often called coefficients, is given by :
- B ± √ B2-4AC
x = ————————
2A
In our case, A = 8
B = -40
C = -5
Accordingly, B2 - 4AC =
1600 - (-160) =
1760
Applying the quadratic formula :
40 ± √ 1760
x = ——————
16
Can √ 1760 be simplified ?
Yes! The prime factorization of 1760 is
2•2•2•2•2•5•11
To be able to remove something from under the radical, there have to be 2 instances of it (because we are taking a square i.e. second root).
√ 1760 = √ 2•2•2•2•2•5•11 =2•2•√ 110 =
± 4 • √ 110
√ 110 , rounded to 4 decimal digits, is 10.4881
So now we are looking at:
x = ( 40 ± 4 • 10.488 ) / 16
Two real solutions:
x =(40+√1760)/16=5/2+1/4√ 110 = 5.122
or:
x =(40-√1760)/16=5/2-1/4√ 110 = -0.122
The triangle below is equilateral. Find the length of side a in simplest radical form
with a rational denominator.
Answers
By using the Pythagorean theorem, we conclude that side x measures (5/2)*√3 units.
How to find the length of side x?
In the image, we can see that the equilateral triangle can be divided into two right triangles.
If each side of the equilateral triangle measures 5 units, then for the right triangles we will have that the hypotenuse measures 5 units, and the bottom side measures half of that: 2.5 units.
Now remember the Pythagorean theorem. It says that the sum of the squares of the cathetus is equal to the square of the hypotenuse. Then we will have:
[tex]x^2 + 2.5^2 = 5^2[/tex]
[tex]x = \sqrt{5^2 - 2.5^2} = \frac{5}{2}\sqrt{3}[/tex]
Then we conclude that side x measures (5/2)*√3 units.
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Simplify 3(2x+6)+4x-1
Answers
Answer: 10+17
Step-by-step explanation:
Distribute:
3(2+6)+4−1
6+18+4−1
Subtract the numbers:
6+18+4−1
6+17+4
Combine like terms:
6+17+4
10+17
solution:
10+17
Five different numbers are such that, 2 are odd, the median is 7, the mean is 8 and all numbers are less than 13. What are the five numbers?
Answers
Solution :
Help me please I beg
Answers
Answer:
see explanation
Step-by-step explanation:
(a)
calculate the gradient (slope) m using the slope formula
m = [tex]\frac{y_{2}-y_{1} }{x_{2}-x_{1} }[/tex]
with (x₁, y₁ ) = O (0, 0 ) and (x₂, y₂ ) = A (- 5, 2 )
[tex]m_{OA}[/tex] = [tex]\frac{2-0}{-5-0}[/tex] = [tex]\frac{2}{-5}[/tex] = - [tex]\frac{2}{5}[/tex]
(b)
the angle between a tangent and a radius at the point of contact is 90°
given a line with slope m then the gradient of a line perpendicular to it is
[tex]m_{perpendicular}[/tex] = - [tex]\frac{1}{m}[/tex] = - [tex]\frac{1}{-\frac{2}{5} }[/tex] = [tex]\frac{5}{2}[/tex]
(c)
the equation of a line in slope- intercept form is
y = mx + c ( m is the slope and c the y- intercept )
here m = [tex]\frac{5}{2}[/tex] , then
y = [tex]\frac{5}{2}[/tex] x + c ← is the partial equation
to find c substitute A (- 5, 2 ) into the partial equation
2 = - [tex]\frac{25}{2}[/tex] + c ⇒ c = 2 + [tex]\frac{25}{2}[/tex] = [tex]\frac{29}{2}[/tex]
y = [tex]\frac{5}{2}[/tex] x + [tex]\frac{29}{2}[/tex] ← equation of tangent
please solve for me. please be correct
Answers
x/12 = -4
=> x = -48
Hope it helps you.
The answer to x is -48. Hope this helps!
in 2010 there were 3200 tigers in the wild in 2016 there were 3890 tigers what is the percentage increase. Give ur answer to the nearest whole number
Answers
A percentage is a way to describe a part of a whole. The percentage increase in the number of tigers is 21.56%.
What are Percentages?A percentage is a way to describe a part of a whole. such as the fraction ¼ can be described as 0.25 which is equal to 25%.
To convert a fraction to a percentage, convert the fraction to decimal form and then multiply by 100 with the '%' symbol.
The percentage change is given by the formula,
Percentage change = |(Intial Value - Final value)|/Initial Value × 100%
Percentage Change = |3200-3890|/3200 × 100% = 21.56%
Hence, the percentage increase in the number of tigers is 21.56%.
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Chen is given the graph below.
What type of graph is shown, and what is the growth factor?
linear function; growth factor of 2
linear function; growth factor of 4
exponential function; growth factor of 2
exponential function; growth factor of 4
Answers
An insurance firm wants to estimate the percentage of senior citizens in a small town with approximately 2,534 residents. it asks a group of 85 randomly selected people in the town about their age.
select the statement that is true.
a. the sample is 2,534 people. the population is 85 people.
b. the sample is 85 people. the population is 2,449 people.
c. the sample is 85 people. the population is 2,534 people.
d. none of the answer choices are true.
Answers
Using sampling concepts, it is found that the correct statement is given by:
c. the sample is 85 people. the population is 2,534 people.
What is sampling?It is a common statistics practice, when we want to study something from a population, we find a sample of this population, which is a group containing elements of a population. A sample has to be representative of the population, that is, it has to involve all segments of the population.
In this problem, a group of 85 people, which is the sample, is taken from the entire population of 2,534 people, hence option c is correct.
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The prism shown represents a storage bin for a barn. The dark face will be open to allow people to place items inside.
A net of a triangular prism. Face A is shaded.
Which face of the net represents the open face of the prism?
A
B
C
D
Answers
Answer:
its A
Step-by-step explanation:
SURFACE AREA QUESTION: the cargo area of the moving truck will be completely filled by 45 identical cube-shaped boxes. What will be the Surface area of one layer of boxes on the floor of the truck bed. (the truck has a height of 6 ft, a length of 6ft, and a width of 10ft.)
Answers
I believe it is 312, hope this helps, sorry if it doesn't!:)
What is the answer F, G, H or J
Answers
Answer:
G its G
Step-by-step explanation:
In the diagram, the radius is 7 and tangent AB has length of 24. Determine the length of OA rounded to the nearest whole number
Answers
Given the radius r and the tangent line AB, the length of the line OA is 24 units
How to determine the length OA?The radius r and the tangent line AB meet at a right angle.
By Pythagoras theorem, we have:
AB² = OA² + r²
So, we have:
24² = OA² + 7²
Rewrite as:
OA² = 24² - 7²
Evaluate
OA² = 527
Take the square root of both sides
OA = 23
Hence, the length of OA is 24 units
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Consider the quadratic function shown in the table below. x y 0 0 1 3 2 12 3 27 Which exponential function grows at a faster rate than the quadratic function for 0< x < 3?
Answers
So values are
(0,0)(1,3)(2,12)(3,27)The rule is
3/1=312/2=627/3=9Explicit formula
x(3x) where x is set of integersEquation here is
y=3x²Answer:
[tex]f(x)=4^x[/tex] grows at a faster rate than the given quadratic function.
Step-by-step explanation:
Given table:
[tex]\large \begin{array}{| c | c |}\cline{1-2} x & y \\\cline{1-2} 0 & 0 \\\cline{1-2} 1 & 3 \\\cline{1-2} 2 & 12 \\\cline{1-2} 3 & 27 \\\cline{1-2}\end{array}[/tex]
First Differences in y-values:
[tex]0 \overset{+3}{\longrightarrow} 3 \overset{+9}{\longrightarrow} 12 \overset{+15}{\longrightarrow} 27[/tex]
Second Differences in y-values:
[tex]3 \overset{+6}{\longrightarrow} 9 \overset{+6}{\longrightarrow} 15[/tex]
As the second differences are the same, the function is quadratic.
The coefficient of [tex]x^2[/tex] is always half of the second difference.
Therefore, the quadratic function is:
[tex]f(x)=3x^2[/tex]
The average rate of change of function f(x) over the interval a ≤ x ≤ b is given by:
[tex]\dfrac{f(b)-f(a)}{b-a}[/tex]
Therefore, the average rate of change for [tex]f(x)=3x^2[/tex] over the interval
0 ≤ x ≤ 3 is:
[tex]\textsf{Average rate of change}=\dfrac{f(3)-f(0)}{3-0}=\dfrac{27-0}{3-0}=9[/tex]
An exponential function that grows at a faster rate than [tex]f(x)=3x^2[/tex] over the interval 0 ≤ x ≤ 3 is [tex]f(x)=4^x[/tex]
[tex]\large \begin{array}{| c | c | c | c | c |}\cline{1-5} x & 0 & 1 & 2 & 3 \\\cline{1-5} f(x)=4^x & 1 & 4 & 16 & 64\\\cline{1-5} \end{array}[/tex]
[tex]\textsf{Average rate of change}=\dfrac{f(3)-f(0)}{3-0}=\dfrac{64-1}{3-0}=21[/tex]
As 21 > 9, [tex]f(x)=4^x[/tex] grows at a faster rate than [tex]f(x)=3x^2[/tex] over the interval 0 ≤ x ≤ 3.
11
The area of a square is 49 cm2. What is the perimeter, in cm, of the square?
Answers
Answer:
28 cmStep-by-step explanation:
The area of a square is 49 cm2. What is the perimeter, in cm, of the square?
first we use the inverse formula to find the side (√49 = 7), then multiply the side by 4 (7 x 4 = 28)
or you can use an expression
4 * √49 = 28
7th grade math!!!!!! HELP!
Morgan begins to use synthetic division to divide x4 + x3 − 6x2 − 4x + 8 by x − 2, as shown below. Which of the following shows the correct values to replace the question marks, and also gives the quotient?
A. 2, 6, 0, −8; x^3 − 3x^2 + 4
B. 2, 6, 0, −8; x^3 + 3x^2 − 4
C. 1, 3, 0, −4; x^2 + 3x − 4
D. 1, 1, −6, −4; x^3 + 3x^2 − 4
Answers
Morgan begins to use synthetic division to divide x4 + x3 − 6x2 − 4x + 8 by x − 2, as shown below. Which of the following shows the correct values to replace the question marks, and also gives the quotient?
A. 2, 6, 0, −8; x^3 − 3x^2 + 4
B. 2, 6, 0, −8; x^3 + 3x^2 − 4
C. 1, 3, 0, −4; x^2 + 3x − 4
D. 1, 1, −6, −4; x^3 + 3x^2 − 4
Answer is a
The correct values to replace will be 2, 6, 0, and − 8 and the quotient is x³ + 3x² − 4. Then the correct option is B.
What is Algebra?Algebra is the study of abstract symbols, while logic is the manipulation of all those ideas.
The acronym PEMDAS stands for Parenthesis, Exponent, Multiplication, Division, Addition, and Subtraction. This approach is used to answer the problem correctly and completely.
P(x) = x⁴ + x³ − 6x² − 4x + 8
P(x) = 1x⁴ + 1x³ − 6x² − 4x + 8
By the synthetic division, we have
2 ║ 1 1 − 6 − 4 8
2 6 0 − 8
1 3 0 − 4 0
x³ 3x² − 4
By the synthetic division, the correct values to replace will be 2, 6, 0, and − 8 and the quotient is x³ + 3x² − 4. Then the correct option is B.
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6•(x•9) simplified please
Answers
Answer:
6x+54 should be the answer
Step-by-step explanation:
Please Help its a math problem !! see image attached below for more info
Answers
Answer:
g(x) = 2ˣ⁻¹ + 3
Step-by-step explanation:
f(x) = 2ˣ
Translated 1 unit right
Represented by (x - 1)f(x - 1) = 2ˣ⁻¹Translated 3 units up
Represented by adding 3g(x) = 2ˣ⁻¹ + 3Answer:
Well if its a translation on the x-axis the formula would be g(x) = -2×
Although Functions are not my strong suit
I hope i got this right!
After the translation, where is A located?
Answers
Answer:
(-3, 13)
Step-by-step explanation:
The transformation that moves a point 4 left and 8 up is ...
(x, y) ⇒ (x -4, y +8)
The transformation that reflects a point across the y-axis is ...
(x, y) ⇒ (-x, y)
Applied after the translation, the transformation of ∆ABC becomes ...
(x, y) ⇒ (-(x -4), y +8) = (4 -x, y +8)
Then point A gets moved to ...
A(7, 5) ⇒ A'(4 -7, 5 +8) = (-3, 13)
What is the surface area of the
triangular prism shown?
Answers
Answer:
1120^2
Step-by-step explanation:
25x17=425
425+(8x25)=625
625+(8x15)=745
745+(15x25)=1120