Answer:
3.75•4=15 TL dir .......
Which x value makes this equation true? Explain how you can tell
2x^2 - x + 10 = 38
a) x=2
b) x=4
c) x=-4
d) x=6
Answer:
b) x = 4
Explanation:
[tex]2x^2 - x + 10 = 38[/tex]
collect variables
[tex]2x^2 - x + 10 - 38 = 0[/tex]
simplify
[tex]2x^2 - x - 28 = 0[/tex]
breakdown
[tex]2x^2 -8x + 7x - 28 = 0[/tex]
factor out
[tex]2x(x - 4) + 7(x - 4) = 0[/tex]
collect into groups
[tex](2x + 7)(x - 4) = 0[/tex]
set to zero
[tex]2x + 7 = 0, x - 4 = 0[/tex]
relocate variable
[tex]2x = -7, x = 4[/tex]
final solutions
[tex]x = -3.5, x = 4[/tex]
The answer is b.
To find the value of x, we need to convert this into the form of a quadratic equation.
Subtract 38 from each side.
2x² - x + 10 - 38 = 38 - 382x² - x - 28 = 0Solve by splitting the middle term.
2x² + 7x - 8x - 28 = 0x (2x + 7) - 4 (2x + 7) = 0x = 4, x = -7/2A freezer is shaped like a rectangular prism. It has a length of 8 feet and a height of 3 feet. The volume is 54 cubic feet. Find the width of the freezer.
Step-by-step explanation:
volume = length • width • height
by making width subject
V=LWH
W=V/LH
W= 54/8×3
W=54/24
W=9/4
W=2.25
what is the equation of the line containing the points (3,1) (9,3) and (27,9)
The equation of the line containing the points (3,1) (9,3) and (27,9) is y = 1 / 3x
How to find equation of a line?The equation of a line can be found as follows:
y = mx + b
where
m = slopeb = y-interceptTherefore,
using (3,1) (9,3)
m = 3 - 1 / 9 - 3 = 2 / 6 = 1 / 3
using (3, 1)
1 = 1 / 3(3) + b
1 = 1 + b
b = 0
Therefore,
y = 1 / 3x
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9. The half-life of aspirin in your bloodstream is 12 hours. Use exponential model to
estimate how long for the 500 mg dosage to decay to 70% in your bloodstream.
after 6.2 hours the dose will decay to 70% in your bloodstream.
How long you must wait for the dosage to decay to 70% in your bloodstream?We know that the half-life is 12 hours. Then the exponential relation for an initial dosage of A is:
[tex]D(t) = A*e^{-t*ln(2)/12h}[/tex]
If the dosage needs to decay to a 70% of the initial dosage, then we must have:
[tex]e^{-t*ln(2)/12h} = 0.7[/tex]
Now we need to solve that for t:
If we apply the natural logarithm in both sides, we get:
[tex]ln(e^{-t*ln(2)/12h}) = ln(0.7)\\\\-t*ln(2)/12h = ln(0.7)\\\\t = -ln(0.7)*12h/ln(2) = 6.2h[/tex]
So after 6.2 hours the dose will decay to 70% in your bloodstream.
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Drag each equation and coordinate to the correct location on the table. Not all equations or coordinates will be used.
In the table below, quadratic equations are given in standard form. Rewrite each equation in the form that reveals the maximum or
minimum value, and then identify the coordinate point of that extreme value.
Completing the squares, we have that:
For the parabola of standard form y = x² - 6x + 17, we have that the equivalent form is (x - 3)² + 8 and the extreme value is (3,8).For the parabola of standard form y = x² + 8x + 21, we have that the equivalent form is (x + 4)² + 5 and the extreme value is (-4,5).For the parabola of standard form y = x² - 16x + 60, we have that the equivalent form is (x - 8)² - 4 and the extreme value is (8,-4).What is the equation of a parabola given it’s vertex?The equation of a quadratic function, of vertex (h,k), is given by:
y = a(x - h)² + k
In which a is the leading coefficient.
For the parabola of standard form y = x² - 6x + 17, we have that it can be written as follows, completing the squares:
y = x² - 6x + 17 = (x - 3)² + 8, hence the extreme value is (3,8).
For the parabola of standard form y = x² + 8x + 21, we have that it can be written as follows, completing the squares:
y = x² + 8x + 21 = (x + 4)² + 5, hence the extreme value is (-4,5).
For the parabola of standard form y = x² - 16x + 60, we have that it can be written as follows, completing the squares:
y = x² - 16x + 60 = (x - 8)² - 4, hence the extreme value is (8,-4).
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A parachute speed free fall reaches 45 meters per second what is this speed in feet per second at this speed how many feet will the parachutist fall during 5 seconds of free fall in your computations assume that 1 meter is equal to 3.3 feet. Don’t round your answers
The speed is:
S = 742.5ft
The distance that the parachutist falls in 5 seconds is:
D = 742.5ft
How to get the speed in feet per second?
We know that the speed in free fall is:
S = 45 m/s.
We know that:
1 m = 3.3ft
Then we can rewrite the speed as:
S = 45 m/s = 45 *(3.28ft)/s = 148.5 ft/s
Then, the distance that the parachutist falls during 5 seconds is:
D = S*5s = (148.5 ft/s)*5s = 742.5ft
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What effect does 'h' have on the graph of a parabola?
Vertical stretch
Vertical compression
Vertical shift
Horizontal shift
The effect that 'h' have on the graph of a parabola is Horizontal shift or translation .
What is translation?A translation is the movement of a shape up, down , this can also be movement from side to side.
Even though there is movement, its appearance remains the same in any other way, hence, h values cause left or right movement with respect to the graph.
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!!!!!!Please please please help!!!!!!!!Drag each equation to the correct location on the table. Not all equations will be used.
Determine which equations represent lines that are parallel or perpendicular to the linear equation provided on the graph
v =
y = -2z + 1 y = − 2 + 4
2 + 3y = ½z+8 y = 2z+ 2 y = −2+5
-8
-6 -4 2
Parallel Line
4
2
-2-
4
4
2
6 B
Perpendicular Line
The equation of that is parallel to the graph is y = 1 / 2 x + 3 and the equation perpendicular to the graph is y = -2x + 1
How to know equation that a parallel and perpendicular?Equation that are parallel have the same slope.
Equation that are perpendicular gives negative 1 when multiplied .
Therefore, using slope intercept equation,
y = mx + b
where
m = slopeb = y-interceptHence, the equation of the graph can be calculated as follows:
(0, 6)(2, 7)
m = 7 - 6 / 2 - 0 = 1 / 2
Therefore,
y = 1 / 2 x + 6
Therefore, the equation that are parallel to the graph are as follows:
y = 1 / 2 x + 3The equation that are perpendicular to the graph is as follows;
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find the y intercept of the line on the graph
Which answer best describes the complex zeros of the polynomial function? f(x)=x3+x2+10x+10
"The function has one real zero and two nonreal zeros. The graph of the function intersects the x-axis at exactly one location."
Polynomial functions are equations such as quadratic and cubic equations that take only the non-negative integer power of a variable or a positive integer exponent. For example, 2x + 5 is a polynomial with an exponent equal to 1.
A polynomial function is an expression that is a combination of variables of different degrees, non-zero coefficients, positive exponents (of variables), and constants. For example, f (b) = 4b2 – 6 is a polynomial of'b'and has a degree of 2.
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how do I solve for x? (the picture has the problem)
Answer:
x = 21.013155617496
Step-by-step explanation:
we have a right triangle then ,
[tex]\cos \left( 36\right) =\frac{17}{x}[/tex]
Then
[tex]x=\frac{17}{\cos \left( 36\right) } = 21.013155617496[/tex]
Then
x ≈ 21
Step-by-step explanation:
imagine this right-angled triangle is the sine and cosine scenario in a circle. just turn it in your mind or on the paper until it looks like this.
the point with the 36° angle is the center of this circle.
x is the radius of the circle, that is under 36° connecting the center of the circle with the arc of the circle.
17 is the cosine of the angle multiplied by the radius (as the standard cosine function is normed for the standard circle with radius 1).
and the other leg is the sine of the angle multiplied by the radius (this is FYI, we don't need that for the solution here).
so,
17 = cos(36) × x
x = 17/cos(36) = 21.01315562...
Examine the first two steps for solving this equation. 3x - 6(5x 3) = 9x 6 1. distribute: 3x - 30x - 18 = 9x 6 2. combine like terms: -27x - 18 = 9x 6 what could be the coefficient of x once the variable term is isolated on one side of the equation? check all that apply. –36 –27 –24 24 27 36
Answer:
-36 and 36
Step-by-step explanation:
moving the 9x to the left it changes to -9x and that plus -27x is -36x
-27-9 = -36
moving -27x to the right it changes to 27x so that plus 9x is 36x
27+9 = 36
Answer:
A. -36
F. 36
Step-by-step explanation:
WILL MAKE BRAINLIEST!! Angles a and b are vertical angles. If m
Answer: 127
Step-by-step explanation:
angle b is 127 as well because they're vertical angles and vertical angles are equal to each other.
A simple random sample of size n is drawn from a normally distributed population, and the mean of the sample is x Overbar, while the standard deviation is s. What is the 90% confidence interval for the population mean
The mean of the sample is x-bar is determined to be 59.2 and population standard deviation, σ, is known to be 3.8. The 90% confidence interval about μ if the sample size, n, is 45 be 58.27< μ<60.13
A simple random sample of size n is drawn from a population whose population standard deviation, σ, is known to be 3.8. The sample mean, x-bar, is determined to be 59.2.
Hence,
n=45
σ=3.8
x-bar=59.2
The z value for the 90% confidence interval is z=1.645.
Then, μ=(x-bar)±(z×σ/[tex]\sqrt{n}[/tex])
μ=59.2±(1.645×3.8/[tex]\sqrt{45}[/tex])
μ=59.2±0.9318
59.2-0.9318<μ<59.2+0.9318
58.27< μ<60.13
Therefore, The 90% confidence interval about μ if the sample size, n, is 45 be 58.27< μ<60.13
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PLEASE HELP AND EXPLAIN
See below for the interpretation of the graph
How to interpret the graph?From the graph, the initial values of x and y are 0
As x increases, y decreases.
This means that the first statement is
Initially, as x increases, y decreases.Slope is calculated as:
[tex]m = \frac{y_2 - y_1}{x_2 -x_1}[/tex]
Using the graph values at the interval x =0 to x = 3, we have:
[tex]m = \frac{-3 - 0}{3 - 0}[/tex]
m = -1
This means that the second statement is
The slope of the graph is equal to -1 for all x between x = 0 and x = 3From the graph, y = -3, when x = 3
As x increases at this point, y increases.
This means that the third statement is
Starting at x = 3, the function value y increases as x increasesUsing the graph values at the interval x = 3 to x = 5, we have:
[tex]m = \frac{3 + 3}{5 - 3}[/tex]
m = 3
This means that the fourth statement is
The slope of the graph is equal to 3 for x between x = 3 and x = 5All y values at x = 0 to x = 4 are less than 0, while all y values at x = 4 to x = 8 are greater than 0
So, the last two statements are
For x between x = 0 and x = 4, the function value y is less than 0For x between x = 4 and x = 8, the function value y is greater than 0Read more about functions at:
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pls help solve this……
Answer:
(a) x = -7, 1
Step-by-step explanation:
In most cases, it is useful to follow the directions. This can be solved easily by completing the square.
Completing the squareThe square is completed by adding the square of the x-term coefficient to both sides.
x² +6x +9 = 7 +9 . . . . . add 9
(x +3)² = 16 . . . . . . . . simplify . . . . write the left side as a square
The square is now complete. We finish the solution by taking the square root.
x +3 = ±√16 = ±4 . . . . take the square root
x = -3 ±4 . . . . . . . . . subtract 3
x = -7, 1
PLS HELP IN SUPER STUCK PLEASE HELP
A printing company charges a fixed rate to set up the printing press, plus a cost of $3.50 for every 100 copies. If 800 copies cost $64.00, how much will it cost to print 1500 copies?
Answer:
88.5
Step-by-step explanation:
3.5 * 8 = 28, this is how much was spent on copies printed. If 800 copies cost $64 and 28 of that was on the 3.5 fee per 100, then the flat rate must be:
64-28 = 36.
Now, let's do 1500. For 1500 copies, you will get charged $3.5 15 times. This amounts to 52.5, then adding the fixed fee of 36 dollars, you get
88.5
CSN SOMEONE PLEASE HELP ASAP
If the ADA guidelines state that a
wheelchair ramps angle of elevation
must equal 4.8°. would a
ramp with the
following dimensions be up to code?
Show your work and explain. (Picture is
not drawn to scale.)
3.5 ft
e°
40 ft
The ramp with the following dimension won't obey the ADA guideline because the angle is more than 4.8 degrees.
How to find the angle of elevation of the ramp?The angle of elevation of the ramp can be found using trigonometric ratios.
Therefore, the angle of elevation must be equal to 4.8 degrees to obey the ADA guidelines .
Hence,
tan ∅ = opposite / adjacent
opposite side = 3.5 ft
adjacent side = 40 ft
Therefore,
tan ∅ = 3.5 / 40
∅ = tan ⁻¹ 0.0875
∅ = 5.00064459756
∅ = 5 degrees
Therefore, the ramp with the following dimension won't obey the ADA guideline because the angle is more than 4.8 degrees.
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Geometry question confused on how to solve this answer
The acute angles of a right triangle are complementary, so [tex]\boxed{m\angle F=34^{\circ}}[/tex].
Using right-angle trigonometry, we know that
[tex]\cos 56^{\circ}=\frac{26}{DF}\\\\DF=\frac{26}{\cos 56^{\circ}}\\\\\boxed{DF \approx 46.5}[/tex]
[tex]\tan 56^{\circ}=\frac{FE}{26}\\\\FE=26 \tan 56^{\circ}\\\\\boxed{FE \approx 38.5}[/tex]
help me to slove this
Answer:
1. pi. 2.49-12.25pi
Step-by-step explanation:
HELP HELP HELP HELP
HELP HELP HELP
A music store owner noted that cd sales had dropped 23% from one quarter to the next. if the owner sold 715 units in the first quarter, how many did she sell in the next quarter?
round your answer to the nearest whole unit of cds. do not include units with your answer.
help please what's the correct answer
If the sales had dropped 23% then music store had sold 551 units in the second quarter.
Given that a music store had sold 715 units in first quarter and sales had dropped by 23%.
We are required to determine the sales in the second quarter.
Percentage is the number or ratio expressed in terms of 100. It is expressed as %.
Sales in first quarter=715 units
Decrease in sales=23%
In units ,decrease=715*23%
=715*23/100
=164.45
Sales of second quarter=715-164.45
=550.55
After rounding we will get 551.
Hence if the music store sold 715 units in first quarter then the units sold by music store in second quarter 551 units.
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Write down the mathematical name of the shape made by each net.
a)
b)
How do I do the picture
Answer:
1. Cube
2. Square-based pyramid
Step-by-step explanation:
Answer:
Below.
Step-by-step explanation:
a) Cube
b Pyramid
Use the distributive property to write an
addition sentence equivalent to:
8(5+2)
Answer:
8(5) + 8(2)
Step-by-step explanation:
8 (5 + 2) is 8 (7) or 56
If I distribute the 8 through the problem, I will get the same answer
8(5) + 8(2)
40 + 16
56
PLEASE HELP ASAP
Determine the number of terms in the sequence. Your work must be shown with fractions not decimals.
2/81, 4/27, 8/9,…,6912
we conclude that the sequence has 8 terms.
How to get the number of terms in the sequence?
Here we have the geometric sequence:
2/81, 4/27, 8/9, ..., 6912
Notice that each term is equal to 6 times the previous term, such that:
2/81*6 = 4/27
4/27*6 = 8/9
Then the n-th term is equal to:
[tex]a_n = a_1*r^{n-1}[/tex]
Where in this case:
[tex]a_1 = 2/81\\\\r = 6[/tex]
Now we need to find the value of n such that:
[tex](2/81)*6^{n-1} = 6912\\\\6^n = 6*6812*(81/2) = 1,679,616[/tex]
If we apply the natural logarithm to both sides, then:
[tex]n*ln(6) = ln(1,679,616)\\n = ln(1,679,616)/ln(6) = 8[/tex]
Then we conclude that the sequence has 8 terms.
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Given that 20=20+18+16+...+x, how many terms are on the right side of the equation
20 terms on the right side of the given equation [tex]20=20+18+16+...+x[/tex].
How we find the sum of n terms?The first n terms of the arithmetic sequence are added together to form the sum of the first n terms of AP.
Therefore, we can only evaluate the sum of n terms in a sequence if we are aware of the type of sequence it is. Usually, when calculating the sum of an n-number of terms, we take into account arithmetic progression. The common distinction between each following term and each preceding term remains unchanged throughout this progression. Natural numbers are an illustration of Arithmetic Progression, where the common difference is 1. We must therefore be familiar with the formula in order to calculate the sum of natural numbers.
We can use formula for sum of n terms-
[tex]S = \frac{n}{2}(2a + (n-1)d)[/tex]
where, S- sum of n terms
n- number of terms
a- first term
d- difference between two consecutive terms
Here, S= 20 , a = 20, d= -2
we have to find n,
[tex]S = 20 = \frac{n}{2}(2(20) + (n-1)(-2)) \\20 = \frac{n}{2}(40-(2n-2))\\40 = n(40-2n+2)\\40 = 42n-2n^2\\2n^2 -42n +40 = 0[/tex]
solving this quadratic equation-
[tex]2n^2 -42n +40 = 0\\2n^2 -40n-2n+40=0\\2n(n-20)-2(n-20) = 0\\(2n-2)(n-20)=0[/tex]
when,
[tex]2n-2 = 0\\n=1[/tex]
When,
[tex]n-20=0\\ n=20[/tex]
as we can see that there are more than 1 terms present in the series so answer will be 20 terms.
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Mrs. fresneda sells homemade soap at the farmers' market for $4.00 per bar. write an expression for how much mrs. fresneda earns selling bars of soap. then, evaluate the expression to determine how much money she will earn if she sells 26 bars of soap.
The expression which shows the earning of Mrs. Fresneda is 4x and the money that she will earn by selling 26 bars of soap is $144.
Given that price of soap is $4.00 per bar.
We have to find the expression which shows the earning of Mrs. Fresneda after selling soap bars and the money that she will earn by selling 26 bars of soap.
let the number of soap bars be x.
We know that the revenue is the product of price and quantity.
Money that Mrs.Fresneda earns is 4*x
=4x
Expression is 4x which shows that money that Mrs. Freneda will earn by selling soap bars.
We have to just put x=26 in the expression to calculate the money after selling 26 bars of soap.
Money=4*26
=$144
Hence the expression is 4x and the money that Mrs.Freneda will earnby selling 26 bars of soap is $144.
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Please help me with this polynomial based questions
Answer:
Hello,
Step-by-step explanation:
All is in the following picture:
A man spends 1/4 of his salary on food and 1/8 on transportation. His salary is Rs. 50,000
i) Find his total expenses as a fraction of the salary
ii) Find the amount of salary he spent
iii) Find the remaining balance of the salary
total expenses= 1/4 + 1/8
the denominators should be equal to add the values.
1/4×2(divide both the numerator and denominator by two)
=2/8
=2/8+1/8
3/8//
3/8(fraction of the salary he spent)
3/8 of the salary
3/8×50,000
R.s 6250
balance = 50,000-6,250
= R.s 43,750//