Answer:
-22 1/3
Step-by-step explanation:
We should start by subtracting both sides of the equality by 21.
After doing this, we get that -67=3m.
Furthermore, we can divide both sides by 3 and get -67/3=m.
However, this is an improper fraction, not a mixed number.
If we divide -67 by 3, we get -22 1/3.
Therefore, m= -22 1/3
giving Brainly show work
Answer:
Step-by-step explanation:
5 1/2 +2x = 25
25- 5 1/2 = 2x
19 1/2 = 2x
x = 9.75
It took him about 9.75 weeks to lose at least 25 pounds.
Answer:
10 or more weeks------------------
Weight lossFirst week - lost 5 and 1/2 pounds,Following weeks - lost 2 pounds per week,Total - at least 25 pounds.Set inequality and find the least whole number2w + 5.5 ≥ 252w ≥ 25 - 2.52w ≥ 19.5w ≥ 19.5/2w ≥ 9.75 ≈ 10It took Mr. Henry at least 10 weeks to lose 25 pounds.
help meeeeeeeeeeee pleaseeeeeeeeeee rn rnnnnnnnnn!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
help meeeeeeeeeeee pleaseeeeeeeeeee rn rnnnnnnnnn!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
maximum height = 32ft
Given function h(t) = -16t^2+40t+7
known data:
[tex]h{0}[/tex] = 7 ft
[tex]v_{0}[/tex] = 40 ft/s
we equate the first derivation to zero
and solve for time.
h(t) = -16t^2 + 40t+7
[tex]\frac{dh}{dt} (t)[/tex] = -32t+40 = 0
t = [tex]\frac{40}{32}[/tex] = 1.25s
second derivative and evaluate:
[tex]\frac{d^{2}h}{dt^{2}}[/tex] [tex]\frac{}{}(t)[/tex] = -32
the maximum height of the rocket with the respect to
the ground can be obtained by evaluating the function
h(1.25) = - 16[tex](1.25)^{2}[/tex]+40(1.25)+7 = 32 ft
therefore the rocket reaches maximum height at h = 32ft.
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PLEASE HELP
*IMAGE BELOW*
A plane has a cruising speed of 200 miles per hour when there is no wind. At this speed, the plane flew 500 miles with the wind in the same
amount of time it flew 300 miles against the wind. Find the speed of the wind.
The speed of the wind is 50 mile per hour .
In the question ,
it is given that
the speed of the plane is [tex]=[/tex] 200 miles per hour .
let the speed of the wind is = "w"
So ,the speed of the plane with wind is [tex]=[/tex] 200 + w
and the speed of the plane against wind is [tex]=[/tex] 200 - w
we know that , distance [tex]=[/tex] speed × time
the plane flew "500 miles" with wind ,
which means ,
500 [tex]=[/tex] (200 + w) × t .....(1)
and the plane flew 300 miles against the wind ,
which means ,
300 [tex]=[/tex] (200 - w) × t ......(2)
adding both the equations ,
we get
800 [tex]=[/tex] t ( 200 [tex]+[/tex] w [tex]+[/tex] 200 - w)
800 = t × 400
t = 2
Substituting , t = 2 in 500 [tex]=[/tex] (200 + w) × t
we get
500 = (200 + w) × 2
500/2 = 200 + w
250 = 200 + w
w = 250 - 200
w = 50
Therefore , The speed of the wind is 50 mile per hour .
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196 prime factorization pls help
p x 3,700=4,070
There was a % percent increase in the number of visitors.
There was 110% percent increase in the number of visitors.
Percent:
Basically, percentage refers the number or ratio that can be expressed as a fraction of 100.
Given,
p x 3,700=4,070
There was a % percent increase in the number of visitors.
Here we need to find the increase in the percentage.
While we looking into the given question we have identified that,
The Old population = 3700
And the new population = 4070
So, the value of P is calculated as,
=> p = 4070/3700
=> p = 1.1
When we convert this into percent then we get 110% as increase.
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3. Suppose that your calculator does not have a square root key. How could you still use your calculator to determine √144?
Answer
12
Step-by-step explanation:
click on square root
click on 144
then your answer will pop out below your equation
The points (4, -3) and (x, 3) lie on the same straight line.
If the slope of the line is 2, what is the value of x ?
answer:
(1,3)
step-by-step explanation:
desmos.
The value of x will be equal to 7 for the given slope of 2 for the line.
What is the slope?Slope or the gradient is the number or the ratio which determines the direction or the steepness of the line.
Given that the points (4, -3) and (x, 3) lie on the same straight line. The slope of the line is 2.
The slope of the line is calculated by the formula,
Slope = ( y₂ - y₁ ) / ( x₂ - x₁ )
2 = ( 3 + 3 ) / ( x - 4)
2(x-4) = 6
2x - 8 = 6
2x = 8 + 6
2x = 14
x = 14 / 2
x = 7
Therefore, the value of x will be equal to 7 for the given slope of 2 for the line.
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Find the area of the circle. Give your answer to two decimal places . Please show work
Answer:
1256.64
Step-by-step explanation:
Determine the length of the line segment shown. line segment from negative 5 comma 5 to 3 comma negative 1 6 units 8 units 10 units 36 units
fist gets brainlyist and 35 points please help asap
The length of the line segment with points (-5, 5) (3, -1) is 10 units
How to find length of lineThe length of line in an ordered pair is calculated using the formula
d = √{(x₂ - x₁)² + (y₂ - y₁)²}
where
d = distance between the points
x₂ and x₁ = points in x coordinates
y₂ and y₁ = points in y coordinates
distance between points (-5, 5) and (3, -1) is calculated as follows
d = √{(x₂ - x₁)² + (y₂ - y₁)²}
d =√{(-5 - 3)² + (5 - -1)²}
d =√{64 + 36}
d = √100
d = 10 units
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A 5-kilogram bag of cat food costs $14.85. What is the unit price?
Answer:
I believe the unit price would be $2.97
Step-by-step explanation:
Hope this helps! :))
Please let me know if its incorrect.
Solve the system of equations.
Answer:
(7,5)
Step-by-step explanation:
[tex]-3y+4x=13 \implies -15y+20x=65 \\ \\ -5y-6x=-67 \implies 15y+18x=201 \\ \\ \therefore 38x=266 \implies x=7 \\ \\ \implies -3y+4(7)=13 \implies y=5 \\ \\ \therefore (7,5)[/tex]
Can anyone write the equation of this graph?
The translated absolute value function graphed is defined as follows:
y = |x - 3| + 5.
What is the absolute value function?The absolute value function, of vertex (h,k), is defined by the following piecewise rule, depending on the input of the function:
f(x) = |x - h| + k = x - h + k, x - h ≥ 0.f(x) = |x - h| + k = -x + h - k, x - h < 0.In this problem, the coordinates of the vertex are given as follows:
h = 3, as the x-coordinate of the vertex is of 3.k = 5, as the y-coordinate of the vertex is of 5.Hence the vertex is given by the following point:
(3,5).
Then the equation graphed is defined by the rule presented as follows:
y = |x - 3| + 5.
Which is a translation of 3 units right and 5 units up of the standard absolute value function.
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Problem 6 Triangle FGH is the image of isosceles triangle FEH after a reflection across line HF. Select all the statements that are a result of corresponding parts of congruent triangles being congruent.
A: EFGH is a rectangle.
B: EFGH is a rhombus.
C: Diagonal FH bisects angles EFG and EHG.
D: Diagonal FH is perpendicular to side FE.
E: Angle EHF is congruent to angle FGH.
F: Angle FEH is congruent to angle FGH.
The statements which are as a result of corresponding parts of congruent triangles being congruent are:
Diagonal FH bisects angles EFG and EHG. Angle EHF is congruent to angle FGH. Proof of congruent triangles being congruent1) EFGH is a rectangle.
The above statements is not true in general. EFGH is a quadrilateral with opposites sides are equal, it may be rectangle in some cases but it is not always be a rectangle.
2). EFGH has 4 congruent sides.
The above statement is also false. EFGH has two opposite sides are congruent.
3). Diagonal FH bisect angles EFG and EHG.
The above statement is true. Triangle EFH and FGH both are isosceles triangles and hence they both have equal angles for the equal sides. Thus, it is true in all cases.
4). Diagonal FH is perpendicular to side Fe.
The above case is not true in general.
5). Angle FEH is congruent to angle FGH.
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The length of a rectangle is twice its width.
If the perimeter of the rectangle is 42 in, find its length and width.
Answer: Width = 7 inches, Length = 14 inches
Step-by-step explanation:
Let the width be [tex]w[/tex]. Then, the length is [tex]2w[/tex].
Using the formula for the perimeter of a rectangle,
[tex]2(w+2w)=42\\\\w+2w=21\\\\3w=21\\\\w=7\\\\\implies 2w=14[/tex]
the radius of a sphere is increasing at a rate of 4 mm/s. how fast is the volume increasing (in mm3/s) when the diameter is 80 mm? (round your answer to two decimal places.)
Increase in volume is 802424.77 cubic mm/s when the diameter is 80 mm.
Let the radius of the sphere be R.
So, the volume of the sphere is given by,
V = [tex]\frac{4}{3}\pi r^3[/tex]
Differentiating the above relation with respect to time 't' we get,
dV/dt = 4[tex]\pi r^2[/tex]. dr/dt
Given that, the change of radius (dr/dt) = 4 mm/s
When the diameter is 80 mm, then the radius = 80/2 = 40 mm
So the volume change when the diameter is 80 mm is given by,
dV/dt [tex]=4\pi\times40^2\times4\approx 802424.77[/tex] cubic mm/s
Hence the volume increase in 802424.77 cubic mm/s.
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please can someone solve this and tell me how at the end, it's gives -2 alpha beta instead of +2 alpha beta
I need answers ASAP pleeeeaase!!!!!
The value for the given expression [tex]\alpha ^{2} + \beta ^{2}[/tex] will be [tex](\alpha +\beta )^{2}-2\alpha \beta[/tex].
What are Algebraic Identities?
Algebraic identities are algebraic equations that hold true for any value of each of their variables. In factoring polynomials, they are also used.
As we know, [tex](a+b)^{2} = a^{2} +2ab + b^{2}[/tex] then,
For the given question, [tex](\alpha +\beta )^{2} = \alpha ^{2} +2\alpha \beta + \beta ^{2}[/tex]
Now, subtracting [tex]2\alpha \beta[/tex] on both sides then, we get
or, [tex](\alpha +\beta )^{2}-2\alpha \beta = \alpha ^{2} +2\alpha \beta + \beta ^{2}-2\alpha \beta[/tex]
or, [tex](\alpha +\beta )^{2}-2\alpha \beta = \alpha ^{2} + \beta ^{2}\\[/tex]
or, [tex]\alpha ^{2} + \beta ^{2}=(\alpha +\beta )^{2}-2\alpha \beta[/tex]
That's how the value [tex]-2\alpha \beta[/tex] comes.
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Determine whether the function is one-to-one. If it is, find a formula for its inverse.
f(x) = 4/9x+8
Answer:
87c
Step-by-step explanation:
I need help with math
The leading coefficients and parabolic equations, considering the vertices, are given as follows:
1. a = 7/4, y = 7/4(x - 4)² - 1.
2. a = -2, y = -2(x + 1)² + 2.
Equation of parabola with vertex (h,k)
The equation of a parabola with vertex given by (h,k) is presented as follows:
y = a(x - h)² + k.
In which a is the leading coeffiicent.
For item 1, the coordinates of the vertex is given as follows:
(4,-1).
Hence:
h = 4, k = -1, and the equation is:
y = a(x - 4)² - 1.
When x = 6, y = 6, hence the leading coefficient is calculated as follows:
6 = a(6 - 4)² - 1
4a = 7
a = 7/4.
Thus the equation is:
y = 7/4(x - 4)² - 1.
For item 2, the vertex is:
(-1,2).
Hence:
y = a(x + 1)² + 2.
When x = 0, y = 0, hence the leading coefficient is calculated as follows:
0 = a(0 + 1)² + 2
a = -2.
Hence the equation is:
y = -2(x + 1)² + 2.
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Write the following equations in slope intercept form
1. 4x - 3y = 2
2. 3x + 2y = -3
1.
The slope intercept form is y=mx+b
4x-3y=2
subtract 4x from both sides
3y=2+(-4x)
Divide by 3
y=2/3+(-4x/3)
simplify:
y=2/3-4x/3
reorder:
y=-4/3x+2/3
slope= -4/3, y intercept= 2/3
2.
In the same way,
3x+2y=-3
2y=-3-3x
y=-3/2 - 3x/2
y+3/2=-3x/2
y=-3x/2-3/2
y=-3/2x-3/2
slope=-3/2, y intercept= -3/2
I hope this helped you.
Graph the line that passes through the points (9,2) and (3,4) and determine the equation of the line ( I need it with graph)
The equation of the line that passes through the points (9,2) and (3,4) is x + 3y = 15 and the graph is shown below .
In the question ,
it is given that
the required line passes through the points (9,2) and (3,4)
in order to find the equation of line we first need to find slope .
so , the slope(m) will be
m = (4-2)/(3-9)
m = 2/(-6)
m = -1/3
The equation of the line passing through the point (3,4) having slope -1/3 is
y - 4 = (-1/3)(x - 3)
3(y - 4) = -1(x - 3)
3y - 12 = -x + 3
x + 3y = 12 + 3
x + 3y = 15
the graph of the line is drawn below .
Therefore ,The equation of the line that passes through the points (9,2) and (3,4) is x + 3y = 15 .
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estimate by rounding
496.1+212.4+301=
a banana weighs 140 g a pineapple weighs 345 g bag a contains 8 bananas and bag b contains 3 pineapples which bag weighs more and by how much show your working
Answer:
Bag a, by 85 grams!
Step-by-step explanation:
1) Work out the weight of bag a
1 banana is 140 grams so to find out 8 you have to multiply them
140 x 8 = 1120
Bag a = 1120 grams
2) Work out the weight of bag b
1 pineapple weight 345 grams so to find out 3 you have to multiply them just like above
345 x 3 = 1035
Bag b = 1035
3) Find the difference
Bag a is 1120 grams and bag b is 1035
To find out out by how much you just have to subtract them
1120 - 1035 = 85
Hope this helps, have a great day!
Help needed with this equation thx
The geometric system has a length of f = 4 cm and a length of g = 6 cm.
How to find the missing lengths of a geometric systemHerein we find a geometric system formed by two rectangles, the rectangle ABCD has an area of 60 square centimeters and the rectangle APQD has an area of 24 square centimeters. The area of a rectangle is equal to the product of the lengths of its base (b) and its height (h), both in centimeters.
First, describe the area formulas for the rectangles ABCD and APQD, both in square centimeters:
Rectangle ABCD
(g + 9) · f = 60 (1)
Rectangle APQD
g · f = 24 (2)
Where:
g - Length of the side QD, in centimeters. f - Length of the side BC, in centimeters.Second, use distributive property in (1):
By (1):
g · f + 9 · f = 60
Third, use substitution by (2) on (1) and determine the value of f:
(2) in (1):
24 + 9 · f = 60
9 · f = 36
f = 4
Fourth, determine the value of g:
By (2):
g = 24 / f
g = 24 / 4
g = 6
The lengths of f and g are 4 and 6 centimeters, respectively.
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If x =-5, what is the value of 2x^+6x
2x^2+6x
2(-5)^2+6(-5)
2(25)+6(-5)
50+6(-5)
50+(-30)
50-30
20
I have been struggling on this for hours now please help
Step-by-step explanation:
-(10x + 2) > 5x - 1 - 8x
combine x terms on right side:
-(10x + 2) > -3x - 1
remove ()'s from left side:
-10x - 2 > -3x - 1
add 10x to both sides:
-10x - 2 + 10x > -3x - 1 + 10x
-2 > 7x - 1
add 1 to both sides:
-2 + 1 > 7x - 1 + 1
-1 > 7x
divide both sides by 7:
-1/7 > 7x /7
-1/7 > x or x < -1/7
in interval notation: (-∞, -1/7)
let x be the exam grade of a random student taking calculus 1 at uiuc. suppose professor smith takes a random sample of 140 students from the calculus 1 class to see how they did on the exam. in his sample, he got a mean of 86 and a standard deviation of 11. approximate the probability that (the sample mean) would be higher than 88.4 or smaller than 84.4?
The probability that the sample mean would be higher than 88.4 or smaller than 84.4 is 0.85582
How to get the required probabilityThe probability is calculated using z score, this is used to determine the amount of standard deviations a sample, X is from the mean
The z score is given by the formula
z = (X - μ) / σ
Definition of variables
mean, μ = 86
sample size, n = 140
standard deviation, σ = 11
The probability
P(z > 88.4) + P(z < 84.4)
z score for z < 88.4
z = (88.4 - 86) / 11
= 0.21818 p value = 0.41364
z score for z < 84.4
z = (84.4 - 86) / 11
= -0.14545
p value for z < -0.14545 = 0.44218
The probability required = 0.41364 + 0.44218 = 0.85582
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A rectangle has an area of 50 square
centimeters. The width is 5 more than 1 times
the length. Find the length and width, in
centimeters, of the rectangle.
Show your work here
The measurements of the rectangle are 10 cm and 5cm.
What is rectangle?
A rectangle could be a quadrilateral with four right angles in geometer geometry. It may be outlined as an angulate quadrilateral as a result of all of its angles square measure equal; or a quadrangle with a right angle.
Main Body:
Let the width be x.
According to question :
width is 5 more than 1 times the length(l), so
length (l) = width -5
Area if rectangle = 50 cm²
Formula for area of rectangle = length * width
⇒50 = x*(x-5)
⇒50 = x² - 5x
⇒x² - 5x - 50 =0
splitting the middle term
⇒x²- 10x +5x -50 = 0
⇒x(x-10) +5(x-10)
⇒(x-10)(x+5)
Hence the value for x = 10 or -5 .
but length can never be -ve so x= 10.
Width = 10 cm
length = width -5
length = 10 -5
l = 5cm
Hence Measurements of rectangle are 10cm and 5cm.
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his table shows the ratio of the number of people to the number of pizzas needed. A 2-column table has 4 rows. Column 1 is labeled People with entries 5, 10, 15, 20. Column 2 is labeled Pizzas with entries 2, 4, 6, 8. Complete the statement about the equivalent ratios shown in this table. When the number of people is multiplied by 4, the number of pizzas is multiplied by .
When the number of people is multiplied by 4, the number of pizzas is multiplied by 4.
What is a ratio?A ratio can be defined as a mathematical expression that's used to denote the proportion of two (2) or more quantities with respect to one another and the total quantities.
What is a proportion?A proportion can be defined as an equation which is typically used to represent (indicate) the equality of two (2) ratios. This ultimately implies that, proportions can be used to establish that two (2) ratios are equivalent and solve for all unknown quantities.
Mathematically, a proportional relationship can be modeled by the following mathematical expression:
y = kx
Where:
x represents the number of people.y represents the number of pizzas needed.k represents the constant of proportionality.If the x-value is multiplied by 4, we have:
x = 5 × 4
x = 20
From the corresponding y-value for 20 is equal to 8 and as such the number of pizzas needed should be multiplied by 4, in order to produce an equivalent ratio.
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Rafe buys a cake for $12. The sales tax is 10%. How much is the sales tax?
A. $1.20
B.$10
C.$12
D.$13.20
Answer:
A $1.20
Step-by-step explanation:
Answer: A) $1.20
Step-by-step explanation: To get 10% of a number, you just need to divide by 10, so 12 ÷ 10 = 1.2.
