Given the following formula, w=x-y/2 -z. The value of y is y = x - 2w + wz .
What is a simplification of an expression?Usually, simplification involves proceeding with the pending operations in the expression.
Like, 5 + 2 is an expression whose simplified form can be obtained by doing the pending addition, which results in 7 as its simplified form.
Simplification usually involves making the expression simple and easy to use later.
Given the following formula,
w=x-y/2 -z
We need to solve for y.
[tex]w = \dfrac{x-y}{2 -z}[/tex]
By cross multiplication
[tex]w\times (2 -z)= {x-y}\\\\2w - wz = x - y[/tex]
subtract x both side
2w - wz -x = x - y -x
y = x - 2w + wz
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Calculate the area of the alarm clock.
Given the diameter of the surface of the clock, the area of the surface of the alarm clock is 3846.5cm².
What is the area of the alarm clock?Note that: Area of a circle is expressed as;
A = πr²
Where r is radius and π is constant pi ( π = 3.14 )
Given that;
Diameter d = 70cm Radius r = d/2 = 70cm/2 = 35cmArea = ?A = πr²
A = 3.14 × ( 35cm )²
A = 3.14 × 1225cm²
A = 3846.5cm²
Therefore, given the diameter of the surface of the clock, the area of the surface of the alarm clock is 3846.5cm².
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If we changed the 3 to a 0 in the equation, what would happen to the graph?
A function assigns the values. The function will move down by 3 units.
What is a Function?A function assigns the value of each element of one set to the other specific element of another set.
The graph of the function is given below. Now if 3 is replaced by a 0, then the y-intercept of the function will become zero while keeping the slope the same. Therefore, the function will move down by 3 units.
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Help for college scholarships! Must be a paragraph.
How has your family background affected the way you see the world?
Family background refers to the culture and tradition of the family into which a person is born.
What is family background?Family background refers to the culture and tradition of the family into which a person is born. it is worthy of note that most of this family traditions are unspoken yet are firmly entrenched in the psyche of individual as he/she grows.
My family is strictly conservative having had a Southern Baptist orientation. My dad believes deeply in religion and a moralist and perfectionist.
As a result of this, I find myself always grappling with the unfortunate disorder in the world; always trying to bring order to my world as much as I can.
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im lost can someone help?
Amalia and Alec are studying the growth of a plant over time. They measure the height of the plant at the end of each week for several weeks and display the data in a scatter plot. They then find the equation for the best-fit line to be y=2.5+ 1.25x
X=the number of weeks that have passed
Y = the height of the plant
How tall will with plant be after 7 weeks?
After 7 weeks the plant will 11.25 units tall if the equation for the best-fit line to be y = 2.5 + 1.25x.
What is the line of best fit?A mathematical notion called the line of the best fit connects points spread throughout a graph. It's a type of linear regression that uses scatter data to figure out the best way to define the dots' relationship.
[tex]\rm m = \dfrac{n\sum xy-\sum x \sum y}{n\sum x^2 - (\sum x)^2} \\\\\rm c = \dfrac{\sum y -m \sum x}{n}[/tex]
We have a line of best fit:
y = 2.5 + 1.25x
Plug x = 7 weeks
y = 2.5 + 1.25(7)
y = 11.25 units
Thus, after 7 weeks the plant will 11.25 units tall if the equation for the best-fit line to be y = 2.5 + 1.25x.
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In triangle ABC, AP is an angle bisector of angle BAC. What is the length of PC? Round you answer to the nearest whole number.
A) 6 B) 7 C) 8 D) 9
Answer:
D) 9
Step-by-step explanation:
x = ½ × 13 = 6.5
y = ½ × 5 = 2.5
6.5 + 2.5 = 9
So the length of PC is 9
HOPE THIS HELPS AND HAVE A NICE DAY <3
Draw and set up the integrals for the area enclosed by the y–axis, the curve y = (x + 1)1/2 and y = 2. Compute one of them.
Region II only please
If the definitions of type I and type II regions is the same as in the link provided, then as a type I region the integration domain is the set
[tex]R_{\rm I} = \left\{(x,y) \mid 0 \le x \le 3 \text{ and } \sqrt{x+1} \le y \le 2\right\}[/tex]
and as a type II region,
[tex]R_{\rm II} = \left\{(x,y) \mid 0 \le x \le y^2-1 \text{ and } 1 \le y \le 2\right\}[/tex]
where we solve y = √(x + 1) for x to get x as a function of y.
A. The area of the type I region is
[tex]\displaystyle \iint_{R_{\rm I}} dA = \int_0^3 \int_{\sqrt{x+1}}^2 dy \, dx = \int_0^3 (2 - \sqrt{x+1}) \, dx = \boxed{\frac43}[/tex]
B. The area of the type II region is of course also
[tex]\displaystyle \iint_{R_{\rm II}} dA = \int_1^2 \int_0^{y^2-1} dx \, dy = \int_1^2 (y^2-1) \, dy = \boxed{\frac43}[/tex]
I've attached a plot of the type II region to give an idea of how it was determined. The black arrows indicate the domain of x as it varies from the line x = 0 (y-axis) to the curve y = √(x + 1).
40 POINTS!!
Which statement matches the vector operation shown on the coordinate grid?
The statement that matches the vector operation shown on the coordinate grid is v + w = u.
How to add two vectors graphically?In order to add two vectors a and b graphically by using the tail and tip method, we must draw the tail of b at the tip of vector a.
Then we must draw a line that goes from the tail of vector a to the tip of vector b.
This line represents the sum of a + b.
In the given problem, we notice that the tail of the vector w is on the tip of the vector v.
The line that joins the tail of vector v with the tip of vector w is vector u.
Therefore we can say that v + w = u
The statement that matches the vector operation shown on the coordinate grid is v + w = u.
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Deion has 62 m of fencing to build a four-sided fence around a rectangular plot of
land. The area of the land is 228 square meters. Solve for the dimensions (length and
width) of the field?
The dimensions of the the plot of land is a length of 19 meters and width of 12 meters.
What is an equation?An equation is an expression that shows the relationship between two or more numbers and variables.
Let x represent the length of the field and y represent the width of the field, hence:
Deion has 62 m of fencing:
2(x + y) = 62
x + y = 31
y = 31 - x (1)
The area of the land is 228 square meters. hence:
xy = 228
x(31 - x) = 228
x² - 31x + 228 = 0
x = 12 or x = 19
when x = 12; y = 31 - 12 = 19
when x = 19; y = 31 - 19 = 12
The dimensions of the the plot of land is a length of 19 meters and width of 12 meters.
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suppose y varies inversely as x and y=12 when x=6 find y if x=8
Answer:
y = 9
Step-by-step explanation:
given that y varies inversely as x then the equation relating them is
y = [tex]\frac{k}{x}[/tex] ← k is the constant of variation
to find k use the condition y = 12 when x = 6
12 = [tex]\frac{k}{6}[/tex] ← multiply both sides by 6 to clear the fraction
72 = k
y = [tex]\frac{72}{x}[/tex] ← equation of variation
when x = 8 , then
y = [tex]\frac{72}{8}[/tex] = 9
solve for x in the following equations
Answer:
2.
[tex]x = \frac{11}{4} = 2 \frac{3}{4} = 2.75[/tex]
3.
[tex]x = \frac{5}{2} = 2 \frac{1}{2} = 2.5[/tex]
4.
[tex]x = \frac{3}{7} ≈0.428571429[/tex]
What is the domain of the piecewise function?
A. x<0, x>4
B. -∞ 4
C. all real numbers
Answer:
C. All real numbers
he triangle on the grid will be translated two units down. On a coordinate plane, triangle A B C has points (2, 1), (0, negative 1), (2, negative 1). Which shows the triangle when it is translated two units down? On a coordinate plane, triangle A prime B prime C prime has points (0, negative 1), (0, negative 3), (2, negative 3). On a coordinate plane, triangle A prime B prime C prime has points (0, 1), (negative 2, negative 1), (0, negative 1). On a coordinate plane, triangle A prime B prime C prime has points (2, negative 1), (2, negative 3), (0, negative 3). On a coordinate plane, triangle A prime B prime C prime has points (2, negative 1), (2, negative 3), (0, negative 1).
If these coordinates are translated two units down, we will subtract 2 units from the y axis to have A(2, -1), B(0, -3) and C(2, -3)
Translation of coordinate pointTranslation is a transformation technique of changing the position of an object on the xy-plane.
Given the following coordinate of a triangle expressed as:
A(2, 1)
B(0, -1)
C(2, -1)
If these coordinates are translated two units down, we will subtract 2 units from the y axis to have:
A(2, -1)
B(0, -3)
C(2, -3)
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WILL MARK BRAINLIEST 50 POINTS Find the area of the regular pentagon if the apothem is 7 ft and a side is 10 ft. Round to the nearest whole number.
175 ft2
350 ft2
35 ft2
70 ft2
Answer:
175 ft^2
Step-by-step explanation:
split the pentagon into 5 triangles with base length 10ft and height 7ft. each triangle then has an area of 10 * 7 * 1/2 = 35 ft^2
then the pentagon has an area 35*5 = 175 ft^2
Without calculating the cubes find 1 cube+2cube+2(4) cube+(-5)cube+(-6)cube .
what is the area of the figure?
Answer:
area = 62ft
Step-by-step explanation
so you section the polygon into a big rectangle and 2 small rectangles
the area of the small rectangle will be 2ft x 3ft which will be 6 ft, and as there are 2 of them the area of it will be 12ft
the area of the big rectangle will be 10ft x 5ft, as 8ft - 3ft is 5ft so 5x10=50ft
now add the areas you got, 50+12 which is 62ft
hope this helps:)
What is true of the function g(x) = -2x² + 5?
O g(x) is the multiplication of g and x.
O-212 +5 is the input of the function.
The variable x represents the independent variable.
The variable g represents the input of the function.
Answer:
C.) The variable x represents the independent variable
Step-by-step explanation:
The variable "x" is the independent variable because that is the value that we can manipulate. We cannot manipulate the dependent variable because it is determined by the independent variable. In that case, "y" would be the dependent variable because its value is dependent on what "x" is.
A.) is incorrect because g(x) symbolizes the input of the variable "x" into the g function.
B.) is incorrect because "x" is the input.
D.) is incorrect because "x" is the input.
what percentage of 5/2 hours is 15 minutes?
Answer:
10 %
Step-by-step explanation:
15 mn = 1/4 h
We have :
[tex]\frac{\frac{1}{4} }{\frac{5}{2} } =\frac{1}{4} \times \frac{2}{5} =\frac{2}{20} =\frac{1}{10}=0.1[/tex]
Then the percentage that 15 mn represents of 5/2 h is :
0.1 × 100 = 10 %
can someone help me with this worksheet please!!!!
(1) The missing term in the sequence, a₁₂ = 0.8.
(2) The missing term in the sequence, a₈ = 102.5.
(3) The missing term in the sequence, a₈ = 111.
(4) The missing term in the sequence, a₁₂ = -19.
(5) The missing term in the sequence, a₁₂ = 94.
(6) The missing term in the sequence, a₆ = 40.
(7) The missing term in the sequence, a₃₆ = -52.
(8) The missing term in the sequence, a₂₁ = -58.
Missing term of the sequenceThe missing term in the sequence is determined as follows;
Tₙ = a + (n - 1)d
1.0 a₄ = 18.4 and a₅ = 16.2, a₁₂ = ?T₄ = a + 3d
18.4 = a + 3d ---(1)
T₅ = a + 4d
16.2 = a + 4d ---(2)
subtract (1) from (2)
-2.2 = d
18.4 = a + 3(-2.2)
a = 25
a₁₂ = a + 11d
a₁₂ = 25 + 11(-2.2)
a₁₂ = 0.8
2.0 a₂ = 57.5 and a₅ = 80, a₈ = ?a₂ = a + d
57.5 = a + d -- (1)
a₅ = a + 4d
80 = a + 4d --- (2)
solve (1) and (2)
d = 7.5
a = 50
a₈ = a + 7d
a₈ = 50 + 7(7.5)
a₈ = 102.5
3.0 a₁₀ = 141 and a₁₃ = 186, a₈ = ?a₁₀ = a + 9d
141 = a + 9d --- (1)
a₁₃ = a + 12d
186 = a + 12d --- (2)
Subtract (1) from (2)
d = 15
a = 6
a₈ = a + 7d
a₈ = 6 + 7(15)
a₈ = 111
4.0 a₂₂ = -49 and a₂₅ = -58, a₁₂ = ?a₂₂ = a + 21d
-49 = a + 21d ---- (1)
a₂₅ = a + 24d
-58 = a + 24d --- (2)
subtract (1) from (2)
d = -3
a = 14
a₁₂ = a + 11d
a₁₂ = 14 + 11(-3)
a₁₂ = -19
5.0 a₄ = -2 and a₈ = 46, a₁₂ = ?a₄ = a + 3d
-2 = a + 3d --- (1)
a₈ = a + 7d
46 = a + 7d ---- (2)
Subtract (1) from (2)
d = 12
a = -38
a₁₂ = a + 11d
a₁₂ = -38 + 11(12)
a₁₂ = 94
6.0 a₉ = 64 and a₁₂ = 88, a₆ = ?a₉ = a + 8d
64 = a + 8d --- (1)
a₁₂ = a + 11d
88 = a + 11d --- (2)
Subtract (1) from (2)
d = 8
a = 0
a₆ = a + 5d
a₆ = 0 + 5(8)
a₆ = 40
7.0 a₂₀ = -4 and a₂₃ = -13, a₃₆ = ?a₂₀ = a + 19d
-4 = a + 19d ---- (1)
a₂₃ = a + 22d
-13 = a + 22d --- (2)
Subtract (1) from (2)
d = -3
a = 53
a₃₆ = a + 35d
a₃₆ = 53 + 35(-3)
a₃₆ = -52
8.0 a₂₈ = 5 and a₃₃ = 50, a₂₁ = ?a₂₈ = a + 27d
5 = a + 27d ---- (1)
a₃₃ = a + 32d
50 = a + 32d --- (2)
Subtract (1) from (2)
d = 9
a = -238
a₂₁ = a + 20d
a₂₁ = -238 + 20(9)
a₂₁ = -58
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Find the probability that a randomly
selected point within the circle falls
in the red shaded area.
r = 4 cm
[?]%
Round to the nearest tenth of a percent.
Enter
Answer:
[tex]31.8\%[/tex]
Step-by-step explanation:
The area of the circle is [tex]A=\pi r^2=\pi(4)^2=16\pi[/tex]
The area of the triangle is [tex]A=\frac{bh}{2}=\frac{8*4}{2}=\frac{32}{2}=16[/tex]
Hence, the probability of a randomly selected point within the circle falls in the red shaded area is [tex]\frac{16}{16\pi}=\frac{1}{\pi}\approx0.318\approx31.8\%[/tex]
Given a polynomial function f(x) = –x2 + 2x + 1 and an exponential function g(x) = 2x, what key features do f(x) and g(x) have in common?
A.)Both f(x) and g(x) decrease over the interval of [1 , ∞).
B.) Both f(x) and g(x) have the same range of (–∞, 2).
C.) Both f(x) and g(x) have the same x-intercept of (–1, 0).
D.)Both f(x) and g(x) have the same y-intercept of (0, 1).
The only key feature that these functions have in common is that they have the same y-intercept. So the correct option is D.
What do these functions have in common?
Here we have the functions:
[tex]f(x) = -x^2 + 2x + 1\\\\g(x) = 2^x[/tex]
f(x) is quadratic, and g(x) is exponential.
Notice that the exponential function has a positive base, so it is increasing. For the quadratic equation we can see a negative leading coefficient, so it opens downwards. So first and second options are false.
Also, g(x) never intersects the x-axis, so third option is false.
Finally, the y-intercepts of the given functions are:
[tex]f(0) = -0^2 + 2*0 + 1 = 1\\\\g(0) = 2^0 = 1[/tex]
So the y-intercepts are equal, meaning that the correct option is D.
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Answer:
Both f(x) and g(x) have the same y-intercept of (0, 1).
Step-by-step explanation:
I got it right on the test.
Two adjacent rooms are rectangles, both of length 13 feet by 10 feet. Jerry wants to change the carpets in both rooms. How many square feet should he order?
Answer:
260 square feet
Step-by-step explanation:
The area of a rectangle is given by the formula ...
A = LW
The area of two same-size rectangular rooms will be double the area of one of them.
__
room areaEach room has an area of ...
A = LW = (13 ft)(10 ft) = 130 ft²
carpet orderThe order for carpet must be for 2 times the area of one room:
carpet order = 2 × 130 ft² = 260 ft²
Jerry should order 260 square feet of carpet.
F. In what order should items weighing
51 pounds, 40 pounds, 48 pounds,
and 44 pounds be stacked if you want
them in order from heaviest to lightest?
Answer:
51 pounds, 48 pounds, 44 pounds and 40 pounds in that chronological order.
Write two numbers that multiply to the value on top and add to the value on bottom.
-84
17
Two numbers multiply the value on top (-84) and add to the value on the bottom (17) is 21 and -4.
What is multiplication?Multiplication is one of the four basic arithmetic operations, alongside addition, subtraction, and division. Multiplication essentially means the repeated addition.
The two given numbers are -84 and 17.
We need to write two numbers that multiply to the value on top (-84) and add to the value on the bottom (17).
If we multiply 21 and -4, we get the product as -84.
That is, 21×(-4)=-84
If we add 21 and -4, we get the sum as -17.
That is, 21+(-4)=21-4=17
Therefore, two numbers multiply the value on top (-84) and add to the value on the bottom (17) is 21 and -4.
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write a Pythagorean triplet whose smallest member is 6
Answer:
6, 8, 10
Step-by-step explanation:
Where:
a = 6
b = 8
c = 10
Pythagorean theorem: [tex]a^2 + b^2 = c^2[/tex]
[tex]6^2 + 8^2 = c^2[/tex]
[tex]36 + 64 = c^2[/tex]
[tex]100 = c^2[/tex]
c = [tex]\sqrt{100}[/tex]
c = 10
Given that 24w = 14ten .Find the unknown base
Answer:
w = 5
Step-by-step explanation:
24w = (14)10
2w + 4 = 10 + 4
2w = 10
w = 5
4. Evaluate e^-2 to one decimal place
A) 0.7
B) -1.4
C) 0.1
D) 1.4
In a year, a hospital admitted 4500 patients. If of the patients had heart or lung diseases,
how many patients had heart or lung diseases?
Answer:
4500
Step-by-step explanation:
all of them were admitted.
Two trains, Train A and Train B, weigh a total of 526 tons. Train A is heavier than Train B. The difference of their weights is 466 tons. What is the weight of each train?
Answer:
Train A = 466
Train B = 60
Step-by-step explanation:
find the sum. 1-2+3-4+5-6+7-8...99-100
Answer:
-50
Step-by-step explanation:
1 - 2 + 3 - 4 + 5 - 6 + 7 - 8...99 - 100
just means,
1 - 2 = -1
3 - 4 = -1
5 - 6 = - 1
7 - 8 = - 1
99 - 100 = -1
basically, -1 + -1 + -1 + -1 + ....+ -1 or -1 - 1 - 1 - 1 - ... - 1
[tex](-1)^{n}[/tex]
Treating Grandi's series as a divergent geometric series we may use the same algebraic methods that evaluate convergent geometric series to obtain a third value:
S = 1 − 1 − 1 + ..., so
1 − S = 1 − (1 − 1 − 1 ...) = 1 − 1 − 1 ... = S
1 - S = S
1 = 2*S
resulting in S = 1/2. The same conclusion results from calculating −S, subtracting the result from S, and solving 2S = 1
1/2 of the last term is 100 x 1/2 = 50
This because you are using 2 numbers per -1
example: 1 - 2 = -1 or 3 - 4 = -1 resulting in 50 of the -1 being subtracted