The required verbal expression : Twice of a variable x when added with 7 will give a constant equal to 35
What is a variable ?An unknown numerical value in an equation or algebraic expression is represented by a symbol (typically a letter) in algebra. A variable is, to put it simply, a quantity that is changeable and not fixed and is frequently represented by an alphabet.
What is a verbal expression ?A verbal statement is a mathematical problem. Algebraic 8 + 6 is an example of using numbers and numeric variables. It is necessary to be familiar with the words used to describe mathematical operations in order to translate between verbal statements and algebraic expressions.
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Which of the expressions below has a 7 in the
tenths place of the sum? Select all that apply.
A) 12.35 + 19.38
B) 9.89 + 4.9
C) 8.135 + 2. 644
D) 3.445 +2.382
Pls tell me!
State the coordinates of the point.
ƒ (x) = 4x + 5, what is the value of f (−3) and ƒ (3)?
Answer:
f(-3) = -7f(3) = 17Step-by-step explanation:
Given functions,
→ f(x) = 4x + 5
Now the value of f(-3) will be,
→ f(x) = 4x + 5
→ f(-3) = 4(-3) + 5
→ f(-3) = -12 + 5
→ [ f(-3) = -7 ]
Then the value of f(3) will be,
→ f(x) = 4x + 5
→ f(3) = 4(3) + 5
→ f(3) = 12 + 5
→ [ f(3) = 17 ]
Hence, the answer of f(3) is 17.
Substitute [tex]x=-3[/tex] into [tex]f(x)=4x+5[/tex] :
[tex]f(-3)=4(-3)+5[/tex]
[tex]=-12+5[/tex]
[tex]=-7[/tex]
Substitute [tex]x=3[/tex] into[tex]f(x)=4x+5[/tex] :
[tex]f(3)=4(3)+5[/tex]
[tex]=12+5[/tex]
[tex]=17[/tex]
[tex]\text{Hence, } f(-3)=-7 \text{ and } f(x)=17.[/tex]
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The vector 〈4,1〉 describes the translation of A(-1, w) to A'(2x+1,\ 4) and B(8y-1,1) onto B'(3,3z) . Find the values of w, x, y, and z .
The values of the variables associated ot translation operations are (w, x, y, z) = (3, 1, 0, 2 / 3).
How to determine the values of the variables associated to translation operations
Herein we find two translation cases of points set on Cartesian plane. Translations are rigid operations of the form:
P'(x, y) = P(x, y) + T(x, y)
Where:
P(x, y) - Original pointP'(x, y) - Resulting pointT(x, y) - Translation vectorNow we proceed to determine the values of the variables w, x, y, z behind each translation operation, substitute on each component and solve the resulting formula:
T(x, y) = A'(x, y) - A(x, y)
(2 · x + 1, 4) - (- 1, w) = (4, 1)
(2 · x + 2, 4 - w) = (4, 1)
(x, w) = (1, 3)
T(x, y) = B'(x, y) - B(x, y)
(3, 3 · z) - (8 · y - 1, 1) = (4, 1)
(4 - 8 · y, 3 · z - 1) = (4, 1)
(y, z) = (0, 2 / 3)
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Linear Equations Word Problems
Sasha spent half of her allowance going to the movies. She washed the family car and earned $6. What is her weekly allowance if she ended with $15?
Answer:
Her weekly allowance is $18
Step-by-step explanation:
We can use an algebraic equation to solve this problem.
x/2 + 6 = 15
x/2 + 6 ( - 6) = 15 ( - 6)
x/2 ( · 2)= 9 ( · 2)
x = 18
Her weekly allowance is $18
determine the sampling error if the grade point averages for 10 randomly selected students from a class of 125 students has a mean of
Answer:
Step-by-step explanation:
x=2.3
Help please. 20 pts WILL MARK BRAINLIEST
Answer:
Subtract 6 from both sides
Question 7 of 15 Garth sells baseball caps outside the stadium. The graph shows the number of caps sold and the income from the sales. It represents a linear function. Income (dollars) 250 225 200 175 150 125 100 75 50 25 Income from Cap Sales (3, 22.5) (5, 37.5) 1 2 3 4 5 6 7 8 9 10 Number of caps sold
Answer:
He gets $7.50 per cap
Step-by-step explanation:
I took the test
Answer:
$17.50
Step-by-step explanation:
Which equation represents a line that has a slope of One-third and passes through point (–2, 1)?
y = one-third x minus 1
y = one-third x + five-thirds
y = one-third x minus five-thirds
The equation of the line with a slope of one third and passes through (-2, 1) is y = one-third x + five-thirds.
How to find the equation of a line?The equation of a line can be represented in a slope intercept form as follows:
y = mx + b
where
m = slopeb = y-interceptTherefore, the equation of the line has a slope of 1 / 3. Let's find the y-intercept using the coordinates (-2, 1)
y = 1 / 3 x + b
1 = 1 / 3 (-2) + b
1 + 2 / 3 = b
b = 3 + 2 / 3
b = 5 / 3
Therefore, the equation is y = 1 / 3 x + 5 / 3
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The water level in a spherical bowl has a diameter of 30 cm. If the horizontal diameter of the bowl is 10 cm below the water level, calculate the radius of the bowl and the depth of the water in the bowl.
Answer:
radius ≈ 18.03 cmdepth ≈ 28.03 cmStep-by-step explanation:
You want the radius and water depth in a spherical bowl in which the water level is 10 cm above the center of the sphere, and the circular surface has a diameter of 30 cm.
Pythagorean theoremThe geometry of the diameter of the water surface can be modeled as shown in the attachment. The radius of that surface forms one leg of a right triangle with the other leg being 10 cm. The hypotenuse of the triangle is the radius of the sphere, so we have ...
r² = 15² +10² = 325
r = √325 = 5√13 ≈ 18.03 . . . . . cm
DepthThe water depth is 10 cm more than the radius, so is ...
d = 10 +r = 10 +5√13 ≈ 28.03 . . . . . cm
The radius of the bowl is about 18.03 cm; the depth of water is about 28.03 cm.
WHOEVER ANSWERS GETS 100 POINTS ASND BRAINLIEST ANSWER PLEASE HELP
GIVEN THE FOLLOWING SITUATION, ANSWER THE QUESTIONS:
The size of shoe a person needs varies linearly with the length of his or her foot. The smallest adult shoe size is Size 5, and fits a 9-inch long foot. An 11-inch long foot takes a Size 11 shoe.
1. Name TWO POINTS on the line that expresses shoe size in terms of foot length:
2. Find the slope of the line that expresses shoe size in terms of foot length.
3. Write the particular equation expressing shoe size in terms of foot length in slope-intercept form.
4. If your foot is a foot long what size shoe do you need?
5. Bob Lanier, who once played basketball for the Detroit Pistons, wears a Size 22 shoe. How long is his foot? Include units!!
6. If plotted the graph of the adult shoe size versus foot length, what would the leftmost point be, based on the information given in bold print above? (the story problem before number 1)
7. If manufacturer decided to begin offering adult shoes in smaller sizes, how long would the foot of a person be who wore size 0? Include units!!
PLEASE HELP
Answer:
The slope is 1/3, calculate the rest from there
Step-by-step explanation:
We can picture this as a graph with the x value being the shoe size and the y being the length of a foot in inches. If we visualize it that way, we have two points on the graph: (5,9) and (11,11). From this, we can calculate the slope. The formula for slope is change in y value/change in x value, or rise/run. The slope in this case would be 2/6, simplified to 1/3. From this, we know that every time the X value increases by 1, the Y value increases by 3. Using this, you can find the two points on the line yourself. The equation formula for slope is y = mx + b. M is the slope, and Y is the y intercept (the value of Y when X = 0). Since the slope is 1/3, the equation is y = 1/3x+(y intercept). I am not going to fully solve this problem for you because I have a feeling you need this answer for a test of sorts (because of the level of urgency) but with this information you can probably solve this yourself! Good luck :)
Write the equation of the line in slope intercept form and given the slope and y-intercept.
1) slope = 3/4 and (0, 4). 2) slope = -1 and (0, -2)
Please,help. Been stuck for two days
The equation of each line in slope-intercept form are:
1. y = 3/4x + 4.
2. y = -x - 2
What is the Equation of a Line in Slope-intercept Form?To express the equation of a line in slope-intercept form, y = mx + b, substitute the value of the slope (m) and the value of the y-intercept (b) into the equation.
1. Slope (m) = 3/4
y-intercept (b) = 4
Substitute m = 3/4 and b = 4 into the equation y = mx + b:
y = 3/4x + 4.
2. Slope (m) = -1
y-intercept (b) = -2
Substitute m = -1 and b = -2 into the equation y = mx + b:
y = -x - 2
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graph into an eqation
The equation of the given values of x and y will be; y = 2x - 2
What does it mean to solve an equation?An equation represents equality of two or more mathematical expression.
Solutions to an equation are those values of the variables involved in that equation for which the equation is true.
We have been given the values of x and y. then we need to find the equations;
First slope
m = (4 +2)/(3 - 0)
m = 6/3 = 2
Now the standard form of the equation is;
y-y₁ = m(x-x₁)
y+ 2 = 2(x- 0)
y = 2x - 2
The graph of the given equation of line is attached below.
Hence, the equation of the given values of x and y will be; y = 2x - 2
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Help me and please explain your answer Act smart
The only equation that represents a piecewise defined function is;
Option A: f(x) = {-2, if x ≥ 4
{x², if x < 4
What is a piecewise function?A piecewise function is defined as a function that consists of multiple subfunctions, whereby each subfunction defined over a specific subset of the domain of the main function which is called a subdomain.
The equation of a piecewise function is usually written with a curly bracket that indicates the fact of being comprised of more than one subfunction. An example of a piecewise function is;
f(x) = {x, x < 0
{x + 1, x ≥ 0
Let us look at each of the given functions;
Function in option A is clearly a piecewise function when compared to the definition given above
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Which is the focus and directrix of the parabola with equation (y + 0.5)² = 4(x - 1)?
O Focus (2, -0.5); directrix x = 0
O Focus (2,-0.5); directrix y = -1.5
O Focus (0, -0.5); directrix y = -1.5
O Focus (0, -0.5); directrix x = 0
The first option Focus(2,-0.5); directrix x=0 of the parabola is the correct answer.
What is a parabola?
A parabola is an approximately U-shaped, mirror-symmetrical plane curve in mathematics. It corresponds to a number of seemingly unrelated mathematical descriptions, all of which can be shown to define the same curves. A parabola can be described using a point and a line.
The general equation of a parabola is as follows:
[tex](y-k)^2=4a(x-h)[/tex]
Now, consider the given equation.
[tex](y+0.5)^2=4(x-1)[/tex]
Now, compare with the standered equation.
a=1, k=-0.5 and h=1
Here, a is positive hence, the parbola opens right side.
Focus is given by the following coordinate:
[tex](h+a,k)=(1+1,-0.5)\\=(2,-0.5)[/tex]
Now, equation of diretrix is given by the following expression:
[tex]x=h-a\\x=1-1\\x=0[/tex]
Hence, the first option Focus(2,-0.5); directrix x=0 is the correct answer.
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Layla is shipping cans of soup and boxes of pasta to a local food pantry. Each can of soup weighs 18.6 ounces and each box of pasta weighs 16 ounces. The maximum weight of the shipping box Layla will use to ship the food is 40 pounds. If Layla plans to put 15 cans of soup in the shipping box, how many boxes of pasta can she put in the same shipping box without going over the maximum weight?
Answer:
23 boxes of pasta
Water Glasses on a shelf are broken and must be replaced.
The replacement cost can be cut in half if you can figure out how many glasses were broken.
Here are your clues:
There were more than 24 glasses, but less than 100 glasses.
If the glasses were in rows of 6, there would be 3 left over.
If the glasses were in rows of 8, there would be 7 left over.
The total number of water glasses on the shelf may be 39, 63 or 87.
Given, that there were more than 24 glasses, but less than 100 glasses.
If the glasses were in rows of 6, there would be 3 left over.
If the glasses were in rows of 8, there would be 7 left over.
Let the number of glasses be x,
So, x = 6k1 + 3
=> (x - 3) is a multiple of 6
x = 8k2 + 7
=> (x - 7) is a multiple of 8
Now, the numbers that can satisfy the given conditions are,
39 , 63 & 87.
So, the total number of glasses may be 39, 63 or 87.
Hence, the total number of water glasses on the shelf may be 39, 63 or 87.
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I need help please!!
Please help
me answer both of them ASAP!! and submit it like this. Example: 1=b and 2=d
8. -a+b-7
9. m=(y-b)/x
Answer:
first one: C
second one: A
Step-by-step explanation:
4a - 5 + 3b - 2 - 2b - 5a
combine a terms:
-a - 5 + 3b - 2 - 2b
combine b terms:
-a - 5 + b - 2
combine numbers:
-a + b - 7 (this is option c)
_____________________
y = mx + b, solve for m
subtract b from both sides:
y - b = mx + b - b
y - b = mx
divide both sides by x:
(y - b)/x = mx/x
m = (y - b)/x (this is option a)
5. What is the independent variable in the following function?
f(c) = 2c + 9
09
Of
0:
Answer:
C
Step-by-step explanation:
C is the input. The input is the independent variable. The output would be the dependent variable.
Can anyone possibly help me?
Function F was transformed by using f(bx) as shown below. Find the value of b
The graph of the transformation of f(x) to f(b·x), where f(1) in f(b·x) is equal to f(5) in f(x) indicates that the value of b is 5
What is the transformation of a function?The transformation of a function is represented by a function that changes one function into another function, such that the size, or position of the graph of the original function is modified
The given transformation of the function f is f(b·x)
A formula for the transformation of a function y = f(x) is the function;
y = a·f(b(x + c)) + d
Where;
The a indicates a vertical translation of the function
b indicates an horizontal dilation of f
c stands for a horizontal translation
d stands for a vertical translation
The translation in the question is f(b·x), which is a horizontal dilation, is expressed as follows;
When b > 1, the graph of f(x) shrinks horizontally
When 0 < b < 1, the graph of f(x) is stretched
At x = 1, f(x) = 1, and f(b·x) = 5
The graph of f(x) shrinks to obtain the graph of f(b·x), such that the value obtained at f(5) in f(x) is obtained at f(1) in f(b·x)
f(5) = f(b·1)
b×1 = 5
b = 5 ÷ 1 = 5
The value of b is 5
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a researcher want to determine an interval estimate for the average weight of adult gorillas in pounds. she wants to be 80% certain that she is within 7.1 of the true average. from past studies, it is known that the standard deviation of the weights of adult gorillas is 18.2 pounds.
The population estimated minimum sample size will be 11 , and the critical value will be 1.28.
The average gorilla weight is being calculated as a range estimate by a researcher (in pounds).
She wants to be within 7.1 pounds of the actual average with 80% accuracy.
Previous research has shown that the standard deviation of the weights of gorillas is 18.2 pounds.
a) Since the confidence is 0.80 or 80% then the value of α is 0.20 and and we can calculate the critical value. Then the value of the z-score will be z = 1.28.
b) The margin of error is given as
M.E.= z*(standard deviation/√n)
We have,
Margin of error = 7.1
From the above formula we get;
n = ((z* standard deviation )/marginal error)²
n = ((1.28*18.2)/7.1)²
= 10.76 ≈ 11
Therefore, the researcher should take 11 samples.
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please help !!!!!!!!!
Answer: Real and Rational
Step-by-step explanation:
2/3 is a fraction. ALL numbers are are considered real numbers. Rational numbers are typically fractions and decimals.
Runners at a cross-country meet run 2 miles south and then 4 miles west from the starting line. Determine the shortest straight path they must run to get back to the
tarting line.
06 miles
√6 miles
O√12 miles
√20 miles
hello hope you are having a good day
the answer to your question would be A 6 miles i took the test and got an 100% also asked the teacher.
Devon and Albert are shelving books at a public library. Devon shelves 6 books at a time, whereas Albert shelves 9 at a time. If they end up shelving the same number of books, what is the smallest number of books each could have shelved?
Given the Quadratic equation y = 2x²- 9x - 13, what is the y intercept?
(0,0)
(0,-13)
(0,2)
(0,-9)
Help please
Answer: (0,-13)
Step-by-step explanation:
The y intercept is x=0
Hence,
y=2(0²)-9*(0)-13
y=2(0)-0-13
y=0-13
y=-13
Thus, (0,-13)
PLEASE HELP ME!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
Cost of 14 apples is Rs. 120, find the cost of 20 apples
Answer:
Rs 171.40
Step-by-step explanation:
For 1 apple we have to divide 120 by 14 which is 8.57 to 2d.p.
So 20 * 8.57 = 171.4
to 2d.p. = Rs 171.40
Pls could you give me brainliest
pls:(
PLEASE HELP ME! I know this is alot to ask but I need someone to complete this study guide for me it's late so I need it asap. if you could answer with a typed pdf that would be the best. I WILL MARK BRAINLIEST! I NEED SOMEONE PLEASE IM BEGGING YOU PLEASE I WOULD GIVE YOU MONEY IF I COULD I WOULD GIVE YOU 10000000000 POINTS I SWEAR TO GOD I NEED HELP AND I HAVE OTHER STUFF DUE AND I WON'T BE ABLE TO GET IT ALL DONE. I FINISHED THE ASSIGNMENT BUT I LOST IT PLEASE HELP ME! I REALLY DID IT AND I SWEAR I WILL FAIL THIS CLASS IF I DON'T HAVE IT SOON ANYTHING HELPS IF YOU ONLY ANSWER LIKE 5 QUESTIONS I DON'T CARE JUST HELP! PLEASE PLEASE
2.Under feudalism, landowners were granted plots of land (called fiefs) by nobles in exchange for their loyalty and military service. The landowner, or vassal, was required to provide the lord with soldiers when needed and give him a portion of the land's produce. In return, the lord provided the vassal with protection from invaders.
Manorialism (how did it work)
Manorialism was an economic system that developed in medieval Europe. It was based on the control of land and the produce of that land by a lord. The lord would grant land to peasants in exchange for their labor and a portion of the produce. This system allowed for the development of large estates and the growth of a class of landowners.
Justinian ( identify and achivements)
Justinian was the Byzantine emperor from 527 to 565. During his reign, Justinian sought to revive the empire's greatness and reconquer the lost western half of the historical Roman Empire.
One of Justinian's most famous achievements was the construction of the Hagia Sophia, which was completed in 537. The Hagia Sophia is a former Greek Orthodox cathedral that was turned into a mosque after the Ottoman conquest of Constantinople in 1453. It is now a museum in Istanbul, Turkey.
Another of Justinian's accomplishments was the compilation of the Justinian Code, a collection of laws that codified Roman law and is still used as a reference today. The Justinian Code was instrumental in the development of modern legal systems.
vassal
The social position and duties of a vassal during the Middle Ages was to provide military service to their lord in exchange for land that they could then cultivate. Vassals were also required to attend their lord's court and give him counsel
Knights
Serve as a military support system for the king
. Helped keep the peace within the kingdom
. Provided protection for the king and queen
. Guarded the king's castle
serf
The serfs were the lowest class of society in medieval Europe and were bound to the land that they worked on. They were required to work for their lord for a certain number of days each week and were given a plot of land to farm for themselves. They were also required to pay taxes and fees to their lord.