Answer:
Y = -X + 5
Step-by-step explanation:
I want this equation in the form
y = mx = b
2x + 2y = 10 Subtract 2x from both sides of the equations
2y = -2x + 10 Now divide everything by 2
y = -1x + 5
or
y = -x + 5
triangle ABC is similar to triangle DEF. Find the perimeter of triangle DEF
The perimeter of tr8angle DEF that is similar to triangle ABC is: 18 cm.
How to Find the Perimeter of Similar Triangles?If two triangles are similar to each other, and the perimeter of one is A with a side length of a, and the perimeter of the other is B with a side length of b, then, the following below is the ratio of their perimeters.
Perimeter of A/perimeter of B = a/b
Given that triangles ABC and DEF are similar triangles, we have the following:
Perimeter of triangle ABC = x
One side length of triangle ABC = 4 cm
Perimeter of triangle DEF = 12 + 6 + 9 = 27 cm
One side length of triangle DEF = 6 cm
Therefore:
x/27 = 4/6
Cross multiply
6x = (27)(4)
6x = 108
6x/6 = 108/6
x = 18
Thus, the perimeter of tr8angle DEF that is similar to triangle ABC is: 18 cm.
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What is the missing side length?
Answer:10
Step-by-step explanation:
6+4=10
solve the following simultaneous equation graphically 2x-y=1 and 3x+y=9
The solution to the system of linear equations is (x, y) = (2, 3).
How to solve graphically a system of linear equation
Graphic methods are useful to solve systems of two linear equations with two variables, as it is seen in the statement of the problem. In accordance with geometry, a line can be constructed by knowing the coordinates of two distinct points on Cartesian plane. First, rewrite each linear equation into its explicit form:
y = 2 · x - 1 (1)
y = - 3 · x + 9 (2)
Second, look for two points lying on each line:
y = 2 · x - 1
(0, - 1) and (1, 1)
y = - 3 · x + 9
(0, 9) and (- 3, 6)
Third, plot the points on a Cartesian plane and pass each line through corresponding pair of points. The result is presented by the image attached below.
The solution to this system is the point of intersection of the two lines. The point of intersection is (2, 3).
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Evaluate the expression. Check all possible sets that
the solution may belong in.*
√0+7
*More than one answer may be correct; mark all that apply.
-rational
-integers
-real
-whole
-natural
-irrational
-none of these
The possible sets of the solution of the expression given as √0 + 7 are integer, whole number, natural number, rational number and real numbers
How to determine the possible set of the solution?The expression is given as
√0 + 7
Start by evaluating the radical expression
So, we have
√0 + 7 = 0 + 7
Continue by evaluating the sum of the terms
So, we have
√0 + 7 = 7
The above implies that the result of the expression √0 + 7 is 7
The sets the number 7 belong to are:
The number 7 is an integer because it does not have any decimal pointThe number 7 is a whole number because it does not have any decimal point and it is not negativeThe number 7 is a natural number because it does not have any decimal point and it is greater than 0The number 7 is a rational number because it can be expressed as a fraction of integersThe number 7 is a real number because it does not have any imaginary partHence, the possible sets of the solution of the expression given as √0 + 7 are integer, whole number, natural number, rational number and real numbers
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How are the values in the
ordered pairs affected by the translation?
In arithmetic, a shape is translated when it is moved up, down, left or right. The translated shapes are congruent to the original shapes because they appear to be the same size. Just one or more of their routes have been changed. No changes to the shape are made because it is simply being moved from one location to another.
By utilizing the aforementioned guidelines, we can move the provided graph to the left, right, up, or down and graph the translated graphs. The coordinates of some points on a graph can be used to translate a graph as an alternative to this. Translation f(x + k) + C for a function graph To get the new x and y coordinates of each point when the graph of the function f(x) is supplied, simply select a few key spots on the graph (where the shape is changing or turning) and proceed as follows.
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7 Write down two square roots for each of these numbers. b 36 d 196 e 225 f 400
The square roots of 36,196,225 and 400 are ±6,±14,±15 and±20
There exits two square roots of any number one with positive sign and one with negative sign
The first number we have is 36
The square roots of 36 = ±√36 = ±6 or it can be written as 6 and -6
The second number we have is 196
The square roots of 196 = ±√196 = ±14 or it can be written as 14 and -14
The third number we have is 225
The square roots of 225 = ±√225 = ±15 or it can be written as 15 and -15
The fourth number we have is 400
The square roots of 400 = ±√400 = ±20 or it can be written as 20 and -20
Hence, the square roots of 36,196,225 and 400 are ±6,±14,±15 and±20
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A
Which of the following does
not have a horizontal line of
symmetry?
E
B
A
C
O
Answer:
A
Step-by-step explanation:
In math, symmetry is when an object, thing, etc is identical on both ends. Split a horizontal(left to right) line through the middle of each letter. Every letter has identical top and bottom sides except for A.
Therefore, the answer is A.
If 0.6 J of work is needed to stretch a spring from 7 cm to 9 cm and another 1 J is needed to stretch it from 9 cm to 11 cm, what is the natural length (in cm) of the spring?
We need to know about concept of work done on spring to solve the question.The natural length of the spring is 5cm.
We will need to make assumptions to solve this problem, we will assume that the natural length of the srping is [tex]x_{0}[/tex] and the work done to stretch the spring from it's natural length to a specific length is given by
W=[tex]\frac{1}{2} k(x-x_{0} )^{2}[/tex] , where W is the work done, x is the final length of the spring
We have to find out the work done to get to 7cma nd 9cm separately and then subtract one from the other to get the work done to stretch from 7cm to 9cm. We repeat the process for 9cm and 11cm and we will find the final result which is the natural length.
W=[tex]\frac{1}{2} k(7-x_{0} )^{2}[/tex]
W=[tex]\frac{1}{2} k(9-x_{0} )^{2}[/tex]
[tex]\frac{1}{2} k(9-x_{0} )^{2} -\frac{1}{2} k(7-x_{0} )^{2} =0.6\\(9-x_{0} )^{2} - (7-x_{0} )^{2} =\frac{1.2}{k}[/tex]...(i)
W=[tex]\frac{1}{2} k(9-x_{0} )^{2}[/tex]
W=[tex]\frac{1}{2} k(11-x_{0} )^{2}[/tex]
[tex]\frac{1}{2} k(11-x_{0} )^{2} -\frac{1}{2} k(9-x_{0} )^{2} =1\\(11-x_{0} )^{2} -(9-x_{0} )^{2} =\frac{2}{k}[/tex]...(ii)
Dividing equation (ii) by (i)
[tex]\frac{(11-x_{0} )^{2} -(9-x_{0} )^{2} }{(9-x_{0} )^{2} -(7-x_{0} )^{2} } =\frac{2}{1.2} \\\frac{(20-2x_{0} )2}{(16-2x_{0})2 } =\frac{1}{0.6} \\12-1.2x_{0} =16-2x_{0} \\0.8x_{0} =4\\x_{0} =5[/tex]
Thus using the concept of work done to stretch a spring we get the natural length of the spring which is 5cm.
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F(x) = 2x-6 and f(7) -9
Answer:
-1
Step-by-step explanation:
Plug 7 in for wherever there's an "x."
f(x) = 2(7) - 6
f(x) = 14 - 6
f(x) = 8
Now subtract 9 from 8.
8 - 9 = -1
Therefore, if Yolanda deposits $1,900 at the end of each six months for 2 years in a savings account earning 8% interest compounded semiannually, to the nearest cent, she can expect to have
$
.
The amount that Yolanda can expect to have in her account at the end of 2 years is $8,068.28.
What is the future value of the amount deposited?The amount of money that Yolanda deposits twice in a year represents an annuity. An annuity is a series of payment that is made over a specified period of time. An ordinary annuity is when payment is made at the end of each period and not at the beginning of the period. Yolanda's deposit is an ordinary annuity.
When the amount deposited in an account earns interest that is compounded semi-annually, it means that both the amount that is invested and the interest that is already accrued increases in value two time in a year, every six month.
The formula that can be used to determine the future value of the amount that was deposited in the account is:
Future value = amount deposited x annuity factor
Annuity factor = {[(1+r)^n] - 1} / r
Where:
r = interest rate : 8 / 2= 4%n = number of periods : 2 x 2 = 41,900 x[ {(1.04^4) - 1} / 0.04] = $8,068.28
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Find the average
rate of change for the given
function from x = -1 to x = 4. (5 points)
Professor Halen has 184 students in his college mathematics lecture class. The scores on the midterm exam are normally distributed with a mean of 72 and standard deviation of 9.
a. How many students in the class can be expected to receive a score over 60?
b. What percent of the class is expected to receive a score between 82 and 90?
Using the normal distribution, it is found that:
a) 167 students in the class can be expected to receive a score over 60.
b) 11.07% of the class is expected to receive a score between 82 and 90.
Normal Probability DistributionThe z-score of a measure X of a normally distributed variable with mean represented by [tex]\mu[/tex] and standard deviation represented by [tex]\sigma[/tex] is given by:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
It measures how many standard deviations the measure is above(in case the score is positive) or below(in case the score is negative) the mean. Looking at the z-score table, the p-value associated with the z-score is found, which represents the percentile of the measure X.The mean and the standard deviation for the scores are given, respectively, by:
[tex]\mu = 72, \sigma = 9[/tex]
The proportion of students who scored over 60 is given by one subtracted by the p-value of Z when X = 60, hence:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
Z = (60 - 72)/9
Z = -1.33.
Z = -1.33 has a p-value of 0.0918.
1 - 0.0918 = 0.9082.
Out of 184 students:
0.9082 x 184 = 167.
167 students in the class can be expected to receive a score over 60.
For item b, the proportion is the p-value of Z when X = 90 subtracted by the p-value of Z when X = 82, hence:
X = 90:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
Z = (90 - 72)/9
Z = 2.
Z = 2 has a p-value of 0.9772.
X = 82:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
Z = (82 - 72)/9
Z = 1.11
Z = 1.11 has a p-value of 0.8665.
0.9772 - 0.8665 = 0.1107.
Hence:
11.07% of the class is expected to receive a score between 82 and 90.
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Simplify 1,999,9990.
The value of 1,999,999 with an exponent of 0 is 1,999,999 × 10⁰
What is an exponent?Exponentiation is a mathematical process that involves the base b and the exponent or power n. It is represented as bn and is pronounced as "b to the n."
Knowing that every number raised to the power of zero equals one is necessary before we can simplify using a zero exponent. Hence:
1,999,999 = 1,999,999 × 1
Since 1 can be expressed as 10⁰, the value becomes:
1,999,999 = 1,999,999 × 10⁰
Therefore, the value of 1,999,999 with an exponent of 0 is 1,999,999 × 10⁰.
The complete question is given below:-
Simplify 1,999,999 with an exponent of 0
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Select the correct answer.
A school conducts 27 tests in 36 weeks. Assume the school conducts tests at a constant rate. What is the slope of the line that represents the
number of tests on the y-axis and the time in weeks on the x axis
The slope of the line representing number of tests on the y-axis and the time in weeks on the x axis is 0.75.
What is the definition of line slope?A line's slope is a measure of its steepness as well as direction. The slope of a line can be calculated using any two separate points on that line.The slope of a line formula calculates the ratio of "vertical change" to "horizontal change" between two distinct points on a line.The net change in y coordinates is Δy while the net change in x coordinates is Δx.As per the given question;
The total number of week is 36 weeks.
The total test conducted is 27.
As, number of tests are represented on the y-axis and the time in weeks on the x axis.
The slope is constant for the text and weeks.
Thus, slope (m) is determined as;
m = Δy/Δx
m = number of tests/time in weeks
Put the values.
m = 27/36
m = 0.75
Therefore, the slope of the line representing number of tests on the y-axis and the time in weeks on the x axis is 0.75.
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Please show work ThankYou very much 25 points to whoever does it
Answer: 3 answer
Step-by-step explanation:
Problem Solving
6. Sandi's school has 1,030 students. If
Karla's school had 43 more students, it
would have 3 times as many students as
Sandi's school. How many students are in
Karla's school?
What is the simplified form of the expression the quantity x squared plus 4x minus 21 end quantity divided by 4 times the quantity x plus 7 end quantity?
the quantity x plus 3 end quantity divided by quantity x plus 7 end quantity
the quantity x minus 3 end quantity divided by quantity x plus 7 end quantity
the quantity x minus 3 end quantity divided by 4
the quantity x plus 3 end quantity divided by 4
Answer:
[tex] \sf \frac{(x^3+4x^2+21x+28)}{4}[/tex]
Step-by-step explanation:
Let's simplify step-by-step.
[tex] \sf \: \frac{ {x}^{2} + 4x - 21}{4} \times x + 7[/tex]
Distribute
[tex] \sf \frac{(x^3+4x^2+21x+28)}{4}[/tex]
Answer:
A) x + 3
4
Step-by-step explanation:
how to simplify 5(2x-8) using distributive property
Answer:
Not 100% sure
Step-by-step explanation:
Image result for how to simplify 5(2x-8) using distributive property
The formula for the distributive property is expressed as, a × (b + c) = (a × b) + (a × c); where, a, b, and c are the operands. Here, the number outside the brackets is multiplied with each term inside the brackets and then the products are added.
8d+14 awnser needed
Answer:
22d
Step-by-step explanation:
A fast food chain buys burgers from a food supplier.
They're given a discount depending on how many they buy.
The table on the right is used to calculate this discount.
between
The full price of a single burger is 27p.
What is the difference in the price to pay
ordering 1100 burgers as a single order or as two
orders of 550? Give your answer in pounds (£).
Quantity
Fewer than 500
Discount
0
Quantity
500 to 1000
Discount
2/15
Quantity
More than 1000
Discount
3/15
Answer:
89.01 calariese is answer
a. Write an inequality that represents the numbers that are not solutions of x+3.8>11.3 .
Inequality:
Question 2
b. Graph the inequality from part (a).
Inequality that represents the coordinates that are not the solutions of this inequality is x < 7.5. The graph of the inequality is attached at the end.
What are the various operators used in inequalities for comparison?The various operators used in inequalities for expression are -
greater than - ' > 'less than - ' < 'greater than or equal to - ' ≥ 'less than or equal to - ' ≤ 'Given is a inequality in one variable which is → x + 3.8 > 11.3.
PART - A
The inequality that represents the coordinates that are not the solutions of this inequality is -
x + 3.8 < 11.3
or
we can simplify it to get -
Subtract 3.8 from both sides -
x + 3.8 - 3.8 < 11.3 - 3.8
x < 7.5
PART - B
In order to plot the graph of this inequality, firstly we will plot the line of equation -
x = 7.5.
Since, the inequality is strict, make a dashed line to represent the equation.
Take the coordinates of origin O(0,0), and substitute it in the inequality -
0 < 7.5
which is true. Therefore, we will shade the complete side where origin lies.
The graph of the inequality is plotted an attached with the answer.
Therefore, inequality that represents the coordinates that are not the solutions of this inequality is x < 7.5. The graph of the inequality is attached at the end.
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I give up I’m so confuse rn pls help answer these
3x+4y-5z=-11
4х+ у- z=-5
x-3y + 3z = 2
Left to right elimination
The solution using the elimination method for the values of x, y and z are -1, 3 and 4 respectively.
To solve multiple equation in three variables using the elimination approach, we can either add or subtract the equations. To eliminate a variable, we add the equations when the coefficients of one variable are in opposition, and subtract the equations when the coefficients of one variable are equal.
Let us classify the given equations as:
3x + 4y - 5z = -11 →→→→ (A)
4х + у- z = -5 →→→→→(B)
x- 3y + 3z = 2 →→→→→(C)
Multiplying equation(C) by 3 and equation (A) by 1 and subtracting we get:
3x + 4y - 5z = -11
3x - 9y + 9z= 6
13y-14z=-17→→→→→→(D)
Multiplying equation(C) by 4 and equation (B) by 1 and subtracting we get:
4x-12y+12z = 8
4x + y - z = -5
-13y+13z=13
or, z-y=1→→→→→→→(E)
Multiplying equation(E) by 13 and equation (D) by 1 and adding we get:
-13y+13z=13
13y-14z =-17
-z=-4
or, z = 4
Substituting the value of z in the equation (E) we get:
z-y=1
or, 4-y = 1
or, -y = -3
or, y = 3
Substituting the value of z and y in the equation (A) we get:
3x+4y-5z=-11
or, 3x+12-20=-11
or, 3x=-11+8
or, x=-1
Hence the solution of x, y and z are -1, 3 and 4 respectively .
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Calculate the price elasticity of supply for Barbie's Bakery's multigrain loaf. When the price changes by 27% , the quantity supplied changes by 59% .
Percentage, a relative value indicating hundredth parts of any quantity. One percent (symbolized 1%) is a hundredth part. Price Elasticity of Supply is 2.185.
What is percentage?Percentage, a relative value indicating hundredth parts of any quantity. One percent (symbolized 1%) is a hundredth part.
Price Elasticity of Supply is buyers' responsive change in quantity supplied due to change in Price.
P Es Formula = % change in quantity supplied / % change in price.
Given : % change in supply = 59 ; % change in price = 27
So, P Es = 59 / 27 = 2.185
% change in supply > % change in price & supply is > 1 . So, Supply is Elastic.
Therefore the price elasticity of supply for Barbie's Bakery's multigrain loaf is 2.185.
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The table shows the linear relationship between the playing time in minutes of high-definition videos and the file size of these videos in megabytes (MB) What is the rate of change of this function?
180
60
120
30
the slope of the linear equation is 120, then the correct option is the third counting from the top.
What is the rate of change of this function?For any linear equation with two points (a, b) and (c, d), the slope (or rate of change) of that line is given by:
s = (d - b)/(c - a)
So here we can use the first two points so we get:
(0.5, 60)
(1.5, 180)
With these two points we will get the slope:
s = (180 - 60)/(1.5 - 0.5) = 129
We conclude that the slope is 120, then the correct option is the third counting from the top.
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(100 POINTS!!! NEED HELP, PLEASE HURRY!!) Valerie estimates that a used vehicle will require regular maintenance every 3 months. The average costs for this is $45. The insurance premiums are estimated at $100 per month. She saves $100 per month for tires and unexpected repairs since there is no warranty on the used vehicle. The interest rate is 11% to finance the vehicle. (Interest rates are traditionally higher on used vehicles.) Valerie can afford $400 per month for four years to buy a vehicle. Excluding tax, tag, and title, approximately what is the most Valerie can pay for a vehicle?
Answer Valerie can afford 21,312 car
Step-by-step explanation:
Suppose you make $5 an hour as a dog walker. Let h represent the number of hours you work in a week. Write an expression that represents the amount of money you earn in a week and evaluate it for h = 20.
Answer:
e = 5h
$100
Step-by-step explanation:
Let e = earnings
e = 5h
For h = 20,
e = 5h = 5(20) = 100
Answer:
$ 100
Step-by-step explanation:
1 hour = $ 5
h (hours worked in a week) = 20 hrs
EXPRESSION: amount of money earned in a week = h × 5
EVALUATION: amount of money earned in a week = 20 × 5
amount of money earned in a week = $ 100 ... answer
hope that helps...
[tex]-5(4-1/2n) + 1/16(-32+8)[/tex]
Answer:
2.5n - 21.5
Step-by-step explanation:
[tex]-5(4 - \frac n2) + \frac1{16}(-32 + 8) \\ \\\to -5 \times 4 + 5 \times \frac n2 - \frac1{16} \times 32 + \frac1{16} \times 8 \\ \\\to -20 + \frac{5n}2 - \frac{32}{16} + \frac{8}{16} \\ \\\to -20 + 2.5n -2 + 0.5 \\ \\\to 2.5n - 21.5[/tex]
wh...
>
<
<
Equivalent ratios with equal groups
Use the following image to complete the sentences describing the ratio of windows with
penguins to total windows.
There are
windows with a penguin for every 18 total windows.
There is 1 window with a penguin for every
total windows.
Second blank is 6 windows for every 1 penguin
given,
there are _18_ windows for every 3 penguins.
There are _6_ windows for every 1 penguin.
its is already given that 3 penguins = 18 windows,
the first blank is 18
To get number of windows for 1 penguin, we divide 18 by 3,
18/3=6
therefore second blank is 6 windows for every 1 penguin.
Window functions—otherwise known as weighting functions, tapering functions, functions—are mathematical functions that are zero-valued outside the chosen interval. They are well established as a vital part of digital signal processing.
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Write the domain and range of the function using interval notation.
The domain of the function is -5 ≤ x < 3 and the range is 0 ≤ y ≤ 2
How to determine th domain and range of the function using interval notation?We have the following endpoints on the graph of the function;
(x, y) = Closed (-5, 2)
(x, y) = Open (3, 2)
Minimum y = 0
Remove the y values to determine the domain
x = Closed -5
x = Open 3
The closed statement represents the inequality ≤, while the closed statement represents the inequality < or >
So, we have
Domain = -5 ≤ x < 3
Also, we have:
(x, y) = Closed (-5, 2)
(x, y) = Open (3, 2)
Minimum y = 0
Remove the x values to determine the range
x = Closed 2
x = Open 2
Minimum y = 0
The above means that the y value does not include a negative value
So, we have
Range = 0 ≤ y ≤ 2
Hence, the domain of the function is -5 ≤ x < 3 and the range is 0 ≤ y ≤ 2
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