Answer:
x = 6, y = 5
Step-by-step explanation:
5x - 4y = 19 -------> equation 1
x + 2 = 8 --------> equation 2
Step 1 : Subtract 2 on both sides in equation 2.
x + 2 - 2 = 8 - 2
x = 6
Step 2 : Substitute the value of x is equation 1.
5 ( 6 ) - 4y = 19
( 5 * 6 ) - 4y = 19
30 - 4y = 10
Step 3 : Subtract 30 on both sides.
30 - 30 - 4y = 10 - 30
- 4y = - 20
Step 4 : Multiply - 1 on both sides.
- 1 * - 4y = - 1 * - 20
4y = 20
Step 5 : Divide 4 on both sides.
4y / 4 = 20 / 4
y = 5
Hence,
x = 6
y = 5
Answer:
x = 5, y = 3/2.
Step-by-step explanation:
5x-4y=19
x+2y =8 Multiply this by 2:
2x + 4y = 16 Adding this to first equation 1:
7x = 35
x = 5
So
5 + 2y = 8
2y = 3
y = 3/2.
PGCPS
Given the function defined in the table below, find the average rate of change, in
simplest form, of the function over the interval 3 ≤ x ≤ 6.
Answer:
X
1
2
3
4
5
6
f(x)
69
64
59
54
49
44
Need Help
Answer: -5
Step-by-step explanation:
[tex]\frac{g(6)-g(3)}{6-3}=\frac{44-59}{3}=-5[/tex]
What is the correlation coefficient for the model that predicts the list price of all homes using population as an explanatory variable
Here, we are concerned about two variables from the above data set, namely, Condo or co-ops and the Unemployment rate. We use the CORREL function of Excel to calculate the correlation coefficient rate and it is = R = -0.01873.
A Weak (negative) correlation exists between the list price of condominiums and co-ops and the unemployment rate.
The correlation coefficient is a statistical measure of the strength of the connection between the relative actions of two variables. The values varied between -1.0 and 1. zero. A calculated wide variety greater than 1. zero or less than -1.zero means that there was an error within the correlation size.
The correlation coefficient is decided with the aid of dividing the covariance by way of the product of the 2 variables' popular deviations.
Correlation values above 0. eight are deemed to signify a strong tremendous linear courting between the variables. Values among zero and 0. three imply a vulnerable relationship or none.
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Describe a new situation that can be modeled by the part-to-part ratio 2:3 and interpret what the ratio means in the situation. Use complete sentences in your answer.
20 girls and 30 boys
What is arithmetic ?
A branch of mathematics that deals usually with the nonnegative real numbers including sometimes the transfinite cardinals and with the application of the operations of addition, subtraction, multiplication, and division to them
To make the new situation:
Suppose A classroom has 50 people.
The ratio of girls to boys is 2:3, so in other words, we need to find out how many boys and girls there are, and there are 2 girls for every three boys, So ,how many boys and girls are there?
The answer would be :
Let the two parts in which we divide 50 be 2x and 3x respectively
2x+3x=50
5x=50
x= [tex]\frac{50}{5}[/tex]
x=10
Here,
2x= 2×10=20
3x =3*10=30
20 girls and 30 boys.
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Question 1 of 40
If f(x) = 4x² - 6 and g(x) = x² - 4x-8, find (f- g)(x).
Answer:
[tex]\huge\boxed{\sf (f-g)(x) = 3x\² + 4x - 14}[/tex]
Step-by-step explanation:
Given functions:f(x) = 4x² - 6g(x) = x² - 4x - 8Solution:Subtract both functions
(f-g)(x) = 4x² - 6 - (x² - 4x - 8)
(f-g)(x) = 4x² - 6 - x² + 4x - 8
Combine like terms
(f-g)(x) = 4x² - x² + 4x - 6 - 8
(f-g)(x) = 3x² + 4x - 14
[tex]\rule[225]{225}{2}[/tex]
Given: f(x)=4x^2-6f(x)=4x2−6g(x)=x^2-4x-8g(x)=x2−4x−8
To find : (f-g)(x)
(f-g)(x)=f(x)-g(x)(f−g)(x)=f(x)−g(x)
(4x^2-6)-(x^2-4x-8)
Using Distributive property:-
4x^2-6-x^2+4x+8
4x^2-x^2+4x+8-6
Combine like term
3x^2+4x+2
(f-g)(x)=3x^2+4x+2
Hence, The composite function is (f-g)(x)=3x^2+4x+2
There are 11 kids at a birthday party. If there are 6 girls and 5 boys at the party, whta fractof the kids are boys?
Answer:
Step-by-step explanation: The answer is 5/11.
Hello!
Fraction of boys = Number of boys / Total kids
Fraction of boys = [tex]\boxed {\frac{5}{11}}[/tex]
Triangle ABC is translated 6 units to the right and 1 units up.
What are the coordinates of C’?
C’(4, –2)
C'(4, –0)
C'(4, 2)
C'(1, 2)
The coordinate of the point C from the given triangle ABC after translation is C' = (4, -2)
Translation of coordinatesA triangle is a 2D figure with 3 sides and angles. Given the coordinate C points of the triangle;
C = (-2, -3)
If these coordinate point is translated 6 units to the right and 1 units up, the resulting coordinate will be at:
C' = (-2 + 6, -3 + 1)
C' = (4, -2)
Hence the coordinate of the point C from the given triangle ABC after translation is C' = (4, -2)
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Answer: the answer is A C'(4, -2)
Step-by-step explanation:
B is the midpoint of AC. AB= 3(3x-1) and AC=5(2x+2) find X, AB, BC, and AC
Answer:
x = 2
Step-by-step explanation:
AB is given as 3(3x-1) multiply inside the parenthesis with 3
AB = 9x - 3
AC is given as 5(2x+2) multiply inside the parenthesis with 5
AC = 10x + 10
if B is midpoint of AC then AB = BC and AC = AB + BC if we write this equation using the given values
9x - 3 + 9x - 3 = 10x + 10 add like terms
18x - 6 = 10x + 10 transfer like terms to the same side of the equation
18x - 10x = 10 + 6
8x = 16 divide both sides by 8
x = 2 replace x with 2 in given expressions to find the value of each component
Answer: x = 2; AB = 15; BC = 15; AC = 30
Step-by-step explanation:
AB = BC = 3(3x - 1) = 9x - 3
AC = 5(2x + 2) = 10x + 10
AB + BC = AC
(9x - 3) + (9x - 3) = 10x + 10
9x - 3 + 9x - 3 = 10x + 10
18x - 6 = 10x + 10
8x - 6 = 10
8x = 16
x = 2
Plug x = 2 to find AB, BC, and AC.
AC = BC = 3(3x - 1) = 9x - 3 = 9(2) - 3 = 18 - 3 = 15
AC = 5(2x + 2) = 10x + 10 = 10(2) + 10 = 20 + 10 = 30
Assume that the hourly cost to operate a commercial airplane follows the normal distribution with a mean of $2,100 per hour and a standard deviation of $250. What is the operating cost for the lowest 3% of the airplanes
Using the normal distribution, it is found that the operating cost for the lowest 3% of the airplanes is of at most $1,630.
Normal Probability DistributionThe z-score of a measure X of a normally distributed variable with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex] is given by:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
The z-score measures how many standard deviations the measure is above or below the mean. Looking at the z-score table, the p-value associated with this z-score is found, which is the percentile of X.The mean and the standard deviation are given, respectively, by:
[tex]\mu = 2100, \sigma = 250[/tex].
The operating cost for the lowest 3% of the airplanes is of at most the 3rd percentile, hence at most X when Z = -1.88.
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]-1.88 = \frac{X - 2100}{250}[/tex]
X - 2100 = -1.88(250)
X = 1630.
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*Written Response Question*
The image below shows two dilated figures with lines KO and K’O’ drawn. If the larger figure was dilated using a scale factor of 5, what relationship do lines KO and K’O’ have?
The relationship between lines KO and K’O’ is given as Line K'O' = 5 * line KO
What is a transformation?Transformation is the movement of a point from its initial point to a new location. Types of transformation are reflection, rotation, translation and dilation.
Dilation is the increase or decrease in size of a figure by a scale factor.
The larger figure was dilated using a scale factor of 5, hence:
Line K'O' = 5 * line KO
The relationship between lines KO and K’O’ is given as Line K'O' = 5 * line KO
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Determine the period.
Answer:
13
Step-by-step explanation:
The graph will start repeating after every 13 degrees
The period of the function is of 12 units.
What is the period of a function?The period of the function is the interval between repetitions of any function. A trigonometric function's period is the length of one whole cycle. As a starting point, we can use x = 0 for any trigonometry graph function.
The period of a function is given by the distance between it's repetitions.
Also, it is the distance between two peak value.
Looking at the graph, the distance between the repetitions is of
= 13- 1
= 12 units, which is the period of the function.
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What is the y-intercept
of this line?
X-10-5 0 5 10 15
yl-6-5-4-3|–2|–1
To find Y-intercept, the x-value must be 0.
In the table you can see x = 0 and y = -4
so, the y-intercept of this line is (0 -4)
Hope it helps!
Help with Geometry :/
For this problem, I will be using the equal sign instead of the congruent sign for segments.
1) AC = AB, CD = DE, m∠ABC = 70°, m∠ECB = 35° (given)
2) ∠ACB is congruent to ∠ABC (base angles theorem)
3) m∠ACB = 70° (congruent angles have equal measure)
4) m∠DCE = 35° (angle subtraction postulate)
5) ∠DCE and ∠DEC are congruent (base angles theorem)
6) m∠DEC = 35° (congruent angles have equal measure)
7) ∠DEC is congruent to ∠ECB (angles with the same measure are congruent)
8) DE is parallel to BC (if two lines are cut by a transversal and the alternate interior angles are congruent, then the lines are parallel)
If 7 times a certain number is decreased by 8 and the result is equal to 20. find the number
Hello,
Answer:
number= 4
Step-by-step explanation:
7x - 8 = 20
⇔ 7x - 8 + 8 = 20 + 8
⇔ 7x = 28
⇔ 7x/7 = 28/7
⇔ x = 4
Answer:
certain number=4
Step-by-step explanation:
7x-8=20 then solve
Determine the length of AB. Write your answer in simplest form.
By using the definition of similarity between triangles and algebraic properties, the length of the segment AB of the system is equal to 4 units.
How to determine the length of the segment AB
In this problem we have two similar triangles and we need first to determine the lengths of segments AC and BC and then subtract the length of the latter from the length of the former, that is:
AC/BC = CE/CD
AC/2 = 15/5
AC = 6
AB = AC - BC
AB = 6 - 2
AB = 4
By using the definition of similarity between triangles and algebraic properties, the length of the segment AB of the system is equal to 4 units.
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Which expression can be used to approximate the expression below, for all positive numbers a, b, and x, where a not-equals 1 and b not-equals 1?
The following logarithmic expression can be used to approximate the given expression,
[tex]\frac{log_{b} x}{log_{b} a}[/tex]
Finding the Logarithmic Expression
It is given that for all positive numbers a, b, and x on the condition that a≠1 and b≠1.
Now, for positive values of m and n, we have the following logarithmic expression,
[tex]\frac{log_{m} x}{log_{n} a}[/tex]
Here, m, n and x are all positive numbers.
The logarithmic property imposes that m and n are not equal to 1.
So, by substituting the values m and n by a and b respectively, we get the following logarithmic expression,
[tex]\frac{log_{b} x}{log_{b} a}[/tex]
Therefore, [tex]\frac{log_{b} x}{log_{b} a}[/tex] is the required expression.
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Given: The
measure of angle B = 31 degrees, measure of angle C
= 121 degrees, and b = 9. Then a =
nearest tenth.
to the
Answer:
a=8.2
Step-by-step explanation:
example : 4(m+4) = 4m + 16
1 6(m+3)=?
Use the Pythagorean identity
to find sin x.
COS X =
sin x =
31
3√13
19
2√[?]
Answer:
2√61/19
Step-by-step explanation:
sin^2 x = 1 - cos^2 x
= 1 - (3√13/ 19)^2
= 1 - 117/361
= 244/361
sin x = √244/19
= 2√61/19.
x and y are numbers between 50 and 100. Both x and y have the same digit but in a different order. the two numbers add up to 187 all their digits add up to 34. find x and y.
By solving a system of equations, we see that:
x = 89 and y = 98.
How to find the two numbers?
First, we can write:
x = a*10 + b
y = b*10 + c
Where a, b, and c are single digit numbers. You can see that b is on both numbers because we know that the numbers share a digit, but on different order.
We also know that:
x + y = 187
a + b + b + c = 34
I we rewrite the first equation, we get:
(a*10 + b) + (b*10 + c) = 187
10a + 11b + c = 187
Then we have two equations:
a + 2b + c = 34
10a + 11b + c = 187
In both equations we can isolate c:
34 -2b -a = c
10a + 11b - 187 = c
Now we have:
-a - 2b + 34 = -10a - 11b + 187
Solving that, we get:
9a + 9b = 153
a + b = 153/9 = 17
Then a and b add up to 17, we can take:
a = 8
b = 9
And:
c = -a - 2b + 34 = -8 - 9 - 9 + 34 = 8
Then the numbers are:
x = 89
y = 98
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5284 Ib = ________ tn ________ Ib. show your work
Answer:
2 tons and 1824 pounds
Step-by-step explanation:
Ton= 2,000 pounds
We know that 2,000 will go into 5824 twice, resulting in 4,000. Subtract 4,000 from 5,284, and you will have an answer of 1284. 1,284 does not go into a ton, therefore you have a remainder of 1,284 pounds.
determine the area of the figure
The area of the trapezoid is x+11 cm.
Given a trapezoid has one side of (x+6) cm, the other side is 5 cm, and the height is 2 cm.
A two-dimensional quadrilateral consisting of the sum of non-adjacent parallel sides and a suitable non-parallel side is denoted as a trapezoid.
Now we will use the formula to find the area of a trapezoid
Area = 1/2 × (base 1 + base 2) × height
Here base 1 = (x+6) cm, base 2 = 5cm and height = 2cm
Substituting the values into the formula, we get
Area = 1/2 × (x+6+5) × 2
Area = 1/2 × (x+11) × 2
Area = x+11
Thus, the area of the given figure when one side is x+6, the other side is 5 cm and the height is 2 cm is x+11 cm.
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Four transformations of the function f(x) are given below. For each transformation, drag the graph that shows the results of that transformation into the box under it.
The graph that has been drag into the box in the image attached are the options that shows the results of that transformation.
What is the Function transformation about?Note that there are 4 types of function transformations which are are:
DilationTranslationRotationReflectionTherefore, The function above is known to have passed through the following points
(1,1) and (0,-1)
The graphs of the functions
(a) Function g(x)
The equation of the function is given as: g (x) = 2 + f (x)
This implies that f(x) is said to be translated up by 2 units.
The graph that shows this is graph (b)
(b) Function h(x) = f (x + 2)
This implies that f(x) is translated left by 2 units.
The graph that shows this is graph (e)
(c) Function k(x) = f (x) -2
This implies that f(x) is translated down by 2 units.
The graph that shows this is graph (c)
(d) Function m(x) = f (x - 2)
This implies that f(x) is translated right by 2 units.
The graph that depicts this is graph (f)
Therefore, The graph that has been drag into the box in the image attached are the options that shows the results of that transformation.
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2- The doctor prescribed 50 grams of sodium polystyrene sulfonate rectally. The medication is supplied as a 15 g/60 mL suspension. How many milliliters of sodium polystyrene sulfonate should the nurse Flora administer? Record your answer as a whole number.
The number of milliliters of sodium polystyrene sulfonate that the nurse Flora should administer is; 200 mL
How to carry out conversion rates?We are told that;
Medication dosage supply = 60mL for each 15 grams
Now, if the doctor prescribes 50 grams of the drug sodium polystyrene sulfonate rectally, then the volume to be administered is;
V = (50 * 60)/15
V = 200 mL
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If the function y = sinx is transformed to y = 3 sine (two-thirds x), how do the amplitude and period change?
Change in Amplitude is 2
Change in Period is π
Transforming sin(x) to [tex]3sin(\frac{2x}{3})[/tex]
y = a(sin(bx+c)) + d
Where, a is Amplitude and [tex]\frac{2}{b}[/tex]π is period
Amplitude of sin(x) =1
Period of sin(x) = 2π
Amplitude of 3sin([tex]\frac{2x}{3}[/tex]) = 3
Period of 3sin([tex]\frac{2x}{3}[/tex]) = [tex]\frac{2}{\frac{2}{3}}[/tex]*π = 3π
Change in Amplitude = 3sin([tex]\frac{2x}{3}[/tex]) - sin(x)
= 3 - 1
= 2
Change in Period = 3sin([tex]\frac{2x}{3}[/tex]) - sin(x)
= 3π - 2π
= π
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Answer: B
Step-by-step explanation:
What is the length of DE?
Answer:
C. 6
Step-by-step explanation:
[tex]\frac{ZY}{FE} =\frac{XY}{DE}[/tex]
[tex]\frac{12}{8} =\frac{9}{DE}[/tex]
[tex]12DE=(9)(8)[/tex]
[tex]DE=\frac{(9)(8)}{12} =\frac{72}{12} =6[/tex]
Hope this helps
Myles is tracking the growth of his palm tree. it was 62 inches when he bought it, and it has grown 6 inches per year. what does the initial value represent? what is the input for the initial value? what is the output for the initial value?
What is initial value?
It is given that,
The height of the palm tree at the time Myles bought it was 62 inches.
He is tracking the growth of the tree and he has observed that it has grown 6 inches per year.
So, the initial value of the tree, here, is representing the height of the palm tree when it was bought.
As can be seen clearly, there is no input for the initial value. And, the output for the initial value is given to be 62 inches.
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A farmer has a house at the point (0, 0). He has a corn field that can be found by driving 2 units down, 3 units right, 3 units up, and 2 units right. If he instead walks diagonally to his corn field, how far has he gone? Round to 2 decimal places.
Answer:
2.45 units
5 units
5.99 units
5.10 units
What are the rigid transformations that will map
△ABC to △DEF?
Translate vertex A to vertex D, and then reflect
△ABC across the line containing AC.
Translate vertex B to vertex D, and then rotate
△ABC around point B to align the sides and angles.
Translate vertex B to vertex D, and then reflect
△ABC across the line containing AC.
Translate vertex A to vertex D, and then rotate
△ABC around point A to align the sides and angles.
The rigid transformations which will map the triangle ABC to triangle DEF is; Translate vertex A to vertex D, and then rotate△ABC around point A to align the sides and angles.
Which transformation best maps △ABC to △DEF?It follows from the task content that the two triangles given are △ABC to △DEF.
Hence, in a bid to map the triangle ABC to DEF, Vertex A is translated to point D which represents vertex D in△DEF. Afterwards, the triangle ABC is simply rotated about the translated vertex A until all sides and angles of both triangles align.
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Find the slope of the line through the points (13,14) and (0,−1)
Answer:
1.15 or [tex]\frac{15}{13}[/tex]
Step-by-step explanation:
1. The slope can be found with this formula: [tex]\frac{y2-y1}{x2-x1}[/tex]
2. Let's plug in the numbers: [tex]\frac{14--1}{13-0}[/tex]
4. [tex]\frac{15}{13}[/tex] ≈ 1.1538
L = 5t + 12
Please choose an answer.
The cost of renting a canoe L depends on the number of hours t of rental. The cost is $12 for equipment rental and $5 per hour of use.
The cost of renting a canoe L depends on the number of hours t of rental. The cost is $5 for equipment rental and $12 per hour of use.
The cost of renting a canoe L depends on the number of hours t of rental. The cost is $5 per rental hour.
The cost of renting a canoe L depends on the number of hours t of rental. The cost is $17 per rental hour.
Answer:
Option 1
Step-by-step explanation:
Hello!
We can see that the base price for a canoe is $12, as you have to spend the $12 to get the canoe.
You also have to spend $5 per hour in the canoe, which is why "t" is being multiplied by 5.
We can also look at this graphically.
The x-axis is the number of hours, while the y-axis is the price. When x is 0 (no hours on canoe), you can see that the price is $12. But as it increases by 1 hour, the price increases by $5.