Answer:
x=-1, y=9.
Explanation:
Given the system of equations
[tex]\begin{gathered} y=-3x+5 \\ 2x+y=6 \end{gathered}[/tex]Substitute y=-3x+5 into 2x+y=6.
[tex]\begin{gathered} 2x+y=6 \\ 2x+(-3x+5)=6 \\ 2x-3x+5=6 \\ -x=6-5 \\ -x=1 \\ x=-1 \end{gathered}[/tex]Next, we solve for y.
[tex]\begin{gathered} y=-3x+5 \\ =-3(-1)+5 \\ =4+5 \\ y=9 \end{gathered}[/tex]The solution to the system of equations are:
x=-1 and y=9.
There are approximately 2.54 cm in 1 inch. what is the distance in inches of 14 cm. use a proportion to solve and round your answer to the nearest 10th of an inch
We know that there are 2.54 cm in 1 inch
2.54 cm ⇔ 1 inch
We want to find what is the distance in inches of 14 cm:
14 cm ⇔ ?? inch
Then, we have the following equivalence:
14 cm ⇔ ?? inches
2.54 cm ⇔ 1 inch
If we divide both sides of the equivalence we would have the same proportion:
[tex]\frac{14}{2.54}=\frac{?\text{?}}{1}[/tex]Solving both sides of the equation:
[tex]\begin{gathered} \frac{14}{2.54}=\frac{?\text{?}}{1} \\ \downarrow \\ 5.51=\text{??} \end{gathered}[/tex]This means that:
14 cm ⇔ 5.51 in
Rounding the answerWe want to round our result to the nearest tenth. This is a number with one digit after the decimal point:
5.51 in ≅ 5.5 in
Answer: the distance in inches of 14 cm is 5.5 in14. What property is used to show that 3(4-6) = 12-18?
Answer:
Distribution property method
1. Given: f(x)=x²-5x +1
A) Which is larger f(2) or f(-2)?
B) Which is smaller f(0) or f(4)?
A. The function f(-2) is larger than f(2)
B. The function f(4) is smaller than f(0)
Given,
The function; f(x) = x²- 5x + 1
We have to find;
A. The larger is f(2) or f(-2)
Here,
f(2) = 2²- 5 x 2 + 1 = 4 - 10 + 1 = - 6 + 1 = -5
f(-2) = -2²- 5 x -2 + 1 = 4 + 10 + 1 = 15
That is,
The function f(-2) is larger than f(2)
B. The smaller is f(0) or f(4)
Here,
f(0) = 0²- 5 x 0 + 1 = 0 - 0 + 1 = 1
f(4) = 4²- 5 x 4 + 1 = 16 - 20 + 1 = - 4 + 1 = -3
That is,
The function f(4) is smaller than f(0)
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write the decimal using number name,and unit form . 317.098
three hundred and seventeen and ninety-eight thousandths
Explanation:3 = hundreds
1 = ten
7 = ones
Number after the decimal point start in ythe tenth place
0 = tenth
9 = hundredths
8 = thousandths
Naming the number:
three hundred and seventeen and ninety-eight thousandths
Evaluate the expression when a =3 and x = - 5-8a + x
We have an expression:
[tex]-8a+x[/tex]We have to evaluate it when a = 3 and x = -5. To do that we replace a and x by its values and calculate:
[tex]\begin{gathered} -8(3)+(-5) \\ -24-5 \\ -29 \end{gathered}[/tex]Answer: the expression value is -29
When you convert a number from decimal notation to scientific notation, how do you know if the exponent will be positive or negative? Explain.
When converting a number from decimal to scientific notation,
The exponent is positive if the movement of the decimal point is to the left
The exponent is negative if the movement of the decimal point is to the right.
Examples :
[tex]1200\rightarrow1.2\times10^3[/tex]The decimal point moves from the right of the last digit to the place between 1 and 2. It moves to the left so the exponent is positive.
[tex]0.0012\rightarrow1.2\times10^{-3}[/tex]The decimal point will move 3 places to the right, so the exponent will be negative.
Which set of numbers includes only integers? o -5, -3 1/4, 1 1/8o -3, -2, 2, 3o-6, -4, -2, -1/2o1/2, 2/3, 6/7, 0
It is important to know that integers refer to the numbers that can be written as a fractional component.
For example: -3, -2, 2, 3 are integers.
Hence, the answer is the second option.Why the other answer choices are wrong?
Mainly because the other answer choices include numbers that are decimals, for example, -3 1/4 is equal to -3.25 which is not an integer.
in quadrilateral ABCD shown below, AD is congruent to BD, m
We will use the next image
the angles in red are equals
The angle in blue is 30°
We need to remember that the sum of the interior angles of a triangle must be 180°
x is the red angle
2x+30=180
2x=180-30
x=150/2
x=75
the angle DBC can be calculated as a complementary angle, the complementary angle is formed with two angles that form an angle of 90°
angle DBC =90-75
angle DBC=15° the angle in green in the image
Tala Abarkowe NAME PERIOD Unit 2 Lesson 5 Cool Down An albatross is a large bird that can fly 400 kilometers in 8 hours at a constant speed. Using d for distance in kilometers and t for number of hours, an equation that represents this situation is d = 50t. = 1) What are two constants of proportionality for the relationship between distance in kilometers and number of hours? Due in this s cose lh sud
Given relation is
[tex]d=50t[/tex]Here, d is the distance in kilometers and t is the number of hours.
Since distance and time both vary, therefore, they are not constants.
The only value which is fixed is 50.
Therefore, the only constant of proportion is 50.
Since the ratio of two valus are constant, therefore, they are in direct proportional relationship.
From the given relation, we can write
[tex]t=\frac{d}{50}[/tex]Hence, another relationship between d and t is
[tex]t=\frac{d}{50}[/tex]i need help with my homework PLEASE CHECK WHEN DONE ANSWERING
Answer:
The sequence is given below as
[tex]8,11,14,17,20[/tex]Step 1:
The nth term of an arithmentic progression is given below as
[tex]\begin{gathered} a_n=a+(n-1)d \\ where, \\ a=first\text{ term} \\ n=number\text{ of terms} \\ d=common\text{ difference} \end{gathered}[/tex]To figure out the common difference, we will use the formula below
[tex]\begin{gathered} d=a_2-a_1=a_3-a_2 \\ d=11-8=14-11=17-14=20-17=3 \\ d=3 \end{gathered}[/tex]Step 2:
The first term of the sequence is given below as
[tex]a=8[/tex]Step 3:
Substitute the value of a and d in the formula below
[tex]\begin{gathered} a_{n}=a+(n-1)d \\ a_n=8+(n-1)3 \\ a_n=8+3n-3 \\ a_n=5+3n \end{gathered}[/tex]Hence,
The final answer is
[tex]a_n=5+3n,where\text{ n=1,2,3,4,...}[/tex]OPTION A is the right answer
HW Score: 77 Score: 0 of 1 pt 15 of 18 (15 complete) v X 7.3.43 On a world globe, the distance between Chy A and Cycles that are actually 10.730 kilometers apart, is 132 inches. The actual distance between City C and City Dis 1500 kilometers How far apart are this globe? chy C and Cny D are inches apart on this giebe (Type an integer ordenalpadd to the manded) More Enter you are All parts showing Type here to search
13.2 inches is. 10,730
1500 km , how far apart are
Find X= (1500/10,730) = 150/1073= 0.14
then multiply by 13.2
13.2X = 1.85
Then ,in a globe , distance between C and D cities is 1.85 inches
Answer is 1.85 inches
Fill in the blanks below.(a) Ivanna lost 40 dollars from her pocket.Write a signed number to represent this change.(b) A car corporation produced 540 more cars this month than last.Write a signed number to represent this month's change in production.
Recall that the signs
[tex]+,\text{ and -}[/tex]helps us indicate if there is an increase or a decrease.
If the number represents a decrease from the previous one, we put a minus sign. If the number represents an increase then we put a plus sign.
Notice that Ivanna lost $40, therefore, the total money she had decreased by 40.
If the company produced 540 more cars this month than last month, then there was an increase of 540 in cars production.
Answer:
(a)
[tex]-40.[/tex](b)
[tex]+540.[/tex]Find the distance between (-5,3) and (-6,6).
simplify using distributive property 4(1 + 9x)
4(1 + 9x)
4 + 36x (Distributing)
The answer is 36x + 4
Use the distributive property to write the following expression as an equivalent product:8x -40a) 8(x - 32)(c) 10(-2x -4)(b) 8(x - 5)(d) 2(6x - 38)would it be answer c?:(
The answer is 8(x - 5)
Explanation
8x - 40
this can be re written as
since 8 is a factor of 40 and 40/8 = 5
factorize out 8
the new equation is
8(x - 5)
Geometry formulas Situation: Find the perimeter of a rectangular area with a length of 13 inches and a width of 7 inches. Calculation With Distribution (Show all steps.) Calculation Without Distribution (Show all steps.) I think is easier: to distribute. to not distribute. Why I think it is Easier
a rectangular area with a length of 13 inches and a width of 7 inches.
Length of rectangle = 13 inches
Width of rectangle = 7 inches
With Distribution:
The perimeter of any polygon is the sum of all the sides of the polygon
In the given rectangle we have 2 lengths and 2 widthSo,
Perimeter = length + width + Length+ width
Substitute the value and solve
Perimeter = 13 + 7 +13 +7
Perimeter = 20 + 20
Perimeter =40inches
Without Distribution
The perimeter of rectangle is express as :
Perimeter = 2(length + Width)
Substitute the value and solve
Perimeter=2(13+7)
Perimeter=2(20)
Perimeter-40 inches
It was easier without distribution because it becomes calculation easy.
Answer: Perimeter = 40 inches
It is easier to not distribute
Because it makes calculation easy and short.
Debra brought a desk on sale for $438. This price was 73% of the original price. What was the original price
Let x = the original price of the desk.
It's known that 73% of the price is $438, thus:
[tex]\frac{73}{100}x=438[/tex]Multiplying by 100 and dividing by 73:
[tex]x=\frac{100\cdot438}{73}=600[/tex]The original price of the desk was $600
You roll a 6 sided die what is p 2 or less than 6
The sample space for one 6-sided die is given by
[tex]{}\lbrace1,2,3,4,5,6\rbrace[/tex]Then, the probability to get the number 2 or a number less than 6 is given by
[tex]P(2\text{ or less than 6\rparen=P\lparen2\rparen+P\lparen less than 6\rparen-P\lparen2 and less than 6\rparen}[/tex]which gives
[tex]P(2\text{ or less than 6\rparen=}\frac{1}{6}+\frac{5}{6}-\frac{1}{6}=\frac{5}{6}[/tex]that is because the probability to get a number 2 is 1/6, the probability to get a number less than 6 is 5/6 because there are 5 numbers less than 6 and the probability to get a number 2 and a number less than 6 is 1/6 because there is only one number 2.
Therefore, the answer is:
[tex]\frac{5}{6}[/tex]Which order pair makes both inequalities true? Y<-2x+3Y< x-2
The ordered pair which makes both inequalities true are (3, 0).
Inequalities are mathematical expressions where neither side is equal.
Contrary to equations, we compare two values in inequality.
Less than, greater than, or not equal to signs are used in place of the equal to sign in between.
Let us consider the ordered pair (3, 0)
In the first inequality
y > -2x + 3
Substituting the values of x and y
0 > -2(3) + 3
0 > -6 + 3
0 > -3
In the second inequality
y < x - 2
Substituting the value of x and y
0 < 3 - 2
0 < 1
Therefore, the ordered pair which makes both inequalities true are (3, 0).
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Simplify each expression using the order of operations. 3+(7−5)2×6= 25(4+4)×2= 8−6÷2+3×5= 7×3−15÷5= 8+2(1+12÷2)2=
Using the order of operation which states
[tex]\begin{gathered} B\Rightarrow Bracket \\ O\Rightarrow Orders \\ D\Rightarrow Division \\ M\Rightarrow Multilication \\ A\Rightarrow Addition \\ S\Rightarrow Subtraction \end{gathered}[/tex]Expressions in brackets/parentheses are evaluted first, followed by expressions involving orders, division, multiplication, addition and subtraction in that order.
Thus,
1)
[tex]\begin{gathered} 3+(7-5)2\times6\text{ = ?} \\ \text{Evaluate expressions in parentheses. thus,} \\ 3+(2)2\times6 \\ \text{Evaluate expressions involving multiplication,} \\ 3+24 \\ \text{Add up the expressions,} \\ 3+24\text{ = 27} \end{gathered}[/tex]thus, 3+(7−5)2×6 = 27
2)
[tex]\begin{gathered} 25\mleft(4+4\mright)\times2=\text{?} \\ \text{Evaluate expressions in parentheses. thus,} \\ 25(8)\times2 \\ \Rightarrow400 \end{gathered}[/tex]thus, 25(4+4)×2 = 400
3)
[tex]\begin{gathered} 8-6\div2+3\times5\text{ = ?} \\ \text{Evaluate expressions involving division. thus,} \\ 8-3+3\times5 \\ \text{Evaluate expressions involving multipliation. thus,} \\ 8-3+15 \\ \text{Evaluate expressions involving addition. thus,} \\ 8+12 \\ \text{Add up the terms,} \\ 8+12\text{ = 20} \end{gathered}[/tex]thus, 8−6÷2+3×5 = 20
4)
[tex]\begin{gathered} 7\times3-15\div5=\text{ ?} \\ \text{Evaluate expressions involving division. thus,} \\ 7\times3-3 \\ \text{Evaluate expressions involving multiplication. thus,} \\ 21-3 \\ \text{Subtract the terms,} \\ 21-3\text{ = }18 \end{gathered}[/tex]thus, 7×3−15÷5 = 18
5)
[tex]\begin{gathered} 8+2\mleft(1+12\div2\mright)2=\text{ ?} \\ \text{Evaluate the terms in parentheses. thus,} \\ 8+2\times\: 7\times\: 2 \\ \text{Evaluate the terms involving multiplication. thus,} \\ 8+28 \\ \text{Add up the terms,} \\ 8+28\text{ = }36 \end{gathered}[/tex]thus, 8+2(1+12÷2)2 = 36.
Let angle D be an acute angle and tan D = 0.72 . Use technology to approximate the measure of D to the nearest 10th of a degree.
D=35.8 °
Explanation
Acute angles measure less than 90 degrees, to solve this we need to use a calculator
Step 1
a) let
[tex]\begin{gathered} angle\text{ =D} \\ tan\text{ angle = }tan\text{ D=0.72} \end{gathered}[/tex], b) now, use the inverse tan function to isolate D
[tex]\begin{gathered} tan\text{ D=0.72} \\ inverse\text{ tan function in both sides} \\ \tan^{-1}(tan\text{ D\rparen=}\tan^{-1}(\text{0.72\rparen} \\ D=35.75388 \\ rounded \\ D=35.8\text{ \degree} \end{gathered}[/tex]so, the answer is
D=35.8 °
I hope this helps you
Write an inequality for the problem and answer the question about the inequality. The square of x is greater than or equal to 10. Is 3 a solution.
"The square of x..." translates to x²
"...is greater than or equal to 10." translates to ≥ 10.
To determine if 3 is a solution, substitute 3 to the inequality.
[tex]\begin{gathered} x^2\ge10 \\ \text{If }x=3 \\ (3)^2\ge10 \\ 9\ge10 \\ 9\ngeq10 \end{gathered}[/tex]The resulting number, 9 is not greater than 10. Therefore, 3 is not a solution.
a recipe calls for 1/4 cup of flour. Carter only has a measuring cup that holds 1/8 cup.How can Carter measuring cup that holds 1/8 cup.How can Carter measure the flour he needs for his recipe?
We are given that we need to measure 1/4 cup of flour with a measuring device that can only hold 1/8 cup.
To determine the 1/4 cup we need to have into account that:
[tex]\frac{1}{8}+\frac{1}{8}=\frac{2}{8}=\frac{1}{4}[/tex]Therefore, two times 1/8 is 1/4 therefore, Carter can fill the 1/8 cup two times to get 1/4 cup.
I need help with this question. I have to show work
PART A:
Let the number of days be represented by t. Let the total cost be represented by C.
FOR COMPANY A:
The equation to represent the total charges will be given as
[tex]C=22t+5[/tex]FOR COMPANY B:
The equation to represent the total charges will be given as
[tex]C=20t+16[/tex]PART B:
Company B will charge less over a 9-day rental period.
To confirm this answer, we will calculate the cost using the equations derived above:
FOR COMPANY A:
[tex]\begin{gathered} C=22(9)+5 \\ C=198+5 \\ C=203 \end{gathered}[/tex]FOR COMPANY B:
[tex]\begin{gathered} C=20(9)+16 \\ C=180+16 \\ C=196 \end{gathered}[/tex]Therefore, COMPANY B will charge less over 9 days.
PART C:
To know how much is saved over a 15-day period, we will first calculate the cost of both companies over the period using the equations derived from Part A.
FOR COMPANY A:
[tex]\begin{gathered} C=22(15)+5 \\ C=330+5 \\ C=335 \end{gathered}[/tex]FOR COMPANY B:
[tex]\begin{gathered} C=20(15)+16 \\ C=300+16 \\ C=316 \end{gathered}[/tex]We can, thus, calculate the difference as
[tex]\begin{gathered} 335-316 \\ =19 \end{gathered}[/tex]Therefore, the amount saved will be $19 over 15 days.
Find the area of this circle please…Use 3 for pi
Given:
The radius of circle is 11 inch
The value for pi is 3
The objective is to find the area of the circle.
The area of the circle is given by the formula:
[tex]A=\pi\times r^2^{}[/tex]Substituting ,r = 11
[tex]\pi=3[/tex]We get:
[tex]\begin{gathered} A=\pi\times r^2 \\ =3\times(11)^2 \\ =3\times121 \\ =363 \end{gathered}[/tex]Hence, the area of the circle is 363 square inches
The picture that I sent to the app would not pick up the greater or less than signs. The instructions say solve the system of inequalities by graphing. I would like someone to walk me through the steps. I had an amazing tutor the last time but my connection got lost she sent me a graph to help me.
See graph below
Explanation:We have two inequalities:
y < 6
y > x + 3
To plot the inequalities on a graph, we change the inequality sign to equal to in order to get points to plot the graph:
y = 6
This means at y = 6, there will be an horizontal line for all values of x. But due to the less than sign, it means the horizontal line will be shaded down.
y = x + 3
We assign values to x inorder to get y values:
let x = -2, 0, 2, 4
when x = -2
y = -2 + 3 = 1
when x = 0
y = 0 + 3 = 3
when x = 2
y = 2 +3 = 5
when x = 4
y = 4 + 3 = 7
When we plot this points, we get a straight line. SInce the sign is greater than, the line will be shaded towards the positive side
plotting the graph:
First inequality
Both inequalities:
The following side lengths, in meters, were given to a carpenter to build a front porch with a triangular design. The carpenter needs to determine which set of lengths will make a triangle to be able to use it in his design. Which of the options would create a triangle for his design?
*
5 points
Side lengths: 4, 4, 8
Side lengths: 6, 8, 10
Side lengths: 6, 6, 13
The pair of side lengths that can create a triangle is 6, 8 , 10.
What is a triangle?A triangle is a polygon with 3 sides. The area of a triangle with base b and height h is given by A = (1/2)bh.
The given pairs of side lengths of the triangle are 4,4,8; 6,8,10; and 6,6,13.
The sum of the lengths of any two sides of a triangle must be greater than the length of the third side.
(1) The side lengths are 4,4,8.
Since 4 + 4 =8 is not greater than the length of the third side, 8, it won't create a triangle.
(2) The side lengths are 6,8,10.
Note that the sum of any two side lengths is greater than the length of the third side, therefore, this pair of side lengths can create a triangle.
(3) The side lengths are 6,6,13
Since 6 + 6 =12 is not greater than 13, the third side length, won't create a triangle.
Hence, the pair of side lengths that can create a triangle is 6, 8 , 10.
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Find the absolute extrema of the function (if any exist) on each interval. (If an answer does not exist, enter DNE.)
Before we can determine the absolute extrema of the function, let's graph the given function first. f(x) = x² - 6x.
For the interval [-1, 6], we can see that the maximum value would be at x = -1.
Let's replace x with -1 in the function above.
[tex]\begin{gathered} f(x)=x^2-6x \\ f(-1)=(-1)^2-6(-1) \\ f(-1)=1+6 \\ f(-1)=7 \end{gathered}[/tex]Therefore, the maximum between the interval [-1, 6] is at (-1, 7).
On the other hand, looking at the interval (3, 7] in the graph, the maximum is found at x = 7. To determine the maximum point, replace "x" with 7 in the function above.
[tex]\begin{gathered} f(7)=7^2-6(7) \\ f(7)=49-42 \\ f(7)=7 \end{gathered}[/tex]Therefore, the maximum at the interval (3, 7] is at point (7, 7).
Put in your own words.What is a quadratic equation?
Answer:
A quadratic equation is an equation that has the following general form:
[tex]ax^2+bx+c=0.[/tex]Any equation that can be rewritten in the above form can be considered a quadratic equation, the important part is that there is a term that includes an
[tex]x^2,[/tex]and that 2 is the greatest exponent of any variable of the equation.
The rectangular foor of a classrom is 30 feet in length and 24 feet in width. A scale drawing of the floor has a length of 5 inches. What is the perimeter, in inches, of the floor in the scale drawing?
The required perimeter of the scale drawing is given as 18 inches.
Given that,
The rectangular floor of a classroom is 30 feet in length and 24 feet in width. A scale drawing of the floor has a length of 5 inches. The perimeter, in inches, of the floor in the scale drawing, is to be determined.
Perimeter is the measure of the figure on its circumference.
Here,
According to the question,
L = 30 feet, W = 24 feet,
for Scaled drawing
l = 5 inch, w = x
Now,
30/5 = 24 / x
6 = 24 / x
x = 24 {1/6}
x = 4,
So the width of the scale drawing is 4 inches,
perimeter of the scaled drawing = 2[l + w]
= 2 [5 + 4] = 18 inches
Thus, the required perimeter of the scale drawing is given as 18 inches.
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