5x + 4 = x + 44
x is adding on the right, then it will subtract on the left
4 is adding on the left, then it will subtract on the right
5x - x = 44 - 4
4x = 40
4 is multiplying on the left, then it will divide on the right
x = 40/4
x = 10
Answer the question below. Be sure to show your work
ANSWER:
We have to find new side-lengths of PQR triangle.
Original sides are.
[tex]\begin{gathered} PQ\text{ = 8cm} \\ QR=17\operatorname{cm} \\ RP=15\operatorname{cm} \end{gathered}[/tex]After multiplying by 2.5 we get
[tex]\begin{gathered} PQ^{\prime}=2.5\times PQ=(8\times2.5)cm=20\operatorname{cm} \\ QR^{\prime}=(17\times2.5)cm=42.5\operatorname{cm} \\ RP^{\prime}=(15\times2.5)cm=37.5\operatorname{cm} \end{gathered}[/tex]These are the new sides of the P'Q'R' triangle.
Determine the coordinates of the midpoint of the segment with given endpoints. J(-3, 2), K(7,10) Midpoint:
drawing and explanation for areaof triangle where h=137 and base = 203
The area of triangle is 13905.5 cm square when height is 137 cm and bae is 203 cm.
Given that,
There is a triangle with height 137 cm and base 203 cm.
We have to find the area of triangle.
We know,
The entire area filled by a triangle's three sides in a two-dimensional plane is referred to as the triangle's area. A straightforward formula can be used to get the area of a triangle by multiplying the sum of the base and height by two.
Area of triangle =1/2×b×h
Area of triangle =1/2×137×203
Area of triangle =1/2×27811
Area of triangle =13905.5
Therefore, The area of triangle is 13905.5 cm square when height is 137 cm and bae is 203 cm.
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Find the x-intercept and y-intercept of the line. - 6x + 4y= 15 Write your answers as exact values. Do not write your answers as ordered pairs. x-intercept: 1 Х ? y -intercept: 1
The equation of a line is line is given as y = mx + c where m is the slope and c is the y-intercept
From the equation
-6x + 4y = 15
Changing into the form of the general equation
4y = 6x + 15
Divide both sides by 4
y = 6y/4 + 15/4
y = 3y/2 + 15/4
the x intercept is 0 while the y intercept is 15/4.
Katie rents a car when spending her vacation in Argentina while she returns the car she has driven 900 miles and used about 36 gallons of gas if you guess cost an average of $4.139 Per gallon estimate how much she spent on fuel
Given that Katie had driven 900 miles and used about 36 gallons of gas.
The average cost of gas per gallon = $4.139
The amount she spent on gas would be:
[tex]\text{ The average cost of gas per gallon x gallons of gas used}[/tex]Hence, the amount Katie spent on gas would be:
[tex]\begin{gathered} \text{ }\frac{\text{\$4.139}}{\text{gallon}}\times\text{ 36 gallons} \\ =\text{ \$149.004} \end{gathered}[/tex]She spent $149.004
CD = 69, BC = 10x + 3. AD = 18x + 44,and AB= 7x- 20. Find BC.
Answer: A) 83
Explanation:
Representing this segments in a number line, and supposing that they are arranged in alphabetical order:
Here we can see that if we sum all of the segments they must be equal to 18x+44:
[tex]7x-20+10x+3+69=18x+44[/tex]Combining like terms:
[tex]17x+52=18x+44[/tex]Now we move all of the terms with x to the right side and all of the independent numbers to the left side:
[tex]\begin{gathered} 52-44=18x-17x \\ 8=x \end{gathered}[/tex]And now that we know the value of x, we can find BC:
[tex]\begin{gathered} BC=10x+3 \\ BC=10(8)+3 \\ BC=80+3 \\ BC=83 \end{gathered}[/tex]Which is option A)
19. Which of the following is equal to V-24 ?O-2iV64i 166i-1/2O21 V6
The given value is,
[tex]\sqrt[]{-24}[/tex]We can write this as,
[tex]\sqrt[]{-24}=\sqrt[]{24\times-1}[/tex]As we know, 24 = 4 x 6 and,
[tex]\sqrt[]{-1}=i[/tex]the above expression can again be rewritten as,
[tex]\sqrt[]{-24\times-1}=\sqrt[]{4\times6}\times i=2i\sqrt[]{6}[/tex]Thus, the last option is correct.
Given that segment AD is congruent to segment BC, and angle DAB is congruent to CBA; Prove: triangle ABE is isosceles
Statement | Reason
AD ≅ BC | Given
∠DAB ≅ ∠CBA | Given
AB ≅ AB | Reflexive property of congruence
ΔADB ≅ ABC | SAS postulate
∠DBA ≅ ∠CAB | CPCTC
ΔABE is isosceles | Any triangle with 2 congruent angles is isosceles
The set consisting of all integers between -2 and -1 will be empty
It is true that the set consisting of all integers between -2 and -1 is empty.
Integers are numbers that are not fraction. They are simply the whole numbers on the number line.
There are positive and negative integers.
Positive Integers are: 1, 2, 3, 4, 5, and so on
Negative Integers are: -1, -2, -3, -4, -5, and so on.
Between -2 and -1, there are no integers. Therefore, the set consisting of all the integers between them is empty.
Can you please help me with this question thank youu.The first one.
Given that:
- Tara has 18 pairs of white socks.
- She has 12 pairs of colored socks.
You can state the proportion of those types of socks using ratios.
By definition, a ratio can be written in this form:
[tex]a\colon b[/tex]And it is read "a to b".
In this case, you need to find the ratio of white socks to colored socks, then you have to set up this ratio:
[tex]18\colon12[/tex]You can simplify the ratio dividing both sides by 6:
[tex]\begin{gathered} 18\div6\colon12\div6 \\ \\ 3\colon2 \end{gathered}[/tex]Hence, the answer is: Option B.
How many red squares will there be if there are 60 squares?
• There are 3 red squares.
,• There are 4 white squares.
To compare them and get the ratio, we can build the following relation:
[tex]\frac{3}{4}=\frac{x}{60}[/tex]where x is the number of red squares it will be when there are 60 white squares.
Solving for x:
[tex]x=\frac{3}{4}\cdot60[/tex][tex]x=45[/tex]Answer: C. 45
The slope of the line below is 2 Write the point-slope equation of the line using the coordinates of the labeled point.
As per given by the question,
there are given that,
The slope of the line is 2, and the point is (3, 10).
Now,
For finding the point slope equation;
From the formula for point slope equation of the line,
[tex]y-y_1=m(x-x_1)[/tex]Here,
[tex]x_1=3,y_1=10,\text{ and m=2}[/tex]Then put the value in above formula,
[tex]undefined[/tex]Hello I am helping my son with independent variable and dependent
It is given that,
As a plane descends, the more time that passes, the lower the plane's altitude is.
So,
Here, x be the time and y the altitude of the plane.
According to the statement, x be the dependent variable and y be the independent variable.
So, the graph is,
I'll give you the pic.
Let's use pythagorean theorem to calculate the remaining side:
[tex]\begin{gathered} c=\sqrt[]{a^2+b^2} \\ c=\sqrt[]{7^2+3^2} \\ c=\sqrt[]{21+9} \\ c=\sqrt[]{30} \end{gathered}[/tex]The area of a square is given by:
[tex]\begin{gathered} A=s^2 \\ \text{Where:} \\ s=\text{One of its sides} \\ A=(\sqrt[]{30})^2 \\ A=30 \end{gathered}[/tex]From the waiting area, they walked another 0.1 miles to board the plane. The plane left the gate 45 min after they arrived at the waiting area. Part C: what was the length from the waiting area to the airplanes takeoff?
C) We have to calculate the distance from the waiting area to the plane.
From the waiting area they walked 0.1 miles to board the plane.
Answer: from the waiting area to the plane there is a distance of 0.1 miles.
Find the answers to fill in blank 1. And blank 2.
EXPLANATION:
We are given the linear equation;
[tex]y-4=3(x+1)[/tex]To graph this equation, we would begin by re-writing the equation in the slope-intercept form, which is;
[tex]y=mx+b[/tex]To do this, we first expand the parenthesis;
[tex]y-4=3x+3[/tex]Next we add 4 to both sides;
[tex]y-4+4=3x+3+4[/tex][tex]y=3x+7[/tex]We can now begin to plot the various points on the line. Starting from, x = -2 we would have;
[tex]\begin{gathered} x=-2: \\ y=3(-2)+7 \\ y=-6+7 \\ y=1 \end{gathered}[/tex]We can now go on and plot other points depending on the limit imposed by the graph page.
However, what we have here shows the coordinates from which we may begin;
ANSWER:
[tex]\begin{gathered} (-2,1) \\ That\text{ is;} \\ x=-2,y=1 \end{gathered}[/tex]To find the length of JK you’d set up and solve:
According to the statement, to find x, it is necessary to use the following expression:
[tex]7x=3x+14[/tex]This expression is set up thanks to the definition of a parallelogram. To solve it isolate x to one of the sides of the equation.
[tex]\begin{gathered} 7x=3x+14 \\ 7x-3x=14 \\ 4x=14 \\ x=\frac{14}{4} \\ x=3.5 \end{gathered}[/tex]x has a value of 14/4 or 3.5.
According to the figure JK measures 7 times x. Use this information to find JK:
[tex]\begin{gathered} JK=7x \\ JK=7(3.5) \\ JK=24.5 \end{gathered}[/tex]JK measures 24.5.
what is the quotient of {24a^4 b^2 + 36a^2 b-36ab^2 +48 ab}÷(12ab)?
To divide this polynomial, we will follow steps below:
Step 1
Arrange
step 2
Divide 24a⁴b² by by 12ab
The result will be 2a³b
Write the result at the top of the root sign
Step 3
Mutiply 12ab by 2a³b, the result will be 24a⁴b²
Write the result in the root sign under 24a⁴b²
step 4
subtract, the result is zero
step 5
Take down 36a²b
Step 6
divide 36a²b by 12ab
The result is 3a
write the result at the top of the root sign
step 7
Multiply 12ab by 3a
The result is 36a²b
Write the result in the root sign under 36a²b
Step8
subtract, the result is 0
step 9
Take down -36ab²
step10
Divide -36ab² by 12ab
The result is -3b
Write the result at the top of the root sign
step11
Multiply 12ab by -3b
The result is -36ab²
Write the result in the root sign under -36ab²
step12
subtract, the result is zero
step 13
Take down 48ab
step 14
divide 48ab by 12 ab
The result is 4
write the result at the top root sign
step 15
Mulltiply 12ab by 4
The result is 48ab
Write the result in the root sign under 48 ab and then subtract
The result is zero
Hence the quotient is : 2a³b + 3a -3b + 4
The Quadratic f(x)=x^2-2x-15Using the functions of your graphing calculator calculate the coordinates of the following points (as shown in the calculator videos in this lesson). If the parabola doesn't intersect the x-axis then write "none." If necessary, round to the nearest hundredths place (2 decimal places).a. The vertex using the min/max calculate function.b. X-intercept(s) using the zero calculate function.c. Y-intercept using the value calculate function (w/ a value of x=0).d. Now, copy down the t-table generated by your calculator for integer input values from-3≤x≤3.
Given: The function below
[tex]f(x)=x^2-2x-15[/tex]To Determine: The vertex, the x-intercept, the y-intercept, and the table for -3≤x≤3
Solution
The graph of the given function is as shown below
Hence:
The vertex is a minimum value at y = -16 and coordinate (1, -16)
(b) The X-intercepets is x = -3, x = 5, coordinates: (-3, 0) and (5, 0)
(c) The Y-intercept is at y = -15, coordinate: (0, - 15)
(d) The table showing the values of f(x) for -3≤x≤3 is as shown below
which of the following equations represent linear functions? A. x^2+y^2=1 B. x+y=14 C. y=6/x D. y=3(2x+1)
A linear function has this form:
[tex]y=ax+b[/tex]Notice that option A cannot be written in this form, because x and y have a square power. If you clear y you'll get:
[tex]y=\sqrt[]{1-x^2}[/tex]Option B you can write it in the form of a linear equation:
[tex]y=14-x[/tex]For this option, a = -1 and b = 14
Option C cannot be written in this form:
[tex]y=\frac{6}{x}[/tex]And option D can be written like that:
[tex]y=6x+3[/tex]Here, a=6 and b=3.
So, options B and D are linear equations
A pair of shoes is on sale for 20% off. I paid $95. How much were the shoes originally? Write an equation and solve.
118.75
0.80 * x = 95
x = 95/ 0.80
x = 118.75
With x being the original cost of the shoes.
which fractions represent how to find the probability to rolling a number less than 5 and a number greater than 2?
Explanation
The probability of an event is the number of favorable outcomes divided by the total number of outcomes possible
Step 1
find the total of favorable possible
[tex]\begin{gathered} \text{for a dice, } \\ a\text{ number less than 5, it is, 1, 2, 3 or 4, ( 4 favorables outcomes}) \\ a\text{ number greater than 2, it is, 3,4 , 5 or 6} \\ \text{the numbers that have the two options are 3 and 4 ( 2 favorable outcomes)} \end{gathered}[/tex]favorable outcomes : 2 ( 3 and 4)
Step 2
find the total number of outcomes possilbe
the dice has 6 faces, (numbers, 1, 2, 3, 4, 5 or 6),
possible outcomes : 6 ( 1,2,3,4,5 and 6)
Step 3
finally replace
[tex]\begin{gathered} P=\frac{favorable\text{ outcomes}}{\text{possible outcomes}} \\ P=\frac{2}{6}=\frac{1}{3} \end{gathered}[/tex]Please Help! Functions and Relations The graph shows the absolute value parent function. which statement best describes the function?
The function is increasing when, if xa > xb, then f(xa) > f(b).
Let's choose values for x < 0 and for x > 0.
First, let's compare x = -2 and x = -1
-1 > -2
f(-1) < f(-2)
Then, the function is decreasing for x < 0.
Second, let's compare x = 1 and x = 2.
2 > 1
f(2) > f(1)
Then, the function is increasing for x > 0.
Answer: c. The function is increasing when x >0.
question 13Consider the following data: 12, 15, 13, 10, 15, 10. Answer the following questicwrite final answers only. [T/I - 4]#1) What is the mean of the data?#2) What is the median of the data?#3) What is the mode of the data?#4) What is the range of the data?
Solution:
Given:
The data;
[tex]12,15,13,10,15,10[/tex]Question 1:
To get the mean:
The mean of a set of numbers, sometimes simply called the average, is the sum of the data divided by the total number of data.
[tex]\begin{gathered} \text{Mean}=\frac{\text{ sum of data}}{n\text{ umber of data}} \\ \text{Mean}=\frac{12+15+13+10+15+10}{6} \\ \text{Mean}=\frac{75}{6} \\ \text{Mean}=12.5 \end{gathered}[/tex]Therefore, the mean is 12.5
Question 2:
To get the median:
The median of a set of numbers is the middle number in the set (after the numbers have been arranged from least to greatest)
If there is an even number of data, the median is the average of the middle two numbers.
[tex]\begin{gathered} R\text{ earranging the data given in rank order,} \\ 10,10,12,13,15,15 \end{gathered}[/tex]
The data indicates an even number of data. There are 6 numbers in the set.
Hence, the median is the mean of the middle two numbers.
[tex]\begin{gathered} \text{The middle two numbers are;} \\ 12\text{ and 13} \\ \text{Hence, the median is the mean of 12 and 13} \\ \text{Median}=\frac{12+13}{2} \\ \text{Median}=\frac{25}{2} \\ \text{Median}=12.5 \end{gathered}[/tex]Therefore, the median is 12.5
Question 3:
To find the mode:
The mode of a set of numbers is the number that occurs the most. Hence, the mode of a set of numbers is the number with the highest frequency.
If a set of data has two modes, the data is said to be bimodal.
[tex]\begin{gathered} 10,10,12,13,15,15 \\ \\ \text{From the above, 10 appears twice} \\ 15\text{ also appears twice} \\ \\ \text{Hence, the mode is 10 and 15. The data has two modes, it is a bimodal data.} \end{gathered}[/tex]
Therefore, the modes are 10 and 15.
Question 4:
The range is the difference between the highest and lowest values in a set of numbers.
[tex]\begin{gathered} 10,10,12,13,15,15 \\ \text{Lowest number=10} \\ \text{Highest number=15} \\ \\ \text{Hence, range=highest number-lowest number} \\ \text{Range}=15-10 \\ \text{Range}=5 \end{gathered}[/tex]Therefore, the range is 5.
Two dice are rolled. What is the probability that the sum of the numbers rolled is either 3 and 8? Express your answer as a fraction in lowest terms or a decimal rounded to the nearest million
The two dice have 6 numbers each.
Look at the image to find the outcomes:
First, we need to find the total of outcomes with the sum of 3:
T. outcomes with the sum of 3 = 2
Now, find the total of outcomes with the sum of 8 = 5
When we ave in probability the expression "or" we add the probabilities:
In this case,
T. outcomes with the sum of 3 + T. outcomes with the sum of 8.
Replace the values and sum:
P = 2 +5
P = 7
Now, to find the probability divide it by the total of outcomes
Total outcomes= 36. because 6 * 6 = 36
P( sum being 3 or 8) = 7/36
X = y - 4-2x + 3y= 6Solve each system by equation
Answer: x=-6 and y=-2
Given:
[tex]\begin{gathered} x=y-4 \\ -2x+3y=6 \end{gathered}[/tex]Having these two equations, we can substitute the first equation with the second equation to solve for y:
[tex]\begin{gathered} -2x+3y=6 \\ \end{gathered}[/tex]Since the first equation says that x = y - 4,
[tex]\begin{gathered} -2x+3y=6 \\ -2(y-4)+3y=6 \\ -2y+8+3y=6 \\ -2y+3y=6-8 \\ y=-2 \end{gathered}[/tex]Then, we will substitute this y-value to the first equation to solve for x.
[tex]\begin{gathered} x=y-4 \\ x=-2-4 \\ x=-6 \end{gathered}[/tex]We now have the values x=-6 and y=-2. To check, let us substitute both values to the second equation
[tex]\begin{gathered} -2x+3y=6 \\ -2(-6)+3(-2)=6 \\ 12-6=6 \\ 6=6 \end{gathered}[/tex]Therefore, the answer is correct, and the answer is x=-6 and y=-2
The equation of the line of best fit of a scatter plot is y = –7x − 2. What is the the y-intercept?
–7
–2
2
7
Answer:
The y-intercept of this line is -2.
Can you pls help me with this question thank you
The Solution:
The difference of c and 7 is either:
[tex]\begin{gathered} c-7\text{ } \\ \text{ or} \\ 7-c \end{gathered}[/tex]Multiplying the result by 10, we get
[tex]\begin{gathered} 10(c-7) \\ \text{ or} \\ 10(7-c) \end{gathered}[/tex]We are asked not to simplify any part of the expression.
So, the correct answer is:
[tex]\begin{gathered} 10(c-7) \\ or \\ 10(7-c) \end{gathered}[/tex]
Look at the construction. Which statement is false? XA = YA XP = PY XA = XY
XA = XY is false. XA and YA are both congruent segments, which means they are equal. The same goes for XP and PY.
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a bakery. needs to pack 48 donuts, 12 pastries, and 24 cinnamon in identical quantities across all of the boxes. What is the maximum quantity of boxes she can utilize?
It requires maximum 12 boxes to put 4 donuts, 1 pastry and 2 cinnamon in each box using the Greatest comon factor.
What is Greatest common factor or GCF?The greatest common factor or GCF is the largest number that can be split into exactly two or more other numbers. It is the "best" thing for reducing the complexity of fractions. A factor is a number that, when multiplied by other numbers, produces the desired numbers in mathematics. Factors are another name for the total that results.
The largest factor that two or more numbers have in common is called the greatest common factor (GCF).
It is given that there are 48 donuts, 12 pastries and 24 cinnamon.
Find the greatest common factor of the given values.
Expand 48,12, and 24 in factors.
48= 2x2x2x2x3
12=2x2x3
24=2x2x2x3
Find the greatest common factors of the three factored-out numbers.
GCF=2x2x3=12
So, it requires maximum 12 boxes to put 4 donuts, 1 pastry and 2 cinnamon in each box using the GCF.
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