Step-by-step explanation:
An integer (pronounced IN-tuh-jer) is a whole number (not a fractional number) that can be positive, negative, or zero. Examples of integers are: -5, 1, 5, 8, 97, and 3,043. Examples of numbers that are not integers are: -1.43, 1 3/4, 3.14, . 09, and 5,643.1.
The slope of the line between the points (2,5) & (5,r) is 2/3. What is the value of r?
(hint: Use the slope formula)
By using the slope formula the required value of r is 7 .
Given : ( 2 , 5 ) and ( 5 , r )
The slope given is 2/ 3
We know that when two values of x and y are given and we are supposed to find the slope of the equation we use the slope formula.
And thus by using the slope formula we get the below :
y₂ - y₁ = m ( x₂ - x₁ )
= > r - 5 = 2/ 3 ( 5 - 2 )
On cross multiplying we get :
3 r - 15 = 10 - 4
Add 15 to both sides of the equation and we will get
3 r = 10 - 4 + 15
3 r = 21
Divide both sides by 7 and we get :
r = 7
Thus by using the slope formula the required value of r is 7 .
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Solve the word problem. Show all the steps.
Two numbers add to 39. One number is 9 less than 7 times the other. What are the numbers?
The numbers represented by the word problems are 33 and 6
How to determine the solution to the word problem?The statements in the question are:
Two numbers add to 39. One number is 9 less than 7 times the other.Let the numbers in the expressions be x and y
So, we have
x + y = 39
x = 7y - 9
Substitute x = 7y - 9 in the equation x + y = 39
So, we have
7y - 9 + y = 39
Evaluate the like terms
8y = 48
Divide both sides by y
y = 6
Substitute y = 6 in x + y = 39
x + 6 = 39
Evaluate the like terms
So, we have
x = 33
Hence, the numbers are 33 and 6
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Sash has $80.000 in a savings account. The interest rate is 4% per year and is not compounded. How much interest will she earn in 5 years??
Answer:$16,000 in interest
Step-by-step explanation: well, you just take 4% of 80,000 which is $3200. (80,000x0.04=3200). Then because it is 5 years, just multiply the 3200 by 5 (there isn't compound interest.) 3200*5=16,000.
Consider the functions f(x) and g(x). The function f(x)=2x-5 and g(x)= -f(x+1)+3. A. Describe the three transformations that are performed on f(x) to create g(x).1.2.3.B. Sketch a graph of g(x):
First we have to take a look at the expression f(x + 1). This represents an horizontal translation. So this is the first transformation:
1. Horizontal translation
Now we can see that we have to multiply f(x + 1) by -1. This represents a reflexion on the y-axis
2. Reflection on y-axis
Finally we can see that -f(x + 1) is added by 3 units. This represents a vertical translation:
3. Vertical translation
Answer:
1. Horizontal translation
2. Reflection on y-axis
3. Vertical translation
Now let's see the final function:
f(x) = 2x - 5
f(x+1) = 2(x + 1) - 5
f(x+1) = 2x + 2 - 5
f(x+1) = 2x - 3
g(x) = -2x + 3 + 3
g(x) = -2x + 6
So let's plot f and g on the same reference system:
Evaluar la expresion numérica -8.5 (9.4 a 6.1
answer: b) - 28.05
Final8. Find the measure of the angle indicated in bold.
Those are supplementary angles, hence:
[tex]\begin{gathered} (12x+8)+(15x+10)=180 \\ 27x+18=180 \\ 27x=180-18 \\ x=\frac{162}{27} \\ x=6 \\ \text{Therefore:} \\ 15x+10=15(6)+10=90+10=100 \\ \end{gathered}[/tex]11.
Write the equation of the line with the points (0, 2) and (4, 10) in standard form.
By definition, the of a line written in Standard form is:
[tex]Ax+By=C[/tex]Where "A", "B" and "C" are Integers ("A" is positive).
The Slope-Intercept form of the equation of a line is:
[tex]y=mx+b[/tex]Where "m" is the slope and "b" is the y-intercept.
You know that this line passes through these points:
[tex](0,2);(4,10)[/tex]By definition, the value of "x" is zero when the line intersects the y-axis. Then, you can identify that, in this case:
[tex]b=2[/tex]Now you can substitute the value of "b" and the coordinates of the second point into the following equation and solve for "m":
[tex]y=mx+b[/tex]Then, the slope of the line is:
[tex]\begin{gathered} 10=m(4)+2 \\ 10-2=4m \\ 8=4m \\ \\ \frac{8}{4}=m \\ \\ m=2 \end{gathered}[/tex]Therefore, the equation of this line in Slope-Intercept form is:
[tex]y=2x+2[/tex]To write it in Standard form, you can follow these steps:
- Subtract 2 from both sides of the equation:
[tex]\begin{gathered} y-(2)=2x+2-(2) \\ y-2=2x \\ \end{gathered}[/tex]- Subtract "y" from both sides of the equation:
[tex]\begin{gathered} y-2-(y)=2x-(y) \\ -2=2x-y \\ 2x-y=-2 \end{gathered}[/tex]The answer is:
[tex]2x-y=-2[/tex]Answer:
2x-y =-2
Step-by-step explanation:
To find the equation of the line in standard form, first, we need to find the slope
m = ( y2-y1)/(x2-x1)
m = (10-2)/(4-0)
= 8/4 = 2
Then we can use the slope intercept form
y = mx+b where m is the slope and y is the y-intercept
y = 2x +b
Using the y-intercept ( 0,2)
y = 2x +2
The standard form is Ax +By =C where A is a positive integer and B is an integer
Subtract 2x from each side
-2x +y = 2
Multiply each side by -1
2x-y =-2
as a group. determine how many different chicken sandwiches he can pick from by taping in the 3 pieces of red yarn to the "chicken " index card and each end of the yarn to the "white", "wheat", or "Italian " cards. what sandwiches options have you created?
Answer:
3 options.
Chicken - White
Chicken - Italian
Chicken - Wheat
Explanation:
This question can be better explained with a graphic:
You have an index card with the word "chicken", and 3 index cards with the words "white", "wheat", and "Italian", which are the options of bread.
Also we have represeted the red yarn with 3 black lines that connect the options.
We can see from the image that we have 3 options of sandwiches:
Chicken - White
Chicken - Italian
Chicken - Wheat
A recipe called for the ratio of sugar to flour to be 7 : 3. If you used 63 ounces of sugar, how many ounces of flour would you need to use? Solve by using equivalent fractions.
Answer:
27 ounces of flour
Step-by-step explanation:
[tex]\frac{7}{3}[/tex] x [tex]\frac{9}{9}[/tex] = [tex]\frac{63}{27}[/tex]
7/3 = 63/x
isolate the so that it is on the top, so multiply by x on the right and on the left
this gives you:
x*7/3 = 63
try to isolate x and multiply by 3 to get rid of the denominator
x*7 = 63 * 3
x*7 = 189
finally isolate x by dividing by 7 and getting rid of the 7 multiplying with it
x= 189/7
x = 27
you need 27 ounces of flour if you have 63 ounces of sugar
I need help with my math
Answer:
Sure
Step-by-step explanation:
Let me know what you want by making me brainliest
graph triangle JKL with vertices j(2,3), k(-2,1), L(-1,5) and its image after the glide reflection: x-axis
Check the picture below.
14. Sort each number of miles and number of hours traveled into the appropriate bin to identify the rate in miles per hour. 6.NS.2 718 miles in 5.95 hours 45.8 miles In 4 hours 2,865 miles in 24.8 hours 419.72 miles in 80.6 hours 935.47 miles in 22.75 hours Las Toan 10 MIO por Hour Between 10 and 99 Miles per Hour Greater Than 100 Miles per Hour
we have
Find the unit rate in each case
so
718/5.95=120.67 miles per hour ---------> greater than 100 miles per hour
45.8/4=11.45 miles per hour ------> between 10 and 96 miles per hour
2,865/24.8=115.52 miles per hour -------> greater than 100 miles per hour
419.72/80.6=5.21 miles per hour ------------> less than 10 miles per hour
935.47/22.75=41.12 miles per hour ------> between 10 and 96 miles per hour
Marco bought 12 roses for
$48. What was the original
cost of EACH rose before
the discount? Set up an
equation and solve to
answer this question
Super Saver
DEALS! Get $2
off each rose
when you buy 12
or more roses
Marco bought 12 roses for $48. Each rose was originally $4 before the discount, and Super Saver Get $2 off each rose when you buy 12 or more roses each rose is $6.
How to calculate discount?The discount formula is as follows: Discount = Marked Price - Selling Price. OR. Formula for Discount Percentage = Marked Price Discount Rate A 10% discount can be calculated in two steps: Step 1 is to convert your percentage to a decimal using the formula 10 / 100 = 0.1. As a decimal, 10% equals 0.1. Step 2 is to multiply your original price by the decimal you chose. The sweaters were originally priced at $80. The store would like to offer a 15% discount on the sweaters. The company converts 15% to the decimal 0.15 to calculate the discount. The result is a figure of $12 after multiplying 0.15 by the original price of $80.Therefore,
Marco bought 12 roses for $48. Each rose was originally $4 before the discount.
∴ 48/12 = $4 and,
Super Saver Get $2 off each rose when you buy 12 or more roses
each rose is $6.
∴ 12/2 = $6
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correctly solve the equation dx + fy=g for x?
Given the expression:
[tex]dx+fy=g[/tex]To solve this expression for x, means that you have to isolate the term "x" in one side of the equal sign and all other terms mus be in the other side of it.
To "pass" a term from one side of the = sign to the other you have to perform the inverse operation to both sides of the equation (this way the equality remains valid)
So, the term "fy" is adding, the inverse operation is to subtract it, first step is to subtract this term of both sides of the equation:
[tex]dx+fy-fy=g-fy[/tex]+fy and -fy cancel each other so that:
[tex]dx=g-fy[/tex]Next, the term "x" is being multiplied by "d" but you need to reach the point were x is alone.
To cancel this multiplication you have to divide it by "d", and to keep the equality valid you have to perform the operation in both sides of the = sign:
[tex]\frac{dx}{d}=\frac{(g-fy)}{d}[/tex]d/d=1, then we get that x is equal to:
[tex]x=\frac{(g-fy)}{d}[/tex]11) Find the length of XZ.If WY = 15x -2 and XZ = 9x + 10,TVZY
Answer:
XZ = 28
Explanation:
The trapezoid is isosceles because it has two equal sides WZ and XY.
The diagonals of isosceles trapezoids have the same length. So, WY is equal to XZ and we can write the following equation:
WY = XZ
15x - 2 = 9x + 10
Then, solving for x, we get:
15x - 2 = 9x + 10
15x - 2 + 2 = 9x + 10 + 2
15x = 9x + 12
15x - 9x = 9x + 12 - 9x
6x = 12
6x/6 = 12/6
x = 2
Therefore, the value of XZ is equal to:
XZ = 9x + 10
XZ = 9(2) + 10
XZ = 18 + 10
XZ = 28
So, the answer is XZ = 28
The points (−7,−4) and (3,8) are the endpoints of the diameter of a circle. Find the length of the radius of the circle.
The length of the radius of the circle is √61.
Here there are two endpoints of the circle (-7,-4) and (3,8)
To find the distance between the two points we have a formula:
Distance = [tex]\sqrt{(x_{2} -x_{1} ^{2} + (y_{2} - y_{1})^{2} }[/tex]
So here we have
([tex]x_{1} , y_{1}[/tex]) = (-7, -4)
([tex]x_{2} , y_{2}[/tex]) = ( 3,8)
Putting the value we have,
=[tex]\sqrt{(3-(-4))^{2} + (8-(-7))^{2} }[/tex]
=[tex]\sqrt{10^{2} + 12^{2} }[/tex]
=√244
=2√61
The diameter is 2√61
radius = diameter/2
= 2√61/2
= √61
Therefore the length of the radius of a circle is √61.
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Help mee pleasee!!
thank you <3
...................
Part II: Constructed Response15. An amusement park has two carousels. The first carousel has a circularplatform with a diameter of 13 meters, and the second carousel has acircular platform with a diameter of 19 meters. How much larger is thearea of the larger carousel's platform than the area of the smallercarousels platform? Show your work, using 3.14 for r.151st find Area of First Carousel:16. Next find Area of Second Carousel:127.6.417. What is the difference between the two areas?
- Area of First Carousel:
diameter = 13 m
[tex]\text{Area}=\pi\cdot\frac{d^2}{4}=(3.14)\cdot\frac{(13)^2}{4}=3.14\cdot\frac{169}{4}=\frac{530.66}{4}=132.7m^2[/tex]- Area of Second Carousel:
diameter = 19 m
[tex]\text{Area}=(3.14)\cdot\frac{(19)^2}{4}=3.14\cdot\frac{361}{4}=\frac{1133.54}{4}=283.4m^2[/tex]- The difference between the two areas is:
[tex]283.4-132.7=150.7m^2[/tex]Answer:
The platform area of the larger carousel is 150.7 m^2 larger than the platform area of the smaller carousel.
Which one of these numbers are greater than 3.2×10-3
3.2 x 10^-3 = 0.0032 ( we have to move the decimal point 3 units to the left since the exponent of 10 is -3)
Express all the options in decimal form
2.1 x 10^-3 = 0.0021
4.2 x 10^-4 = 0.00042
5.2 x 10^-2 = 0.052
5.2 x 10^-1= 0.52
0.052 > 0.0032
0.52> 0.0032
So, correct options are:
5.2 x 10^-2
5.2 x 10^-1
look at the circle below. identify an example of radius
we have taht
radius is
HG
HA
HE
HD
The radius is the distance from the center of the circle to any point that lies on the circle
In this problem
point H is the center of the circle
so
the distance from H to any point on the circumference of the circle is a radius
see the attached image
All those segments are radius
Part 2
Remember that
the circumference is equal to
[tex]C=\pi\cdot D[/tex]so
In the table
the value of C is about 3 times the diameter
therefore
the values of flying disc are inaccurate
because
if D=23 cm the circunference must be about 69 cm, not 28 cm
What type of quadrilateral is given? (Note: The red hash marks denote congruent sides. The sides with one hash mark are congruent to each other. The sides with two hash marks are congruent to each other.)a.) Parallelogramb. b) Rectangle.c ) Rhombus.d ) Square.e) Trapezoid
Given the image we have a Parallelogram. Because it is a four-sided plane figure with opposite sides parallel.
ANSWER
a) Parallelogram
The distance, y, in miles, traveled by a car for a certain amount of time, x, in hours, is shown in the graph below:Motion of a Car7865Distance 52from Starting39Point(mi)261301562314Time (hr)Which of the following best describes the motion of the car shown? It travels for 2 hours, then stops for 3 hours, and finally travels again for 2 hours.lt travels for 2 hours, then stops for 3 hours, and finally travels again for 5 hours. lt travels for 2 hours, then stops for 1 hour, and finally travels again for 5 hours.lt travels for 2 hours, then stops for 1 hour, and finally travels again for 2 hours.
From the graph we can conclude:
The cars travels for 2 hours, then stops for 1 hour and finally travels again for 2 hours.
-------------------------------------
[tex]undefined[/tex]Help needed! please help math
Answer:
1.147×10^-2 cm
Step-by-step explanation:
You want the difference between the two values 1.87×10^-2 and 7.23×10^-3 expressed in scientific notation.
DifferenceAddition and subtraction of numbers in scientific notation requires that the multipliers have the same exponent. That exponent can be chosen so no adjustment of the exponent is required in the answer.
[tex]1.87\times10^{-2}-7.23\times10^{-3}= 1.87\times10^{-2}-0.723\times10^{-2}\\\\=(1.87-0.723)\times10^{-2}=\boxed{1.147\times10^{-2}}[/tex]
This measurement is in centimeters.
__
Additional comment
A calculator or spreadsheet can accept input and display results in scientific notation.
The difference in the diameter of of G and H is 1.147x 10⁻² cm
What are mathematics operations?
• An operation is a function in mathematics that converts zero or more input values (also known as "operands" or "arguments") to a well-defined output value.
• The operation's arity is determined by the number of operands.
• Binary operations (i.e., operations of arity 2), such as addition and multiplication, and unary operations (i.e., operations of arity 1), such as additive inverse and multiplicative inverse, are the most commonly studied operations.
• A zero-arity operation, also known as a nullary operation, is a constant.
• The mixed product is an example of an arity 3 operation, also known as a ternary operation.
it is given that :
the diameter of cell G is = 1.87 x 10⁻² cm
the diameter of cell H is = 7.23 x 10⁻³ cm
Now, to find the difference between the diameter of two cells simply subtract the diameter of cell G and H :
difference in the diameter of of G and H = 1.87 x 10⁻² cm - 7.23 x 10⁻³ cm
difference in the diameter of of G and H=1.87 x 10⁻² cm - 0.723 x 10⁻² cm
= 1.147x 10⁻² cm
Therefore, the difference in the diameter of of G and H is 1.147x 10⁻² cm
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(3^9)/(3^-9)simpilfy. write your answer using a positive exponent
Simplifying:
[tex]\frac{3^9}{3^{-9}}\rightarrow3^{9-(-9)}\rightarrow3^{9+9}\rightarrow3^{18}[/tex]***I NEED TO FIND THE SLOPE OF THE LINE THOUGH THESE POINTS****
We need to find the slope of a segment that joins the points (5, -2), and (-5, -8)
Therefore we use the formula for the slope:
[tex]\text{slope}=\frac{y_2-y_1}{x_2-x_1}=\frac{-8-(-2)}{-5-5}=\frac{-6}{-10}=0.6[/tex]Therefore the value of the slope is 0.6 = 6/10 = 3/5
You may need to enter the answer in a particular format (all three values above are the same, but expressed differently)
Then if we want the expression for the equation of the line, we use this slope, and either one of the points that they give us. for example the point (5, -2)
We write the general form of the equation of a line in slope-intercept form:
[tex]y=mx+b[/tex]and use for "m" 3/5, and require that the point (5, -2) be part of the line:
[tex]\begin{gathered} y=\frac{3}{5}x+b \\ -2=\frac{3}{5}(5)+b \\ -2=3+b \\ -2-3=b \\ b=-5 \end{gathered}[/tex]Therefore, the equation of the line (in slope intercept form) is:
[tex]y=\frac{3}{5}x-5[/tex]What is the approximate area of a clock face with a diameter of eight inches?
The area formula of a circle is :
[tex]A=\frac{1}{4}\pi D^2[/tex]From the problem, the diameter is 8 inches.
The area will be :
[tex]\begin{gathered} A=\frac{1}{4}\pi(8)^2 \\ A=50.27 \end{gathered}[/tex]The answer is 50.27 in^2
I can’t figure this equation out. -2(x + 1) = -2x + 5
Since equality is false there is no solution.
variables review find w if 67.1=29.7-0.2w
Given the following equation:
[tex]67.1=29.7-0.2w[/tex]You need to solve for the variable "w" in order to find its value. To do this, you can follow the steps shown below:
1. You can apply the Subtraction property of equality by subtracting 29.7 from both sides of the equation. Then:
[tex]\begin{gathered} 67.1-(29.7)=29.7-0.2w-(29.7) \\ 37.4=-0.2w \end{gathered}[/tex]2. Finally, you need to apply the Division property of equality by dividing both sides of the equation by -0.2. Then, you get:
[tex]\begin{gathered} \frac{37.4}{-0.2}=\frac{-0.2w}{-0.2} \\ \\ w=-187 \end{gathered}[/tex]The answer is:
[tex]w=-187[/tex]PLEASE HURRY ILL GIVE BRAINALIEST!!!
Almost 7 over 16 of the total water supplied to a household is wasted because of leaky faucets. Determine the decimal equivalent of 7 over 16 .
Use words to explain if the decimal terminates or repeats.
The decimal equivalent of 7 over 16 is 0.4375 .
What is 7/16 as a decimal?Fractions and decimals are two ways to represent the same numbers. A decimal number can be defined as a number whose whole number part and the fractional part is separated by a decimal point. A fraction is represented as a numerical value that is defined as a part of a whole.
We will convert the given fraction 7/16 to a decimal number.
To convert any fraction to a decimal, we just need to divide its numerator by denominator.
Here the fraction is 7/16 which means we need to perform 7 ÷ 16 = 0.4375.
So, 7/16 as a decimal is 0.4375.
Thus, 7/16 as a decimal is equal to 0.4375
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Line r passes through the point (3,6) and is parallel to line s is 3y=-6x+9 enter the equation of line r in y=ax+b form
Answer:
y = -6/3 + 12
Step-by-step explanation:
Step 1: Plot the point
Step 2: Simplify the given function then graph it
3y = -6x + 9 becomes:
y = -6/3x + 3
Step 3: Using the slope of -6/3 (because parallel lines will ALWAYS have the same slope) find 1 more point on the graph.
Step 4: Draw a line thru those points and find the y-int
y = ax + b, x and y are variables, a is the slope and b is the y-int
y = -6/3 + 12
