A easy way to operate fractions is convert the integer in a fraction, to operate fractions with the same denominator:
[tex]6\cdot\frac{3}{3}-\frac{2}{3}=\frac{18}{3}-\frac{2}{3}=\frac{16}{3}[/tex]In ATUV, the measure of ZV=90°, VU = 7, UT = 25, and TV = 24. What ratiorepresents the sine of ZU?U25NVT24Answer:Submit Answer
1) Since the sine is the ratio between the opposite leg and the hypotenuse.
And the hypotenuse is always opposite to the right angle
Then we can write
2) The sine of ∠ U can be written as the following ratio
sine (∠U) = 24/25
sine(∠U)= 0.96
Write the quadratic function in standard form. g(x) = x2 − 10x
The quadratic function in standard form is g(x)= x²-10x+0
What is a quadratic function?Quadratic functions are polynomial functions of the second degree, meaning they contain at least one squared term.
Quadratic functions are another name called quadratics. The quadratic function has the following general form: f(x)=ax² + bx + c.
An quadratic function is given as g(x)= x²-10x
In the standard form of the quadratic equation, there should be three terms, terms with power two, one and a constant.
In the given equation, there is a constant term missing.
So, we add a zero to the end because it brings no change to the function quantitatively.
So, the standard form of the given quadratic function will be g(x)= x²-10x+0
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A 56-inch board is to be cut into three pieces so that the second piece is 3 times as long as the first piece and the third piece is 4 times as long as the first piece. If x represents the length of the first piece, find the lengths of all three pieces.
A 56-inch board is to be cut into three pieces so that the second piece is 3 times as long as the first piece and the third piece is 4 times as long as the first piece. The length of all the three pieces are : 7, 21, 18.
LengthThere are 3 pieces:
Length of first piece = x
Length of second piece = 3x
Length of third piece = 4x
Total length = 8x
Now, 8x = 56
Divide both side by 8x
x = 56 /8
x = 7
Length of second piece = 3x where x = 7
3x = 3 ( 7)
= 21
Length of third piece = 4x where x = 7'
4x = 4 ( 7)
= 28
Therefore we can conclude that the length are : 7, 21, 18.
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4
An ice cream shop has a sign in the shape
of an ice cream cone. The sign is made
using a semicircle and a triangle, as
modeled below.
The base of the
triangle is the
6 in.
diameter of the
semicircle.
12 in.
Which is the best estimate of the area of
the sign in square inches?
F 150 in.2
F
G 14 in.2
H 36 in.2
J 50 in.2
In order to determine the total area of the sign, we need to calculate the area of the triangle, and the area of the semicircle. The expressions we need to use are described below:
[tex]\begin{gathered} A_{\text{semicircle}}=\frac{\pi\cdot r^2}{2} \\ A_{\text{triangle}}=\frac{b\cdot h}{2} \end{gathered}[/tex]We were given the diameter of the semicircle, it's radius is half of the diameter, therefore:
[tex]r=\frac{6}{2}=3\text{ in}[/tex]The base of the triangle is equal to the diameter of the semicircle. With this we can calculate both areas:
[tex]\begin{gathered} A_{\text{triangle}}=\frac{6\cdot12}{2}=36\text{ square inches} \\ A_{\text{semicircle}}=\frac{\pi\cdot3^2}{2}=14.13\text{ square inches} \end{gathered}[/tex]The total area of the figure is the sum of the above, therefore:
[tex]\begin{gathered} A=A_{\text{triangle}}+A_{\text{semicircle}} \\ A=36+14.13=50.13 \end{gathered}[/tex]The area is approximately 50 in². The correct option is J.
for each equation give for solution. Then, graph the solution set on the graph provided.
Given the equation x+2y=8
[tex]\begin{gathered} \text{When x=-4} \\ x+2y=8 \\ -4+2y=8 \\ 2y=8+4 \\ 2y=12 \\ y=6 \\ (-4,\text{ 6)} \end{gathered}[/tex]When x = -2
[tex]\begin{gathered} \\ x+2y=8 \\ -2+2y=8 \\ 2y=8+2 \\ 2y=10 \\ y=5 \\ (-2,\text{ 5)} \end{gathered}[/tex]When x=0
[tex]\begin{gathered} \\ x+2y=8 \\ 0+2y=8 \\ 2y=8 \\ y=4 \\ (0,\text{ 4)} \\ \end{gathered}[/tex]When x=2
[tex]\begin{gathered} \\ x+2y=8 \\ 2+2y=8 \\ 2y=8-2 \\ 2y=6 \\ (2,\text{ 3)} \end{gathered}[/tex]We then plot these points.
Two planes, which are 2505 2505 miles apart, fly toward each other. Their speeds differ by 85mph 85 mph . If they pass each other in 3 3 hours, what is the speed of each?
When two planes which are 2505 miles apart and fly toward each other. if their speeds differ by 85mph and If they pass each other in 3 hours, then the speed of first plane is 372.5 mph and the speed of second plane is 462.5 mph
Their speeds differ by 85mph
Consider the speed of first plane = x mph
The speed of second plane = 90+x mph
The relative speed = sum of both speed
= x + x+90
= 2x+90 mph
The distance between the planes = 2505 miles
Time taken to pass each other = 3 hours
Therefore in 3 hours
3(2x+90) = 2505
6x+270 = 2505
6x = 2505-270
6x = 2235
x = 2235/6
x = 372.5 mph
The speed of second plane = 90+x
= 90+372.5
= 462.5 mph
Hence, when two planes which are 2505 miles apart and fly toward each other. if their speeds differ by 85mph and If they pass each other in 3 hours, then the speed of first plane is 372.5 mph and the speed of second plane is 462.5 mph.
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x= -13 will this line be horizontal or vertical? based on this expression
EXPLANATION
The equation x=-13 represents a vertical line.
The access code for a gym locker consists of three digits. Each digit can be any number from 1 through 6, and each digit can be repeated. Complete parts (a) through (c).(a) Find the number of possible access codes. (b) What is the probability of randomly selecting the correct access code on the first try? (c) What is the probability of not selecting the correct access code on the first try?
A.The number of the possible access codes:
[tex]6\cdot6\cdot6=216[/tex]B. The probability of randomly select the correct access code on the first try:
[tex]P=\frac{1}{216}[/tex]C. The probability of not selecting the correct access code on the first try :
[tex]P=\frac{99}{216}[/tex]
Brian split 4/5 pounds of candy among 5 people. What is the unit rate in pounds per person. Write the answer in simplest form.
SOLUTION:
Case: Unit rates
Given: Brian split 4/5 pounds of candy among 5 people
Method:
The unit rate in pounds per person
[tex]\begin{gathered} rate=\frac{4}{5}\div5 \\ rate=\frac{4}{5}\times\frac{1}{5} \\ rate=\frac{4}{25} \end{gathered}[/tex]Final answer:
The rate in pounds per person is:
4/25 pounds
Enter your answer as an integer or as a reduced fraction in the form A/B.
From the given graph, let's find the slope of the line.
To find the slope of the line, apply the slope formula:
[tex]m=\frac{y2-y1}{x2-x1}[/tex]Take two points on the line:
(x1, y1) ==> (-6, 4)
(x2, y2) ==> (3, -2)
To find the slope, we have:
[tex]\begin{gathered} m=\frac{-2-4}{3-(-6)} \\ \\ m=\frac{-6}{3+6} \\ \\ m=\frac{-6}{9} \\ \\ m=-\frac{2}{3} \end{gathered}[/tex]Therefore, the slope of the line is:
[tex]-\frac{2}{3}[/tex]
ANSWER:
[tex]-\frac{2}{3}[/tex]
What’s the correct answer answer asap
Answer:
Serbia
Step-by-step explanation:
Austria-Hungary declares war on Serbia, effectively beggining the first world war
one integer is 7 less than 5 times another. Their product is 24. Find the integers.
Answer:
3, 8
Step-by-step explanation:
Let's make the first integer x and the second integer y.
Now, you take the information given and convert it into a system of equations:
xy = 24
x = 5y - 7
y = 24 / x
Now, we substitute:
(5y - 7) · y = 24
Distribute y
5y² - 7y = 24
Rearrange it into a quadratic equation:
ax² + bx + c = 0
5y² - y - 24 = 0
Use the quadratic formula (shown in image) and plug in the values:
x = (- (7) ± [tex]\sqrt{(-7^})^{2} -4(5)(-24)}[/tex] ) / 2(5)
[tex]\sqrt{(-7)^{2} -4(5)(-24)}[/tex] = [tex]\sqrt{49 - (-480)} = \sqrt{529} = 23[/tex]
Remember that ± means there are two y values
[tex]x = \frac{7+23}{10} = \frac{30}{10} = 3[/tex]
and
[tex]x = \frac{7-23}{10} = \frac{-16}{10} = -1.6[/tex]
Since y must be an integer, we know that y = 3
Now, plug in y:
5(3) - y = 24
15 - y = 24
- y = -24
y = 8
Let's check to see if we are right:
5y - 7 = 5(3) - 7 = 15 - 7 = 8
It works!
Jonah saw a news report that stated that 72% of children in his town played a sport last year. If there are 4,000 children in his town, how many children in his town played a sport last year?(1 point) children in his town played a sport last year.
a person weighs 140 pounds has 4 quarts if blood. estimate the number of quarts of blood in a person who weighs 120 pounds
The number of quarts of blood in a person who weighs 120 pounds is 3.4
How to calculate the number of quarts of blood ?The expression can be written as
W= kV
W represents the weight in pounds
V= number of quarts
k= 140/4
= 35
The number of quarts of blood in a person that weighs 120 pounds can be calculated as follows
= 120/35
= 3.4
Hence 3.4 quarts of blood is gotten from a person who weighs 120 pounds. This was done by dividing 120 by 35
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x 0 1 9
P(X = x) 0.14 0.35 0.51
Answer:
Step-by-step explanation:
k = 0.2
4. Which function will translate f(x) = x2 right 3 units and down 2 units?a. f(x) = (x - 2)2 – 3b. B. f(x) = (x - 3)2 – 2c. C. f(x) = (x - 3)2 + 2d. D. f(x) = (x + 3)2 – 2
f(x) = x^2
To translate the function 2 units down (along the y axis) subtract 2
F(x) = x^2 -2
To translate the function 3 units to the right (along the x-axis) subtract 3 units inside the parentheses.
f(x) = (x-3)^2 - 2
Ally has a square backyard with an area of 169 square feet. What is the length of one side of thebackyard?Sut
Ally has a square backyard with an area of 169 square feet.
Given a square of side length, s
[tex]\text{Area of a Square}=s^2[/tex]Therefore:
[tex]\begin{gathered} s^2=169\text{ square feet} \\ \text{Take the square root of both sides} \\ \sqrt{s^2}=\sqrt{169} \\ s=13\text{ feet} \end{gathered}[/tex]Therefore, the length of one side of the backyard is 13 feet.
find the distance the points (-3,-5) and (9,-10). Enter the exact value of the answer.
00:00 Jayden evaluated the expression a = (2 + 1.5) for a = 14. He said that the answer was 8.5. Choose True or False for each statement Choose... Jayden's solution is incorrect. Choose... Jayden added in the parentheses before dividing. Choose... Jayden substituted the wrong value for a. Choose... Jayden divided 14 by 2 and added 1.5.
Explanation:
Let's see what's the value of the expression if we substitute a = 14:
[tex]14\colon(2+1.5)=14\colon3.5=4[/tex]So definetly Jayden's solution is not correct.
Let's check the second statement: that's what we just did - add the parentheses before dividing. If Jayden would've done that he would have arrieved at the same solution we did, so definetly this statement is false
The third statement could be true. Let's see which value of a gives 8.5 as a result:
[tex]\begin{gathered} a\colon(2+1.5)=8.5 \\ a\colon3.5=8.5 \\ a=8.5\times3.5 \\ a=29.75 \end{gathered}[/tex]If 'a' were 29.75, Jayden would be correct.
Let's see what happens if we divide 14 by 2 and then add 1.5:
[tex](14\colon2)+1.5=7+1.5=8.5[/tex]This is the result Jayden got, so definetly this is one option for what he did wrong.
Answer:
• Jayden's solution is incorrect: ,true
,• Jayden added in the parentheses before dividing:, ,false
,• Jayden substituted the wrong value for a: ,true
,• Jayden divided 14 by 2 and then added 1.5: ,true
Lucas is riding his rocket-powered big wheel. He rides at a constant speed. After riding for 5 hours, Lucashas travelled 46.5 miles. After 8 hours, he has travelled 74.4 miles.a. What is the dependent variable?b. What is the independent variable?c. What is Lucas' speed?d. If you were to graph Lucas' travel, what would the y-intercept be? Why?
a. Distance travelled
Given that he rides at a constant speed and after riding for 5 hours, he had travelled 46.5 miles. Per review, the distance travelled is dependent on time hence distance or miles covered is the dependent variable
PLEASE HELP ITS DUE SOON! I DONT GET ANY OF THIS! HELP WOULD BE MUCH APPRECIATED! NEED THIS DONE BEEN STUCK ON THIS FOR WAY TO LONG!
YOU WILL GET 100 POINTS IF YOU HELP! QUESTION DOWN BELOW!!!!!
THIS IS MY LAST QUESTION!!
Answer:
See below.
Step-by-step explanation:
Vertical Angles Theorem
When two straight lines intersect, the opposite vertical angles are congruent.
Alternate Interior Angles Theorem
If a line intersects a set of parallel lines in the same plane at two distinct points, the alternate interior angles that are formed are congruent.
Transitive Property of Equality
If a=b and c=b, then a=c.
Proof that ∠1=∠2
∠3 is equal to ∠4 (Vertical Angle Theorem).As BC intersects the set of parallel lines AB and CD (given), ∠3 is equal to ∠2 (Alternate Interior Angles Theorem).If ∠3=∠4 and ∠3=∠2 then ∠2=∠4 (Transitive Property of Equality).Given that ∠1=∠4 and ∠2=∠4 then ∠1=∠2 (Transitive Property of Equality).[tex]\begin{array}{c|c}\sf Statement & \sf Reason\\\cline{1-2}\\ \angle 3 = \angle 4 & \textsf{Vertical Angle Theorem}\\\\AB \parallel CD & \textsf{Given}\\\\\angle 3 = \angle 2 & \textsf{Alternate Interior Angles Theorem}\\\\\angle 2 = \angle 4 & \textsf{Transitive Property of Equality}\\\\\angle 1 = \angle 4 & \textsf{Given}\\\\\angle 1 = \angle 2 & \textsf{Transitive Property of Equality}\\\\\end{array}[/tex]
Henry is shipping a package that weighs 7 7/8 lbs. What is the weight of the package expressed as a decimal?
Answer:
7.875
Step-by-step explanation:
help meeeeeeeeee pleaseeeeeeeeeee!!!
thank youu
For the given ques, the graph is mention in the question.
As, domain are the all set of values lying on the x-axis.
Thus,
A. Domain {-1 to infinity} (In integer or fraction form.)
B. Domain [-1, ∞), (interval notation; half closed half open)
Range of the relation of function are-
A. Range {- infinity to infinity} (In integer or fraction form.)
B. Range (- ∞, ∞), (interval notation open interval both sides)
Thus, the value of domain and range of the function are found.
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Which method is best to solve this system?
y = -6x + 5
-2x + y = 5
Option 1: Guess and Check
Option 2: Elimination
Option 3: SUbstitution
Option 4: Graphing
Answer: I'm sure Option 4 Could help you find your answer.
Step-by-step explanation:
y=−6x+5−2x+y=5
Hope this helps.
at the pet store 25 bunnies were examined and 7 of them had blue eyes.
Given
[tex]\begin{gathered} 25\text{ }bunnies=7blue\text{ }eyes \\ 60\text{ }bunnies=xblue\text{ }eyes \\ \\ x=\frac{60\times7}{25} \\ \\ x=16.8 \\ \\ x\approx17 \end{gathered}[/tex]The final answer is 17 bunnies
Solve the system by using the substitution method.y = 2x + 184x + 5y = 20
Let:
y=2x+18 (1)
4x+5y=20 (2)
replace (1) into (2)
4x+5(2x+18)=20
Using distributive property:
4x+10x+90=20
Add like terms:
(4x+10x)+90=20
14x+90=20
subtract 90 from both sides:
14x+90-90=20-90
14x=-70
Divide both sides by 14:
14x/14=-70/14
x=-5
Finally, replace the value of x into (1)
y=2(-5)+18
y=-10+18
y=8
Let:
2x+2y=6 (1)
3x-5y=25 (2)
From (1) let's solve for x:
subtract 2y from both sides:
2x+2y-2y=6-2y
2x=6-2y
Divide both sides by 2:
x=(6-2y)/2
x=3-y (3)
Replace (3) into (2)
3(3-y)-5y=25
Using distributive property:
9-3y-5y=25
Add like terms:
9+(-3y-5y)=25
9-8y=25
subtract 9 from both sides:
9-8y-9=25-9
-8y=16
Divide both sides by -8:
(-8y)/(-8)=(16)/(-8)
y=-2
Finally, replace the value of y into (3)
x=3-(-2)
x=3+2
x=5
Factor differences of square m^4 - n^4
Remember that a difference of squares can be written as the product of two conjugate binomials:
[tex]a^2-b^2=(a+b)(a-b)[/tex]In the given expression, notice that m^4 and n^4 can be written as (m^2)^2 and (n^2)^2:
[tex]m^4-n^4=(m^2)^2-(n^2)^2[/tex]Once written as a difference of squares, we can factor the expression:
[tex](m^2)^2-(n^2)^2=(m^2+n^2)(m^2-n^2)[/tex]Therefore:
[tex]m^4-n^4=(m^2+n^2)(m^2-n^2)[/tex]What are two ordered pairs that the midpoints (4, -10)? Please show that your points work.
In order to find any pair of points that have a midpoint of (4, -10), we can choose any two values p and q. Then, one of the endpoints will be (4+p, -10+q) and the other endpoint will be (4-p, -10-q).
For example, let's choose p = q = 2, so we have:
[tex]\begin{gathered} midpoint\text{ \lparen4,-10\rparen}\\ \\ \\ \\ 1st\text{ endpoint:}\\ \\ (4+2,-10+2)=(6,-8)\\ \\ \\ \\ 2nd\text{ endpoint:}\\ \\ (4-2,-10-2)=(2,-12) \end{gathered}[/tex]Therefore the ordered pairs (6, -8) and (2, -12) have a midpoint of (4, -10).
Describe a series of transformations Matt can perform to decide if the two windows are congruent
The three transformations—rotations, reflections, and translations—can be combined to produce congruent shapes. The truth is that any pair of congruent shapes can be matched to one another by combining one or more of these three transformations.
Explain transformations.
A point, line, or geometric figure has four different transformations that can be applied to alter its appearance. While the term "Image" refers to the position and final shape of the object, "Pre-Image" refers to the object's shape before transformation.
Given Information
The size and shape of the figures are preserved during stiff transformations, as we already know (reflections, translations, and rotations). Always in harmony with one another is the pre-image.
These transformational skills are all possessed by Matt:
Reflection
The reason a reflection maintains its original form Comparable locations between the pre-image and the picture remain apart from the line of reflection.
Rotations as a Transformation of Congruence
When a figure rotates, it twists. Despite being the same size and shape, the figurine appears to have toppled over. A clock is an excellent example of how the globe rotates in reality. Every hour or every day, the connecting arms of a clock revolve around its axis. The degree of a rotation determines what kind of rotation it is; popular rotations include 90, 180, and 270 degrees. Before spinning around completely and going back to where it started, the figure rotates 360 degrees. the clockwise or counterclockwise direction in which a rotation is made. This data can be used to determine the degree, amount, a revolution's speed and direction.
Congruence translational transformation
When an object or shape is transferred from one location to another without altering its size, shape, or orientation, we refer to the transfer as a movement. A translation, often known as a slide, involves moving every point on an object or shape uniformly and in one direction.
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#15If you do not know college algebra, please say so and let me move on.
In order to graph the functiom we need to identify the parent function and the vertical and horizontal shifts that might be done to the function.
In this case we see that the parent function is a cubic function since the greater degree is 3
[tex]g(x)=x^3[/tex]this means that f(x) is a transformation of g(x)
then
the horizontal shifts since there is sum inside the parentheses the shift will be 1 unit to the left.
the vertical shift will be 1 unit up since there is a sum outside the parentheses.
and finally since there is a - it means that the function is reflected over the x-axis
the parent function will be the red line and the function #15 is the blue line.
In order to find points we can tabulate the values for given xs' and construct the graph.
Start by making a table like this:
now since the function is given we can replace x with the values and find y
[tex]\begin{gathered} y=-(x+1)^3+1 \\ y=-(-6+1)^3+1 \\ y=-(-5)^3+1 \\ y=-(-125)+1 \\ y=125+1 \\ y=126 \end{gathered}[/tex]then after tabulating values should look like this
Now looking at the graph on the blue function we can see that the function is decreasing until reaching x=-1, however after that the function will continue to decrease but at a different rate, which means that over the interval
[tex](-\infty,\infty)[/tex]the function will be decreasing