Answer:
Step-by-step explanation:
We graph the function.
Final answer:
Plotting points that satisfy an equation or inequality creates a graph representing their relationship, with lines or curves like parabolas depending on the equation type.
Explanation:
When we plot all the points that satisfy an equation or inequality, we create a visual representation of the relationship between variables that are described by that equation or inequality. For instance, if the equation is linear and we plot its solutions on a graph, we will see a line. The y-intercept is an important feature of this line, indicating the point where the plot crosses the y-axis. In the case of a quadratic equation, plotting its solutions results in a parabola. If we want to determine whether the plot crosses a particular axis, such as the t-axis, we may need to analyze the discriminant (D) of the quadratic equation, which tells us whether the equation has real roots and, consequently, intersects with the axis.
counting backwards from 5, what number is 4?
Answer:
The number 4 is the first term of the sequence
Step-by-step explanation:
we know that
Counting backwards is when the numbers are count in reverse sequence
Is also know as 1 less
In this problem the sequence of counting backwards from 5 is equal to
4,3,2,1,0
therefore
The number 4 is the first term of the sequence
Mrs Jenkins picked some tomatoes from her garden. She used 5/9 of the tomatoes to make pasta sauce. Then she used 3/4 of the remainder to make a salad. What fraction of the tomatoes did mrs Jenkins use to make the salad?
Answer:
Final answer is 1/3.
Step-by-step explanation:
Given that Mrs Jenkins picked some tomatoes from her garden. She used 5/9 of the tomatoes to make pasta sauce. Then she used 3/4 of the remainder to make a salad. Now we need to find about what fraction of the tomatoes did Mrs Jenkins use to make the salad.
Since she used 5/9 of the tomatoes to make pasta sauce.
Then remaining amount of tomatoes = 1- 5/9 = 9/9 -5/9 = 4/9
Then she used 3/4 of the remainder to make a salad. So fraction of the tomatoes did Mrs Jenkins use to make the salad = (4/9)(3/4)=12/36=1/3
Hence final answer is 1/3.
The measurement of the smallest angle in a right triangle is 45° less than the measure of the next larger angle. Find the measures of all three angles.
Hey there!
The interior angles of a triangle always have to add up to 180 degrees.
We are told that this is a right triangle, so one of the angles must be 90 degrees. This means that the measures of the other two angles must add up to 90.
90 + m<1 + m<2 = 180
If the smallest angle is 45 degrees less than the next largest angle, the only option for this would be for both of the remaining angles to be 45 degrees. The next largest angle would be the right angle, and 90 - 45 = 45.
We can't have any of the other angles be more than 90 degrees because then it wouldn't be a proper triangle.
So, the measures of the angles are going to be 90, 45, and 45.
Hope this helps!
The measurement of the smallest angle in a right triangle is 45° less than the measure of the next larger angle. The three angle of right are ( [tex]90^o, 45^o, 45^o[/tex] )
What is right angle triangle property?In a right angle triangle, the largest angle is equal to the 90 degrees, and the some of the other two angle is equal to the 90 degrees.
Given information-
The smallest angle in a right triangle is 45° less than the measure of the larger angle.
Suppose the smallest angle of the right triangle is x degrees.
Now as the smallest angle in a right triangle is 45° less than the measure of the larger angle and the value of largest angle is 90 degrees in the right angle triangle. Thus,
[tex]x=90-45\\x=45^o[/tex]
Hence, the measurement of the smallest angle is 45 degrees.
Let the other angle of the right angle triangle is y degrees.
As the some of the all the angles of a triangle is equal the 180 degrees. Thus,
[tex]x+y+90=180\\45+y=180-90\\y=90-45\\y=45[/tex]
Thus, the measurement of the other angle is 45 degrees.
Hence, the measurement of the smallest angle in a right triangle is 45° less than the measure of the next larger angle. The three angle of right are ( [tex]90^o, 45^o, 45^o[/tex] )
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Frank left his house at 7 a.m. and drove to the airport at a speed of 50 mph. Lance left his house at 6 a.m. and drove to the same airport at a speed of 55 mph. Frank's house is 150 miles from the airport and Lance's house is 220 miles from the airport. At what time did Frank arrive at the airport?
Answer:
10:00 AM
Step-by-step explanation:
Frank drove at a speed of 50 mph, and traveled a distance of 150 miles. This means he traveled for
150/50 = 3 hours.
7 AM + 3 hours = 10 AM
The solution is, at 10:00 AM Frank will arrive at the airport.
What is speed?Speed is measured as distance moved over time. The formula for speed is speed = distance ÷ time. To work out what the units are for speed, you need to know the units for distance and time. In this example, distance is in metres (m) and time is in seconds (s), so the units will be in metres per second (m/s).
Speed = Distance/ Time.
here, we have,
given that,
Frank left his house at 7 a.m. and drove to the airport at a speed of 50 mph.
Lance left his house at 6 a.m. and drove to the same airport at a speed of 55 mph.
Frank's house is 150 miles from the airport and Lance's house is 220 miles from the airport.
so, we get,
Frank drove at a speed of 50 mph,
and traveled a distance of 150 miles. This means he traveled for
150/50 = 3 hours.
Thus, it takes Frank 3 hours to reach the airport.
so, we get,
since he departed at 7:00 AM, he will arrive at the airport at
7 AM + 3 hours = 10 AM
Hence, The solution is, at 10:00 AM Frank will arrive at the airport.
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What happens to the graph of y=|x| when the equation changes to y=|x+3| - 1
Solve the system of linear equations below. x − 3y = -3 x + 3y = 9 A. x = -12, y = 7 B. x = 3, y = 2 C. x = 6, y = 1 D. x = 6, y = 2
ANSWER
B. x=3,y=2
EXPLANATION
The given equations are
[tex]x - 3y = - 3...(1)[/tex]
and
[tex]x + 3y = 9...(2)[/tex]
We add the two equations to eliminate y.
This implies that that:
[tex] x + x - 3y + 3y = 9 + - 3[/tex]
Simplify:
[tex]2x = 6[/tex]
Divide both sides by 2.
[tex]x = 3[/tex]
We put x=3 into any of the equations to find y.
Let us substitute x=3 into equation (1) to get:
[tex]3 - 3y = - 3[/tex]
[tex] - 3y = - 3 - 3[/tex]
[tex] - 3y = - 6[/tex]
Divide both sides by -3 to get;
[tex]y = 2[/tex]
The solution is therefore x=,y=2.
What is the equation written in slope intercept
Answer:
[tex]\large\boxed{1.\ y=-\dfrac{3}{5}x+\dfrac{12}{5}}\\\boxed{2.\ y=\dfrac{5}{4}x-\dfrac{3}{2}}[/tex]
Step-by-step explanation:
The slope-intercept form:
[tex]y=mx+b[/tex]
m - slope
b - y-intercept
[tex]1.\\3x+5y=12\qquad\text{subtract 3x from both sides}\\\\5y=-3x+12\qquad\text{divide both sides by 5}\\\\\boxed{y=-\dfrac{3}{5}x+\dfrac{12}{5}}\\\\2.\\5x-4y=6\qquad\text{subtract 5x from both sides}\\\\-4y=-5x+6\qquad\text{divide both sides by (-4)}\\\\y=\dfrac{5}{4}x-\dfrac{6}{4}\\\\\boxed{y=\dfrac{5}{4}x-\dfrac{3}{2}}[/tex]
What is the value of x?
Answer:
x = 12.8
Step-by-step explanation:
To find the value of x, set up a proportion between the two similar triangles. Then solve for x.
[tex]\frac{32}{32+x} = \frac{40}{56}[/tex]
Solve by cross multiplying and isolating x.
32(56) = 40(32+x)
1792 = 1280 + 40x
512 = 40x
12.8 = x
measure each rectangle to the nearest 1/4 in with your ruler and label the dimensions use the area model to find the area
Answer:
can you attach a picture
Step-by-step explanation:
Do u have a picture so i could solve it
All rectangles are parallelograms
A diagonal path divides a square park in half. If the park is 50 yards on each side, how long is the path?
The length of the diagonal path is approximately 70.71 yards.
To find the length of the diagonal path that divides the square park in half, we can use the Pythagorean theorem. A square park of 50 yards on each side means we are dealing with a right-angled triangle with both legs equal to 50 yards.
The Pythagorean theorem states that in a right-angled triangle, the square of the length of the hypotenuse (c) is equal to the sum of the squares of the lengths of the other two sides (a and b):
[tex]c^2 = a^2 + b^2[/tex]
Here, both a and b are 50 yards, so the equation becomes:
[tex]c^2[/tex] = 502 + 502 = 2500 + 2500 = 5000
Now we find the square root of 5000 to get the length of the diagonal:
c = √5000 ≈ 70.71 yards
Therefore, the length of the diagonal path is approximately 70.71 yards.
Which of the following numbers is irrational?
Answer:
it is the 3rd choice
Step-by-step explanation:
3
➷ An irrational number cannot be written in the form of a fraction.
As you can see, the first two are already in fraction form, so it can't be those.
The square root of 4 is 2 which can be written as 2/1
This leaves the square root of 3, which is the answer.
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I need to know how to find the mean for 77,82,87,85,32,78?
Answer:
73.5
Step-by-step explanation:
To find the mean, sum the data and divide by the amount of data
mean = [tex]\frac{77+82+87+85+32+78}{6}[/tex]
= [tex]\frac{441}{6}[/tex] = 73.5
The answer is 73.5. Just add all the numbers and divided by how many numbers there are. So you would add all the numbers and then divided by 6 since there are 6 numbers.
(20pts) Pls I need help with my hw, pls show work
4. Just look at the graph, and see which coordinates are on the line.
D, E, and F are on the line.
5. The y-coordinate is (0,4), and the slope is (4 + 8)/(0 - 4) = -3. Therefore, the equation of the line is y = -3x + 4. Plugging in the numbers we know gives us b = -3*8 + 4. b = -20.
6. Find the number of times P is on a line. There are two lines that do so.
If m > n, which inequalities must be true? Check all that apply.
m + 2.1 > n + 2.1
m - (-4) > n -(-4)
m + 3 > n - 3
16.5 + m > 16.5 + n
m > n + 1/2
9 + m > 6 + n
Will give a rank if can be answered in 5 min
Answer:
It's A B and D, the brainliest is incorrect.
Step-by-step explanation:
Final answer:
If m is greater than n, then all the provided inequalities must be true, as they involve either adding the same amount to both sides or increasing the positive difference between m and n.
Explanation:
If m > n, then certain inequalities must hold true when we add, subtract, or compare these variables while keeping the inequality relationship consistent. Here are the inequalities that must be true based on the given condition:
m + 2.1 > n + 2.1: Adding the same number to both sides of an inequality does not change the relationship, thus this inequality must be true.
m - (-4) > n -(-4): Subtracting a negative is the same as adding a positive, so this inequality will also hold true.
m + 3 > n - 3: Adding a positive number to m and a negative to n will increase the difference between them, making this inequality true.
16.5 + m > 16.5 + n: Similar to the first point, adding the same number to both sides of an inequality maintains the inequality.
m > n + 1/2: Since m is greater than n, adding a positive fraction to n would still keep m greater than the modified n.
9 + m > 6 + n: Adding different numbers to m and n still preserves the inequality, if the number added to m is not smaller than the number added to n.
A rectangle has an area of 24 square centimeters. Select the three choices that show pairs of possible side lengths of the rectangle
Answer:
A, B, and C
Step-by-step explanation:
We can use guess-and-check.
A rectangle with the area 24 cm² has the sides that make the product of 24 (A = l * w)
1 * 24 is 24.
2 * 12 is 24.
3 * 8 is 24.
4 * 20 is 80.
12 * 12 is 144.
help me please, match the number to the letter
Answer: 1b 2c 3e? 4d 5a
Step-by-step explanation:
There are 2 items that need to be checked.
The midpoint of the coordinates is the center of the circleThe diameter of the coordinates is the diameter of the circle.Midpoint:
[tex]Midpoint = \bigg(\dfrac{x_1+x_2}{2},\dfrac{y_1+y_2}{2}\bigg)\\\\\\1)\ \bigg(\dfrac{-4+2}{2},\dfrac{-1+10}{2}\bigg)=\bigg(\dfrac{-2}{2},\dfrac{9}{2}\bigg)=(-1, 4.5)\implies \text{equation b}\\\\\\2)\ \bigg(\dfrac{1+7}{2},\dfrac{3-10}{2}\bigg)=\bigg(\dfrac{8}{2},\dfrac{-7}{2}\bigg)=(4, -3.5)\implies \text{equation c}\\\\\\3)\ \bigg(\dfrac{4-8}{2},\dfrac{-2+6}{2}\bigg)=\bigg(\dfrac{-4}{2},\dfrac{4}{2}\bigg)=(-2,2 )\implies \text{none of the equations}[/tex]
[tex]4)\ \bigg(\dfrac{6-4}{2},\dfrac{3-13}{2}\bigg)=\bigg(\dfrac{2}{2},\dfrac{-10}{2}\bigg)=(1, -5)\implies \text{equation d}\\\\\\5)\ \bigg(\dfrac{7-1}{2},\dfrac{5+8}{2}\bigg)=\bigg(\dfrac{6}{2},\dfrac{13}{2}\bigg)=(3, 6.5)\implies \text{equation a}[/tex]
Diameter:
distance between coordinates = 2√r² (from circle equation)
[tex]\text{formula for coordinates is: }d=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}\\\\1)\ \text{Coordinates: } d=\sqrt{(-4-2)^2+(-1-10)^2}=\sqrt{36+121}=12.5\\b)\ \text{Circle: }2\sqrt{39.25}=12.5\\\\\\2)\ \text{Coordinates: } d=\sqrt{(1-7)^2+(3+10)^2}=\sqrt{36+169}=14.3\\c)\ \text{Circle: }2\sqrt{51.25}=14.3\\\\\\4)\ \text{Coordinates: } d=\sqrt{(6+4)^2+(3+13)^2}=\sqrt{100+256}=18.9\\d)\ \text{Circle: }2\sqrt{89}=18.9[/tex]
[tex]5)\ \text{Coordinates: } d=\sqrt{(7+1)^2+(5-8)^2}=\sqrt{64+9}=8.5\\a)\ \text{Circle: }2\sqrt{18.25}=8.5[/tex]
Check:
Graph to confirm your answers are correct (see attached)
A bag contains 12 counters. 7 of them are white. A counter is taken at random and not replaced. A second counter is taken out of the bag at random. Calculate the probability that only one of the two counters is white
➷ First calculate how many counters are 'not white'
12 - 7 = 5
We have 5 counters that are 'not white'
The probability of taking a white counter the first time is 7/12
For the next pick, there would be 1 less of the total counters as it is not being replaced
The probability of then taking a 'not white' counter is 5/11
The other way you could still get one white counter is:
The first counter (non white) probability would be 5/12
The second counter (white) probability would be 7/11
Multiply these values:
7/12 x 5/11 = 35/132
5/12 x 7/11 = 35/132
Add these two values together:
35/132 + 35/132 = 70/132
Your answer is 70/132
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Solve the system of linear equations by elimination.
4x+3y= -5
-x+3y= -10
The solution of given system of linear equations are x = 1 and y = -3.
Given system of linear equations are,
[tex]4x+3y=-5 ..........(1)\\\\ -x+3y=-10..............(2)[/tex]
Subtract equation 2 from equation 1.
[tex]4x+3y-(-x+3y)=-5+10\\ \\ 4x+3y+x-3y=5\\ \\ 5x=5\\ \\ x=5/5=1[/tex]
Substituting value of x in equation 1.
[tex]4(1)+3y=-5\\ \\ 3y=-5-4=-9\\ \\ y=-9/3=-3[/tex]
Hence, The solution of given system of linear equations are x = 1 and y = -3.
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How many groups of 5 can u make out of 670
Answer:
134
Step-by-step explanation:
670/5 = 134
The answer is 130=5*130
Given that √x = -4, what is x?
Square on both sides..
x=16 !!!
[tex] \sqrt{x} = - 4 \\ { \sqrt{x} }^{2} = {( - 4)}^{2} \\ x = 16 [/tex]
(-) +(-) =+
math help 20 points and brainliest
find the roots, and list the steps correctly
you need to show work and list the steps please
f(n)=n^2 -6n-16
ANSWER
[tex]n = 8 \: or \: n = - 2[/tex]
EXPLANATION
The given function is
[tex]f(n) = {n}^{2} - 6n - 16[/tex]
To find roots of the equation, we set the equation to zero.
[tex]{n}^{2} - 8n + 2n- 16 = 0[/tex]
Split the middle term with -8n+2n
We now factor to get,
[tex]n(n - 8) + 2(n- 8) = 0[/tex]
[tex](n - 8)(n + 2) = 0[/tex]
Using the zero product property,
[tex]n - 8 = 0 \: or \: n + 2 = 0[/tex]
[tex]n = 8 \: or \: n = - 2[/tex]
The sign below is located at the start of Pinecone trail and shows the distances from the sign to different points of interest along the trail. Sage hiked from the start of the trail to Lookout Point. She then hiked back to Giant Boulder to camp for the night. What was the total distance, in miles, that Sage hiked?
Answer:
Total distance = 53/4 miles = 13.25 miles
Step-by-step explanation:
Sage hiked from the start of the trail to Lookout Point.
Distance = 8 3/4 miles = 35/4 miles
She then hiked back to Giant Boulder
This means she traveled an additional
8 3/4 miles - 4 1/4 miles = 35/4 mi - 17/4 mi = 18/4 mi = 9/2 mi
The total distance traveled by sage is the sum of both trajectories
Total distance = 35/4 miles + 9/2 miles = 53/4 miles
Total distance = 13.25 miles
A recipe calls for 3/4 cup of sugar for every 1 1/2 cups of flour. How much sugar would be needed if the baker uses 4 1/2 cups of flour?
Answer:
Step-by-step explanation:
Please help quickly, I don't understand.
Image attached
Answer:
ok so
Step-by-step explanation:
you basically hafta calulate funtion f w factor two
hope this helps!
If a figure is a square, then it is a regular quadrilateral. True or false? Explain.
Answer:
Yes, because a quadrilateral have four sided figure. So True.
Answer + Explanation:
True, because all quadrilaterals are four-sided figures. Squares have four equal sides, so they are regular quadrilaterals.
if a number is increased by 100%, how does the increased number compare with the original number? explain
how many different pairs can you make with four colors: red, blue, green purple?
Answer:
6
Step-by-step explanation:
red blue green purple
red red/blue red/green red/purple
blue red/blue blue/green blue/purple
green red/green blue/green green/purple
purple red/ purple purple blue purple/green
i did not include red/red since the question asks for DIFFERENT PAIRS. same with the combinations that are repeated
plz give me a brainliesttttttt
To find the number of different pairs that can be made with four colors, we use the combinations formula C(4, 2), which calculates to 6. Thus, there are 6 different color pairs that can be made with red, blue, green, and purple.
To determine how many different pairs can be made with four colors: red, blue, green, purple, we use the concept of combinations from mathematics. A combination is a selection of items where the order does not matter. In this case, we are selecting two colors from the four available to form a pair.
To calculate the number of combinations without repetition, we can use the combination formula which is [tex]C(n, k) = \frac{n! }{ (k!(n - k)!)}[/tex], where n is the total number of items to choose from, k is the number of items to choose, and '!' represents the factorial of a number. For this scenario, n = 4 (four colors) and k = 2 (since we are forming pairs).
So, the number of combinations is C(4, 2) = [tex]\frac{4! }{2!(4 - 2)!} = \frac{4 \times 3 \times 2 \times 1 }{ 2 \times 1 \times 2 \times 1}[/tex] = 6. Therefore, there are 6 different color pairs that can be made with the colors red, blue, green, and purple.
Area of regular hexagon
Check the picture below.
let's recall that a circle has 360°, so that means every two radii coming from the center of the hexagon, will split those 360° in 6 even pieces, 360/6 = 60, namely those two radii make up a 60° central angle, as you see in the picture.
running a perpendicular from the center, we end up with a 30-60-90 triangle, as you see there, and thus we can use the 30-60-90 rule to get the length of "a".
now, keeping in mind that the perimeter of the polygon is simply 4+4+4+4+4+4 = 24.
[tex]\bf \textit{area of a regular polygon}\\\\ A=\cfrac{1}{2}dp~~ \begin{cases} d=apothem\\ p=perimeter\\[-0.5em] \hrulefill\\ d=2\sqrt{3}\\ p=24 \end{cases}\implies A=\cfrac{1}{2}(2\sqrt{3})(24)\implies A=24\sqrt{3}[/tex]
If you had 150 subjects to work on and had 28 Days How many per day do you need to do?
Divide the total subjects by total days:
150 / 28 = 5.357 per day. Round the answer as needed.
Answer: Approximately 5 subjects per days.
Step-by-step explanation:
To solve the exercise and calculate the number of subjects you need to do per day you must keep on mind the information given in the problem. You know that:
- The total number of subjects is 150.
- You had 28 days left.
Therefore, you need to divide 150 subjects by 28 days.
Then, you obtain the following result:
[tex]=\frac{150subjects}{28days}=5.35\frac{subjects}{day}[/tex]≈ 5 subjects per days.