Answer:
[tex]x = \frac{2}{3} + \frac{\sqrt{10} }{3} , x = \frac{2}{3} - \frac{\sqrt{10} }{3}[/tex]
Step-by-step explanation:
Multiplying the coefficient of x by the constant to get:
3 x (-2) = -6
Find factors of -6 that equal the middle term -4.
Since, no such factors can be found so we can solve the equation by completing the square.
To complete the square, divide the equation by the coefficient of x^2 which is 3 to get:
[tex]x^{2} - \frac{4}{3} x - \frac{2}{3} = 0[/tex]
[tex]x^{2} - \frac{4}{3} x = \frac{2}{3}[/tex]
Now divide the coefficient of x by 2 and add the square of the result to both sides of the equation:
[tex]x^{2} - \frac{4}{3} x + (-\frac{2}{3} )^{2} = \frac{2}{3} + (-\frac{2}{3} )^{2}[/tex]
[tex](x - \frac{2}{3} )^2 = \frac{2}{3} + \frac{4}{9}[/tex]
[tex](x - \frac{2}{3} )^2 = \frac{4}{9}[/tex]
[tex]\sqrt{(x - \frac{2}{3} )^2} = \sqrt{\frac{4}{9} }[/tex]
[tex]x - \frac{2}{3} = \sqrt{\frac{10}{9} }[/tex] , [tex]x - \frac{2}{3} = -\sqrt{\frac{10}{9} }[/tex]
[tex]x = \frac{2}{3} + \frac{\sqrt{10} }{3} , x = \frac{2}{3} - \frac{\sqrt{10} }{3}[/tex]
The table shows the height of a soccer ball that has been kicked from the ground over time. (For reference: h(t) = −16t2 + 40t) Time (seconds) Height (feet) 0 0 0.5 16 1 24 1.25 25 1.5 24 2 16 2.5 0 Which statement describes the rate of change of the height of the ball over time? The rate of change is not constant and decreases over the entire time. Between 0 and 0.5 second the ball rises 16 feet, but between 0.5 and 1 second it rises only 8 more feet. The rate of change is not constant and increases over the entire time. Between 1.5 and 2 seconds the ball falls 8 feet, but between 2 and 12.5 seconds it falls 16 more feet. The rate of change is not constant and decreases then increases over time. The ball rises by 16 in the first half second, but only 8 feet over the next one. After it reaches 25 feet in the air, the ball drops. The rate of change is not constant and increases then decreases over time. The height of the ball above ground gets larger until 1.25 seconds and then gets smaller after that time.
Answer:
- Between 0 and 0.5 second the ball rises 16 feet, but between 0.5 and 1 second it rises only 8 more feet
- The ball rises by 16 in the first half second, but only 8 feet over the next one
- After it reaches 25 feet in the air, the ball drops
- The height of the ball above ground gets larger until 1.25 seconds and then gets smaller after that time.
Step-by-step explanation:
Let's rewrite the table:
Time (seconds) Height (feet)
0 0
0.5 16
1 24
1.25 25
1.5 24
2 16
2.5 0
By simply looking at the table, we can see that the following statements are all correct:
- Between 0 and 0.5 second the ball rises 16 feet, but between 0.5 and 1 second it rises only 8 more feet
- The ball rises by 16 in the first half second, but only 8 feet over the next one
- After it reaches 25 feet in the air, the ball drops
- The height of the ball above ground gets larger until 1.25 seconds and then gets smaller after that time.
Vector ahs 4 orange picks for every 3 green picks.If 8 of the picks are orange, how many picks are green?
If 8 of the picks are orange, then 6 of the picks will be green
Solve v=1/3bh for h the height of the cone
The volume of the cone can be calculated using fofmula
[tex]V=\dfrac{1}{3}\cdot b\cdot h,[/tex] wher b is the area of the base and h is the hieght.
Multiply the whole equation by 3:
[tex]3V=b\cdot h.[/tex]
Divide this equation by b:
[tex]h=\dfrac{3V}{b}.[/tex]
Answer: [tex]h=\dfrac{3V}{b}.[/tex]
We rearranged the equation v=1/3bh to solve for h, the height of the cone, by first multiplying by 3 to cancel the 1/3 and then dividing by b, resulting in h=3v/b.
The question is asking to Solving for Variable for h in the formula v=1/3bh, where v is the volume of a cone, b is the base area, and h is the height.
To find h, we need to rearrange the equation by first multiplying both sides by 3 to cancel out the 1/3 in front of bh.
So, it becomes 3v=bh.
Then, we divide both sides by b to isolate h, which gives us h=3v/b.
So the height of the cone is h=3v/b.
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Which equation represents y = x^2 − 8x + 5 in vertex form?
A) y = (x − 4)^2 − 9
B) y = (x − 4)^2 + 11
C) y = (x − 4)^2 + 21
D) y = (x − 4)^2 − 11
Answer: D
Step-by-step explanation:
y = x² - 8x + 5
-5 -5
y - 5 = x² - 8x complete the square by adding [tex](\frac{-8}{2})^{2}[/tex] to both sides
y - 5 + 16 = x² - 8x + 16 the right side is a perfect square: (x - 4)²
y + 11 = (x - 4)²
-11 -11
y = (x - 4)² - 11
Joanne is in Miami with her parents. The image shows a thermometer at a restaurant on the beach. What is the temperature on the thermometer?
C. 26 degrees Celsius
Answer:
The temperature on the thermometer is 26°C
Step-by-step explanation:
The image is very clear.
To answer this question you need to know the scale of the thermometer.
As between 20 and 30 there are 5 "spaces" (four lines) , we should divide
10 (the difference between 30 and 20) by 5.
10/5= 2
So each line means 2 °C
As there are 3 lines painted in red after 20, the answer is:
20+3*2= 26°C
1. Rodrigo has a ladder that is 13 ft long. The ladder is leaned against a vertical wall. The top of the ladder is 10.8 ft above the ground. The angle the ladder makes with the ground needs to be 60o or less for safety purposes. a. Is this ladder in a safe position? (1 point) b. Show your work (3 points) and draw a diagram (1 point) to support your answer. Answer:
Answer:
As per the given condition: Rodrigo has a ladder that is 13 ft long. The ladder is leaned against a vertical wall. The top of the ladder is 10.8 ft above the ground.
The Orientation of the ladder with the wall forms a right triangle.
The ladder length is the hypotenuse of the triangle,
the distance between the ladder at ground level and the base of the wall is the horizontal leg of the triangle,
and the height of the ladder is the vertical leg of the triangle.
⇒ Height of the ladder = 10.8 ft and hypotenuse = 13 ft
Using sine ratio formula;
[tex]\sin \theta = \frac{\text{Opposite side}}{\text{Hypotenuse side}}[/tex]
Opposite side = height of the ladder = 10.8 ft and
Hypotenuse side = 13 ft.
then;
[tex]\sin \theta = \frac{10.8}{13} =0.830769230769[/tex]
or
[tex]\theta = \sin^{-1}(0.830769230769)[/tex]
Simplify:
[tex]\theta = 56.2^{\circ}[/tex] (nearest to tenth place)
Since, it is given that the angle the ladder makes with the ground needs to be 60 degree or less for safety purposes.
(a)
Yes, this ladder in a safe position.
as [tex]\theta = 56.2^{\circ} < 60^{\circ}[/tex]
(b)
You can see the diagram as shown below in the attachment.
Alex is building a rectangular fence around his yard. The total perimeter of the fence is 68 feet and the area of the yard is 240 square feet. Based on this information, what are the dimensions of the fence?
Perimeter (P) = 2L + 2w
68 = 2L + 2w
68 - 2L = 2w
2(34 - L) = 2(w)
34 - L = w
********************
Area (A) = L * w
240 = L (34 - L)
240 = 34L - L²
L² - 34L + 240 = 0
(L - 10)(L - 24) = 0
L = 10 or L = 24
w = 34 - L = 34 - 10 = 24 or w = 34 - 24 = 10
Answer: width = 10, length = 24 assuming length is bigger than the width
Perimeter (P) = 2L + 2w
68 = 2L + 2w
68 - 2L = 2w
2(34 - L) = 2(w)
34 - L = w
********************
Area (A) = L * w
240 = L (34 - L)
240 = 34L - L²
L² - 34L + 240 = 0
(L - 10)(L - 24) = 0
L = 10 or L = 24
w = 34 - L = 34 - 10 = 24 or w = 34 - 24 = 10
Answer: width = 10, length = 24 assuming length is bigger than the width
Point A is on a line that has a slope of 3. Which of these could be the coordinates of another point on the line?
The fromula of a slope:
[tex]m=\dfrac{y_2-y_1}{x_2-x_1}[/tex]
We have A(4, 3) and m = 3.
(0, 3)
[tex]\dfrac{3-3}{0-4}=0\neq3[/tex]
(5, 0)
[tex]\dfrac{0-3}{5-4}=\dfrac{-3}{1}=-3\neq3[/tex]
(3, 0)
[tex]\dfrac{0-3}{3-4}=\dfrac{-3}{-1}=3\qquad CORRECT[/tex]
(0, 0)
[tex]\dfrac{0-3}{0-4}=\dfrac{-3}{-4}=\dfrac{3}{4}\neq3[/tex]
Answer: (3, 0).Sandra has a photo that is 9 inches by 12 inches. She wants to resize the photo by the scale factor of 3/4. What will be the dimensions of the new photo
The new dimensions are 6.75 inches by 9 inches
The dimensions of the new photo if, Sandra has a photo that is 9 inches by 12 inches, and The scale factor is 3 / 4, is 6.75 inches by 9 inches.
What is the scale factor?To adjust the size of a figure without altering its shape, a scale factor is a number or conversion factor that is utilized. It is employed to change the size of an object.
Given:
Sandra has a photo that is 9 inches by 12 inches,
The scale factor is, s = 3 / 4
Calculate the dimensions of the new photo as shown below,
The length = 9 × 3 / 4
The length = 27 / 4
The length = 6.75 inches,
The width of photo = 12 × 3 / 4
The width of the photo = 36 / 4
The width of the photo = 9 inches
Thus, the dimensions of the new photo will be 6.75 inches by 9 inches.
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In a math class, the teacher asked the students to find the approximate value of one of the x-coordinates of a point of intersection of two functions: f(x) = 2x2 − 3x + 4 g(x) = 5x − 1 Her students gave her different answers. Which answer is the most accurate? A. 0.8 B. 0.9 C. 1.9 D. 1.1
Set the polynomial equal to each other.
x2 - 2x - 5 = x3 - 2x2 - 5x - 9
Move all the terms to the right side of the equation to make the left side equal to zero.
0 = x3 - 3x2 - 3x - 4
Now we use synthetic division to factor.
4 | 1 -3 -3 -4
4 4 4
___________________________
1 1 1 0
0 = (x - 4)(x2 + x + 1)
Now you can set the factors equal to zero and solve for x. Since the quadratic factor has no real solutions, we ignore and focus on the linear factor. x = 4
Evaluate any of the function when x=4 to get the y-coordinate of the intersection point.
Answer:
The answer is 0.8 so A
Step-by-step explanation:
50q + 43 > −11q + 70
Answer:
The solution in the attached figure
Step-by-step explanation:
we have
[tex]50q+43 > -11q+70[/tex]
Solve for q
Adds 11 q both sides
[tex]50q+43 +11q > 70[/tex]
[tex]61q+43 > 70[/tex]
Subtract 43 both sides
[tex]61q > 70-43[/tex]
[tex]61q > 27[/tex]
Divide by 61 both sides
[tex]q > \frac{27}{61}[/tex]
The solution is the interval ------> (27/61,∞)
All real numbers greater than 27/61
In a number line the solution is the shaded area at right of 27/61 (open circle)
Math graph please help 35 points
In order to better find the points on this graph, we need to convert it from standard form to slope-intercept.
We can do that by solving for y.
-7y + 8 = 21x - 6
Subtract 8 from both sides.
-7y = 21x - 14
Divide both sides by -7
y = -3x + 2
Now that the equation is in slope-intercept, we can find two points on the line.
We know that (0, 2) will be the first point, because 2 is the y-intercept.
We can plug 1 into the x value of the equation to find the corresponding y value.
y = -3(1) + 2
y = -3 + 2
y = -1
The second point is (1, -1)
It's the linear function.
The slope-intercept form: y = mx + b.
-7y + 8 = 21x - 6 subtract 8 from both sides
-7y = 21x - 14 divide both sides by (-7)
y = -3x + 2
We need only two points:
for x = 0 → y = -3(0) + 2 = 0 + 2 = 2 → (0, 2)
for x = 2 → y = -3(2) + 2 = -6 + 2 = -4 → (2, -4)
Evaluate the expression 3xy-2x^2 x=4 and y=3
3 × 4 × 3 - 2 × 4²
36 - 2 × 4²
36 - 2 × 16
36 - 32
The answer is 4
Is that right? I hoped it helped...
which statement about -2h^2-15h-7 is true?
The answer is C) 2h + 1
First i factored out the negative sign, then i split the second term into two terms, then i factored out the common terms and i got -(h + 7) (2h + 1).
Answer:
One of the factor is (2h+1)
Step-by-step explanation:
[tex]-2h^2-15h-7[/tex]
Take out negative sign in common
[tex]-(2h^2+15h+7)[/tex]
Now factor the parenthesis
To factor this , we find out two factors whose product is 14 and sum is 15
[tex]-(2h^2+h+14h+7)[/tex]
Break first two terms and last two terms
[tex]-(2h^2+h)+(14h+7)[/tex]
[tex]-h(2h+1)+7(2h+1)[/tex]
[tex](-h+7)(2h+1)[/tex]
[tex](7-h)(2h+1)[/tex]
One of the factor is (2h+1)
Describe the difference between vertical angles and linear pairs of angles
Vertical angles are opposite each other when two lines intersect and are equal. Linear pairs of angles are adjacent angles that form a straight line and their sum is always 180 degrees. The difference lies both in their position and their angle sum.
Explanation:The main difference between vertical angles and linear pairs of angles derives from their positioning and sums. Vertical angles are angles opposite each other when two lines intersect. Vertical angles are always congruent, meaning they have the same measure.On the other hand, linear pairs of angles are adjacent angles whose non-common sides are opposite rays or in other words, they form a straight line. The sum of a linear pair of angles is always 180 degrees.
So, in sum, the difference lies in their positioning (vertical angles are opposite, linear pair angles are adjacent) and in their sum (vertical angles are equal, linear pair angles sum to 180 degrees).
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use the function rule to complete the table
-10x+y=4
the chart is below i coppied it
X= -2, -1, 0, 1, 2
y=is blank so you have to complet the bottom part witch is y.
The sun is about 93 * 10^6 miles from earth.What is this distance written as a whole number?
Multiplication time!
10^6 = 1,000,000
93 × 1,000,000 = 93,000,000
Hope this helps!!!
A grocery store gives away a $10 gift card to every 25th customer and a $20 gift card to every 60th customer. Which customer will be the first to receive both gift cards? Customer # b. After this customer receives both gift cards, what is the total amount in gift cards that the store has given away? $
Four more than three times a number t t is written as
"More" means you're adding. So the problem would look like this...
3t + 4
I hope this is what you're looking for. :)
What is 0.275 0.20 0.572 and 0.725 greatest to least
help me find the line of best fit ??
positive correlation
plz rate me
Answer:
Hello! I believe that this will help you find the line best fit.
Step-by-step explanation:
Remember, for it to be a line best fit, you must find the two points that you think will be on the "line best fit".
please help 20 points!
What is the truth value for the following conditional statement?
1.)
p: true
q: true
p → q
2.)
p: true
q: false
p → q
3.)
p: false
q: false
p → q
4.)
p: true
q: true
∼p → q
The truth value for the following conditional i.e., conjunction statement P is false and Q is true is False.
Answer:
1) True2) False3) True4) TrueStep-by-step explanation:
This conditional statement:
If a its true, then b its true.Has a truth value of true if:
both a and b are true.a its false, besides the truth value of bAnd has a truth value of false, if
a is true and b is falseThen, for this statements:
1. p -> qAs both p and q are true, then, this statement is true.
2. p -> qAs p is true and q is false, this statement is false.
3. p->qAs p is false, this statement is true, no matter the truth value of q.
4. ∼p -> q∼p its the negation of p. if p is true, then ∼p is false. And this statement is true, no matter the truth value of q.
A rectangular field is 65 meters wide and 115 meters long. Give the length and width of another rectangular field that has the same perimeter but a smaller area.
Answer: width = 30 m, length = 150 is one possible answer
Step-by-step explanation:
P = 2L + 2w A = L x w
= 2(65) + 2(115) = 65 x 115
= 130 + 230 = 7,475
= 360
360 ÷ 2 = 180
Find 2 numbers whose sum equals 180 and product is less than 7475
Sum: L + w = 180 ⇒ w = 180 - L
Product: Lw < 7475
Graph these 2 equations to see which coordinates of the sum fall into the shaded region of the product.
The denarius was a unit of currency in ancient Rome. Suppose it costs the Roman government 10 denarius per day to support 3 legionaries and 3archers. It only costs 3 denarius per day to support one legionary and one archer. Use a system of linear equations in two variables. Can we solve for a unique cost for each soldier?
Answer:
We can not solve for a unique cost for each soldier.
Step-by-step explanation:
Let x be the daily cost for legionaries and y be the daily cost for archers.
Upon using our given information we will get a system of linear equations as:
[tex]3x+3y=10...(1)[/tex]
[tex]x+y=3...(2)[/tex]
Now we will solve for x from our 2nd equation,
[tex]x = 3-y[/tex]
Now we will substitute this value in our 1st equation.
[tex]3(3-y)+3y=10[/tex]
[tex]9-3y+3y=10[/tex]
We can see that -3y cancels out with 3y and 9 is not equal to 10. So this is an unsolvable system. Therefore, we can not find a unique cost for each soldier.
Answer: No solutions
Step-by-step explanation:
HELP PLEASE!! 70 POINTS AND BRAINLIEST IF YOU ANSWER THESE MATH QUESTIONS!!
2 1/9 divided by 2/3
3/5 divided by 1 1/4
7 9/16 divided by 2 3/4
2 1/9 divided 2/3 = 19/6 OR 3 1/6
3/5 divided 1 1/4 = 12/25
7 9/16 divided 2 3/4 = 11/4 OR 2 3/4
Answer:
2 1/9 divided 2/3 = 19/6 OR 3 1/6
3/5 divided 1 1/4 = 12/25
7 9/16 divided 2 3/4 = 11/4 OR 2 3/4
Step-by-step explanation:
Out of 50 us states 4 haves names starting with a w what is the precentage starting with a w
Azul has 4 green picks and no orange picks. You add ornage picks so that there are 2 ornage picks for every 1 green pick. How many picks are there now?
Answer:
12 total picks, 4 green and 8 orange
Step-by-step explanation:
green(g)=4
orange(O)=2g
since g=4,
O=2(4)
O=8
8+4=12
Which expressions are polynomials?
What is the LCM of xy(x + 1) and x(x + 2)?
A.x2(x + 3)
B.x2(x + 1)(x + 2)
C.xy(x + 1)(x + 2)
D.xy(x + 3)
The answer is (C)
Explanation[tex]xy (x + 1), x(x+2)[/tex]
By multiplying x in equation
[tex]y(x^2 + x), x^2 + 2x[/tex]
[tex]y(x^2 + x), x(x+2)[/tex]
All the 4 factors are (x^2 + x), y, x, (x + 2)
So, the LCM is
[tex]xy(x + 1)(x + 2)[/tex]
Final answer:
The LCM of xy(x + 1) and x(x + 2) is found by including the highest powers of all variables and unique factors from both expressions, yielding x²y(x + 1)(x + 2).
Explanation:
The Least Common Multiple (LCM) of two algebraic expressions is the smallest expression that both original expressions can divide into evenly without leaving a remainder. To find the LCM of xy(x + 1) and x(x + 2), we look for the highest power of all the variables and factors included in both expressions.
The factor x appears in both expressions, but with different powers. The highest power of x in the given expressions is x² as seen in the second expression.
The factor y appears only in the first expression, so it must also be included in the LCM.
Next, the factors (x + 1) and (x + 2) are both unique, so they are also included in the LCM.
Therefore, the LCM of xy(x + 1) and x(x + 2) is x²y(x + 1)(x + 2), which corresponds to choice C. Hence, the correct answer is C.xy(x + 1)(x + 2).
Lily wrote the equation n + (-11)=24 find the value of n and explain how you found it
note that +(-) is equivalent to -
thus the equation can be written as
n - 11 = 24 ( add 11 to both sides )
n = 24 + 11 = 35