Answer:
[tex]y=-\frac{3+\sqrt{5}}{2}[/tex] AND [tex]y=-\frac{3-\sqrt{5}}{2}[/tex]
Step-by-step explanation:
Given: [tex]y^2+3y=-1[/tex]
To solve for [tex]y[/tex], we need to get everything on one side of the equal sign and set it to zero. We can do this by adding 1 to both sides. We then get:
[tex]y^2+3y+1=0[/tex]
We can solve for [tex]y[/tex] by using the quadratic formula:
[tex]y=\frac{-b+\sqrt{(b)^2-4(a)(c)}}{2a}[/tex] AND [tex]y=\frac{-b-\sqrt{(b)^2-4(a)(c)}}{2a}[/tex]
Let's identify our values:
[tex]a: 1\\b: 3\\c: 1[/tex]
Plug in the values and simplify.
[tex]y=\frac{-3+\sqrt{(3)^2-4(1)(1)}}{2(1)}\\y=\frac{-3+\sqrt{5}}{2}\\-------------------------\\y=\frac{-3-\sqrt{(3)^2-4(1)(1)}}{2(1)}\\\\y=\frac{-3-\sqrt{5}}{2}\\[/tex]
Your final answers are:
[tex]y=-\frac{3+\sqrt{5}}{2}[/tex] AND [tex]y=-\frac{3-\sqrt{5}}{2}[/tex]
please help I will give brainless.
15% answered swimming.
39 people said swimming, so 39 people is 15% of the total people surveyed.
To find the total number of people, divide 39 by 15%:
39 / 0.15 = 260
There were 260 total people surveyed.
6 is 30% of, please answer
Answer:
20
Step-by-step explanation:
30% × ? = 6
? =
6 ÷ 30% =
6 ÷ (30 ÷ 100) =
(100 × 6) ÷ 30 =
600 ÷ 30 =
20
a small baseball stadium 6552 seats the seats are evenly distributed among 18 different section. how many seats are in each section of the stadium
Answer:
3. 364
4. F 11.45
Step-by-step explanation:
3. 1/18 of the total number of seats in the stadium are found in each section. That number is ...
1/18 · 6552 = 364 . . . . seats in one section
__
4. The numbers round to tenths as follows:
F — 11.5
G — 11.6
H — 11.3
J — 12.5
Perhaps you can see that the one that rounds to 11.5 is ...
F 11.45
Answer:
364
Step-by-step explanation:
6552/ 18
The bear population of yellowstone national park goes from 230 bear to 300 bears. What is the percent of change?
so the difference is 300 - 230 = 70.
now, if we take 230 to be the 100%, what is 70 off of in percentage?
[tex]\bf \hspace{34em}|\\\\ \begin{array}{ccll} amount&\%\\ \cline{1-2} 230&100\\ 70&x \end{array}\implies \cfrac{230}{70}=\cfrac{100}{x}\implies \cfrac{23}{7}=\cfrac{100}{x} \\\\\\ 23x=700\implies x=\cfrac{700}{23}\implies x\approx 30.43[/tex]
Answer:23%
Step-by-step explanation:
300-230=70
70/300=0.23(3 goes on forever)
So 23%
subtract the original with the decreased value, then divide the answer you get with 300. That should equal 0.23 or 23%
Determine whether the solids are similar.
Answer:
The solids are similar.
Step-by-step explanation:
Every linear dimension of the larger solid is twice that of the smaller solid. Since the scale factor is the same in every direction, the figures are similar.
Vivian is solving the equation 0=x2−5x−4 0 = x 2 − 5 x − 4 using the quadratic formula. Which value is the negative real number solution to her quadratic equation? Round to the nearest tenth if necessary. -5.7 -4 -1 -0.7
-0.7
steps:the quadratic formula is
[tex] \frac{ - b + - \sqrt{ {b}^{2} - 4ac } }{2a} [/tex]
substitute the correct values in
[tex] \frac{ - ( - 5) + - \sqrt{ {( - 5)}^{2} - 4(1)( - 4) } }{2(1)} [/tex]
where it says +- you would type this into your calculator with + AND THEN - to get two separate answers.
when you type + you get the answer of: 5.701562119...
when you type - you get the answer of:
-0.7015621187...
when you round to the nearest tenth you get -0.7
hope this helps! :)
have a great day ~ •lipika•
Given the function f(x) = 4|x – 5| + 3, for what values of x is f(x) = 15?
Start with the definition of absolute value |x|:
|x| = x for x>=0
|x| = -x for x<0
We are given a function f(x) and are asking when is that function = 15.
This means we are asking:
4|x-5| + 3 = 15, or simplified:
|x-5| = 3
but at this point further simplification seems stuck on the absolute value. Time to use the above definition, and we split this into two cases:
|x-5| = 3 -->
Case 1: (x-5) = 3 for (x-5)>=0
Case 2: -(x-5) = 3 for (x-5)<0
and now we can proceed and solve each case separately:
Case 1: x = 8 for x >= 5
Case 2: x = 2 for x < 5
Give it sharp look and realize that both cases are valid because each case has a solution of an x that is "allowed" by the inequality condition (meaning it is not contradicting it), therefore both solutions
x1 = 2 and x2 = 8
are valid solutions to the equation 4|x-5|+3=15. For both the function f(x) will have the value 15 (and please do verify for yourself!)
Read the statement.
Doubling the dimensions of a rectangle increases the area by a factor of 4.
If p represents doubling the dimensions of a rectangle and q represents the area increasing by a factor of 4, which are true? Check all that apply.
1)p → q represents the original conditional statement.
2)~p → ~q represents the inverse of the original conditional statement.
3)q → p represents the original conditional statement.
4)~q → ~p represents the converse of the original conditional statement.
5)p → ~q represents the contrapositive of the original conditional statement.
Answer:
1) and 2)
Step-by-step explanation:
Let us see the correction in the rest of the statements.
3) p→q represent the original conditional statement.
4) ~q → ~p represents the contrapositive of the original conditional statement
5) contrapositive of the original conditional statement will be ~q → ~p
There is one more implication called Converse of the original conditional statement . It is represented as q→p
You have a coin bank in the shape of a cylinder. It has a radius of 1.5 inches and a height of 5 inches. What is the surface area of the coin bank? Use 3.14 to approximate pi. Round your answer to the nearest hundredth.
Answer:
Step-by-step explanation:
The top and the bottom are easiest to find.
Area_top = pi*r^2
r = 1.5
Area_top = 3.14 * 1.5^2
Area_top = 3.14 * 2.25
Area_top = 7.065
But there are 2 of them (top and bottom) which is 14.13
================
Area of the body of the cylinder
Area body = circumference of the circle * height
C = 2*pi*r
r = 1.5
C = 2 * 3.14 * 1.5
C = 9.42
Area body = 9.42 * 5
Area body = 47.1
===================
The sum of both of these is the answer you want
47.1 + 14.13 = 61.23 square inches.
I found the answer!
6 points! Markin Brainliest! 3D Geometry! rectangular prism has a length of 6 cm and a width of 2 cm and a height of 5 cm what is the surface area of the prism enter your answer in the Box.
[ 104 ] cm^2
^
Thats the box btw
The surface area is 104 cm²
Step-by-step explanation:The surface area of rectangular prism is given by
A=2 (wl + hl + hw)
by putting the values we get
A =2 ( 2x6 + 5x6 + 5x2)
A = 104
I NEED HELP NOW!!!
Monelle started an arithmetic sequence. The first four terms of her sequence are shown below.
13,9,5,1,...
1.) What is the common difference for Monelle's sequence? Show or explain how you got the answer
2.) What is the sixth term of Monelle's sequence? Show or explain how you got the answer.
Fin started a geometric sequence. The first four terms of his sequence are show below.
162,54,18,6,...
3.) What is the sixth therm of Fins sequence? Show or explain how you got the answer.
4.) Write an expression that represents the ᵗʰ term of Fins sequence.
Answer: 1. Common difference= 4 . 2.The sixth term would be -7.
Step-by-step explanation: 1. 13-9=4 and 9-5=4 and 5-1=4. 2. Sixth term: 1-4=-3 And -3-4=-7.
The common difference in Monelle's arithmetic sequence is -4, and the sixth term is -7. For Fin's geometric sequence, the ratio is 1/3, with the sixth term being 2. The formula for the nth term of Fin's sequence is 162 * (1/3)^(n-1).
Explanation:In mathematical terms, an arithmetic sequence is a number sequence in which the difference between every two successive members is a constant. From the first part of your question, in Monelle's arithmetic sequence: 13, 9, 5, 1,... the common difference can be calculated by subtracting any term from the one that comes after it. In this case, 9 - 13 or 5 - 9 will give us the common difference, which is -4.
Once you've found the common difference, you can calculate the sixth term by taking the first term (13) and adding the common difference (-4) times the number of terms minus 1 (for the sixth term, this would be 5 times). This gives us 13 - 4 * 5 = -7 for the sixth term of Monelle's sequence.
Conversely, a geometric sequence is a sequence of numbers where each term after the first is found by multiplying the previous term by a fixed, non-zero number called the 'ratio'. Looking at Fin's sequence: 162, 54, 18, 6, ..., we can find the ratio by dividing any term by the one before it. So 54 divided by 162, or 18 divided by 54, gives us the common ratio of 1/3. To find the sixth term, we multiply the first term by the ratio raised to the power of (the term's position number minus 1). The sixth term then is 162 * (1/3)^5 = 2.
The expression that represents the ᵗʰ term of Fin's sequence can be written general form as a * r^(n-1), where 'a' is the first term, 'r' is the ratio, and 'n' is the term's position number. In this case, the formula for the nth term of Fin's sequence would be 162 * (1/3)^(n-1).
Learn more about Sequences here:https://brainly.com/question/36944481
#SPJ2
The container that holds the water for the football team is 3/4
full. After pouring out 7 gallons of water, it is 1/2 full. How many gallons can the container hold?
Answer:
28 Gallons
Step-by-step explanation:
This one is really easy, so i want you to look at my steps:
1. Gather all given information, container is 3/4, 7 gallons are poured out to make it 1/2 full.
2. Find a common denominator for the fractions 1/2 and 3/4, this would be 4.
3. Make them both the same denominator, 2/4 and 3/4.
4. Subtract the remaining amount from the original amount to see how much 7 gallons made up, 3/4 - 2/4 = 1/4
5. Now that you know that 7 gallons made up 1/4 of the container, you can just multiply 7 by 4 to get the total amount of gallons that can fit in the container.
7 * 4 = 28 gallons is the max that the container can hold.
Answer:
28 gallons
Step-by-step explanation:
Got it right on test
Before it started to rain, Bobby cut 1 8 of the grass in his yard and Danny cut 1 5 of the grass in the yard. Both boys were disappointed because they were not able to cut the entire yard.
Which statement is TRUE?
A)Together the boys didn't even cut half the yard. B) The boys were able to cut more than half the yard. C) The boys cut almost three-fourths of the yard. D) Together the boys cut almost the entire yard.
It’s B. The boys were able to cut more than half the yard.
Answer:
A) Together the boys didn't even cut half the yard.
Step-by-step explanation:
The amount cut was ...
1/8 + 1/5 = 5/40 +8/40 = 13/40
This amount is less than half = 20/40, so choice A is appropriate.
_____
You can reason about these fractions several ways:
1. half is 2 1/2 fifths. 1/8 is less than 1/5, so 1/5+1/8 < (2 1/2)/5.
2. half is 4/8. 1/5 is more than 1/8 but is less than 2/8. 1/8 + 1/5 < 3/8 < 1/2
3. 1/5 < 1/4; 1/8 < 1/4; 1/2 = 2/4, so two amounts less than 1/4 cannot be more than 1/2.
can someone help me with 2.5
Answer:
A
Step-by-step explanation:
Givens
The board has been placed 1/2 the length of the 10 foot ladder across to 1/2 the length of the 15 foot ladder. That means that the rung holding the board on the 10 foot ladder is 1/2 up the length of the 10 foot ladder. That makes the hypotenuse of the small triangle = 5The distance from where the ladders meet to the paint = xFind x
x^2 + 3^2 = 5^2
x^2 + 9 = 25 Subtract 9 from both sides
x^2 = 25 - 9 Combine
x^2 = 16 Take the sqrt of both sides
x = 4
Find the height
The ratio of all dimensions involving the 2 ladders and the board is 1 to 2.
So the total height from where the ladders meet to the ground is 2*4 = 8
Answer: The distance from the bucket to the ground is 1/2 * 8 = 4
Answer: A
I need some help plz
Answer:
one solution is (0, -2)
Step-by-step explanation:
The line y = -x is the boundary of the solution space of the first inequality. The less-than symbol (<) tells you that the line will be dashed and the shading will be below it. The line has a slope of -1 and goes through the y-intercept point (0, 0).
The line y = x - 2 is the boundary of the solution space for the second inequality. The less-than-or-equal-to symbol (≤) tells you the line will be solid (or equal to) and the shading will be below it (less than). The line has a slope of +1 and goes through the y-intercept point (0, -2).
The area of the graph where the shadings overlap is the solution space for the system of inequalities. Any point in that area will do, including points on the solid line where y < -x. (0, -2) is one such point.
Graph the line passing through the given point and having the indicated slope. through (3, negative 2) with slope minus−three fifths 3/5
Answer:
See the attachment
Step-by-step explanation:
A slope of -3/5 means the line drops 3 units for each 5 units it goes to the right. Then you can find another point on the line by going 5 uints to the left (to x=-2) and 3 units up (to y=1).
Plot the given point and the one just computed and draw the line through them.
If two legs of a right triangle are 2 inches and 3 inches, can the hypotenuse be 4 inches? Justify your answer.
Answer in complete sentences and include all relevant calculations.
Answer:
No
Step-by-step explanation:
The only consecutive integers that satisfy the Pythagorean theorem are 3, 4, and 5.
___
4^2 ≠ 2^2 + 3^2
16 ≠ 4 + 9 . . . . . . . an attempt at applying the Pythagorean theorem to the given numbers fails.
Final answer:
Using the Pythagorean theorem, a right triangle with legs of 2 inches and 3 inches cannot have a hypotenuse of 4 inches. The correct length of the hypotenuse is the square root of 13, which is approximately 3.61 inches.
Explanation:
To determine whether a right triangle can have sides of 2 inches, 3 inches, and a hypotenuse of 4 inches, we use the Pythagorean theorem. This theorem states that for any right 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). Mathematically, it's expressed as a² + b² = c².
Let's input the given values into this equation. For the legs measuring 2 inches and 3 inches, the equation would look like this: 2² + 3² = c², which simplifies to 4 + 9 = c². This results in 13 = c². Taking the square root of both sides gives us c = √13. Therefore, the hypotenuse must be the square root of 13, which is approximately 3.61 inches, not 4 inches.
Thus, a right triangle with legs of 2 inches and 3 inches cannot have a hypotenuse of 4 inches. The actual length of the hypotenuse according to the Pythagorean theorem is approximately 3.61 inches.
( l = P + P • r • t )
Answer:
$19,720
Step-by-step explanation:
Put the given numbers into the formula and do the arithmetic.
P = principal amount, $17,000
r = interest rate, 8% = 0.08
t = 2 years
"I" = P + Prt
I = $17000 + $17000·0.08·2 = $17000 +2720
I = $19,720
_____
I put "I" in quotes because the variable capital-I is usually used in this context to refer to the amount of interest paid, not the entire repayment amount. However, that is what your formula is. It works for what you want.
a survey was given on hours of practice per week and the number of math questions answered correctly. The graph shows the results of the survey. The scatter plot indicates which of the following A.) a positive correlation B.) a negative correlation C.) no correlation
A) a positive correlation
What linear function represents the line given by the point slope equation y+7= 2/3(x+6)?
Answer:
the correct answer is the 3rd one
Answer:
the third option is correct
Step-by-step explanation:
How do I solve this, and what is the answer? please and thank you.
Answer:
A. (x +8) + (-4x+31)/(x^2+2x+1)
Step-by-step explanation:
When you perform long division of polynomials, the first quotient term is the ratio of the highest-degree terms in the numerator and denominator: x^3/x^2 = x.
This fact eliminates all but choices A and C.
The denominator of the remainder term is the denominator of the original expression, so will be x^2 +2x +1, as shown in choice A.
__
So, simply based on a couple of facts about long division (that you learned in the early elementary grades), you can make the correct choice of answer without actually working the problem in detail.
_____
This is a polynomial long division problem. It is worked in virtually the same way that numerical long division problems are worked: first you find a quotient term, then you multiply that by the divisor and subtract the result from the dividend. The difference is the new dividend. These steps are identical to numerical long division.
For polynomial long division, instead of lining up the digits with the same place value, you line up the terms with the same degree of the variable.
As mentioned above, the quotient term is computed only from the highest-degree terms of dividend and divisor, so that part is actually simpler than for numerical long division.
A dividend that is of lower degree than the divisor is considered to be the remainder. As with numerical long division, it can be expressed as a fraction with the divisor as the denominator.
Numerical example: 18/7 = 2 remainder 4 or 2 4/7.
A manufacturer uses a mold to make a part in the shape of a triangular prism. The dimensions of this part are shown below.
Which estimate is closest to the volume in cubic millimeters of the part?
A. 65
B. 125
C. 249
D. 446
Answer:
B. 125
Step-by-step explanation:
If you compute the actual volume as the product of the area of the triangle and the length of the piece, you get ...
V = Bh = (1/2)(14.4 mm)(2.1 mm)·(8.25 mm) = 124.74 mm
That is closest to choice B, 125 mm.
___
You can estimate the volume by rounding the dimensions. The triangle can be considered to be a rectangle of the same base width and half the height, so you are looking to estimate the product ...
(8.25 mm)(14.4 mm)(1.05 mm)
That's about 8 × 15 × 1 = 120 . . . . mm³.
Certainly, this is an estimate sufficiently close to allow you to choose the correct answer.
fill 350 milliliter bottles from a 30 liter drum how many bottles
Answer:
85
Step-by-step explanation:
0.350 L × n = 30 L . . . . . where n is the number of bottles.
Divide by 0.350:
n = (30 L)/(0.350 L) ≈ 85.7
85 bottles can be filled, and one can be partially filled.
_____
Of course, you know the SI prefix milli- means 1/1000, so 350 mL = 350/1000 L = 0.350 L. When you do the division indicated above, ...
(30 L)/(0.350 L)
the units of liters cancel, and you are left with the number of bottles.
what is the area of this figure
Answer:
54 square units
Step-by-step explanation:
A line (red in the attachment) can divide the figure into two triangles and a trapezoid. The formulas for the areas of these are ...
area of a triangle = (1/2)bh . . . . . where b is the base and h is the height
The triangle on the upper left has a base of 3 and a height of 2, so an area of ...
upper left triangle area = (1/2)(3)(2) = 3 square units . . . . area shown in red
The triangle on the upper right has a base of 6 and a height of 1, so an area of ...
upper right triangle area = (1/2)(6)(1) = 3 square units . . . . area shown in yellow
___
The formula for the area of a trapezoid is ...
area of a trapezoid = (1/2)(b1 +b2)h . . . . where b1 and b2 are the lengths of the parallel bases, and h is the height
The trapezoid has an upper base length of 9 and a lower base length of 7, and a height of 6, so its area is ...
area of bottom trapezoid = (1/2)(9 + 7)(6) = 48 square units . . . . area shown in green
___
Then the total area of the figure is the sum of the areas of its non-overlapping parts:
total area = upper left triangle area + upper right triangle area + trapezoid area
= (3 + 3 + 48) square units = 54 square units
Factor form of x^2-x-30
Answer:
(x - 6)(x + 5)
Step-by-step explanation:
You know that in order to get x^2 there has to be two x's so you get:
(x ...)(x...)
Then you also know that two numbers have to multiply together and equal 30 but also have a sume of -1. So you get:
(x - 6)(x + 5)
Answer: [tex](x+5)(x-6)[/tex]
Step-by-step explanation:
To solve the exercise you must keep on mind the following:
- You must find two numbers whose sum is -1 and whose product is -30.
- These numbers would be 5 and -6.
Therefore, you can factor the quadratic equation given in the problem above [tex]x^2-x-30[/tex], as you can see below:
[tex]x^2-x-30\\(x+5)(x-6)[/tex]
write the point intercept form and the slope-intercept form.
(-5,1) and (2,-5)
Can someone help me out??
Answer:
see below
Step-by-step explanation:
The figure is completely symmetrical about line RT so ...
ST = UT = 23
RU = RS = 8
SV = UV = 5
SU = SV + UV = 10
Solve the word problem.
Lee can frame a cabin in 4 days less than Ron. When they work together, they will do the job in 4 days. How long would each of them take to frame the cabin alone?
Ron
a0 days
Lee
a1 days
Answer:
Ron: 6+2√5 days ≈ 10.47 days
Lee: 2+2√5 days ≈ 6.47 days
Step-by-step explanation:
Let L represent the number of days it takes Lee to frame a cabin. Then it take L+4 days for Ron to frame it. Working together, they take 4 days. Then their rates, in cabins per day, add up as ...
1/L + 1/(L+4) = 1/4
Multiplying by the product of denominators, we get ...
4(L+4) +4L = L(L+4)
Subtracting the left side gives ...
L^2 -4L -16 = 0
Completing the square, we can write this as ...
L^2 -4L +4 = 20
(L -2)^2 = 20
L = 2 + √20 = 2 +2√5 ≈ 6.47
Lee takes 2+2√5 ≈ 6.47 days to frame a cabin.
Ron takes 6+2√5 ≈ 10.47 days to frame a cabin.
Plzzz answer all of these questions to get 100 pointd
Answer:
1. 42.8 °C
2. Aceves' class: $133.33; Baca's class: $266.67; Canyon's class: $200.
Step-by-step explanation:
1.) The difference between two numbers is found by subtraction. Since we want to report the positive difference, we can subtract the smaller number from the larger:
-21.2 °C - (-64 °C) = (64 -21.2) °C = 42.8 °C
The temperature must drop 42.8 °C more for the antifreeze to solidify.
_____
2.) We want to divide the prize money in the ratio
1200 : 2400 : 1800 = 2 : 4 : 3
There are 2+4+3 = 9 total ratio units, so each one must stand for $600/9 = $66 2/3.
Then the money to Aceves' class is ...
2 × $66 2/3 = $133 1/3 = $133.33
And the money to Baca's class is ...
4 × $66 2/3 = $266 2/3 = $266.67
Finally, the money to Canyon's class is ...
3 × $66 2/3 = $200.00
___
Note on the division:
The 1/3 cent that Aceves' class should have gotten goes to Baca's class in the above scenario. It might make sense for the classes to donate $6 to the school and divide the remaining $594 as $132 : $264 : $198. If they actually want the pennies, they could donate $0.06 to the school and split the result as $133.32 : $266.64 : $199.98.
Answer:
Step-by-step explanation:
Answer:
1. 42.8 °C
2. Aceves' class: $133.33; Baca's class: $266.67; Canyon's class: $200.
Step-by-step explanation:
1.) The difference between two numbers is found by subtraction. Since we want to report the positive difference, we can subtract the smaller number from the larger:
-21.2 °C - (-64 °C) = (64 -21.2) °C = 42.8 °C
The temperature must drop 42.8 °C more for the antifreeze to solidify.
_____
2.) We want to divide the prize money in the ratio
1200 : 2400 : 1800 = 2 : 4 : 3
There are 2+4+3 = 9 total ratio units, so each one must stand for $600/9 = $66 2/3.
Then the money to Aceves' class is ...
2 × $66 2/3 = $133 1/3 = $133.33
And the money to Baca's class is ...
4 × $66 2/3 = $266 2/3 = $266.67
Finally, the money to Canyon's class is ...
3 × $66 2/3 = $200.00
___
Note on the division:
The 1/3 cent that Aceves' class should have gotten goes to Baca's class in the above scenario. It might make sense for the classes to donate $6 to the school and divide the remaining $594 as $132 : $264 : $198. If they actually want the pennies, they could donate $0.06 to the school and split the result as $133.32 : $266.64 : $199.98.
How can you use a point on the graph of f –1(x) = 9x to determine a point on the graph of f(x) = log9x?
Whenever you can invert a function, you have that the graphs of [tex]f(x)[/tex] and its inverse [tex]f^{-1}(x)[/tex] are reflected with respect to the line [tex]y=x[/tex]
So, given any point on the graph of [tex]f^{-1}(x)[/tex], you can simply swap its coordinates to get the correspondent point on the original function [tex]f(x)[/tex]
As an example, all exponential functions pass through the point [tex](0,1)[/tex], while all the logarithmic functions pass through the point [tex](1,0)[/tex]
Answer: switch x and y coordinates
Step-by-step explanation: