The value of b is -6.
Explanation:To find the value of b, we need to solve the quadratic equation b2 + 2b - 24 = 0.
Since b < 0, we can eliminate the positive solution.
We can factor the equation by finding two numbers whose product is -24 and sum is 2.
The numbers are -4 and 6.
So, the factored form of the equation is (b - 4)(b + 6) = 0.
Setting each factor equal to zero, we find that b = -6 or b = 4.
Since b < 0, the value of b is -6.
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Final answer:
Using the quadratic formula, we find that b = -6 (option A), considering the requirement that b < 0 for the equation b² + 2b - 24 = 0.
Explanation:
To find the value of b given the quadratic equation b² + 2b − 24 = 0 and knowing that b is less than zero, we can use the quadratic formula:
The quadratic formula is −b ± √(b² − 4ac /2a), where a, b, and c are coefficients from the quadratic equation in the form ax2 + bx + c = 0.
In this case, a = 1, b = 2, and c = −24. Applying these values to the quadratic formula, we have:
−(2) ± √((2)² − 4(1)(−24) /2(1))
The discriminant part of the formula, b² − 4ac, equals (2)² − 4(1)(−24) = 4 + 96 = 100. Therefore, the square root of the discriminant is 10.
Simplifying further, we have:
(−2 ± 10) / 2 = −6 or +8
Since b < 0, we disregard the positive solution and consider b = −6, which is option A.
The value of a car decreases as shown in the table below. Which statements are true? Check all that apply.
well.. what are the statements?
Answer: The function that best represents the data is f(x)=24,512(0.755)^x.
The function decrease indefinitely.
It is reasonable to interpolate to the value of the car at 4.5 years.
Step-by-step explanation:
took the test
jorge solves the equation 4x-(x+2)+6
Answer:
Step-by-step explanation:
2x+6
<3
Callie
Answer:
The equation that is solved by George is
=4 x - (x+2) +6
=4 x -x -2 +6-------Using Distributive property of Multiplication with respect to Addition→ a×(b+c)=a×b+a×c
→Adding and subtracting like terms
=3 x+4
Show work please!!! Solve the equation by completing the square. If necessary, round to the nearest hundredth.
x^2-18x=19
A. 1;19
B.-1;19
C.3;6
D.-3;1
Solve x^2-81=0
A.0
B.-9
C.-9,9
D.9
Answer:
1. B 2. C
Step-by-step explanation:
1. x^2-18x+(18/2)^2=19+(18/2)^2
(x-18/2)^2=100
(x-9)^2=100
x1= -1 x2= 19
2. x^2=81
x=+-9
x1=-9 x2=9
Olivia is making bead bracelets for her friends. She can make 3 bracelets in 15 minutes.What does the proportionality constant represent in this situation?
Answer:
The amount of time it takes for her to make 1 bracelet.
Step-by-step explanation:
You can set up an equation as 3k = 15, and then solve it by dividing by 3 on both sides, getting an answer of 5.
Answer:
Step-by-step explanation:
The proportionality constant of 5 minutes per bracelet means it takes Olivia 5 minutes to make 1 bracelet.
what is the product of (a + 3)(a - 2)
Answer: [tex]a^2+a-6[/tex]
Step-by-step explanation:
To solve the exercise you must apply the following proccedure:
- Apply the distributive property.
- Keepn on mind that when you multiply two powers with equal base, you must add the exponents.
- Add like terms.
Then:
[tex](a)(a)-(a)(2)+(3)(a)-(3)(2)=a^2-2a+3a-6=a^2+a-6[/tex]
Answer:
[tex]\large\boxed{(a+3)(a-2)=a^2+a-6}[/tex]
Step-by-step explanation:
Use FOIL: (a + b)(c + d) = ac + ad + bc + bd
[tex](a+3)(a-2)=(a)(a)+(a)(-2)+(3)(a)+(3)(-2)\\\\=a^2-2a+3a-6\qquad\text{combine like terms}\\\\=a^2+a-6[/tex]
Which of the following equations describes a relationship of inverse variation between input and out put
Answer:
option (A)
output = constant / input
Step-by-step explanation:
Inverse relationship between two input and output means that they both moves in opposite directions, if one increases than other decreases.
Equation to describe relationship of inverse variation between input and output will be as following
output ∝ 1 / inputto remove this sign of proportionality
output = k / inputwhere k is a constant
PLZ HELP! Need this DESPERATELY! Worth 15 points and will mark Brainliest! Thx so much :)
Answer:
#1 (1,10),(2,9),(2,8),(4,7),(5,6),(6,5),(7,4),(8,3),(9,2),(10,1). #2 (1,18),(2,9),(3,6),(6,3),(9,2),(18,1)
In a lab, a 30% acid solution is being mixed with a 5% acid solution to create a 10% acid solution. What is the ratio of the amount of the 30% solution to the amount of 5% solution used to create the 10% solution? 1:3 1:4 1:5 1:6
Answer:
1 : 4
Step-by-step explanation:
Let x represent the amount of 30% solution for 1 unit of 5% solution. Then the amount of acid in the mix is ...
0.30x + 0.05·1 = 0.10·(x +1)
0.30x + 0.05 = 0.10x + 0.10 . . . . eliminate parentheses
0.20x = 0.05 . . . . . . . . . . . . . . . . subtract 0.05+0.10x
x = 0.05/0.20 = 1/4
That is, the ratio x : 1 is 1 : 4.
Answer:
The ratio of the amount of the 30% solution to the amount of 5% solution will be 1 : 4.
Step-by-step explanation:
Suppose, the amount of 30% acid solution is [tex]x[/tex] and the amount of 5% acid solution is [tex]y[/tex].
So, the total amount of the mixture [tex]= x+y[/tex], which is 10% acid solution.
Amount of acid in 30% solution [tex]= 30\%\ of\ x=0.30x[/tex]
Amount of acid in 5% solution [tex]=5\%\ of\ y= 0.05y[/tex]
Amount of acid in the mixture [tex]=10\%\ of\ (x+y)=0.10(x+y)[/tex]
Now, the equation will be......
[tex]0.30x+0.05y=0.10(x+y)\\ \\ 0.30x+0.05y=0.10x+0.10y\\ \\ 0.30x-0.10x=0.10y-0.05y\\ \\ 0.20x=0.05y\\ \\ \frac{x}{y} =\frac{0.05}{0.20} =\frac{5}{20}=\frac{1}{4}\\ \\ x:y=1:4[/tex]
So, the ratio of the amount of the 30% solution to the amount of 5% solution will be 1 : 4.
penny and luc have found a treasure chest in the garden. The chest contains 150 gold couns . Penny and luc share the coins between them in the ratio 2:1 . how many gold coins do they each get?
75 coins because you take 150/2 and get 75 coins
Rewrite in standard form |x|-4=0
Answer:
x = ±4
Step-by-step explanation:
we are given |x|-4=0
The first step is to add 4 on both sides of the equation;
|x|-4+4=0+4
|x|=4
Getting rid of the absolute symbol implies we have to add the positive and negative symbols to the right hand side of the equation;
x = ±4
1. Find the area of the composite figure.
2. The previous diagram represents a scale drawing of a hexagonal garden. The scale factor is 1cm=0.5m. What is the area of the garden? A=a12m2 B=a16m2 C=a24m2 D=a240m2
3. For which shape would you use the formula (bh)+(1/2bh) to find the area?
4. Which shapes could this hexagon be decomposed into to find its area? Choose all that apply. A. Two trapezoids B. Six triangles C. One rectangle and two triangles D. Two parallelograms
5. Which formulas could be use to find the area of the composite shape? Choose all that apply. A=2bh A=2(1/2bh) A=bh+bh A=1/2bh+bh
The correct formulas for the composite shape are A. [tex]\( A = 2bh \)[/tex] and B. [tex]\( A = 2\left(\frac{1}{2}bh\right) \)[/tex].
1. Find the area of the composite figure.
You can use the formula for the area of a parallelogram: [tex]$A = bh$[/tex]. Since there are two parallelograms, you add their areas:
[tex]\[ A = 2bh \][/tex]
2. The previous diagram represents a scale drawing of a hexagonal garden. The scale factor is 1cm=0.5m. What is the area of the garden?
If the scale factor is 1 cm = 0.5 m, the area in the drawing needs to be scaled up. The scale factor squared is used for areas. Therefore,
[tex]\[ \text{Area in meters}^2 = (\text{Area in centimeters}^2) \times (\text{Scale factor})^2 \][/tex]
3. For which shape would you use the formula [tex]\((bh) + \left(\frac{1}{2}bh\right)\)[/tex] to find the area?
This formula represents the sum of the areas of a parallelogram and a triangle. So, you would use this formula for a shape that consists of both a parallelogram and a triangle.
4. Which shapes could this hexagon be decomposed into to find its area? Choose all that apply.
Since a hexagon has six sides, it can be decomposed into various combinations of shapes. All the given options are valid:
- A. Two trapezoids
- B. Six triangles
- C. One rectangle and two triangles
- D. Two parallelograms
5. Which formulas could be used to find the area of the composite shape? Choose all that apply.
The correct formulas for finding the area of the composite shape (made up of two parallelograms) are:
- A. [tex]\(A = 2bh\)[/tex]
- B. [tex]\(A = 2\left(\frac{1}{2}bh\right)\)[/tex]
So, the correct choices are A and B.
Raffaello Sanzio’s bank granted him a single-payment loan of $9,650. He agreed to repay the loan in 146 days at an ordinary interest rate of 7.75%. What is the maturity value of the loan?
Answer:c
Step-by-step explanation:
$9953.30
What are the x intercepts of the quadratic function? Y=-x^2+2x-1
Answer:
x = 1
Step-by-step explanation:
Given in the question the equation
y = -x² + 2x - 1
To find the x-intercept, substitute in 0 for y
0 = -x² + 2x - 1
To find value of x use quadratic equation
x = -b ± √b²-4ac / 2a
here a = -1
b = 2
c = -1
x1 = -2 + √2²-4(-1)(-1) / 2(-1)
= -2 + 0 / -2
= -2 / -2
= 1
x2 = -2 - √2²-4(-1)(-1) / 2(-1)
= -2 - 0 / -2
= -2 / -2
= 1
a football player attempts two passes in overtime. each pass attempt results in a completion, an incompletion, or a turnover.
The correct answer is C) 7.
In order to determine the number of different outcomes for the two pass attempts in overtime, we need to consider the possibilities for each pass attempt. Let's break it down step by step:
For the first pass attempt, there are three possible outcomes: completion, incompletion, or turnover. Let's say the first pass attempt resulted in a completion.
For the second pass attempt, again there are three possible outcomes: completion, incompletion, or turnover. Since we are considering all possible outcomes, we will consider each possibility for the second pass attempt separately.
If the first pass attempt was a completion and the second pass attempt is also a completion, then we have one possible outcome.
If the first pass attempt was a completion and the second pass attempt is an incompletion, then we have one possible outcome.
If the first pass attempt was a completion and the second pass attempt is a turnover, then we have one possible outcome.
Now, let's consider the other possibilities for the first pass attempt.
If the first pass attempt was an incompletion and the second pass attempt is a completion, then we have one possible outcome.
If the first pass attempt was an incompletion and the second pass attempt is also an incompletion, then we have one possible outcome.
If the first pass attempt was an incompletion and the second pass attempt is a turnover, then we have one possible outcome.
Lastly, let's consider the remaining possibility for the first pass attempt.
If the first pass attempt was a turnover, then it does not matter what the outcome of the second pass attempt is, as the possession has already changed. Therefore, we have one possible outcome in this case.
Adding up all the possible outcomes, we have a total of 7 different outcomes for the two pass attempts in overtime.
Therefore, the correct answer is C) 7.
Complete question :-
A football player attempts two passes in overtime. Each pass attempt results in a completion, an incompletion, or a turnover. A) 8 B) 14 C) 7 D) 6
a rectangular Garden has a length of 6.8 M and a perimeter of 20.6 M what is the width of the garden
Answer:
First, you add 6.8 and 6.8 together, since it's a rectangular garden and the length is the same on both sides of the rectangle. This will equal 13.6. Then you subtract 13.6 from 20.6. You will get 7. Divide this in half and you will get 3.5. 3.5 is the width.
Step-by-step explanation:
My question is 33 divided by 6789 so yeah and need the steps
33÷6789 or 6789÷33? 33÷6789 would give you a decimal less than 1, 6789÷33 would give you a number greater than 1 possibly with a remainder.
In similar polygon, corresponding angles should not have equal measures.
True or False
Answer: False
Step-by-step explanation: Similar means the ability for two shapes to be congruent to each other if dilated.
Also, corresponding angles are angles that have the same length. This means that this statement is indeed False.
What is the value of X in the diagram
Answer:
X = 25.28
Step-by-step explanation:
By Pitagoras Theorem:
9^2 + Y^2 =24^2
81 + Y^2 = 576
Y^2 = 495
Y = 22.25
Now Y is one catet for to find X
X^2 = 12^2 + 22.5^2
X^2 = 144 + 495
X^2 = 639
X = 25.28
Best regards
Answer:
x = 32
Step-by-step explanation:
The segments formed by the angle bisector will form a correct proportion when paired with their adjacent triangle sides
so
9/24 = 12/x
Cross multiply
9x = 24 * 12
9x = 288
x = 32
Jeff makes fruit punch using 1 quart of orange juice 2 pints of pineapple juice 8 cups of tropical punch and 8 pints of ginger ale. How many gallons of fruit punch does Jeff make.
Answer:
2 gallons
Step-by-step explanation:
So say we make everything into cups. We know there is 4 cups in a quart and 2 cups in a pint. So if we do the math you are really adding
4 cups + 4 cups + 8 cups + 16 cups
So that would be 32 cups.
We also know there is 16 cups in a gallon. Since we know that then we can do
32 cups ÷ 16 cups
That would be 2 gallons!
Hope this helps!
Final answer:
Jeff makes 2 gallons of fruit punch by converting all the liquid measurements to pints and then summing them up to convert to gallons.
Explanation:
To determine how many gallons of fruit punch Jeff makes, we need to convert all the measurements to the same unit and then add them together. Here are the conversions we'll use:
1 quart = 2 pints
1 pint = 2 cups
1 gallon = 4 quarts
1 gallon = 8 pints
1 gallon = 16 cups
Now let's convert everything to pints since most of the units provided are in pints:
Orange juice: 1 quart = 2 pints
Pineapple juice: 2 pints
Tropical punch: 8 cups = 4 pints
Ginger ale: 8 pints
Add all the pints together:
2 pints (orange juice) + 2 pints (pineapple juice) + 4 pints (tropical punch) + 8 pints (ginger ale) = 16 pints total
Now convert pints to gallons:
16 pints ÷ 8 pints/gallon = 2 gallons
So, Jeff makes 2 gallons of fruit punch.
Which lines in the graph have a slope greater than 1 but less than 2?
line 1
line 2
line 3
line 4
line 5
I think that is line 5
Answer:
Lines 3 & 4
Step-by-step explanation: To find slope you calculate rise/run.
Line 1: 6/2= 3
Line 2: 6/3= 2
Line 3: 6/4= 1.5
Line 4: 6/5 = 1.2
Line 5: 6/6= 1
Lines 3 and 4 are the only two that have a slope that fall between 1 and 2. Notice it said greater than and less than but not equal to.
if the surface area is 6.8ft what is the area in each triangle
1.7 ft2 If the surface area is 6.8 ft2 then 1.7ft2 x 4 =6.8FT2
The area of each Triangle is 1.7 ft².
What is Surface Area?A 3-dimensional solid prism's surface area is determined by the form of its base. A prism's surface area is the total area occupied by the prism's faces. A prism is a flat-faced polyhedron. It lacks curves.
The surface area of a prism is the amount of total space occupied by the prism's flat faces. Determining a prism's surface area entails calculating the total space occupied by all the faces of that particular type of prism or the sum of the areas of all faces (or surfaces) in a 3D plane.
We have
Surface Area = 6.8 ft²
As, the Figure have 4 Triangle.
Then, the Area of each Triangle
= 6.8 / 4
= 1.7 ft²
Thus, the required Surface Area is 1.7 ft².
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5 + (7-7) + 4 is what property. A: identity property B: associative property
Answer:
A
Step-by-step explanation:
Solve the equation.
3.4 = –13.6 + (–3.4c) + 1.7c
Answer:
c= (-10)
Step-by-step explanation:
Simplify both sides of the equation then isolate the variable.
Answer:
c= 15.9
Step-by-step explanation:
Find the slope of the line through each pair of points.
(-14, -18), (6, 18)
Answer:
9/5
Step-by-step explanation:
To find the slope, use the slope formula.
[tex]m = \frac{y_2 - y_1}{x_2-x_1} = \frac{18 - -18}{6--14} = \frac{36}{20} =\frac{9}{5}[/tex]
Ms. Oliver sells bookmarks for $0.90 each to raise money to purchase new library books. So far, she has collected a total of $69.12. Ms.Oliver uses the equation below to represent her bookmark sales. Which of the following could represent the number of bookmarks Ms.Oliver has sold so far?
0.96b=69.12
A) 7 bookmarks
B) 69 bookmarks
C) 68 bookmarks
D) 72 bookmarks
The answer to you question is = c) 68 bookmarks
The correct answer is D.
0.96 x 72 = 69.12
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solve the sysyem of equations 3x+y=3 x+y=2
Answer:
{x = 1/2 , y = 3/2
Step-by-step explanation:
Solve the following system:
{3 x + y = 3 | (equation 1)
{x + y = 2 | (equation 2)
Subtract 1/3 × (equation 1) from equation 2:
{3 x + y = 3 | (equation 1)
{0 x+(2 y)/3 = 1 | (equation 2)
Multiply equation 2 by 3:
{3 x + y = 3 | (equation 1)
{0 x+2 y = 3 | (equation 2)
Divide equation 2 by 2:
{3 x + y = 3 | (equation 1)
{0 x+y = 3/2 | (equation 2)
Subtract equation 2 from equation 1:
{3 x+0 y = 3/2 | (equation 1)
{0 x+y = 3/2 | (equation 2)
Divide equation 1 by 3:
{x+0 y = 1/2 | (equation 1)
{0 x+y = 3/2 | (equation 2)
Collect results:
Answer: {x = 1/2 , y = 3/2
Answer:
[tex]\large\boxed{x=\dfrac{1}{2}\ and\ y=1\dfrac{1}{2}\to\left(\dfrac{1}{2},\ 1\dfrac{1}{2}\right)}[/tex]
Step-by-step explanation:
[tex]\left\{\begin{array}{ccc}3x+y=3\\x+y=2&\text{change the signs}\end{array}\right\\\\\underline{+\left\{\begin{array}{ccc}3x+y=3\\-x-y=-2\end{array}\right}\qquad\text{add both sides of the equations}\\.\qquad2x=1\qquad\text{divide both sides by 2}\\.\qquad\boxed{x=\dfrac{1}{2}}\\\\\text{Put the value of x to the second equation:}\\\dfrac{1}{2}+y=2\qquad\text{subtract}\ \dfrac{1}{2}\ \text{from both sides}\\\boxed{y=1\dfrac{1}{2}}[/tex]
the circumference of a circle is 34 pi. Find the diameter and radius
If the circumference is 34 Times PI that means that 34 is the diameter.
So that means that you can just divide the diameter by 2 to get the radius (Because the radius is half of the diameter.)
So the answer is the diameter is 34 and the radius is 17
Final answer:
The diameter of the circle with a circumference of 34π is 34 units, and the radius is half the diameter, which is 17 units.
Explanation:
The circumference of a circle is given by the formula C = πd, where C is the circumference, π (Pi) is approximately 3.14159, and d is the diameter of the circle. Given that the circumference of the circle is 34π, we can find the diameter by dividing the circumference by π:
d = C / π = 34π / π = 34
Therefore, the diameter is 34 units. The radius r is half of the diameter, so:
r = d / 2 = 34 / 2 = 17
Thus, the radius of the circle is 17 units.
Diane Has to give medicine to her cat every morning for the next 21 days. How many weeks is this?
? Weeks
Answer:
it would be 3 weeks because there are 7 days in a wekk so if u divide 21 by 7 it would give u 3
Step-by-step explanation:
1 week = 7 days
weeks = 21/7 days
Weeks = 3
21 days is 3 weeks.
Plz help !!!!!!!!!!!!
Answer: a) x² - 3x - 18 = 0
Step-by-step explanation:
[tex]\dfrac{x}{3}-\dfrac{6}{x}=1\\\\\\\text{Multiply everything by the LCD (3x) to clear the denominator:}\\\\\dfrac{x}{3}(3x)-\dfrac{6}{x}(3x)=1(3x)\\\\\\x^2-18=3x\\\\\\\text{Subtract 3x from both sides:}\\x^2-3x-18=0[/tex]
Write an equation of the line that is parallel to y = 1 2 x + 3 and passes through the point (10, -5). A) y = 2x - 15 B) y = -2x + 15 C) y = - 1 2 x Eliminate D) y = 1 2 x - 10
Answer:
B) y = -2x + 15Step-by-step explanation:
[tex]\text{Let}\ k:y=m_1x+b_1\ \text{and}\ l:y=m_2x+b_2,\ \text{then}\\\\k\ \parallel\ l\iff m_1=m_2\\\\k\ \perp\ l\iff m_1m_2=-1\to m_2=-\dfrac{1}{m_1}\\=============================\\\\\text{We have the equation}\ y=\dfrac{1}{2}x+3\to m_1=\dfrac{1}{2}.\ \text{Therefore}\ m_2=-\dfrac{1}{\frac{1}{2}}=-2.\\\\\text{We have the equation}\ y=-2x+b\\\\\text{Put the coordinates of the point (10, -5) to the equation and solve}\\\text{for}\ b:\\\\-5=-2(10)+b\\-5=-20+b\qquad\text{add 20 to both sides}\\15=b\\\\\text{Finally we have:}\\\\y=-2x+15[/tex]