The equivalent equation to 3x² + 24x + 15 = 0 is 3(x² + 8x + 5) = 0. It was found by factoring the given quadratic equation.
Explanation:The equation you're asked to simplify is a quadratic equation, which has the form ax² + bx + c = 0. Here, a = 3, b = 24, and c = 15. The equivalent equation can be found by factoring the given equation.
The quadratic formula -b ± √b² - 4ac / 2a can be used to find the solutions of the equation, but we are asked to provide an equivalent form of the original equation. Factoring the original equation, we get: 3(x² + 8x + 5) = 0. That is the equivalent equation.
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The equation 3x^2 + 24x + 15 = 0 can be factored using the ac method. The factored form is (x + 3)(3x + 5) = 0. Solving the factored equations gives x = -3 and x = -5/3.
Explanation:The equation 3x^2 + 24x + 15 = 0 can be factored.
Start by finding two numbers that multiply to give ac (a = 3, c = 15) and add to give b (b = 24).
In this case, the two numbers are 3 and 5. So we can factor the quadratic equation as (x + 3)(3x + 5) = 0.
Setting each factor equal to zero, we get x + 3 = 0 and 3x + 5 = 0.
Solving these equations gives x = -3 and x = -5/3.
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How much is 81% of 403?
Answer:
81% of 403 is.....326.43! (Rounding it to the nearest hundred gives '326')
Step-by-step explanation:
(P= Percentage / X= The number your finding the percentage of...)
Formula : X = P% * X
X = 81% * 403
Converting percent to decimal:
Converting percent to decimal:p = 81% ÷ 100 = 0.81
X = 0.81 x 403
X = 326.43
35. A 60° angle is complementary to an ang
that measures xº. Which of the following
equations represents this situation?
A 60 + X = 90
B 60 = x + 90
C 60+ x = 180
D. 60 = x + 180
Answer:
A. 60+x°=90
Step-by-step explanation:
Complementary angles add up to 90°.
Which coordinate pair identifies a point in the third quadrant of the coordinate plane?
A) (0, 6)
B) (−6, 2)
C) (2, −6)
D) (−6, −2)
Answer:
D, (-6,-2)
Step-by-step explanation:
the first quadrant of a coordinate plane has the x coordinate being a negative number, and the y coordinate being a positive number
the second quadrant of a coordinate plane has the x and y coordinates being a positive number
the third quadrant of a coordinate plane has the x and y coordinates being a negative number
the fourth quadrant of a coordinate plane has the x coordinate being a positive number, and the y coordinate being a negative number
i have attached a graph showing the quadrants for a visual point of view
The coordinate pair that identifies a point in the third quadrant of the coordinate plane, where both x and y coordinates are negative, is (-6,-2)
Explanation:The question is asking about identifying which pair of coordinates falls into the third quadrant of the coordinate plane in mathematics. The third quadrant in a coordinate plane is the bottom-left quadrant, where both the x and y coordinates are negative.
Looking at the options: A) (0,6), B) (-6,2), C) (2,-6), and D) (-6,-2); we can clearly see that option D) (-6,-2) is the point in the third quadrant, as both coordinates are negative. The pair (-6,-2) meets this description, with -6 on the x-axis and -2 on the y-axis. So, the correct answer is option D).
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Consider the following graph of a piecewise-defined function.
Choose the correct expression to represent the piecewise-defined function.
Answer:
Step-by-step explanation:
When x<-2, f(x)=5
When -2<x<3, f(x)=2x+2
When x>3, f(x)=-3
Answer:
Step-by-step explanation:
Given is a graph of piecewise function.
We are given a horizontal line for
[tex]x<-2[/tex]
Hence [tex]f(x) = 5, x<-2[/tex] ... I
Whenever
[tex]-2\leq x<3[/tex], the graph is a line passing through (-2,-2) and (3,8)
Hence using two point equation we get
[tex]\frac{y+2}{8+2} =\frac{x+2}{3+2}\\5(y+2)=10(x+2)\\y=2x+2[/tex]...II
Again for
[tex]x>3\\y=-3[/tex]... III
I,II and III together give the piecewise funciton
Two vertices of a right triangle have the coordinates (-2, 5) and (9,5)
What is the length of the side formed by these vertices?
Answer:
The length of the formed by these vertices is 11 units.
Step-by-step explanation:
We are given the following coordinates of two vertices of a right angled triangle and we are to find the length of the side formed by these vertices:
[tex](-2, 5)[/tex] and [tex](9,5)[/tex]
Using the distance formula to find the side length:
Side length = [tex] \sqrt { ( 9 - ( - 2 ) ) ^ 2 + ( 5 - 5 ) ^ 2 } [/tex] = [tex]\sqrt{121}[/tex] = 11 units
Answer:
11
Step-by-step explanation:
Note that the horizontal line y = 5 goes through both vertices, and that the length of the side formed by those vertices is the distance between the vertices in this case. That distance would be 9 - (-2), or 11.
Pls help asap....tia
Answer:
2541 peanut cookies were sold
Step-by-step explanation:
A system of equations can be written to match the problem description. Let p and c represent the initial numbers of peanut and chocolate cookies, respectively. Then we have ...
p - c = 1820 . . . . Lyn had 1820 more peanut cookies
After selling 35% of her peanut cookies, Lyn had 1-0.35 = 0.65 of the original number left. Likewise, after selling 15% of her chocolate cookies, she had 1-0.15 = 0.85 of the original number left. Then after the sales, the difference in cookie count was 95:
0.65p -0.85c = 95
We only need to know the original number of peanut cookies (p), so we can use Cramer's rule to find the solution for p.
p = (-95 +0.85·1820)/(-0.65+0.85) = 1452/0.20 = 7260
The original number of peanut cookies Lyn had was 7260, so the number she sold is ...
0.35 · 7260 = 2541
_____
Cramer's rule says the solution to ...
ax +by =c
dx +ey =f
is given by ...
x = (ec-bf)/(ea-bd)
y = (fa-cd)/(ea-bd)
Answer:
2541 cookie were sold
Step-by-step explanation:
given that (9,2) is on the graph of f(x), find the corresponding point for the function f(-3/4x)
Given the point (9,2) is on the graph of f(x), the corresponding point for the function f(-3/4x) is found by multiplying the x-coordinate of the given point by -3/4. This yields the corresponding point (-6.75, 2).
Explanation:The given point is (9,2). In the function f(-3/4x), the variable is multiplied by the factor -3/4. We apply this factor to the x-coordinate of the given point to find the x-coordinate of the corresponding point in the function f(-3/4x).
Therefore, the x-coordinate of the corresponding point is 9×-3/4 = -27/4 = -6.75. The y-coordinate remains the same because the transformation corresponds only to the x-coordinates of points. So, the corresponding point in the function f(-3/4x) is (-6.75,2).
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NEED HELP ASAP SHOW WORK AND PLZ EXPLAIN
Answer:
x = 12
Step-by-step explanation:
Given
4(x - 5) = 8x + 4 - 6x ← distribute left side and simplify right side
4x - 20 = 2x + 4 ( subtract 2x from both sides )
2x - 20 = 4 ( add 20 to both sides )
2x = 24 ( divide both sides by 2 )
x = 12
Part 1
The ratio table shows the amounts of sand and water in a concrete mixture. Which fraction represents the ratio for the gallons of water to bags of sand?
A)3/6
B)3/7
C)5/3
D)7/3
Part 2
How many bags of sand should be mixed with 12 gallons of water?
A)22 bags
B)24 bags
C)28 bags
D)30 bags
Please help
Divide bags of sand by gallons of water:
14 /6 = 2.33
21/9 = 2.33
The ratio is the same, so this means for every gallon of water you need 2.33 bags of sand.
Convert the fractions into decimals and you will get 7/3 = 2.33
The answer for Part 1 is D) 7/3
For part 2, multiply the gallons of water by 2.33 to get the number of sand bags needed:
12 x 2.33 = 27.99, which rounds to 28.
The answer is C) 28 bags.
Answer:
A) [tex]\frac{3}{7}[/tex]
C) 28 bags
Step-by-step explanation:
Part 1 :
By the given table,
[tex]\frac{\text{Gallon of water}}{\text{bags of sand}}=\frac{6}{14}=\frac{9}{21}=\frac{15}{35}=\frac{3}{7}[/tex]
Hence, the proportion of gallons of water to bags of sand is same,
Which is [tex]\frac{3}{7}[/tex]
OPTION A) is correct.
Part 2 : Let x bags of sand should be mixed with 12 gallon of water,
Then the ratio of gallon of water and number of bags of sand = [tex]\frac{12}{x}[/tex]
By part 1,
[tex]\frac{12}{x}=\frac{3}{7}[/tex]
[tex]84 = 3x[/tex] ( by cross multiplication )
[tex]\implies x = \frac{84}{3}=28[/tex]
Hence, 28 bags of sand should be mixed.
OPTION C) is correct.
What is the average rate of change for this exponential function for the interval from x=1 to x=3
The answer for this question is 3
Answer:
B. 3
Step-by-step explanation:
x=1 ; y = 2
x=3; y =8
the average rate of change = (8-2)/(3-1) = 6/2 = 3
Answer
B. 3
Find an equivalent fraction for the decimal number. In your final answer, include all of your work.
0.901 recurring
Answer:
[tex]\frac{901}{999}[/tex]
Step-by-step explanation:
we know that
A Recurring Decimal, is a decimal number with a digit (or group of digits) that repeats forever.
In this problem we have
0.901 recurring
that means
0.901901901..
Let
[tex]x=0.901901901..[/tex]
Multiply x by a power of [tex]10[/tex], one that keeps the decimal part of the number the same:
[tex]1,000x=901.901901..[/tex]
Subtract [tex]x[/tex] from [tex]\\1000x[/tex]
[tex]1,000x-x=901.901901..-0.901901..=901[/tex]
The repeating decimals should cancel out
[tex]\\999x=901[/tex]
solve for x
Divide by [tex]999[/tex] both sides
[tex]990x/990=135/990[/tex]
[tex]x=\frac{901}{999}[/tex]
which answer best describes the shape of this distribution
A. skewed right
B. skewed left
C. uniform
D. bell-shaped
Answer:
B.. skewed left
Step-by-step explanation:
Answer:
Option B. skewed left.
Step-by-step explanation:
In the figure attached maximum frequency of the data is at the 45. Distribution on the right side of the maximum frequency is upto 48 and in the left it is upto 36.
As we can see point 36 is more distant from peak point 45 as compared to point 48.
Therefore, distribution of the data is more in the left than in the right.
Therefore, the shape of this distribution is skewed left.
Option B. skewed left is the correct answer.
A class student council election was held on Monday and 15 of the 20 students decided to vote. On Tuesday, another election was held, but only 16 students were in the class that day. Use the ratio of students who voted in Monday's election to the total number of students in class on Monday to predict the number of students who voted in Tuesday's election.
Answer:
12
Step-by-step explanation:
We know that 15/20 students voted in the StuCo election on the first go around.
Using this ratio for 16 student is as simple as multiplying 15/20 by 16
(15/20)*16=12
Based on the voting ratio of 3:4 from Monday's election, we predict that 12 out of the 16 students present on Tuesday voted.
The question asks to predict the number of students who voted in Tuesday's election based on the ratio of students who voted on Monday. On Monday, 15 out of 20 students voted, which establishes a voting ratio of 15:20, or 3:4 when simplified. To predict Tuesday's voter turnout, we apply this ratio to the 16 students present on Tuesday.
Using the simplified ratio of 3:4, for every 4 students, 3 vote. Since 16 students were in class on Tuesday:
Divide 16 by 4 to find how many groups of 4 there are, which is 4.Multiply the number of groups (4) by the number of voters per group (3), which equals 12.Therefore, we predict that 12 students voted in Tuesday's election.
Find the missing part
Answer:
[tex]\large\boxed{z=\dfrac{15\sqrt3}{2}[/tex]
Step-by-step explanation:
Lookat the picture.
We have
[tex]2a=15\to a=\dfrac{15}{2}\to a\sqrt3=\dfrac{15\sqrt3}{2}[/tex]
small triangle:
[tex]x=2a=\dfrac{15}{2}\to a=\dfrac{15}{4}\to y=\dfrac{15\sqrt3}{4}[/tex]
[tex]a+b=15\to b=15-\dfrac{15}{4}=\dfrac{60}{4}-\dfrac{15}{4}=\dfrac{45}{4}[/tex]
[tex]a=\dfrac{15}{4}\\\\b=\dfrac{45}{4}\\\\x=\dfrac{15}{2}\\\\y=\dfrac{15\sqrt3}{4}\\\\z=\dfrac{15\sqrt3}{2}[/tex]
which polynomial is prime?
a) x^3+3x^2-2x-6 b)x^3-2x^2+3x-6 c)4x^4+4x^3-2x-2
d)2x^4+x^3-x+2
Answer: D. 2x4+x3–x+2 is prime
Step-by-step explanation:
a number y increased by 5 is at most 28
The answer to your question is this:
[tex]y + 5\leq 28\\y\leq 23[/tex]
Monica found the volume of the prism below using the expression
What errors did Monica make? Check all that apply.
For this case we have that by definition, the volume of a regular prism is given by:
V = B * h
Where:
B: It is the area of the base
h: It is the height of the prism
We have to:
[tex]B = 2 * 2 = 4 \ cm ^ 2\\h = 1 \frac {2} {3} = \frac {3 * 1 + 2} {3} = \frac {5} {3}[/tex]
Thus, the volume will be:
[tex]V = 4 * \frac {5} {3}\\V = \frac {20} {3} \ cm ^ 3[/tex]
ANswer:
[tex]V = \frac {20} {3} \ cm ^ 3[/tex]
Answer:
The answer is b and c
hope this helps!
Step-by-step explanation:
What’s is the answer?
Answer:
Option D)
Step-by-step explanation:
Given:
x= {2,3,4}
y={49,343,2401}
Points with coordinates (x,log(y)) are required to be plotted
Finding (x,log(y)):
log(y)= {log(49),log(343),log(2401)}
Log(49)=1.69020
log(343)=2.53529
log(2401)=3.38039
Now the transformed data set will be written in coordinates form:
(2,1.690),(3,2.535),(4,3.380)
Which is option D !
What is the initial value of the exponential function shown
on the graph?
a.0
b.1
c.2
d.4
Answer:
a.0
Step-by-step explanation:
The exponential function levels at 0
Please give brainliest
lauri's cat had a litter of 4 kittens. What is the probability that there were 3 males
Answer:
The probability that there were 3 males is 1/4.
Step-by-step explanation:
Total Number of kitten = 4
Probability of a kitten to be male = 1/2
Probability of a kitten to be female = 1/2
Probability that out of 3 were male = 4 × 1/2 × 1/2 × 1/2 × 1/2
= 1/4
Therefore, The probability that there were 3 males is 1/4.
What is the square of 16
Answer:
Square root of 16 = 4
Square of 16 = 256
Hope this helps :)
Have a great day !
5INGH
Step-by-step explanation:
Please help!!!!!!!!!!!!!!
Answer:
12.5, not 100% sure though.
Answer:
Step-by-step explanation:
12.5 is right. Because it say similar to triangle XYZ
What is the perimeter of triangle ABC ? 11 units 14 units 16 units 20 units Coordinate graph showing triangle A B C. Triangle A B C has vertex A at negative 1 comma 1, vertex B at 2 comma 5, and vertex C at 5 comma 1.
Answer:
The perimeter is equal to [tex]16\ units[/tex]
Step-by-step explanation:
we have that
[tex]A(-1,1),B(2,5),C(5,1)[/tex]
The perimeter of triangle ABC is equal to
[tex]P=AB+BC+AC[/tex]
the formula to calculate the distance between two points is equal to
[tex]d=\sqrt{(y2-y1)^{2}+(x2-x1)^{2}}[/tex]
step 1
Find the distance AB
[tex]A(-1,1),B(2,5)[/tex]
[tex]AB=\sqrt{(5-1)^{2}+(2+1)^{2}}[/tex]
[tex]AB=\sqrt{(4)^{2}+(3)^{2}}[/tex]
[tex]AB=\sqrt{25}[/tex]
[tex]AB=5\ units[/tex]
step 2
Find the distance BC
[tex]B(2,5),C(5,1)[/tex]
[tex]BC=\sqrt{(1-5)^{2}+(5-2)^{2}}[/tex]
[tex]BC=\sqrt{(-4)^{2}+(3)^{2}}[/tex]
[tex]BC=\sqrt{25}[/tex]
[tex]BC=5\ units[/tex]
step 3
Find the distance AC
[tex]A(-1,1),C(5,1)[/tex]
[tex]AC=\sqrt{(1-1)^{2}+(5+1)^{2}}[/tex]
[tex]AC=\sqrt{(0)^{2}+(6)^{2}}[/tex]
[tex]AC=\sqrt{36}[/tex]
[tex]AC=6\ units[/tex]
step 4
Find the perimeter
[tex]P=5+5+6=16\ units[/tex]
Answer:
The answer is 16 untis
Step-by-step explanation:
Help !!
Which transformation can not be used to prove that ABC is congruent to DEF ?
D
the answer is D. dilation cannot be used to prove this
The answer is D since dialation only beating to increase in size
What is the value of X? Please help me with geometry.
Answer:
x=61
Step-by-step explanation:
X=61
Because (52+67)-180=61
Select the expression below that is equal to 6(9 - m).
Answer:
The answer would be m= -9
Step-by-step explanation:
6(9-m)
You will multiply the 6 with the 9 and -m inside of the parenthesis
54-6m
Divide by -6 on both sides and you will get m= -9
I hope this helps you with this question and have a nice weekend
The equivalent expression to 6(9 - m) is 54 - 6m, determined by applying the distributive property of multiplication over addition and subtraction.
The expression given is 6(9 - m). To identify an expression equal to this, we should look for expressions that maintain the same relationship between the numbers and the variable m. When we distribute the 6 across the parentheses, we multiply 6 by 9, and 6 by -m, resulting in 54 - 6m.
Distributing a number across a subtraction in a parenthesis follows the distributive property of multiplication over addition and subtraction, which allows us to multiply each term inside the parentheses by the number outside.
PLZ Help. It will be very appreciated.
when the two books were published
Answer: It would be (B) because you don't actually have to know the date unless it is a part of the equation which you dont have to know in this question :)
Hope this will help you out :)
a jar contains 32 red marbles and 28 blue marbles. what is the probability that a randomly selected marble is red
Answer:
The answer is 7/8 chance.
Step-by-step explanation:
To find this answer, you have to divide the blue marbles by red marbles. Then, you will get 28/32.
You can simplify it, so simplify it to the smallest possible number, therefore getting 7/8.
The equation of line AB is (y-3) = 5(x-4) what is the slope
Answer:
slope = 5
Step-by-step explanation:
The equation of a line in point- slope form is
y - b = m(x - a)
where m is the slope and (a, b) a point on the line
y - 3 = 5(x - 4) ← is in point- slope form
with slope m = 5
How to evaluate 8(2/3)
8 times 2/3 is 16/3, which when simplified is 5 1/3
To evaluate 8(2/3), you need to multiply 8 by 2/3. The value of 8(2/3) is 16/3.
Explanation:To evaluate 8(2/3), you need to multiply 8 by 2/3. To do this, you can simplify 2/3 by dividing both the numerator and denominator by their greatest common factor, which is 1.
This simplifies 2/3 to 2/3. Then, multiply 8 by 2/3 to get the final answer.
8 x 2/3 = 16/3Therefore, the value of 8(2/3) is 16/3.
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