Subtract x from both sides
2x + 3 - x = -4
Simplify 2x + 3 - x to x + 3
x + 3 = -4
Subtract 3 from both sides
x = -4 - 3
Simplify -4 - 3 to -7
x = -7
2x+3=x-4
2x-x= -4-3
x= -7
Check answer by using substitution method
2(-7)+3= -7-4
-14+3=-11
-11=-11
Answer is x=-7
what are the roots of this equation?
x²-4x+9=0
a. 1±i√5
b. 2±i√5
c. 2±i√3
d. 1±i√52
Answer:
x = 2 ± (i)√5 (Answer b)
Step-by-step explanation:
x²-4x+9=0 can be solved in a variety of ways; the first two that come to mind that are also appropriate are (1) completing the square and (2) using the quadratic formula.
Completing the square is fast here:
Rewrite x²-4x+9=0 as x²-4x +9=0
Identify the coefficient of the x term: it is -4
Take half of that, obtaining -2
Square this result, obtaining 4
Add 4 to x²-4x +9=0, in the blank space in the middle, and then subtract 4: x²-4x +4 -4 +9=0
Rewrite x²-4x +4 as the square of a binomial:
(x - 2)² - 4 + 9 = 0 → (x - 2)² = -5
Take the square root of both sides: x - 2 = ±√(-5) = ± (i)√5
Then x = 2 ± (i)√5
The scatterplot shows the sales, in dollars, of snow cones in relation to the outside temperature, in degrees Celsius. According to the line of best fit, which is the closest approximation of sales when the outside temperature is 21 °C?
A) $420
B) $450
C) $480
D) $520
B) it is 450 dollars
Answer: C: 480
Step-by-step explanation:
trust me its this answer not the other guys
Lillian is trying to determine how people feel about the new act Congress is trying to put through. Which question would be the MOST appropriate for her survey?
A) How do you feel about the new Act Congress is trying to pass?
B) How do you feel about Congress spending billions of dollars on this new Act?
C) Which is better Congress passing this new Act or trying to erase national debt?
D) How do you feel about Congress raising federal taxes in order for the Act to be financed?
Answer:
A
Explanation:
Lillian is trying to find out how people feel about the new act Congress is trying to put through. I would go with A because the question is literally what she is trying to determine through the survey.
B, C, D are asking about certain things(issues) about the act or comparing it with other issues, and with A you get a broader answer. (or the question is straight to the point)
A mother who is 40 years old has a daughter and a son. The son is twice as old as the daughter. In 15 years the sum of all their ages will be 100 years. How old are the siblings now?
Answer:
the son is 30 and the daughter is 15
Step-by-step explanation:
the mom is 55 in 15 years
100-55=45
45-30=15
15x2=30
Answer:
15 and 5
Step-by-step explanation:
Mother's current age: 40
daughter's age: d
son's age: s
son is 2x as old as daughter: s = 2d
Then, 15 years from now, the sum of their ages will be:
(40 + 15) + (2d + 15) + (d + 15) = 100
or
55 + 15 + 15 + 3d = 100
85 + 3d = 100, or 3d = 15, or d = 5.
Then the son's age is 3(5) = 15 and the daughter's is 5.
HELP! The answer is 3 but I can't seem to get to the answer, instead I keep getting -3.
Answer:
x=3
Step-by-step explanation:
[tex]45-\frac{90}{x} = 15[/tex]
Minus 45 from both sides
[tex]-\frac{90}{x}=-30[/tex]
Multiply both sides x
[tex]-90=-30x[/tex]
Divide both sides by -30
[tex]3=x[/tex]
Answer:
3
Step-by-step explanation:
To eliminate the x on the denominator, multiply all terms by x
45x - 90 = 15x ( subtract 45x from both sides )
- 90 = - 30x ( divide both sides by - 30 )
3 = x ⇒ x = 3
what is the value of x?
• 7
• 7√2
• 14
• 14√2
The value of [tex]\(x\)[/tex] is [tex]\(14\)[/tex]. The correct option is [tex]\(14\)[/tex].
In a right triangle with a 45-degree angle, the sides are related by the special angles of 45-45-90 triangles. In such triangles, the sides are in the ratio [tex]\(1:1:\sqrt{2}\)[/tex].
Given that the height is [tex]\(7\sqrt{2}\)[/tex] and the hypotenuse is [tex]\(x\),[/tex] we can identify the relationship as follows:
[tex]\[ \text{Height} : \text{Base} : \text{Hypotenuse} = 1 : 1 : \sqrt{2} \][/tex]
So, the height is [tex]\(7\sqrt{2}\)[/tex], and the base would be [tex]\(7\sqrt{2}\)[/tex]as well, and the hypotenuse [tex](\(x\))[/tex] would be [tex]\(7\sqrt{2} \times \sqrt{2} = 7 \times 2 = 14\)[/tex].
Therefore, the value of [tex]\(x\)[/tex] is [tex]\(14\)[/tex], and the correct option is:
• [tex]\(14\)[/tex]
The correct answer is [tex]\boxed{14}[/tex]. The value of x is [tex]\boxed{14}[/tex].
To determine the value of [tex]\( x \)[/tex], we need to consider the given options and the context of the question, which involves the square root of 2. The options provided are [tex]\( 7 \), \( 7\sqrt{2} \), \( 14 \), and \( 14\sqrt{2} \).[/tex]
Let's analyze the options:
1. [tex]\( 7 \)[/tex] is a straightforward integer.
2. [tex]\( 7\sqrt{2} \) is \( 7 \)[/tex] times the square root of 2, which is an irrational number approximately equal to [tex]\( 1.414 \)[/tex].
3.[tex]\( 14 \) is \( 7 \)[/tex] times [tex]\( 2 \)[/tex], which is a simple integer multiplication.
4. [tex]\( 14\sqrt{2} \) is \( 14 \)[/tex] times the square root of 2.
Given that the question is asking for the value of [tex]\( x \)[/tex] and the options involve multiples of [tex]\( 7 \)[/tex] and [tex]\( 14 \)[/tex], it is reasonable to suspect that the answer might involve the square root of 2, since it is the only mathematical operation present in all the options.
However, without additional context or a mathematical equation to solve for [tex]\( x \)[/tex], we cannot definitively determine which of these options is correct based solely on the information given. In mathematics, problems involving square roots typically require an equation or a geometric representation to provide a clear path to the solution.
Since the question does not provide an equation or additional context, we must rely on the principle that the most straightforward answer is often correct when dealing with multiple-choice questions. In this case, the simplest option that does not involve an irrational number is [tex]\( 14 \)[/tex].
Therefore, without further information, the most logical and simple choice is [tex]\( 14 \)[/tex], as it is a whole number and does not introduce the complexity of an irrational number like [tex]\( \sqrt{2} \)[/tex].
Thus, the final answer is [tex]\boxed{14}[/tex].
student government members survey every 15th student who enters the school building and asks whether students favor the school’s new school mascot. the sample statistics show that 57% oppose the new school mascot., 37% favor the school mascot, and 6% have no opinion.
The student's question pertains to a survey on students' opinions about a new school mascot. The survey results showed varying levels of support and opposition, which are crucial for decision-making in educational policy. This demonstrates the real-world application of mathematics in understanding public opinion through statistics.
The student's question deals with a survey conducted by student government members to understand the school community's stance on the new school mascot. This survey follows a systematic sampling method by asking every 15th student entering the school. The outcome showed that 57% oppose, 37% are in favor, and 6% have no opinion regarding the new mascot. Such a poll is useful for making decisions related to public policy and ensuring that actions consider community preferences.
Another key component is understanding the methodology behind this survey. If we consider a similar scenario where 600 students are surveyed with 480 opposing new legislation (as mentioned in one of the examples), we could calculate the percentage opposing the legislation and use this to propose actions or influence decision-making processes regarding school policies.
In the context of educational institutions, conducting polls or surveys is a practical way to involve student bodies in decision-making processes, reflecting a democratic practice in school governance. This kind of statistical analysis forms a crucial part of mathematics in the real world, particularly within the fields of statistics and probability.
HELP!
There are 6 seniors on student council . Two of them will be chosen to go to an all district meeting. how many ways are there to choose the students who will go to the meeting?
Answer:
U think the answer is C.
Answer:
Number of ways of selecting two students is 15
Step-by-step explanation:
number of ways of selecting n out of r is given by
[tex]n_{C_{r} } =\frac{n!}{r!(n-r)!}[/tex]
It is given that there are 6 seniors on student council.
2 students are selected for district meeting
So we have [tex]n= 6[/tex] and [tex]r=2[/tex]
number of ways of selecting two students =[tex]6_{C_{2} } [/tex]
=[tex]\frac{6!}{2!(6-2)!}[/tex]
=[tex]\frac{6!}{2!4!}=15[/tex]
So we have number of ways of selecting two students is 15
Please help me ll give you 40 branily
Answer: Figure 2
Step-by-step explanation: A translation of the blue shaded shape would be figure 2
On a blueprint with a scale of 1 cm = 4 ft, the length of the wall is 9 cm. If the scale of the blueprint were 1 cm = 3 ft, what would the length of the wall be
Final answer:
To find the length of the wall on the new blueprint with a scale of 1 cm = 3 ft, a proportion can be used. The length of the wall on the new blueprint would be 0.75 ft.
Explanation:
To find the length of the wall on the new blueprint with a scale of 1 cm = 3 ft, we can use a proportion.
In the original blueprint with a scale of 1 cm = 4 ft, the length of the wall is 9 cm. Let's let x represent the length of the wall on the new blueprint.
Set up the proportion: 1 cm/4 ft = x cm/3 ft
Cross multiply: 1 * 3 = 4 * x
Solve for x: x = 3/4
Therefore, the length of the wall on the new blueprint would be 3/4 ft or 0.75 ft.
The levels of mercury in two different bodies of water are rising. In one body of water the initial measure of mercury is 0.05 parts per billion (ppb) and is rising at a rate of 0.1 ppb each year. In the second body of water the initial measure is 0.12 ppb and the rate of increase is 0.06 ppb each year.
Answer:
y=6
Step-by-step explanation:
The complete question is as follows:-
The levels of mercury in two different bodies of water are rising. In one body of water, the initial measure of mercury is 0.05 parts per billion (ppb) and is rising at a rate of 0.1 ppb each year. In the second body of water, the initial measure is 0.12 ppb and the rate of increase is 0.06 ppb each year. Which equation can be used to find y, the year in which both bodies of water have the same amount of mercury?
An equation can be used to find y, the year in which both bodies of water have the same amount of mercury will be given as below:-
0.05 + 0.1y = 0.12 + 0.06y
What is an equation?It is defined as the relation between two variables, if we plot the graph of the linear equation we will get a straight line.
Here, we want to find y which is the heat in which the amount of mercury in each of the water bodies is the same.
Now for the first water body:
Initial is 0.05 ppb and after y years, we have a rise of 0.1 x y = 0.1y ppb
So the amount of mercury in ppb after y years would be;
0.05 + 0.1y
For the second water body;
Initial is 0.12 and a rise of 0.06 ppb per year for y years. The rise would be
0.06 x y = 0.06y
So the total amount of mercury here is
0.12 + 0.06y
So to find y which is the year the amount of mercury in each water body is the same, we simple equate both and that would be;
0.05 + 0.1y = 0.12 + 0.06y
Therefore an equation can be used to find y, the year in which both bodies of water have the same amount of mercury is 0.05 + 0.1y = 0.12 + 0.06y
To know more about equations follow
https://brainly.com/question/2972832
#SPJ2
There are 10 students in a class. The teacher chooses three students to go to the library. The order in which they are chosen does not matter. How many ways are there to choose the students?
Answer:
I think the answer is C.
Answer:B. 120
Step-by-step explanation:
Help please and need to show the work!
To find how many small cubes can fit inside a larger cube, you need to find the volume of both.
Once you have the volumes, divide the volume of the larger cube, by the volume of the smaller cube.
Volume = L x W x H
Small cube: Volume = 3/4 x 3/4 x 3/4 = 0.421875 cm^3
Large cube: Volume = 3 x 3 x 2 = 18 cm^3
Number of small cubes that can fit: 18 / 0.421875 = 42.67 Cubes.
Since you can't have a partial cube ( 0.67) round down to a whole number:
That means you can fit 42 cubes.
The triangle will be dilated by a scale factor of 1.5.
Center of dilation
(a) calculate the length of each side of the dilated image.
(b) draw the new image and label it a'b'c
Answer:
Part a) A'B'=15 units, B'C'=12 units, A'C'=21 units
Part b) The graph in the attached figure
Step-by-step explanation:
Part a) calculate the length of each side of the dilated image
we know that
To calculate the length of each side of the dilated image, multiply the scale factor by the original length
we have
scale factor=1.5
so
A'B'=AB*1.5=10*1.5=15 units
B'C'=BC*1.5=8*1.5=12 units
A'C'=AC*1.5=14*1.5=21 units
Part b) draw the new image and label it a'b'c
The graph in the attached figure
A 5 inch tall bamboo shoot doubles in height every 3 days. If the equation y=ab^x, where x is the number of doubling periods, represent the height of the bamboo shoot,what are the values of a and b
Answer:
a = 5 and b = 2
Step-by-step explanation:
y = ab^x
If x is the number of double periods, then b is the rate of growth (2), and a is the initial height (5).
a = 5 and b = 2
You can buy 4 bottles of water from a vending machine for $7. At this rate, how many bottles of water can you buy for $28
Answer:
16
Step-by-step explanation:
Divide 7 by 4, which gives you 1.75 . Multiply 1.75 & 28 and you get 16.
Answer:
16 bottles
Step-by-step explanation:
We can write a ratio, dollars over bottles of water
7 28
-------- = ----------
4 x
Using cross products
7x = 4*28
Divide each side by 7
7x/7 = 4*28/7
x = 4 * 4
x = 16
Which are true about the area of the circle? Check all that apply
Answer:
Step-by-step explanation:
2, 3, 5
Answer:
Answers:2, 3, 5
Step-by-step explanation:
If x2 + mx + m is a perfect-square trinomial, which equation must be true?
x2 + mx + m = (x – 1)2
x2 + mx + m = (x + 1)2
x2 + mx + m = (x + 2)2
x2 + mx + m = (x + 4)2
The answer is:
The third option,
[tex]x^{2}+mx+m=(x+2)^{2}[/tex]
Why?We are looking for an equation that establishes a relationship between the perfect-square trinomial and the givens notable products.
So, we are looking for a notable product that gives us a value of "m" that is the coefficient of the linear term (x) and it's also the constant term.
- Trying with the two first options, we have:
[tex](x+1)^{2}=x^{2}+2x+ 1\\\\(x-1)^{2}=x^{2}-2x+ 1[/tex]
We can see that for these first two options, the value of m has not the same value for the coefficient of the linear term and the constant term since m is equal 2 and the constant number is not 2.
- Trying with the third option, we have:
[tex](x+2)^{2}=x^{2}+2*(2*x)+2^{2}=x^{2} +4x+4[/tex]
Now, we can see that the value of m is the same for the coefficient of the linear term and the constant term, we can see that m is equal to 4.
So, the correct option is the third option, because
[tex]m=4[/tex]
[tex]x^{2} +mx+m=(x+2)^{2}=x^{2} +4x+4=x^{2} +mx+m[/tex]
Have a nice day!
What is the solution to log 5 (x+30)= 3
Answer:
x = 95
Step-by-step explanation:
Using the rule of logarithms
• [tex]log_{b}[/tex] x = n ⇔ x = [tex]b^{n}[/tex]
Given
[tex]log_{5}[/tex](x + 30) = 3, then
x + 30 = 5³ = 125 ( subtract 30 from both sides )
x = 95
PLEASE HELP ASAP!!
What is the probability that the first spinner will land on 7 and the second spinner will land on C?
A. 1/3
B. 1/6
C. 1/12
D. 1/4
i believe the answer is c. 1/12
hope this helped! have a good day!
The required probability is 1/12 that the first spinner will land on 7 and the second spinner will land on C.
What is probability?Probability is defined as the possibility of an event being equal to the ratio of the number of favorable outcomes and the total number of outcomes.
The probability that the first spinner will land on 7
P(7) = favorable outcomes / total outcomes
P(7) = 1/4
The probability that the second spinner will land on C
P(C) = 1/3
As per the given question, the required probability will be as:
⇒ P(7) × P(C)
⇒ 1/4 × 1/3
⇒ 1/12
Hence, the correct answer would be an option (C).
Learn more about probability here:
brainly.com/question/11234923
#SPJ2
Find the volume of a cylinder with a radius of 6 cm and height 15 cm?
The volume of the cylinder is defined (as usual) as the base area times the height. The base is a circle, so the base area is [tex]\pi r^2[/tex]
So, the volume is
[tex]h\pi r^2 = 15\cdot \pi \cdot 36 = 540\pi[/tex]
Answer:
[tex]
1696.46 {cm}^{3}
[/tex]
Step-by-step explanation:
[tex]V
=
π
{r}^{2}
h
\\ =
π
·
{6}^{2}
·
15
\\
≈
1696.46003
[/tex]
On a map of the United States the line from Portland, Oregon, to Twin Falls, Idaho, is 11 centimeters long. If the scale of the map is 2 centimeters to 100 miles, how far is it from Portland to Twin Falls?
Not sure what to do about Oregon and Idaho but the 2/100 gives you a 50 unit rate 50x11= 550
Answer:
using the information we have we can see that each mile centimeter is 50 miles. 11 x 50 is 550 so that is your answer
550 miles
Drag the tiles to the correct boxes to complete the pairs.
Match each inequality to the number line that represents its solution
The answer is:
- First inequality: The fourth number line.
- Second inequality: The second number line.
- Third inequality: The first number line.
- Fourth inequality: The third number line.
Why?To be able to match each inequality to the number line that represents its solution, we need to solve each inequality.
So, solving we have:
- First inequality:
[tex]\frac{7x}{9}>-\frac{14}{3}\\\\x>-\frac{14}{3}*\frac{9}{7}>-\frac{126}{21}>-6 \\\\x>-6[/tex]
Therefore, the solution for the first inequality is the x greaters than 6, and the solution matchs with the fourth number line.
- Second inequality:
[tex]-\frac{75x}{4}>\frac{225}{2}\\\\\frac{75x}{4}<-\frac{225}{2}\\\\x<-\frac{225}{2}*\frac{4}{75}<-6[/tex]
Therefore, the solution for the first inequality is the x less than 6, and the solution matchs with the second number line.
- Third inequality:
[tex]\frac{x}{4}\leq -\frac{3}{2}\\\\x\leq -\frac{3}{2}*4\leq -\frac{12}{2}=-6[/tex]
Therefore, the solution for the first inequality is the x less or equals than 6, and the solution matchs with the first number line.
- Fourth inequality:
[tex]\frac{2x}{3}>-\frac{16}{3}\\\\x>-\frac{16}{3}*\frac{3}{2}>-\frac{48}{6}>-8\\\\x>-8[/tex]
Therefore, the solution for the first inequality is the x greater than 6, and the solution matchs with the third number line.
Have a nice day!
Three equivalent ratios for 8/16
Answer:
48 : 96 88 : 17656 : 11224 : 48 208 : 416 32 : 64 40 : 80* Hopefully this helps:) Mark me the brainliest:)!!!
4:8
2:4
1:2
16:32
Good luck!!!
please help w precalculus will mark brainliest!
-see attachment-
ANSWER
x=-3, y=6
EXPLANATION
The given equation is
[tex] - 3 + yi = x + 6i[/tex]
We can rewrite this equation as:
[tex]x - yi = - 3 - 6i[/tex]
The two complex number equations are equal therefore their corresponding parts are also equal.
Comparing the real number parts,
[tex]x = - 3[/tex]
Comparing the complex number part,
[tex] - y = - 6[/tex]
y=6.
What is the common difference between consecutive terms in the following arithmetic sequence -11, -8, -5, -2, 1
Answer:
The common difference is +3
Step-by-step explanation:
When you add 3 to -11 it becomes -8, add 3 again and you get -5, keep doing this and you'll notice that +3 is the common difference.
Answer:
The common difference is +3
Step-by-step explanation:
If you add "3" since -11 you obtain this arithmetic sequence.
(-11+3) = -8
(-8+3) = -5
(-5+3) = -2
(-2+3) = 1
-11, -8, -5, -2, 1
If sin(x+y) - sin(x-y) = 2f(x)sin(y), then f(x) equals?????
From the function sin(x+y) - sin(x-y) = 2f(x)sin(y), we can deduce that f(x) = cosx
But sin(x + y) = sinxcosy + cosxsiny.
Also, sin(x - y) = sinxcosy - cosxsiny..
Hence:
sin(x+y) - sin(x-y)
= sinxcosy + cosxsiny - (sinxcosy - cosxsiny)
= sinxcosy - sinxcosy + cosxsiny + cosxsiny
= 2cosxsiny
2cosxsiny = 2f(x)sin(y)
Hence, f(x) = cosx
Find out more at: https://brainly.com/question/14418346
In the metric system, the numbers 10, 100, 1,000, 10,000, and so on serve as
Answer:
prefixes
Step-by-step explanation:
The exact response will depend a lot on what you learned in your manual and the terms used in it, but the metric system is all based on the base of 10, like the numbers system you use every day.
Unlike the US/Imperial system where there's no clear relation between an inch, a yard and a mile for example, in the metric system everything is related by the factor 10 somehow.
The unit multiplier is also used as a prefix to identify measurements. Like for meter...
10 meters = 1 decameter
100 meters = 1 hectometer
1000 meters = 1 kilometer
and so on.
Answer:
what he said
Step-by-step explanation:
Describe the trend in the scatter plot.
A:Negative trend
B:positive trend
C:no trend
It is positive . Every time it’s to the right it’s positive when it’s to the left it’s negative and when the points are all over the place it’s no Trend
Answer: Positive trend
Step-by-step explanation: In this scatter plot, notice that we can draw a line of best fit to represent the data. This means that we have a trend. Notice the x-values increase while the y-values increase which means we have a positive correlation between x and y.
Therefore, this scatter plot represents a positive trend.
Image provided.
Find the value of x. Write your answer as a decimal.
ANSWER
[tex]x = 75.5 \degree[/tex]
EXPLANATION
Lines WO and WX are tangents to the circle.
The angle subtended at the center, Z by minor arc XO is the angle subtended at the circumcenter by the same arc.
Therefore the central angle is 2x°.
The two radii ZX and ZO meets the tangents at right angles.
This implies that:
[tex]2x + 90 + 90 + 29 = 360 \degree[/tex]
Or
[tex]2x + 29 = 180 \degree[/tex]
[tex]2x = 180 - 29[/tex]
[tex]2x = 151[/tex]
Divide both sides by 2
[tex]x = \frac{151}{2} = 75.5[/tex]
The value of x using the quadratic equation is 0.00139. When adjusting exponential notations, move the decimal left or right, depending on whether the exponent is positive or negative. Verifying precision to a certain number of decimal places can be achieved by altering the increment and observing changes beyond the desired precision.
Explanation:To find the value of x when using the quadratic equation, we have two potential solutions, which are x= -0.0024 and x= 0.00139. In practical applications, a negative result may not be viable, which indicates that x would equal to 0.00139. When dealing with exponential notation, moving the decimal to adjust for the exponent is necessary. For instance, 4.5 x 10¹ would become 0.45 when the decimal is moved one place to the left. Similarly, 1.6 x 10² would adjust to 160 by moving the decimal place to the right two places. Conversely, a negative exponent like in 2.4 x 10⁻² requires moving the decimal to the left twice to get 0.024. Understanding this concept is crucial when working with numbers written in scientific notation.
If we're verifying to three decimal places and see a change beyond the third decimal (such as with Ax=10⁻⁵ resulting in 1.00001), we can deduce that the initial three decimal places are indeed accurate. Hence, an answer like 1.00001 confirms that 1.000 is valid up to three decimal places. Additionally, using Newton's method can improve approximations, such as refining an initial estimate of the solution to tan x = x from about 4.5 to a more precise six decimal places.