Answer:
[tex]x=1[/tex]
Step-by-step explanation:
Remember:
[tex](\sqrt[n]{a})^n=a\\\\(a+b)=a^2+2ab+b^2[/tex]
Given the equation [tex]\sqrt{17-x}=x+3[/tex], you need to solve for the variable "x" to find its value.
You need to square both sides of the equation:
[tex](\sqrt{17-x})^2=(x+3)^2[/tex]
[tex]17-x=(x+3)^2[/tex]
Simplifying, you get:
[tex]17-x=x^2+2(x)(3)+3^2\\\\17-x=x^2+6x+9\\\\x^2+6x+9+x-17=0\\\\x^2+7x-8=0[/tex]
Factor the quadratic equation. Find two numbers whose sum be 7 and whose product be -8. These are: -1 and 8:
[tex](x-1)(x+8)=0[/tex]
Then:
[tex]x_1=1\\x_2=-8[/tex]
Let's check if the first solution is correct:
[tex]\sqrt{17-(1)}=(1)+3[/tex]
[tex]4=4[/tex] (It checks)
Let's check if the second solution is correct:
[tex]\sqrt{17-(-8)}=(-8)+3[/tex]
[tex]5\neq-5[/tex] (It does not checks)
Therefore, the solution is:
[tex]x=1[/tex]
the only solution is x = 1.
To solve the equation sqrt(17-x) = x+3, we first eliminate the square root by squaring both sides of the equation. Doing so yields:
17 - x = (x + 3)2
17 - x = x2 + 6x + 9
Next, we rearrange the equation to set it equal to zero, thus forming a quadratic equation:
x2 + 6x + 9 + x - 17 = 0
x2 + 7x - 8 = 0
Now, we factor the quadratic:
(x + 8)(x - 1) = 0
Hence, the solutions are:
x = -8
x = 1
To verify that these solutions satisfy the original equation, we perform a check by substituting them back into the original equation. However, we notice that the solution x = -8 does not work because it would result in taking the square root of a negative number, which is not possible in real numbers. So the only solution is x = 1.
a newspaper is curious about the satisfaction of their readers. when a person visits the newspaper's webpage, they are asked to complete a brief summary online. Biased or Unbiased?
A newspaper asking readers to complete a survey on their webpage is not conclusively biased or unbiased without knowing more about the survey's design and intention. Surveys can be a method to engage with and understand the readership better, but the potential for selection bias and the phrasing of questions could introduce bias. Whether the survey is biased or not depends on its execution and underlying methodological rigor.
Explanation:The question "Is a newspaper asking readers to complete a brief survey on their webpage biased or unbiased" revolves around evaluating the intentions and methodology behind collecting reader satisfaction feedback. Given the nature of the survey is to collect feedback directly from readers on the newspaper webpage this can initially seem like a genuine effort to improve their service.
For evaluating the unbiased information based on research, it is crucial to consider the intent behind the survey and the potential for selection bias. It might inadvertently capture only the opinions of those willing to participate, or primarily those with strong opinions, positive or negative. Despite these considerations, the effort to engage with the readership directly can also be seen as a step towards transparency and improvement, indicating a potential to balance partiality with constructive feedback.
However, to ensure the process is unbiased, the newspaper would need to follow rigorous methodological standards, like random sampling, to ensure that the survey findings reflect the actual population of readers accurately. It's also essential to ensure that questions are phrased neutrally to avoid leading respondents towards a particular answer.
Our basketball team has 10 players. we need to divide into two teams of 5 for an intra-squad scrimmage. in how many ways can we do this without restriction?
There are 252 ways to divide the 10 players into two teams of 5 without any restriction.
To determine the number of ways you can divide 10 players into two teams of 5 without any restriction,
Using the formula, C(n, k) = [tex]\frac{n!}{k!(n-k)!}[/tex]
By finding the number of ways to choose 5 players out of 10, which is the same as choosing the other 5 players who are not on the first team.
Where n = 10
k = 5
C(10, 5) = [tex]\frac{10!}{5!(10-5)!}[/tex]
C(10, 5) = [tex]\frac{10!}{5!(5)!}[/tex]
C(10, 5) = 10*9*8*7*6*5*4*3*2*1/5*4*3*2*1(5*4*3*2*1)
C(10, 5) = 30240/5*4*3*2*1
C(10, 5) = 252 ways
Therefore, there are 252 ways to divide the 10 players into two teams of 5 without any restriction.
What will happen to the mean if the outlier is removed?
4, 5, 5, 7, 9, 17
It will not change.
It will be the same as the median.
It will decrease.
It will increase.
The mean is the average. The outlier is a number way bigger or smaller than the rest of the data. The outlier here would be 17. If you remove 17 and then find the average again, it will be smaller because all the numbers left are around the same range.
Answer: It will decrease
I have SAT's tomorrow and need help with math...
Antonina needs to have worked at least 90 volunteer hours to graduate. She has already volunteered with a housing organization over the summer for 52 hours. Antonina needs to tutor after school for 3 hours per week to complete the remainder of her volunteer hours. If w is the number of weeks that Antonina needs to tutor in order to complete her volunteer hours, which of the following inequalities best models the situation described above?
Answer:
3w + 52 ≥ 90
Step-by-step explanation:
If she volunteers 3 hours per week for w weeks, then the number of hours from tutoring is 3w. Add the 52 hours from her summer volunteering, and her total hours is 3w + 52. This needs to be at least 90 hours for her to graduate, so:
3w + 52 ≥ 90
Please help me out please
Answer:
20°
Step-by-step explanation:
40=2x,x=20°
A airplane travels at 150 miles per hour the number of hours at that rate is h what is an expression for the number of miles traveled?
Final answer:
The expression for the number of miles traveled by the airplane is 150h.
Explanation:
The expression for the number of miles traveled by the airplane is 150h. This expression represents the distance covered by the airplane based on the number of hours, h, it has been traveling at a speed of 150 miles per hour.
The expression for the number of miles traveled is [tex]\[ \text{Distance} = 150h \][/tex].
To determine the number of miles an airplane travels given its speed and the duration of travel, we can use a basic formula from physics that relates distance, speed, and time. The formula is:
[tex]\[ \text{Distance} = \text{Speed} \times \text{Time} \][/tex]
Here, the speed of the airplane is given as 150 miles per hour, and the time is represented by ( h ) hours.
Step 1.Identify the given values:
Speed ( v ) = 150 miles per hour
Time ( h ) = number of hours
Step 2. Apply the formula for distance:
Distance ( d ) = [tex]Speed (\( v \)) \(\times\) Time (\( h \))[/tex]
Step 3. Substitute the given values into the formula:
[tex]\( d = 150 \text{ miles per hour} \times h \text{ hours} \)[/tex]
[tex]\( d = 150h \)[/tex]
Thus, the expression for the number of miles traveled by the airplane, when it travels at 150 miles per hour for ( h ) hours, is:
[tex]\[ \text{Distance} = 150h \][/tex]
what is the range of the data set?
69
49
40
19
Answer:
19
Step-by-step explanation:
to find the range, you have to subtract the smaller number from the biggest number
In this case it would be 45-26
45-26=19
range=19
Can someone show me the steps to do this :( please
Answer:
Step-by-step explanation:
Use the sum of angle formula:
cos(a+b) = cos(a)cos(b) -sin(a)sin(b)
This gives you ...
cos(x)cos(-π/6) -sin(x)sin(-π/6) = 1 + cos(x)cos(π/6) -sin(x)sin(π/6)
Subtracting the right-side trig function terms and factoring, we have ...
cos(x)(cos(-π/6) -cos(π/6)) -sin(x)(sin(-π/6) -sin(π/6)) = 1
Since the cosine is an even function, cos(-π/6) = cos(π/6). Since the sine is an odd function, sin(-π/6) = -sin(π/6). This gives us ...
cos(x)·0 -sin(x)(-2sin(π/6)) = 1
sin(x) = 1/(2·sin(π/6)) = 1/(2·1/2) = 1
x = arcsin(1)
x = π/2
_____
When solving these by using a graphing calculator, it is convenient to subtract one side of the equation so you have a function of x that you want to find the zeros of. Here, we subtracted the right side. The graph shows the result is zero for x=π/2, as we know.
(99 POINTS AND BRAINLIEST NEED HELP ASAP)
A prism and two nets are shown below:
Part A: Which is the correct net for the prism? Explain your answer.
Part B: Write the measurements of Sides AB, BC, and CD of the correct net.
Part C: What is the surface area of the prism? Show your work.
I know that the answer is A, however I can not answer the rest
19. Heather invests $4,900 in an account with a 3.5% interest rate, making no other deposits or withdrawals. What will Heather’s account balance be after 5 years if the interest is compounded 2 times each year?
Answer:
[tex]\$5,828.28[/tex]
Step-by-step explanation:
we know that
The compound interest formula is equal to
[tex]A=P(1+\frac{r}{n})^{nt}[/tex]
where
A is the Final Investment Value
P is the Principal amount of money to be invested
r is the rate of interest in decimal
t is Number of Time Periods
n is the number of times interest is compounded per year
in this problem we have
[tex]t=5\ years\\ P=\$4,900\\ r=0.035\\n=2[/tex]
substitute in the formula above
[tex]A=\$4,900(1+\frac{0.035}{2})^{2*5}[/tex]
[tex]A=\$4,900(1.0175)^{10}=\$5,828.28[/tex]
Answer:
5,828.28
Step-by-step explanation:
Miss Stoner purchase a new computer for $1,150 at the Apple store if sales tax is 7.5% what is the total of her purchase
Answer:
$1236.25
Step-by-step explanation:
We can convert the percentage to 0.075 to make it easier. Then, multiply 1150 by 1.075 to get 1236.25. We add the one because we need to include the initial $1150.
A bag contains 40 marble ,4 of which are blue , 10 are red ,25 are green , and 1 purple Shawna takes a marble out of the bag, records the color and returns it to the bag . How many green marbles should she exepect after 400 trials
She should expect 250 green marbles.
She has a 25 out of 40 chance of selecting a green marble each time since she is putting it back in the bag each time. 25/40 reduces to 5/8. Multiply 5/8 by 400 and you get 2000/8. Reduce the fraction to 250/1 or 250.
Yvonne is a salesperson who earns a fixed amount of $1,850 per month. She also earns a commission of 4% on the amount of goods that she sells. If she wants to earn more than $2,300 in one month, how many dollars (x) in goods must she sell?
Answer: $11,250
1850 + (4/100)x = 1850 + 0.04x.
1850 + 0.04x > 2300
0.04x > 2300 - 1850
0.04x > 450
x > 450 / 0.04
x > $11,250
Answer
x> 11,250
yyyyyyyyyyyyyyyyyeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeee
A pentagonal prism is cut be a plane perpendicular to the base . What is the shape of the cross section that is formed?
Answer:
Step-by-step explanation:
The cross section will have the same shape as the base of the pentagonal prism; the dimensions will be proportionally smaller.
An object moves along a circular path with radius 10 inches and makes 5 revolutions in 1 minute. What is the linear velocity, in inches per minute, of a point on the edge of the wheel?
10π
20π
50π
100π
Answer:
100π
Step-by-step explanation:
step 1
Find the circumference
The circumference is equal to
[tex]C=2\pi r[/tex]
we have
[tex]r=10\ in[/tex]
substitute
[tex]C=2\pi (10)[/tex]
[tex]C=20\pi\ in[/tex]
step 2
we know that
An object moves along a circular path and makes 5 revolutions in 1 minute
Remember that
[tex]1\ rev=2\pi r[/tex] ----> circumference of the circle
therefore
[tex]5\ rev=5(20\pi)=100\pi\frac{in}{minute} [/tex]
If John can drive his car for 343.8 miles on 9 gallons of gas, how far can he drive on 1 gallon of gas
Answer:
38.2 miles
Step-by-step explanation:
343.8 miles divided by 9 gallons equals 32.2 miles per gallon.
A coal car on a train weighs 30 tons plus 1 ton per cubic yard of coal x that it carries. The total weight of a coal car is: f(x) = x + 30. How will the graph of this function change if the coal car weight is changed to 26 tons?
Answer:
every point will be 4 tons lower than it was
Step-by-step explanation:
26 is 4 less than 30, so the new function g(x) is ...
g(x) = f(x) -4
It is shifted down 4 units (tons) from the original function.
You pick a card at random, put it back, and then pick another card at random. 3 4 5 What is the probability of picking a number greater than 3 and then picking an even number?
Final answer:
To find the probability of drawing a four and then a five from a standard deck with replacement, multiply the probabilities of the independent events: (1/13) × (1/13) = 1/169.
Explanation:
The question involves calculating the probability of two independent events when drawing cards from a standard deck. The first event (A) is drawing a card that is a four, and the second event (B) is drawing a card that is a five. The probability of each of these events is calculated separately since the card is replaced after each draw, making the draws independent of each other.
The probability of drawing a four (P(A)) from a standard deck is 1/13, as there are four fours in a 52-card deck. Similarly, the probability of drawing a five (P(B)) is also 1/13. Since the events are independent, the combined probability is the product of the two probabilities: P(A) × P(B) = (1/13) × (1/13) = 1/169.
If secx = -2, then in which quadrants do the solutions lie?
ANSWER
2nd and 3rd quadrant.
EXPLANATION
The given trigonometric equation is:
[tex] \sec(x) = - 2[/tex]
The secant ratio is negative in the second and third quadrant.
But it is positive in the first and fourth quadrants.
The given secant ratio is negative.
This implies that , the solution to given equation lies in the second and third quadrant.
Identify m∠F. PLEASE HELP!!
Answer:
D. <F = 65 degrees
Step-by-step explanation:
First off, we know that the measures of <F and the angle adjacent to it add to 90 degrees, as indicated by the right angle. They are complementary angles.
The complementary angle of <F has an intercepted arc of 50 degrees. Because the angle is on the opposite end of the circle, it is half of the measure of the arc. Therefore, it is 25 degrees.
Because this angle and <F sum to 90, just subtract 90-25 to find <F.
<F = 65 degrees
Answer:
F is equal to 65 (option D)
The table below shows the values for the function y = f(x).
| x | y |
-4 7
-1 -2
0 3
3 -4
6 5
Complete the table for the function y = f(1/5x).
Answer:
(x, y) = (-20, 7), (-5, -2), (0, 3), (15, -4), (30, 5)
Step-by-step explanation:
You want 1/5x to match the x-value in the given table. To make that happen, multiply the given x by 5.
Example: when (1/5x) = -4, f(1/5x) = 7, so x = -4·5 = -20 for y = 7.
The transformation f(1/5x) is a horizontal expansion by a factor of 5, so each point of f(x) is now 5 times farther from the y-axis than it was.
The completed table for the function [tex]\(y = f\left(\frac{1}{5}x\right)\)[/tex] is as follows:
x
−4
−1
0
3
6
y
3
−2
3
7
5
To complete the table for the function [tex]\(y = f\left(\frac{1}{5}x\right)\),[/tex] we need to substitute the given \(x\) values into the function [tex]\(y = f\left(\frac{1}{5}x\right)\)[/tex] and calculate the corresponding \(y\) values.
The function [tex]\(y = f\left(\frac{1}{5}x\right)\)[/tex]implies that we are scaling the input \(x\) by a factor of 5. This means the \(x\) values in the original table need to be multiplied by 5 to find the corresponding values for the new function. Let's calculate the values step by step:
1. For [tex]\(x = -4\):[/tex]
[tex]\[y = f\left(\frac{1}{5}(-4)\right) = f(-0.8)\][/tex]
Looking at the original table, when [tex]\(x = -0.8\), \(y = 3\).[/tex]
2. For [tex]\(x = -1\):[/tex]
[tex]\[y = f\left(\frac{1}{5}(-1)\right) = f(-0.2)\][/tex]
When [tex]\(x = -0.2\), \(y = -2\).[/tex]
3. For [tex]\(x = 0\):[/tex]
[tex]\[y = f\left(\frac{1}{5}(0)\right) = f(0)\][/tex]
When [tex]\(x = 0\), \(y = 3\).[/tex]
4. For [tex]\(x = 3\):[/tex]
[tex]\[y = f\left(\frac{1}{5}(3)\right) = f(0.6)\][/tex]
When [tex]\(x = 0.6\), \(y = 7\).[/tex]
5. For [tex]\(x = 6\):[/tex]
[tex]\[y = f\left(\frac{1}{5}(6)\right) = f(1.2)\][/tex]
When [tex]\(x = 1.2\), \(y = 5\).[/tex]
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Please answer this correctly
The answer is 8......
Answer:
The answer is 8
Step-by-step explanation:
Just add the rest of the numbers and then subtract from the answer
Please Help!!
Which function has zeroes at npi, where n is an integer? Select 2.
y=cos x
y=cot x
y=csc x
y=sec x
y=sin x
y=tan x
ANSWER
[tex]y = \sin(x) [/tex]
EXPLANATION
The trigonometric function that is zero at integral values is the sine function.
That is;
[tex]y = \sin(x) [/tex]
has x-intercepts at
[tex] n\pi[/tex]
where n is an integer.
In other words, the solution to the equation:
[tex] \sin(x) = 0[/tex]
is
[tex]x = n\pi[/tex]
where n is an integer.
Answer:
y=sin x
y=tan x
these are correct....
use an appropriate technology to simulate 35 rolls of a six sided number cube according to this data,what is the experimental probability of a roll of 3? what is the theoretical probability that a roll of the number cube will yield a result of 3? explain any differences between the theoretical probability and the experimental probability.
Explanation of experimental and theoretical probability of rolling a 3 on a six-sided number cube.
The experimental probability of rolling a 3:
Simulate 35 rolls of a six-sided number cube to get results.
Count the number of times a 3 is rolled and calculate the experimental probability by dividing the number of 3s rolled by 35.
The theoretical probability of rolling a 3:
Theoretical probability = Number of favorable outcomes / Total number of outcomes = 1/6 (since there is 1 favorable outcome out of 6 possible outcomes).
Differences between theoretical and experimental probabilities:
Theoretical probability is based on calculations and assumptions, while experimental probability is based on actual observations. Discrepancies between the two can occur due to sample size, random variations, or errors in the simulation.
Hey I am struggling with this question and was hoping someone could help me before 7:00PM CST.
11.) 5x/x^2+2x÷30x^2/x+2
Thanks! I will post a picture if I can figure out how to.
Answer: x^3+30x+75
-----------------------------
15x
Step-by-step explanation:
5x/x^2+2x÷30x^2/x+2
1/15x^5+2x^3+5x^2
---------------------------
x^3
x^3+30x+75
-----------------------------
15x
[tex]\bf \cfrac{5x}{x^2+2x}\div \cfrac{30x^2}{x+2}\implies \cfrac{5x}{x^2+2x}\cdot \cfrac{x+2}{30x^2}\implies \cfrac{\begin{matrix} 5x \\[-0.7em]\cline{1-1}\\[-5pt]\end{matrix}}{x~~\begin{matrix} (x+2) \\[-0.7em]\cline{1-1}\\[-5pt]\end{matrix}}\cdot \cfrac{\begin{matrix} x+2\\[-0.7em]\cline{1-1}\\[-5pt]\end{matrix} }{\begin{matrix} 5x \\[-0.7em]\cline{1-1}\\[-5pt]\end{matrix}\cdot 6x} \\\\[-0.35em] \rule{34em}{0.25pt}\\\\ ~\hfill \cfrac{1}{6x^2}~\hfill[/tex]
The person at (0, 1) needs a bottled water. He moved to the right on a slope of -4. Where can you find him to give him the water he ordered
Final answer:
To locate the person who moved from (0, 1) with a slope of -4, we need to know the specific horizontal distance they moved. Without this, we can only say they moved downward 4 units for every 1 unit they moved to the right.
Explanation:
The student's question involves determining the position of a person who has moved along a slope on a coordinate plane. Since the individual started at the point (0, 1) and moved to the right with a slope of -4, we can assume they are moving in the negative y-direction (downward), as the negative slope indicates a decrease in y for every increase in x. The specific horizontal distance isn't given, so we cannot provide an exact new coordinate without more information. However, if we had a specific horizontal distance the person moved, we could calculate the new position using the slope (-4), which means for every 1 unit moved horizontally to the right, the person would move 4 units down.
You are getting ready to watch a fireworks display and are sitting about 300 feet away from the launch pad. The angle for you to see the fireworks is about 35°. If the fireworks are launched vertically into the sky, what is the height of the fireworks when they explode?
Answer:
210.06 feet
Step-by-step explanation:
This is a classic right triangle trig problem. The distance from the launch pad is the measure of the base of the right triangle. The angle of elevation, 35, is the base angle (not the right angle). How high the fireworks go up is the height of the triangle. You have the reference angle of 35, the side adjacent to it, 300, and you're looking for the side length across from it, y. The trig ratio that relates a reference angle to the sides opposite it and adjacent to it is the tangent ratio. Setting that up:
[tex]tan(35)=\frac{y}{300}[/tex]
Solving for y:
y = 300 tan(35)
On your calculator in degree mode find y to be 210.06 feet.
By using basic trigonometry, specifically the tangent of the viewing angle, we can determine that the height of the fireworks when they explode is approximately 210 feet.
Explanation:You are asking how to use trigonometry to find the height of the fireworks when they explode. If we combine your conditions that the launch was vertical and the viewing angle was 35°, we can use the tangent of that angle to find the height of the fireworks. The tangent of an angle in a right triangle is the opposite side (height in this case) divided by the adjacent side (distance from the launch, 300 feet in this case). So setting up the equation, we have: tan(35°) = height / 300. Solving for 'height', we get: height = 300 * tan(35°). Using a calculator, we find that tan(35°) is roughly 0.70021. Multiplying that by 300, we find that the height of the fireworks when they explode is approximately 210 feet.
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Please please help !
Answer:
13.74
Step-by-step explanation:
the top right angle is 90 (opposite angles in a quadrilateral add up to 180). use the sine rule. x = 47/sin 90 × sin 17
= 13.74
Answer:
x = 13.7
Step-by-step explanation:
The angle at the top of the triangle = 90° - 17° = 73°
The left side of the triangle is x ( opposite sides of a rectangle )
Using the cosine ratio in the right triangle
cos73° = [tex]\frac{adjacent}{hypotenuse}[/tex] = [tex]\frac{x}{47}[/tex]
Multiply both sides by 47
47 × cos73° = x, hence
x ≈ 13.7
What else would need to be congruent to show that STU is congruent to JKL by SAS? tysm! :)
Answer:
Choice C.
Step-by-step explanation:
You already have two sides and two angles. Now you need the other two sides that include the angle. Choice C is correct.
Answer: C. [tex]\overline{SU}\cong\overline{JL}[/tex]
Step-by-step explanation:
SAS congruence postulate tells that if two sides and the included angle of a triangle are congruent to corresponding two sides and the included angle of other triangle, then the triangles are congruent.In the given picture , we have two triangles ΔSTU and Δ JKL , in which we have
[tex]\overline{ST}\cong\overline{JK}[/tex]
[tex]\angle{S}\cong\angle{J}[/tex]
To prove ΔSTU is congruent to Δ JKL, we need [tex]\overline{SU}\cong\overline{JL}[/tex] such that [tex]\angle{S}\text{ and }\angle{J}[/tex] becomes congruent the included angles between pair of congruent sides.
Hence, C is the right option.
Suppose f(x)—>300 and g(x)—>0 with g(x)< 0 as x —>5. Determine lim x—>5 f(x)/g(x)
Given the conditions: f(x) approaches 300 and g(x) approaches 0 (and is less than zero as x approaches 5), the limit as x approaches 5 of the quotient f(x)/g(x) is negative infinity.
Explanation:Based on the given conditions: f(x) approaches 300 and g(x) approaches 0 as x approaches 5. Moreover, g(x) is less than zero, and therefore negative, as x approaches 5. When you divide f(x) by g(x), the sign of the outcome is determined by the signs of the numerator (f(x)) and the denominator (g(x)).
As f(x) is positive and g(x) is negative, the quotient will be negative. Since f(x) is approaching a finite value and g(x) is approaching 0, the quotient f(x)/g(x) tends toward negative infinity as per the properties of limits.
Therefore, the value of lim x→5 f(x)/g(x) is negative infinity.
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