From the problem we can get that the y intercept of the line of travel is the y coordinate of the spaceship.
Given,
You have discovered another alien. Find the correct rescue path .
When the spaceship starts from a point on the y axis, we have to find the y intercept of the line of travel.
y-intercept;
A y-intercept, also known as a vertical intercept, is the location where the graph of a function or relation intersects the coordinate system's y-axis. This is done in analytic geometry using the common convention that the horizontal axis represents the variable x and the vertical axis the variable y. These points satisfy x = 0 because of this.
Here,
From the problem we can get that the y intercept of the line of travel is the y coordinate of the spaceship.
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-15/2 = 3x solve for x and simplify your answer as much as possible
Answer:
x = -5/2
Step-by-step explanation:
-15/2 = 3x
multiply both sides by 2:
2(-15/2) = 2(3x)
-15 = 6x
divide both sides by 6:
-15/6 = 6x/6
x = -15/6
this can be reduced to:
x = -5/2
Please solve this quickly. Thanks!
Applying the trapezoid midsegment theorem, the diameter of the bottom layer of the cake = KS = 26 inches.
What is the Diameter of a Circular Shape?The diameter of any circular shape is the length of the line segment that divides the shape into two equal halves and runs through its center.
What is the Trapezoid Midsegment Theorem?The trapezoid midsegment theorem states that the length of the midsegment of a trapezoid that is parallel to its bases is equal to half of the sum of the bases.
Using the trapezoid midsegment theorem we have:
MQ = 1/2(NP + LR)
Substitute
MQ = 1/2(8 + 20)
MQ = 1/2(28)
MQ = 14 inches
Also, we would also have:
LR = 1/2(MQ + KS) [trapezoid midsegment theorem]
Substitute
20 = 1/2(14 + KS)
40 = 14 + KS
40 - 14 = KS
26 = KS
KS = 26
The diameter = KS = 26 inches.
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The diameter(KS) of the cake's bottom layer is calculated using the trapezoid midsegment theorem is 26 inches.
What is a Diameter?The diameter of a circle is equal to the length of the line segment running through its center and dividing it into two equal halves.
According to the trapezoid midsegment theorem the length of a trapezoid's midsegment that is parallel to its bases is equal to half of the sum of the bases.
MQ = 1/2(NP + LR)
MQ = 1/2(8 + 20)
MQ = 1/2(28)
MQ = 14 inches.
And,
LR = 1/2(MQ + KS).
20 = 1/2(14 + KS)
40 = 14 + KS
40 - 14 = KS
26 = KS
KS = 26
The diameter(KS) is 26 inches.
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What is the equation of a line that passes through the point (5, −3) and is parallel to 6x+3y=−12?
Enter your answer in the box.
Answer: Slope= -2.000
x-intercept= -2
y-intercept= -4.000
Hope this helps !
The measures of the angles of a triangle are shown in the figure below. Solve for x.
54°
(7x+1)°
The value of x according to the complete task content as given is; 5.
Sum of interior angles in a triangle.It follows from the complete task content that a right angled triangle is given(in which case one of the angles is a right angle = 90°).
Hence, the required value of x can be determined from the; sum of interior angles of a triangle as follows;
90° + 54° + 7x + 1° = 180°
7x = 180° - 90° - 54° - 1°
Evaluate the right side of the equation;
7x = 35°
Divide both sides by; 7;
x = 35°/7
x = 5.
Ultimately, the value of x according to the task content is; 5.
Remark:
The completed task content is; The measures of the angles of a triangle are shown in the figure below. Solve for x. The figure is a right triangle with the other two interior angles 54° and (7x + 1)°.
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a cyber hacker is trying to identify the mean age of customers that make frequent purchases on the online retail platform. the hacker does not have access to the raw data, however, the hacker had guessed that the age of customers is normally distributed with a standard deviation of 5 years. in addition to the above, the hacker knows that 70% of the time the age of the customers does not exceed 30 years old. calculate the mean age of customers, relying on the above information.
The mean age of customers is 27.35 years.
It is well known that age has a normal distribution with a 5-year standard deviation. Additionally, 30% of the time, customers are under the age of 30.
Mathematically,
P (age ≤ 30) = 0.70
Let μ be the mean age of the customer.
P [z ≤ (30 - μ) / σ] = 0.70
The equivalent of "age" in a conventional normal distribution is the z-score or z. It is evident from the usual normal distribution table that when z=0.53, 0.70 probability is reached.
Thus,
z = (30 - μ) / σ
⇒ 0.53 = (30 - μ) / 5
⇒ μ = 27.35
As a result, the average consumer is 27.35 years old.
The probability at each z-score in a standard normal table is represented by the associated z-score. We will look for the number 0.70 in the table, then the row value of 0.5 and the associated column value of 0.03 will be examined. They add up to 0.53 when combined.
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A food truck vendor determined that 42% of his customers order a beverage with their food. What is the ratio of customers who order a beverage to customers who do not order a beverage?
Answer:29
Step-by-step explanation:
need help on this, thanks
In the pair of given angles, the value of 2x and x is 52° and 26°.
What are angles?When two straight lines or rays intersect at a single endpoint, an angle is created. The vertex of an angle is the location where two points come together. The Latin word "angulus," which means "corner," is where the word "angle" originates. The names of fundamental angles include acute, obtuse, right, straight, reflex, and full rotation. A geometrical shape called an angle is created by joining two rays at their termini. In most cases, an angle is expressed in degrees. In geometry, there are several different kinds of angles.So, the value of 2x and x:
We know that the given pair of angles is an exterior alternate angle.A pair of exterior alternate angles is always 180°.Now, solve for x and 2x as follows:
2x + 128 = 1802x = 180 - 1282x = 52°x = 52/2x = 26°Therefore, in the pair of given angles, the value of 2x and x is 52° and 26°.
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What is the exponential form of sq.rt (5^x)?
Answer:
Step-by-step explanation:
Comment and Answer
√5^x
The square root is really 0.5 as a decimal or 1/2 as a fraction. Both are powers.
So the square root of 23 can be written as 23^.5
For your question, you divide the power (x) by 2 so it looks like this.
5^(x/2)
A new pet store is offering 12% off for their grand opening! A parakeet originally costs $17. What is the sale price after the discount?
Let:
Oc = original cost = $17
Sp = Sale price
D = Discount percent = 12% = 12/100 = 0.12
The sale price will be:
[tex]\begin{gathered} Sp=Oc-0.12\cdot Oc \\ Sp=17-0.12\cdot17 \\ Sp=17-2.04 \\ Sp=14.96 \end{gathered}[/tex]The sale price is $14.96
Convert the rectangular equation to polar form
2x - y =3
Answer:
[tex]\dfrac{3}{2\cos\theta - r\sin\theta}[/tex]
Step-by-step explanation:
The polar coordinate system uses two parameters r and θ where r is the magnitude of the radius of the circle in polar form(also known as the radial coordinate) and θ the angle which the which the radius makes relative to the x=axis
The following equations are used to convert from cartesian coordinate to polar coordinates
[tex]r = \sqrt{x^2 + y^2}\\\\\\x = r\cos\theta\\\\y= r\sin\theta\\\\[/tex]
Substituting for x and y in terms of r and θ into the equation 2x - 3y = 3 gives
[tex]2x - y = 3\\\\2r\cos\theta - r\sin\theta = 3\\\\r(2\cos\theta - r\sin\theta = 3\\\\r = \dfrac{3}{2\cos\theta - r\sin\theta}[/tex]
Which of the following values are solutions to the inequality 9 ≤ -7+ 4x?
I. - 4
II. O
III. 4
Answer: Inequality Form: x ≥ 4
lll. 4
Step-by-step explanation:
Isolate the variable by dividing each side by factors that don't contain the variable.
Answer:
Your answer is x ≥ 4
Step-by-step explanation:
a) Simplify both sides of the inequality.
9 ≤ 4x − 7
b) Flip the equation.
4x − 7 ≥ 9
c) Add 7 to both sides.
4x − 7 + 7 ≥ 9 + 7
4x ≥ 16
d) Divide both sides by 4.
4x/4 ≥ 14/4
x ≥ 4
if f(3)=6, what is the value of f^-1(6)?
If the function f(3) has a value of 6, then the value of f⁻¹(6) is 3
How to determine the composite function?From the question, the definition of the function is given as
f(x)
Such that
The value of f(3) is 6
This is represented as
f(3) = 6
Also, the function can be represented as
y = f(x)
In f(3) = 6, we have
x = 3 and y = 6
When the inverse function is calculated, we have
f⁻¹(y) = x
This means that
f⁻¹(6) = 3
Express as an inverse function
f⁻¹(6) = 3
Hence, the inverse function f⁻¹(6) has a value of 3
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What is the answer for this as the y- intercept of two points? (-6,-5) and (-4,-4)
The slope intercept form of the equation that passes through (-6, -5) and (-4, -4) is y = 1 / 2x - 2
How to represent equation in slope intercept form?The equation in slope intercept form can be represented as follows:
y = mx + b
where
m = slopeb = y-interceptTherefore, let's find the slope of the lines using (-6, -5) and (-4, -4).
m = y₂ - y₁ / x₂ - x₁
m = -4 + 5 / -4 + 6
m = 1 / 2
Therefore, lets find the y-intercept using (-4, -4)
-4 = 1 / 2 (-4) + b
-4 = -2 + b
b = -4 + 2
b = -2
Therefore, y = 1 / 2x - 2
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The slope-intercept form of the equation that passes through (-6, -5) and (-4, -4) will be; y = 1 / 2x - 2
What is slope intercept form?The equation in slope intercept form can be represented as :
y = MX + b
where m is the slope, b is the y-intercept
Therefore, to determine the slope of the lines using (-6, -5) and (-4, -4).
m = y₂ - y₁ / x₂ - x₁
m = -4 + 5 / -4 + 6
m = 1 / 2
Therefore, the y-intercept using (-4, -4)
-4 = 1 / 2 (-4) + b
-4 = -2 + b
b = -4 + 2
b = -2
Thus, y = 1 / 2x - 2
The slope-intercept form of the equation that passes through (-6, -5) and (-4, -4) will be; y = 1 / 2x - 2
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is the equation below represent a direct proportion. if so what is the constant 3x + 4 = y
The expression for a linear equation in thee slope-intercept form is ,
y = mx + b
the slope = m= (y2-y1)/ (x2-x1)
y-intercept is (0, b)
___________________
Rearreging tha expresion
y = 3x + 4
The rate is the slope (m) = 3
__________________________
Answer
the constant, in this case, is 3
If Santa drives at an average speed of 60 miles per hour for a distance of 1,260 miles, how long will Santa's trip take?
Step 1: Speed is defined as the rate of covering a distance, mathematically it is given by
[tex]\begin{gathered} S\text{peed}=\frac{\text{distance}}{\text{time}} \\ S=\frac{d}{t} \end{gathered}[/tex]Step 2: Make the time (t) of the subject in the above speed formula
[tex]t=\frac{d}{S}[/tex]Step 3: Given the distance covered and the average speed used during the trip as
[tex]\begin{gathered} S=60\text{miles per hour} \\ d=1260\text{ miles} \end{gathered}[/tex]Step 4: Substitute the values for distance and speed in the time formula in step 2
[tex]\begin{gathered} t=\frac{d}{S} \\ t=\frac{1260}{60} \\ t=21\text{ hours} \end{gathered}[/tex]Hence, Santa's trip will take up to 21 hours
Answer:
To find out the time required to travel the distance of 1260 miles we need to divide the total distance travelled by the distance travelled in one hour.
[tex]1260/60=21[/tex]
So, it tool 21 hours for Santa to complete the trip
What are the Missing Angles? Are these triangles the similar or Not similar?
Answer:
The missing angle in Triangle A is 66 degrees
The missing angle in Triangle B is 34 degrees
Because Triangle A has measures of 34 degrees, 80 degrees, and 66 degrees
and
Triangle B has measures of 80 degrees, 66 degrees, and 34 degrees, we can conclude that THEY ARE SIMILAR TRIANGLES
Explanation:
The sum of angles in a triangle is 180 degrees.
Given that triangle A has m<1 = 34 degrees, m<2 = 80 degrees. Let the missing angle be x, then
x + 34 + 80 = 180
x + 114 = 180
Subtract 114 from both sides
x = 180 - 114
= 66 degrees
Triangle B has m<1 = 80 degrees, m<2 = 66 degreess. Let the missing angle be y, then
y + 80 + 66 = 180
y + 146 = `180
Subtract 146 from both sides
y = 180 - 146
= 34 degrees
Triangles A and B are similar, since they have similar measure of angles.
NEED HELP ASAP THIS IS OVERDUE !!!
Answer:
A
Step-by-step explanation:
The slope goes up by 11 and over by 1.
Answer: D
Step-by-step explanation:
y= [tex]\frac{1}{55}[/tex]×
sin(40 + 2°) csc(30 + 5°) = 1
sin(40 + 2°) cosec(30 + 5°) = 1 we proved that by the values.
Given,
sin(40 + 2°) cosec(30 + 5°) = 1
To prove the trigonometry function equal to 1.
Now, According to the question:
We know that
Sin 42° = 0.66913061
Cosec 35° = 1.7434468
sin(40 + 2°) cosec(30 + 5°) = 1
sin 42° × cosec 35° = 1
Plug the values of sin and cosec in above function:
0.66913061 × 1.7434468
= 1.16659
But we take the before decimal value i.e., 1
Hence, sin(40 + 2°) cosec(30 + 5°) = 1 we proved that by the values.
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1/2 (7/10-3/5) + -1.9
Answer: -1 17/20
Step-by-step explanation: use order of operations to solve, parenthesis, multiplication, addition/subtraction
12 friends are sharing 8 packs of pencils. What fraction of a package will each friend receive?
Answer:
33/50
Step-by-step explanation:
8/12=.66666667
.6666667=33/50
33/50 in simplest form is 33/50
hope this helped
have a good day ^^
Point(2,8) , (4,7.5) rise over run so what's the answer
The slope of the line with the given coordinates (2,8) and (4,7.5) is -0.25.
What is the slope of the line with the given coordinates?Slope is simply expressed as change in y over the change in x.
Rise over run.
Slope m = ( y₂ - y₁ )/( x₂ - x₁ )
Given the data in the question;
Point 1( 2,8) )
x₁ = 2y₁ = 8Point 2( 4,7.5 )
x₂ = 4y₂ = 7.5To find the slope, plug the given x and y values into the slope formula and simplify.
Slope m = ( y₂ - y₁ )/( x₂ - x₁ )
Slope m = ( 7.5 - 8 )/( 4 - 2 )
Slope m = ( -0.5 )/( 2 )
Slope m = -0.5 / 2
Slope m = -0.25
Therefore, the slope of the line is -0.25.
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How many 5's ar in 125 ?
Answer:
There are 25 5's in 125.
Step-by-step explanation:
5 can go in 125 25 times.
(unless you are talking about literally-- there is one 5 in 125)
in your own words explain angle addition postulate
This postulate tells us that when we put two angles side by side with a ray touching the ray of the other angle, we are creating a new angle which is the addition of the two, and whose measure is the addition of the measures of the two angles we are contacting via a common ray.
An exterior angle of a rectangle polygon cannot have the measure
The sum of the measures of an exterior angle of a polygon is 360°.
If the given angle divides 360 evenly, then it can be a measure of an exterior angle of a polygon. If otherwise, then it cannot be.
[tex]\begin{gathered} 360\div30=12 \\ 360\div50=7.2 \\ 360\div120=3 \\ 360\div90=4 \\ 360\div40=9 \end{gathered}[/tex]Out of the given angles, only 50 does not divide 360 evenly. Therefore, a regular polygon cannot have an exterior angle measuring 50°. (Option B)
What is the value of this expression.
this is the answer to your equation hope it helps thanks
Answer:
D. [tex]\dfrac{27}{4}\\\\[/tex]
Step-by-step explanation:
[tex]\mathrm{With\;x=\dfrac{1}{8}\;and\;y = \dfrac{3}{16}\;we\;get}\\\\[/tex]
[tex]2\left(\dfrac{1}{8}+4\right)-\left(\dfrac{3}{16}\cdot 8\right)\\\\[/tex]
[tex]\mathrm{Calculate\:within\:parentheses}\:\left(\dfrac{1}{8}+4\right) = \dfrac{1}{8}+\dfrac{32}{8}} = \dfrac{33}{8}\\\\[/tex]
[tex]2\left(\dfrac{1}{8}+4\right) = 2\cdot \dfrac{33}{8} = \dfrac{33}{4}[/tex]
[tex]y \cdot 8 = \dfrac{3}{16} \cdot 8} = \dfrac{3}{2}\\\\[/tex]
So
[tex]2(x + 4) - y\cdot 8 = \dfrac{33}{4} - \dfrac{3}{2}\\\\\\= \dfrac{33-6}{4}\\\\= \dfrac{27}{4}\\\\[/tex]
professor smith loves dark chocolate, and she would like to find out the proportion of the population that shares her preference. she randomly sampled 150 people, and 120 people choose dark chocolate. to construct a 95% confidence interval, she should use:
Use 1-Prop Z Int to create a 95% confidence interval.
Z test should be employed because there is only one set of samples collected and the sample size is huge.
An observed percentage is compared to a theoretical one using a one proportion z-test. The test statistic is determined as follows:
z = (p-p0) / √(p0(1-p0)/n)
where:
p = observed sample proportion
p0 = hypothesized population proportion
n = sample size
You can reject the null hypothesis if the p-value associated with the test statistic z is less than your selected level of significance (popular choices are 0.10, 0.05, and 0.01).
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$20 off, 30% original price
Answer:
20%
Explanation:
To know the percentage, we need to identify what percentage of $50 represents $10. So, we can calculate the percentage as:
[tex]\frac{\text{ \$10}}{\text{ \$50}}\times100=0.2\times100=20\text{ \%}[/tex]Therefore, the answer is 20%
HELP ASAP-GETS BRAINIEST GETS 100 POINTS.
In a theater with 30 rows the number of seats in a row increases by two with successive row. the front has 15 seats find the total seating capacity of the theater.
Answer:
75
Step-by-step explanation:
15 + 2 × 30
Answer:
1320 seats.
Step-by-step explanation:
The given scenario can be modeled as an arithmetic series.
[tex]\boxed{\begin{minipage}{7.3 cm}\underline{Sum of the first $n$ terms of an arithmetic series}\\\\$S_n=\dfrac{1}{2}n[2a+(n-1)d]$\\\\where:\\\phantom{ww}$\bullet$ $a$ is the first term. \\ \phantom{ww}$\bullet$ $d$ is the common difference.\\ \phantom{ww}$\bullet$ $n$ is the position of the term.\\\end{minipage}}[/tex]
The first term is the number of seats in the front row.
Given that the number of seats in a row increases by 2 with each successive row, the common difference is 2.
The nth term is 30 since there are 30 rows in the theater.
Therefore:
a = 15d = 2n = 30Substitute the values into the arithmetic series formula and solve:
[tex]\implies S_{30}=\dfrac{1}{2}(30)[2(15)+(30-1)2][/tex]
[tex]\implies S_{30}=15[30+(29)2][/tex]
[tex]\implies S_{30}=15[30+58][/tex]
[tex]\implies S_{30}=15[88][/tex]
[tex]\implies S_{30}=1320[/tex]
Therefore, the total seating capacity of the theater is 1320 seats.
Triangle ABC is congruent to triangle XYZ. In AABC, AB = 12 cm and AC = 14 cm. In AXYZ, YZ = 10 cm and XZ = 14
!
cm.
What is the perimeter of AABC?
O 36 cm
O 38 cm
О 40 cm
• 50 cm
The perimeter of the triangle ABC is 36 cm. Then the correct option is A.
What is the triangle?A triangle is a three-sided polygon with three angles. The angles of the triangle add up to 180 degrees. If two triangles are similar, then the ratio of the corresponding sides will remain one.
Triangle ABC is congruent to triangle XYZ. In AABC, AB = 12 cm and AC = 14 cm. In AXYZ, YZ = 10 cm and XZ = 14 cm.
AB = XY = 12 cm
BC = YZ = 10 cm
AC = XZ = 14 cm
Then the perimeter of the triangle ABC is given as,
P = 12 + 10 + 14
P = 36 cm
The perimeter of the triangle ABC is 36 cm. Then the correct option is A.
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aghwhelrrotiuugggdddd
Solution
We have the following info:
Grades Credits
B 2
B 5
B 5
C 2
And we know that A= 4, B= 3, C=2
So we can do this:
[tex]\operatorname{mean}=\frac{3\cdot2+3\cdot5+3\cdot5+2\cdot2}{2+5+5+2}=2.86[/tex]then the weighted average is 2.86