-4x - y = 24
Let y = 8
-4x - 8 = 24
-4x = 24 + 8
-4x = 32
You finish.
Look at the unit circle shown below.
Which statement is TRUE? A The x-coordinate of P corresponds to cosθ , which has a period of 2π . B The x-coordinate of P corresponds to cosθ , which has a period of π . C The y-coordinate of P corresponds to cosθ , which has a period of 2π . D The y-coordinate of P corresponds to cosθ , which has a period of π .
Answer:
A is true.
Step-by-step explanation:
Cos θ = adjacent / hypotenuse = x/1 = x.
Cosθ has a period pf 2π.
Answer:
The correct option is A.
Step-by-step explanation:
Draw a perpendicular form point P on x-axis.
Radius of unit circle is 1 . It means in triangle OPA
Hypotenuse = OP = 1 units
Adjacent= OA = x
Perpendicular = PA = y
In a circle angled triangle,
[tex]\cos \theta = \frac{adjacent}{hypotenuse}[/tex]
In triangle OPA,
[tex]\cos \theta = \frac{x}{1}[/tex]
[tex]\cos \theta =x[/tex]
The x-coordinate of P corresponds to cosθ.
The period of a unit circle is 2π.
Therefore, the correct option is A.
This box holds 4 crates of eggs each holds 6 dozen eggs how many eggs are in a eggs are in the box when it is full.
Each crate holds 6 dozen eggs.
1 dozen = 12 eggs.
Multiply 12 by 6 to get the total number of eggs per crate:
6 x 12 = 72 eggs per crate.
The box holds 4 crates, multiply the number of each in a crate by the number of crates:
72 eggs x 4 crates = 288 total eggs.
Please help and explain I’m very confused thank you
Answer:
31° = x
Step-by-step explanation:
According to the Supplementary Angles Theorem, 123° and that acute angle right up against it, form a straight angle, so you do this:
[tex] - 123 + 180 = 57[/tex]
Now that the second angle measure is found, according to the Triangular Interior Angles Theorem, the sum of the interior angles of all triangles add up to 180°:
180° = 57° + 92° + x°
|________|
180° = 149° + x°
-149° - 149°
________________
31° = x
I am joyous to assist you anytime.
a television with a 5:4 screen shows an image with a ratio of 20:12 which creates a letter boxed image. What percent of the screen area is occupied
Answer: [tex]75\%[/tex]
Step-by-step explanation:
You know that the ratio of the television's screen is [tex]5:4[/tex] . This ratio can be also written as the following fraction:
[tex]\frac{5}{4}[/tex]
The television shows an image with a ratio of [tex]20:12[/tex] which can be also written as a fraction:
[tex]\frac{20}{12}[/tex]
Set up the following proportion and solve for "x":
[tex]\frac{20}{x}=\frac{5}{4}\\\\x=\frac{4*20}{5}\\\\x=16[/tex]
Now, in order to find the percent of the screen area occupied make the following division:
[tex]\% occupied=\frac{12}{16}*100=75\%[/tex]
Ellie colors 20% of the total shapes on her paper. She colors 10 shapes. Enter the number of shapes on Ellie's paper.
Answer:
50 shapes
Step-by-step explanation:
If 20% is 10 shapes, then 30% would be 15, 40% would be 20, and so forth. when you get to 100%, the answer would be 50 shapes because the numbers of shapes is half the percentage. For example, 5% is 2.5 shapes, 10% is 5 shapes, 60% is 30 shapes.
CAN EXPLAIN FURTHER
would appreciate brainliest, but I am content with just giving you an answer :)
On a number line, the square root of two falls between which two consecutive integers
Graph the rational function. F(x)=x^2+4x+4/x^3+5x^2
Answer:
[tex]F(x)=\frac{x^2+4x+4}{x^3+5x^2}[/tex]
Step-by-step explanation:
Graph the rational function.
A driveway is in the shape of a rectangle 3.0 meters wide by 5.0 meters long. What is its perimeter?
Answer: I believe the answer is 18 meters
Step-by-step explanation:
Answer:
The perimeter would be 16.
Step-by-step explanation:
3.0+3.0=6
5.0+5.0=10
10+6=16
what is 4127*28324
please anwser now
Answer:
116,893,148
Hope this helps :)
The product of 4127 and 28324 is 116884748.
To find the product of 4127 and 28324:
Write down the numbers vertically aligning the digits:
4127 x 28324
Multiply each digit of the second number by the entire first number, remembering to shift each subsequent multiplication one place to the left:
4127 × 4 = 16508
4127 × 2 = 8254 (shift one place to the left, becomes 82540)
4127 × 3 = 12381 (shift two places to the left, becomes 1238100)
4127 × 8 = 33016 (shift three places to the left, becomes 33016000)
4127 × 2 = 8254 (shift four places to the left, becomes 82540000)
Add all these partial products together:
16508 + 82540 +1238100 +33016000 +82540000
= 116884748
So, the product of 4127 and 28324 is 116884748.
If the discriminant of a quadratic equation is equal to -8, which statement describes the roots?
Answer:
Roots are complex numbers
Step-by-step explanation:
we know that
In a quadratic equation of the form [tex]ax^{2} +bx+c=0[/tex]
The discriminant is equal to [tex]b^{2} -4ac[/tex]
If [tex]b^{2} -4ac=0[/tex] -----> The equation has only one real root
If [tex]b^{2} -4ac>0[/tex] -----> The equation has two real roots
If [tex]b^{2} -4ac<0[/tex] -----> The equation has complex roots
In this problem the discriminant is -8
so
-8 < 0
therefore
Roots are complex numbers
Answer:
A) There are two complex roots
Step-by-step explanation:
took the test
A student has these scores on their assignments. The teacher is considering dropping a
lowest score.
0, 40, 60, 70, 75, 80, 85, 95, 95, 100
a) What effect does eliminating the lowest value, 0, from the data set have on the mean
and median?
b) Would there be more of a significant change on the IQR or Standard Deviation?
Explain why.
The answers are shown below:
What is mean and median?The arithmetic mean of a given data is the sum of all observations divided by the number of observations. For example, a cricketer's scores in five ODI matches are as follows: 12, 34, 45, 50, 24. To find his average score in a match, we calculate the arithmetic mean of data using the mean formula:
Mean = Sum of all observations/Number of observations
Mean = Sum of all observations/Number of observations
Mean = (12 + 34 + 45 + 50 + 24)/5
Mean = 165/5 = 33
The value of the middlemost observation, obtained after arranging the data in ascending or descending order, is called the median of the data.
For example, consider the data: 4, 4, 6, 3, 2. Let's arrange this data in ascending order: 2, 3, 4, 4, 6. There are 5 observations. Thus, median = middle value i.e. 4.
Given data:
0, 40, 60, 70, 75, 80, 85, 95, 95, 100
a)Mean without '0' = 40+ 60+ 70+ 75+ 80+ 85+ 95+ 95+ 100/9
= 700/9
= 77.777
Median without '0' = 80
Mean with ' 0' = 0+ 40+ 60+ 70+ 75+ 80+ 85+ 95+ 95+ 100/10 = 70
Median with '0' = 80
b)standard deviation= 18.121673811445. (without '0')
standard deviation with 0 = 28.982753492379
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Your grades on four exams are 78, 85, 97, and 92
What grade do you need on the next exam to have an
average of 90 on the five exams?
Let g = grade needed
(78 + 85 + 92 + 97 + g)/5 = 90
Solve for g.
1. The scatterplot below shows the fuel efficiency (in
miles per gallon) and weight (in pounds) of
twenty subcompact cars.
91
3000
(a) Is there a clear explanatory variable and
response variable in this setting? If so, tell
which is which. If not, explain why not.
Car weight
(b) Does the scatterplot show a positive association, negative association, or neither? Explain why this
makes sense.
(c) How would you describe the form of the relationship?
(d) Which of the following is closest to the correlation between car weight and fuel efficiency for these
20 vehicles? Explain.
r=-0.9
r=-0.6
r=0 r=0.4
(e) There is one "unusual point" on the graph. Explain what is "unusual" about this car.
(
What effect would removing the “unusual point” have on the correlation? Justify your answer.
(g) If we converted the car weights to metric tons (1 metric ton -2,205 pounds). How would the
correlation change? Explain.
The explanatory variable is the car's weight, with fuel efficiency as the response variable; a likely negative association may exist, possibly linear or non-linear; a correlation like r=-0.9 or r=-0.6 is plausible; an 'unusual point' could be an outlier affecting the correlation; removing it might strengthen or weaken the correlation; converting weights to metric tons wouldn't alter the correlation.
(a) In this context, the explanatory variable is the car's weight (in pounds) and the fuel efficiency (in miles per gallon) is the response variable. This is because we are typically interested in determining the effect of a car's weight on its fuel efficiency.
(b) Based on the context, a scatterplot might show a negative association between the car's weight and its fuel efficiency. This would make sense as heavier cars often require more fuel to operate efficiently, leading to lower miles per gallon.
(c) The form of the relationship between car weight and fuel efficiency can vary. For instance, it could be linear (indicating a constant rate of change) or non-linear (indicating a rate of change that varies with weight).
(d) Without viewing the scatterplot it's not possible to definitively answer this, but based on the proposed negative relationship, a correlation of r=-0.9 or r=-0.6 would be plausible. Correlations range from -1 to 1, and a negative sign indicates an inverse relationship.
(e) An 'unusual point’ could be an outlier on the scatterplot that doesn't model the relationship between car weight and fuel efficiency like the rest of the data. This could be due to factors unique to this car, such as a highly efficient engine that gets more miles per gallon despite its weight
(f) Depending on the unique characteristics of the 'unusual point', its removal could either increase or decrease the correlation. If this point were causing the correlation to be weaker, its removal would cause the correlation to strengthen, and vice-versa.
(g) Converting the car weights to metric tons wouldn't change the correlation between weight and fuel efficiency. Correlation is unitless and depends only on the relationship between variables, not the scale they're measured on. Thus, while the specific values for weight would change, the strength, direction, and form of the relationship between weight and fuel efficiency would remain the same.
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What is the solution to this equation?
7x – 3(х – 6) = 30
A.x= 12
B.х = 6
C. х = 3
D. x= 9û
Answer:
x = 3
Step-by-step explanation:
[tex]7x-3(x+6)=30[/tex]
Isolate the variable by dividing each side by factors that don't contain the variable.
263 grams dental stone powder
80 milliliters of water
If you use 70 grams of stone, how many milliliters of water are needed?
Answer:
21.29 milliliters
Step-by-step explanation:
First find how much water is need for 1 gram of stone by dividing both numbers by 263. Then multiplying both numbers by 70.
Grams : Milliliters
263 80
1 : 0.3042 (Rounded to 4 decimal places)
70 : 21.29 (Rounded to 2 decimal places)
The amount of water needed when using 70 grams of dental stone powder is approximately 21.29 milliliters. This is based on the ratio of stone powder to water in the original mixture.
Explanation:The question is asking for the calculation of the amount of water needed if 70 grams of dental stone powder is used. This can be resolved by determining the ratio of water to dental stone powder in the initial mixture, and then applying this ratio to the lesser quantity of 70 grams. In the original mixture, there are 263 grams of dental stone powder to 80 milliliters of water which simplifies to approximately 1 gram to 0.3042 milliliters of water. Therefore, if you use 70 grams of stone powder, you multiply 70 grams by 0.3042 milliliters/g, which equates to approximately 21.29 milliliters of water.
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If it is known that a+b/a−b =c, find the following.
3a+3b/2a−2b
Answer:
[tex]\frac{3}{2}[/tex] c
Step-by-step explanation:
Given
[tex]\frac{3a+3b}{2a-2b}[/tex] ← factor numerator and denominator
= [tex]\frac{3(a+b)}{2(a-b)}[/tex]
= [tex]\frac{3}{2}[/tex] × [tex]\frac{a+b}{a-b}[/tex] = [tex]\frac{3}{2}[/tex] c
Please help
Use p(x)=x^2+4x+9. Find a polynomial r(x) such that p(x)+r(x)=2x^2-6x+14.
Find a polynomial s(x) such that p(x)+s(x)=2x^2+14
Find a polynomial t(x) such that p(x) + t(x) has degree 2 and p(x) * t(x) has degree 3.
How do you solve |x-4| is less than or equal to 2?
Answer:
|x - 4| ≤ 2
-2 ≤ x - 4 ≤ 2
2 ≤ x ≤ 6
is 0.9 repeating a rational or irrational number
Answer:
rational
Step-by-step explanation:
it is rational
a rational number is that which is non-terminating (a number which cannot be terminated) and repeating . So 0.99999…. aquires both repeating and non-terminating property . Hence it is a rational number .
What is 7ab(2a+4b-6)
Answer:
[tex]14a^{2}b[/tex] + [tex]28ab^{2}[/tex] - 42ab
Step-by-step explanation:
The expression 7ab(2a+4b-6) simplifies as 14a^2b + 28ab^2 - 42ab by distributing 7ab to each number within the parentheses.
Explanation:This question involves distribution which is a property in Mathematics. To simplify the expression
7ab(2a+4b-6), you need to distribute or multiply 7ab with each number within the parentheses. When we do this step-by-step:
7ab times 2a = 14a2b7ab times 4b = 28ab27ab times -6 = -42abSo, the expression 7ab(2a+4b-6) simplifies as 14a2b + 28ab2 - 42ab.
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Help find the distance between two points?
Answer:
4
Step-by-step explanation:
Calculate the distance using the distance formula
d = √ (x₂ - x₁ )² + (y₂ - y₁ )²
with (x₁, y₁ ) = B(0, 0) and (x₂, y₂ ) = ([tex]\frac{\sqrt{6} }{2}[/tex], [tex]\frac{\sqrt{58} }{2}[/tex] )
AB = [tex]\sqrt{((\frac{\sqrt{6} }{2})^2 }[/tex] + [tex]\{(\frac{\sqrt{58} }{2})^2 }[/tex]
= [tex]\sqrt{\frac{6}{4} }[/tex] + [tex]\frac{58}{4}[/tex]
= [tex]\sqrt{\frac{64}{4} }[/tex]
= [tex]\sqrt{16}[/tex]
= 4
Is 4x-3=2x+13 a true statement?
Answer:
It is ture.
4x-3=2x+13
2x-3=13
2x=16
x=8
5k - 7 > 5k + 8
guys I really need help!!
Answer:
Step-by-step explanation:
Classify each number below as an integer or not.
Answer:
1. yes
2. no
3. yes
4. no
5. yes
Step-by-step explanation:
The method i use is if the number is not a fraction than it is an integer. besides 6 for some reason.
Here is the catch if the fraction can be simplified into a whole number than it is an integer.
find the coordinates of the midpoint of the segment with the given endpoints. Y(-13,8) and Z (2,-10)
[tex]\bf ~~~~~~~~~~~~\textit{middle point of 2 points } \\\\ Y(\stackrel{x_1}{-13}~,~\stackrel{y_1}{8})\qquad Z(\stackrel{x_2}{2}~,~\stackrel{y_2}{-10}) \qquad \left(\cfrac{ x_2 + x_1}{2}~~~ ,~~~ \cfrac{ y_2 + y_1}{2} \right) \\\\\\ \left( \cfrac{2-13}{2}~~,~~\cfrac{-10+8}{2} \right)\implies \left( \cfrac{-11}{2}~,~\cfrac{-2}{2} \right)\implies \left(-5\frac{1}{2}~,~-1 \right)[/tex]
The area of a rectangular rug is 18.7 Square yards the width of the rug is 2.75 yards Isabell found the length of the rug by dividing its area by its width what is the length in yards of the rug?
Thank you so much for helping me Have a blessed night/day!
Factor the following expression
10x^5+5x^3-14x^2-7-
Answer:
C. (5x^3-7)(2x^2+1)
Step-by-step explanation:
Given expression is,
10x^5+5x^3-14x^2-7
=10x^5-14x^2 + 5x^3 - 7 (By the commutative property)
=2x^2(5x^3-7)+5x^3-7 (Taking 2x^3 common from first two terms )
=(5x^3-7)(2x^2+1) (Taking 5x^3-7 common from both terms)
\implies 10x^5+5x^3-14x^2-7=(5x^3-7)(2x^2+1)
Hence, Option C is correct
What is the relationship between the independent and dependent variable?
Answer: Direct proportion because as the time goes up the distance goes up
Solve for C: S = C+RC
Answer:
factoring c is the best way to solve this
Step-by-step explanation:
S = C ( 1 + R )
C = S/( 1 + R )
The equation after solving is C = S / (1 + R).
To solve for C in the equation S = C + RC, we can factor out C on the right side:
S = C + RC
S = C(1 + R)
Then, we can divide both sides by (1 + R) to isolate C:
S / (1 + R) = C
Therefore, the solution is:
C = S / (1 + R)
For example, if S = 100 and R = 0.1, then C would be:
C = 100 / (1 + 0.1)
C = 100 / 1.1
C = 90.9090909090909
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Can you draw two triangles each having two 45° angles and one. 90° angle that are not similar justify her answer
No, you cannot draw two triangles each having two 45° angles and one 90° angle that are not similar. All 45-45-90 triangles are similar by definition because they have the same shape, i.e., their angles are the same (two 45° angles and one 90° angle). These similar figures can differ in size, but not in shape.
Explanation:No, it is not possible to draw two triangles each having two 45° angles and one 90° angle that are not similar. Let's break this down.
All triangles that have two 45° angles and one 90° angle are called 45-45-90 triangles. In a 45-45-90 triangle, the angles are always the same, so they are always similar by the definition of similar figures. Similar figures have the same shape, but not necessarily the same size. Their corresponding angles are congruent (the same) and their corresponding sides are in proportion.
Since all 45-45-90 triangles have the same angles - two 45° angles and one 90° angle - they are all similar to each other, regardless of their size. The size of the triangle does not matter, because the definition of similar figures is based on the shape, not the size. Hence, it is impossible to draw two 45-45-90 triangles that are not similar.
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