Answer: Look at the explanation:
Step-by-step explanation: First, you start at -3 on the number line. Then, since we are adding 7, we would add 7 spaces to the right. That should lead us to our answer; 4. Another way how to model this is 7 + -3 or 7-3. They all equal 4. I hope this helped!
Graph Y= -1/4 x + 6.
The x-intercept and y-intercept of the line will be at (24, 0) and (0, 6). And the line is drawn below.
What is a linear equation?A connection between a number of variables results in a linear model when a graph is displayed. The variable will have a degree of one.
The linear equation is given as,
x/a + y/b = 1
Where 'a' is the x-intercept of the line and ‘b’ is the y-intercept of the line.
The linear equation is given below.
y = -(1/4)x + 6
Convert the equation into intercept form, then we have
y = -(1/4)x + 6
4y = - x + 24
x + 4y = 24
x / 24 + y / 6 = 1
The x-catch and y-capture of the line will be at (24, 0) and (0, 6) and the line is drawn underneath.
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Triangle OPQ is shown below with line RS passing through points R and S:
R
S
If triangle OPQ is dilated about the center of the triangle to create triangle O'P'Q', what can you
conclude about segments RS and R'S'? (6 points)
Segment O'Q' is perpendicular to segment R'S'.
Line RS is parallel to line R'S'.
Line RS is perpendicular to line R'S:
Point P' passes through line RS.
Dilation is a type of transformation. So it can concluded that: Line RS is parallel to line R'S'.
Transformation is a method required to either increase or decrease the size of a given object, or change its orientation. Types of transformation are dilation, translation, rotation and reflection.
Dilation is a process in which the size of a given shape or figure is reduced or increased appropriately to form an image.
Two lines are said to be perpendicular when the measure of angle between is a right angle. While two or more lines are said to be parallel is the measure of angle between them is that of a straight line.
Thus, the appropriate statement that would be concluded considering the conditions in the question is line RS is parallel to line R'S'.
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Increasing Functions
30
27.5
25
20
175
15
10
y = 2
(y=x
y = 2x
Consider the graph shown, which func
the other functions?
4x A
{x B
C
D
y=2
y=z²
y = 2x
cannot be determined
Which function will eventually surpass
Answer:
b
Step-by-step explanation:
i know ..
A line passes through the point (6,-1) and is perpendicular to the line with the equation -2x + 3y = -6.
Answer: A
Step-by-step explanation:
Before we find the equation of the perpendicular line, we have to find the slope of the original line.
The slope-intercept form of the equation is y=mx+b, so let's change that.
[tex]-2x+3y=-6[/tex] [add both sides by 2x]
[tex]3y=2x-6[/tex] [divide both sides by 3]
[tex]y=\frac{2}{3} x-2[/tex]
This gives slope as [tex]\frac{2}{3}[/tex].
There are 2 things for us to do to find the slope of a perpendicular line.
1. reciprocal
2. change sign
Let's apply those rules.
1. [tex]\frac{3}{2}[/tex]
2. [tex]-\frac{3}{2}[/tex]
Now, we can find the perpendicular lines by plugging in our new point.
[tex]y=-\frac{3}{2} x+b[/tex] [plug in x and y]
[tex]-1=-\frac{3}{2}(6)+b[/tex] [multiply]
[tex]-1=-9+b[/tex] [add both sides by 9]
[tex]b=8[/tex]
Now we can plug in for our slope-intercept equation.
[tex]y=-\frac{3}{2} x+8[/tex]
Since answers are in standard form, we have to manipulate it.
[tex]y=-\frac{3}{2} x+8[/tex] [add both sides by [tex]\frac{3}{2} x[/tex]]
[tex]\frac{3}{2}x+y=8[/tex] [multiply both sides by 2]
[tex]3x+2y=16[/tex]
Therefore, our final answer is A.
if a point is characterized as having both a nonzero x and y coordinate and oppositely signed coordinates, then the point must be in which of the labeled quadrants in the standard xy coordinate plane?
The labeled quadrants in the standard xy coordinate plane is Quadrant II
What is Quadrants?
The intersection of the x-axis (the horizontal number line) and the y-axis in the cartesian system divides the coordinate plane into four equal pieces (the vertical number line). Because each of these four areas occupies a quarter of the entire coordinate plane, they are collectively referred to as quadrants.
Concept:
The x and y coordinates are both positive in quadrant I. In quadrant II, the x and y coordinates are oppositely positive. The x and y coordinates are both negative in quadrant III. The x-coordinate is positive and the y-coordinate is negative in quadrant IV.
The origin, or the point where the x- and y-axes connect, is where both the x and y coordinates are zero (0, 0).
The point is in the first quadrant if both x and y are positive. If both x and y are negative, the point will be in the second quadrant. In the third quadrant if both x and y are negatives, the point is located.
The labeled quadrants in the standard xy coordinate plane is Quadrant II
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a) Shashwat obtained an average marks of 15 in 3 subjects. When the marks obtained in another subject is also included, the average marks is increased by 1. Find the marks obtained in the fourth subject.
The mark obtained in the fourth subject is 19
How to determine the mark obtained in the fourth subject?From the question, we have the following parameters that can be used in our computation:
Average marks in 3 subjects = 15
Average marks in 4 subjects = 15 + 1
When the number of subjects is increased by 1, we have the following equation
Average = Sum of subjects/Number of subjects
Substitute the known values in the above equation, so, we have the following representation
15 + 1 = (3 * 15 + Score in 4th subject)/4
So, we have
16 = (3 * 15 + Score in 4th subject)/4
Evaluate the products
16 = (45 + Score in 4th subject)/4
So, we have
45 + Score in 4th subject = 64
Subtract 45 from both sides
Score in 4th subject = 19
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the table shows the number of stickers three friends have, Hannah has fewer stickers than Marco but more stickers than Addison. how many stickers could Hannah have?
How can we use the formula M= 58h + 135 to determine the mile marker that Sam passed at hour 6
Sam passed the marker of 483 miles, in 6 hours.
What are equation models?The equation model is defined as the model of the given situation in the form of an equation using variables and constants.
Here,
An expression is given as M = 58h + 135. shows how many miles the same has traveled for h hours,
To evaluate the mile marker that sam passed at 6 hours, substitute the value with h in a given expression.
M = 58×6 +135
Simplifying the above expression gives the mile marker
M = 483 miles
Thus, the required miles are 483.
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1. Which of the following is equivalent to 5a³ + 4a³??
O (5+4) a³+3
O (5+4) a³
(5.4) a³+3
O (5.4) a³
ہے
The equivalent to 5a³ + 4a³ is (5+4) a³, according to the question.
What do you mean by Equivalent ?
Equivalent refers to the mathematical notion that distinct terms and expressions having a similar value are treated equally.
According to the given question,
We have the given options are:
O (5+4) a³+3
O (5+4) a³
O (5.4) a³+3
O (5.4) a³
Now, we will find the equivalent,
5a³ + 4a³
Then, we will taking common factor from the given equation:
5a³ + 4a³
= a³(5+4)
So that is same as (5+4)a³.
Therefore, the equivalent to 5a³ + 4a³ is (5+4) a³.
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What does y equal, in this picture with 30 60 90 triangles?
The value of y= 5.49≈ 5.5cm
What is 30-60-90 traingle?
The 30-60-90 triangle is cut straight through the middle along its altitude, like one half of an equilateral triangle. Its name is derived from its three angles of 30 degrees, 60 degrees, and 90 degrees. Any triangle with angles of 30-60-90 will look like this: The hypotenuse is always twice as long as the shortest leg, and the length of the long leg can be calculated by multiplying the short leg by the square root of three. The shortest leg is across from the 30-degree angle.
By 30-60-90 triangle rule,
Side across 60° angle = x
Hypotenuse side = 2x= 15
Side across 30° angle = x√3
By solving,
2x= 15
x= 7.5cm
So side across 60° angle= 7.5 cm
Side across 30° angle = 7.5×√3
= 7.5× 1.732= 12.99≈ 13cm
As the figure given us square so,
13= 7.5+y
y= 13-7.5
y= 5.5 cm
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If a plane can travel 480 miles per hour with the wind and 380 miles per hours against the wind, find the speed of the wind and the speed of the plane in still air
Answer:
Step-by-step explanation:
I am not super sure about this one
an irs auditor randomly selects 3 tax returns from59returns of which7contain errors. what is the probabilitythat she selects none of those containing errors?
Therefore , the probability that she selects none of those containing errors is 0.6798.
What does probability really mean?Calculating how likely or "possible" it is for an event to occur is the subject of probability. Words like "definitely," "impossible," or "likely" may be used to communicate the likelihood that a particular event will occur. Mathematics always expresses probabilities as fractions, decimals, or percentages, with values ranging from 0 to 1.
Here,
Number of ways of selecting 3 returns out of 59 is C(59,3).
Out of 59 returns, 59-7 = 52 returns has no error so number of ways of selecting 3 returns out fo 52 is C(52,3).
The probability that she selects none of those containing errors is
P( No errors )=[tex]\frac{C(52,3)}{C(59,3)}[/tex]=0.6798
Therefore , the probability that she selects none of those containing errors is 0.6798.
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2. The basic advertising package has a value of $1,000
and the premium package has a value of $2,500. The
goal of the agency is to sell more than $60,000 worth
of small-business advertising packages.
If you know that exactly 10 premium packages were
sold, what can you say about the number of basic
packages the agency needs to sell to meet its goal?
1000b + 2500p = 60,000
1000b + 2500(10) = 60,000
1000b + 25000 = 60,000
1000b = 35,000
b = 35
they need to sell 35 basic packages to reach their goal of 60,000 dollars
2
Write the answer in each blank.
Of these numbers
745 281 578 170
is the smallest
is the largest
Frank gets a Lamborghini for Christmas from Bill Nye for $225,000. Frank crashes the Lamborghini and survives. But his car is damaged. His repairs will cost 55% of the original price, but 30% of the price is covered by insurance. How much money does Frank owe?
Answer: Frank has to pay 56,250 dollars
Step-by-step explanation: If Frank's repair costs 55% of the original price, that means he'll have to pay 123,750 dollars because 55% of 225,000 is 123,750. But he doesn't have to pay that amount because the car insurance is paying 30% of 225,000 which is 67,500 dollars. So the car insurance is paying 67,500 dollars out of the 123,750 dollars in damage. So you'll have the subtract 123,750 by 67,500 which is 56,250 dollars.
If f(x) = 3x-1 and g(x) = x^2+2, what is (f ° g)(x)?
Answer:
(f ○ g)(x) = 3x² + 5
Step-by-step explanation:
substitute x = g(x) into f(x) , that is
(f ○ g)(x)
= f(g(x))
= f(x² + 2)
= 3(x² + 2) - 1
= 3x² + 6 - 1
= 3x² + 5
suppose that CDE IS ISOSCELES WITH THE BASE ED suppose also that m<E=(2x+37) and m<D=4x+23)
find the degrees measure of each angle in the triangle
Answer:
the measure of angle a is 51.43 degrees, the measure of angles C and E is also 51.43 degrees. The measure of angle D is 77.14 degrees.
Step-by-step explanation:
Since CDE is an isosceles triangle with the base ED, the two angles at C and E are equal. Let's call this angle a. This means that the angles at D and E are also equal and have a measure of 180 - 2a.
We know that the measure of angle D is 4x + 23. Since the angles at D and E are equal, the measure of angle E is also 4x + 23. Therefore, the measure of angle a is 2x + 23.
To find the measure of each angle in the triangle, we need to use the fact that the sum of the angles in a triangle is 180 degrees. Since we already know the measure of angle D and angle E, we can use this information to find the measure of angle C.
Since the sum of the angles in the triangle is 180 degrees, we can write the following equation:
a + (180 - 2a) + (180 - 2a) = 180
Solving for a, we get:
a = 180 - 2(180 - 2a)
a = 360 - 4(180 - 2a)
a = 360 - 720 + 8a
a = -360 + 8a
7a = 360
a = 51.43 degrees
Since the measure of angle a is 51.43 degrees, the measure of angles C and E is also 51.43 degrees. The measure of angle D is 4x + 23, as given in the problem statement.
Write and equation of the line in slope-intercept form. (0,-2) (1,3)
Answer:
y=5x−2
I hope this helps!
Michael is building a skateboard
ramp. The ramp needs to include a
right angle to be safe. If the side
lengths are 10 feet, 2.5 feet, and 10.5
feet, will the ramp be safe? Prove
your answer with an inequality.
Given that the side lengths of the ramp are 10 feet, 2.5 feet, and 10.5 feet.
We know that for making a right angle A Pythagoras triplet must follow
So, a² + b² = c²
Where a, b, c are the lengths of the triangle and a, b <=c
So, on applying the above formula
We have,
2.5² + 10² = 10.5²
6.25 + 100 = 110.25
But 106.25 is not equal to 110.25
So all these sides are not good for making the ramp safe.
There are three types of the triangle based on angle -
1. Acute angled triangle
2. Right-angled triangle
3. Obtuse angled triangle
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A) Q''(−5, 6), R''(−2, 1), S''(1, 5)
B) Q''(7, 11), R''(10, 16), S''(13, 12)
C) Q''(−5, 2), R''(−2, 7), S''(1, 3)
D) Q''(13, 2), R''(10, 7), S''(7, 3)
The correct answer is C.
fast as you can. point slope form. algebra 1)
Answer: Y=mx+b
Step-by-step explanation:
Which of the following represents the least value?
1/3 of 1,212
1/5 of 1,212
25% of 1,212
30% of 1,212
Answer:
1/5 of 1,212
Step-by-step explanation:
Note that 25% = 1/4 and 30% = 3/10.
The least value is achieved when we take the smallest fraction, which is 1/5.
Answer:
1/5 of 1212 is the smallest value
Step-by-step explanation:
if we convert 25% to a fraction we have 1/4
if we convert 30% to a fraction we have 3/10
now we convert each of the four fractions into equivalent fractions using lowest common denominator of 60
1/3 = 20/60
1/5 = 12/60
1/4 = 15/60
3/10 = 18/60
the smallest fraction is 12/60, or 1/5
therefore 1/5 of 1212 is the smallest value
Inequality
x + y > 11
.05x + .10y < .95
the inequality model will be x+2y<19
What is inequality?
Inequalities are mathematical expressions where neither side is equal. In inequality, as opposed to equations, we compare two values. Less than (or less than or equal to), greater than (or greater than or equal to), or not equal to signs are used in place of the equal sign in between. Sometimes it can be about a "not equal to" relationship, where one thing is more than the other or less than. In mathematics, an inequality is a relationship that results in a non-equal comparison between two numbers or other mathematical expressions.
x + y > 11
.05x + .10y < .95
by multiplying 20 in inequality we get x+2y<19
Hence, the inequality model will be x+2y<19
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you walk to the subway station for your morning commute. given that you always leave your apartment at the same time, there is a probability of 1/2 that you will wait 3 minutes for the train and a probability of 1/2 that you will wait 7 minutes for the train. find the expected value of your wait time
To find the expected value of your wait time, we need to multiply the value of each possible outcome by its probability and then add up all the products. In this case, there are two possible outcomes: waiting 3 minutes or waiting 7 minutes.
The probability of waiting 3 minutes is 1/2, and the probability of waiting 7 minutes is also 1/2. Therefore, the expected value of your wait time is:
(3 minutes * 1/2) + (7 minutes * 1/2) = 5 minutes
So, on average, you can expect to wait about 5 minutes for the train.
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A quadrilateral with vertices A(-2, 2), 8(-3, 6), C(-7, 7), and D(-4, 1) is rotated 180° about the origin. Which of
the vertices is NOT correct?
A quadrilateral with vertices A(-2, 2), 8(-3, 6), C(-7, 7), and D(-4, 1) is rotated 180° about the origin is Coordinates of D' (-6,3).
What is quadrilateral?
A quadrilateral is a flat shape with four edges and four corners, also known as vertices. The quadrilateral has angles at each of its four vertices, or corners. The angles at the vertices of a quadrilateral ABCD are ∠A, ∠B, ∠C and ∠D. A quadrilateral has the following sides: AB, BC, CD, and DA.
When any figure is rotated 180° in the counterclockwise direction, then the coordinates of the vertices is changed into its opposite sign.
(x, y) → (-x, -y)
The coordinates of the vertices of quadrilateral ABCD is changed when it is rotated 180 degrees counterclockwise about the origin as,
A (7,-7) → A'(-7,7)
B (4,-10) → B' (-4,10)
C (1.5, -2.5) → C' (-1.5, 2.5)
D (6, -3) → D'(-6,3)
So the coordinates of D' will be (-6,3).
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If 1.5 liters of washing up liquid is 2.70$ find the cost of 1 liter
The cost of one liter of washing up liquid would be = $1.8
What is liters?Liters is a variable that is can be used to denote the measurement of a liquid.
The quantity of the washing up liquid that was given= 1.5 liters.
The cost of 1.5 liters of washing up liquid =$2.70
If 1.5 L = 2.70
1 L = X
Make X the subject of formula;
X = 1× 2.70/1.5
X = $1.8
Therefore, the cost of one liter of washing up liquid would be = $1.8
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If you roll a fair die, what is the probability you will roll a 5 or a number less than 3?
Answer:
1/2
Step-by-step explanation:
Since 5 is one of the six possible numbers available, rolling a 5 is a 1/6 probability.
Since rolling a number less than 3 means rolling a 1 or 2, rolling a 1 or 2 is a 2/6 probability.
Add those probabilities up since you can get either of those outcomes and you get 1/6+2/6=3/6
3/6=1/2
Sam and Bethan share £54 in the ratio 5 : 4
work out how much each person gets
The amount of money Sam and Bethan share is $30 and $24 respectively.
Describe the term ratio of the number?The term "to" is used to convey ratios verbally; we phrase "the ratio of one thing to of something." Ratios can be expressed as a fraction, by using the word "to," or by using a colon. Let's study more about ratios using this example of a form.For the stated question-
Adding 5 and 4 results in 9.54 divided by 9 equals 6. This is because, for every five that Sam receives, Bethan receives four.You may calculate the entire cost of one share by adding those. When you increase the number of eros Sams by the fact that there are 6 shares, Bethan receives each share.Thus, Sam's share = 5 x 54 /9
Sam's share = $30
Similarly, Bethan's share = 4 x 54 /9
Bethan's share = $24
Thus, the amount of money Sam and Bethan share is $30 and $24 respectively.
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Identify the rate of decay r (as a percent) of the exponential function f(x) = 0.3(0.82)^x
a. r = 30%
b. r = 18%
c. r = 70%
d. r = 82%
Answer:
b. r = 18%
Step-by-step explanation:
0.3(0.82)^x:
0.3(0.82)^x:
The 0.82 is getting affected since it is raised to the power of x
Hence, for every iteration of x, the object is becoming 82% of itself.
100%-82%=18%
r = 18% ==> b
Option B is correct, 18% is the rate of decay of the exponential function f(x) = 0.3(0.82)ˣ
What is a function?A relation is a function if it has only One y-value for each x-value.
The exponential function f(x) = 0.3(0.82)^x can be written in the form f(x) = a(b)ˣ, where a = 0.3 and b = 0.82.
In an exponential function of the form f(x) = a(b)ˣ
the base b represents the rate of change.
If b is between 0 and 1, then the function represents exponential decay. The rate of decay r can be found using the formula:
r = (1 - b) x 100%
In this case, b = 0.82, so the rate of decay is:
r = (1 - 0.82) x 100%
= 0.18 x 100%
= 18%
Hence, option B is correct, 18% is the rate of decay of the exponential function f(x) = 0.3(0.82)ˣ
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HELP WITH NUMBER 4 PLEASE
Amount = $404.01
Second Period Interest = $ 2.01.
What is Compound Interest ?The interest that is computed using both the principal and the interest that has accrued during the previous period is called compound interest. It differs from simple interest in that the principal is not taken into account when determining the interest for the subsequent period with simple interest. Compound interest is commonly abbreviated C.I. in mathematics.
Different methods can be used to compute compound interest depending on the circumstance. To make the computations simpler, we may utilise the compound interest formula. We need to know the quantity and the principal in order to compute compound interest. The difference between the two is the principle.
In this problem,
Principal = $ 400
Rate(r) = 6% (annually)
Compounded monthly., n =12
Second Period of interest is the 2nd Month = [tex]\frac{2}{12} \ of \ a \ year = \frac{1}{6} \ of \ a \ year[/tex].(t)
Amount Generated (A)
= [tex]P(1 + \frac{r}{n})^{nt}[/tex] = [tex]400(1 + \frac{6}{12 * 100})^{12*\frac{1}{6} } = 400(1 + \frac{1}{200})^{2} = 404.01[/tex]
Amount = $404.01
Second Period Interest = 2nd Period Amount - 1st period Amount = 404.01 - 402 = $ 2.01.
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