Step-by-step explanation:
Our straight line has the same gradient as that of the line,
[tex]2y=5x+7[/tex]
Dividing each term by 2,
[tex]y=\dfrac{5}{2}\,x+\dfrac{7}{2}[/tex]
Now this equation is in the form [tex]y=mx+c,[/tex] so the gradient of this line is 5/2.
So the gradient of our straight line is,
[tex]m=\dfrac{5}{2}[/tex]
Given our straight line passes through the point,
[tex](x_1,\ y_1)=(3,\ -2)[/tex]
The equation of a straight line passing through a point [tex](x_1,\ y_1)[/tex] and having gradient [tex]m[/tex] is given by,
[tex]\longrightarrow\large\boxed{\quad y-y_1=m(x-x_1)\quad}[/tex]
This form of equation of a straight line is called point - slope form.
By this point - slope form, the equation of our straight line will be given by,
[tex]\longrightarrow y-(-2)=\dfrac{5}{2}\,(x-3)[/tex]
[tex]\longrightarrow y+2=\dfrac{5}{2}\,(x-3)[/tex]
[tex]\longrightarrow2(y+2)=5(x-3)[/tex]
[tex]\longrightarrow2y+4=5x-15[/tex]
[tex]\longrightarrow\underline{\underline{5x-2y-19=0}}[/tex]
This is the equation of our straight line, written in the form [tex]Ax+By+C=0.[/tex]
Congruent triangles. What does x equal?
The value of x for the congruent triangles will be equal to 10.
What is congruency?In geometry, two figures or objects are said to be congruent if their shapes and sizes match, or if one is the mirror image of the other. The meaning of congruency is that the two shapes are similar as well as equal in size.
Given that the angles are ∠E = 95, ∠F = 32 and ∠R=4x +13. The value of x will be calculated as,
Calculate the value of angle ∠G,
∠G = 180 - 32 - 95
∠G = 53
The value of x will be,
4x + 13 = 53
4x = 40
x = 10
Therefore, the value of x for the congruent triangles will be equal to 10.
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What is the median of 1 to 99?
The median of 1 to 99 is 50.
The midway value in a given set of figures or data is referred to as the median. To get the average value for a given group of integers, three distinct metrics are employed in mathematics.
The data set's median is the value in the center. Put all the numbers in ascending or descending order, and then choose the middle number to determine the median. There will only be one middle integer if the number of data points is odd. If the number of data points is even, you must choose the middle two numbers, add them together, and divide by two. Your median will be that value.
Median= 99+1/2 = 100/2 = 50th term, which in this case is 50.
Thus, the median of 1 to 99 is 50.
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This year, a small business had a total revenue of $16,500. If this is 34% less than their total revenue the previous year, what was their total revenue the previous year?
Answer:
$25000
Step-by-step explanation:
100% - 34% = 66%
We know that
66% = $16,500
We have to find 1%
16500 divided by 66 = $250
Then we have to find the 34%
250 times 34 = $8500
Then we add both numbers to find their previous year's revenue
$16500 + $8500 = $25000
So, their previous year's revenue is $25000
How many gallons of paint do I need to cover 2000 square feet?
5.7 gallons of paint is required to cover an area of 2000 square feet
Given,
The quantity of paint = 2 gallons
Area covered by 2 gallons of paint = 700 square feet
We have to find the quantity of paint required to cover 2,000 square feet;
Here,
Area covered by 1 gallon of paint = Given area / Quantity of paint
= 700 / 2 = 350 square feet
Now,
Quantity of paint required to cover 2000 square feet;
2000 / Area covered by 1 gallon of paint = 2000 / 350 = 40 / 7 = 5.7 gallons
That is,
We need 5.7 gallons of paint to cover 2000 square feet.
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The given question is incomplete. Completed question is given below;
two gallons of paint will cover 700 square feet. How many gallons of paint are needed to cover 2,000 square feet ?
Does 2 equal square root?
Therefore , it means if an equation have 2 roots , it means it is a quadratic function .
How to define square root ?The outcome of multiplying a number by itself produces the original number, which is the square root of that number. Squares and square roots are a few of examples of exponents. Try to visualize nine. Furthermore, this can be written as 3x3.
Here,
A quadratic function is one where an equation has two roots.
A quadratic function's two roots are equal if D=0.
D (discriminant) = 0 such that b24ac = 0 is needed in order for the roots of a polynomial function to be equal.
As a result, if an equation has two roots, a quadratic function is what it is.
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Make Sense and Persevere Neil and Yuki run a data entry service. Neil starts at 9:00 A.M can type 45 words per minute. Yuki arrives at 10:30 A.M. and can type 60 words per minute. Write and solve an inequality to find at what time Yuki will have typed more words than Neil. Let x represent the time in minutes. MP.1 . and
Yuki would have typed more than Neil at 10:30 AM and the inequality is 45×90+45 × x < 90 × x
We know that Neil started 90 minutes earlier than Yuki by subtracting the time difference So that tells us that
at 10:30 AM Neil would have typed 45 times 90. After x minutes he would have typed 45*90+45*x and Yuki would have typed 60*x.
Words typed by Yuki will be greater than those that will be Words typed by Neil
45×90+45 × x < 90 × x
When we will try in Solving the above inequality would give us
x >90
it means that 90 minutes after 10:30 AM
Yuki would type more than Neil.
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Determine the Domain and Range
Answer:
Step-by-step explanation:
domain
all real numbers, because the graph keeps going to the left and to the right
range
y ≥ 1 because the function starts in y = 1 and then keeps going up
list the data in the following stem-and-leaf plot. the leaf represents the tenths digit.
As per the given stem and leaf plot, the range of the stem and leaf plot is 4.
The term stem and leaf plot in math is referred as a type of table where the stem (or first column) represents the first place values of numbers and the leaves (or second column) represent the final place value of the numbers.
Here we given the following stem and leaf plot data.
Now we have to find the range of the stem and plot.
As we all know that range is defined as the maximum and minimum number in the data set.
While we looking into the given data, we have identified the the minimum number is 14 and the maximum number is 18.
Then the range is calculated as,
=> 18 - 14 = 4.
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What are the factors of X² 11x 42?
Therefore , the solution to the problem is factors of the given equation comes out be (x-14)(x+3).
Describe the equation.By joining two expressions with the equivalent sign, a mathematical statement known as an equation is produced. The equation 3x - 5 = 17 is an illustration. By solving this equation, we can determine that the value of the variable x is 4.
Here,
In the given question the equation is given as [tex]x^{2}[/tex]-11x-42.
Given polynomial : [tex]x^{2}[/tex]-11x-42
Thus we factorise the given equation
First:
=> [tex]x^{2}[/tex]-14x+3x-42
Second:
=> x(x-14)+3(x-14)
=> (x-14)(x+3)
thus factors comes out to be
(x-14) and (x+3)
Therefore , the solution to the problem is factors of the given equation comes out be (x-14)(x+3).
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Is asymptote the same as discontinuity?
An asymptote is not the same as discontinuity.
What is asymptote and discontinuity?An asymptote is a line or curve to which a function's graph draws closer without touching it. A vertical asymptote is a line that a function approaches but never quite touches. A vertical asymptote isn't always a discontinuity. It only matters if there's something "on the other side" since then how are you supposed to get across that gap without picking up your pencil? For instance ln(x) has a vertical asymptote at x=0 but it's no big thIng. But ln(|x|) (which is just ln(x) together with its "mirror image" on the negative side) is discontinuous.
An asymptote is not the same as discontinuity.
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What is AAS and AES?
Answer:
⭐ AAS = Angle-Angle-Side
⭐ I don't know what AES is.
Step-by-step explanation:
AAS is a triangle congruence statement you use to say that 2 triangles are congruent ≅ (the same).
Here's how to determine if 2 triangles are congruent by AAS:
One of their corresponding side lengths is congruentOne of their corresponding angles is congruentAnother one of their corresponding angles is congruentOne of the corresponding, congruent angles is in between another corresponding, congruent angle and a corresponding, congruent side lengthCongruent side lengths and congruent angles are often denoted by tick marks.
⭐ Example:
What are examples of inverse relationships?
Examples of inverse relationships are : As the speed of the car increases the time taken to cover certain distance decreases and More buses on the road less space on the road.
inverse relationships
An inverse relationship, also known as a negative relationship, is a contrary correlation between two variables such that they move in opposite directions. For example, we have two variables X and Y. As X increases, Y decreases and as Y increases, X decreases .The inverse of a relation is a relation obtained by interchanging or swapping the elements or coordinates of each ordered pair in the relation.
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How do you read mean and SD?
The variability in your data collection is measured by the standard deviation. It reveals the average distance between each score and the mean.
How to interpret a standard deviation?
The term "standard deviation" (or "") refers to the degree of dispersion of the data from the mean. Data are grouped around the mean when the standard deviation is low, and are more dispersed when the standard deviation is high.
What are the mean, median, and example?
The most frequent number, or the one that happens the most frequently, is known as the mode.
Example: Since the number 2 appears three times, more than any other number, it is the mode of the numbers 4, 2, 4, 3, and 2.
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What is the first step when adding and subtracting rational expressions?
The First step in adding and subtracting the rational expression is making the denominator equal .
The Rational Expression is defined as the expression that is written in the p/q form , where q ≠ 0 .
Let us understand adding and subtracting of the rational expression by an Example .
For Example : add the rational expressions 2/3 and 1/4 .
The First Step in adding them is to make the denominator equal ,
to make the denominator equal , we take LCM ,
the LCM of 3 and 4 is 12 ,
the rational expression become ⇒ 8/12 and 3/12 .
On adding , we get ; (8 + 3)/12 = 11/12 .
On subtracting , we get ; (8 - 3)/12 = 5/12 .
Therefore , making the denominator equal is the first step for adding and subtracting rational expressions .
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How do you find the height of a pyramid when given the volume and area?
The height of pyramid when given the volume and area is estimated as; H = 3 * V / a²
Define the meaning of the term pyramid?A solid object having four flat, triangular sides that slope inward and come together to form a point at the top, as well as a flat, square base. A triangular-shaped pile of objects is sometimes known as a pyramid: By balancing on each other's shoulders, the acrobats created a pyramid.How is the height of the a square pyramid determined?
To find the base area, first square the base edge.Next, divide the base area by the known volume.Finally, divide the result by three to determine the height of the pyramid.H = 3 * V / A_b
In which,
H - height of pyramid;
V- volume of pyramid
A_b - base area of pyramid; A_b = a²,
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Siti bought the bag at a dicount 7%. The original price of a bag wa $50. How much did iti pay for the bag
The amount that should be paid by Siti for the bag is $46.50. A discount is a reduction in the price of a product or service. It can be expressed as a percentage or as a fixed amount.
Discounts can be offered for a variety of reasons, such as to encourage customers to buy a product or to clear out inventory. They may be offered to certain groups of customers, such as students or seniors, or they may be available to all customers.
To find out how much Siti paid for the bag, you can use the following formula:
Discounted price = Original price * (1 - discount percentage)
Plugging in the values given in the problem, we get:
Discounted price = $50 * (1 - 7%) = $50 * 0.93 = $46.50
Therefore, Siti paid $46.50 for the bag.
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Which equation has an X intercept of 5 and a Y intercept of 10?
C) 2x+y=10 is the line has an X intercept of 5 and Y intercept of 10
To find the eqaution of line whose X intercept and Y intercept is given we will use line intercept form of line
The equation of line with A units of X intercept and B units of
Y intersect is given by:
[tex]\frac{x}{A} + \frac{y}{B} =1[/tex] ----(i)
given that A= 5 (X intercept) and B= 10 (Y intercept)
so equation (i) reduces to
[tex]\frac{x}{5}+\frac{y}{10} =1[/tex]
so 2x + y = 1*10
so the equation of the line is 2x+y=10
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Complete question:
Which equation has an X intercept of 5 and a Y intercept of 10?
A) 3x+2y=10
B) 5x+7y=2
C) 2x+y=10
D) 11x+7y=9
Write an equation for nth 45, 30, 15, 0 sequences and series
Answer:
a_n = -15 (n - 4) (for all terms given)
Step-by-step explanation:
a_n = -15 (n - 4) (for all terms given)
45, 30, 15, 0, -15, -30, -45, -60, -75, -90, -105, -120, -135, -150, -165, ...
To search for the nth sequence, replace n with the desired term.
need help on these questions. Help anyone, please!
Step-by-step explanation:
a linear function is defined as
y = ax + b
the variable x is only occurring with the exponent of 1.
this represents a straight line in a graphic representation (hence the name "linear").
if the exponent of the variable x is not 1, then it is not a linear function
P : y = 3/x + 2³
it is not linear.
the exponent of x = -1, as 1/x = x^-1. -1 is different to 1, which would be needed as exponent of x to make it linear.
Q : y = (1/3)x² + 3
it is not linear.
the exponent of x = 2. and 2 is different to 1, which would be needed as exponent of x to make it linear.
a person goes to store to buy clothes. the probability of the events are independent. the probability of buying a hat is 0.25. the probability of buying a pair of gloves is 0.72. what is the probability of both events occurring?
The probability of both events occurring is 0.18.
How to calculate the probability?Probability is the occurence of likely events. It is the area of mathematics that deals with numerical estimates of the likelihood that an event will occur or that a statement is true.
Since the person goes to store to buy clothes. the probability of the events are independent. the probability of buying a hat is 0.25. the probability of buying a pair of gloves is 0.72.
The probability of both events occurring will be:
= P(hat) × P(glove)
= 0.25 × 0.72
= 0.18
The probability is 0.18.
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A zookeeper predicted the weight of a new baby elephant to be 232 pounds when it was born. The elephant actually weighed 264 pounds at birth. What was the percent error of the zookeeper's prediction?
The percent error in zookeeper's prediction on baby elephant's weight is 13.79%.
What is percentage error?
Percentage error is the difference between the estimated value and the actual value compared to the actual value, expressed as a percentage. So the percent error is the relative error multiplied by 100.
Uses of percentage error:
The main purpose of calculating percent error is to analyze how close the measured value is to the actual value. This is part of a comprehensive error analysis.
Solution:
Percent error = (Actual weight - Predicted weight/Predicted weight)x100
Percent error = (264 - 232/232) x 100
Percent error = ( 32/232) x 100
Percent error = 0.1379 x 100
Percent error = 13.79%
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i need to find the similarity ratio of the first polygon to the second polygon because i forgot how to do this
The similarity ratio of first polygon to second polygon is 4 : 1.
Define similarity ratio.If two figures have the same shape, they are said to be comparable. In more formal terms, two figures are said to be comparable if their respective angles are congruent and their corresponding side length ratios are identical. The scale factor is the name given to this usual ratio. The ratio of any pair of corresponding sides is the ratio of any two similar figures. Simply put, when two figures are found to be similar, all of their associated side pairs have the same ratio.
Given,
Two polygons given,
Ratio of PQRS polygon = 20
Ratio of EFGH polygon = 5
Similarity ratio,
20 : 5
Simplifying,
4 : 1
The similarity ratio of first polygon to second polygon is 4 : 1.
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What is the factorization of the polynomial below 3x² 36x 81?
The factorized form of the formula is (3x+9)(x+9) of [tex]3x^{2}[/tex]+ 36x + 81 = 0 . Quadratics can be defined using a polynomial equation of the second degree.
what is a quadratic equation ?The mathematical action known as "squaring," which is typically used to describe a quadratic problem, involves multiplying a variable by itself. This lexicon is based on the idea that the area of a square is equal to the product of the lengths of its sides. The Latin term quadratum, which means square, is where the word "quadratic" comes from.
here ,
= [tex]3x^{2}[/tex] + 36x + 81 = 0
= 3x² + 27x + 9x + 81
= 3x(x+9) + 9(x+9)
= (3x+9)(x+9)
= 3(x+3)(x+9)
The factorized form of the formula is (3x+9)(x+9) of [tex]3x^{2}[/tex]+ 36x + 81 = 0 .
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solve | x + 4 | = -6
Answer:
Option D. No solution
Step-by-step explanation:
There is no value of x that makes the equation be true since an absolute value can never be negative.
No solution
Answer:
OptionD)
Step-by-step explanation:
[tex]x + 4 = -6\\x=-6-4\\x=-10\\[/tex]
Since there is no options with -10 only
The correct answer is OptionD)
Giving 25 points!!!!!! PLEASE HELP
describe the correlation for this scatter plot
Answer: Strong Negative Correlation
Step-by-step explanation:
Please help me solve
I will mark as brainliest
Answer:
3. B
4. C
Tell me if you need an explanation, I can add it for you :D
Killian used blocks to create this figure.
Complete the statement below.
Lily finds some dimes and quarters in her piggy bank. How much money (in dollars) does she have if she has 5 dimes and 12 quarters? How much money (in dollars) does she have if she has x dimes and y quarters?
Answer: 7 dollars
Step-by-step explanation:
i think
Answer: A dollar is 100 cents, so you would add the 5 dimes and 12 quarters together. A dime is 10 cents so 10x5 is 50, so you would have 50 cents in dimes. A quarter is 25 cents, so you would multiply 12x25 and you would get 300 and you add those both together to get 350 cents. A dollar is 100 cents so you would have 3 dollars and the remaining 50 cents would stay 50 cents! <33
Step-by-step explanation:
Type the correct answer in the box. Use numerals instead of words. What percentage of a radioactive substance remains after two half-lives?.
Answer:
25%
Step-by-step explanation:
[tex](1/2)^2=1/4 \\ \\ \frac{1}{4} \times 100=25\%[/tex]
algebra 1-
The admission fee at a small fair is $1.50 for children and $4.00 for adults. On a certain day, 2,200 people enter the fair and $5,050 is collected. Determine how many children and adults attended?