Based on the slope formula for a line, the value of a is: a = -3.
How to Calculate the Slope of a Line?If two points on a line have the following coordinates, (x1, y1) and (x2, y2), to find the slope (m) of the line, the formula that is applied is given as:
Slope (m) = change in y /change in x = [tex]\frac{y_2 - y_1}{x_2 - x_1}[/tex] = rise/run.
The given line has the following:
(-10, 0) = (x1, y1)
(a, -6) = (x2, y2)
Slope (m) of the line = -6/7.
Plug in the values into the slope formula for a line:
(-6 - 0) / (a - (-10)) = -6/7
-6/(a + 10) = -6/7
Cross multiply and solve to find the value of a in the equation:
-6(a + 10) = -6(7)
Apply the distributive property
-6a - 60 = -42
Add 60 to both sides
-6a - 60 + 60 = -42 + 60 [addition property of equality]
-6a = 18
Divide both sides by -6
-6a/-6 = 18/-6 [division property of equality]
a = -3
Therefore, the value of a is -3.
The line that has a slope of -6/7 will have the following points, (-10, 0) and (-3, -6).
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2,175/12 what is the answer
Answer: 2,175 divided by 12 will give you 181.25.
25. Susan is an electrician. She charges $75 for each repair appointmentand an additional $42 for each hour needed during the appointmentto make the repair. The expression shown can be used to calculate thetotal charge, in dollars, for each repair appointment,75 + 421where: h = the number of hours Susan works on a repair duringthe appointmentWhat is the total charge, in dollars, for a repair appointment if Susanworks for 6 hours?
Given:
Charge for each repair = $75
Additional charge per hour = $42
The expression is used to calculate the total charge, in dollars, for each repair appointment:
75 + 42h
Let h represent the number of hours Susna works during an appointment.
To find the total charge if Susan works for 6 hours, substitute 6 for h in the expression and evaluate.
Thus, we have:
h = 6
75 + 42h
75 + 42(6) = 75 + 252 = 327
Therefore, the total charge in dollars if Susan works for 6 hours is = $327
ANSWER:
$327
I really need help with number 3
3.To find:
The right angle congruence theorem is used to prove that two triangles are congruent.
Solution:
In the given triangles, the corresponding hypotenuse and the corresponding angle are equal. So, the congruence used here is the Hypotenuse-Angle congruence that implies ABC is congruent to DEF.
Thus, the answer is Hypotenuse-Angle congruence.
Where is the function f(x) = 2/6x^3 not differentiable?
at X= 0 the function f(x) = 2/6x^3 is not differentiable
Since 1/0 cannot be differentiated and the denominator will become zero when x=O, the function is not defined. Sharp points, cusps, and discontinuities in the graph indicate that a function is "not differentiable." Additionally, it implies that at that same location, we can draw an endless number of tangents. There is therefore no special tangent at that place. Even at x=0, the provided function is not defined. (If you plug in x=0, you get (1/0), which is undefined and leaves you with nothing to do.)) Only after a function is clearly defined at a certain moment do we discuss its continuation. And only if the function is continuous at the place do we talk about differentiability.
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Mary runs 4 laps around the track inb8 minutes. Paul runs 12 laps in 18 minutes. Who ran faster
Answer:
Step-by-step explanation:
thanks
Parul ran the fastest.
For Mary,
4/8 = x/1
4/8 or 1/2 laps per minute.
x= 0.5
For Paul,
12/18 = y/1
12/18 or 2/3 laps per minute.
y=0.666
Hence, Parul ran faster.
The SI unit of speed is m/s, and speed is defined as the ratio of distance to time.
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Find the compound amount and interest on 40,000 naira at 15% for 2 years
Answer: 52900 Naira
Step-by-step explanation:
1) Use the equation A = P(1+r/n)^nt
A = Ammount
(Starting Cash) P = 40,000
(Intrest rate) R = 15%
(Number of periods) n = N/A
(Time) t = 2
2) Make an equation
A = 40,000(1+15%)^2
3) Solve the equation.
A = 40,000(1+0.15)^2
A = 40,000(1.15)^2
A = 40,000(1.3225)
A = 52900
PLS HELP MEEEEEEEEEEEEEEEEEEEEE PLS I BEG U
how could you use a graph of a proportional relationship to find any ratio in the the proportional relationship why does this work?
Find the equation of a line perpendicular to y=-3x - 4 that contains the point (3, 0). Write the equation in slope-
intercept form.
Answer:
y = 1/3 x + 3
Step-by-step explanation:
1) when finding a perpendicular line, you take the slope and use the reciprocal (you flip it) and change the sign (from negative to positive or positive to negative)
-3 ---> 1/3
2) plug in the slope into a new equation
y=1/3 x + b
3) plug in the points
3= 1/3 (0) + b
b=3
4) rewrite the equation
y=1/3 x + 3
Answers: 5 to the square root of y^2 1/10 to the square root of y 10 to the square root of y 1/ square root of y^5
This is a case of indices
[tex]\begin{gathered} (\frac{1}{\sqrt[]{y}})^{-\frac{1}{5}} \\ =(\frac{1}{y^{\frac{1}{2}}})^{-\frac{1}{5}} \\ =y^{-\frac{1}{2}\times-\frac{1}{5}} \\ =y^{\frac{1}{10}} \\ =\sqrt[10]{y} \end{gathered}[/tex]The third option is the right answer.
175% of what number is 23?
Answer: 13
Step-by-step explanation:
The graph of a linear function is a horizontal line. When x = -3, y = 4. What is the equation for
this linear function? Explain.
For the graph of a linear function x=-3 and y=4 is horizontal line , the equation for this linear function is y = 0(x) +4.
As given in the question,
Graph of a required linear function is a horizontal line.
Given :
When x=-3 y=4
Two coordinates of the required linear function are :
(x₁ ,y₁) = (-3, 4)
(x₂, y₂) = ( 0,4)
Equation of the linear function :
(y -y₁) /(x-x₁) = (y₂ -y₁) / (x₂- x₁)
⇒( y-4)/(x+3) =(4-4)/(0+3)
⇒ (y-4)/(x+3) = 0/3
⇒ y = 0(x) +4
Therefore, for the graph of a linear function x=-3 and y=4 is horizontal line , the equation for this linear function is y = 0(x) +4.
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what is the fraction if the denominator is 8
Step-by-step explanation:
1/8, 2/8, 3/8, 4/8, etc...
(3/8, - (sqrt(55))/8) Find csc t.
The CSC of the expression [tex]\left(\frac{3}{8},-\frac{\sqrt{55}}{8}\right)[/tex] is mathematically given as
[tex]\csc (\theta)=-\frac{8 \sqrt{55}}{55}[/tex]
This is further explained below.
What is the CSC ?Generally, the equation for the Problem is mathematically given as
[tex]\left(\frac{3}{8},-\frac{\sqrt{55}}{8}\right)[/tex]
Therefore
To find the [tex]$\csc (\theta)$[/tex] between the x-axis and the line between the points (0,0) and [tex]\left(\frac{3}{8},-\frac{\sqrt{55}}{8}\right),[/tex] draw the triangle between the three points [tex](0,0),\left(\frac{3}{8}, 0\right)$, and $\left(\frac{3}{8},-\frac{\sqrt{55}}{8}\right)$[/tex]
Opposite [tex]$:-\frac{\sqrt{55}}{8}$[/tex]
Adjacent :[tex]$\frac{3}{8}$[/tex]
Find the hypotenuse using the Pythagorean theorem [tex]$c=\sqrt{a^2+b^2}.[/tex]
[tex]$\csc (\theta)=\frac{\text { Hypotenuse }}{\text { Opposite }}$[/tex]
therefore
[tex]\csc (\theta)=\frac{1}{-\frac{\sqrt{65}}{8}}$.[/tex]
[tex]\frac{1}{-\frac{\sqrt{55}}{8}}[/tex]
Simplify[tex]\csc (\theta)[/tex]
[tex]\csc (\theta)=-\frac{8 \sqrt{55}}{55}[/tex]
Approximate the result.
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Question 1 options:
Is the relation in this set of points a function?
{(-2, 6) , (4, 5) , (3, -3) , (6, 9), (4, -4)}
State whether the statement is true of false.
1. The relation is a function.
2. An element from the domain is paired with more than one element from the range.
Answers:
FalseTrue================================================
Explanation:
Focus on (4,5) and (4,-4)
The input x = 4 leads to simultaneous outputs y = 5 and y = -4 at the same time. This is not allowed in a function. For a function to be possible, each input x must lead to exactly one y output.
Therefore, this given relation is not a function.
-----------
Domain = set of possible x inputs
Range = set of possible y outputs
The statement "An element from the domain is paired with more than one element from the range" basically means we have an x value paired with more than one y value. Therefore, this statement is true since I mentioned (4,5) and (4,-4) earlier.
Answer:
This answer is correct!
Find the angle measures of the inscribed quadrilateralm
In an inscribed quadrilateral, the sum of the opposite angles are always equal to 180 degrees
so that
10z +
(14z-7) + 8z = 180 degrees-------------(2)
From equation (2)
14z+8z= 180+7
22z = 187
22z/22 = 187/22
z= 8.5
From equation (1) and substituting for z
10(8.5) + 85 +
Assume that a procedure yields a binomial distribution with a trial repeated n times. Use the binomial probability formula to find the
probability of x successes given the probability p of success on a single trial. Round to three decimal places.
n = 6, X = 3, p = 1/6
Probability of x successes given the probability p of success on a single trial is 0.0154.
What is binomial probability?When a process is repeated a certain number of times (for example, in a set of patients), the result for each patient can either be a success or a failure, the binomial distribution model enables us to calculate the probability of witnessing a defined number of "successes." In probability theory and statistics, the discrete probability distribution of the number of successes in a series of n independent experiments, each asking a yes-or-no question and each with its own Boolean-valued outcome: success or failure, is known as the binomial distribution with parameters n and p.
Given Data
n = 6
X = 3
p = [tex]\frac{1}{6}[/tex]
Binomial distribution
P(X = x) = ₙCₓ(pˣ)(qⁿ⁻ˣ)
ₙCₓ =[tex]\frac{n!}{(n-x)!x!}[/tex]
P(X = 3) = ₃C₄(0.1667³)(1-0.1667)¹
P(X=3) = 0.0154
Probability of x successes given the probability p of success on a single trial is 0.0154.
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Select the three equations that pass through the points (–4, –16) and (5, 2):
y + 4 = 2(x – 16)
y – 2 = 2(x – 5)
y = 2x – 8
y + 16 = 2(x + 4)
The equation of line passing through (-4, -16) and (5, 2) are y = 2x – 8, y - 2 = 2(x - 5) and y + 16 = 2(x + 4)
What is an equation?An equation is an expression that shows the relationship between two or more numbers and variables.
Equations are classified based on degree (value of highest exponents) as linear, quadratic, cubic and so on. Variables can be dependent or independent. Dependent variables depend on other variable while an independent variable do not depend.
The standard form for linear equation is:
y = mx + b
Where m is the slope and b is the y intercept
The equation of line passing through (5, 2) and (-4, -16) is:
y - 2 = [(-16-2)/(-4-5)](x - 5)
y - 2 = 2(x - 5)
y = 2x - 8
y + 16 = 2(x + 4)
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Question
Given that the terminal side of angle 0 goes through the point (-4, 3), find csc(0).
Answer: -4/3
Step-by-step explanation:
[tex]\csc \theta=\frac{1}{\sin \theta}=\frac{1}{-3/4}=-4/3[/tex]
Which graph represents the solution to the inequality 2(b + 2) < 24?
number line with open point at 10 with arrow pointing left
number line with closed point at 10 with arrow pointing left
number line with closed point at 10 with arrow pointing right
number line with open point at 10 with arrow pointing right
The solution to the inequality shows that the circle will be on 10 and pointing to the left.
Solving inequalityInequality are expressions not separates by an equal sign.
Given the inequality expression below:
2(b + 2) < 24
Expand
2b + 4 < 24
2b < 24 - 4
2b < 20
Divide both sides by 2
2b/2 < 20/2
b < 10
Hence the number line with open point at 10 with arrow pointing left.
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What’s the answer to this question
The value of (fg)(6) is -6x³ + 72x² + 72x - 864 after doing the mathematical operations.
What do we mean by mathematical operations?A mathematical function called an operation, also known as an "operand" or "argument," transforms zero or more input values into a precisely defined output value.The quantity of operands affects the operation's arity.The operations that are most frequently studied are unary operations (i.e., operations of arity 1), such as additive inverse and multiplicative inverse, and binary operations (i.e., operations of arity 2), such as addition and multiplication.An operation of arity zero also referred to as a nullary operation, is a constant.The mixed product is an illustration of an operation of arity 3, also referred to as a ternary operation.So, f(x) = x² - 12 and g(x) = 12 - x.
Then, (fg)(6) will be:
[(x² - 12)(12 - x)]6[x²(12 - x) - 12(12 - x)]6[12x² - x³ - 144 + 12x]6-6x³ + 72x² + 72x - 864Therefore, the value of (fg)(6) is -6x³ + 72x² + 72x - 864 after doing the mathematical operations.
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The width of a garden is 19.5 feet, and the perimeter of the garden is 84 feet. What is the area of the garden?
Rectangular garden has sides:
width, length, width, length
The perimeter is sum of all the 4 sides.
So, we can say:
84 = 2w + 2l
Where
w is width
l is length
Width is 19.5, so we find length:
84 = 2(19.5) + 2l
84 = 39 + 2l
2l = 45
l = 22.5 feet
Now, area is given by:
Area = length * width
Area = 22.5 * 19.5 = 438.75 sq. ft.
Can you please solve this.
Answer:
x^8
Step-by-step explanation:
You want to simplify x^10/x^2.
Rule of exponentsThe applicable rule of exponents is ...
(a^b)/(a^c) = a^(b-c)
ApplicationUsing this rule on the given expression, we find ...
(x^10)/(x^2) = x^(10-2) = x^8
__
Additional comment
An exponent can be considered to be an indicator of repeated multiplication. That is, it tells how many times the base is a factor in the product. Knowing this, you can use the usual rules of division to cancel common factors:
[tex]\dfrac{x^{10}}{x^2}=\dfrac{x\cdot x\cdot x\cdot x\cdot x\cdot x\cdot x\cdot x\cdot x\cdot x}{x\cdot x}=x\cdot x\cdot x\cdot x\cdot x\cdot x\cdot x\cdot x=x^8[/tex]
Sades dinner cost $30 she had a coupon to save 40% off the price of the
dinner
Answer:
The dinner costs $18
Step-by-step explanation:
30x0.40=discount
discount=12
30-12=dinner price
dinner price=$18
Are these rational numbers?
1) -1098.15
2) -2,784.75
Yes, these -1098.15 and -2,784.75 are rational numbers.
Rational number is the one that can be stated mathematically as the ratio or fraction p/q of two numbers, where p and q are the numerator and denominator, respectively
What is a rational numbers?A rational number is the one that can be stated mathematically as the ratio or fraction p/q of two numbers, where p and q are the numerator and denominator, respectively. Every integer (e.g., 5 = 5/1) and, for instance, the number 3/7 are rational numbers. Boldface Q, also known as blackboard bold, is typically used to signify the set of all rational numbers, also known as "the rationals," the field of rationals, or the field of rational numbers.
Real numbers are those that are sensible. The rational real numbers are those whose decimal expansion either ends after a finite number of digits (for instance, 3/4=0.75) or eventually starts to repeatedly repeat the same finite sequence of digits (9/44=0.204545454). This assertion is accurate not just in base 10, but also in every other integer base, such as the binary and hexadecimal ones
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Please help I’ll mark you as brainliest if correct!!
filled in the blanks : -
348
* 784
_____________
1392
2784
2436
______________
272832
What is multiplication ?a mathematical operation that, at its most basic, is the quick addition of an integer to zero a certain number of times, expanded to other numbers using principles that apply to integers.
Calculation348
* 784
_____________
1392
2784
2436
______________
272832
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Which of the following questions describes the equation 4 =-20? What number, when multiplied by negative twenty, is equal to four? What number, when divided by four, is equal to negative twenty? What number, when multiplied by four, is equal to negative twenty? What number, when divided by negative four, is equal to twenty?
The option that describes the equation 4x =-20 will be C. What number, when multiplied by four, is equal to negative twenty?
How to illustrate the information?It should be noted that an equation is used to show the relationship between the variables.
In this case, the equation given us illustrated as:
4x = -20
The appropriate question that fits this will be that what number, when multiplied by four, is equal to negative twenty. This can be illustrated as:
4x = -20
Divide through
x = -20 / 4
x = -5
In conclusion, the correct option is C.
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Answer:
Step-by-step explanation:
(-2,-3), (4,3) in point slope form
Answer: y + 3 = 1 ⋅ (x + 2)
Step-by-step explanation:
terrance plants a garden that has 8 rows of flowers, with 28 flowers in each row. how many flowers did terance plant
Answer:
224
Step-by-step explanation:
The answer is 224 since 8 x 28 = 224
Answer: Terrence planted 224 flowers in total
Step-by-step explanation: 8x28
Given the two rectangles below. Find the area of the shaded region?
Answer:
Step-by-step explanation:
34 units.
Find the value of f (8).
Answer:
4
Step-by-step explanation:
first we go over where 8 is on the x-axis then we move up to the line, and look at the corresponding y value, which is 4