Volume = Area of the base * height
Area of the base = (7 * 6) / 2
Area of the base = 42/2
Area of the base = 21ft^2
Volume of the prism = 21 * 13
Volume of the prism = 273 ft^3 The thi
Simplify the expression.
the expression negative six sevenths times k minus 7 plus the expression 5 plus one half times k
negative 19 over 14 times k plus negative 12
negative 5 over 14 times k plus negative 2
negative 5 over 9 times k plus negative 12
5 over 14 times k plus negative 2
The simplified form of the expression, negative six sevenths times k minus 7 plus the expression 5 plus one half times k is negative 5 over 14 times k plus negative 2.
Hence, the correct option is option (B).
What is an algebraic expression?An algebraic expression is consists of variables, numbers with various mathematical operations,
The given expression is,
negative six sevenths times k minus 7 plus the expression 5 plus one half times k.
The expression can be written in mathematical term,
(-6/7)k - 7 + 5 + 1/2(k)
Simplify the expression,
(-6/7)k + 1/2(k) - 7 + 5
((-12 + 7)/14) k - 2
(-5/14) k - 2.
-(5/14)k + (-2)
The simplified form is, negative 5 over 14 times k plus negative 2.
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Write a polynomial function f of least degree that has rational coefficients, a leading
coefficient of 1, and the given zeros of -1, 2, and -3i. Show all work.
The least degree polynomial function with rational coefficients and the given zeros, -1, 2 and 3i is f(x) =[tex]x^{2} -x -2(\sqrt{x} -9)[/tex]
What do we mean by polynomial function?
A polynomial function is one that involves only non-negative integer powers or positive integer exponents of a variable in an equation such as the quadratic equation, cubic equation, and so on.
For example, 2x+5 is a polynomial with an exponent of one.
So given zeroes are -1 , 2 and 3i
We have,
x = -1
x +1 =0
Similarly for 2
x = 2
x -2 = 0
Again, For 3i
We have, x = 3i
Rewrite as x = [tex]\sqrt{-9}[/tex]
For easy calculation, squaring on both sides
[tex]x^{2} = -9[/tex]
[tex]x^{2} +9[/tex] =0
So, the polynomial has the function:
(x + 1)(x - 2) ([tex]\sqrt{x} -9[/tex])
[tex]x^{2} - 2x +x -2 (\sqrt{x} -9)\\x^{2} -x -2(\sqrt{x} -9)\\[/tex]
Therefore, the least degree polynomial function with rational coefficients and the given zeros, -1, 2 and 3i is f(x) =[tex]x^{2} -x -2(\sqrt{x} -9)[/tex].
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Hi Please help me with math
Answer:12
Step-by-step explanation:
NEED HELP URGENTLY!!!!!
20. Write a word problem such that the equation
to be formed for solving the problem is
QUESTION 6x +4(x - 10) = 140.
OPEN
In linear equation, x = 18 is the value of x in equation .
What is a linear equation example?
Ax+By=C is the usual form for two-variable linear equations.As an illustration, the conventional form of the linear equation 2x+3y=5 When an equation is given in this format, finding both intercepts is rather simple (x and y).A linear equation is a first-order (linear) term plus a constant in the algebraic form y=mx+b, where m is the slope and b is the y-intercept.The variables in the previous sentence, y and x, are referred to as a "linear equation with two variables" at times.6x +4(x - 10) = 140.
6X + 4X - 40 = 140
10X = 140 + 40
10x = 180
x = 180/10
x = 18
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Tank B, which initially contained 80 liters of water, is being drained at a rate of 2.5 liters per minute. For how many minutes has the water been draining when Tank B contains 75 liters of water?
We get that the function that models this situation is
[tex]L=80-2.5m[/tex]where L is the liters the tank contains and m is the minutes that has passed. So we get:
[tex]75=80-2.5m\rightarrow m=\frac{-80+75}{-2.5}=2[/tex]so the tank has been drained for 2 minutes
Maleri Designs sells cartons of cloth face masks ($18) and cartons of hand-sanitizer ($9) on eBay. One of their
customers, Mod World, purchased 21 cartons for $297. How many of cartons of each did Mod World purchase?
Check your answer. Hint: Let F= Face masks.
Answer:
F=12 C=9
Step-by-step explanation:
$18 12 times is $216 $9 9 times is $81 $216+81=$297
LOTS OF POINTS!!!!! The table of values represents a linear function g(x), where x is the number of weeks that have passed and g(x) is the balance in the bank account. Find the slope of the function.
A.
-500
B.
-1/100
C.
-100
D.
-1/500
Answer: easy it's A -500
The slope of the function (x) is -500!! :D
What is the contrapositive of the following sentence?If two triangles are congruent, then their corresponding angles are congruent.
Given:
If two triangles are congruent, then their corresponding angles are congruent.
Contapositive statement:
If two triangles are not congruent , then their corresponding angles are not congruent.
Option C is the correct answer
help meeeeeee pleaseee !!!!
The equation of the line that passes through point (8,-1) and perpendicular to 8y = x - 16 is f(x) = -8x + 63.
What is the equation of line that passes through the given points and is perpendicular to the given line?Given the data in the question;
Equation of line: 8y = x - 16Point: (8,-1)First we determine the slope of the initial line using the slope intercept-form. y = mx + b
8y = x - 16
y = (1/8)x - 2
Compared with the slope intercept form,
Slope m = 1/8
Now, for the equation of line perpendicular to the initial line, its slope must be a negative reciprocal of the initial slope.
Hence, slope of the perpendicular line is;
Slope m = -1/1/8 = -8
To find the equation of the perpendicular line, we use the point slope formula.
y - y₁ = m( x - x₁ )
Plug in the slope m ( -8) and point (8,-1).
y - (-1) = (-8)( x - 8 )
y+1 = -8x + 64
y = -8x + 64 - 1
y = -8x + 63
Therefore, the equation of the perpendicular line is y = 8x + 63
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Please help! Will give brainliest!
g(9)+h(-14) if g(x)=14-2/3x and h(x)=-x-7?
The value of g(9) + h(-14) is 15.
We are given two functions, h(x) and g(x).The function h(x) is defined as given below:The function h(x) equals -x - 7.The function g(x) is defined as given below:The function g(x) equals 14 - (2/3)x.We have to find the sum of g(9) and h(-14).To find g(9), replace "x" with 9 in the definition of function "g".g(9) = 14 - (2/3)*9g(9) = 14 - (2*3)g(9) = 14 - 6g(9) = 8To find h(-14), replace "x" with -14 in the definition of function "h".h(-14) = -(-14) - 7h(-14) = 14 - 7h(-14) = 7g(9) + h(-14) = 8 + 7g(9) + h(-14) = 15To learn more about functions, visit :
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I need it in slope intercept form and it has to be PERPENDICULAR to the equation it gives.
The equation of the line in slope intercept form perpendicular to 6x - 2y = 12 and has the same y-intercept is y = - 1 / 3 x - 6
How to find equation in slope intercept form?The equation in slope intercept form can be represented as follows:
y = mx + b
where
m = slopeb = y-interceptTherefore, the equation of the line is perpendicular to 6x - 2y = 12 and have the same y-intercept.
Hence, perpendicular lines follows the rule below:
m₁m₂ = -1
6x - 2y = 12
6x - 12 = 2y
y = 3x - 6
Hence,
3m₂ = -1
m₂ = - 1 / 3
Therefore, the slope of the line is - 1 / 3.
The y-intercept is -6
Therefore,
the equation of the line is y = - 1 / 3 x - 6
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using trig to find sides
Step 1: Problem
Find the measure of
Step 2: Concept
Use trigonometry ratio to find the value of angle x.
Step 3: Method
Given data
Opposite = 3.2 side facing given angle
Adjacent = 5
[tex]\begin{gathered} U\sin g\text{ tagent formula} \\ \tan \theta\text{ = }\frac{Opposite}{\text{Adjacent}} \\ \tan x\text{ = }\frac{3.2}{5} \\ \tan x\text{ = 0.64} \\ x\text{ = }\tan ^{-1}\text{ 0.64} \\ x\text{ = 32.6} \end{gathered}[/tex]Step 4: Final answer
Due to increased mailing costs, the new rate will cost publishers $50 million; this is 12.5% more than they
paid the previous year. How much did it cost publishers last year? Round to the nearest hundreds.
The amount it will cost the publishers last year is 44.4 million
How to calculate the amount it will cost the publishers?The first step is to write out the parameters
The cost of mailing increased for the last one year
Due to this increase, it will cost the publishers $50 million for this current year
The increase is at the rate of 12.5%
The amount it will cost the publishers last year can be calculated as follows
= 12.5/100
= 0.125 + 1
= 1.125
The next step is to calculate last year cost
last year cost= 50/1.125
= 44.4 million
Hence the publishers spent 44.4 million last year
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Given the following expression: 8x2 + 26x – 15 One of its simplified factors is: NOTE: If an answer is (x + 1), then do not use any spaces in your answer and be sure to include the parentheses. Your answer would look like this: (x+1)
We have the following:
[tex]8x^2+26x-15[/tex]simplify:
[tex]\begin{gathered} 8x^2-4x+30x-15 \\ 4x(2x-1)+15(2x-1) \\ (2x-1)\cdot(4x+15) \end{gathered}[/tex]The answer are (2x - 1) or (4x + 15)
Find the length of the minor axis of the ellipse described by the equation:x squared over 12 plus y squared over 13 equals 1
This equation of the ellipse can be modeled by
[tex]\frac{x^2}{a^2}+\frac{y^2}{b^2}=1[/tex]The major axis is the y-axis and minor axis is the x-axis.
So, the length of the minor axis of this ellipse is "2a".
First, let's find "a",
[tex]\begin{gathered} a^2=12 \\ a=\sqrt[]{12} \end{gathered}[/tex]The length of the minor axis is >>>
[tex]\begin{gathered} 2a \\ =2(\sqrt[]{12}) \\ =2\sqrt[]{12} \end{gathered}[/tex]Answer[tex]2\sqrt[]{12}[/tex]For what values of x is the expression below defined?x+5+ v1 -O A. 5 >x>1B. 5 sxs1C. -5 s x < 1D. 5 > XS-1SUBMIT
The correct range of definition is;
[tex]C;\text{ -5}\leq x<1[/tex]Here, we want to get the range of values of x for which the given expression is defined
The key here is that any value of x that will make us have a negative value inside the root will make the expression undefined as that would give us a non-real root
Now, let us take a look at the options;
a) if x is greater than 1, we will have a negative root on the right, making the expression undefined. This option is wrong
b) This is also wrong; if 5 is less than x, then x might be 6 , which would give a negative root value
c) If -5 is less than x, x could take values of -4, -3, -2 and the root on the right will never be negative. But in cases like this, we have the spectrum upto positive values of x such as 5 which would make the root on the right negative and undefined. This range here is the correct answer
d) Here, 5 is greater than x, so the root on the left can never be negative. For values less than -1, like -6, what we have on the left will be undefined
Which of the following activities are examples of data gathering?Check all that apply.
Answer.
D.
Step by step explanation.
It's defined as the procedure of collecting, measuring, and analyzing accurate insights for research using standard validated techniques.
The most critical objective is ensuring that information rich and reliable data is collected dor statistical analysis so that data-driven decisions can be made for research
A triangular pane of glass has a height of 48 inches and an area of 432 square inches. What is the length of the base of the pane? The length of the base of the pane is inches.
We can express the area of a triangle as half the product of its base and height:
[tex]A=\frac{b\cdot h}{2}[/tex]Then, we can express the base in function of the known variables (area and height) as:
[tex]\begin{gathered} A=\frac{b\cdot h}{2} \\ 2A=b\cdot h \\ b=\frac{2A}{h} \end{gathered}[/tex]We replace with the known values (A=432 sq in, h=48 in) and calculate the base b:
[tex]b=\frac{2\cdot432\text{ in}^2}{48\text{ in}}=18\text{ in}[/tex]Answer: the base is 18 inches.
Equation: y =
Write an equation of the line that passes through the given point and is parallel to the given I
(-4, 2); y = 1/4x + 1
The equation of the line that passes through the point (-4,2) and the parallel to the line y = 1/4x + 1 is y = (1/4)x+3
The equation of the line parallel to the line is
y = 1/4 x +1
The slope intercept form is
y = mx + b
Where m is the slope of the line and b is the y intercept
By comparing the given equation and slope intercept form of the line
The slope of the line is m = 1/4
Then the point slope form is
[tex](y-y_1)= m(x-x_1)[/tex]
The line is passing through the point (-4,2)
Substitute the values in the equation
(y-2) = 1/4(x-(-4))
y-2 = 1/4(x+4)
y-2 = (1/4)x+1
y = (1/4)x+3
Hence, the equation of the line that passes through the point (-4,2) and the parallel to the line y = 1/4x + 1 is y = (1/4)x+3
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State a conclusion that seems reasonable 6+06, 8+0=8, 9 -9, 100-0-100 Conclusion:
Answer
The most obvious conclusion from this is that
Adding 0 to any number gives that number itself.
This concept is known as the additive identity property of 0.
Hope this Helps!!!
Can someone please help me solve this pleaseeee, I’m struggling and depressed
Step-by-step explanation:
your teacher gave you the formula, the values, even did the tricky part by telling you that 63 months are 5.25 years.
all you need to do is put everything into the formula and calculate.
so, calm down, breathe and just use common sense :
1.
after 2 years (means t = 2) :
2000 × (1.025)^(2×2) = 2000 × (1.025)⁴ =
= 2000 × 1.103812890625 =
= $2,207.62578125 ≈ $2,207.63
as rounding to the nearest cent means rounding to 2 positions after the decimal point.
2.
after 63 months = 5.25 years (t = 5.25)
2000 × (1.025)^(2×5.25) = 2000 × (1.025)^10.5 =
= 2000 × 1.295986825... =
= $2,591.973651... ≈ $2,591.97
3.
$2,000
because, even t = 0 we have
2000 × (1.025)^(2×0) = 2000 × (1.025)⁰ = 2000 × 1 =
= $2,000
one afternoon the shadow of a flagpole is 21 feet long at the same time the shadow of 109 foot high building is 54 feet long what is the approximate Height of the flag pole
Coplanar lines are referred to as parallel lines because they may be extended indefinitely without ever intersecting. || is the sign meaning "parallel to." If two lines are drawn, they don't have to be parallel, and a third line runs across them as seen in the diagram below. We may obtain eight distinct angles by drawing two parallel lines, and then drawing a transverse line through them.
Four pairs of matching angles will be created from all eight angles. One of the pairings is represented by angles F and B in the preceding diagram. If the two lines are parallel, corresponding angles are congruent.
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Evaluate the following expression when x =2 and z=5
The given expression is
[tex]\frac{z}{5x}[/tex]Let's replace x = 2, and z = 5.
[tex]\frac{5}{5\cdot2}=\frac{1}{2}[/tex]Hence, the answer is 1/2.find the x and y intercepts of 2x-5y=12 (write all answers as points)
Here, we want to find the x and y intercepts of the given line
We start by writing the equation of the line in the standard form
The standard form is;
[tex]y\text{ = mx + b}[/tex]where m is the slope and b is the y-intercept
We have the equation re-written as;
[tex]\begin{gathered} 5y\text{ = 2x - 12} \\ y\text{ = }\frac{2}{5}x\text{ - }\frac{12}{5} \end{gathered}[/tex]As we can see, we have the y-intercept at the point y = -12/5
The coordinate form at this point is (0,-12/5)
To find the x-intercept, we simply set y to zero
This is;
[tex]\begin{gathered} 0\text{ = }\frac{2}{5}x\text{ - }\frac{12}{5} \\ \\ \frac{2}{5}x\text{ = }\frac{12}{5} \\ \\ 2x\text{ = 12} \\ x\text{ = }\frac{12}{2} \\ x\text{ = 6} \end{gathered}[/tex]The x-intercept is thus (6,0)
help help hellpppppp
The equation of the line will be y = 2x + 1.
What do we mean by the equation of the line?The set of points that make up a line in a coordinate system is represented algebraically by a line's equation. An equation of a line is an algebraic expression that represents the many points that together make up a line in the coordinate axis as a set of variables, x, and y.So, the equation of the line:
The equation is parallel to y = 2x -2 and the slopes equation is y = mx + b where m is the slope.So, the slope is 2.Then, y = 2x + b
Now, substitute x = 1 and y = 3 in the above equation to find b:
y = 2x + b3 = 2(1) + bb = 3 - 2b = 1So, the equation of the line will be: y = 2x + 1
Therefore, the equation of the line will be y = 2x + 1.
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Polygon KLMN is drawn with vertices at K(1, 5), L(1, 0), M(−1, −1), N(−4, 2). Determine the image vertices of N′ if the preimage is rotated 90° counterclockwise. N′(−4, 2) N′(4, −2) N′(−2, −4) N′(2, 4)
ANSWER
N'(-2 , -4) Option C
EXPLANATION
Given:
A polygon KLMN with vertices at K(1, 5), L(1, 0), M(−1, −1), N(−4, 2).
Desired Outcome:
Image vertices of N′ if the preimage is rotated 90° counterclockwise
Answer: The correct answer is C
Step-by-step explanation:
I was correct on the quiz. WOWWWW
Which situation represents a proportional relationship?
O Renting a movie for $2 per day
O Renting a movie for $2 per day with a coupon for $0.50 off for the first day
O Renting a movie for $2 per day along with paying a $5 membership fee
O Renting a movie for $2 for the first day and $1 for each day after the first day
Answer:
renting a movie for 2 dollars a day
Step-by-step explanation:
the y does not repeat
Find the equation of a parabola with a focus of (0, 15) and directrix y = –15.
The equation of the parabola is x² = 60y after applying the concept of the parabola.
What is a parabola?It is defined as the graph of a quadratic function that has something bowl-shaped.
(x - h)² = 4a(y - k)
(h, k) is the vertex of the parabola:
a = √[(c-h)² + (d-k²]
(c, d) is the focus of the parabola:
It is given that:
Focus of (0, 15) and directrix y = –15.
Let (x, y) be on the parabola:
The distance between focus and (x, y):
The distance formula can be given as:
[tex]\rm d=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}[/tex]
[tex]\rm d=\sqrt{(x-0)^2+(y-15)^2}[/tex]
[tex]\rm d=\sqrt{x^2+(y-15)^2}[/tex]
Directrix y = -15
y + 15 = 0
[tex]\rm \sqrt{x^2+(y-15)^2} = |y + 5|[/tex]
Squaring both sides:
x² + (y - 15)² = (y + 15)²
x² + y² -30y + 225 = y² + 30y + 225
x² -30y = 30y
x² = 30y + 30y
x² = 60y
Thus, the equation of the parabola is x² = 60y after applying the concept of the parabola.
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If 35% of your candies was 42 candies, how many candies do you have?
Answer:
120 candles
Step-by-step explanation:
42/35 = x/100 and solve for x
x = 120
Answer:
120
Step-by-step explanation:
35%/100=42/x