Answer: 6x-5
5 less is just subtract 5 from whatever follows
Write a slope-intercept equation for a line that passes through (7,0) and (-5,3).
Answer:
y = -1/4x + 7/4
Step-by-step explanation:
m = (y2-y1)/(x2-x1)
m = (3 - 0)/(-5 - 7) = 3/(-12) = -1/4
using m = -1/4, y = 0 , x = 7
y = mx + b
0 = -1/4(7) + b
0 = -7/4 + b
b = 7/4
y = -1/4x + 7/4
Evaluate the function /(x) = 5x²+2x for the given value of x. Simplify your answer.
h(-4)
Answer:
h(-4) = 72
Step-by-step explanation:
Given:
h(x) = 5x² +2x
Evaluate the function h(x) = 5x²+2x for x=-4 means to
find h(-4) by substituting x with -4:
h(-4) = 5·(-4)² +2·(-4)
h(-4) = 5·16 -2·4
h(-4) = 5·16 -2·4
h(-4) = 80 -8
h(-4) = 72
Find the length of the missing side. Leave your answer in the simplest radical form.
Length of the missing side. Leave your answer in the simplest radical form b= root of 69 feet
Pythagorean theorem:
Pythagorean theorem is the well-known geometric theorem that the sum of the squares on the legs of a right triangle is equal to the square on the hypotenuse (the side opposite the right angle)—or, in familiar algebraic notation, a2 + b2 = c2
The Pythagorean Theorem is tremendously useful. In many realistic scenarios it is possible to measure a and b with ease, but it is often difficult to measure c. For instance, c might pass through a lake or private property or might be up in the air! We'll do a few example puzzles in class together to show you how this works.
Nonetheless, the Pythagorean Theorem still presents a substantial limitation to utility. Specifically, it requires that the angle between a and b is 90 degrees. If the angle is not 90 degrees, the Pythagorean Theorem doesn't help.
This is where the Law of Cosines comes in. The Law of Cosines allows us to find c even when the angle between a and b is not 90 degrees. Check out this applet which illustrates the relationship between a2 and b2 and c2 that also takes into account the angle C (note the angle is capital C to distinguish it from lower case c, the side opposite angle C) between the legs a and b.
Adjust the blue dots in the triangle on the right right side of the screen to see the relationship. At the outset, when angle C is 90 degrees, a2+b2 is exactly equal to c2. However, when you move any of the three vertices of the triangle, note that the equality is not maintained. The problem is that angle C becomes not 90 degrees.
Now ,
a= 10
c= 13
b=?
a2 + b2 = c2
[tex]10^{2} +b^{2} = 13^{2} \\\\100+ b^{2} = 169\\\\b^{2} = 169-100\\\\b=\sqrt{69}[/tex]
Length of the missing side. Leave your answer in the simplest radical form
b= root of 69 feet
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The circle graph on the right shows the uses of corn production. Use this graph to answer the question. What percent of corn production is used for ethanol or exports?
Answer:
37%
Step-by-step explanation
Reading the graph we see:
The percent of corn production is used for ethanol is 18%
The percent of corn production is used for exports is 19%
Answer the question:
The percent of corn production used for ethanol OR exports is the sum of the two 18%+19% = 37%
please help
please hurry
From the given table, the relationship that is an inverse variation is the fourth relationship with (1, -2) and (3, -6).
What is an inverse variation?An inverse variation refers to when the values of x and y move in opposite directions.
For instance, when x increases, y decreases. The decrease will have to be constant however which is why the fourth relationship is an inverse variation.
When x increases by 1, the value of y decreases by 2.
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Vartan was paid $25,000 for a cell phone app that he wrote and wants to invest it to save for his son’s education. He wants to put some of the money into a bond that pays 4% annual interest and the rest into stocks that pay 9% annual interest. If he wants to earn 7.4% annual interest on the total amount, how much money should he invest in each account?
If the polygons are similar, write similar on the blank. If they are not similar, write not similar on the blank. Consider all angles are congruent. First square is 5 by 7 by 5 by 7, the second square is 2.5 by 3.5 by 2.5 by 3.5
What is the 7 1/2 divided by 1 9/10 in the simplest form
Answer:
3 18/19
Step-by-step explanation:
7 1/2 ÷ 1 9/10 =
= 15/2 × 10/19
= 150/38
= 75/19
= 3 18/19
Which expression is equivalent to the image below.
Answer:
t - s
------------
t + s
Step-by-step explanation:
To solve a problem like this you need to flip the denominator and multiply
Step 1: Write the equation
s
1 - ------
t
--------------
s
1 + -------
t
Step 2: Flip it and multiply
s t
1 - ------ × 1 + -------
t s
Step 3: Multiply Across
s t -s + t t - s
1 - ------ × 1 + ------- = -------------- or ---------------
t s t + s t + s
I hope this helps!
the length of a rectangle is 5 feet longer than the width if the perimeter is 94 feet find the length and width of the rectangle
The length and width of the rectangle with the given perimeter are 26ft and 21ft respectively.
What is the length and width of the rectangle?The perimeter of rectangle is expressed as;
P = 2( l + w )
Given the data in the question;
Let 'x' represent the width of the rectangle.
Width w = xLength = x+5Perimeter = 94ftPlug these values into the equation above.
P = 2( l + w )
94 = 2( (x+5) + x )
94 = 2x + 10 + 2x
94 = 4x + 10
4x = 94 - 10
4x = 84
x = 84/4
x = 21
Hence;
Width of the rectangle = x = 21ft
Length of the rectangle = x+5 = 21+5 = 26ft
Therefore the length and width of the rectangle with the given perimeter are 26ft and 21ft respectively.
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simplify 20/64 into simplest form
Answer:
Ahmm I guess it is
[tex] \frac{5}{16} \\ [/tex]
Step-by-step explanation:
Cuz I did like
[tex] \frac{20}{64} = \frac{20}{64} \div \frac{2}{2} = \frac{10}{32} = \frac{5}{16} \\ \\ \\ \\ \frac{20}{64} = \frac{20}{64} \div \frac{4}{4} = \frac{5}{16 \\ \\ \\ \\ \\ \\ } [/tex]
so I guess it's correct
Eric walks around a man made circular lake three times how far in km has he walked ?
Considering the circumference of a circle, it is found that Eric has walked 151.68 km.
What is the missing information?The missing information is that the lake is a circle of radius 5 miles.
What is the measure of the circumference of a circle?The circumference of a circle of radius r is given by:
C = 2πr.
Hence the circumference in miles of the circle is:
C = 2π x 5 = 10π miles.
This is the length of one lap, hence the length of 3 laps is:
3 x 10π = 30π miles.
In kilometers, the distance is:
30π x 1.60934 = 151.68 km.
Hence Eric has walked 151.68 km.
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E
3
A. bd
If a, b, c, and d are four different numbers and the proportion
a C
B. a b
C
I
C. b
a
11
IL
D. a+b
b
d
C
HE
3
c+d
d
E
a
11
U
bd
40:09
is true, which of the following is false?
If a, b, c, and d are four different numbers and the proportion. The given statement is true.
We take one example,
When you split them, they will all equal the same thing.
A = 5 ,B = 20 20 divided by 5 equals 4
C = 28 ,D = 7 28 divided by 7 equals 4
The ratio is used to compare two amounts of the same type. For two numbers, a and b, the ratio formula is written as a: b or a/b. The ratio and proportion concepts are based on fractions. Ratio and proportion are the fundamental building blocks for many other notions in mathematics. Ratio and proportion are useful in addressing many everyday difficulties, such as comparing heights, weights, distance, or time, or when combining ingredients in cookery, and so on.
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Can a table 9 feet wide (legs folded) fit through a rectangular doorway 4 feet by 8
Yes , it is possible to fit a table 9 feet wide through a rectangular doorway 4 feet by 8.
The Pythagorean theorem states, "In a right triangle, the square of the hypotenuse equals the sum of the squares of the other two sides." The sides of this triangle were called the perpendicular, the base, and the hypotenuse. Here, the hypotenuse is on the opposite side of the 90° angle, so it is the longest side. The sides of a right triangle (a, b, c, etc.) with positive integer squared values are put into the equation, also known as the Pythagorean triple. which is given by [tex]c^2=a^2+b^2[/tex] here “a” is the perpendicular, “b” is the base, “c” is the hypotenuse.A table with folded legs can pass through a rectangular door at an angle of 45°, forming a triangle to which the Pythagorean theorem can be applied.
Let the two sides of the door be the two sides of triangles a and b, then
[tex]c^2=4^2+8^2\\c^2=16+64\\c^2=80\\c=8.94[/tex]
Conclusion: Using the Pythagorean theorem, we know that an 8.94 foot table can pass through the door. And we know that 8.94 ≈ 9
Hence , a 9-feet table can pass through a rectangular door.
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50 POINTS!!!!
Answer the questions by drawing on the coordinate plane below.
(a) Draw the image of ∆ABC under the dilation with scale factor 3 and the origin as the center of dilation. Label the image ∆A'B'C'. Make sure to include the coordinates of A’, B’, and C’.
(b) Draw the image of ∆DEF under the dilation with scale factor -1/2 and the origin as the center of dilation. Label the image ∆D'E'F'. Make sure to include the coordinates of D’, E’, and F’.
Using dilation rules, the dilated triangle is given at the end of the answer. The coordinates of the vertices are as follows:
A'(-6,6), B'(-3,0), C'(3,6).
What is the rule for a dilation?To dilate a figure by a factor of a, each coordinate of each vertex of the image is multiplied by a, that is, the following rule is applied:
(x,y) -> (ax, ay).
The coordinates of the vertices of ABC are given as follows:
A(-2,2), B(-1,0), C(1,2).
After a dilation with a scale factor of 3, the coordinates of the vertices of A'B'C' will be given as follows:
A'(-6,6), B'(-3,0), C'(3,6).
These coordinates are derived multiplying the coordinates of A, B and C by 3.
The image of the triangle is given at the graph at the end of the answer.
For the image of triangle DEF, each of the coordinates of D, E and F will be multiplied by -1/2 to generate the dilated triangle.
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Triangle ABC is an equilateral triangle. Use the figure to find the value of x
The value of x in the equilateral triangle is 10
The equilateral triangle's three characteristics are: Equal on all three sides. The three angles are identical. Three symmetry lines may be seen in the figure. Additionally, each inside angle is identical (60 degrees).
A unique isosceles triangle with three equal sides is called an equilateral triangle. The formulas that we take into account most frequently for a triangle are: Dimensions of an equilateral triangle , the equilateral triangle's circumference, Equilateral triangle's height
An equiangular triangle's area can be calculated using the following formula:
If A=√3a2/4, then ABC's perimeter 3a
where a is the triangle's side length.
In equilateral triangle, the sum of the 3 angles are 180°.then the angle of each side is 60°
From the given data,
(7x-10)°=60°
7x=60+10
7x=70, x=10
Hence the value of x is 10
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Rosita paid $32.08, including tax, for her family to eat dinner at a restaurant. She wants to tip a whole dollar amount that is close to 20%. What is a reasonable tip that Rosita should leave?
Answer:
$6
Step-by-step explanation
$32 is the total(100%)
in order to find what she needs to tip, you have to divide by 5 because 100% / 5=20%
now, to find 20% of 32, you divide 32 by 5.
32 you can just round to 30, so that you can divide it by 5.
30/5=$6
you could've rounded the total up to 35, but 30 was closer, therefore $6 was the closest whole number tip rosita could've left.
hope this helps
A flag measures 475 feet by 220 feet. Find its area answer
Answer:104,500
Step-by-step explanation:
Area = l × w= 475 × 220= 104500 feet2
solve for y 3x-7y=21
A. y=-3/7x+21
B. y=3/7x-21
C. y=3/7x-3
D. y=-3/7x+3
Answer:
Y = 3/7x-3
Step-by-step explanation:
I don't have an explanation other than the fact I put this into a calculator and this is what it gave me.
Find the area of a quadrilateral formed by the points of intersection of the graphs f(x) = (x − 3)(x + 1) and g(x) = 4x − 2x^2 + 6 and the points of extrema of f(x) and g(x).
Answer:
24
Step-by-step explanation:
The extrema is halfway between the roots, so for f(x), it has coordinates (1, f(1)) = (1, -4).
For g(x), we can rewrite it as -2(x²-2x-3) = -2(x-3)(x+1). We can see that the extrema has coordinates (1, 8).
Finding the intersection,
[tex](x-3)(x+1)=-2(x-3)(x+1) \\ \\ 3(x-3)(x+1)=0 \\ \\ x=-1, 3 \\ \\ x=-1 \implies f(x)=g(x)=0 \\ \\ x=3 \implies f(x)=g(x)=0[/tex]
So, we need to find the quadrilateral with vertices (1,-4), (1,8), (-1,0), and (3,0).
We observe this is a kite with diagonals of lengths 4 and 12. So, using the formula for the area of a kite, the area is 24.
Grayson's retirement party will cost $60 if he invites 10 guests. If there are 86 guests, how much will Grayson's retirement party cost? Solve using unit rates.
Answer:
Grayson's party will cost $516.
Step-by-step explanation:
Start with putting a unit rate for money per person
60/10
Divide by 10
6/1 (6$ per person)
Then multiply by 86 (# of guests attending)
86 x 6 = 516
Which sequence of transformations can joseph perform to show that figure A and figure B are congruent
Step-by-step explanation:
If rigid transformations can be used to map two shapes onto one another, they are said to be congruent (a sequence of one or more rotations, translations, and reflections). Any series of rigid transformations performed on a triangle results in a congruent triangle.
Let's now analyze rigid transformation.
An isometry, also known as a rigid transformation of the plane, preserves length. Reflections, translations, rotations, and combinations of these three transformations are all considered "rigid transformations".
Example: Congruent shapes include, for instance, the right angle triangle and its preimage.
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Type an equation for the following pattern.
Solve for x 8x + 12 = 2x - 18
Answer:
[tex] \sf \Large x=−5 [/tex]
Step-by-step explanation:
Let's solve your equation step-by-step.
8x+12=2x−18
Step 1: Subtract 2x from both sides.
8x+12−2x=2x−18−2x
6x+12=−18
Step 2: Subtract 12 from both sides.
6x+12−12=−18−12
6x=−30
Step 3: Divide both sides by 6.
6x/6 = −30/6
x=−5
Step-by-step explanation:
8x + 12 = 2x -18
8x - 2x = -18 - 12
6x = -30
6x/6 = -30÷6
x = - 5
Please help me i need help with this i dont understand it see photo whats the name of the equations
Answer:
commutative property of multiplicationassociative property of additionadditive inverse propertymultiplication property of zeroStep-by-step explanation:
You are asked to identify the real number properties that justify various changes in the way an expression is written.
Properties of numbersIn general, there are associative, commutative, identity, and inverse properties of addition and multiplication. You can use these properties to simplify and rewrite expressions, and to help perform arithmetic.
This is basically a vocabulary question, to see if you know the names associated with the behaviors these properties describe.
Commutative propertiesWhen an operation (such as addition or multiplication) has the commutative property, it means the order of its operands does not matter
addition: a + b = b + a
multiplication: a × b = b × a
Associative propertiesWhen an operation has the associative property, it means that grouping of operands does not matter.
addition: (a + b) + c = a + (b + c)
multiplication: (ab)c = a(bc)
Identity propertiesWhen an operation is performed using its identity element, the value of the other operand is not changed:
addition: a + 0 = a
multiplication: a × 1 = a
Inverse propertiesWhen an operation has an inverse, performing the operation with the inverse produces the identity element.
addition: a + (-a) = 0
multiplication: a × (1/a) = 1
Note: these last two properties are used to simplify and solve algebraic expressions. They let you "undo" operations done to variables or expressions.
Questions at handYou can match the given expressions to the example expressions shown above. The "multiplication property of zero" is also known as the "zero product rule": a product is zero if and only if a factor is zero.
[tex]\begin{aligned}d\cdot4=4\cdot d\quad&\text{commutative property, multiplication}\\(2+a)+8=2+(a+8)\quad&\text{associative property, addition}\\m+(-m)=0\quad&\text{additive inverse property}\\0\cdot b=0\quad&\text{multiplication property of 0}\end{aligned}[/tex]
Select the correct answer.
Which function defines (g. f)(z)?
f(z)
g(z)
log(5z)
5z + 4
OA
(9. f)(z)
OB.
(g-f)(z): = 5x + 4+ log(5z)
OC (g. f)(z) = 5z log(5z) +4
OD. (g. f)(z) = 5z - 4-log(5z)
5z log(52) + 4log(5z)
Answer: A. (g•f)(x)= log(5x) ( 5x + 4)=5x log(5x) + 4log(5x)
Step-by-step explanation:
Hope this helps :)
Please help me please please please!!!!
Step-by-step explanation:
total number of people are 40
take teach takeaway category and divide it by 40
eg)3÷40 / 11÷40
since there are 360⁰ in a circle, multiply your answer by 360 to get your angle
(3÷40)×360 = a
(11÷40)×360 = b
(9÷40)×360 = c
(2÷40)×360 = d
(15÷40)×360 = e
those are your angles. use a protractor to measure the angles
note : if all your angles add up to 360 the you've done everything correctly
Use the graph of the function to find its domain and range. Write the domain and range in interval notation.
I’m not sure if I did it right
Answer:
you did it right!
Step-by-step explanation:
47=
\,\,-\frac{x}{11}+43
−
11
x
+43
Answer:
x=−44
Step-by-step explanation:
Rewrite the equation as
−x11+43=47.−x11+43=47
Move all terms not containing
x
to the right side of the equation.
−x11=4
Multiply both sides of the equation by
−11.−11(−x11)=−11⋅4
Simplify the following (1/7x+3/8) + (2x - 1/8)
