4 gallons of paint will be used to paint the inside of the barn.
What is equation?In algebra, an equation is a declaration of equivalence that includes one or more variables or unknowable quantities.
Given Data
Jay needs 19 quarts more paint for the outside of his barn than for the inside.
he uses 107 quarts in all
Paint needed for Inside = x
Paint needed for outside = x + 19
So,
Total paint = Paint for outside + Paint for inside
107 = x + x+ 19
107 = 2x + 19
2x = 88
x = 44
Number of gallon = [tex]\frac{44}{4}[/tex]
Number of gallon = 4
4 gallons of paint will be used to paint the inside of the barn.
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A pet store has 3 bird cages with 2 birds in each cage, and 10 aquariums with 4 fish in each aquarium. Which of the following expressions represents how many birds and fish the pet store owns?
(3+2)+(10 + 4)
(3+2) x (10+4)
(3 x 2) × (10 x 4)
(3 x 2) + (10 x 4)
Answer:
(3 × 2) + (10 × 4) is the correct expression.
What is the value of x in the equation x^2 + 2 = 0
Answer:
[tex]{ \tt{ {x}^{2} + 2 = 0 }} \\ \\ { \tt{ {x}^{2} = - 2 }} \\ \\ { \tt{x = \sqrt{ - 2} }}[/tex]
- At this point, we can't operate the square root. Let's introduce the imaginary part of a value
From complex numbers;
[tex]{ \boxed{ \tt{{ \red{note} \: {\rightarrow{i \times i = - 1 = {i}^{2} }}}}}}[/tex]
Therefore;
[tex]{ \tt{x = \sqrt{2 \times {i}^{2} } }} \\ \\ { \boxed{ \rm{ \: x = i \sqrt{2} \: \: }}}[/tex]
I want to place an order of 253,625 books. How can I estimate the number to make sure it’s enough books
The estimate where the number of books is enough is 254,000
What is the estimation of a number?The estimation of numbers is the approximation of the said number.
This means that the estimation of a number is close to the said number, but it has a slight different value
How to estimate the number of books?The number of books is given as
Number of books = 253,625
From the question, we understand that:
You want to make sure that the number of books is enough
This means that we estimate the number of books to a number greater than 253,625
A good way to do this is to approximate to the nearest thousand
When the number is approximated to the nearest thousand, we have
Estimate = 254,000
Hence, the estimate is 254,000
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Which of the following is the graph of (g-f)(x)?
The graph (g-f)(x)=-4x complies with the query.
Graph example: What is it?An edge denotes the connection between the x and y vertices and is represented by the pair (x ,y). In the examples that follow, circles stand in for vertices and lines for edges.
The graph indicates that line generated by function f(x) passes through the points (1,-3) and (0,0) and that line similarly passes through the points (1,1) and (0,0).
With the use of the formula Y-Y1 = y2-y1/x2-x1, we can thus determine the equation of the lines (x-x2)
Therefore, the equation of the line produced by the function f(x) y+3= 3-0/0-1 (x-1)
Function f(x) Equals 3x since y+3=-3x+3 y=-3x.
the line drawn by the function g(x) has the equation y=x, hence function g(x)=x.
We now need to figure out, (g-f) (x) = g(x)- f(x) = -3x-x = -4x
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Plot (−3 1/2, −1 1/4) on the coordinate plane.
The point is located at 3 1/2 points to the left of the origin and 1 1/4 points below the origin
How to plot the point on a coordinate plane?The coordinate of the point on a coordinate plane is given as
Point = (-3 1/2, -1 1/4)
Rewrite the above coordinate as follows:
(x, y) = (-3 1/2, -1 1/4)
Split the coordinates into x and y coordinates
So, we have the following equations
x = -3 1/2
y = -1 1/4
The above means that:
(-3 1/2, -1 1/4) is located at 3 1/2 points to the left of the origin (-3 1/2, -1 1/4) is located 1 1/4 points below the originNext, we plot the points
See attachment for the plot of the points on a coordinate plane
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Answer this question find angle a,b,c,d,e,f
We can determine the values of the angles as follows:
*By opposite by angle we will have that angle f is equal to:
[tex]f=180-44-78\Rightarrow f=58[/tex]angle f has a measurement of 58°.
*By supplementary angles we will have that angle e is equal to:
[tex]e=90-64\Rightarrow e=26[/tex]angle e has a measurement of 26°.
*As is indicated (Two lines have the same markings indicating they are parallel) we will have that the measurement of angle b is 78°.
*By complementary angles, the measurement of angle a is:
[tex]a=180-78\Rightarrow a=102[/tex]angle a has a measurement of 102°.
*We will have by alternate exterior angles that c has a measurement of 58°.
*By supplementary angles, we will have that the measurement of angle d equals:
[tex]d=180-58\Rightarrow d=122[/tex]angle d has a measurement of 122°.
I really need to know how to solve for this question!! I have no idea what to do
Given:
Cost of Truck = $16000
Down payment amount = $3000
EMI = $250
Duration of EMI = 60 Months
Required:
a) Total amount financed
b) Total finance charge paid at the end of 60 months
Explanation:
Total cost of Truck = $16000
The total amount taken from other source = Total Amount - Down payment
=$16000-$3000
=$13000
EMI = $ 250
[tex]Total\text{ }amount\text{ }paid\text{ }at\text{ }the\text{ }end\text{ }of\text{ }60\text{ }months=250\times60[/tex][tex]Total\text{ }amount\text{ }paid\text{ }at\text{ }the\text{ }end\text{ }of\text{ }60\text{ }months=15000[/tex]Total amount paid at the end of 60 months = $15000
The total amount financed = Actual price -Down payment
=$16,000- $3000
=$13000
a) Total amount financed =3$18000
The total finance charged = Actual price - amount paid monthly for 60 months.
=$16000-$15000
=$1000
b)The total finance charged =1$20
Answer
Hence the total amount finance is 13000 dollar.
The total finance charged is 1000 dollar.00
????????????????????
Answer:
536
Explanation:
rom the given table:
If an individual and spouse enroll in the low deductible plan, the monthly premium will be $536.
helppppppp 20 points
C) Triangle ABC is equilateral.
E) Segment AB is the same length as segment AC because they are both radii of the same circle centered at point A.
F) Segment AB is the same length as segment BC because they are both radii of the same circle centered at point B.
What are Euclid's Axioms?Euclidean geometry, sometimes referred to as Euclid's geometry is the study of solid and flat shapes based on many axioms and theorems. The assumptions of the evident universal truths that have not been verified are known as Euclid's axioms or common conceptions.In the given figure,
A and B are the centres of the two intersecting circles.
In a circle having centre at A, we have
AC = AB = radius
In a circle having centre at B, we have
BC = BA = radius
According to Euclid's first axiom, things that are equal to the same thing are equal to one another.
Therefore, AC = AB = BC
Hence, the triangle is an equilateral triangle.
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11) Increase 763.685 by 0.1
Answer: its 243
Step-by-step explanation:
write the sum in sigma notation [tex]\frac{1}{3} +\frac{1}{15} +\frac{1}{35} +\frac{1}{63}[/tex]
Sum in the sigma notation of the given series is equal to
∑[1 /(2n +1)(2n + 3)] , n =0,1,2,3.
As given in the question,
Given series :
(1 /3) + ( 1/ 15) + ( 1/ 35) + ( 1/ 63)
Simplify the given series
= [1/ (1 ×3)] + [1/ (3 ×5)] + [1/ (5 ×7)] + [1/ (7×9)]
1, 3, 5, 7 can be expressed as ( 2n + 1) , where n = 0, 1, 2, 3
3, 5, 7, 9 can be expressed as ( 2n + 3) , where n = 0, 1, 2, 3
Express the given series as a sum in the sigma notation form
(1 /3) + ( 1/ 15) + ( 1/ 35) + ( 1/ 63)
=∑ [ 1/ (2n +1) (2n + 3) ] where n = 0,1,2,3
Therefore, sum in the sigma notation of the given series is equal to
∑[1 /(2n +1)(2n + 3)] , n =0,1,2,3.
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Find the x-and y-intercepts of the line:3x - 4y = 12A.x-int: (-4,0)y-int: (0,3)B. x-int: (4,0)y-int: (0, -3)C. x-int: (0,4)y-int:(-3,0)D. x-int: (0,-4)y-int: (3,0)
To find the x-intercept, simply but y=0 in the equation given and solve for x
That is;
3x - 4y = 12
3x - 4(0) = 12
3x = 12
Divide both-side of the equation by 3
x= 4
The x-intercept is;
(4, 0)
To find the y-intercept, simply put y=0 in the equation given and then solve for y
That is;
3x - 4y = 12
3(0) - 4y = 12
-4y = 12
Divide both-side of the equation by -4
y = -3
The y-intercept is (0, -3)
Hence, the correct option is B.
x-int: (4,0)
y-int: (0, -3)
x + 9.27 = 21
I need help answer this questions
Answer:
x = 11.73 is what i got
Step-by-step explanation:
Need help thanks. Due today
Answer:
The answer would be D(x/y)= -(11/8) / -(11/4)
Step-by-step explanation:
Construct a polynomial function with the stated properties. Reduce all fractions to lowest terms.
Third-degree, with zeros of -2,-1, and 5, and a y-intercept of -10.
Answer:
y = x³ -2x² -13x -10
Step-by-step explanation:
You want a polynomial with x-intercepts -2, -1, and 5, and a y-intercept of -10.
Polynomial factorsA polynomial with zero x = p will have a factor of (x -p). The three given zeros mean factors of the desired polynomial will be ...
p(x) = (x -(-2))(x -(-1))(x -5) = (x +2)(x +1)(x -5)
Expanding this gives ...
p(x) = (x +2)(x² -4x -5) = x³ -2x² -13x -10
This polynomial has a constant of -10, which will be its y-intercept. No additional scaling is needed.
The polynomial function is ...
y = x³ -2x² -13x -10
Jane, Alan, and Ravi sent a total of 146 text messages over their cell phones during the weekend. Ravi sent 8 fewer
messages than Jane. Alan sent 4 times as many messages as Ravi. How many messages did they each send?
Jane, Alan, and Ravi sent a total of 146 text messages over their cell phones during weekend, Ravi sent 8 fewer messages than Jane. Alan sent 4 times as many messages as Ravi. So as per question data,
Jane sent= 31 messages
Ravi sent= x-8= 31-8 = 23 messages
Alan sent= 4(x-8) = 92 messages
What operations are used here?The best way to solve an expression is from left to right if all the operations are the same (for instance, only addition, only subtraction, only multiplication, or only division). However, we must adhere to the order of operations for expressions including several operations.
The rule that dictates how to solve an expression involving numerous operations is known as the order of operations.
PEMDAS can help you remember that sequence. In PEMDAS, each letter denotes a mathematical operation.
Let, Jane sent x number of messages
Then, Ravi sent x-8 number of messages
and, Alan sent 4(x-8) number of messages
Total number of messages by them = 146
now,
x+(x-8)+4(x-8)=146
6x-40=146
x=31
so, Jane sent= 31 messages
Ravi sent= x-8= 31-8 = 23
Alan sent= 4(x-8) = 92
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The polynomial passes through the
X-intercepts of (-5, 0), (-3, 0), and (1, 0). The end behavior of the graph is down, up.
Finally, it passes through the point of (3, 14).
The equation of the polynomial is P(x) = 6.86(x + 5) (x + 3) (x - 1)
Given,
x intercepts which the polynomial passes though = (-5, 0), (-3, 0), and (1, 0).
Point = (3, 14).
We have to find the polynomial equation;
A polynomial is defined as;-
P(x) = a(x - c₁) (x - c₂)....(x - cₙ)
Here,
a is a constant
c₁, c₂,...cₙ are the zeros of the polynomial
Here,
-5, -3 and 1 are the zeros of the given polynomial
(x + 5), (x + 3) and (x - 1) are the factors of the given polynomial.
Then the equation of polynomial be like;
P(x) = a(x + 5) (x + 3) (x - 1)
This polynomial passes through point (3, 14)
That is,
14 = a(3 + 5) (3 + 3) (3 - 1)
14 = a x 8 x 6 x 2
14 = 96a
a = 96/14
a = 6.86
Substitute this in equation of polynomial;
That is,
P(x) = 6.86(x + 5) (x + 3) (x - 1)
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Solve 7|14i-10|+9 = 37
Answer:
i = 1, (3/7)
Step-by-step explanation:
7|14i-10|+9 = 37,
-9 -9
------------------------
7|14i - 10| = 28
÷7 ÷7
---------------------
|14i - 10| = 4
14i - 10 = 4
+10 +10
------------------
14i = 14
÷14 ÷14
--------------
i = 1
|14i - 10| = -4
14i - 10 = -4
+10 +10
---------------------
14i = 6
÷14 ÷14
--------------
i = (3/7)
I hope this helps!
Order the function from the least steep slope to the steepest slope.
y=2x-3
y = 4x+0.5
y=-2x+3
y=x+42
y=-0.5x+7
How are the given functions ordered based on their slopes?
1. y = -2x+ 3
slope = m= -2
tanФ = -2 -----(1) Least steep slope
Ф = -63.4°
2. y= 3/4x-3
slope = m = 3/4 ------(3)
tanФ = 3/4
Ф= 36.9°
3. y= 4x+0.5
slope = m = 4 ------(5) Steepest
tanФ = 4
Ф = 75.9°
4. y= x+42
slope = m= 1 ------(4)
tanФ= 1
Ф= 45°
5. y = - 0.5x+ 7
slop = m= -0.5 -----(2)
tanФ = -0.5
Ф = -26.56°
What is a slope?
An indication of how steep a line is is its slope. Nowhere on the line there is a different slope as it is constant. The gradient may be used to refer to it.The ratio of vertical change to horizontal change between any two separate points on a line, or any two points, is used to compute slope.Indicating a steeper line is a slope with a higher absolute value.A line can have upward, downward, horizontal, or vertical directions.To learn more about steep slope, refer:
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Fill in the blanks below.
Find the slope of the line passing through the points (6, 4) and (6, -7).
slope:
Find the slope of the line passing through the points (-9,-5) and (-9, 5).
slope:
The entered points (6,4) and (6,-7) belong to a vertical line, There is no slope and The entered points (-9,-5) and (-9,5)belong to a vertical line. There is no slope.
How to find slope of the coordinates ?The slope, which is essentially how slanted a line is, might be positive, negative, zero, or both (x1,y1) and (x2,y2). The slope equation is (y2 - y1) / (x2 - x1). A vertical line is formed by the points entered. Nothing slopes.Formula: x = 6.
Angle (θ)=90°
Location (d) = 11
(x)=0 Distance between x's
d = (y2 + x2) = (-112 + 02) = 121 = 11 is the distance between y's (y)=11.
A vertical line is formed by the points entered. Nothing slopes.Formula: x = -9.
Location (d) = 10
(x)=0 Distance between x's
Distance between y's (d) = y2 + x2 = 102 + 02 = 100 = 10
A vertical line, on the other hand, will have an ill-defined slope since the x-coordinates are constant. As a result, there will be a division-by-zero error when using the formula.To more learn about coordinates refers to:
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180
94
112
90
68
56
100
(x+18)° is vertical opposite 112° and vertical opposite angles are equal meaning
⇒(x+18)°=112°
x+18°=112°
x=112°-18°
∴x=94°
(2y)° is in a straight line with 112° meaning their sum is 180°
[tex]2y+112=180\\2y=180-112\\2y=68\\\frac{2y}{2} =\frac{68}{2} \\y=34[/tex]
∴y=34°
Study Island Math Help Worth 40 PTS
Answer:
B
Step-by-step explanation:
using the rules of exponents
• [tex]a^{m}[/tex] × [tex]a^{n}[/tex] = [tex]a^{(m+n)}[/tex]
• [tex]a^{-m}[/tex] = [tex]\frac{1}{a^{m} }[/tex]
• [tex](a^m)^{n}[/tex] = [tex]a^{mn}[/tex]
given
[tex]5^{8}[/tex] × [tex](5^{12}) ^{-4}[/tex]
= [tex]5^{8}[/tex] × [tex]5^{(12(-4))}[/tex]
= [tex]5^{8}[/tex] × [tex]5^{-48}[/tex]
= [tex]5^{(8-48)}[/tex]
= [tex]5^{-40}[/tex]
= [tex]\frac{1}{5^{40} }[/tex]
You reflect the triangle below over the x-axis.
The coordinates of P' are ( , )
Answer:
P' (- 5, 3 )
Step-by-step explanation:
under a reflection in the x- axis
a point (x, y ) → (x , - y ) , then
P (- 5, - 3 ) → P' (- 5, 3 )
The water pressure on a submerged object is given by P = 64d, where P is the pressure in pounds per square foot, and d is the depth of the object in feet. a. solve the formula for d. b. Find the depth of a submerged object if the pressure is 672 pounds per square foot.
The water pressure on a submerged object is given by P = 64d, then the
a. The answer to the subject of the formula, "d," is d = P/64.
b. The depth of a submerged object if the pressure is 672 pounds per square foot is 10. 5 feet
A function can be defined as an expression, law or rule that shows the relationship between two variables.
These variables are namely;
Independent variableDependent variableGiven the role as;
P = 64d
Where;
P stands for pounds per square foot of pressure.
d represents the object's depth in feet.
Let's now make the variable "d" the focus of the formula.
The coefficient of the variable "d," which is 64, is used to divide both sides of the equation. So that the variable can stand on its own, this is done.
(a) We get,
P/64 = 64d/64
d = P/ 64
(b) P equals 672 pounds per square foot if there is pressure.
When the variable's value is substituted into the formula, we get;
d = P/64
Then,
d = 672/64
Discover the quotient,
d = 10. 5 ft.
The value is 10.5 feet .
Therefore,
a. The answer to the subject of the formula, "d," is d = P/64.
b. The depth of a submerged object if the pressure is 672 pounds per square foot is 10. 5 feet.
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the numbers between 1 to 2022 are written on a piece of paper.Caitlin circles the even numbers with red circles and nicole circles the multiples of 5 with yellow circles.How many numbers are circled with only one color?
The number of numbers circled with only one color found using arithmetic progression formula are 809 numbers
What is an arithmetic progression?An arithmetic progression is a sequence of numbers in which the difference between any two consecutive terms in the sequence is constant
The given parameters are;
The set of the numbers written on the paper = Numbers from 1 to 2022
Numbers circled with red circles by Caitlin = All even numbers between 1 and 2022
Numbers Nicole circles using yellow = Numbers that are multiples of 5
Required; The number of numbers that are circled with one colour only
Solution; The even numbers are numbers that are a multiple of 2
The number of even numbers between 1 and 2022 are found using arithmetic progression formula as follows;
[tex] a_{n} = a_{1} + (n - 1)\cdot d[/tex]
Where;
[tex]a_{1}[/tex] = The first term = 2 (First even number)
d = The common difference = 2
n = The number of terms
Given that 2022 is an even number, we have;
[tex] a_{n} = 2022 = 2 + (n - 1)\cdot 2[/tex]
Which gives;
[tex] \displaystyle {n = \frac{(2022 - 2)}{2} + 1 = 1011} [/tex]
We note that 10 is the lowest common multiple of 2 and 5, which gives;
Multiples of 10 have two colors, therefore, the numbers that have only one color is given by the difference between the number of even numbers and the number of multiples of 10 as follows;
The number of multiples of 10 are;
[tex] \displaystyle {n = \frac{(2020 - 10)}{10} + 1 = 202} [/tex]
Which gives;
The numbers having only one colour = 1011 - 202 = 809
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Solve for x.
√x + 20 = 9
Answer:
x = 61
Step-by-step explanation:
sqrt = square root
sqrt(x + 20) = 9 square both sides to cancel out sqrt
x + 20 = 81 subtract 20 to get x alone
x = 61
15x=75Write which property of equality you used.
1) Given this equality,
15x = 75 Divide both sides by 15
x=5
2) Then we can write that since x = 5 and 15x = 75 we have here is the Division Property of Equality.
Because in this case, we divided both sides by 15, which is different from zero to find equivalent equality.
3) So
Distribute the following perfect square: 6x(8x - 9y)² = ?
Answer:
384x² - 486xy²
Step-by-step explanation:
I think this is the answer all I did us first i solved the brackets then I multiplied them by 6x
what is the period of the graph of y=5sin(4piex)+3
The period of the graph is π/2.
What is the period of the graph?The length of one function wave is referred to as the period. One entire wave in this situation is 180 degrees, or radians. Without using a graph, you can get this simply dividing 2 by the frequency, which in this case is 2.
Given: 5 sin (4πx)+3
Period = 2π / 4
⇒ period = π/2
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Help PLEASE!!! How do I solve this?
Two similar boxes A and B are given with box B created by dividing box A's dimensions by 2.
Recall that the scale factor, k is the ratio of lengths of two corresponding sides of similar figures.
Since the dimensions of A were divided by 2 to form B, it follows that the scale factor of box A to box B is:
[tex]k=\frac{2}{1}[/tex]Also, recall the Similar Solids Theorem
It follows that the ratio of the volumes of the given solids is:
[tex]\frac{\text{Volume of A}}{\text{Volume of B }}=k^3=(\frac{2}{1})^3=\frac{2^3}{1^3}=\frac{8}{1}[/tex]Let the volume of box A be V₁ and let the volume of box B be V₂, it, therefore, implies that:
[tex]\frac{V_1}{V_2}=\frac{8}{1}[/tex]Substitute the value for the volume of box A into the equation, V₁=64:
[tex]\begin{gathered} \frac{64}{V_2}=\frac{8}{1} \\ Cross-Multiply_{} \\ \Rightarrow8V_2=64 \\ Divide\text{ both sides by 8:} \\ \Rightarrow\frac{8V_2}{8}=\frac{64}{8}\Rightarrow V_2=8\text{ cubic meters} \end{gathered}[/tex]Hence, the volume of box B is 8 m³.