Answer:
the correct answer is 27.5 feet
Step-by-step explanation:
The scale of a blueprint is a ratio that represents the relationship between the size of an object on the blueprint and the size of the actual object. In this case, the scale is 1:55, which means that for every 1 unit of length on the blueprint, the actual object is 55 units long.
If a wall on the blueprint is 6 inches long, then the actual wall is 55 times longer, or 6 inches * 55 = 330 inches. Since there are 12 inches in a foot, the actual wall is 330 inches / 12 inches/foot = 27.5 feet long. Therefore, the correct answer is 27.5 feet
How many solutions exist for the system of equations graphed below?
none
one
two
infinitely many
The number of solutions that exist for the system of equations graphed as shown is B . One .
How to find the number of solutions ?To find the number of solutions that exist in a system of graphs, you need to look at the number of points of intersection that there are.
The number of points of intersection shows the number of solutions. If there is one point of intersection, then there is one solution.
The system of equations graphed, has one point of intersection so there is only one solution .
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Simplify −7g(2g + 3).
−14g2 − 21g
−14g2 + 3
−14g − 21g
−14g + 3
Answer:
The first answer
Step-by-step explanation:
-7g(2g + 3) Distribute the -7g
(-7g)(2g) + (-7g)(3)
-14[tex]g^{2}[/tex] - 21g
Answer:
Option A; [tex]-14g^{2}[/tex] - 21g
Step-by-step explanation:
-7g(2g + 3)[tex]-14g^{2}[/tex] - 21g (Use the distributive property)Answer: [tex]-14g^{2}[/tex] - 21gHope this helped! :D
Pls help…………………………….
Answer:
m = 3
Step-by-step explanation:
4 - - 2/ 3 - 1
m = 6/2
m = 3
Gina charges an initial fee and an hourly fee to babysit. Using the table below find the hourly fee and the initial fee that
Gina charges to babysit. Show work.
Cost in Dollars
Answer:
13 dollars
Step-by-step explanation:
Mrs. Anna has 96 puzzles to share with 14 students. She wants to give each child the same number of puzzles and keep the remaining puzzles in the classroom.
How many puzzles will she have left over?
A
6 puzzles
B
8 puzzles
C
12 puzzles
D
13 puzzles
Answer
6
because, 96 / 14 is 6.8
so unless you round it to 8 it should be 6
At an end of the year sale, Gabriela bought more than 12 bottles of hand soaps and lotions. If x represents the number of hand soaps and y represents the number of lotions she bought, which inequality best represents her purchase?
x + y < 12
x + y > 12
x + y ≤ 12
x + y ≥ 12
The inequality which best represents her purchase is x + y > 12.
How to write expressions with inequalities?
Equations and inequalities are both mathematical sentences formed by relating two expressions to each other.
When two expressions are equal, we use the equal sign ( = ). But when we are trying to compare two values or expressions, we use the inequality signs like greater than (>), less than (<), greater than or equal to ( ≥ ) and less than or equal to (≤) .
If x represents the number of hand soaps and y represents the number of lotions she bought. And Gabriela bought more than 12 bottles of hand soaps and lotions
This means the sum of the bottles of hand soaps and lotions she bought is greater than 12. This can be written as follows:
x + y > 12
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Can y’all pls answer both questions
The number of times of Puerto Rico is 5/6
No earthquake released 10³ of Colombia
How to determine the number of timesFrom the question, we have the following parameters that can be used in our computation:
The table of values
On the table of values, we have
Colombia = 6.0M
Puerto Rico = 5.0M
This means that
Number of times = Puerto Rico/Colombia
Substitute the known values in the above equation, so, we have the following representation
Number of times = 5/6
The earthquake that released 10³ of ColombiaHere, we have
Colombia = 6.0M
So, we have
Earthquake = Colombia * 10³
This gives
Earthquake = 6 * 10³
From the table of values, we have no entries with the readings 6 * 10³
Hence, no earthquake released 10³ of Colombia
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a right rectangular prism has a base of 20cm2 and a height of 9.2cm what is the volume of the prism
A right rectangular prism has a base of 20cm² and a height of 9.2cm will have a volume of 184 cm³
What is a right rectangular prism?The right rectangular prism has four rectangle-shaped lateral faces, each of which is perpendicular to one of its bases, and two parallel end faces.
A non-right rectangular prism (oblique prism) has parallelograms for its faces. The term "cuboid" can also refer to a right rectangular prism.
In the given problem the formula used for volume of prism is
= are of base * height
= 20 * 9.2
= 184 cm³
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The area of a rectangle is 8w-18 square units.
Factor this expression.
Given your answer in part A, describe what you can conclude about the dimensions of the rectangle in two or more complete sentences.
Can anyone please find the slope of the lines? Picture below
Thank you!
The slope of the first and second lines will be - 3/2 and 3/5, respectively.
What is a linear equation?A connection between a number of variables results in a linear model when a graph is displayed. The variable will have a degree of one.
The slope of the line is given as,
m = (y₂ - y₁) / (x₂ - x₁)
The points are (1, 2) and (3, -1). Then the slope of the first line is given as,
m = (-1 - 2) / (3 - 1)
m = - 3 / 2
The points are (-3, 1) and (2, 4). Then the slope of the second line is given as,
m = (4 - 1) / (2 + 3)
m = 3 / 5
The slope of the first and second lines will be - 3/2 and 3/5, respectively.
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What is the diameter of a circle that has an area of 14,400
Answer: ≈425.39
Step-by-step explanation: First, let's recall the formula for finding the circumference of a circle with the area:
C = 2 [tex]\pi[/tex] r
So, let's set up our equation:
2·[tex]\sqrt{\pi 14,400}[/tex]
So, we need to multiply pi (3.14 [rounded]) by 14,400 and find the square root of that times 2.
We'd get about 425.39.
Graph the image of this figure after a dilation with a scale factor of 2 centered at the origin.
Use the polygon tool to graph the dilated figure.
With point at (-2,5), (-2,2), (2,5), (2,2)
The vertices of the quadrilateral after dilation of 2 are
(-4, 10), (-4, 4), (4, 10), (4, 4).
What are transformations?Two-dimensional figures can be transformed mathematically in order to travel about a plane or coordinate system.
Dilation: The preimage is scaled up or down to create the image.
Reflection: The picture is a preimage that has been reversed.
Rotation: Around a given point, the preimage is rotated to create the final image.
Translation: The image is translated and moved a fixed amount from the preimage.
Given, A quadrilateral with vertices (-2,5), (-2,2), (2,5), (2,2).
Now, Dialating this quadrilateral with a scale factor of 2 centered at the origin would multiply every vertices points by 2.
Therefore, The dilated quadrilateral has vertices,
2[ (-2,5), (-2,2), (2,5), (2,2)].
(-4, 10), (-4, 4), (4, 10), (4, 4).
The figure of this dilated quadrilateral is attached.
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Alanna purchases 12 packets of vegetable seeds, 15 packets of flower seeds, and 9 bags of topsoil. Each packet of vegetable seeds costs $1.50, each packet of flower seeds costs $2.20, and each bag of topsoil costs $12.10.how much does she pay for all of the seeds and topsoil
Answer: $159.90
Step-by-step explanation:
Assigning a variable: V=Vegetable seeds F=Flower seeds T=Top soil
Assigning a value to each variable: V=1.5 F=2.2 T=12.1
The equation:
v(12)+f(15)+t(9)=
1.5(12)+2.2(15)+12.1(9)=
1.5*12=18 2.2*15=33 12.1*9=108.9
18+33+108.9=159.9
Total cost = $159.90
Hope this helps!
Simplify 6 + 8 / 2* | -3| + 7
The simplification of the given expression 6 + 8 / 2* | -3| + 7 is 25
The process of simplifying arithmetic operations.The process of simplifying a complex expression with an equivalent, simpler one is known as simplification. There are several strategies for simplifying expressions, depending on the exact expression and what you are attempting to accomplish.
To simplify the given expression:
6 + 8 / 2* | -3| + 7
Divide 2 by 8 = 4
6 + 4 * |-3| + 7
Take the absolute value of |-3| = 3
6 + 4 + 3 + 7
= 25
Therefore, we can conclude that the simplification of the given expression is 25.
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Triangles ACD and BCD are isosceles. Angle BAC has a measure of 20 degrees and angles BDC has a measure of 25 degrees. Find the measure of angle ABD
The measure of angle ABD of the described Isosceles triangles is; 115°
What is the measure of the angle in the triangle?The parameters are;
Triangle ΔACD is Isosceles triangle
Triangle ΔBCD is Isosceles triangle
m∠BAC = 20°
m∠BDC = 25°
Whereby ΔBCD and ΔACD have their vertex in the same direction, we can have;
AD ≅ AC Given sides legs of triangle ACD
BD ≅ BC Given sides legs of triangle BCD
BA ≅ BA Reflexive property
Therefore, we can say that;
ΔDAB ≅ ΔCAB by SSS congruency rule
By the CPCTC (Congruent Parts of Congruent Triangles are Congruent), we can say that;
m∠BAC ≅ m∠BAD
Thus;
m∠BAC ≅ m∠BAD = 20°
Therefore;
m∠BAC + m∠BAD = 20° + 20°
m∠BAC + m∠BAD = 40°
Thus, m∠DAC = 40° by the Angle addition postulate
m∠ADC = m∠ACD = (180 - m∠DAC)/2
= (180 - 40)/2 = 70° This is because they are base angles of an isosceles triangle
∴ m∠ADC = m∠ACD = 70°
Similarly;
m∠BDC = 25° = m∠BCD Base angles of isosceles triangle ΔBCD
m∠BCD + m∠DBC + m∠BCD = 180° Sum of the interior angles of a triangle theorem
m∠DBC = 180° - (m∠BCD + m∠BCD)
= 180° - (25° + 25°)
= 130°
m∠DBC = 130°
m∠ABD ≅ m∠ABC by CPCTC
m∠ABD = m∠ABC
Therefore;
m∠DBC + m∠ABD + m∠ABC = 360° Sum of angles at a point
m∠DBC + 2 × m∠ABD = 360°
130° + (2 × m∠ABD) = 360°
2 × m∠ABD = 360° - 130°
2 × m∠ABD = 230°
m∠ABD = 230°/2
m∠ABD = 115°
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Square ABCD has a diagonal AC with vertices A(-2, 1) and C(2, 4). Find the coordinates of the remaining vertices. Express your answers as decimals, if necessary.
The coordinates are and D.
Answer: To find the coordinates of the remaining vertices of square ABCD, we can use the information given about diagonal AC and the properties of a square. Since a square has equal side lengths and right angles, we know that the distance between opposite vertices on a diagonal must be equal to the side length of the square.
Given the coordinates of vertex A and C, we can use the distance formula to find the length of AC:
Distance = sqrt((x2 - x1)^2 + (y2 - y1)^2)
AC = sqrt((2 - (-2))^2 + (4 - 1)^2)
AC = sqrt(4 + 9) = sqrt(13)
Now that we know the side length of the square, we can use this information to find the coordinates of the remaining vertices. We know that vertex B has the same y-coordinate as vertex A, but the x-coordinate is 2 units to the left of vertex C. Therefore, the coordinates of vertex B are (-2 + 2sqrt(13), 1).
Similarly, we know that vertex D has the same x-coordinate as vertex A, but the y-coordinate is 4 units down from vertex C. Therefore, the coordinates of vertex D are (-2, 1 + 4sqrt(13))
So, the coordinates of the remaining vertices are (2sqrt(13),1) and (-2, 4sqrt(13)) respectively.
Step-by-step explanation:
3-(-7) find the difference
Answer:
Step-by-step explanation:
So 3 minus 7. 3 – 7 = -4 *just trust me on that one ;) So the difference of 3 and 7 is -4.
Find the term that must be added to the equation 2 - 8x = 9 to make it into a perfect square.
A. 64
B.-9
C. 16
D. 32
The solution is Option C.
The term that must be added to the equation x² - 8x = 9 is 16 and the equation will be ( x - 4 )² = 5²
What is an Equation?Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.
It demonstrates the equality of the relationship between the expressions printed on the left and right sides.
Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.
Given data ,
Let the equation be represented as A
Now , the value of A is
x² - 8x = 9 be equation (1)
( x - a )² = x² + a² - 2ax
So , 2ax = 8x
a = 4
So , the equation will be
( x - 4 )² = x² - 8x + 16
And , adding 16 on both sides of the equation (1) , we get
x² - 8x + 16 = 9 + 16
On simplifying the equation , we get
( x - 4 )² = 25
( x - 4 )² = 5²
Taking square roots on both sides of the equation , we get
x- 4 = 5
Adding 4 on both sides of the equation , we get
x = 9
Therefore , the value of x is 9
Hence , the number to be added to the equation is 16
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The base of a right pyramid is a triangle with base and a height of 17cm. If the volume of the pyramid is 11120 cubic cm, find the slant height of the pyramid
The height of the triangular pyramid will be 154 cm.
What is a triangular pyramid?A pyramid with a triangle base is referred to as a triangular pyramid. Vertices are essentially corners in geometry. Both regular and irregular triangular-based pyramids contain four vertices.
Pyramids with triangular bases have six edges, three of which run along the base and three of which rise above the base.
The volume of the triangular pyramid will be,
Volume = 1/2 x Base x h
11120 = 1/2 x ( 17 x 17 /2 ) x h
h = ( 11120 x 2 x 2 ) / ( 17 x 17 )
h = 44480 / 289
h = 154 cm
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a unit fraction that has 1 as its numerator. write the four greatest unit fractions that are repeating decimals. then write each fraction as a decimal.
Answer:
Here, we use an underscore preceding the repeating digit(s).
1/3 = 0.3_3
1/6 = 0.16_6
1/7 = 0.142857_142857
1/9 = 0.1_1
Step-by-step explanation:
You want the four largest unit fractions that are repeating decimals, and their decimal equivalents.
Repeating decimalThe decimal equivalent of a fraction will repeat if the denominator of that fraction has factors other than 2 and 5.
Larger fractionsA fraction with a given numerator will be larger if its denominator is smaller.
Largest repeating decimalsThe fractions of interest will have denominators that are the smallest integers greater than 1 that have factors other than 2 and 5. Consider the integers:
2 . . . . factor is 2
3 . . . . suitable denominator
4 = 2² . . . . factors are 2
5 . . . . factor is 5
6 = 2·3 . . . . suitable denominator
7 . . . . suitable denominator
8 = 2³ . . . . factors are 2
9 = 3² . . . . suitable denominator
Using an overline to signify the repeating digits, the fractions of interest are ...
[tex]\dfrac{1}{3}=0.\overline{3}\\\\\text{ }\dfrac{1}{6}=0.1\overline{6}\\\\\dfrac{1}{7}=0.\overline{142857}\\\\\text{ }\dfrac{1}{9}=0.\overline{1}[/tex]
__
Additional comment
The number of repeating digits may be as many as one less than the denominator. This is the case for 1/7, which has 6 repeating digits. 1/17 is another example, with 16 repeating digits.
The four unit fraction that has its numerator as 1 and a repeating decimal is
1/3, 1/6, 1/7, and 1/9What are repeating decimals?A repeating decimal are also called recurring decimal, is a time of decimal number with only digits that repeat after the decimal at regular intervals.
In mathematics, a repeating decimal is written in short form with an overline on the number that repeats
In the problem, the repeating fraction requires to have a unit numerator and the greatest. from knowledge of fractions, the ones with lesser numerators are the greatest.
The greatest is 1/3 = 0. 333.....
others are
1/6 = 0.166.....
1/7 = 0.142957142957.......
1/9 = 0.111111.........
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Is the relation represented in this table a function?
This is a function
This is not a function
The given function table is found not to be a function.
How to identify a function table?A function is defined as a relation in which each possible input value leads to exactly one output value. That means that “the output is a function of the input.” Meanwhile, the input values make up the domain, and the output values make up the range.
Now, the coordinates from the given function table are as follows;
(2, 3)
(3, 3)
(4, 3)
(5, 3)
(6, 3)
This shows that all the range values are the same for different x-values and as such it doesn't fit the definition of a function as stated above.
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2. Is the following proportion true? Simplify both ratios to determine the answer.
26
18 =
39
36
a. Rewrite the ratio 26
18
in simplest form.
b. Rewrite the ratio 39
36
in simplest form.
c. Are the ratios equivalent? Explain.
d. Are the ratios proportional? Justify your answers.
The ratios in their simplest forms are 13:9 and 13:12 respectively and the two ratios are not proportional
What is proportional ratio?You should understand that two ratios are proportional if their cross-product give the same result.
The cross product of two ratios entails multiplying the numerator of the first by the denominator of the second and the numerator of the second by the denominator of the first
a. Rewrite the ratio 26: 18 in simplest form.
This is expressed as follow = 26/2 : 18/2
= 13:9
b. Rewrite the ratio 39 : 36 in simplest form.
= 39/3 : 36/3
= 13 : 12
The corss product of the two ratios is
13/9 ≠13/12
this is because 156≠108
Conclusively, they are not proportional
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Angel has a deck that measures 20 feet by 25 feet. He wants to increase each dimension by equal lengths so that its area is increased by 50%. By how much should he increase each dimension?
Angel should increase the dimensions of the deck by 5 feet each
How to determine by how much the lengths should be increasedFrom the question, we have the following parameters that can be used in our computation:
Length = 20 feet
Width = 25 feet
So, the area is
Area = 20 * 25
Evaluate
Area = 500
When increased by 50%, we have
(20 + x) *(25 + x) = 500 * 1.50
Evaluate
(20 + x) * (25 + x) = 750
Express 750 as 25 * 30
So, we have
(20 + x) * (25 + x) = 25 * 30
This means that
20 + x = 25
25 + x = 30
Solve for x
x = 5 and x = 5
This means that
Increment = 5
Hence, the lengths should be increased by 5 feet
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A number decreased by 20 is 10 less than twice the number
Answer:
the number is 40
Step-by-step explanation:
A number decreased by 20 is 10 less than twice the number
10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40
Can someone answer 1-4 please and thank you.
The value for x is 10; the perimeter is 56 inches; a possible area the area is 7 square feet (option c); and a possible perimeter is 25 m (option a).
What is the value for x?To find the correct value for x, let's replace the possible values and verify if the total is >11.
2x + 9
(2 x 0) + 9 = 0 + 9 = 9
(2 x -5) + 9 = -10 + 9 = 1
(2 x 10) + 9 =20 + 9 = 29
(2 x -8) + 9 = -16 + 9 = 7
Based on this, the correct value for x is 10
What is the perimeter of an octagon if each side is 7 inches?The perimeter of an octagon can be calculated using this formula:
8 x lengh of one side
8 x 7 inches = 56 inches
What could be the area of a shape?The area of a shape is calculated by multiplying side x side. Due to this, areas are always expressed using square meters, square feet, square kilometers, etc. Based on this principle, a possible area is 7 square feet (option c).
What could be the perimeter of a shape?The perimeter is found by adding the lengh of all the sides in a shape. Due to this, it is expected a perimeter is expressed in meters, kilometers, centimeters, etc. Based on this a possible perimeter is 25 m (option a).
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need assistance!!!!!
Answer:
100 ft^2
Step-by-step explanation:
first we can make this a complete rectangle that is 10 by 12
so we find the area of it
10x12
120
now we have to subtract the triangle from it
we first find the area of the missing piece using triangle formula
bxh/2
the base is 10 and height is 4
10x4/2
40/2
20
now we subtract the area of the triangle from the area of the rectangle
120-20
100 ft^2
hopes this helps
i need help with #3 pleaseee!
The new equations are:
a) g(x) = (1/2x)^(1/3)-3
b) j(x) = 2((x+4)^(1/3))
c) h(x) = (8x-24)^(1/3)
What is transformation function and how to write new equation from transformation function? A transformation function is a mathematical function used to transform a set of data points from one coordinate system to another. The transformation function takes the form of an equation that expresses a relation between two variables. It is commonly used in sciences such as physics and engineering to convert data from one coordinate system to another.For example, if one measure the position of an object in Cartesian coordinates (x,y), the transformation function allows one to express the position of the same object in polar coordinates (r,θ). This can be written as: r = sqrt(x2 + y2); θ = arctan(y/x)To write a new equation from a transformation function, one must first determine the desired coordinate system. Then, one can use the transformation function to find the relation between the two variables in the given coordinate system. For example, if one wants to express the position of an object in Cartesian coordinates from polar coordinates, the equation would take the form: x = r*cos(θ) ; y = r*sin(θ)This equation expresses the relation between the two variables in Cartesian coordinates. Then, one can use this equation to determine the position of any object in Cartesian coordinates given its position in polar coordinates.To learn more about transformation function refer to:
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The new equations are:
a) g(x) = (1/2x)^(1/3)-3
b) j(x) = 2((x+4)^(1/3))
c) h(x) = (8x-24)^(1/3)
What is transformation function and how to write new equation from transformation function?A transformation function is a mathematical function used to transform a set of data points from one coordinate system to another. The transformation function takes the form of an equation that expresses a relation between two variables. It is commonly used in sciences such as physics and engineering to convert data from one coordinate system to another.
For example, if one measure the position of an object in Cartesian coordinates (x,y), the transformation function allows one to express the position of the same object in polar coordinates (r,θ). This can be written as: r = sqrt(x2 + y2); θ = arctan(y/x)
To write a new equation from a transformation function, one must first determine the desired coordinate system. Then, one can use the transformation function to find the relation between the two variables in the given coordinate system. For example, if one wants to express the position of an object in Cartesian coordinates from polar coordinates, the equation would take the form: x = r*cos(θ) ; y = r*sin(θ)
This equation expresses the relation between the two variables in Cartesian coordinates. Then, one can use this equation to determine the position of any object in Cartesian coordinates given its position in polar coordinates.
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2/5k + 1/6 = 3/10k + 1/3
Answer: k = 5/3
Step-by-step explanation:
To solve, we will isolate the variable, k, by using inverse operations.
Given:
2/5k + 1/6 = 3/10k + 1/3
Subtract 1/6 from both sides of the equation:
2/5k = 3/10k + 1/6
Subtract 3/10k from both sides of the equation:
1/10k = 1/6
Divide both sides of the equation by (1/10), which is the same as multiplying both sides by 10:
k = 5/3
Answer:
k=5/3
Step-by-step explanation:
2/5k+1/6=3/10k+1/3
Move the 3/10k to the left side with subtraction
1/10k+1/6=1/3
Move the 1/6 to the right with subtraction
1/10k=1/6
Divide the 1/10 from each side
Getting K=5/3
A machine running at 100 percent capacity produces 13,000 products each shift. Each product weighs about 2.2 ounces.
How many ounces of product can the machine produce during a shift if it is running at 85 percent capacity?
See attached Screenshot
The expression ∛(t⁴m²) / (m³t) in the simplified form will be written as [tex]\rm \frac{t^{1/3}}{m^{7/3}}[/tex].
What is Algebra?Algebra is the study of abstract symbols, while logic is the manipulation of all those ideas.
The acronym PEMDAS stands for Parenthesis, Exponent, Multiplication, Division, Addition, and Subtraction. This approach is used to answer the problem correctly and completely.
The expression is given below.
⇒ ∛(t⁴m²) / (m³t)
Simplify the expression, then we have
⇒ ∛(t⁴m²) / (m³t)
⇒ t∛(tm²) / (m³t)
⇒ ∛(tm²) / (m³)
Simplify the equation further, then we have
[tex]\rm \rightarrow \dfrac{\sqrt[3]{\rm tm^2} }{m^3}\\\\\rightarrow \dfrac{t^{1/3}m^{2/3}}{m^3}\\\\\rightarrow \dfrac{t^{1/3}}{m^{7/3}}[/tex]
The expression ∛(t⁴m²) / (m³t) in the simplified form will be written as [tex]\rm \frac{t^{1/3}}{m^{7/3}}[/tex].
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