Using proportions, we find that the hedgehog loses 3.45 ounces after 115 days of hibernation.
Here, we are given a table shows the proportional relationship between a hedgehog's weight loss and the number of days of hibernation
A proportional relationship is mathematically represented as-
y = kx
where k is the constant of proportionality.
Here x = days in hibernation and y = loss in weight
From the table we see that when x = 8, y = 0.24
⇒ 0.24 = 8k
8k = 0.24
k = 0.24/ 8
k = 24/ 800
k = 3/100
k = 0.03
Now, when x = 115, y will be-
y = 0.03*115
y = 3.45
Thus, using proportions, we have found that the hedgehog loses 3.45 ounces after 115 days of hibernation.
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Your question was incomplete. Check for full content below-
The table shows the proportional relationship between a hedgehog's weight loss and the number of days of hibernation. How much weight does the hedgehog lose during 115 days of hibernation? Use pencil and paper. Explain how you know that the relationship between the hedgehog's weight loss and the number of days of hibernation is proportional.
Weight Loss of Hedgehog
Days of Hibernation 8 28 75 93
Loss in Weight (oz) 0.24 0.84 2.25 2.79
What is the horizontal distance in inches covered by 12 stair steps if each is 11 in. wide?
The total horizontal distance covered by 12 stair steps is 132 inches.
What is an equation?An equation is an expression that can be used to show the relationship between numbers and variables.
Given that:
Each stair step is 11 inches wideThere are 12 stair stepsTotal horizontal distance = 12 stairs * 11 in/stair = 132 inches
Total horizontal distance is 132 inches
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a quarter of which is 15
The triangular prism has a volume 120 yards^3
Please tell me the height of the prism.
In the picture there is a prism. The volume of the prism is 120 yards³. The prism stands 8 yards height.
Given that,
In the picture there is a prism.
The volume of the prism is 120 yards³.
The base is 6 yards and the length is 5 yards.
We have to find the height of the prism.
Take the height of the prism as h.
The volume of a prism is the space that it occupies.
The formula for volume of the prism is (base×height×length)/2
120=(6×h×5)/2
120×2=30×h
240=30h
h=240/30
h=8
Therefore, The prism stands 8 yards height.
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factor (GCF) the binomial 25x^2 -15x and find one of its factors.
The most appropriate choice for factorization will be given by
[tex]\\5x(5x - 3)\\[/tex] is the required factorization.
(5x - 3) is one of the factor of [tex]25x^2 - 15x[/tex]
What is factorization?
Algebraic expression consist of number and variables connected with addition, subtraction, multiplication and division.
Factorization is the process of breaking of algebraic expression into algebraic expressions of smaller degree.
The algebraic expressions of smaller degree are called factors.
Here,
[tex]25x^2 - 15x\\5x(5x - 3)\\[/tex]
This is the required factorization.
(5x - 3) is one of the factor of [tex]25x^2 - 15x[/tex]
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What is the area of a triangle whose vertices are J(-2, 1), K(0,3), and L(4, -4)?
Enter your answer in the box.
According to the given coordinates, the area of the triangle is 11 units².
What are triangles?A polygon with three edges and three vertices is called a triangle. It is one of the fundamental geometric shapes. Triangle ABC is the designation for a triangle with vertices A, B, and C. In Euclidean geometry, any three points that are not collinear produce a distinct triangle and a distinct plane.So, the area of the triangle:
The formula for the area of the triangle: 1/2|x₁(y₂-y₃) + x₂(y₃-y₁) + x₃(y₁-y₂)|
Now, insert the values in the formula as follows
1/2|x₁(y₂-y₃) + x₂(y₃-y₁) + x₃(y₁-y₂)|1/2|-2(3+4) + 0(-4-1) + 4(1-3)|1/2|-2(7) + 0(-5) + 4(-2)|1/2|-14 + 0 + -8|1/2|-22|-11Since the area cannot be negative, the area of the triangle will be 11 units².
Therefore, according to the given coordinates, the area of the triangle is 11 units².
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Answer: 11 units squared
Step-by-step explanation: You can use an interactive coordinate plane like I did to plot the points and then find the area.
_1) Given: L = √2
M-3√3
N =√16
P = √9
Which expression results in a rational number?
(3) N + P
(4) P+L
(1) L + M
(2) M + N
The expression that results in rational number is P+N
What is rational numbers?Any integer that can be expressed as p/q, where q ≠ 0, is referred to as rational.
The form of a rational number, which is a type of real number in mathematics, is p/q when q is not equal to 0. Examples of rational numbers include 1/2, 1/5, 3/4, and other such values. For example, any integer is a rational number. The number one can be written as 10,000/10000, -2 over -2, or 1/1.
Here, L = √2
M=3√3
N =√16
P = √9
we know [tex]\sqrt{16} =4 , \sqrt{9} =3[/tex]
only P and N are rational numbers.
P+N = 4+3 = 7/1
which is a rational number.
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Find the measures of the numbered angles in the figure, shown to the right. Name the theorem that justifies each answer.
Question content area bottom
Part 1
Complete the table below.
Measure
Justification
The measurement of all four angles is 105°
What is an angle?
When two solid lines or rays intersect at a single endpoint, an angle is created. The vertex about an angle is the location where two points come together.Vertex: The intersection of two lines or sides at an angle is called a vertex. In the diagram, O is the vertex.Arms: The angle's two sides are linked at a single end. The arms of just an angle are OA and OB.180° [Linear pair with angles] = m1 + 75°
The opposite angles of either a rectangle are equal: m1 = 180° - 75° = 105° m2 = m1.
[Vertically opposing angles] m2 = m1 = 105° m2 = m3 = 105°
m∠3 = m∠4 = 105° Coordinating angles
As a result, the measurement of all four angles is 105°.
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NEED ANSWER ASAP. please help
what is the value of x?
- 20
- 40
- 8
- 12
Answer:
8
Step-by-step explanation:
8x-4=60
8x=64
x=64/8
x=8
Answer:
x = 8
Step-by-step explanation:
Alternate Interior Angles Theorem
If a line intersects a set of parallel lines in the same plane at two distinct points, the alternate interior angles that are formed are congruent.
Therefore, equate the two angles and solve for x:
⇒ (8x - 4)° = 60°
⇒ 8x - 4 = 60
⇒ 8x - 4 + 4 = 60 + 4
⇒ 8x = 64
⇒ 8x ÷ 8 = 64 ÷ 8
⇒ x = 8
Alex earns a \$35{,}000$35,000dollar sign, 35, comma, 000 salary in the first year of his career. Each year, he gets a 3\%3%3, percent raise. Which expression gives the total amount Alex has earned in his first nnn years of his career?
The expression which represents the total amount Alex has earned in his first n years of his career is; F(n) = 35,000 (1.03)^n.
Which expression gives the total amount Alex has earned in his first n years of his career?The expression which represents the total amount earned in n years of Alex's career is to be determined.
Since the percent raise in Alex's earning each year is 3%, it follows that the required expression would be an exponential function.
It is therefore noteworthy to note the standard form of exponential models at this point, 2whuch is as follows;
F(n) = a(b)^n
Hence, the value of a which is the starting value is; 35,000 while b = (100% + 3%) = (1 + 0.03) = 1.03.
The required expression is therefore;
F(n) = 35,000 (1.03)^n.
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what is the process of getting 10b+7<8b+7<9b+10 down to -3<b<0 because I have my solution graphed already but I genuinely couldn't track my friend helping me on my homework assignment so can somebody please explain?
What is the process of getting 10b+7 <8b+7 <9b+10 down to -3 <b <0?
Transforming the inequalities,
(a) Consider 10b+7<8b+7,
10b+7<8b+7
Combining like terms,
10b - 8b < 7-7
2b< 0
Dividing both sides of the inequality by the coefficient of the variable,
b< 0
(b) Consider 8b+7<9b+10,
8b+7<9b+10
Combining like terms,
8b- 9b < 10-7
-b < 3
Dividing both sides of the inequality by the coefficient of the variable,
b > -3
The intersection of the inequality is given by,
-3 < b < 0
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how could you determine the number of feet per second a squirrel can run?
We are asked that how could we determine the number of feet per second a squirrel can run?
Recall that rate (also known as speed) is given by
[tex]r=\frac{d}{t}[/tex]Where d is the distance in feet.
t is
In this truss bridge, AABC~ AXYZ BASED ON THE GIVEN INFORMATION WHAT IS YZ??A.) 10 FTB.) 20 FTC.) 30 FTD.) 40 FT
Given that the triangles are similar, then their corresponding sides are in proportion, that is,
[tex]\frac{XY}{AB}=\frac{YZ}{BC}[/tex]Substituting with data:
[tex]\begin{gathered} \frac{40\text{ ft}}{10\text{ ft}}=\frac{YZ}{10\text{ ft}} \\ 40\cdot10=YZ\cdot10 \\ \frac{400}{10}=YZ \\ 40\text{ ft = YZ} \end{gathered}[/tex]Scale Factor And Scale Drawing
Explain Please
The explanation of the scalar factor and scalar drawing is given below.
Given that
We have to explain what is scalar factor and scalar drawing.
What is a scalar factor?
To adjust the size of a figure without altering its shape, a scalar factor is a number or conversion factor that is utilized. It is employed to change the size of an object. If the original figure's dimensions and the dilated (increased or lowered) figure's dimensions are known, the scalar factor can be determined.
The original rectangle's dimensions in the accompanying figure are 3 units and 2 units. The formula: Dimensions of the new shape = Dimensions of the old shape Scalar factor is used to multiply the dimensions by the scalar factor of 3 to produce an expanded figure. The revised dimensions are thus given as 9 units and 6 units, respectively. In a similar manner, we multiply the original dimensions by a scalar factor of half to produce a reduced figure. As a result, the reduced dimensions are given as 1.5 units and 1.
What is a scalar drawing?
An accurate portrayal of an object or location in two dimensions is called a scalar drawing. Scalar drawings include, but are not limited to, maps and floor plans.
The scalar describes the actual length that each length on the scalar graphic corresponds to.
A scalar of "1 inch to 5 miles," for instance, indicates that 1 inch on the figure corresponds to 5 actual miles. If a road is depicted on a drawing as being 2 inches long, it is actually 10 miles long.
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Which expressions represent the volume of the cube? Select all that apply.
A cube with side length 3-fourths foot.
3343ft3
(34)3ft3
2716ft3
2764ft3
916ft2
(34)2ft2
The volume of cube with side length 3/4 of a foot is (27/64) square feet which is the fourth option.
We know that the formula for the volume of a cube is given by:-
Volume of cube = (side)*(side)*(side) = [tex]side^3[/tex]
Cube
In geometry, a cube is a three-dimensional solid object bounded by six square faces, facets or sides, with three meeting at each vertex.
The cube is the only regular hexahedron and is one of the five Platonic solids. It has 6 faces, 12 edges, and 8 vertices.
We have,
side = (3/4) foot
Hence, we can write,
Volume of cube = (3/4)*(3/4)*(3/4) = (27/64) square feet.
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Find the distance between the parallel lines. If necessary, round to the nearest whole number y=2x+7 y=2x-2
The distance between the two parallel lines are found as 9 units.
What is defined as the parallel lines?Parallel lines are two or more lines which lie within the same plane but never intersect. They are equal in distance and share the same slope. Many pairs of angles are formed when two parallel lines are intersected by some other line known as a transversal.For the given question;
The two equation of the lines are given as;
y = 2x + 7 ; y = 2x - 2
Complaining both equation with standard form of line in point slope form.
y - y1 = m(x - x1)
The equations are in slope intercept form, yielding two points (0,7) and (0,7). (0, -2).
Now, find the distance using the distance formula.
d = √(x₂ - x₁)² + (y₂ - y₁)²
Put the values in the equation.
d = √(0 - 0)² + (-2 - 7)²
d = √(-9)²
d = 9
Thus, the distance between the two parallel lines are found as 9 units.
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100 points need asap
Determine the solutions to the equation below. 5|x−2|+3=8
x=1 and x=3
x=−9 and x=13
x=−3 and x=−1
Answer: X = 1 and X = 3
Step-by-step explanation:
By filling in both the possible X values (1 and 3) you get two equations.
5|1-2| + 3 = 8
5|3-2| + 3 = 8
Both of these equations when simplified equal eight on both sides because the first one has the absolute value of -1 times 5 plus 3 which is eight. The second equation is the same besides the fact that it's the absolute value of 1, not -1 but it makes no difference.
If4x-2y=6, then y =?
Rick used 4-2-3 yards to sew 3-1-2 shirts what is the unit rate of cloth he used in terms of yards per shirt Mathematics 7th grade
If Rick used 4 2/3 yards of fabric to sew 3 1/2 shirts. The unit rate of cloth he used in terms of yards per shirt will be 4/3.
What is an arithmetic operation?It is defined as the operation in which we do the addition of numbers, subtraction, multiplication, and division. It has basic four operators that are +, -, ×, and ÷.
It is given that, Rick used 4 2/3 yards of fabric to sew 3 1/2 shirts.
We'll apply division by Splitting into equal halves or groups, the division may be used to decide how to distribute a dish of cookies evenly among a group.
The unit rate of cloth he used in terms of yards per shirt is found by dividing the 3 1/2 shirts by 4 2/3 yards,
[tex]= 4 \dfrac{2}{3} / 3 \dfrac{1}{2} \\\\ = \dfrac{14}{3} / \dfrac{7}{2} \\\\ = \dfrac{14}{3} \times \dfrac{2}{7} \\\\ = \dfrac{4}{3}[/tex]
Thus, if Rick used 4 2/3 yards of fabric to sew 3 1/2 shirts. The unit rate of cloth he used in terms of yards per shirt will be 4/3.
The question is incomplete
The complete question is"Rick used 4 2/3 yards of fabric to sew 3 1/2 shirts. What is the unit rate of cloth he used in terms of yards per shirt?"
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a right triangle has one angle that measures 70°. what is the measure of the other acute angle?
1. A right triangle is a triangle with an angle measuring 90 degrees
2. 3 angles in a triangle add up to 180 degrees
We have the measurements of 2 angles, and because of 2., we can find the measure of the other acute angle : 180 - 90 - 70 = 20 degrees.
Answer: 20°
Step-by-step explanation:
Right triangle means one angle is 90°
One angle is given, 70°
A triangle adds up to 180°
90° + 70° + X = 180°
160° + X = 180°
X = 20°
Evaluate the expression shown below and write your answer as a mixed number in simplest form.
-5 9/10 divided by 9/10
The most appropriate choice for fraction will be given by -
The quotient obtained on performing the division is [tex]-6\frac{5}{9}[/tex]
What is fraction?
Suppose there is a whole collection of objects and some parts of the objects are taken from the whole collection. Fraction represents those parts which are taken. In other words, part of a whole is called fraction. The upper part of the fraction is the numerator and the lower part of the fraction is the denominator.
We can do addition, subtraction, multiplication and division on fractions.
Here,
The given division is
[tex]-5\frac{9}{10} \div \frac{9}{10}[/tex]
Now,
[tex]-5\frac{9}{10} \div \frac{9}{10}\\\\-\frac{59}{10} \div \frac{9}{10}\\\\-\frac{59}{10} \times \frac{10}{9}\\\\-\frac{59}{9}\\\\-6\frac{5}{9}[/tex]
The quotient obtained on performing the division is [tex]-6\frac{5}{9}[/tex]
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16. The greatest distance between the Sun and
greatest distance between the Sun and Saturn
Jupiter is about 8.166 x 10^8 kilometers. The
is about 1.515 x 10⁹ kilometers. What is the
difference of these two distances?
The difference of the distance given for Sun, Saturn and Jupiter is 6.984 x 10⁸ kilometers.
What is termed as the scientific notations?Every day, we use numbers in our lives. Scientific notation is a method of writing extremely large and extremely small numbers. Scientific notation consists of two parts: a coefficient between 1 and 10 and a power of ten. The mantissa is the difference between the whole part (left of a decimal point) and also the decimal part (right of a decimal point) of the coefficient. The exponent would be positive or negative depending on which way the decimal point is moved.For the given question;
The greatest distance between the Sun and Jupiter is about 8.166 x 10⁸ kilometers.
The greatest distance between the Sun and Saturn is about 1.515 x 10⁹ kilometers.
Write this distance in the form of 10⁸ , the point will shift towards right one decimal.
Sun and Saturn distance = 15.15 x 10⁸ kilometers.
Difference = Sun and Saturn distance - Sun and Jupiter distance
Put the values,
Difference = 15.15 x 10⁸ - 8.166 x 10⁸
Difference = 6.984 x 10⁸ kilometers.
Thus, the difference of the distances is found as 6.984 x 10⁸ kilometers.
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Estimate a 10% tip on a bill of $159.63 by first rounding the bill amount to the nearest ten dollars.
Answer: Tip Total: $ 16.00Total (Bill + Tip): $ 176.00
Which rounding to the dearest ten dollars will be 186.00
help pleeeaseee i don’t understand what to do!
Answer:
The difference of a number and seven ⇒ n - 7
The product of seven and a number ⇒ 7n
The quotient of a number and seven ⇒ n/7
The sum of seven and a number ⇒ n + 7
Step-by-step explanation:
Difference ⇒ subtraction.
Product ⇒ multiplication.
Quotient ⇒ division.
Sum ⇒ addition.
Angie Simon is a single palmetto county deputy sheriff. she has $103.92 in federal income tax withheld from her weekly salary. her weekly salary exceeds $645.00. she calms 2 allowances the county computes her federal income tax using the percentage method.
Lucia ordered a set of beads. She received 35 beads in all. 7 of the beads were green. What percentage of the beads were green?
Write your answer using a percent sign (%).
The percentage of the beads were green is 20% .
A figure or ratio that may be stated as a fraction of 100 is a percentage. If we need to calculate a percentage of a number, we should divide it by its entirety and then multiply it by 100. The proportion therefore refers to a component per hundred. Per 100 is what the word percent means.
Given that
Total number of beads = 35
In which Number of green beads = 7
Find out What percentage of the beads were green?
By dividing the value by the entire value and multiplying the result by 100, one may determine the percentage. The percentage calculation formula is (value/total value)100%.
So here total value = 35
Value = 7
Put the values in the formula
(value/total value)100%
= (7/35) × 100 %
= 1/5 × 100 %
= 100 / 5 %
= 20 %
Hence , Twenty percent (20%) of the beads were green.
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URGENT!! ILL GIVE
BRAINLIEST! AND 100 POINTS
Is the function y=x^2-x linear or not?
Answer:
NOT linear
Step-by-step explanation:
Your equation is:
y = x^2 - x
Since the y has no exponent, (which is a power of 1) and the x has an exponent of 2, this function is a parabola. It is not linear. (Linear functions have a graph that is a line)
Functions that are NOT linear have exponents greater than 1, or variables in the denominator, or, variables inside a radical.
Can you please help me find the limit and identify any vertical asymptotes? Thanks
Given: The limit below
[tex]\lim_{x\to7^-}(\frac{1}{x-7})[/tex]To Determine: The limit and the vertical asymptotes
Solution
[tex]\begin{gathered} \lim_{x\to7^-}(\frac{1}{x-7}) \\ \mathrm{For}\:x\:\mathrm{approaching}\:7\:\mathrm{from\:the\:left},\:x<7\quad \Rightarrow \quad \:x-7<0 \\ The\:denominator\:is\:a\:negative\:quantity\:approaching\:0\:from\:the\:left \\ Hence \\ \operatorname{\lim}_{x\to7^-}(\frac{1}{x-7})=-\infty \end{gathered}[/tex]For the vertical asymptote
[tex]\begin{gathered} Vertical-asymptote \\ For\:rational\:functions,\:the\:vertical\:asymptotes\:are\:the\:undefined\:points \\ also\:known\:as\:the\:zeros\:of\:the\:denominator,\:of\:the\:simplified\:function. \end{gathered}[/tex]The denominator of the rational function given is
[tex]\begin{gathered} denominator:x-7 \\ x-7=0 \\ x=7 \end{gathered}[/tex]Hence:
limit = - ∞
Vertical asymptote: x = 7
which cards are equivalent to 2/3 - 1/4 choose all the correct answers
6/12-4/12
8/12-3/12
2/7-1/7
1/7
2/7
5/12
work out m and c for the line: y = 6x
After using equation of line the value of m = 6 and c = 0.
The equation of line is an algebraic form of representing the set of points, which together form a line in a coordinate system. The numerous points which together form a line in the coordinate axis are represented as a set of variables x, y to form an algebraic equation, which is referred to as an equation of a line.
Given that,
The equation of line
y = 6x
Compare the given equation by the standard equation of line.
y = mx+c
m = 6 and c = 0
Hence, The value of m = 6 and c = 0.
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