Solution: X-value of vertex=-3
Y-value of vertex=-4
Zeros of the parabola: X=-5 and x=-1
Analysis
We can find the x-coordinate of the vertex, calculating -b/2a. First, we identify the a and b values of y=ax^2+bx+c of your quadratic equation.
b=6
a=1
[tex]\begin{gathered} -\frac{b}{2a}=-\frac{6}{2(1)}=-3 \\ \\ After\text{ we find x-coordinate, we can find y-coordinate of the vertex replacing x-value.} \\ f(x)=x^2+6x+5\text{ = }^^(-3\text{ }^2)+6(-3)+5 \\ f(x)\text{ = 9}-18+5 \\ f(x)=-4 \end{gathered}[/tex]Now, let's find the zeros of the parabola. We factorize the quadratic equation:
[tex]\begin{gathered} f(x)=x^2+6x+5 \\ f(x)=(x+5)(x+1) \\ Let^{\prime}s\text{ equal to zero} \\ (x+5)(x+1)=0 \\ (x+5)=\text{ 0 }(x+1)=0 \\ x=-5\text{ }x=-1 \end{gathered}[/tex]What's the correct letter name for this below?
The correct letter name for ∠1 is ∠ABC.
How to name angles?There are various ways of naming angles . One can name an angle by its vertex, by the three points of the angle (the middle point must be the vertex), or by a letter or number written within the opening of the angle.
The method adopted to name the angle below is the three points of the angle.
Therefore, using the three points, the ∠1 can be named as follows:
∠1 = ∠ABC
The middle point is usually the vertex.
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Use the list below to complete each sentence.
factor
product
1. -3- (-12)=-12-(-3)
positive
negative
a. This equation is written using the
of Multiplication.
additive inverses
Distributive Property
b. Both factors in this equation are Poritiv
c. The product will be Distributive property
3. (5 (-9))-6-5-((-9). 6)
b. One
2. -7 (-8+8)=[-7 (-8)] + [-7.8]
a. This equation is written using the
b. The product of this equation is 0. This is because the sum of the
,-8 and 8, is equal to 0.
a. This equation is written using the
of Multiplication.
are positive.
c. The
negative
Commutative Property
Associative Property
is negative, while the other two
will be negative.
1a) This equation is written using the Distributive Property of Multiplication.
b) Both factors in this equation are negative.
c) The product will be positive.
2a) This equation is written using the Additive inverses of Multiplication.
b) The product of this equation is 0.
c) This is because the sum of (-8+8) is equal to 0.
3a) This equation is written using the Commutative Property of Multiplication.
b) The products of the commutative multiplications do not change.
c) This is because changing the order of factors does not affect the solution.
What are the properties of multiplication?The properties of multiplication are:
Identity Property of Multiplication (product of 1 and another factor remains the factor.)Associative Property of Multiplication (grouping order of factors does not change the product.)Distributive Property of MultiplicationCommutative Property of Multiplication (the order of factors does not change the product.)For the distributive property, multiplying the sum of two numbers by another number gives the same result as distributing the first number to both other numbers and multiplying them separately and adding.
1) -3(-12) = -12(-3)
= 36 = 36
2) -7 (-8+8) = [-7 (-8)] + [-7 (8)]
= -7(0) = [56 + - 56
0 = 0
3. (5 (-9))-6 = -5 ((-9) +6)
(-45)-6 = -5(-54)
270 = 270
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Question Completion:2) -7 (-8+8) = [-7 (-8)] + [-7 (8)]
3. (5 (-9))-6 = -5 ((-9) +6)
Calculate Sample Variance for the following data collection: 10, 11,12, 13, 14, 18.
To calculate the variance follow these steps:
1. Work out the Mean
2. Then for each number: subtract the Mean and square the result .
3. Then work out the average of those squared differences.
The data are 10, 11, 12, 13, 14, 18
The first step find the mean
The mean = sum of data/number of data
The sum = 10 + 11 + 12+ 13 +14 + 18 = 78
The number =
Triangles W U V and X Z Y are shown. Angles V U W and Y X Z are congruent. Angles U W V and X Z Y are congruent. Angles U V W and Z Y X are congruent. The length of side V W is 60 and the length of side Z Y is 48. The length of side Y X is 40 and the length of V U is 50. The length of side U W is 40 and the length of X Z is 32.
How can the triangles be proven similar by the SAS similarity theorem?
The triangles can be proven similar by the SAS similarity theorem based on this: B. Show that the ratios are equivalent, and ∠V ≅ ∠Y.
The properties of similar triangles.In Mathematics, two (2) triangles are said to be similar when the ratio of their corresponding side lengths are equal and their corresponding angles are congruent.
Based on the side, angle, side (SAS) similarity theorem, in order to prove that theses two (2) triangles are similar, it needs to be shown that the ratio of the corresponding side lengths of these triangles are equal and that their corresponding angles are congruent as shown below:
Side UV = side XY
∠V ≅ ∠Y
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Complete Question:
Consider the two triangles.
How can the triangles be proven similar by the SAS similarity theorem?
Show that the ratios are equivalent, and ∠U ≅ ∠X.
Show that the ratios are equivalent, and ∠V ≅ ∠Y.
Show that the ratios are equivalent, and ∠W ≅ ∠X.
Show that the ratios are equivalent, and ∠U ≅ ∠Z.
question 11, rewrite the formulaThe area of a triangle is A-a. Rewrite the formula for b.b. Rewrite the formula for h.
Given the formula:
[tex]A\text{ = }\frac{1}{2}bh[/tex]a) Rewrite for b:
First step: Multiply 2 to both sides
[tex]\begin{gathered} 2A\text{ = }\frac{1}{2}bh\text{ }\ast2 \\ \\ 2A\text{ = bh} \end{gathered}[/tex]Second step: divide both sides by h
[tex]\frac{2A}{h}\text{ = b}[/tex][tex]\begin{gathered} \text{Thus,} \\ b\text{ = }\frac{2A}{h} \end{gathered}[/tex]B) Rewrite for h:
First step: Multiply 2 to both sides
[tex]\begin{gathered} 2A\text{ = }\frac{1}{2}bh\ast2 \\ \\ 2A\text{ = bh} \end{gathered}[/tex]Second step: divide both sides by b
[tex]\begin{gathered} \frac{2A}{b}\text{ = }\frac{bh}{b} \\ \\ \frac{2A}{b}\text{ = h} \end{gathered}[/tex][tex]h\text{ = }\frac{2A}{b}[/tex]What is the equal number for 2 tens and 15 ones
A certain species of fish require 1.5 cubic feet of water per fish to maintain a healthy environment. Find the maximum number of fish you could put in a tank measuring 5 feet by 3 feet by 4 feet.
Answer:
40
Step-by-step explanation:
Given information:
1.5 ft³ = Volume of water required per fish.Dimensions of the tank = 5 ft × 3 ft × 4 ftModel the tank as a rectangular prism.
[tex]\begin{aligned}\textsf{Volume of a rectangular prism}&=\sf width \times length \times height\\\\\implies \textsf{Volume of tank}&=\sf 5 \; ft \times 3\; ft \times 4 \; ft\\& = \sf 15\;ft^2 \times 4\;ft\\& = \sf 60 \; ft^3\end{aligned}[/tex]
To find the maximum number of fish that can be put in the tank, divide the found volume of the tank by the given volume of water required per fish:
[tex]\begin{aligned}\textsf{Maximum number of fish}&=\textsf{Volume of tank} \div \textsf{Water per fish}\\& = \sf 60\;ft^3 \div 1.5 \; ft^3\\& = \sf 60 \div 1.5\\& = \sf 40\end{aligned}[/tex]
Therefore, the maximum number of fish that can be put in the tank is 40.
CAN SOMEONE HELP WITH THIS QUESTION?✨
The value of P = $5000, r = 3.6%/4 = 0.9%, n = 4n and amount after 10 years is $5450.
Compound interest may be defined as the interest which can be applied by any institution on any individual in which the interest amount after a year becomes principle for the next year. The formula for compound interest is given as A = P(1 + r/n) ^ nt where A is the amount, P is the principle, r is the interest rate, n is compounding frequency and t is the time. If compounded quarterly the principle will be same as in the question that is $5000, the interest rate will be divided by 4 that is r = 0.9% and the compounding frequency will be 4 times that is 4n. Now, we need to find the amount after 10 years that is t = 10 years. The amount will be
A = P(1 + r/4n) ^ 4nt
A = 5000(1 + 0.9/100×4×12) ^4×12×10
A = 5000(1.09)
A = $5450 which will be amount after 10 years.
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Describe a series of transformations Matt can perform to decide if the two windows are congruent
Congruent shapes are produced by combining rotations, reflections, and translations. In fact, any pair of congruent shapes can be matched to one another by combining one or more of these three transformations.
Define transformations.A point, line, or geometric figure can be transformed into one of four different shapes or locations. Pre-Image refers to the shape of the object prior to transformation, whereas Image refers to the location and shape of the object after transformation.
Given information
We now know that the size and shape of the figures are preserved during stiff transformations (reflections, translations, and rotations). The pre-image and the actual image concur completely.
The following Matt's transformative skills:
Reflection
Because the The line of reflection remains the same distance away from comparable points from the pre-image to the image.
As a Congruence Transformation - rotations
Rotating a figure causes it to twist. Even though the figure is the same size and shape as before, it appears to have toppled over. A clock is a fantastic example of how the earth actually rotates. Every hour or every day, the clock's connecting arms revolve around their axis. A rotation's degree determines what it is, and common rotations include 90, 180, and 270 degrees. Before going back to its original position, the figure rotates a full 360 degrees. the direction of a rotation, whether it is counterclockwise or clockwise. It is possible to determine the degree, amount, and and the direction of a revolution.
Translational congruence transformation
When an object or shape is transported from one location to another without altering its size, shape, or orientation, the movement is referred to as a translation. During a translation, also known as a slide occasionally, every point on an object or shape is moved by the same amount and in the same direction.
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Factor the expression over the complex numbers. x^2+25 Enter your answer in the box.
please help
The complex number factors are (x+5i) and (x-5i).
The term a + bi, where a and b are real numbers, can be used to represent any complex number.
A complex number is a component of a number system that includes an element with the symbol I, sometimes known as the imaginary unit, and that extends the real numbers by satisfying the equation i² = -1. Since no real number can fulfil the conditions in the previous equation, i was referred to as an imaginary number. The complex number a + bi is known as having real and imaginary parts, respectively, a and b. The group of complex numbers is represented by the letter C.The given expression is x² + 25
Now this can be written as :
x² - [(i)²×(5)²] as we know that i² = -1.
Now we use the algebraic form of a²-b² =(a + b)(a - b) to separate it into complex factors.
or , (x+5i)(x-5i)
Therefore the complex number factors are (x+5i) and (x-5i).
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samuel carries three sacks of gravel to his motorcycle which weigh 800 cm³ cube how many liters did he carry?Plss answer it now I need help
Explanation:
To be able to determine the number of liters Samuel carried, let's convert first the 800 cm³ to liters.
The conversion formula is 1 cm³ = 0.001 liters.
So, to convert 800 cm³ to liters, let's multiply 800 by 0.001.
[tex]800cm^3\times\frac{0.001L}{1cm^3}=0.8L[/tex]Answer:
Which set of values belong to the domain and range of a relation?
Domain is x values of the set and range is y values of the set.
What is domain and range?
Domain is the set of all first numbers of the ordered pairs in a relation and range is the set of second numbers of the ordered pair in relation.
The domain is the set of independent values, meaning the set of x-coordinates of the ordered pair as x is an independent variable.
The range is set of dependent values, meaning the set of y-coordinates of the ordered pair as y is an independent variable.
For example- we have a set
(1,2) (0,6) (2,3) (4,5)
Domain = {1,0,2,4}
Range = {2,0,3,5}
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Write the statement as a conditional statement, then tell which part is the hypothesis and which is the conclusion. Write the inverse, converse, and contrapositive of your conditional statement:
People who reduce their time in the shower will save money on water.
Conditional Statement: If people reduce their time in the shower then they will save money on water.
Hypothesis: "If people reduce their time in the shower"
Conclusion: "they will save money on water"
What is the conditional statement?A conditional statement is defined as the two fundamental components that make up a conditional statement are Hypothesis (if) and Conclusion (then).
Conditional Statement: If people reduce their time in the shower then they will save money on water.
Hypothesis: "If people reduce their time in the shower"
Conclusion: "they will save money on water"
Inverse Statement: If people did not reduce their time in the shower, then they will not save money on water.
Converse Statement: If they will save money on water then people reduce their time in the shower.
Contrapositive Statement: If they will not save money on water then people do not reduce their time in the shower.
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How would you write the phrase, “I do not want fries with my burger” in spanish?
The phrase, “I do not want fries with my burger” in Spanish is “No quiero papas fritas con mi hamburguesa".
What is a phrase?A phrase is a group of words or a single word that functions as a grammatical unit in syntax and grammar. The English phrase "the extremely happy squirrel," for instance, is a noun phrase that also incorporates the adjective phrase "very happy." A phrase may be made up of a single word or a whole sentence.
A phrase is typically a group of words with a specific idiomatic meaning or other importance, such as "all rights reserved," "economical with the truth," "kick the bucket," and the like. It could be a euphemism, a proverb, a permanent word, a figure of speech, or anything else. These are referred to as phrasemes in linguistics.
A phrase is a group of words that together convey one or more speech elements. They are crucial because they enhance your ability to communicate verbally and in writing. In this case, the phrase has been translated into Spanish.
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2. Calculate each surface area to the nearest tenth of a square centimetre ) r = 10 cm b) a) d=7 cm 30 cm 22 cm 3. bbelow 1
The formula to find the surface area of a cylinder is:
[tex]\begin{gathered} S.A.=2\pi r^2+2\pi rh \\ \text{ Where} \\ S.A\text{. is the surface area,} \\ r\text{ is the radius, and} \\ h\text{ is the height of the cylinder} \end{gathered}[/tex]So, in this case, we have:
[tex]\begin{gathered} r=10\operatorname{cm} \\ h=22\operatorname{cm} \\ S.A.=2\pi r^2+2\pi rh \\ S.A.=2\pi(10cm)^2+2\pi(10cm)(22cm) \\ S.A.=2\pi(10cm)(10cm)+2\pi(10cm)(22cm) \\ S.A.=628.3cm^2+1382.3cm^2 \\ S.A.=2010.6cm^2 \end{gathered}[/tex]Therefore, the surface area of the given cylinder rounded to the nearest square centimetre is 2010.6 cm².
The triangle below will be translated 2 units up and 5 units to the right.3АA22-4-3045- 1Bс2What will be the coordinates of point A'?O (4,4)O (1,7)O (-3,-3)O (-6,0)
In general, a translation:
• in the x-direction by n units is given by: (x, y) → (x + n, y),
,• in the y-direction by m units is given by: (x, y) → (x, y + m),
,• the combination of both translations is: (x, y) → (x + n, y + m).
In this problem, we want to translate a triangle 2 units up and 5 units to the right, so we want to translate the points of the triangle in the following way:
[tex](x,y)\rightarrow(x+5,y+2)[/tex]From the graph we see that the coordinates of point A are:
[tex](x_A,y_A)=(-1,2)[/tex]Making the translation we get:
[tex](x_A+5,y_A+2)=(-1+5,2+2)=(4,4)[/tex]Answer
(4,4)
The deer population in the united states can be predicted by the expression 523(1.099)^t where t is the number of years since 1990 . what does the value 523 represent?
The exponential growth or decay function is a function that grows or shrinks at a constant percent growth rate. The equation can be written in the following form:
[tex]f(x)=a(1+r)^x[/tex]or
[tex]f(x)=ab^x\text{ where b= 1+r}[/tex]here
a is the initial or starting value of the function or initial population.
r is the percent growth or decay rate, written as a decimal
and
b is the growth factor or growth multiplier.
Now, consider the following exponential model:
[tex]f(t)=523\left(1.099\right)^t[/tex]notice that in this case:
a = 523
according to the definition of exponential growth, we can conclude that the correct answer is:
Answer:523 is the initial population of deers.Determine the interval(s) for which the function shown below is decreasing.
When x increases the value of f(x) decreases called decreasing function thus the interval on which the function is decreasing is (-∞, -5] ∪ [-2, 2].
What is a function?A certain kind of relationship called a function binds inputs to essentially one output.
The machine will only accept specified inputs, described as the function's domain, and will potentially produce one output for each input.
As per the given graph of a random function,
The value of f(x) decreasing when x is increasing is the interval on which we can say that function is decreasing.
If we look at the extreme left of the graph and come towards the right then the curve is going downward till x = -5.
Therefore, in interval (-∞, -5] function is decreasing.
The function is again going down in intervals [-2,2].
Therefore in inteval (-∞, -5] ∪ [-2, 2] the function is decreasing.
Hence "When x increases the value of f(x) decreases called decreasing function thus the interval on which the function is decreasing is (-∞, -5] ∪ [-2, 2]".
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The given question is incomplete complete question is attached below ;
Jayla plays on the Strikers soccer team. The team worked on 5 new drills at yesterday's
practice, spending the same amount of time on each drill. Jayla was 15 minutes late and only
practiced for 40 minutes.
) Which equation can you use to find how long, x, the team spent on each drill?
The equation that can be use to find how long, x the team spent on each drill is 55 = 5x
How to represent equation?Jayla plays on the Strikers soccer team.
The team worked on 5 new drills at yesterday's practice, spending the same amount of time on each drill.
Jayla was 15 minutes late and only practiced for 40 minutes.
The equation that can be used to represent the situation is as follows:
where
x = time the team spent on each training drill
Therefore, the equation is as follows:
15 + 40 = 5x
55 = 5x
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Sam has a piece of rope that is 3 1/2 feet long. He cuts the rope so that one piece is 1 1/3 feet long what is the length of the other half?
The length of the other half is:
[tex]\frac{7}{2}-\frac{4}{3}=\frac{7\cdot3-4\cdot2}{2\cdot3}=\frac{21-8}{6}=\frac{13}{6}[/tex][tex]\frac{13}{6}=\frac{12+1}{6}=\frac{12}{6}+\frac{1}{6}=2+\frac{1}{6}=2\frac{1}{6}\text{ fe}et[/tex]Write an equation of the line passing through point P(3,8) that is parallel to the line y\ ={1}{5}(x+4) NEEP HELP ASAP
Answer:
y = (1/5)(x + 37)Step-by-step explanation:
Slope-intercept form:
y = mx + bGiven line has a slope of m = 1/5.
Parallel lines have equal slopes, so the line we are looking for is:
y = (1/5)x + b and passing through point P(3,8).Substitute the coordinates and slope and find b:
8 = (1/5)*3 + bb = 8 - 3/5b = 7 2/5The line is:
y = 1/5x + 7 2/5 ory = (1/5)(x + 37)Evaluate (m³ + 4) -n² if m= -4 and n=-6. Write your answer as an integer.
Answer:
-96
Step-by-step explanation:
m = -4
n = -6
(m³ + 4) - n² =
= [(-4)³ + 4] - (-6)²
= -64 + 4 - 36
= -60 - 36
= -96
Without using a calculator, order the
following expressions from least to greatest.
29 2
3
64
The expressions from least to greatest is (√3)² < 8² < 29².
How to compare expressions with indices?
Expressions with indices are of three types:
(1) when bases are equal and powers are different;
(2) when powers are equal but bases are different;
(3) when both powers and bases are unequal.
To solve an expression of type (1), we compare the powers for the given expressions only to determine the greater number efficiently, no heed needs to be given to the base.
To solve an expression of type (2), we compare the bases for the given expressions only to determine the greater number efficiently, no heed needs to be given to the powers.
To solve an expression of type (3), we reduce the power of an expression until it matches the other, so that for comparison only bases are to be taken into consideration without any heed to powers.
Given the expressions are 29², 3 and 64
The given expressions can be re-written as: 29², (√3)² and 8².
On comparing the expressions with the above literature, they match type (2), thus following the assertions we should compare the bases only to find the greatest number.
Thus, the correct order for expressions is: (√3)² < 8² < 29²
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Is the ordered pair a solution of the equation? 4x+5y=-1; (1,-1) And 2x-3y=7; (8,-3)
The given equations are:
4x + 5y = - 1
2x - 3y = 7
For the ordered pairs to be a solution of the equation, the equation must be true when the points are substituted into the equation. That is, the right hand side must equal the left hand side.
For 4x + 5y = -1
To test if (1, -1) is a solution, substitute x = 1, and y = -1 into the equation.
4(1) + 5(-1) = -1
4 - 5 = -1 (True)
Therefore, (1, -1) is a solution for the equation 4x + 5y = -1
For 2x - 3y = 7
To test if (8, -3) is a solution, substitute x = 8, and y = -3 into the equation
2(8) - 3(-3) = 7
16 + 9 = 7 ( False)
Therefore, (8, -3) is not a solution for 2x - 3y = 7
Hey I need help I got stuck I am struggling
According to the trigonometric relations in a right triangle, the following relation is valid:
[tex]\begin{gathered} \sin x\degree=\frac{\text{opposite leg}}{hypotenuse}=\frac{4.9}{7.5} \\ \sin x\degree=0.6533\ldots \\ x\degree=\arcsin 0.6533\ldots \\ x\degree\approx40.8\degree \end{gathered}[/tex]2. The slope of a line is -4. Find the value of x so that the line passes through the points
(-1,7) and (x,-9). A graph
is provided if needed.
The value of the variable 'x' is calculated by solving equation of the line by using slope value is: x = 3
What is slope of a line?
The slope of a line explain the steepness of the line segment. It is ration of the coordinates of the y-axis and the vertical coordinates of the x-axis. Depending upon the slope value, it is classified as whether lines are parallel or perpendicular.
According to the question, the given parameters for the line segment is as written below:
Slope of a line = (-4) and the coordinate points = (-1, 7)(x,-9): (x1 = -1; y1 = 7)
Now, by using standard equation for the line segment: y = mx + c
where, 'm' is the slope; c is the y-intercept; (x, y) are coordinates
Substituting given values that is slope and y-intercept in the standard equation, we get:
y = mx + c
⇒ 7 = (-4)(-1) + c
⇒ c = 7 - 4 = 3
Therefore, the value of the y-intercept is: c = (3)
Equation of the line by substituting the value of the y-intercept as well as slope value in another equation whose coordinates are (x, -9):
-9 = (-4)x + (3) ⇒ -12 = -4x ⇒ x =3
Hence, the value of the variable 'x' is calculated by solving equation of the line by using slope value is: x = 3
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The volume of this cylinder is approximately 12,468.94 cubic feet.The radius is ___ feet.Use π = 3.14.
we have that
the volume of the cylinder is
V=pi(r^2)h
the radius is given
r=57 cm
Remember that
1 ft=30.48 cm
so
57 cm=57/30.48=1.87 ft
the radius is 1.87 ftI need help finding the vortex angle with these three sides. I don’t really know how to do this sort of thing with an isosceles triangle. Once I know the vortex angle I can figure out the base angles.
Answer:
[tex]\begin{gathered} \text{ Smalles angle in the triangle}\colon \\ D=14.36\degree \\ \text{ The measure of the two congruent angles:} \\ Step-by-step explanation:To find the angle D, use the law of cosines, which is represented as:
[tex]\begin{gathered} d^2=e^2+f^2-2(e)(f)\cos D \\ 3^2=12^2+12^2-2(12)(12)\cos D \\ 9=144+144-288\cos D \\ -279==-288\cos D \\ \frac{-279}{-288}=\cos D \\ D=\cos ^{-1}(\frac{-279}{-288}) \\ D=14.36\degree \end{gathered}[/tex]Then, since the base angles are equal in measure:
[tex]\begin{gathered}use the recipe to find the ratio of bananas to tomatoes in simplest form. put the ratio data in the first row of the ratio table below. the fill in the ratio table to create two equivalent ratios
Answer:
Bananas Tomatoes
1 3
2 6
3 9
4 12
Explanation:
The ratio of bananas to tomatoes can be calculated as the division of the number of bananas in the recipe over the number of tomatoes in the recipe. So, the ratio is:
[tex]\frac{2\text{ bananas}}{6\text{ tomatoes}}[/tex]Therefore, to find the simplest form, we can divide the numerator and denominator by 2 as:
[tex]\frac{2\div2}{6\div2}=\frac{1\text{ bananas}}{3\text{ tomatoes}}[/tex]Then, we can fill the table as:
Bananas Tomatoes Ratio
1 3 1/3
2 6 2/6 = 1/3
3 9 3/9 = 1/3
4 12 4/12 = 1/3
Where every ratio is equivalent to 1/3
What is the domain of the function shown in the graph below? y 10 OSCO 7 6 5 4 3 2 1 I 1 -10 -8 -9 -5 -4 -3 -2 1 2 3 4 8 ON 5 9 10 - 2 -3 -4 -5 -8 -9 10
The function is define for all values of x greater than or equal -3 and less than or equal 3
Hence the domain of the function is;
-3 ≤ x ≤ 3