Answer:
(6.25, 10)
Step-by-step explanation:
red = x. blue = y
Jackie: 4x + 5y = 75
Sam: 4x + 4y = 65
Solving by elimination
4x + 5y = 75
4x + 4y = 65
--------------------
(4x + 5y = 75) × -1
-4x - 5y = -75
-4x - 5y = -75
4x + 4y = 65
------------------------
-y = -10
÷-1 ÷-1
--------------
y = 10
4x + 4y = 65
4x + 4(10) = 65
4x + 40 = 65
-40 -40
--------------------
4x = 25
÷4 ÷4
-------------
x = 6.25
(6.25, 10)
Each red block weighs 6.25 ounces.
Each blue block weighs 10 ounces.
I hope this helps!
3
Point A(7, 3) is translated to A'(16.-9), Which rule describes the translation?
Oo (x,y)-(x-9.y-12)
O(x,y)-(x-9y+12)
O (x,y) →(x+9y+12)
O (x,y) →(x+9y-12)
The Rule of translation of the point is (x, y) → (x+8, y - 12)
What is the coordinate rule for translation?The translation is a transformation of a figure on the coordinate plane without changing its shape, or size.
The Coordinate rule for translation is (x, y) → (x ± h, y ± k)
where h and k are the units of horizontal and vertical shifting. Here if the movement is left then h will be negative. If movement is downwards then k will be negative.
Here we have
Point A(7, 3) is translated to A'(16, -9)
If we plot the given points in a graph the will as given below the graph
There we can observe that,
The x coordinate is moved left 8 units further and y is moved 12 units downward
Therefore,
The Rule of translation of the point is (x, y) → (x+8, y - 12)
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Determine the value of the expression −2(36−8)+(−3).
Answer:-59
Step-by-step explanation:
-2*36 + -2*-8
-72+16-3
-56-3
-59
Are closed under addition True or false?
Integers are closed under addition by all the properties. Hence, the answer is True.
Integers are set of zero, positive, and negative numbers. The set of integers is represented by the symbol ‘Z’.
Z= {……-8,-7,-6, -5, -4, -3, -2, -1, 0, 1, 2, 3, 4, 5, 6, 7, 8,……}
To check if the integers are closed under addition or not we will check out the four properties namely, the closure property, the commutative property, the associative property, and the distributive property.
Let us consider each property one by one -
1. The closure property-
let's take two integers say 5 and 2.
now 5+2=7, but -2+5= -3 which is an integer.
Thus, integers are closed under addition by closure property.
2. The commutative property-
let's take two integers say 5 and 2.
now 5+2=7 and 2+5=-7
hence, we get 2+5 = 5+2.
Thus, integers are closed under addition by commutative property.
3. The associative property-
let's take three integers say 5, 3, and 2.
now (5+3)+2 = 10 and 5+(3+2)= 10
hence, we get (5+3)+2 = 5+(3+2).
Thus, integers are closed under addition by associative property.
4. The distributive property-
let's take three integers say -2, 6, and 5.
now, -2 × ( 6 + 5 ) = -2 × 6 + (-2) × 5 = -12 - 10 = -22
and -2 × ( 6 + 5 ) = -2 × 11 = -22
Hence, -22 = -22
Thus, integers are closed under addition by distributive property.
Hence, we can conclude that integers are closed under addition by all the properties.
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The complete question is-
Are Integers closed under addition. True or false?
Given a set of data and a corresponding regression line, describe all values of x that provide meaningful predictions for y. O A. Prediction values are meaningful for all X-values that are realistic in the context of the original data set. O B. Prediction values are meaningful only for x-values that are not included in the original data set. O c. Prediction values are meaningful only for X-values in (or close to the range of the original data.
The values of x that provide meaningful predictions for the output value y are given as follows:
c. Prediction values are meaningful only for X-values in (or close to the range of the original data.
What are regression equations?Regression equations are built from a sample of a data-set, and are used to model the entire data.
Depending on the behavior of the data, the regression equation can be linear, quadratic, logistic, exponential, and so on...
These regression equations are not valid for all values of the input x, some conditions are given as follows:
Values of x that are realistic in the data-set -> time cannot be negative, for example.Values of x that are close to the range of the data-set. -> a linear function from the previous 5 years can preview the measure in 5 years but it is unlikely to be accurate in 100 years.More can be learned about regression equations at https://brainly.com/question/26755306
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Multiply:
-6 x -10 =??
Answer: 60
6 x 10 is 60 and a negative times a negative is positive.
Answer: 60 hope this helps
a rectangular horse pasture is bounded on one side by a stone wall and on the other three sides by a single wire strand of electric fence. using 400 feet of wire, what is the largest area, in square feet, that can be enclosed?
The rectangular horse pasture's largest area, in square feet, can be enclosed in [tex]80000m^{2}[/tex]
Let the sides of the rectangle-shaped fence be a and b.
We have to use wire for the three sides of the fence.
[tex]a+b*2=800[/tex]
Area A is given by
[tex]A=a*b[/tex]
Also, we can write A as a function of b
[tex]A=A(b)\\=(800-2*b)b=800b-2b^{2}[/tex]
Taking the derivative of A
[tex]A'=800-4b\\A'=0\\b=200m[/tex]
Then the length of the other side
[tex]a=800-2*200\\=400m[/tex]
The largest area
[tex]A=400*200\\=80000m^{2}[/tex]
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Inequality (please check the attached image)
Let the number of pens be p and number of pencil cases be c.
Each pen costs php 20 and all pens cost 20p.Each pencil case costs php 40 and all pencil cases cost 40c.Total amount Dona needs to make is at least 2000.Use given information and set inequality:
20p + 40c ≥ 2000Simplify it by dividing all terms by 20:
p + 2c ≥ 100If number of pens is more than 100, we get:
p > 100Substitute this into inequality:
100 + 2c ≥ 100 Subtract 100 from both sides2c ≥ 0 Divide both sides by 2c ≥ 0If Dona sells more than 100 pens then she will exceed php 2000 regardless the number of pencil cases sold.
the dashed-lined figure is a dilation image of the solid-lined figure. is the dilation an enlargement, or a reduction? what is the scale factor of the dilation?
3 enlargement is the scale factor of the dilation.
What is dilation?
resizing an object is accomplished through a change called dilation. The objects can be enlarged or shrunk via dilation. A shape identical to the source image is created by this transformation. The size of the form does, however, differ. A dilatation ought to either extend or contract the original form. The scale factor is a phrase used to describe this transition.
The scale factor is defined as the difference in size between the new and old images. An established location in the plane is the center of dilatation. The dilation transformation is determined by the scale factor and the center of dilation.
The options for this question are missing. Here are the missing options:
enlargement; 6
enlargement; 3
reduction; 3
reduction; 1/3
Hence, 3 enlargement is the scale factor of the dilation.
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The angles of a quadrilateral are 4x,7x,15x and 10x. find the smallest and largest angle of the quadrilateral
A quadrilateral has angles of 4x, 7x, 15x, and 10x.The smallest angle of the quadrilateral is 4x and the largest angle is 15x.
A quadrilateral is a polygon with four vertices, four sides, and four angles, all of which add up to 360 degrees. The quadrilateral is formed into two triangles when the diagonals are drawn. The angle total for these two triangles is 180°. As a result, the quadrilateral has a 360° total angle. TA quadrilateral has angles that total 360 degrees. This information can be used to find the value of x.
360
= 4x + 7x + 15x + 10x
x = 360 / 36
x = 10
Therefore, the smallest angle is 40 degrees and the largest angle is 150 degrees.
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16/6 = 3d/9 solving proportions
what expression is equivalent to
5-(6g-7)+5g
Answer:
-g+12
Step-by-step explanation:
The price of a video game was reduced from $70.00 to $40.00. By what percentage was the price of the video game reduced?
Latanya has $1.90 worth of nickels and dimes. She has a total of 24 nickels and dimes altogether. Determine the number of nickels and the number of dimes that Latanya has.
The number of nickels and dimes Latanys have is 10 and 14.
What is an equation?An equation is a mathematical statement of two expressions connected by an equal sign.
We have,
Total coins = 24
$1 = 20 nickels
$1 = 10 dimes
Now,
Number of nickels = N
Number of dimes = D
Now,
N + D = 24 ____(1)
N = 24 - D _____(2)
0.05N + 0.1D = 1.90 ____(3)
Putting (2) in (3) we get,
0.05(24 - D) + 0.1D = 1.90
1.2 - 0.05D + 0.1D = 1.90
0.05D = 1.90 - 1.2
0.05D = 0.7
D = 0.7 / 0.05
D = 14
Now,
N = 24 - D
N = 24 - 14
N = 10
Thus,
The number of nickels is 10.
The number of dimes is 14.
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the area of a rectangle is 105 sq in and the length of one side is 7 in. what is the length of the perimeter?
The length of the perimeter is 44cm if the area of a rectangle is 105sq in and length of one of the side is 7 in.
What is meant by perimeter?A perimeter is a closed path that encompasses, surrounds, or delineates something, whether it be a two-dimensional shape or a one-dimensional length. The outermost border of an ellipse or circle is its circumference.
Knowing the perimeter is helpful in a variety of circumstances. Calculated perimeter refers to the length of fence required to entirely enclose a yard or garden.
Given,
Area of a rectangle=105cm²
And also given that,
Width w=7cm
Area= Length× Width
Length=Area/Width
Length-105/7
Length=15cm
Here, Now we have to calculate the perimeter of a rectangle
Perimeter=2(Width+ Length)
Perimeter=2(7cm+15cm)
Perimeter=44cm.
Hence, the length of the perimeter is 44cm.
Therefore, the length of the perimeter is 44cm if the area of a rectangle is 105sq in and length of one of the side is 7 in.
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Isla sells baked good from her home kitchen. She offers decorated cookies for $15 per dozen and cupcakes for $13 per dozen. It takes her an hour to decorate a dozen cookies, but only 20 minutes to decorate a dozen cupcakes. She would like to make at least $300 per week and not put in more than 20 hours of work per week.
A: Create a system of linear inequalities that fits the situation.
B: Isla just discovered that she is running out of cake mix for the cupcakes and royal icing for the cookies. She can make a maximum of 40 dozen cupcakes and 12 dozen cookies. What are the new inequalities you need to add to your problem?
C: What is the maximum amount of baked goods that she could make? (cupcakes, cookies)
D: How much will she earn if she made the maximum amount of baked goods?
E: How long will it take her to make the maximum amount of baked goods? (minutes and hours)
F: What is the least amount of time she could work and still earn $300? What baked goods would she make?
Answer:
A: The system of linear inequalities that fits the situation is:
15x + 13y >= 300
60x + 20y <= 1200
Where x is the number of dozen cookies and y is the number of dozen cupcakes.
B: The new inequalities that need to be added to the problem are:
x <= 12
y <= 40
C: The maximum amount of baked goods that she could make is:
x = 12
y = 40
D: The amount she will earn if she made the maximum amount of baked goods is:
15x + 13y = 15 * 12 + 13 * 40 = $660
E: The time it will take her to make the maximum amount of baked goods is:
60x + 20y = 60 * 12 + 20 * 40 = 960 minutes = 16 hours
F: The least amount of time she could work and still earn $300 is:
15x + 13y = 300
x + y = 20
Solving this system of equations, we get:
x = 8
y = 12
In this case, she would make 8 dozen cookies and 12 dozen cupcakes in a minimum of 8 hours.
Step-by-step explanation:
Please help!! Thank you!!
Answer:
The cellular plan allows you to use 4 gigabytes and charges you a flat $90. After 4 gigabytes have been used then, every gigabyte after that is an extra $20.
the following measurements from yaw marks left at scene of an accident were taken by law enforcement officers. using a 31 ft-long chord, the middle ordinate measured approximately 3ft. the drag factor of the road surface was determined to be 1.13. determine the radius of the yaw mark to the nearest tenth of a foot. determine the minimum speed that the car was going when the skid occurred to the nearest tenth.
The yaw mark's radius is 11.2 feet, or one foot to the nearest tenth.
11.1634 miles per hour is considered the minimum speed.
what is yaw marks?Yaw marks are always curved. They are, initiated by a steering input. They're the remains of a tire that's still moving while also slapping sideways.
Using a chord and middle ordinate, you can calculate the radius using the following formula:
We must apply the algorithm to get the yaw mark's radius.
where the middle ordinate is m and the chord's length is c
With a 31 foot chord and a 3 foot middle ordinate, the tires leave a yaw mark.
so,
[tex]r^{2}=\frac{31^{2} }{8*3} + \frac{3}{2}[/tex]
[tex]r^{2} =[/tex] 40.041 + 1.5
[tex]r^{2}[/tex] = 41.041
We will now apply the following formula to get the minimum speed:
where 'f' is the drag factor and 'r' is the radius
0.2 is the drag factor, hence f=0.2
and r=41.541 feet
[tex]s= \sqrt{15*0.2*41.041}[/tex]
[tex]s=\sqrt{124.623}[/tex]
s= 11.1634 mph
11.1634 miles per hour was the lowest speed at which the brakes could be applied.
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4. What is the ratio of the sides for triangle HIL?
The ratio of the sides for triangle HIL is 1:1:√3.
What is Triangle?A triangle is a three-sided polygon that consists of three edges and three vertices.
We need to find the ratio of HIL triangle.
In the triangle JKL, IL is perpendicular to the JH.
At I the angle is 90 degrees.
The length of JI is 11cm.
The angle of JKL is x degrees.
JK is 22 cm and the angle of ILJ is y degrees.
the ratio of the sides for triangle HIL is 1:1:√3.
Hence, 1:1:√3 is the ratio of the sides for triangle HIL
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HELP
A=1
b=2
c=3
d=4
e=5
f=6
g=7
h=8
i=9
j=10
k=11
Answer:
x = -15
Step-by-step explanation:
[tex]\frac{x - 9}{3}[/tex] = -8 Multiply all the say through by 3
x - 9 = -24 Add 9 to each sides
x = -15
In a city, there are 16 swimming pools. On weekends, 6 of the pools are open.
George says the ratio of pools open on weekends to the total number of pools is 6:16.
Emma says the ratio of pools open on weekends to the total number of pools is 6:10.
Which student is correct? PLEASE....... Explain.
The student that is correct is George as the ratio of pools open on weekends to the total number of pools is 6:16.
What is the ratio?Ratio is the relationship between two or more numbers. It is the number of times that one value is contained within other value(s). The sign that is used to represent ratio is :.
In order to determine the ratio between the number of pools open on the weekend to the total number of pools express the numbers that represent each value as ratios.
This will be:
= number of pools open on weekends: total number of pools
= 6 : 16
George is correct.
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Which must be true? line segment a n is-congruent-to line segment l b line segment n c is-congruent-to line segment b z anglebmz is-congruent-to anglecmz anglezbm is-congruent-to anglezcm
The lines or angles with measure must be true for the lines and angles.
To predict the truthfulness of the statements, we must understand the concept of congruency. Any two entities will be congruent if they measure the same. In the question, the line AN will be congruent to line segment LB and line NC will be congruent to line BZ.
Similarly, the angle measurements should also be same to the angles to be congruent. In case of same angles, the Angle BMZ will be congruent to Angle CMZ and Angle ZBM will be congruent to Angle ZCM.
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Answer: D
Step-by-step explanation:
The novel is 216 pages long. If Sergio continues to read at the same rate, how long will it take him to finish reading the entire novel
please help asap thank u so muchhh
The answer is 7h and 12m
Step-by-step explanation:
To solve for time, divide the distance traveled by the rate. For example, if Sergio continues reading the total of 216 pages, then he had finish reading for 7 hours and 12 minutes!
How do you find the center and scale factor of a dilation?
Center point of dilation is a fixed point in a plane about which all the points of the figure expanded or contract. And scale factor of a dilation is the ratio of new formed image to the old given image.
Explanation:
Center of a dilation is considered as a fixed point in the given plane.Around the center point of dilation all the points of the given and new figure expanded or contracts.Translate the center of dilation and the given figure , now origin becomes the center and translate back to get the center of dilation.Scale factor can be calculated as the ratio of the dimension of the new image formed to the dimensions of the old given image.If new or old images not defined then ratio of larger to the smaller image gives the scale factor.Therefore, the center of the dilation can be find using the translation and scale factor can be calculated using the ratio of the new to the old images.
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6.2.9 Check Your Understanding
The University of Florida has a surf club. Assuming it has 11 females and 12 males and h represents the
height of a team member, the inequality, 300 < 5.25h-15 ≤ 368.25, represents the range of heights of
the surfers, in inches.
Select all possible heights for the University of Florida's Surf Club.
The possible heights of the students in the surf club will be -
73 inches ≥ h > 60 inches
What is a function? What is equation modelling? What is a mathematical equation and expression?In mathematics, a function from a set X to a set Y assigns to each element of X exactly one element of Y. The set X is called the domain of the function and the set Y is called the codomain of the functionEquation modelling is the process of writing a mathematical verbal expression in the form of a mathematical expression for correct analysis of the given problem.A mathematical expression is made up of terms (constants and variables) separated by mathematical operators.A mathematical equation is used to equate two expressions.
Given is the University of Florida that has a surf club. It has 11 females and 12 males and [h] represents the height of a team member.
The given inequality is -
300 < 5.25h - 15 ≤ 368.25
So, we can write -
5.25h - 15 > 300
5.25h > 315
h > (315/5.25)
h > 60 inches
and
5.25h - 15 ≤ 368.25
5.25h ≤ 368.25 + 15
5.25h ≤ 383.25
h ≤ 73 inches
So, we can write the range as -
73 inches ≥ h > 60 inches.
Therefore, the height range of the students in the surf club will be between 73 inches ≥ h > 60 inches.
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defined by miles as ""a requirement of the activities of one subunit that is affected by the activities of other subunits"" is a _________.
A contingency is defined by miles as " a requirement of the activities belongs to one subunit which is affected by the activities of other subunits.
Step to Step Explanation:
Contingency is a noun which represent the chances of fulfillment of an activity.Contingency represents the activity may or may not happen .It is dependable activity.Requirement of one activity belongs to one subunit may affect the subunits of other activities.Example: you want to buy a home but due to certain conditions in future you are unable to purchase.Therefore, the contingency is defined by miles as " a requirement of the activities of one given subunit which is affected by the activities of other subunits.
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There were 425 guests at a hotel. 170 guests ordered food. What percentage of the guests ordered food?
A lion weighs 7 times as much as a leopard. The combined weight of the cats is 480 pounds. What is the weight of each cat?
Answer:
Leopard: 60 lb
Lion: 420 lb
Step-by-step explanation:
Let x = weight of leopard.
Weight of lion = 7x.
Sum of the weights = x + 7x = 8x
Total weight = 480 lb
8x = 480
x = 60
7x = 7 × 60 = 420
Answer:
Leopard: 60 lb
Lion: 420 lb
Answer: shown below
Step-by-step explanation:
x = 7y
x+y+ 480
7y+y = 480
8y = 480
y = 480/8 = 60 pounds for the leopard
x = 7(60) = 420 pounds for the lion
Two mountain bikers leave from the same parking lot and head in opposite directions on two different trails. The first rider goes 8 km due East, then rides due south for 15 km. The second rider goes 8 km due West, then changes direction and rides 20 degrees west of due north for 15 km. (See the picture below.) Both riders have been traveling for 23 km, but when they stopped, which one was further away from the parking lot?
When both riders have stopped, the person that is further away from the parking lot is; The second rider.
How to use Pythagoras theorem and law of cosine?Let the required distance be represented by x.
Using Pythagoras theorem, we have:
hypotenuse² = opposite² + adjacent²
x = √(8² + 15²)
x = √289
x = 17 km
This means that the first biker is 17.0 km from the starting point.
Using the law of cosine which is given by the expression;
c² = a² + b² - 2ab cos C
x² = 8² + 15² - 2(8*15) cos (160)
x = 20.22 km
This means that the second biker is 20.22 km from the starting point.
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The tangent of O in this triangle is Which equation must be true? (MGSE9-
12.G.SRT.8)
a®
19°
A. sin a = 2
B. tan a = 2
C. sina = 1/2
D. . tan a = 1/2
The correct answer is option D, which states tan∝ = 1/2
What is Trigonometry?
The field of mathematics concerned with the relationships between triangle sides and angles, as well as the pertinent functions of any angles is Trigonometry.
Solution:
we are given that tanθ = 1/2
this implies θ = 45°
We know that the sum of all interior angle of triangle is 180°
so, it can be calculated that the value of
angle ∝ = 45°
Therefore, tan∝ = 1/2
The correct answer is option D, which states tan∝ = 1/2
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Is dilate getting bigger or smaller?
The dilation will change the size of the figure, so it can be getting bigger or smaller
The dilation is the process of changing the size of the figure, but the shape of the figure will be same. Therefore we can say that the dilation is one form of the transformation of the figure
The dilation can be increase the size or decrease the size
If you consider the case of dilation with scale factor, when the scale factor is greater than 1 the size will be bigger and if the scale factor is between 0 and 1 the size will be smaller than original size
Therefore, the dilation can be getting bigger or smaller
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