Answer:
Hence the expression [tex]$(y+7)(y+4)=y^{2}+11 y+28$[/tex]
Step-by-step explanation:
- The given expression is (y+7)(y+4).
- We have to multiply the given expression.
- Multiply the (y+7) by 4 , multiply the (y+7) by y then add like terms.
[tex]\begin{array}{r}y+7 \\\underline {\times \quad y+28} \\4 y+28 \\\underline {y^{2}+7 y }\\y^{2}+11 y+28\end{array}[/tex]
Suppose A and B are 2x2 matrices and that AB = BA =
which of the following statements is correct?
Based on the matrices given, the true statement on matrices AB = BA is A. A⁻¹ = ¹/₃B.
What is true on AB = BA?If:
AB = BA = [3 0]
[0 3]
Then:
AB = BA = 3 [1 0]
[0 1]
This can be further written as:
AB = BA = 3I₂
And again as:
A (¹/₃ B) = I
This then allows us to either write this as:
A⁻¹ = ¹/₃ B
Or:
B⁻¹ = ¹/₃ A
In conclusion, option A is correct.
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Which of the following systems of linear inequalities is represented by the
solution graphed below?
The inequalities represented by the graph are; y > -1 and y <= -x.
What are the inequalities described by the graph?The graph as shown in the task content includes the horizontal line; y = -1 and the line; y = -x.
However, the area shaded in the graph coincides with the upper area of y = -1 with broken lines as boundary and the lower area of line; y = -x with a solid boundary line.
Ultimately, the graph represents the inequalities y > -1 and y <= -x.
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Answer:The inequalities represented by the graph are; y > -1 and y <= -x.
What are the inequalities described by the graph?
The graph as shown in the task content includes the horizontal line; y = -1 and the line; y = -x.
However, the area shaded in the graph coincides with the upper area of y = -1 with broken lines as boundary and the lower area of line; y = -x with a solid boundary line.
Ultimately, the graph represents the inequalities y > -1 and y <= -x.
Step-by-step explanation:
In a right triangle, a and b are the lengths of the legs and c is the length of the hypotenuse. If a=21 miles and c=75 miles, what is b? If necessary, round to the nearest tenth.
Answer:
C = 29.7
Step-by-step explanation:
Remember to use a^2 + b^2 = c^2
21^2+ 21^2 = c^2
441 + 441 = c^2
882 = c^2
you square root both sides
c= 29.6984
Round it
C = 29.7
how did the temperature change if it decreased by 60% and then increased by 80%
Answer:
The temperature decreased by 28%
Step-by-step explanation:
How did the temperature change if :
At first it decreased by 60%
Then increased by 80%
Assume that the temperature before decreasing is 100%
∵ The temperature before decreasing = 100%
∵ It decreased by 60%
→ Before decreasing : decreasing : after decreasing
→ 100% : 60% : 100% - 60% = 40%
∴ The temperature after decreasing = 40%
Assume that the temperature after decreasing is 100%
∵ The temperature after decreasing = 100%
∵ It increased by 80%
By using the ratio method
→ After decreasing : increasing : after increasing
→ 100% : 80% : 100% + 80% = 180%
→ 40% : : x%
By using cross multiplication
∴ 100% × x% = 40% × 180%
- Divide both sides by 100%
∴ x% =
∴ x% = 72%
∵ At first the temperature = 100%
∵ At last the temperature = 72%
∵ The first the temperature > the last the temperature
∴ The decreasing in temperature = 100% - 72% = 28%
GEOMETRY HELP ME PLS PLS!!!! THE FOLLOWING ROMBUS!!
Answer:
12
Step-by-step explanation:
Diagonals of a rhombus bisect each other at right angles, so in triangle JNK, we have JK=20 and JN=16.
Using the Pythagorean theorem, it follows that KN = 12.
is 4(2r-1)=-2(3r+16) a no solution or infinite solutions
Answer: Infinite
Step-by-step explanation:
Answer:
one solution, r = - 2
Step-by-step explanation:
4(2r - 1) = - 2(3r + 16) ← distribute parenthesis on both sides
8r - 4 = - 6r - 32 ( add 6r to both sides )
14r - 4 = - 32 ( add 4 to both sides )
14r = - 28 ( divide both sides by 14 )
r = - 2
What is the slope of the line represented by the equation y=x/6 −5 ?
−5
1/6
5/6
6
Answer:
slope is the gradient(coefficient of (x) in the equation .We have [tex] \frac{x}{6} [/tex]which can also be written as [tex] \frac{1}{6} x \: therefore \: the \: slope \: is \: \frac{1}{6} [/tex]Answer:
1/6
Step-by-step explanation:
Solution:
The given equation is:y=x/6 -5
arranging the equation :x/6-y=5
Given,
Coefficient of x=1/6
coefficient of y=-1
So,
Slope(m)=-(Coefficient of x/coefficient of y))
= -(1/6 / -1) {minus divided by - becomes plus }
1 by 6 whole divide by 1
= 1/6 ans✓
The concession stand at a local high school sells nachos for $4 each and popcorn for $2 each. At the next event, the manager of the stand expects sales of a minimum of 100 items, totaling at least $225. Let x represent the number of nachos sold and let y represent the number of popcorn sold. Which of the following systems correctly represents the scenario?
The system of inequalities that correctly represents this scenario is given by:
[tex]x + y \geq 100[/tex].[tex]4x + 2y \geq 225[/tex].What is a system of inequalities?A system of inequalities is when two or more variables are related, and inequalities are built to find the values of each variable.
In this problem, the variables are given as follows:
Variable x: number of nachos sold.Variable y: number of popcorn sold.The manager of the stand expects sales of a minimum of 100 items, hence:
[tex]x + y \geq 100[/tex].
The concession stand at a local high school sells nachos for $4 each and popcorn for $2 each. The manager wants a total of at least $225, hence:
[tex]4x + 2y \geq 225[/tex]
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Susan's Coffee Shop makes a blend that is a mixture of two types of coffee. Type A coffee costs Susan $5.45 per pound, and type B coffee
costs $4.05 per pound. This month's blend used three times as many pounds of type B coffee as type A, for a total cost of $633.60. How
many pounds of type A coffee were used?
The amount in pounds of Type A coffee used is 36 pounds.
Using equation to find the number of pounds?Type A coffee costs Susan $5.45 per pound, and type B coffee
costs $4.05 per pound.
Therefore,
Let x = the number of pounds of Type A coffee.
total pounds = x + 3x
total cost = 5.45(x) + 3x(4.05)
633.60 = 5.45(x) + 3x(4.05)
633.60 = 5.45x + 12.15x
633.60 = 17.6x
divide both sides by 17.6
x = 633.60 / 17.6
x = 36
Pounds of Type A coffee used = 36 pounds
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Dylan examines 10 different brands of yogurt. He lists the amount of yogurt in one container of each brand to the nearest 18 of a cup. The results are recorded in this frequency table. Create a line plot to display the data. To create a line plot, hover over each number on the number line. Then click and drag up to plot the data.
The attached graph represents the line plot of the dataset
How to create the line plot?The frequency table is given as:
Amount 3 3.5 4 4.5 5
Frequency 1 2 3 3 1
To create the line plot, we represent the frequency by dots.
Take for instance:
The amount 3 will be represented by 1 dot because it has a frequency of 1The amount 3.5 will be represented by 2 dots because it has a frequency of 2See attachment for the line plot
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PLEASE HEELPPPPPP
in circle A, AT = AE =7cm & BR= 48 CM
FIND AS
Answer:
Step-by-step explanation:
Comments
AE = AT = 7 Given
AT is a perpendicular bisector of OS Property of a circle
AE is a perpendicular bisector of BR Property of a circle
ER = 1/2 BR = 48/2 = 24 Property of a bisector
TS = ER Property of a bisector and chord
TS = 24 ER = 24 so TS = 24
AS^2 = TS^2 + TA^2 Pythagorean Theorem + rt angle
AS^2 = 24^2 + 7^2 Substitute values
AS^2 = 576 + 49 Combine
AS^2 = 625 Take sqrt of both sides
√AS^2 = √625
AS = 25
Answer
AS = 25
-10 -8 -6 -42
10
8
6
41
2
-2
-4
-6
-8
+10
y
2
4 6 8 10
x
Study th
to find its
The equ
Answer: [tex]y=x+2[/tex]
Step-by-step explanation:
The slope is
[tex]\frac{0-2}{-2-0}=1[/tex]
since the y-intercept is 2, the equation is [tex]y=x+2[/tex]
A man is dealt 4 spade cards from an ordinary deck of 52 cards. If he is given five more, what is the probability that none of them are spades
The probability that none of them are spades is c(39,5) / c(48,5).
Probability is without a doubt how probable something is to show up. whenever we are uncertain about the final results of an occasion, we can talk about the possibilities of sure outcomes and how probable they are. The analysis of events governed by opportunity is referred to as records.
A chain of moves in which the results are usually unsure. The tossing of a coin, selecting a card from a deck of playing cards, throwing a cube. occasion. it is a single final result of an experiment. Getting a Head whilst tossing a coin is an event.
Simple chance is the calculation of an outcome or the chance of an event ever taking place. Coverage companies use possibility statistics to determine the possibility of having to pay out a declaration. A simple chance is calculated by way of dividing a particular outcome by all of the feasible outcomes.
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If a and b are integers such that -6
a x b?
(A)-36
(B)-30
(C)-24
(D)-12
Does this graph show a function? Explain how you know.
• A. Yes; the graph passes the vertical line test.
• B. No; there are y values that have more than one x-value.
• C. No; the graph fails the vertical line test.
• D. Yes; there are no y-values that have more than one x-value.
The graph doesn't show a function as C. No; the graph fails the vertical line test.
What is a graph?It should be noted that a graph is the diagrammatic representation of data.
In this case, the graph doesn't show a function as the graph fails the vertical line test.
The vertical line test is a visual way that's uses to determine if the curve is a graph of the function.
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pls help me answer this
Diagram 3 shows a composite solid, formed by joining a half m-cylinder with a right prism. ABKJ is the cross - section of the right prism. MK is the diameter of the half - cylinder Given BK 28 cm, AJ = 14 and AE = 20 cm, The volume of the composite solid is 17000 cm³
Using
[tex]\pi = \frac{22}{7} [/tex]
calculate the value of h
Answer: 30 cm
Step-by-step explanation:
The volume of the composite solid is 17000 cm³. To find h, we must first subtract the volume of the half cylinder from the composite volume.
From the figure, AE = MK, and so the radius of the half cylinder is 10cm. The volume of the half cylinder is thus [tex]\frac{1}{2}[/tex] the volume of a cylinder. The volume of a cylinder is πr²h. So a half cylinder is 1/2 πr²h. This gives us a volume of [tex]\frac{1}{2} (\frac{22}{7})(10 cm)^2(28 cm) = 4400 cm^3[/tex].
Thus, the volume of the right prism is 17000cm³ - 4400cm³ = 12600cm³. Consider the cross-section ABKJ. If we multiply this by AE, we'll have the volume of the right prism.
The ABKJ is a trapezoid so it's area is [tex]\frac{1}{2}(AJ + BK) \cdot AB[/tex]. Thus the volume of the right prism is [tex]\frac{1}{2}(AJ + BK) \cdot AB \cdot AE[/tex]. This gives us [tex]\frac{1}{2}(28 + 14) \cdot h \cdot 20 = 12600[/tex], and thus h = 30 cm.
The point-slope form of the equation of of the line that passes through (-4, -3) and (12, 1) is y - 1 = 1/4(x - 12). What
is the standard form of the equation for this line?
O x- 4y = 8
O x-4y=2
O 4x-y= 8
O 4x-y=2
Answer: [tex]\frac{1}{4}[/tex]x - y = 2
Step-by-step explanation:
Standard form is Ax + By = C where A, B, and C, are integers.
Given:
y - 1 = 1/4(x - 12)
Distribute:
y - 1 = [tex]\frac{1}{4}[/tex]x - 3
Add 3 to both sides of the equation:
y + 2 = [tex]\frac{1}{4}[/tex]x
Subtract y from both sides of the equation:
2 = [tex]\frac{1}{4}[/tex]x - y
Apply the reflexive property:
[tex]\frac{1}{4}[/tex]x - y = 2
Geometry question I need help with this one
First part;
Following the transformation (x, y) → (3•x, 2•y), the images are;
A'(9, 10), B'(15, 6), C'(6, 4)
Second part;
The distance between points A and B is 2•√2 which is different from the distance between the image A' and B' which indicates that the transformation is a non rigid transformation.
How can the images and the type of transformation be found?First part;
The given points are;
A(3, 5), B(5, 3), C(2, 2)The given transformation is presented as follows;
(x, y) → (3•x, 2•y)
Therefore, the images are;
A(3, 5) → A'(3 × 3, 2 × 5) = A'(9, 10)
B(5, 3) → B'(3 × 5, 2 × 3) = B'(15, 6)
C(2, 2) → C'(3 × 2, 2 × 2) = C'(6, 4)
A(3, 5) → A'(9, 10)B(5, 3) → B'(15, 6)C(2, 2) → C'(6, 4)Second part;
Length of AB = √((5-3)² + (3-5)²) = 2•√2
Length of A'B' = √((15-9)² + (6-10)²) = 2•√13
2•√2 ≠ 2•√13AB ≠ A'B'Given that the length of AB ≠ the length of A'B' then we have;
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The points of the image are (9, 10), (15, 6) and (6, 4) and the resulting image is a nonrigid motion.
How to determine the image of the points?The points are given as:
A = (3, 5)
B = (5, 3)
C = (2, 2)
The transformation is given as:
(x, y) ⇒ (3x, 2y)
So, we have:
A' = (9, 10)
B' = (15, 6)
C' = (6, 4)
Hence, the image of the transformation is (9, 10), (15, 6) and (6, 4)
See attachment for the image
Also, the resulting image is a nonrigid motion.
This is so because the lengths of the image and the preimage are not equal
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given cos data = 0.7620, approximate the acute angle to the following
a. the nearest 0.01
The acute angle is 40.40 degrees
How to determine the acute angle?The cosine of the angle is given as:
cos(x) = 0.7620
Take the arc cos of both sides
[tex]x = \cos^{-1}(0.7620)[/tex]
Evaluate the arc cos
x = 40.359
Approximate
x = 40.40
Hence, the acute angle is 40.40 degrees
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Which is the equivalent expression of 78?
2 × (10 × 3 + 32)
2 × (13 + 32)
(10 × 3 + 32)
2 × (10 × 3 + 3)
None of the expressions is equivalent to 78
How to determine the equivalent expression?The number is given as:
Number = 78
Next, we evaluate the expressions in the options using a calculator
2 × (10 × 3 + 32) = 124
2 × (13 + 32) = 90
(10 × 3 + 32) =62
2 × (10 × 3 + 3) = 66
None of the options equals 78
Hence, none of the expressions is equivalent to 78
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Rectangle ABCD is congruent to rectangle URST.
Rectangles A B C D and U R S T are congruent. The length of sides A B is 9 millimeters and the length of sides R S is 15 millimeters.
What is the area of rectangle URST?
24 mm
48 mm
135 mm2
The area of the rectangle URST is 135 mm². so the option C is correct.
What are Congruent rectangles?Congruent rectangles have the same lengths of sides, same measures of angles and same areas and same perimeters
The Rectangle ABCD is congruent to rectangle URST
Given; Rectangle ABCD ≅ rectangle URST
AB = UR , BC = RS , CD = ST , AD = UT
AB = 9 millimeters
UR = 9 millimeters
We know that, The area of any rectangle = l × w,
In rectangle URST
∵ UR = 9 millimeters
∵ RS = 15 millimeters
- Assume that UR = l and RS = w
The area of rectangle URST = UR × RS
The area of rectangle URST = 9 × 15 = 135 millimeters²
Hence, The area of rectangle URST is 135 mm²
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choosing a spade, not replacing it, then choosing a jack
Answer:
Probability means Possibility. It states how likely an event is about to happen. The probability of an event can exist only between 0 and 1 where 0 indicates that event is not going to happen i.e. Impossibility and 1 indicates that it is going to happen for sure i.e. Certainty.
The higher or lesser the probability of an event, the more likely it is that the event will occur or not respectively. For example – An unbiased coin is tossed once. So the total number of outcomes can be 2 only i.e. either “heads” or “tails”. The probability of both outcomes is equal i.e. 50% or 1/2.
(01.04 LC)Multiply negative 1 over 6 multiplied by negative 1 over 5. negative 1 over 11 negative 1 over 30 1 over 30 1 over 11
The expression is -1/6 x (-1/5) = 1/30.
What is expression?An expression or mathematical expression is a finite combination of symbols that is well-formed according to rules that depend on the context.
Given:
negative 1 over 6 multiplied by negative 1 over 5.
As per the data,
if -1/6 is multiplied with -1/5 then the resultant value will be
=-1/6 * -1/5
= 1/5*6
=1/30
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suppose g(x)=f(x+2)-3 wich statement best compares the graph of g(x) with the graph of f(x)
Answer:
xyucyxxhc9gohjpbkvicucucuc7vucuc7cucuc7cuvuv8v8
Step-by-step explanation:
q+++
55. TECHNOLOGY
If f is a linear function, f(0.1) = 11.5, and f(0.4) = -5.9, find an equation for the function.
Considering the expression of a line, the equation for the function that is represented through the points f(0.1) = 11.5, and f(0.4) = -5.9 is y= -58x +17.3.
Linear equation o lineA linear equation o line can be expressed in the form y = mx + b.
where
x and y are coordinates of a point.m is the slope.b is the ordinate to the origin and represents the coordinate of the point where the line crosses the y axis.Knowing two points (x1, y1) and (x2, y2) of a line, the slope m of said line can be calculated using the following expression:
[tex]m=\frac{y2-y1}{x2-x1}[/tex]
Substituting the value of the slope m and the value of one of the points in the expression of a linear equation, y = mx + b, the value of the ordinate to the origin b can be obtained.
Equation for the function in this caseIn this case, the function f(x) is represented through the points f(0.1) = 11.5, and f(0.4) = -5.9. This is:
(x1, y1)= (0.1, 11.5) (x2, y2)= (0.4, -5.9)So, the slope m can be calculated as:
[tex]m=\frac{-5.9-11.5}{0.4-0.1}[/tex]
Solving:
m= -58
Considering point 1 and the slope m, you obtain:
11.5= -58×0.1 +b
11.5= -5.8 + b
11.5 + 5.8= b
17.3= b
Finally, the equation for the function that is represented through the points f(0.1) = 11.5, and f(0.4) = -5.9 is y= -58x +17.3.
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In the diagram below, ΔPQR ≅ ΔSTR. Complete the statement RQ⎯⎯⎯⎯⎯⎯⎯⎯≅ R Q ¯ ≅ ___
Based on the CPCTC theorem, the complete statement is: RQ ≅ RT.
What is the CPCTC Theorem?According to the CPCTC theorem, if two triangles are said to be congruent, then all the corresponding parts of both triangles are congruent.
Given that ΔPQR ≅ ΔSTR, RQ corresponds to RT. Therefore, both sides are congruent to each other.
Thus, the complete statement is: RQ ≅ RT.
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A sock drawer contains 5 different colors of socks. it has 20 white, 10 black, 6 red, and 4 purple. if you reach into the drawer and choose a sock randomly, what is the probability you will get a a black sock? (write your final answer as a fraction.)
The probability of selecting a black sock is 1/4.
What is the required probability?The area of mathematics known as probability deals with numerical representations of the likelihood that an event will occur or that a statement is true. An event's probability is a number between 0 and 1, where, roughly speaking, 0 denotes the event's impossibility and 1 denotes certainty. It is more likely that an event will occur if its probability is higher.
Number of white socks=20
Number of black socks=10
Number of red socks=6
Number of purple socks=4
Total number of socks=20+10+6+4
=40
Probability of getting a black sock=Number of black socks/Total number of socks
=10/40
=1/4
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Riddle-if you solve it i will delete your answer and you have to post the riddle. Riddle-you enter a room. 2 dogs, 4 horses, 1 giraffe and a duck are lying on the bed. 3 chickens are flying over a chair. How many legs are on the ground? don’t play if you’re not to continue.
Answer:
28
Step-by-step explanation:
please help! i will give u 20 points I need the answer with the method
Answer:
6 mm
Step-by-step explanation:
So, the area he needs to fill isn't really important, you don't need to calculate it. What is necessary is the individual dimensions of that area (width/length). The width and the length must be divisible by the lengths of the tiles. This is so you don't need to cut anything. For example let's say the area needed to be filled was 15 mm (width) by 10 mm (length). If I chose 3mm square tiles, it could perfectly fill up the width, but when it came to the length there would be a small 1 mm gap. And you would need to cut one of the square tiles, so it would have a length of 1 mm. In this case the 15mm was divisible by 3, but the 10 mm wasn't. So using this logic, it can't be the 4 mm square tile since 150mm / 4 mm = 37.5. It can be the 6m since 150mm / 6mm = 25 and 180 mm / 6mm = 30. It can't be the 8 mm since 150 mm / 8mm = 18.75 mm
if ace had 6 grapes and he gave 3 to mason how many will he have left
Answer:
its 3 grapes
Step-by-step explanation:
6-3=3 therefore the answer is 3
Answer:
3 grapes are left
Step-by-step explanation:
if you subtract 3 from 6 (6 - 3) you will find the answer you need to find how many grapes you have left.