Answer:
(6,-1)
Step-by-step explanation:
The ordered pair on the line will have the same slope. To find this, substitute the original point (-2,5) and each listed point into the slope formula. Simplify to see if the slope is the same.
[tex]m = \frac{y_2-y_1}{x_2-x_1} = \frac{-1 - 5}{6 --2} = \frac{-6}{8} = -\frac{3}{4}[/tex]
The pair (2,8) gives a slope of 3/4.
The pair (-5,1) gives a slope of 4/3.
The pair (1,1) gives a slope of -4/3.
The solution is (6,-1).
Show that sin (x + pi) = -sin x.
Answer:
The answer in the procedure
Step-by-step explanation:
we know that
[tex]sin(A + B) = sin A cos B + cos A sin B[/tex]
In this problem we have
[tex]sin(x + \pi)=sin (x)cos(\pi) + cos(x)sin(\pi)[/tex]
Remember that
[tex]sin(\pi) = 0[/tex]
[tex]cos(\pi) = -1[/tex]
substitute
[tex]sin(x + \pi) = sin(x)(-1) + cos(x)(0)[/tex]
[tex]sin(x + \pi) = -sin(x)[/tex]
Final answer:
To prove that sin (x + π) = -sin x, the trigonometric identity for the sine of a sum is used, and by considering the specific values for cos π and sin π, the identity simplifies to the required expression.
Explanation:
To show that sin (x + π) = -sin x, we can use the trigonometric identity for the sine of a sum:
sin (α + β) = sin α cos β + cos α sin β
Applying this identity to sin (x + π):
sin (x + π) = sin x cos π + cos x sin π
Since cos π = -1 and sin π = 0, we substitute these values:
sin (x + π) = sin x (−1) + cos x (0)
sin (x + π) = −sin x + 0
Hence, sin (x + π) = −sin x, demonstrating the original statement.
Find the radius of a circle with a circumference of 35 π yards
Answer:
17.5 yds because Radius is half of the circumference
Step-by-step explanation:
The radius of the circle with a circumference of 35 π yards is 17.5 yards.
Circumference of a circle:The circumference of a circle is the perimeter of a circle. Therefore,
circumference = 2πrwhere
r =radius
Therefore,
circumference = 35πyard
35π = 2πr
divide both sides by 2π
35π / 2π = 2πr / 2π
r = 17.5 yards
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. Evaluate the following expression: 24 ÷ 3 + 7 ⋅ 2 – 15 ÷ 5 + 6 ⋅ 2 A. 31 B. –31 C. 30 D. 21
To evaluate the expression, we follow the order of operations (PEMDAS). The result of the expression is 31.
Explanation:To evaluate the expression 24 ÷ 3 + 7 ⋅ 2 – 15 ÷ 5 + 6 ⋅ 2, we need to follow the order of operations, also known as PEMDAS. PEMDAS stands for Parentheses, Exponents, Multiplication and Division (from left to right), and Addition and Subtraction (from left to right).
First, we perform the division: 24 ÷ 3 = 8.Next, we perform the multiplication: 7 ⋅ 2 = 14 and 6 ⋅ 2 = 12.Now, we can write the expression with the values we found: 8 + 14 - 15 ÷ 5 + 12.Then, we perform the division: 15 ÷ 5 = 3.Finally, we perform the addition and subtraction from left to right: 8 + 14 - 3 + 12 = 31.Therefore, the evaluated expression is equal to 31.
identify the center and the radius of a circle with equation (x-4)^2+(y+2)^2=9
Answer:
center:(4,-2)
Radius: 3 units
Step-by-step explanation:
The standard equation of a circle is given as [tex](x-h)^2+(y-k)^2=r^2[/tex], where (h,k) is the center and r is the radius of the circle.
The given equation is [tex](x-4)^2+(y+2)^2=9[/tex].
We compare to the standard equation of the circle to get;
[tex]x-h=x-4[/tex]
[tex]\Rightarrow -h=-4[/tex]
[tex]\Rightarrow h=4[/tex]
and
[tex]y-k=y+2[/tex]
[tex]\Rightarrow -k=2[/tex]
[tex]\Rightarrow k=-2[/tex]
Hence the center of the circle is (4,-2).
Also, we have [tex]r^2=9[/tex]
Therefore [tex]r=\sqrt{9}[/tex]
[tex]r=3[/tex] units.
Answer:
Center at (4,-2); radius: 3
Step-by-step explanation:
NEEDED ASAP!
A rectangular prism is 1 1/2 ft long, 2/3 ft wide, and 5/6 ft high. What is the surface area of the prism in square inches? show your work.
♫ - - - - - - - - - - - - - - - ~Hello There!~ - - - - - - - - - - - - - - - ♫
➷ There are 6 surfaces:
2 of them have an area of 84 square inches
2 of them have an area of 37 1/3 square inches
2 of them have an area of 1
You add them all together, and you get:
Final answer:
244 2/3 square inches
✽
➶ Hope This Helps You!
➶ Good Luck (:
➶ Have A Great Day ^-^
TROLLER
The total surface area for the given prism is 808 square inches.
The question asks to calculate the surface area of a rectangular prism in square inches. The dimensions given are 1 1/2 ft (length), 2/3 ft (width), and 5/6 ft (height). To convert these measurements to inches, we multiply by 12 since there are 12 inches in a foot. Thus, the dimensions in inches are:
Length: 1 1/2 ft x 12 = 18 inchesWidth: 2/3 ft x 12 = 8 inchesHeight: 5/6 ft x 12 = 10 inchesTo find the surface area, we calculate the area of each face and then sum them:
Area of the front/back faces: Length x Height = 18 inches x 10 inches = 180 square inches (two faces, so 2 x 180 = 360 square inches)Area of the top/bottom faces: Length x Width = 18 inches x 8 inches = 144 square inches (two faces, so 2 x 144 = 288 square inches)Area of the side faces: Width x Height = 8 inches x 10 inches = 80 square inches (two faces, so 2 x 80 = 160 square inches)Now, add up all the areas of the faces to get the total surface area:
Surface Area = 360 + 288 + 160 = 808 square inches.
Rewrite the quadratic function in standard form and give the vertex f(x)=3x^2-6x-9
Answer:
y=3(x-1)^2-12
Step-by-step explanation:
HELP PLS HELP!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
Answer: C.
Step-by-step explanation:
All we need to do is add all the number together:
Convert to decimals for easier adding:
2.5+2.5+(3.5*5)+4.25+4.25+5.5=36.50km
Now we convert to a fraction: 36.50=36 2/4km
So the answer is 36 2/4km
I really need help with this, my teacher doesn't really teach and I'm stumped again.
Answer:
JMK = 54
JKH = 126
HLK = 90
HJL = 27
LHK = 63
JLK = 27
Step-by-step explanation:
Just use 180 for total angles in each triangle. Vertical angles mean the opposite to 126 is 126 and the other two that make up the inner vertices are (360- 126*2)/2 = 54
So, 126, `16, 54 , 54 are the inner angles in the circle. Just go from there.
Gabriella has $300 in her checking account and $125 in her savings account if Gabriella transferred enough money from my checking account to her savings account to double the savings account balance what is her new checking account balance
Answer:
Step-by-step explanation:
$300-$125=$175
What is a scientifically-based theory on finding perimeter?
Answer:
The concep of rectilinean line between point A and point B.
Search about euclidean laws.
Besr regards
The line between is point A and point B.
Item 1
Plot and connect the points to make a picture.
1 (5,0) 2 (2,−3) 3 (2,−2) 4 (0,−2)
5 (−3,−2) 6 (−3,0) 7 (−3,2) 8 (0,2)
9 (2,2) 10 (2,3)
Which graph represents an exponential function?
Answer:
The first graph.
Step-by-step explanation:
An exponential function has a graph that is a smooth curve; it either increases at an ever increasing rate or decreases at an ever increasing rate.
The only graph that fits these characteristics is the first one.
Answer:
First graph is the exponential function
Step-by-step explanation:
The x value of exponential function is all real numbers
x can take any value positive or negative numbers
In the first graph , as x value increases the graph goes down
The first graph is an exponential function .
Second graph is the cubic function as the graph goes from left and it goes down on the right .
Third graph is an rational function because we have two graph on both sides of vertical asymptote
The fourth graph is not an exponential function as the domain is not all real numbers.
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HELP PLZ (30 POINTS)
Answer: I think 1 or 2
Answer:
4: 3 and 2
5: 1 and 4
You are making identical gift bags using 12 candles and 28 bottles of lotion. What is the greatest number of gift bags you can make with no items left over?
Answer:
I believe the answer would be 4 gift bags.
Step-by-step explanation:
The highest number both numbers can be divided by and get a a whole number is 4. Four is the greatest common factor. So there will be 4 bags with 7 bottles of lotion and 3 candles inn each bag.
Answer:
4Step-by-step explanation:
Factoring the number of items
12 = 4*328 = 4*7Common factor is 4, so the number of gift bags is 4 the greatest
A group of art students are painting a mural on a walls the rectangular wall has dimensions of (6x+7) by (8x+5) and they are planning the mural to be (x+4) by(2x+5). What is the area of the remaining wall after the mural has been painted
Answer:
46x^2 + 73x + 15
Step-by-step explanation:
Expand both equations
Wall = (6x + 7)(8x + 5) = 48x^2 + 56x + 30x + 35 = 48x^2 + 86x + 35
Mural = (x + 4)(2x + 5) = 2x^2 + 5x + 8x + 20 = 2x^2 + 13x + 20
Minus them.
Wall - Mural =
(48x^2 + 86x + 35) - (2x^2 + 13x + 20)
(48x^2 - 2x^2) + (86x - 13x) + (35 - 20)
46x^2 + 73x + 15
Answer:
46x^2 + 73x + 15
Step-by-step explanation:
Expand both equations
Wall = (6x + 7)(8x + 5) = 48x^2 + 56x + 30x + 35 = 48x^2 + 86x + 35
Mural = (x + 4)(2x + 5) = 2x^2 + 5x + 8x + 20 = 2x^2 + 13x + 20
Minus them.
Wall - Mural =
(48x^2 + 86x + 35) - (2x^2 + 13x + 20)
(48x^2 - 2x^2) + (86x - 13x) + (35 - 20)
46x^2 + 73x + 15
What is the volume of the pyramid in cubic inches?
48 and 81 basically you just have to multiply
Answer:
144 cubic inches
Step-by-step explanation:
We are given a diagram of a pyramid with length = 8 inches, height = 9 inches and width = 6 inches.
We are to find the volume of this pyramid.
We know that the formula of volume of a pyramid is given by:
[tex] \frac { l \times w \times h } { 3 } [/tex]
Substituting the given values in the above formula to get:
Volume of pyramid = [tex] \frac { 8 \times 6 \times 9 } { 3 } [/tex] [tex]=\frac{432}{3}[/tex] = 144 cubic inches
In the number 3,657,892 which digit is in the millions place
The number that is in the millions place is 3
The value of each digit in a number is known as the place value. The correct option is C, 3.
What is the place value of a digit in a number?The value of each digit in a number is known as the place value. The 5 in 350, for example, represents 5 tens, or 50, whereas the 5 in 5,006 represents 5 thousand, or 5,000. It is critical that children that while a digit can be the same, its value is determined by its position in the number.
Identification of the place value of a digit in a number:
The place values on the left of the decimal point start as ones, tens, hundreds, and so on.The place value on the right of the decimal point starts from the point and goes to the right as tenths, hundredths and so onThe tens mean multiply by 10The tenth means the tenth part of that digit which is that digit divided by 10The million in a digit is represented by the sixth digit from the right in a number. Therefore, In the number 3,657,892, the digit that is in the millions of places is 3.
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As shown in the diagram of the right triangles below, Triangle: ABC ~ Triangle: DEF, AB = 7x, BC = 4, DE = 7, EF = x. What is thr perimeter of Triangle: DEF to the nearest hundredth?
since triangles are similar
4/x = 7x/7
=》 4/x = x
=》x^2 = 4
=》 x = 2
for right triangles a^2 = b^2+c^2
DF^2 = 7^2+2^2 = 53
=》 DF = 7.28
perimeter of DEF = 7 +2+7.28 = 16.28
what value is equivalent to
Answer:
D
Step-by-step explanation:
An absolute value is measuring how far away the value is from 0.
Since -1/4 is 1/4 away from 0, D is the answer.
Which is more, 1 yard or 64 inches?
Answer:
64 inches
Step-by-step explanation:
12 x 3ft (1yard)=36in
Mrs siebenaller recorded the average number of points a student earned on unit 3 and unit4 quizzes Unit 3 {2,4,2,3,5,2} Unit 4 {5,1,1,5 1,5} a. what is the mean point value for each unit? Please help
Which unit is the largest?
decameter
millimeter
meter
centimeter
A decameter is the longest, as it has a length equal to 10 meters.
Hope this helps!
Answer:
Decameter
Step-by-step explanation:
A decameter = 10 meter
millimeter = 0.001 meter
meter = meter
centimeter = 0.01 meter
Best regars
Define the following terms
a. Dividend
b. Divisor
c. Quotient
d. Remainder
Answer:
Dividend- The number that is divided is called the dividend
Divisor- a number that divides a integer ( It is the number that is divided by the Dividend)
Quotient- is the result when dividing.
Remainder- is the amount that is left over after dividing
Step-by-step explanation:
Example
36 ÷ 6 = 6
36 is the Dividend
6 is the Divisor
6 is the Quotient
No remainder
Hopes this helps!
which of the figures shown above polygons?
Answer:
the one with 5anglesinterior angles are 5What is the value of the expression below? (4/5+3/5)+3.5*5
Step-by-step explanation:
(4/5+3/5)+3.5*5
= 7/5+7/2*5
= 7/5+35/2
= 14/10+175/10
= 189/10
= 18.9
Answer:
The value of the expression is 18.9
Step-by-step explanation:
The expression is:
[tex]\bigg( \frac{4}{5}+\frac{3}{5}\bigg)+3.5\times 5[/tex]
The first step is to solve the parenthesis. As both fractions have the same denominator, the numerators must be added:
[tex]\bigg( \frac{4+3}{5}\bigg)+3.5\times 5[/tex]
[tex]\bigg( \frac{7}{5}\bigg)+3.5\times 5[/tex]
The second step is to perform the division between 7 and 5, it is 1.4:
[tex]1.4+3.5\times 5[/tex]
The third step is to perform the multiplication between 3.5 and 5, it is 17.5:
[tex]1.4+17.5[/tex]
The last step is to perform the sum, it is 18.9:
[tex]1.4+17.5=18.9[/tex]
Thus, the value of the expression is 18.9.
What is the value of the expression |3x-y| + |2y-x| if x= -4 and y= -1?
A. -13
B. -11
C. 11
D. 13
Answer:
D) 13
Step-by-step explanation:
3(-4)=-12+1=-11
2(-1)=-2+4=-2
11+2=13
some of the dimensions, in meters, of a different swimming pool that is a rectangular from the top and trapezoidal from the side are shown. what is the volume, in cubic meters, if the water in the pool when it is completely full?
Answer:
[tex]4,151.25\ m^{3}[/tex]
Step-by-step explanation:
we know that
The volume of the trapezoidal prism (swimming pool) is equal to
[tex]V=BL[/tex]
where
B is the area of the trapezoidal base
L is the length (distance between the two trapezoidal faces)
Find the area B
[tex]B=\frac{1}{2}(4+8)(30.75)=184.5\ m^{2}[/tex]
[tex]L=22.5\ m[/tex]
Find the volume
[tex]V=184.5(22.5)=4,151.25\ m^{3}[/tex]
A frog catches insects for his lunch. The frog likes to eat flies and mosquitoes in a certain ratio, which is shown in the diagram.
The table shows the number of flies and the number of mosquitoes that the frog eats for two lunches.
Based on the ratio, complete the missing values in the table.
Day Flies Mosquitoes
Monday 151515
Tuesday
141414
Disregard Above
Use Picture
Answer:
ON MONDAY: 35 mosquitos.
ON TUESDAY: 6 flies.
Step-by-step explanation:
As you can see in the diagram, the frog eats 3 flies for every 7 mosquitoes (for lunch). Then you can expresed this ratio as following:
3:7 or [tex]\frac{3}{7}[/tex]
Based on the table:
-If the frog eats 15 flies on monday, then the number of mosquitos that it eats can be calculated as following:
[tex]\frac{3}{7}=\frac{15}{mosquitoes}\\\\mosquitoes=\frac{15*7}{3}\\\\mosquitoes=35[/tex]
-If the frog eats 14 mosquitoes on tuesday, then the number of flies that it eats can be calculated as following:
[tex]\frac{3}{7}=\frac{flies}{14}\\\\flies=\frac{14*3}{7}\\\\flies=6[/tex]
Evaluate g(x)= 2/3x + 7 For x=9
A. 9
B. 25
C. 12.5
D. 13
Answer: 13
Step-by-step explanation:
In order to solve this equation you need to replace x with 9.
2/3 x 9 + 7=
6 + 7=
13
Brianna spent a total of $52 on 4 used video games. What was the average cost of a game?
52 divided by 4 then you’ll get 13