Answers
Explanation
Step 1
Vertical angles are formed when two lines intersect each other. Out of the 4 angles that are formed, the angles that are opposite to each other are vertical angles. vertical angles are congruent so
[tex]\begin{gathered} m\angle5=m\angle7\rightarrow reason\text{ vertical angles} \\ \end{gathered}[/tex]Step 1
replace the given values
[tex]\begin{gathered} m\angle5=m\angle7\rightarrow reason\text{ vertical angles} \\ -2(3x-4)=3(x-3)-1 \end{gathered}[/tex]now, we need to solve for x
a)
[tex]\begin{gathered} -2(3x-4)=3(x-3)-1 \\ \text{apply distributive property} \\ -6x+8=3x-9-1 \\ \text{add like terms} \\ -6x+8=3x-10\rightarrow reason\text{ distributive property} \end{gathered}[/tex]b)subtract 3x in both sides( additioin or subtraction property of equality)
[tex]\begin{gathered} -6x+8=3x-10 \\ subtract\text{ 3x in both sides} \\ -6x+8-3x=3x-10-3x \\ -9x+8=-10 \\ \text{subtract 8 in both sides} \\ -9x+8-8=-10-8 \\ -9x=-18 \\ -9x=-18\rightarrow reason\colon\text{ addition and subtraction property of equality} \end{gathered}[/tex]c) finally, divide both sides by (-9) division property of equality
[tex]\begin{gathered} -9x=-18 \\ \text{divide both side by -9} \\ \frac{-9x}{-9}=\frac{-18}{-9} \\ x=2\rightarrow\text{prove} \end{gathered}[/tex]i hope this helps you
Related Questions
Oaks Hardware purchases an extension ladder list priced at $120. It is available at a 15% discount. What is the available price?
Answers
A 15% discount means that the retail price is 85% of the original price.
To calculate said retail price, we'll use a rule of three:
Thereby,
[tex]x=\frac{120\cdot85}{100}\rightarrow x=102[/tex]Therefore, we can conclude that the available price is $102
French cooks usually weigh ingredients. A French recipe uses 225 grams of granulated sugar.How many cups are needed if there are 2 cups of sugar per pound: (Note that you are changingfrom units of weight, grams, to units of volume, cups. There are 453.5 grams/pound)cups
Answers
Given:
The amount of granulated sugar used fo French fries, x=225 g.
1 pound=2cups.
1 pound=453.5g.
Since 1 pound =453.5 g,
[tex]1\text{ g=}\frac{1}{453.5}\text{ pound}[/tex]Therefore, 225 grams can be expressed in pound as,
[tex]\begin{gathered} 225\text{ g=}225\text{ g}\times\frac{\frac{1}{453.5}pound}{1\text{ g}} \\ =\frac{225}{453.5}pound \\ \cong0.496\text{ pound} \end{gathered}[/tex]Since 1 pound =2 cups, we can write
[tex]\begin{gathered} 0.496pound=0.496pound\times\frac{2cup}{1\text{ pound}} \\ =0.992\text{ cups} \\ \cong1\text{ cup} \end{gathered}[/tex]Therefore, 1 cup is needed.
Drag each tile to the correct box.The figures in the graph below can be shown to be similar by a sequence of transformations.Choose the correct sequence of transformations that take figure A to figure B.
Answers
Answer
Rotate 270 degrees clockwise about the origin → Translate 3 units right and 3 units up → Dilate by a scale factor of 3
Step-by-step explanation
Rotation 270 degrees clockwise about the origin transforms the point (x, y) into (-y, x). Applying this rule to the vertices of figure A, we get:
(-5, 5) → (-5, -5)
(-4, 4) → (-4, -4)
(-5, 1) → (-1, -5)
(-4, 1) → (-1, -4)
Translation 3 units right and 3 units up transform the point (x, y) into (x+3, y+3). Applying this rule to the previous points, we get:
(-5, -5) → (-5+3, -5+3) → (-2, -2)
(-4, -4) → (-4+3, -4+3) → (-1, -1)
(-1, -5) → (-1+3, -5+3) → (2, -2)
(-1, -4) → (-1+3, -4+3) → (2, -1)
Dilation by a factor of 3 transforms the point (x, y) into (3x, 3y). Applying this rule to the previous points, we get:
(-2, -2) → (3x-2, 3x-2) → (-6, -6)
(-1, -1) → (3x-1, 3x-1) → (-3, -3)
(2, -2) → (3x2, 3x-2) → (6, -6)
(2, -1) → (3x2, 3x-1) → (6, -3)
These vertices coincide with the vertices in figure B
Solve for basic equation x2x+3=-3x-12
Answers
Solution
We have the following equation:
2x +3 = -3x-12
We can solve for x on this way:
5x = -12-3
5x = -15
Dividing both sides by 5 we got:
x= -3
divide the sum of z and 3 by 7
Answers
Answer:
4 divide the sum of z and 3 by 7
Step-by-step explanation:
z+3=7
or,z=7-3
or,z=4
A flower bed is in the shape of a rectangle. It measures7 yd long and 4 yd wide. Chris wants to use mulch tocover the flower bed. The mulch is sold by the squarefoot. Use the facts to find the area of the flower bed insquare feet.2ftX 5?Conversion facts for length1 foot (ft)1 yard (yd)1 yard (yd)===12 inches (in)3 feet (ft)36 inches (in) i need help with this math problem.
Answers
Answer
252 ft²
Step-by-step explanation
1 yard is equivalent to 3 feet. Using this conversion factor, the equivalence of 7 yd is:
[tex]\begin{gathered} 7\text{ yd =}7\text{ yd}\cdot\frac{3\text{ ft}}{1\text{ yd}} \\ \text{ Simplifying the units:} \\ 7\text{ yd =}\frac{7\cdot3}{1}\text{ ft} \\ 7\text{ yd }=21\text{ ft} \end{gathered}[/tex]Similarly, the equivalence of 4 yards is:
[tex]\begin{gathered} 4\text{ yd }=4\text{ yd}{}\cdot\frac{3\text{ ft}}{1\text{ yd}} \\ 4\text{ yd }=4\cdot3\text{ ft} \\ 4\text{ yd}=12\text{ ft} \end{gathered}[/tex]Therefore, the length of the bed is 21 ft and the width is 12 ft.
Finally, the area of the bed (a rectangle) is calculated as follows:
[tex]\begin{gathered} A=legnth\cdot width \\ A=21\cdot12 \\ A=252\text{ ft}^2 \end{gathered}[/tex]What’s the correct answer answer asap for brainlist
Answers
Answer:
Answer is B. Harding, Coolidge, and Hoover
:)
Write a linear function f with f(0) = 3.75 and f(-6) =3.75
f(x) = ???
Answers
The linear function will be;
⇒ f (x) = 3.75
What is an expression?
Mathematical expression is defined as the collection of the numbers variables and functions by using operations like addition, subtraction, multiplication, and division.
Given that;
The values are,
⇒ f (0) = 3.75
And, f (-6) = 3.75
Now,
Let the linear function is,
f (x) = ax + b
Since, The values is given as;
f (0) = 3.75
And, f (-6) = 3.75
So, We can substitute the given values in the linear function, we get;
f (x) = ax + b
Substitute x = 0 we get;
f (0) = a × 0 + b
f (0) = b
3.75 = b
b = 3.75
And, We can substitute x = -6 and f(0) = 3.75 we get;
f (-6) = a × -6 + b
3.75 = -6a + 3.75
- 6a = 0
a = 0
So, Substitute a = 0 and b = 3.75 in linear function we get;
f (x) = ax + b
f (x) = a × 0 + 3.75
f (x) = 3.75
Therefore,
The linear function will be;
⇒ f (x) = 3.75
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I need help on this please! Assignment is called “Periods and Amplitudes” not sure if that helps lol
Answers
Solution:
The sine function is generally expressed as
[tex]\begin{gathered} y=A\sin(B(x+C))+D\text{ ---- equation 1} \\ where \\ A\Rightarrow amplitude \\ C\Rightarrow phase\text{ shift} \\ D\Rightarrow vertical\text{ shift} \\ \end{gathered}[/tex]The period of the function is expressed as
[tex]period=\frac{2\pi}{B}[/tex]Given the function:
[tex]y=\sin((\frac{7\pi}{4}x))\text{ ---- equation 2}[/tex]Comparing equations 1 and 2, we see that
[tex]B=\frac{7\pi}{4}[/tex]Thus, by substituting the value of B into the period formula, we have
[tex]\begin{gathered} period=\frac{2\pi}{\frac{7\pi}{4}} \\ =2\pi\times\frac{4}{7\pi} \\ =\frac{2\times\text{4}}{7} \\ =\frac{8}{7} \end{gathered}[/tex]Hence, the period of the function is
[tex]\frac{8}{7}[/tex]Y=-4 graph each equation by making a table
Answers
The graph of the equation and the table is attached below.
Graph:
Graph means the pictorial representation of the given set of data or the equation.
Given,
Here we have the equation
y = -4.
Now, we need to plot the graph for this equation and we have also draw the table for that.
Here we have the equation y = -4. This one can't take any value for the calculation,
Which means it we take any value on the x coordinate, the given equation will result only the value of y as -4.
Which means, if we take x as -2, the value of y is -4.
If we take x as -1, it will also have the value of y as -4.
If we take x as 0, then again we will get the value of y as -4.
Therefore, it will continuous at infinity.
So, the table for this equation is look like the following.
And the graph of the equation is attached below.
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URGENT!! ILL GIVE
BRAINLIEST!!!!! AND 100
POINTS!!!!!
Answers
the rriangle is 3 4 5 triangle so 5×5 is 25
can anyone help me i have a picture of my math question
Answers
Answer:
-8, -5, -2, 1, 4
Explanation:
The given sequence is an arithmetic sequence -8, -5, -2 ....
The nth term of the sequence is expressed as;
Tn = a+ (n-1)d
a is the first term = -8
d is the common difference = -5 -(-8) = -2-(-5)
d = -5+8 = -2+5 = 3
Get the 4th term;
n = 4
T4 = -8+(4-1)*(3)
T4 = -8+3(3)
T4 = -8+9
T4 = 1
Get the 5th term:
n = 5
T5 = -8 + (5-1)*3
T5 = -8+4(3)
T5 = -8 + 12
T5 = 4
Hence the next two terms of the sequence are 1 and 4
que es el producto para (x+5) (2x-1)?
Answers
the given expression is,
(x+ 5) (2x -1)
so the answer is
[tex]\begin{gathered} \mleft(x+5\mright)(2x-1)=2x^2-x+10x-5 \\ \end{gathered}[/tex][tex]=2x^2+9x-5[/tex]so the answer is
2x^2 + 9x - 5
Order the following integers from least to greatest.-41, -53, -73, -78 A. -78, -53, -73, -41 B. -78, -73, -41, -53 C. -73, -78, -53, -41 D. -78, -73, -53, -41
Answers
The value of negative integers decreases the further we get from the 0 point on the number line.
Therefore, if we arrange the numbers in ascending order ignoring the negative sign, the numbers will be in descending order when the negative sign is included.
By the definition above, we can say that the smallest number of the lot is -78 and the largest one is -41.
The numbers can be ordered from least to greatest as shown below:
[tex]-78,-73,-53,-41[/tex]OPTION D is the correct answer.
If the calculator gives us the following values number 7
Answers
we know that
The equation is of the form
y=ax+b
The given values are
a=0.872
b=25.263
substitute
therefore
The equation is
y=0.872x+25.263what is a youth group that
Answers
(3+ 1i) (2 - 2i)
open the parenthesis
3(2 - 2i) + 1i(2 - 2i) (note: i² = -1)
6 - 6i + 2i + 2
Rearrange
6 + 2 - 6i + 2i
8 - 4i
comparing with a + bi
The real number a equals 8
The real number b equals -4
Problem 14.f(2)(a) Determine the equations of the perpendicular bisectors througheach side of the triangle.C(4,6)B(7,3)A(2,2)I
Answers
The product of the slopes of the perpendicular lines is -1, which means if the slope of one of them is m, then the slope of the perpendicular line is -1/m
In triangle ABC
The perpendicular bisector of the side BC is drawn from the opposite vertex A
Then to find it find the slope of BC and reciprocal it and change its sign to get its slope and find the midpoint of BC to use it in the equation of the perpendicular bisector
Since B = (7, 3) and C = (4, 6)
Let us find the slope of BC, using the rule of the slope
[tex]m=\frac{y2-y1}{x2-x1}[/tex]Let (x1, y1) = (7, 3) and (x2, y2) = (4, 6)
[tex]\begin{gathered} m_{BC}=\frac{6-3}{4-7} \\ m_{BC}=\frac{3}{-3} \\ m_{BC}=-1 \end{gathered}[/tex]Now to find the slope of the perpendicular line to BC reciprocal it and change its sign
Since the reciprocal of 1 is 1 and the opposite of negative is positive, then
Then the slope of the perpendicular line is 1
Now, let us find the mid-point of BC
The rule of the midpoint is
[tex]M=(\frac{x1+x2}{2},\frac{y1+y2}{2})[/tex]Then the mid-point of BC is
[tex]\begin{gathered} M_{BC}=(\frac{7+4}{2},\frac{3+6}{2}) \\ M_{BC}=(\frac{11}{2},\frac{9}{2}) \\ M_{BC}=(5.5,4.5) \end{gathered}[/tex]Now we can form the equation of the perpendicular bisector of BC using its slope 1 and the point (5.5, 4.5)
The form of the equation using a point and a slope is
[tex]y-y1=m(x-x1)[/tex]m is the slope and (x1, y1) is a point on the line
Since m = 1 and (x1, y1) = (5.5, 4.5), then
[tex]\begin{gathered} m=1,x1=5.5,y1=4.5 \\ y-4.5=1(x-5.5) \\ y-4.5=x-5.5 \end{gathered}[/tex]Add 4.5 to both sides
[tex]\begin{gathered} y-4.5+4.5=x-5.5+4.5 \\ y=x-1 \end{gathered}[/tex]The equation of the perpendicular bisector of BC is
[tex]y=x-1[/tex]We will do the same to AB and AC
Which of these tables doesn't show a proportional relationship? MY 2 B 4 12. 18 X 1 2 2 4 3 6 X Y 0 - 2 1 에 1 2 4 X Y 0 0 1 1 2 2
Answers
Answer:
The third table.
Explanation:
In a proportional relationship, the and y values are in a constant ratio.
If the rectangle below were to be enlarged by a scale factor of 5, what would the new size be? 2 10 x 15 10 X 6 8 X 15 Od 2 X 3
Answers
To dilate a shape by a determined scale factor, you have to multiply each side of the said shape by the scale factor.
The figure is a rectangle with length l=3 and width w=2, to enlarge it using factor 5, you have to multiply both lengths by 5:
[tex]\begin{gathered} l=3\cdot5 \\ l=15 \end{gathered}[/tex][tex]\begin{gathered} w=2\cdot5 \\ w=10 \end{gathered}[/tex]After dilating the rectangle by scale factor 5, the new size will be 10 x 15
Convert the binary number ( 365.24 ) into decimal number.
Answers
Given:
The given deciaml number is 365.24.
Required:
We need to convert the given decimal number into a binary number.
Explanation:
Consider the integer part of the given number.
[tex]365[/tex]Divide the number 365.
Consider the fraction part of the given number.
[tex]0.24[/tex]Multiply the number 0.24 by 2.
The binary number of the decimal number is
[tex]365.24_{10}=101101101.0011110101_2[/tex]Final answer:
[tex]101101101.0011110101[/tex]Can you write on the paper/photo? So can write on my paper too and write it down
Answers
Answer:
1) 4x + 12
2) new area = 16x + 48
3) Yes, the ratio is the same for positive values of x
Explanation:
The distributive property of multiplication is shown below
a(b + c) = ab + ac
The area of the given rectangle is expressed as
Area = 4(x + 3)
By applying the distributive property, it becomes
4 * x + 4 * 3
= 4x + 12
The equivalent expression is
4x + 12
If the dimensions of the rectangle are doubled, then
new length = 2(x + 3) = 2x + 6
new width = 4 * 2 = 8
Thus,
new area = 8(2x + 6) = 8 * 2x + 8 * 6
new area = 16x + 48
We would input values of x into both areas and find their ratios
For x = 1,
area = 4(1) + 12 = 16
new area = 16(1) + 48 = 64
ratio = 16/64 = 1/4
For x = 2,
area = 4(2) + 12 = 20
new area = 16(2) + 48 = 80
ratio = 20/80 = 1/4
For x = 3,
area = 4(3) + 12 = 24
new area = 16(3) + 48 = 96
ratio = 24/96 = 1/4
Thus, the ratio is the same for positive values of x
I need help with this practice from my ACT prep guide Having trouble
Answers
Given:
[tex]f(x)=-4\cos (\frac{2}{3}x+\frac{\pi}{3})-3[/tex]If $2,000 is invested at 6% compounded monthly, what is the amount after 5 years?
Answers
Remember that
The compound interest formula is equal to
[tex]A=P(1+\frac{r}{n})^{nt}[/tex]
where
A is the Final Investment Value
P is the Principal amount of money to be invested
r is the rate of interest in decimal
t is the number of Time Periods
n is the number of times interest is compounded per year
in this problem we have
P=$2,000
t=5 years
r=6%=6/100=0.06
n=12
substitute the given values in the above formula
[tex]\begin{gathered} A=2,000(1+\frac{0.06}{12})^{12*5} \\ \\ A=\$2,697.70 \end{gathered}[/tex]therefore
The answer is $2,697.70Find the real part and the imaginary part of the following complex number. (sqrt(6) - sqrt(6i))/4
Answers
In this case, we'll have to carry out several steps to find the solution.
Step 01:
data:
(√6 - √6i) / 4
Step 02:
complex numbers:
[tex]\frac{\sqrt{6}-\sqrt{6}i}{4}=\frac{\sqrt{6}}{4}-\frac{\sqrt{6}i}{4}[/tex]real part:
√6 / 4
imaginary part:
- √6i / 4
That is the full solution.
mathematics assignment
Answers
Examining the function the graph that is correct is the graph in option C
What is graph ?A graph is a representation of data using accepted means of presentation.
The graph used in the question is in cartesian coordinate and it a parabolic graph
How to find the correct graphThe given data is h(x) = -x² - 4
Examining the given function
The term -x² is a negative term hence the graph opens downwards
The value of h(x) when x = 0 is -4. Therefore the graph will have an intercept at -4
The graph of option C is the one that meets the required criteria hence the nest option
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Use an inequality to represent the corresponding Celsius temperature that is at or below 32° F.
Answers
C ≤ 0
Explanations:The given equation is:
[tex]F\text{ = }\frac{9}{5}C\text{ + 32}[/tex]Make C the subject of the equation
[tex]\begin{gathered} F\text{ - 32 = }\frac{9}{5}C \\ 9C\text{ = 5(F - 32)} \\ C\text{ = }\frac{5}{9}(F-32) \end{gathered}[/tex]At 32°F, substitute F = 32 into the equation above to get the corresponding temperature in °C
[tex]\begin{gathered} C\text{ = }\frac{5}{9}(32-32) \\ C\text{ = }\frac{5}{9}(0) \\ C\text{ = 0} \end{gathered}[/tex]The inequality representing the corresponding temperature that is at or below 32°F is C ≤ 0
Samantha received a loan from the bank for $4,500. She plans on payinyoff the loan in 4 years. At the end of 4 years, Samantha will have paid$900 in interest. What is the simple interest rate on the bank loan?
Answers
The simple interest rate formular is;
I = A - P
A= I + P
A = P ( 1 + rt )
A is the amount after t years
P is the initial amount = $4,500
r is the rate in percent = ?
t is the time in years = 4
A = $4,500 + $900 = $5,400
Therefore to obtain the rate (r)
5400 = 4500 (1 + r x 4 )
1 + 4r = 5400/4500
1 + 4r = 1.2
4r = 1.2 - 1
4r = 0.2
r = 0.2/4 = 0.05
In percentage;
r = 0.05 x 100 = 5%
Thus, the simple interest rate is 5%
4. At a shelter, 15% of the dogs are puppies. If there are 60 dogs at the shelter, how many are puppies? * O 400 O 25 O 9 O 42
Answers
4. At a shelter, 15% of the dogs are puppies. If there are 60 dogs at the shelter, how many are puppies? * O 400 O 25 O 9 O 42
_____________________________________________________
60* (0.15) = 9
_______________________________
Answer
There are 9 puppies
· A) A highway noise barrier is 120 m long is constructed in 2pieces. One piece is 45 m longer than the other one. Findthe length of each piece. B) If you are to construct arectangle with each of the sizes of the pieces being thelength and width then what is the perimeter? c) What would bethe area of that rectangle? (Note: Use an Equation to solve)
Answers
A) Let the length of one piece be x. if one piece is 45 m longer than the other one, it means that the length of the other one would be (x + 45) m
Given that the total length of both pieces is 120m, then the equation would be
x + x + 45 = 120
2x + 45 = 120
2x = 120 - 45 = 75
x = 75/2
x = 37.5
Thus, the length of each piece are
37.5 m
37.5 + 45 = 82.5 m
B) The formula for determining the perimeter of a rectangle is expressed as
Perimeter = 2(length + width)
Given that
length = 82.5
width = 37.5
then
perimeter = 2(82.5 + 37.5) = 2 * 120
perimeter of rectangle= 240 m
C) the formula for determining area of a rectangle is expressed as
Area = length * width
Area of rectangle = 82.5 * 37.5 = 3093.75 cm^2
A person has 29 1/2 -yd of material available to make a doll outfit. Each outfit requires 3/4 yd of material. a. How many outfits can be made? b. How much material will be left over?
