Answer: [tex]x > 4[/tex]
Step-by-step explanation:
[tex]8x-2x+7 > 21+10\\\\6x+7 > 31\\\\6x > 24\\\\x > 4[/tex]
The denominator of a fraction is five more than twice the numerator if both the numerator and the denominator are decreased by three the simplified result is 1/4 find the original fraction
Answer:
7/19
Step-by-step explanation: we could get two equations from the question if we set the denominator as x and the numerator as y:
1: x=2y+5
2:(y-3)/(x-3)=1/4
cross multiply
4(y-3)=1(x-3)
4y-12=x-3
x=4y-9
3: Then we can choose one of them and minus by another one
x-x=4y-2y-(9+5)
0=2y-14
2y=14
y=7
Then we only have to plug in
x=2*7+5
x=14+5
x=19
Question is attached in photo Function : f(x)=x+2 sin x
Answer:
The function is given below as
[tex]f(x)=x+2\sin x[/tex]Using the interval below
[tex]0\leq x\leq2\pi[/tex]A relative maximum point is a point where the function changes direction from increasing to decreasing (making that point a "peak" in the graph).
Similarly, a relative minimum point is a point where the function changes direction from decreasing to increasing (making that point a "bottom" in the graph).
Using a graphing tool, we will have the relative maximum and relative minimum to be
Hence,
The relative maximum is at
[tex](\frac{2\pi}{3},3.826)[/tex]The relative minimum is at
[tex](\frac{4\pi}{3},2.457)[/tex]1 1 10 1 b. What fraction of the whole square is shaded? Explain how you know.
1/100
Explanation:To get the fraction of the square shaded we would use the rows and columns
For the row:
The total on the 1st row = 1
The first row is divided into 10. This means each box in the first row: 1/10
One of the box is shaded. This implies the fraction shaded in the first row is 1/10
For the column:
The total on the 1st column = 1
The column is also divided into 10 box which means each box represent 1/10
Since one of the box in the column is shaded, it represent 1/10
Fraction of the whole square shaded = fraction shaded in the row × fraction shaded in the column
Fraction of the whole square shaded = 1/10 × 1/10
Fraction of the whole square shaded = 1/100
the points (-4,-2) and (8,r) lie on a line with slope 1/4 . Find the missing coordinate r.
The points (-4, -2) and (8, r) are located on a line of slope 1/4, We are asked to find the value of "r" that would make suche possible.
So we recall the definition of the slope of the segment that joins two points on the plane as:
slope = (y2 - y1) / (x2 - x1)
in our case:
1/4 = ( r - -2) / (8 - -4)
1/4 = (r + 2) / (8 + 4)
1/4 = (r + 2) / 12
multiply by 12 both sides to cancel all denominators:
12 / 4 = r + 2
operate the division on the left:
3 = r + 2
subtract 2 from both sides to isolate "r":
3 - 2 = r
Then r = 1
What is the midpoint of the line segment graphed below?10(5,9)(2-1)-1010- 10O A. (7,8)OB.OC (34)OD (710
ANSWER:
[tex](\frac{7}{2},4)[/tex]STEP-BY-STEP EXPLANATION:
To calculate the value of the midpoint, we use the formula of the midpoint which is the following:
[tex](x_m,y_m)=(\frac{x_1+x_2}{2},\frac{y_1+y_2}{2})[/tex]Replacing and solving the midpoint:
[tex]\begin{gathered} (x_m,y_m)=(\frac{5+2_{}}{2},\frac{9-1_{}}{2}) \\ (x_m,y_m)=(\frac{7_{}}{2},\frac{8_{}}{2})=(\frac{7}{2},4) \end{gathered}[/tex]Find the product of -0.6 and -2/5
Express your answer as a fraction or
mixed number in simplest form.
Answer:
6/25Step-by-step explanation:
1) -0.6 = -6/10
= -3/5
2) -0.6*-2/5 = (-3/5)*(-2/5)
=(-3*-2)/(5*5)
=6/25Find all the solutions and if there is an extraneous solution, identify them and explain why they are extraneous.
ANSWER
Solution: b = 3
It is extraneous
EXPLANATION
We want to solve the equation given and to see if there are any extraneous solutions.
We have:
[tex]\begin{gathered} \frac{7}{b\text{ + 3}}\text{ + }\frac{5}{b\text{ - 3}}\text{ = }\frac{10b}{b^2\text{ - 9}} \\ \Rightarrow\text{ }\frac{7}{b\text{ + 3}}\text{ + }\frac{5}{b\text{ - 3}}\text{ = }\frac{10b}{(b\text{ + 3)(b - 3)}} \\ \text{Multiply both sides by (b + 3)(b - 3):} \\ \Rightarrow\text{ }\frac{7(b+3)(b\text{ - 3)}}{b\text{ + 3}}\text{ + }\frac{5(b\text{ + 3)(b - 3)}}{b\text{ - 3}}\text{ = }\frac{10b(b\text{ + 3)(b - 3)}}{(b\text{ + 3)(b - 3)}} \\ 7(b\text{ - 3) + 5(b + 3) = 10b} \\ 7b\text{ - 21 + 5b + 15 = 10b} \\ \text{Collect like terms:} \\ 7b\text{ + 5b - 10b = 21 - 15} \\ 2b\text{ = 6} \\ Divide\text{ both sides by 2:} \\ b\text{ = }\frac{6}{2} \\ b\text{ = 3} \end{gathered}[/tex]That is the solution to the equation.
To find if the solution is extraneous, we will insert the value of b = 3 into the original equation.
That is:
[tex]\begin{gathered} \Rightarrow\text{ }\frac{7}{3\text{ + 3}}\text{ + }\frac{5}{3\text{ - 3}}\text{ = }\frac{10(3)}{(3\text{ + 3)(3 - 3)}} \\ \frac{7}{6}\text{ + }\frac{5}{0}\text{ = }\frac{30}{(6)(0)} \\ \frac{7}{6}\text{ + }\frac{5}{0}\text{ = }\frac{30}{0} \end{gathered}[/tex]An extraneous solution is a solution that derives from solving a rational equation but does not exactly satisfy the original equation, that is, it is invalid for the equation.
By inserting b = 3 into the equation, we see that the equation is undefined.
Therefore, since b = 3 is a solution, but it does not satisfy the equation, it is an extraneous solution.
What is the product of 8i and 4i
The product of given complex number that is 8i and 4i will be -32 by the properties of complex number that states i*i will be -1 and 8*4 will be 32.
What is complex number?Every complex number can be expressed in the form a + bi, where a and b are real numbers. A complex number is an element of a number system that extends the real numbers with a specific element denoted I also known as the imaginary unit, and satisfying the equation i²=-1.
What are the property of complex number?Commutative, Associative, Distributive Properties: All complex numbers are commutative and associative under addition and multiplication, and multiplication distributes over addition.
Here,
The product of 8i*4i=-32
as 8*4=32
and i²=-1
32*-1=-32
Due to the properties of complex numbers, which state that i*i will be -1 and 8*4 will be 32, the product of the given complex number, which is 8i and 4i, will be -32.
To know more about complex numbers,
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Yesterday, Alan had k baseball cards. Today, he gave 19 away. Using k, write an expression for the number of cards Alan has left.
Answer:
k-19
Step-by-step explanation:
If Alan had k baseball card and gave 19 away then he would have 19 less then k
Answer:
K - 19= X
Step-by-step explanation:
I hope this helps!
960 watts hour per how many watts hour does it consume in 4 days and 6 hours
Answer:
Explanation:
[tex]undefined[/tex]Point P is in the interior of
∵ m< OZQ = m[tex]\because m\angle OZP=62[/tex]Substitute the measures of the given angles in the equation above
[tex]\therefore125=62+m\angle PZQ[/tex]Subtract 62 from both sides
[tex]\begin{gathered} \therefore125-62=62-62+m\angle PZQ \\ \therefore63=m\angle PZQ \end{gathered}[/tex]The measure of angle PZQ is 63 degrees
Note:enter your answer and show all steps that you use to solve this problem3.jaoquin buys 3 dozen lightbulbs.after changing the lightbulbs in his house, he has 15 lightbulbs left how many lightbulbs did he use?*btw the not is the same thing to my question I have for number 6*6. the empire state building in new York City is 1,250 feet tall. it has 103 floors. rounded to the nearest whole, what is the height of each floor?
Answer: Number of lightbulbs that he used = 21 lightbulbs
1 dozen of light bulbs = 12 light bulbs
Jaoquin buys 3 dozens
3 dozens of lightbulbs = 3 * 12 lightbulbs
3 dozens of lightbulbs = 36 lightbulbs
This means that :
The number of light bulbs Jaoquin bought = 36
The number of lightbulbs that remain = 15
The number of lightbulbs that he used = (Number of lightbulbs that he buys) - (Number of lightbulbs that remains)
Number of lightbulbs that he used = 36 - 15
Number of lightbulbs that he used = 21 lightbulbs
Find the midpoint of the coordinates (3. -18) and (-5, -10) WHAT IS THE XVALUE?
Given the points (3, -18) and (-5, -10)
Let the midpoint of the given coordinates is (x , y)
[tex]x=\frac{3+(-5)}{2}=\frac{-2}{2}=-1[/tex][tex]y=\frac{(-18)+(-10)}{2}=\frac{-28}{2}=-14[/tex]So, the coordinates of the midpoint is (-1 , -14)
Which value of x proves that the two triangles above are similar? 42.7 ft 26.7 ft 10 ft 25.6 ft
Explanation
Step 1
we have two triangles
ACE and BCD
if the triangles are similar, then the ratio of the sides must be the same:
[tex]\begin{gathered} \frac{\text{red line}}{purple\text{ line}}=\frac{blue\text{ line}}{\text{green line}} \\ \text{replacing} \\ \frac{16+x}{32}=\frac{x}{20} \end{gathered}[/tex]Step 2
solve for x
[tex]\begin{gathered} \frac{16+x}{32}=\frac{x}{20} \\ \text{cross multiply} \\ 20(16+x)=32\cdot x \\ 320+20x=32x \\ \text{subtrac 20x in both sides} \\ 320+20x-20x=32x-20x \\ 320=12x \\ \text{divide both sides y 12} \\ \frac{320}{12}=\frac{12x}{12} \\ \text{ x=26.66} \end{gathered}[/tex]rounded
[tex]x=26.7\text{ }[/tex]I hope this helps you
For triangle ABC, AB = 3 cm and BC = 5 cm.Which could be the measure of AC?A 2 cmB 4 cmC 8 cmD 15 cm
ANSWER
2, 4 and 8
EXPLANATION
We have that in a triangle ABC, AB = 3 cm and BC = 5 cm.
To find the possible length of AC, we can apply the triangle inequality theorem.
It states that in any triangle, the sum of the lengths of any two sides must be greater than or equal to the length of the remaining side.
This means that:
[tex]\begin{gathered} AB\text{ + AC }\ge\text{ BC} \\ \text{and } \\ AB\text{ + BC }\ge\text{ AC} \\ \text{and} \\ AC\text{ + BC }\ge\text{ AB} \end{gathered}[/tex]So, we have that:
[tex]\begin{gathered} 3\text{ + AC }\ge\text{ 5 }\Rightarrow\text{ AC }\ge\text{ 2} \\ 3\text{ + 5 }\ge\text{ AC }\Rightarrow\text{ AC }\leq\text{ 8} \\ AC\text{ + 5 }\ge3\Rightarrow\text{ AC }\ge\text{ -2} \end{gathered}[/tex]We have to disregard the third line, since the length of a triangle side can only be positive.
So, using the first 2 lines, we see that:
[tex]2\text{ }\leq\text{ AC }\leq\text{ 8}[/tex]This means that from the options, the measure of AC can either be 2, 4 or 8.
Jane invested her savings in two investment funds. The $2000 that she invested in Fund A returned a 3% profit. The amount that she invested in Fund B returned a 10% profit. How much did she invest in fund B, if both funds together returned a 8% profit?
Fund A, Jane invested $2000 and has a profit of 3%
Profit at Fund A is :
[tex]\$2000\times0.03=\$60[/tex]at Fund B, let $x be the amount she invested that gives her a profit of 10%
The profit at Fund B is :
[tex]\$x\times0.10=\$0.10x[/tex]It is said that the total amount she invested returned a 8% profit
The total amount she invested is :
[tex]\$2000+\$x[/tex]and the 8% profit of her total investment is :
[tex](2000+x)\times0.08=160+0.08x[/tex]Now we need to equate the sum of her profits from Fund A and Fund B, and this must be equal to the 8% profit.
3% Profit at Fund A = $60
10% Profit at Fund B = $0.10x
8% Profit at both funds together = 160 + 0.08x
[tex]\begin{gathered} 60+0.10x=160+0.08x \\ 0.10x-0.08x=160-60 \\ 0.02x=100 \\ x=\frac{100}{0.02}=5000 \end{gathered}[/tex]Therefore, the amount she invested in Fund B is $5000
Determine if the two triangles shown are similar. If so, write the similarity statement.Question options:A) Impossible to determine.B) ΔBCG ∼ ΔEFGC) ΔGCB ∼ ΔGFED) The triangles are not similar.
ANSWER
Option D: The triangles are not similar
STEP BY STEP EXPLANATION
Now, two (2) triangles are said to be similar if the three (3) angles of triangle A are congruent or equal to the corresponding three (3) angles of triangle B.
If you take a close look at the two (2) triangles, you will notice that the only angle in ∆BCG that is equal to the corresponding angles in ∆EFG is ∆BGC; the two (2) remaining angles in ∆BCG are not congruent with the two (2) corresponding angles in ∆EFG
Hence, it can be concluded that both triangles are not similar.
If the formula x=1/n, is used to find the mean of the following sample, what is the value of n? 2, 63, 88, 10, 72, 99, 38, 19
Given:
The formula is:
[tex]x=\frac{1}{n}\sum_{i=1}^nx_i[/tex]Series is:
[tex]2,63,88,10,72,99,38,19[/tex]Find-:
The value of "n"
Explanation-:
In the given formula "n" represent the number of member in a series.
Given series is:
[tex]2,63,88,10,72,99,38,19[/tex]The number of members is:
The members are 8.
So the value of "n" is:
[tex]n=8[/tex]The value of "n" is 8.
Answer: The answer to this problem is 6
Step-by-step explanation: i took the quiz, this is the correct answer.
Evaluate. 7⋅5+42−23÷4
The result that can be gotten from the evaluation here is 6.625
How to solve the problemWe would have to solve the problem following the order that the operations are. The reason why it would have to be solve this way is because the operations are not in a bracket.
If it was in brackets, the brackets would have to be solved first using the bodmas rule
so we would have
7⋅5+42 = 49.5
49.5 - 23 = 26.5
26.5 / 4 = 6.625
The value that we got from the evaluation is 6.625
Read more on mathematical operators here:
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Carolina wants to find out how many different ways can she arrange the apps on her Iphone on the first row. The first row has space for 4 apps, and she has 12 apps to choose from
ANSWER
495 ways
EXPLANATION
Carolina has 12 apps to choose from and she only has space for 4 apps.
To find out how many ways she can do it, we will need to use combination.
That is:
[tex]^{12}C_4[/tex]Note: we use combination because the order of the apps is not a factor
So, we have that:
[tex]\begin{gathered} ^{12}C_4\text{ = }\frac{12!}{(12\text{ - 4)! 4!}}\text{ = }\frac{12!}{8!\text{ 4!}} \\ =\text{ 495 ways} \end{gathered}[/tex]She can arrange them in 495 ways.
Eddie brought his DVD set to the secondhand store to sell he was paid for all three DVDs in the set before he left Eddie used $15.70 of his earnings to purchase a pair of headphones had $2.30 remaining which equation can you use to find the amount of money Eddie received for each DVD
15.70(d-3)=2.30
3d-15.70=2.30
15.70d-3=2.30
3(d-15.70)=2.30
Eddie brought his DVD set to the secondhand store to sell he was paid for all three DVDs in the set before he left Eddie used $15.70 of his earnings to purchase a pair of headphones had $2.30 remaining which equation can you use to find the amount of money Eddie received for each DVD:
15.70(d-3)=2.30
3d - 15.70 = 2.30
15.70d-3=2.30
3(d-15.70)=2.30
the digits 1through 6 are used for a set of locker codes. suppose the digits cannot repeat. find the number of possible two digit codes and three digit codes. describe any pattern and use it to predict the number of possible five digit codes
SOLUTION
This is a permutation problem.
a) To find the number of possible two digits codes
[tex]^6P_2[/tex][tex]^6P_2=\frac{6!}{(6-2)!}[/tex][tex]\begin{gathered} =\frac{6!}{4!} \\ =\frac{720}{24} \\ =30\text{ ways} \end{gathered}[/tex]There are 30 possible two-digit codes pattern.
b) To find the number of three digits codes
[tex]\begin{gathered} ^6P_3=\text{ }\frac{6!}{(6-3)!} \\ \text{ =}\frac{6!}{3!} \\ \text{ =}\frac{720}{6} \\ \text{ = 120 ways} \end{gathered}[/tex]There are 120 possible three-digit codes pattern.
Any other pattern can be calculated using
[tex]\begin{gathered} ^6P_r \\ \text{where r is the number of digits code (1,2,3,4,5,6)} \end{gathered}[/tex]So to predict the number of possible five-digit codes will be:
[tex]^6P_5[/tex][tex]\begin{gathered} =\frac{6!}{(6-5)!} \\ =\frac{6!}{1!} \\ =720\text{ways} \end{gathered}[/tex]There are 720 different possible five-digit codes
the answer of this question is 720 ways
Solve for c.
6>c+8>5
Step-by-step explanation:
Fill in the table using this function rule. y = -10x +3 y X 6 ? 1 0 a 1
the function is
[tex]y=-10x+3[/tex]we must replace the value of x and obtain y
x=-5
[tex]\begin{gathered} y=-10(-5)+3 \\ y=50+3 \\ y=53 \end{gathered}[/tex]x=-1
[tex]\begin{gathered} y=-10(-1)+3 \\ y=13 \end{gathered}[/tex]x=0
[tex]\begin{gathered} y=-10(0)+3 \\ y=3 \end{gathered}[/tex]x=1
[tex]\begin{gathered} y=-10(1)+3 \\ y=-7 \end{gathered}[/tex]UsetheprimefactorsmethodtofindtheGCFof76,190,and931.
There are several ways to calculate the GCF
Let's use the Prime Factorization.
1) List the numbers in a row. As we can see, 76, 190 are both divisible by 2
So le's start dividing by the prime number 2, up to next divisible prime number as it follows:
As we can see the Greatest Common Divisor to both 76,190 and 931 is the prime number 19
Therefore, we can state the GCD of 76,190, 931 as 19
7. Reflect AABC over the y-axis, translate by (2, -1), and rotate the result 180° counterclockwise aboutthe origin. Plot AA'B'C' on the grid below. (1 point)tyTransformation rule:420А,PreimageABCImage A'B'CImage A"B"C"Image A'B'C'-22,-12,44, 2lifelongGeometry ACredit 2L4L - Geometry A (2020)Page 57
Reflection rule over y - axis is given as
(x , y) ------------ (-x, y)
This implies that the y - axis will remain the same and the x - axis will be negated
Pre image ABC at point (2, -1)
The reflection over y - axis will be
ABC A'B'C' A''B''C'' A'''B'''C'''
(2, -1) -----------------(-2, -1) ----------------------(2, -1) -------------------(-2, -1)
ABC A'B'C' A''B''C'' A'''B'''C'''
(2, -4) (-2, -4) (2, -4) (-2, -4)
The ratio of 1.2 to 32 is equal to the ratio of 3.6 to____.
Answer:
96
Step-by-step explanation:
let the number be x then
1.2x=32
x=80/3
again
3.6x
3.6×80/3
96
Nick skates 2 1/8 miles in 1/2 of an hour. What is Nick's average speed, in miles per hour ?
Average speed = distance / time
From the question;
distance = 2 1/8 miles = 17/8 miles
time = 1/2
substitute the values into the formula;
[tex]\text{Average sp}eed\text{ =}\frac{\frac{17}{8}}{\frac{1}{2}}[/tex][tex]=\frac{17}{8}\times\frac{2}{1}[/tex][tex]=\frac{17}{4}[/tex][tex]=4\frac{1}{4}\text{ miles per hour}[/tex]How to tell if a sequence is linear, exponential, quadratic or absolute value as simply as possible without graphing (8th grade algebra) examples will be greatly appreciated
We will have the following:
We will be able to tel apart sequences as follows:
Linear sequence: We have that linear sequences follow the form:
[tex]y=mx+b[/tex]Here "x" represents the iteration value for the sequence, "m" the ratio (slope) and "b" a value that modifies the "position" of the sequence. This sequences grows in a linear manner.
Example:
[tex]\begin{cases}y_{}=2x+2 \\ \\ y_1=4 \\ y_2=6 \\ y_3=8 \\ \ldots\end{cases}[/tex]Exponential sequence: We have that exponential sequences follow the form:
[tex]y=a_1(r)^{x-1}[/tex]Here "a1" is the first term of the sequence, "r" is the ratio and "x" the iteration of the sequence.
We obtain the ratio as follows:
[tex]r=\frac{y_n}{y_{n-1}}[/tex]Example:
[tex]\begin{cases}y=1(5)^{x-1}_{} \\ \\ y_1=1 \\ y_2=5 \\ y_3=25 \\ \\ \ldots\end{cases}[/tex]The ratio for this case:
[tex]r=\frac{y_3}{y_2}\Rightarrow r=\frac{25}{5}\Rightarrow r=5[/tex]Quadratic sequence: A quadratic sequence follows the general form
A family of four went to an amusement park for their vacation. They started the vacation with $426.They spent a total of $198 the first three days.If they divided the remainder of the money evenly between the family members for souvenirs, how much did each person have to spend?
They started the vacation with $426
After spending $198 the first three days, the remainder is $426 - $198 = $228
Given that there are 4 family members, we have to divide this remainder by 4, that is, $228/4 = $57
Each person has $57 to spend
