Answer:
[tex] {b}^{10} \div {b}^{6} = {b}^{4} \\ \\ \frac{ {b}^{10} }{ {b}^{6} } = b^{10 - 6} = {b}^{4} [/tex]
I hope I helped you^_^
11. Find the solutions of x^2-x-30 = 0.
Please give a walkthrough/step by step I am trying to learn how to do it!
To find the solutions of quadratic equation, there are two ways to do which are:
FactorizeQuadratic FormulaStep 1
- Factor the expression.
To factor the expression, refer below:
[tex] \displaystyle \large{ (x - a)(x - b) = {x}^{2} - bx - ax + ab}[/tex]
For bx and ax, both can be common-factored. Therefore
[tex] \displaystyle \large{ (x - a)(x - b) = {x}^{2} - (b + a)x + ab}[/tex]
From the above, we conclude that:
The middle term is b+aThe last term is a×bThus, we have to find two numbers that satisfy a+b and a×bFrom the expression, 30 comes from 5×6 and when 5-6 = -1. Therefore, a can be 5 and b can be 6.
[tex] \displaystyle \large{{x}^{2} - x - 30 = (x + 5)(x - 6)}[/tex]
Because in the middle term, it is -x which is negative, we have to let the highest number become negative.
From the factored expression:
The middle term = 5x + (-6x) = -xThe last term = 5 × (-6) = -30Then we replace the standard equation with factored form.
[tex] \displaystyle \large{ (x + 5)(x - 6) = 0}[/tex]
For this part, we solve like a linear equation where we isolate x. Just think you are solving two linear equations!
Hence
[tex] \displaystyle \large{ x = - 5, 6}[/tex]
Therefore, the solutions are x = -5, 6.
15) A small rectangular block of land has a perimeter of 100 m and an area of 225 m². Find the dimensions of the block of land.
Answer:
45 and 5 are the dimensions of the block of land.
Step-by-step explanation:
2(x + y) = 100, x + y = 100/2, y = (50 - x)
xy = 225
x (50 — x) = 225
0 = x^2 — 50x + 225
0 = (x — 45) (x -5)
45 and 5 are the roots of the above polynomial, thus they are the sides or dimensions of the block of land.
Which statement is true about the climbers’ heights?
What is the value of a in the equation 3 a plus b equals 54, when b equals 9?
15
18
21
27
Can someone help me please :00
Answer:
according to the dark spots which shows where each number goes to, it would be D.-2
Consider the points below. P(â1, 4, 1), Q(0, 6, 2), R(4, 3, â1)
a. Find a nonzero vector orthogonal to the plane through the points P, Q, and R.
b. Find the area of the triangle PQR.
Answer:
B. Find the area of the triangle PQR.
Select the matrix multiplication that transforms vector A to
vector B
Answer:
Option C.
Step-by-step explanation:
Notice that only option B and C involves the vectors in transformation
[tex]A=\begin{bmatrix}4\\2\end{bmatrix}, B=\begin{bmatrix}-8\\-4\end{bmatrix}[/tex]
However, option B is not a defined multification since the dimension of both matrices are not matching. Vector A is 2x1 but the second matrix is 2x2.
WILL MARK BRAINIEST IF FAST!
Kane's Furniture Store advertised a table at a 11% discount. The original selling price was $111, and the sale price was $100. Was the sale price consistent with the ad? Explain.
Select the correct choice below and, if necessary, fill in the answer box within your choice.
O A. No, the sale price was s higher than it should have been
(Round to the nearest cent.)
OB. No, the sale price was $ lower than it should have been
(Round to the nearest cent.)
OC. Yes, the sale price was consistent with the ad, because it represents a 11% discount.
va
Vi
(11)
More
Click to select and enter your answer(s) and then click Check Answer.
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Answer:
A. No, the sale price was 1.21 higher than it should have been
Step-by-step explanation:
First find the discount
111 * 11%
111 * .11
12.21
Subtract this from 111
111-12.21
98.79
The sale price should have been 98.79
100-98.79
1.21
help me now where are you all helppppp
Q7
7/25
(Decimal: 0.28)
Step-by-step explanation:
Here's the little secret you can use to instantly transform any fraction to a decimal: Simply divide the numerator by the denominator:
= 7/25
= 7 ÷ 25
= 0.28
In Evan's math class, there are 7 boys and 10 girls. Which of the following is the ratio of boys to girls in Evan's math class?
Answer:
7/17
Step-by-step explanation:
Vito avido is a sales representative for a company that sells roofing material. he receives a graduated commission of 5 percent on the first $5,000 of sales, 6.5 percent on the next $15,000, and a 7 percent on sales over $20,000. What is his commission on $23,458 in sales?
Hence commission will be 7%
[tex]\\ \rm\longmapsto 23458\times \dfrac{7}{100}[/tex]
[tex]\\ \rm\longmapsto \dfrac{164206}{100}[/tex]
[tex]\\ \rm\longmapsto 1642.06[/tex]
Vito Avido's commission on $23,458 in sales is $1466.06.
Here, we have to calculate Vito Avido's commission on $23,458 in sales, we'll break down the sales amount into different ranges and apply the respective commission rates for each range.
For the first $5,000 of sales: 5% commission
Commission = 5% of $5,000 = 0.05 * $5,000 = $250
For the next $15,000 of sales: 6.5% commission
Commission = 6.5% of $15,000 = 0.065 * $15,000 = $975
For the remaining amount over $20,000: 7% commission
Sales above $20,000 = $23,458 - $20,000 = $3,458
Commission = 7% of $3,458 = 0.07 * $3,458 = $241.06
Now, add up the commissions from each range:
Total Commission = $250 + $975 + $241.06 = $1466.06
Vito Avido's commission on $23,458 in sales is $1466.06.
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Which set of ordered pairs represents a function?
{(3,6), (3, 1), (9,0), (2, 2)}
{(2,-5), (-3, 6), (-1, -8), (-3,-4)}
{(4, -7), (-2, -1), (-7,4), (9, -1)}
{(3,8), (-2,-9), (1,4), (1,9)}
Answer:
{(4, -7), (-2, -1), (-7,4), (9, -1)}
Step-by-step explanation:
Every other set of ordered pairs has an x-value that has more than one y-value. This is against the rules of a function. Therefore, {(4, -7), (-2, -1), (-7,4), (9, -1)} represents a function.
Write 96% as a fraction.
Answer:
Directly, it would be 96/100. However, we can reduce it to become 48/50 = 24/25.
(underlined is simplest answer)
24/25
Step-by-step explanation:
96%
=96/100
=24/25
answer
The graph represents a function.
Which ordered pair can be plotted together with these four points, so that the resulting graph still represents a function?
O (0,0)
0 (-3,1)
0 (1,3)
O (31)
If we consider the ordered pair (0,0) then only the graph still represents a function.
How to define a graph represent a function?
In a function, there can not be two different values of x corresponding to the same value of y.
Here, the points on the graph are (0,0), (-3,1), (1,3) and (3, 1).
If we consider point (-3,1) then there will be two points corresponding to the same y value i.e. (-3,1) and (3, 1).
The values of x for a single value of y.
i.e. y = 1.
So, if we consider the ordered pair (0,0) then only the graph still represents a function. Therefore, the correct answer is option (a) (0,0).
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If angle DEG is 8x + 14 and angle GEF is 8x - 7, the measure of angle DEG is ___ degrees.
Answer:
100.5
Step-by-step explanation:
As it's a straight line, the angles should add up to 180. So 8x+14+8x-7=180, 16x+7=180, x=10.8125, DEG will be 8x+14=100.5
your monthly salary increases from $2,200 to $2,376. what percent is your raise?
Answer:
8%
Step-by-step explanation:
(2376-2200):2200x100%=8%
solve -5x+y=1 and 9x-2y=4 using multiplication and then elimination.
Answer:
x = - 6, y = - 29
Step-by-step explanation:
Elimination:
2*(-5x + y = 1) = -10x + 2y = 2
9x - 2y = 4 = + (9x - 2y = 4) =
-x = 6
x = -6
9(-6)-2y=4
-54-2y=4
-2y=58
y=-29
simplify (2/3 of 21/4)
Answer: 3 1/2
Step-by-step explanation:
"Of" is the same as multiplication so,
2/3 × 21/4=?
For fraction multiplication, multiply the numerators and then multiply the denominators to get
2 × 2/13 × 4 = 42/12
This fraction can be reduced by dividing both the numerator and denominator by the Greatest Common Factor of 42 and 12 using
GCF(4/2 , 1/2) = 6
4/2 ÷ 6 1/2 ÷ 6 = 7/2
The fraction
7/2
is the same as
7÷2
Convert to a mixed number using
long division for 7 ÷ 2 = 3R1, so
7/2 = 3 1/2
Therefore:
2/3 of 21/4 = 3 1/2
Hopefully, I Helped
1/2. Divided by 2/12 picture
1/2 divided by 2/12 or 1/6 would be 3.The reciprocal of 1/6 is 6 and multiplied with 1/2 = 3.
Answer:
3
Step-by-step explanation:
[tex] \frac{1}{2} \div \frac{2}{12} [/tex]
➡️ [tex] \frac{1}{2} \times \frac{12}{2} [/tex]
➡️ [tex] \frac{1}{2} \times 6[/tex]
➡️ [tex] = 3[/tex] ✅
Which word begins with an open syllable?
silly
sister
sofa
softer
The word sofa begins with an open syllable.
Phonetics is the study of the sound of words/ speeches. This branch of linguistics deals with how words and letters sound and classifies them accordingly.
In phonetics, open and closed syllables refer to the specific nature of how the words end. This means that the words that end with a vowel are known as open syllables while the words that end with a consonant are known as closed syllables. Now, looking at the individual words given in the question, we can ascertain that the initial syllables of the words "silly, sister, softer" all ends in a consonant word. On the other hand, the word "sofa" begins with a vowel "o", thereby making it an open syllable.The easiest way to detect an open and closed syllable is by identifying the position or use of the vowels and consonants in a syllable. This makes the word "sofa" an open syllable.
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The ratio of red beads to blue beads on a necklace is 4:7. What fraction of the beads are blue?
Answer:
fraction of blue beads = 7/(4+7)
= 7/11
Answer:
3:5
Step-by-step explanation:
find a common numeral
suppose the functions u and w are defined as follows u(x)=x+9 w(x)=the square root of x+8 find the following (wou)(8)= (uow)(8)=
Answer:
5 and 13
Step-by-step explanation:
To evaluate (w ￮ u)(8) , evaluate u(8) then substitute the value obtained into w(x) , that is
u(8) = = 8 + 9 = 17 , then
w(17) = [tex]\sqrt{17+8}[/tex] = [tex]\sqrt{25}[/tex] = 5
---------------------------------------
To evaluate (u ￮ w )(8) , evaluate w(8) then substitute the value obtained into u(x) , that is
w(8) = [tex]\sqrt{8+8}[/tex] = [tex]\sqrt{16}[/tex] = 4 , then
u(4) = 4 + 9 = 13
Answer:
Step-by-step explanation:
[tex]u(x)=x+9\\\\w(x)=\sqrt{x+8} \\\\(wou)(x)=u(w(x))=u(\sqrt{x+8} )=\sqrt{x+8}+9\\(wou)(8)= \sqrt{8+8}+9=4+9=13\\\\\\(uow)(x)=w(u(x))=w(x+9)=\sqrt{x+9+8}=\sqrt{x+17}\\(wou)(8)= \sqrt{8+17}=\sqrt{25}=5\\\\[/tex]
I left home at 5:30 am
7.250m and arrived at school at 7:25am how many seconds did I take to reach school
Zip codes are numerical designations of locations for the purpose of mail delivery. The following histogram summarizes the number, in hundreds, of zip codes assigned to each state in the United States.
According to the 1.5 IQR rule for outliers, how many low outliers are there in the data set?
Choose 1 answer:
There are zero number of outliers in data set.
What are [tex]1.5[/tex] IQR rule for outliers ?The [tex]1.5[/tex] IQR rule for outliers says that any data point below [tex]Q_{1} -1.5\ IQR[/tex] is a low outlier. or lower than this are a low outliers.
And,
[tex]IQR=Q_{3} -Q_{1}[/tex]
We have,
[tex]Q_{1}= 275[/tex]
[tex]Q_{3} = 933[/tex]
Minimum [tex]= 1[/tex]
Maximum [tex]= 2596[/tex]
Median [tex]= 533[/tex]
Now,
[tex]IQR=Q_{3} -Q_{1}[/tex]
IQR [tex]=933-275=658[/tex]
So,
[tex]Q_{1} -1.5\ IQR[/tex]
[tex]=275-1.5*658[/tex]
[tex]=-712[/tex]
So, any data point lower than this is the low outlier.
As we see the given histogram, there is no point below this outlier so, in the given histogram there is no low outlier.
Hence, we can say that here are zero number of outliers in data set.
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Answer:
The correct answer is 3.
Step-by-step explanation:
how many litters is in a gallon
Answer:3.785 liters
Step-by-step explanation:
Answer:
1 gal = 3.78541
Step-by-step explanation:
A quick search will do it.
Find the area of this circle
Answer:
314ft²
Step-by-step explanation:
A = 3.14(10²)
A = 3.14 x 100
A = 314ft²
Answer:
Area is 314 ft²
Step-by-step explanation:
[tex]A = \pi {r}^{2} [/tex]
r is radius,
[tex]r = \frac{diameter}{2} = \frac{20}{2} = 10 \: ft[/tex]
therefore:
[tex]A = 3.14 \times {10}^{2} \\ A = 3.14 \times 100 \\ A = 314 \: {ft}^{2} [/tex]
You go to the grocery store to buy milk and some eggs. Milk costs $3.67 and eggs cost $2.40. You want to make sure you have enough money. Estimate the cost of these two items to the nearest ones place.
Answer:
Step-by-step explanation:
Let's start by round 3.67. We look at the key digit which is 6 in this case. Since 6 is greater than 5, 3.67 will round up to 4.
The key digit in 2.40 is 4. 4 is not greater than 5, so we round down to 2.
2+4=6
Therefore, an estimate of these two items to the nearest ones place is $6.
Answer:
$2 for the eggs and $4 for the milk
Step-by-step explanation:
Since the eggs cost $2.40 and after the 2 you can see that there is a 4, " 5 or more we add one more, 4 or less just ignore", so it stays $2. However the milk costs $3.67, and here you can see that after the 3 there is a 4, so since it's more than 5 we change the estimated amount to $4.
I hope you understood, and I hope the answer is right :)
GH = 4x - 1, and DH = 8. Find x.
Help
Answer:
x=4.25
------------------------------------------
8+8=4x-1
16=4x-1
4x=16+1
4x=17
x= 17/4
I have no idea if i am correct just a guesstimate
Have a good day
The table shows the times for the 100-meter dash. What is the
difference between the men'stime and the women's time?
Write your answer in both decimal and fraction form.
Times for 100-meter Dash
Men's winner
9.58
2009
Women's winner
10.49
1988
Answer:
0.91 (make sure to include unit of measurement)
Step-by-step explanation:
10.49 - 9.58 = 0.91
express 3x-x^2 as m-(x-n)^2. Ill give brainliest to correct answer!
Answer:
(i) 2x+3y=9.3
5
ˉ
⇒2x+3y−9.3
5
ˉ
Comparing the equation with ax+by+c=0
a=2,b=3,c=−9.3
5
ˉ
Answer:
[tex]\frac{9}{4}[/tex] - (x - [tex]\frac{3}{2}[/tex] )²
Step-by-step explanation:
Given
3x - x² ← factor out - 1 from each term
= - (x² - 3x)
Using the method of completing the square
add/subtract ( half the coefficient of the x- term)² to x² - 3x
= - (x² + 2(- [tex]\frac{3}{2}[/tex])x + [tex]\frac{9}{4}[/tex] - [tex]\frac{9}{4}[/tex] )
= - (x - [tex]\frac{3}{2}[/tex] )² - 1(- [tex]\frac{9}{4}[/tex] )
= [tex]\frac{9}{4}[/tex] - (x - [tex]\frac{3}{2}[/tex] )²
What is the slope of a line parallel to a line with equation -4y + 7x = 20?
Answer:
[tex]{ \underline{ \sf{slope \: is \: \frac{7}{4} }}}[/tex]
Step-by-step explanation:
Parallel lines have same slopes.
General equation of line:
[tex]y = mx + c[/tex]
the line given:
[tex] - 4y + 7x = 20 \\ 4y = 7x - 20 \\ y = \frac{7}{4} x - 5[/tex]
