Answer:
Step-by-step explanation:
(x-4) (x+10) ⇒ (x+a)(x+b)=x²+(a+b)x+ab
a=-4 , b=10
x²+(-4+10)x+-4(10)
x²+6x-40
(3x+4) (3x +5)
3(x+4/3) *3(x+5/3) ⇒ identity : (x+a)(x+b)=x²+(a+b)x+ab
a=4/3 b=5/3
3*3=9
9[x²+(4/3 +5/3)x+4/3(5/3)]
9[x²+9/3 x+20/9]
9x²+27x+20
(-3a +5b +4c)^2 ⇒
suitable identity is (a+b+c)²= a² + b² + c² + 2ab + 2bc + 2ca
a=-3a , b=5b , c=4c
9a²+25b²+16c²- 30ab +40bc - 24ca
Solve two-step equations. -5/2 a + 5 = 25
Answer:
a = -8
Step-by-step explanation:
-5/2 a + 5 = 25
Subtract 5 from each side
-5/2 a + 5-5 = 25-5
-5/2 a = 20
Multiply each side by -2/5
-2/5 *-5/2 a = 20*-2/5
a = -8
A rectangular box with a square base contains 24 cubic feet. if the height of the box is 18 inches, how many feet are there in each side of the base?
Answer:
4
Step-by-step explanation:
V = Lwh
the volume (given) = 24 ft^3
the height (given) = 18" = 1.5'
24 = L*w*1.5
divide both sides by 1.5
16 = Lw
You need to find the number of feet in each side of the base
since the box has a square base
L = W
AND, found above, L*w = 16
so 4*4= 16
Answer - 4
someone help me really quick
Answer:
u^18
Step-by-step explanation:
(u^3)^6
=
u^(3*6)
=
u^18
Hope this helps!
Jess receives a $15000 salary for working as an engineer. If Jess has to spend $6000 of her salary on expenses each year, then what percent of Jess's money does she have to spend? Round your answer to the nearest whole number if necessary.
Answer:
Jess will have to spend 40% of her salary
Step-by-step explanation:
Jess salary = $15,000
Jess expenses = $6,000
what percent of Jess's money does she have to spend
Percentage of Jess expenses = Jess expenses / Total salary × 100
= 6,000 / 15,000 × 100
= 0.4 × 100
= 40%
Jess will have to spend 40% of her salary
\large 6\cdot\frac{6+2^2}{6+2-6}
Answer:
30Step-by-step explanation:
Given the expression [tex]\large 6\cdot\frac{6+2^2}{6+2-6}[/tex], on simplification we have;
[tex]= \large 6\cdot\frac{6+2^2}{6+2-6}\\\\= \large 6\cdot\frac{6+4}{8-6}\\\\= \large 6\cdot\frac{10}{2}\\\\= 6* 5\\\\= 30[/tex]
Hence the equivalent value of the expression is 30
Help now for brainliest,5stars and thanks.Find the values of x in the range 0≤x≤180° for which 15sin^2 x+11cox-17=0
Answer:
[tex]\bold{x = 66.42^\circ, 70.53^\circ}[/tex]
Step-by-step explanation:
Given equation is:
[tex]15sin^2 x+11cosx-17=0[/tex]
To find:
Values of [tex]x[/tex] in the range [tex]0^\circ\leq x\leq180^\circ[/tex].
Solution:
First of all, let us recall one identity of square of sine and square of cosine.
Sum of square of sine of an angle and square of cosine of the same angle is equal to 1.
[tex]\bold{sin^2\theta+cos^2\theta=1}[/tex]
So
Putting [tex]sin^2x=1-cos^2x[/tex] in the given equation.
[tex]15(1-cos^2x)+11cosx-17=0\\\Rightarrow 15-15cos^2x+11cosx-17=0\\\Rightarrow -15cos^2x+11cosx-2=0\\\Rightarrow 15cos^2x-11cosx+2=0\\\Rightarrow 15cos^2x-5cosx-6cosx+2=0\\\Rightarrow 5cosx(3cosx-1)-2(3cosx-1)=0\\\Rightarrow (5cosx-2)(3cosx-1)=0\\\Rightarrow cosx=\dfrac{2}{5}, \dfrac{1}{3}[/tex]
So, in the range [tex]0^\circ\leq x\leq180^\circ[/tex]
[tex]\bold{x = 66.42^\circ, 70.53^\circ}[/tex]
NEED IN 10 MIN. WILL GIVE BRAINLEST Solve the triangle. B = 36°, a = 41, c = 17
Answer:
Yes this is a Triangle
36 degrees of any side then 41 would connct to 36 and 17 would connects to 36 and 41! If this is Khan Academy your asking out of its a Yes, it is a Triangle
HOPE IM THE BRANLIESS UwUAnswer:
It is a triangle:
Step-by-step explanation:
b² = a² + c² - 2(a)(c)cos(B)
b² = 41² + 20² - 2(41)(20)cos(36)
b² = 754.2121292
b = 27.46292281
b = 27.463
A = 41, B = 27.4, C = 17
Jake ran 4 1/4 miles on Monday and 2 2/3 miles on Tuesday. On Wednesday he ran 1 fewer miles then he ran on Monday. How many miles did he run in all? PLEASE SHOW YOUR WORK I WILL MARK YOU BRAINLIEST AND PLEASE EXPLAIN
Answer:
Jake ran 10 1/6 miles in total
Step-by-step explanation:
4 1/4 + 2 2/3 - (4 1/4-1).
v
6 11/12 + 3 1/4
v
6 11/12 + 3 3/12 = 10 1/6
Jake ran 10 1/6 miles in total (Mon, Tues, Wed).
Answer:
61/6 or 10.1666666667
Step-by-step explanation:
Monday = 4 1/4
Tuesday = 2 2/3
Wednesday = Monday - 1
=> Monday = 17/4 miles
=> Tuesday = 8/3 miles
=> Wednesday = 17/4 - 4/4 = 13/4 miles.
=> (17/4 + 13/4) + 8/3
=> 30/4 + 8/3
=> Take the LCM of the denominators.
=> LCM = 12
=> 90/12 + 32/12
=> 122/12
SImplify 122/12
=> 61/6 or 10.1666666667
explain how the phrase oh heck another hour of algebra can help a student recall the trigonometric ratios
Answer:
its a mnemonic
Oh Heck Another Hour Of Algebra
(O = opposite side, H = hypotenuse ) = sine
(A = adjacent side, H = hypotenuse ) = cosine
(O = opposite side, A = adjacent ) = tangent
Today I would like for you to work one of the following problems and explain your process/reasoning clearly and thoroughly.
Answer:
Step-by-step explanation:
A line from the center of the circle to bisect a chord is perpendicular to the chord.
Therefore, OA⊥ AS
Join O & R
OR is radius of the circle
ΔOAR is right angled triangle.
Use Pythagorean theorem to find OR
OR² = OA² + RA²
= 3² + 4²
= 9 +16
OR² = 25
OR = √25
OR = 5 cm
OP is radius. Therefore, OP = OR = 5 cm
PA = OP + OA
= 5 + 3
PA = 8 cm
Drag each label to the correct location on the table. Each label can be used more than once. A cross country coach records the number of miles his athletes on the Junior Varsity and Varsity teams ran today and displays the data in the provided dot plots. Given the shape of each distribution, determine which measures of center and spread are appropriate for him to use to summarize the data from each team. mean mean interquartile range interquartile range standard deviation standard deviation median median
Answer:
a.) For the Junior Varsity Team, mean would be the appropriate measure of center since the data is symmetric or well-proportioned while we should use standard deviation for getting the measure of spread since it also measures the center and how far the values are from the mean.
b.) For the Varsity Team, the median would be the appropriate measure of the center since the data is skewed left and not evenly distributed so median could be used since it does not account for outliers while we use IQR or interquartile range in measuring the spread of data since IQR does not account for the data that is skewed.
For the Junior Varsity Team, the mean would be the appropriate measure of the center since the data is symmetric or well-proportioned .
What is median?Median represents the middle value of the given data when arranged in a particular order.
Since the data for the Junior Varsity Team is symmetric or well-proportioned, the mean would be the best way to determine the center, and standard deviation, which also measures the center and how far the values deviate from the mean, should be used to determine the spread.
The median could be utilized for the Varsity Team since the data is not evenly distributed and skewed to the left, and it does not take into account outliers.
We can use the interquartile range (IQR) to quantify the spread of the data because IQR does not take into account the skewed data.
Therefore, the varsity squad competes in intercollegiate or international competitions on behalf of the high school or institution while we should use standard deviation for getting the measure of spread since it also measures the center and how far the values are from the mean.
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hello, i need help pleaseeeeeeeeeeeeeeee
Answer:
f₁(x) = -3x + 2
f₂(x) = x - 4
f₃(x) = x + 8
f₄(x) = -2x - 6
f₅(x) = -3x
Step-by-step explanation:
1). Since function f₁ (blue line) passes through a point (0, 2) and (-2, 8)
Let the equation of the blue line is,
y = mx + b
Since slope of the line 'm' = [tex]\frac{y_2-y_1}{x_2-x_1}[/tex]
m = [tex]\frac{8-2}{-2-0}[/tex]
m = -3
Y-intercept 'b' = 2
Therefore, equation of the line will be,
y = -3x + 2
Linear function representing the line will be,
f₁(x) = -3x + 2
2). Let the equation of the red line passing through (0, -4) and (2, -2) is,
y = mx + b
Slope of the line 'm' = [tex]\frac{y_2-y_1}{x_2-x_1}[/tex]
m = [tex]\frac{-4+2}{0-2}[/tex]
m = 1
y-intercept 'b' = -4
Therefore, the linear function will be,
f₂(x) = x - 4
3). Let the equation of the green line passing through (-6, 2) and (-2, 6) is,
y = mx + b
Slope of the line 'm' = [tex]\frac{6-2}{-2+6}[/tex]
m = 1
y-intercept 'b' = 8
Therefore, linear function will be,
f₃(x) = x + 8
4). Let the equation of the yellow line passing through (-6, 6) and (-4, 2) is,
y = mx + b
Slope of the line = [tex]\frac{6-2}{-6+4}[/tex]
m = -2
y-intercept of the line 'b' = -6
Therefore, function representing the line will be,
f₄(x) = -2x - 6
5). Let the equation of the pink line is passing through (0, 0) and (-2, 6) is,
y = mx + b
Since the line is passing through origin, y-intercept 'b' = 0
Slope of the line = [tex]\frac{6-0}{-2-0}[/tex]
m = -3
Therefore, equation of the linear function will be,
f₅(x) = -3x
A trader bought a bag for 125gh cedis. he later sold it at a profit of 30%. What is his selling price
Answer:
162.5 Cedis
Step-by-step explanation:
Cost Price= 125
Profit % = 30%
Selling price=?
Selling price= Cost price+ profit
Profit = ?
[tex]profit \% = \frac{profit}{cost \: price} \times 100[/tex]
[tex]30 \% = \frac{x}{125} \times 100[/tex]
[tex]30 \% = \frac{100x}{125} \\ 30 \times 125 = 100x[/tex]
[tex]3750 = 100x \\ \frac{3750}{100} = \frac{100x}{100} \\ x = 37.5[/tex]
Profit = 37.5 gh Cedis
Selling price= 125+37.5
Selling price= 162.5 gh Cedis
The selling price of a bag is 162.5Cedis.
It is required to find the selling price.
What is profit?The profit is defined as the amount gained by selling a product, and it should be more than the cost price of the product.
Given that :
Let the profit be x.
Cost Price= 125
Profit % = 30%
profit%=profit/cp*100
30=profit/125*100
3750=100x
x=37.5
profit=37.5
Selling price= Cost price+ profit
Selling price=125+37.5
Selling price=162.5ghcedis
So, the selling price of a bag is 162.5Cedis.
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how many words can be formed by using the W,X,Y,Z if repetitions is not allowed?
- 30
- 24
- 18
- 12
Answer:
24
Step-by-step explanation:
What you have here is a permutation, seeing as each element can only be used once.
We have 4 letters initially, so we can choose any 1 as our first letter. We have 4 choices for our first letter
However, once we choose our first letter, we can't use it anymore, so, for our second letter, we can only choose from the remaining 3 letters.
Furthermore, once we choose our second letter, we can only choose our 3rd letter from the remaining two letters we didn't choose yet.
Finally, our last letter will always be the one we didn't choose the last 3 times. So there is only one choice here.
Going off of this, we have four choices for the 1st letter, three choices for the 2nd letter, two choices for the 3rd letter, and one choice for the 4th letter
The way to calculate how many permutations we have without repetition is using factorials
N!
Where N is the number of elements you have.
In this case, it would be 4!
4! is 4 * 3 * 2 * 1
Which equals 24
If you notice, each number in 4! is the number of options we have for each choice. 4, then 3, and so on
.You deposit $200 in an account earning 3.5% simple interest. How long will it take for the
balance of the account to be $221?
Answer:
3 times the percent for the balance to be $221
Step-by-step explanation:
Write each fraction as a decimal and a percent. A) 7/8 B) 9/75 C/ 120/75
Answer:
A) 0.875, 87.5%
B) 0.12, 12%
C) 1.6, 160%
Step-by-step explanation:
Answer:
A) 0.875, 87.5%
B) 0.001, 0.1%
C) 1.6, 160%
Step-by-step explanation:
I honestly just used a calculator, but it could also be solved using the butterfly technique. For percentages just move the decimal to the left two places.
The temperature in Anchorage, Alaska at 6:00 am was 2°C. If the temperature drops 2 degrees each hour, what is the temperature in degrees celsius at 2:00 pm
Answer:
-12°C
Step-by-step explanation:
6AM = 2°C
8AM= -2°C
10AM= -6°C
12AM= -8°C
2PM= -12°C
the temperature in degrees Celsius at 2:00 pm would be -14°C.
To find the temperature in degrees Celsius at 2:00 pm, we need to determine the number of hours that have passed from 6:00 am to 2:00 pm, and then calculate the temperature decrease accordingly.
From 6:00 am to 2:00 pm, a total of 8 hours have passed (6 hours from 6:00 am to 12:00 pm, and 2 hours from 12:00 pm to 2:00 pm).
Given that the temperature drops 2 degrees Celsius each hour, we can multiply the number of hours (8) by the rate of temperature decrease (2 degrees/hour):
Temperature decrease = 8 hours × 2 degrees/hour = 16 degrees
Starting with a temperature of 2°C at 6:00 am, if the temperature drops 16 degrees Celsius over 8 hours, we can subtract 16 from the initial temperature:
Temperature at 2:00 pm = 2°C - 16°C = -14°C
Therefore, the temperature in degrees Celsius at 2:00 pm would be -14°C.
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In the figure shown, what is the measure of angle x? (5 points) 115 degrees 130 degrees 145 degrees 150 degrees
Answer:
x=115
Step-by-step explanation:
180 - (115) =65(triangle)
65 + x = 180(on a line)
x=180-65
x = 115
Answer:
115 degrees
Step-by-step explanation:
the person above me is right, but there is an easier way.
Just add 50 and 65 degrees and boom you have your answer.
The teacher wants to make a fruit punch for the class party. She needs 30 quarts of juice. If there are 15 kids bringing in juice, how many pints should each person bring?
Answer:
4 pints
Step-by-step explanation:
30 quarts ÷ 15 kids = 2 quarts per kid
there are 2 pints in a quart so..
2 quarts per kid x 2 pints per quarter = 4 pints
Hello, a quick question which number is least to greatest 0.359, 0.35, 1
Answer:
0.35, 0.359, 1
Step-by-step explanation:
0.359 = 359 thousandths
0.35 = 0.350 = 350 thousandths
1 = 1.000 = 1000 thousandths
Since 350 < 359 < 1000, then from least to greatest you get
0.35, 0.359, 1
Someone pls help . Thank you sm☄️ .
1) 3 is the Coefficient.
2) 10 is the constant.
3) 10.8 is the ans.
In comparing two distributions, which attribute would you not compare?
A. Shape
B. Center
C. Marginal frequency
D. Spread
Answer:
The correct option is;
C. Marginal frequency
Step-by-step explanation:
The objective of comparison of two distributions is to check the significant difference from each other
The general measures used to compare the difference between distributions are the measures of centers such as the mean, the measures of spread such as the standard deviation and the shape of the compared distribution curves
Marginal frequencies are the values found in the total row and total column portion of a two way frequency distribution table
The marginal frequency is used to calculate the marginal relative frequency
The values of the marginal frequency, which is a sum, does not characterize the details of a distribution to a large extent.
Answer:
C. Marginal frequency
Step-by-step explanation:
Find the midpoint of the segment below and enter its coordinates as an ordered pair. If necessary, express coordinates as fractions, using the slash mark (/) for the fraction bar. (-12, -3) (3, -8)
Answer:
[tex]=\left(-\frac{9}{2},\:-\frac{11}{2}\right)[/tex]
Step-by-step explanation:
[tex]\mathrm{Midpoint\:of\:}\left(x_1,\:y_1\right),\:\left(x_2,\:y_2\right):\\\quad \left(\frac{x_2+x_1}{2},\:\:\frac{y_2+y_1}{2}\right)\\\\\left(x_1,\:y_1\right)=\left(-12,\:-3\right),\:\left(x_2,\:y_2\right)=\left(3,\:-8\right)\\\\=\left(\frac{3-12}{2},\:\frac{-8-3}{2}\right)\\\\=\left(-\frac{9}{2},\:-\frac{11}{2}\right)[/tex]
What’s up guys, pls help 19b)
Thanks
Answer:
90°
Step-by-step explanation:
As given in the figure:
[tex]AC \perp CE\\
\therefore m\angle ACE = 90\degree \\ [/tex]
is this right? someone please check?
Answer:
The answer looks correct.
Step-by-step explanation:
All the other option doesn't match the above question's statement.
The last answer is the correct (in my opinion)
Answer:
Absolutely Correct
Step-by-step explanation:
Based on the definition of midpoint;
It is equidistant from both endpoints, and it is the centroid both of the segment and of the endpoints.
meaning the distance from the midpoint to one end is the same as the distance to the other end
Simplify. Can you explain it also?
[tex] \frac{9 {c}^{3} {de}^{2} }{12 {c}^{2}d {e}^{3} }[/tex]
Answer:
The answer is
[tex] \frac{3c}{4e}[/tex]Step-by-step explanation:
[tex] \frac{9 {c}^{3}d {e}^{2} }{12 {c}^{2} d {e}^{3} } [/tex]To solve the fraction reduce the fraction with d
That's we have
[tex] \frac{9 {c}^{3} {e}^{2} }{12 {c}^{2} {e}^{3} } [/tex]Next simplify the expression using the rules of indices to simplify the letters in the fraction
For c
Since they are dividing we subtract the exponents
We have
[tex] {c}^{3} \div {c}^{2} = {c}^{3 - 2} = c^{1} = c[/tex]For e
[tex]e^{2} \div {e}^{3} = e^{2 - 3} = {e}^{ - 1} = \frac{1}{e} [/tex]Substituting them into the expression we have
[tex] \frac{9c}{12e} [/tex]Reduce the fraction by 3
We have the final answer as
[tex] \frac{3c}{4e} [/tex]Hope this helps you
What is the center of the circle with the equation (x+4)2 + (y - 2)2 = 16?
Answer:
The center of the circle is
( - 4 , 2)Step-by-step explanation:
Equation of a circle is given by
(x - h)² + ( y - k)² = r²where r is the radius
(h, k) is the center of the circle
The center of a circle is given by
( - h , - k)
From the question equation of the circle is
( x + 4)² + ( y - 2)² = 16
Comparing with the general equation above
( h , k) = ( 4 , - 2)
The center of the circle is
( - h , - k) = ( - 4 , -(-2))
We have the final answer as
( - 4 , 2)Hope this helps you
Kyle rides his bicycle 15 mph for 2 hours how far does he travel
━━━━━━━☆☆━━━━━━━
▹ Answer
30 miles
▹ Step-by-Step Explanation
Multiply mph by hours:
15 mph * 2 hrs = 30 miles
Hope this helps!
CloutAnswers ❁
━━━━━━━☆☆━━━━━━━
Given \qquad m \angle LONm∠LONm, angle, L, O, N is a straight angle. \qquad m \angle MON = 8x - 13^\circm∠MON=8x−13 ∘ m, angle, M, O, N, equals, 8, x, minus, 13, degrees \qquad m \angle LOM = 7x - 17^\circm∠LOM=7x−17 ∘ m, angle, L, O, M, equals, 7, x, minus, 17, degrees Find m\angle MONm∠MONm, angle, M, O, N:
Answer:
[tex] \boxed{99°}[/tex]Step-by-step explanation:
m<MON = 8x - 13°
m<LOM = 7x - 17°
To find : m <MON
First, we have to find the value of x :
Create an equation
[tex] \mathrm{8x - 13 + 7x - 17 = 180}[/tex] ( sum of angle in straight line )
Collect like terms
[tex] \mathrm{15x - 13 - 17 = 180}[/tex]
Calculate
[tex] \mathrm{15x - 30 = 180}[/tex]
Move constant to R.H.S and change its sign
[tex] \mathrm{15x = 180 + 30}[/tex]
Calculate the sum
[tex] \mathrm{15x = 210}[/tex]
Divide both sides of the equation by 15
[tex] \mathrm{ \frac{15x}{15} = \frac{210}{15} }[/tex]
Calculate
[tex] \mathrm{x = 14}[/tex]
Now, let's find the value of m<MON
[tex] \mathrm{8x - 13}[/tex]
Plug the value of x
[tex] \mathrm{ = 8 \times 14 - 13}[/tex]
Calculate the product
[tex] \mathrm{ = 112 - 13}[/tex]
Calculate the difference
[tex] \mathrm{ = 99}[/tex] °
Hope I helped!
Best regards!
Answer:
48
Step-by-step explanation:
because i say so
What is the tangent ratio of KJL? (Question and answers provided in picture.)
Answer:
Option (1)
Step-by-step explanation:
The given triangle JKL is an equilateral triangle.
Therefore, all three sides of this triangle will be equal in measure.
Side JK = JL = KL = 48 units
Perpendicular LM drawn to the base JK bisects the base in two equal parts JM and MK.
By applying tangent rule in ΔJML,
tan(∠KJL) = [tex]\frac{\text{Opposite side}}{\text{Adjacent side}}[/tex]
= [tex]\frac{\text{LM}}{\text{JM}}[/tex]
= [tex]\frac{\text{LM}}{24}[/tex]
Since, Sin(K) = [tex]\frac{\text{Opposite side}}{\text{Hypotenuse}}[/tex]
Sin(60)° = [tex]\frac{\text{LM}}{48}[/tex]
[tex]\frac{\sqrt{3}}{2}=\frac{\text{LM}}{48}[/tex]
LM = 24√3
Now, tan(∠KJL) = [tex]\frac{\text{LM}}{24}[/tex]
= [tex]\frac{24\sqrt{3} }{24}[/tex]
Therefore, Option (1) will be the answer.
