Answer:
-4 -5x
Step-by-step explanation:
4(1 – 3x) + 7x – 8.
Distribute
4 -12x +7x -8
Combine like terms
-4 -5x
Answer:
The simplified answer of this expression is -5x - 4
Step-by-step explanation:
4(1 - 3x) + 7x - 8
Distribute 4 to (1 - 3x)
4 - 12x + 7x - 8
Rearrange the terms so it'll be easier to combine them.
4 - 8 - 12x + 7x
Combine like terms.
-4 - 5x
Put the equation in standard form.
-5x - 4
On the circle below, tangent line BC¯¯¯¯¯ is constructed by striking an arc from point D that intersects circle A at point B. The measure of EC¯¯¯¯¯ is 8 units and other measures are shown on the diagram below. Enter the distance from point D to point B.
Answer:
[tex]\huge\boxed{BD = 12\ units}[/tex]
Step-by-step explanation:
If AB = 5 , then AE = 5 [Radii of the same circle]
So,
AC = AE + EC
AC = 8+5
AC = 13 units
Now, Using Pythagorean theorem to find the missing side i.e. BD because tangent strikes the circle at 90 degrees making the triangle a right angled triangle
[tex]c^2=a^2+b^2[/tex]
Where c = AC , a = BD and b = AB
[tex]13^2 = BD^2+5^2[/tex]
169 = BD² + 25
Subtracting 25 to both sides
169 - 25 = BD²
BD² = 144
Taking square root on both sides
BD = 12 units
Raj tested his new flashlight by shining it on his bedroom wall. The beam of light can be described by the equation . How many inches wide is the beam of light on the wall?
Answer:
12 inches
Step-by-step explanation:
Raj tested his new flashlight by shinning it on his bedroom wall the beam of the light can be described by the equation (x^2-2x) + (y^2-4y) - 31=0. how many inches wide is the beam of light on the wall
Solution
Given:
(x^2-2x) + (y^2-4y) - 31=0
By completing the square
(x^2-2x) + (y^2-4y) - 31=0
(x^2-2x+1-1) + (y^2-4y+4-4)-31=0
(x-1)^2 -1 + (y-2)^2 - 4 - 31=0
(x-1)^2 + (y-2)^2 - 1 - 4 - 31=0
(x-1)^2 + (y-2)^2 - 36=0
(x-1)^2 + (y-2)^2=36
Writing the equation in the form: (x-h)^2+(y-k)^2=r^2
(x-1)^2+(y-2)^2=6^2
From the above, r=6
Where,
r=radius
how wide is the diameter ?
radius=6
Diameter= 2 × radius
=2×6
=12 inches
Answer:
12
Step-by-step explanation:
to graph it just scan the equation on photo math!!
Which graph represents the solution set of this inequality?
10c + 5 < 45?
Answer:
see below
Step-by-step explanation:
10c + 5 < 45
Subtract 5 from each side
10c + 5-5 < 45-5
10c < 40
Divide by 10 on each side
10c/10 < 40/10
c < 4
Open circle at 4 and the line going to the left
Avani is building a rectangular play area. The length of the play area is 7.5 meters. The width of the play area is 5.3 meters. If she wants to cover the area in foam, how much foam does she need to buy? Due to the accuracy of the tape measure Avani used, the amount of foam needed to cover the play area is A.39 B.39.75 C.39.8 D.40
Answer:
Step-by-step explanation:
Area of the rectangle length x width
7.5x5.3 =39.75 sq.m
so, B is the correct answer.
A study was conducted on students from a particular high school over the last 8 years. The following information was found regarding standardized tests used for college admitance. Scores on the SAT test are normally distributed with a mean of 982 and a standard deviation of 198. Scores on the ACT test are normally distributed with a mean of 19.6 and a standard deviation of 4.5. It is assumed that the two tests measure the same aptitude, but use different scales.If a student gets an SAT score that is the 20-percentile, find the actual SAT score.SAT score =What would be the equivalent ACT score for this student?ACT score =If a student gets an SAT score of 1437, find the equivalent ACT score.ACT score =
Answer:
Actual SAT Score = 815.284
Equivalent ACT Score = 15.811
The equivalent ACT Score = 29.95
Step-by-step explanation:
From the given information:
Scores on the SAT test are normally distributed with :
Mean = 982
Standard deviation = 198
If a student gets an SAT score that is the 20-percentile
Then ;
P(Z ≤ z ) = 0.20
From the standard z-score for percentile distribution.
z = -0.842
Therefore, the actual SAT Score can be computed as follows:
Actual SAT score = Mean + (z score × Standard deviation)
Actual SAT score = 982 + (- 0.842 × 198)
Actual SAT score = 982 + ( - 166.716)
Actual SAT score = 982 - 166.716
Actual SAT Score = 815.284
Scores on the ACT test are normally distributed with a mean of 19.6 and a standard deviation of 4.5.
Mean = 19.6
Standard deviation = 4.5
Equivalent ACT Score = 19.6 + (- 0.842 × 4.5)
Equivalent ACT Score = 19.6 + ( - 3.789)
Equivalent ACT Score = 15.811
If a student gets an SAT score of 1437, find the equivalent ACT score.
So , if the SAT Score = 1437
Then , using the z formula , we can determine the equivalent ACT Score
[tex]z = \dfrac{X - \mu}{\sigma}[/tex]
[tex]z = \dfrac{1437 - 982}{198}[/tex]
[tex]z = \dfrac{455}{198}[/tex]
z =2.30
The equivalent ACT Score = 19.6 + (2.30 × 4.5)
The equivalent ACT Score = 19.6 + 10.35
The equivalent ACT Score = 29.95
A number rounded to the nearest hundred thousand is 400,00. The same number rounded to the nearest ten thousand is 350,000. What could be the number?
Answer:
the number could be between 350,000 and 354,999
Step-by-step explanation:
when calculating to the nearest hundred thousand
for instance, your number is in this format abc,def, the hundred thousand place is determined by "b".
So if the value of b is over 5, when approximating, 1 is added to a.
if the value of b is below 5, when approximating, 0 is added to a.
Therefore, 354,999 to the nearest hundred thousand is 400,000
when calculating to the nearest ten thousand
for instance, your number is in this format abc,def, the ten thousand place is determined by "c".
So if the value of c is over 5, when approximating, 1 is added to b.
if the value of c is below 5, when approximating, 0 is added to b.
Therefore, 354,999 to the nearest ten thousand is 350,000
The width of a rectangle measures (6.8d-4.2)(6.8d−4.2) centimeters, and its length measures (9.2d+8.7)(9.2d+8.7) centimeters. Which expression represents the perimeter, in centimeters, of the rectangle?
Answer:
The perimeter of the rectangle is represented by [tex]p = 32\cdot d + 9[/tex], measured in centimeters.
Step-by-step explanation:
The perimeter ([tex]p[/tex]) of a rectangle, measured in centimeters, is represented by this formula:
[tex]p = 2\cdot (w+l)[/tex]
Where [tex]w[/tex] and [tex]l[/tex] are width and length, measured in centimeters.
If [tex]w = 6.8\cdot d-4.2[/tex] and [tex]l = 9.2\cdot d+8.7[/tex], the expression that represents the perimeter is:
[tex]p = 2\cdot (16\cdot d +4.5)[/tex]
[tex]p = 32\cdot d + 9[/tex]
The perimeter of the rectangle is represented by [tex]p = 32\cdot d + 9[/tex], measured in centimeters.
Events A and B are mutually exclusive. Find the missing probability.
P(A) = 1/4 P(B) = 13/20 P(A or B) = ?
4/5
1/2
9/10
3/8
Answer:
Option C.
Step-by-step explanation:
It is given that,
[tex]P(A)=\dfrac{1}{4}[/tex]
[tex]P(B)=\dfrac{13}{20}[/tex]
It is given that events A and B are mutually exclusive. It means they have no common elements.
[tex]P(A\cap B)=0[/tex]
We know that,
[tex]P(A\ or\ B)=P(A\cup B)=P(A)+P(B)-P(A\cap B)[/tex]
On substituting the values, we get
[tex]P(A\cup B)=\dfrac{1}{4}+\dfrac{13}{20}-0[/tex]
[tex]P(A\cup B)=\dfrac{5+13}{20}[/tex]
[tex]P(A\cup B)=\dfrac{18}{20}[/tex]
[tex]P(A\cup B)=\dfrac{9}{10}[/tex]
Therefore, the correct option is C.
The P (A or B) should be [tex]\frac{9}{10}[/tex]
Given that,
P(A) = 1 by 4 P(B) = 13 by 20Based on the above information, the calculation is as follows:
[tex]= \frac{1}{4} + \frac{13}{20}\\\\= \frac{5+13}{20} \\\\= \frac{18}{20}\\\\= \frac{9}{10}[/tex]
Learn more: https://brainly.com/question/17429689?referrer=searchResults
Starting at the same spot on a circular track that is 80 meters in diameter, Hillary and Eugene run in opposite directions, at 300 meters per minute and 240 meters per minute, respectively. They run for 50 minutes. What distance separates Hillary and Eugene when they finish
Answer:
143.32 m
Step-by-step explanation:
Given the following :
Diameter of circular track = 80m
Hillary's speed = 300m per minute
Eugene's speed = 240m per minute
Run time = 50 minutes
Note: they both run in opposite direction.
Calculate the Circumference(C) of the circle :
C = 2πr or πd
Where r = radius ; d = diameter
Using C = πd
C = πd
C = π * 80
C = 251.327
Eugene's distance covered = (240 * 50) = 12000
Hillary's distance covered = (300 * 50) = 15000
Number turns :
Eugene = 12000/ 251.327 = 47.746561
Hillary = 15000/251.327 = 59.683201
Therefore ;
48 - 47.746561 = 0.253439
60 - 59.683201 = 0.316799
(0.253439+0.316799) = 0.570238
Distance which separates Eugene and Hillary when they finish :
0.570238 * 251.327 = 143.32 m
The 100-meter dash times in the girls track meet were normally distributed with a mean of 13 seconds and a standard deviation of 0.3 seconds. What is the probability that a runner finished between 12.4 and 14 seconds?
Answer:
The probability is 0.97682
Step-by-step explanation:
We start by finding the z-values of the runner times given.
Mathematically;
z-score = (x-mean)/SD
From the question, mean = 13 seconds and SD = 0.3 seconds
So for 12.4 seconds, we have;
z = (12.4-13)/0.3 = -0.6/0.3 = -2
For 14 seconds, we have;
z = (14-13)/0.3= 1/0.3 = 3.33
So the probability we want to calculate is;
P(-2<z<3.33)
We can find this using the standard normal distribution table
Mathematically;
P(-2<z<3.33) = P(z<3.33) - P(z < -2)
Using the standard normal distribution table, the value of this is;
P(-2<z<3.33) = 0.97682
What is happening to this graph when the x-values are between - 1 and 1?
A. It is decreasing.
B. It is constant
C. It is increasing
Answer:
A. It’s decreasing
Step-by-step explanation:
Hey there!
Well on the graph at points -1 and 1 we can tell the line is going down,
meaning the line is decreasing.
Hope this helps :)
Answer:it is increasing
Step-by-step explanation:
the function f(x)=-(x5+)(x+1) is shown. what is the range of the function
Answer:
all real numbers less than or equals to 4
Suppose you start at the origin, move along the x-axis a distance of 5 units in the positive direction, and then move downward along the z-axis a distance of 3 units. What are the coordinates of your position
Answer:(x,z)=(5,-3)
Step-by-step explanation:
Given
We move 5 units in x-axis
3 units in downward along z-axis
Suppose a z-axis is vertical and x -axis is horizontal as shown in fig.
So, coordinates after movement is given by the movement along x-axis and z-axis.
So, final coordinates is (5,-3) in x-z Plane .
As there is no movement in z-axis , so Y-coordinate will remain zero.
PLEASE ANSWER QUICKLY ASAP
READ QUESTIONS CAREFULLY
Answer:
see details below
Step-by-step explanation:
a) week 1 : #10" / (#10"+#12") = 509 / 736 = 69% (to nearest percent)
b) week 2 : #10" / (#10"+#12") = 766 / 1076 = 383/538 = 71% (to nearest percent)
A).69% for week 1
B)71% for week 2
How many solutions does the following equation have? 4(y-30)=4y+124(y−30)=4y+12
Answer:
A. No solution
Step-by-step explanation:
Choose 1 answer:
A. No solutions
B. Exactly one solution
C. Infinitely many solutions
Solution
Given:
4(y-30)=4y+12
Open parenthesis
4y-120=4y+12
Collect like terms
4y-4y=12+120
0=142
There is no solution to the equation, therefore, the answer is A
Please help me with this question asap!!!
Answer:
Choice A
Step-by-step explanation:
A fair coin is tossed 5 times in a row. The exact probability of the coin landing heads exactly 2 times is?
[tex]|\Omega|=2^5=32\\|A|=10\\\\P(A)=\dfrac{10}{32}=\dfrac{5}{16}[/tex]
Answer:
answer is 5/16
Step-by-step explanation: i did plato
Write the explicit rule by writing each term as the product of the first term.
1.) N 1 2 3 4
F(n) 3 15 75 375
2.) 40, 60, 90, 135,
Answer:
1 f(n) = 3(5)^x-1
2 f(n) = 40(3/2)^x-1
Step-by-step explanation:
The first number in the sequence, times the (multiplicative factor)^ x-1 is the rule for geometric sequences.
Answer:
graph A on edge 2020
Step-by-step explanation:
I took the test
Find y.
A. √2/2
B. 4
C. √6/2
D. √2
Answer:
Step-by-step explanation:
the answer is option D
WHEN YOU SUBSTITUTE THE VALUES YOU WILL GET IT............
Shireen starts from 100 and writes a series of numbers in which EACH NUMBER IS 4 MORE THAN THE NUMBER AFTER IT. Shireen's series will be A.100, 104, 108, 112, B.100, 104, 100, 104, C.100, 96, 92, 88, D.100, 400, 800, 1200,
Answer:C. 100, 96, 94, 90.
Step-by-step explanation:
If shireen starts at 100, and if the number is 4 more than the number after it. You must subtract 4 to the previous number to get the next number.
So= 100-4= 96
= 96-4= 94
=94-4 = 90
ANSWER IS= 100, 96, 94, 90, etc....
I hope this helps!
WILL AWARD BRAINLIEST IF CORRECT!!!!! ALSO PLEASR HURRY I'M ON A TIMER!! Which graph represents the following piecewise defined function? (images attatched)
Answer:
The last one.
Step-by-step explanation:
For x>3, the graph should start at x=3 and y = 2*3-3 = 3 with an open circle, since x must not be equal to 3.
The last graph is the only one that has that.
Furthermore, the middle part is a straight line from -2 ≤ x ≤ 3. The 'or equals' part in there reveals that the straight line segment should have closed circles, all solutions that don't have that can be discarded. So that hint alone points you to the last solution.
Tuesday 8 hours and 18 hours minutes Wednesday 7 hours and 54 minutes how many hours did Brett work in total this week
Answer:
(if you just add them together), it is 16 hours and 12 minutes
Step-by-step explanation:
8 hours plus 7 hours is 15 hours. 54 minutes plus 6 minutes is another hour. We then have 12 minutes left over. This could also be 16 1/5 hrs.
Which statement is true about the solutions to x^2 - 1 = 24
A. There are two distinct irrational solutions.
B. There are two distinct rational solutions
C. There is only one rational solution
D. There is only one irrational solution
Answer:
B. There are two distinct rational solutions
Step-by-step explanation:
x^2 -1 = 24
Add 1 to each side
x^2 -1+1 = 24+1
x^2 = 25
Take the square root of each side
sqrt(x^2) = ±sqrt(25)
x = ±5
Answer:
B.
Step-by-step explanation:
x^2 - 1 = 24
x^2 = 25
Taking the square root of both sides:
x = -5, 5.
2 distinct rational solutions.
In the figure above, O is a circle. What is the
measure of obtuse angle AOB, in degrees?
Answer:
An obtuse angle is an angle that is bigger than 90° degrees, but doesn’t reach a straight line at 180°.
Step-by-step explanation:
i didnt see a figure above but this is the answer to "what is the measure if obtuse angle in degrees?"
Write the event as set of outcomes. We flip three coins and obtain more tails than heads.
A. {ttt}
B. {ttt, tth, tht, htt}
C. {ttt, tth}
D. {tth, tht, htt}
Answer:
B.
Step-by-step explanation:
All the possible outcomes are listed on choice B.
The event is a set of outcomes. if we flip three coins and obtain more tails than heads is E = {ttt, tth, tht, htt} option (B) is correct.
What is set?A set is a collection of clearly - defined unique items. The term "well-defined" applies to a property that makes it simple to establish whether an entity actually belongs to a set. The term 'unique' denotes that all the objects in a set must be different.
We have three coins.
As we know, in a coin there are two sides head and a tail.
If we flip three coins then the set of all the possible outcomes:
O = {HHH,HHT,HTH,HTT,THH,THT,TTH,TTT}
The set of outcomes has more tails than heads.
E = {ttt, tth, tht, htt}
We can find the probability, the probability can be defined as the ratio of the number of favorable outcomes to the total number of outcomes, in other words, the probability is the number that shows the happening of the event.
Probability = 4/8 = 1/2
Thus, the event is a set of outcomes. if we flip three coins and obtain more tails than heads is E = {ttt, tth, tht, htt} option (B) is correct.
Learn more about the set here:
brainly.com/question/8053622
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Hmm What's 2⁄3 of 90cm?
Answer:
Hey there!
2/3 of 90 cm would be 60 cm.
Hope this helps :)
Answer
[tex] \boxed{60}[/tex]
Step by step explanation
To multiply one fraction by another, multiply the numerators for the numerator and multiply the denominators for its denominator and reduce the fraction obtained after multiplication into lowest term :
[tex] \mathsf{ \frac{2}{3} \times 90}[/tex]
⇒[tex] \mathsf{ \frac{2 \times 90}{3 \times 1} }[/tex]
⇒[tex] \mathsf{ \frac{180}{3} }[/tex]
⇒[tex]60[/tex]
Hope I helped!
Best regards!!
Please answer this question now
Answer:
Measure of arc CD = 112°
Step-by-step explanation:
Since quadrilateral ABCD is a cyclic quadrilateral,
m∠A + m∠C = 180°
129° + m∠C = 180°
m∠C = 180° - 129°
m∠C = 51°
Since, m(arc BD) = 2(m∠C) [Since measure of the arc is double of its inscribed angle]
= 2(51°)
= 102°
Since, m(arc BD) + m(arc CD) + m(arc BC) = 360°
102° + m(arc CD) + 146° = 360°
m(arc CD) = 360° - (102° + 146°)
= 112°
Therefore, measure of arc CD is 112°.
We want to build a swimming pool that is 2m by 6m. On our page it measured out to be 8cm by 24cm. What is tge scale that can be used
Answer:
1:25
Step-by-step explanation:
Given
Dimensions of swimming pool:
W = 2 mL = 6 mDimensions on paper:
w = 8 cml = 24 cmScale is the ratio of same measurements:
w/W = 8 cm/2 m = 8 cm / 200 cm = 1/25So the scale is 1:25
Tori and Gavin were trying to solve the equation: (x+1)^2-3=13(x+1) 2 −3=13left parenthesis, x, plus, 1, right parenthesis, squared, minus, 3, equals, 13 Tori said, "I'll add 333 to both sides of the equation and solve using square roots." Gavin said, "I'll multiply (x+1)^2(x+1) 2 left parenthesis, x, plus, 1, right parenthesis, squared and rewrite the equation as x^2+2x+1-3=13x 2 +2x+1−3=13x, squared, plus, 2, x, plus, 1, minus, 3, equals, 13. Then I'll subtract 131313 from both sides, combine like terms, and solve using the quadratic formula with a=1a=1a, equals, 1, b=2b=2b, equals, 2, and c=-15c=−15c, equals, minus, 15."
The other answer is correct, its both !<3
Answer:
Both
Step-by-step explanation:
Both Tori and Gavin are correct, the two methods work. Completed this in Khan Academy, it's correct.
A traveler explores the regions of Mexico. She travels from Sonora to Colima, and
Colima to Tamaulipas. Write two inequalities that represent the two possible distances
from Tamaulipas back to Sonora.
Answer:
809mi
Step-by-step explanation:
There are two ways to travel form Tamaulipas to Sorona. The first if the direct route from Sorona to Tamaulipas which is 809mi. The another route is to travel to Colima from Sorona and then travel to Tamaulipas from Colima. This is the long distance routes in which there are two destination points. The direct route is shorter in length therefore preferable.
