Answers
Answer:
x = -9, 4
Step-by-step explanation:
The sides are marked congruent, so you have ...
x^2 +5x = 36
Subtracting 36 puts this in standard form:
x^2 +5x -36 = 0
To factor this, you need to find factors of -36 that have a sum of 5.
-36 = (-1)(36) = (-2)(18) = (-3)(12) = (-4)(9) = (-6)(6)
The sums of these factor pairs are 35, 16, 9, 5, 0.
The pair with a sum of 5 is (-4)(9), so the factorization of the quadratic is ...
(x -4)(x +9) = 0
The solutions are the values of x that make the factors zero:
x = 4, x = -9
Both of these solutions work in this problem.
Related Questions
When two pipes fill a pool together, they can finish in 4 hours. If one of the pipes fills half the pool then the other takes over and finishes filling the pool, it will take them 9 hours. How long will it take each pipe to fill the pool if it were working alone?
One pipe takes __ hours alone.
The other pipe takes __ hours alone.
Answers
One pipe takes 6 hours working alone.
The other pipe takes 12 hours working alone.
This is a rate of work problem. The formula utilized is
[tex]w=r\times t[/tex]
where
[tex]w[/tex] is the work done[tex]r[/tex] is the rate of work done[tex]t[/tex] is the time taken to do the workWe are looking for how long it will take each pipe to completely fill the pool
For pipe 1 working alone to fill 1 pool, the work done is 1;
[tex]w=r\times t\\\\1 = r_1 \times t_1\\\\t_1=\frac{1}{r_1}[/tex]
For pipe 2 working alone to fill 1 pool, the work done is 1;
[tex]w=r\times t\\\\1 = r_2 \times t_2\\\\t_2=\frac{1}{r_2}[/tex]
From the question, it would take 9 hours if each pipe took turns to fill half the pool. That is;
[tex]\frac{t_1}{2}+\frac{t_2}{2}=9\\\\t_1+t_2=18[/tex]
However, if both pipes worked together, it would take 4 hours for each pipe. That is;
[tex]w_1+w_2=w\\\\r_1t_1+r_2t_2=w\\\\4r_1+4r_2=1\\\\r_1+r_2=\frac{1}{4}[/tex]
Remember that [tex]r_1=\frac{1}{t_1}[/tex] and [tex]r_2=\frac{1}{t_2}[/tex]. So,
[tex]\frac{1}{t_1}+\frac{1}{t_2}=\frac{1}{4}\\\\\frac{t_1+t_2}{t_1t_2}=\frac{1}{4}[/tex]
Also recall that [tex]t_1+t_2=18[/tex]. So,
[tex]\frac{18}{t_1t_2}=\frac{1}{4}\\\\t_1t_2=72[/tex]
The only factors of 72 that satisfy the conditions
[tex]t_1+t_2=18\\\\t_1t_2=72[/tex]
are 6 and 12.
Therefore, pipe 1 will take 6 hours, and pipe 2 will take 12 hours to fill the pool if working alone.
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please, help!!!! Bussines Calc. I give 20 points. I need a full explanation.
Answers
I believe you are trying to find the most Cheapest cost?
Since the area had to be 1200m^2 the most biggest numbers we could divide with is 30 x 40, which equals to 1200.
30 x 20 (expensive one the lower) = 600 (wall 3) + 20 x 20 = 1000 (wall 3 + wall 1)
40 x 13 (cheapter one the higher) = 520 (wall 4) + 32 x 13 = 936 (wall 4 + wall 2)
Add all together, $1936 to build the whole fence.
(I don't know for sure if I am right. If I am right, can I have a brainliest?)
Blake was listening to his favorite radio station. He noticed that during one hour, 15 songs were played and 3 of them were by a group from Michigan.
A. What is the ratio of songs by the group from Michigan to the number of songs played?
B. Write the ratio in simplest form.
C. Suppose the station continues to play the ratio of songs. How many songs from the Michigan group will Blake hear in the next three hours?
Answers
Answer:
Step-by-step explanation:
A. What is the ratio of songs by the group from Michigan to the number of songs played? 3/15
B. In lowest terms, 3/15 is 1/5.
C. Suppose the station continues to play the ratio of songs. How many songs from the Michigan group will Blake hear in the next three hours? To answer this, multiply the 1-hour unit rate by 3: 3*3 = 9 Michigan group songs over the next 3 hours.
Cereal is on sale this week. Is it a better buy to get the 10-ounce box for $2.12 or the 14-ounce box for $2.74?
Answers
The 14-ounce box is cheaper at a cost of $2.74 than the 10-ounce box.
What is the division operation?In mathematics, divides left-hand operands into right-hand operands in the division operation. The primary purpose of the division is to generate equal groupings or to determine how many people are in each category after a fair distribution.
For example 4/2 = 2
First, we have to find the price for each ounce.
So for the 10-ounce box:
⇒ 2.12 / 10
Apply the division operation,
⇒ $0.212 per ounce.
Now for the 14-ounce box:
⇒ 2.74/ 14
Apply the division operation,
⇒ $0.19 per ounce.
Here the cost of the 14-ounce box is less than the 10-ounce box as 0.19 < 0.21
Therefore, the 14-ounce box is cheaper at a cost of $2.74.
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Si se duplica el radio(2) del círculo anterior, el número de veces que aumenta el area del círculo es?
Answers
Answer:
4
Step-by-step explanation:
Use the pattern in the sequence to determine the next two terms.
-16, 8, -4, 2. . .
Answers
Answer:
-1 , 1/2
Step-by-step explanation:
Each term is obtained by dividing by (-2)
-16/-2 = 8
So, the next two terms are:
2/-2 = -1
-1/-2 = 1/2
A city council acquired 3,437.5 acres of land to add to their park system. The city plans to divide the acreage evenly into 22 separate parks.
There will be ___ acres in each park.
please help
Answers
Today, Petland sold 8 times as many dogs as cats. If a total of 72 dogs and cats were sold, how many cats were sold?
Answers
9 cats were sold
solve pls brainliest
Answers
Answer:
48.95
Step-by-step explanation:
Please help me with this, im kinda struggling
Answers
Answer:
X=4
Step-by-step explanation:
Let's make an equation,
7/4 ÷ 14 = x ÷ 3
We can cross multiply
7/4 * 32 = x * 14
Now we have 56 = 14x
Divide both sides by 14
56 ÷ 14 = 4, 14x ÷ 14 = x
4 = x
x = 4
BRAINLIEST
please help me finish these
Answers
Answer:
15) 44.6 inches
16) 77.8 degrees
Step-by-step explanation:
15) we are given the angle and length of 16, drawing this out, 16 inches (the height) would be opposite of the angle and the length of the ramp would be hypotenuse.
we know that sine is opposite over hypotenuse, so we can use that to help find the length.
Rearrange:
sin21degrees = opposite/hypotenuse
hypotenuse*sin21degrees = opposite
hypotenuse = opposite/sin21degrees
Sub in values:
hypotenuse = 16/sin21degrees
hypotenuse = 44.6468 inches
16) we are given two side lengths and expected to find an angle, we now need to use the inverse of one of the trigonometric ratios.
Drawing this out, we are given the hypotenuse and adjacent lengths, so we can use the inverse cosine to find the angle
angle = cos^-1 adjacent/hypotenuse
angle = cos^-1 (7/26)
angle = 74.381 degrees
y + 2x = 2 and y + 4x = 0?
Answers
Answer:
y=4
Step-by-step explanation:
y+2x=2
2(y+2x)=2(2)
2y+4x=4
(2y+4x)-(y+4x)=4-0
y=4
100 points plus brainiest to right answer.
Answers
Answer:e d
Step-by-step explanation:
During a closeout sale, some television models are discounted 40%. If a television is on sale for $1,485, what is the original price of the television to the nearest dollar?
Answers
Answer: it should be 70
Step-by-step explanation:
because the re adding of the dollars
1485 x 1.4 = 2079
Find the minimum and maximum possible values for area of the garden
Answers
Answer:
Smallest: 12.8 square meters
Largest: 13.5 square meters
Step-by-step explanation:
I'm not 100% sure I understand this correctly as it seems like a very strange problem, but here it goes.
The smallest number that rounds to 3.2 is 3.15, and the smallest number that rounds to 4.1 is 4.05.
[tex]3.15*4.05=12.7575[/tex]
The smallest possible area is 12.8 rounded to the nearest 10th.
The largest number that rounds to 3.2 is 3.24999... and the largest that rounds to 4.1 is 4.14999...
[tex]3.24999*4.14999=13.4875[/tex]
That rounds to 13.5.
1. Two angles added together to produce 90 degrees a) Supplementary b) Complementary c) Right od) Vertical
Answers
Answer: B: complementary
Step-by-step explanation: :)
A recipe calls for
23
cup of sugar for every 4 teaspoons of vanilla. How much vanilla should be used for every 1 cup of sugar?
Answers
Answer:
.....
Step-by-step explanation:
Write the expression 83⋅83⋅83⋅83⋅83⋅83 as a power.Enter your answer by filling in the boxes.$$
Answers
Answer:
It's (8/3) 6 I took the test and that was the answer. Your Welcome!!!!!!!!!!!!!
Answer:
Its 83 the power of 6. Also Please choose my anwer as brainliest
Use the quadratic formula to solve x2 – 3x - 2 = 0
Answers
Answer:
C
Step-by-step explanation:
C
Answer:
c
Step-by-step explanation:
c is the answer to this problem
ABC is a triangle
AB = AC and BA is parallel to CD
Work out the size of the angle marked x
Answers
Step-by-step explanation:
so as ∆BCE is a right angled triangle
angle BEC = 90°
angle CBE = 22° (given)
apply angle sum property of triangle
so according to that
BCE + CBE + ECB = 180
22° + 90° + ECB = 180
102° + ECB = 180
ECB = 180 - 102
ECB = 78°
and also we know, that exterior angle of a triangle is equal to 2 interior angle of triangle,
so ,
x = 78°
hope this answer helps you dear! take care
Find the slope of the line that passes through point A (-2,0)and point B (0,10) using m=rise/run
Answers
Answer:
m = 5
Step-by-step explanation:
The x-coordinate of A is -2 and that of B is 0. The increase in this coordinate from A to B is 2. Similarly, the y-coordinate increases by 10. The slope is therefore m = rise / run = 10/2, or m = 5
PLS HELP ASAP ILL GIVE BRAINLKEST
Answers
Answer:
number 5
Step-by-step explanation:
an equal sign means "is not equal to"
A watch company estimates that the profit (in peso)
for selling a particular model is given by
P(x)=4x^3-31x^3-10058x+158040 for 0 < x < 50
where x is the advertising expense (in tens of thousands of pesos).
What kind of polynomial is described by the equation?
A.quadratic
B.constant
C.cubic
D.quintic
I need an answer right now thank you.
Answers
The leading degree of the polynomial is 3. This shows that the polynomial described by the equation is a cubic polynomial
The standard form of a polynomial expression is written as:
[tex]a_nx^n+ a_{n-1}x^{n-1}+ a_{n-2}x^{n-2}+...[/tex]
A polynomial function has a leading degree that is greater than 2;
Given the polynomial function
[tex]P(x)=4x^3-31x^3-10058x+158040[/tex]
From the given polynomial, the leading degree of the polynomial is 3. This shows that the polynomial described by the equation is a cubic polynomial
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GIVING BRAINLIEST
In the figure below, if AB=11√7 , what is CD?
Answers
CD is 11 square root of 14.
The measure of the side length CD in the given right angled triangle as per the measurements is equal to option C. 11√14 .
In right triangle ABE,
Measure of angle ABE = 90 degrees
Measure of angle AEB = 60 degrees
AB = 11√7
Using trigonometric ratio we have,
tan 60° = AB / BE
⇒ √3 = 11√7 / BE
⇒ BE = 11√7 / √3
⇒BE = 11√21 / 3
In right triangle BED,
Measure of angle BED = 90 degrees
Measure of angle EBD= 45°
⇒Measure of angle EDB= 45°
BE ≅ ED
BE = 11√21 / 3
⇒ED = 11√21 / 3
Using Pythagoras theorem,
BD² = BE² + ED²
⇒BD = √ 2 (11√21 / 3 )²
⇒BD = 11√21 / 3 × √2
⇒ BD = 11√42 / 3
In right triangle CDB,
Measure of ∠CDB = 90°
Measure of ∠DCB = 30°
tan 30° = BD / CD
⇒ ( 1/ √3) = 11√42 / 3 / CD
⇒ CD = [11√42 / 3 ] × √3
⇒ CD = 11√14
Therefore, the length of the side CD in the triangle is equal to option C. 11√14 .
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Three bowls of frozen yogurt cost 8.25. At the same rate how much do 9 bowls of frozen yogurt cost.
Answers
Answer:
$24.75
Step-by-step explanation:
$8.25 is for 3. So triple that cost gets you $24.75
Michael can swim 5 lengths of a swimming pool in 130 seconds.
Use this information to show that he could swim 100 lengths in under 45 minutes
Answers
Answer:
Yes, he can swim 100 lengths in under 45 minutes.
Step-by-step explanation:
First we divide 100 by 5
100 ÷ 5 = 20
Now we can multiply this by 130 seconds
Now we have 2600 seconds
Since 1 minute is 60 seconds we divide 2600 by 60 seconds
2600 ÷ 60, this gets us 43.33... minutes, which is less than 45 minutes.
This is all assuming his rate is constant.
Micheal takes 43.333 minutes to swim 100 lengths.
What is length?Length is a measurement or extent of something from one end to another end.
The SI unit of length is meter.
Given that,
To cover 5 lengths, time taken by Micheal = 130 seconds,
Therefore,
Time taken by Micheal to cover 1 length = 130/5 = 26 seconds
Time to cover 100 length = 26×100=2600 seconds
1 minute = 60 seconds
100 length is covered = 2600×1/60 minute
= 43.333 minute
So, To swim 100 lengths Micheal takes 43.333 minutes, which is under 45 minutes.
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si el largo de un rectangulo es 2 cm más que el ancho y tiene un perimetro de 52 cm cual es el largo y cual es el ancho?
Answers
Answer:
ancho: 12 cm
Largo: 14 cm
Step-by-step explanation:
[tex]P=2a+2l[/tex]
[tex]l=a+2[/tex]
[tex]P=2a+2(a+2)=2a+2a+4[/tex]
[tex]P=4a+4[/tex]
[tex]52=4a+4[/tex]
[tex]52-4=4a[/tex]
[tex]48=4a[/tex]
[tex]48/4=a[/tex]
[tex]12=a[/tex]
largo = ancho + 2 = 12 +12 = 14 cm
Hope this helps
Use elimination to solve the system of equations.
x+y=−3
2x−3y=29
Answers
Answer:
(4,-7)
Step-by-step explanation:
Answer:
(4,-7)
Step-by-step explanation:
2x-3y=29
2x+2y=-6
subtracting gives us -5y=35 so y is -7 and x-7=-3 so x is 4. therefore the ordered pair is (4,-7)
At the craft store, Patty bought a bag of yellow and brown marbles. The bag contained 85
marbles, and 60% of them were yellow. How many yellow marbles did Patty receive?
Answers
Answer:
51 yellow marbles
Step-by-step explanation:
60% of 85 can be found by multiplying 85 and 0.6 to get 51
Answer:
i got 51 marbles! simple.
The price of the trail mix at the health food store is $7.50 per pound at this rate what is total cost of 8 ounces bags of trail mix
Answers
Answer:
Below
Step-by-step explanation:
1 pound = 16 ounces
Therefore if you're looking for 8 ounces, divide $7.50 in half.
You get $3.75
Answer:
At this rate, the total cost of 8 ounce bag of trail mix would be $3.75.
Step-by-step explanation:
So first I found that for 1 LB (pound), there is 16 ounces so 8 oz is half of 16. If we know that, we have to divide 7.5 by 2 to get 3.75.