Extraneous solutions are untrue solution of an equation
Mike does not obtain any extraneous solutions
How to determine the extraneous solutions
The equation is given as:
[tex]\sqrt{z^2+2z-3}=z-3[/tex]
When squared, it becomes
[tex]z^2+2z-3=z^2-6z + 9[/tex]
Evaluate the like terms
[tex]2z-3=-6z + 9[/tex]
Collect like terns
[tex]6z + 2z = 9 + 3[/tex]
Evaluate the like terms
[tex]8z = 12[/tex]
Divide through by 8
[tex]z = 1.5[/tex]
Substitute 1.5 for z in the given equation
[tex]\sqrt{z^2+2z-3}=z-3[/tex]
[tex]\sqrt{1.5^2+2*1.5-3}=1.5-3[/tex]
Evaluate
[tex]\sqrt{2.25}=-1.5[/tex]
Determine the square root of 2.25
[tex]-1.5=-1.5[/tex]
Hence, Mike does not obtain any extraneous solutions
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Use the distributive property to write an equivalent expression. 6(f+2)
Answer: 6f + 12
Step-by-step explanation:
6(f+2)
Multiply 6 times f : 6f
Multiply 6 times 2 : 12
6f + 12
Given the circle below with secants PQR and TSR, find the length of PQ. round to the nearest tenth if necessary
Answer:
PQ ≈ 20.5
Step-by-step explanation:
The product of lengths from R to the intersection points with the circle is the same for each secant:
RS×RT = RQ×RP
40(40 +31) = (44)(PQ +44)
40(71)/44 = PQ +44
PQ = 2840/44 -44 = 64 6/11 -44 = 20 6/11
PQ ≈ 20.5
Demi is working on a presentation about a famous mathematician for her class. She decides to make her poster in a shape of a + sign
Answer: 1360 in^2
Step-by-step explanation:
Each of the four rectangles on the side is 20x12 inches. Therefore, the total area of the 4 rectangles is 4*20*12 = 960 in^2.
The area of the square in the middle is 20*20 = 400 in^2.
Therefore, the total area = 960 + 400 in^2 = 1360 in^2
which is bigger 7/8 or 1
Answer:
1
Step-by-step explanation:
1 is larger because 7/8 = 0.875 which is less than 1
i hope this helps! have a wonderful rest of ur day :)
and if its not too much to ask could you mark me as brainliest pls, im trying to rank up this month and i only need 3 more, if not then its no big deal! ty and let me know if you need anything else!!
Answer:
1
Step-by-step explanation
If you had a pizza that was cut into eights, and there was 1 slice gone, there would be 7/8 pizza left. If you had a whole pizza, it would represent 8/8 which is one slice more than 7/8.
i need help with this question please look at the picture attached
Answer:
i think its 1.42857143/6
Step-by-step explanation:
hope this helps. If it does, can i have brainliest?
What is this area of this rectangle
Step-by-step explanation:
To find the area of a rectangle, we simply need to multiply its length by its width. The area is simply the width of a rectangle times height. Area = h × h, Area = h2. Hence for a square, the area is the square of its sides.
A worker uses exactly 4 screws and 7
bolts to put a metal desk together. If each metal desk requires the same ratio of screws to bolts, which statement is true?
Answer:
well i dont know the options and is there a picture? but some advice is to see how many holes there are and that can help you find the answer
Step-by-step explanation:
Tell me if there is a picture or something else so i can help further :)
Answer:
The worker uses exactly 140 screws and 80 bolts to make 20 metal desks.
The worker uses exactly 140 screws and 80 bolts to make 20 metal desks.
The worker uses exactly 80 screws and 140 bolts to make
2 metal desks.
The worker uses exactly 80 screws and 140 bolts to make 20 metal desks.
The worker uses exactly 17screws and 14bolts to make 10
metal desks.
The worker uses exactly 17 screws and 14 bolts to make 10 metal desks.
The worker uses exactly 14 screws and 17 bolts to make 10 metal desks.
Step-by-step explanation:
these our the answers
Which conclusions are valid given that ABCD is a parallelogram? Select True or False for each statement.
it is true not false true
A skier IS skiing down a slope on the mountain.
Is the mechanical energy conserved? Why or why not?
Answer:
The mechanical energy isn't conserved.
Step-by-step explanation:
Honeslty I think you should Start cheatin on your Hw
Answer:
The mechanical energy is not conserved
Step-by-step explanation:
Recall that the law of conservation of energy states that in an isolated system (no external forces acting on it), the mechanical energy is conserved.
A skier skiing down a slope is not an isolated system in this case because the friction of the snow causes some of the mechanical energy to convert to thermal energy.
There are 10 yellow cards, 6 green, 9 orange and 5 red cards in a stack turned face down. Once a card is selected it is not replaced. Find each probability.
P(two cards that are not orange)
Answer:
yellow = 33.3 %
green = 20%
orange = 30%
red = 16.6%
Step-by-step explanation:
all in all there are 30 cards
10 ➗ 30 = 0.333 = 33.3%
6 ➗ 30 = 0.20 = 20%
9 ➗ 30 = 0.30 = 30%
5 ➗ 30 = 0.166 = 16.6%
A boat is heading towards a lighthouse, whose beacon-light is 141 feet above the water. The boat’s crew measures the angle of elevation to the beacon, 12 degrees
. What is the ship’s horizontal distance from the lighthouse (and the shore)? Round your answer to the nearest hundredth of a foot if necessary
Step-by-step explanation:
we have a right-angled triangle here.
there is the ground distance boat to lighthouse.
there is the height of the lighthouse = 141 ft.
and there is the line of sight boat to lighthouse light.
the angle at the boat is 12°.
the angle at the lighthouse bottom is 90°.
therefore, the angle at the lighthouse light is 180 - 90 - 12 = 78°
we use the law of sine to solve this.
a/sin(A) = b/sin(B) = c/sin(C)
with the sides and correlated angles being always opposite.
so, we have here
141/sin(12) = ground distance/sin(78)
ground distance = 141×sin(78)/sin(12) = 663.3528454... ft
≈ 663.35 ft
Which of the following could be the equation of a line parallel to the line y =-2/3x-1
36^2+b^2=45^2 ? Can someone pls help me
Answer:
[tex]b = 27[/tex]
Step-by-step explanation:
Formula: [tex]a^{2} + b^{2} = c^{2}[/tex]
[tex]36^{2} + b^{2} = 45^{2}[/tex]
[tex]b^{2} + 1296 = 2025[/tex]
[tex]b^{2} = 729[/tex]
[tex]b = 27[/tex]
HsiwksjrINEEEDHELPPONTHISSS
Answer: 2) 2/7, 11/72 3) 2 2/5 licorice pieces
Step-by-step explanation:
2)
A fraction of another fraction is essentially the two fractions multiplied.
Therefore, 2/3 of 3/7 = (2*3)/(3*7) = 6/21 = 2/7
1/6 of 11/12 = (1*11)/(6*12) = 11/72
3) If the licorice is divided equally, that means each person would get 12/5 of licorice pieces. 12/5 as a mixed number would become 2 2/5.
Answer:
We will get 12 divided by 5 which it equals to 1.5 licornie will each person get.
Step-by-step explanation:
12/5 =2.4 2 and 1/3 of it
Rachel needs to stop at the florist shop on her way to the hospital to see her Uncle Joey. Each square's side length is 1 block. How many blocks will she need to walk to reach the hospital?
A.
17 blocks
B.
19 blocks
C.
20 blocks
D.
24 blocks
Reset Next
Answer:
D is the correct answer.
(next time add a image)
Hence, write down the equation with y as subject (in terms of x) to represent the production cost. [The value of a, b and c must be indicated.]
The production cost is an illustration of a quadratic function
The equation of the production cost is [tex]y= ax^2 + bx - c[/tex]
How to determine the equationFrom the complete question, we have the following parameters:
Computing components (a)Number of devices (x),Labor (b)Savings on reusable material (c)Using the instructions in the complete question, the equation of the production cost would be: [tex]y= ax^2 + bx - c[/tex]
Hence, the equation of the production cost is [tex]y= ax^2 + bx - c[/tex]
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A rectangular prism has a volume of 1280 cubic units. The length is 32 units and the width is 5 units.
What is the height of the prism?
Enter your answer in the box.
units
Answer:
huh
Step-by-step explanation:
Makayla spent $29.99 plus 8.875% tax and also tipped 15% at the car wash. How much did she spent?
(Discount, tax, extra money paid, money saved, and final price can be included)
Answer:
37.1501125
Step-by-step explanation:
29.99+23.875÷100×29.99 amount then tax+tip divided by 100 ×amount
What is the surface area of the rectangular prism below?
Answer:
700 (units[tex]^{3\\[/tex])Step-by-step explanation:
Surface Area =2 length x width + 2 length x height + 2 height x weight
so we do:
7 x 12 = 84 84 x 2 = 168
7 x 14 = 98 98 x 2 = + 196
14 x 12 = 168 168 x 2= + 336
700
700
From Times Square in New York City, you can see Central Park and the Empire State Building. The approximate distance from Times Square to Central Park is 2 miles, Central Park to the Empire State Building is 1.3 miles, and Empire State Building to Times Square is 0.9 miles. What is the approximate angle to the other two landmarks from the Empire State Building
The approximate angle to the other two landmarks from the Empire State Building is 129.868°
What is cosine rule?
Cosine rule is used to show the relationship between the sides and angles of a triangle. It is given by:
a² = b² + b² - 2bc*cosA
Where a, b, c are the sides and A is the angle opposite to side A.
Let A represent the angle to the other two landmarks from the Empire State Building. Hence:
2² = 1.3² + 0.9² - 2(1.3)(0.9)cosA
A = 129.868°
The approximate angle to the other two landmarks from the Empire State Building is 129.868°
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Can you help me please
Answer:
Step-by-step explanation:
When we subtracting variables with exponent, both should have same exponents
6.28 * 10⁶ - 1.256*10⁵ = 62.8 *10⁵ - 1.256*10⁵
= (62.8 - 1.256) *10⁵
= 61.544 *10⁵
= 6.1544 *10⁶
4(2m-5)=2(3m-4)-6m what is the value of M
Answer:
[tex] \frac{3}{2} [/tex]
Step-by-step explanation:
[tex]4(2x - 5) = 2(3x - 4) - 6x = \\ 8x - 20 = 6x - 8 - 6x = \\ 8x = 20 - 6 \\ \frac{8x}{8} = \frac{20 - 8}{8} \\ x = \frac{3}{2} [/tex]
hope its clear ♡
What is the value of X. I will mark brainliest to the first 1 week right
The two angles form a straight line and need to equal 180 when added together:
7x + 28 + 33 = 180
Simplify:
7x + 61 = 180
Subtract 61 from both sides
7x = 119
Divide both sides by 7
X = 17
Answer: B.17
Find the indicated z score. The graph depicts the standard normal distribution with mean 0 and standard deviation. Shaded area is 0.06945
Please show work!
Answer:
z ≈ 1.48
Step-by-step explanation:
A suitable calculator requires only the "work" of data entry. For a TI-83, you can find the result from ...
invNorm(.06945,0,1,RIGHT-tail) = 1.479899759
The z-value is about 1.48.
_____
Additional comment
My iOS TI-83/84 "work-alike" app reportedly gives more accurate results than an actual TI-83 calculator. YMMV
12
11. Quadrilateral ABCD with vertices A(4,0),
B(6, 2), C(8, -7), and D(0, -5): 270°
าา
A” (
B' (
C” (
D'(
Answer:a because i dont know
If a > b and b > C, what is true about the
relationship between a and c? Explain your reasoning.
Answer:
a > c
Step-by-step explanation:
The Transitive Property of Inequality can be written as ...
If a > b and b > c, then a > c.
Based on the above, we can conclude from your premises that a > c.
Which 2 accounts cannot be merged or made inactive?
Answer:
Credit Card Receivables. Undeposited Funds. Opening Balance Equity. Retained Earnings
Step-by-step explanation:
The 2 accounts which cannot be merged or made inactive are Credit Card Receivables and Undeposited Funds.
What is placebo group?A placebo group is defined as the statement "an inactive substance or treatment that cannot be distinguished from a real, active substance or treatment"
From an experiment, "subjects respond differently after they receive a treatment, even if the treatment is neutral".
When we have a neutral treatment that has no effect on the dependent variable is called a "placebo".
The 2 accounts which cannot be merged or made inactive are Credit Card Receivables and Undeposited Funds.
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thank you for the help <3
Answer:
21.6
Step-by-step explanation:
Connect U and X, V and Y
Note ∠XUW = ∠VYW (facing same arc VX) and ∠W = ∠W
so ΔUXW ~ ΔVYW
then VW : YW = XW : UW
VW : YW = (YW - YX) : (UV + VW)
22 : 40 = (40 - 16) : (UV + 22)
11: 20 = 24 : (UV + 22)
11 * ( UV + 22) = 20 * 24
11* UV + 242 = 480
11 * UV = 480 - 242 = 238
so UV = 238/11 = 21.6
find , the correct 1 decimal , the volume of the following
V=BH=PIr2h
Answer:
Answer: 2413 cm^3
Step-by-step explanation:
Knowns:
V=πr^2h
r= 8
h= 12
Work:
- π · 8^2 · 12 = 2412.74cm^3
- Round .7 into a 1 because it is >4, this turns 2412.74 cm^3 into 2413cm^3
Answer: 2413 cm^3
Segment AB has endpoints at A(-14, 12) and B(10, – 4). Point C lies on AB at C(-5,6). Which of the following
represents the ratio of AC to BC?
The ratio of the length AC to BC is 11:18
Distance between two pointsThe formula for calculating the distance between two points is expressed as:
[tex]D = \sqrt{(x_2-x_1)^2+(y_2-y_1)^2}[/tex]
For the length AC
[tex]AC = \sqrt{(-9)^2+(6)^2} \\AC = \sqrt{(-14+5)^2+(12-6)^2} \\AC = \sqrt{81+36} \\AC\approx 11[/tex]
For the length of BC
[tex]BC = \sqrt{(15)^2+(10)^2} \\BC = \sqrt{225+100} \\BC\approx 18[/tex]
Hence the ratio of the length AC to BC is 11:18
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