Answer:
[tex]\begin{pmatrix}x=-3,\:&y=-7\\ x=-5,\:&y=-15\end{pmatrix}\\[/tex]
Step-by-step explanation:
[tex]\begin{bmatrix}y=x^2+12x+20\\ y=4x+5\end{bmatrix}[/tex]
[tex]\mathrm{Subtract\:the\:equations}[/tex]
[tex]y=x^2+12x+20[/tex]
[tex]y-y=x^2+12x+20-\left(4x+5\right)[/tex]
[tex]\mathrm{Simplify}[/tex]
[tex]0=x^2+8x+15[/tex]
The length of a rectangle is equal to triple the width. Write a system of equations can be used to tind the dimensions of the rectangle if the perimeter is 98 centimeters?
Answer:
98 = 2w + 2L,
L = 3w
Step-by-step explanation:
Use the perimeter formula:
2) Perimeter = 2w + 2L (where w is the width and L is the length)
Since the length is three times the width we can write:
L = 3w
We can substitue L with 3w:
Perimeter is equal to 98 so,
98 = 2w + 6w = 8w
W = 98/8
Therefore w is 12.25, and L is 36.75
Factor 12r^2+70+72 completely
[tex]y = 14r^2 + 70r + 72\\\text{let}\ y = 0\\12r^2 + 70r + 72 = 0\\6r^2 + 35r + 36 = 0\\(2r + 9)(3r + 4)\\[/tex]
The diameter of a circle is 3 in. Find its area to the nearest hundredth.
Answer:
Step-by-step explanation:
7.07 in2.
Can y’all help me pls
Answer:
2. The change in expected height for every one additional centimeter of femur length.
Step-by-step explanation:
1. The expected height for someone with a femur length of 65 centimeters.
Doesn't make sense, that would be height value when centimeters = 65.
2. The change in expected height for every one additional centimeter of femur length.
Makes sense, for every increase in one additional centimeter, we can expect the height to be proportional to the slope.
3. The femur length for someone with an expected height of 2.5 centimeters.
Doesn't make sense, the linear relationship relies on the femur length to get the height.
4. The change in expected femur length for every one additional centimeter of height.
Doesn't make sense, again, the linear relationship relies on the femur length.
9. Arianna has two piles of newspapers
to take to recycling. The first pile
weighs 10 pounds 7 ounces. The
second pile weighs 148 ounces. What
is the total weight of the newspapers?
A. 19 pounds 11 ounces
B. 22 pounds 11 ounces
C. 25 pounds 3 ounces
D. 29 pounds 3 ounces
Answer:
(D) 29 pounds 3 ounces
Step-by-step explanation:
1 pound = 16 ounces
Therefore 10 pounds = 16 * 10 = 160 ounces
160 + 7 = 167 ounces (first pile)
Total Weight of Newspapers = Weight of First Pile + Weight of Second Pile
= 167 + 148 = 315 ounces
As 16 ounces = 1 pound
1 ounce = 1/16 pound
315 ounces = (1/16) * 315 = 19.6875 pounds
1 pound = 16 ounces
0.6875 pounds = 16 * 0.6875 = 11
19 + 11 = 30 pounds, which is close to ans (D)
Need help with this question
Answer:
y=14,x=8
Step-by-step explanation:
We know that in congruent triangles, angle measures and side lengths are equal.
Therefore <b=<e and AB=DE
80=6y-4
84=6y
y=14
3x-y=10
3x-14=10
3x=24
x=8
What is the factorization of the polynomial below?
x2 + 6x + 8
O A. (x + 2)(x+4)
O x6
B. (x + 2)(x+6)
O C. (x + 4)(x+4)
O D. (x+8)(x + 1)
The factorization of the polynomial [tex]x^2 + 6x + 8 is (x + 2)(x + 4)[/tex], which is option A.
To factor the polynomial[tex]x^2 + 6x + 8[/tex], we need to find two numbers whose product is 8 and whose sum is 6, since we're looking for two terms that add up to the middle coefficient of the quadratic expression.
The factors of 8 are ±1, ±2, ±4, and ±8. The pairs of factors that add up to 6 are (2, 4) and (-2, -4). Since the second coefficient is positive, we can select the pair (2, 4), since their sum is positive 6.
Using these factors, we can rewrite the quadratic expression as:
x^2 + 6x + 8 = (x + 2)(x + 4)
We can check our work by expanding the factors using the distributive property:
(x + 2)(x + 4) =[tex]x^2 + 4x + 2x + 8 = x^2 + 6x + 8[/tex]
This confirms that the factorization is correct.(option-a)
For such more questions on polynomial
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Factor the trinomial 6x² + 5x - 25. Which of the following is a factor?
O (3x + 5)
O (2x - 5)
O (3x - 5)
O (2-25)
Answer:
(3x - 5 )
(2x + 5)
Step-by-step explanation:
f(x) = 6x² + 5x - 25
Let's factor it:-
We need 2 numbers whose product = ( 6*-25) = -150 and whose sum = + 5.
These are 15 and -10. So we write:
f(x) = 6x^2 + 15x - 10x - 25
= (3x - 5)(2x + 5)
= 3x(2x + 5) - 5(2x + 5)
So the factors are (3x - 5) and (2x + 5)
Please answer the first question
Answer:
12 inches
Step-by-step explanation:
Given
Volume = 763 cubic inchesDiameter = 9 inches ⇒ Radius = 9/2 inchesFormula for Volume of a Cylinder
V = πr²hSolving
763 = 3.14 x (9/2)² x h763 = 3.14 x 81/4 x h763 = 3.14 x 20.25 x h763 = 63.585hh = 11.99 ≅ 12 inchesAnswer:
The height is 12 inches
Step-by-step explanation:
Step 1: Determine the knowns a formula
[tex]Volume = 764\ in^3[/tex]
[tex]Diameter = 9\ in[/tex]
[tex]Formula: V = \pi r^2h[/tex]
Step 2: Input the values and solve
[tex]V = \pi r^2h[/tex]
[tex]764\ in^3 = \pi (9/2\ in)^2h[/tex]
[tex]764\ in^3 = \pi (20.25\ in^2)h[/tex]
[tex]764\ in^3 =63.617\ in^2 * h[/tex]
[tex]\frac{764\ in^3}{63.617\ in^2} = \frac{63.617\ in^2 * h}{63.617\ in^2}[/tex]
[tex]12.0\ in = h[/tex]
Answer: The height is 12 inches
PLEASE I NEED HELP ASAP
An electrician charges $80 for a house visit and $70 per hour. If the electrician gets paid $430, how many hours did he stay at your house?
solve for x ～
[tex]14x - 196 = 0[/tex]
thankyou! :)
Answer:
x = 14
Step-by-step explanation:
14x - 196 = 0
14x = 0 + 196
14x = 196
x = 196 ÷ 14
x = 14
[tex]14x - 196 = 0 \\ \\ \implies14x = 0 + 196 \\ \\ \implies 14x = 196 \\ \\ \implies \: x = \frac{196}{14} \\ \\ \implies \: x = 14[/tex]
Therefore the required value of "x" will be 14.Hope it helpsI need help with this
Answer:
144 ft³
Step-by-step explanation:
This "irregular shape" is a composite shape that can be considered to be any of these compositions:
extending the middle horizontal surface cuts the shape into two blocks: upper left: 2 ft high, 3 ft wide, 6 ft deep; and lower: 2 ft high, 9 ft wide, and 6 ft deep.extending the middle vertical surface cuts the shape into two blocks: left: 4 ft high, 3 ft wide, and 6 ft deep; and right: 2 ft high, 6 ft wide, and 6 ft deep.A larger block with a smaller block cut out of the upper left: larger block: 4 ft high, 9 ft wide, and 6 ft deep; cutout: 2 ft high, 6 ft wide, and 6 ft deep.The volume of any one of these blocks is the product of height, width, and depth. The above decompositions are evaluated here.
1.V = HWD
V = (2 ft)(3 ft)(6 ft) +(2 ft)(9 ft)(6 ft) = 36 ft³ + 108 ft³ = 144 ft³
__
2.V = (4 ft)(3 ft)(6 ft) +(2 ft)(6 ft)(6 ft) = 72 ft³ +72 ft³ = 144 ft³
__
3.V = (4 ft)(9 ft)(6 ft) -(2 ft)(6 ft)(6 ft) = 216 ft³ -72 ft³ = 144 ft³
Travis must use 144 ft³ of concrete to make the block.
the volume of this right trapezoidal prism is 380.25ft^3. what is the height ,x, of the prism? 5, 5, 8, 5.8, x.
Answer:
Hence, the height of the trapezoidal base is 7.2 ft.
Step-by-step explanation:
The height of the trapezoidal base is 7.2 ft.
Step-by-step explanation:
Consider the provided information.
The volume of trapezoidal prism is the area of the cross-section × the length.
Where B is the area of base, H is the length and V is the volume.
The length of the prism is 25.2ft and volume is 1279.152
Hence, the base area is 50.76 ft².
The base is trapezoid.
The area of trapezoid is
Substitute B=50.76, in above formula.
Hence, the height of the trapezoidal base is 7.2 ft.
In a batch of 860 calculators, 9 were found to be defective. What is the probability that a calculator chosen at random will be defective? Write the probability as a percent. Round to the nearest tenth of a percent if necessary.
Answer:
Number of calculators n(C)=860
Number of defectives n(D)=9
The probability of a random number being defective=n(D)/n(C)
p=9/860.
converting this to a percentage gives us, 9/860×100%
=90/86
=45/43
=1.0465%
Therefore rounding this number to the nearest tenth gives us 1.0 % since the hundredth digit is 4 which is less than 5.
so, the probability of choosing a random defective calculator is 1.0%
The lateral surface area of cone A is exactly 1/2
the lateral surface area of
cylinder B.
true or false?
The lateral surface area of cone A is exactly 1/2 the lateral surface area of cylinder B is option (A) true.
What is lateral surface area?The lateral surface area of a figure is the area of the non-base faces only. The lateral surface of an object is all of the sides of the object, excluding its base and top.
For the given situation,
The diagram shows the cone A and the cylinder B.
Cone A has the radius r and the slant height as h.
Cylinder B has the radius r and the height as h.
The lateral surface area of cone is [tex]\pi rh[/tex]
The lateral surface area of cylinder is [tex]2\pi rh[/tex]
1/2 × lateral surface area of cylinder B,
⇒ [tex]\frac{1}{2} (2\pi rh)[/tex]
⇒ [tex]\pi rh[/tex] = lateral surface area of cone A.
Hence we can conclude that the lateral surface area of cone A is exactly 1/2 the lateral surface area of cylinder B is option (A) true.
Learn more about lateral surface area here
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Determine the interval(s) on the function that is increasing in the picture I attached
(–∞, –1) ∪ (1,∞)
(–1, ∞)
(–∞, 0) ∪ (1, ∞)
(0, 1)
Answer:
(–∞, 0) ∪ (1, ∞)
Step-by-step explanation:
From (0, 1) the graph goes down, or decreases. From (–∞, 0) ∪ (1, ∞) the graph goes up, or increases.
I hope this helps!
The function increases where the slope is positive.
The graph starts out by increasing: -infinity
The graph switches to decreasing at x = 0
The graph switches to increasing at x = 1
The graph increases until infinity
(-infinity, 0) U (1, infinity)
Correct Answer: Option 3
Hope this helps!
Two angles have measures of (x + 14)º and (3x – 15). What value of x will make the angles congruent?
Answer:
x = 14º 30' OR 14.5º
Step-by-step explanation:
(x + 14)º = (3x – 15)º
3x -x = 14º +15º
2x = 29º
x = 14º 30' OR 14.5º
NO LINKS!! Please help me part 2
Answer:
UY = 20
WX = 15
VW = 15
Step-by-step explanation:
Given: UVWXY ~ HDEFG
From inspection of the diagram, the corresponding sides are:
UV~HD
VW~DE
WX~EF
XY~FG
UY~HG
The only pair of sides that both have side lengths are XY and FG. Therefore, we can use these to figure out the scale factor of dilation.
XY = 10 and FG = 20
⇒ FG/XY= 20/10 = 2
Therefore, HDEFG is an enlargement of UVWXY by a scale factor of 2
If HG = 40
⇒ UY = 40 ÷ 2 = 20
If EF = 30
⇒ WX = 30 ÷ 2 = 15
If DE = 30
⇒ VW = 30 ÷ 2 = 15
Answer:
UY = 20, WX = 15, VW = 15
Step-by-step explanation:
Step 1: Determine the scale
XY = 10 and FG = 20
[tex]10/20 = 0.5[/tex]
Step 2: Determine UY
We can determine UY by multipliying GF by 0.5 which will give us the upscaled ratio which will produce UY.
[tex]UY = GF * 0.5[/tex]
[tex]UY = 40 * 0.5[/tex]
[tex]UY = 20[/tex]
Step 3: Determine WX
We can determine WX by multipliying FE by 0.5 which will give us the upscaled ratio which will produce WX.
[tex]WX = FE * 0.5[/tex]
[tex]WX = 30 * 0.5[/tex]
[tex]WX = 15[/tex]
Step 4: Determine VW
We can determine VW by multipliying ED by 0.5 which will give us the upscaled ratio which will produce VW.
[tex]VW = ED * 0.5[/tex]
[tex]VW = 30 * 0.5[/tex]
[tex]VW = 15[/tex]
Answer: UY = 20, WX = 15, VW = 15
Out of the three answers, which one is correct?
I would also appreciate an explanation
Answer:
69
Step-by-step explanation:
All angles in a triangle = 180°
35 + x + (x+7) = 180
42 + 2x = 180
2x = 138
x = 69
Hope this helps!
Describe the spread, center, and shape of the data distribution.
Answer:
Free point 3 weeks ago.
Step-by-step explanation:
Express the interval in set-builder notation and graph the interval on a number line. [3, 6]
Easy math pls help quick
Answer:
opal : 5
lynette : 7.5 (7 hrs and 30 mins)
Step-by-step explanation:
Question 3 of
What is the solution to the inequality?
17 < 9 + x
A. X8
B. X>8
C. x < 26
D. X > 26
Answer:
B
Step-by-step explanation:
17<9 + x
group like them
17-9 < x
the sign changes due to the negative
8>x
Find the missing length indicate
Answer:
2.99973 but i would put 3 just incase
Step-by-step explanation:
just search on the internet "right triangle calculator" and click one of the links
write in natural logarithmic form x=e^-4
Answer
-4=lnx
Step-by-step explanation:
So if you raise both side to the ln then the e's cancel out and you are left with lnx=-4
another way to think about it is this:
Help please with this question
Answer:
5
Step-by-step explanation:
in each sample there were 50 students, in a group of 800 there would be 16 samples taken, if you divide the total amount of kids with Novemeber birthdays, 80 by the amount of samples, 16, youll learn that in each sample there are 5 students to have a birthday in november within each sample, hope this helps.
Find the radius of a regular hexagon with perimeter 48 units
Infinitely Many Solutions
2x+9+3x+x
2x+9+3x+x=6x+9
⇒ INFINITE SOLUTUIONS
How many solutions are there to the equation below?
√√√x = 16
Ο Α. 0
OB. 2
C. 1
OD. 4
Answer:
C. 1
Step-by-step explanation:
Given:
[tex]\displaystyle \large{\sqrt{\sqrt{\sqrt{x}}} = 16}[/tex]
The equation can be rewritten as:
[tex]\displaystyle \large{\sqrt[8]{x} = 16}[/tex] via surd property.
Since it’s an even surd, that means there only exists zero-positive numbers for value of x.
To solve this surd equation, simply clear out the surd by powering both sides by 8:
[tex]\displaystyle \large{\left(\sqrt[8]{x}\right )^8=(16)^8}[/tex]
Cancel the surd:
[tex]\displaystyle \large{x=16^8}[/tex]
Now, evaluating 16^8 will give up a million and that’s not necessary because we are finding how many solutions this equation has. Since theee only exists one value of x, which is the solution to this equation. Therefore:
Your answer is 1 solution
I WILL GIVE 20 POINTS TO THOSE WHO ANSWER THIS QUESTION RIGHT NOOOO SCAMS AND EXPLAIN WHY THAT IS THE ANSWER
Answer:
x = 15 , y = 15√(2)
Step-by-step explanation:
The triangle is isosceles where two angles are the same which mean two sides are also the same.
x = 15°
Pythagorean Theorem: a^2 + b^2 = c^2
15^2 + x^2 = y^2
15^2 + 15^2 = y^2
225 + 225 = y^2
450 = y^2
y = √(450) = 15√(2)
Answer:
x=15 and y=15root2
Step-by-step explanation:
tan45=p/b
1=x/15
x=15
again for right angle trangle
h=root (p+b)
=15root2 ans