The difference of the grandson's age in years and the grandfather's age in years is 77. Therefore, the age of the grandson is 7 years.
How to use equations to find the age?
A grandson's age in months is equal to his grandfather's age in years.
Recall,
12 months = 1 year
Hence,
let
x = age of grandson in month
It is the same age in years for the grandfather.
Therefore,
x = age of grand father in years
The difference of the grandson's age in years and the grandfather's age in years is 77. Therefore,
x - x / 12 = 77
12x - x/12 = 77
11x / 12 = 77
cross multiply
11x = 924
x = 924 / 11
x = 84
Therefore, the grandson age in in years is 84 / 12 = 7 years.
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4. Which of the following is a true statement?
A. -4(2x - 3) = -8x - 12
B.-7(4x - 8) = -28x + 56
=
C. 5(3x + 6) = 15x + 6
D. 10-2(x + 5) = -2x + 20
1.) Prove that PAT is an isosceles triangle.
2.) State The Coordinates of R so that quadrilateral PART is a parallelogram.
( The image of the Question Is Given )
First one to answer with the correct answer gets marked
The triangle PAT is an isosceles triangle because the side lengths PA and AT are congruent
How to prove that the triangle is an isosceles triangle?The points are given as:
P = (1,6)
A = (4,5)
T = (5,2)
Calculate the distance between both points as follows:
[tex]d = \sqrt{(x_2 -x_1)^2 + (y_2 -y_1)^2}[/tex]
So, we have:
[tex]PA = \sqrt{(1 -4)^2 + (6-5)^2}[/tex]
[tex]PA = \sqrt{10}[/tex]
[tex]PT = \sqrt{(1 -5)^2 + (6-2)^2}[/tex]
[tex]PT = \sqrt{32}[/tex]
[tex]AT = \sqrt{(4 -5)^2 + (5-2)^2}[/tex]
[tex]AT = \sqrt{10}[/tex]
Because the side lengths PA and AT are congruent, i.e. √10, then the triangle is an isosceles triangle
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simplify √(x^2-10x+25) if -5≤x<5
[tex]\qquad\qquad\huge\underline{{\sf Answer}}[/tex]
Let's simplify ~
[tex]\qquad \sf \dashrightarrow \: \sqrt{ {x}^{2} - 10x + 25 } [/tex]
[tex]\qquad \sf \dashrightarrow \: \sqrt{ {x}^{2} - 5x - 5x + 25 } [/tex]
[tex]\qquad \sf \dashrightarrow \: \sqrt{ {x}^{} (x- 5) - 5(x - 5) } [/tex]
[tex]\qquad \sf \dashrightarrow \: \sqrt{ (x- 5) (x - 5) } [/tex]
[tex]\qquad \sf \dashrightarrow \: \sqrt{ (x- 5) {}^{2} } [/tex]
[tex]\qquad \sf \dashrightarrow \: (x- 5) [/tex]
value x lies between :
[tex]\qquad \sf \dashrightarrow \: - 5 \leqslant x \leqslant 5[/tex]
if the value of x is taken -5
[tex]\qquad \sf \dashrightarrow \: - 5 - 5[/tex]
[tex]\qquad \sf \dashrightarrow \: - 10[/tex]
if value of x is taken as 5
[tex]\qquad \sf \dashrightarrow \:5 - 5[/tex]
[tex]\qquad \sf \dashrightarrow \:0[/tex]
So, the possible values of the required expression lies between ~
[tex]\qquad \sf \dashrightarrow \: - 10 \leqslant \sqrt{ {x}^{2} - 10x + 25 } < 0[/tex]
I hope you understood the whole procedure. let me know if you have any doubts in given steps ~
Consider parallelogram ABCD below.
Use the information given in the figure to find m of angle B, x, and m of angle BCA.
Answer:
Step-by-step explanation:
1) Opposite angles in a parallelogram are congruent, so angle B measures 82 degrees.
2) Opposite sides of a parallelogram are congruent, so 12=6x. Hence, x=2.
3) Opposite sides of a parallelogram are congruent, so by the alternate interior angles theorem, the answer is 62 degrees.
Answer:
see explanation
Step-by-step explanation:
the opposite angles of a parallelogram are congruent , then
∠ B = ∠ D = 82°
the opposite sides of a parallelogram are parallel and congruent , then
AD = BC , that is
6x = 12 ( divide both sides by 6 )
x = 2
∠ BCA and ∠ DAC are alternate angles and are congruent , then
∠ BCA = ∠ DAC = 62°
The volume of this rectangular prism is 2,016 cubic millimeters. What is the value of y?
Answer:
y = 12 mm
Step-by-step explanation:
Volume of a rectangular prism: length × width × height
V = L×W×H
v = 2,016 mm³l = 14 mmw = 12 mmh = y mmSubstitute the values above and solve for y:
2,016 = 14 × 12 × y
2,016 = 168y
2,016/168 = 1395v/168
12 = y
Final answer: 12 mm
Hope this helps!
How can you prove that csc^2(θ)tan^2(θ)-1=tan^2(θ)
Answer:
Make use of the fact that as long as [tex]\sin(\theta) \ne 0[/tex] and [tex]\cos(\theta) \ne 0[/tex]:
[tex]\displaystyle \tan(\theta) = \frac{\sin(\theta)}{\cos(\theta)}[/tex].
[tex]\displaystyle \csc(\theta) = \frac{1}{\sin(\theta)}[/tex].
[tex]\sin^{2}(\theta) + \cos^{2}(\theta) = 1[/tex].
Step-by-step explanation:
Assume that [tex]\sin(\theta) \ne 0[/tex] and [tex]\cos(\theta) \ne 0[/tex].
Make use of the fact that [tex]\tan(\theta) = (\sin(\theta)) / (\cos(\theta))[/tex] and [tex]\csc(\theta) = (1) / (\sin(\theta))[/tex] to rewrite the given expression as a combination of [tex]\sin(\theta)[/tex] and [tex]\cos(\theta)[/tex].
[tex]\begin{aligned}& \csc^{2}(\theta) \, \tan^{2}(\theta) - 1\\ =\; & \left(\frac{1}{\sin(\theta)}\right)^{2} \, \left(\frac{\sin(\theta)}{\cos(\theta)}\right)^{2} - 1 \\ =\; & \frac{\sin^{2}(\theta)}{\sin^{2}(\theta)\, \cos^{2}(\theta)} - 1\\ =\; & \frac{1}{\cos^{2}(\theta)} - 1\end{aligned}[/tex].
Since [tex]\cos(\theta) \ne 0[/tex]:
[tex]\displaystyle 1 = \frac{\cos^{2}(\theta)}{\cos^{2}(\theta)}[/tex].
Substitute this equality into the expression:
[tex]\begin{aligned}& \csc^{2}(\theta) \, \tan^{2}(\theta) - 1\\ =\; & \cdots\\ =\; & \frac{1}{\cos^{2}(\theta)} - 1 \\ =\; & \frac{1}{\cos^{2}(\theta)} - \frac{\cos^{2}(\theta)}{\cos^{2}(\theta)} \\ =\; & \frac{1 - \cos^{2}(\theta)}{\cos^{2}(\theta)}\end{aligned}[/tex].
By the Pythagorean identity, [tex]\sin^{2}(\theta) + \cos^{2}(\theta) = 1[/tex]. Rearrange this identity to obtain:
[tex]\sin^{2}(\theta) = 1 - \cos^{2}(\theta)[/tex].
Substitute this equality into the expression:
[tex]\begin{aligned}& \csc^{2}(\theta) \, \tan^{2}(\theta) - 1\\ =\; & \cdots \\ =\; & \frac{1 - \cos^{2}(\theta)}{\cos^{2}(\theta)} \\ =\; & \frac{\sin^{2}(\theta)}{\cos^{2}(\theta)}\end{aligned}[/tex].
Again, make use of the fact that [tex]\tan(\theta) = (\sin(\theta)) / (\cos(\theta))[/tex] to obtain the desired result:
[tex]\begin{aligned}& \csc^{2}(\theta) \, \tan^{2}(\theta) - 1\\ =\; & \cdots \\ =\; & \frac{\sin^{2}(\theta)}{\cos^{2}(\theta)}\\ =\; & \left(\frac{\sin(\theta)}{\cos(\theta)}\right)^{2} \\ =\; & \tan^{2}(\theta)\end{aligned}[/tex].
Y=|x+2|-1
Y<0
Please help ASAP!
Answer:
x=-1
Step-by-step explanation:
x+2-1=0
-1+2=1
1-1=0
y=0
Answer:
X = -2
Step-by-step explanation:
Y = | (-2) + 2 | - 1
Y = |0| - 1
y = -1
Lance rides his bike at an average speed of 32 mph.
If he has 3072 miles to ride, how many hours will it take him?
How many days is that?
Answer:
96 days. Divide 3072 by 32 and you get 96.
2
3 D
5
6
8
9
10
x²-4
Which shows all the critical points for the inequality ²-5x+6
<<0?
O x=-2 and x = 2
Ox= 2 and x = 3
Ox=-3, x = -2, and x = 2
O x= -2, x = 2, and x = 3
The critical points for the inequality x²-5x+6 is x= 2 and x = 3.
What is critical point?In calculus, a critical point of a function is a point where the derivative of the function is either zero or undefined.
These points are important in determining the maximum and minimum values of a function, and can also help identify points of inflection and other important features of a curve.
To find the critical points for the inequality x²-5x+6, we need to find the values of x that make the expression equal to zero (i.e., the roots of the quadratic equation).
We can factor the expression as (x-2)(x-3) and set each factor to zero to find the critical points:
x-2 = 0 or x-3 = 0
x = 2 or x = 3
So the critical points are x = 2 and x = 3.
Therefore, the answer is x= 2 and x = 3.
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What are the measures of the numbered angles?
Answer:
m<1 = 94
m<2 = 132
Step-by-step explanation:
This is a right trapezoid
Since the base lines are parallel, the facing angles would be supplementary and their sum is equal to 180 which means:
m<1 + 86 = 180 so m<1 = 94
and
m<2 + 48 = 180 so m<2 = 132
Can somebody help me with this
Probability = option(s) that we want / total number of possibilities
Options that we want = cash or credit card = 50 + 4 = 54
Total number of possibilities = cash, debit card, credit card = 50 + 2 + 4 = 56
54 / 56 = 0.96
Answer: 0.96
Hope this helps!
A can of vegetables with no label has a 1/8 chance of being green beans, and a
1/5 chance of being corn. What is the probability the can is green beans or
corn?
Answer:
13/40.
Step-by-step explanation:
We add the probability in this case.
So it is 1/5 + 1/8
= 8/40 + 5/40
= 13/40.
what is the value of X, Z, and Y.
Answer:
x= -64°, y= -63°, z=-57°
Step-by-step explanation:
→Solution,
Here,
60°=(-y-3)°[The opposite sides of a parallelogram are equal]
⇒y= -60°-3°
⇒y= -63°
⇒60°+(-2x-8)°=180°[Sum of co-interior angles is 180°]
⇒52°-2x=180°
⇒52°-180°=2x
⇒x= -128°/2
⇒x= -64°
⇒60°+(-2z+6)°=180°[Sum of co-interior angles is 180°]
⇒66°-2z=180°
⇒66°-180°=2z
⇒z= -114°/2
⇒z= -57°
y
5
4
32
2
1
-5 -4 -3 -2 -1 0
-1
-2
Type here to search
လ ရာ
-3
1 2 3 4 5
What is the equation of the blue line?
X
hp
14°C
Answer:
y=4x-3
Step-by-step explanation:
Using y - intercept form:
y=mx+b
Slope goes up by 4 squares and to the right by 2 squares. This means the slope is 4. The y intercept is -3, thus b is -3.
A triangle has sides with lengths of 20 yards, 48 yards, and 52 yards. Is it a right triangle?
yes
no
Yes
Step-by-step explanation:
Because the sides of this triangle follow the Pythagorean Theorem.
i.e.
[tex]52^{2} = {20}^{2} + {48}^{2} [/tex]
[tex]\boxed{\textbf{Therefore it IS a right triangle}} [/tex]
Identify the image of ∆XYZ for a composition of a 10 degree rotation and 80 degree rotation, both about point X.
Soup A has 8 grams of sodium in 10 cups. Soup B has 7 grams of sodium in 14 cups. Which soup has more sodium per cup?
Answer:
Soup A
Step-by-step explanation:
For this we need to find the number of sodium per cup. To do this, we divide the ratios by the number of cups. 8:10 would be 10/10 (1 cup) and 8/10 (.8 g per cup). 7:14 would be 14/14 (1 cup) and 7/14 (.5 g per cup). So, soup A has .8 g of sodium per cup and soup B has .5 g of sodium per cup. .8>.5, so soup A has more sodium.
Hope this helps!
Explain how to identify the restrictions on the variable when adding or
subtracting rational expressions.
Rational expressions are those that have fractional terms. We state restrictions because it may cause the equation to be undefined in some values of x. The most common restriction for rational expressions is N/0. This means any number divided by zero is undefined.
What is rational expressions and examples?A rational expression is nothing more than a fraction in which the numerator and/or the denominator are polynomials. Here are some examples of rational expressions.
To find the restrictions on a rational function, find the values of the variable that make the denominator equal 0.
[tex]6x-1z2-1z2+5m4+18m+1m2-m-64*2+6*-101[/tex]Learn more about rational expressions here:
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if spur gear system has a driver gear with 100 teeth and rotates at a speed of 10 RPM and is meshed with a driven gear of 20 teeth, then the driven gear will rotate at a speed of:
A. 200 RPM
B. 100 RPM
C. 50 RPM
D. 20 RPM
E. none of the above
100 teeth / 20 teeth = 5
5 x 10 rpm = 50 rpm
answer: 50 rpm
Please help!!!!!!!! Thank you sooo much!
Answer:
see explanation
Step-by-step explanation:
(a)
∠ XBC = 55° because it corresponds to ∠ AXY
(b)
since XB = XC then Δ XBC is isosceles with base angles congruent, that is
∠ XBC = ∠ XCB = 55°
the sum of the 3 angles in Δ XBC = 180° , then
∠ BXC + 55° + 55° = 180°
∠ XBC + 110° =180° ( subtract 110° from both sides )
∠ XBC = 70°
A random sample of college football players had an average height of 66.35 inches. Based on this sample, (65.6, 67.1) found to be a 90% confidence interval for the population mean height of college football players. Choose the correct answer to interpret this interval. i. We are 90% confident that the population mean height of college football players is between 65.6 and 67.1 inches. ii. There is a 90% chance that the population mean height of college football players is between 65.6 and 67.1 inches. iii. We are 90% confident that the population mean height of college football palyers is 66.35 inches. iv. A 90% of college football players have height between 65.6 and 67.1 inches.
Answer:
We are 90% confident that the population mean height of college football players is between 65.6 and 67.1 inches.
Step-by-step explanation:
90% Confidence interval means that out of 100 different samples, for example, 90 out of 100 confidence intervals with include the true mean value (average height).
please help me with this
A B and F seem like questions that make sense :)
Answer:
Abc
Step-by-step explanation:
they make the most reasonable answers
6•(x•9) simplified please
Answer:
6x+54 should be the answer
Step-by-step explanation:
What type of slope is demonstrated by the line below?
(-1,3)
A. Positive slope
B. Negative slope
C. Undefined slope
D. Zero slope
(0,-2)
(05.01 LC)
NEED HELP ASAP ILL MARK BRAINLIEST IF CORRECT
What is the slope of the line segment?
1/4
-1/4
4
−4
Answer:
We can tell by looking at the graph that it is a positive slope, so we can eliminate answers b and d.
It is rise over run. from a point, it goes up 4, and over 1.
4/1
which would be 4. The answer is C! Hope this helps!
Step-by-step explanation:
[tex]\qquad\qquad\huge\underline{{\sf Answer}}[/tex]
Let's consider two points on the line and calculate its Slope ~
(4 , 1)(8 , 2)Slope (m) of a line is :
[tex]\qquad \sf \dashrightarrow \: m = \dfrac{y_2 - y_1}{x_2 - x_1} [/tex]
[tex]\qquad \sf \dashrightarrow \:m = \dfrac{2 - 1}{8 - 4} [/tex]
[tex]\qquad \sf \dashrightarrow \:m = \dfrac{1}{4} [/tex]
Zendaya has $700 to spend at a bicycle store for some new gear and biking outfits. assume all prices listed include tax. she buys a new bicycle for $242.33. she buys 3 bicycle reflectors for $7.17 each and a pair of bike gloves for $33.68. she plans to spend some or all of the money she has left to buy new biking outfits for $77.40 each. write and solve an inequality which can be used to determine xx, the number of outfits zendaya can purchase while staying within her budget.
Answer:
she could buy 5 outfits
Step-by-step explanation:
you multiply 7.17 by 3 = 21.51
700 - 21.51 = 678.49
678.49 - 242.33 = 436.16
436.16 - 33.68 = 402.48
402.48 divided by 77.40 = 5
Which two answer choices below would give you a value of 4 times smaller than (20 x 100)? A) (20 x 100) 4 B) 204 x 100 C) 20 - 25 D) 5 x 25
The option (C) 20 – 25, and option (D) 5×25 are 4 times smaller than (20 × 100) option (C) and (D) are correct.
What is an arithmetic operation?It is defined as the operation in which we do the addition of numbers, subtraction, multiplication, and division. It has a basic four operators that is +, —, ×, and ÷.
We have:
= (20 x 100)
= 2000
4 times smaller will be:
=2000/4
= 500
A) (20×100) 4 = 4000
B) 204×100 = 20400
C) 20 – 25 = -5
D) 5×25 = 100
-5 < 500
100 < 500
Thus, the option (C) 20 – 25, and option (D) 5×25 are 4 times smaller than (20 × 100) option (C) and (D) are correct.
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help answer this pls
answer with procedure
Answer:
2
Step-by-step explanation:
there needs to be qtr with 88 by 779900
E
Describe the transformation that maps figure RSTU onto figure RSTU
611
6
4
S
U
S2
R
E
R
6-4-2 O
2
4
6
Drag the labels to explain your answer. Labels may be used once more than once, or not at all
Figure RSTU is the image of figure RSTU after a translation
units left and
units down, and a reflection across
the
#1
.: 2
14
+ X-axis
- y-axis
Answer:
8 then 2 and reflection on y axes
